id	sid	tid	token	lemma	pos
ejpam-6752	1	1	european	european	PROPN
ejpam-6752	1	2	journal	journal	PROPN
ejpam-6752	1	3	of	of	ADP
ejpam-6752	1	4	pure	pure	ADJ
ejpam-6752	1	5	and	and	CCONJ
ejpam-6752	1	6	applied	applied	ADJ
ejpam-6752	1	7	mathematics	mathematic	NOUN
ejpam-6752	1	8	2025	2025	NUM
ejpam-6752	1	9	,	,	PUNCT
ejpam-6752	1	10	vol	vol	NOUN
ejpam-6752	1	11	.	.	PROPN
ejpam-6752	1	12	18	18	NUM
ejpam-6752	1	13	,	,	PUNCT
ejpam-6752	1	14	issue	issue	NOUN
ejpam-6752	1	15	4	4	NUM
ejpam-6752	1	16	,	,	PUNCT
ejpam-6752	1	17	article	article	NOUN
ejpam-6752	1	18	number	number	NOUN
ejpam-6752	1	19	6752	6752	NUM
ejpam-6752	1	20	issn	issn	PROPN
ejpam-6752	1	21	1307	1307	NUM
ejpam-6752	1	22	-	-	SYM
ejpam-6752	1	23	5543	5543	NUM
ejpam-6752	1	24	–	–	PUNCT
ejpam-6752	1	25	ejpam.com	ejpam.com	X
ejpam-6752	1	26	published	publish	VERB
ejpam-6752	1	27	by	by	ADP
ejpam-6752	1	28	new	new	PROPN
ejpam-6752	1	29	york	york	PROPN
ejpam-6752	1	30	business	business	PROPN
ejpam-6752	1	31	global	global	ADJ
ejpam-6752	1	32	center	center	NOUN
ejpam-6752	1	33	bifurcation	bifurcation	NOUN
ejpam-6752	1	34	for	for	ADP
ejpam-6752	1	35	the	the	DET
ejpam-6752	1	36	smallest	small	ADJ
ejpam-6752	1	37	bimolecular	bimolecular	ADJ
ejpam-6752	1	38	mass	mass	ADJ
ejpam-6752	1	39	-	-	PUNCT
ejpam-6752	1	40	action	action	NOUN
ejpam-6752	1	41	system	system	NOUN
ejpam-6752	1	42	rizgar	rizgar	PROPN
ejpam-6752	1	43	h.	h.	PROPN
ejpam-6752	1	44	salih	salih	PROPN
ejpam-6752	1	45	department	department	PROPN
ejpam-6752	1	46	of	of	ADP
ejpam-6752	1	47	mathematics	mathematics	PROPN
ejpam-6752	1	48	,	,	PUNCT
ejpam-6752	1	49	college	college	NOUN
ejpam-6752	1	50	of	of	ADP
ejpam-6752	1	51	basic	basic	ADJ
ejpam-6752	1	52	education	education	NOUN
ejpam-6752	1	53	,	,	PUNCT
ejpam-6752	1	54	university	university	NOUN
ejpam-6752	1	55	of	of	ADP
ejpam-6752	1	56	raparin	raparin	PROPN
ejpam-6752	1	57	,	,	PUNCT
ejpam-6752	1	58	rania	rania	PROPN
ejpam-6752	1	59	,	,	PUNCT
ejpam-6752	1	60	kurdistan	kurdistan	PROPN
ejpam-6752	1	61	region	region	NOUN
ejpam-6752	1	62	,	,	PUNCT
ejpam-6752	1	63	iraq	iraq	PROPN
ejpam-6752	1	64	abstract	abstract	NOUN
ejpam-6752	1	65	.	.	PUNCT
ejpam-6752	2	1	this	this	DET
ejpam-6752	2	2	paper	paper	NOUN
ejpam-6752	2	3	investigates	investigate	VERB
ejpam-6752	2	4	the	the	DET
ejpam-6752	2	5	center	center	NOUN
ejpam-6752	2	6	bifurcation	bifurcation	NOUN
ejpam-6752	2	7	of	of	ADP
ejpam-6752	2	8	the	the	DET
ejpam-6752	2	9	smallest	small	ADJ
ejpam-6752	2	10	bimolecular	bimolecular	ADJ
ejpam-6752	2	11	mass	mass	ADJ
ejpam-6752	2	12	-	-	PUNCT
ejpam-6752	2	13	action	action	NOUN
ejpam-6752	2	14	system	system	NOUN
ejpam-6752	2	15	.	.	PUNCT
ejpam-6752	3	1	a	a	DET
ejpam-6752	3	2	three	three	NUM
ejpam-6752	3	3	-	-	PUNCT
ejpam-6752	3	4	dimensional	dimensional	ADJ
ejpam-6752	3	5	reaction	reaction	NOUN
ejpam-6752	3	6	network	network	NOUN
ejpam-6752	3	7	,	,	PUNCT
ejpam-6752	3	8	consisting	consist	VERB
ejpam-6752	3	9	of	of	ADP
ejpam-6752	3	10	three	three	NUM
ejpam-6752	3	11	species	specie	NOUN
ejpam-6752	3	12	and	and	CCONJ
ejpam-6752	3	13	four	four	NUM
ejpam-6752	3	14	reactions	reaction	NOUN
ejpam-6752	3	15	,	,	PUNCT
ejpam-6752	3	16	governed	govern	VERB
ejpam-6752	3	17	by	by	ADP
ejpam-6752	3	18	mass	mass	ADJ
ejpam-6752	3	19	-	-	PUNCT
ejpam-6752	3	20	action	action	NOUN
ejpam-6752	3	21	kinetics	kinetic	NOUN
ejpam-6752	3	22	with	with	ADP
ejpam-6752	3	23	a	a	DET
ejpam-6752	3	24	positive	positive	ADJ
ejpam-6752	3	25	equilibrium	equilibrium	NOUN
ejpam-6752	3	26	point	point	NOUN
ejpam-6752	3	27	,	,	PUNCT
ejpam-6752	3	28	is	be	AUX
ejpam-6752	3	29	considered	consider	VERB
ejpam-6752	3	30	.	.	PUNCT
ejpam-6752	4	1	in	in	ADP
ejpam-6752	4	2	addition	addition	NOUN
ejpam-6752	4	3	to	to	ADP
ejpam-6752	4	4	the	the	DET
ejpam-6752	4	5	stability	stability	NOUN
ejpam-6752	4	6	analysis	analysis	NOUN
ejpam-6752	4	7	of	of	ADP
ejpam-6752	4	8	the	the	DET
ejpam-6752	4	9	equilibrium	equilibrium	NOUN
ejpam-6752	4	10	point	point	NOUN
ejpam-6752	4	11	,	,	PUNCT
ejpam-6752	4	12	the	the	DET
ejpam-6752	4	13	dynamic	dynamic	ADJ
ejpam-6752	4	14	directions	direction	NOUN
ejpam-6752	4	15	of	of	ADP
ejpam-6752	4	16	the	the	DET
ejpam-6752	4	17	model	model	NOUN
ejpam-6752	4	18	in	in	ADP
ejpam-6752	4	19	its	its	PRON
ejpam-6752	4	20	planes	plane	NOUN
ejpam-6752	4	21	are	be	AUX
ejpam-6752	4	22	examined	examine	VERB
ejpam-6752	4	23	.	.	PUNCT
ejpam-6752	5	1	it	it	PRON
ejpam-6752	5	2	has	have	AUX
