id	sid	tid	token	lemma	pos
ejpam-2287	1	1	compile	compile	NOUN
ejpam-2287	1	2	/	/	SYM
ejpam-2287	1	3	output.dvi	output.dvi	NOUN
ejpam-2287	1	4	european	european	ADJ
ejpam-2287	1	5	journal	journal	NOUN
ejpam-2287	1	6	of	of	ADP
ejpam-2287	1	7	pure	pure	ADJ
ejpam-2287	1	8	and	and	CCONJ
ejpam-2287	1	9	applied	apply	VERB
ejpam-2287	1	10	mathematics	mathematic	NOUN
ejpam-2287	1	11	vol	vol	NOUN
ejpam-2287	1	12	.	.	PUNCT
ejpam-2287	2	1	7	7	NUM
ejpam-2287	2	2	,	,	PUNCT
ejpam-2287	2	3	no	no	INTJ
ejpam-2287	2	4	.	.	NOUN
ejpam-2287	2	5	4	4	NUM
ejpam-2287	2	6	,	,	PUNCT
ejpam-2287	2	7	2014	2014	NUM
ejpam-2287	2	8	,	,	PUNCT
ejpam-2287	2	9	442	442	NUM
ejpam-2287	2	10	-	-	SYM
ejpam-2287	2	11	461	461	NUM
ejpam-2287	2	12	issn	issn	PROPN
ejpam-2287	2	13	1307	1307	NUM
ejpam-2287	2	14	-	-	SYM
ejpam-2287	2	15	5543	5543	NUM
ejpam-2287	2	16	–	–	PUNCT
ejpam-2287	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-2287	2	18	analyzing	analyze	VERB
ejpam-2287	2	19	periodic	periodic	ADJ
ejpam-2287	2	20	solutions	solution	NOUN
ejpam-2287	2	21	of	of	ADP
ejpam-2287	2	22	an	an	DET
ejpam-2287	2	23	ode	ode	ADJ
ejpam-2287	2	24	suspension	suspension	NOUN
ejpam-2287	2	25	bridge	bridge	NOUN
ejpam-2287	2	26	model	model	NOUN
ejpam-2287	2	27	using	use	VERB
ejpam-2287	2	28	difference	difference	NOUN
ejpam-2287	2	29	equations	equation	NOUN
ejpam-2287	2	30	and	and	CCONJ
ejpam-2287	2	31	polynomial	polynomial	ADJ
ejpam-2287	2	32	methods	method	NOUN
ejpam-2287	3	1	sukanya	sukanya	VERB
ejpam-2287	3	2	basu1	basu1	PROPN
ejpam-2287	4	1	1	1	NUM
ejpam-2287	4	2	independent	independent	ADJ
ejpam-2287	4	3	,	,	PUNCT
ejpam-2287	4	4	grand	grand	ADJ
ejpam-2287	4	5	rapids	rapids	PROPN
ejpam-2287	4	6	,	,	PUNCT
ejpam-2287	4	7	michigan	michigan	PROPN
ejpam-2287	4	8	,	,	PUNCT
ejpam-2287	4	9	usa	usa	PROPN
ejpam-2287	4	10	abstract	abstract	NOUN
ejpam-2287	4	11	.	.	PUNCT
ejpam-2287	5	1	in	in	ADP
ejpam-2287	5	2	[	[	X
ejpam-2287	5	3	13	13	NUM
ejpam-2287	5	4	]	]	PUNCT
ejpam-2287	5	5	,	,	PUNCT
ejpam-2287	5	6	mckenna	mckenna	PROPN
ejpam-2287	5	7	and	and	CCONJ
ejpam-2287	5	8	moore	moore	PROPN
ejpam-2287	5	9	studied	study	VERB
ejpam-2287	5	10	oscillations	oscillation	NOUN
ejpam-2287	5	11	in	in	ADP
ejpam-2287	5	12	a	a	DET
ejpam-2287	5	13	suspension	suspension	NOUN
ejpam-2287	5	14	bridge	bridge	NOUN
ejpam-2287	5	15	by	by	ADP
ejpam-2287	5	16	investigating	investigate	VERB
ejpam-2287	5	17	periodic	periodic	ADJ
ejpam-2287	5	18	solutions	solution	NOUN
ejpam-2287	5	19	to	to	ADP
ejpam-2287	5	20	a	a	DET
ejpam-2287	5	21	differential	differential	ADJ
ejpam-2287	5	22	equations	equation	NOUN
ejpam-2287	5	23	model	model	NOUN
ejpam-2287	5	24	for	for	ADP
ejpam-2287	5	25	the	the	DET
ejpam-2287	5	26	bridge	bridge	NOUN
ejpam-2287	5	27	and	and	CCONJ
ejpam-2287	5	28	its	its	PRON
ejpam-2287	5	29	linearized	linearize	VERB
ejpam-2287	5	30	version	version	NOUN
ejpam-2287	5	31	numerically	numerically	ADV
ejpam-2287	5	32	.	.	PUNCT
ejpam-2287	6	1	in	in	ADP
ejpam-2287	6	2	this	this	DET
ejpam-2287	6	3	paper	paper	NOUN
ejpam-2287	6	4	,	,	PUNCT
ejpam-2287	6	5	the	the	DET
ejpam-2287	6	6	author	author	NOUN
ejpam-2287	6	7	seeks	seek	VERB
ejpam-2287	6	8	to	to	PART
ejpam-2287	6	9	build	build	VERB
ejpam-2287	6	10	a	a	DET
ejpam-2287	6	11	rigorous	rigorous	ADJ
ejpam-2287	6	12	mathematical	mathematical	ADJ
ejpam-2287	6	13	foundation	foundation	NOUN
ejpam-2287	6	14	for	for	ADP
ejpam-2287	6	15	the	the	DET
ejpam-2287	6	16	numerical	numerical	ADJ
ejpam-2287	6	17	experiments	experiment	NOUN
ejpam-2287	6	18	of	of	ADP
ejpam-2287	6	19	mckenna	mckenna	NOUN
ejpam-2287	6	20	and	and	CCONJ
ejpam-2287	6	21	moore	moore	NOUN
ejpam-2287	6	22	in	in	ADP
ejpam-2287	6	23	[	[	X
ejpam-2287	6	24	13	13	NUM
ejpam-2287	6	25	]	]	PUNCT
ejpam-2287	6	26	by	by	ADP
ejpam-2287	6	27	studying	study	VERB
ejpam-2287	6	28	an	an	DET
ejpam-2287	6	29	associated	associate	VERB
ejpam-2287	6	30	discrete	discrete	ADJ
ejpam-2287	6	31	difference	difference	NOUN
ejpam-2287	6	32	equations	equation	NOUN
ejpam-2287	6	33	model	model	NOUN
ejpam-2287	6	34	using	use	VERB
ejpam-2287	6	35	an	an	DET
ejpam-2287	6	36	interplay	interplay	NOUN
ejpam-2287	6	37	of	of	ADP
ejpam-2287	6	38	ideas	idea	NOUN
ejpam-2287	6	39	from	from	ADP
ejpam-2287	6	40	engineering	engineering	NOUN
ejpam-2287	6	41	,	,	PUNCT
ejpam-2287	6	42	discrete	discrete	ADJ
ejpam-2287	6	43	dynamical	dynamical	ADJ
ejpam-2287	6	44	systems	system	NOUN
ejpam-2287	6	45	,	,	PUNCT
ejpam-2287	6	46	algebraic	algebraic	ADJ
ejpam-2287	6	47	geometry	geometry	NOUN
ejpam-2287	6	48	and	and	CCONJ
ejpam-2287	6	49	the	the	DET
ejpam-2287	6	50	theory	theory	NOUN
ejpam-2287	6	51	of	of	ADP
ejpam-2287	6	52	polynomials	polynomial	NOUN
ejpam-2287	6	53	.	.	PUNCT
ejpam-2287	7	1	2010	2010	NUM
ejpam-2287	7	2	mathematics	mathematic	NOUN
ejpam-2287	7	3	subject	subject	NOUN
ejpam-2287	7	4	classifications	classification	NOUN
ejpam-2287	7	5	:	:	PUNCT
ejpam-2287	7	6	39a05	39a05	NUM
ejpam-2287	7	7	,	,	PUNCT
ejpam-2287	7	8	39a11	39a11	NUM
ejpam-2287	7	9	key	key	ADJ
ejpam-2287	7	10	words	word	NOUN
ejpam-2287	7	11	and	and	CCONJ
ejpam-2287	7	12	phrases	phrase	NOUN
ejpam-2287	7	13	:	:	PUNCT
ejpam-2287	7	14	suspension	suspension	NOUN
ejpam-2287	7	15	bridge	bridge	NOUN
ejpam-2287	7	16	,	,	PUNCT
ejpam-2287	7	17	torsional	torsional	ADJ
ejpam-2287	7	18	angle	angle	NOUN
ejpam-2287	7	19	,	,	PUNCT
ejpam-2287	7	20	discrete	discrete	ADJ
ejpam-2287	7	21	model	model	NOUN
ejpam-2287	7	22	,	,	PUNCT
ejpam-2287	7	23	periodic	periodic	ADJ
ejpam-2287	7	24	solution	solution	NOUN
ejpam-2287	7	25	,	,	PUNCT
ejpam-2287	7	26	equilibrium	equilibrium	NOUN
ejpam-2287	7	27	,	,	PUNCT
ejpam-2287	7	28	bifurcation	bifurcation	NOUN
ejpam-2287	7	29	,	,	PUNCT
ejpam-2287	7	30	elliptic	elliptic	ADJ
ejpam-2287	7	31	curve	curve	NOUN
ejpam-2287	7	32	,	,	PUNCT
ejpam-2287	7	33	basin	basin	NOUN
ejpam-2287	7	34	of	of	ADP
ejpam-2287	7	35	attraction	attraction	NOUN
ejpam-2287	7	36	,	,	PUNCT
ejpam-2287	7	37	global	global	ADJ
ejpam-2287	7	38	attractivity	attractivity	NOUN
ejpam-2287	7	39	,	,	PUNCT
ejpam-2287	7	40	eigenvalues	eigenvalue	VERB
ejpam-2287	7	41	1	1	NUM
ejpam-2287	7	42	.	.	PUNCT
ejpam-2287	7	43	introduction	introduction	NOUN
ejpam-2287	7	44	suspension	suspension	NOUN
ejpam-2287	7	45	bridge	bridge	NOUN
ejpam-2287	7	46	dynamics	dynamic	NOUN
ejpam-2287	7	47	such	such	ADJ
ejpam-2287	7	48	as	as	ADP
ejpam-2287	7	49	factors	factor	NOUN
ejpam-2287	7	50	leading	lead	VERB
ejpam-2287	7	51	to	to	ADP
ejpam-2287	7	52	the	the	DET
ejpam-2287	7	53	1940	1940	NUM
ejpam-2287	7	54	tacoma	tacoma	NOUN
ejpam-2287	7	55	narrows	narrow	VERB
ejpam-2287	7	56	bridge	bridge	NOUN
ejpam-2287	7	57	collapse	collapse	NOUN
ejpam-2287	7	58	in	in	ADP
ejpam-2287	7	59	washington	washington	PROPN
ejpam-2287	7	60	,	,	PUNCT
ejpam-2287	7	61	usa	usa	PROPN
ejpam-2287	7	62	,	,	PUNCT
ejpam-2287	7	63	have	have	AUX
ejpam-2287	7	64	been	be	AUX
ejpam-2287	7	65	widely	widely	ADV
ejpam-2287	7	66	studied	study	VERB
ejpam-2287	7	67	by	by	ADP
ejpam-2287	7	68	civil	civil	ADJ
ejpam-2287	7	69	engineers	engineer	NOUN
ejpam-2287	7	70	,	,	PUNCT
ejpam-2287	7	71	architects	architect	NOUN
ejpam-2287	7	72	and	and	CCONJ
ejpam-2287	7	73	applied	apply	VERB
ejpam-2287	7	74	mathematicians	mathematician	NOUN
ejpam-2287	7	75	all	all	ADV
ejpam-2287	7	76	across	across	ADP
ejpam-2287	7	77	the	the	DET
ejpam-2287	7	78	world	world	NOUN
ejpam-2287	7	79	(	(	PUNCT
ejpam-2287	7	80	see	see	VERB
ejpam-2287	7	81	[	[	X
ejpam-2287	7	82	1	1	NUM
ejpam-2287	7	83	,	,	PUNCT
ejpam-2287	7	84	6–8	6–8	NOUN
ejpam-2287	7	85	,	,	PUNCT
ejpam-2287	7	86	13	13	NUM
ejpam-2287	7	87	,	,	PUNCT
ejpam-2287	7	88	14	14	NUM
ejpam-2287	7	89	]	]	PUNCT
ejpam-2287	7	90	)	)	PUNCT
ejpam-2287	7	91	.	.	PUNCT
ejpam-2287	8	1	some	some	DET
ejpam-2287	8	2	researchers	researcher	NOUN
ejpam-2287	8	3	prefer	prefer	VERB
ejpam-2287	8	4	to	to	PART
ejpam-2287	8	5	use	use	VERB
ejpam-2287	8	6	suspension	suspension	NOUN
ejpam-2287	8	7	bridge	bridge	NOUN
ejpam-2287	8	8	models	model	NOUN
ejpam-2287	8	9	involving	involve	VERB
ejpam-2287	8	10	ordinary	ordinary	ADJ
ejpam-2287	8	11	differential	differential	ADJ
ejpam-2287	8	12	equations	equation	NOUN
ejpam-2287	8	13	(	(	PUNCT
ejpam-2287	8	14	see	see	VERB
ejpam-2287	8	15	[	[	X
ejpam-2287	8	16	1	1	NUM
ejpam-2287	8	17	,	,	PUNCT
ejpam-2287	8	18	13	13	NUM
ejpam-2287	8	19	,	,	PUNCT
ejpam-2287	8	20	14	14	NUM
ejpam-2287	8	21	]	]	PUNCT
ejpam-2287	8	22	)	)	PUNCT
ejpam-2287	8	23	while	while	SCONJ
ejpam-2287	8	24	others	other	NOUN
ejpam-2287	8	25	prefer	prefer	VERB
ejpam-2287	8	26	to	to	PART
ejpam-2287	8	27	use	use	VERB
ejpam-2287	8	28	partial	partial	ADJ
ejpam-2287	8	29	differential	differential	NOUN
ejpam-2287	8	30	equations	equation	NOUN
ejpam-2287	8	31	models	model	NOUN
ejpam-2287	8	32	(	(	PUNCT
ejpam-2287	8	33	see	see	VERB
ejpam-2287	8	34	[	[	X
ejpam-2287	8	35	6–8	6–8	NOUN
ejpam-2287	8	36	]	]	X
ejpam-2287	8	37	)	)	PUNCT
ejpam-2287	8	38	to	to	PART
ejpam-2287	8	39	study	study	VERB
ejpam-2287	8	40	the	the	DET
ejpam-2287	8	41	dynamics	dynamic	NOUN
ejpam-2287	8	42	of	of	ADP
ejpam-2287	8	43	suspension	suspension	NOUN
ejpam-2287	8	44	bridges	bridge	NOUN
ejpam-2287	8	45	.	.	PUNCT
ejpam-2287	9	1	often	often	ADV
ejpam-2287	9	2	both	both	DET
ejpam-2287	9	3	groups	group	NOUN
ejpam-2287	9	4	of	of	ADP
ejpam-2287	9	5	researchers	researcher	NOUN
ejpam-2287	9	6	turn	turn	VERB
ejpam-2287	9	7	to	to	ADP
ejpam-2287	9	8	numerical	numerical	ADJ
ejpam-2287	9	9	algorithms	algorithm	NOUN
ejpam-2287	9	10	to	to	PART
ejpam-2287	9	11	gain	gain	VERB
ejpam-2287	9	12	further	further	ADJ
ejpam-2287	9	13	insight	insight	NOUN
ejpam-2287	9	14	into	into	ADP
ejpam-2287	9	15	their	their	PRON
ejpam-2287	9	16	model	model	NOUN
ejpam-2287	9	17	dynamics	dynamic	NOUN
ejpam-2287	9	18	.	.	PUNCT
ejpam-2287	10	1	more	more	ADV
ejpam-2287	10	2	specifically	specifically	ADV
ejpam-2287	10	3	,	,	PUNCT
ejpam-2287	10	4	they	they	PRON
ejpam-2287	10	5	run	run	VERB
ejpam-2287	10	6	their	their	PRON
ejpam-2287	10	7	numerical	numerical	ADJ
ejpam-2287	10	8	algorithms	algorithm	NOUN
ejpam-2287	10	9	on	on	ADP
ejpam-2287	10	10	discretized	discretized	ADJ
ejpam-2287	10	11	versions	version	NOUN
ejpam-2287	10	12	of	of	ADP
ejpam-2287	10	13	their	their	PRON
ejpam-2287	10	14	original	original	ADJ
ejpam-2287	10	15	model	model	NOUN
ejpam-2287	10	16	for	for	ADP
ejpam-2287	10	17	a	a	DET
ejpam-2287	10	18	finite	finite	ADJ
ejpam-2287	10	19	number	number	NOUN
ejpam-2287	10	20	of	of	ADP
ejpam-2287	10	21	initial	initial	ADJ
ejpam-2287	10	22	conditions	condition	NOUN
ejpam-2287	10	23	to	to	PART
ejpam-2287	10	24	get	get	VERB
ejpam-2287	10	25	approximate	approximate	ADJ
ejpam-2287	10	26	solutions	solution	NOUN
ejpam-2287	10	27	.	.	PUNCT
ejpam-2287	11	1	some	some	DET
ejpam-2287	11	2	exceptions	exception	NOUN
ejpam-2287	11	3	to	to	ADP
ejpam-2287	11	4	this	this	DET
ejpam-2287	11	5	rule	rule	NOUN
ejpam-2287	11	6	are	be	AUX
ejpam-2287	11	7	paper	paper	NOUN
ejpam-2287	11	8	[	[	X
ejpam-2287	11	9	14	14	NUM
ejpam-2287	11	10	]	]	PUNCT
ejpam-2287	11	11	by	by	ADP
ejpam-2287	11	12	a.	a.	NOUN
ejpam-2287	11	13	pascoletti	pascoletti	PROPN
ejpam-2287	11	14	and	and	CCONJ
ejpam-2287	11	15	f.	f.	PROPN
ejpam-2287	11	16	zanolin	zanolin	PROPN
ejpam-2287	11	17	and	and	CCONJ
ejpam-2287	11	18	paper	paper	NOUN
ejpam-2287	12	1	[	[	X
ejpam-2287	12	2	8	8	NUM
ejpam-2287	12	3	]	]	PUNCT
ejpam-2287	12	4	by	by	ADP
ejpam-2287	12	5	z.	z.	PROPN
ejpam-2287	12	6	ding	ding	PROPN
ejpam-2287	12	7	in	in	ADP
ejpam-2287	12	8	which	which	PRON
ejpam-2287	12	9	they	they	PRON
ejpam-2287	12	10	present	present	VERB
ejpam-2287	12	11	rigorous	rigorous	ADJ
ejpam-2287	12	12	mathematical	mathematical	ADJ
ejpam-2287	12	13	proofs	proof	NOUN
ejpam-2287	12	14	to	to	PART
ejpam-2287	12	15	back	back	VERB
ejpam-2287	12	16	their	their	PRON
ejpam-2287	12	17	results	result	NOUN
ejpam-2287	12	18	.	.	PUNCT
ejpam-2287	13	1	a	a	DET
ejpam-2287	13	2	danger	danger	NOUN
ejpam-2287	13	3	in	in	ADP
ejpam-2287	13	4	relying	rely	VERB
ejpam-2287	13	5	too	too	ADV
ejpam-2287	13	6	heavily	heavily	ADV
ejpam-2287	13	7	on	on	ADP
ejpam-2287	13	8	numerical	numerical	ADJ
ejpam-2287	13	9	algorithms	algorithm	NOUN
ejpam-2287	13	10	to	to	PART
ejpam-2287	13	11	study	study	VERB
ejpam-2287	13	12	the	the	DET
ejpam-2287	13	13	dynamics	dynamic	NOUN
ejpam-2287	13	14	of	of	ADP
ejpam-2287	13	15	actual	actual	ADJ
ejpam-2287	13	16	suspension	suspension	NOUN
ejpam-2287	13	17	bridges	bridge	NOUN
ejpam-2287	13	18	is	be	AUX
ejpam-2287	13	19	that	that	SCONJ
ejpam-2287	13	20	one	one	PRON
ejpam-2287	13	21	can	can	AUX
ejpam-2287	13	22	very	very	ADV
ejpam-2287	13	23	easily	easily	ADV
ejpam-2287	13	24	miss	miss	VERB
ejpam-2287	13	25	those	those	DET
ejpam-2287	13	26	few	few	ADJ
ejpam-2287	13	27	useful	useful	ADJ
ejpam-2287	13	28	initial	initial	ADJ
ejpam-2287	13	29	points	point	NOUN
ejpam-2287	13	30	which	which	PRON
ejpam-2287	13	31	lead	lead	VERB
ejpam-2287	13	32	to	to	ADP
ejpam-2287	13	33	extraordinary	extraordinary	ADJ
ejpam-2287	13	34	or	or	CCONJ
ejpam-2287	13	35	unusual	unusual	ADJ
ejpam-2287	13	36	bridge	bridge	NOUN
ejpam-2287	13	37	dynamics	dynamic	NOUN
ejpam-2287	13	38	from	from	ADP
ejpam-2287	13	39	the	the	DET
ejpam-2287	13	40	point	point	NOUN
ejpam-2287	13	41	of	of	ADP
ejpam-2287	13	42	view	view	NOUN
ejpam-2287	13	43	of	of	ADP
ejpam-2287	13	44	applications	application	NOUN
ejpam-2287	13	45	(	(	PUNCT
ejpam-2287	13	46	see	see	VERB
ejpam-2287	13	47	[	[	X
ejpam-2287	13	48	13	13	NUM
ejpam-2287	13	49	]	]	PUNCT
ejpam-2287	13	50	)	)	PUNCT
ejpam-2287	13	51	since	since	SCONJ
ejpam-2287	13	52	computers	computer	NOUN
ejpam-2287	13	53	do	do	AUX
ejpam-2287	13	54	not	not	PART
ejpam-2287	13	55	possess	possess	VERB
ejpam-2287	13	56	the	the	DET
ejpam-2287	13	57	mathematical	mathematical	ADJ
ejpam-2287	13	58	intuition	intuition	NOUN
ejpam-2287	13	59	needed	need	VERB
ejpam-2287	13	60	to	to	PART
ejpam-2287	13	61	look	look	VERB
ejpam-2287	13	62	for	for	ADP
ejpam-2287	13	63	special	special	ADJ
ejpam-2287	13	64	initial	initial	ADJ
ejpam-2287	13	65	email	email	NOUN
ejpam-2287	13	66	address	address	NOUN
ejpam-2287	13	67	:	:	PUNCT
ejpam-2287	13	68	sukanyabasu49@yahoo.in	sukanyabasu49@yahoo.in	CCONJ
ejpam-2287	13	69	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2287	14	1	442	442	NUM
ejpam-2287	14	2	c	c	X
ejpam-2287	14	3	©	©	PROPN
ejpam-2287	14	4	2014	2014	NUM
ejpam-2287	14	5	ejpam	ejpam	NOUN
ejpam-2287	14	6	all	all	DET
ejpam-2287	14	7	rights	right	NOUN
ejpam-2287	14	8	reserved	reserve	VERB
ejpam-2287	14	9	.	.	PUNCT
ejpam-2287	15	1	s.	s.	PROPN
ejpam-2287	15	2	basu	basu	PROPN
ejpam-2287	15	3	/	/	SYM
ejpam-2287	15	4	eur	eur	PROPN
ejpam-2287	15	5	.	.	PUNCT
ejpam-2287	16	1	j.	j.	PROPN
ejpam-2287	16	2	pure	pure	PROPN
ejpam-2287	16	3	appl	appl	PROPN
ejpam-2287	16	4	.	.	PROPN
ejpam-2287	16	5	math	math	PROPN
ejpam-2287	16	6	,	,	PUNCT
ejpam-2287	16	7	7	7	NUM
ejpam-2287	16	8	(	(	PUNCT
ejpam-2287	16	9	2014	2014	NUM
ejpam-2287	16	10	)	)	PUNCT
ejpam-2287	16	11	,	,	PUNCT
ejpam-2287	16	12	442	442	NUM
ejpam-2287	16	13	-	-	SYM
ejpam-2287	16	14	461	461	NUM
ejpam-2287	16	15	443	443	NUM
ejpam-2287	16	16	conditions	condition	NOUN
ejpam-2287	16	17	.	.	PUNCT
ejpam-2287	17	1	it	it	PRON
ejpam-2287	17	2	is	be	AUX
ejpam-2287	17	3	also	also	ADV
ejpam-2287	17	4	extremely	extremely	ADV
ejpam-2287	17	5	difficult	difficult	ADJ
ejpam-2287	17	6	to	to	PART
ejpam-2287	17	7	predict	predict	VERB
ejpam-2287	17	8	exact	exact	ADJ
ejpam-2287	17	9	bifurcation	bifurcation	NOUN
ejpam-2287	17	10	values	value	NOUN
ejpam-2287	17	11	for	for	ADP
ejpam-2287	17	12	parameters	parameter	NOUN
ejpam-2287	17	13	by	by	ADP
ejpam-2287	17	14	relying	rely	VERB
ejpam-2287	17	15	solely	solely	ADV
ejpam-2287	17	16	on	on	ADP
ejpam-2287	17	17	computer	computer	NOUN
ejpam-2287	17	18	-	-	PUNCT
ejpam-2287	17	19	aided	aid	VERB
ejpam-2287	17	20	numerical	numerical	ADJ
ejpam-2287	17	21	simulations	simulation	NOUN
ejpam-2287	17	22	(	(	PUNCT
ejpam-2287	17	23	see	see	VERB
ejpam-2287	17	24	[	[	X
ejpam-2287	17	25	13	13	NUM
ejpam-2287	17	26	]	]	NUM
ejpam-2287	17	27	)	)	PUNCT
ejpam-2287	17	28	.	.	PUNCT
ejpam-2287	18	1	in	in	ADP
ejpam-2287	18	2	this	this	DET
ejpam-2287	18	3	paper	paper	NOUN
ejpam-2287	18	4	,	,	PUNCT
ejpam-2287	18	5	the	the	DET
ejpam-2287	18	6	author	author	NOUN
ejpam-2287	18	7	studies	study	VERB
ejpam-2287	18	8	the	the	DET
ejpam-2287	18	9	dynamics	dynamic	NOUN
ejpam-2287	18	10	of	of	ADP
ejpam-2287	18	11	a	a	DET
ejpam-2287	18	12	discrete	discrete	ADJ
ejpam-2287	18	13	difference	difference	NOUN
ejpam-2287	18	14	equations	equation	NOUN
ejpam-2287	18	15	model	model	NOUN
ejpam-2287	18	16	for	for	ADP
ejpam-2287	18	17	a	a	DET
ejpam-2287	18	18	suspension	suspension	NOUN
ejpam-2287	18	19	bridge	bridge	NOUN
ejpam-2287	18	20	using	use	VERB
ejpam-2287	18	21	a	a	DET
ejpam-2287	18	22	rigorous	rigorous	ADJ
ejpam-2287	18	23	mathematical	mathematical	ADJ
ejpam-2287	18	24	approach	approach	NOUN
ejpam-2287	18	25	involving	involve	VERB
ejpam-2287	18	26	the	the	DET
ejpam-2287	18	27	theory	theory	NOUN
ejpam-2287	18	28	of	of	ADP
ejpam-2287	18	29	difference	difference	NOUN
ejpam-2287	18	30	equations	equation	NOUN
ejpam-2287	18	31	(	(	PUNCT
ejpam-2287	18	32	see	see	VERB
ejpam-2287	18	33	[	[	X
ejpam-2287	18	34	2–4	2–4	NUM
ejpam-2287	18	35	,	,	PUNCT
ejpam-2287	18	36	9	9	NUM
ejpam-2287	18	37	–	–	SYM
ejpam-2287	18	38	12	12	NUM
ejpam-2287	18	39	,	,	PUNCT
ejpam-2287	18	40	15	15	NUM
ejpam-2287	18	41	]	]	PUNCT
ejpam-2287	18	42	)	)	PUNCT
ejpam-2287	18	43	to	to	PART
ejpam-2287	18	44	get	get	VERB
ejpam-2287	18	45	useful	useful	ADJ
ejpam-2287	18	46	global	global	ADJ
ejpam-2287	18	47	attractivity	attractivity	NOUN
ejpam-2287	18	48	results	result	NOUN
ejpam-2287	18	49	and	and	CCONJ
ejpam-2287	18	50	parameter	parameter	NOUN
ejpam-2287	18	51	bifurcation	bifurcation	NOUN
ejpam-2287	18	52	values	value	NOUN
ejpam-2287	18	53	backed	back	VERB
ejpam-2287	18	54	by	by	ADP
ejpam-2287	18	55	mathematical	mathematical	ADJ
ejpam-2287	18	56	theorems	theorem	NOUN
ejpam-2287	18	57	and	and	CCONJ
ejpam-2287	18	58	proofs	proof	NOUN
ejpam-2287	18	59	.	.	PUNCT
ejpam-2287	19	1	in	in	ADP
ejpam-2287	19	2	[	[	X
ejpam-2287	19	3	13	13	NUM
ejpam-2287	19	4	]	]	PUNCT
ejpam-2287	19	5	,	,	PUNCT
ejpam-2287	19	6	p.	p.	PROPN
ejpam-2287	19	7	j.	j.	PROPN
ejpam-2287	19	8	mckenna	mckenna	PROPN
ejpam-2287	19	9	and	and	CCONJ
ejpam-2287	19	10	k.	k.	PROPN
ejpam-2287	19	11	s.	s.	PROPN
ejpam-2287	19	12	moore	moore	PROPN
ejpam-2287	19	13	studied	study	VERB
ejpam-2287	19	14	oscillations	oscillation	NOUN
ejpam-2287	19	15	in	in	ADP
ejpam-2287	19	16	a	a	DET
ejpam-2287	19	17	suspension	suspension	NOUN
ejpam-2287	19	18	bridge	bridge	NOUN
ejpam-2287	19	19	by	by	ADP
ejpam-2287	19	20	analyzing	analyze	VERB
ejpam-2287	19	21	periodic	periodic	ADJ
ejpam-2287	19	22	solutions	solution	NOUN
ejpam-2287	19	23	to	to	ADP
ejpam-2287	19	24	the	the	DET
ejpam-2287	19	25	system	system	NOUN
ejpam-2287	19	26	of	of	ADP
ejpam-2287	19	27	nonlinear	nonlinear	ADJ
ejpam-2287	19	28	ordinary	ordinary	ADJ
ejpam-2287	19	29	differential	differential	ADJ
ejpam-2287	19	30	equations	equation	NOUN
ejpam-2287	19	31	θ	θ	X
ejpam-2287	20	1	′′	′′	NOUN
ejpam-2287	20	2	=	=	PRON
ejpam-2287	20	3	−	−	PROPN
ejpam-2287	20	4	6k	6k	NOUN
ejpam-2287	20	5	m	m	NOUN
ejpam-2287	20	6	cosθ	cosθ	PROPN
ejpam-2287	20	7	sinθ	sinθ	PROPN
ejpam-2287	20	8	−δ1θ	−δ1θ	PROPN
ejpam-2287	20	9	′	′	NUM
ejpam-2287	21	1	+	+	PUNCT
ejpam-2287	21	2	λ	λ	NOUN
ejpam-2287	21	3	sinµt	sinµt	VERB
ejpam-2287	21	4	y	y	PROPN
ejpam-2287	21	5	′′	′′	PROPN
ejpam-2287	22	1	=	=	PROPN
ejpam-2287	23	1	−	−	PROPN
ejpam-2287	23	2	2k	2k	NUM
ejpam-2287	23	3	m	m	VERB
ejpam-2287	23	4	y	y	PROPN
ejpam-2287	23	5	−δ2	−δ2	NOUN
ejpam-2287	23	6	y	y	PROPN
ejpam-2287	24	1	′	′	NUM
ejpam-2287	25	1	+	+	CCONJ
ejpam-2287	25	2	g	g	PROPN
ejpam-2287	25	3	(	(	PUNCT
ejpam-2287	25	4	1	1	NUM
ejpam-2287	25	5	)	)	PUNCT
ejpam-2287	25	6	where	where	SCONJ
ejpam-2287	25	7	δ1	δ1	NOUN
ejpam-2287	25	8	,	,	PUNCT
ejpam-2287	25	9	δ2	δ2	VERB
ejpam-2287	25	10	are	be	AUX
ejpam-2287	25	11	damping	damp	VERB
ejpam-2287	25	12	constants	constant	NOUN
ejpam-2287	25	13	,	,	PUNCT
ejpam-2287	25	14	k	k	PROPN
ejpam-2287	25	15	,	,	PUNCT
ejpam-2287	25	16	m	m	PROPN
ejpam-2287	25	17	,	,	PUNCT
ejpam-2287	25	18	λ	λ	NOUN
ejpam-2287	25	19	and	and	CCONJ
ejpam-2287	25	20	µ	µ	X
ejpam-2287	25	21	are	be	AUX
ejpam-2287	25	22	positive	positive	ADJ
ejpam-2287	25	23	parameters	parameter	NOUN
ejpam-2287	25	24	,	,	PUNCT
ejpam-2287	25	25	g	g	PROPN
ejpam-2287	25	26	is	be	AUX
ejpam-2287	25	27	the	the	DET
ejpam-2287	25	28	force	force	NOUN
ejpam-2287	25	29	due	due	ADP
ejpam-2287	25	30	to	to	ADP
ejpam-2287	25	31	gravity	gravity	NOUN
ejpam-2287	25	32	and	and	CCONJ
ejpam-2287	25	33	λ	λ	PROPN
ejpam-2287	25	34	sinµt	sinµt	NOUN
ejpam-2287	25	35	is	be	AUX
ejpam-2287	25	36	an	an	DET
ejpam-2287	25	37	external	external	ADJ
ejpam-2287	25	38	force	force	NOUN
ejpam-2287	25	39	at	at	ADP
ejpam-2287	25	40	time	time	NOUN
ejpam-2287	25	41	t.	t.	PROPN
ejpam-2287	25	42	they	they	PRON
ejpam-2287	25	43	used	use	VERB
ejpam-2287	25	44	a	a	DET
ejpam-2287	25	45	numerical	numerical	ADJ
ejpam-2287	25	46	continuation	continuation	NOUN
ejpam-2287	25	47	algorithm	algorithm	NOUN
ejpam-2287	25	48	to	to	PART
ejpam-2287	25	49	demonstrate	demonstrate	VERB
ejpam-2287	25	50	the	the	DET
ejpam-2287	25	51	existence	existence	NOUN
ejpam-2287	25	52	of	of	ADP
ejpam-2287	25	53	three	three	NUM
ejpam-2287	25	54	periodic	periodic	ADJ
ejpam-2287	25	55	solutions	solution	NOUN
ejpam-2287	25	56	.	.	PUNCT
ejpam-2287	26	1	the	the	DET
ejpam-2287	26	2	paper	paper	NOUN
ejpam-2287	26	3	relied	rely	VERB
ejpam-2287	26	4	heavily	heavily	ADV
ejpam-2287	26	5	on	on	ADP
ejpam-2287	26	6	numerical	numerical	ADJ
ejpam-2287	26	7	experiments	experiment	NOUN
ejpam-2287	26	8	and	and	CCONJ
ejpam-2287	26	9	did	do	AUX
ejpam-2287	26	10	not	not	PART
ejpam-2287	26	11	focus	focus	VERB
ejpam-2287	26	12	as	as	ADV
ejpam-2287	26	13	much	much	ADV
ejpam-2287	26	14	on	on	ADP
ejpam-2287	26	15	developing	develop	VERB
ejpam-2287	26	16	the	the	DET
ejpam-2287	26	17	mathematical	mathematical	ADJ
ejpam-2287	26	18	theory	theory	NOUN
ejpam-2287	26	19	to	to	PART
ejpam-2287	26	20	back	back	VERB
ejpam-2287	26	21	their	their	PRON
ejpam-2287	26	22	numerical	numerical	ADJ
ejpam-2287	26	23	observations	observation	NOUN
ejpam-2287	26	24	.	.	PUNCT
ejpam-2287	27	1	it	it	PRON
ejpam-2287	27	2	was	be	AUX
ejpam-2287	27	3	also	also	ADV
ejpam-2287	27	4	missing	miss	VERB
ejpam-2287	27	5	three	three	NUM
ejpam-2287	27	6	key	key	ADJ
ejpam-2287	27	7	aspects	aspect	NOUN
ejpam-2287	27	8	,	,	PUNCT
ejpam-2287	27	9	namely	namely	ADV
ejpam-2287	27	10	,	,	PUNCT
ejpam-2287	27	11	(	(	PUNCT
ejpam-2287	27	12	a	a	X
ejpam-2287	27	13	)	)	PUNCT
ejpam-2287	27	14	bounds	bound	NOUN
ejpam-2287	27	15	on	on	ADP
ejpam-2287	27	16	the	the	DET
ejpam-2287	27	17	number	number	NOUN
ejpam-2287	27	18	of	of	ADP
ejpam-2287	27	19	real	real	ADJ
ejpam-2287	27	20	equilibria	equilibrium	NOUN
ejpam-2287	27	21	and	and	CCONJ
ejpam-2287	27	22	real	real	ADJ
ejpam-2287	27	23	periodic	periodic	ADJ
ejpam-2287	27	24	solutions	solution	NOUN
ejpam-2287	27	25	,	,	PUNCT
ejpam-2287	27	26	(	(	PUNCT
ejpam-2287	27	27	b	b	X
ejpam-2287	27	28	)	)	PUNCT
ejpam-2287	27	29	existence	existence	NOUN
ejpam-2287	27	30	conditions	condition	NOUN
ejpam-2287	27	31	for	for	ADP
ejpam-2287	27	32	the	the	DET
ejpam-2287	27	33	real	real	ADJ
ejpam-2287	27	34	equilibria	equilibrium	NOUN
ejpam-2287	27	35	and	and	CCONJ
ejpam-2287	27	36	periodic	periodic	ADJ
ejpam-2287	27	37	solutions	solution	NOUN
ejpam-2287	27	38	,	,	PUNCT
ejpam-2287	27	39	and	and	CCONJ
ejpam-2287	27	40	(	(	PUNCT
ejpam-2287	27	41	c	c	X
ejpam-2287	27	42	)	)	PUNCT
ejpam-2287	27	43	global	global	ADJ
ejpam-2287	27	44	attractivity	attractivity	PROPN
ejpam-2287	27	45	results	result	NOUN
ejpam-2287	27	46	for	for	ADP
ejpam-2287	27	47	these	these	DET
ejpam-2287	27	48	solutions	solution	NOUN
ejpam-2287	27	49	including	include	VERB
ejpam-2287	27	50	basins	basin	NOUN
ejpam-2287	27	51	of	of	ADP
ejpam-2287	27	52	attraction	attraction	NOUN
ejpam-2287	27	53	and	and	CCONJ
ejpam-2287	27	54	precise	precise	ADJ
ejpam-2287	27	55	bifurcation	bifurcation	NOUN
ejpam-2287	27	56	values	value	NOUN
ejpam-2287	27	57	for	for	ADP
ejpam-2287	27	58	the	the	DET
ejpam-2287	27	59	parameters	parameter	NOUN
ejpam-2287	27	60	λ	λ	PROPN
ejpam-2287	27	61	and	and	CCONJ
ejpam-2287	27	62	µ.	µ.	NOUN
ejpam-2287	27	63	in	in	ADP
ejpam-2287	27	64	this	this	DET
ejpam-2287	27	65	paper	paper	NOUN
ejpam-2287	27	66	,	,	PUNCT
ejpam-2287	27	67	the	the	DET
ejpam-2287	27	68	author	author	NOUN
ejpam-2287	27	69	will	will	AUX
ejpam-2287	27	70	set	set	VERB
ejpam-2287	27	71	up	up	ADP
ejpam-2287	27	72	a	a	DET
ejpam-2287	27	73	rigorous	rigorous	ADJ
ejpam-2287	27	74	mathematical	mathematical	ADJ
ejpam-2287	27	75	foundation	foundation	NOUN
ejpam-2287	27	76	for	for	ADP
ejpam-2287	27	77	the	the	DET
ejpam-2287	27	78	mckennamoore	mckennamoore	NOUN
ejpam-2287	27	79	suspension	suspension	NOUN
ejpam-2287	27	80	bridge	bridge	NOUN
ejpam-2287	27	81	model	model	NOUN
ejpam-2287	27	82	(	(	PUNCT
ejpam-2287	27	83	1	1	NUM
ejpam-2287	27	84	)	)	PUNCT
ejpam-2287	27	85	by	by	ADP
ejpam-2287	27	86	first	first	ADV
ejpam-2287	27	87	discretizing	discretize	VERB
ejpam-2287	27	88	it	it	PRON
ejpam-2287	27	89	and	and	CCONJ
ejpam-2287	27	90	then	then	ADV
ejpam-2287	27	91	employing	employ	VERB
ejpam-2287	27	92	analytical	analytical	ADJ
ejpam-2287	27	93	and	and	CCONJ
ejpam-2287	27	94	geometrical	geometrical	ADJ
ejpam-2287	27	95	methods	method	NOUN
ejpam-2287	27	96	from	from	ADP
ejpam-2287	27	97	the	the	DET
ejpam-2287	27	98	theory	theory	NOUN
ejpam-2287	27	99	of	of	ADP
ejpam-2287	27	100	difference	difference	NOUN
ejpam-2287	27	101	equations	equation	NOUN
ejpam-2287	27	102	(	(	PUNCT
ejpam-2287	27	103	see	see	VERB
ejpam-2287	27	104	[	[	X
ejpam-2287	27	105	2–4	2–4	NUM
ejpam-2287	27	106	,	,	PUNCT
ejpam-2287	27	107	9–12	9–12	NOUN
ejpam-2287	27	108	,	,	PUNCT
ejpam-2287	27	109	15	15	NUM
ejpam-2287	27	110	]	]	PUNCT
ejpam-2287	27	111	)	)	PUNCT
ejpam-2287	27	112	to	to	PART
ejpam-2287	27	113	analyze	analyze	VERB
ejpam-2287	27	114	equilibria	equilibrium	NOUN
ejpam-2287	27	115	and	and	CCONJ
ejpam-2287	27	116	periodic	periodic	ADJ
ejpam-2287	27	117	solutions	solution	NOUN
ejpam-2287	27	118	of	of	ADP
ejpam-2287	27	119	the	the	DET
ejpam-2287	27	120	resulting	result	VERB
ejpam-2287	27	121	difference	difference	NOUN
ejpam-2287	27	122	equation	equation	NOUN
ejpam-2287	27	123	.	.	PUNCT
ejpam-2287	28	1	for	for	ADP
ejpam-2287	28	2	the	the	DET
ejpam-2287	28	3	rest	rest	NOUN
ejpam-2287	28	4	of	of	ADP
ejpam-2287	28	5	this	this	DET
ejpam-2287	28	6	paper	paper	NOUN
ejpam-2287	28	7	,	,	PUNCT
ejpam-2287	28	8	the	the	DET
ejpam-2287	28	9	author	author	NOUN
ejpam-2287	28	10	will	will	AUX
ejpam-2287	28	11	use	use	VERB
ejpam-2287	28	12	the	the	DET
ejpam-2287	28	13	term	term	NOUN
ejpam-2287	28	14	’	'	PUNCT
ejpam-2287	28	15	periodic	periodic	ADJ
ejpam-2287	28	16	solutions	solution	NOUN
ejpam-2287	28	17	’	'	PUNCT
ejpam-2287	28	18	to	to	PART
ejpam-2287	28	19	mean	mean	VERB
ejpam-2287	28	20	periodic	periodic	ADJ
ejpam-2287	28	21	solutions	solution	NOUN
ejpam-2287	28	22	of	of	ADP
ejpam-2287	28	23	minimal	minimal	ADJ
ejpam-2287	28	24	period	period	NOUN
ejpam-2287	28	25	two	two	NUM
ejpam-2287	28	26	.	.	PUNCT
ejpam-2287	29	1	using	use	VERB
ejpam-2287	29	2	this	this	DET
ejpam-2287	29	3	approach	approach	NOUN
ejpam-2287	29	4	,	,	PUNCT
ejpam-2287	29	5	the	the	DET
ejpam-2287	29	6	author	author	NOUN
ejpam-2287	29	7	will	will	AUX
ejpam-2287	29	8	successfully	successfully	ADV
ejpam-2287	29	9	come	come	VERB
ejpam-2287	29	10	up	up	ADP
ejpam-2287	29	11	with	with	ADP
ejpam-2287	29	12	missing	miss	VERB
ejpam-2287	29	13	mathematical	mathematical	ADJ
ejpam-2287	29	14	explanations	explanation	NOUN
ejpam-2287	29	15	for	for	ADP
ejpam-2287	29	16	numerical	numerical	ADJ
ejpam-2287	29	17	phenomena	phenomenon	NOUN
ejpam-2287	29	18	observed	observe	VERB
ejpam-2287	29	19	by	by	ADP
ejpam-2287	29	20	mckenna	mckenna	PROPN
ejpam-2287	29	21	and	and	CCONJ
ejpam-2287	29	22	moore	moore	PROPN
ejpam-2287	29	23	in	in	ADP
ejpam-2287	29	24	[	[	X
ejpam-2287	29	25	13	13	NUM
ejpam-2287	29	26	]	]	PUNCT
ejpam-2287	29	27	.	.	PUNCT
ejpam-2287	30	1	she	she	PRON
ejpam-2287	30	2	will	will	AUX
ejpam-2287	30	3	also	also	ADV
ejpam-2287	30	4	successfully	successfully	ADV
ejpam-2287	30	5	resolve	resolve	VERB
ejpam-2287	30	6	the	the	DET
ejpam-2287	30	7	three	three	NUM
ejpam-2287	30	8	key	key	ADJ
ejpam-2287	30	9	aspects	aspect	NOUN
ejpam-2287	30	10	missing	miss	VERB
ejpam-2287	30	11	from	from	ADP
ejpam-2287	30	12	[	[	X
ejpam-2287	30	13	13	13	NUM
ejpam-2287	30	14	]	]	PUNCT
ejpam-2287	30	15	,	,	PUNCT
ejpam-2287	30	16	namely	namely	ADV
ejpam-2287	30	17	,	,	PUNCT
ejpam-2287	30	18	bounds	bound	NOUN
ejpam-2287	30	19	,	,	PUNCT
ejpam-2287	30	20	existence	existence	NOUN
ejpam-2287	30	21	conditions	condition	NOUN
ejpam-2287	30	22	and	and	CCONJ
ejpam-2287	30	23	global	global	ADJ
ejpam-2287	30	24	attractivity	attractivity	NOUN
ejpam-2287	30	25	of	of	ADP
ejpam-2287	30	26	the	the	DET
ejpam-2287	30	27	real	real	ADJ
ejpam-2287	30	28	equilibria	equilibrium	NOUN
ejpam-2287	30	29	and	and	CCONJ
ejpam-2287	30	30	periodic	periodic	ADJ
ejpam-2287	30	31	solutions	solution	NOUN
ejpam-2287	30	32	of	of	ADP
ejpam-2287	30	33	equation	equation	NOUN
ejpam-2287	30	34	(	(	PUNCT
ejpam-2287	30	35	1	1	NUM
ejpam-2287	30	36	)	)	PUNCT
ejpam-2287	30	37	in	in	ADP
ejpam-2287	30	38	this	this	DET
ejpam-2287	30	39	paper	paper	NOUN
ejpam-2287	30	40	.	.	PUNCT
ejpam-2287	31	1	this	this	DET
ejpam-2287	31	2	paper	paper	NOUN
ejpam-2287	31	3	is	be	AUX
ejpam-2287	31	4	organized	organize	VERB
ejpam-2287	31	5	as	as	SCONJ
ejpam-2287	31	6	follows	follow	VERB
ejpam-2287	31	7	.	.	PUNCT
ejpam-2287	32	1	in	in	ADP
ejpam-2287	32	2	section	section	NOUN
ejpam-2287	32	3	2	2	NUM
ejpam-2287	32	4	,	,	PUNCT
ejpam-2287	32	5	we	we	PRON
ejpam-2287	32	6	introduce	introduce	VERB
ejpam-2287	32	7	a	a	DET
ejpam-2287	32	8	discretization	discretization	NOUN
ejpam-2287	32	9	of	of	ADP
ejpam-2287	32	10	the	the	DET
ejpam-2287	32	11	the	the	DET
ejpam-2287	32	12	mckenna	mckenna	NOUN
ejpam-2287	32	13	-	-	PUNCT
ejpam-2287	32	14	moore	moore	PROPN
ejpam-2287	32	15	suspension	suspension	PROPN
ejpam-2287	32	16	bridge	bridge	NOUN
ejpam-2287	32	17	model	model	NOUN
ejpam-2287	32	18	(	(	PUNCT
ejpam-2287	32	19	1	1	NUM
ejpam-2287	32	20	)	)	PUNCT
ejpam-2287	32	21	involving	involve	VERB
ejpam-2287	32	22	a	a	DET
ejpam-2287	32	23	second	second	ADJ
ejpam-2287	32	24	-	-	PUNCT
ejpam-2287	32	25	order	order	NOUN
ejpam-2287	32	26	nonlinear	nonlinear	ADJ
ejpam-2287	32	27	difference	difference	NOUN
ejpam-2287	32	28	equation	equation	NOUN
ejpam-2287	32	29	.	.	PUNCT
ejpam-2287	33	1	in	in	ADP
ejpam-2287	33	2	section	section	NOUN
ejpam-2287	33	3	3	3	NUM
ejpam-2287	33	4	,	,	PUNCT
ejpam-2287	33	5	we	we	PRON
ejpam-2287	33	6	look	look	VERB
ejpam-2287	33	7	at	at	ADP
ejpam-2287	33	8	the	the	DET
ejpam-2287	33	9	linearization	linearization	NOUN
ejpam-2287	33	10	of	of	ADP
ejpam-2287	33	11	the	the	DET
ejpam-2287	33	12	discrete	discrete	ADJ
ejpam-2287	33	13	nonlinear	nonlinear	ADJ
ejpam-2287	33	14	model	model	NOUN
ejpam-2287	33	15	introduced	introduce	VERB
ejpam-2287	33	16	in	in	ADP
ejpam-2287	33	17	section	section	NOUN
ejpam-2287	33	18	2	2	NUM
ejpam-2287	33	19	.	.	PUNCT
ejpam-2287	34	1	in	in	ADP
ejpam-2287	34	2	section	section	NOUN
ejpam-2287	34	3	4	4	NUM
ejpam-2287	34	4	,	,	PUNCT
ejpam-2287	34	5	we	we	PRON
ejpam-2287	34	6	introduce	introduce	VERB
ejpam-2287	34	7	a	a	DET
ejpam-2287	34	8	modification	modification	NOUN
ejpam-2287	34	9	to	to	ADP
ejpam-2287	34	10	our	our	PRON
ejpam-2287	34	11	discrete	discrete	ADJ
ejpam-2287	34	12	model	model	NOUN
ejpam-2287	34	13	to	to	PART
ejpam-2287	34	14	make	make	VERB
ejpam-2287	34	15	it	it	PRON
ejpam-2287	34	16	more	more	ADV
ejpam-2287	34	17	realistic	realistic	ADJ
ejpam-2287	34	18	.	.	PUNCT
ejpam-2287	35	1	in	in	ADP
ejpam-2287	35	2	section	section	NOUN
ejpam-2287	35	3	5	5	NUM
ejpam-2287	35	4	,	,	PUNCT
ejpam-2287	35	5	we	we	PRON
ejpam-2287	35	6	establish	establish	VERB
ejpam-2287	35	7	the	the	DET
ejpam-2287	35	8	number	number	NOUN
ejpam-2287	35	9	of	of	ADP
ejpam-2287	35	10	real	real	ADJ
ejpam-2287	35	11	equilibria	equilibrium	NOUN
ejpam-2287	35	12	and	and	CCONJ
ejpam-2287	35	13	real	real	ADJ
ejpam-2287	35	14	periodic	periodic	ADJ
ejpam-2287	35	15	solutions	solution	NOUN
ejpam-2287	35	16	one	one	PRON
ejpam-2287	35	17	can	can	AUX
ejpam-2287	35	18	expect	expect	VERB
ejpam-2287	35	19	to	to	PART
ejpam-2287	35	20	see	see	VERB
ejpam-2287	35	21	in	in	ADP
ejpam-2287	35	22	our	our	PRON
ejpam-2287	35	23	modified	modify	VERB
ejpam-2287	35	24	discrete	discrete	ADJ
ejpam-2287	35	25	model	model	NOUN
ejpam-2287	35	26	.	.	PUNCT
ejpam-2287	36	1	in	in	ADP
ejpam-2287	36	2	section	section	NOUN
ejpam-2287	36	3	6	6	NUM
ejpam-2287	36	4	,	,	PUNCT
ejpam-2287	36	5	we	we	PRON
ejpam-2287	36	6	establish	establish	VERB
ejpam-2287	36	7	local	local	ADJ
ejpam-2287	36	8	and	and	CCONJ
ejpam-2287	36	9	global	global	ADJ
ejpam-2287	36	10	attractivity	attractivity	PROPN
ejpam-2287	36	11	results	result	NOUN
ejpam-2287	36	12	for	for	ADP
ejpam-2287	36	13	our	our	PRON
ejpam-2287	36	14	model	model	NOUN
ejpam-2287	36	15	,	,	PUNCT
ejpam-2287	36	16	including	include	VERB
ejpam-2287	36	17	basins	basin	NOUN
ejpam-2287	36	18	of	of	ADP
ejpam-2287	36	19	attraction	attraction	NOUN
ejpam-2287	36	20	and	and	CCONJ
ejpam-2287	36	21	bifurcation	bifurcation	NOUN
ejpam-2287	36	22	values	value	NOUN
ejpam-2287	36	23	for	for	ADP
ejpam-2287	36	24	the	the	DET
ejpam-2287	36	25	parameters	parameter	NOUN
ejpam-2287	36	26	λ	λ	PROPN
ejpam-2287	36	27	and	and	CCONJ
ejpam-2287	36	28	µ.	µ.	NOUN
ejpam-2287	36	29	in	in	ADP
ejpam-2287	36	30	section	section	NOUN
ejpam-2287	36	31	7	7	NUM
ejpam-2287	36	32	,	,	PUNCT
ejpam-2287	36	33	we	we	PRON
ejpam-2287	36	34	give	give	VERB
ejpam-2287	36	35	a	a	DET
ejpam-2287	36	36	physical	physical	ADJ
ejpam-2287	36	37	interpretation	interpretation	NOUN
ejpam-2287	36	38	of	of	ADP
ejpam-2287	36	39	our	our	PRON
ejpam-2287	36	40	mathematical	mathematical	ADJ
ejpam-2287	36	41	results	result	NOUN
ejpam-2287	36	42	for	for	ADP
ejpam-2287	36	43	our	our	PRON
ejpam-2287	36	44	modified	modify	VERB
ejpam-2287	36	45	discrete	discrete	ADJ
ejpam-2287	36	46	suspension	suspension	NOUN
ejpam-2287	36	47	bridge	bridge	NOUN
ejpam-2287	36	48	model	model	NOUN
ejpam-2287	36	49	from	from	ADP
ejpam-2287	36	50	section	section	NOUN
ejpam-2287	36	51	4	4	NUM
ejpam-2287	36	52	.	.	PUNCT
ejpam-2287	37	1	s.	s.	PROPN
ejpam-2287	37	2	basu	basu	PROPN
ejpam-2287	37	3	/	/	SYM
ejpam-2287	37	4	eur	eur	PROPN
ejpam-2287	37	5	.	.	PUNCT
ejpam-2287	38	1	j.	j.	PROPN
ejpam-2287	38	2	pure	pure	PROPN
ejpam-2287	38	3	appl	appl	PROPN
ejpam-2287	38	4	.	.	PROPN
ejpam-2287	38	5	math	math	PROPN
ejpam-2287	38	6	,	,	PUNCT
ejpam-2287	38	7	7	7	NUM
ejpam-2287	38	8	(	(	PUNCT
ejpam-2287	38	9	2014	2014	NUM
ejpam-2287	38	10	)	)	PUNCT
ejpam-2287	38	11	,	,	PUNCT
ejpam-2287	38	12	442	442	NUM
ejpam-2287	38	13	-	-	SYM
ejpam-2287	38	14	461	461	NUM
ejpam-2287	38	15	444	444	NUM
ejpam-2287	38	16	2	2	NUM
ejpam-2287	38	17	.	.	PUNCT
ejpam-2287	39	1	a	a	DET
ejpam-2287	39	2	discrete	discrete	ADJ
ejpam-2287	39	3	nonlinear	nonlinear	ADJ
ejpam-2287	39	4	suspension	suspension	NOUN
ejpam-2287	39	5	bridge	bridge	NOUN
ejpam-2287	39	6	model	model	NOUN
ejpam-2287	39	7	we	we	PRON
ejpam-2287	39	8	start	start	VERB
ejpam-2287	39	9	with	with	ADP
ejpam-2287	39	10	the	the	DET
ejpam-2287	39	11	mckenna	mckenna	NOUN
ejpam-2287	39	12	-	-	PUNCT
ejpam-2287	39	13	moore	moore	PROPN
ejpam-2287	39	14	suspension	suspension	PROPN
ejpam-2287	39	15	bridge	bridge	NOUN
ejpam-2287	39	16	model	model	NOUN
ejpam-2287	39	17	(	(	PUNCT
ejpam-2287	39	18	1	1	NUM
ejpam-2287	39	19	)	)	PUNCT
ejpam-2287	39	20	from	from	ADP
ejpam-2287	39	21	the	the	DET
ejpam-2287	39	22	previous	previous	ADJ
ejpam-2287	39	23	section	section	NOUN
ejpam-2287	39	24	.	.	PUNCT
ejpam-2287	40	1	replacing	replace	VERB
ejpam-2287	40	2	the	the	DET
ejpam-2287	40	3	parameters	parameter	NOUN
ejpam-2287	40	4	in	in	ADP
ejpam-2287	40	5	(	(	PUNCT
ejpam-2287	40	6	1	1	NUM
ejpam-2287	40	7	)	)	PUNCT
ejpam-2287	40	8	by	by	ADP
ejpam-2287	40	9	actual	actual	ADJ
ejpam-2287	40	10	numerical	numerical	ADJ
ejpam-2287	40	11	values	value	NOUN
ejpam-2287	40	12	from	from	ADP
ejpam-2287	40	13	engineers	engineer	NOUN
ejpam-2287	40	14	’	’	PART
ejpam-2287	40	15	reports	report	NOUN
ejpam-2287	40	16	of	of	ADP
ejpam-2287	40	17	the	the	DET
ejpam-2287	40	18	1940	1940	NUM
ejpam-2287	40	19	tacoma	tacoma	NOUN
ejpam-2287	40	20	narrows	narrow	VERB
ejpam-2287	40	21	bridge	bridge	NOUN
ejpam-2287	40	22	collapse	collapse	NOUN
ejpam-2287	40	23	which	which	PRON
ejpam-2287	40	24	were	be	AUX
ejpam-2287	40	25	used	use	VERB
ejpam-2287	40	26	by	by	ADP
ejpam-2287	40	27	mckenna	mckenna	PROPN
ejpam-2287	40	28	and	and	CCONJ
ejpam-2287	40	29	moore	moore	PROPN
ejpam-2287	40	30	in	in	ADP
ejpam-2287	40	31	their	their	PRON
ejpam-2287	40	32	paper	paper	NOUN
ejpam-2287	41	1	[	[	X
ejpam-2287	41	2	13	13	NUM
ejpam-2287	41	3	]	]	PUNCT
ejpam-2287	41	4	and	and	CCONJ
ejpam-2287	41	5	discretizing	discretize	VERB
ejpam-2287	41	6	the	the	DET
ejpam-2287	41	7	first	first	ADJ
ejpam-2287	41	8	equation	equation	NOUN
ejpam-2287	41	9	in	in	ADP
ejpam-2287	41	10	(	(	PUNCT
ejpam-2287	41	11	1	1	NUM
ejpam-2287	41	12	)	)	PUNCT
ejpam-2287	41	13	by	by	ADP
ejpam-2287	41	14	setting	set	VERB
ejpam-2287	41	15	θ	θ	PROPN
ejpam-2287	41	16	′	′	NUM
ejpam-2287	41	17	:	:	PUNCT
ejpam-2287	41	18	=	=	SYM
ejpam-2287	41	19	θn+1	θn+1	VERB
ejpam-2287	41	20	−	−	PROPN
ejpam-2287	41	21	θn	θn	NOUN
ejpam-2287	41	22	,	,	PUNCT
ejpam-2287	41	23	we	we	PRON
ejpam-2287	41	24	get	get	VERB
ejpam-2287	41	25	the	the	DET
ejpam-2287	41	26	nonlinear	nonlinear	ADJ
ejpam-2287	41	27	nonautonomous	nonautonomous	ADJ
ejpam-2287	41	28	difference	difference	NOUN
ejpam-2287	41	29	equation	equation	NOUN
ejpam-2287	41	30	θn+1	θn+1	NOUN
ejpam-2287	41	31	=	=	SYM
ejpam-2287	41	32	1.99θn	1.99θn	NUM
ejpam-2287	41	33	−	−	NOUN
ejpam-2287	41	34	0.99θn−1	0.99θn−1	NUM
ejpam-2287	42	1	−	−	PROPN
ejpam-2287	42	2	2.4	2.4	NUM
ejpam-2287	42	3	cosθn−1	cosθn−1	PROPN
ejpam-2287	42	4	sinθn−1	sinθn−1	PROPN
ejpam-2287	43	1	+	+	PUNCT
ejpam-2287	43	2	λ	λ	PROPN
ejpam-2287	43	3	sinµ(n−	sinµ(n−	ADJ
ejpam-2287	43	4	1	1	NUM
ejpam-2287	43	5	)	)	PUNCT
ejpam-2287	43	6	(	(	PUNCT
ejpam-2287	43	7	2	2	X
ejpam-2287	43	8	)	)	PUNCT
ejpam-2287	43	9	where	where	SCONJ
ejpam-2287	43	10	λ	λ	NOUN
ejpam-2287	43	11	,	,	PUNCT
ejpam-2287	43	12	µ	µ	X
ejpam-2287	43	13	are	be	AUX
ejpam-2287	43	14	positive	positive	ADJ
ejpam-2287	43	15	parameters	parameter	NOUN
ejpam-2287	43	16	and	and	CCONJ
ejpam-2287	43	17	−π/2	−π/2	PROPN
ejpam-2287	43	18	<	<	X