ejpam-6752	5	3	been	be	AUX
ejpam-6752	5	4	previously	previously	ADV
ejpam-6752	5	5	shown	show	VERB
ejpam-6752	5	6	that	that	SCONJ
ejpam-6752	5	7	the	the	DET
ejpam-6752	5	8	equilibrium	equilibrium	NOUN
ejpam-6752	5	9	point	point	NOUN
ejpam-6752	5	10	is	be	AUX
ejpam-6752	5	11	classified	classify	VERB
ejpam-6752	5	12	as	as	ADP
ejpam-6752	5	13	a	a	DET
ejpam-6752	5	14	center	center	NOUN
ejpam-6752	5	15	when	when	SCONJ
ejpam-6752	5	16	the	the	DET
ejpam-6752	5	17	reaction	reaction	NOUN
ejpam-6752	5	18	rate	rate	NOUN
ejpam-6752	5	19	constants	constant	NOUN
ejpam-6752	5	20	satisfy	satisfy	VERB
ejpam-6752	5	21	a	a	DET
ejpam-6752	5	22	specific	specific	ADJ
ejpam-6752	5	23	condition	condition	NOUN
ejpam-6752	5	24	,	,	PUNCT
ejpam-6752	5	25	leading	lead	VERB
ejpam-6752	5	26	to	to	ADP
ejpam-6752	5	27	a	a	DET
ejpam-6752	5	28	vertical	vertical	ADJ
ejpam-6752	5	29	andronov	andronov	NOUN
ejpam-6752	5	30	-	-	PUNCT
ejpam-6752	5	31	hopf	hopf	ADJ
ejpam-6752	5	32	bifurcation	bifurcation	NOUN
ejpam-6752	5	33	.	.	PUNCT
ejpam-6752	6	1	furthermore	furthermore	ADV
ejpam-6752	6	2	,	,	PUNCT
ejpam-6752	6	3	it	it	PRON
ejpam-6752	6	4	is	be	AUX
ejpam-6752	6	5	demonstrated	demonstrate	VERB
ejpam-6752	6	6	that	that	SCONJ
ejpam-6752	6	7	only	only	ADV
ejpam-6752	6	8	one	one	NUM
ejpam-6752	6	9	limit	limit	NOUN
ejpam-6752	6	10	cycle	cycle	NOUN
ejpam-6752	6	11	can	can	AUX
ejpam-6752	6	12	bifurcate	bifurcate	VERB
ejpam-6752	6	13	from	from	ADP
ejpam-6752	6	14	the	the	DET
ejpam-6752	6	15	center	center	NOUN
ejpam-6752	6	16	equilibrium	equilibrium	NOUN
ejpam-6752	6	17	point	point	NOUN
ejpam-6752	6	18	using	use	VERB
ejpam-6752	6	19	a	a	DET
ejpam-6752	6	20	bifurcation	bifurcation	NOUN
ejpam-6752	6	21	technique	technique	NOUN
ejpam-6752	6	22	.	.	PUNCT
ejpam-6752	7	1	2020	2020	NUM
ejpam-6752	7	2	mathematics	mathematic	NOUN
ejpam-6752	7	3	subject	subject	NOUN
ejpam-6752	7	4	classifications	classification	NOUN
ejpam-6752	7	5	:	:	PUNCT
ejpam-6752	7	6	37g10	37g10	NUM
ejpam-6752	7	7	,	,	PUNCT
ejpam-6752	7	8	37g15	37g15	NUM
ejpam-6752	7	9	,	,	PUNCT
ejpam-6752	7	10	34c23	34c23	NUM
ejpam-6752	7	11	key	key	ADJ
ejpam-6752	7	12	words	word	NOUN
ejpam-6752	7	13	and	and	CCONJ
ejpam-6752	7	14	phrases	phrase	NOUN
ejpam-6752	7	15	:	:	PUNCT
ejpam-6752	7	16	bimolecular	bimolecular	ADJ
ejpam-6752	7	17	mass	mass	ADJ
ejpam-6752	7	18	-	-	PUNCT
ejpam-6752	7	19	action	action	NOUN
ejpam-6752	7	20	system	system	NOUN
ejpam-6752	7	21	,	,	PUNCT
ejpam-6752	7	22	hopf	hopf	ADJ
ejpam-6752	7	23	bifurcation	bifurcation	NOUN
ejpam-6752	7	24	,	,	PUNCT
ejpam-6752	7	25	limit	limit	VERB
ejpam-6752	7	26	cycle	cycle	NOUN
ejpam-6752	7	27	,	,	PUNCT
ejpam-6752	7	28	center	center	NOUN
ejpam-6752	7	29	bifurcation	bifurcation	NOUN
ejpam-6752	7	30	1	1	NUM
ejpam-6752	7	31	.	.	PUNCT
ejpam-6752	8	1	introduction	introduction	NOUN
ejpam-6752	8	2	chemical	chemical	NOUN
ejpam-6752	8	3	reaction	reaction	NOUN
ejpam-6752	8	4	networks	network	NOUN
ejpam-6752	8	5	are	be	AUX
ejpam-6752	8	6	fascinating	fascinating	ADJ
ejpam-6752	8	7	for	for	ADP
ejpam-6752	8	8	both	both	CCONJ
ejpam-6752	8	9	practical	practical	ADJ
ejpam-6752	8	10	and	and	CCONJ
ejpam-6752	8	11	theoretical	theoretical	ADJ
ejpam-6752	8	12	reasons	reason	NOUN
ejpam-6752	8	13	.	.	PUNCT
ejpam-6752	9	1	they	they	PRON
ejpam-6752	9	2	are	be	AUX
ejpam-6752	9	3	essential	essential	ADJ
ejpam-6752	9	4	components	component	NOUN
ejpam-6752	9	5	of	of	ADP
ejpam-6752	9	6	various	various	ADJ
ejpam-6752	9	7	biological	biological	ADJ
ejpam-6752	9	8	models	model	NOUN
ejpam-6752	9	9	and	and	CCONJ
ejpam-6752	9	10	significantly	significantly	ADV
ejpam-6752	9	11	impact	impact	VERB
ejpam-6752	9	12	other	other	ADJ
ejpam-6752	9	13	fields	field	NOUN
ejpam-6752	9	14	of	of	ADP
ejpam-6752	9	15	science	science	NOUN
ejpam-6752	9	16	and	and	CCONJ
ejpam-6752	9	17	engineering	engineering	NOUN
ejpam-6752	9	18	.	.	PUNCT
ejpam-6752	10	1	numerous	numerous	ADJ
ejpam-6752	10	2	important	important	ADJ
ejpam-6752	10	3	findings	finding	NOUN
ejpam-6752	10	4	,	,	PUNCT
ejpam-6752	10	5	both	both	PRON
ejpam-6752	10	6	traditional	traditional	ADJ
ejpam-6752	10	7	and	and	CCONJ
ejpam-6752	10	8	contemporary	contemporary	ADJ
ejpam-6752	10	9	,	,	PUNCT
ejpam-6752	10	10	provide	provide	VERB
ejpam-6752	10	11	insights	insight	NOUN
ejpam-6752	10	12	into	into	ADP
ejpam-6752	10	13	the	the	DET
ejpam-6752	10	14	dynamics	dynamic	NOUN
ejpam-6752	10	15	of	of	ADP
ejpam-6752	10	16	a	a	DET
ejpam-6752	10	17	chemical	chemical	NOUN
ejpam-6752	10	18	reaction	reaction	NOUN
ejpam-6752	10	19	network	network	NOUN
ejpam-6752	10	20	based	base	VERB
ejpam-6752	10	21	on	on	ADP
ejpam-6752	10	22	its	its	PRON
ejpam-6752	10	23	combinatorial	combinatorial	ADJ
ejpam-6752	10	24	structure	structure	NOUN
ejpam-6752	10	25	[	[	X
ejpam-6752	10	26	1	1	NUM
ejpam-6752	10	27	]	]	PUNCT
ejpam-6752	10	28	.	.	PUNCT
ejpam-6752	11	1	wilhelm	wilhelm	PROPN
ejpam-6752	11	2	described	describe	VERB
ejpam-6752	11	3	a	a	DET
ejpam-6752	11	4	bimolecular	bimolecular	ADJ
ejpam-6752	11	5	chemical	chemical	NOUN
ejpam-6752	11	6	reaction	reaction	NOUN
ejpam-6752	11	7	network	network	NOUN
ejpam-6752	11	8	with	with	ADP
ejpam-6752	11	9	three	three	NUM
ejpam-6752	11	10	species	specie	NOUN
ejpam-6752	11	11	and	and	CCONJ
ejpam-6752	11	12	four	four	NUM
ejpam-6752	11	13	reactions	reaction	NOUN
ejpam-6752	11	14	,	,	PUNCT
ejpam-6752	11	15	having	have	VERB
ejpam-6752	11	16	rank	rank	NOUN
ejpam-6752	11	17	three	three	NUM
ejpam-6752	11	18	,	,	PUNCT
ejpam-6752	11	19	that	that	PRON
ejpam-6752	11	20	exhibits	exhibit	VERB
ejpam-6752	11	21	hopf	hopf	ADJ
ejpam-6752	11	22	bifurcation	bifurcation	NOUN
ejpam-6752	11	23	due	due	ADP
ejpam-6752	11	24	to	to	ADP
ejpam-6752	11	25	mass	mass	ADJ
ejpam-6752	11	26	action	action	NOUN
ejpam-6752	11	27	dynamics	dynamic	NOUN
ejpam-6752	11	28	[	[	X
ejpam-6752	11	29	2	2	NUM
ejpam-6752	11	30	]	]	PUNCT
ejpam-6752	11	31	.	.	PUNCT
ejpam-6752	12	1	his	his	PRON
ejpam-6752	12	2	example	example	NOUN
ejpam-6752	12	3	demonstrated	demonstrate	VERB
ejpam-6752	12	4	that	that	SCONJ
ejpam-6752	12	5	the	the	DET
ejpam-6752	12	6	set	set	NOUN
ejpam-6752	12	7	of	of	ADP
ejpam-6752	12	8	bimolecular	bimolecular	ADJ
ejpam-6752	12	9	networks	network	NOUN
ejpam-6752	12	10	with	with	ADP
ejpam-6752	12	11	hopf	hopf	ADJ
ejpam-6752	12	12	bifurcation	bifurcation	NOUN
ejpam-6752	12	13	is	be	AUX
ejpam-6752	12	14	not	not	PART
ejpam-6752	12	15	empty	empty	ADJ
ejpam-6752	12	16	.	.	PUNCT
ejpam-6752	13	1	however	however	ADV
ejpam-6752	13	2	,	,	PUNCT
ejpam-6752	13	3	there	there	PRON
ejpam-6752	13	4	are	be	VERB
ejpam-6752	13	5	,	,	PUNCT
ejpam-6752	13	6	up	up	ADP
ejpam-6752	13	7	to	to	ADP
ejpam-6752	13	8	isomorphism	isomorphism	NOUN
ejpam-6752	13	9	,	,	PUNCT
ejpam-6752	13	10	14670	14670	NUM
ejpam-6752	13	11	bimolecular	bimolecular	ADJ
ejpam-6752	13	12	networks	network	NOUN
ejpam-6752	13	13	(	(	PUNCT
ejpam-6752	13	14	with	with	ADP
ejpam-6752	13	15	three	three	NUM
ejpam-6752	13	16	species	specie	NOUN
ejpam-6752	13	17	and	and	CCONJ
ejpam-6752	13	18	four	four	NUM
ejpam-6752	13	19	reactions	reaction	NOUN
ejpam-6752	13	20	of	of	ADP
ejpam-6752	13	21	rank	rank	PROPN
ejpam-6752	13	22	three	three	NUM
ejpam-6752	13	23	)	)	PUNCT
ejpam-6752	13	24	that	that	PRON
ejpam-6752	13	25	permit	permit	VERB
ejpam-6752	13	26	positive	positive	ADJ
ejpam-6752	13	27	equilibria	equilibrium	NOUN
ejpam-6752	14	1	[	[	X
ejpam-6752	14	2	3	3	NUM
ejpam-6752	14	3	]	]	PUNCT
ejpam-6752	14	4	.	.	PUNCT
ejpam-6752	15	1	the	the	DET
ejpam-6752	15	2	main	main	ADJ
ejpam-6752	15	3	question	question	NOUN
ejpam-6752	15	4	:	:	PUNCT
ejpam-6752	15	5	is	be	AUX
ejpam-6752	15	6	how	how	SCONJ
ejpam-6752	15	7	many	many	ADJ
ejpam-6752	15	8	of	of	ADP
ejpam-6752	15	9	these	these	DET
ejpam-6752	15	10	networks	network	NOUN
ejpam-6752	15	11	allow	allow	VERB
ejpam-6752	15	12	for	for	ADP
ejpam-6752	15	13	hopf	hopf	ADJ
ejpam-6752	15	14	bifurcation	bifurcation	NOUN
ejpam-6752	15	15	due	due	ADP
ejpam-6752	15	16	to	to	ADP
ejpam-6752	15	17	mass	mass	ADJ
ejpam-6752	15	18	action	action	NOUN
ejpam-6752	15	19	dynamics	dynamic	NOUN
ejpam-6752	15	20	?	?	PUNCT
ejpam-6752	16	1	to	to	PART
ejpam-6752	16	2	answer	answer	VERB
ejpam-6752	16	3	this	this	DET
ejpam-6752	16	4	question	question	NOUN
ejpam-6752	16	5	,	,	PUNCT
ejpam-6752	16	6	a	a	DET
ejpam-6752	16	7	scientific	scientific	ADJ
ejpam-6752	16	8	study	study	NOUN
ejpam-6752	16	9	by	by	ADP
ejpam-6752	16	10	banaji	banaji	PROPN
ejpam-6752	16	11	and	and	CCONJ
ejpam-6752	16	12	boros	boro	NOUN
ejpam-6752	16	13	investigated	investigate	VERB
ejpam-6752	16	14	the	the	DET
ejpam-6752	16	15	smallest	small	ADJ
ejpam-6752	16	16	doi	doi	NOUN
ejpam-6752	16	17	:	:	PUNCT
ejpam-6752	16	18	https://doi.org/10.29020/nybg.ejpam.v18i4.6752	https://doi.org/10.29020/nybg.ejpam.v18i4.6752	NOUN
ejpam-6752	16	19	email	email	NOUN
ejpam-6752	16	20	address	address	NOUN
ejpam-6752	16	21	:	:	PUNCT