ejpam-2287	43	19	θn	θn	X
ejpam-2287	43	20	<	<	X
ejpam-2287	43	21	π/2	π/2	PROPN
ejpam-2287	43	22	for	for	ADP
ejpam-2287	43	23	all	all	DET
ejpam-2287	43	24	n	n	PRON
ejpam-2287	43	25	∈	∈	PROPN
ejpam-2287	43	26	n.	n.	NOUN
ejpam-2287	43	27	note	note	VERB
ejpam-2287	43	28	that	that	SCONJ
ejpam-2287	43	29	the	the	DET
ejpam-2287	43	30	periodic	periodic	ADJ
ejpam-2287	43	31	external	external	ADJ
ejpam-2287	43	32	forcing	force	VERB
ejpam-2287	43	33	term	term	NOUN
ejpam-2287	43	34	λ	λ	NOUN
ejpam-2287	43	35	sinµ(n−	sinµ(n−	ADJ
ejpam-2287	43	36	1	1	NUM
ejpam-2287	43	37	)	)	PUNCT
ejpam-2287	43	38	depends	depend	VERB
ejpam-2287	43	39	on	on	ADP
ejpam-2287	43	40	the	the	DET
ejpam-2287	43	41	step	step	NOUN
ejpam-2287	43	42	number	number	NOUN
ejpam-2287	43	43	n	n	CCONJ
ejpam-2287	43	44	−	−	PROPN
ejpam-2287	43	45	1	1	NUM
ejpam-2287	43	46	.	.	PUNCT
ejpam-2287	44	1	more	more	ADV
ejpam-2287	44	2	precisely	precisely	ADV
ejpam-2287	44	3	,	,	PUNCT
ejpam-2287	44	4	it	it	PRON
ejpam-2287	44	5	depends	depend	VERB
ejpam-2287	44	6	on	on	ADP
ejpam-2287	44	7	the	the	DET
ejpam-2287	44	8	position	position	NOUN
ejpam-2287	44	9	of	of	ADP
ejpam-2287	44	10	the	the	DET
ejpam-2287	44	11	suspension	suspension	NOUN
ejpam-2287	44	12	bridge	bridge	NOUN
ejpam-2287	44	13	and	and	CCONJ
ejpam-2287	44	14	hence	hence	ADV
ejpam-2287	44	15	on	on	ADP
ejpam-2287	44	16	its	its	PRON
ejpam-2287	44	17	torsional	torsional	ADJ
ejpam-2287	44	18	angle	angle	NOUN
ejpam-2287	44	19	θn−1	θn−1	ADJ
ejpam-2287	44	20	at	at	ADP
ejpam-2287	44	21	step	step	NOUN
ejpam-2287	44	22	number	number	NOUN
ejpam-2287	44	23	n−1	n−1	PROPN
ejpam-2287	44	24	.	.	PROPN
ejpam-2287	45	1	for	for	ADP
ejpam-2287	45	2	example	example	NOUN
ejpam-2287	45	3	,	,	PUNCT
ejpam-2287	45	4	if	if	SCONJ
ejpam-2287	45	5	the	the	DET
ejpam-2287	45	6	periodic	periodic	ADJ
ejpam-2287	45	7	external	external	ADJ
ejpam-2287	45	8	forcing	force	VERB
ejpam-2287	45	9	term	term	NOUN
ejpam-2287	45	10	is	be	AUX
ejpam-2287	45	11	due	due	ADJ
ejpam-2287	45	12	to	to	ADP
ejpam-2287	45	13	blowing	blow	VERB
ejpam-2287	45	14	wind	wind	NOUN
ejpam-2287	45	15	,	,	PUNCT
ejpam-2287	45	16	then	then	ADV
ejpam-2287	45	17	the	the	DET
ejpam-2287	45	18	effect	effect	NOUN
ejpam-2287	45	19	of	of	ADP
ejpam-2287	45	20	the	the	DET
ejpam-2287	45	21	wind	wind	NOUN
ejpam-2287	45	22	on	on	ADP
ejpam-2287	45	23	the	the	DET
ejpam-2287	45	24	bridge	bridge	NOUN
ejpam-2287	45	25	would	would	AUX
ejpam-2287	45	26	depend	depend	VERB
ejpam-2287	45	27	on	on	ADP
ejpam-2287	45	28	the	the	DET
ejpam-2287	45	29	position	position	NOUN
ejpam-2287	45	30	of	of	ADP
ejpam-2287	45	31	the	the	DET
ejpam-2287	45	32	bridge	bridge	NOUN
ejpam-2287	45	33	with	with	ADP
ejpam-2287	45	34	respect	respect	NOUN
ejpam-2287	45	35	to	to	ADP
ejpam-2287	45	36	the	the	DET
ejpam-2287	45	37	direction	direction	NOUN
ejpam-2287	45	38	of	of	ADP
ejpam-2287	45	39	the	the	DET
ejpam-2287	45	40	wind	wind	NOUN
ejpam-2287	45	41	gusts	gust	NOUN
ejpam-2287	45	42	.	.	PUNCT
ejpam-2287	46	1	incorporating	incorporate	VERB
ejpam-2287	46	2	this	this	PRON
ejpam-2287	46	3	in	in	ADP
ejpam-2287	46	4	(	(	PUNCT
ejpam-2287	46	5	2	2	NUM
ejpam-2287	46	6	)	)	PUNCT
ejpam-2287	46	7	,	,	PUNCT
ejpam-2287	46	8	we	we	PRON
ejpam-2287	46	9	get	get	VERB
ejpam-2287	46	10	the	the	DET
ejpam-2287	46	11	updated	update	VERB
ejpam-2287	46	12	autonomous	autonomous	ADJ
ejpam-2287	46	13	difference	difference	NOUN
ejpam-2287	46	14	equation	equation	NOUN
ejpam-2287	46	15	θn+1	θn+1	X
ejpam-2287	46	16	=	=	SYM
ejpam-2287	46	17	1.99θn	1.99θn	NUM
ejpam-2287	46	18	−	−	NOUN
ejpam-2287	46	19	0.99θn−1	0.99θn−1	NUM
ejpam-2287	47	1	−	−	PROPN
ejpam-2287	47	2	2.4	2.4	NUM
ejpam-2287	47	3	cosθn−1	cosθn−1	PROPN
ejpam-2287	47	4	sinθn−1	sinθn−1	PROPN
ejpam-2287	48	1	+	+	PROPN
ejpam-2287	48	2	λ	λ	X
ejpam-2287	48	3	sinµθn−1	sinµθn−1	PROPN
ejpam-2287	48	4	=	=	NOUN
ejpam-2287	48	5	:	:	PUNCT
ejpam-2287	48	6	f	f	PROPN
ejpam-2287	48	7	(	(	PUNCT
ejpam-2287	48	8	θn−1,θn	θn−1,θn	PROPN
ejpam-2287	48	9	)	)	PUNCT
ejpam-2287	48	10	(	(	PUNCT
ejpam-2287	48	11	3	3	X
ejpam-2287	48	12	)	)	PUNCT
ejpam-2287	48	13	applying	apply	VERB
ejpam-2287	48	14	the	the	DET
ejpam-2287	48	15	transformation	transformation	NOUN
ejpam-2287	48	16	θn+1	θn+1	PUNCT
ejpam-2287	48	17	:	:	PUNCT
ejpam-2287	48	18	=	=	SYM
ejpam-2287	48	19	un	un	PROPN
ejpam-2287	48	20	and	and	CCONJ
ejpam-2287	48	21	un+1	un+1	ADV
ejpam-2287	48	22	:	:	PUNCT
ejpam-2287	48	23	=	=	SYM
ejpam-2287	48	24	f	f	X
ejpam-2287	48	25	(	(	PUNCT
ejpam-2287	48	26	θn	θn	PROPN
ejpam-2287	48	27	,	,	PUNCT
ejpam-2287	48	28	un	un	PROPN
ejpam-2287	48	29	)	)	PUNCT
ejpam-2287	48	30	to	to	ADP
ejpam-2287	48	31	(	(	PUNCT
ejpam-2287	48	32	3	3	X
ejpam-2287	48	33	)	)	PUNCT
ejpam-2287	48	34	changes	change	VERB
ejpam-2287	48	35	it	it	PRON
ejpam-2287	48	36	to	to	ADP
ejpam-2287	48	37	the	the	DET
ejpam-2287	48	38	nonlinear	nonlinear	ADJ
ejpam-2287	48	39	system	system	NOUN
ejpam-2287	48	40	of	of	ADP
ejpam-2287	48	41	two	two	NUM
ejpam-2287	48	42	difference	difference	NOUN
ejpam-2287	48	43	equations	equation	NOUN
ejpam-2287	48	44	¨	¨	NOUN
ejpam-2287	48	45	θn+1	θn+1	PROPN
ejpam-2287	48	46	=	=	SYM
ejpam-2287	48	47	un	un	PROPN
ejpam-2287	48	48	un+1	un+1	PROPN
ejpam-2287	48	49	=	=	SYM
ejpam-2287	49	1	1.99un	1.99un	NOUN
ejpam-2287	50	1	−	−	NOUN
ejpam-2287	50	2	0.99θn	0.99θn	NUM
ejpam-2287	50	3	−	−	PROPN
ejpam-2287	50	4	2.4	2.4	NUM
ejpam-2287	50	5	cosθn	cosθn	NOUN
ejpam-2287	50	6	sinθn	sinθn	NOUN
ejpam-2287	50	7	+	+	PROPN
ejpam-2287	50	8	λ	λ	PROPN
ejpam-2287	50	9	sinµθn	sinµθn	NOUN
ejpam-2287	50	10	(	(	PUNCT
ejpam-2287	50	11	4	4	NUM
ejpam-2287	50	12	)	)	PUNCT
ejpam-2287	50	13	whose	whose	DET
ejpam-2287	50	14	associated	associated	ADJ
ejpam-2287	50	15	map	map	NOUN
ejpam-2287	50	16	t	t	PROPN
ejpam-2287	50	17	(	(	PUNCT
ejpam-2287	50	18	θ	θ	PROPN
ejpam-2287	50	19	,	,	PUNCT
ejpam-2287	50	20	u	u	NOUN
ejpam-2287	50	21	)	)	PUNCT
ejpam-2287	50	22	is	be	AUX
ejpam-2287	50	23	defined	define	VERB
ejpam-2287	50	24	as	as	ADP
ejpam-2287	50	25	t	t	PROPN
ejpam-2287	50	26	�	�	PROPN
ejpam-2287	50	27	θ	θ	PROPN
ejpam-2287	50	28	u	u	PROPN
ejpam-2287	50	29	�	�	PROPN
ejpam-2287	50	30	=	=	SYM
ejpam-2287	50	31	�	�	PROPN
ejpam-2287	50	32	u	u	NOUN
ejpam-2287	50	33	1.99u−	1.99u−	NUM
ejpam-2287	50	34	0.99θ	0.99θ	NUM
ejpam-2287	50	35	−	−	PROPN
ejpam-2287	50	36	2.4	2.4	NUM
ejpam-2287	50	37	cosθ	cosθ	PROPN
ejpam-2287	50	38	sinθ	sinθ	PROPN
ejpam-2287	50	39	+	+	PROPN
ejpam-2287	50	40	λ	λ	PROPN
ejpam-2287	50	41	sinµθ	sinµθ	PROPN
ejpam-2287	50	42	�	�	PROPN
ejpam-2287	50	43	(	(	PUNCT
ejpam-2287	50	44	5	5	NUM
ejpam-2287	50	45	)	)	PUNCT
ejpam-2287	50	46	note	note	NOUN
ejpam-2287	50	47	that	that	SCONJ
ejpam-2287	50	48	the	the	DET
ejpam-2287	50	49	periodic	periodic	ADJ
ejpam-2287	50	50	solutions	solution	NOUN
ejpam-2287	50	51	of	of	ADP
ejpam-2287	50	52	(	(	PUNCT
ejpam-2287	50	53	3	3	X
ejpam-2287	50	54	)	)	PUNCT
ejpam-2287	50	55	are	be	AUX
ejpam-2287	50	56	precisely	precisely	ADV
ejpam-2287	50	57	the	the	DET
ejpam-2287	50	58	intersection	intersection	NOUN
ejpam-2287	50	59	points	point	NOUN
ejpam-2287	50	60	of	of	ADP
ejpam-2287	50	61	the	the	DET
ejpam-2287	50	62	equilibrium	equilibrium	NOUN
ejpam-2287	50	63	curves	curve	NOUN
ejpam-2287	50	64	of	of	ADP
ejpam-2287	50	65	the	the	DET
ejpam-2287	50	66	map	map	NOUN
ejpam-2287	50	67	t2(θ	t2(θ	X
ejpam-2287	50	68	,	,	PUNCT
ejpam-2287	50	69	u	u	NOUN
ejpam-2287	50	70	)	)	PUNCT
ejpam-2287	50	71	:	:	PUNCT
ejpam-2287	51	1	=	=	SYM
ejpam-2287	51	2	(	(	PUNCT
ejpam-2287	51	3	f(θ	f(θ	PROPN
ejpam-2287	51	4	,	,	PUNCT
ejpam-2287	51	5	u	u	NOUN
ejpam-2287	51	6	)	)	PUNCT
ejpam-2287	51	7	,	,	PUNCT
ejpam-2287	51	8	g(θ	g(θ	ADP
ejpam-2287	51	9	,	,	PUNCT
ejpam-2287	51	10	u	u	NOUN
ejpam-2287	51	11	)	)	PUNCT
ejpam-2287	51	12	)	)	PUNCT
ejpam-2287	51	13	which	which	PRON
ejpam-2287	51	14	are	be	AUX
ejpam-2287	51	15	defined	define	VERB
ejpam-2287	51	16	by	by	ADP
ejpam-2287	51	17	the	the	DET
ejpam-2287	51	18	equations	equation	NOUN
ejpam-2287	51	19	¨	¨	NOUN
ejpam-2287	51	20	f(θ	f(θ	X
ejpam-2287	51	21	,	,	PUNCT
ejpam-2287	51	22	u	u	NOUN
ejpam-2287	51	23	)	)	PUNCT
ejpam-2287	51	24	=	=	SYM
ejpam-2287	52	1	θ	θ	X
ejpam-2287	52	2	g(θ	g(θ	PROPN
ejpam-2287	52	3	,	,	PUNCT
ejpam-2287	52	4	u	u	NOUN
ejpam-2287	52	5	)	)	PUNCT
ejpam-2287	53	1	=	=	SYM
ejpam-2287	53	2	u	u	NOUN
ejpam-2287	53	3	(	(	PUNCT
ejpam-2287	53	4	6	6	NUM
ejpam-2287	53	5	)	)	PUNCT
ejpam-2287	53	6	in	in	ADP
ejpam-2287	53	7	particular	particular	ADJ
ejpam-2287	53	8	,	,	PUNCT
ejpam-2287	53	9	the	the	DET
ejpam-2287	53	10	map	map	NOUN
ejpam-2287	53	11	t2(θ	t2(θ	X
ejpam-2287	53	12	,	,	PUNCT
ejpam-2287	53	13	u	u	NOUN
ejpam-2287	53	14	)	)	PUNCT
ejpam-2287	53	15	for	for	ADP
ejpam-2287	53	16	equation	equation	NOUN
ejpam-2287	53	17	(	(	PUNCT
ejpam-2287	53	18	3	3	X
ejpam-2287	53	19	)	)	PUNCT
ejpam-2287	53	20	has	have	VERB
ejpam-2287	53	21	the	the	DET
ejpam-2287	53	22	form	form	NOUN
ejpam-2287	53	23	t2	t2	NOUN
ejpam-2287	53	24	�	�	PROPN
ejpam-2287	53	25	θ	θ	PROPN
ejpam-2287	53	26	u	u	PROPN
ejpam-2287	53	27	�	�	PROPN
ejpam-2287	53	28	=	=	SYM
ejpam-2287	53	29			NOUN
ejpam-2287	53	30			PUNCT
ejpam-2287	53	31	−0.99(−1.0101λ	−0.99(−1.0101λ	PROPN
ejpam-2287	53	32	sinµθ	sinµθ	PROPN
ejpam-2287	53	33	+	+	NUM
ejpam-2287	53	34	θ	θ	PROPN
ejpam-2287	53	35	+	+	NUM
ejpam-2287	53	36	2.42424	2.42424	NUM
ejpam-2287	53	37	sinθ	sinθ	NOUN
ejpam-2287	53	38	cosθ	cosθ	PROPN
ejpam-2287	53	39	−	−	PROPN
ejpam-2287	54	1	2.0101u	2.0101u	NOUN
ejpam-2287	54	2	)	)	PUNCT
ejpam-2287	54	3	2.9701(0.670011λ	2.9701(0.670011λ	NOUN
ejpam-2287	54	4	sinµθ	sinµθ	NOUN
ejpam-2287	54	5	+	+	CCONJ
ejpam-2287	54	6	0.336689λ	0.336689λ	NUM
ejpam-2287	54	7	sinµu−	sinµu−	NOUN
ejpam-2287	54	8	0.663311θ−	0.663311θ−	PROPN
ejpam-2287	54	9	1.60803	1.60803	NUM
ejpam-2287	54	10	sinθ	sinθ	PROPN
ejpam-2287	54	11	cosθ	cosθ	PROPN
ejpam-2287	54	12	+	+	CCONJ
ejpam-2287	54	13	u−	u−	PROPN
ejpam-2287	54	14	0.808054	0.808054	NUM
ejpam-2287	54	15	sin	sin	NOUN
ejpam-2287	54	16	u	u	PROPN
ejpam-2287	54	17	cos	cos	PROPN
ejpam-2287	54	18	u	u	NOUN
ejpam-2287	54	19	)	)	PUNCT
ejpam-2287	54	20			PROPN
ejpam-2287	54	21			NOUN
ejpam-2287	54	22	(	(	PUNCT
ejpam-2287	54	23	7	7	NUM
ejpam-2287	54	24	)	)	PUNCT
ejpam-2287	54	25	s.	s.	PROPN
ejpam-2287	54	26	basu	basu	PROPN
ejpam-2287	54	27	/	/	SYM
ejpam-2287	54	28	eur	eur	PROPN
ejpam-2287	54	29	.	.	PUNCT
ejpam-2287	55	1	j.	j.	PROPN
ejpam-2287	55	2	pure	pure	PROPN
ejpam-2287	55	3	appl	appl	PROPN
ejpam-2287	55	4	.	.	PROPN
ejpam-2287	55	5	math	math	PROPN
ejpam-2287	55	6	,	,	PUNCT
ejpam-2287	55	7	7	7	NUM
ejpam-2287	55	8	(	(	PUNCT
ejpam-2287	55	9	2014	2014	NUM
ejpam-2287	55	10	)	)	PUNCT
ejpam-2287	55	11	,	,	PUNCT
ejpam-2287	55	12	442	442	NUM
ejpam-2287	55	13	-	-	SYM
ejpam-2287	55	14	461	461	NUM
ejpam-2287	55	15	445	445	NUM
ejpam-2287	55	16	with	with	ADP
ejpam-2287	55	17	its	its	PRON
ejpam-2287	55	18	associated	associated	ADJ
ejpam-2287	55	19	equilibrium	equilibrium	NOUN
ejpam-2287	55	20	curves	curve	NOUN
ejpam-2287	55	21	given	give	VERB
ejpam-2287	55	22	by	by	ADP
ejpam-2287	55	23			PROPN
ejpam-2287	55	24			NOUN
ejpam-2287	55	25			NOUN
ejpam-2287	55	26	e1	e1	VERB
ejpam-2287	55	27	:	:	PUNCT
ejpam-2287	55	28	−0.99(−1.0101λ	−0.99(−1.0101λ	PROPN
ejpam-2287	55	29	sinµθ	sinµθ	PROPN
ejpam-2287	55	30	+	+	NUM
ejpam-2287	55	31	θ	θ	PROPN
ejpam-2287	55	32	+	+	NUM
ejpam-2287	55	33	2.42424	2.42424	NUM
ejpam-2287	55	34	sinθ	sinθ	NOUN
ejpam-2287	55	35	cosθ	cosθ	PROPN
ejpam-2287	55	36	−	−	PROPN
ejpam-2287	55	37	2.0101u)−	2.0101u)−	NUM
ejpam-2287	55	38	θ	θ	NOUN
ejpam-2287	55	39	=	=	SYM
ejpam-2287	55	40	0	0	NUM
ejpam-2287	55	41	e2	e2	PROPN
ejpam-2287	55	42	:	:	PUNCT
ejpam-2287	55	43	2.9701(0.670011λ	2.9701(0.670011λ	NUM
ejpam-2287	55	44	sinµθ	sinµθ	NOUN
ejpam-2287	55	45	+	+	CCONJ
ejpam-2287	55	46	0.336689λ	0.336689λ	PROPN
ejpam-2287	55	47	sinµu−	sinµu−	NOUN
ejpam-2287	55	48	0.663311θ	0.663311θ	X
ejpam-2287	55	49	−1.60803	−1.60803	PROPN
ejpam-2287	55	50	sinθ	sinθ	PROPN
ejpam-2287	55	51	cosθ	cosθ	PROPN
ejpam-2287	56	1	−	−	PROPN
ejpam-2287	57	1	0.808054	0.808054	NUM
ejpam-2287	57	2	sin	sin	NOUN
ejpam-2287	57	3	u	u	X
ejpam-2287	57	4	cos	cos	PROPN
ejpam-2287	57	5	u	u	NOUN
ejpam-2287	57	6	)	)	PUNCT
ejpam-2287	57	7	=	=	SYM
ejpam-2287	57	8	0	0	PUNCT
ejpam-2287	57	9	(	(	PUNCT
ejpam-2287	57	10	8)	8)	NUM
ejpam-2287	57	11	replacing	replace	VERB
ejpam-2287	57	12	sinθ	sinθ	PROPN
ejpam-2287	57	13	,	,	PUNCT
ejpam-2287	57	14	cosθ	cosθ	PROPN
ejpam-2287	57	15	,	,	PUNCT
ejpam-2287	57	16	sin	sin	NOUN
ejpam-2287	57	17	u	u	NOUN
ejpam-2287	57	18	and	and	CCONJ
ejpam-2287	57	19	cos	cos	ADP
ejpam-2287	57	20	u	u	NOUN
ejpam-2287	57	21	by	by	ADP
ejpam-2287	57	22	their	their	PRON
ejpam-2287	57	23	taylor	taylor	PROPN
ejpam-2287	57	24	series	series	NOUN
ejpam-2287	57	25	expansions	expansion	NOUN
ejpam-2287	57	26	in	in	ADP
ejpam-2287	57	27	(	(	PUNCT
ejpam-2287	57	28	8)	8)	NUM
ejpam-2287	57	29	,	,	PUNCT
ejpam-2287	57	30	one	one	PRON
ejpam-2287	57	31	can	can	AUX
ejpam-2287	57	32	think	think	VERB
ejpam-2287	57	33	of	of	ADP
ejpam-2287	57	34	the	the	DET
ejpam-2287	57	35	curves	curve	NOUN
ejpam-2287	57	36	e1	e1	PROPN
ejpam-2287	57	37	and	and	CCONJ
ejpam-2287	57	38	e2	e2	NOUN
ejpam-2287	57	39	as	as	ADP
ejpam-2287	57	40	polynomials	polynomial	NOUN
ejpam-2287	57	41	of	of	ADP
ejpam-2287	57	42	infinite	infinite	ADJ
ejpam-2287	57	43	degrees	degree	NOUN
ejpam-2287	57	44	,	,	PUNCT
ejpam-2287	57	45	that	that	ADV
ejpam-2287	57	46	is	is	ADV
ejpam-2287	57	47	,	,	PUNCT
ejpam-2287	57	48	of	of	ADP
ejpam-2287	57	49	degrees	degree	NOUN
ejpam-2287	57	50	n1	n1	NOUN
ejpam-2287	57	51	and	and	CCONJ
ejpam-2287	57	52	n2	n2	ADJ
ejpam-2287	57	53	where	where	SCONJ
ejpam-2287	57	54	n1→∞	n1→∞	NOUN
ejpam-2287	57	55	and	and	CCONJ
ejpam-2287	57	56	n2→∞.	n2→∞.	NOUN
ejpam-2287	57	57	it	it	PRON
ejpam-2287	57	58	follows	follow	VERB
ejpam-2287	57	59	from	from	ADP
ejpam-2287	57	60	bézout	bézout	NOUN
ejpam-2287	57	61	’s	’s	PART
ejpam-2287	57	62	theorem	theorem	NOUN
ejpam-2287	57	63	[	[	X
ejpam-2287	57	64	16	16	NUM
ejpam-2287	57	65	]	]	PUNCT
ejpam-2287	57	66	that	that	SCONJ
ejpam-2287	57	67	the	the	DET
ejpam-2287	57	68	number	number	NOUN
ejpam-2287	57	69	of	of	ADP
ejpam-2287	57	70	intersections	intersection	NOUN
ejpam-2287	57	71	of	of	ADP
ejpam-2287	57	72	e1	e1	PROPN
ejpam-2287	57	73	and	and	CCONJ
ejpam-2287	57	74	e2	e2	PROPN
ejpam-2287	57	75	is	be	AUX
ejpam-2287	57	76	bounded	bound	VERB
ejpam-2287	57	77	by	by	ADP
ejpam-2287	57	78	the	the	DET
ejpam-2287	57	79	product	product	NOUN
ejpam-2287	57	80	n1n2	n1n2	NOUN
ejpam-2287	57	81	→∞.	→∞.	X
ejpam-2287	57	82	in	in	ADP
ejpam-2287	57	83	other	other	ADJ
ejpam-2287	57	84	words	word	NOUN
ejpam-2287	57	85	,	,	PUNCT
ejpam-2287	57	86	one	one	PRON
ejpam-2287	57	87	can	can	AUX
ejpam-2287	57	88	expect	expect	VERB
ejpam-2287	57	89	to	to	PART
ejpam-2287	57	90	see	see	VERB
ejpam-2287	57	91	infinitely	infinitely	ADV
ejpam-2287	57	92	many	many	ADJ
ejpam-2287	57	93	periodic	periodic	ADJ
ejpam-2287	57	94	solutions	solution	NOUN
ejpam-2287	57	95	for	for	ADP
ejpam-2287	57	96	equation	equation	NOUN
ejpam-2287	57	97	(	(	PUNCT
ejpam-2287	57	98	3	3	NUM
ejpam-2287	57	99	)	)	PUNCT
ejpam-2287	57	100	.	.	PUNCT
ejpam-2287	58	1	however	however	ADV
ejpam-2287	58	2	this	this	PRON
ejpam-2287	58	3	is	be	AUX
ejpam-2287	58	4	not	not	PART
ejpam-2287	58	5	a	a	DET
ejpam-2287	58	6	realistic	realistic	ADJ
ejpam-2287	58	7	scenario	scenario	NOUN
ejpam-2287	58	8	from	from	ADP
ejpam-2287	58	9	the	the	DET
ejpam-2287	58	10	applications	application	NOUN
ejpam-2287	58	11	point	point	NOUN
ejpam-2287	58	12	of	of	ADP
ejpam-2287	58	13	view	view	NOUN
ejpam-2287	58	14	.	.	PUNCT
ejpam-2287	59	1	in	in	ADP
ejpam-2287	59	2	section	section	NOUN
ejpam-2287	59	3	4	4	NUM
ejpam-2287	59	4	,	,	PUNCT
ejpam-2287	59	5	we	we	PRON
ejpam-2287	59	6	will	will	AUX
ejpam-2287	59	7	consider	consider	VERB
ejpam-2287	59	8	a	a	DET
ejpam-2287	59	9	modification	modification	NOUN
ejpam-2287	59	10	of	of	ADP
ejpam-2287	59	11	equation	equation	NOUN
ejpam-2287	59	12	(	(	PUNCT
ejpam-2287	59	13	3	3	NUM
ejpam-2287	59	14	)	)	PUNCT
ejpam-2287	59	15	with	with	ADP
ejpam-2287	59	16	a	a	DET
ejpam-2287	59	17	finite	finite	ADJ
ejpam-2287	59	18	number	number	NOUN
ejpam-2287	59	19	of	of	ADP
ejpam-2287	59	20	periodic	periodic	ADJ
ejpam-2287	59	21	solutions	solution	NOUN
ejpam-2287	59	22	.	.	PUNCT
ejpam-2287	60	1	in	in	ADP
ejpam-2287	60	2	the	the	DET
ejpam-2287	60	3	next	next	ADJ
ejpam-2287	60	4	section	section	NOUN
ejpam-2287	60	5	,	,	PUNCT
ejpam-2287	60	6	we	we	PRON
ejpam-2287	60	7	consider	consider	VERB
ejpam-2287	60	8	a	a	DET
ejpam-2287	60	9	linearization	linearization	NOUN
ejpam-2287	60	10	of	of	ADP
ejpam-2287	60	11	(	(	PUNCT
ejpam-2287	60	12	3	3	X
ejpam-2287	60	13	)	)	PUNCT
ejpam-2287	60	14	which	which	PRON
ejpam-2287	60	15	will	will	AUX
ejpam-2287	60	16	be	be	AUX
ejpam-2287	60	17	used	use	VERB
ejpam-2287	60	18	to	to	PART
ejpam-2287	60	19	give	give	VERB
ejpam-2287	60	20	mathematical	mathematical	ADJ
ejpam-2287	60	21	explanations	explanation	NOUN
ejpam-2287	60	22	for	for	ADP
ejpam-2287	60	23	certain	certain	ADJ
ejpam-2287	60	24	numerical	numerical	ADJ
ejpam-2287	60	25	observations	observation	NOUN
ejpam-2287	60	26	of	of	ADP
ejpam-2287	60	27	mckenna	mckenna	PROPN
ejpam-2287	60	28	and	and	CCONJ
ejpam-2287	60	29	moore	moore	NOUN
ejpam-2287	60	30	in	in	ADP
ejpam-2287	60	31	[	[	X
ejpam-2287	60	32	13	13	NUM
ejpam-2287	60	33	]	]	PUNCT
ejpam-2287	60	34	.	.	PUNCT
ejpam-2287	61	1	3	3	X
ejpam-2287	61	2	.	.	X
ejpam-2287	61	3	a	a	DET
ejpam-2287	61	4	linearization	linearization	NOUN
ejpam-2287	61	5	of	of	ADP
ejpam-2287	61	6	the	the	DET
ejpam-2287	61	7	discrete	discrete	ADJ
ejpam-2287	61	8	nonlinear	nonlinear	PROPN
ejpam-2287	61	9	model	model	NOUN
ejpam-2287	61	10	recall	recall	VERB
ejpam-2287	61	11	that	that	SCONJ
ejpam-2287	61	12	for	for	ADP
ejpam-2287	61	13	small	small	ADJ
ejpam-2287	61	14	θ	θ	PROPN
ejpam-2287	61	15	values	value	NOUN
ejpam-2287	61	16	,	,	PUNCT
ejpam-2287	61	17	cosθ	cosθ	PROPN
ejpam-2287	61	18	≈	≈	PROPN
ejpam-2287	61	19	1	1	NUM
ejpam-2287	61	20	and	and	CCONJ
ejpam-2287	61	21	sinθ	sinθ	PROPN
ejpam-2287	61	22	≈	≈	PROPN
ejpam-2287	61	23	θ	θ	PROPN
ejpam-2287	61	24	.	.	PUNCT
ejpam-2287	62	1	putting	put	VERB
ejpam-2287	62	2	these	these	DET
ejpam-2287	62	3	changes	change	NOUN
ejpam-2287	62	4	in	in	ADP
ejpam-2287	62	5	equation	equation	NOUN
ejpam-2287	62	6	(	(	PUNCT
ejpam-2287	62	7	3	3	X
ejpam-2287	62	8	)	)	PUNCT
ejpam-2287	62	9	gives	give	VERB
ejpam-2287	62	10	the	the	DET
ejpam-2287	62	11	following	follow	VERB
ejpam-2287	62	12	linearization	linearization	NOUN
ejpam-2287	62	13	of	of	ADP
ejpam-2287	62	14	(	(	PUNCT
ejpam-2287	62	15	3	3	NUM
ejpam-2287	62	16	)	)	PUNCT
ejpam-2287	62	17	θn+1	θn+1	X
ejpam-2287	62	18	=	=	SYM
ejpam-2287	62	19	1.99θn	1.99θn	NUM
ejpam-2287	62	20	−	−	NOUN
ejpam-2287	62	21	0.99θn−1	0.99θn−1	NUM
ejpam-2287	63	1	−	−	NUM
ejpam-2287	63	2	2.4θn−1	2.4θn−1	NUM
ejpam-2287	64	1	+	+	PUNCT
ejpam-2287	64	2	λµθn−1	λµθn−1	X
ejpam-2287	64	3	(	(	PUNCT
ejpam-2287	64	4	9	9	NUM
ejpam-2287	64	5	)	)	PUNCT
ejpam-2287	64	6	where	where	SCONJ
ejpam-2287	64	7	λ	λ	NOUN
ejpam-2287	64	8	,	,	PUNCT
ejpam-2287	64	9	µ	µ	X
ejpam-2287	64	10	are	be	AUX
ejpam-2287	64	11	positive	positive	ADJ
ejpam-2287	64	12	parameters	parameter	NOUN
ejpam-2287	64	13	and	and	CCONJ
ejpam-2287	64	14	−π/2	−π/2	PROPN
ejpam-2287	64	15	<	<	X
ejpam-2287	64	16	θn	θn	X
ejpam-2287	64	17	<	<	X
ejpam-2287	64	18	π/2	π/2	PROPN
ejpam-2287	64	19	for	for	ADP
ejpam-2287	64	20	all	all	PRON
ejpam-2287	64	21	n	n	DET
ejpam-2287	64	22	∈	∈	PROPN
ejpam-2287	64	23	n.	n.	NOUN
ejpam-2287	64	24	its	its	PRON
ejpam-2287	64	25	associated	associated	ADJ
ejpam-2287	64	26	linearized	linearize	VERB
ejpam-2287	64	27	system	system	NOUN
ejpam-2287	64	28	has	have	VERB
ejpam-2287	64	29	the	the	DET
ejpam-2287	64	30	form	form	NOUN
ejpam-2287	64	31	¨	¨	NOUN
ejpam-2287	64	32	θn+1	θn+1	X
ejpam-2287	64	33	=	=	SYM
ejpam-2287	64	34	un	un	PROPN
ejpam-2287	64	35	un+1	un+1	PROPN
ejpam-2287	64	36	=	=	SYM
ejpam-2287	64	37	1.99un	1.99un	NOUN
ejpam-2287	65	1	−	−	NOUN
ejpam-2287	65	2	0.99θn	0.99θn	NUM
ejpam-2287	66	1	−	−	PROPN
ejpam-2287	66	2	2.4θn	2.4θn	NUM
ejpam-2287	67	1	+	+	NOUN
ejpam-2287	67	2	λµθn	λµθn	ADJ
ejpam-2287	67	3	(	(	PUNCT
ejpam-2287	67	4	10	10	NUM
ejpam-2287	67	5	)	)	PUNCT
ejpam-2287	67	6	it	it	PRON
ejpam-2287	67	7	is	be	AUX
ejpam-2287	67	8	straightforward	straightforward	ADJ
ejpam-2287	67	9	to	to	PART
ejpam-2287	67	10	see	see	VERB
ejpam-2287	67	11	that	that	SCONJ
ejpam-2287	67	12	the	the	DET
ejpam-2287	67	13	equilibrium	equilibrium	NOUN
ejpam-2287	67	14	curves	curve	NOUN
ejpam-2287	67	15	(	(	PUNCT
ejpam-2287	67	16	6	6	NUM
ejpam-2287	67	17	)	)	PUNCT
ejpam-2287	67	18	of	of	ADP
ejpam-2287	67	19	the	the	DET
ejpam-2287	67	20	map	map	NOUN
ejpam-2287	67	21	t2(θ	t2(θ	X
ejpam-2287	67	22	,	,	PUNCT
ejpam-2287	67	23	u	u	NOUN
ejpam-2287	67	24	)	)	PUNCT
ejpam-2287	67	25	of	of	ADP
ejpam-2287	67	26	(	(	PUNCT
ejpam-2287	67	27	10	10	NUM
ejpam-2287	67	28	)	)	PUNCT
ejpam-2287	67	29	belong	belong	VERB
ejpam-2287	67	30	to	to	ADP
ejpam-2287	67	31	straight	straight	ADJ
ejpam-2287	67	32	lines	line	NOUN
ejpam-2287	67	33	passing	pass	VERB
ejpam-2287	67	34	through	through	ADP
ejpam-2287	67	35	the	the	DET
ejpam-2287	67	36	origin	origin	NOUN
ejpam-2287	67	37	with	with	ADP
ejpam-2287	67	38	explicit	explicit	ADJ
ejpam-2287	67	39	formulas	formula	NOUN
ejpam-2287	67	40	¨	¨	NOUN
ejpam-2287	67	41	e1	e1	NOUN
ejpam-2287	67	42	:	:	PUNCT
ejpam-2287	67	43	u=	u=	NOUN
ejpam-2287	67	44	0.502513(4.39−λµ)t	0.502513(4.39−λµ)t	PROPN
ejpam-2287	67	45	e2	e2	PROPN
ejpam-2287	67	46	:	:	PUNCT
ejpam-2287	67	47	u=	u=	NOUN
ejpam-2287	67	48	1.99(3.39−λµ	1.99(3.39−λµ	NUM
ejpam-2287	67	49	)	)	PUNCT
ejpam-2287	67	50	λµ−0.4299	λµ−0.4299	NOUN
ejpam-2287	68	1	t	t	PROPN
ejpam-2287	68	2	moreover	moreover	ADV
ejpam-2287	68	3	it	it	PRON
ejpam-2287	68	4	is	be	AUX
ejpam-2287	68	5	easy	easy	ADJ
ejpam-2287	68	6	to	to	PART
ejpam-2287	68	7	see	see	VERB
ejpam-2287	68	8	that	that	SCONJ
ejpam-2287	68	9	e1	e1	PROPN
ejpam-2287	68	10	and	and	CCONJ
ejpam-2287	68	11	e2	e2	PROPN
ejpam-2287	68	12	intersect	intersect	NOUN
ejpam-2287	68	13	at	at	ADP
ejpam-2287	68	14	infinitely	infinitely	ADV
ejpam-2287	68	15	many	many	ADJ
ejpam-2287	68	16	points	point	NOUN
ejpam-2287	68	17	exactly	exactly	ADV
ejpam-2287	68	18	when	when	SCONJ
ejpam-2287	68	19	they	they	PRON
ejpam-2287	68	20	have	have	VERB
ejpam-2287	68	21	the	the	DET
ejpam-2287	68	22	same	same	ADJ
ejpam-2287	68	23	slope	slope	NOUN
ejpam-2287	68	24	,	,	PUNCT
ejpam-2287	68	25	that	that	PRON
ejpam-2287	68	26	is	be	AUX
ejpam-2287	68	27	exactly	exactly	ADV
ejpam-2287	68	28	when	when	SCONJ
ejpam-2287	68	29	λµ	λµ	ADP
ejpam-2287	68	30	=	=	NOUN
ejpam-2287	68	31	2.4,6.38	2.4,6.38	NUM
ejpam-2287	68	32	.	.	PUNCT
ejpam-2287	69	1	for	for	ADP
ejpam-2287	69	2	all	all	DET
ejpam-2287	69	3	other	other	ADJ
ejpam-2287	69	4	λµ-values	λµ-value	NOUN
ejpam-2287	69	5	,	,	PUNCT
ejpam-2287	69	6	e1	e1	PROPN
ejpam-2287	69	7	and	and	CCONJ
ejpam-2287	69	8	e2	e2	PROPN
ejpam-2287	69	9	intersect	intersect	NOUN
ejpam-2287	69	10	only	only	ADV
ejpam-2287	69	11	at	at	ADP
ejpam-2287	69	12	the	the	DET
ejpam-2287	69	13	origin	origin	NOUN
ejpam-2287	69	14	which	which	PRON
ejpam-2287	69	15	also	also	ADV
ejpam-2287	69	16	happens	happen	VERB
ejpam-2287	69	17	to	to	PART
ejpam-2287	69	18	be	be	AUX
ejpam-2287	69	19	the	the	DET
ejpam-2287	69	20	equilibrium	equilibrium	NOUN
ejpam-2287	69	21	solution	solution	NOUN
ejpam-2287	69	22	of	of	ADP
ejpam-2287	69	23	the	the	DET
ejpam-2287	69	24	map	map	NOUN
ejpam-2287	69	25	t2(θ	t2(θ	X
ejpam-2287	69	26	,	,	PUNCT
ejpam-2287	69	27	u	u	NOUN
ejpam-2287	69	28	)	)	PUNCT
ejpam-2287	69	29	.	.	PUNCT
ejpam-2287	70	1	it	it	PRON
ejpam-2287	70	2	follows	follow	VERB
ejpam-2287	70	3	that	that	SCONJ
ejpam-2287	70	4	the	the	DET
ejpam-2287	70	5	linearization	linearization	NOUN
ejpam-2287	70	6	(	(	PUNCT
ejpam-2287	70	7	9	9	NUM
ejpam-2287	70	8	)	)	PUNCT
ejpam-2287	70	9	of	of	ADP
ejpam-2287	70	10	equation	equation	NOUN
ejpam-2287	70	11	(	(	PUNCT
ejpam-2287	70	12	3	3	X
ejpam-2287	70	13	)	)	PUNCT
ejpam-2287	70	14	has	have	VERB
ejpam-2287	70	15	infinitely	infinitely	ADV
ejpam-2287	70	16	many	many	ADJ
ejpam-2287	70	17	periodic	periodic	ADJ
ejpam-2287	70	18	solutions	solution	NOUN
ejpam-2287	70	19	for	for	ADP
ejpam-2287	70	20	λµ=	λµ=	NOUN
ejpam-2287	70	21	2.4	2.4	NUM
ejpam-2287	70	22	and	and	CCONJ
ejpam-2287	70	23	6.38	6.38	NUM
ejpam-2287	70	24	,	,	PUNCT
ejpam-2287	70	25	and	and	CCONJ
ejpam-2287	70	26	no	no	DET
ejpam-2287	70	27	nontrivial	nontrivial	ADJ
ejpam-2287	70	28	periodic	periodic	ADJ
ejpam-2287	70	29	solutions	solution	NOUN
ejpam-2287	70	30	for	for	ADP
ejpam-2287	70	31	all	all	DET
ejpam-2287	70	32	other	other	ADJ
ejpam-2287	70	33	λµ-values	λµ-value	NOUN
ejpam-2287	70	34	.	.	PUNCT
ejpam-2287	71	1	this	this	PRON
ejpam-2287	71	2	suggests	suggest	VERB
ejpam-2287	71	3	that	that	SCONJ
ejpam-2287	71	4	linearization	linearization	NOUN
ejpam-2287	71	5	is	be	AUX
ejpam-2287	71	6	not	not	PART
ejpam-2287	71	7	a	a	DET
ejpam-2287	71	8	very	very	ADV
ejpam-2287	71	9	practical	practical	ADJ
ejpam-2287	71	10	way	way	NOUN
ejpam-2287	71	11	to	to	PART
ejpam-2287	71	12	study	study	VERB
ejpam-2287	71	13	oscillations	oscillation	NOUN
ejpam-2287	71	14	in	in	ADP
ejpam-2287	71	15	a	a	DET
ejpam-2287	71	16	suspension	suspension	NOUN
ejpam-2287	71	17	bridge	bridge	NOUN
ejpam-2287	71	18	since	since	SCONJ
ejpam-2287	71	19	the	the	DET
ejpam-2287	71	20	dynamics	dynamic	NOUN
ejpam-2287	71	21	in	in	ADP
ejpam-2287	71	22	this	this	DET
ejpam-2287	71	23	case	case	NOUN
ejpam-2287	71	24	are	be	AUX
ejpam-2287	71	25	too	too	ADV
ejpam-2287	71	26	extreme	extreme	ADJ
ejpam-2287	71	27	to	to	PART
ejpam-2287	71	28	occur	occur	VERB
ejpam-2287	71	29	in	in	ADP
ejpam-2287	71	30	real	real	ADJ
ejpam-2287	71	31	life	life	NOUN
ejpam-2287	71	32	.	.	PUNCT
ejpam-2287	72	1	but	but	CCONJ
ejpam-2287	72	2	it	it	PRON
ejpam-2287	72	3	does	do	AUX
ejpam-2287	72	4	help	help	VERB
ejpam-2287	72	5	to	to	PART
ejpam-2287	72	6	explain	explain	VERB
ejpam-2287	72	7	mathematically	mathematically	ADV
ejpam-2287	72	8	the	the	DET
ejpam-2287	72	9	numerical	numerical	ADJ
ejpam-2287	72	10	observations	observation	NOUN
ejpam-2287	72	11	of	of	ADP
ejpam-2287	72	12	mckenna	mckenna	PROPN
ejpam-2287	72	13	and	and	CCONJ
ejpam-2287	72	14	moore	moore	NOUN
ejpam-2287	72	15	in	in	ADP
ejpam-2287	72	16	[	[	X
ejpam-2287	72	17	13	13	NUM
ejpam-2287	72	18	]	]	PUNCT
ejpam-2287	72	19	,	,	PUNCT
ejpam-2287	72	20	an	an	DET
ejpam-2287	72	21	s.	s.	PROPN
ejpam-2287	72	22	basu	basu	PROPN
ejpam-2287	72	23	/	/	SYM
ejpam-2287	72	24	eur	eur	PROPN
ejpam-2287	72	25	.	.	PUNCT
ejpam-2287	73	1	j.	j.	PROPN
ejpam-2287	73	2	pure	pure	PROPN
ejpam-2287	73	3	appl	appl	PROPN
ejpam-2287	73	4	.	.	PROPN
ejpam-2287	73	5	math	math	PROPN
ejpam-2287	73	6	,	,	PUNCT
ejpam-2287	73	7	7	7	NUM
ejpam-2287	73	8	(	(	PUNCT
ejpam-2287	73	9	2014	2014	NUM
ejpam-2287	73	10	)	)	PUNCT
ejpam-2287	73	11	,	,	PUNCT
ejpam-2287	73	12	442	442	NUM
ejpam-2287	73	13	-	-	SYM
ejpam-2287	73	14	461	461	NUM
ejpam-2287	73	15	446	446	NUM
ejpam-2287	73	16	explanation	explanation	NOUN
ejpam-2287	73	17	that	that	PRON
ejpam-2287	73	18	was	be	AUX
ejpam-2287	73	19	missing	miss	VERB
ejpam-2287	73	20	from	from	ADP
ejpam-2287	73	21	their	their	PRON
ejpam-2287	73	22	paper	paper	NOUN
ejpam-2287	73	23	.	.	PUNCT
ejpam-2287	74	1	more	more	ADV
ejpam-2287	74	2	specifically	specifically	ADV
ejpam-2287	74	3	,	,	PUNCT
ejpam-2287	74	4	mckenna	mckenna	PROPN
ejpam-2287	74	5	and	and	CCONJ
ejpam-2287	74	6	moore	moore	PROPN
ejpam-2287	74	7	noted	note	VERB
ejpam-2287	74	8	in	in	ADP
ejpam-2287	74	9	their	their	PRON
ejpam-2287	74	10	paper	paper	NOUN
ejpam-2287	74	11	that	that	PRON
ejpam-2287	74	12	for	for	ADP
ejpam-2287	74	13	their	their	PRON
ejpam-2287	74	14	linearized	linearize	VERB
ejpam-2287	74	15	differential	differential	ADJ
ejpam-2287	74	16	equation	equation	NOUN
ejpam-2287	74	17	θ	θ	X
ejpam-2287	74	18	′′	′′	PROPN
ejpam-2287	74	19	=	=	PUNCT
ejpam-2287	74	20	−2.4θ	−2.4θ	PRON
ejpam-2287	74	21	−	−	NUM
ejpam-2287	74	22	0.01θ	0.01θ	NUM
ejpam-2287	74	23	′	′	NUM
ejpam-2287	75	1	+	+	PUNCT
ejpam-2287	75	2	λ	λ	NOUN
ejpam-2287	75	3	sinµt	sinµt	NOUN
ejpam-2287	75	4	(	(	PUNCT
ejpam-2287	75	5	11	11	NUM
ejpam-2287	75	6	)	)	PUNCT
ejpam-2287	75	7	periodic	periodic	ADJ
ejpam-2287	75	8	solutions	solution	NOUN
ejpam-2287	75	9	occur	occur	VERB
ejpam-2287	75	10	for	for	ADP
ejpam-2287	75	11	µ	µ	PROPN
ejpam-2287	75	12	≈	≈	PROPN
ejpam-2287	75	13	1.55	1.55	NUM
ejpam-2287	75	14	and	and	CCONJ
ejpam-2287	75	15	for	for	ADP
ejpam-2287	75	16	small	small	ADJ
ejpam-2287	75	17	λ	λ	NOUN
ejpam-2287	75	18	whose	whose	DET
ejpam-2287	75	19	exact	exact	ADJ
ejpam-2287	75	20	range	range	NOUN
ejpam-2287	75	21	was	be	AUX
ejpam-2287	75	22	unspecified	unspecified	ADJ
ejpam-2287	75	23	in	in	ADP
ejpam-2287	75	24	the	the	DET
ejpam-2287	75	25	paper	paper	NOUN
ejpam-2287	75	26	.	.	PUNCT
ejpam-2287	76	1	moreover	moreover	ADV
ejpam-2287	76	2	for	for	ADP
ejpam-2287	76	3	µ	µ	X
ejpam-2287	76	4	>	>	X
ejpam-2287	76	5	1.55	1.55	NUM
ejpam-2287	76	6	,	,	PUNCT
ejpam-2287	76	7	they	they	PRON
ejpam-2287	76	8	observed	observe	VERB
ejpam-2287	76	9	no	no	DET
ejpam-2287	76	10	bifurcation	bifurcation	NOUN
ejpam-2287	76	11	from	from	ADP
ejpam-2287	76	12	one	one	NUM
ejpam-2287	76	13	to	to	ADP
ejpam-2287	76	14	many	many	ADJ
ejpam-2287	76	15	periodic	periodic	ADJ
ejpam-2287	76	16	solutions	solution	NOUN
ejpam-2287	76	17	.	.	PUNCT
ejpam-2287	77	1	they	they	PRON
ejpam-2287	77	2	also	also	ADV
ejpam-2287	77	3	noted	note	VERB
ejpam-2287	77	4	that	that	SCONJ
ejpam-2287	77	5	for	for	ADP
ejpam-2287	77	6	µ	µ	X
ejpam-2287	77	7	<	<	X
ejpam-2287	77	8	1.55	1.55	NUM
ejpam-2287	77	9	but	but	CCONJ
ejpam-2287	77	10	close	close	ADJ
ejpam-2287	77	11	to	to	ADP
ejpam-2287	77	12	this	this	DET
ejpam-2287	77	13	value	value	NOUN
ejpam-2287	77	14	,	,	PUNCT
ejpam-2287	77	15	their	their	PRON
ejpam-2287	77	16	numerical	numerical	ADJ
ejpam-2287	77	17	algorithm	algorithm	NOUN
ejpam-2287	77	18	did	do	AUX
ejpam-2287	77	19	not	not	PART
ejpam-2287	77	20	converge	converge	VERB
ejpam-2287	77	21	to	to	ADP
ejpam-2287	77	22	a	a	DET
ejpam-2287	77	23	periodic	periodic	ADJ
ejpam-2287	77	24	solution	solution	NOUN
ejpam-2287	77	25	.	.	PUNCT
ejpam-2287	78	1	they	they	PRON
ejpam-2287	78	2	did	do	AUX
ejpam-2287	78	3	not	not	PART
ejpam-2287	78	4	address	address	VERB
ejpam-2287	78	5	the	the	DET
ejpam-2287	78	6	case	case	NOUN
ejpam-2287	78	7	where	where	SCONJ
ejpam-2287	78	8	µ	µ	X
ejpam-2287	78	9	<	<	X
ejpam-2287	78	10	1.55	1.55	NUM
ejpam-2287	78	11	and	and	CCONJ
ejpam-2287	78	12	far	far	ADV
ejpam-2287	78	13	away	away	ADV
ejpam-2287	78	14	from	from	ADP
ejpam-2287	78	15	this	this	DET
ejpam-2287	78	16	value	value	NOUN
ejpam-2287	78	17	at	at	ADV
ejpam-2287	78	18	all	all	ADV
ejpam-2287	78	19	in	in	ADP
ejpam-2287	78	20	their	their	PRON
ejpam-2287	78	21	paper	paper	NOUN
ejpam-2287	78	22	[	[	X
ejpam-2287	78	23	13	13	NUM
ejpam-2287	78	24	]	]	PUNCT
ejpam-2287	78	25	.	.	PUNCT
ejpam-2287	79	1	in	in	ADP
ejpam-2287	79	2	short	short	ADJ
ejpam-2287	79	3	,	,	PUNCT
ejpam-2287	79	4	the	the	DET
ejpam-2287	79	5	case	case	NOUN
ejpam-2287	79	6	µ	µ	X
ejpam-2287	79	7	<	<	X
ejpam-2287	79	8	1.55	1.55	NUM
ejpam-2287	79	9	was	be	AUX
ejpam-2287	79	10	pretty	pretty	ADV
ejpam-2287	79	11	much	much	ADV
ejpam-2287	79	12	left	leave	VERB
ejpam-2287	79	13	unanalyzed	unanalyzed	ADJ
ejpam-2287	79	14	in	in	ADP
ejpam-2287	79	15	their	their	PRON
ejpam-2287	79	16	paper	paper	NOUN
ejpam-2287	79	17	.	.	PUNCT
ejpam-2287	80	1	for	for	ADP
ejpam-2287	80	2	their	their	PRON
ejpam-2287	80	3	numerical	numerical	ADJ
ejpam-2287	80	4	experiments	experiment	NOUN
ejpam-2287	80	5	,	,	PUNCT
ejpam-2287	80	6	mckenna	mckenna	PROPN
ejpam-2287	80	7	and	and	CCONJ
ejpam-2287	80	8	moore	moore	PROPN
ejpam-2287	80	9	used	use	VERB
ejpam-2287	80	10	the	the	DET
ejpam-2287	80	11	four	four	NUM
ejpam-2287	80	12	sets	set	NOUN
ejpam-2287	80	13	of	of	ADP
ejpam-2287	80	14	λµ-values	λµ-value	NOUN
ejpam-2287	80	15	given	give	VERB
ejpam-2287	80	16	below	below	ADV
ejpam-2287	80	17	to	to	PART
ejpam-2287	80	18	study	study	VERB
ejpam-2287	80	19	the	the	DET
ejpam-2287	80	20	occurrence	occurrence	NOUN
ejpam-2287	80	21	of	of	ADP
ejpam-2287	80	22	periodic	periodic	ADJ
ejpam-2287	80	23	solutions	solution	NOUN
ejpam-2287	80	24	in	in	ADP
ejpam-2287	80	25	(	(	PUNCT
ejpam-2287	80	26	11	11	NUM
ejpam-2287	80	27	)	)	PUNCT
ejpam-2287	80	28	.	.	PUNCT
ejpam-2287	81	1	{	{	PUNCT
ejpam-2287	81	2	λ,µ	λ,µ	NOUN
ejpam-2287	81	3	}	}	PUNCT
ejpam-2287	81	4	=	=	PUNCT
ejpam-2287	81	5	{	{	PUNCT
ejpam-2287	81	6	0.0126,1	0.0126,1	NOUN
ejpam-2287	81	7	}	}	PUNCT
ejpam-2287	81	8	,	,	PUNCT
ejpam-2287	81	9	{	{	PUNCT
ejpam-2287	81	10	0.0117,1.2	0.0117,1.2	NOUN
ejpam-2287	81	11	}	}	PUNCT
ejpam-2287	81	12	,	,	PUNCT
ejpam-2287	81	13	{	{	PUNCT
ejpam-2287	81	14	0.0088,1.4	0.0088,1.4	NOUN
ejpam-2287	81	15	}	}	PUNCT
ejpam-2287	81	16	,	,	PUNCT
ejpam-2287	81	17	{	{	PUNCT
ejpam-2287	81	18	0.0197,1.5	0.0197,1.5	NUM
ejpam-2287	81	19	}	}	PUNCT
ejpam-2287	81	20	in	in	ADP
ejpam-2287	81	21	the	the	DET
ejpam-2287	81	22	first	first	ADJ
ejpam-2287	81	23	three	three	NUM
ejpam-2287	81	24	cases	case	NOUN
ejpam-2287	81	25	,	,	PUNCT
ejpam-2287	81	26	they	they	PRON
ejpam-2287	81	27	observed	observe	VERB
ejpam-2287	81	28	bifurcations	bifurcation	NOUN
ejpam-2287	81	29	from	from	ADP
ejpam-2287	81	30	single	single	ADJ
ejpam-2287	81	31	to	to	ADP
ejpam-2287	81	32	multiple	multiple	ADJ
ejpam-2287	81	33	periodic	periodic	ADJ
ejpam-2287	81	34	solutions	solution	NOUN
ejpam-2287	81	35	while	while	SCONJ
ejpam-2287	81	36	in	in	ADP
ejpam-2287	81	37	the	the	DET
ejpam-2287	81	38	fourth	fourth	ADJ
ejpam-2287	81	39	case	case	NOUN
ejpam-2287	81	40	,	,	PUNCT
ejpam-2287	81	41	they	they	PRON
ejpam-2287	81	42	simply	simply	ADV
ejpam-2287	81	43	noted	note	VERB
ejpam-2287	81	44	the	the	DET
ejpam-2287	81	45	existence	existence	NOUN
ejpam-2287	81	46	of	of	ADP
ejpam-2287	81	47	multiple	multiple	ADJ
ejpam-2287	81	48	periodic	periodic	ADJ
ejpam-2287	81	49	solutions	solution	NOUN
ejpam-2287	81	50	.	.	PUNCT
ejpam-2287	82	1	a	a	DET
ejpam-2287	82	2	quick	quick	ADJ
ejpam-2287	82	3	check	check	NOUN
ejpam-2287	82	4	shows	show	VERB
ejpam-2287	82	5	that	that	SCONJ
ejpam-2287	82	6	in	in	ADP
ejpam-2287	82	7	the	the	DET
ejpam-2287	82	8	first	first	ADJ
ejpam-2287	82	9	three	three	NUM
ejpam-2287	82	10	cases	case	NOUN
ejpam-2287	82	11	,	,	PUNCT
ejpam-2287	82	12	the	the	DET
ejpam-2287	82	13	product	product	NOUN
ejpam-2287	82	14	λµ	λµ	NOUN
ejpam-2287	82	15	is	be	AUX
ejpam-2287	82	16	roughly	roughly	ADV
ejpam-2287	82	17	constant	constant	ADJ
ejpam-2287	82	18	with	with	ADP
ejpam-2287	82	19	λµ	λµ	PRON
ejpam-2287	82	20	≈	≈	PROPN
ejpam-2287	82	21	0.013	0.013	NUM
ejpam-2287	82	22	or	or	CCONJ
ejpam-2287	82	23	0.014	0.014	NUM
ejpam-2287	82	24	with	with	ADP
ejpam-2287	82	25	3	3	NUM
ejpam-2287	82	26	-	-	PUNCT
ejpam-2287	82	27	digit	digit	NOUN
ejpam-2287	82	28	rounding	rounding	NOUN
ejpam-2287	82	29	and	and	CCONJ
ejpam-2287	82	30	in	in	ADP
ejpam-2287	82	31	the	the	DET
ejpam-2287	82	32	fourth	fourth	ADJ
ejpam-2287	82	33	case	case	NOUN
ejpam-2287	82	34	,	,	PUNCT
ejpam-2287	82	35	λµ≈	λµ≈	NOUN
ejpam-2287	82	36	0.03	0.03	NUM
ejpam-2287	82	37	.	.	PUNCT
ejpam-2287	83	1	drawing	draw	VERB
ejpam-2287	83	2	analogy	analogy	NOUN
ejpam-2287	83	3	to	to	ADP
ejpam-2287	83	4	the	the	DET
ejpam-2287	83	5	bifurcation	bifurcation	NOUN
ejpam-2287	83	6	analysis	analysis	NOUN
ejpam-2287	83	7	of	of	ADP
ejpam-2287	83	8	the	the	DET
ejpam-2287	83	9	discrete	discrete	ADJ
ejpam-2287	83	10	linearized	linearize	VERB
ejpam-2287	83	11	difference	difference	NOUN
ejpam-2287	83	12	equations	equation	NOUN
ejpam-2287	83	13	model	model	NOUN
ejpam-2287	83	14	(	(	PUNCT
ejpam-2287	83	15	9	9	X
ejpam-2287	83	16	)	)	PUNCT
ejpam-2287	83	17	presented	present	VERB
ejpam-2287	83	18	earlier	early	ADV
ejpam-2287	83	19	in	in	ADP
ejpam-2287	83	20	this	this	DET
ejpam-2287	83	21	section	section	NOUN
ejpam-2287	83	22	,	,	PUNCT
ejpam-2287	83	23	one	one	PRON
ejpam-2287	83	24	can	can	AUX
ejpam-2287	83	25	conclude	conclude	VERB
ejpam-2287	83	26	that	that	SCONJ
ejpam-2287	83	27	the	the	DET
ejpam-2287	83	28	mckenna	mckenna	NOUN
ejpam-2287	83	29	-	-	PUNCT
ejpam-2287	83	30	moore	moore	NOUN
ejpam-2287	83	31	linearized	linearize	VERB
ejpam-2287	83	32	equation	equation	NOUN
ejpam-2287	83	33	(	(	PUNCT
ejpam-2287	83	34	11	11	NUM
ejpam-2287	83	35	)	)	PUNCT
ejpam-2287	83	36	has	have	VERB
ejpam-2287	83	37	infinitely	infinitely	ADV
ejpam-2287	83	38	many	many	ADJ
ejpam-2287	83	39	periodic	periodic	ADJ
ejpam-2287	83	40	solutions	solution	NOUN
ejpam-2287	83	41	for	for	ADP
ejpam-2287	83	42	λµ	λµ	PRON
ejpam-2287	84	1	≈	≈	PROPN
ejpam-2287	84	2	0.013	0.013	NUM
ejpam-2287	84	3	(	(	PUNCT
ejpam-2287	84	4	or	or	CCONJ
ejpam-2287	84	5	0.014	0.014	NUM
ejpam-2287	84	6	)	)	PUNCT
ejpam-2287	84	7	and	and	CCONJ
ejpam-2287	84	8	0.03	0.03	NUM
ejpam-2287	84	9	,	,	PUNCT
ejpam-2287	84	10	and	and	CCONJ
ejpam-2287	84	11	no	no	DET
ejpam-2287	84	12	nontrivial	nontrivial	ADJ
ejpam-2287	84	13	periodic	periodic	ADJ
ejpam-2287	84	14	solutions	solution	NOUN
ejpam-2287	84	15	for	for	ADP
ejpam-2287	84	16	all	all	DET
ejpam-2287	84	17	other	other	ADJ
ejpam-2287	84	18	λµ-values	λµ-value	NOUN
ejpam-2287	84	19	.	.	PUNCT
ejpam-2287	85	1	this	this	PRON
ejpam-2287	85	2	would	would	AUX
ejpam-2287	85	3	explain	explain	VERB
ejpam-2287	85	4	why	why	SCONJ
ejpam-2287	85	5	their	their	PRON
ejpam-2287	85	6	numerical	numerical	ADJ
ejpam-2287	85	7	algorithm	algorithm	NOUN
ejpam-2287	85	8	did	do	AUX
ejpam-2287	85	9	not	not	PART
ejpam-2287	85	10	converge	converge	VERB
ejpam-2287	85	11	to	to	ADP
ejpam-2287	85	12	a	a	DET
ejpam-2287	85	13	periodic	periodic	ADJ
ejpam-2287	85	14	solution	solution	NOUN
ejpam-2287	85	15	in	in	ADP
ejpam-2287	85	16	some	some	DET
ejpam-2287	85	17	cases	case	NOUN
ejpam-2287	85	18	(	(	PUNCT
ejpam-2287	85	19	no	no	DET
ejpam-2287	85	20	nontrivial	nontrivial	ADJ
ejpam-2287	85	21	periodic	periodic	ADJ
ejpam-2287	85	22	solutions	solution	NOUN
ejpam-2287	85	23	in	in	ADP
ejpam-2287	85	24	theses	thesis	NOUN
ejpam-2287	85	25	cases	case	NOUN
ejpam-2287	85	26	!	!	PUNCT
ejpam-2287	85	27	)	)	PUNCT
ejpam-2287	86	1	while	while	SCONJ
ejpam-2287	86	2	in	in	ADP
ejpam-2287	86	3	other	other	ADJ
ejpam-2287	86	4	cases	case	NOUN
ejpam-2287	86	5	they	they	PRON
ejpam-2287	86	6	observed	observe	VERB
ejpam-2287	86	7	no	no	DET
ejpam-2287	86	8	bifurcation	bifurcation	NOUN
ejpam-2287	86	9	from	from	ADP
ejpam-2287	86	10	one	one	NUM
ejpam-2287	86	11	to	to	ADP
ejpam-2287	86	12	many	many	ADJ
ejpam-2287	86	13	periodic	periodic	ADJ
ejpam-2287	86	14	solutions	solution	NOUN
ejpam-2287	86	15	(	(	PUNCT
ejpam-2287	86	16	infinitely	infinitely	ADV
ejpam-2287	86	17	many	many	ADJ
ejpam-2287	86	18	periodic	periodic	ADJ
ejpam-2287	86	19	solutions	solution	NOUN
ejpam-2287	86	20	in	in	ADP
ejpam-2287	86	21	these	these	DET
ejpam-2287	86	22	cases	case	NOUN
ejpam-2287	86	23	!	!	PUNCT
ejpam-2287	86	24	)	)	PUNCT
ejpam-2287	86	25	.	.	PUNCT
ejpam-2287	87	1	to	to	PART
ejpam-2287	87	2	summarize	summarize	VERB
ejpam-2287	87	3	,	,	PUNCT
ejpam-2287	87	4	the	the	DET
ejpam-2287	87	5	authors	author	NOUN
ejpam-2287	87	6	in	in	ADP
ejpam-2287	87	7	[	[	X
ejpam-2287	87	8	13	13	NUM
ejpam-2287	87	9	]	]	PUNCT
ejpam-2287	87	10	missed	miss	VERB
ejpam-2287	87	11	the	the	DET
ejpam-2287	87	12	fact	fact	NOUN
ejpam-2287	87	13	that	that	SCONJ
ejpam-2287	87	14	the	the	DET
ejpam-2287	87	15	observed	observed	ADJ
ejpam-2287	87	16	bifurcations	bifurcation	NOUN
ejpam-2287	87	17	from	from	ADP
ejpam-2287	87	18	one	one	NUM
ejpam-2287	87	19	to	to	ADP
ejpam-2287	87	20	multiple	multiple	ADJ
ejpam-2287	87	21	periodic	periodic	ADJ
ejpam-2287	87	22	solutions	solution	NOUN
ejpam-2287	87	23	in	in	ADP
ejpam-2287	87	24	equation	equation	NOUN
ejpam-2287	87	25	(	(	PUNCT
ejpam-2287	87	26	11	11	NUM
ejpam-2287	87	27	)	)	PUNCT
ejpam-2287	87	28	were	be	AUX
ejpam-2287	87	29	being	be	AUX
ejpam-2287	87	30	caused	cause	VERB
ejpam-2287	87	31	not	not	PART
ejpam-2287	87	32	separately	separately	ADV
ejpam-2287	87	33	by	by	ADP
ejpam-2287	87	34	the	the	DET
ejpam-2287	87	35	parameters	parameter	NOUN
ejpam-2287	87	36	λ	λ	PROPN
ejpam-2287	87	37	or	or	CCONJ
ejpam-2287	87	38	µ	µ	NOUN
ejpam-2287	87	39	but	but	CCONJ
ejpam-2287	87	40	rather	rather	ADV
ejpam-2287	87	41	by	by	ADP
ejpam-2287	87	42	their	their	PRON
ejpam-2287	87	43	joint	joint	ADJ
ejpam-2287	87	44	product	product	NOUN
ejpam-2287	87	45	λµ.	λµ.	NOUN
ejpam-2287	87	46	analyzing	analyze	VERB
ejpam-2287	87	47	its	its	PRON
ejpam-2287	87	48	associated	associated	ADJ
ejpam-2287	87	49	discrete	discrete	ADJ
ejpam-2287	87	50	linearized	linearize	VERB
ejpam-2287	87	51	difference	difference	NOUN
ejpam-2287	87	52	equation	equation	NOUN
ejpam-2287	87	53	(	(	PUNCT
ejpam-2287	87	54	9	9	NUM
ejpam-2287	87	55	)	)	PUNCT
ejpam-2287	87	56	as	as	SCONJ
ejpam-2287	87	57	shown	show	VERB
ejpam-2287	87	58	above	above	ADV
ejpam-2287	87	59	helped	help	VERB
ejpam-2287	87	60	to	to	PART
ejpam-2287	87	61	figure	figure	VERB
ejpam-2287	87	62	this	this	PRON
ejpam-2287	87	63	out	out	ADP
ejpam-2287	87	64	.	.	PUNCT
ejpam-2287	88	1	in	in	ADP
ejpam-2287	88	2	the	the	DET
ejpam-2287	88	3	next	next	ADJ
ejpam-2287	88	4	section	section	NOUN
ejpam-2287	88	5	,	,	PUNCT
ejpam-2287	88	6	we	we	PRON
ejpam-2287	88	7	look	look	VERB
ejpam-2287	88	8	at	at	ADP
ejpam-2287	88	9	a	a	DET
ejpam-2287	88	10	modification	modification	NOUN
ejpam-2287	88	11	of	of	ADP
ejpam-2287	88	12	equation	equation	NOUN
ejpam-2287	88	13	(	(	PUNCT
ejpam-2287	88	14	3	3	NUM
ejpam-2287	88	15	)	)	PUNCT
ejpam-2287	88	16	.	.	PUNCT
ejpam-2287	89	1	4	4	X
ejpam-2287	89	2	.	.	X
ejpam-2287	89	3	a	a	DET
ejpam-2287	89	4	modified	modify	VERB
ejpam-2287	89	5	discrete	discrete	ADJ
ejpam-2287	89	6	nonlinear	nonlinear	ADJ
ejpam-2287	89	7	suspension	suspension	NOUN
ejpam-2287	89	8	bridge	bridge	NOUN
ejpam-2287	89	9	model	model	NOUN
ejpam-2287	89	10	in	in	ADP
ejpam-2287	89	11	this	this	DET
ejpam-2287	89	12	section	section	NOUN
ejpam-2287	89	13	,	,	PUNCT
ejpam-2287	89	14	we	we	PRON
ejpam-2287	89	15	will	will	AUX
ejpam-2287	89	16	consider	consider	VERB
ejpam-2287	89	17	a	a	DET
ejpam-2287	89	18	modified	modified	ADJ
ejpam-2287	89	19	nonlinear	nonlinear	ADJ
ejpam-2287	89	20	discrete	discrete	ADJ
ejpam-2287	89	21	difference	difference	NOUN
ejpam-2287	89	22	equations	equation	NOUN
ejpam-2287	89	23	model	model	NOUN
ejpam-2287	89	24	for	for	ADP
ejpam-2287	89	25	a	a	DET
ejpam-2287	89	26	suspension	suspension	NOUN
ejpam-2287	89	27	bridge	bridge	NOUN
ejpam-2287	89	28	with	with	ADP
ejpam-2287	89	29	a	a	DET
ejpam-2287	89	30	finite	finite	ADJ
ejpam-2287	89	31	number	number	NOUN
ejpam-2287	89	32	of	of	ADP
ejpam-2287	89	33	periodic	periodic	ADJ
ejpam-2287	89	34	solutions	solution	NOUN
ejpam-2287	89	35	.	.	PUNCT
ejpam-2287	90	1	the	the	DET
ejpam-2287	90	2	goal	goal	NOUN
ejpam-2287	90	3	is	be	AUX
ejpam-2287	90	4	to	to	PART
ejpam-2287	90	5	come	come	VERB
ejpam-2287	90	6	up	up	ADP
ejpam-2287	90	7	with	with	ADP
ejpam-2287	90	8	a	a	DET
ejpam-2287	90	9	more	more	ADV
ejpam-2287	90	10	realistic	realistic	ADJ
ejpam-2287	90	11	model	model	NOUN
ejpam-2287	90	12	from	from	ADP
ejpam-2287	90	13	an	an	DET
ejpam-2287	90	14	applications	application	NOUN
ejpam-2287	90	15	point	point	NOUN
ejpam-2287	90	16	of	of	ADP
ejpam-2287	90	17	view	view	NOUN
ejpam-2287	90	18	than	than	ADP
ejpam-2287	90	19	the	the	DET
ejpam-2287	90	20	original	original	ADJ
ejpam-2287	90	21	discrete	discrete	ADJ
ejpam-2287	90	22	nonlinear	nonlinear	NOUN
ejpam-2287	90	23	model	model	NOUN
ejpam-2287	90	24	(	(	PUNCT
ejpam-2287	90	25	3	3	NUM
ejpam-2287	90	26	)	)	PUNCT
ejpam-2287	90	27	with	with	ADP
ejpam-2287	90	28	the	the	DET
ejpam-2287	90	29	infinite	infinite	ADJ
ejpam-2287	90	30	number	number	NOUN
ejpam-2287	90	31	of	of	ADP
ejpam-2287	90	32	periodic	periodic	ADJ
ejpam-2287	90	33	solutions	solution	NOUN
ejpam-2287	90	34	which	which	PRON
ejpam-2287	90	35	was	be	AUX
ejpam-2287	90	36	introduced	introduce	VERB
ejpam-2287	90	37	in	in	ADP
ejpam-2287	90	38	section	section	NOUN
ejpam-2287	90	39	2	2	NUM
ejpam-2287	90	40	.	.	PUNCT
ejpam-2287	91	1	the	the	DET
ejpam-2287	91	2	strategy	strategy	NOUN
ejpam-2287	91	3	will	will	AUX
ejpam-2287	91	4	be	be	AUX
ejpam-2287	91	5	to	to	PART
ejpam-2287	91	6	replace	replace	VERB
ejpam-2287	91	7	cosθ	cosθ	PROPN
ejpam-2287	91	8	and	and	CCONJ
ejpam-2287	91	9	sinθ	sinθ	PROPN
ejpam-2287	91	10	by	by	ADP
ejpam-2287	91	11	their	their	PRON
ejpam-2287	91	12	second	second	ADJ
ejpam-2287	91	13	-	-	PUNCT
ejpam-2287	91	14	order	order	NOUN
ejpam-2287	91	15	taylor	taylor	PROPN
ejpam-2287	91	16	polynomial	polynomial	ADJ
ejpam-2287	91	17	approximations	approximation	NOUN
ejpam-2287	91	18	in	in	ADP
ejpam-2287	91	19	(	(	PUNCT
ejpam-2287	91	20	3	3	NUM
ejpam-2287	91	21	)	)	PUNCT
ejpam-2287	91	22	and	and	CCONJ
ejpam-2287	91	23	analyze	analyze	VERB
ejpam-2287	91	24	the	the	DET
ejpam-2287	91	25	resulting	result	VERB
ejpam-2287	91	26	model	model	NOUN
ejpam-2287	91	27	mathematically	mathematically	ADV
ejpam-2287	91	28	.	.	PUNCT
ejpam-2287	92	1	the	the	DET
ejpam-2287	92	2	proofs	proof	NOUN
ejpam-2287	92	3	for	for	ADP
ejpam-2287	92	4	higherorder	higherorder	NOUN
ejpam-2287	92	5	taylor	taylor	PROPN
ejpam-2287	92	6	polynomial	polynomial	ADJ
ejpam-2287	92	7	approximations	approximation	NOUN
ejpam-2287	92	8	are	be	AUX
ejpam-2287	92	9	essentially	essentially	ADV
ejpam-2287	92	10	the	the	DET
ejpam-2287	92	11	same	same	ADJ
ejpam-2287	92	12	and	and	CCONJ
ejpam-2287	92	13	will	will	AUX
ejpam-2287	92	14	be	be	AUX
ejpam-2287	92	15	omitted	omit	VERB
ejpam-2287	92	16	.	.	PUNCT
ejpam-2287	93	1	one	one	NUM
ejpam-2287	93	2	way	way	NOUN
ejpam-2287	93	3	to	to	PART
ejpam-2287	93	4	decide	decide	VERB
ejpam-2287	93	5	which	which	DET
ejpam-2287	93	6	order	order	NOUN
ejpam-2287	93	7	taylor	taylor	PROPN
ejpam-2287	93	8	polynomial	polynomial	NOUN
ejpam-2287	93	9	to	to	PART
ejpam-2287	93	10	use	use	VERB
ejpam-2287	93	11	is	be	AUX
ejpam-2287	93	12	to	to	PART
ejpam-2287	93	13	see	see	VERB
ejpam-2287	93	14	which	which	DET
ejpam-2287	93	15	order	order	NOUN
ejpam-2287	93	16	best	good	ADJ
ejpam-2287	93	17	approximates	approximate	VERB
ejpam-2287	93	18	an	an	DET
ejpam-2287	93	19	actual	actual	ADJ
ejpam-2287	93	20	data	datum	NOUN
ejpam-2287	93	21	set	set	VERB
ejpam-2287	93	22	of	of	ADP
ejpam-2287	93	23	torsional	torsional	ADJ
ejpam-2287	93	24	angle	angle	NOUN
ejpam-2287	93	25	values	value	NOUN
ejpam-2287	93	26	for	for	ADP
ejpam-2287	93	27	a	a	DET
ejpam-2287	93	28	given	give	VERB
ejpam-2287	93	29	suspension	suspension	NOUN
ejpam-2287	93	30	bridge	bridge	NOUN
ejpam-2287	93	31	taken	take	VERB
ejpam-2287	93	32	s.	s.	PROPN
ejpam-2287	93	33	basu	basu	PROPN
ejpam-2287	93	34	/	/	SYM
ejpam-2287	93	35	eur	eur	PROPN
ejpam-2287	93	36	.	.	PUNCT
ejpam-2287	94	1	j.	j.	PROPN
ejpam-2287	94	2	pure	pure	PROPN
ejpam-2287	94	3	appl	appl	PROPN
ejpam-2287	94	4	.	.	PROPN
ejpam-2287	94	5	math	math	PROPN
ejpam-2287	94	6	,	,	PUNCT
ejpam-2287	94	7	7	7	NUM
ejpam-2287	94	8	(	(	PUNCT
ejpam-2287	94	9	2014	2014	NUM
ejpam-2287	94	10	)	)	PUNCT
ejpam-2287	94	11	,	,	PUNCT
ejpam-2287	94	12	442	442	NUM
ejpam-2287	94	13	-	-	SYM
ejpam-2287	94	14	461	461	NUM
ejpam-2287	94	15	447	447	NUM
ejpam-2287	94	16	at	at	ADP
ejpam-2287	94	17	different	different	ADJ
ejpam-2287	94	18	time	time	NOUN
ejpam-2287	94	19	intervals	interval	NOUN
ejpam-2287	94	20	.	.	PUNCT
ejpam-2287	95	1	replacing	replace	VERB
ejpam-2287	95	2	cosθ	cosθ	PROPN
ejpam-2287	95	3	and	and	CCONJ
ejpam-2287	95	4	sinθ	sinθ	PROPN
ejpam-2287	95	5	by	by	ADP
ejpam-2287	95	6	their	their	PRON
ejpam-2287	95	7	respective	respective	ADJ
ejpam-2287	95	8	second	second	ADJ
ejpam-2287	95	9	-	-	PUNCT
ejpam-2287	95	10	order	order	NOUN
ejpam-2287	95	11	taylor	taylor	PROPN
ejpam-2287	95	12	polynomial	polynomial	ADJ
ejpam-2287	95	13	approximations	approximation	NOUN
ejpam-2287	95	14	1−	1−	NUM
ejpam-2287	95	15	θ2	θ2	ADV
ejpam-2287	95	16	and	and	CCONJ
ejpam-2287	95	17	θ	θ	PROPN
ejpam-2287	95	18	in	in	ADP
ejpam-2287	95	19	(	(	PUNCT
ejpam-2287	95	20	3	3	NUM
ejpam-2287	95	21	)	)	PUNCT
ejpam-2287	95	22	,	,	PUNCT
ejpam-2287	95	23	we	we	PRON
ejpam-2287	95	24	get	get	VERB
ejpam-2287	95	25	the	the	DET
ejpam-2287	95	26	new	new	ADJ
ejpam-2287	95	27	equation	equation	NOUN
ejpam-2287	95	28	θn+1	θn+1	X
ejpam-2287	95	29	=	=	SYM
ejpam-2287	95	30	1.99θn	1.99θn	NUM
ejpam-2287	95	31	−	−	NOUN
ejpam-2287	95	32	0.99θn−1	0.99θn−1	NUM
ejpam-2287	95	33	−	−	PROPN
ejpam-2287	96	1	2.4(1−	2.4(1−	NUM
ejpam-2287	96	2	θ2	θ2	ADP
ejpam-2287	96	3	n−1)θn−1	n−1)θn−1	PROPN
ejpam-2287	97	1	+	+	PROPN
ejpam-2287	97	2	λµθn−1	λµθn−1	X
ejpam-2287	97	3	(	(	PUNCT
ejpam-2287	97	4	12	12	NUM
ejpam-2287	97	5	)	)	PUNCT
ejpam-2287	97	6	where	where	SCONJ
ejpam-2287	97	7	λ	λ	NOUN
ejpam-2287	97	8	,	,	PUNCT
ejpam-2287	97	9	µ	µ	X
ejpam-2287	97	10	are	be	AUX
ejpam-2287	97	11	positive	positive	ADJ
ejpam-2287	97	12	parameters	parameter	NOUN
ejpam-2287	97	13	and	and	CCONJ
ejpam-2287	97	14	−π/2	−π/2	PROPN
ejpam-2287	97	15	<	<	X
ejpam-2287	97	16	θn	θn	X
ejpam-2287	97	17	<	<	X
ejpam-2287	97	18	π/2	π/2	PROPN
ejpam-2287	97	19	for	for	ADP
ejpam-2287	97	20	all	all	PRON
ejpam-2287	97	21	n	n	DET
ejpam-2287	97	22	∈	∈	PROPN
ejpam-2287	97	23	n.	n.	NOUN
ejpam-2287	97	24	its	its	PRON
ejpam-2287	97	25	associated	associated	ADJ
ejpam-2287	97	26	2dsystem	2dsystem	PROPN
ejpam-2287	97	27	is	be	AUX
ejpam-2287	97	28	¨	¨	NOUN
ejpam-2287	97	29	θn+1	θn+1	NUM
ejpam-2287	97	30	=	=	SYM
ejpam-2287	97	31	un	un	PROPN
ejpam-2287	97	32	un+1	un+1	PROPN
ejpam-2287	97	33	=	=	SYM
ejpam-2287	98	1	1.99un	1.99un	NOUN
ejpam-2287	99	1	−	−	NOUN
ejpam-2287	99	2	0.99θn	0.99θn	NOUN
ejpam-2287	99	3	−	−	PROPN
ejpam-2287	99	4	2.4(1−	2.4(1−	NUM
ejpam-2287	99	5	θ2	θ2	ADP
ejpam-2287	99	6	n	n	PROPN
ejpam-2287	99	7	)	)	PUNCT
ejpam-2287	99	8	θn	θn	X
ejpam-2287	100	1	+	+	NOUN
ejpam-2287	100	2	λµθn	λµθn	ADJ
ejpam-2287	100	3	(	(	PUNCT
ejpam-2287	100	4	13	13	NUM
ejpam-2287	100	5	)	)	PUNCT
ejpam-2287	100	6	with	with	ADP
ejpam-2287	100	7	associated	associated	ADJ
ejpam-2287	100	8	map	map	NOUN
ejpam-2287	100	9	t	t	PROPN
ejpam-2287	100	10	(	(	PUNCT
ejpam-2287	100	11	θ	θ	PROPN
ejpam-2287	100	12	,	,	PUNCT
ejpam-2287	100	13	u	u	NOUN
ejpam-2287	100	14	)	)	PUNCT
ejpam-2287	100	15	defined	define	VERB
ejpam-2287	100	16	as	as	ADP
ejpam-2287	100	17	t	t	PROPN
ejpam-2287	100	18	�	�	PROPN
ejpam-2287	100	19	θ	θ	PROPN
ejpam-2287	100	20	u	u	PROPN
ejpam-2287	100	21	�	�	PROPN
ejpam-2287	100	22	=	=	SYM
ejpam-2287	100	23	�	�	PROPN
ejpam-2287	100	24	u	u	NOUN
ejpam-2287	100	25	1.99u−	1.99u−	NUM
ejpam-2287	100	26	0.99θ	0.99θ	NUM
ejpam-2287	100	27	−	−	NUM
ejpam-2287	100	28	2.4(1−	2.4(1−	NUM
ejpam-2287	100	29	θ2)θ	θ2)θ	NOUN
ejpam-2287	100	30	+	+	NOUN
ejpam-2287	100	31	λµθ	λµθ	NOUN
ejpam-2287	100	32	�	�	NOUN
ejpam-2287	100	33	(	(	PUNCT
ejpam-2287	100	34	14	14	NUM
ejpam-2287	100	35	)	)	PUNCT
ejpam-2287	100	36	setting	set	VERB
ejpam-2287	100	37	t	t	PROPN
ejpam-2287	100	38	(	(	PUNCT
ejpam-2287	100	39	θ	θ	PROPN
ejpam-2287	100	40	,	,	PUNCT
ejpam-2287	100	41	u	u	NOUN
ejpam-2287	100	42	)	)	PUNCT
ejpam-2287	100	43	=	=	SYM
ejpam-2287	100	44	(	(	PUNCT
ejpam-2287	100	45	θ	θ	PROPN
ejpam-2287	100	46	,	,	PUNCT
ejpam-2287	100	47	u	u	NOUN
ejpam-2287	100	48	)	)	PUNCT
ejpam-2287	100	49	and	and	CCONJ
ejpam-2287	100	50	solving	solve	VERB
ejpam-2287	100	51	for	for	ADP
ejpam-2287	100	52	θ	θ	PROPN
ejpam-2287	100	53	in	in	ADP
ejpam-2287	100	54	(	(	PUNCT
ejpam-2287	100	55	14	14	NUM
ejpam-2287	100	56	)	)	PUNCT
ejpam-2287	100	57	gives	give	VERB
ejpam-2287	100	58	the	the	DET
ejpam-2287	100	59	formulas	formula	NOUN
ejpam-2287	100	60	for	for	ADP
ejpam-2287	100	61	the	the	DET
ejpam-2287	100	62	three	three	NUM
ejpam-2287	100	63	equilibria	equilibrium	NOUN
ejpam-2287	100	64	of	of	ADP
ejpam-2287	100	65	(	(	PUNCT
ejpam-2287	100	66	12	12	NUM
ejpam-2287	100	67	)	)	PUNCT
ejpam-2287	100	68	as	as	ADP
ejpam-2287	100	69	e1	e1	NOUN
ejpam-2287	100	70	:	:	PUNCT
ejpam-2287	100	71	=	=	SYM
ejpam-2287	100	72	(	(	PUNCT
ejpam-2287	100	73	0,0	0,0	NUM
ejpam-2287	100	74	)	)	PUNCT
ejpam-2287	100	75	e2	e2	NOUN
ejpam-2287	100	76	:	:	PUNCT
ejpam-2287	100	77	=	=	SYM
ejpam-2287	100	78	(	(	PUNCT
ejpam-2287	100	79	0.645497	0.645497	NUM
ejpam-2287	100	80	æ	æ	SYM
ejpam-2287	100	81	2.4−λµ	2.4−λµ	NUM
ejpam-2287	100	82	,	,	PUNCT
ejpam-2287	100	83	0.645497	0.645497	NUM
ejpam-2287	100	84	æ	æ	SYM
ejpam-2287	100	85	2.4−λµ	2.4−λµ	NUM
ejpam-2287	100	86	)	)	PUNCT
ejpam-2287	100	87	e3	e3	NOUN
ejpam-2287	100	88	:	:	PUNCT
ejpam-2287	100	89	=	=	SYM
ejpam-2287	100	90	(	(	PUNCT
ejpam-2287	100	91	−0.645497	−0.645497	PROPN
ejpam-2287	100	92	æ	æ	PROPN
ejpam-2287	101	1	2.4−λµ,−0.645497	2.4−λµ,−0.645497	NUM
ejpam-2287	101	2	æ	æ	SYM
ejpam-2287	101	3	2.4−λµ	2.4−λµ	NUM
ejpam-2287	101	4	)	)	PUNCT
ejpam-2287	102	1	to	to	PART
ejpam-2287	102	2	find	find	VERB
ejpam-2287	102	3	the	the	DET
ejpam-2287	102	4	number	number	NOUN
ejpam-2287	102	5	of	of	ADP
ejpam-2287	102	6	real	real	ADJ
ejpam-2287	102	7	periodic	periodic	ADJ
ejpam-2287	102	8	solutions	solution	NOUN
ejpam-2287	102	9	of	of	ADP
ejpam-2287	102	10	(	(	PUNCT
ejpam-2287	102	11	12	12	NUM
ejpam-2287	102	12	)	)	PUNCT
ejpam-2287	102	13	,	,	PUNCT
ejpam-2287	102	14	note	note	VERB
ejpam-2287	102	15	that	that	SCONJ
ejpam-2287	102	16	these	these	PRON
ejpam-2287	102	17	are	be	AUX
ejpam-2287	102	18	precisely	precisely	ADV
ejpam-2287	102	19	the	the	DET
ejpam-2287	102	20	intersection	intersection	NOUN
ejpam-2287	102	21	points	point	NOUN
ejpam-2287	102	22	of	of	ADP
ejpam-2287	102	23	the	the	DET
ejpam-2287	102	24	equilibrium	equilibrium	NOUN
ejpam-2287	102	25	curves	curve	NOUN
ejpam-2287	102	26	of	of	ADP
ejpam-2287	102	27	the	the	DET
ejpam-2287	102	28	map	map	NOUN
ejpam-2287	102	29	t2(θ	t2(θ	X
ejpam-2287	102	30	,	,	PUNCT
ejpam-2287	102	31	u	u	NOUN
ejpam-2287	102	32	)	)	PUNCT
ejpam-2287	102	33	whose	whose	DET
ejpam-2287	102	34	explicit	explicit	ADJ
ejpam-2287	102	35	formulas	formula	NOUN
ejpam-2287	102	36	can	can	AUX
ejpam-2287	102	37	be	be	AUX
ejpam-2287	102	38	found	find	VERB
ejpam-2287	102	39	by	by	ADP
ejpam-2287	102	40	solving	solve	VERB
ejpam-2287	102	41	the	the	DET
ejpam-2287	102	42	equation	equation	NOUN
ejpam-2287	102	43	t2(θ	t2(θ	X
ejpam-2287	102	44	,	,	PUNCT
ejpam-2287	102	45	u	u	NOUN
ejpam-2287	102	46	)	)	PUNCT
ejpam-2287	102	47	=	=	SYM
ejpam-2287	102	48	(	(	PUNCT
ejpam-2287	102	49	θ	θ	PROPN
ejpam-2287	102	50	,	,	PUNCT
ejpam-2287	102	51	u	u	NOUN
ejpam-2287	102	52	)	)	PUNCT
ejpam-2287	102	53	where	where	SCONJ
ejpam-2287	102	54	t2	t2	PROPN
ejpam-2287	102	55	�	�	PROPN
ejpam-2287	102	56	θ	θ	PROPN
ejpam-2287	102	57	u	u	NOUN
ejpam-2287	102	58	�	�	PROPN
ejpam-2287	102	59	=	=	SYM
ejpam-2287	102	60	�	�	PROPN
ejpam-2287	102	61	1.99u−	1.99u−	NUM
ejpam-2287	102	62	0.99θ	0.99θ	NUM
ejpam-2287	103	1	−	−	NUM
ejpam-2287	103	2	2.4(1−	2.4(1−	NUM
ejpam-2287	103	3	θ2)θ	θ2)θ	NOUN
ejpam-2287	104	1	+	+	NOUN
ejpam-2287	104	2	λµθ	λµθ	NOUN
ejpam-2287	104	3	1.99(1.99u−	1.99(1.99u−	NUM
ejpam-2287	104	4	0.99θ	0.99θ	NUM
ejpam-2287	104	5	−	−	NOUN
ejpam-2287	105	1	2.4(1−	2.4(1−	NUM
ejpam-2287	105	2	θ2)θ	θ2)θ	NOUN
ejpam-2287	105	3	+	+	NOUN
ejpam-2287	105	4	λµθ	λµθ	NOUN
ejpam-2287	105	5	)	)	PUNCT
ejpam-2287	106	1	+	+	NOUN
ejpam-2287	106	2	λµu−	λµu−	PROPN
ejpam-2287	106	3	2.4	2.4	NUM
ejpam-2287	106	4	�	�	PROPN
ejpam-2287	106	5	1−	1−	NUM
ejpam-2287	106	6	u2	u2	PROPN
ejpam-2287	106	7	�	�	PROPN
ejpam-2287	106	8	u−	u−	PROPN
ejpam-2287	106	9	0.99u	0.99u	ADJ
ejpam-2287	106	10	�	�	PROPN
ejpam-2287	106	11	(	(	PUNCT
ejpam-2287	106	12	15	15	NUM
ejpam-2287	106	13	)	)	PUNCT
ejpam-2287	106	14	a	a	DET
ejpam-2287	106	15	simple	simple	ADJ
ejpam-2287	106	16	calculation	calculation	NOUN
ejpam-2287	106	17	shows	show	VERB
ejpam-2287	106	18	that	that	SCONJ
ejpam-2287	106	19	the	the	DET
ejpam-2287	106	20	equilibrium	equilibrium	NOUN
ejpam-2287	106	21	curves	curve	NOUN
ejpam-2287	106	22	of	of	ADP
ejpam-2287	106	23	t2(θ	t2(θ	PROPN
ejpam-2287	106	24	,	,	PUNCT
ejpam-2287	106	25	u	u	NOUN
ejpam-2287	106	26	)	)	PUNCT
ejpam-2287	106	27	are	be	AUX
ejpam-2287	106	28	elliptic	elliptic	ADJ
ejpam-2287	106	29	curves	curve	NOUN
ejpam-2287	106	30	with	with	ADP
ejpam-2287	106	31	formulas	formula	NOUN
ejpam-2287	106	32			VERB
ejpam-2287	106	33			NOUN
ejpam-2287	106	34			NOUN
ejpam-2287	106	35	e1	e1	PROPN
ejpam-2287	106	36	:	:	PUNCT
ejpam-2287	107	1	−0.99(−1.0101λµθ	−0.99(−1.0101λµθ	PROPN
ejpam-2287	107	2	+	+	CCONJ
ejpam-2287	107	3	θ	θ	X
ejpam-2287	108	1	+	+	X
ejpam-2287	108	2	2.42424θ	2.42424θ	X
ejpam-2287	108	3	(	(	PUNCT
ejpam-2287	108	4	1−	1−	NUM
ejpam-2287	108	5	θ2)−	θ2)−	NOUN
ejpam-2287	108	6	2.0101u)−	2.0101u)−	NUM
ejpam-2287	108	7	θ	θ	NOUN
ejpam-2287	108	8	=	=	SYM
ejpam-2287	108	9	0	0	NUM
ejpam-2287	108	10	e2	e2	PROPN
ejpam-2287	108	11	:	:	PUNCT
ejpam-2287	108	12	2.9701(0.670011λµθ	2.9701(0.670011λµθ	NUM
ejpam-2287	108	13	+	+	NUM
ejpam-2287	108	14	0.336689λµu−	0.336689λµu−	NUM
ejpam-2287	109	1	0.663311θ	0.663311θ	NUM
ejpam-2287	109	2	−	−	PROPN
ejpam-2287	109	3	1.60803θ	1.60803θ	PROPN
ejpam-2287	109	4	(	(	PUNCT
ejpam-2287	109	5	1−	1−	NUM
ejpam-2287	109	6	θ2	θ2	PROPN
ejpam-2287	109	7	)	)	PUNCT
ejpam-2287	109	8	−0.808054u(1−	−0.808054u(1−	ADJ
ejpam-2287	109	9	u2	u2	NOUN
ejpam-2287	109	10	)	)	PUNCT
ejpam-2287	109	11	=	=	SYM
ejpam-2287	109	12	0	0	NUM
ejpam-2287	109	13	(	(	PUNCT
ejpam-2287	109	14	16	16	NUM
ejpam-2287	109	15	)	)	PUNCT
ejpam-2287	109	16	the	the	DET
ejpam-2287	109	17	equilibrium	equilibrium	NOUN
ejpam-2287	109	18	curves	curve	NOUN
ejpam-2287	109	19	for	for	ADP
ejpam-2287	109	20	the	the	DET
ejpam-2287	109	21	maps	map	NOUN
ejpam-2287	109	22	t	t	PROPN
ejpam-2287	109	23	(	(	PUNCT
ejpam-2287	109	24	θ	θ	PROPN
ejpam-2287	109	25	,	,	PUNCT
ejpam-2287	109	26	u	u	NOUN
ejpam-2287	109	27	)	)	PUNCT
ejpam-2287	109	28	and	and	CCONJ
ejpam-2287	109	29	t2(θ	t2(θ	PROPN
ejpam-2287	109	30	,	,	PUNCT
ejpam-2287	109	31	u	u	NOUN
ejpam-2287	109	32	)	)	PUNCT
ejpam-2287	109	33	are	be	AUX
ejpam-2287	109	34	shown	show	VERB
ejpam-2287	109	35	in	in	ADP
ejpam-2287	109	36	figure	figure	NOUN
ejpam-2287	109	37	1	1	NUM
ejpam-2287	109	38	.	.	PUNCT
ejpam-2287	109	39	according	accord	VERB
ejpam-2287	109	40	to	to	ADP
ejpam-2287	109	41	bézout	bézout	NOUN
ejpam-2287	109	42	’s	’s	PART
ejpam-2287	109	43	theorem	theorem	PROPN
ejpam-2287	109	44	,	,	PUNCT
ejpam-2287	109	45	the	the	DET
ejpam-2287	109	46	maximum	maximum	ADJ
ejpam-2287	109	47	number	number	NOUN
ejpam-2287	109	48	of	of	ADP
ejpam-2287	109	49	intersections	intersection	NOUN
ejpam-2287	109	50	of	of	ADP
ejpam-2287	109	51	the	the	DET
ejpam-2287	109	52	third	third	ADJ
ejpam-2287	109	53	-	-	PUNCT
ejpam-2287	109	54	degree	degree	NOUN
ejpam-2287	109	55	elliptic	elliptic	ADJ
ejpam-2287	109	56	curves	curve	NOUN
ejpam-2287	109	57	e1	e1	PROPN
ejpam-2287	109	58	and	and	CCONJ
ejpam-2287	109	59	e2	e2	NOUN
ejpam-2287	109	60	counting	counting	NOUN
ejpam-2287	109	61	complex	complex	ADJ
ejpam-2287	109	62	intersections	intersection	NOUN
ejpam-2287	109	63	and	and	CCONJ
ejpam-2287	109	64	multiplicities	multiplicity	NOUN
ejpam-2287	109	65	is	be	AUX
ejpam-2287	109	66	3×3=	3×3=	NUM
ejpam-2287	109	67	9	9	NUM
ejpam-2287	109	68	.	.	PUNCT
ejpam-2287	110	1	thus	thus	ADV
ejpam-2287	110	2	bézout	bézout	NOUN
ejpam-2287	110	3	’s	’s	PART
ejpam-2287	110	4	theorem	theorem	NOUN
ejpam-2287	110	5	gives	give	VERB
ejpam-2287	110	6	an	an	DET
ejpam-2287	110	7	upper	upper	ADJ
ejpam-2287	110	8	bound	bind	VERB
ejpam-2287	110	9	for	for	ADP
ejpam-2287	110	10	the	the	DET
ejpam-2287	110	11	number	number	NOUN
ejpam-2287	110	12	of	of	ADP
ejpam-2287	110	13	real	real	ADJ
ejpam-2287	110	14	periodic	periodic	ADJ
ejpam-2287	110	15	solutions	solution	NOUN
ejpam-2287	110	16	to	to	ADP
ejpam-2287	110	17	(	(	PUNCT
ejpam-2287	110	18	12	12	NUM
ejpam-2287	110	19	)	)	PUNCT
ejpam-2287	110	20	,	,	PUNCT
ejpam-2287	110	21	which	which	PRON
ejpam-2287	110	22	is	be	AUX
ejpam-2287	110	23	what	what	PRON
ejpam-2287	110	24	we	we	PRON
ejpam-2287	110	25	are	be	AUX
ejpam-2287	110	26	interested	interested	ADJ
ejpam-2287	110	27	in	in	ADP
ejpam-2287	110	28	for	for	ADP
ejpam-2287	110	29	studying	study	VERB
ejpam-2287	110	30	real	real	ADJ
ejpam-2287	110	31	oscillations	oscillation	NOUN
ejpam-2287	110	32	in	in	ADP
ejpam-2287	110	33	a	a	DET
ejpam-2287	110	34	suspension	suspension	NOUN
ejpam-2287	110	35	bridge	bridge	NOUN
ejpam-2287	110	36	.	.	PUNCT
ejpam-2287	111	1	in	in	ADP
ejpam-2287	111	2	the	the	DET
ejpam-2287	111	3	next	next	ADJ
ejpam-2287	111	4	section	section	NOUN
ejpam-2287	111	5	,	,	PUNCT
ejpam-2287	111	6	we	we	PRON
ejpam-2287	111	7	will	will	AUX
ejpam-2287	111	8	apply	apply	VERB
ejpam-2287	111	9	descartes	descarte	NOUN
ejpam-2287	111	10	’	'	PUNCT
ejpam-2287	111	11	rule	rule	NOUN
ejpam-2287	111	12	of	of	ADP
ejpam-2287	111	13	signs	sign	NOUN
ejpam-2287	111	14	for	for	ADP
ejpam-2287	111	15	real	real	ADJ
ejpam-2287	111	16	roots	root	NOUN
ejpam-2287	111	17	of	of	ADP
ejpam-2287	111	18	polynomials	polynomial	NOUN
ejpam-2287	111	19	(	(	PUNCT
ejpam-2287	111	20	see	see	VERB
ejpam-2287	111	21	[	[	X
ejpam-2287	111	22	16	16	NUM
ejpam-2287	111	23	]	]	PUNCT
ejpam-2287	111	24	)	)	PUNCT
ejpam-2287	111	25	to	to	PART
ejpam-2287	111	26	predict	predict	VERB
ejpam-2287	111	27	the	the	DET
ejpam-2287	111	28	number	number	NOUN
ejpam-2287	111	29	of	of	ADP
ejpam-2287	111	30	real	real	ADJ
ejpam-2287	111	31	periodic	periodic	ADJ
ejpam-2287	111	32	solutions	solution	NOUN
ejpam-2287	111	33	of	of	ADP
ejpam-2287	111	34	(	(	PUNCT
ejpam-2287	111	35	12	12	NUM
ejpam-2287	111	36	)	)	PUNCT
ejpam-2287	111	37	for	for	ADP
ejpam-2287	111	38	different	different	ADJ
ejpam-2287	111	39	λµ-parameter	λµ-parameter	NOUN
ejpam-2287	111	40	regions	region	NOUN
ejpam-2287	111	41	.	.	PUNCT
ejpam-2287	112	1	s.	s.	PROPN
ejpam-2287	112	2	basu	basu	PROPN
ejpam-2287	112	3	/	/	SYM
ejpam-2287	112	4	eur	eur	PROPN
ejpam-2287	112	5	.	.	PUNCT
ejpam-2287	113	1	j.	j.	PROPN
ejpam-2287	113	2	pure	pure	PROPN
ejpam-2287	113	3	appl	appl	PROPN
ejpam-2287	113	4	.	.	PROPN
ejpam-2287	113	5	math	math	PROPN
ejpam-2287	113	6	,	,	PUNCT
ejpam-2287	113	7	7	7	NUM
ejpam-2287	113	8	(	(	PUNCT
ejpam-2287	113	9	2014	2014	NUM
ejpam-2287	113	10	)	)	PUNCT
ejpam-2287	113	11	,	,	PUNCT
ejpam-2287	113	12	442	442	NUM
ejpam-2287	113	13	-	-	SYM
ejpam-2287	113	14	461	461	NUM
ejpam-2287	113	15	448	448	NUM
ejpam-2287	113	16	-3	-3	INTJ
ejpam-2287	113	17	-2	-2	INTJ
ejpam-2287	114	1	-1	-1	SYM
ejpam-2287	114	2	0	0	NUM
ejpam-2287	115	1	1	1	NUM
ejpam-2287	115	2	2	2	NUM
ejpam-2287	115	3	3	3	NUM
ejpam-2287	115	4	-3	-3	INTJ
ejpam-2287	115	5	-2	-2	NOUN
ejpam-2287	115	6	-1	-1	SYM
ejpam-2287	115	7	0	0	NUM
ejpam-2287	115	8	1	1	NUM
ejpam-2287	115	9	2	2	NUM
ejpam-2287	115	10	3	3	NUM
ejpam-2287	115	11	(	(	PUNCT
ejpam-2287	115	12	a	a	NOUN
ejpam-2287	115	13	)	)	PUNCT
ejpam-2287	115	14	-2	-2	PUNCT
ejpam-2287	115	15	-1	-1	SYM
ejpam-2287	115	16	0	0	NUM
ejpam-2287	115	17	1	1	NUM
ejpam-2287	115	18	2	2	NUM
ejpam-2287	115	19	-3	-3	INTJ
ejpam-2287	115	20	-2	-2	NOUN
ejpam-2287	115	21	-1	-1	SYM
ejpam-2287	115	22	0	0	NUM
ejpam-2287	116	1	1	1	NUM
ejpam-2287	116	2	2	2	NUM
ejpam-2287	116	3	3	3	NUM
ejpam-2287	116	4	(	(	PUNCT
ejpam-2287	116	5	b	b	NOUN
ejpam-2287	116	6	)	)	PUNCT
ejpam-2287	116	7	figure	figure	NOUN
ejpam-2287	116	8	1	1	NUM
ejpam-2287	116	9	:	:	PUNCT
ejpam-2287	116	10	equilibrium	equilibrium	NOUN
ejpam-2287	116	11	curves	curve	NOUN
ejpam-2287	116	12	for	for	ADP
ejpam-2287	116	13	the	the	DET
ejpam-2287	116	14	maps	map	NOUN
ejpam-2287	116	15	t	t	PROPN
ejpam-2287	116	16	(	(	PUNCT
ejpam-2287	116	17	θ	θ	PROPN
ejpam-2287	116	18	,	,	PUNCT
ejpam-2287	116	19	u	u	NOUN
ejpam-2287	116	20	)	)	PUNCT
ejpam-2287	116	21	(	(	PUNCT
ejpam-2287	116	22	on	on	ADP
ejpam-2287	116	23	the	the	DET
ejpam-2287	116	24	left	left	NOUN
ejpam-2287	116	25	)	)	PUNCT
ejpam-2287	116	26	and	and	CCONJ
ejpam-2287	116	27	t2(θ	t2(θ	NUM
ejpam-2287	116	28	,	,	PUNCT
ejpam-2287	116	29	u	u	NOUN
ejpam-2287	116	30	)	)	PUNCT
ejpam-2287	116	31	(	(	PUNCT
ejpam-2287	116	32	on	on	ADP
ejpam-2287	116	33	the	the	DET
ejpam-2287	116	34	right	right	NOUN
ejpam-2287	116	35	)	)	PUNCT
ejpam-2287	116	36	.	.	PUNCT
ejpam-2287	117	1	the	the	DET
ejpam-2287	117	2	black	black	ADJ
ejpam-2287	117	3	dots	dot	NOUN
ejpam-2287	117	4	represent	represent	VERB
ejpam-2287	117	5	equilibria	equilibrium	NOUN
ejpam-2287	117	6	(	(	PUNCT
ejpam-2287	117	7	left	leave	VERB
ejpam-2287	117	8	)	)	PUNCT
ejpam-2287	117	9	and	and	CCONJ
ejpam-2287	117	10	periodic	periodic	ADJ
ejpam-2287	117	11	solutions	solution	NOUN
ejpam-2287	117	12	(	(	PUNCT
ejpam-2287	117	13	right	right	NOUN
ejpam-2287	117	14	)	)	PUNCT
ejpam-2287	117	15	of	of	ADP
ejpam-2287	117	16	equation	equation	NOUN
ejpam-2287	117	17	(	(	PUNCT
ejpam-2287	117	18	12	12	NUM
ejpam-2287	117	19	)	)	PUNCT
ejpam-2287	117	20	.	.	PUNCT
ejpam-2287	118	1	5	5	X
ejpam-2287	118	2	.	.	X
ejpam-2287	118	3	number	number	NOUN
ejpam-2287	118	4	of	of	ADP
ejpam-2287	118	5	real	real	ADJ
ejpam-2287	118	6	equilibria	equilibrium	NOUN
ejpam-2287	118	7	and	and	CCONJ
ejpam-2287	118	8	periodic	periodic	ADJ
ejpam-2287	118	9	solutions	solution	NOUN
ejpam-2287	118	10	in	in	ADP
ejpam-2287	118	11	[	[	X
ejpam-2287	118	12	13	13	NUM
ejpam-2287	118	13	]	]	PUNCT
ejpam-2287	118	14	,	,	PUNCT
ejpam-2287	118	15	mckenna	mckenna	PROPN
ejpam-2287	118	16	and	and	CCONJ
ejpam-2287	118	17	moore	moore	PROPN
ejpam-2287	118	18	used	use	VERB
ejpam-2287	118	19	a	a	DET
ejpam-2287	118	20	numerical	numerical	ADJ
ejpam-2287	118	21	continuation	continuation	NOUN
ejpam-2287	118	22	algorithm	algorithm	NOUN
ejpam-2287	118	23	to	to	PART
ejpam-2287	118	24	demonstrate	demonstrate	VERB
ejpam-2287	118	25	the	the	DET
ejpam-2287	118	26	existence	existence	NOUN
ejpam-2287	118	27	of	of	ADP
ejpam-2287	118	28	three	three	NUM
ejpam-2287	118	29	periodic	periodic	ADJ
ejpam-2287	118	30	solutions	solution	NOUN
ejpam-2287	118	31	to	to	ADP
ejpam-2287	118	32	their	their	PRON
ejpam-2287	118	33	continuous	continuous	ADJ
ejpam-2287	118	34	suspension	suspension	NOUN
ejpam-2287	118	35	bridge	bridge	NOUN
ejpam-2287	118	36	model	model	NOUN
ejpam-2287	118	37	(	(	PUNCT
ejpam-2287	118	38	1	1	NUM
ejpam-2287	118	39	)	)	PUNCT
ejpam-2287	118	40	through	through	ADP
ejpam-2287	118	41	a	a	DET
ejpam-2287	118	42	finite	finite	ADJ
ejpam-2287	118	43	number	number	NOUN
ejpam-2287	118	44	of	of	ADP
ejpam-2287	118	45	numerical	numerical	ADJ
ejpam-2287	118	46	experiments	experiment	NOUN
ejpam-2287	118	47	(	(	PUNCT
ejpam-2287	118	48	five	five	NUM
ejpam-2287	118	49	in	in	ADP
ejpam-2287	118	50	their	their	PRON
ejpam-2287	118	51	paper	paper	NOUN
ejpam-2287	118	52	)	)	PUNCT
ejpam-2287	118	53	.	.	PUNCT
ejpam-2287	119	1	however	however	ADV
ejpam-2287	119	2	,	,	PUNCT
ejpam-2287	119	3	they	they	PRON
ejpam-2287	119	4	did	do	AUX
ejpam-2287	119	5	not	not	PART
ejpam-2287	119	6	give	give	VERB
ejpam-2287	119	7	a	a	DET
ejpam-2287	119	8	rigorous	rigorous	ADJ
ejpam-2287	119	9	mathematical	mathematical	ADJ
ejpam-2287	119	10	proof	proof	NOUN
ejpam-2287	119	11	for	for	ADP
ejpam-2287	119	12	the	the	DET
ejpam-2287	119	13	existence	existence	NOUN
ejpam-2287	119	14	of	of	ADP
ejpam-2287	119	15	(	(	PUNCT
ejpam-2287	119	16	or	or	CCONJ
ejpam-2287	119	17	lack	lack	NOUN
ejpam-2287	119	18	of	of	ADP
ejpam-2287	119	19	)	)	PUNCT
ejpam-2287	119	20	three	three	NUM
ejpam-2287	119	21	periodic	periodic	ADJ
ejpam-2287	119	22	solutions	solution	NOUN
ejpam-2287	119	23	in	in	ADP
ejpam-2287	119	24	all	all	DET
ejpam-2287	119	25	cases	case	NOUN
ejpam-2287	119	26	not	not	PART
ejpam-2287	119	27	covered	cover	VERB
ejpam-2287	119	28	by	by	ADP
ejpam-2287	119	29	their	their	PRON
ejpam-2287	119	30	finite	finite	ADJ
ejpam-2287	119	31	number	number	NOUN
ejpam-2287	119	32	of	of	ADP
ejpam-2287	119	33	simulations	simulation	NOUN
ejpam-2287	119	34	.	.	PUNCT
ejpam-2287	120	1	more	more	ADV
ejpam-2287	120	2	specifically	specifically	ADV
ejpam-2287	120	3	,	,	PUNCT
ejpam-2287	120	4	they	they	PRON
ejpam-2287	120	5	did	do	AUX
ejpam-2287	120	6	not	not	PART
ejpam-2287	120	7	address	address	VERB
ejpam-2287	120	8	the	the	DET
ejpam-2287	120	9	question	question	NOUN
ejpam-2287	120	10	of	of	ADP
ejpam-2287	120	11	whether	whether	SCONJ
ejpam-2287	120	12	to	to	PART
ejpam-2287	120	13	expect	expect	VERB
ejpam-2287	120	14	more	more	ADV
ejpam-2287	120	15	or	or	CCONJ
ejpam-2287	120	16	less	less	ADJ
ejpam-2287	120	17	than	than	ADP
ejpam-2287	120	18	three	three	NUM
ejpam-2287	120	19	periodic	periodic	ADJ
ejpam-2287	120	20	solutions	solution	NOUN
ejpam-2287	120	21	for	for	ADP
ejpam-2287	120	22	some	some	DET
ejpam-2287	120	23	λµparameter	λµparameter	NOUN
ejpam-2287	120	24	regions	region	NOUN
ejpam-2287	120	25	.	.	PUNCT
ejpam-2287	121	1	they	they	PRON
ejpam-2287	121	2	also	also	ADV
ejpam-2287	121	3	did	do	AUX
ejpam-2287	121	4	not	not	PART
ejpam-2287	121	5	distinguish	distinguish	VERB
ejpam-2287	121	6	between	between	ADP
ejpam-2287	121	7	trivial	trivial	ADJ
ejpam-2287	121	8	periodic	periodic	ADJ
ejpam-2287	121	9	solutions	solution	NOUN
ejpam-2287	121	10	,	,	PUNCT
ejpam-2287	121	11	namely	namely	ADV
ejpam-2287	121	12	,	,	PUNCT
ejpam-2287	121	13	equilibrium	equilibrium	NOUN
ejpam-2287	121	14	solutions	solution	NOUN
ejpam-2287	121	15	,	,	PUNCT
ejpam-2287	121	16	and	and	CCONJ
ejpam-2287	121	17	nontrivial	nontrivial	ADJ
ejpam-2287	121	18	periodic	periodic	ADJ
ejpam-2287	121	19	solutions	solution	NOUN
ejpam-2287	121	20	for	for	ADP
ejpam-2287	121	21	their	their	PRON
ejpam-2287	121	22	model	model	NOUN
ejpam-2287	121	23	(	(	PUNCT
ejpam-2287	121	24	1	1	NUM
ejpam-2287	121	25	)	)	PUNCT
ejpam-2287	121	26	.	.	PUNCT
ejpam-2287	122	1	in	in	ADP
ejpam-2287	122	2	this	this	DET
ejpam-2287	122	3	section	section	NOUN
ejpam-2287	122	4	,	,	PUNCT
ejpam-2287	122	5	we	we	PRON
ejpam-2287	122	6	will	will	AUX
ejpam-2287	122	7	rigorously	rigorously	ADV
ejpam-2287	122	8	prove	prove	VERB
ejpam-2287	122	9	that	that	SCONJ
ejpam-2287	122	10	our	our	PRON
ejpam-2287	122	11	suspension	suspension	NOUN
ejpam-2287	122	12	bridge	bridge	NOUN
ejpam-2287	122	13	model	model	NOUN
ejpam-2287	122	14	(	(	PUNCT
ejpam-2287	122	15	12	12	NUM
ejpam-2287	122	16	)	)	PUNCT
ejpam-2287	122	17	can	can	AUX
ejpam-2287	122	18	have	have	VERB
ejpam-2287	122	19	at	at	ADP
ejpam-2287	122	20	most	most	ADV
ejpam-2287	122	21	three	three	NUM
ejpam-2287	122	22	real	real	ADJ
ejpam-2287	122	23	equilibria	equilibrium	NOUN
ejpam-2287	122	24	and	and	CCONJ
ejpam-2287	122	25	at	at	ADP
ejpam-2287	122	26	most	most	ADJ
ejpam-2287	122	27	four	four	NUM
ejpam-2287	122	28	real	real	ADJ
ejpam-2287	122	29	nontrivial	nontrivial	ADJ
ejpam-2287	122	30	periodic	periodic	ADJ
ejpam-2287	122	31	solutions	solution	NOUN
ejpam-2287	122	32	for	for	ADP
ejpam-2287	122	33	0	0	NUM
ejpam-2287	122	34	<	<	X
ejpam-2287	122	35	λµ≤	λµ≤	X
ejpam-2287	122	36	6.38	6.38	NUM
ejpam-2287	122	37	.	.	PUNCT
ejpam-2287	123	1	moreover	moreover	ADV
ejpam-2287	123	2	,	,	PUNCT
ejpam-2287	123	3	we	we	PRON
ejpam-2287	123	4	will	will	AUX
ejpam-2287	123	5	show	show	VERB
ejpam-2287	123	6	that	that	SCONJ
ejpam-2287	123	7	it	it	PRON
ejpam-2287	123	8	is	be	AUX
ejpam-2287	123	9	possible	possible	ADJ
ejpam-2287	123	10	to	to	PART
ejpam-2287	123	11	have	have	VERB
ejpam-2287	123	12	λµ-parameter	λµ-parameter	NOUN
ejpam-2287	123	13	regions	region	NOUN
ejpam-2287	123	14	where	where	SCONJ
ejpam-2287	123	15	at	at	ADP
ejpam-2287	123	16	most	most	ADV
ejpam-2287	123	17	one	one	NUM
ejpam-2287	123	18	or	or	CCONJ
ejpam-2287	123	19	even	even	ADV
ejpam-2287	123	20	no	no	DET
ejpam-2287	123	21	real	real	ADJ
ejpam-2287	123	22	nontrivial	nontrivial	ADJ
ejpam-2287	123	23	periodic	periodic	ADJ
ejpam-2287	123	24	solutions	solution	NOUN
ejpam-2287	123	25	exist	exist	VERB
ejpam-2287	123	26	.	.	PUNCT
ejpam-2287	124	1	the	the	DET
ejpam-2287	124	2	main	main	ADJ
ejpam-2287	124	3	theorem	theorem	NOUN
ejpam-2287	124	4	of	of	ADP
ejpam-2287	124	5	this	this	DET
ejpam-2287	124	6	section	section	NOUN
ejpam-2287	124	7	is	be	AUX
ejpam-2287	124	8	as	as	SCONJ
ejpam-2287	124	9	follows	follow	VERB
ejpam-2287	124	10	.	.	PUNCT
ejpam-2287	125	1	theorem	theorem	NOUN
ejpam-2287	125	2	1	1	NUM
ejpam-2287	125	3	.	.	PUNCT
ejpam-2287	126	1	the	the	DET
ejpam-2287	126	2	number	number	NOUN
ejpam-2287	126	3	of	of	ADP
ejpam-2287	126	4	real	real	ADJ
ejpam-2287	126	5	equilibria	equilibrium	NOUN
ejpam-2287	126	6	and	and	CCONJ
ejpam-2287	126	7	real	real	ADJ
ejpam-2287	126	8	nontrivial	nontrivial	ADJ
ejpam-2287	126	9	periodic	periodic	ADJ
ejpam-2287	126	10	solutions	solution	NOUN
ejpam-2287	126	11	of	of	ADP
ejpam-2287	126	12	equation	equation	NOUN
ejpam-2287	126	13	(	(	PUNCT
ejpam-2287	126	14	12	12	NUM
ejpam-2287	126	15	)	)	PUNCT
ejpam-2287	126	16	for	for	ADP
ejpam-2287	126	17	various	various	ADJ
ejpam-2287	126	18	λµ-parameter	λµ-parameter	NOUN
ejpam-2287	126	19	regions	region	NOUN
ejpam-2287	126	20	is	be	AUX
ejpam-2287	126	21	as	as	SCONJ
ejpam-2287	126	22	shown	show	VERB
ejpam-2287	126	23	in	in	ADP
ejpam-2287	126	24	table	table	NOUN
ejpam-2287	126	25	1	1	NUM
ejpam-2287	126	26	.	.	PUNCT
ejpam-2287	126	27	table	table	NOUN
ejpam-2287	126	28	1	1	NUM
ejpam-2287	126	29	:	:	PUNCT
ejpam-2287	126	30	table	table	NOUN
ejpam-2287	126	31	showing	show	VERB
ejpam-2287	126	32	the	the	DET
ejpam-2287	126	33	number	number	NOUN
ejpam-2287	126	34	of	of	ADP
ejpam-2287	126	35	real	real	ADJ
ejpam-2287	126	36	equilibria	equilibrium	NOUN
ejpam-2287	126	37	and	and	CCONJ
ejpam-2287	126	38	real	real	ADJ
ejpam-2287	126	39	nontrivial	nontrivial	ADJ
ejpam-2287	126	40	periodic	periodic	ADJ
ejpam-2287	126	41	solutions	solution	NOUN
ejpam-2287	126	42	of	of	ADP
ejpam-2287	126	43	equation	equation	NOUN
ejpam-2287	126	44	(	(	PUNCT
ejpam-2287	126	45	12	12	NUM
ejpam-2287	126	46	)	)	PUNCT
ejpam-2287	126	47	.	.	PUNCT
ejpam-2287	127	1	λµ	λµ	PRON
ejpam-2287	127	2	region	region	NOUN
ejpam-2287	128	1	no	no	INTJ
ejpam-2287	128	2	.	.	PROPN
ejpam-2287	128	3	of	of	ADP
ejpam-2287	128	4	real	real	ADJ
ejpam-2287	128	5	equilibria	equilibrium	NOUN
ejpam-2287	129	1	no	no	INTJ
ejpam-2287	129	2	.	.	PUNCT
ejpam-2287	130	1	of	of	ADP
ejpam-2287	130	2	real	real	ADJ
ejpam-2287	130	3	periodic	periodic	ADJ
ejpam-2287	130	4	solns	solns	NOUN
ejpam-2287	130	5	.	.	PUNCT
ejpam-2287	131	1	0	0	PUNCT
ejpam-2287	131	2	<	<	X
ejpam-2287	131	3	λµ	λµ	X
ejpam-2287	131	4	<	<	X
ejpam-2287	131	5	2.4	2.4	NUM
ejpam-2287	131	6	three	three	NUM
ejpam-2287	131	7	≤	≤	NUM
ejpam-2287	131	8	four	four	NUM
ejpam-2287	131	9	pairs	pair	NOUN
ejpam-2287	131	10	λµ=	λµ=	VERB
ejpam-2287	131	11	2.4	2.4	NUM
ejpam-2287	131	12	(	(	PUNCT
ejpam-2287	131	13	0,0	0,0	NOUN
ejpam-2287	131	14	)	)	PUNCT
ejpam-2287	131	15	unique	unique	ADJ
ejpam-2287	131	16	equilibrium	equilibrium	NOUN
ejpam-2287	131	17	≤	≤	NUM
ejpam-2287	131	18	three	three	NUM
ejpam-2287	131	19	pairs	pair	NOUN
ejpam-2287	131	20	2.4	2.4	NUM
ejpam-2287	131	21	<	<	X
ejpam-2287	131	22	λµ	λµ	X
ejpam-2287	131	23	<	<	X
ejpam-2287	131	24	4.39	4.39	NUM
ejpam-2287	131	25	(	(	PUNCT
ejpam-2287	131	26	0,0	0,0	NOUN
ejpam-2287	131	27	)	)	PUNCT
ejpam-2287	131	28	unique	unique	ADJ
ejpam-2287	131	29	equilibrium	equilibrium	NOUN
ejpam-2287	131	30	≤	≤	NUM
ejpam-2287	131	31	three	three	NUM
ejpam-2287	131	32	pairs	pair	NOUN
ejpam-2287	131	33	λµ=	λµ=	VERB
ejpam-2287	131	34	4.39	4.39	NUM
ejpam-2287	131	35	(	(	PUNCT
ejpam-2287	131	36	0,0	0,0	NOUN
ejpam-2287	131	37	)	)	PUNCT
ejpam-2287	132	1	unique	unique	ADJ
ejpam-2287	132	2	equilibrium	equilibrium	NOUN
ejpam-2287	132	3	≤	≤	NUM
ejpam-2287	132	4	one	one	NUM
ejpam-2287	132	5	pair	pair	NOUN
ejpam-2287	132	6	4.39	4.39	NUM
ejpam-2287	132	7	<	<	X
ejpam-2287	132	8	λµ	λµ	X
ejpam-2287	132	9	<	<	X
ejpam-2287	132	10	6.38	6.38	NUM
ejpam-2287	132	11	(	(	PUNCT
ejpam-2287	132	12	0,0	0,0	NOUN
ejpam-2287	132	13	)	)	PUNCT
ejpam-2287	132	14	unique	unique	ADJ
ejpam-2287	132	15	equilibrium	equilibrium	NOUN
ejpam-2287	132	16	≤	≤	NUM
ejpam-2287	132	17	one	one	NUM
ejpam-2287	132	18	pair	pair	NOUN
ejpam-2287	132	19	λµ=	λµ=	VERB
ejpam-2287	132	20	6.38	6.38	NUM
ejpam-2287	132	21	(	(	PUNCT
ejpam-2287	132	22	0,0	0,0	NOUN
ejpam-2287	132	23	)	)	PUNCT
ejpam-2287	132	24	unique	unique	ADJ
ejpam-2287	132	25	equilibrium	equilibrium	NOUN
ejpam-2287	132	26	none	none	NOUN
ejpam-2287	132	27	λµ	λµ	ADP
ejpam-2287	132	28	>	>	X
ejpam-2287	132	29	6.38	6.38	NUM
ejpam-2287	132	30	(	(	PUNCT
ejpam-2287	132	31	0,0	0,0	NOUN
ejpam-2287	132	32	)	)	PUNCT
ejpam-2287	132	33	unique	unique	ADJ
ejpam-2287	132	34	equilibrium	equilibrium	NOUN
ejpam-2287	132	35	none	none	NOUN
ejpam-2287	132	36	s.	s.	PROPN
ejpam-2287	132	37	basu	basu	PROPN
ejpam-2287	132	38	/	/	SYM
ejpam-2287	132	39	eur	eur	PROPN
ejpam-2287	132	40	.	.	PUNCT
ejpam-2287	133	1	j.	j.	PROPN
ejpam-2287	133	2	pure	pure	PROPN
ejpam-2287	133	3	appl	appl	PROPN
ejpam-2287	133	4	.	.	PROPN
ejpam-2287	133	5	math	math	PROPN
ejpam-2287	133	6	,	,	PUNCT
ejpam-2287	133	7	7	7	NUM
ejpam-2287	133	8	(	(	PUNCT
ejpam-2287	133	9	2014	2014	NUM
ejpam-2287	133	10	)	)	PUNCT
ejpam-2287	133	11	,	,	PUNCT
ejpam-2287	133	12	442	442	NUM
ejpam-2287	133	13	-	-	SYM
ejpam-2287	133	14	461	461	NUM
ejpam-2287	133	15	449	449	NUM
ejpam-2287	133	16	proof	proof	NOUN
ejpam-2287	133	17	.	.	PUNCT
ejpam-2287	134	1	the	the	DET
ejpam-2287	134	2	number	number	NOUN
ejpam-2287	134	3	of	of	ADP
ejpam-2287	134	4	real	real	ADJ
ejpam-2287	134	5	equilibria	equilibrium	NOUN
ejpam-2287	134	6	in	in	ADP
ejpam-2287	134	7	table	table	NOUN
ejpam-2287	134	8	1	1	NUM
ejpam-2287	134	9	follows	follow	VERB
ejpam-2287	134	10	directly	directly	ADV
ejpam-2287	134	11	from	from	ADP
ejpam-2287	134	12	their	their	PRON
ejpam-2287	134	13	formulas	formula	NOUN
ejpam-2287	134	14	given	give	VERB
ejpam-2287	134	15	in	in	ADP