ejpam-6752	17	1	rizgar.salih@uor.edu.krd	rizgar.salih@uor.edu.krd	PROPN
ejpam-6752	17	2	(	(	PUNCT
ejpam-6752	17	3	r.	r.	PROPN
ejpam-6752	17	4	h.	h.	PROPN
ejpam-6752	17	5	salih	salih	PROPN
ejpam-6752	17	6	)	)	PUNCT
ejpam-6752	17	7	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6752	18	1	1	1	NUM
ejpam-6752	18	2	copyright	copyright	NOUN
ejpam-6752	18	3	:	:	PUNCT
ejpam-6752	18	4	©	©	PROPN
ejpam-6752	18	5	2025	2025	NUM
ejpam-6752	18	6	the	the	DET
ejpam-6752	18	7	author(s	author(s	NOUN
ejpam-6752	18	8	)	)	PUNCT
ejpam-6752	18	9	.	.	PUNCT
ejpam-6752	19	1	(	(	PUNCT
ejpam-6752	19	2	cc	cc	NOUN
ejpam-6752	19	3	by	by	ADP
ejpam-6752	19	4	-	-	PUNCT
ejpam-6752	19	5	nc	nc	PROPN
ejpam-6752	19	6	4.0	4.0	NUM
ejpam-6752	19	7	)	)	PUNCT
ejpam-6752	19	8	r.	r.	PROPN
ejpam-6752	19	9	h.	h.	PROPN
ejpam-6752	19	10	salih	salih	PROPN
ejpam-6752	19	11	/	/	SYM
ejpam-6752	19	12	eur	eur	PROPN
ejpam-6752	19	13	.	.	PUNCT
ejpam-6752	20	1	j.	j.	PROPN
ejpam-6752	20	2	pure	pure	PROPN
ejpam-6752	20	3	appl	appl	PROPN
ejpam-6752	20	4	.	.	PROPN
ejpam-6752	20	5	math	math	PROPN
ejpam-6752	20	6	,	,	PUNCT
ejpam-6752	20	7	18	18	NUM
ejpam-6752	20	8	(	(	PUNCT
ejpam-6752	20	9	4	4	NUM
ejpam-6752	20	10	)	)	PUNCT
ejpam-6752	20	11	(	(	PUNCT
ejpam-6752	20	12	2025	2025	NUM
ejpam-6752	20	13	)	)	PUNCT
ejpam-6752	20	14	,	,	PUNCT
ejpam-6752	20	15	6752	6752	NUM
ejpam-6752	20	16	2	2	NUM
ejpam-6752	20	17	of	of	ADP
ejpam-6752	20	18	14	14	NUM
ejpam-6752	20	19	bimolecular	bimolecular	ADJ
ejpam-6752	20	20	chemical	chemical	NOUN
ejpam-6752	20	21	reaction	reaction	NOUN
ejpam-6752	20	22	networks	network	NOUN
ejpam-6752	20	23	with	with	ADP
ejpam-6752	20	24	hopf	hopf	ADJ
ejpam-6752	20	25	bifurcation	bifurcation	NOUN
ejpam-6752	20	26	[	[	X
ejpam-6752	20	27	3	3	NUM
ejpam-6752	20	28	]	]	PUNCT
ejpam-6752	20	29	.	.	PUNCT
ejpam-6752	21	1	this	this	PRON
ejpam-6752	21	2	means	mean	VERB
ejpam-6752	21	3	that	that	SCONJ
ejpam-6752	21	4	these	these	DET
ejpam-6752	21	5	networks	network	NOUN
ejpam-6752	21	6	have	have	VERB
ejpam-6752	21	7	the	the	DET
ejpam-6752	21	8	fewest	few	ADJ
ejpam-6752	21	9	species	specie	NOUN
ejpam-6752	21	10	and	and	CCONJ
ejpam-6752	21	11	reactions	reaction	NOUN
ejpam-6752	21	12	.	.	PUNCT
ejpam-6752	22	1	the	the	DET
ejpam-6752	22	2	results	result	NOUN
ejpam-6752	22	3	show	show	VERB
ejpam-6752	22	4	that	that	SCONJ
ejpam-6752	22	5	the	the	DET
ejpam-6752	22	6	smallest	small	ADJ
ejpam-6752	22	7	bimolecular	bimolecular	ADJ
ejpam-6752	22	8	mass	mass	ADJ
ejpam-6752	22	9	-	-	PUNCT
ejpam-6752	22	10	action	action	NOUN
ejpam-6752	22	11	network	network	NOUN
ejpam-6752	22	12	allowing	allow	VERB
ejpam-6752	22	13	hopf	hopf	ADJ
ejpam-6752	22	14	bifurcation	bifurcation	NOUN
ejpam-6752	22	15	must	must	AUX
ejpam-6752	22	16	have	have	VERB
ejpam-6752	22	17	at	at	ADV
ejpam-6752	22	18	least	least	ADV
ejpam-6752	22	19	three	three	NUM
ejpam-6752	22	20	species	specie	NOUN
ejpam-6752	22	21	and	and	CCONJ
ejpam-6752	22	22	at	at	ADP
ejpam-6752	22	23	least	least	ADJ
ejpam-6752	22	24	four	four	NUM
ejpam-6752	22	25	reactions	reaction	NOUN
ejpam-6752	22	26	.	.	PUNCT
ejpam-6752	23	1	they	they	PRON
ejpam-6752	23	2	found	find	VERB
ejpam-6752	23	3	that	that	SCONJ
ejpam-6752	23	4	138	138	NUM
ejpam-6752	23	5	non	non	ADJ
ejpam-6752	23	6	-	-	ADJ
ejpam-6752	23	7	isomorphic	isomorphic	ADJ
ejpam-6752	23	8	bimolecular	bimolecular	ADJ
ejpam-6752	23	9	networks	network	NOUN
ejpam-6752	23	10	allow	allow	VERB
ejpam-6752	23	11	for	for	ADP
ejpam-6752	23	12	andronov	andronov	ADJ
ejpam-6752	23	13	-	-	PUNCT
ejpam-6752	23	14	hopf	hopf	ADJ
ejpam-6752	23	15	bifurcation	bifurcation	NOUN
ejpam-6752	23	16	.	.	PUNCT
ejpam-6752	24	1	these	these	DET
ejpam-6752	24	2	networks	network	NOUN
ejpam-6752	24	3	can	can	AUX
ejpam-6752	24	4	be	be	AUX
ejpam-6752	24	5	dynamically	dynamically	ADV
ejpam-6752	24	6	divided	divide	VERB
ejpam-6752	24	7	into	into	ADP
ejpam-6752	24	8	87	87	NUM
ejpam-6752	24	9	non	non	ADJ
ejpam-6752	24	10	-	-	ADJ
ejpam-6752	24	11	equivalent	equivalent	ADJ
ejpam-6752	24	12	classes	class	NOUN
ejpam-6752	24	13	.	.	PUNCT
ejpam-6752	25	1	of	of	ADP
ejpam-6752	25	2	these	these	DET
ejpam-6752	25	3	classes	class	NOUN
ejpam-6752	25	4	,	,	PUNCT
ejpam-6752	25	5	86	86	NUM
ejpam-6752	25	6	admit	admit	VERB
ejpam-6752	25	7	non	non	ADJ
ejpam-6752	25	8	-	-	ADJ
ejpam-6752	25	9	degenerate	degenerate	ADJ
ejpam-6752	25	10	andronov	andronov	ADJ
ejpam-6752	25	11	-	-	PUNCT
ejpam-6752	25	12	hopf	hopf	ADJ