ejpam-2287	134	16	the	the	DET
ejpam-2287	134	17	previous	previous	ADJ
ejpam-2287	134	18	section	section	NOUN
ejpam-2287	134	19	.	.	PUNCT
ejpam-2287	135	1	recall	recall	VERB
ejpam-2287	135	2	that	that	SCONJ
ejpam-2287	135	3	the	the	DET
ejpam-2287	135	4	periodic	periodic	ADJ
ejpam-2287	135	5	solutions	solution	NOUN
ejpam-2287	135	6	of	of	ADP
ejpam-2287	135	7	equation	equation	NOUN
ejpam-2287	135	8	(	(	PUNCT
ejpam-2287	135	9	12	12	NUM
ejpam-2287	135	10	)	)	PUNCT
ejpam-2287	135	11	are	be	AUX
ejpam-2287	135	12	precisely	precisely	ADV
ejpam-2287	135	13	the	the	DET
ejpam-2287	135	14	intersection	intersection	NOUN
ejpam-2287	135	15	points	point	NOUN
ejpam-2287	135	16	of	of	ADP
ejpam-2287	135	17	the	the	DET
ejpam-2287	135	18	elliptic	elliptic	ADJ
ejpam-2287	135	19	curves	curve	NOUN
ejpam-2287	135	20	e1	e1	PROPN
ejpam-2287	135	21	and	and	CCONJ
ejpam-2287	135	22	e2	e2	PROPN
ejpam-2287	135	23	which	which	PRON
ejpam-2287	135	24	were	be	AUX
ejpam-2287	135	25	defined	define	VERB
ejpam-2287	135	26	in	in	ADP
ejpam-2287	135	27	(	(	PUNCT
ejpam-2287	135	28	16	16	NUM
ejpam-2287	135	29	)	)	PUNCT
ejpam-2287	135	30	.	.	PUNCT
ejpam-2287	136	1	solving	solve	VERB
ejpam-2287	136	2	the	the	DET
ejpam-2287	136	3	equations	equation	NOUN
ejpam-2287	136	4	for	for	ADP
ejpam-2287	136	5	e1	e1	PROPN
ejpam-2287	136	6	and	and	CCONJ
ejpam-2287	136	7	e2	e2	PROPN
ejpam-2287	136	8	simultaneously	simultaneously	ADV
ejpam-2287	136	9	for	for	ADP
ejpam-2287	136	10	the	the	DET
ejpam-2287	136	11	variable	variable	ADJ
ejpam-2287	136	12	θ	θ	PROPN
ejpam-2287	136	13	gives	give	VERB
ejpam-2287	136	14	rise	rise	NOUN
ejpam-2287	136	15	to	to	ADP
ejpam-2287	136	16	the	the	DET
ejpam-2287	136	17	ninth	ninth	ADJ
ejpam-2287	136	18	-	-	PUNCT
ejpam-2287	136	19	degree	degree	NOUN
ejpam-2287	136	20	polynomial	polynomial	ADJ
ejpam-2287	136	21	equation	equation	NOUN
ejpam-2287	136	22	g(θ	g(θ	VERB
ejpam-2287	136	23	)	)	PUNCT
ejpam-2287	137	1	=	=	SYM
ejpam-2287	137	2	−	−	NOUN
ejpam-2287	137	3	4.21004θ[θ8	4.21004θ[θ8	NUM
ejpam-2287	137	4	+	+	CCONJ
ejpam-2287	137	5	(	(	PUNCT
ejpam-2287	137	6	−5.4875	−5.4875	NOUN
ejpam-2287	137	7	+	+	NUM
ejpam-2287	137	8	1.25λµ)θ6	1.25λµ)θ6	NUM
ejpam-2287	137	9	+	+	CCONJ
ejpam-2287	137	10	(	(	PUNCT
ejpam-2287	137	11	10.0376−	10.0376−	NUM
ejpam-2287	137	12	4.57292λµ+	4.57292λµ+	NOUN
ejpam-2287	137	13	0.520833λ2µ2)θ4	0.520833λ2µ2)θ4	NOUN
ejpam-2287	138	1	+	+	CCONJ
ejpam-2287	138	2	(	(	PUNCT
ejpam-2287	138	3	−7.3777	−7.3777	ADJ
ejpam-2287	138	4	+	+	NOUN
ejpam-2287	138	5	4.46878λµ−	4.46878λµ−	NUM
ejpam-2287	138	6	0.952691λ2µ2	0.952691λ2µ2	NUM
ejpam-2287	139	1	+	+	CCONJ
ejpam-2287	139	2	0.072338λ3µ3)θ2	0.072338λ3µ3)θ2	X
ejpam-2287	140	1	+	+	CCONJ
ejpam-2287	140	2	(	(	PUNCT
ejpam-2287	140	3	1.82765−	1.82765−	NUM
ejpam-2287	140	4	1.04799λµ+	1.04799λµ+	NUM
ejpam-2287	140	5	0.119361λ2µ2	0.119361λ2µ2	NUM
ejpam-2287	140	6	)	)	PUNCT
ejpam-2287	140	7	]	]	PUNCT
ejpam-2287	141	1	=	=	X
ejpam-2287	141	2	:	:	PUNCT
ejpam-2287	141	3	−	−	PROPN
ejpam-2287	141	4	4.21004θh(θ	4.21004θh(θ	NUM
ejpam-2287	141	5	)	)	PUNCT
ejpam-2287	141	6	(	(	PUNCT
ejpam-2287	141	7	17	17	NUM
ejpam-2287	141	8	)	)	PUNCT
ejpam-2287	141	9	where	where	SCONJ
ejpam-2287	141	10	h(θ	h(θ	PROPN
ejpam-2287	141	11	)	)	PUNCT
ejpam-2287	142	1	=	=	NOUN
ejpam-2287	142	2	θ8	θ8	ADJ
ejpam-2287	142	3	+	+	CCONJ
ejpam-2287	142	4	(	(	PUNCT
ejpam-2287	142	5	−5.4875	−5.4875	X
ejpam-2287	142	6	+	+	NUM
ejpam-2287	142	7	1.25λµ)θ6	1.25λµ)θ6	NUM
ejpam-2287	142	8	+	+	CCONJ
ejpam-2287	142	9	(	(	PUNCT
ejpam-2287	142	10	10.0376−	10.0376−	NUM
ejpam-2287	142	11	4.57292λµ+	4.57292λµ+	NOUN
ejpam-2287	142	12	0.520833λ2µ2)θ4	0.520833λ2µ2)θ4	NOUN
ejpam-2287	143	1	+	+	CCONJ
ejpam-2287	143	2	(	(	PUNCT
ejpam-2287	143	3	−7.3777	−7.3777	ADJ
ejpam-2287	143	4	+	+	NOUN
ejpam-2287	143	5	4.46878λµ−	4.46878λµ−	NUM
ejpam-2287	143	6	0.952691λ2µ2	0.952691λ2µ2	NUM
ejpam-2287	144	1	+	+	CCONJ
ejpam-2287	144	2	0.072338λ3µ3)θ2	0.072338λ3µ3)θ2	X
ejpam-2287	145	1	+	+	CCONJ
ejpam-2287	145	2	(	(	PUNCT
ejpam-2287	145	3	1.82765−	1.82765−	NUM
ejpam-2287	145	4	1.04799λµ+	1.04799λµ+	NUM
ejpam-2287	145	5	0.119361λ2µ2	0.119361λ2µ2	NUM
ejpam-2287	145	6	)	)	PUNCT
ejpam-2287	145	7	(	(	PUNCT
ejpam-2287	145	8	18	18	NUM
ejpam-2287	145	9	)	)	PUNCT
ejpam-2287	145	10	observe	observe	VERB
ejpam-2287	145	11	that	that	SCONJ
ejpam-2287	145	12	the	the	DET
ejpam-2287	145	13	coefficients	coefficient	NOUN
ejpam-2287	145	14	of	of	ADP
ejpam-2287	145	15	all	all	DET
ejpam-2287	145	16	terms	term	NOUN
ejpam-2287	145	17	except	except	SCONJ
ejpam-2287	145	18	the	the	DET
ejpam-2287	145	19	leading	lead	VERB
ejpam-2287	145	20	θ8	θ8	NOUN
ejpam-2287	145	21	-	-	PUNCT
ejpam-2287	145	22	term	term	NOUN
ejpam-2287	145	23	in	in	ADP
ejpam-2287	145	24	h(θ	h(θ	PROPN
ejpam-2287	145	25	)	)	PUNCT
ejpam-2287	145	26	are	be	AUX
ejpam-2287	145	27	polynomials	polynomial	NOUN
ejpam-2287	145	28	in	in	ADP
ejpam-2287	145	29	the	the	DET
ejpam-2287	145	30	’	'	PUNCT
ejpam-2287	145	31	new	new	ADJ
ejpam-2287	145	32	’	'	PUNCT
ejpam-2287	145	33	variable	variable	ADJ
ejpam-2287	145	34	λµ.	λµ.	NOUN
ejpam-2287	145	35	renaming	rename	VERB
ejpam-2287	145	36	λµ→	λµ→	X
ejpam-2287	145	37	s	s	PROPN
ejpam-2287	145	38	,	,	PUNCT
ejpam-2287	145	39	one	one	PRON
ejpam-2287	145	40	can	can	AUX
ejpam-2287	145	41	rewrite	rewrite	VERB
ejpam-2287	145	42	h(θ	h(θ	PROPN
ejpam-2287	145	43	)	)	PUNCT
ejpam-2287	145	44	in	in	ADP
ejpam-2287	145	45	(	(	PUNCT
ejpam-2287	145	46	18	18	NUM
ejpam-2287	145	47	)	)	PUNCT
ejpam-2287	145	48	as	as	SCONJ
ejpam-2287	145	49	follows	follow	VERB
ejpam-2287	145	50	.	.	PUNCT
ejpam-2287	146	1	h(θ	h(θ	NUM
ejpam-2287	146	2	)	)	PUNCT
ejpam-2287	147	1	=	=	PUNCT
ejpam-2287	147	2	θ8	θ8	ADJ
ejpam-2287	147	3	+	+	CCONJ
ejpam-2287	147	4	p1(s)θ	p1(s)θ	PUNCT
ejpam-2287	147	5	6	6	NUM
ejpam-2287	147	6	+	+	NOUN
ejpam-2287	147	7	p2(s)θ	p2(s)θ	NUM
ejpam-2287	147	8	4	4	NUM
ejpam-2287	147	9	+	+	NUM
ejpam-2287	147	10	p3(s)θ	p3(s)θ	SYM
ejpam-2287	147	11	2	2	NUM
ejpam-2287	147	12	+	+	CCONJ
ejpam-2287	147	13	p4(s	p4(s	NOUN
ejpam-2287	147	14	)	)	PUNCT
ejpam-2287	147	15	(	(	PUNCT
ejpam-2287	147	16	19	19	NUM
ejpam-2287	147	17	)	)	PUNCT
ejpam-2287	147	18	where	where	SCONJ
ejpam-2287	147	19	p1(s	p1(s	NOUN
ejpam-2287	147	20	)	)	PUNCT
ejpam-2287	147	21	:	:	PUNCT
ejpam-2287	147	22	=	=	PUNCT
ejpam-2287	148	1	−5.4875	−5.4875	X
ejpam-2287	148	2	+	+	NUM
ejpam-2287	148	3	1.25s	1.25s	NUM
ejpam-2287	148	4	p2(s	p2(s	NOUN
ejpam-2287	148	5	)	)	PUNCT
ejpam-2287	148	6	:	:	PUNCT
ejpam-2287	149	1	=	=	SYM
ejpam-2287	149	2	10.0376−	10.0376−	NUM
ejpam-2287	149	3	4.57292s+	4.57292s+	NUM
ejpam-2287	149	4	0.520833s2	0.520833s2	NUM
ejpam-2287	149	5	p3(s	p3(	NOUN
ejpam-2287	149	6	)	)	PUNCT
ejpam-2287	149	7	:	:	PUNCT
ejpam-2287	149	8	=	=	PUNCT
ejpam-2287	149	9	−7.3777	−7.3777	PROPN
ejpam-2287	149	10	+	+	NUM
ejpam-2287	149	11	4.46878s−	4.46878s−	NOUN
ejpam-2287	149	12	0.952691s2	0.952691s2	NUM
ejpam-2287	149	13	+	+	CCONJ
ejpam-2287	149	14	0.072338s3	0.072338s3	NUM
ejpam-2287	149	15	p4(s	p4(s	X
ejpam-2287	149	16	)	)	PUNCT
ejpam-2287	149	17	:	:	PUNCT
ejpam-2287	149	18	=	=	NOUN
ejpam-2287	149	19	1.82765−	1.82765−	NUM
ejpam-2287	149	20	1.04799s+	1.04799s+	NUM
ejpam-2287	149	21	0.119361s2	0.119361s2	NUM
ejpam-2287	149	22	the	the	DET
ejpam-2287	149	23	graphs	graph	NOUN
ejpam-2287	149	24	of	of	ADP
ejpam-2287	149	25	p1(s	p1(s	PROPN
ejpam-2287	149	26	)	)	PUNCT
ejpam-2287	149	27	,	,	PUNCT
ejpam-2287	149	28	p2(s	p2(s	NOUN
ejpam-2287	149	29	)	)	PUNCT
ejpam-2287	149	30	,	,	PUNCT
ejpam-2287	149	31	p3(s	p3(s	NOUN
ejpam-2287	149	32	)	)	PUNCT
ejpam-2287	149	33	and	and	CCONJ
ejpam-2287	149	34	p4(s	p4(	NOUN
ejpam-2287	149	35	)	)	PUNCT
ejpam-2287	149	36	are	be	AUX
ejpam-2287	149	37	shown	show	VERB
ejpam-2287	149	38	in	in	ADP
ejpam-2287	149	39	figure	figure	NOUN
ejpam-2287	149	40	2	2	NUM
ejpam-2287	149	41	.	.	PUNCT
ejpam-2287	149	42	solving	solve	VERB
ejpam-2287	149	43	the	the	DET
ejpam-2287	149	44	equations	equation	NOUN
ejpam-2287	149	45	p1(s	p1(s	NOUN
ejpam-2287	149	46	)	)	PUNCT
ejpam-2287	149	47	=	=	SYM
ejpam-2287	149	48	0	0	NUM
ejpam-2287	149	49	,	,	PUNCT
ejpam-2287	149	50	p2(s	p2(s	NOUN
ejpam-2287	149	51	)	)	PUNCT
ejpam-2287	149	52	=	=	SYM
ejpam-2287	149	53	0	0	NUM
ejpam-2287	149	54	and	and	CCONJ
ejpam-2287	149	55	p3(s	p3(	NOUN
ejpam-2287	149	56	)	)	PUNCT
ejpam-2287	149	57	=	=	SYM
ejpam-2287	149	58	0	0	NUM
ejpam-2287	149	59	simultaneously	simultaneously	ADV
ejpam-2287	149	60	,	,	PUNCT
ejpam-2287	149	61	we	we	PRON
ejpam-2287	149	62	see	see	VERB
ejpam-2287	149	63	that	that	SCONJ
ejpam-2287	149	64	the	the	DET
ejpam-2287	149	65	common	common	ADJ
ejpam-2287	149	66	s	s	NOUN
ejpam-2287	149	67	-	-	PUNCT
ejpam-2287	149	68	intercept	intercept	NOUN
ejpam-2287	149	69	of	of	ADP
ejpam-2287	149	70	the	the	DET
ejpam-2287	149	71	three	three	NUM
ejpam-2287	149	72	polynomial	polynomial	ADJ
ejpam-2287	149	73	curves	curve	NOUN
ejpam-2287	149	74	p1(s	p1(s	NOUN
ejpam-2287	149	75	)	)	PUNCT
ejpam-2287	149	76	,	,	PUNCT
ejpam-2287	149	77	p2(s	p2(s	NOUN
ejpam-2287	149	78	)	)	PUNCT
ejpam-2287	149	79	and	and	CCONJ
ejpam-2287	149	80	p3(s	p3(	NOUN
ejpam-2287	149	81	)	)	PUNCT
ejpam-2287	149	82	is	be	AUX
ejpam-2287	149	83	at	at	ADP
ejpam-2287	149	84	s	s	NOUN
ejpam-2287	149	85	=	=	NOUN
ejpam-2287	149	86	4.39	4.39	NUM
ejpam-2287	149	87	,	,	PUNCT
ejpam-2287	149	88	that	that	ADV
ejpam-2287	149	89	is	is	ADV
ejpam-2287	149	90	,	,	PUNCT
ejpam-2287	149	91	at	at	ADP
ejpam-2287	149	92	λµ	λµ	ADP
ejpam-2287	149	93	=	=	NOUN
ejpam-2287	149	94	4.39	4.39	NUM
ejpam-2287	149	95	.	.	PUNCT
ejpam-2287	150	1	moreover	moreover	ADV
ejpam-2287	150	2	,	,	PUNCT
ejpam-2287	150	3	the	the	DET
ejpam-2287	150	4	parabola	parabola	PROPN
ejpam-2287	150	5	p2(s	p2(s	PROPN
ejpam-2287	150	6	)	)	PUNCT
ejpam-2287	150	7	has	have	VERB
ejpam-2287	150	8	a	a	DET
ejpam-2287	150	9	real	real	ADJ
ejpam-2287	150	10	,	,	PUNCT
ejpam-2287	150	11	repeated	repeat	VERB
ejpam-2287	150	12	root	root	NOUN
ejpam-2287	150	13	at	at	ADP
ejpam-2287	150	14	s	s	NOUN
ejpam-2287	150	15	=	=	NOUN
ejpam-2287	150	16	4.39	4.39	NUM
ejpam-2287	150	17	and	and	CCONJ
ejpam-2287	150	18	is	be	AUX
ejpam-2287	150	19	positive	positive	ADJ
ejpam-2287	150	20	everywhere	everywhere	ADV
ejpam-2287	150	21	else	else	ADV
ejpam-2287	150	22	.	.	PUNCT
ejpam-2287	151	1	the	the	DET
ejpam-2287	151	2	line	line	NOUN
ejpam-2287	151	3	p1(s	p1(s	PROPN
ejpam-2287	151	4	)	)	PUNCT
ejpam-2287	151	5	and	and	CCONJ
ejpam-2287	151	6	the	the	DET
ejpam-2287	151	7	cubic	cubic	PROPN
ejpam-2287	151	8	p3(s	p3(	NOUN
ejpam-2287	151	9	)	)	PUNCT
ejpam-2287	151	10	are	be	AUX
ejpam-2287	151	11	clearly	clearly	ADV
ejpam-2287	151	12	positive	positive	ADJ
ejpam-2287	151	13	for	for	ADP
ejpam-2287	151	14	s	s	PROPN
ejpam-2287	151	15	>	>	X
ejpam-2287	151	16	4.39	4.39	NUM
ejpam-2287	151	17	and	and	CCONJ
ejpam-2287	151	18	negative	negative	ADJ
ejpam-2287	151	19	elsewhere	elsewhere	ADV
ejpam-2287	151	20	.	.	PUNCT
ejpam-2287	152	1	moreover	moreover	ADV
ejpam-2287	152	2	,	,	PUNCT
ejpam-2287	152	3	the	the	DET
ejpam-2287	152	4	two	two	NUM
ejpam-2287	152	5	s	s	NOUN
ejpam-2287	152	6	-	-	NOUN
ejpam-2287	152	7	intercepts	intercept	NOUN
ejpam-2287	152	8	of	of	ADP
ejpam-2287	152	9	the	the	DET
ejpam-2287	152	10	parabola	parabola	PROPN
ejpam-2287	152	11	p4(s	p4(s	PROPN
ejpam-2287	152	12	)	)	PUNCT
ejpam-2287	152	13	are	be	AUX
ejpam-2287	152	14	given	give	VERB
ejpam-2287	152	15	by	by	ADP
ejpam-2287	152	16	s	s	NOUN
ejpam-2287	152	17	=	=	SYM
ejpam-2287	152	18	2.4	2.4	NUM
ejpam-2287	152	19	and	and	CCONJ
ejpam-2287	152	20	s	s	NOUN
ejpam-2287	152	21	=	=	NOUN
ejpam-2287	152	22	6.38	6.38	NUM
ejpam-2287	152	23	.	.	PUNCT
ejpam-2287	153	1	in	in	ADP
ejpam-2287	153	2	particular	particular	ADJ
ejpam-2287	153	3	,	,	PUNCT
ejpam-2287	153	4	p4(s	p4(s	NOUN
ejpam-2287	153	5	)	)	PUNCT
ejpam-2287	153	6	is	be	AUX
ejpam-2287	153	7	negative	negative	ADJ
ejpam-2287	153	8	between	between	ADP
ejpam-2287	153	9	these	these	DET
ejpam-2287	153	10	two	two	NUM
ejpam-2287	153	11	s	s	NOUN
ejpam-2287	153	12	-	-	PUNCT
ejpam-2287	153	13	values	value	NOUN
ejpam-2287	153	14	and	and	CCONJ
ejpam-2287	153	15	positive	positive	ADJ
ejpam-2287	153	16	everywhere	everywhere	ADV
ejpam-2287	153	17	else	else	ADV
ejpam-2287	153	18	.	.	PUNCT
ejpam-2287	154	1	these	these	DET
ejpam-2287	154	2	observations	observation	NOUN
ejpam-2287	154	3	are	be	AUX
ejpam-2287	154	4	summarized	summarize	VERB
ejpam-2287	154	5	in	in	ADP
ejpam-2287	154	6	table	table	NOUN
ejpam-2287	154	7	2	2	NUM
ejpam-2287	154	8	in	in	ADP
ejpam-2287	154	9	terms	term	NOUN
ejpam-2287	154	10	of	of	ADP
ejpam-2287	154	11	the	the	DET
ejpam-2287	154	12	coefficients	coefficient	NOUN
ejpam-2287	154	13	of	of	ADP
ejpam-2287	154	14	the	the	DET
ejpam-2287	154	15	polynomial	polynomial	ADJ
ejpam-2287	154	16	h(θ	h(θ	PROPN
ejpam-2287	154	17	)	)	PUNCT
ejpam-2287	154	18	given	give	VERB
ejpam-2287	154	19	in	in	ADP
ejpam-2287	154	20	(	(	PUNCT
ejpam-2287	154	21	19	19	NUM
ejpam-2287	154	22	)	)	PUNCT
ejpam-2287	154	23	.	.	PUNCT
ejpam-2287	155	1	s.	s.	PROPN
ejpam-2287	155	2	basu	basu	PROPN
ejpam-2287	155	3	/	/	SYM
ejpam-2287	155	4	eur	eur	PROPN
ejpam-2287	155	5	.	.	PUNCT
ejpam-2287	156	1	j.	j.	PROPN
ejpam-2287	156	2	pure	pure	PROPN
ejpam-2287	156	3	appl	appl	PROPN
ejpam-2287	156	4	.	.	PROPN
ejpam-2287	156	5	math	math	PROPN
ejpam-2287	156	6	,	,	PUNCT
ejpam-2287	156	7	7	7	NUM
ejpam-2287	156	8	(	(	PUNCT
ejpam-2287	156	9	2014	2014	NUM
ejpam-2287	156	10	)	)	PUNCT
ejpam-2287	156	11	,	,	PUNCT
ejpam-2287	156	12	442	442	NUM
ejpam-2287	156	13	-	-	SYM
ejpam-2287	156	14	461	461	NUM
ejpam-2287	156	15	450	450	NUM
ejpam-2287	156	16	-5	-5	NUM
ejpam-2287	156	17	5	5	NUM
ejpam-2287	156	18	10	10	NUM
ejpam-2287	156	19	-2	-2	NOUN
ejpam-2287	156	20	2	2	NUM
ejpam-2287	156	21	4	4	NUM
ejpam-2287	156	22	6	6	NUM
ejpam-2287	156	23	8	8	NUM
ejpam-2287	156	24	10	10	NUM
ejpam-2287	156	25	figure	figure	NOUN
ejpam-2287	156	26	2	2	NUM
ejpam-2287	156	27	:	:	PUNCT
ejpam-2287	156	28	diagram	diagram	NOUN
ejpam-2287	156	29	showing	show	VERB
ejpam-2287	156	30	the	the	DET
ejpam-2287	156	31	polynomials	polynomial	NOUN
ejpam-2287	156	32	p1(s	p1(s	NOUN
ejpam-2287	156	33	)	)	PUNCT
ejpam-2287	156	34	in	in	ADP
ejpam-2287	156	35	black	black	ADJ
ejpam-2287	156	36	,	,	PUNCT
ejpam-2287	156	37	p2(s	p2(s	NOUN
ejpam-2287	156	38	)	)	PUNCT
ejpam-2287	156	39	in	in	ADP
ejpam-2287	156	40	red	red	ADJ
ejpam-2287	156	41	,	,	PUNCT
ejpam-2287	156	42	p3(s	p3(s	NOUN
ejpam-2287	156	43	)	)	PUNCT
ejpam-2287	156	44	in	in	ADP
ejpam-2287	156	45	blue	blue	ADJ
ejpam-2287	156	46	and	and	CCONJ
ejpam-2287	156	47	p4(s	p4(s	NOUN
ejpam-2287	156	48	)	)	PUNCT
ejpam-2287	156	49	in	in	ADP
ejpam-2287	156	50	green	green	ADJ
ejpam-2287	156	51	.	.	PUNCT
ejpam-2287	157	1	table	table	NOUN
ejpam-2287	157	2	2	2	NUM
ejpam-2287	157	3	:	:	PUNCT
ejpam-2287	157	4	table	table	NOUN
ejpam-2287	157	5	showing	show	VERB
ejpam-2287	157	6	the	the	DET
ejpam-2287	157	7	signs	sign	NOUN
ejpam-2287	157	8	of	of	ADP
ejpam-2287	157	9	the	the	DET
ejpam-2287	157	10	coefficients	coefficient	NOUN
ejpam-2287	157	11	of	of	ADP
ejpam-2287	157	12	h(θ	h(θ	PROPN
ejpam-2287	157	13	)	)	PUNCT
ejpam-2287	157	14	for	for	ADP
ejpam-2287	157	15	various	various	ADJ
ejpam-2287	157	16	λµ-parameter	λµ-parameter	NOUN
ejpam-2287	157	17	regions	region	NOUN
ejpam-2287	157	18	.	.	PUNCT
ejpam-2287	158	1	λµ	λµ	PRON
ejpam-2287	158	2	region	region	NOUN
ejpam-2287	158	3	θ8	θ8	PROPN
ejpam-2287	158	4	coeff	coeff	PROPN
ejpam-2287	158	5	.	.	PUNCT
ejpam-2287	159	1	θ6	θ6	PROPN
ejpam-2287	159	2	coeff	coeff	PROPN
ejpam-2287	159	3	.	.	PUNCT
ejpam-2287	159	4	:	:	PUNCT
ejpam-2287	160	1	p1(s	p1(s	X
ejpam-2287	160	2	)	)	PUNCT
ejpam-2287	160	3	θ4	θ4	PROPN
ejpam-2287	160	4	coeff	coeff	PROPN
ejpam-2287	160	5	.	.	PUNCT
ejpam-2287	160	6	:	:	PUNCT
ejpam-2287	161	1	p2(s	p2(s	NOUN
ejpam-2287	161	2	)	)	PUNCT
ejpam-2287	161	3	θ2	θ2	PROPN
ejpam-2287	161	4	coeff	coeff	PROPN
ejpam-2287	161	5	.	.	PUNCT
ejpam-2287	161	6	:	:	PUNCT
ejpam-2287	162	1	p3(s	p3(s	X
ejpam-2287	162	2	)	)	PUNCT
ejpam-2287	162	3	constant	constant	ADJ
ejpam-2287	162	4	:	:	PUNCT
ejpam-2287	162	5	p4(s	p4(s	X
ejpam-2287	162	6	)	)	PUNCT
ejpam-2287	162	7	0	0	NUM
ejpam-2287	162	8	<	<	X
ejpam-2287	162	9	λµ	λµ	X
ejpam-2287	162	10	<	<	X
ejpam-2287	162	11	2.4	2.4	NUM
ejpam-2287	162	12	+	+	SYM
ejpam-2287	162	13	+	+	CCONJ
ejpam-2287	162	14	+	+	NUM
ejpam-2287	162	15	λµ=	λµ=	PROPN
ejpam-2287	162	16	2.4	2.4	NUM
ejpam-2287	162	17	+	+	CCONJ
ejpam-2287	163	1	+	+	CCONJ
ejpam-2287	163	2	0	0	NUM
ejpam-2287	163	3	2.4	2.4	NUM
ejpam-2287	163	4	<	<	X
ejpam-2287	163	5	λµ	λµ	X
ejpam-2287	163	6	<	<	X
ejpam-2287	163	7	4.39	4.39	NUM
ejpam-2287	163	8	+	+	CCONJ
ejpam-2287	163	9	+	+	NUM
ejpam-2287	163	10	λµ=	λµ=	NOUN
ejpam-2287	163	11	4.39	4.39	NUM
ejpam-2287	163	12	+	+	CCONJ
ejpam-2287	163	13	0	0	NUM
ejpam-2287	163	14	0	0	NUM
ejpam-2287	163	15	0	0	NUM
ejpam-2287	163	16	4.39	4.39	NUM
ejpam-2287	163	17	<	<	X
ejpam-2287	163	18	λµ	λµ	X
ejpam-2287	163	19	<	<	X
ejpam-2287	163	20	6.38	6.38	NUM
ejpam-2287	163	21	+	+	PUNCT
ejpam-2287	164	1	+	+	PUNCT
ejpam-2287	164	2	+	+	CCONJ
ejpam-2287	164	3	+	+	NUM
ejpam-2287	164	4	λµ=	λµ=	NOUN
ejpam-2287	164	5	6.38	6.38	NUM
ejpam-2287	164	6	+	+	NOUN
ejpam-2287	165	1	+	+	PUNCT
ejpam-2287	166	1	+	+	PUNCT
ejpam-2287	166	2	+	+	SYM
ejpam-2287	166	3	0	0	NUM
ejpam-2287	166	4	λµ	λµ	PRON
ejpam-2287	166	5	>	>	X
ejpam-2287	166	6	6.38	6.38	NUM
ejpam-2287	166	7	+	+	PUNCT
ejpam-2287	166	8	+	+	PUNCT
ejpam-2287	167	1	+	+	PUNCT
ejpam-2287	167	2	+	+	CCONJ
ejpam-2287	167	3	+	+	CCONJ
ejpam-2287	167	4	it	it	PRON
ejpam-2287	167	5	follows	follow	VERB
ejpam-2287	167	6	from	from	ADP
ejpam-2287	167	7	table	table	NOUN
ejpam-2287	167	8	2	2	NUM
ejpam-2287	167	9	that	that	PRON
ejpam-2287	167	10	for	for	ADP
ejpam-2287	167	11	0	0	NUM
ejpam-2287	167	12	<	<	X
ejpam-2287	167	13	λµ	λµ	X
ejpam-2287	167	14	<	<	X
ejpam-2287	167	15	2.4	2.4	NUM
ejpam-2287	167	16	,	,	PUNCT
ejpam-2287	167	17	there	there	PRON
ejpam-2287	167	18	are	be	VERB
ejpam-2287	167	19	four	four	NUM
ejpam-2287	167	20	sign	sign	NOUN
ejpam-2287	167	21	changes	change	NOUN
ejpam-2287	167	22	between	between	ADP
ejpam-2287	167	23	the	the	DET
ejpam-2287	167	24	coefficients	coefficient	NOUN
ejpam-2287	167	25	of	of	ADP
ejpam-2287	167	26	h(θ	h(θ	PROPN
ejpam-2287	167	27	)	)	PUNCT
ejpam-2287	167	28	.	.	PUNCT
ejpam-2287	168	1	hence	hence	ADV
ejpam-2287	168	2	by	by	ADP
ejpam-2287	168	3	descartes	descarte	NOUN
ejpam-2287	168	4	’	'	PUNCT
ejpam-2287	168	5	rule	rule	NOUN
ejpam-2287	168	6	of	of	ADP
ejpam-2287	168	7	signs	sign	NOUN
ejpam-2287	168	8	[	[	X
ejpam-2287	168	9	16	16	NUM
ejpam-2287	168	10	]	]	X
ejpam-2287	168	11	,	,	PUNCT
ejpam-2287	168	12	there	there	PRON
ejpam-2287	168	13	exist	exist	VERB
ejpam-2287	168	14	at	at	ADP
ejpam-2287	168	15	most	most	ADJ
ejpam-2287	168	16	four	four	NUM
ejpam-2287	168	17	positive	positive	ADJ
ejpam-2287	168	18	periodic	periodic	ADJ
ejpam-2287	168	19	solutions	solution	NOUN
ejpam-2287	168	20	of	of	ADP
ejpam-2287	168	21	equation	equation	NOUN
ejpam-2287	168	22	(	(	PUNCT
ejpam-2287	168	23	12	12	NUM
ejpam-2287	168	24	)	)	PUNCT
ejpam-2287	168	25	.	.	PUNCT
ejpam-2287	169	1	we	we	PRON
ejpam-2287	169	2	also	also	ADV
ejpam-2287	169	3	saw	see	VERB
ejpam-2287	169	4	in	in	ADP
ejpam-2287	169	5	section	section	NOUN
ejpam-2287	169	6	4	4	NUM
ejpam-2287	169	7	that	that	PRON
ejpam-2287	169	8	(	(	PUNCT
ejpam-2287	169	9	12	12	NUM
ejpam-2287	169	10	)	)	PUNCT
ejpam-2287	169	11	has	have	VERB
ejpam-2287	169	12	a	a	DET
ejpam-2287	169	13	positive	positive	ADJ
ejpam-2287	169	14	equilibrium	equilibrium	NOUN
ejpam-2287	169	15	θ	θ	NOUN
ejpam-2287	169	16	=	=	PUNCT
ejpam-2287	170	1	0.645497	0.645497	NUM
ejpam-2287	170	2	p	p	NOUN
ejpam-2287	170	3	2.4−λµ	2.4−λµ	NUM
ejpam-2287	170	4	for	for	ADP
ejpam-2287	170	5	λµ	λµ	PRON
ejpam-2287	170	6	<	<	X
ejpam-2287	170	7	2.4	2.4	NUM
ejpam-2287	170	8	.	.	PUNCT
ejpam-2287	171	1	since	since	SCONJ
ejpam-2287	171	2	equilibria	equilibrium	NOUN
ejpam-2287	171	3	are	be	AUX
ejpam-2287	171	4	trivially	trivially	ADV
ejpam-2287	171	5	periodic	periodic	ADJ
ejpam-2287	171	6	solutions	solution	NOUN
ejpam-2287	171	7	,	,	PUNCT
ejpam-2287	171	8	equation	equation	NOUN
ejpam-2287	171	9	(	(	PUNCT
ejpam-2287	171	10	12	12	NUM
ejpam-2287	171	11	)	)	PUNCT
ejpam-2287	171	12	has	have	VERB
ejpam-2287	171	13	at	at	ADP
ejpam-2287	171	14	most	most	ADJ
ejpam-2287	171	15	4−	4−	NOUN
ejpam-2287	171	16	1	1	NUM
ejpam-2287	171	17	=	=	SYM
ejpam-2287	171	18	3	3	NUM
ejpam-2287	171	19	nontrivial	nontrivial	NOUN
ejpam-2287	171	20	positive	positive	ADJ
ejpam-2287	171	21	periodic	periodic	ADJ
ejpam-2287	171	22	solutions	solution	NOUN
ejpam-2287	171	23	for	for	ADP
ejpam-2287	171	24	λµ	λµ	PRON
ejpam-2287	171	25	<	<	X
ejpam-2287	171	26	2.4	2.4	NUM
ejpam-2287	171	27	.	.	PUNCT
ejpam-2287	172	1	also	also	ADV
ejpam-2287	172	2	note	note	VERB
ejpam-2287	172	3	that	that	SCONJ
ejpam-2287	172	4	h(−θ	h(−θ	NOUN
ejpam-2287	172	5	)	)	PUNCT
ejpam-2287	172	6	has	have	VERB
ejpam-2287	172	7	the	the	DET
ejpam-2287	172	8	same	same	ADJ
ejpam-2287	172	9	number	number	NOUN
ejpam-2287	172	10	of	of	ADP
ejpam-2287	172	11	sign	sign	NOUN
ejpam-2287	172	12	changes	change	NOUN
ejpam-2287	172	13	between	between	ADP
ejpam-2287	172	14	its	its	PRON
ejpam-2287	172	15	coefficients	coefficient	NOUN
ejpam-2287	172	16	as	as	ADP
ejpam-2287	172	17	h(θ	h(θ	PROPN
ejpam-2287	172	18	)	)	PUNCT
ejpam-2287	172	19	.	.	PUNCT
ejpam-2287	173	1	hence	hence	ADV
ejpam-2287	173	2	one	one	PRON
ejpam-2287	173	3	has	have	VERB
ejpam-2287	173	4	from	from	ADP
ejpam-2287	173	5	descartes	descarte	NOUN
ejpam-2287	173	6	’	'	PUNCT
ejpam-2287	173	7	rule	rule	NOUN
ejpam-2287	173	8	of	of	ADP
ejpam-2287	173	9	signs	sign	NOUN
ejpam-2287	173	10	that	that	SCONJ
ejpam-2287	173	11	(	(	PUNCT
ejpam-2287	173	12	12	12	NUM
ejpam-2287	173	13	)	)	PUNCT
ejpam-2287	173	14	has	have	VERB
ejpam-2287	173	15	at	at	ADP
ejpam-2287	173	16	most	most	ADJ
ejpam-2287	173	17	3	3	NUM
ejpam-2287	173	18	nontrivial	nontrivial	ADJ
ejpam-2287	173	19	negative	negative	ADJ
ejpam-2287	173	20	periodic	periodic	ADJ
ejpam-2287	173	21	solutions	solution	NOUN
ejpam-2287	173	22	for	for	ADP
ejpam-2287	173	23	λµ	λµ	PRON
ejpam-2287	173	24	<	<	X
ejpam-2287	173	25	2.4	2.4	NUM
ejpam-2287	173	26	.	.	PUNCT
ejpam-2287	174	1	since	since	SCONJ
ejpam-2287	174	2	periodic	periodic	ADJ
ejpam-2287	174	3	solutions	solution	NOUN
ejpam-2287	174	4	of	of	ADP
ejpam-2287	174	5	discrete	discrete	ADJ
ejpam-2287	174	6	2d	2d	NOUN
ejpam-2287	174	7	-	-	PUNCT
ejpam-2287	174	8	systems	system	NOUN
ejpam-2287	174	9	occur	occur	VERB
ejpam-2287	174	10	in	in	ADP
ejpam-2287	174	11	pairs	pair	NOUN
ejpam-2287	174	12	,	,	PUNCT
ejpam-2287	174	13	one	one	PRON
ejpam-2287	174	14	can	can	AUX
ejpam-2287	174	15	conclude	conclude	VERB
ejpam-2287	174	16	that	that	SCONJ
ejpam-2287	174	17	there	there	PRON
ejpam-2287	174	18	exist	exist	VERB
ejpam-2287	174	19	at	at	ADP
ejpam-2287	174	20	most	most	ADV
ejpam-2287	174	21	three	three	NUM
ejpam-2287	174	22	pairs	pair	NOUN
ejpam-2287	174	23	of	of	ADP
ejpam-2287	174	24	real	real	ADJ
ejpam-2287	174	25	nontrivial	nontrivial	ADJ
ejpam-2287	174	26	periodic	periodic	ADJ
ejpam-2287	174	27	solutions	solution	NOUN
ejpam-2287	174	28	of	of	ADP
ejpam-2287	174	29	equation	equation	NOUN
ejpam-2287	174	30	(	(	PUNCT
ejpam-2287	174	31	12	12	NUM
ejpam-2287	174	32	)	)	PUNCT
ejpam-2287	174	33	for	for	ADP
ejpam-2287	174	34	0	0	NUM
ejpam-2287	174	35	<	<	X
ejpam-2287	174	36	λµ	λµ	ADP
ejpam-2287	174	37	<	<	X
ejpam-2287	174	38	2.4	2.4	NUM
ejpam-2287	174	39	.	.	PUNCT
ejpam-2287	175	1	similar	similar	ADJ
ejpam-2287	175	2	arguments	argument	NOUN
ejpam-2287	175	3	can	can	AUX
ejpam-2287	175	4	be	be	AUX
ejpam-2287	175	5	given	give	VERB
ejpam-2287	175	6	for	for	ADP
ejpam-2287	175	7	the	the	DET
ejpam-2287	175	8	remaining	remain	VERB
ejpam-2287	175	9	λµ-parameter	λµ-parameter	NOUN
ejpam-2287	175	10	cases	case	NOUN
ejpam-2287	175	11	in	in	ADP
ejpam-2287	175	12	table	table	NOUN
ejpam-2287	175	13	2	2	NUM
ejpam-2287	175	14	.	.	PUNCT
ejpam-2287	175	15	to	to	PART
ejpam-2287	175	16	summarize	summarize	VERB
ejpam-2287	175	17	,	,	PUNCT
ejpam-2287	175	18	in	in	ADP
ejpam-2287	175	19	this	this	DET
ejpam-2287	175	20	section	section	NOUN
ejpam-2287	175	21	we	we	PRON
ejpam-2287	175	22	looked	look	VERB
ejpam-2287	175	23	at	at	ADP
ejpam-2287	175	24	the	the	DET
ejpam-2287	175	25	exact	exact	ADJ
ejpam-2287	175	26	number	number	NOUN
ejpam-2287	175	27	of	of	ADP
ejpam-2287	175	28	equilibria	equilibrium	NOUN
ejpam-2287	175	29	for	for	ADP
ejpam-2287	175	30	equation	equation	NOUN
ejpam-2287	175	31	(	(	PUNCT
ejpam-2287	175	32	12	12	NUM
ejpam-2287	175	33	)	)	PUNCT
ejpam-2287	175	34	and	and	CCONJ
ejpam-2287	175	35	computed	compute	VERB
ejpam-2287	175	36	strict	strict	ADJ
ejpam-2287	175	37	upper	upper	ADJ
ejpam-2287	175	38	bounds	bound	NOUN
ejpam-2287	175	39	for	for	ADP
ejpam-2287	175	40	the	the	DET
ejpam-2287	175	41	number	number	NOUN
ejpam-2287	175	42	of	of	ADP
ejpam-2287	175	43	real	real	ADJ
ejpam-2287	175	44	nontrivial	nontrivial	ADJ
ejpam-2287	175	45	periodic	periodic	ADJ
ejpam-2287	175	46	solutions	solution	NOUN
ejpam-2287	175	47	of	of	ADP
ejpam-2287	175	48	(	(	PUNCT
ejpam-2287	175	49	12	12	NUM
ejpam-2287	175	50	)	)	PUNCT
ejpam-2287	175	51	in	in	ADP
ejpam-2287	175	52	the	the	DET
ejpam-2287	175	53	parameter	parameter	NOUN
ejpam-2287	175	54	region	region	NOUN
ejpam-2287	175	55	0	0	PUNCT
ejpam-2287	175	56	<	<	X
ejpam-2287	175	57	λµ	λµ	X
ejpam-2287	175	58	<	<	X
ejpam-2287	175	59	2.4	2.4	NUM
ejpam-2287	175	60	.	.	PUNCT
ejpam-2287	176	1	in	in	ADP
ejpam-2287	176	2	the	the	DET
ejpam-2287	176	3	next	next	ADJ
ejpam-2287	176	4	section	section	NOUN
ejpam-2287	176	5	,	,	PUNCT
ejpam-2287	176	6	we	we	PRON
ejpam-2287	176	7	will	will	AUX
ejpam-2287	176	8	address	address	VERB
ejpam-2287	176	9	global	global	ADJ
ejpam-2287	176	10	attractivity	attractivity	NOUN
ejpam-2287	176	11	and	and	CCONJ
ejpam-2287	176	12	basins	basin	NOUN
ejpam-2287	176	13	of	of	ADP
ejpam-2287	176	14	attraction	attraction	NOUN
ejpam-2287	176	15	of	of	ADP
ejpam-2287	176	16	these	these	DET
ejpam-2287	176	17	real	real	ADJ
ejpam-2287	176	18	equilibria	equilibrium	NOUN
ejpam-2287	176	19	and	and	CCONJ
ejpam-2287	176	20	periodic	periodic	ADJ
ejpam-2287	176	21	solutions	solution	NOUN
ejpam-2287	176	22	.	.	PUNCT
ejpam-2287	177	1	s.	s.	PROPN
ejpam-2287	177	2	basu	basu	PROPN
ejpam-2287	177	3	/	/	SYM
ejpam-2287	177	4	eur	eur	PROPN
ejpam-2287	177	5	.	.	PUNCT
ejpam-2287	178	1	j.	j.	PROPN
ejpam-2287	178	2	pure	pure	PROPN
ejpam-2287	178	3	appl	appl	PROPN
ejpam-2287	178	4	.	.	PROPN
ejpam-2287	178	5	math	math	PROPN
ejpam-2287	178	6	,	,	PUNCT
ejpam-2287	178	7	7	7	NUM
ejpam-2287	178	8	(	(	PUNCT
ejpam-2287	178	9	2014	2014	NUM
ejpam-2287	178	10	)	)	PUNCT
ejpam-2287	178	11	,	,	PUNCT
ejpam-2287	178	12	442	442	NUM
ejpam-2287	178	13	-	-	SYM
ejpam-2287	178	14	461	461	NUM
ejpam-2287	178	15	451	451	NUM
ejpam-2287	178	16	6	6	NUM
ejpam-2287	178	17	.	.	PUNCT
ejpam-2287	178	18	global	global	ADJ
ejpam-2287	178	19	attractivity	attractivity	NOUN
ejpam-2287	178	20	and	and	CCONJ
ejpam-2287	178	21	basins	basin	NOUN
ejpam-2287	178	22	of	of	ADP
ejpam-2287	178	23	attraction	attraction	NOUN
ejpam-2287	178	24	of	of	ADP
ejpam-2287	178	25	the	the	DET
ejpam-2287	178	26	real	real	ADJ
ejpam-2287	178	27	equilibria	equilibrium	NOUN
ejpam-2287	178	28	and	and	CCONJ
ejpam-2287	178	29	periodic	periodic	ADJ
ejpam-2287	178	30	solutions	solution	NOUN
ejpam-2287	178	31	an	an	DET
ejpam-2287	178	32	important	important	ADJ
ejpam-2287	178	33	question	question	NOUN
ejpam-2287	178	34	that	that	SCONJ
ejpam-2287	178	35	mckenna	mckenna	PROPN
ejpam-2287	178	36	and	and	CCONJ
ejpam-2287	178	37	moore	moore	PROPN
ejpam-2287	178	38	failed	fail	VERB
ejpam-2287	178	39	to	to	PART
ejpam-2287	178	40	address	address	VERB
ejpam-2287	178	41	in	in	ADP
ejpam-2287	178	42	[	[	X
ejpam-2287	178	43	13	13	NUM
ejpam-2287	178	44	]	]	PUNCT
ejpam-2287	178	45	was	be	AUX
ejpam-2287	178	46	global	global	ADJ
ejpam-2287	178	47	attractivity	attractivity	NOUN
ejpam-2287	178	48	properties	property	NOUN
ejpam-2287	178	49	of	of	ADP
ejpam-2287	178	50	the	the	DET
ejpam-2287	178	51	real	real	ADJ
ejpam-2287	178	52	equilibria	equilibrium	NOUN
ejpam-2287	178	53	and	and	CCONJ
ejpam-2287	178	54	periodic	periodic	ADJ
ejpam-2287	178	55	solutions	solution	NOUN
ejpam-2287	178	56	of	of	ADP
ejpam-2287	178	57	their	their	PRON
ejpam-2287	178	58	continuous	continuous	ADJ
ejpam-2287	178	59	suspension	suspension	NOUN
ejpam-2287	178	60	bridge	bridge	NOUN
ejpam-2287	178	61	model	model	NOUN
ejpam-2287	178	62	(	(	PUNCT
ejpam-2287	178	63	1	1	NUM
ejpam-2287	178	64	)	)	PUNCT
ejpam-2287	178	65	,	,	PUNCT
ejpam-2287	178	66	including	include	VERB
ejpam-2287	178	67	basins	basin	NOUN
ejpam-2287	178	68	of	of	ADP
ejpam-2287	178	69	attraction	attraction	NOUN
ejpam-2287	178	70	of	of	ADP
ejpam-2287	178	71	these	these	DET
ejpam-2287	178	72	solutions	solution	NOUN
ejpam-2287	178	73	.	.	PUNCT
ejpam-2287	179	1	one	one	PRON
ejpam-2287	179	2	can	can	AUX
ejpam-2287	179	3	expect	expect	VERB
ejpam-2287	179	4	global	global	ADJ
ejpam-2287	179	5	attractivity	attractivity	NOUN
ejpam-2287	179	6	properties	property	NOUN
ejpam-2287	179	7	of	of	ADP
ejpam-2287	179	8	real	real	ADJ
ejpam-2287	179	9	periodic	periodic	ADJ
ejpam-2287	179	10	solutions	solution	NOUN
ejpam-2287	179	11	to	to	PART
ejpam-2287	179	12	play	play	VERB
ejpam-2287	179	13	a	a	DET
ejpam-2287	179	14	very	very	ADV
ejpam-2287	179	15	important	important	ADJ
ejpam-2287	179	16	role	role	NOUN
ejpam-2287	179	17	in	in	ADP
ejpam-2287	179	18	predicting	predict	VERB
ejpam-2287	179	19	the	the	DET
ejpam-2287	179	20	stability	stability	NOUN
ejpam-2287	179	21	of	of	ADP
ejpam-2287	179	22	a	a	DET
ejpam-2287	179	23	swaying	sway	VERB
ejpam-2287	179	24	bridge	bridge	NOUN
ejpam-2287	179	25	,	,	PUNCT
ejpam-2287	179	26	with	with	ADP
ejpam-2287	179	27	an	an	DET
ejpam-2287	179	28	attracting	attract	VERB
ejpam-2287	179	29	periodic	periodic	ADJ
ejpam-2287	179	30	solution	solution	NOUN
ejpam-2287	179	31	implying	imply	VERB
ejpam-2287	179	32	stable	stable	ADJ
ejpam-2287	179	33	bridge	bridge	NOUN
ejpam-2287	179	34	oscillations	oscillation	NOUN
ejpam-2287	179	35	in	in	ADP
ejpam-2287	179	36	the	the	DET
ejpam-2287	179	37	long	long	ADJ
ejpam-2287	179	38	run	run	NOUN
ejpam-2287	179	39	and	and	CCONJ
ejpam-2287	179	40	a	a	DET
ejpam-2287	179	41	repelling	repelling	NOUN
ejpam-2287	179	42	or	or	CCONJ
ejpam-2287	179	43	saddle	saddle	NOUN
ejpam-2287	179	44	point	point	NOUN
ejpam-2287	179	45	periodic	periodic	ADJ
ejpam-2287	179	46	solution	solution	NOUN
ejpam-2287	179	47	signifying	signify	VERB
ejpam-2287	179	48	the	the	DET
ejpam-2287	179	49	onset	onset	NOUN
ejpam-2287	179	50	of	of	ADP
ejpam-2287	179	51	unstable	unstable	ADJ
ejpam-2287	179	52	or	or	CCONJ
ejpam-2287	179	53	even	even	ADV
ejpam-2287	179	54	chaotic	chaotic	ADJ
ejpam-2287	179	55	bridge	bridge	NOUN
ejpam-2287	179	56	oscillations	oscillation	NOUN
ejpam-2287	179	57	in	in	ADP
ejpam-2287	179	58	the	the	DET
ejpam-2287	179	59	long	long	ADJ
ejpam-2287	179	60	run	run	NOUN
ejpam-2287	179	61	possibly	possibly	ADV
ejpam-2287	179	62	leading	lead	VERB
ejpam-2287	179	63	to	to	ADP
ejpam-2287	179	64	disastrous	disastrous	ADJ
ejpam-2287	179	65	consequences	consequence	NOUN
ejpam-2287	179	66	such	such	ADJ
ejpam-2287	179	67	as	as	ADP
ejpam-2287	179	68	the	the	DET
ejpam-2287	179	69	1940	1940	NUM
ejpam-2287	179	70	tacoma	tacoma	NOUN
ejpam-2287	179	71	narrows	narrow	VERB
ejpam-2287	179	72	bridge	bridge	NOUN
ejpam-2287	179	73	collapse	collapse	NOUN
ejpam-2287	179	74	in	in	ADP
ejpam-2287	179	75	washington	washington	PROPN
ejpam-2287	179	76	,	,	PUNCT
ejpam-2287	179	77	usa	usa	PROPN
ejpam-2287	179	78	.	.	PROPN
ejpam-2287	180	1	in	in	ADP
ejpam-2287	180	2	this	this	DET
ejpam-2287	180	3	section	section	NOUN
ejpam-2287	180	4	,	,	PUNCT
ejpam-2287	180	5	we	we	PRON
ejpam-2287	180	6	will	will	AUX
ejpam-2287	180	7	compute	compute	VERB
ejpam-2287	180	8	for	for	ADP
ejpam-2287	180	9	our	our	PRON
ejpam-2287	180	10	discrete	discrete	ADJ
ejpam-2287	180	11	suspension	suspension	NOUN
ejpam-2287	180	12	bridge	bridge	NOUN
ejpam-2287	180	13	model	model	NOUN
ejpam-2287	180	14	(	(	PUNCT
ejpam-2287	180	15	12	12	NUM
ejpam-2287	180	16	)	)	PUNCT
ejpam-2287	180	17	precise	precise	ADJ
ejpam-2287	180	18	λµ-parameter	λµ-parameter	NOUN
ejpam-2287	180	19	regions	region	NOUN
ejpam-2287	180	20	where	where	SCONJ
ejpam-2287	180	21	there	there	PRON
ejpam-2287	180	22	exist	exist	VERB
ejpam-2287	180	23	a	a	DET
ejpam-2287	180	24	unique	unique	ADJ
ejpam-2287	180	25	equilibrium	equilibrium	NOUN
ejpam-2287	180	26	,	,	PUNCT
ejpam-2287	180	27	multiple	multiple	ADJ
ejpam-2287	180	28	equilibria	equilibrium	NOUN
ejpam-2287	180	29	,	,	PUNCT
ejpam-2287	180	30	a	a	DET
ejpam-2287	180	31	unique	unique	ADJ
ejpam-2287	180	32	real	real	ADJ
ejpam-2287	180	33	periodic	periodic	ADJ
ejpam-2287	180	34	solution	solution	NOUN
ejpam-2287	180	35	and	and	CCONJ
ejpam-2287	180	36	multiple	multiple	ADJ
ejpam-2287	180	37	real	real	ADJ
ejpam-2287	180	38	periodic	periodic	ADJ
ejpam-2287	180	39	solutions	solution	NOUN
ejpam-2287	180	40	.	.	PUNCT
ejpam-2287	181	1	we	we	PRON
ejpam-2287	181	2	will	will	AUX
ejpam-2287	181	3	also	also	ADV
ejpam-2287	181	4	compute	compute	VERB
ejpam-2287	181	5	basins	basin	NOUN
ejpam-2287	181	6	of	of	ADP
ejpam-2287	181	7	attraction	attraction	NOUN
ejpam-2287	181	8	for	for	ADP
ejpam-2287	181	9	these	these	PRON
ejpam-2287	181	10	.	.	PUNCT
ejpam-2287	182	1	we	we	PRON
ejpam-2287	182	2	start	start	VERB
ejpam-2287	182	3	by	by	ADP
ejpam-2287	182	4	stating	state	VERB
ejpam-2287	182	5	a	a	DET
ejpam-2287	182	6	local	local	ADJ
ejpam-2287	182	7	stability	stability	NOUN
ejpam-2287	182	8	result	result	NOUN
ejpam-2287	182	9	for	for	ADP
ejpam-2287	182	10	the	the	DET
ejpam-2287	182	11	equilibria	equilibria	PROPN
ejpam-2287	182	12	e1	e1	PROPN
ejpam-2287	182	13	,	,	PUNCT
ejpam-2287	182	14	e2	e2	PROPN
ejpam-2287	182	15	,	,	PUNCT
ejpam-2287	182	16	and	and	CCONJ
ejpam-2287	182	17	e3	e3	NOUN
ejpam-2287	182	18	of	of	ADP
ejpam-2287	182	19	(	(	PUNCT
ejpam-2287	182	20	12	12	NUM
ejpam-2287	182	21	)	)	PUNCT
ejpam-2287	182	22	whose	whose	DET
ejpam-2287	182	23	formulas	formula	NOUN
ejpam-2287	182	24	were	be	AUX
ejpam-2287	182	25	first	first	ADV
ejpam-2287	182	26	introduced	introduce	VERB
ejpam-2287	182	27	in	in	ADP
ejpam-2287	182	28	section	section	NOUN
ejpam-2287	182	29	4	4	NUM
ejpam-2287	182	30	and	and	CCONJ
ejpam-2287	182	31	are	be	AUX
ejpam-2287	182	32	given	give	VERB
ejpam-2287	182	33	below	below	ADP
ejpam-2287	182	34	for	for	ADP
ejpam-2287	182	35	easy	easy	ADJ
ejpam-2287	182	36	reference	reference	NOUN
ejpam-2287	182	37	.	.	PUNCT
ejpam-2287	183	1	e1	e1	NOUN
ejpam-2287	183	2	:	:	PUNCT
ejpam-2287	183	3	=	=	SYM
ejpam-2287	183	4	(	(	PUNCT
ejpam-2287	183	5	0,0	0,0	NUM
ejpam-2287	183	6	)	)	PUNCT
ejpam-2287	183	7	e2	e2	NOUN
ejpam-2287	183	8	:	:	PUNCT
ejpam-2287	183	9	=	=	SYM
ejpam-2287	183	10	(	(	PUNCT
ejpam-2287	183	11	0.645497	0.645497	NUM
ejpam-2287	183	12	æ	æ	SYM
ejpam-2287	183	13	2.4−λµ	2.4−λµ	NUM
ejpam-2287	183	14	,	,	PUNCT
ejpam-2287	183	15	0.645497	0.645497	NUM
ejpam-2287	183	16	æ	æ	SYM
ejpam-2287	183	17	2.4−λµ	2.4−λµ	NUM
ejpam-2287	183	18	)	)	PUNCT
ejpam-2287	183	19	e3	e3	NOUN
ejpam-2287	183	20	:	:	PUNCT
ejpam-2287	183	21	=	=	SYM
ejpam-2287	183	22	(	(	PUNCT
ejpam-2287	183	23	−0.645497	−0.645497	PROPN
ejpam-2287	183	24	æ	æ	PROPN
ejpam-2287	184	1	2.4−λµ,−0.645497	2.4−λµ,−0.645497	NUM
ejpam-2287	184	2	æ	æ	SYM
ejpam-2287	184	3	2.4−λµ	2.4−λµ	NUM
ejpam-2287	184	4	)	)	PUNCT
ejpam-2287	184	5	(	(	PUNCT
ejpam-2287	184	6	20	20	X
ejpam-2287	184	7	)	)	PUNCT
ejpam-2287	184	8	lemma	lemma	PROPN
ejpam-2287	184	9	1	1	NUM
ejpam-2287	184	10	.	.	PUNCT
ejpam-2287	185	1	the	the	DET
ejpam-2287	185	2	equilibria	equilibria	PROPN
ejpam-2287	185	3	e1	e1	PROPN
ejpam-2287	185	4	,	,	PUNCT
ejpam-2287	185	5	e2	e2	PROPN
ejpam-2287	185	6	,	,	PUNCT
ejpam-2287	185	7	and	and	CCONJ
ejpam-2287	185	8	e3	e3	NOUN
ejpam-2287	185	9	are	be	AUX
ejpam-2287	185	10	unstable	unstable	ADJ
ejpam-2287	185	11	for	for	ADP
ejpam-2287	185	12	all	all	DET
ejpam-2287	185	13	admissible	admissible	ADJ
ejpam-2287	185	14	λµ-parameter	λµ-parameter	NOUN
ejpam-2287	185	15	regions	region	NOUN
ejpam-2287	185	16	.	.	PUNCT
ejpam-2287	186	1	proof	proof	NOUN
ejpam-2287	186	2	.	.	PUNCT
ejpam-2287	187	1	it	it	PRON
ejpam-2287	187	2	is	be	AUX
ejpam-2287	187	3	easy	easy	ADJ
ejpam-2287	187	4	to	to	PART
ejpam-2287	187	5	check	check	VERB
ejpam-2287	187	6	that	that	SCONJ
ejpam-2287	187	7	the	the	DET
ejpam-2287	187	8	eigenvalues	eigenvalues	PROPN
ejpam-2287	187	9	λ1	λ1	ADJ
ejpam-2287	187	10	and	and	CCONJ
ejpam-2287	187	11	λ2	λ2	PROPN
ejpam-2287	187	12	(	(	PUNCT
ejpam-2287	187	13	with	with	ADP
ejpam-2287	187	14	λ1	λ1	ADJ
ejpam-2287	187	15	≤	≤	NOUN
ejpam-2287	187	16	λ2	λ2	NOUN
ejpam-2287	187	17	)	)	PUNCT
ejpam-2287	187	18	of	of	ADP
ejpam-2287	187	19	the	the	DET
ejpam-2287	187	20	jacobian	jacobian	NOUN
ejpam-2287	187	21	of	of	ADP
ejpam-2287	187	22	the	the	DET
ejpam-2287	187	23	map	map	NOUN
ejpam-2287	187	24	t	t	PROPN
ejpam-2287	187	25	(	(	PUNCT
ejpam-2287	187	26	θ	θ	PROPN
ejpam-2287	187	27	,	,	PUNCT
ejpam-2287	187	28	u	u	NOUN
ejpam-2287	187	29	)	)	PUNCT
ejpam-2287	187	30	evaluated	evaluate	VERB
ejpam-2287	187	31	at	at	ADP
ejpam-2287	187	32	the	the	DET
ejpam-2287	187	33	three	three	NUM
ejpam-2287	187	34	equilibria	equilibrium	NOUN
ejpam-2287	187	35	are	be	AUX
ejpam-2287	187	36	as	as	SCONJ
ejpam-2287	187	37	follows	follow	VERB
ejpam-2287	187	38	:	:	PUNCT
ejpam-2287	187	39	e1	e1	NOUN
ejpam-2287	187	40	:	:	PUNCT
ejpam-2287	187	41	λ1	λ1	PROPN
ejpam-2287	187	42	=	=	SYM
ejpam-2287	187	43	1−	1−	NUM
ejpam-2287	187	44	æ	æ	X
ejpam-2287	187	45	λµ−	λµ−	PUNCT
ejpam-2287	187	46	2.4,λ2	2.4,λ2	NUM
ejpam-2287	187	47	=	=	SYM
ejpam-2287	187	48	1	1	NUM
ejpam-2287	187	49	+	+	NUM
ejpam-2287	187	50	æ	æ	X
ejpam-2287	187	51	λµ−	λµ−	NUM
ejpam-2287	187	52	2.4	2.4	NUM
ejpam-2287	187	53	e2	e2	NOUN
ejpam-2287	187	54	:	:	PUNCT
ejpam-2287	187	55	λ1	λ1	PROPN
ejpam-2287	187	56	=	=	SYM
ejpam-2287	187	57	1−	1−	NUM
ejpam-2287	187	58	1.414	1.414	NUM
ejpam-2287	187	59	æ	æ	SYM
ejpam-2287	187	60	2.4−λµ,λ2	2.4−λµ,λ2	NUM
ejpam-2287	187	61	=	=	SYM
ejpam-2287	187	62	1	1	NUM
ejpam-2287	187	63	+	+	NOUN
ejpam-2287	187	64	1.414	1.414	NUM
ejpam-2287	187	65	æ	æ	X
ejpam-2287	187	66	2.4−λµ	2.4−λµ	NUM
ejpam-2287	187	67	e3	e3	NOUN
ejpam-2287	187	68	:	:	PUNCT
ejpam-2287	187	69	λ1	λ1	ADJ
ejpam-2287	187	70	=	=	SYM
ejpam-2287	187	71	1−	1−	NUM
ejpam-2287	187	72	1.414	1.414	NUM
ejpam-2287	187	73	æ	æ	SYM
ejpam-2287	187	74	2.4−λµ,λ2	2.4−λµ,λ2	NUM
ejpam-2287	187	75	=	=	SYM
ejpam-2287	187	76	1	1	NUM
ejpam-2287	187	77	+	+	NOUN
ejpam-2287	187	78	1.414	1.414	NUM
ejpam-2287	187	79	æ	æ	SYM
ejpam-2287	187	80	2.4−λµ	2.4−λµ	NUM
ejpam-2287	187	81	note	note	VERB
ejpam-2287	187	82	that	that	SCONJ