ejpam-6752	25	13	bifurcations	bifurcation	NOUN
ejpam-6752	25	14	,	,	PUNCT
ejpam-6752	25	15	leading	lead	VERB
ejpam-6752	25	16	to	to	ADP
ejpam-6752	25	17	isolated	isolated	ADJ
ejpam-6752	25	18	limit	limit	NOUN
ejpam-6752	25	19	cycles	cycle	NOUN
ejpam-6752	25	20	.	.	PUNCT
ejpam-6752	26	1	however	however	ADV
ejpam-6752	26	2	,	,	PUNCT
ejpam-6752	26	3	in	in	ADP
ejpam-6752	26	4	the	the	DET
ejpam-6752	26	5	remaining	remain	VERB
ejpam-6752	26	6	class	class	NOUN
ejpam-6752	26	7	,	,	PUNCT
ejpam-6752	26	8	andronov	andronov	ADJ
ejpam-6752	26	9	-	-	PUNCT
ejpam-6752	26	10	hopf	hopf	ADJ
ejpam-6752	26	11	bifurcations	bifurcation	NOUN
ejpam-6752	26	12	can	can	AUX
ejpam-6752	26	13	only	only	ADV
ejpam-6752	26	14	be	be	AUX
ejpam-6752	26	15	degenerate	degenerate	ADJ
ejpam-6752	26	16	.	.	PUNCT
ejpam-6752	27	1	the	the	DET
ejpam-6752	27	2	three	three	NUM
ejpam-6752	27	3	-	-	PUNCT
ejpam-6752	27	4	dimensional	dimensional	ADJ
ejpam-6752	27	5	system	system	NOUN
ejpam-6752	27	6	corresponding	correspond	VERB
ejpam-6752	27	7	to	to	ADP
ejpam-6752	27	8	the	the	DET
ejpam-6752	27	9	last	last	ADJ
ejpam-6752	27	10	class	class	NOUN
ejpam-6752	27	11	of	of	ADP
ejpam-6752	27	12	the	the	DET
ejpam-6752	27	13	reaction	reaction	NOUN
ejpam-6752	27	14	network	network	NOUN
ejpam-6752	27	15	is	be	AUX
ejpam-6752	27	16	ẋ1	ẋ1	PROPN
ejpam-6752	27	17	=	=	PUNCT
ejpam-6752	27	18	x1(k1x3	x1(k1x3	PROPN
ejpam-6752	27	19	−	−	PROPN
ejpam-6752	27	20	k2x2	k2x2	NOUN
ejpam-6752	27	21	)	)	PUNCT
ejpam-6752	27	22	,	,	PUNCT
ejpam-6752	28	1	ẋ2	ẋ2	PROPN
ejpam-6752	28	2	=	=	SYM
ejpam-6752	28	3	x2(k2x1	x2(k2x1	PROPN
ejpam-6752	28	4	−	−	NOUN
ejpam-6752	28	5	k3x3	k3x3	NOUN
ejpam-6752	28	6	)	)	PUNCT
ejpam-6752	28	7	.	.	PUNCT
ejpam-6752	29	1	(	(	PUNCT
ejpam-6752	29	2	1	1	X
ejpam-6752	29	3	)	)	PUNCT
ejpam-6752	29	4	ẋ3	ẋ3	X
ejpam-6752	29	5	=	=	SYM
ejpam-6752	29	6	−x3(k1x1	−x3(k1x1	ADP
ejpam-6752	29	7	+	+	CCONJ
ejpam-6752	29	8	k3x2	k3x2	NOUN
ejpam-6752	29	9	)	)	PUNCT
ejpam-6752	29	10	+	+	NUM
ejpam-6752	29	11	2k4	2k4	NUM
ejpam-6752	29	12	,	,	PUNCT
ejpam-6752	29	13	where	where	SCONJ
ejpam-6752	29	14	ki	ki	PROPN
ejpam-6752	29	15	,	,	PUNCT
ejpam-6752	29	16	i	i	PRON
ejpam-6752	29	17	=	=	NOUN
ejpam-6752	29	18	1	1	NUM
ejpam-6752	29	19	,	,	PUNCT
ejpam-6752	29	20	2	2	NUM
ejpam-6752	29	21	,	,	PUNCT
ejpam-6752	29	22	3	3	NUM
ejpam-6752	29	23	,	,	PUNCT
ejpam-6752	29	24	4	4	NUM
ejpam-6752	29	25	are	be	AUX
ejpam-6752	29	26	real	real	ADJ
ejpam-6752	29	27	positive	positive	ADJ
ejpam-6752	29	28	parameters	parameter	NOUN
ejpam-6752	29	29	called	call	VERB
ejpam-6752	29	30	the	the	DET
ejpam-6752	29	31	reaction	reaction	NOUN
ejpam-6752	29	32	rate	rate	NOUN
ejpam-6752	29	33	constants	constant	NOUN
ejpam-6752	29	34	and	and	CCONJ
ejpam-6752	29	35	xi	xi	PRON
ejpam-6752	29	36	≥	≥	NUM
ejpam-6752	29	37	0	0	NUM
ejpam-6752	29	38	.	.	PUNCT
ejpam-6752	30	1	system	system	NOUN
ejpam-6752	30	2	(	(	PUNCT
ejpam-6752	30	3	1	1	X
ejpam-6752	30	4	)	)	PUNCT
ejpam-6752	30	5	has	have	VERB
ejpam-6752	30	6	a	a	DET
ejpam-6752	30	7	unique	unique	ADJ
ejpam-6752	30	8	positive	positive	ADJ
ejpam-6752	30	9	equilibrium	equilibrium	NOUN
ejpam-6752	30	10	point	point	NOUN
ejpam-6752	30	11	,	,	PUNCT
ejpam-6752	30	12	which	which	PRON
ejpam-6752	30	13	is	be	AUX
ejpam-6752	30	14	of	of	ADP
ejpam-6752	30	15	type	type	NOUN
ejpam-6752	30	16	center	center	NOUN
ejpam-6752	30	17	when	when	SCONJ
ejpam-6752	30	18	the	the	DET
ejpam-6752	30	19	parameters	parameter	NOUN
ejpam-6752	30	20	satisfy	satisfy	VERB
ejpam-6752	30	21	k1	k1	PROPN
ejpam-6752	30	22	=	=	PUNCT
ejpam-6752	31	1	k2+k3	k2+k3	PROPN
ejpam-6752	32	1	[	[	X
ejpam-6752	32	2	4	4	NUM
ejpam-6752	32	3	]	]	PUNCT
ejpam-6752	32	4	.	.	PUNCT
ejpam-6752	33	1	it	it	PRON
ejpam-6752	33	2	is	be	AUX
ejpam-6752	33	3	proven	prove	VERB
ejpam-6752	33	4	by	by	ADP
ejpam-6752	33	5	finding	find	VERB
ejpam-6752	33	6	a	a	DET
ejpam-6752	33	7	constant	constant	NOUN
ejpam-6752	33	8	of	of	ADP
ejpam-6752	33	9	motion	motion	NOUN
ejpam-6752	33	10	.	.	PUNCT
ejpam-6752	34	1	they	they	PRON
ejpam-6752	34	2	also	also	ADV
ejpam-6752	34	3	proved	prove	VERB
ejpam-6752	34	4	the	the	DET
ejpam-6752	34	5	existence	existence	NOUN
ejpam-6752	34	6	of	of	ADP
ejpam-6752	34	7	a	a	DET
ejpam-6752	34	8	global	global	ADJ
ejpam-6752	34	9	center	center	NOUN
ejpam-6752	34	10	manifold	manifold	ADJ
ejpam-6752	34	11	that	that	PRON
ejpam-6752	34	12	attracts	attract	VERB
ejpam-6752	34	13	all	all	DET