ejpam-2287	187	83	e2	e2	PROPN
ejpam-2287	187	84	and	and	CCONJ
ejpam-2287	187	85	e3	e3	NOUN
ejpam-2287	187	86	have	have	VERB
ejpam-2287	187	87	the	the	DET
ejpam-2287	187	88	same	same	ADJ
ejpam-2287	187	89	set	set	NOUN
ejpam-2287	187	90	of	of	ADP
ejpam-2287	187	91	eigenvalues	eigenvalue	NOUN
ejpam-2287	187	92	.	.	PUNCT
ejpam-2287	188	1	moreover	moreover	ADV
ejpam-2287	188	2	,	,	PUNCT
ejpam-2287	188	3	an	an	DET
ejpam-2287	188	4	easy	easy	ADJ
ejpam-2287	188	5	calculation	calculation	NOUN
ejpam-2287	188	6	shows	show	VERB
ejpam-2287	188	7	that	that	SCONJ
ejpam-2287	188	8	the	the	DET
ejpam-2287	188	9	eigenvalues	eigenvalue	NOUN
ejpam-2287	188	10	of	of	ADP
ejpam-2287	188	11	e1	e1	NOUN
ejpam-2287	188	12	satisfy	satisfy	VERB
ejpam-2287	188	13	the	the	DET
ejpam-2287	188	14	following	follow	VERB
ejpam-2287	188	15	inequalities	inequality	NOUN
ejpam-2287	188	16	for	for	ADP
ejpam-2287	188	17	the	the	DET
ejpam-2287	188	18	given	give	VERB
ejpam-2287	188	19	λµ-parameter	λµ-parameter	NOUN
ejpam-2287	188	20	regions	region	NOUN
ejpam-2287	188	21	:	:	PUNCT
ejpam-2287	188	22			VERB
ejpam-2287	188	23			NOUN
ejpam-2287	188	24			PROPN
ejpam-2287	188	25	0	0	NUM
ejpam-2287	188	26	<	<	X
ejpam-2287	188	27	λµ	λµ	ADP
ejpam-2287	188	28	<	<	X
ejpam-2287	188	29	2.4	2.4	NUM
ejpam-2287	188	30	:	:	PUNCT
ejpam-2287	188	31	|λ1|	|λ1|	ADP
ejpam-2287	188	32	>	>	X
ejpam-2287	188	33	1	1	NUM
ejpam-2287	188	34	,	,	PUNCT
ejpam-2287	188	35	|λ2|	|λ2|	NOUN
ejpam-2287	188	36	>	>	X
ejpam-2287	188	37	1	1	NUM
ejpam-2287	188	38	(	(	PUNCT
ejpam-2287	188	39	a	a	NOUN
ejpam-2287	188	40	)	)	PUNCT
ejpam-2287	188	41	λµ=	λµ=	PROPN
ejpam-2287	188	42	2.4	2.4	NUM
ejpam-2287	188	43	:	:	PUNCT
ejpam-2287	188	44	|λ1|=	|λ1|=	PROPN
ejpam-2287	188	45	|λ2|=	|λ2|=	PROPN
ejpam-2287	188	46	1	1	NUM
ejpam-2287	188	47	(	(	PUNCT
ejpam-2287	188	48	b	b	NOUN
ejpam-2287	188	49	)	)	PUNCT
ejpam-2287	188	50	2.4	2.4	NUM
ejpam-2287	188	51	<	<	X
ejpam-2287	188	52	λµ	λµ	X
ejpam-2287	188	53	<	<	X
ejpam-2287	188	54	6.38	6.38	NUM
ejpam-2287	188	55	:	:	PUNCT
ejpam-2287	188	56	|λ1|	|λ1|	ADP
ejpam-2287	188	57	<	<	X
ejpam-2287	188	58	1	1	NUM
ejpam-2287	188	59	,	,	PUNCT
ejpam-2287	188	60	|λ2|	|λ2|	NOUN
ejpam-2287	188	61	>	>	X
ejpam-2287	188	62	1	1	NUM
ejpam-2287	188	63	(	(	PUNCT
ejpam-2287	188	64	c	c	NOUN
ejpam-2287	188	65	)	)	PUNCT
ejpam-2287	188	66	λµ=	λµ=	PROPN
ejpam-2287	188	67	6.38	6.38	NUM
ejpam-2287	188	68	:	:	PUNCT
ejpam-2287	188	69	|λ1|=	|λ1|=	PROPN
ejpam-2287	188	70	1	1	NUM
ejpam-2287	188	71	,	,	PUNCT
ejpam-2287	188	72	|λ2|	|λ2|	NOUN
ejpam-2287	188	73	>	>	X
ejpam-2287	188	74	1	1	NUM
ejpam-2287	188	75	(	(	PUNCT
ejpam-2287	188	76	d	d	NOUN
ejpam-2287	188	77	)	)	PUNCT
ejpam-2287	188	78	λµ	λµ	ADP
ejpam-2287	188	79	>	>	X
ejpam-2287	188	80	6.38	6.38	NUM
ejpam-2287	188	81	:	:	PUNCT
ejpam-2287	188	82	|λ1|	|λ1|	ADP
ejpam-2287	188	83	>	>	X
ejpam-2287	188	84	1	1	NUM
ejpam-2287	188	85	,	,	PUNCT
ejpam-2287	188	86	|λ2|	|λ2|	NOUN
ejpam-2287	188	87	>	>	X
ejpam-2287	188	88	1	1	NUM
ejpam-2287	188	89	(	(	PUNCT
ejpam-2287	188	90	e	e	NOUN
ejpam-2287	188	91	)	)	PUNCT
ejpam-2287	188	92	(	(	PUNCT
ejpam-2287	188	93	21	21	NUM
ejpam-2287	188	94	)	)	PUNCT
ejpam-2287	188	95	hence	hence	ADV
ejpam-2287	188	96	e1	e1	PROPN
ejpam-2287	188	97	is	be	AUX
ejpam-2287	188	98	a	a	DET
ejpam-2287	188	99	repeller	repeller	NOUN
ejpam-2287	188	100	in	in	ADP
ejpam-2287	188	101	cases	case	NOUN
ejpam-2287	188	102	(	(	PUNCT
ejpam-2287	188	103	a	a	NOUN
ejpam-2287	188	104	)	)	PUNCT
ejpam-2287	188	105	and	and	CCONJ
ejpam-2287	188	106	(	(	PUNCT
ejpam-2287	188	107	e	e	NOUN
ejpam-2287	188	108	)	)	PUNCT
ejpam-2287	188	109	,	,	PUNCT
ejpam-2287	188	110	a	a	DET
ejpam-2287	188	111	saddle	saddle	NOUN
ejpam-2287	188	112	point	point	NOUN
ejpam-2287	188	113	equilibrium	equilibrium	NOUN
ejpam-2287	188	114	in	in	ADP
ejpam-2287	188	115	case	case	NOUN
ejpam-2287	188	116	(	(	PUNCT
ejpam-2287	188	117	c	c	NOUN
ejpam-2287	188	118	)	)	PUNCT
ejpam-2287	188	119	and	and	CCONJ
ejpam-2287	188	120	a	a	DET
ejpam-2287	188	121	nonhyperbolic	nonhyperbolic	ADJ
ejpam-2287	188	122	equilibrium	equilibrium	NOUN
ejpam-2287	188	123	in	in	ADP
ejpam-2287	188	124	cases	case	NOUN
ejpam-2287	188	125	(	(	PUNCT
ejpam-2287	188	126	b	b	NOUN
ejpam-2287	188	127	)	)	PUNCT
ejpam-2287	188	128	and	and	CCONJ
ejpam-2287	188	129	(	(	PUNCT
ejpam-2287	188	130	d	d	NOUN
ejpam-2287	188	131	)	)	PUNCT
ejpam-2287	188	132	.	.	PUNCT
ejpam-2287	189	1	similarly	similarly	ADV
ejpam-2287	189	2	,	,	PUNCT
ejpam-2287	189	3	one	one	PRON
ejpam-2287	189	4	can	can	AUX
ejpam-2287	189	5	show	show	VERB
ejpam-2287	189	6	that	that	SCONJ
ejpam-2287	189	7	the	the	DET
ejpam-2287	189	8	eigenvalues	eigenvalue	NOUN
ejpam-2287	189	9	of	of	ADP
ejpam-2287	189	10	e2	e2	PROPN
ejpam-2287	189	11	s.	s.	PROPN
ejpam-2287	189	12	basu	basu	PROPN
ejpam-2287	189	13	/	/	SYM
ejpam-2287	189	14	eur	eur	PROPN
ejpam-2287	189	15	.	.	PUNCT
ejpam-2287	190	1	j.	j.	PROPN
ejpam-2287	190	2	pure	pure	PROPN
ejpam-2287	190	3	appl	appl	PROPN
ejpam-2287	190	4	.	.	PROPN
ejpam-2287	190	5	math	math	PROPN
ejpam-2287	190	6	,	,	PUNCT
ejpam-2287	190	7	7	7	NUM
ejpam-2287	190	8	(	(	PUNCT
ejpam-2287	190	9	2014	2014	NUM
ejpam-2287	190	10	)	)	PUNCT
ejpam-2287	190	11	,	,	PUNCT
ejpam-2287	190	12	442	442	NUM
ejpam-2287	190	13	-	-	SYM
ejpam-2287	190	14	461	461	NUM
ejpam-2287	190	15	452	452	NUM
ejpam-2287	190	16	and	and	CCONJ
ejpam-2287	190	17	e3	e3	VERB
ejpam-2287	190	18	satisfy	satisfy	NOUN
ejpam-2287	190	19			VERB
ejpam-2287	190	20			NOUN
ejpam-2287	190	21			ADP
ejpam-2287	190	22	0	0	X
ejpam-2287	190	23	<	<	X
ejpam-2287	190	24	λµ	λµ	X
ejpam-2287	190	25	<	<	X
ejpam-2287	190	26	0.41	0.41	NUM
ejpam-2287	190	27	:	:	PUNCT
ejpam-2287	190	28	|λ1|	|λ1|	ADP
ejpam-2287	190	29	>	>	X
ejpam-2287	190	30	1	1	NUM
ejpam-2287	190	31	,	,	PUNCT
ejpam-2287	190	32	|λ2|	|λ2|	NOUN
ejpam-2287	190	33	>	>	SYM
ejpam-2287	190	34	1	1	NUM
ejpam-2287	190	35	λµ=	λµ=	NOUN
ejpam-2287	190	36	0.41	0.41	NUM
ejpam-2287	190	37	:	:	PUNCT
ejpam-2287	190	38	|λ1|=	|λ1|=	PROPN
ejpam-2287	190	39	1	1	NUM
ejpam-2287	190	40	,	,	PUNCT
ejpam-2287	190	41	|λ2|	|λ2|	NOUN
ejpam-2287	190	42	>	>	X
ejpam-2287	190	43	1	1	NUM
ejpam-2287	190	44	0.41	0.41	NUM
ejpam-2287	190	45	<	<	X
ejpam-2287	190	46	λµ	λµ	ADP
ejpam-2287	190	47	<	<	X
ejpam-2287	190	48	2.4	2.4	NUM
ejpam-2287	190	49	:	:	PUNCT
ejpam-2287	190	50	|λ1|	|λ1|	ADP
ejpam-2287	190	51	<	<	X
ejpam-2287	190	52	1	1	NUM
ejpam-2287	190	53	,	,	PUNCT
ejpam-2287	190	54	|λ2|	|λ2|	NOUN
ejpam-2287	190	55	>	>	X
ejpam-2287	190	56	1	1	NUM
ejpam-2287	190	57	(	(	PUNCT
ejpam-2287	190	58	22	22	NUM
ejpam-2287	190	59	)	)	PUNCT
ejpam-2287	190	60	hence	hence	ADV
ejpam-2287	190	61	e2	e2	PROPN
ejpam-2287	190	62	and	and	CCONJ
ejpam-2287	190	63	e3	e3	NOUN
ejpam-2287	190	64	are	be	AUX
ejpam-2287	190	65	both	both	DET
ejpam-2287	190	66	repellers	repeller	NOUN
ejpam-2287	190	67	,	,	PUNCT
ejpam-2287	190	68	saddle	saddle	NOUN
ejpam-2287	190	69	point	point	NOUN
ejpam-2287	190	70	equilibria	equilibrium	NOUN
ejpam-2287	190	71	or	or	CCONJ
ejpam-2287	190	72	nonhyperbolic	nonhyperbolic	ADJ
ejpam-2287	190	73	equilibria	equilibrium	NOUN
ejpam-2287	190	74	.	.	PUNCT
ejpam-2287	191	1	the	the	DET
ejpam-2287	191	2	next	next	ADJ
ejpam-2287	191	3	theorem	theorem	NOUN
ejpam-2287	191	4	follows	follow	VERB
ejpam-2287	191	5	directly	directly	ADV
ejpam-2287	191	6	from	from	ADP
ejpam-2287	191	7	(	(	PUNCT
ejpam-2287	191	8	20	20	NUM
ejpam-2287	191	9	)	)	PUNCT
ejpam-2287	191	10	,	,	PUNCT
ejpam-2287	191	11	(	(	PUNCT
ejpam-2287	191	12	21	21	NUM
ejpam-2287	191	13	)	)	PUNCT
ejpam-2287	191	14	and	and	CCONJ
ejpam-2287	191	15	(	(	PUNCT
ejpam-2287	191	16	22	22	NUM
ejpam-2287	191	17	)	)	PUNCT
ejpam-2287	191	18	.	.	PUNCT
ejpam-2287	192	1	theorem	theorem	NOUN
ejpam-2287	192	2	2	2	NUM
ejpam-2287	192	3	.	.	PUNCT
ejpam-2287	193	1	the	the	DET
ejpam-2287	193	2	following	follow	VERB
ejpam-2287	193	3	are	be	AUX
ejpam-2287	193	4	true	true	ADJ
ejpam-2287	193	5	for	for	ADP
ejpam-2287	193	6	the	the	DET
ejpam-2287	193	7	equilibria	equilibria	PROPN
ejpam-2287	193	8	e1	e1	PROPN
ejpam-2287	193	9	,	,	PUNCT
ejpam-2287	193	10	e2	e2	PROPN
ejpam-2287	193	11	and	and	CCONJ
ejpam-2287	193	12	e3	e3	NOUN
ejpam-2287	193	13	of	of	ADP
ejpam-2287	193	14	equation	equation	NOUN
ejpam-2287	193	15	(	(	PUNCT
ejpam-2287	193	16	12	12	NUM
ejpam-2287	193	17	):	):	PUNCT
ejpam-2287	193	18	1	1	NUM
ejpam-2287	193	19	.	.	PUNCT
ejpam-2287	194	1	if	if	SCONJ
ejpam-2287	194	2	0	0	NUM
ejpam-2287	194	3	<	<	X
ejpam-2287	194	4	λµ	λµ	X
ejpam-2287	194	5	<	<	X
ejpam-2287	194	6	2.4	2.4	NUM
ejpam-2287	194	7	,	,	PUNCT
ejpam-2287	194	8	then	then	ADV
ejpam-2287	194	9	all	all	DET
ejpam-2287	194	10	three	three	NUM
ejpam-2287	194	11	equilibria	equilibrium	NOUN
ejpam-2287	194	12	e1	e1	PROPN
ejpam-2287	194	13	,	,	PUNCT
ejpam-2287	194	14	e2	e2	NOUN
ejpam-2287	194	15	and	and	CCONJ
ejpam-2287	194	16	e3	e3	NOUN
ejpam-2287	194	17	exist	exist	NOUN
ejpam-2287	194	18	.	.	PUNCT
ejpam-2287	195	1	the	the	DET
ejpam-2287	195	2	zero	zero	NUM
ejpam-2287	195	3	equilibrium	equilibrium	NOUN
ejpam-2287	195	4	e1	e1	NOUN
ejpam-2287	195	5	is	be	AUX
ejpam-2287	195	6	a	a	DET
ejpam-2287	195	7	repelling	repelling	NOUN
ejpam-2287	195	8	equilibrium	equilibrium	NOUN
ejpam-2287	195	9	.	.	PUNCT
ejpam-2287	196	1	the	the	DET
ejpam-2287	196	2	nonzero	nonzero	PROPN
ejpam-2287	196	3	equilibria	equilibria	PROPN
ejpam-2287	196	4	e2	e2	PROPN
ejpam-2287	196	5	and	and	CCONJ
ejpam-2287	196	6	e3	e3	NOUN
ejpam-2287	196	7	satisfy	satisfy	NOUN
ejpam-2287	196	8	:	:	PUNCT
ejpam-2287	196	9	i.	i.	NOUN
ejpam-2287	196	10	if	if	SCONJ
ejpam-2287	196	11	0	0	NUM
ejpam-2287	196	12	<	<	X
ejpam-2287	196	13	λµ	λµ	X
ejpam-2287	196	14	<	<	X
ejpam-2287	196	15	0.41	0.41	NUM
ejpam-2287	196	16	,	,	PUNCT
ejpam-2287	196	17	then	then	ADV
ejpam-2287	196	18	they	they	PRON
ejpam-2287	196	19	are	be	AUX
ejpam-2287	196	20	both	both	PRON
ejpam-2287	196	21	repelling	repel	VERB
ejpam-2287	196	22	equilibria	equilibrium	NOUN
ejpam-2287	196	23	.	.	PUNCT
ejpam-2287	197	1	ii	ii	PROPN
ejpam-2287	197	2	.	.	PUNCT
ejpam-2287	198	1	if	if	SCONJ
ejpam-2287	198	2	0.41	0.41	NUM
ejpam-2287	198	3	<	<	X
ejpam-2287	198	4	λµ	λµ	X
ejpam-2287	198	5	<	<	X
ejpam-2287	198	6	2.4	2.4	NUM
ejpam-2287	198	7	,	,	PUNCT
ejpam-2287	198	8	then	then	ADV
ejpam-2287	198	9	they	they	PRON
ejpam-2287	198	10	are	be	AUX
ejpam-2287	198	11	both	both	PRON
ejpam-2287	198	12	saddle	saddle	NOUN
ejpam-2287	198	13	point	point	NOUN
ejpam-2287	198	14	equilibria	equilibrium	NOUN
ejpam-2287	198	15	.	.	PUNCT
ejpam-2287	199	1	iii	iii	X
ejpam-2287	199	2	.	.	PUNCT
ejpam-2287	200	1	if	if	SCONJ
ejpam-2287	200	2	λµ=	λµ=	PROPN
ejpam-2287	200	3	0.41	0.41	NUM
ejpam-2287	200	4	,	,	PUNCT
ejpam-2287	200	5	then	then	ADV
ejpam-2287	200	6	they	they	PRON
ejpam-2287	200	7	are	be	AUX
ejpam-2287	200	8	both	both	ADV
ejpam-2287	200	9	nonhyperbolic	nonhyperbolic	ADJ
ejpam-2287	200	10	equilibria	equilibrium	NOUN
ejpam-2287	200	11	.	.	PUNCT
ejpam-2287	201	1	2	2	X
ejpam-2287	201	2	.	.	X
ejpam-2287	202	1	if	if	SCONJ
ejpam-2287	202	2	2.4≤	2.4≤	PROPN
ejpam-2287	202	3	λµ	λµ	VERB
ejpam-2287	202	4	<	<	X
ejpam-2287	202	5	6.38	6.38	NUM
ejpam-2287	202	6	,	,	PUNCT
ejpam-2287	202	7	then	then	ADV
ejpam-2287	202	8	e1	e1	NOUN
ejpam-2287	202	9	is	be	AUX
ejpam-2287	202	10	a	a	DET
ejpam-2287	202	11	unique	unique	ADJ
ejpam-2287	202	12	saddle	saddle	NOUN
ejpam-2287	202	13	point	point	NOUN
ejpam-2287	202	14	equilibrium	equilibrium	NOUN
ejpam-2287	202	15	.	.	PUNCT
ejpam-2287	203	1	3	3	X
ejpam-2287	203	2	.	.	X
ejpam-2287	204	1	if	if	SCONJ
ejpam-2287	204	2	λµ≥	λµ≥	PROPN
ejpam-2287	204	3	6.38	6.38	NUM
ejpam-2287	204	4	,	,	PUNCT
ejpam-2287	204	5	then	then	ADV
ejpam-2287	204	6	e1	e1	NOUN
ejpam-2287	204	7	is	be	AUX
ejpam-2287	204	8	a	a	DET
ejpam-2287	204	9	repelling	repelling	NOUN
ejpam-2287	204	10	equilibrium	equilibrium	NOUN
ejpam-2287	204	11	.	.	PUNCT
ejpam-2287	205	1	note	note	VERB
ejpam-2287	205	2	that	that	SCONJ
ejpam-2287	205	3	the	the	DET
ejpam-2287	205	4	south	south	ADJ
ejpam-2287	205	5	-	-	PUNCT
ejpam-2287	205	6	east	east	NOUN
ejpam-2287	205	7	partial	partial	ADJ
ejpam-2287	205	8	ordering	ordering	NOUN
ejpam-2287	205	9	“	"	PUNCT
ejpam-2287	205	10	�	�	PROPN
ejpam-2287	205	11	se	se	NOUN
ejpam-2287	205	12	”	"	PUNCT
ejpam-2287	205	13	and	and	CCONJ
ejpam-2287	205	14	the	the	DET
ejpam-2287	205	15	north	north	NOUN
ejpam-2287	205	16	-	-	PUNCT
ejpam-2287	205	17	east	east	NOUN
ejpam-2287	205	18	partial	partial	ADJ
ejpam-2287	205	19	ordering	ordering	NOUN
ejpam-2287	205	20	“	"	PUNCT
ejpam-2287	205	21	�	�	PROPN
ejpam-2287	205	22	ne	ne	PROPN
ejpam-2287	205	23	”	"	PUNCT
ejpam-2287	205	24	from	from	ADP
ejpam-2287	205	25	the	the	DET
ejpam-2287	205	26	theory	theory	NOUN
ejpam-2287	205	27	of	of	ADP
ejpam-2287	205	28	cooperative	cooperative	ADJ
ejpam-2287	205	29	and	and	CCONJ
ejpam-2287	205	30	competitive	competitive	ADJ
ejpam-2287	205	31	maps	map	NOUN
ejpam-2287	205	32	(	(	PUNCT
ejpam-2287	205	33	see	see	VERB
ejpam-2287	205	34	see	see	VERB
ejpam-2287	205	35	[	[	X
ejpam-2287	205	36	5	5	NUM
ejpam-2287	205	37	,	,	PUNCT
ejpam-2287	205	38	11	11	NUM
ejpam-2287	205	39	,	,	PUNCT
ejpam-2287	205	40	12	12	NUM
ejpam-2287	205	41	,	,	PUNCT
ejpam-2287	205	42	15	15	NUM
ejpam-2287	205	43	]	]	PUNCT
ejpam-2287	205	44	)	)	PUNCT
ejpam-2287	205	45	are	be	AUX
ejpam-2287	205	46	defined	define	VERB
ejpam-2287	205	47	as	as	SCONJ
ejpam-2287	205	48	follows	follow	VERB
ejpam-2287	205	49	:	:	PUNCT
ejpam-2287	205	50	(	(	PUNCT
ejpam-2287	205	51	x1	x1	PROPN
ejpam-2287	205	52	,	,	PUNCT
ejpam-2287	205	53	y1)	y1)	PROPN
ejpam-2287	205	54	�	�	PROPN
ejpam-2287	205	55	se	se	X
ejpam-2287	205	56	(	(	PUNCT
ejpam-2287	205	57	x2	x2	PROPN
ejpam-2287	205	58	,	,	PUNCT
ejpam-2287	205	59	y2	y2	PROPN
ejpam-2287	205	60	)	)	PUNCT
ejpam-2287	206	1	if	if	SCONJ
ejpam-2287	206	2	and	and	CCONJ
ejpam-2287	206	3	only	only	ADV
ejpam-2287	206	4	if	if	SCONJ
ejpam-2287	206	5	x1	x1	ADJ
ejpam-2287	206	6	≤	≤	NUM
ejpam-2287	206	7	x2	x2	PROPN
ejpam-2287	206	8	and	and	CCONJ
ejpam-2287	206	9	y1	y1	INTJ
ejpam-2287	206	10	≥	≥	NOUN
ejpam-2287	206	11	y2	y2	INTJ
ejpam-2287	206	12	(	(	PUNCT
ejpam-2287	206	13	x1	x1	PROPN
ejpam-2287	206	14	,	,	PUNCT
ejpam-2287	206	15	y1)	y1)	PROPN
ejpam-2287	206	16	�	�	PROPN
ejpam-2287	206	17	ne	ne	PROPN
ejpam-2287	206	18	(	(	PUNCT
ejpam-2287	206	19	x2	x2	PROPN
ejpam-2287	206	20	,	,	PUNCT
ejpam-2287	206	21	y2	y2	PROPN
ejpam-2287	206	22	)	)	PUNCT
ejpam-2287	206	23	if	if	SCONJ
ejpam-2287	206	24	and	and	CCONJ
ejpam-2287	206	25	only	only	ADV
ejpam-2287	206	26	if	if	SCONJ
ejpam-2287	206	27	x1	x1	ADJ
ejpam-2287	206	28	≤	≤	NUM
ejpam-2287	206	29	x2	x2	PROPN
ejpam-2287	206	30	and	and	CCONJ
ejpam-2287	206	31	y1	y1	ADJ
ejpam-2287	206	32	≤	≤	ADJ
ejpam-2287	207	1	y2	y2	INTJ
ejpam-2287	207	2	(	(	PUNCT
ejpam-2287	207	3	23	23	NUM
ejpam-2287	207	4	)	)	PUNCT
ejpam-2287	207	5	it	it	PRON
ejpam-2287	207	6	is	be	AUX
ejpam-2287	207	7	a	a	DET
ejpam-2287	207	8	well	well	ADV
ejpam-2287	207	9	-	-	PUNCT
ejpam-2287	207	10	known	know	VERB
ejpam-2287	207	11	fact	fact	NOUN
ejpam-2287	207	12	that	that	SCONJ
ejpam-2287	207	13	cooperative	cooperative	ADJ
ejpam-2287	207	14	maps	map	NOUN
ejpam-2287	207	15	preserve	preserve	VERB
ejpam-2287	207	16	the	the	DET
ejpam-2287	207	17	“	"	PUNCT
ejpam-2287	207	18	�	�	PROPN
ejpam-2287	207	19	ne	ne	NOUN
ejpam-2287	207	20	”	"	PUNCT
ejpam-2287	207	21	ordering	order	VERB
ejpam-2287	207	22	(	(	PUNCT
ejpam-2287	207	23	see	see	VERB
ejpam-2287	207	24	[	[	X
ejpam-2287	207	25	5	5	NUM
ejpam-2287	207	26	,	,	PUNCT
ejpam-2287	207	27	11	11	NUM
ejpam-2287	207	28	,	,	PUNCT
ejpam-2287	207	29	12	12	NUM
ejpam-2287	207	30	,	,	PUNCT
ejpam-2287	207	31	15	15	NUM
ejpam-2287	207	32	]	]	NUM
ejpam-2287	207	33	)	)	PUNCT
ejpam-2287	207	34	.	.	PUNCT
ejpam-2287	208	1	our	our	PRON
ejpam-2287	208	2	next	next	ADJ
ejpam-2287	208	3	lemma	lemma	PROPN
ejpam-2287	208	4	gives	give	VERB
ejpam-2287	208	5	precise	precise	ADJ
ejpam-2287	208	6	parameter	parameter	NOUN
ejpam-2287	208	7	and	and	CCONJ
ejpam-2287	208	8	initial	initial	ADJ
ejpam-2287	208	9	value	value	NOUN
ejpam-2287	208	10	conditions	condition	NOUN
ejpam-2287	208	11	for	for	ADP
ejpam-2287	208	12	t2(θ	t2(θ	PROPN
ejpam-2287	208	13	,	,	PUNCT
ejpam-2287	208	14	u	u	NOUN
ejpam-2287	208	15	)	)	PUNCT
ejpam-2287	208	16	to	to	PART
ejpam-2287	208	17	be	be	AUX
ejpam-2287	208	18	cooperative	cooperative	ADJ
ejpam-2287	208	19	.	.	PUNCT
ejpam-2287	209	1	it	it	PRON
ejpam-2287	209	2	will	will	AUX
ejpam-2287	209	3	play	play	VERB
ejpam-2287	209	4	a	a	DET
ejpam-2287	209	5	key	key	ADJ
ejpam-2287	209	6	role	role	NOUN
ejpam-2287	209	7	in	in	ADP
ejpam-2287	209	8	the	the	DET
ejpam-2287	209	9	proof	proof	NOUN
ejpam-2287	209	10	of	of	ADP
ejpam-2287	209	11	our	our	PRON
ejpam-2287	209	12	main	main	ADJ
ejpam-2287	209	13	theorem	theorem	NOUN
ejpam-2287	209	14	for	for	ADP
ejpam-2287	209	15	this	this	DET
ejpam-2287	209	16	section	section	NOUN
ejpam-2287	209	17	.	.	PUNCT
ejpam-2287	210	1	lemma	lemma	PROPN
ejpam-2287	210	2	2	2	NUM
ejpam-2287	210	3	.	.	PUNCT
ejpam-2287	211	1	the	the	DET
ejpam-2287	211	2	map	map	NOUN
ejpam-2287	211	3	t2(θ	t2(θ	X
ejpam-2287	211	4	,	,	PUNCT
ejpam-2287	211	5	u	u	NOUN
ejpam-2287	211	6	)	)	PUNCT
ejpam-2287	211	7	is	be	AUX
ejpam-2287	211	8	cooperative	cooperative	ADJ
ejpam-2287	211	9	exactly	exactly	ADV
ejpam-2287	211	10	when	when	SCONJ
ejpam-2287	211	11	one	one	NUM
ejpam-2287	211	12	of	of	ADP
ejpam-2287	211	13	the	the	DET
ejpam-2287	211	14	following	follow	VERB
ejpam-2287	211	15	holds	hold	NOUN
ejpam-2287	211	16	:	:	PUNCT
ejpam-2287	211	17	i.	i.	PROPN
ejpam-2287	211	18	3.39≤	3.39≤	PROPN
ejpam-2287	211	19	λµ≤	λµ≤	PROPN
ejpam-2287	211	20	6.38	6.38	NUM
ejpam-2287	211	21	ii	ii	NOUN
ejpam-2287	211	22	.	.	PROPN
ejpam-2287	211	23	0≤	0≤	PUNCT
ejpam-2287	212	1	λµ	λµ	ADP
ejpam-2287	212	2	<	<	X
ejpam-2287	212	3	3.39	3.39	NUM
ejpam-2287	212	4	and	and	CCONJ
ejpam-2287	212	5	θ	θ	PROPN
ejpam-2287	212	6	6∈	6∈	PROPN
ejpam-2287	212	7	(	(	PUNCT
ejpam-2287	212	8	θ1,θ2	θ1,θ2	PROPN
ejpam-2287	212	9	)	)	PUNCT
ejpam-2287	212	10	,	,	PUNCT
ejpam-2287	212	11	where	where	SCONJ
ejpam-2287	212	12	θ1	θ1	NOUN
ejpam-2287	212	13	and	and	CCONJ
ejpam-2287	212	14	θ2	θ2	PROPN
ejpam-2287	212	15	are	be	AUX
ejpam-2287	212	16	given	give	VERB
ejpam-2287	212	17	by	by	ADP
ejpam-2287	212	18	the	the	DET
ejpam-2287	212	19	formulas	formulas	ADJ
ejpam-2287	212	20	θ1	θ1	NOUN
ejpam-2287	212	21	:	:	PUNCT
ejpam-2287	212	22	=	=	PUNCT
ejpam-2287	212	23	−0.372678	−0.372678	X
ejpam-2287	212	24	p	p	NOUN
ejpam-2287	212	25	3.39−λµ	3.39−λµ	NUM
ejpam-2287	212	26	and	and	CCONJ
ejpam-2287	212	27	θ2	θ2	ADV
ejpam-2287	212	28	:	:	PUNCT
ejpam-2287	212	29	=	=	X
ejpam-2287	213	1	0.372678	0.372678	NUM
ejpam-2287	213	2	p	p	NOUN
ejpam-2287	213	3	3.39−λµ	3.39−λµ	NUM
ejpam-2287	213	4	proof	proof	NOUN
ejpam-2287	213	5	.	.	PUNCT
ejpam-2287	214	1	note	note	VERB
ejpam-2287	214	2	that	that	SCONJ
ejpam-2287	214	3	the	the	DET
ejpam-2287	214	4	jacobian	jacobian	NOUN
ejpam-2287	214	5	of	of	ADP
ejpam-2287	214	6	the	the	DET
ejpam-2287	214	7	map	map	NOUN
ejpam-2287	214	8	t2(θ	t2(θ	X
ejpam-2287	214	9	,	,	PUNCT
ejpam-2287	214	10	u	u	NOUN
ejpam-2287	214	11	)	)	PUNCT
ejpam-2287	214	12	is	be	AUX
ejpam-2287	214	13	given	give	VERB
ejpam-2287	214	14	by	by	ADP
ejpam-2287	214	15	jact2	jact2	PROPN
ejpam-2287	214	16	=	=	SYM
ejpam-2287	214	17	�	�	PROPN
ejpam-2287	214	18	7.2θ2	7.2θ2	NUM
ejpam-2287	214	19	+	+	PROPN
ejpam-2287	214	20	λµ−	λµ−	PROPN
ejpam-2287	214	21	3.39	3.39	NUM
ejpam-2287	214	22	1.99	1.99	NUM
ejpam-2287	214	23	1.99(7.2θ2	1.99(7.2θ2	NUM
ejpam-2287	215	1	+	+	ADJ
ejpam-2287	216	1	λµ−	λµ−	PROPN
ejpam-2287	216	2	3.39	3.39	NUM
ejpam-2287	216	3	)	)	PUNCT
ejpam-2287	216	4	λµ+	λµ+	ADJ
ejpam-2287	216	5	7.2u2	7.2u2	NUM
ejpam-2287	217	1	+	+	CCONJ
ejpam-2287	217	2	0.5701	0.5701	NUM
ejpam-2287	217	3	�	�	PROPN
ejpam-2287	217	4	(	(	PUNCT
ejpam-2287	217	5	24	24	NUM
ejpam-2287	217	6	)	)	PUNCT
ejpam-2287	217	7	if	if	SCONJ
ejpam-2287	217	8	3.39	3.39	NUM
ejpam-2287	217	9	≤	≤	NUM
ejpam-2287	217	10	λµ	λµ	DET
ejpam-2287	217	11	≤	≤	NUM
ejpam-2287	217	12	6.38	6.38	NUM
ejpam-2287	217	13	,	,	PUNCT
ejpam-2287	217	14	then	then	ADV
ejpam-2287	217	15	all	all	DET
ejpam-2287	217	16	entries	entry	NOUN
ejpam-2287	217	17	of	of	ADP
ejpam-2287	217	18	the	the	DET
ejpam-2287	217	19	jacobian	jacobian	PROPN
ejpam-2287	217	20	are	be	AUX
ejpam-2287	217	21	positive	positive	ADJ
ejpam-2287	217	22	which	which	PRON
ejpam-2287	217	23	implies	imply	VERB
ejpam-2287	217	24	that	that	SCONJ
ejpam-2287	217	25	the	the	DET
ejpam-2287	217	26	associated	associated	ADJ
ejpam-2287	217	27	map	map	NOUN
ejpam-2287	217	28	t2(θ	t2(θ	X
ejpam-2287	217	29	,	,	PUNCT
ejpam-2287	217	30	u	u	NOUN
ejpam-2287	217	31	)	)	PUNCT
ejpam-2287	217	32	is	be	AUX
ejpam-2287	217	33	cooperative	cooperative	ADJ
ejpam-2287	217	34	(	(	PUNCT
ejpam-2287	217	35	see	see	VERB
ejpam-2287	217	36	[	[	X
ejpam-2287	217	37	11	11	NUM
ejpam-2287	217	38	,	,	PUNCT
ejpam-2287	217	39	12	12	NUM
ejpam-2287	217	40	,	,	PUNCT
ejpam-2287	217	41	15	15	NUM
ejpam-2287	217	42	]	]	NUM
ejpam-2287	217	43	)	)	PUNCT
ejpam-2287	217	44	.	.	PUNCT
ejpam-2287	218	1	if	if	SCONJ
ejpam-2287	218	2	0	0	NUM
ejpam-2287	218	3	<	<	X
ejpam-2287	218	4	λµ	λµ	X
ejpam-2287	218	5	<	<	X
ejpam-2287	218	6	3.39	3.39	NUM
ejpam-2287	218	7	,	,	PUNCT
ejpam-2287	218	8	then	then	ADV
ejpam-2287	218	9	the	the	DET
ejpam-2287	218	10	1,1	1,1	NUM
ejpam-2287	218	11	-	-	PUNCT
ejpam-2287	218	12	entry	entry	NOUN
ejpam-2287	218	13	of	of	ADP
ejpam-2287	218	14	the	the	DET
ejpam-2287	218	15	jacobian	jacobian	PROPN
ejpam-2287	218	16	in	in	ADP
ejpam-2287	218	17	(	(	PUNCT
ejpam-2287	218	18	24	24	NUM
ejpam-2287	218	19	)	)	PUNCT
ejpam-2287	218	20	,	,	PUNCT
ejpam-2287	218	21	f	f	PROPN
ejpam-2287	218	22	(	(	PUNCT
ejpam-2287	218	23	θ	θ	PROPN
ejpam-2287	218	24	)	)	PUNCT
ejpam-2287	218	25	:	:	PUNCT
ejpam-2287	219	1	=	=	X
ejpam-2287	219	2	7.2θ2	7.2θ2	NUM
ejpam-2287	219	3	+	+	PROPN
ejpam-2287	219	4	λµ−	λµ−	PROPN
ejpam-2287	219	5	3.39	3.39	NUM
ejpam-2287	219	6	s.	s.	PROPN
ejpam-2287	219	7	basu	basu	PROPN
ejpam-2287	219	8	/	/	SYM
ejpam-2287	219	9	eur	eur	PROPN
ejpam-2287	219	10	.	.	PUNCT
ejpam-2287	220	1	j.	j.	PROPN
ejpam-2287	220	2	pure	pure	PROPN
ejpam-2287	220	3	appl	appl	PROPN
ejpam-2287	220	4	.	.	PROPN
ejpam-2287	220	5	math	math	PROPN
ejpam-2287	220	6	,	,	PUNCT
ejpam-2287	220	7	7	7	NUM
ejpam-2287	220	8	(	(	PUNCT
ejpam-2287	220	9	2014	2014	NUM
ejpam-2287	220	10	)	)	PUNCT
ejpam-2287	220	11	,	,	PUNCT
ejpam-2287	220	12	442	442	NUM
ejpam-2287	220	13	-	-	SYM
ejpam-2287	220	14	461	461	NUM
ejpam-2287	220	15	453	453	NUM
ejpam-2287	220	16	is	be	AUX
ejpam-2287	220	17	a	a	DET
ejpam-2287	220	18	parabola	parabola	NOUN
ejpam-2287	220	19	with	with	ADP
ejpam-2287	220	20	positive	positive	ADJ
ejpam-2287	220	21	leading	lead	VERB
ejpam-2287	220	22	coefficient	coefficient	NOUN
ejpam-2287	220	23	whose	whose	DET
ejpam-2287	220	24	θ	θ	NOUN
ejpam-2287	220	25	-axis	-axis	PROPN
ejpam-2287	220	26	intercepts	intercept	NOUN
ejpam-2287	220	27	are	be	AUX
ejpam-2287	220	28	given	give	VERB
ejpam-2287	220	29	by	by	ADP
ejpam-2287	220	30	the	the	DET
ejpam-2287	220	31	formulas	formula	NOUN
ejpam-2287	220	32	θ1,θ2	θ1,θ2	PROPN
ejpam-2287	220	33	=	=	PUNCT
ejpam-2287	220	34	±0.372678	±0.372678	X
ejpam-2287	220	35	æ	æ	PROPN
ejpam-2287	220	36	3.39−λµ	3.39−λµ	NUM
ejpam-2287	220	37	,	,	PUNCT
ejpam-2287	220	38	θ1	θ1	NOUN
ejpam-2287	220	39	<	<	X
ejpam-2287	220	40	θ2	θ2	PROPN
ejpam-2287	220	41	(	(	PUNCT
ejpam-2287	220	42	25	25	NUM
ejpam-2287	220	43	)	)	PUNCT
ejpam-2287	220	44	clearly	clearly	ADV
ejpam-2287	220	45	f	f	X
ejpam-2287	220	46	(	(	PUNCT
ejpam-2287	220	47	θ	θ	PROPN
ejpam-2287	220	48	)	)	PUNCT
ejpam-2287	220	49	≥	≥	NOUN
ejpam-2287	220	50	0	0	NUM
ejpam-2287	220	51	for	for	ADP
ejpam-2287	220	52	θ	θ	PROPN
ejpam-2287	220	53	∈	∈	PROPN
ejpam-2287	220	54	(	(	PUNCT
ejpam-2287	220	55	−∞,θ1	−∞,θ1	PROPN
ejpam-2287	220	56	]	]	X
ejpam-2287	220	57	⋃	⋃	PROPN
ejpam-2287	220	58	[	[	X
ejpam-2287	220	59	θ2,∞	θ2,∞	NOUN
ejpam-2287	220	60	)	)	PUNCT
ejpam-2287	220	61	.	.	PUNCT
ejpam-2287	221	1	hence	hence	ADV
ejpam-2287	221	2	the	the	DET
ejpam-2287	221	3	map	map	NOUN
ejpam-2287	221	4	t2(θ	t2(θ	X
ejpam-2287	221	5	,	,	PUNCT
ejpam-2287	221	6	u	u	NOUN
ejpam-2287	221	7	)	)	PUNCT
ejpam-2287	221	8	is	be	AUX
ejpam-2287	221	9	cooperative	cooperative	ADJ
ejpam-2287	221	10	in	in	ADP
ejpam-2287	221	11	this	this	DET
ejpam-2287	221	12	θ	θ	PROPN
ejpam-2287	221	13	-range	-range	PROPN
ejpam-2287	221	14	.	.	PUNCT
ejpam-2287	222	1	the	the	DET
ejpam-2287	222	2	main	main	ADJ
ejpam-2287	222	3	theorem	theorem	NOUN
ejpam-2287	222	4	of	of	ADP
ejpam-2287	222	5	this	this	DET
ejpam-2287	222	6	paper	paper	NOUN
ejpam-2287	222	7	is	be	AUX
ejpam-2287	222	8	as	as	SCONJ
ejpam-2287	222	9	follows	follow	VERB
ejpam-2287	222	10	:	:	PUNCT
ejpam-2287	222	11	theorem	theorem	NOUN
ejpam-2287	222	12	3	3	NUM
ejpam-2287	222	13	.	.	PUNCT
ejpam-2287	223	1	under	under	ADP
ejpam-2287	223	2	the	the	DET
ejpam-2287	223	3	hypotheses	hypothesis	NOUN
ejpam-2287	223	4	of	of	ADP
ejpam-2287	223	5	lemma	lemma	PROPN
ejpam-2287	223	6	2	2	NUM
ejpam-2287	223	7	,	,	PUNCT
ejpam-2287	223	8	equation	equation	NOUN
ejpam-2287	223	9	(	(	PUNCT
ejpam-2287	223	10	12	12	NUM
ejpam-2287	223	11	)	)	PUNCT
ejpam-2287	223	12	has	have	VERB
ejpam-2287	223	13	exactly	exactly	ADV
ejpam-2287	223	14	two	two	NUM
ejpam-2287	223	15	real	real	ADJ
ejpam-2287	223	16	nontrivial	nontrivial	ADJ
ejpam-2287	223	17	periodic	periodic	ADJ
ejpam-2287	223	18	solutions	solution	NOUN
ejpam-2287	223	19	{	{	PUNCT
ejpam-2287	223	20	{	{	PUNCT
ejpam-2287	223	21	p1,q1	p1,q1	PROPN
ejpam-2287	223	22	}	}	PUNCT
ejpam-2287	223	23	,	,	PUNCT
ejpam-2287	223	24	{	{	PUNCT
ejpam-2287	223	25	p2,q2	p2,q2	PROPN
ejpam-2287	223	26	}	}	PUNCT
ejpam-2287	223	27	}	}	PUNCT
ejpam-2287	223	28	and	and	CCONJ
ejpam-2287	223	29	{	{	PUNCT
ejpam-2287	223	30	{	{	PUNCT
ejpam-2287	223	31	s1	s1	NOUN
ejpam-2287	223	32	,	,	PUNCT
ejpam-2287	223	33	t1	t1	NOUN
ejpam-2287	223	34	}	}	PUNCT
ejpam-2287	223	35	,	,	PUNCT
ejpam-2287	223	36	{	{	PUNCT
ejpam-2287	223	37	s2	s2	NOUN
ejpam-2287	223	38	,	,	PUNCT
ejpam-2287	223	39	t2	t2	NOUN
ejpam-2287	223	40	}	}	PUNCT
ejpam-2287	223	41	}	}	PUNCT
ejpam-2287	223	42	where	where	SCONJ
ejpam-2287	223	43	{	{	PUNCT
ejpam-2287	223	44	p1,q1	p1,q1	PROPN
ejpam-2287	223	45	}	}	PUNCT
ejpam-2287	223	46	�	�	PROPN
ejpam-2287	223	47	se	se	X
ejpam-2287	223	48	(	(	PUNCT
ejpam-2287	223	49	0,0)	0,0)	PROPN
ejpam-2287	223	50	�	�	PROPN
ejpam-2287	223	51	se	se	X
ejpam-2287	223	52	{	{	PUNCT
ejpam-2287	223	53	p2,q2	p2,q2	PROPN
ejpam-2287	223	54	}	}	PUNCT
ejpam-2287	223	55	and	and	CCONJ
ejpam-2287	223	56	{	{	PUNCT
ejpam-2287	223	57	s1	s1	NOUN
ejpam-2287	223	58	,	,	PUNCT
ejpam-2287	223	59	t1	t1	NOUN
ejpam-2287	223	60	}	}	PUNCT
ejpam-2287	223	61	�	�	PROPN
ejpam-2287	223	62	ne	ne	PROPN
ejpam-2287	223	63	(	(	PUNCT
ejpam-2287	223	64	0,0)	0,0)	PROPN
ejpam-2287	223	65	�	�	PROPN
ejpam-2287	223	66	ne	ne	PROPN
ejpam-2287	223	67	{	{	PUNCT
ejpam-2287	223	68	s2	s2	PROPN
ejpam-2287	223	69	,	,	PUNCT
ejpam-2287	223	70	t2	t2	NOUN
ejpam-2287	223	71	}	}	PUNCT
ejpam-2287	223	72	{	{	PUNCT
ejpam-2287	223	73	{	{	PUNCT
ejpam-2287	223	74	p1,q1	p1,q1	PROPN
ejpam-2287	223	75	}	}	PUNCT
ejpam-2287	223	76	,	,	PUNCT
ejpam-2287	223	77	{	{	PUNCT
ejpam-2287	223	78	p2,q2	p2,q2	PROPN
ejpam-2287	223	79	}	}	PUNCT
ejpam-2287	223	80	}	}	PUNCT
ejpam-2287	223	81	is	be	AUX
ejpam-2287	223	82	a	a	DET
ejpam-2287	223	83	repelling	repel	VERB
ejpam-2287	223	84	periodic	periodic	ADJ
ejpam-2287	223	85	solution	solution	NOUN
ejpam-2287	223	86	and	and	CCONJ
ejpam-2287	223	87	{	{	PUNCT
ejpam-2287	223	88	{	{	PUNCT
ejpam-2287	223	89	s1	s1	NOUN
ejpam-2287	223	90	,	,	PUNCT
ejpam-2287	223	91	t1	t1	NOUN
ejpam-2287	223	92	}	}	PUNCT
ejpam-2287	223	93	,	,	PUNCT
ejpam-2287	223	94	{	{	PUNCT
ejpam-2287	223	95	s2	s2	NOUN
ejpam-2287	223	96	,	,	PUNCT
ejpam-2287	223	97	t2	t2	NOUN
ejpam-2287	223	98	}	}	PUNCT
ejpam-2287	223	99	}	}	PUNCT
ejpam-2287	223	100	is	be	AUX
ejpam-2287	223	101	locally	locally	ADV
ejpam-2287	223	102	asymptotically	asymptotically	ADV
ejpam-2287	223	103	stable	stable	ADJ
ejpam-2287	223	104	.	.	PUNCT
ejpam-2287	224	1	the	the	DET
ejpam-2287	224	2	global	global	ADJ
ejpam-2287	224	3	dynamics	dynamic	NOUN
ejpam-2287	224	4	of	of	ADP
ejpam-2287	224	5	equation	equation	NOUN
ejpam-2287	224	6	(	(	PUNCT
ejpam-2287	224	7	12	12	NUM
ejpam-2287	224	8	)	)	PUNCT
ejpam-2287	224	9	is	be	AUX
ejpam-2287	224	10	as	as	SCONJ
ejpam-2287	224	11	follows	follow	VERB
ejpam-2287	224	12	:	:	PUNCT
ejpam-2287	225	1	1	1	X
ejpam-2287	225	2	.	.	X
ejpam-2287	226	1	if	if	SCONJ
ejpam-2287	226	2	0	0	NUM
ejpam-2287	226	3	<	<	X
ejpam-2287	226	4	λµ	λµ	X
ejpam-2287	226	5	<	<	X
ejpam-2287	226	6	2.4	2.4	NUM
ejpam-2287	226	7	,	,	PUNCT
ejpam-2287	226	8	then	then	ADV
ejpam-2287	226	9	both	both	DET
ejpam-2287	226	10	pairs	pair	NOUN
ejpam-2287	226	11	of	of	ADP
ejpam-2287	226	12	periodic	periodic	ADJ
ejpam-2287	226	13	solutions	solution	NOUN
ejpam-2287	226	14	are	be	AUX
ejpam-2287	226	15	present	present	ADJ
ejpam-2287	226	16	.	.	PUNCT
ejpam-2287	227	1	moreover	moreover	ADV
ejpam-2287	227	2	,	,	PUNCT
ejpam-2287	227	3	i.	i.	NOUN
ejpam-2287	227	4	if	if	SCONJ
ejpam-2287	227	5	0	0	NUM
ejpam-2287	227	6	<	<	X
ejpam-2287	227	7	λµ	λµ	X
ejpam-2287	227	8	<	<	X
ejpam-2287	227	9	0.41	0.41	NUM
ejpam-2287	227	10	,	,	PUNCT
ejpam-2287	227	11	then	then	ADV
ejpam-2287	227	12	every	every	DET
ejpam-2287	227	13	solution	solution	NOUN
ejpam-2287	227	14	converges	converge	VERB
ejpam-2287	227	15	to	to	ADP
ejpam-2287	227	16	the	the	DET
ejpam-2287	227	17	stable	stable	ADJ
ejpam-2287	227	18	periodic	periodic	ADJ
ejpam-2287	227	19	solution	solution	NOUN
ejpam-2287	227	20	{	{	PUNCT
ejpam-2287	227	21	{	{	PUNCT
ejpam-2287	227	22	s1	s1	NOUN
ejpam-2287	227	23	,	,	PUNCT
ejpam-2287	227	24	t1	t1	NOUN
ejpam-2287	227	25	}	}	PUNCT
ejpam-2287	227	26	,	,	PUNCT
ejpam-2287	227	27	{	{	PUNCT
ejpam-2287	227	28	s2	s2	NOUN
ejpam-2287	227	29	,	,	PUNCT
ejpam-2287	227	30	t2	t2	NOUN
ejpam-2287	227	31	}	}	PUNCT
ejpam-2287	227	32	}	}	PUNCT
ejpam-2287	227	33	.	.	PUNCT
ejpam-2287	228	1	ii	ii	PROPN
ejpam-2287	228	2	.	.	PUNCT
ejpam-2287	229	1	if	if	SCONJ
ejpam-2287	229	2	0.41≤	0.41≤	NOUN
ejpam-2287	229	3	λµ	λµ	ADP
ejpam-2287	229	4	<	<	X
ejpam-2287	229	5	2.4	2.4	NUM
ejpam-2287	229	6	,	,	PUNCT
ejpam-2287	229	7	then	then	ADV
ejpam-2287	229	8	every	every	DET
ejpam-2287	229	9	solution	solution	NOUN
ejpam-2287	229	10	converges	converge	VERB
ejpam-2287	229	11	to	to	ADP
ejpam-2287	229	12	the	the	DET
ejpam-2287	229	13	stable	stable	ADJ
ejpam-2287	229	14	periodic	periodic	ADJ
ejpam-2287	229	15	solution	solution	NOUN
ejpam-2287	229	16	{	{	PUNCT
ejpam-2287	229	17	{	{	PUNCT
ejpam-2287	229	18	s1	s1	NOUN
ejpam-2287	229	19	,	,	PUNCT
ejpam-2287	229	20	t1	t1	NOUN
ejpam-2287	229	21	}	}	PUNCT
ejpam-2287	229	22	,	,	PUNCT
ejpam-2287	229	23	{	{	PUNCT
ejpam-2287	229	24	s2	s2	NOUN
ejpam-2287	229	25	,	,	PUNCT
ejpam-2287	229	26	t2	t2	NOUN
ejpam-2287	229	27	}	}	PUNCT
ejpam-2287	229	28	}	}	PUNCT
ejpam-2287	229	29	or	or	CCONJ
ejpam-2287	229	30	to	to	ADP
ejpam-2287	229	31	the	the	DET
ejpam-2287	229	32	saddle	saddle	NOUN
ejpam-2287	229	33	point	point	NOUN
ejpam-2287	229	34	equilibria	equilibrium	NOUN
ejpam-2287	229	35	e2	e2	PROPN
ejpam-2287	229	36	or	or	CCONJ
ejpam-2287	229	37	e3	e3	NOUN
ejpam-2287	229	38	.	.	PUNCT
ejpam-2287	230	1	2	2	X
ejpam-2287	230	2	.	.	X
ejpam-2287	231	1	if	if	SCONJ
ejpam-2287	231	2	2.4	2.4	NUM
ejpam-2287	231	3	≤	≤	NOUN
ejpam-2287	231	4	λµ	λµ	ADP
ejpam-2287	231	5	<	<	X
ejpam-2287	231	6	6.38	6.38	NUM
ejpam-2287	231	7	,	,	PUNCT
ejpam-2287	231	8	then	then	ADV
ejpam-2287	231	9	the	the	DET
ejpam-2287	231	10	repelling	repel	VERB
ejpam-2287	231	11	periodic	periodic	ADJ
ejpam-2287	231	12	solution	solution	NOUN
ejpam-2287	231	13	{	{	PUNCT
ejpam-2287	231	14	{	{	PUNCT
ejpam-2287	231	15	p1,q1	p1,q1	PROPN
ejpam-2287	231	16	}	}	PUNCT
ejpam-2287	231	17	,	,	PUNCT
ejpam-2287	231	18	{	{	PUNCT
ejpam-2287	231	19	p2,q2	p2,q2	PROPN
ejpam-2287	231	20	}	}	PUNCT
ejpam-2287	231	21	}	}	PUNCT
ejpam-2287	231	22	is	be	AUX
ejpam-2287	231	23	the	the	DET
ejpam-2287	231	24	only	only	ADJ
ejpam-2287	231	25	one	one	NUM
ejpam-2287	231	26	present	present	NOUN
ejpam-2287	231	27	.	.	PUNCT
ejpam-2287	232	1	every	every	DET
ejpam-2287	232	2	solution	solution	NOUN
ejpam-2287	232	3	converges	converge	VERB
ejpam-2287	232	4	to	to	ADP
ejpam-2287	232	5	the	the	DET
ejpam-2287	232	6	zero	zero	NUM
ejpam-2287	232	7	saddle	saddle	NOUN
ejpam-2287	232	8	point	point	NOUN
ejpam-2287	232	9	equilibrium	equilibrium	NOUN
ejpam-2287	232	10	e1	e1	NOUN
ejpam-2287	232	11	.	.	PUNCT
ejpam-2287	233	1	3	3	X
ejpam-2287	233	2	.	.	X
ejpam-2287	234	1	if	if	SCONJ
ejpam-2287	234	2	λµ	λµ	PRON
ejpam-2287	234	3	≥	≥	NOUN
ejpam-2287	234	4	6.38	6.38	NUM
ejpam-2287	234	5	,	,	PUNCT
ejpam-2287	234	6	then	then	ADV
ejpam-2287	234	7	equation	equation	NOUN
ejpam-2287	234	8	(	(	PUNCT
ejpam-2287	234	9	12	12	NUM
ejpam-2287	234	10	)	)	PUNCT
ejpam-2287	234	11	does	do	AUX
ejpam-2287	234	12	not	not	PART
ejpam-2287	234	13	possess	possess	VERB
ejpam-2287	234	14	any	any	DET
ejpam-2287	234	15	periodic	periodic	ADJ
ejpam-2287	234	16	solutions	solution	NOUN
ejpam-2287	234	17	.	.	PUNCT
ejpam-2287	235	1	the	the	DET
ejpam-2287	235	2	zero	zero	NUM
ejpam-2287	235	3	equilibrium	equilibrium	NOUN
ejpam-2287	235	4	e1	e1	NOUN
ejpam-2287	235	5	is	be	AUX
ejpam-2287	235	6	a	a	DET
ejpam-2287	235	7	repelling	repelling	NOUN
ejpam-2287	235	8	equilibrium	equilibrium	NOUN
ejpam-2287	235	9	.	.	PUNCT
ejpam-2287	236	1	every	every	DET
ejpam-2287	236	2	solution	solution	NOUN
ejpam-2287	236	3	escapes	escape	VERB
ejpam-2287	236	4	to	to	PART
ejpam-2287	236	5	infinity	infinity	VERB
ejpam-2287	236	6	.	.	PUNCT
ejpam-2287	237	1	the	the	DET
ejpam-2287	237	2	proof	proof	NOUN
ejpam-2287	237	3	of	of	ADP
ejpam-2287	237	4	theorem	theorem	ADJ
ejpam-2287	237	5	3	3	NUM
ejpam-2287	237	6	follows	follow	VERB
ejpam-2287	237	7	from	from	ADP
ejpam-2287	237	8	the	the	DET
ejpam-2287	237	9	statements	statement	NOUN
ejpam-2287	237	10	of	of	ADP
ejpam-2287	237	11	theorem	theorem	ADJ
ejpam-2287	237	12	2	2	NUM
ejpam-2287	237	13	,	,	PUNCT
ejpam-2287	237	14	lemmas	lemma	VERB
ejpam-2287	237	15	3	3	NUM
ejpam-2287	237	16	-	-	SYM
ejpam-2287	237	17	5	5	NUM
ejpam-2287	237	18	,	,	PUNCT
ejpam-2287	237	19	propositions	proposition	NOUN
ejpam-2287	237	20	1	1	NUM
ejpam-2287	237	21	-	-	SYM
ejpam-2287	237	22	2	2	NUM
ejpam-2287	237	23	,	,	PUNCT
ejpam-2287	237	24	corollaries	corollary	NOUN
ejpam-2287	237	25	1	1	NUM
ejpam-2287	237	26	-	-	SYM
ejpam-2287	237	27	2	2	NUM
ejpam-2287	237	28	and	and	CCONJ
ejpam-2287	237	29	the	the	DET
ejpam-2287	237	30	fact	fact	NOUN
ejpam-2287	237	31	that	that	SCONJ
ejpam-2287	237	32	all	all	DET
ejpam-2287	237	33	orbits	orbit	NOUN
ejpam-2287	237	34	of	of	ADP
ejpam-2287	237	35	a	a	DET
ejpam-2287	237	36	bounded	bounded	ADJ
ejpam-2287	237	37	cooperative	cooperative	ADJ
ejpam-2287	237	38	map	map	NOUN
ejpam-2287	237	39	must	must	AUX
ejpam-2287	237	40	converge	converge	VERB
ejpam-2287	237	41	to	to	ADP
ejpam-2287	237	42	a	a	DET
ejpam-2287	237	43	locally	locally	ADV
ejpam-2287	237	44	asymptotically	asymptotically	ADV
ejpam-2287	237	45	stable	stable	ADJ
ejpam-2287	237	46	equilibrium	equilibrium	NOUN
ejpam-2287	237	47	or	or	CCONJ
ejpam-2287	237	48	to	to	ADP
ejpam-2287	237	49	a	a	DET
ejpam-2287	237	50	saddle	saddle	NOUN
ejpam-2287	237	51	point	point	NOUN
ejpam-2287	237	52	equilibrium	equilibrium	NOUN
ejpam-2287	237	53	(	(	PUNCT
ejpam-2287	237	54	see	see	VERB
ejpam-2287	237	55	for	for	ADP
ejpam-2287	237	56	example	example	NOUN
ejpam-2287	237	57	[	[	X
ejpam-2287	237	58	5	5	NUM
ejpam-2287	237	59	,	,	PUNCT
ejpam-2287	237	60	11	11	NUM
ejpam-2287	237	61	,	,	PUNCT
ejpam-2287	237	62	12	12	NUM
ejpam-2287	237	63	,	,	PUNCT
ejpam-2287	237	64	15	15	NUM
ejpam-2287	237	65	]	]	NUM
ejpam-2287	237	66	)	)	PUNCT
ejpam-2287	237	67	.	.	PUNCT
ejpam-2287	238	1	the	the	DET
ejpam-2287	238	2	next	next	ADJ
ejpam-2287	238	3	lemma	lemma	PROPN
ejpam-2287	238	4	gives	give	VERB
ejpam-2287	238	5	bounds	bound	NOUN
ejpam-2287	238	6	for	for	ADP
ejpam-2287	238	7	the	the	DET
ejpam-2287	238	8	coordinates	coordinate	NOUN
ejpam-2287	238	9	of	of	ADP
ejpam-2287	238	10	the	the	DET
ejpam-2287	238	11	map	map	NOUN
ejpam-2287	238	12	t2(θ	t2(θ	X
ejpam-2287	238	13	,	,	PUNCT
ejpam-2287	238	14	u	u	NOUN
ejpam-2287	238	15	)	)	PUNCT
ejpam-2287	238	16	.	.	PUNCT
ejpam-2287	239	1	it	it	PRON
ejpam-2287	239	2	will	will	AUX
ejpam-2287	239	3	be	be	AUX
ejpam-2287	239	4	crucial	crucial	ADJ
ejpam-2287	239	5	for	for	ADP
ejpam-2287	239	6	the	the	DET
ejpam-2287	239	7	rest	rest	NOUN
ejpam-2287	239	8	of	of	ADP
ejpam-2287	239	9	the	the	DET
ejpam-2287	239	10	proofs	proof	NOUN
ejpam-2287	239	11	in	in	ADP
ejpam-2287	239	12	this	this	DET
ejpam-2287	239	13	section	section	NOUN
ejpam-2287	239	14	.	.	PUNCT
ejpam-2287	240	1	lemma	lemma	PROPN
ejpam-2287	241	1	3	3	X
ejpam-2287	241	2	.	.	PUNCT
ejpam-2287	242	1	under	under	ADP
ejpam-2287	242	2	the	the	DET
ejpam-2287	242	3	assumptions	assumption	NOUN
ejpam-2287	242	4	−π/2	−π/2	PROPN
ejpam-2287	242	5	≤	≤	NUM
ejpam-2287	242	6	θ	θ	PROPN
ejpam-2287	242	7	≤	≤	NOUN
ejpam-2287	242	8	π/2	π/2	PUNCT
ejpam-2287	242	9	and	and	CCONJ
ejpam-2287	242	10	0	0	NUM
ejpam-2287	242	11	<	<	X
ejpam-2287	242	12	λµ	λµ	DET
ejpam-2287	242	13	≤	≤	NOUN
ejpam-2287	242	14	6.38	6.38	NUM
ejpam-2287	242	15	,	,	PUNCT
ejpam-2287	242	16	there	there	PRON
ejpam-2287	242	17	exist	exist	VERB
ejpam-2287	242	18	two	two	NUM
ejpam-2287	242	19	real	real	ADJ
ejpam-2287	242	20	numbers	number	NOUN
ejpam-2287	242	21	m1	m1	PROPN
ejpam-2287	242	22	and	and	CCONJ
ejpam-2287	242	23	m2	m2	PROPN
ejpam-2287	242	24	for	for	ADP
ejpam-2287	242	25	which	which	PRON
ejpam-2287	242	26	the	the	DET
ejpam-2287	242	27	map	map	NOUN
ejpam-2287	242	28	t2(θ	t2(θ	X
ejpam-2287	242	29	,	,	PUNCT
ejpam-2287	242	30	u	u	NOUN
ejpam-2287	242	31	)	)	PUNCT
ejpam-2287	242	32	=	=	SYM
ejpam-2287	242	33	(	(	PUNCT
ejpam-2287	242	34	f(θ	f(θ	PROPN
ejpam-2287	242	35	,	,	PUNCT
ejpam-2287	242	36	u	u	NOUN
ejpam-2287	242	37	)	)	PUNCT
ejpam-2287	242	38	,	,	PUNCT
ejpam-2287	243	1	g(θ	g(θ	ADP
ejpam-2287	243	2	,	,	PUNCT
ejpam-2287	243	3	u	u	NOUN
ejpam-2287	243	4	)	)	PUNCT
ejpam-2287	243	5	)	)	PUNCT
ejpam-2287	243	6	satisfies	satisfy	VERB
ejpam-2287	243	7	−m1	−m1	PROPN
ejpam-2287	243	8	≤	≤	PROPN
ejpam-2287	243	9	f(θ	f(θ	PROPN
ejpam-2287	243	10	,	,	PUNCT
ejpam-2287	243	11	u	u	NOUN
ejpam-2287	243	12	)	)	PUNCT
ejpam-2287	243	13	≤	≤	NOUN
ejpam-2287	243	14	m1	m1	NOUN
ejpam-2287	243	15	and	and	CCONJ
ejpam-2287	243	16	−m2	−m2	NOUN
ejpam-2287	243	17	≤	≤	NUM
ejpam-2287	243	18	g(θ	g(θ	PROPN
ejpam-2287	243	19	,	,	PUNCT
ejpam-2287	243	20	u)≤	u)≤	DET
ejpam-2287	243	21	m2	m2	PROPN
ejpam-2287	243	22	proof	proof	NOUN
ejpam-2287	243	23	.	.	PUNCT
ejpam-2287	244	1	note	note	VERB
ejpam-2287	244	2	that	that	SCONJ