ejpam-6752	34	14	positive	positive	ADJ
ejpam-6752	34	15	solutions	solution	NOUN
ejpam-6752	34	16	.	.	PUNCT
ejpam-6752	35	1	to	to	PART
ejpam-6752	35	2	gain	gain	VERB
ejpam-6752	35	3	information	information	NOUN
ejpam-6752	35	4	about	about	ADP
ejpam-6752	35	5	bimolecular	bimolecular	ADJ
ejpam-6752	35	6	networks	network	NOUN
ejpam-6752	35	7	with	with	ADP
ejpam-6752	35	8	hopf	hopf	ADJ
ejpam-6752	35	9	bifurcation	bifurcation	NOUN
ejpam-6752	35	10	,	,	PUNCT
ejpam-6752	35	11	the	the	DET
ejpam-6752	35	12	reader	reader	NOUN
ejpam-6752	35	13	should	should	AUX
ejpam-6752	35	14	consult	consult	VERB
ejpam-6752	35	15	the	the	DET
ejpam-6752	35	16	references	reference	NOUN
ejpam-6752	35	17	[	[	X
ejpam-6752	35	18	5–10	5–10	ADJ
ejpam-6752	35	19	]	]	X
ejpam-6752	35	20	.	.	PUNCT
ejpam-6752	36	1	an	an	DET
ejpam-6752	36	2	important	important	ADJ
ejpam-6752	36	3	question	question	NOUN
ejpam-6752	36	4	arises	arise	VERB
ejpam-6752	36	5	:	:	PUNCT
ejpam-6752	36	6	if	if	SCONJ
ejpam-6752	36	7	we	we	PRON
ejpam-6752	36	8	perturb	perturb	VERB
ejpam-6752	36	9	the	the	DET
ejpam-6752	36	10	parameters	parameter	NOUN
ejpam-6752	36	11	in	in	ADP
ejpam-6752	36	12	system	system	NOUN
ejpam-6752	36	13	(	(	PUNCT
ejpam-6752	36	14	1	1	NUM
ejpam-6752	36	15	)	)	PUNCT
ejpam-6752	36	16	,	,	PUNCT
ejpam-6752	36	17	how	how	SCONJ
ejpam-6752	36	18	many	many	ADJ
ejpam-6752	36	19	periodic	periodic	ADJ
ejpam-6752	36	20	orbits	orbit	NOUN
ejpam-6752	36	21	can	can	AUX
ejpam-6752	36	22	bifurcate	bifurcate	VERB
ejpam-6752	36	23	from	from	ADP
ejpam-6752	36	24	the	the	DET
ejpam-6752	36	25	positive	positive	ADJ
ejpam-6752	36	26	equilibrium	equilibrium	NOUN
ejpam-6752	36	27	point	point	NOUN
ejpam-6752	36	28	?	?	PUNCT
ejpam-6752	37	1	to	to	PART
ejpam-6752	37	2	address	address	VERB
ejpam-6752	37	3	this	this	PRON
ejpam-6752	37	4	,	,	PUNCT
ejpam-6752	37	5	a	a	DET
ejpam-6752	37	6	technique	technique	NOUN
ejpam-6752	37	7	is	be	AUX
ejpam-6752	37	8	applied	apply	VERB
ejpam-6752	37	9	to	to	ADP
ejpam-6752	37	10	system	system	NOUN
ejpam-6752	37	11	(	(	PUNCT
ejpam-6752	37	12	1	1	NUM
ejpam-6752	37	13	)	)	PUNCT
ejpam-6752	37	14	to	to	PART
ejpam-6752	37	15	estimate	estimate	VERB
ejpam-6752	37	16	the	the	DET
ejpam-6752	37	17	cyclicity	cyclicity	NOUN
ejpam-6752	37	18	bifurcating	bifurcate	VERB
ejpam-6752	37	19	from	from	ADP
ejpam-6752	37	20	the	the	DET
ejpam-6752	37	21	center	center	NOUN
ejpam-6752	37	22	.	.	PUNCT
ejpam-6752	38	1	this	this	DET
ejpam-6752	38	2	method	method	NOUN
ejpam-6752	38	3	was	be	AUX
ejpam-6752	38	4	first	first	ADV
ejpam-6752	38	5	employed	employ	VERB
ejpam-6752	38	6	in	in	ADP
ejpam-6752	38	7	three	three	NUM
ejpam-6752	38	8	dimensions	dimension	NOUN
ejpam-6752	38	9	by	by	ADP
ejpam-6752	38	10	salih	salih	PROPN
ejpam-6752	39	1	[	[	X
ejpam-6752	39	2	11	11	NUM
ejpam-6752	39	3	]	]	PUNCT
ejpam-6752	39	4	.	.	PUNCT
ejpam-6752	40	1	it	it	PRON
ejpam-6752	40	2	has	have	AUX
ejpam-6752	40	3	since	since	ADV
ejpam-6752	40	4	been	be	AUX
ejpam-6752	40	5	utilized	utilize	VERB
ejpam-6752	40	6	in	in	ADP
ejpam-6752	40	7	various	various	ADJ
ejpam-6752	40	8	scientific	scientific	ADJ
ejpam-6752	40	9	studies	study	NOUN
ejpam-6752	40	10	.	.	PUNCT
ejpam-6752	41	1	salih	salih	PROPN
ejpam-6752	41	2	demonstrated	demonstrate	VERB
ejpam-6752	41	3	that	that	SCONJ
ejpam-6752	41	4	four	four	NUM
ejpam-6752	41	5	limit	limit	NOUN
ejpam-6752	41	6	cycles	cycle	NOUN
ejpam-6752	41	7	can	can	AUX
ejpam-6752	41	8	bifurcate	bifurcate	VERB
ejpam-6752	41	9	from	from	ADP
ejpam-6752	41	10	the	the	DET
ejpam-6752	41	11	center	center	NOUN
ejpam-6752	41	12	of	of	ADP
ejpam-6752	41	13	the	the	DET
ejpam-6752	41	14	3d	3d	PROPN
ejpam-6752	41	15	lotka	lotka	PROPN
ejpam-6752	41	16	-	-	PUNCT
ejpam-6752	41	17	volterra	volterra	NOUN
ejpam-6752	41	18	system	system	NOUN
ejpam-6752	41	19	[	[	X
ejpam-6752	41	20	11	11	NUM
ejpam-6752	41	21	]	]	PUNCT
ejpam-6752	41	22	.	.	PUNCT
ejpam-6752	42	1	additionally	additionally	ADV
ejpam-6752	42	2	,	,	PUNCT
ejpam-6752	42	3	salih	salih	PROPN
ejpam-6752	42	4	et	et	PROPN
ejpam-6752	42	5	al	al	PROPN
ejpam-6752	42	6	.	.	PUNCT
ejpam-6752	43	1	[	[	X
ejpam-6752	43	2	12	12	NUM
ejpam-6752	43	3	]	]	PUNCT
ejpam-6752	43	4	applied	apply	VERB
ejpam-6752	43	5	the	the	DET
ejpam-6752	43	6	technique	technique	NOUN
ejpam-6752	43	7	to	to	ADP
ejpam-6752	43	8	two	two	NUM
ejpam-6752	43	9	differential	differential	ADJ
ejpam-6752	43	10	systems	system	NOUN
ejpam-6752	43	11	,	,	PUNCT
ejpam-6752	43	12	showing	show	VERB
ejpam-6752	43	13	that	that	SCONJ
ejpam-6752	43	14	one	one	NUM
ejpam-6752	43	15	and	and	CCONJ
ejpam-6752	43	16	five	five	NUM
ejpam-6752	43	17	limit	limit	NOUN
ejpam-6752	43	18	cycles	cycle	NOUN
ejpam-6752	43	19	can	can	AUX
ejpam-6752	43	20	bifurcate	bifurcate	VERB
ejpam-6752	43	21	from	from	ADP
ejpam-6752	43	22	the	the	DET
ejpam-6752	43	23	quadratic	quadratic	ADJ
ejpam-6752	43	24	polynomial	polynomial	ADJ
ejpam-6752	43	25	system	system	NOUN
ejpam-6752	43	26	and	and	CCONJ
ejpam-6752	43	27	the	the	DET
ejpam-6752	43	28	lü	lü	X
ejpam-6752	43	29	system	system	NOUN
ejpam-6752	43	30	,	,	PUNCT
ejpam-6752	43	31	respectively	respectively	ADV
ejpam-6752	43	32	.	.	PUNCT
ejpam-6752	44	1	salih	salih	PROPN
ejpam-6752	44	2	et	et	PROPN
ejpam-6752	44	3	al	al	PROPN
ejpam-6752	44	4	.	.	PUNCT
ejpam-6752	45	1	[	[	X
ejpam-6752	45	2	13	13	NUM
ejpam-6752	45	3	]	]	PUNCT
ejpam-6752	45	4	examined	examine	VERB
ejpam-6752	45	5	a	a	DET
ejpam-6752	45	6	specific	specific	ADJ
ejpam-6752	45	7	type	type	NOUN
ejpam-6752	45	8	of	of	ADP
ejpam-6752	45	9	the	the	DET
ejpam-6752	45	10	jerk	jerk	NOUN
ejpam-6752	45	11	system	system	NOUN
ejpam-6752	45	12	,	,	PUNCT
ejpam-6752	45	13	revealing	reveal	VERB
ejpam-6752	45	14	that	that	SCONJ
ejpam-6752	45	15	three	three	NUM
ejpam-6752	45	16	and	and	CCONJ
ejpam-6752	45	17	four	four	NUM
ejpam-6752	45	18	limit	limit	NOUN
ejpam-6752	45	19	cycles	cycle	NOUN
ejpam-6752	45	20	can	can	AUX
ejpam-6752	45	21	bifurcate	bifurcate	VERB
ejpam-6752	45	22	from	from	ADP
ejpam-6752	45	23	the	the	DET
ejpam-6752	45	24	center	center	NOUN
ejpam-6752	45	25	equilibrium	equilibrium	NOUN
ejpam-6752	45	26	point	point	NOUN
ejpam-6752	45	27	under	under	ADP
ejpam-6752	45	28	two	two	NUM
ejpam-6752	45	29	different	different	ADJ
ejpam-6752	45	30	sets	set	NOUN
ejpam-6752	45	31	of	of	ADP
ejpam-6752	45	32	conditions	condition	NOUN
ejpam-6752	45	33	.	.	PUNCT
ejpam-6752	46	1	this	this	DET
ejpam-6752	46	2	paper	paper	NOUN
ejpam-6752	46	3	is	be	AUX
ejpam-6752	46	4	organized	organize	VERB
ejpam-6752	46	5	as	as	SCONJ
ejpam-6752	46	6	follows	follow	VERB
ejpam-6752	46	7	:	:	PUNCT
ejpam-6752	46	8	section	section	NOUN
ejpam-6752	46	9	2	2	NUM
ejpam-6752	46	10	focuses	focus	VERB
ejpam-6752	46	11	on	on	ADP
ejpam-6752	46	12	identifying	identify	VERB
ejpam-6752	46	13	the	the	DET
ejpam-6752	46	14	existence	existence	NOUN
ejpam-6752	46	15	of	of	ADP
ejpam-6752	46	16	equilibrium	equilibrium	NOUN
ejpam-6752	46	17	points	point	NOUN
ejpam-6752	46	18	in	in	ADP
ejpam-6752	46	19	system	system	NOUN
ejpam-6752	46	20	(	(	PUNCT
ejpam-6752	46	21	1	1	NUM
ejpam-6752	46	22	)	)	PUNCT
ejpam-6752	46	23	and	and	CCONJ
ejpam-6752	46	24	studying	study	VERB
ejpam-6752	46	25	their	their	PRON
ejpam-6752	46	26	stability	stability	NOUN
ejpam-6752	46	27	.	.	PUNCT
ejpam-6752	47	1	the	the	DET
ejpam-6752	47	2	trajectory	trajectory	NOUN
ejpam-6752	47	3	directions	direction	NOUN
ejpam-6752	47	4	in	in	ADP
ejpam-6752	47	5	the	the	DET
ejpam-6752	47	6	planes	plane	NOUN
ejpam-6752	47	7	are	be	AUX
ejpam-6752	47	8	investigated	investigate	VERB
ejpam-6752	47	9	in	in	ADP
ejpam-6752	47	10	section	section	NOUN
ejpam-6752	47	11	3	3	NUM
ejpam-6752	47	12	.	.	PUNCT
ejpam-6752	48	1	the	the	DET
ejpam-6752	48	2	next	next	ADJ
ejpam-6752	48	3	section	section	NOUN
ejpam-6752	48	4	is	be	AUX
ejpam-6752	48	5	dedicated	dedicate	VERB
ejpam-6752	48	6	to	to	ADP
ejpam-6752	48	7	the	the	DET
ejpam-6752	48	8	study	study	NOUN
ejpam-6752	48	9	of	of	ADP
ejpam-6752	48	10	both	both	CCONJ
ejpam-6752	48	11	hopf	hopf	ADJ
ejpam-6752	48	12	and	and	CCONJ
ejpam-6752	48	13	center	center	NOUN
ejpam-6752	48	14	bifurcations	bifurcation	NOUN
ejpam-6752	48	15	.	.	PUNCT
ejpam-6752	49	1	lastly	lastly	ADV
ejpam-6752	49	2	,	,	PUNCT
ejpam-6752	49	3	the	the	DET
ejpam-6752	49	4	conclusions	conclusion	NOUN
ejpam-6752	49	5	are	be	AUX
ejpam-6752	49	6	presented	present	VERB
ejpam-6752	49	7	.	.	PUNCT
ejpam-6752	50	1	2	2	X
ejpam-6752	50	2	.	.	X
ejpam-6752	50	3	equilibrium	equilibrium	NOUN
ejpam-6752	50	4	point	point	NOUN
ejpam-6752	50	5	and	and	CCONJ
ejpam-6752	50	6	its	its	PRON
ejpam-6752	50	7	stability	stability	NOUN
ejpam-6752	50	8	equilibrium	equilibrium	NOUN
ejpam-6752	50	9	points	point	NOUN
ejpam-6752	50	10	are	be	AUX
ejpam-6752	50	11	fundamental	fundamental	ADJ
ejpam-6752	50	12	to	to	ADP
ejpam-6752	50	13	understanding	understand	VERB
ejpam-6752	50	14	various	various	ADJ
ejpam-6752	50	15	aspects	aspect	NOUN