ejpam-2287	244	3	under	under	ADP
ejpam-2287	244	4	the	the	DET
ejpam-2287	244	5	given	give	VERB
ejpam-2287	244	6	assumptions	assumption	NOUN
ejpam-2287	244	7	,	,	PUNCT
ejpam-2287	244	8	the	the	DET
ejpam-2287	244	9	first	first	ADJ
ejpam-2287	244	10	coordinate	coordinate	NOUN
ejpam-2287	244	11	of	of	ADP
ejpam-2287	244	12	the	the	DET
ejpam-2287	244	13	map	map	NOUN
ejpam-2287	244	14	t2	t2	NOUN
ejpam-2287	244	15	�	�	PROPN
ejpam-2287	244	16	θ	θ	PROPN
ejpam-2287	244	17	u	u	NOUN
ejpam-2287	244	18	�	�	PROPN
ejpam-2287	244	19	=	=	SYM
ejpam-2287	244	20	�	�	PROPN
ejpam-2287	244	21	1.99u−	1.99u−	NUM
ejpam-2287	244	22	0.99θ	0.99θ	NUM
ejpam-2287	244	23	−	−	NUM
ejpam-2287	244	24	2.4(1−	2.4(1−	NUM
ejpam-2287	244	25	θ2)θ	θ2)θ	NOUN
ejpam-2287	245	1	+	+	NOUN
ejpam-2287	245	2	λµθ	λµθ	NOUN
ejpam-2287	245	3	1.99(1.99u−	1.99(1.99u−	NUM
ejpam-2287	245	4	0.99θ	0.99θ	NUM
ejpam-2287	245	5	−	−	NOUN
ejpam-2287	246	1	2.4(1−	2.4(1−	NUM
ejpam-2287	246	2	θ2)θ	θ2)θ	NOUN
ejpam-2287	246	3	+	+	NOUN
ejpam-2287	246	4	λµθ	λµθ	NOUN
ejpam-2287	246	5	)	)	PUNCT
ejpam-2287	247	1	+	+	NOUN
ejpam-2287	247	2	λµu−	λµu−	PROPN
ejpam-2287	247	3	2.4	2.4	NUM
ejpam-2287	247	4	�	�	PROPN
ejpam-2287	247	5	1−	1−	NUM
ejpam-2287	247	6	u2	u2	PROPN
ejpam-2287	247	7	�	�	PROPN
ejpam-2287	247	8	u−	u−	PROPN
ejpam-2287	247	9	0.99u	0.99u	ADJ
ejpam-2287	247	10	�	�	PROPN
ejpam-2287	247	11	s.	s.	PROPN
ejpam-2287	247	12	basu	basu	PROPN
ejpam-2287	247	13	/	/	SYM
ejpam-2287	247	14	eur	eur	PROPN
ejpam-2287	247	15	.	.	PUNCT
ejpam-2287	248	1	j.	j.	PROPN
ejpam-2287	248	2	pure	pure	PROPN
ejpam-2287	248	3	appl	appl	PROPN
ejpam-2287	248	4	.	.	PROPN
ejpam-2287	248	5	math	math	PROPN
ejpam-2287	248	6	,	,	PUNCT
ejpam-2287	248	7	7	7	NUM
ejpam-2287	248	8	(	(	PUNCT
ejpam-2287	248	9	2014	2014	NUM
ejpam-2287	248	10	)	)	PUNCT
ejpam-2287	248	11	,	,	PUNCT
ejpam-2287	248	12	442	442	NUM
ejpam-2287	248	13	-	-	SYM
ejpam-2287	248	14	461	461	NUM
ejpam-2287	248	15	454	454	NUM
ejpam-2287	248	16	which	which	PRON
ejpam-2287	248	17	was	be	AUX
ejpam-2287	248	18	defined	define	VERB
ejpam-2287	248	19	in	in	ADP
ejpam-2287	248	20	(	(	PUNCT
ejpam-2287	248	21	15	15	NUM
ejpam-2287	248	22	)	)	PUNCT
ejpam-2287	248	23	has	have	VERB
ejpam-2287	248	24	bounds	bound	NOUN
ejpam-2287	248	25	given	give	VERB
ejpam-2287	248	26	by	by	ADP
ejpam-2287	248	27	−17.7528≤	−17.7528≤	DET
ejpam-2287	248	28	1.99u−	1.99u−	NUM
ejpam-2287	249	1	0.99θ	0.99θ	NOUN
ejpam-2287	249	2	−	−	NUM
ejpam-2287	249	3	2.4(1−	2.4(1−	NUM
ejpam-2287	249	4	θ2)θ	θ2)θ	NOUN
ejpam-2287	250	1	+	+	NOUN
ejpam-2287	250	2	λµθ	λµθ	NOUN
ejpam-2287	250	3	≤	≤	ADJ
ejpam-2287	250	4	17.7528	17.7528	NUM
ejpam-2287	250	5	(	(	PUNCT
ejpam-2287	250	6	26	26	NUM
ejpam-2287	250	7	)	)	PUNCT
ejpam-2287	250	8	and	and	CCONJ
ejpam-2287	250	9	its	its	PRON
ejpam-2287	250	10	second	second	ADJ
ejpam-2287	250	11	coordinate	coordinate	NOUN
ejpam-2287	250	12	has	have	VERB
ejpam-2287	250	13	bounds	bound	NOUN
ejpam-2287	250	14	given	give	VERB
ejpam-2287	250	15	by	by	ADP
ejpam-2287	250	16	−9.09491≤1.99(1.99u−	−9.09491≤1.99(1.99u−	X
ejpam-2287	250	17	0.99θ	0.99θ	NUM
ejpam-2287	250	18	−	−	PROPN
ejpam-2287	250	19	2.4(1−	2.4(1−	NUM
ejpam-2287	250	20	θ2)θ	θ2)θ	NOUN
ejpam-2287	250	21	+	+	NOUN
ejpam-2287	250	22	λµθ	λµθ	NOUN
ejpam-2287	250	23	)	)	PUNCT
ejpam-2287	251	1	+	+	NOUN
ejpam-2287	251	2	λµu−	λµu−	PROPN
ejpam-2287	251	3	2.4	2.4	NUM
ejpam-2287	251	4	�	�	PROPN
ejpam-2287	251	5	1−	1−	NUM
ejpam-2287	251	6	u2	u2	PROPN
ejpam-2287	251	7	�	�	PROPN
ejpam-2287	251	8	u	u	PROPN
ejpam-2287	251	9	−0.99u≤9.09491	−0.99u≤9.09491	X
ejpam-2287	251	10	(	(	PUNCT
ejpam-2287	251	11	27	27	NUM
ejpam-2287	251	12	)	)	PUNCT
ejpam-2287	251	13	choose	choose	VERB
ejpam-2287	251	14	m1	m1	PROPN
ejpam-2287	251	15	=	=	PUNCT
ejpam-2287	251	16	17.7528	17.7528	NUM
ejpam-2287	251	17	and	and	CCONJ
ejpam-2287	251	18	m2	m2	PROPN
ejpam-2287	251	19	=	=	PROPN
ejpam-2287	251	20	9.09491	9.09491	NUM
ejpam-2287	251	21	in	in	ADP
ejpam-2287	251	22	the	the	DET
ejpam-2287	251	23	statement	statement	NOUN
ejpam-2287	251	24	of	of	ADP
ejpam-2287	251	25	the	the	DET
ejpam-2287	251	26	lemma	lemma	PROPN
ejpam-2287	251	27	.	.	PUNCT
ejpam-2287	252	1	define	define	VERB
ejpam-2287	252	2	the	the	DET
ejpam-2287	252	3	four	four	NUM
ejpam-2287	252	4	regions	region	NOUN
ejpam-2287	252	5	r1	r1	NOUN
ejpam-2287	252	6	,	,	PUNCT
ejpam-2287	252	7	r2	r2	PROPN
ejpam-2287	252	8	,	,	PUNCT
ejpam-2287	252	9	r3	r3	PROPN
ejpam-2287	252	10	and	and	CCONJ
ejpam-2287	252	11	r4	r4	NOUN
ejpam-2287	252	12	as	as	SCONJ
ejpam-2287	252	13	follows	follow	VERB
ejpam-2287	252	14	.	.	PUNCT
ejpam-2287	253	1	r1	r1	NOUN
ejpam-2287	253	2	:	:	PUNCT
ejpam-2287	253	3	=	=	PUNCT
ejpam-2287	254	1	[	[	X
ejpam-2287	254	2	0	0	NUM
ejpam-2287	254	3	,	,	PUNCT
ejpam-2287	254	4	m1]×	m1]×	ADJ
ejpam-2287	254	5	[	[	X
ejpam-2287	254	6	0	0	NUM
ejpam-2287	254	7	,	,	PUNCT
ejpam-2287	254	8	m2	m2	PROPN
ejpam-2287	254	9	]	]	X
ejpam-2287	254	10	r2	r2	NOUN
ejpam-2287	254	11	:	:	PUNCT
ejpam-2287	255	1	=	=	PUNCT
ejpam-2287	256	1	[	[	X
ejpam-2287	256	2	−m1	−m1	NOUN
ejpam-2287	256	3	,	,	PUNCT
ejpam-2287	256	4	0]×	0]×	NUM
ejpam-2287	257	1	[	[	X
ejpam-2287	257	2	0	0	NUM
ejpam-2287	257	3	,	,	PUNCT
ejpam-2287	257	4	m2	m2	PROPN
ejpam-2287	257	5	]	]	X
ejpam-2287	257	6	r3	r3	PROPN
ejpam-2287	257	7	:	:	PUNCT
ejpam-2287	257	8	=	=	PUNCT
ejpam-2287	258	1	[	[	X
ejpam-2287	258	2	−m1	−m1	X
ejpam-2287	258	3	,	,	PUNCT
ejpam-2287	258	4	0]×	0]×	NUM
ejpam-2287	258	5	[	[	X
ejpam-2287	258	6	−m2	−m2	NOUN
ejpam-2287	258	7	,	,	PUNCT
ejpam-2287	258	8	0	0	NUM
ejpam-2287	258	9	]	]	PUNCT
ejpam-2287	258	10	r4	r4	NOUN
ejpam-2287	258	11	:	:	PUNCT
ejpam-2287	258	12	=	=	PUNCT
ejpam-2287	259	1	[	[	X
ejpam-2287	259	2	0	0	NUM
ejpam-2287	259	3	,	,	PUNCT
ejpam-2287	259	4	m1]×	m1]×	ADJ
ejpam-2287	259	5	[	[	X
ejpam-2287	259	6	−m2	−m2	NOUN
ejpam-2287	259	7	,	,	PUNCT
ejpam-2287	259	8	0	0	NUM
ejpam-2287	259	9	]	]	X
ejpam-2287	259	10	(	(	PUNCT
ejpam-2287	259	11	28	28	NUM
ejpam-2287	259	12	)	)	PUNCT
ejpam-2287	259	13	the	the	DET
ejpam-2287	259	14	following	follow	VERB
ejpam-2287	259	15	lemma	lemma	PROPN
ejpam-2287	259	16	establishes	establish	VERB
ejpam-2287	259	17	an	an	DET
ejpam-2287	259	18	invariant	invariant	ADJ
ejpam-2287	259	19	attracting	attract	VERB
ejpam-2287	259	20	set	set	NOUN
ejpam-2287	259	21	for	for	ADP
ejpam-2287	259	22	the	the	DET
ejpam-2287	259	23	map	map	NOUN
ejpam-2287	259	24	t2(θ	t2(θ	X
ejpam-2287	259	25	,	,	PUNCT
ejpam-2287	259	26	u	u	NOUN
ejpam-2287	259	27	)	)	PUNCT
ejpam-2287	259	28	when	when	SCONJ
ejpam-2287	259	29	the	the	DET
ejpam-2287	259	30	latter	latter	NOUN
ejpam-2287	259	31	is	be	AUX
ejpam-2287	259	32	cooperative	cooperative	ADJ
ejpam-2287	259	33	.	.	PUNCT
ejpam-2287	260	1	it	it	PRON
ejpam-2287	260	2	will	will	AUX
ejpam-2287	260	3	play	play	VERB
ejpam-2287	260	4	a	a	DET
ejpam-2287	260	5	key	key	ADJ
ejpam-2287	260	6	role	role	NOUN
ejpam-2287	260	7	in	in	ADP
ejpam-2287	260	8	establishing	establish	VERB
ejpam-2287	260	9	global	global	ADJ
ejpam-2287	260	10	attractivity	attractivity	NOUN
ejpam-2287	260	11	results	result	NOUN
ejpam-2287	260	12	for	for	ADP
ejpam-2287	260	13	equation	equation	NOUN
ejpam-2287	260	14	(	(	PUNCT
ejpam-2287	260	15	12	12	NUM
ejpam-2287	260	16	)	)	PUNCT
ejpam-2287	260	17	later	later	ADV
ejpam-2287	260	18	on	on	ADV
ejpam-2287	260	19	in	in	ADP
ejpam-2287	260	20	this	this	DET
ejpam-2287	260	21	section	section	NOUN
ejpam-2287	260	22	.	.	PUNCT
ejpam-2287	261	1	lemma	lemma	PROPN
ejpam-2287	261	2	4	4	NUM
ejpam-2287	261	3	.	.	PUNCT
ejpam-2287	262	1	under	under	ADP
ejpam-2287	262	2	the	the	DET
ejpam-2287	262	3	hypotheses	hypothesis	NOUN
ejpam-2287	262	4	of	of	ADP
ejpam-2287	262	5	lemma	lemma	PROPN
ejpam-2287	262	6	2	2	NUM
ejpam-2287	262	7	,	,	PUNCT
ejpam-2287	262	8	the	the	DET
ejpam-2287	262	9	regions	region	NOUN
ejpam-2287	262	10	r1	r1	NOUN
ejpam-2287	262	11	,	,	PUNCT
ejpam-2287	262	12	r2	r2	PROPN
ejpam-2287	262	13	,	,	PUNCT
ejpam-2287	262	14	r3	r3	PROPN
ejpam-2287	262	15	and	and	CCONJ
ejpam-2287	262	16	r4	r4	PROPN
ejpam-2287	262	17	satisfy	satisfy	NOUN
ejpam-2287	262	18	:	:	PUNCT
ejpam-2287	262	19	t2(r1	t2(r1	NUM
ejpam-2287	262	20	)	)	PUNCT
ejpam-2287	262	21	⊆r1	⊆r1	PROPN
ejpam-2287	262	22	,	,	PUNCT
ejpam-2287	262	23	t	t	PROPN
ejpam-2287	262	24	(	(	PUNCT
ejpam-2287	262	25	r2	r2	PROPN
ejpam-2287	262	26	)	)	PUNCT
ejpam-2287	262	27	⊆r1	⊆r1	NOUN
ejpam-2287	262	28	,	,	PUNCT
ejpam-2287	262	29	t2(r3	t2(r3	ADV
ejpam-2287	262	30	)	)	PUNCT
ejpam-2287	262	31	⊆r3	⊆r3	PROPN
ejpam-2287	262	32	,	,	PUNCT
ejpam-2287	262	33	t	t	PROPN
ejpam-2287	262	34	(	(	PUNCT
ejpam-2287	262	35	r4	r4	PROPN
ejpam-2287	262	36	)	)	PUNCT
ejpam-2287	262	37	⊆r3	⊆r3	PROPN
ejpam-2287	262	38	in	in	ADP
ejpam-2287	262	39	particular	particular	ADJ
ejpam-2287	262	40	,	,	PUNCT
ejpam-2287	262	41	r1	r1	PROPN
ejpam-2287	262	42	∪r3	∪r3	NOUN
ejpam-2287	262	43	is	be	AUX
ejpam-2287	262	44	an	an	DET
ejpam-2287	262	45	invariant	invariant	ADJ
ejpam-2287	262	46	attracting	attract	VERB
ejpam-2287	262	47	set	set	NOUN
ejpam-2287	262	48	for	for	ADP
ejpam-2287	262	49	the	the	DET
ejpam-2287	262	50	map	map	NOUN
ejpam-2287	262	51	t2(θ	t2(θ	X
ejpam-2287	262	52	,	,	PUNCT
ejpam-2287	262	53	u	u	NOUN
ejpam-2287	262	54	)	)	PUNCT
ejpam-2287	262	55	.	.	PUNCT
ejpam-2287	263	1	proof	proof	NOUN
ejpam-2287	263	2	.	.	PUNCT
ejpam-2287	264	1	to	to	PART
ejpam-2287	264	2	see	see	VERB
ejpam-2287	264	3	that	that	SCONJ
ejpam-2287	264	4	t2(r1	t2(r1	NOUN
ejpam-2287	264	5	)	)	PUNCT
ejpam-2287	264	6	⊆r1	⊆r1	NUM
ejpam-2287	264	7	,	,	PUNCT
ejpam-2287	264	8	observe	observe	VERB
ejpam-2287	264	9	that	that	SCONJ
ejpam-2287	264	10	all	all	PRON
ejpam-2287	264	11	(	(	PUNCT
ejpam-2287	264	12	θ	θ	PROPN
ejpam-2287	264	13	,	,	PUNCT
ejpam-2287	264	14	u	u	NOUN
ejpam-2287	264	15	)	)	PUNCT
ejpam-2287	264	16	∈	∈	PROPN
ejpam-2287	264	17	r1	r1	PROPN
ejpam-2287	264	18	satisfy	satisfy	NOUN
ejpam-2287	264	19	(	(	PUNCT
ejpam-2287	264	20	0,0)	0,0)	NOUN
ejpam-2287	264	21	�	�	PROPN
ejpam-2287	264	22	ne	ne	PROPN
ejpam-2287	264	23	(	(	PUNCT
ejpam-2287	264	24	θ	θ	PROPN
ejpam-2287	264	25	,	,	PUNCT
ejpam-2287	264	26	u)	u)	PROPN
ejpam-2287	264	27	�	�	SYM
ejpam-2287	264	28	ne	ne	PROPN
ejpam-2287	264	29	(	(	PUNCT
ejpam-2287	264	30	m1	m1	PROPN
ejpam-2287	264	31	,	,	PUNCT
ejpam-2287	264	32	m2	m2	PROPN
ejpam-2287	264	33	)	)	PUNCT
ejpam-2287	264	34	under	under	ADP
ejpam-2287	264	35	the	the	DET
ejpam-2287	264	36	hypotheses	hypothesis	NOUN
ejpam-2287	264	37	of	of	ADP
ejpam-2287	264	38	lemma	lemma	PROPN
ejpam-2287	264	39	2	2	NUM
ejpam-2287	264	40	,	,	PUNCT
ejpam-2287	264	41	the	the	DET
ejpam-2287	264	42	map	map	NOUN
ejpam-2287	264	43	t2(θ	t2(θ	X
ejpam-2287	264	44	,	,	PUNCT
ejpam-2287	264	45	u	u	NOUN
ejpam-2287	264	46	)	)	PUNCT
ejpam-2287	264	47	is	be	AUX
ejpam-2287	264	48	cooperative	cooperative	ADJ
ejpam-2287	264	49	.	.	PUNCT
ejpam-2287	265	1	since	since	SCONJ
ejpam-2287	265	2	it	it	PRON
ejpam-2287	265	3	also	also	ADV
ejpam-2287	265	4	has	have	VERB
ejpam-2287	265	5	(	(	PUNCT
ejpam-2287	265	6	0,0	0,0	NOUN
ejpam-2287	265	7	)	)	PUNCT
ejpam-2287	265	8	as	as	ADP
ejpam-2287	265	9	a	a	DET
ejpam-2287	265	10	fixed	fix	VERB
ejpam-2287	265	11	point	point	NOUN
ejpam-2287	265	12	,	,	PUNCT
ejpam-2287	265	13	it	it	PRON
ejpam-2287	265	14	follows	follow	VERB
ejpam-2287	265	15	from	from	ADP
ejpam-2287	265	16	the	the	DET
ejpam-2287	265	17	“	"	PUNCT
ejpam-2287	265	18	�	�	PROPN
ejpam-2287	265	19	ne	ne	NOUN
ejpam-2287	265	20	”	"	PUNCT
ejpam-2287	265	21	order	order	NOUN
ejpam-2287	265	22	-	-	PUNCT
ejpam-2287	265	23	preserving	preserve	VERB
ejpam-2287	265	24	property	property	NOUN
ejpam-2287	265	25	of	of	ADP
ejpam-2287	265	26	cooperative	cooperative	ADJ
ejpam-2287	265	27	maps	map	NOUN
ejpam-2287	265	28	(	(	PUNCT
ejpam-2287	265	29	see	see	VERB
ejpam-2287	265	30	[	[	X
ejpam-2287	265	31	12	12	NUM
ejpam-2287	265	32	,	,	PUNCT
ejpam-2287	265	33	15	15	NUM
ejpam-2287	265	34	]	]	PUNCT
ejpam-2287	265	35	)	)	PUNCT
ejpam-2287	266	1	that	that	SCONJ
ejpam-2287	266	2	(	(	PUNCT
ejpam-2287	266	3	0,0	0,0	NOUN
ejpam-2287	266	4	)	)	PUNCT
ejpam-2287	266	5	=	=	SYM
ejpam-2287	266	6	t2(0,0)	t2(0,0)	PROPN
ejpam-2287	266	7	�	�	PROPN
ejpam-2287	266	8	ne	ne	PROPN
ejpam-2287	266	9	t2(θ	t2(θ	PROPN
ejpam-2287	266	10	,	,	PUNCT
ejpam-2287	266	11	u)	u)	PROPN
ejpam-2287	266	12	�	�	PROPN
ejpam-2287	266	13	ne	ne	NOUN
ejpam-2287	266	14	t2(m1	t2(m1	PROPN
ejpam-2287	266	15	,	,	PUNCT
ejpam-2287	266	16	m2)	m2)	PROPN
ejpam-2287	266	17	�	�	SYM
ejpam-2287	266	18	ne	ne	X
ejpam-2287	266	19	(	(	PUNCT
ejpam-2287	266	20	m1	m1	PROPN
ejpam-2287	266	21	,	,	PUNCT
ejpam-2287	266	22	m2	m2	PROPN
ejpam-2287	266	23	)	)	PUNCT
ejpam-2287	266	24	which	which	PRON
ejpam-2287	266	25	is	be	AUX
ejpam-2287	266	26	what	what	PRON
ejpam-2287	266	27	we	we	PRON
ejpam-2287	266	28	wanted	want	VERB
ejpam-2287	266	29	to	to	PART
ejpam-2287	266	30	prove	prove	VERB
ejpam-2287	266	31	.	.	PUNCT
ejpam-2287	267	1	the	the	DET
ejpam-2287	267	2	proof	proof	NOUN
ejpam-2287	267	3	of	of	ADP
ejpam-2287	267	4	t2(r3	t2(r3	NOUN
ejpam-2287	267	5	)	)	PUNCT
ejpam-2287	268	1	⊆r3	⊆r3	PRON
ejpam-2287	268	2	is	be	AUX
ejpam-2287	268	3	similar	similar	ADJ
ejpam-2287	268	4	and	and	CCONJ
ejpam-2287	268	5	we	we	PRON
ejpam-2287	268	6	skip	skip	VERB
ejpam-2287	268	7	it	it	PRON
ejpam-2287	268	8	.	.	PUNCT
ejpam-2287	269	1	to	to	PART
ejpam-2287	269	2	see	see	VERB
ejpam-2287	269	3	that	that	PRON
ejpam-2287	269	4	t	t	PROPN
ejpam-2287	269	5	(	(	PUNCT
ejpam-2287	269	6	r2	r2	PROPN
ejpam-2287	269	7	)	)	PUNCT
ejpam-2287	269	8	⊆r1	⊆r1	NOUN
ejpam-2287	269	9	,	,	PUNCT
ejpam-2287	269	10	note	note	VERB
ejpam-2287	269	11	that	that	SCONJ
ejpam-2287	269	12	the	the	DET
ejpam-2287	269	13	equilibrium	equilibrium	NOUN
ejpam-2287	269	14	curves	curve	VERB
ejpam-2287	269	15	θ	θ	NOUN
ejpam-2287	270	1	=	=	SYM
ejpam-2287	270	2	f	f	PROPN
ejpam-2287	270	3	(	(	PUNCT
ejpam-2287	270	4	θ	θ	PROPN
ejpam-2287	270	5	,	,	PUNCT
ejpam-2287	270	6	u	u	NOUN
ejpam-2287	270	7	)	)	PUNCT
ejpam-2287	270	8	and	and	CCONJ
ejpam-2287	270	9	u=	u=	ADV
ejpam-2287	270	10	g(θ	g(θ	PROPN
ejpam-2287	270	11	,	,	PUNCT
ejpam-2287	270	12	u	u	NOUN
ejpam-2287	270	13	)	)	PUNCT
ejpam-2287	270	14	of	of	ADP
ejpam-2287	270	15	the	the	DET
ejpam-2287	270	16	map	map	NOUN
ejpam-2287	270	17	t	t	PROPN
ejpam-2287	270	18	(	(	PUNCT
ejpam-2287	270	19	θ	θ	PROPN
ejpam-2287	270	20	,	,	PUNCT
ejpam-2287	270	21	u	u	NOUN
ejpam-2287	270	22	)	)	PUNCT
ejpam-2287	270	23	=	=	SYM
ejpam-2287	270	24	(	(	PUNCT
ejpam-2287	270	25	f	f	X
ejpam-2287	270	26	(	(	PUNCT
ejpam-2287	270	27	θ	θ	PROPN
ejpam-2287	270	28	,	,	PUNCT
ejpam-2287	270	29	u	u	NOUN
ejpam-2287	270	30	)	)	PUNCT
ejpam-2287	270	31	,	,	PUNCT
ejpam-2287	270	32	g(θ	g(θ	ADP
ejpam-2287	270	33	,	,	PUNCT
ejpam-2287	270	34	u	u	NOUN
ejpam-2287	270	35	)	)	PUNCT
ejpam-2287	270	36	)	)	PUNCT
ejpam-2287	270	37	defined	define	VERB
ejpam-2287	270	38	in	in	ADP
ejpam-2287	270	39	(	(	PUNCT
ejpam-2287	270	40	14	14	NUM
ejpam-2287	270	41	)	)	PUNCT
ejpam-2287	270	42	are	be	AUX
ejpam-2287	270	43	both	both	PRON
ejpam-2287	270	44	increasing	increase	VERB
ejpam-2287	270	45	curves	curve	NOUN
ejpam-2287	270	46	passing	pass	VERB
ejpam-2287	270	47	through	through	ADP
ejpam-2287	270	48	the	the	DET
ejpam-2287	270	49	origin	origin	NOUN
ejpam-2287	270	50	.	.	PUNCT
ejpam-2287	271	1	in	in	ADP
ejpam-2287	271	2	particular	particular	ADJ
ejpam-2287	271	3	,	,	PUNCT
ejpam-2287	271	4	the	the	DET
ejpam-2287	271	5	region	region	NOUN
ejpam-2287	271	6	r2	r2	PROPN
ejpam-2287	271	7	lies	lie	VERB
ejpam-2287	271	8	entirely	entirely	ADV
ejpam-2287	271	9	above	above	ADP
ejpam-2287	271	10	them	they	PRON
ejpam-2287	271	11	.	.	PUNCT
ejpam-2287	272	1	moreover	moreover	ADV
ejpam-2287	272	2	,	,	PUNCT
ejpam-2287	272	3	all	all	PRON
ejpam-2287	272	4	(	(	PUNCT
ejpam-2287	272	5	θ	θ	PROPN
ejpam-2287	272	6	,	,	PUNCT
ejpam-2287	272	7	u	u	NOUN
ejpam-2287	272	8	)	)	PUNCT
ejpam-2287	272	9	∈	∈	PROPN
ejpam-2287	272	10	r2	r2	PROPN
ejpam-2287	272	11	satisfy	satisfy	NOUN
ejpam-2287	272	12	(	(	PUNCT
ejpam-2287	272	13	θ	θ	NOUN
ejpam-2287	272	14	,	,	PUNCT
ejpam-2287	272	15	u	u	NOUN
ejpam-2287	272	16	)	)	PUNCT
ejpam-2287	272	17	�	�	PROPN
ejpam-2287	272	18	ne	ne	PROPN
ejpam-2287	272	19	t	t	PROPN
ejpam-2287	272	20	(	(	PUNCT
ejpam-2287	272	21	θ	θ	PROPN
ejpam-2287	272	22	,	,	PUNCT
ejpam-2287	272	23	u	u	NOUN
ejpam-2287	272	24	)	)	PUNCT
ejpam-2287	272	25	.	.	PUNCT
ejpam-2287	273	1	for	for	ADP
ejpam-2287	273	2	example	example	NOUN
ejpam-2287	273	3	,	,	PUNCT
ejpam-2287	273	4	one	one	PRON
ejpam-2287	273	5	can	can	AUX
ejpam-2287	273	6	check	check	VERB
ejpam-2287	273	7	that	that	DET
ejpam-2287	273	8	(	(	PUNCT
ejpam-2287	273	9	0,u	0,u	NUM
ejpam-2287	273	10	)	)	PUNCT
ejpam-2287	273	11	�	�	PROPN
ejpam-2287	273	12	ne	ne	PROPN
ejpam-2287	273	13	t	t	PROPN
ejpam-2287	273	14	(	(	PUNCT
ejpam-2287	273	15	0,u	0,u	NUM
ejpam-2287	273	16	)	)	PUNCT
ejpam-2287	273	17	for	for	ADP
ejpam-2287	273	18	u	u	NOUN
ejpam-2287	273	19	>	>	X
ejpam-2287	273	20	0	0	X
ejpam-2287	273	21	.	.	PUNCT
ejpam-2287	274	1	it	it	PRON
ejpam-2287	274	2	is	be	AUX
ejpam-2287	274	3	also	also	ADV
ejpam-2287	274	4	easy	easy	ADJ
ejpam-2287	274	5	to	to	PART
ejpam-2287	274	6	check	check	VERB
ejpam-2287	274	7	that	that	DET
ejpam-2287	274	8	t	t	NOUN
ejpam-2287	274	9	(	(	PUNCT
ejpam-2287	274	10	θ	θ	PROPN
ejpam-2287	274	11	,	,	PUNCT
ejpam-2287	274	12	u	u	NOUN
ejpam-2287	274	13	)	)	PUNCT
ejpam-2287	274	14	is	be	AUX
ejpam-2287	274	15	a	a	DET
ejpam-2287	274	16	cooperative	cooperative	ADJ
ejpam-2287	274	17	map	map	NOUN
ejpam-2287	274	18	by	by	ADP
ejpam-2287	274	19	looking	look	VERB
ejpam-2287	274	20	at	at	ADP
ejpam-2287	274	21	its	its	PRON
ejpam-2287	274	22	jacobian	jacobian	ADJ
ejpam-2287	274	23	.	.	PUNCT
ejpam-2287	275	1	hence	hence	ADV
ejpam-2287	275	2	for	for	ADP
ejpam-2287	275	3	all	all	DET
ejpam-2287	275	4	(	(	PUNCT
ejpam-2287	275	5	θ	θ	PROPN
ejpam-2287	275	6	,	,	PUNCT
ejpam-2287	275	7	u	u	NOUN
ejpam-2287	275	8	)	)	PUNCT
ejpam-2287	275	9	∈	∈	PROPN
ejpam-2287	275	10	r2	r2	NOUN
ejpam-2287	275	11	,	,	PUNCT
ejpam-2287	275	12	one	one	NUM
ejpam-2287	275	13	has	have	VERB
ejpam-2287	275	14	(	(	PUNCT
ejpam-2287	275	15	θ	θ	PROPN
ejpam-2287	275	16	,	,	PUNCT
ejpam-2287	275	17	u)	u)	PROPN
ejpam-2287	275	18	�	�	PROPN
ejpam-2287	275	19	ne	ne	PROPN
ejpam-2287	275	20	t	t	PROPN
ejpam-2287	275	21	(	(	PUNCT
ejpam-2287	275	22	θ	θ	PROPN
ejpam-2287	275	23	,	,	PUNCT
ejpam-2287	275	24	u	u	NOUN
ejpam-2287	275	25	)	)	PUNCT
ejpam-2287	275	26	�	�	PROPN
ejpam-2287	275	27	ne	ne	PROPN
ejpam-2287	275	28	t2(θ	t2(θ	PROPN
ejpam-2287	275	29	,	,	PUNCT
ejpam-2287	275	30	u)	u)	PROPN
ejpam-2287	275	31	�	�	PROPN
ejpam-2287	275	32	ne	ne	PROPN
ejpam-2287	275	33	.	.	PUNCT
ejpam-2287	275	34	.	.	PUNCT
ejpam-2287	275	35	.	.	PUNCT
ejpam-2287	276	1	s.	s.	PROPN
ejpam-2287	276	2	basu	basu	PROPN
ejpam-2287	276	3	/	/	SYM
ejpam-2287	276	4	eur	eur	PROPN
ejpam-2287	276	5	.	.	PUNCT
ejpam-2287	277	1	j.	j.	PROPN
ejpam-2287	277	2	pure	pure	PROPN
ejpam-2287	277	3	appl	appl	PROPN
ejpam-2287	277	4	.	.	PROPN
ejpam-2287	277	5	math	math	PROPN
ejpam-2287	277	6	,	,	PUNCT
ejpam-2287	277	7	7	7	NUM
ejpam-2287	277	8	(	(	PUNCT
ejpam-2287	277	9	2014	2014	NUM
ejpam-2287	277	10	)	)	PUNCT
ejpam-2287	277	11	,	,	PUNCT
ejpam-2287	277	12	442	442	NUM
ejpam-2287	277	13	-	-	SYM
ejpam-2287	277	14	461	461	NUM
ejpam-2287	277	15	455	455	NUM
ejpam-2287	277	16	the	the	DET
ejpam-2287	277	17	monotone	monotone	NOUN
ejpam-2287	277	18	increasing	increase	VERB
ejpam-2287	277	19	sequence	sequence	NOUN
ejpam-2287	277	20	given	give	VERB
ejpam-2287	277	21	above	above	ADV
ejpam-2287	277	22	must	must	AUX
ejpam-2287	277	23	enter	enter	VERB
ejpam-2287	277	24	the	the	DET
ejpam-2287	277	25	region	region	NOUN
ejpam-2287	277	26	r1	r1	NOUN
ejpam-2287	277	27	since	since	SCONJ
ejpam-2287	277	28	otherwise	otherwise	ADV
ejpam-2287	277	29	it	it	PRON
ejpam-2287	277	30	would	would	AUX
ejpam-2287	277	31	have	have	VERB
ejpam-2287	277	32	to	to	PART
ejpam-2287	277	33	converge	converge	VERB
ejpam-2287	277	34	to	to	ADP
ejpam-2287	277	35	a	a	DET
ejpam-2287	277	36	fixed	fix	VERB
ejpam-2287	277	37	point	point	NOUN
ejpam-2287	277	38	of	of	ADP
ejpam-2287	277	39	t	t	PROPN
ejpam-2287	277	40	(	(	PUNCT
ejpam-2287	277	41	θ	θ	PROPN
ejpam-2287	277	42	,	,	PUNCT
ejpam-2287	277	43	u	u	NOUN
ejpam-2287	277	44	)	)	PUNCT
ejpam-2287	277	45	in	in	ADP
ejpam-2287	277	46	r2	r2	PROPN
ejpam-2287	277	47	,	,	PUNCT
ejpam-2287	277	48	contradicting	contradict	VERB
ejpam-2287	277	49	the	the	DET
ejpam-2287	277	50	fact	fact	NOUN
ejpam-2287	277	51	that	that	SCONJ
ejpam-2287	277	52	the	the	DET
ejpam-2287	277	53	equilibrium	equilibrium	NOUN
ejpam-2287	277	54	curves	curve	NOUN
ejpam-2287	277	55	of	of	ADP
ejpam-2287	277	56	t	t	PROPN
ejpam-2287	277	57	(	(	PUNCT
ejpam-2287	277	58	θ	θ	PROPN
ejpam-2287	277	59	,	,	PUNCT
ejpam-2287	277	60	u	u	NOUN
ejpam-2287	277	61	)	)	PUNCT
ejpam-2287	277	62	do	do	AUX
ejpam-2287	277	63	not	not	PART
ejpam-2287	277	64	lie	lie	VERB
ejpam-2287	277	65	in	in	ADP
ejpam-2287	277	66	this	this	DET
ejpam-2287	277	67	region	region	NOUN
ejpam-2287	277	68	by	by	ADP
ejpam-2287	277	69	our	our	PRON
ejpam-2287	277	70	previous	previous	ADJ
ejpam-2287	277	71	discussion	discussion	NOUN
ejpam-2287	277	72	.	.	PUNCT
ejpam-2287	278	1	the	the	DET
ejpam-2287	278	2	proof	proof	NOUN
ejpam-2287	278	3	of	of	ADP
ejpam-2287	278	4	t	t	PROPN
ejpam-2287	278	5	(	(	PUNCT
ejpam-2287	278	6	r4	r4	PROPN
ejpam-2287	278	7	)	)	PUNCT
ejpam-2287	278	8	⊆r3	⊆r3	PRON
ejpam-2287	278	9	is	be	AUX
ejpam-2287	278	10	similar	similar	ADJ
ejpam-2287	278	11	and	and	CCONJ
ejpam-2287	278	12	we	we	PRON
ejpam-2287	278	13	skip	skip	VERB
ejpam-2287	278	14	it	it	PRON
ejpam-2287	278	15	.	.	PUNCT
ejpam-2287	279	1	our	our	PRON
ejpam-2287	279	2	next	next	ADJ
ejpam-2287	279	3	lemma	lemma	PROPN
ejpam-2287	279	4	establishes	establish	VERB
ejpam-2287	279	5	the	the	DET
ejpam-2287	279	6	fact	fact	NOUN
ejpam-2287	279	7	that	that	SCONJ
ejpam-2287	279	8	any	any	DET
ejpam-2287	279	9	region	region	NOUN
ejpam-2287	279	10	bounded	bound	VERB
ejpam-2287	279	11	by	by	ADP
ejpam-2287	279	12	two	two	NUM
ejpam-2287	279	13	fixed	fix	VERB
ejpam-2287	279	14	points	point	NOUN
ejpam-2287	279	15	of	of	ADP
ejpam-2287	279	16	a	a	DET
ejpam-2287	279	17	cooperative	cooperative	ADJ
ejpam-2287	279	18	map	map	NOUN
ejpam-2287	279	19	in	in	ADP
ejpam-2287	279	20	the	the	DET
ejpam-2287	279	21	“	"	PUNCT
ejpam-2287	279	22	�	�	PROPN
ejpam-2287	279	23	ne	ne	NOUN
ejpam-2287	279	24	”	"	PUNCT
ejpam-2287	279	25	ordering	ordering	NOUN
ejpam-2287	279	26	must	must	AUX
ejpam-2287	279	27	contain	contain	VERB
ejpam-2287	279	28	a	a	DET
ejpam-2287	279	29	locally	locally	ADV
ejpam-2287	279	30	asymptotically	asymptotically	ADV
ejpam-2287	279	31	stable	stable	ADJ
ejpam-2287	279	32	fixed	fix	VERB
ejpam-2287	279	33	point	point	NOUN
ejpam-2287	279	34	of	of	ADP
ejpam-2287	279	35	this	this	DET
ejpam-2287	279	36	map	map	NOUN
ejpam-2287	279	37	.	.	PUNCT
ejpam-2287	280	1	lemma	lemma	PROPN
ejpam-2287	280	2	5	5	NUM
ejpam-2287	280	3	.	.	PUNCT
ejpam-2287	280	4	suppose	suppose	VERB
ejpam-2287	280	5	et	et	NOUN
ejpam-2287	280	6	:	:	PUNCT
ejpam-2287	280	7	r→	r→	PROPN
ejpam-2287	280	8	r	r	NOUN
ejpam-2287	280	9	is	be	AUX
ejpam-2287	280	10	a	a	DET
ejpam-2287	280	11	cooperative	cooperative	ADJ
ejpam-2287	280	12	map	map	NOUN
ejpam-2287	280	13	.	.	PUNCT
ejpam-2287	281	1	in	in	ADP
ejpam-2287	281	2	addition	addition	NOUN
ejpam-2287	281	3	,	,	PUNCT
ejpam-2287	281	4	suppose	suppose	VERB
ejpam-2287	281	5	there	there	PRON
ejpam-2287	281	6	exist	exist	VERB
ejpam-2287	281	7	two	two	NUM
ejpam-2287	281	8	points	point	NOUN
ejpam-2287	281	9	(	(	PUNCT
ejpam-2287	281	10	x∗1	x∗1	ADJ
ejpam-2287	281	11	,	,	PUNCT
ejpam-2287	281	12	y∗1	y∗1	NOUN
ejpam-2287	281	13	)	)	PUNCT
ejpam-2287	281	14	and	and	CCONJ
ejpam-2287	281	15	(	(	PUNCT
ejpam-2287	281	16	x∗2	x∗2	PROPN
ejpam-2287	281	17	,	,	PUNCT
ejpam-2287	281	18	y∗2	y∗2	PROPN
ejpam-2287	281	19	)	)	PUNCT
ejpam-2287	281	20	with	with	ADP
ejpam-2287	281	21	(	(	PUNCT
ejpam-2287	281	22	x∗1	x∗1	ADV
ejpam-2287	281	23	,	,	PUNCT
ejpam-2287	281	24	y∗1)	y∗1)	PROPN
ejpam-2287	281	25	�	�	PROPN
ejpam-2287	281	26	ne	ne	PROPN
ejpam-2287	281	27	(	(	PUNCT
ejpam-2287	281	28	x	x	NOUN
ejpam-2287	281	29	∗	∗	NOUN
ejpam-2287	281	30	2	2	NUM
ejpam-2287	281	31	,	,	PUNCT
ejpam-2287	281	32	y∗2	y∗2	NOUN
ejpam-2287	281	33	)	)	PUNCT
ejpam-2287	281	34	in	in	ADP
ejpam-2287	281	35	r×r	r×r	PROPN
ejpam-2287	281	36	such	such	ADJ
ejpam-2287	281	37	that	that	PRON
ejpam-2287	281	38	et	et	PROPN
ejpam-2287	281	39	(	(	PUNCT
ejpam-2287	281	40	x∗1	x∗1	PROPN
ejpam-2287	281	41	,	,	PUNCT
ejpam-2287	281	42	y∗1	y∗1	NOUN
ejpam-2287	281	43	)	)	PUNCT
ejpam-2287	281	44	=	=	PUNCT
ejpam-2287	282	1	(	(	PUNCT
ejpam-2287	282	2	x	x	X
ejpam-2287	282	3	∗	∗	NOUN
ejpam-2287	282	4	1	1	NUM
ejpam-2287	282	5	,	,	PUNCT
ejpam-2287	282	6	y∗1	y∗1	NOUN
ejpam-2287	282	7	)	)	PUNCT
ejpam-2287	282	8	and	and	CCONJ
ejpam-2287	282	9	et	et	PROPN
ejpam-2287	282	10	(	(	PUNCT
ejpam-2287	282	11	x∗2	x∗2	PROPN
ejpam-2287	282	12	,	,	PUNCT
ejpam-2287	282	13	y∗2	y∗2	NOUN
ejpam-2287	282	14	)	)	PUNCT
ejpam-2287	282	15	=	=	PRON
ejpam-2287	283	1	(	(	PUNCT
ejpam-2287	283	2	x	x	X
ejpam-2287	283	3	∗	∗	NOUN
ejpam-2287	283	4	2	2	NUM
ejpam-2287	283	5	,	,	PUNCT
ejpam-2287	283	6	y∗2	y∗2	NOUN
ejpam-2287	283	7	)	)	PUNCT
ejpam-2287	283	8	then	then	ADV
ejpam-2287	283	9	there	there	PRON
ejpam-2287	283	10	exists	exist	VERB
ejpam-2287	283	11	a	a	DET
ejpam-2287	283	12	point	point	NOUN
ejpam-2287	283	13	(	(	PUNCT
ejpam-2287	283	14	p∗,q∗	p∗,q∗	PROPN
ejpam-2287	283	15	)	)	PUNCT
ejpam-2287	283	16	∈	∈	PROPN
ejpam-2287	284	1	[	[	X
ejpam-2287	284	2	x∗1	x∗1	ADV
ejpam-2287	284	3	,	,	PUNCT
ejpam-2287	284	4	x∗2]×	x∗2]×	PROPN
ejpam-2287	285	1	[	[	X
ejpam-2287	285	2	y	y	PROPN
ejpam-2287	285	3	∗	∗	PROPN
ejpam-2287	285	4	1	1	NUM
ejpam-2287	285	5	,	,	PUNCT
ejpam-2287	285	6	y∗2	y∗2	NOUN
ejpam-2287	285	7	]	]	PUNCT
ejpam-2287	285	8	such	such	ADJ
ejpam-2287	285	9	that	that	SCONJ
ejpam-2287	285	10	et	et	NOUN
ejpam-2287	285	11	(	(	PUNCT
ejpam-2287	285	12	p∗,q∗	p∗,q∗	PROPN
ejpam-2287	285	13	)	)	PUNCT
ejpam-2287	285	14	=	=	SYM
ejpam-2287	285	15	(	(	PUNCT
ejpam-2287	285	16	p∗,q∗	p∗,q∗	PROPN
ejpam-2287	285	17	)	)	PUNCT
ejpam-2287	285	18	.	.	PUNCT
ejpam-2287	286	1	moreover	moreover	ADV
ejpam-2287	286	2	,	,	PUNCT
ejpam-2287	286	3	(	(	PUNCT
ejpam-2287	286	4	p∗,q∗	p∗,q∗	PROPN
ejpam-2287	286	5	)	)	PUNCT
ejpam-2287	286	6	must	must	AUX
ejpam-2287	286	7	be	be	AUX
ejpam-2287	286	8	a	a	DET
ejpam-2287	286	9	locally	locally	ADV
ejpam-2287	286	10	asymptotically	asymptotically	ADV
ejpam-2287	286	11	stable	stable	ADJ
ejpam-2287	286	12	fixed	fix	VERB
ejpam-2287	286	13	point	point	NOUN
ejpam-2287	286	14	of	of	ADP
ejpam-2287	286	15	the	the	DET
ejpam-2287	286	16	map	map	NOUN
ejpam-2287	286	17	et	et	NOUN
ejpam-2287	286	18	.	.	PUNCT
ejpam-2287	287	1	proof	proof	NOUN
ejpam-2287	287	2	.	.	PUNCT
ejpam-2287	288	1	it	it	PRON
ejpam-2287	288	2	is	be	AUX
ejpam-2287	288	3	easy	easy	ADJ
ejpam-2287	288	4	to	to	PART
ejpam-2287	288	5	see	see	VERB
ejpam-2287	288	6	that	that	PRON
ejpam-2287	289	1	[	[	X
ejpam-2287	289	2	x∗1	x∗1	ADV
ejpam-2287	289	3	,	,	PUNCT
ejpam-2287	289	4	x∗2]×	x∗2]×	PROPN
ejpam-2287	290	1	[	[	X
ejpam-2287	290	2	y	y	PROPN
ejpam-2287	290	3	∗	∗	PROPN
ejpam-2287	290	4	1	1	NUM
ejpam-2287	290	5	,	,	PUNCT
ejpam-2287	290	6	y∗2	y∗2	NOUN
ejpam-2287	290	7	]	]	PUNCT
ejpam-2287	290	8	is	be	AUX
ejpam-2287	290	9	an	an	DET
ejpam-2287	290	10	invariant	invariant	ADJ
ejpam-2287	290	11	region	region	NOUN
ejpam-2287	290	12	for	for	ADP
ejpam-2287	290	13	et	et	PROPN
ejpam-2287	290	14	since	since	SCONJ
ejpam-2287	290	15	(	(	PUNCT
ejpam-2287	290	16	x∗1	x∗1	ADJ
ejpam-2287	290	17	,	,	PUNCT
ejpam-2287	290	18	y∗1	y∗1	NOUN
ejpam-2287	290	19	)	)	PUNCT
ejpam-2287	290	20	=	=	SYM
ejpam-2287	290	21	et	et	PROPN
ejpam-2287	290	22	(	(	PUNCT
ejpam-2287	290	23	x∗1	x∗1	ADV
ejpam-2287	290	24	,	,	PUNCT
ejpam-2287	290	25	y∗1)	y∗1)	PROPN
ejpam-2287	290	26	�	�	PROPN
ejpam-2287	290	27	ne	ne	PROPN
ejpam-2287	290	28	(	(	PUNCT
ejpam-2287	290	29	x	x	INTJ
ejpam-2287	290	30	,	,	PUNCT
ejpam-2287	290	31	y)	y)	PROPN
ejpam-2287	290	32	�	�	PROPN
ejpam-2287	290	33	ne	ne	VERB
ejpam-2287	290	34	et	et	PROPN
ejpam-2287	290	35	(	(	PUNCT
ejpam-2287	290	36	x	x	PROPN
ejpam-2287	290	37	,	,	PUNCT
ejpam-2287	290	38	y)	y)	PROPN
ejpam-2287	290	39	�	�	PROPN
ejpam-2287	290	40	ne	ne	PROPN
ejpam-2287	290	41	et	et	PROPN
ejpam-2287	290	42	(	(	PUNCT
ejpam-2287	290	43	x∗2	x∗2	PROPN
ejpam-2287	290	44	,	,	PUNCT
ejpam-2287	290	45	y∗2	y∗2	NOUN
ejpam-2287	290	46	)	)	PUNCT
ejpam-2287	290	47	=	=	PRON
ejpam-2287	291	1	(	(	PUNCT
ejpam-2287	291	2	x	x	X
ejpam-2287	291	3	∗	∗	NOUN
ejpam-2287	291	4	2	2	NUM
ejpam-2287	291	5	,	,	PUNCT
ejpam-2287	291	6	y∗2	y∗2	NOUN
ejpam-2287	291	7	)	)	PUNCT
ejpam-2287	291	8	for	for	ADP
ejpam-2287	291	9	all	all	DET
ejpam-2287	291	10	(	(	PUNCT
ejpam-2287	291	11	x	x	INTJ
ejpam-2287	291	12	,	,	PUNCT
ejpam-2287	291	13	y	y	PROPN
ejpam-2287	291	14	)	)	PUNCT
ejpam-2287	291	15	∈	∈	PROPN
ejpam-2287	292	1	[	[	X
ejpam-2287	292	2	x∗1	x∗1	ADV
ejpam-2287	292	3	,	,	PUNCT
ejpam-2287	292	4	x∗2]×	x∗2]×	PROPN
ejpam-2287	293	1	[	[	X
ejpam-2287	293	2	y	y	PROPN
ejpam-2287	293	3	∗	∗	PROPN
ejpam-2287	293	4	1	1	NUM
ejpam-2287	293	5	,	,	PUNCT
ejpam-2287	293	6	[	[	X
ejpam-2287	293	7	y∗2	y∗2	NOUN
ejpam-2287	293	8	]	]	X
ejpam-2287	293	9	.	.	PUNCT
ejpam-2287	294	1	the	the	DET
ejpam-2287	294	2	proof	proof	NOUN
ejpam-2287	294	3	follows	follow	VERB
ejpam-2287	294	4	from	from	ADP
ejpam-2287	294	5	this	this	PRON
ejpam-2287	294	6	and	and	CCONJ
ejpam-2287	294	7	the	the	DET
ejpam-2287	294	8	theory	theory	NOUN
ejpam-2287	294	9	of	of	ADP
ejpam-2287	294	10	cooperative	cooperative	ADJ
ejpam-2287	294	11	maps	map	NOUN
ejpam-2287	294	12	.	.	PUNCT
ejpam-2287	295	1	the	the	DET
ejpam-2287	295	2	next	next	ADJ
ejpam-2287	295	3	two	two	NUM
ejpam-2287	295	4	propositions	proposition	NOUN
ejpam-2287	295	5	give	give	VERB
ejpam-2287	295	6	existence	existence	NOUN
ejpam-2287	295	7	and	and	CCONJ
ejpam-2287	295	8	uniqueness	uniqueness	ADJ
ejpam-2287	295	9	conditions	condition	NOUN
ejpam-2287	295	10	for	for	ADP
ejpam-2287	295	11	the	the	DET
ejpam-2287	295	12	real	real	ADJ
ejpam-2287	295	13	periodic	periodic	ADJ
ejpam-2287	295	14	solutions	solution	NOUN
ejpam-2287	295	15	of	of	ADP
ejpam-2287	295	16	equation	equation	NOUN
ejpam-2287	295	17	(	(	PUNCT
ejpam-2287	295	18	12	12	NUM
ejpam-2287	295	19	)	)	PUNCT
ejpam-2287	295	20	.	.	PUNCT
ejpam-2287	296	1	they	they	PRON
ejpam-2287	296	2	complete	complete	VERB
ejpam-2287	296	3	the	the	DET
ejpam-2287	296	4	proof	proof	NOUN
ejpam-2287	296	5	of	of	ADP
ejpam-2287	296	6	theorem	theorem	ADJ
ejpam-2287	296	7	3	3	NUM
ejpam-2287	296	8	and	and	CCONJ
ejpam-2287	296	9	are	be	AUX
ejpam-2287	296	10	as	as	SCONJ
ejpam-2287	296	11	follows	follow	VERB
ejpam-2287	296	12	.	.	PUNCT
ejpam-2287	297	1	proposition	proposition	NOUN
ejpam-2287	297	2	1	1	NUM
ejpam-2287	297	3	.	.	PUNCT
ejpam-2287	297	4	suppose	suppose	VERB
ejpam-2287	297	5	the	the	DET
ejpam-2287	297	6	hypotheses	hypothesis	NOUN
ejpam-2287	297	7	of	of	ADP
ejpam-2287	297	8	lemma	lemma	PROPN
ejpam-2287	297	9	2	2	NUM
ejpam-2287	297	10	hold	hold	NOUN
ejpam-2287	297	11	.	.	PUNCT
ejpam-2287	298	1	if	if	SCONJ
ejpam-2287	298	2	0	0	NUM
ejpam-2287	298	3	<	<	X
ejpam-2287	298	4	λµ	λµ	X
ejpam-2287	298	5	<	<	X
ejpam-2287	298	6	6.38	6.38	NUM
ejpam-2287	298	7	,	,	PUNCT
ejpam-2287	298	8	then	then	ADV
ejpam-2287	298	9	there	there	PRON
ejpam-2287	298	10	always	always	ADV
ejpam-2287	298	11	exists	exist	VERB
ejpam-2287	298	12	a	a	DET
ejpam-2287	298	13	unique	unique	ADJ
ejpam-2287	298	14	periodic	periodic	ADJ
ejpam-2287	298	15	solution	solution	NOUN
ejpam-2287	298	16	{	{	PUNCT
ejpam-2287	298	17	{	{	PUNCT
ejpam-2287	298	18	p1,q1	p1,q1	PROPN
ejpam-2287	298	19	}	}	PUNCT
ejpam-2287	298	20	,	,	PUNCT
ejpam-2287	298	21	{	{	PUNCT
ejpam-2287	298	22	p2,q2	p2,q2	PROPN
ejpam-2287	298	23	}	}	PUNCT
ejpam-2287	298	24	}	}	PUNCT
ejpam-2287	298	25	of	of	ADP
ejpam-2287	298	26	equation	equation	NOUN
ejpam-2287	298	27	(	(	PUNCT
ejpam-2287	298	28	12	12	NUM
ejpam-2287	298	29	)	)	PUNCT
ejpam-2287	298	30	in	in	ADP
ejpam-2287	298	31	the	the	DET
ejpam-2287	298	32	bounded	bounded	ADJ
ejpam-2287	298	33	regionr2∪	regionr2∪	NOUN
ejpam-2287	298	34	r4	r4	VERB
ejpam-2287	298	35	defined	define	VERB
ejpam-2287	298	36	by	by	ADP
ejpam-2287	298	37	(	(	PUNCT
ejpam-2287	298	38	28	28	NUM
ejpam-2287	298	39	)	)	PUNCT
ejpam-2287	298	40	.	.	PUNCT
ejpam-2287	299	1	this	this	DET
ejpam-2287	299	2	periodic	periodic	ADJ
ejpam-2287	299	3	solution	solution	NOUN
ejpam-2287	299	4	is	be	AUX
ejpam-2287	299	5	repelling	repel	VERB
ejpam-2287	299	6	in	in	ADP
ejpam-2287	299	7	nature	nature	NOUN
ejpam-2287	299	8	and	and	CCONJ
ejpam-2287	299	9	disappears	disappear	VERB
ejpam-2287	299	10	for	for	ADP
ejpam-2287	299	11	λµ≥	λµ≥	NOUN
ejpam-2287	299	12	6.38	6.38	NUM
ejpam-2287	299	13	.	.	PUNCT
ejpam-2287	300	1	proof	proof	NOUN
ejpam-2287	300	2	.	.	PUNCT
ejpam-2287	301	1	observe	observe	VERB
ejpam-2287	301	2	that	that	SCONJ
ejpam-2287	301	3	the	the	DET
ejpam-2287	301	4	θ	θ	PROPN
ejpam-2287	301	5	-intercepts	-intercept	NOUN
ejpam-2287	301	6	of	of	ADP
ejpam-2287	301	7	the	the	DET
ejpam-2287	301	8	equilibrium	equilibrium	NOUN
ejpam-2287	301	9	curves	curve	NOUN
ejpam-2287	301	10	e1	e1	PROPN
ejpam-2287	301	11	and	and	CCONJ
ejpam-2287	301	12	e2	e2	PROPN
ejpam-2287	301	13	of	of	ADP
ejpam-2287	301	14	the	the	DET
ejpam-2287	301	15	map	map	NOUN
ejpam-2287	301	16	t2(θ	t2(θ	X
ejpam-2287	301	17	,	,	PUNCT
ejpam-2287	301	18	u	u	NOUN
ejpam-2287	301	19	)	)	PUNCT
ejpam-2287	301	20	defined	define	VERB
ejpam-2287	301	21	in	in	ADP
ejpam-2287	301	22	(	(	PUNCT
ejpam-2287	301	23	16	16	NUM
ejpam-2287	301	24	)	)	PUNCT
ejpam-2287	301	25	are	be	AUX
ejpam-2287	301	26	respectively	respectively	ADV
ejpam-2287	301	27	given	give	VERB
ejpam-2287	301	28	by	by	ADP
ejpam-2287	301	29	e1	e1	NOUN
ejpam-2287	301	30	:	:	PUNCT
ejpam-2287	301	31	θ	θ	X
ejpam-2287	301	32	=	=	SYM
ejpam-2287	301	33	0	0	NUM
ejpam-2287	301	34	,	,	PUNCT
ejpam-2287	301	35	±0.645497	±0.645497	PROPN
ejpam-2287	301	36	æ	æ	PROPN
ejpam-2287	301	37	4.39−λµ	4.39−λµ	NUM
ejpam-2287	301	38	e2	e2	PROPN
ejpam-2287	301	39	:	:	PUNCT
ejpam-2287	302	1	θ	θ	X
ejpam-2287	302	2	=	=	SYM
ejpam-2287	302	3	0	0	NUM
ejpam-2287	302	4	,	,	PUNCT
ejpam-2287	302	5	±0.645497	±0.645497	PROPN
ejpam-2287	302	6	æ	æ	PROPN
ejpam-2287	302	7	3.39−λµ	3.39−λµ	NUM
ejpam-2287	302	8	(	(	PUNCT
ejpam-2287	302	9	29	29	NUM
ejpam-2287	302	10	)	)	PUNCT
ejpam-2287	302	11	it	it	PRON
ejpam-2287	302	12	follows	follow	VERB
ejpam-2287	302	13	that	that	SCONJ
ejpam-2287	302	14	if	if	SCONJ
ejpam-2287	302	15	0	0	NUM
ejpam-2287	302	16	<	<	X
ejpam-2287	302	17	λµ	λµ	X
ejpam-2287	302	18	<	<	X
ejpam-2287	302	19	3.39	3.39	NUM
ejpam-2287	302	20	,	,	PUNCT
ejpam-2287	302	21	then	then	ADV
ejpam-2287	302	22	both	both	DET
ejpam-2287	302	23	e1	e1	PROPN
ejpam-2287	302	24	and	and	CCONJ
ejpam-2287	302	25	e2	e2	PROPN
ejpam-2287	302	26	have	have	VERB
ejpam-2287	302	27	a	a	DET
ejpam-2287	302	28	positive	positive	ADJ
ejpam-2287	302	29	θ	θ	NOUN
ejpam-2287	302	30	-axis	-axis	NOUN
ejpam-2287	302	31	intercept	intercept	NOUN
ejpam-2287	302	32	and	and	CCONJ
ejpam-2287	302	33	a	a	DET
ejpam-2287	302	34	negative	negative	ADJ
ejpam-2287	302	35	θ	θ	PROPN
ejpam-2287	302	36	-axis	-axis	NOUN
ejpam-2287	302	37	intercept	intercept	NOUN
ejpam-2287	302	38	in	in	ADP
ejpam-2287	302	39	addition	addition	NOUN
ejpam-2287	302	40	to	to	ADP
ejpam-2287	302	41	the	the	DET
ejpam-2287	302	42	(	(	PUNCT
ejpam-2287	302	43	0,0)-intercept	0,0)-intercept	NUM
ejpam-2287	302	44	.	.	PUNCT
ejpam-2287	303	1	if	if	SCONJ
ejpam-2287	303	2	3.39≤	3.39≤	NOUN
ejpam-2287	303	3	λµ	λµ	X
ejpam-2287	303	4	<	<	X
ejpam-2287	303	5	4.39	4.39	NUM
ejpam-2287	303	6	,	,	PUNCT
ejpam-2287	303	7	then	then	ADV
ejpam-2287	303	8	only	only	ADV
ejpam-2287	303	9	e1	e1	NOUN
ejpam-2287	303	10	has	have	VERB
ejpam-2287	303	11	the	the	DET
ejpam-2287	303	12	two	two	NUM
ejpam-2287	303	13	nonzero	nonzero	ADJ
ejpam-2287	303	14	θ	θ	NUM
ejpam-2287	303	15	-axis	-axis	PROPN
ejpam-2287	303	16	intercepts	intercept	NOUN
ejpam-2287	303	17	.	.	PUNCT
ejpam-2287	304	1	and	and	CCONJ
ejpam-2287	304	2	if	if	SCONJ
ejpam-2287	304	3	4.39≤	4.39≤	PROPN
ejpam-2287	304	4	λµ	λµ	X
ejpam-2287	304	5	<	<	X
ejpam-2287	304	6	6.38	6.38	NUM
ejpam-2287	304	7	,	,	PUNCT
ejpam-2287	304	8	then	then	ADV
ejpam-2287	304	9	both	both	DET
ejpam-2287	304	10	e1	e1	PROPN
ejpam-2287	304	11	and	and	CCONJ
ejpam-2287	304	12	e2	e2	PROPN
ejpam-2287	304	13	have	have	VERB
ejpam-2287	304	14	only	only	ADV
ejpam-2287	304	15	the	the	DET
ejpam-2287	304	16	(	(	PUNCT
ejpam-2287	304	17	0,0)-intercept	0,0)-intercept	NUM
ejpam-2287	304	18	.	.	PUNCT
ejpam-2287	305	1	moreover	moreover	ADV
ejpam-2287	305	2	,	,	PUNCT
ejpam-2287	305	3	it	it	PRON
ejpam-2287	305	4	is	be	AUX
ejpam-2287	305	5	straightforward	straightforward	ADJ
ejpam-2287	305	6	to	to	PART
ejpam-2287	305	7	check	check	VERB
ejpam-2287	305	8	that	that	SCONJ
ejpam-2287	305	9	both	both	CCONJ
ejpam-2287	305	10	e1	e1	PROPN
ejpam-2287	305	11	and	and	CCONJ
ejpam-2287	305	12	e2	e2	PROPN
ejpam-2287	305	13	have	have	VERB
ejpam-2287	305	14	negative	negative	ADJ
ejpam-2287	305	15	slopes	slope	NOUN
ejpam-2287	305	16	inr2∪r4	inr2∪r4	NOUN
ejpam-2287	305	17	which	which	PRON
ejpam-2287	305	18	satisfy	satisfy	VERB
ejpam-2287	305	19	slope(e1	slope(e1	ADV
ejpam-2287	305	20	)	)	PUNCT
ejpam-2287	306	1	<	<	X
ejpam-2287	306	2	slope	slope	PROPN
ejpam-2287	306	3	(	(	PUNCT
ejpam-2287	306	4	e2	e2	PROPN
ejpam-2287	306	5	)	)	PUNCT
ejpam-2287	306	6	at	at	ADP
ejpam-2287	306	7	all	all	DET
ejpam-2287	306	8	three	three	NUM
ejpam-2287	306	9	θ	θ	PROPN
ejpam-2287	306	10	-intercepts	-intercept	NOUN
ejpam-2287	306	11	.	.	PUNCT
ejpam-2287	307	1	hence	hence	ADV
ejpam-2287	307	2	e1	e1	PROPN
ejpam-2287	307	3	and	and	CCONJ
ejpam-2287	307	4	e2	e2	PROPN
ejpam-2287	307	5	must	must	AUX
ejpam-2287	307	6	intersect	intersect	VERB
ejpam-2287	307	7	transversally	transversally	ADV
ejpam-2287	307	8	inr2∪r4	inr2∪r4	NOUN
ejpam-2287	307	9	whenever	whenever	SCONJ
ejpam-2287	307	10	0	0	NUM
ejpam-2287	307	11	<	<	X
ejpam-2287	307	12	λµ	λµ	X
ejpam-2287	307	13	<	<	X
ejpam-2287	307	14	6.38	6.38	NUM
ejpam-2287	307	15	.	.	PUNCT
ejpam-2287	308	1	if	if	SCONJ
ejpam-2287	308	2	λµ≥	λµ≥	PROPN
ejpam-2287	308	3	6.38	6.38	NUM
ejpam-2287	308	4	,	,	PUNCT
ejpam-2287	308	5	then	then	ADV
ejpam-2287	308	6	this	this	PRON
ejpam-2287	308	7	is	be	AUX
ejpam-2287	308	8	no	no	ADV
ejpam-2287	308	9	longer	long	ADV
ejpam-2287	308	10	true	true	ADJ
ejpam-2287	308	11	since	since	SCONJ
ejpam-2287	308	12	the	the	DET
ejpam-2287	308	13	slopes	slope	NOUN
ejpam-2287	308	14	of	of	ADP
ejpam-2287	308	15	e1	e1	PROPN
ejpam-2287	308	16	and	and	CCONJ
ejpam-2287	308	17	e2	e2	PROPN
ejpam-2287	308	18	now	now	ADV
ejpam-2287	308	19	satisfy	satisfy	VERB
ejpam-2287	308	20	slope(e1	slope(e1	ADV
ejpam-2287	308	21	)	)	PUNCT
ejpam-2287	309	1	=	=	SYM
ejpam-2287	309	2	slope	slope	NOUN
ejpam-2287	309	3	(	(	PUNCT
ejpam-2287	309	4	e2	e2	PROPN
ejpam-2287	309	5	)	)	PUNCT
ejpam-2287	309	6	at	at	ADP
ejpam-2287	309	7	the	the	DET
ejpam-2287	309	8	origin	origin	NOUN
ejpam-2287	309	9	.	.	PUNCT
ejpam-2287	310	1	the	the	DET
ejpam-2287	310	2	various	various	ADJ
ejpam-2287	310	3	scenarios	scenario	NOUN
ejpam-2287	310	4	are	be	AUX
ejpam-2287	310	5	shown	show	VERB
ejpam-2287	310	6	in	in	ADP
ejpam-2287	310	7	figure	figure	NOUN
ejpam-2287	310	8	3	3	NUM
ejpam-2287	310	9	.	.	PUNCT
ejpam-2287	311	1	the	the	DET
ejpam-2287	311	2	repelling	repel	VERB
ejpam-2287	311	3	nature	nature	NOUN
ejpam-2287	311	4	of	of	ADP
ejpam-2287	311	5	{	{	PUNCT
ejpam-2287	311	6	{	{	PUNCT
ejpam-2287	311	7	p1,q1	p1,q1	PROPN
ejpam-2287	311	8	}	}	PUNCT
ejpam-2287	311	9	,	,	PUNCT
ejpam-2287	311	10	{	{	PUNCT
ejpam-2287	311	11	p2,q2	p2,q2	PROPN
ejpam-2287	311	12	}	}	PUNCT
ejpam-2287	311	13	}	}	PUNCT
ejpam-2287	311	14	is	be	AUX
ejpam-2287	311	15	a	a	DET
ejpam-2287	311	16	direct	direct	ADJ
ejpam-2287	311	17	consequence	consequence	NOUN
ejpam-2287	311	18	of	of	ADP
ejpam-2287	311	19	the	the	DET
ejpam-2287	311	20	fact	fact	NOUN
ejpam-2287	311	21	that	that	SCONJ
ejpam-2287	311	22	t	t	PROPN
ejpam-2287	311	23	(	(	PUNCT
ejpam-2287	311	24	r2	r2	PROPN
ejpam-2287	311	25	)	)	PUNCT
ejpam-2287	311	26	⊆r1	⊆r1	PROPN
ejpam-2287	311	27	and	and	CCONJ
ejpam-2287	311	28	t	t	PROPN
ejpam-2287	311	29	(	(	PUNCT
ejpam-2287	311	30	r4	r4	PROPN
ejpam-2287	311	31	)	)	PUNCT
ejpam-2287	311	32	⊆r3	⊆r3	NUM
ejpam-2287	311	33	by	by	ADP
ejpam-2287	311	34	lemma	lemma	PROPN
ejpam-2287	311	35	4	4	NUM
ejpam-2287	311	36	.	.	PUNCT
ejpam-2287	311	37	s.	s.	PROPN
ejpam-2287	311	38	basu	basu	PROPN
ejpam-2287	311	39	/	/	SYM
ejpam-2287	311	40	eur	eur	PROPN
ejpam-2287	311	41	.	.	PUNCT
ejpam-2287	312	1	j.	j.	PROPN
ejpam-2287	312	2	pure	pure	PROPN
ejpam-2287	312	3	appl	appl	PROPN
ejpam-2287	312	4	.	.	PROPN
ejpam-2287	312	5	math	math	PROPN
ejpam-2287	312	6	,	,	PUNCT
ejpam-2287	312	7	7	7	NUM
ejpam-2287	312	8	(	(	PUNCT
ejpam-2287	312	9	2014	2014	NUM
ejpam-2287	312	10	)	)	PUNCT
ejpam-2287	312	11	,	,	PUNCT
ejpam-2287	312	12	442	442	NUM
ejpam-2287	312	13	-	-	SYM
ejpam-2287	312	14	461	461	NUM
ejpam-2287	312	15	456	456	NUM
ejpam-2287	312	16	-2	-2	INTJ
ejpam-2287	312	17	-1	-1	SYM
ejpam-2287	312	18	0	0	NUM
ejpam-2287	312	19	1	1	NUM
ejpam-2287	312	20	2	2	NUM
ejpam-2287	312	21	-3	-3	INTJ
ejpam-2287	312	22	-2	-2	NOUN
ejpam-2287	313	1	-1	-1	SYM
ejpam-2287	313	2	0	0	NUM
ejpam-2287	314	1	1	1	NUM
ejpam-2287	314	2	2	2	NUM
ejpam-2287	314	3	3	3	NUM
ejpam-2287	314	4	(	(	PUNCT
ejpam-2287	314	5	a	a	X
ejpam-2287	314	6	)	)	PUNCT
ejpam-2287	314	7	0	0	NUM
ejpam-2287	314	8	<	<	X
ejpam-2287	314	9	λµ	λµ	X
ejpam-2287	314	10	<	<	X
ejpam-2287	314	11	3.39	3.39	NUM
ejpam-2287	314	12	-2	-2	INTJ
ejpam-2287	314	13	-1	-1	NOUN
ejpam-2287	314	14	0	0	NUM
ejpam-2287	314	15	1	1	NUM
ejpam-2287	314	16	2	2	NUM
ejpam-2287	314	17	-3	-3	INTJ
ejpam-2287	314	18	-2	-2	NOUN
ejpam-2287	314	19	-1	-1	SYM
ejpam-2287	314	20	0	0	NUM
ejpam-2287	315	1	1	1	NUM
ejpam-2287	315	2	2	2	NUM
ejpam-2287	315	3	3	3	NUM
ejpam-2287	315	4	(	(	PUNCT
ejpam-2287	315	5	b	b	NOUN
ejpam-2287	315	6	)	)	PUNCT
ejpam-2287	315	7	3.39≤	3.39≤	NOUN
ejpam-2287	315	8	λµ	λµ	ADP
ejpam-2287	315	9	<	<	X
ejpam-2287	315	10	4.39	4.39	NUM
ejpam-2287	315	11	-2	-2	INTJ
ejpam-2287	315	12	-1	-1	NOUN
ejpam-2287	315	13	0	0	NUM
ejpam-2287	315	14	1	1	NUM
ejpam-2287	315	15	2	2	NUM
ejpam-2287	315	16	-3	-3	INTJ
ejpam-2287	315	17	-2	-2	NOUN
ejpam-2287	316	1	-1	-1	SYM
ejpam-2287	316	2	0	0	NUM
ejpam-2287	317	1	1	1	NUM
ejpam-2287	317	2	2	2	NUM
ejpam-2287	317	3	3	3	NUM
ejpam-2287	317	4	(	(	PUNCT
ejpam-2287	317	5	c	c	NOUN
ejpam-2287	317	6	)	)	PUNCT
ejpam-2287	317	7	4.39≤	4.39≤	NOUN
ejpam-2287	317	8	λµ	λµ	ADP
ejpam-2287	317	9	<	<	X
ejpam-2287	317	10	6.38	6.38	NUM
ejpam-2287	317	11	-2	-2	NOUN
ejpam-2287	317	12	-1	-1	NOUN
ejpam-2287	317	13	0	0	NUM
ejpam-2287	317	14	1	1	NUM
ejpam-2287	317	15	2	2	NUM
ejpam-2287	317	16	-3	-3	INTJ
ejpam-2287	317	17	-2	-2	NOUN
ejpam-2287	317	18	-1	-1	SYM
ejpam-2287	317	19	0	0	NUM
ejpam-2287	318	1	1	1	NUM
ejpam-2287	318	2	2	2	NUM
ejpam-2287	318	3	3	3	NUM
ejpam-2287	318	4	(	(	PUNCT
ejpam-2287	318	5	d	d	NOUN
ejpam-2287	318	6	)	)	PUNCT
ejpam-2287	318	7	λµ≥	λµ≥	NOUN
ejpam-2287	318	8	6.38	6.38	NUM
ejpam-2287	318	9	figure	figure	NOUN
ejpam-2287	318	10	3	3	NUM
ejpam-2287	318	11	:	:	PUNCT
ejpam-2287	318	12	diagram	diagram	NOUN
ejpam-2287	318	13	showing	show	VERB
ejpam-2287	318	14	the	the	DET
ejpam-2287	318	15	nontrivial	nontrivial	ADJ
ejpam-2287	318	16	periodic	periodic	ADJ
ejpam-2287	318	17	solution	solution	NOUN
ejpam-2287	318	18	in	in	ADP
ejpam-2287	318	19	r2	r2	PROPN
ejpam-2287	318	20	∪r4	∪r4	PROPN
ejpam-2287	318	21	along	along	ADP
ejpam-2287	318	22	with	with	ADP
ejpam-2287	318	23	the	the	DET
ejpam-2287	318	24	(	(	PUNCT
ejpam-2287	318	25	0,0	0,0	NOUN
ejpam-2287	318	26	)	)	PUNCT
ejpam-2287	318	27	equilibrium	equilibrium	NOUN
ejpam-2287	318	28	.	.	PUNCT
ejpam-2287	319	1	proposition	proposition	NOUN
ejpam-2287	319	2	2	2	NUM
ejpam-2287	319	3	.	.	PUNCT
ejpam-2287	319	4	suppose	suppose	VERB
ejpam-2287	319	5	the	the	DET
ejpam-2287	319	6	hypotheses	hypothesis	NOUN
ejpam-2287	319	7	of	of	ADP
ejpam-2287	319	8	lemma	lemma	PROPN
ejpam-2287	319	9	2	2	NUM
ejpam-2287	319	10	hold	hold	NOUN
ejpam-2287	319	11	.	.	PUNCT
ejpam-2287	320	1	if	if	SCONJ
ejpam-2287	320	2	0	0	NUM
ejpam-2287	320	3	<	<	X
ejpam-2287	320	4	λµ	λµ	X
ejpam-2287	320	5	<	<	X
ejpam-2287	320	6	2.4	2.4	NUM
ejpam-2287	320	7	,	,	PUNCT
ejpam-2287	320	8	then	then	ADV
ejpam-2287	320	9	there	there	PRON
ejpam-2287	320	10	always	always	ADV
ejpam-2287	320	11	exists	exist	VERB
ejpam-2287	320	12	a	a	DET
ejpam-2287	320	13	unique	unique	ADJ
ejpam-2287	320	14	periodic	periodic	ADJ
ejpam-2287	320	15	solution	solution	NOUN
ejpam-2287	320	16	{	{	PUNCT
ejpam-2287	320	17	{	{	PUNCT
ejpam-2287	320	18	s1	s1	NOUN
ejpam-2287	320	19	,	,	PUNCT
ejpam-2287	320	20	t1	t1	NOUN
ejpam-2287	320	21	}	}	PUNCT
ejpam-2287	320	22	,	,	PUNCT
ejpam-2287	320	23	{	{	PUNCT
ejpam-2287	320	24	s2	s2	NOUN
ejpam-2287	320	25	,	,	PUNCT
ejpam-2287	320	26	t2	t2	NOUN
ejpam-2287	320	27	}	}	PUNCT
ejpam-2287	320	28	}	}	PUNCT
ejpam-2287	320	29	of	of	ADP
ejpam-2287	320	30	equation	equation	NOUN
ejpam-2287	320	31	(	(	PUNCT
ejpam-2287	320	32	12	12	NUM
ejpam-2287	320	33	)	)	PUNCT
ejpam-2287	320	34	in	in	ADP
ejpam-2287	320	35	the	the	DET
ejpam-2287	320	36	bounded	bounded	ADJ
ejpam-2287	320	37	regionr1∪r3	regionr1∪r3	PROPN
ejpam-2287	320	38	defined	define	VERB
ejpam-2287	320	39	by	by	ADP
ejpam-2287	320	40	(	(	PUNCT
ejpam-2287	320	41	28	28	NUM
ejpam-2287	320	42	)	)	PUNCT
ejpam-2287	320	43	.	.	PUNCT
ejpam-2287	321	1	this	this	DET
ejpam-2287	321	2	periodic	periodic	ADJ
ejpam-2287	321	3	solution	solution	NOUN
ejpam-2287	321	4	is	be	AUX
ejpam-2287	321	5	locally	locally	ADV
ejpam-2287	321	6	asymptotically	asymptotically	ADV
ejpam-2287	321	7	stable	stable	ADJ
ejpam-2287	321	8	and	and	CCONJ
ejpam-2287	321	9	disappears	disappear	VERB
ejpam-2287	321	10	for	for	ADP
ejpam-2287	321	11	λµ≥	λµ≥	NOUN
ejpam-2287	321	12	2.4	2.4	NUM
ejpam-2287	321	13	.	.	PUNCT
ejpam-2287	322	1	proof	proof	NOUN
ejpam-2287	322	2	.	.	PUNCT
ejpam-2287	323	1	we	we	PRON
ejpam-2287	323	2	prove	prove	VERB
ejpam-2287	323	3	uniqueness	uniqueness	NOUN
ejpam-2287	323	4	of	of	ADP
ejpam-2287	323	5	the	the	DET
ejpam-2287	323	6	locally	locally	ADV
ejpam-2287	323	7	asymptotically	asymptotically	ADV
ejpam-2287	323	8	stable	stable	ADJ
ejpam-2287	323	9	periodic	periodic	ADJ
ejpam-2287	323	10	solution	solution	NOUN
ejpam-2287	323	11	{	{	PUNCT
ejpam-2287	323	12	{	{	PUNCT
ejpam-2287	323	13	s1	s1	NOUN
ejpam-2287	323	14	,	,	PUNCT
ejpam-2287	323	15	t1	t1	NOUN
ejpam-2287	323	16	}	}	PUNCT
ejpam-2287	323	17	,	,	PUNCT
ejpam-2287	323	18	{	{	PUNCT
ejpam-2287	323	19	s2	s2	NOUN
ejpam-2287	323	20	,	,	PUNCT
ejpam-2287	323	21	t2	t2	NOUN
ejpam-2287	323	22	}	}	PUNCT
ejpam-2287	323	23	}	}	PUNCT
ejpam-2287	323	24	by	by	ADP
ejpam-2287	323	25	contradiction	contradiction	NOUN
ejpam-2287	323	26	.	.	PUNCT
ejpam-2287	324	1	suppose	suppose	VERB
ejpam-2287	324	2	there	there	PRON
ejpam-2287	324	3	exists	exist	VERB
ejpam-2287	324	4	a	a	DET
ejpam-2287	324	5	second	second	ADJ
ejpam-2287	324	6	periodic	periodic	ADJ
ejpam-2287	324	7	solution	solution	NOUN
ejpam-2287	324	8	,	,	PUNCT
ejpam-2287	324	9	say	say	VERB
ejpam-2287	324	10	{	{	PUNCT
ejpam-2287	324	11	{	{	PUNCT
ejpam-2287	324	12	v1	v1	NOUN
ejpam-2287	324	13	,	,	PUNCT
ejpam-2287	324	14	w1	w1	NOUN
ejpam-2287	324	15	}	}	PUNCT
ejpam-2287	324	16	,	,	PUNCT
ejpam-2287	324	17	{	{	PUNCT
ejpam-2287	324	18	v2	v2	NOUN
ejpam-2287	324	19	,	,	PUNCT
ejpam-2287	324	20	w2	w2	NOUN
ejpam-2287	324	21	}	}	PUNCT
ejpam-2287	324	22	}	}	PUNCT
ejpam-2287	324	23	,	,	PUNCT
ejpam-2287	324	24	of	of	ADP
ejpam-2287	324	25	equation	equation	NOUN
ejpam-2287	324	26	(	(	PUNCT
ejpam-2287	324	27	2	2	NUM
ejpam-2287	324	28	)	)	PUNCT
ejpam-2287	324	29	in	in	ADP
ejpam-2287	324	30	r1	r1	PROPN
ejpam-2287	324	31	∪r3	∪r3	NUM
ejpam-2287	324	32	.	.	PUNCT
ejpam-2287	325	1	then	then	ADV
ejpam-2287	325	2	it	it	PRON
ejpam-2287	325	3	must	must	AUX
ejpam-2287	325	4	satisfy	satisfy	VERB
ejpam-2287	325	5	{	{	PUNCT
ejpam-2287	325	6	v1	v1	PROPN
ejpam-2287	325	7	,	,	PUNCT
ejpam-2287	325	8	w1	w1	NOUN
ejpam-2287	325	9	}	}	PUNCT
ejpam-2287	325	10	�	�	PROPN
ejpam-2287	325	11	ne	ne	PROPN
ejpam-2287	325	12	{	{	PUNCT
ejpam-2287	325	13	s1	s1	PROPN
ejpam-2287	325	14	,	,	PUNCT
ejpam-2287	325	15	t1	t1	NOUN
ejpam-2287	325	16	}	}	PUNCT
ejpam-2287	325	17	�	�	PROPN
ejpam-2287	325	18	ne	ne	PROPN
ejpam-2287	325	19	(	(	PUNCT
ejpam-2287	325	20	0,0)	0,0)	PROPN
ejpam-2287	325	21	�	�	PROPN
ejpam-2287	325	22	ne	ne	PROPN
ejpam-2287	325	23	{	{	PUNCT
ejpam-2287	325	24	s2	s2	PROPN
ejpam-2287	325	25	,	,	PUNCT
ejpam-2287	325	26	t2	t2	NOUN
ejpam-2287	325	27	}	}	PUNCT
ejpam-2287	325	28	�	�	PROPN
ejpam-2287	325	29	ne	ne	PROPN
ejpam-2287	325	30	{	{	PUNCT
ejpam-2287	325	31	v2	v2	PROPN
ejpam-2287	325	32	,	,	PUNCT
ejpam-2287	325	33	w2	w2	NOUN
ejpam-2287	325	34	}	}	PUNCT
ejpam-2287	325	35	(	(	PUNCT
ejpam-2287	325	36	30	30	NUM
ejpam-2287	325	37	)	)	PUNCT
ejpam-2287	325	38	otherwise	otherwise	ADV
ejpam-2287	325	39	if	if	SCONJ
ejpam-2287	325	40	{	{	PUNCT
ejpam-2287	325	41	v1	v1	NOUN
ejpam-2287	325	42	,	,	PUNCT
ejpam-2287	325	43	w1	w1	NOUN
ejpam-2287	325	44	}	}	PUNCT
ejpam-2287	325	45	�	�	PROPN
ejpam-2287	325	46	se	se	PROPN
ejpam-2287	325	47	{	{	PUNCT
ejpam-2287	325	48	s1	s1	PROPN
ejpam-2287	325	49	,	,	PUNCT
ejpam-2287	325	50	t1	t1	NOUN
ejpam-2287	325	51	}	}	PUNCT
ejpam-2287	325	52	,	,	PUNCT
ejpam-2287	325	53	then	then	ADV
ejpam-2287	325	54	the	the	DET
ejpam-2287	325	55	fact	fact	NOUN
ejpam-2287	325	56	that	that	SCONJ
ejpam-2287	325	57	{	{	PUNCT
ejpam-2287	325	58	v1	v1	NOUN
ejpam-2287	325	59	,	,	PUNCT
ejpam-2287	325	60	w1	w1	NOUN
ejpam-2287	325	61	}	}	PUNCT
ejpam-2287	325	62	�	�	PROPN
ejpam-2287	325	63	ne	ne	PROPN
ejpam-2287	325	64	(	(	PUNCT
ejpam-2287	325	65	0,0	0,0	NOUN
ejpam-2287	325	66	)	)	PUNCT
ejpam-2287	325	67	,	,	PUNCT
ejpam-2287	325	68	an	an	DET
ejpam-2287	325	69	unstable	unstable	ADJ
ejpam-2287	325	70	fixed	fix	VERB
ejpam-2287	325	71	point	point	NOUN
ejpam-2287	325	72	of	of	ADP
ejpam-2287	325	73	t2(θ	t2(θ	PROPN
ejpam-2287	325	74	,	,	PUNCT
ejpam-2287	325	75	u	u	NOUN
ejpam-2287	325	76	)	)	PUNCT
ejpam-2287	325	77	by	by	ADP
ejpam-2287	325	78	lemma	lemma	PROPN
ejpam-2287	325	79	1	1	NUM
ejpam-2287	325	80	,	,	PUNCT
ejpam-2287	325	81	along	along	ADP
ejpam-2287	325	82	with	with	ADP
ejpam-2287	325	83	lemma	lemma	PROPN
ejpam-2287	325	84	5	5	NUM
ejpam-2287	325	85	would	would	AUX
ejpam-2287	325	86	imply	imply	VERB
ejpam-2287	325	87	that	that	SCONJ
ejpam-2287	325	88	{	{	PUNCT
ejpam-2287	325	89	v1	v1	NOUN
ejpam-2287	325	90	,	,	PUNCT
ejpam-2287	325	91	w1	w1	NOUN
ejpam-2287	325	92	}	}	PUNCT
ejpam-2287	325	93	is	be	AUX
ejpam-2287	325	94	locally	locally	ADV
ejpam-2287	325	95	asymptotically	asymptotically	ADV
ejpam-2287	325	96	stable	stable	ADJ
ejpam-2287	325	97	.	.	PUNCT
ejpam-2287	326	1	this	this	PRON
ejpam-2287	326	2	would	would	AUX
ejpam-2287	326	3	make	make	VERB
ejpam-2287	326	4	{	{	PUNCT
ejpam-2287	326	5	v1	v1	NOUN
ejpam-2287	326	6	,	,	PUNCT
ejpam-2287	326	7	w1	w1	NOUN
ejpam-2287	326	8	}	}	PUNCT
ejpam-2287	326	9	and	and	CCONJ
ejpam-2287	326	10	{	{	PUNCT
ejpam-2287	326	11	s1	s1	NOUN
ejpam-2287	326	12	,	,	PUNCT
ejpam-2287	326	13	t1	t1	NOUN
ejpam-2287	326	14	}	}	PUNCT
ejpam-2287	326	15	locally	locally	ADV
ejpam-2287	326	16	asymptotically	asymptotically	ADV
ejpam-2287	326	17	stable	stable	ADJ
ejpam-2287	326	18	neighbors	neighbor	NOUN
ejpam-2287	326	19	in	in	ADP
ejpam-2287	326	20	the	the	DET
ejpam-2287	326	21	“	"	PUNCT
ejpam-2287	326	22	�	�	PROPN
ejpam-2287	326	23	se	se	NOUN
ejpam-2287	326	24	”	"	PUNCT
ejpam-2287	326	25	ordering	ordering	NOUN
ejpam-2287	326	26	,	,	PUNCT
ejpam-2287	326	27	contradicting	contradict	VERB
ejpam-2287	326	28	a	a	DET
ejpam-2287	326	29	theorem	theorem	NOUN
ejpam-2287	326	30	by	by	ADP
ejpam-2287	326	31	dancer	dancer	NOUN
ejpam-2287	326	32	and	and	CCONJ
ejpam-2287	326	33	hess	hess	NOUN
ejpam-2287	326	34	in	in	ADP
ejpam-2287	326	35	[	[	X
ejpam-2287	326	36	5	5	NUM
ejpam-2287	326	37	]	]	PUNCT
ejpam-2287	326	38	which	which	PRON
ejpam-2287	326	39	says	say	VERB
ejpam-2287	326	40	that	that	SCONJ
ejpam-2287	326	41	stable	stable	ADJ
ejpam-2287	326	42	and	and	CCONJ
ejpam-2287	326	43	unstable	unstable	ADJ
ejpam-2287	326	44	fixed	fix	VERB
ejpam-2287	326	45	points	point	NOUN
ejpam-2287	326	46	of	of	ADP
ejpam-2287	326	47	an	an	DET
ejpam-2287	326	48	order	order	NOUN
ejpam-2287	326	49	-	-	PUNCT
ejpam-2287	326	50	preserving	preserve	VERB
ejpam-2287	326	51	map	map	NOUN
ejpam-2287	326	52	must	must	AUX
ejpam-2287	326	53	alternate	alternate	VERB
ejpam-2287	326	54	.	.	PUNCT
ejpam-2287	327	1	hence	hence	ADV
ejpam-2287	327	2	{	{	PUNCT
ejpam-2287	327	3	{	{	PUNCT
ejpam-2287	327	4	v1	v1	NOUN
ejpam-2287	327	5	,	,	PUNCT
ejpam-2287	327	6	w1	w1	NOUN
ejpam-2287	327	7	}	}	PUNCT
ejpam-2287	327	8	,	,	PUNCT
ejpam-2287	327	9	{	{	PUNCT
ejpam-2287	327	10	v2	v2	NOUN
ejpam-2287	327	11	,	,	PUNCT
ejpam-2287	327	12	w2}}must	w2}}must	AUX
ejpam-2287	327	13	be	be	AUX
ejpam-2287	327	14	an	an	DET
ejpam-2287	327	15	unstable	unstable	ADJ
ejpam-2287	327	16	periodic	periodic	ADJ
ejpam-2287	327	17	solution	solution	NOUN
ejpam-2287	327	18	of	of	ADP
ejpam-2287	327	19	(	(	PUNCT
ejpam-2287	327	20	28	28	NUM
ejpam-2287	327	21	)	)	PUNCT
ejpam-2287	327	22	satisfying	satisfy	VERB
ejpam-2287	327	23	the	the	DET
ejpam-2287	327	24	“	"	PUNCT
ejpam-2287	327	25	�	�	PROPN
ejpam-2287	327	26	ne	ne	PROPN
ejpam-2287	327	27	”	"	PUNCT
ejpam-2287	327	28	ordering	order	VERB
ejpam-2287	327	29	s.	s.	PROPN
ejpam-2287	327	30	basu	basu	PROPN
ejpam-2287	327	31	/	/	SYM
ejpam-2287	327	32	eur	eur	PROPN
ejpam-2287	327	33	.	.	PUNCT
ejpam-2287	328	1	j.	j.	PROPN
ejpam-2287	328	2	pure	pure	PROPN
ejpam-2287	328	3	appl	appl	PROPN
ejpam-2287	328	4	.	.	PROPN
ejpam-2287	328	5	math	math	PROPN
ejpam-2287	328	6	,	,	PUNCT
ejpam-2287	328	7	7	7	NUM
ejpam-2287	328	8	(	(	PUNCT
ejpam-2287	328	9	2014	2014	NUM
ejpam-2287	328	10	)	)	PUNCT
ejpam-2287	328	11	,	,	PUNCT
ejpam-2287	328	12	442	442	NUM
ejpam-2287	328	13	-	-	SYM
ejpam-2287	328	14	461	461	NUM
ejpam-2287	328	15	457	457	NUM
ejpam-2287	328	16	in	in	ADP
ejpam-2287	328	17	(	(	PUNCT
ejpam-2287	328	18	30	30	NUM
ejpam-2287	328	19	)	)	PUNCT
ejpam-2287	328	20	.	.	PUNCT
ejpam-2287	329	1	however	however	ADV
ejpam-2287	329	2	in	in	ADP
ejpam-2287	329	3	this	this	DET
ejpam-2287	329	4	case	case	NOUN
ejpam-2287	329	5	,	,	PUNCT
ejpam-2287	329	6	the	the	DET
ejpam-2287	329	7	invariant	invariant	ADJ
ejpam-2287	329	8	region	region	NOUN
ejpam-2287	329	9	defined	define	VERB
ejpam-2287	329	10	by	by	ADP
ejpam-2287	329	11	[	[	X
ejpam-2287	329	12	−m1	−m1	PROPN
ejpam-2287	329	13	,	,	PUNCT
ejpam-2287	329	14	v1]×	v1]×	PROPN
ejpam-2287	329	15	[	[	X
ejpam-2287	329	16	−m2	−m2	PROPN
ejpam-2287	329	17	,	,	PUNCT
ejpam-2287	329	18	w1	w1	NOUN
ejpam-2287	329	19	]	]	PUNCT
ejpam-2287	329	20	can	can	AUX
ejpam-2287	329	21	not	not	PART
ejpam-2287	329	22	contain	contain	VERB
ejpam-2287	329	23	a	a	DET
ejpam-2287	329	24	locally	locally	ADV
ejpam-2287	329	25	asymptotically	asymptotically	ADV
ejpam-2287	329	26	stable	stable	ADJ
ejpam-2287	329	27	fixed	fix	VERB
ejpam-2287	329	28	point	point	NOUN
ejpam-2287	329	29	of	of	ADP
ejpam-2287	329	30	the	the	DET
ejpam-2287	329	31	cooperative	cooperative	ADJ
ejpam-2287	329	32	map	map	NOUN
ejpam-2287	329	33	t2	t2	NOUN
ejpam-2287	329	34	,	,	PUNCT
ejpam-2287	329	35	contradicting	contradict	VERB
ejpam-2287	329	36	lemma	lemma	PROPN
ejpam-2287	329	37	5	5	NUM
ejpam-2287	329	38	.	.	PUNCT
ejpam-2287	329	39	there	there	PRON
ejpam-2287	329	40	also	also	ADV
ejpam-2287	329	41	can	can	AUX
ejpam-2287	329	42	not	not	PART
ejpam-2287	329	43	exist	exist	VERB
ejpam-2287	329	44	an	an	DET
ejpam-2287	329	45	additional	additional	ADJ
ejpam-2287	329	46	stable	stable	ADJ
ejpam-2287	329	47	periodic	periodic	ADJ
ejpam-2287	329	48	solution	solution	NOUN
ejpam-2287	329	49	to	to	PART
ejpam-2287	329	50	get	get	VERB
ejpam-2287	329	51	around	around	ADP
ejpam-2287	329	52	this	this	DET
ejpam-2287	329	53	problem	problem	NOUN
ejpam-2287	329	54	because	because	SCONJ
ejpam-2287	329	55	if	if	SCONJ
ejpam-2287	329	56	it	it	PRON
ejpam-2287	329	57	did	do	VERB
ejpam-2287	329	58	,	,	PUNCT
ejpam-2287	329	59	then	then	ADV
ejpam-2287	329	60	we	we	PRON
ejpam-2287	329	61	would	would	AUX
ejpam-2287	329	62	have	have	VERB
ejpam-2287	329	63	two	two	NUM
ejpam-2287	329	64	unstable	unstable	ADJ
ejpam-2287	329	65	periodic	periodic	ADJ
ejpam-2287	329	66	solutions	solution	NOUN
ejpam-2287	329	67	including	include	VERB
ejpam-2287	329	68	the	the	DET
ejpam-2287	329	69	repelling	repelling	NOUN
ejpam-2287	329	70	equilibrium	equilibrium	NOUN
ejpam-2287	329	71	(	(	PUNCT
ejpam-2287	329	72	0,0	0,0	NUM
ejpam-2287	329	73	)	)	PUNCT
ejpam-2287	329	74	alternating	alternate	VERB
ejpam-2287	329	75	with	with	ADP
ejpam-2287	329	76	two	two	NUM
ejpam-2287	329	77	stable	stable	ADJ
ejpam-2287	329	78	periodic	periodic	ADJ
ejpam-2287	329	79	solutions	solution	NOUN
ejpam-2287	329	80	including	include	VERB
ejpam-2287	329	81	{	{	PUNCT
ejpam-2287	329	82	{	{	PUNCT
ejpam-2287	329	83	s1	s1	NOUN
ejpam-2287	329	84	,	,	PUNCT
ejpam-2287	329	85	t1	t1	NOUN
ejpam-2287	329	86	}	}	PUNCT
ejpam-2287	329	87	,	,	PUNCT
ejpam-2287	329	88	{	{	PUNCT
ejpam-2287	329	89	s2	s2	NOUN
ejpam-2287	329	90	,	,	PUNCT
ejpam-2287	329	91	t2	t2	NOUN
ejpam-2287	329	92	}	}	PUNCT
ejpam-2287	329	93	}	}	PUNCT
ejpam-2287	329	94	in	in	ADP
ejpam-2287	329	95	the	the	DET
ejpam-2287	329	96	�	�	PROPN
ejpam-2287	329	97	ne	ne	PROPN
ejpam-2287	329	98	ordering	ordering	NOUN
ejpam-2287	329	99	of	of	ADP
ejpam-2287	329	100	periodic	periodic	ADJ
ejpam-2287	329	101	solutions	solution	NOUN
ejpam-2287	329	102	.	.	PUNCT
ejpam-2287	330	1	however	however	ADV
ejpam-2287	330	2	,	,	PUNCT
ejpam-2287	330	3	this	this	PRON
ejpam-2287	330	4	would	would	AUX
ejpam-2287	330	5	leave	leave	VERB
ejpam-2287	330	6	no	no	DET
ejpam-2287	330	7	room	room	NOUN
ejpam-2287	330	8	to	to	PART
ejpam-2287	330	9	fit	fit	VERB
ejpam-2287	330	10	the	the	DET
ejpam-2287	330	11	two	two	NUM
ejpam-2287	330	12	nonzero	nonzero	ADJ
ejpam-2287	330	13	unstable	unstable	ADJ
ejpam-2287	330	14	equilibria	equilibrium	NOUN
ejpam-2287	330	15	e2	e2	NOUN
ejpam-2287	330	16	and	and	CCONJ
ejpam-2287	330	17	e3	e3	PROPN
ejpam-2287	330	18	,	,	PUNCT
ejpam-2287	330	19	which	which	PRON
ejpam-2287	330	20	also	also	ADV
ejpam-2287	330	21	exist	exist	VERB
ejpam-2287	330	22	in	in	ADP
ejpam-2287	330	23	this	this	DET
ejpam-2287	330	24	case	case	NOUN
ejpam-2287	330	25	by	by	ADP
ejpam-2287	330	26	theorem	theorem	NOUN
ejpam-2287	330	27	2	2	NUM
ejpam-2287	330	28	part	part	NOUN
ejpam-2287	330	29	1	1	NUM
ejpam-2287	330	30	,	,	PUNCT
ejpam-2287	330	31	in	in	ADP
ejpam-2287	330	32	this	this	DET
ejpam-2287	330	33	ordering	ordering	NOUN
ejpam-2287	330	34	without	without	ADP
ejpam-2287	330	35	having	have	VERB
ejpam-2287	330	36	two	two	NUM
ejpam-2287	330	37	unstable	unstable	ADJ
ejpam-2287	330	38	equilibria	equilibrium	NOUN
ejpam-2287	330	39	as	as	ADP
ejpam-2287	330	40	neighbors	neighbor	NOUN
ejpam-2287	330	41	,	,	PUNCT
ejpam-2287	330	42	thus	thus	ADV
ejpam-2287	330	43	violating	violate	VERB
ejpam-2287	330	44	dancer	dancer	NOUN
ejpam-2287	330	45	and	and	CCONJ
ejpam-2287	330	46	hess	hess	NOUN
ejpam-2287	330	47	’	'	PUNCT
ejpam-2287	330	48	result	result	NOUN
ejpam-2287	330	49	in	in	ADP
ejpam-2287	330	50	[	[	X
ejpam-2287	330	51	5	5	NUM
ejpam-2287	330	52	]	]	PUNCT
ejpam-2287	330	53	once	once	ADV
ejpam-2287	330	54	again	again	ADV
ejpam-2287	330	55	.	.	PUNCT
ejpam-2287	331	1	the	the	DET
ejpam-2287	331	2	fact	fact	NOUN
ejpam-2287	331	3	that	that	SCONJ
ejpam-2287	331	4	the	the	DET
ejpam-2287	331	5	unique	unique	ADJ
ejpam-2287	331	6	periodic	periodic	ADJ
ejpam-2287	331	7	solution	solution	NOUN
ejpam-2287	331	8	{	{	PUNCT
ejpam-2287	331	9	{	{	PUNCT
ejpam-2287	331	10	s1	s1	NOUN
ejpam-2287	331	11	,	,	PUNCT
ejpam-2287	331	12	t1	t1	NOUN
ejpam-2287	331	13	}	}	PUNCT
ejpam-2287	331	14	,	,	PUNCT
ejpam-2287	331	15	{	{	PUNCT
ejpam-2287	331	16	s2	s2	NOUN
ejpam-2287	331	17	,	,	PUNCT
ejpam-2287	331	18	t2	t2	NOUN
ejpam-2287	331	19	}	}	PUNCT
ejpam-2287	331	20	}	}	PUNCT
ejpam-2287	331	21	must	must	AUX
ejpam-2287	331	22	be	be	AUX
ejpam-2287	331	23	locally	locally	ADV
ejpam-2287	331	24	asymptotically	asymptotically	ADV
ejpam-2287	331	25	stable	stable	ADJ
ejpam-2287	331	26	follows	follow	VERB
ejpam-2287	331	27	directly	directly	ADV
ejpam-2287	331	28	from	from	ADP
ejpam-2287	331	29	the	the	DET
ejpam-2287	331	30	theory	theory	NOUN
ejpam-2287	331	31	of	of	ADP
ejpam-2287	331	32	cooperative	cooperative	ADJ
ejpam-2287	331	33	maps	map	NOUN
ejpam-2287	331	34	which	which	PRON
ejpam-2287	331	35	guarantees	guarantee	VERB
ejpam-2287	331	36	the	the	DET
ejpam-2287	331	37	existence	existence	NOUN
ejpam-2287	331	38	of	of	ADP
ejpam-2287	331	39	a	a	DET
ejpam-2287	331	40	stable	stable	ADJ
ejpam-2287	331	41	fixed	fix	VERB
ejpam-2287	331	42	point	point	NOUN
ejpam-2287	331	43	of	of	ADP
ejpam-2287	331	44	the	the	DET
ejpam-2287	331	45	cooperative	cooperative	ADJ
ejpam-2287	331	46	map	map	NOUN
ejpam-2287	331	47	t2(θ	t2(θ	X
ejpam-2287	331	48	,	,	PUNCT
ejpam-2287	331	49	u	u	NOUN
ejpam-2287	331	50	)	)	PUNCT
ejpam-2287	331	51	in	in	ADP
ejpam-2287	331	52	the	the	DET
ejpam-2287	331	53	invariant	invariant	ADJ
ejpam-2287	331	54	attracting	attract	VERB
ejpam-2287	331	55	regionr1∪r3	regionr1∪r3	PROPN
ejpam-2287	331	56	.	.	PUNCT
ejpam-2287	332	1	to	to	PART
ejpam-2287	332	2	see	see	VERB
ejpam-2287	332	3	that	that	SCONJ
ejpam-2287	332	4	the	the	DET
ejpam-2287	332	5	periodic	periodic	ADJ
ejpam-2287	332	6	solution	solution	NOUN
ejpam-2287	332	7	disappears	disappear	VERB
ejpam-2287	332	8	for	for	ADP
ejpam-2287	332	9	λµ	λµ	DET
ejpam-2287	332	10	≥	≥	NOUN
ejpam-2287	332	11	2.4	2.4	NUM
ejpam-2287	332	12	,	,	PUNCT
ejpam-2287	332	13	one	one	NUM
ejpam-2287	332	14	just	just	ADV
ejpam-2287	332	15	needs	need	VERB
ejpam-2287	332	16	to	to	PART
ejpam-2287	332	17	observe	observe	VERB
ejpam-2287	332	18	that	that	SCONJ
ejpam-2287	332	19	in	in	ADP
ejpam-2287	332	20	this	this	DET
ejpam-2287	332	21	case	case	NOUN
ejpam-2287	332	22	,	,	PUNCT
ejpam-2287	332	23	the	the	DET
ejpam-2287	332	24	critical	critical	ADJ
ejpam-2287	332	25	points	point	NOUN
ejpam-2287	332	26	and	and	CCONJ
ejpam-2287	332	27	θ	θ	NOUN
ejpam-2287	332	28	-intercepts	-intercept	NOUN
ejpam-2287	332	29	of	of	ADP
ejpam-2287	332	30	the	the	DET
ejpam-2287	332	31	equilibrium	equilibrium	NOUN
ejpam-2287	332	32	curve	curve	NOUN
ejpam-2287	332	33	e2	e2	PROPN
ejpam-2287	332	34	are	be	AUX
ejpam-2287	332	35	smaller	small	ADJ
ejpam-2287	332	36	in	in	ADP
ejpam-2287	332	37	magnitude	magnitude	NOUN
ejpam-2287	332	38	than	than	ADP
ejpam-2287	332	39	those	those	PRON
ejpam-2287	332	40	of	of	ADP
ejpam-2287	332	41	the	the	DET
ejpam-2287	332	42	equilibrium	equilibrium	NOUN
ejpam-2287	332	43	curve	curve	NOUN
ejpam-2287	332	44	e1	e1	PROPN
ejpam-2287	332	45	.	.	PUNCT
ejpam-2287	333	1	since	since	SCONJ
ejpam-2287	333	2	the	the	DET
ejpam-2287	333	3	critical	critical	ADJ
ejpam-2287	333	4	points	point	NOUN
ejpam-2287	333	5	of	of	ADP
ejpam-2287	333	6	both	both	DET
ejpam-2287	333	7	curves	curve	NOUN
ejpam-2287	333	8	lie	lie	VERB
ejpam-2287	333	9	in	in	ADP
ejpam-2287	333	10	r1	r1	PROPN
ejpam-2287	333	11	∪r3	∪r3	NUM
ejpam-2287	333	12	,	,	PUNCT
ejpam-2287	333	13	it	it	PRON
ejpam-2287	333	14	follows	follow	VERB
ejpam-2287	333	15	that	that	SCONJ
ejpam-2287	333	16	they	they	PRON
ejpam-2287	333	17	can	can	AUX
ejpam-2287	333	18	not	not	PART
ejpam-2287	333	19	intersect	intersect	VERB
ejpam-2287	333	20	here	here	ADV
ejpam-2287	333	21	.	.	PUNCT
ejpam-2287	334	1	the	the	DET
ejpam-2287	334	2	next	next	ADJ
ejpam-2287	334	3	corollary	corollary	NOUN
ejpam-2287	334	4	is	be	AUX
ejpam-2287	334	5	a	a	DET
ejpam-2287	334	6	direct	direct	ADJ
ejpam-2287	334	7	consequence	consequence	NOUN
ejpam-2287	334	8	of	of	ADP
ejpam-2287	334	9	theorem	theorem	ADJ
ejpam-2287	334	10	3	3	NUM
ejpam-2287	334	11	.	.	PUNCT
ejpam-2287	334	12	corollary	corollary	ADJ
ejpam-2287	334	13	1	1	NUM
ejpam-2287	334	14	.	.	PUNCT
ejpam-2287	335	1	if	if	SCONJ
ejpam-2287	335	2	the	the	DET
ejpam-2287	335	3	hypotheses	hypothesis	NOUN
ejpam-2287	335	4	of	of	ADP
ejpam-2287	335	5	lemma	lemma	PROPN
ejpam-2287	335	6	2	2	NUM
ejpam-2287	335	7	are	be	AUX
ejpam-2287	335	8	not	not	PART
ejpam-2287	335	9	satisfied	satisfied	ADJ
ejpam-2287	335	10	,	,	PUNCT
ejpam-2287	335	11	i.e.	i.e.	X
ejpam-2287	335	12	,	,	PUNCT
ejpam-2287	335	13	if	if	SCONJ
ejpam-2287	335	14	the	the	DET
ejpam-2287	335	15	map	map	NOUN
ejpam-2287	335	16	t2(θ	t2(θ	X
ejpam-2287	335	17	,	,	PUNCT
ejpam-2287	335	18	u	u	NOUN
ejpam-2287	335	19	)	)	PUNCT
ejpam-2287	335	20	is	be	AUX
ejpam-2287	335	21	not	not	PART
ejpam-2287	335	22	cooperative	cooperative	ADJ
ejpam-2287	335	23	or	or	CCONJ
ejpam-2287	335	24	is	be	AUX
ejpam-2287	335	25	unbounded	unbounde	VERB
ejpam-2287	335	26	,	,	PUNCT
ejpam-2287	335	27	then	then	ADV
ejpam-2287	335	28	the	the	DET
ejpam-2287	335	29	solutions	solution	NOUN
ejpam-2287	335	30	of	of	ADP
ejpam-2287	335	31	equation	equation	NOUN
ejpam-2287	335	32	(	(	PUNCT
ejpam-2287	335	33	12	12	NUM
ejpam-2287	335	34	)	)	PUNCT
ejpam-2287	335	35	may	may	AUX
ejpam-2287	335	36	exhibit	exhibit	VERB
ejpam-2287	335	37	unpredictable	unpredictable	ADJ
ejpam-2287	335	38	or	or	CCONJ
ejpam-2287	335	39	even	even	ADV
ejpam-2287	335	40	chaotic	chaotic	ADJ
ejpam-2287	335	41	behavior	behavior	NOUN
ejpam-2287	335	42	.	.	PUNCT
ejpam-2287	336	1	the	the	DET
ejpam-2287	336	2	next	next	ADJ
ejpam-2287	336	3	corollary	corollary	ADJ
ejpam-2287	336	4	addresses	address	NOUN
ejpam-2287	336	5	bifurcation	bifurcation	NOUN
ejpam-2287	336	6	values	value	NOUN
ejpam-2287	336	7	of	of	ADP
ejpam-2287	336	8	the	the	DET
ejpam-2287	336	9	parameters	parameter	NOUN
ejpam-2287	336	10	λ	λ	PROPN
ejpam-2287	336	11	and	and	CCONJ
ejpam-2287	336	12	µ.	µ.	PROPN
ejpam-2287	336	13	corollary	corollary	ADJ
ejpam-2287	336	14	2	2	NUM
ejpam-2287	336	15	.	.	PUNCT
ejpam-2287	337	1	at	at	ADP
ejpam-2287	337	2	λµ	λµ	ADP
ejpam-2287	337	3	=	=	SYM
ejpam-2287	337	4	2.4	2.4	NUM
ejpam-2287	337	5	and	and	CCONJ
ejpam-2287	337	6	6.38	6.38	NUM
ejpam-2287	337	7	,	,	PUNCT
ejpam-2287	337	8	the	the	DET
ejpam-2287	337	9	point	point	NOUN
ejpam-2287	337	10	(	(	PUNCT
ejpam-2287	337	11	0,0	0,0	NOUN
ejpam-2287	337	12	)	)	PUNCT
ejpam-2287	337	13	is	be	AUX
ejpam-2287	337	14	a	a	DET
ejpam-2287	337	15	unique	unique	ADJ
ejpam-2287	337	16	nonhyperbolic	nonhyperbolic	ADJ
ejpam-2287	337	17	equilibrium	equilibrium	NOUN
ejpam-2287	337	18	and	and	CCONJ
ejpam-2287	337	19	undergoes	undergo	VERB
ejpam-2287	337	20	a	a	DET
ejpam-2287	337	21	neimark	neimark	NOUN
ejpam-2287	337	22	-	-	PUNCT
ejpam-2287	337	23	sacker	sacker	NOUN
ejpam-2287	337	24	bifurcation	bifurcation	NOUN
ejpam-2287	337	25	.	.	PUNCT
ejpam-2287	338	1	moreover	moreover	ADV
ejpam-2287	338	2	if	if	SCONJ
ejpam-2287	338	3	λµ	λµ	INTJ
ejpam-2287	338	4	>	>	X
ejpam-2287	338	5	6.38	6.38	NUM
ejpam-2287	338	6	,	,	PUNCT
ejpam-2287	338	7	then	then	ADV
ejpam-2287	338	8	every	every	DET
ejpam-2287	338	9	nonzero	nonzero	NOUN
ejpam-2287	338	10	solution	solution	NOUN
ejpam-2287	338	11	escapes	escape	VERB
ejpam-2287	338	12	to	to	PART
ejpam-2287	338	13	infinity	infinity	VERB
ejpam-2287	338	14	.	.	PUNCT
ejpam-2287	339	1	proof	proof	NOUN
ejpam-2287	339	2	.	.	PUNCT
ejpam-2287	340	1	the	the	DET
ejpam-2287	340	2	proof	proof	NOUN
ejpam-2287	340	3	of	of	ADP
ejpam-2287	340	4	the	the	DET
ejpam-2287	340	5	first	first	ADJ
ejpam-2287	340	6	statement	statement	NOUN
ejpam-2287	340	7	is	be	AUX
ejpam-2287	340	8	a	a	DET
ejpam-2287	340	9	direct	direct	ADJ
ejpam-2287	340	10	consequence	consequence	NOUN
ejpam-2287	340	11	of	of	ADP
ejpam-2287	340	12	table	table	NOUN
ejpam-2287	340	13	1	1	NUM
ejpam-2287	340	14	and	and	CCONJ
ejpam-2287	340	15	(	(	PUNCT
ejpam-2287	340	16	21)-(22	21)-(22	NOUN
ejpam-2287	340	17	)	)	PUNCT
ejpam-2287	340	18	in	in	ADP
ejpam-2287	340	19	the	the	DET
ejpam-2287	340	20	proof	proof	NOUN
ejpam-2287	340	21	of	of	ADP
ejpam-2287	340	22	lemma	lemma	PROPN
ejpam-2287	340	23	1	1	NUM
ejpam-2287	340	24	.	.	PUNCT
ejpam-2287	341	1	in	in	ADP
ejpam-2287	341	2	particular	particular	ADJ
ejpam-2287	341	3	,	,	PUNCT
ejpam-2287	341	4	note	note	VERB
ejpam-2287	341	5	that	that	SCONJ
ejpam-2287	341	6	at	at	ADP
ejpam-2287	341	7	λµ	λµ	ADP
ejpam-2287	341	8	=	=	NOUN
ejpam-2287	341	9	6.38	6.38	NUM
ejpam-2287	341	10	,	,	PUNCT
ejpam-2287	341	11	the	the	DET
ejpam-2287	341	12	(	(	PUNCT
ejpam-2287	341	13	0,0	0,0	NOUN
ejpam-2287	341	14	)	)	PUNCT
ejpam-2287	341	15	equilibrium	equilibrium	NOUN
ejpam-2287	341	16	changes	change	NOUN
ejpam-2287	341	17	from	from	ADP
ejpam-2287	341	18	a	a	DET
ejpam-2287	341	19	repeller	repeller	NOUN
ejpam-2287	341	20	to	to	ADP
ejpam-2287	341	21	a	a	DET
ejpam-2287	341	22	saddle	saddle	NOUN
ejpam-2287	341	23	point	point	NOUN
ejpam-2287	341	24	and	and	CCONJ
ejpam-2287	341	25	a	a	DET
ejpam-2287	341	26	new	new	ADJ
ejpam-2287	341	27	pair	pair	NOUN
ejpam-2287	341	28	of	of	ADP
ejpam-2287	341	29	periodic	periodic	ADJ
ejpam-2287	341	30	solutions	solution	NOUN
ejpam-2287	341	31	is	be	AUX
ejpam-2287	341	32	created	create	VERB
ejpam-2287	341	33	.	.	PUNCT
ejpam-2287	342	1	similarly	similarly	ADV
ejpam-2287	342	2	at	at	ADP
ejpam-2287	342	3	λµ	λµ	ADP
ejpam-2287	342	4	=	=	SYM
ejpam-2287	342	5	2.4	2.4	NUM
ejpam-2287	342	6	,	,	PUNCT
ejpam-2287	342	7	(	(	PUNCT
ejpam-2287	342	8	0,0	0,0	NOUN
ejpam-2287	342	9	)	)	PUNCT
ejpam-2287	342	10	changes	change	NOUN
ejpam-2287	342	11	from	from	ADP
ejpam-2287	342	12	a	a	DET
ejpam-2287	342	13	saddle	saddle	NOUN
ejpam-2287	342	14	point	point	NOUN
ejpam-2287	342	15	to	to	ADP
ejpam-2287	342	16	a	a	DET
ejpam-2287	342	17	repeller	repeller	NOUN
ejpam-2287	342	18	and	and	CCONJ
ejpam-2287	342	19	a	a	DET
ejpam-2287	342	20	new	new	ADJ
ejpam-2287	342	21	pair	pair	NOUN
ejpam-2287	342	22	of	of	ADP
ejpam-2287	342	23	of	of	ADP
ejpam-2287	342	24	periodic	periodic	ADJ
ejpam-2287	342	25	solutions	solution	NOUN
ejpam-2287	342	26	is	be	AUX
ejpam-2287	342	27	created	create	VERB
ejpam-2287	342	28	.	.	PUNCT
ejpam-2287	343	1	thus	thus	ADV
ejpam-2287	343	2	the	the	DET
ejpam-2287	343	3	nonhyperbolic	nonhyperbolic	ADJ
ejpam-2287	343	4	equilibrium	equilibrium	NOUN
ejpam-2287	343	5	(	(	PUNCT
ejpam-2287	343	6	0,0	0,0	NOUN
ejpam-2287	343	7	)	)	PUNCT
ejpam-2287	343	8	undergoes	undergo	VERB
ejpam-2287	343	9	a	a	DET
ejpam-2287	343	10	neimark	neimark	NOUN
ejpam-2287	343	11	-	-	PUNCT
ejpam-2287	343	12	sacker	sacker	NOUN
ejpam-2287	343	13	bifurcation	bifurcation	NOUN
ejpam-2287	343	14	at	at	ADP
ejpam-2287	343	15	both	both	DET
ejpam-2287	343	16	these	these	DET
ejpam-2287	343	17	λµ-values	λµ-value	NOUN
ejpam-2287	343	18	.	.	PUNCT
ejpam-2287	344	1	it	it	PRON
ejpam-2287	344	2	is	be	AUX
ejpam-2287	344	3	easy	easy	ADJ
ejpam-2287	344	4	to	to	PART
ejpam-2287	344	5	see	see	VERB
ejpam-2287	344	6	that	that	SCONJ
ejpam-2287	344	7	the	the	DET
ejpam-2287	344	8	map	map	NOUN
ejpam-2287	344	9	t2(θ	t2(θ	X
ejpam-2287	344	10	,	,	PUNCT
ejpam-2287	344	11	u	u	NOUN
ejpam-2287	344	12	)	)	PUNCT
ejpam-2287	344	13	in	in	ADP
ejpam-2287	344	14	(	(	PUNCT
ejpam-2287	344	15	15	15	NUM
ejpam-2287	344	16	)	)	PUNCT
ejpam-2287	344	17	is	be	AUX
ejpam-2287	344	18	unbounded	unbounded	ADJ
ejpam-2287	344	19	for	for	ADP
ejpam-2287	344	20	λµ	λµ	INTJ
ejpam-2287	344	21	>	>	X
ejpam-2287	344	22	6.38	6.38	NUM
ejpam-2287	344	23	.	.	PUNCT
ejpam-2287	345	1	this	this	PRON
ejpam-2287	345	2	and	and	CCONJ
ejpam-2287	345	3	the	the	DET
ejpam-2287	345	4	fact	fact	NOUN
ejpam-2287	345	5	that	that	SCONJ
ejpam-2287	345	6	t2(θ	t2(θ	X
ejpam-2287	345	7	,	,	PUNCT
ejpam-2287	345	8	u	u	NOUN
ejpam-2287	345	9	)	)	PUNCT
ejpam-2287	345	10	is	be	AUX
ejpam-2287	345	11	cooperative	cooperative	ADJ
ejpam-2287	345	12	guarantee	guarantee	NOUN
ejpam-2287	345	13	unbounded	unbounded	ADJ
ejpam-2287	345	14	growth	growth	NOUN
ejpam-2287	345	15	for	for	ADP
ejpam-2287	345	16	the	the	DET
ejpam-2287	345	17	orbits	orbit	NOUN
ejpam-2287	345	18	of	of	ADP
ejpam-2287	345	19	t2(θ	t2(θ	PROPN
ejpam-2287	345	20	,	,	PUNCT
ejpam-2287	345	21	u	u	NOUN
ejpam-2287	345	22	)	)	PUNCT
ejpam-2287	345	23	.	.	PUNCT
ejpam-2287	346	1	as	as	ADP
ejpam-2287	346	2	a	a	DET
ejpam-2287	346	3	result	result	NOUN
ejpam-2287	346	4	,	,	PUNCT
ejpam-2287	346	5	every	every	DET
ejpam-2287	346	6	nonzero	nonzero	NOUN
ejpam-2287	346	7	solution	solution	NOUN
ejpam-2287	346	8	escapes	escape	VERB
ejpam-2287	346	9	to	to	PART
ejpam-2287	346	10	infinity	infinity	VERB
ejpam-2287	346	11	.	.	PUNCT
ejpam-2287	347	1	in	in	ADP
ejpam-2287	347	2	the	the	DET
ejpam-2287	347	3	next	next	ADJ
ejpam-2287	347	4	section	section	NOUN
ejpam-2287	347	5	,	,	PUNCT
ejpam-2287	347	6	we	we	PRON
ejpam-2287	347	7	give	give	VERB
ejpam-2287	347	8	a	a	DET
ejpam-2287	347	9	summary	summary	NOUN
ejpam-2287	347	10	of	of	ADP
ejpam-2287	347	11	our	our	PRON
ejpam-2287	347	12	mathematical	mathematical	ADJ
ejpam-2287	347	13	results	result	NOUN
ejpam-2287	347	14	in	in	ADP
ejpam-2287	347	15	this	this	DET
ejpam-2287	347	16	paper	paper	NOUN
ejpam-2287	347	17	and	and	CCONJ
ejpam-2287	347	18	their	their	PRON
ejpam-2287	347	19	physical	physical	ADJ
ejpam-2287	347	20	interpretation	interpretation	NOUN
ejpam-2287	347	21	for	for	ADP
ejpam-2287	347	22	our	our	PRON
ejpam-2287	347	23	discrete	discrete	ADJ
ejpam-2287	347	24	suspension	suspension	NOUN
ejpam-2287	347	25	bridge	bridge	NOUN
ejpam-2287	347	26	model	model	NOUN
ejpam-2287	347	27	(	(	PUNCT
ejpam-2287	347	28	12	12	NUM
ejpam-2287	347	29	)	)	PUNCT
ejpam-2287	347	30	.	.	PUNCT
ejpam-2287	348	1	7	7	X
ejpam-2287	348	2	.	.	X
ejpam-2287	348	3	conclusion	conclusion	NOUN
ejpam-2287	348	4	and	and	CCONJ
ejpam-2287	348	5	model	model	NOUN
ejpam-2287	348	6	interpretation	interpretation	NOUN
ejpam-2287	348	7	in	in	ADP
ejpam-2287	348	8	this	this	DET
ejpam-2287	348	9	paper	paper	NOUN
ejpam-2287	348	10	,	,	PUNCT
ejpam-2287	348	11	we	we	PRON
ejpam-2287	348	12	mathematically	mathematically	ADV
ejpam-2287	348	13	analyzed	analyze	VERB
ejpam-2287	348	14	a	a	DET
ejpam-2287	348	15	discrete	discrete	ADJ
ejpam-2287	348	16	difference	difference	NOUN
ejpam-2287	348	17	equations	equation	NOUN
ejpam-2287	348	18	version	version	NOUN
ejpam-2287	348	19	of	of	ADP
ejpam-2287	348	20	mckenna	mckenna	PROPN
ejpam-2287	348	21	and	and	CCONJ
ejpam-2287	348	22	moore	moore	PROPN
ejpam-2287	348	23	’s	’s	PART
ejpam-2287	348	24	continuous	continuous	ADJ
ejpam-2287	348	25	nonlinear	nonlinear	ADJ
ejpam-2287	348	26	differential	differential	ADJ
ejpam-2287	348	27	equations	equation	NOUN
ejpam-2287	348	28	model	model	NOUN
ejpam-2287	348	29	for	for	ADP
ejpam-2287	348	30	a	a	DET
ejpam-2287	348	31	suspension	suspension	NOUN
ejpam-2287	348	32	bridge	bridge	NOUN
ejpam-2287	348	33	in	in	ADP
ejpam-2287	348	34	[	[	X
ejpam-2287	348	35	13	13	NUM
ejpam-2287	348	36	]	]	PUNCT
ejpam-2287	348	37	.	.	PUNCT
ejpam-2287	349	1	s.	s.	PROPN
ejpam-2287	349	2	basu	basu	PROPN
ejpam-2287	349	3	/	/	SYM
ejpam-2287	349	4	eur	eur	PROPN
ejpam-2287	349	5	.	.	PUNCT
ejpam-2287	350	1	j.	j.	PROPN
ejpam-2287	350	2	pure	pure	PROPN
ejpam-2287	350	3	appl	appl	PROPN
ejpam-2287	350	4	.	.	PROPN
ejpam-2287	350	5	math	math	PROPN
ejpam-2287	350	6	,	,	PUNCT
ejpam-2287	350	7	7	7	NUM
ejpam-2287	350	8	(	(	PUNCT
ejpam-2287	350	9	2014	2014	NUM
ejpam-2287	350	10	)	)	PUNCT
ejpam-2287	350	11	,	,	PUNCT
ejpam-2287	350	12	442	442	NUM
ejpam-2287	350	13	-	-	SYM
ejpam-2287	350	14	461	461	NUM
ejpam-2287	350	15	458	458	NUM
ejpam-2287	350	16	more	more	ADV
ejpam-2287	350	17	specifically	specifically	ADV
ejpam-2287	350	18	,	,	PUNCT
ejpam-2287	350	19	we	we	PRON
ejpam-2287	350	20	computed	compute	VERB
ejpam-2287	350	21	the	the	DET
ejpam-2287	350	22	exact	exact	ADJ
ejpam-2287	350	23	number	number	NOUN
ejpam-2287	350	24	of	of	ADP
ejpam-2287	350	25	real	real	ADJ
ejpam-2287	350	26	equilibria	equilibrium	NOUN
ejpam-2287	350	27	and	and	CCONJ
ejpam-2287	350	28	real	real	ADJ
ejpam-2287	350	29	nontrivial	nontrivial	ADJ
ejpam-2287	350	30	periodic	periodic	ADJ
ejpam-2287	350	31	solutions	solution	NOUN
ejpam-2287	350	32	for	for	ADP
ejpam-2287	350	33	our	our	PRON
ejpam-2287	350	34	discrete	discrete	ADJ
ejpam-2287	350	35	suspension	suspension	NOUN
ejpam-2287	350	36	bridge	bridge	NOUN
ejpam-2287	350	37	model	model	NOUN
ejpam-2287	350	38	under	under	ADP
ejpam-2287	350	39	some	some	DET
ejpam-2287	350	40	very	very	ADV
ejpam-2287	350	41	general	general	ADJ
ejpam-2287	350	42	hypotheses	hypothesis	NOUN
ejpam-2287	350	43	.	.	PUNCT
ejpam-2287	351	1	we	we	PRON
ejpam-2287	351	2	also	also	ADV
ejpam-2287	351	3	gave	give	VERB
ejpam-2287	351	4	precise	precise	ADJ
ejpam-2287	351	5	parameter	parameter	NOUN
ejpam-2287	351	6	regions	region	NOUN
ejpam-2287	351	7	for	for	ADP
ejpam-2287	351	8	our	our	PRON
ejpam-2287	351	9	model	model	NOUN
ejpam-2287	351	10	to	to	PART
ejpam-2287	351	11	have	have	VERB
ejpam-2287	351	12	(	(	PUNCT
ejpam-2287	351	13	a	a	PRON
ejpam-2287	351	14	)	)	PUNCT
ejpam-2287	351	15	unique	unique	ADJ
ejpam-2287	351	16	and	and	CCONJ
ejpam-2287	351	17	multiple	multiple	ADJ
ejpam-2287	351	18	equilibria	equilibrium	NOUN
ejpam-2287	351	19	,	,	PUNCT
ejpam-2287	351	20	and	and	CCONJ
ejpam-2287	351	21	(	(	PUNCT
ejpam-2287	351	22	b	b	NOUN
ejpam-2287	351	23	)	)	PUNCT
ejpam-2287	351	24	unique	unique	ADJ
ejpam-2287	351	25	and	and	CCONJ
ejpam-2287	351	26	multiple	multiple	ADJ
ejpam-2287	351	27	real	real	ADJ
ejpam-2287	351	28	periodic	periodic	ADJ
ejpam-2287	351	29	solutions	solution	NOUN
ejpam-2287	351	30	.	.	PUNCT
ejpam-2287	352	1	in	in	ADP
ejpam-2287	352	2	addition	addition	NOUN
ejpam-2287	352	3	,	,	PUNCT
ejpam-2287	352	4	we	we	PRON
ejpam-2287	352	5	established	establish	VERB
ejpam-2287	352	6	the	the	DET
ejpam-2287	352	7	different	different	ADJ
ejpam-2287	352	8	types	type	NOUN
ejpam-2287	352	9	of	of	ADP
ejpam-2287	352	10	local	local	ADJ
ejpam-2287	352	11	and	and	CCONJ
ejpam-2287	352	12	global	global	ADJ
ejpam-2287	352	13	attractivity	attractivity	NOUN
ejpam-2287	352	14	behaviors	behavior	NOUN
ejpam-2287	352	15	that	that	PRON
ejpam-2287	352	16	these	these	DET
ejpam-2287	352	17	equilibria	equilibrium	NOUN
ejpam-2287	352	18	and	and	CCONJ
ejpam-2287	352	19	real	real	ADJ
ejpam-2287	352	20	periodic	periodic	ADJ
ejpam-2287	352	21	solutions	solution	NOUN
ejpam-2287	352	22	exhibit	exhibit	VERB
ejpam-2287	352	23	along	along	ADP
ejpam-2287	352	24	with	with	ADP
ejpam-2287	352	25	the	the	DET
ejpam-2287	352	26	precise	precise	ADJ
ejpam-2287	352	27	parameter	parameter	NOUN
ejpam-2287	352	28	regions	region	NOUN
ejpam-2287	352	29	where	where	SCONJ
ejpam-2287	352	30	they	they	PRON
ejpam-2287	352	31	exhibit	exhibit	VERB
ejpam-2287	352	32	these	these	DET
ejpam-2287	352	33	behaviors	behavior	NOUN
ejpam-2287	352	34	.	.	PUNCT
ejpam-2287	353	1	finally	finally	ADV
ejpam-2287	353	2	,	,	PUNCT
ejpam-2287	353	3	we	we	PRON
ejpam-2287	353	4	used	use	VERB
ejpam-2287	353	5	a	a	DET
ejpam-2287	353	6	linearization	linearization	NOUN
ejpam-2287	353	7	of	of	ADP
ejpam-2287	353	8	our	our	PRON
ejpam-2287	353	9	discrete	discrete	ADJ
ejpam-2287	353	10	model	model	NOUN
ejpam-2287	353	11	to	to	PART
ejpam-2287	353	12	gain	gain	VERB
ejpam-2287	353	13	valuable	valuable	ADJ
ejpam-2287	353	14	insights	insight	NOUN
ejpam-2287	353	15	that	that	PRON
ejpam-2287	353	16	helped	help	VERB
ejpam-2287	353	17	us	we	PRON
ejpam-2287	353	18	offer	offer	VERB
ejpam-2287	353	19	missing	miss	VERB
ejpam-2287	353	20	mathematical	mathematical	ADJ
ejpam-2287	353	21	explanations	explanation	NOUN
ejpam-2287	353	22	for	for	ADP
ejpam-2287	353	23	phenomena	phenomenon	NOUN
ejpam-2287	353	24	that	that	SCONJ
ejpam-2287	353	25	mckenna	mckenna	PROPN
ejpam-2287	353	26	and	and	CCONJ
ejpam-2287	353	27	moore	moore	PROPN
ejpam-2287	353	28	observed	observe	VERB
ejpam-2287	353	29	for	for	ADP
ejpam-2287	353	30	their	their	PRON
ejpam-2287	353	31	linearized	linearize	VERB
ejpam-2287	353	32	continuous	continuous	ADJ
ejpam-2287	353	33	model	model	NOUN
ejpam-2287	353	34	in	in	ADP
ejpam-2287	353	35	[	[	X
ejpam-2287	353	36	13	13	NUM
ejpam-2287	353	37	]	]	PUNCT
ejpam-2287	353	38	via	via	ADP
ejpam-2287	353	39	numerical	numerical	ADJ
ejpam-2287	353	40	simulations	simulation	NOUN
ejpam-2287	353	41	.	.	PUNCT
ejpam-2287	354	1	our	our	PRON
ejpam-2287	354	2	results	result	NOUN
ejpam-2287	354	3	are	be	AUX
ejpam-2287	354	4	summarized	summarize	VERB
ejpam-2287	354	5	in	in	ADP
ejpam-2287	354	6	table	table	NOUN
ejpam-2287	354	7	3	3	NUM
ejpam-2287	354	8	.	.	PUNCT
ejpam-2287	355	1	the	the	DET
ejpam-2287	355	2	physical	physical	ADJ
ejpam-2287	355	3	interpretation	interpretation	NOUN
ejpam-2287	355	4	of	of	ADP
ejpam-2287	355	5	our	our	PRON
ejpam-2287	355	6	mathematical	mathematical	ADJ
ejpam-2287	355	7	results	result	NOUN
ejpam-2287	355	8	for	for	ADP
ejpam-2287	355	9	the	the	DET
ejpam-2287	355	10	discrete	discrete	ADJ
ejpam-2287	355	11	suspension	suspension	NOUN
ejpam-2287	355	12	bridge	bridge	NOUN
ejpam-2287	355	13	model	model	NOUN
ejpam-2287	355	14	(	(	PUNCT
ejpam-2287	355	15	12	12	NUM
ejpam-2287	355	16	)	)	PUNCT
ejpam-2287	355	17	is	be	AUX
ejpam-2287	355	18	that	that	SCONJ
ejpam-2287	355	19	the	the	DET
ejpam-2287	355	20	suspension	suspension	NOUN
ejpam-2287	355	21	bridge	bridge	NOUN
ejpam-2287	355	22	will	will	AUX
ejpam-2287	355	23	eventually	eventually	ADV
ejpam-2287	355	24	stop	stop	VERB
ejpam-2287	355	25	oscillating	oscillate	VERB
ejpam-2287	355	26	and	and	CCONJ
ejpam-2287	355	27	come	come	VERB
ejpam-2287	355	28	to	to	PART
ejpam-2287	355	29	rest	rest	VERB
ejpam-2287	355	30	at	at	ADP
ejpam-2287	355	31	its	its	PRON
ejpam-2287	355	32	original	original	ADJ
ejpam-2287	355	33	position	position	NOUN
ejpam-2287	355	34	for	for	ADP
ejpam-2287	355	35	all	all	DET
ejpam-2287	355	36	initial	initial	ADJ
ejpam-2287	355	37	conditions	condition	NOUN
ejpam-2287	355	38	θ	θ	PROPN
ejpam-2287	355	39	∈	∈	PROPN
ejpam-2287	355	40	�	�	PROPN
ejpam-2287	355	41	−π2	−π2	PROPN
ejpam-2287	355	42	,	,	PUNCT
ejpam-2287	355	43	π2	π2	PROPN
ejpam-2287	355	44	�	�	PROPN
ejpam-2287	355	45	if	if	SCONJ
ejpam-2287	355	46	2.4	2.4	NUM
ejpam-2287	355	47	<	<	X
ejpam-2287	355	48	λµ≤	λµ≤	X
ejpam-2287	355	49	6.38	6.38	NUM
ejpam-2287	355	50	.	.	PUNCT
ejpam-2287	356	1	it	it	PRON
ejpam-2287	356	2	will	will	AUX
ejpam-2287	356	3	either	either	CCONJ
ejpam-2287	356	4	come	come	VERB
ejpam-2287	356	5	to	to	ADP
ejpam-2287	356	6	a	a	DET
ejpam-2287	356	7	complete	complete	ADJ
ejpam-2287	356	8	rest	rest	NOUN
ejpam-2287	356	9	at	at	ADP
ejpam-2287	356	10	one	one	NUM
ejpam-2287	356	11	of	of	ADP
ejpam-2287	356	12	two	two	NUM
ejpam-2287	356	13	nonzero	nonzero	PROPN
ejpam-2287	356	14	equilibrium	equilibrium	NOUN
ejpam-2287	356	15	positions	position	NOUN
ejpam-2287	356	16	or	or	CCONJ
ejpam-2287	356	17	its	its	PRON
ejpam-2287	356	18	oscillations	oscillation	NOUN
ejpam-2287	356	19	will	will	AUX
ejpam-2287	356	20	eventually	eventually	ADV
ejpam-2287	356	21	settle	settle	VERB
ejpam-2287	356	22	down	down	ADP
ejpam-2287	356	23	to	to	ADP
ejpam-2287	356	24	one	one	NUM
ejpam-2287	356	25	of	of	ADP
ejpam-2287	356	26	two	two	NUM
ejpam-2287	356	27	stable	stable	ADJ
ejpam-2287	356	28	periodic	periodic	ADJ
ejpam-2287	356	29	motions	motion	NOUN
ejpam-2287	356	30	for	for	ADP
ejpam-2287	356	31	all	all	DET
ejpam-2287	356	32	initial	initial	ADJ
ejpam-2287	356	33	conditions	condition	NOUN
ejpam-2287	356	34	θ	θ	PROPN
ejpam-2287	356	35	∈	∈	PROPN
ejpam-2287	356	36	�	�	PROPN
ejpam-2287	356	37	−π2	−π2	PROPN
ejpam-2287	356	38	,	,	PUNCT
ejpam-2287	356	39	π2	π2	X
ejpam-2287	356	40	�	�	PROPN
ejpam-2287	356	41	if	if	SCONJ
ejpam-2287	356	42	0.41	0.41	NUM
ejpam-2287	356	43	<	<	X
ejpam-2287	356	44	λµ	λµ	DET
ejpam-2287	356	45	≤	≤	NUM
ejpam-2287	356	46	2.4	2.4	NUM
ejpam-2287	356	47	.	.	PUNCT
ejpam-2287	357	1	its	its	PRON
ejpam-2287	357	2	oscillations	oscillation	NOUN
ejpam-2287	357	3	will	will	AUX
ejpam-2287	357	4	eventually	eventually	ADV
ejpam-2287	357	5	settle	settle	VERB
ejpam-2287	357	6	down	down	ADP
ejpam-2287	357	7	to	to	ADP
ejpam-2287	357	8	one	one	NUM
ejpam-2287	357	9	of	of	ADP
ejpam-2287	357	10	two	two	NUM
ejpam-2287	357	11	stable	stable	ADJ
ejpam-2287	357	12	periodic	periodic	ADJ
ejpam-2287	357	13	motions	motion	NOUN
ejpam-2287	357	14	for	for	ADP
ejpam-2287	357	15	all	all	DET
ejpam-2287	357	16	initial	initial	ADJ
ejpam-2287	357	17	conditions	condition	NOUN
ejpam-2287	357	18	θ	θ	PROPN
ejpam-2287	357	19	∈	∈	PROPN
ejpam-2287	357	20	�	�	PROPN
ejpam-2287	357	21	−π2	−π2	PROPN
ejpam-2287	357	22	,	,	PUNCT
ejpam-2287	357	23	π2	π2	PROPN
ejpam-2287	357	24	�	�	PROPN
ejpam-2287	357	25	if	if	SCONJ
ejpam-2287	357	26	0	0	NUM
ejpam-2287	357	27	≤	≤	NUM
ejpam-2287	357	28	λµ	λµ	DET
ejpam-2287	357	29	≤	≤	NUM
ejpam-2287	357	30	0.41	0.41	NUM
ejpam-2287	357	31	.	.	PUNCT
ejpam-2287	358	1	the	the	DET
ejpam-2287	358	2	model	model	NOUN
ejpam-2287	358	3	breaks	break	VERB
ejpam-2287	358	4	down	down	ADP
ejpam-2287	358	5	for	for	ADP
ejpam-2287	358	6	λµ	λµ	INTJ
ejpam-2287	358	7	>	>	X
ejpam-2287	358	8	6.38	6.38	NUM
ejpam-2287	358	9	.	.	PUNCT
ejpam-2287	359	1	acknowledgements	acknowledgement	NOUN
ejpam-2287	359	2	the	the	DET
ejpam-2287	359	3	author	author	NOUN
ejpam-2287	359	4	is	be	AUX
ejpam-2287	359	5	deeply	deeply	ADV
ejpam-2287	359	6	indebted	indebted	ADJ
ejpam-2287	359	7	to	to	ADP
ejpam-2287	359	8	dr	dr	PROPN
ejpam-2287	359	9	.	.	PROPN
ejpam-2287	359	10	edward	edward	PROPN
ejpam-2287	359	11	f.	f.	PROPN
ejpam-2287	359	12	aboufadel	aboufadel	PROPN
ejpam-2287	359	13	from	from	ADP
ejpam-2287	359	14	the	the	DET
ejpam-2287	359	15	math	math	PROPN
ejpam-2287	359	16	department	department	PROPN
ejpam-2287	359	17	of	of	ADP
ejpam-2287	359	18	grand	grand	PROPN
ejpam-2287	359	19	valley	valley	PROPN
ejpam-2287	359	20	state	state	PROPN
ejpam-2287	359	21	university	university	PROPN
ejpam-2287	359	22	in	in	ADP
ejpam-2287	359	23	allendale	allendale	PROPN
ejpam-2287	359	24	,	,	PUNCT
ejpam-2287	359	25	mi	mi	PROPN
ejpam-2287	359	26	,	,	PUNCT
ejpam-2287	359	27	usa	usa	PROPN
ejpam-2287	359	28	,	,	PUNCT
ejpam-2287	359	29	for	for	ADP
ejpam-2287	359	30	his	his	PRON
ejpam-2287	359	31	constant	constant	ADJ
ejpam-2287	359	32	encouragement	encouragement	NOUN
ejpam-2287	359	33	,	,	PUNCT
ejpam-2287	359	34	support	support	NOUN
ejpam-2287	359	35	and	and	CCONJ
ejpam-2287	359	36	mentoring	mentor	VERB
ejpam-2287	359	37	over	over	ADP
ejpam-2287	359	38	the	the	DET
ejpam-2287	359	39	years	year	NOUN
ejpam-2287	359	40	.	.	PUNCT
ejpam-2287	360	1	she	she	PRON
ejpam-2287	360	2	would	would	AUX
ejpam-2287	360	3	also	also	ADV
ejpam-2287	360	4	like	like	VERB
ejpam-2287	360	5	to	to	PART
ejpam-2287	360	6	thank	thank	VERB
ejpam-2287	360	7	dr	dr	PROPN
ejpam-2287	360	8	.	.	PROPN
ejpam-2287	360	9	orlando	orlando	PROPN
ejpam-2287	360	10	merino	merino	PROPN
ejpam-2287	360	11	from	from	ADP
ejpam-2287	360	12	the	the	DET
ejpam-2287	360	13	math	math	PROPN
ejpam-2287	360	14	department	department	PROPN
ejpam-2287	360	15	of	of	ADP
ejpam-2287	360	16	the	the	DET
ejpam-2287	360	17	university	university	PROPN
ejpam-2287	360	18	of	of	ADP
ejpam-2287	360	19	rhode	rhode	PROPN
ejpam-2287	360	20	island	island	NOUN
ejpam-2287	360	21	in	in	ADP
ejpam-2287	360	22	kingston	kingston	PROPN
ejpam-2287	360	23	,	,	PUNCT
ejpam-2287	360	24	ri	ri	PROPN
ejpam-2287	360	25	,	,	PUNCT
ejpam-2287	360	26	usa	usa	PROPN
ejpam-2287	360	27	,	,	PUNCT
ejpam-2287	360	28	for	for	ADP
ejpam-2287	360	29	making	make	VERB
ejpam-2287	360	30	her	she	PRON
ejpam-2287	360	31	the	the	DET
ejpam-2287	360	32	mathematician	mathematician	NOUN
ejpam-2287	360	33	that	that	SCONJ
ejpam-2287	360	34	she	she	PRON
ejpam-2287	360	35	is	be	AUX
ejpam-2287	360	36	today	today	NOUN
ejpam-2287	360	37	.	.	PUNCT
ejpam-2287	361	1	s	s	PART
ejpam-2287	361	2	.	.	PUNCT
ejpam-2287	362	1	b	b	X
ejpam-2287	362	2	a	a	DET
ejpam-2287	362	3	su	su	PROPN
ejpam-2287	362	4	/	/	SYM
ejpam-2287	362	5	e	e	PROPN
ejpam-2287	362	6	u	u	PROPN
ejpam-2287	362	7	r.	r.	PROPN
ejpam-2287	362	8	j.	j.	PROPN
ejpam-2287	363	1	p	p	PROPN
ejpam-2287	363	2	u	u	PROPN
ejpam-2287	363	3	re	re	ADP
ejpam-2287	363	4	a	a	DET
ejpam-2287	363	5	p	p	X
ejpam-2287	363	6	p	p	X
ejpam-2287	363	7	l.	l.	PROPN
ejpam-2287	363	8	m	m	PROPN
ejpam-2287	363	9	a	a	DET
ejpam-2287	363	10	th	th	X
ejpam-2287	363	11	,	,	PUNCT
ejpam-2287	363	12	7	7	NUM
ejpam-2287	363	13	(	(	PUNCT
ejpam-2287	363	14	2	2	NUM
ejpam-2287	363	15	0	0	NUM
ejpam-2287	363	16	1	1	NUM
ejpam-2287	363	17	4	4	NUM
ejpam-2287	363	18	)	)	PUNCT
ejpam-2287	363	19	,	,	PUNCT
ejpam-2287	363	20	4	4	NUM
ejpam-2287	363	21	4	4	NUM
ejpam-2287	363	22	2	2	NUM
ejpam-2287	363	23	-4	-4	SYM
ejpam-2287	363	24	6	6	NUM
ejpam-2287	363	25	1	1	NUM
ejpam-2287	363	26	4	4	NUM
ejpam-2287	363	27	5	5	NUM
ejpam-2287	363	28	9	9	NUM
ejpam-2287	363	29	table	table	NOUN
ejpam-2287	363	30	3	3	NUM
ejpam-2287	363	31	:	:	PUNCT
ejpam-2287	363	32	table	table	NOUN
ejpam-2287	363	33	summarizing	summarize	VERB
ejpam-2287	363	34	our	our	PRON
ejpam-2287	363	35	results	result	NOUN
ejpam-2287	363	36	in	in	ADP
ejpam-2287	363	37	this	this	DET
ejpam-2287	363	38	paper	paper	NOUN
ejpam-2287	363	39	.	.	PUNCT
ejpam-2287	364	1	λµ	λµ	PROPN
ejpam-2287	364	2	parameter	parameter	PROPN
ejpam-2287	364	3	region	region	PROPN
ejpam-2287	364	4	no	no	INTJ
ejpam-2287	364	5	.	.	PUNCT
ejpam-2287	364	6	of	of	ADP
ejpam-2287	364	7	equilibria	equilibria	PROPN
ejpam-2287	364	8	local	local	ADJ
ejpam-2287	364	9	attractivity	attractivity	NOUN
ejpam-2287	364	10	no	no	PROPN
ejpam-2287	364	11	.	.	PUNCT
ejpam-2287	365	1	of	of	ADP
ejpam-2287	365	2	periodic	periodic	ADJ
ejpam-2287	365	3	solns	solns	NOUN
ejpam-2287	365	4	local	local	ADJ
ejpam-2287	365	5	attractivity	attractivity	NOUN
ejpam-2287	365	6	global	global	ADJ
ejpam-2287	365	7	dynamics	dynamic	NOUN
ejpam-2287	365	8	0	0	NUM
ejpam-2287	365	9	<	<	X
ejpam-2287	365	10	λµ	λµ	X
ejpam-2287	365	11	<	<	X
ejpam-2287	365	12	0.41	0.41	NUM
ejpam-2287	365	13	3	3	NUM
ejpam-2287	365	14	3	3	NUM
ejpam-2287	365	15	repelling	repelling	NOUN
ejpam-2287	365	16	equilibria	equilibrium	NOUN
ejpam-2287	365	17	2	2	NUM
ejpam-2287	365	18	at	at	ADV
ejpam-2287	365	19	least	least	ADJ
ejpam-2287	365	20	one	one	NUM
ejpam-2287	365	21	is	be	AUX
ejpam-2287	365	22	locally	locally	ADV
ejpam-2287	365	23	asymptotically	asymptotically	ADV
ejpam-2287	365	24	stable	stable	ADJ
ejpam-2287	365	25	every	every	DET
ejpam-2287	365	26	solution	solution	NOUN
ejpam-2287	365	27	↓	↓	NOUN
ejpam-2287	365	28	λµ=	λµ=	VERB
ejpam-2287	365	29	0.414	0.414	NUM
ejpam-2287	365	30	3	3	NUM
ejpam-2287	365	31	(	(	PUNCT
ejpam-2287	365	32	0,0	0,0	NOUN
ejpam-2287	365	33	)	)	PUNCT
ejpam-2287	365	34	a	a	DET
ejpam-2287	365	35	repeller	repeller	NOUN
ejpam-2287	365	36	,	,	PUNCT
ejpam-2287	365	37	2	2	NUM
ejpam-2287	365	38	nonhyperbolic	nonhyperbolic	ADJ
ejpam-2287	365	39	equilibria	equilibrium	NOUN
ejpam-2287	365	40	2	2	NUM
ejpam-2287	365	41	at	at	ADV
ejpam-2287	365	42	least	least	ADJ
ejpam-2287	365	43	one	one	NUM
ejpam-2287	365	44	is	be	AUX
ejpam-2287	365	45	locally	locally	ADV
ejpam-2287	365	46	asymptotically	asymptotically	ADV
ejpam-2287	365	47	stable	stable	ADJ
ejpam-2287	365	48	converges	converge	NOUN
ejpam-2287	365	49	to	to	ADP
ejpam-2287	365	50	↓	↓	PROPN
ejpam-2287	365	51	0.41	0.41	NUM
ejpam-2287	365	52	<	<	X
ejpam-2287	365	53	λµ	λµ	X
ejpam-2287	365	54	<	<	X
ejpam-2287	365	55	2.4	2.4	NUM
ejpam-2287	365	56	3	3	NUM
ejpam-2287	365	57	(	(	PUNCT
ejpam-2287	365	58	0,0	0,0	NOUN
ejpam-2287	365	59	)	)	PUNCT
ejpam-2287	365	60	a	a	DET
ejpam-2287	365	61	repeller	repeller	NOUN
ejpam-2287	365	62	,	,	PUNCT
ejpam-2287	365	63	2	2	NUM
ejpam-2287	365	64	saddle	saddle	NOUN
ejpam-2287	365	65	point	point	NOUN
ejpam-2287	365	66	equilibria	equilibrium	NOUN
ejpam-2287	365	67	2	2	NUM
ejpam-2287	365	68	at	at	ADV
ejpam-2287	365	69	least	least	ADJ
ejpam-2287	365	70	one	one	NUM
ejpam-2287	365	71	is	be	AUX
ejpam-2287	365	72	locally	locally	ADV
ejpam-2287	365	73	asymptotically	asymptotically	ADV
ejpam-2287	365	74	stable	stable	ADJ
ejpam-2287	365	75	an	an	DET
ejpam-2287	365	76	equilibrium	equilibrium	NOUN
ejpam-2287	365	77	or	or	CCONJ
ejpam-2287	365	78	a	a	DET
ejpam-2287	365	79	periodic	periodic	ADJ
ejpam-2287	365	80	soln	soln	NOUN
ejpam-2287	365	81	.	.	PUNCT
ejpam-2287	366	1	↓	↓	PROPN
ejpam-2287	366	2	λµ=	λµ=	VERB
ejpam-2287	366	3	2.4	2.4	NUM
ejpam-2287	366	4	1	1	NUM
ejpam-2287	366	5	(	(	PUNCT
ejpam-2287	366	6	0,0	0,0	NOUN
ejpam-2287	366	7	)	)	PUNCT
ejpam-2287	366	8	nonhyperbolic	nonhyperbolic	ADJ
ejpam-2287	366	9	,	,	PUNCT
ejpam-2287	366	10	neimark	neimark	NOUN
ejpam-2287	366	11	-	-	PUNCT
ejpam-2287	366	12	sacker	sacker	NOUN
ejpam-2287	366	13	bifurcation	bifurcation	NOUN
ejpam-2287	366	14	occurs	occur	VERB
ejpam-2287	366	15	1	1	NUM
ejpam-2287	366	16	it	it	PRON
ejpam-2287	366	17	is	be	AUX
ejpam-2287	366	18	a	a	DET
ejpam-2287	366	19	repelling	repel	VERB
ejpam-2287	366	20	periodic	periodic	ADJ
ejpam-2287	366	21	solution	solution	NOUN
ejpam-2287	366	22	for	for	ADP
ejpam-2287	366	23	θ	θ	PROPN
ejpam-2287	366	24	-values	-value	NOUN
ejpam-2287	366	25	not	not	PART
ejpam-2287	366	26	in	in	ADP
ejpam-2287	366	27	↓	↓	NOUN
ejpam-2287	366	28	2.4	2.4	NUM
ejpam-2287	366	29	<	<	X
ejpam-2287	366	30	λµ≤	λµ≤	X
ejpam-2287	366	31	3.39	3.39	NUM
ejpam-2287	366	32	1	1	NUM
ejpam-2287	366	33	the	the	DET
ejpam-2287	366	34	(	(	PUNCT
ejpam-2287	366	35	0,0	0,0	NOUN
ejpam-2287	366	36	)	)	PUNCT
ejpam-2287	366	37	equil	equil	PROPN
ejpam-2287	366	38	.	.	PUNCT
ejpam-2287	367	1	is	be	AUX
ejpam-2287	367	2	a	a	DET
ejpam-2287	367	3	saddle	saddle	NOUN
ejpam-2287	367	4	point	point	NOUN
ejpam-2287	367	5	1	1	NUM
ejpam-2287	367	6	it	it	PRON
ejpam-2287	367	7	is	be	AUX
ejpam-2287	367	8	a	a	DET
ejpam-2287	367	9	repelling	repel	VERB
ejpam-2287	367	10	periodic	periodic	ADJ
ejpam-2287	367	11	solution	solution	NOUN
ejpam-2287	367	12	(	(	PUNCT
ejpam-2287	367	13	θ1,θ2	θ1,θ2	PROPN
ejpam-2287	367	14	)	)	PUNCT
ejpam-2287	367	15	3.39	3.39	NUM
ejpam-2287	367	16	<	<	X
ejpam-2287	367	17	λµ	λµ	X
ejpam-2287	367	18	<	<	X
ejpam-2287	367	19	4.39	4.39	NUM
ejpam-2287	367	20	1	1	NUM
ejpam-2287	367	21	the	the	DET
ejpam-2287	367	22	(	(	PUNCT
ejpam-2287	367	23	0,0	0,0	NOUN
ejpam-2287	367	24	)	)	PUNCT
ejpam-2287	367	25	equil	equil	PROPN
ejpam-2287	367	26	.	.	PUNCT
ejpam-2287	368	1	is	be	AUX
ejpam-2287	368	2	a	a	DET
ejpam-2287	368	3	saddle	saddle	NOUN
ejpam-2287	368	4	point	point	NOUN
ejpam-2287	368	5	1	1	NUM
ejpam-2287	368	6	it	it	PRON
ejpam-2287	368	7	is	be	AUX
ejpam-2287	368	8	a	a	DET
ejpam-2287	368	9	repelling	repel	VERB
ejpam-2287	368	10	periodic	periodic	ADJ
ejpam-2287	368	11	solution	solution	NOUN
ejpam-2287	368	12	every	every	DET
ejpam-2287	368	13	soln	soln	NOUN
ejpam-2287	368	14	.	.	PUNCT
ejpam-2287	369	1	converges	converge	NOUN
ejpam-2287	369	2	to	to	ADP
ejpam-2287	369	3	(	(	PUNCT
ejpam-2287	369	4	0,0	0,0	NOUN
ejpam-2287	369	5	)	)	PUNCT
ejpam-2287	369	6	λµ=	λµ=	VERB
ejpam-2287	369	7	4.39	4.39	NUM
ejpam-2287	369	8	1	1	NUM
ejpam-2287	370	1	the	the	DET
ejpam-2287	370	2	(	(	PUNCT
ejpam-2287	370	3	0,0	0,0	NOUN
ejpam-2287	370	4	)	)	PUNCT
ejpam-2287	370	5	equil	equil	PROPN
ejpam-2287	370	6	.	.	PUNCT
ejpam-2287	370	7	is	be	AUX
ejpam-2287	370	8	a	a	DET
ejpam-2287	370	9	saddle	saddle	NOUN
ejpam-2287	370	10	point	point	NOUN
ejpam-2287	370	11	1	1	NUM
ejpam-2287	370	12	it	it	PRON
ejpam-2287	370	13	is	be	AUX
ejpam-2287	370	14	a	a	DET
ejpam-2287	370	15	repelling	repel	VERB
ejpam-2287	370	16	periodic	periodic	ADJ
ejpam-2287	370	17	solution	solution	NOUN
ejpam-2287	370	18	every	every	DET
ejpam-2287	370	19	soln	soln	NOUN
ejpam-2287	370	20	.	.	PUNCT
ejpam-2287	371	1	converges	converge	NOUN
ejpam-2287	371	2	to	to	ADP
ejpam-2287	371	3	(	(	PUNCT
ejpam-2287	371	4	0,0	0,0	NOUN
ejpam-2287	371	5	)	)	PUNCT
ejpam-2287	371	6	4.39≤	4.39≤	NOUN
ejpam-2287	371	7	λµ	λµ	ADP
ejpam-2287	371	8	<	<	X
ejpam-2287	371	9	6.38	6.38	NUM
ejpam-2287	371	10	1	1	NUM
ejpam-2287	371	11	the	the	DET
ejpam-2287	371	12	(	(	PUNCT
ejpam-2287	371	13	0,0	0,0	NOUN
ejpam-2287	371	14	)	)	PUNCT
ejpam-2287	371	15	equil	equil	PROPN
ejpam-2287	371	16	.	.	PUNCT
ejpam-2287	372	1	is	be	AUX
ejpam-2287	372	2	a	a	DET
ejpam-2287	372	3	saddle	saddle	NOUN
ejpam-2287	372	4	point	point	NOUN
ejpam-2287	372	5	1	1	NUM
ejpam-2287	372	6	it	it	PRON
ejpam-2287	372	7	is	be	AUX
ejpam-2287	372	8	a	a	DET
ejpam-2287	372	9	repelling	repel	VERB
ejpam-2287	372	10	periodic	periodic	ADJ
ejpam-2287	372	11	solution	solution	NOUN
ejpam-2287	372	12	every	every	DET
ejpam-2287	372	13	soln	soln	NOUN
ejpam-2287	372	14	.	.	PUNCT
ejpam-2287	373	1	converges	converge	NOUN
ejpam-2287	373	2	to	to	ADP
ejpam-2287	373	3	(	(	PUNCT
ejpam-2287	373	4	0,0	0,0	NOUN
ejpam-2287	373	5	)	)	PUNCT
ejpam-2287	373	6	λµ=	λµ=	VERB
ejpam-2287	373	7	6.38	6.38	NUM
ejpam-2287	373	8	1	1	NUM
ejpam-2287	373	9	(	(	PUNCT
ejpam-2287	373	10	0,0	0,0	NOUN
ejpam-2287	373	11	)	)	PUNCT
ejpam-2287	373	12	nonhyperbolic	nonhyperbolic	ADJ
ejpam-2287	373	13	,	,	PUNCT
ejpam-2287	373	14	neimark	neimark	NOUN
ejpam-2287	373	15	-	-	PUNCT
ejpam-2287	373	16	sacker	sacker	NOUN
ejpam-2287	373	17	bifurcation	bifurcation	NOUN
ejpam-2287	373	18	occurs	occur	VERB
ejpam-2287	373	19	0	0	NUM
ejpam-2287	373	20	−−−	−−−	NUM
ejpam-2287	374	1	every	every	DET
ejpam-2287	374	2	soln	soln	NOUN
ejpam-2287	374	3	.	.	PUNCT
ejpam-2287	375	1	converges	converge	NOUN
ejpam-2287	375	2	to	to	ADP
ejpam-2287	375	3	(	(	PUNCT
ejpam-2287	375	4	0,0	0,0	NOUN
ejpam-2287	375	5	)	)	PUNCT
ejpam-2287	375	6	λµ	λµ	ADP
ejpam-2287	375	7	>	>	X
ejpam-2287	375	8	6.38	6.38	NUM
ejpam-2287	375	9	1	1	NUM
ejpam-2287	375	10	(	(	PUNCT
ejpam-2287	375	11	0,0	0,0	NOUN
ejpam-2287	375	12	)	)	PUNCT
ejpam-2287	375	13	is	be	AUX
ejpam-2287	375	14	a	a	DET
ejpam-2287	375	15	repelling	repelling	NOUN
ejpam-2287	375	16	equilibrium	equilibrium	NOUN
ejpam-2287	375	17	0	0	NUM
ejpam-2287	375	18	−−−	−−−	NOUN
ejpam-2287	375	19	every	every	DET
ejpam-2287	375	20	soln	soln	NOUN
ejpam-2287	375	21	.	.	PUNCT
ejpam-2287	376	1	escapes	escape	VERB
ejpam-2287	376	2	to∞	to∞	PROPN
ejpam-2287	376	3	references	reference	VERB
ejpam-2287	376	4	460	460	NUM
ejpam-2287	376	5	references	reference	NOUN
ejpam-2287	376	6	[	[	X
ejpam-2287	376	7	1	1	NUM
ejpam-2287	376	8	]	]	PUNCT
ejpam-2287	376	9	s.	s.	PROPN
ejpam-2287	376	10	altin	altin	PROPN
ejpam-2287	376	11	,	,	PUNCT
ejpam-2287	376	12	k.	k.	PROPN
ejpam-2287	376	13	kaptan	kaptan	PROPN
ejpam-2287	376	14	and	and	CCONJ
ejpam-2287	376	15	s.	s.	PROPN
ejpam-2287	376	16	s.	s.	PROPN
ejpam-2287	376	17	tezcan	tezcan	PROPN
ejpam-2287	376	18	.	.	PUNCT
ejpam-2287	377	1	dynamic	dynamic	ADJ
ejpam-2287	377	2	analysis	analysis	NOUN
ejpam-2287	377	3	of	of	ADP
ejpam-2287	377	4	suspension	suspension	NOUN
ejpam-2287	377	5	bridges	bridge	NOUN
ejpam-2287	377	6	and	and	CCONJ
ejpam-2287	377	7	full	full	ADJ
ejpam-2287	377	8	scale	scale	NOUN
ejpam-2287	377	9	testing	testing	NOUN
ejpam-2287	377	10	,	,	PUNCT
ejpam-2287	377	11	open	open	ADJ
ejpam-2287	377	12	journal	journal	NOUN
ejpam-2287	377	13	of	of	ADP
ejpam-2287	377	14	civil	civil	ADJ
ejpam-2287	377	15	engineering	engineering	NOUN
ejpam-2287	377	16	2	2	NUM
ejpam-2287	377	17	,	,	PUNCT
ejpam-2287	377	18	58	58	NUM
ejpam-2287	377	19	-	-	SYM
ejpam-2287	377	20	67	67	NUM
ejpam-2287	377	21	,	,	PUNCT
ejpam-2287	377	22	2012	2012	NUM
ejpam-2287	377	23	.	.	PUNCT
ejpam-2287	378	1	[	[	X
ejpam-2287	378	2	2	2	X
ejpam-2287	378	3	]	]	PUNCT
ejpam-2287	378	4	s.	s.	PROPN
ejpam-2287	378	5	basu	basu	PROPN
ejpam-2287	378	6	and	and	CCONJ
ejpam-2287	378	7	o.	o.	PROPN
ejpam-2287	378	8	merino	merino	NOUN
ejpam-2287	378	9	.	.	PUNCT
ejpam-2287	379	1	on	on	ADP
ejpam-2287	379	2	the	the	DET
ejpam-2287	379	3	global	global	ADJ
ejpam-2287	379	4	behavior	behavior	NOUN
ejpam-2287	379	5	of	of	ADP
ejpam-2287	379	6	solutions	solution	NOUN
ejpam-2287	379	7	to	to	ADP
ejpam-2287	379	8	a	a	DET
ejpam-2287	379	9	planar	planar	ADJ
ejpam-2287	379	10	system	system	NOUN
ejpam-2287	379	11	of	of	ADP
ejpam-2287	379	12	difference	difference	NOUN
ejpam-2287	379	13	equations	equation	NOUN
ejpam-2287	379	14	,	,	PUNCT
ejpam-2287	379	15	communications	communication	NOUN
ejpam-2287	379	16	on	on	ADP
ejpam-2287	379	17	applied	apply	VERB
ejpam-2287	379	18	nonlinear	nonlinear	ADJ
ejpam-2287	379	19	analysis	analysis	NOUN
ejpam-2287	379	20	16(1	16(1	NOUN
ejpam-2287	379	21	)	)	PUNCT
ejpam-2287	379	22	,	,	PUNCT
ejpam-2287	379	23	89	89	NUM
ejpam-2287	379	24	-	-	SYM
ejpam-2287	379	25	101	101	NUM
ejpam-2287	379	26	,	,	PUNCT
ejpam-2287	379	27	2009	2009	NUM
ejpam-2287	379	28	.	.	PUNCT
ejpam-2287	380	1	[	[	X
ejpam-2287	380	2	3	3	X
ejpam-2287	380	3	]	]	PUNCT
ejpam-2287	380	4	s.	s.	PROPN
ejpam-2287	380	5	basu	basu	PROPN
ejpam-2287	380	6	.	.	PUNCT
ejpam-2287	381	1	the	the	DET
ejpam-2287	381	2	role	role	NOUN
ejpam-2287	381	3	of	of	ADP
ejpam-2287	381	4	plane	plane	NOUN
ejpam-2287	381	5	algebraic	algebraic	ADJ
ejpam-2287	381	6	curves	curve	NOUN
ejpam-2287	381	7	in	in	ADP
ejpam-2287	381	8	the	the	DET
ejpam-2287	381	9	global	global	ADJ
ejpam-2287	381	10	dynamics	dynamic	NOUN
ejpam-2287	381	11	of	of	ADP
ejpam-2287	381	12	a	a	DET
ejpam-2287	381	13	class	class	NOUN
ejpam-2287	381	14	of	of	ADP
ejpam-2287	381	15	planar	planar	ADJ
ejpam-2287	381	16	nonlinear	nonlinear	ADJ
ejpam-2287	381	17	discrete	discrete	ADJ
ejpam-2287	381	18	dynamical	dynamical	ADJ
ejpam-2287	381	19	systems	system	NOUN
ejpam-2287	381	20	,	,	PUNCT
ejpam-2287	381	21	advances	advance	NOUN
ejpam-2287	381	22	in	in	ADP
ejpam-2287	381	23	difference	difference	NOUN
ejpam-2287	381	24	equations	equation	NOUN
ejpam-2287	381	25	2013:292	2013:292	NUM
ejpam-2287	381	26	,	,	PUNCT
ejpam-2287	381	27	2013	2013	NUM
ejpam-2287	381	28	.	.	PUNCT
ejpam-2287	382	1	[	[	X
ejpam-2287	382	2	4	4	X
ejpam-2287	382	3	]	]	PUNCT
ejpam-2287	382	4	s.	s.	PROPN
ejpam-2287	382	5	basu	basu	PROPN
ejpam-2287	382	6	.	.	PUNCT
ejpam-2287	383	1	global	global	ADJ
ejpam-2287	383	2	behavior	behavior	NOUN
ejpam-2287	383	3	of	of	ADP
ejpam-2287	383	4	solutions	solution	NOUN
ejpam-2287	383	5	to	to	ADP
ejpam-2287	383	6	a	a	DET
ejpam-2287	383	7	class	class	NOUN
ejpam-2287	383	8	of	of	ADP
ejpam-2287	383	9	second	second	ADJ
ejpam-2287	383	10	-	-	PUNCT
ejpam-2287	383	11	order	order	NOUN
ejpam-2287	383	12	rational	rational	ADJ
ejpam-2287	383	13	difference	difference	NOUN
ejpam-2287	383	14	equations	equation	NOUN
ejpam-2287	383	15	when	when	SCONJ
ejpam-2287	383	16	prime	prime	ADJ
ejpam-2287	383	17	period	period	NOUN
ejpam-2287	383	18	-	-	PUNCT
ejpam-2287	383	19	two	two	NUM
ejpam-2287	383	20	solutions	solution	NOUN
ejpam-2287	383	21	exist	exist	VERB
ejpam-2287	383	22	,	,	PUNCT
ejpam-2287	383	23	journal	journal	NOUN
ejpam-2287	383	24	of	of	ADP
ejpam-2287	383	25	difference	difference	NOUN
ejpam-2287	383	26	equations	equation	NOUN
ejpam-2287	383	27	and	and	CCONJ
ejpam-2287	383	28	applications	application	NOUN
ejpam-2287	383	29	18,issue	18,issue	PROPN
ejpam-2287	383	30	5	5	NUM
ejpam-2287	383	31	,	,	PUNCT
ejpam-2287	383	32	1	1	NUM
ejpam-2287	383	33	-	-	SYM
ejpam-2287	383	34	29	29	NUM
ejpam-2287	383	35	,	,	PUNCT
ejpam-2287	383	36	2012	2012	NUM
ejpam-2287	383	37	.	.	PUNCT
ejpam-2287	384	1	[	[	X
ejpam-2287	384	2	5	5	X
ejpam-2287	384	3	]	]	PUNCT
ejpam-2287	384	4	e.	e.	PROPN
ejpam-2287	384	5	dancer	dancer	PROPN
ejpam-2287	384	6	and	and	CCONJ
ejpam-2287	384	7	p.	p.	PROPN
ejpam-2287	384	8	hess	hess	PROPN
ejpam-2287	384	9	.	.	PUNCT
ejpam-2287	385	1	stability	stability	NOUN
ejpam-2287	385	2	of	of	ADP
ejpam-2287	385	3	fixed	fix	VERB
ejpam-2287	385	4	points	point	NOUN
ejpam-2287	385	5	for	for	ADP
ejpam-2287	385	6	order	order	NOUN
ejpam-2287	385	7	preserving	preserve	VERB
ejpam-2287	385	8	discrete	discrete	ADJ
ejpam-2287	385	9	-	-	PUNCT
ejpam-2287	385	10	time	time	NOUN
ejpam-2287	385	11	dynamical	dynamical	ADJ
ejpam-2287	385	12	systems	system	NOUN
ejpam-2287	385	13	,	,	PUNCT
ejpam-2287	385	14	journal	journal	NOUN
ejpam-2287	385	15	für	für	PROPN
ejpam-2287	385	16	die	die	VERB
ejpam-2287	385	17	reine	reine	PROPN
ejpam-2287	385	18	und	und	PROPN
ejpam-2287	385	19	angewandte	angewandte	PROPN
ejpam-2287	385	20	mathematik	mathematik	PROPN
ejpam-2287	385	21	419	419	NUM
ejpam-2287	385	22	,	,	PUNCT
ejpam-2287	385	23	125	125	NUM
ejpam-2287	385	24	-	-	SYM
ejpam-2287	385	25	139	139	NUM
ejpam-2287	385	26	,	,	PUNCT
ejpam-2287	385	27	1991	1991	NUM
ejpam-2287	385	28	.	.	PUNCT
ejpam-2287	386	1	[	[	X
ejpam-2287	386	2	6	6	NUM
ejpam-2287	386	3	]	]	PUNCT
ejpam-2287	386	4	m.	m.	NOUN
ejpam-2287	386	5	s.	s.	PROPN
ejpam-2287	386	6	t.	t.	PROPN
ejpam-2287	386	7	de	de	PROPN
ejpam-2287	386	8	freitas	freitas	PROPN
ejpam-2287	386	9	,	,	PUNCT
ejpam-2287	386	10	r.	r.	PROPN
ejpam-2287	386	11	l.	l.	PROPN
ejpam-2287	386	12	viana	viana	PROPN
ejpam-2287	386	13	and	and	CCONJ
ejpam-2287	386	14	c.	c.	PROPN
ejpam-2287	386	15	grebogi	grebogi	PROPN
ejpam-2287	386	16	.	.	PUNCT
ejpam-2287	387	1	basins	basin	NOUN
ejpam-2287	387	2	of	of	ADP
ejpam-2287	387	3	attraction	attraction	NOUN
ejpam-2287	387	4	of	of	ADP
ejpam-2287	387	5	periodic	periodic	ADJ
ejpam-2287	387	6	oscillations	oscillation	NOUN
ejpam-2287	387	7	in	in	ADP
ejpam-2287	387	8	suspension	suspension	NOUN
ejpam-2287	387	9	bridges	bridge	NOUN
ejpam-2287	387	10	,	,	PUNCT
ejpam-2287	387	11	nonlinear	nonlinear	ADJ
ejpam-2287	387	12	dynamics	dynamic	NOUN
ejpam-2287	387	13	37	37	NUM
ejpam-2287	387	14	,	,	PUNCT
ejpam-2287	387	15	207	207	NUM
ejpam-2287	387	16	-	-	SYM
ejpam-2287	387	17	226,2004	226,2004	NUM
ejpam-2287	387	18	.	.	PUNCT
ejpam-2287	388	1	[	[	X
ejpam-2287	388	2	7	7	X
ejpam-2287	388	3	]	]	PUNCT
ejpam-2287	388	4	m.	m.	NOUN
ejpam-2287	388	5	s.	s.	PROPN
ejpam-2287	388	6	t.	t.	PROPN
ejpam-2287	388	7	de	de	PROPN
ejpam-2287	388	8	freitas	freitas	PROPN
ejpam-2287	388	9	,	,	PUNCT
ejpam-2287	388	10	r.	r.	PROPN
ejpam-2287	388	11	l.	l.	PROPN
ejpam-2287	388	12	viana	viana	PROPN
ejpam-2287	388	13	and	and	CCONJ
ejpam-2287	388	14	c.	c.	PROPN
ejpam-2287	388	15	grebogi	grebogi	PROPN
ejpam-2287	388	16	.	.	PUNCT
ejpam-2287	389	1	multistability	multistability	NOUN
ejpam-2287	389	2	,	,	PUNCT
ejpam-2287	389	3	basin	basin	NOUN
ejpam-2287	389	4	boundary	boundary	ADJ
ejpam-2287	389	5	structure	structure	NOUN
ejpam-2287	389	6	,	,	PUNCT
ejpam-2287	389	7	and	and	CCONJ
ejpam-2287	389	8	chaotic	chaotic	ADJ
ejpam-2287	389	9	behavior	behavior	NOUN
ejpam-2287	389	10	in	in	ADP
ejpam-2287	389	11	a	a	DET
ejpam-2287	389	12	suspension	suspension	NOUN
ejpam-2287	389	13	bridge	bridge	NOUN
ejpam-2287	389	14	model	model	NOUN
ejpam-2287	389	15	,	,	PUNCT
ejpam-2287	389	16	international	international	ADJ
ejpam-2287	389	17	journal	journal	NOUN
ejpam-2287	389	18	of	of	ADP
ejpam-2287	389	19	bifurcation	bifurcation	NOUN
ejpam-2287	389	20	and	and	CCONJ
ejpam-2287	389	21	chaos	chaos	NOUN
ejpam-2287	389	22	14(3	14(3	NUM
ejpam-2287	389	23	)	)	PUNCT
ejpam-2287	389	24	,	,	PUNCT
ejpam-2287	389	25	927	927	NUM
ejpam-2287	389	26	-	-	SYM
ejpam-2287	389	27	950	950	NUM
ejpam-2287	389	28	,	,	PUNCT
ejpam-2287	389	29	2004	2004	NUM
ejpam-2287	389	30	.	.	PUNCT
ejpam-2287	390	1	[	[	X
ejpam-2287	390	2	8	8	NUM
ejpam-2287	390	3	]	]	PUNCT
ejpam-2287	390	4	z.	z.	PROPN
ejpam-2287	390	5	ding	ding	PROPN
ejpam-2287	390	6	.	.	PUNCT
ejpam-2287	391	1	on	on	ADP
ejpam-2287	391	2	nonlinear	nonlinear	ADJ
ejpam-2287	391	3	oscillations	oscillation	NOUN
ejpam-2287	391	4	in	in	ADP
ejpam-2287	391	5	a	a	DET
ejpam-2287	391	6	suspension	suspension	NOUN
ejpam-2287	391	7	bridge	bridge	NOUN
ejpam-2287	391	8	system	system	NOUN
ejpam-2287	391	9	,	,	PUNCT
ejpam-2287	391	10	transactions	transaction	NOUN
ejpam-2287	391	11	of	of	ADP
ejpam-2287	391	12	the	the	DET
ejpam-2287	391	13	american	american	PROPN
ejpam-2287	391	14	mathematical	mathematical	PROPN
ejpam-2287	391	15	society	society	NOUN
ejpam-2287	391	16	354(1	354(1	NUM
ejpam-2287	391	17	)	)	PUNCT
ejpam-2287	391	18	,	,	PUNCT
ejpam-2287	391	19	265	265	NUM
ejpam-2287	391	20	-	-	SYM
ejpam-2287	391	21	274	274	NUM
ejpam-2287	391	22	,	,	PUNCT
ejpam-2287	391	23	2001	2001	NUM
ejpam-2287	391	24	.	.	PUNCT
ejpam-2287	392	1	[	[	X
ejpam-2287	392	2	9	9	NUM
ejpam-2287	392	3	]	]	PUNCT
ejpam-2287	392	4	s.	s.	PROPN
ejpam-2287	392	5	elaydi	elaydi	VERB
ejpam-2287	392	6	.	.	PUNCT
ejpam-2287	393	1	an	an	DET
ejpam-2287	393	2	introduction	introduction	NOUN
ejpam-2287	393	3	to	to	ADP
ejpam-2287	393	4	difference	difference	NOUN
ejpam-2287	393	5	equations	equation	NOUN
ejpam-2287	393	6	,	,	PUNCT
ejpam-2287	393	7	2nd	2nd	ADJ
ejpam-2287	393	8	ed	ed	NOUN
ejpam-2287	393	9	.	.	PROPN
ejpam-2287	393	10	,	,	PUNCT
ejpam-2287	393	11	springer	springer	NOUN
ejpam-2287	393	12	-	-	PUNCT
ejpam-2287	393	13	verlag	verlag	PROPN
ejpam-2287	393	14	,	,	PUNCT
ejpam-2287	393	15	new	new	PROPN
ejpam-2287	393	16	york	york	PROPN
ejpam-2287	393	17	,	,	PUNCT
ejpam-2287	393	18	1999	1999	NUM
ejpam-2287	393	19	.	.	PUNCT
ejpam-2287	394	1	[	[	X
ejpam-2287	394	2	10	10	NUM
ejpam-2287	394	3	]	]	X
ejpam-2287	394	4	s.	s.	PROPN
ejpam-2287	394	5	elaydi	elaydi	VERB
ejpam-2287	394	6	.	.	PUNCT
ejpam-2287	395	1	discrete	discrete	ADJ
ejpam-2287	395	2	chaos	chaos	NOUN
ejpam-2287	395	3	with	with	ADP
ejpam-2287	395	4	applications	application	NOUN
ejpam-2287	395	5	in	in	ADP
ejpam-2287	395	6	science	science	NOUN
ejpam-2287	395	7	and	and	CCONJ
ejpam-2287	395	8	engineering	engineering	NOUN
ejpam-2287	395	9	,	,	PUNCT
ejpam-2287	395	10	2nd	2nd	ADJ
ejpam-2287	395	11	ed	ed	NOUN
ejpam-2287	395	12	.	.	PROPN
ejpam-2287	395	13	,	,	PUNCT
ejpam-2287	395	14	chapmanhall	chapmanhall	PROPN
ejpam-2287	395	15	,	,	PUNCT
ejpam-2287	395	16	boca	boca	PROPN
ejpam-2287	395	17	raton	raton	PROPN
ejpam-2287	395	18	,	,	PUNCT
ejpam-2287	395	19	fl	fl	PROPN
ejpam-2287	395	20	,	,	PUNCT
ejpam-2287	395	21	2008	2008	NUM
ejpam-2287	395	22	.	.	PUNCT
ejpam-2287	396	1	[	[	X
ejpam-2287	396	2	11	11	NUM
ejpam-2287	396	3	]	]	PUNCT
ejpam-2287	396	4	m.	m.	NOUN
ejpam-2287	396	5	hirsch	hirsch	PROPN
ejpam-2287	396	6	and	and	CCONJ
ejpam-2287	396	7	h.	h.	PROPN
ejpam-2287	396	8	smith	smith	PROPN
ejpam-2287	396	9	.	.	PUNCT
ejpam-2287	397	1	monotone	monotone	ADJ
ejpam-2287	397	2	dynamical	dynamical	ADJ
ejpam-2287	397	3	systems	system	NOUN
ejpam-2287	397	4	,	,	PUNCT
ejpam-2287	397	5	handbook	handbook	NOUN
ejpam-2287	397	6	of	of	ADP
ejpam-2287	397	7	differential	differential	ADJ
ejpam-2287	397	8	equations	equation	NOUN
ejpam-2287	397	9	:	:	PUNCT
ejpam-2287	397	10	ordinary	ordinary	ADJ
ejpam-2287	397	11	differential	differential	ADJ
ejpam-2287	397	12	equations	equation	NOUN
ejpam-2287	397	13	.	.	PUNCT
ejpam-2287	398	1	vol	vol	NOUN
ejpam-2287	398	2	.	.	PUNCT
ejpam-2287	398	3	ii	ii	PROPN
ejpam-2287	398	4	,	,	PUNCT
ejpam-2287	398	5	239	239	NUM
ejpam-2287	398	6	-	-	SYM
ejpam-2287	398	7	357	357	NUM
ejpam-2287	398	8	,	,	PUNCT
ejpam-2287	398	9	elsevier	elsevier	PROPN
ejpam-2287	398	10	b.	b.	PROPN
ejpam-2287	398	11	v.	v.	PROPN
ejpam-2287	398	12	,	,	PUNCT
ejpam-2287	398	13	amsterdam	amsterdam	PROPN
ejpam-2287	398	14	,	,	PUNCT
ejpam-2287	398	15	2005	2005	NUM
ejpam-2287	398	16	.	.	PUNCT
ejpam-2287	399	1	[	[	X
ejpam-2287	399	2	12	12	NUM
ejpam-2287	399	3	]	]	PUNCT
ejpam-2287	399	4	m.	m.	PROPN
ejpam-2287	399	5	r.	r.	PROPN
ejpam-2287	399	6	s.	s.	PROPN
ejpam-2287	399	7	kulenović	kulenović	PROPN
ejpam-2287	399	8	and	and	CCONJ
ejpam-2287	399	9	o.	o.	PROPN
ejpam-2287	399	10	merino	merino	PROPN
ejpam-2287	399	11	.	.	PUNCT
ejpam-2287	400	1	competitive	competitive	ADJ
ejpam-2287	400	2	-	-	PUNCT
ejpam-2287	400	3	exclusion	exclusion	NOUN
ejpam-2287	400	4	versus	versus	ADP
ejpam-2287	400	5	competitive	competitive	ADJ
ejpam-2287	400	6	-	-	PUNCT
ejpam-2287	400	7	coexistence	coexistence	NOUN
ejpam-2287	400	8	for	for	ADP
ejpam-2287	400	9	systems	system	NOUN
ejpam-2287	400	10	in	in	ADP
ejpam-2287	400	11	the	the	DET
ejpam-2287	400	12	plane	plane	NOUN
ejpam-2287	400	13	,	,	PUNCT
ejpam-2287	400	14	discrete	discrete	ADJ
ejpam-2287	400	15	and	and	CCONJ
ejpam-2287	400	16	continuous	continuous	ADJ
ejpam-2287	400	17	dynamical	dynamical	ADJ
ejpam-2287	400	18	systems	system	NOUN
ejpam-2287	400	19	series	series	PROPN
ejpam-2287	400	20	b	b	PROPN
ejpam-2287	400	21	6	6	NUM
ejpam-2287	400	22	,	,	PUNCT
ejpam-2287	400	23	11411156	11411156	NUM
ejpam-2287	400	24	,	,	PUNCT
ejpam-2287	400	25	2006	2006	NUM
ejpam-2287	400	26	.	.	PUNCT
ejpam-2287	401	1	[	[	X
ejpam-2287	401	2	13	13	NUM
ejpam-2287	401	3	]	]	PUNCT
ejpam-2287	401	4	p.	p.	NOUN
ejpam-2287	401	5	j.	j.	PROPN
ejpam-2287	401	6	mckenna	mckenna	PROPN
ejpam-2287	401	7	and	and	CCONJ
ejpam-2287	401	8	k.	k.	PROPN
ejpam-2287	401	9	s.	s.	PROPN
ejpam-2287	401	10	moore	moore	PROPN
ejpam-2287	401	11	.	.	PUNCT
ejpam-2287	402	1	multiple	multiple	ADJ
ejpam-2287	402	2	periodic	periodic	ADJ
ejpam-2287	402	3	solutions	solution	NOUN
ejpam-2287	402	4	to	to	ADP
ejpam-2287	402	5	a	a	DET
ejpam-2287	402	6	suspension	suspension	NOUN
ejpam-2287	402	7	bridge	bridge	NOUN
ejpam-2287	402	8	ordinary	ordinary	ADJ
ejpam-2287	402	9	differential	differential	ADJ
ejpam-2287	402	10	equation	equation	NOUN
ejpam-2287	402	11	,	,	PUNCT
ejpam-2287	402	12	proceedings	proceeding	NOUN
ejpam-2287	402	13	of	of	ADP
ejpam-2287	402	14	the	the	DET
ejpam-2287	402	15	conference	conference	NOUN
ejpam-2287	402	16	on	on	ADP
ejpam-2287	402	17	nonlinear	nonlinear	ADJ
ejpam-2287	402	18	differential	differential	ADJ
ejpam-2287	402	19	equations	equation	NOUN
ejpam-2287	402	20	(	(	PUNCT
ejpam-2287	402	21	coral	coral	ADJ
ejpam-2287	402	22	gables	gable	NOUN
ejpam-2287	402	23	,	,	PUNCT
ejpam-2287	402	24	fl	fl	NOUN
ejpam-2287	402	25	,	,	PUNCT
ejpam-2287	402	26	1999	1999	NUM
ejpam-2287	402	27	)	)	PUNCT
ejpam-2287	402	28	.	.	PUNCT
ejpam-2287	403	1	vol	vol	NOUN
ejpam-2287	403	2	.	.	PROPN
ejpam-2287	403	3	5	5	NUM
ejpam-2287	403	4	,	,	PUNCT
ejpam-2287	403	5	2000	2000	NUM
ejpam-2287	403	6	.	.	PUNCT
ejpam-2287	404	1	[	[	X
ejpam-2287	404	2	14	14	NUM
ejpam-2287	404	3	]	]	PUNCT
ejpam-2287	404	4	a.	a.	NOUN
ejpam-2287	404	5	pascoletti	pascoletti	PROPN
ejpam-2287	404	6	and	and	CCONJ
ejpam-2287	404	7	f.	f.	PROPN
ejpam-2287	404	8	zanolin	zanolin	PROPN
ejpam-2287	404	9	.	.	PUNCT
ejpam-2287	405	1	example	example	NOUN
ejpam-2287	405	2	of	of	ADP
ejpam-2287	405	3	a	a	DET
ejpam-2287	405	4	suspension	suspension	NOUN
ejpam-2287	405	5	bridge	bridge	NOUN
ejpam-2287	405	6	ode	ode	PROPN
ejpam-2287	405	7	model	model	NOUN
ejpam-2287	405	8	exhibiting	exhibit	VERB
ejpam-2287	405	9	chaotic	chaotic	ADJ
ejpam-2287	405	10	dynamics	dynamic	NOUN
ejpam-2287	405	11	:	:	PUNCT
ejpam-2287	405	12	a	a	DET
ejpam-2287	405	13	topological	topological	ADJ
ejpam-2287	405	14	approach	approach	NOUN
ejpam-2287	405	15	,	,	PUNCT
ejpam-2287	405	16	journal	journal	NOUN
ejpam-2287	405	17	of	of	ADP
ejpam-2287	405	18	mathematical	mathematical	ADJ
ejpam-2287	405	19	analysis	analysis	NOUN
ejpam-2287	405	20	and	and	CCONJ
ejpam-2287	405	21	applications	application	NOUN
ejpam-2287	405	22	339	339	NUM
ejpam-2287	405	23	,	,	PUNCT
ejpam-2287	405	24	1179	1179	NUM
ejpam-2287	405	25	-	-	SYM
ejpam-2287	405	26	1198	1198	NUM
ejpam-2287	405	27	,	,	PUNCT
ejpam-2287	405	28	2008	2008	NUM
ejpam-2287	405	29	.	.	PUNCT
ejpam-2287	406	1	references	reference	NOUN
ejpam-2287	406	2	461	461	NUM
ejpam-2287	407	1	[	[	X
ejpam-2287	407	2	15	15	NUM
ejpam-2287	407	3	]	]	X
ejpam-2287	407	4	h.	h.	PROPN
ejpam-2287	407	5	smith	smith	PROPN
ejpam-2287	407	6	.	.	PUNCT
ejpam-2287	408	1	planar	planar	ADJ
ejpam-2287	408	2	competitive	competitive	ADJ
ejpam-2287	408	3	and	and	CCONJ
ejpam-2287	408	4	cooperative	cooperative	ADJ
ejpam-2287	408	5	difference	difference	NOUN
ejpam-2287	408	6	equations	equation	NOUN
ejpam-2287	408	7	,	,	PUNCT
ejpam-2287	408	8	journal	journal	NOUN
ejpam-2287	408	9	of	of	ADP
ejpam-2287	408	10	difference	difference	NOUN
ejpam-2287	408	11	equations	equation	NOUN
ejpam-2287	408	12	and	and	CCONJ
ejpam-2287	408	13	applications	application	NOUN
ejpam-2287	408	14	3	3	NUM
ejpam-2287	408	15	,	,	PUNCT
ejpam-2287	408	16	335	335	NUM
ejpam-2287	408	17	-	-	SYM
ejpam-2287	408	18	357	357	NUM
ejpam-2287	408	19	,	,	PUNCT
ejpam-2287	408	20	1998	1998	NUM
ejpam-2287	408	21	.	.	PUNCT
ejpam-2287	409	1	[	[	X
ejpam-2287	409	2	16	16	NUM
ejpam-2287	409	3	]	]	PUNCT
ejpam-2287	409	4	r.	r.	PROPN
ejpam-2287	409	5	j.	j.	PROPN
ejpam-2287	409	6	walker	walker	PROPN
ejpam-2287	409	7	.	.	PUNCT
ejpam-2287	410	1	algebraic	algebraic	ADJ
ejpam-2287	410	2	curves	curve	NOUN
ejpam-2287	410	3	,	,	PUNCT
ejpam-2287	410	4	princeton	princeton	PROPN
ejpam-2287	410	5	university	university	PROPN
ejpam-2287	410	6	press	press	NOUN
ejpam-2287	410	7	,	,	PUNCT
ejpam-2287	410	8	1950	1950	NUM
ejpam-2287	410	9	.	.	PUNCT