ejpam-6752	50	16	of	of	ADP
ejpam-6752	50	17	dynamical	dynamical	ADJ
ejpam-6752	50	18	systems	system	NOUN
ejpam-6752	50	19	.	.	PUNCT
ejpam-6752	51	1	to	to	PART
ejpam-6752	51	2	identify	identify	VERB
ejpam-6752	51	3	the	the	DET
ejpam-6752	51	4	equilibrium	equilibrium	NOUN
ejpam-6752	51	5	points	point	NOUN
ejpam-6752	51	6	of	of	ADP
ejpam-6752	51	7	system	system	NOUN
ejpam-6752	51	8	(	(	PUNCT
ejpam-6752	51	9	1	1	NUM
ejpam-6752	51	10	)	)	PUNCT
ejpam-6752	51	11	,	,	PUNCT
ejpam-6752	51	12	the	the	DET
ejpam-6752	51	13	right	right	ADJ
ejpam-6752	51	14	-	-	PUNCT
ejpam-6752	51	15	hand	hand	NOUN
ejpam-6752	51	16	sides	side	NOUN
ejpam-6752	51	17	of	of	ADP
ejpam-6752	51	18	the	the	DET
ejpam-6752	51	19	equations	equation	NOUN
ejpam-6752	51	20	are	be	AUX
ejpam-6752	51	21	set	set	VERB
ejpam-6752	51	22	to	to	ADP
ejpam-6752	51	23	zero	zero	NUM
ejpam-6752	51	24	.	.	PUNCT
ejpam-6752	52	1	it	it	PRON
ejpam-6752	52	2	is	be	AUX
ejpam-6752	52	3	found	find	VERB
ejpam-6752	52	4	that	that	SCONJ
ejpam-6752	52	5	there	there	PRON
ejpam-6752	52	6	is	be	VERB
ejpam-6752	52	7	one	one	NUM
ejpam-6752	52	8	positive	positive	ADJ
ejpam-6752	52	9	equilibrium	equilibrium	NOUN
ejpam-6752	52	10	point	point	NOUN
ejpam-6752	52	11	,	,	PUNCT
ejpam-6752	52	12	given	give	VERB
ejpam-6752	52	13	by	by	ADP
ejpam-6752	52	14	e	e	PROPN
ejpam-6752	52	15	=	=	PUNCT
ejpam-6752	52	16	(	(	PUNCT
ejpam-6752	52	17	√	√	INTJ
ejpam-6752	52	18	k3k4	k3k4	PROPN
ejpam-6752	52	19	k1k2	k1k2	PROPN
ejpam-6752	52	20	,	,	PUNCT
ejpam-6752	52	21	√	√	INTJ
ejpam-6752	52	22	k1k4	k1k4	PROPN
ejpam-6752	53	1	k2k3	k2k3	INTJ
ejpam-6752	53	2	,	,	PUNCT
ejpam-6752	53	3	√	√	INTJ
ejpam-6752	53	4	k2k4	k2k4	SYM
ejpam-6752	53	5	k1k3	k1k3	PROPN
ejpam-6752	53	6	)	)	PUNCT
ejpam-6752	53	7	.	.	PUNCT
ejpam-6752	54	1	through	through	ADP
ejpam-6752	54	2	simple	simple	ADJ
ejpam-6752	54	3	analysis	analysis	NOUN
ejpam-6752	54	4	,	,	PUNCT
ejpam-6752	54	5	one	one	PRON
ejpam-6752	54	6	can	can	AUX
ejpam-6752	54	7	easily	easily	ADV
ejpam-6752	54	8	derive	derive	VERB
ejpam-6752	54	9	the	the	DET
ejpam-6752	54	10	following	follow	VERB
ejpam-6752	54	11	conclusion	conclusion	NOUN
ejpam-6752	54	12	.	.	PUNCT
ejpam-6752	55	1	r.	r.	PROPN
ejpam-6752	55	2	h.	h.	PROPN
ejpam-6752	55	3	salih	salih	PROPN
ejpam-6752	55	4	/	/	SYM
ejpam-6752	55	5	eur	eur	PROPN
ejpam-6752	55	6	.	.	PUNCT
ejpam-6752	56	1	j.	j.	PROPN
ejpam-6752	56	2	pure	pure	PROPN
ejpam-6752	56	3	appl	appl	PROPN
ejpam-6752	56	4	.	.	PROPN
ejpam-6752	56	5	math	math	PROPN
ejpam-6752	56	6	,	,	PUNCT
ejpam-6752	56	7	18	18	NUM
ejpam-6752	56	8	(	(	PUNCT
ejpam-6752	56	9	4	4	NUM
ejpam-6752	56	10	)	)	PUNCT
ejpam-6752	56	11	(	(	PUNCT
ejpam-6752	56	12	2025	2025	NUM
ejpam-6752	56	13	)	)	PUNCT
ejpam-6752	56	14	,	,	PUNCT
ejpam-6752	56	15	6752	6752	NUM
ejpam-6752	56	16	3	3	NUM
ejpam-6752	56	17	of	of	ADP
ejpam-6752	56	18	14	14	NUM
ejpam-6752	56	19	proposition	proposition	NOUN
ejpam-6752	56	20	1	1	NUM
ejpam-6752	56	21	.	.	X
ejpam-6752	57	1	for	for	ADP
ejpam-6752	57	2	system	system	NOUN
ejpam-6752	57	3	(	(	PUNCT
ejpam-6752	57	4	1	1	NUM
ejpam-6752	57	5	)	)	PUNCT
ejpam-6752	57	6	,	,	PUNCT
ejpam-6752	57	7	the	the	DET
ejpam-6752	57	8	stability	stability	NOUN
ejpam-6752	57	9	of	of	ADP
ejpam-6752	57	10	the	the	DET
ejpam-6752	57	11	equilibrium	equilibrium	NOUN
ejpam-6752	57	12	point	point	NOUN
ejpam-6752	57	13	e	e	NOUN
ejpam-6752	57	14	is	be	AUX
ejpam-6752	57	15	determined	determine	VERB
ejpam-6752	57	16	as	as	SCONJ
ejpam-6752	57	17	follows	follow	VERB
ejpam-6752	57	18	:	:	PUNCT
ejpam-6752	57	19	i.	i.	NOUN
ejpam-6752	57	20	it	it	PRON
ejpam-6752	57	21	is	be	AUX
ejpam-6752	57	22	asymptotically	asymptotically	ADV
ejpam-6752	57	23	stable	stable	ADJ
ejpam-6752	57	24	if	if	SCONJ
ejpam-6752	58	1	and	and	CCONJ
ejpam-6752	58	2	only	only	ADV
ejpam-6752	58	3	if	if	SCONJ
ejpam-6752	58	4	k1	k1	PROPN
ejpam-6752	58	5	>	>	X
ejpam-6752	58	6	k2	k2	PROPN
ejpam-6752	58	7	+	+	CCONJ
ejpam-6752	58	8	k3	k3	PROPN
ejpam-6752	58	9	.	.	PUNCT
ejpam-6752	58	10	ii	ii	PROPN
ejpam-6752	58	11	.	.	PUNCT
ejpam-6752	59	1	it	it	PRON
ejpam-6752	59	2	is	be	AUX
ejpam-6752	59	3	a	a	DET
ejpam-6752	59	4	center	center	NOUN
ejpam-6752	59	5	when	when	SCONJ
ejpam-6752	59	6	k1	k1	PROPN
ejpam-6752	59	7	=	=	SYM
ejpam-6752	59	8	k2	k2	PROPN
ejpam-6752	59	9	+	+	CCONJ
ejpam-6752	59	10	k3	k3	PROPN
ejpam-6752	59	11	.	.	PUNCT
ejpam-6752	59	12	iii	iii	X
ejpam-6752	59	13	.	.	PUNCT
ejpam-6752	60	1	it	it	PRON
ejpam-6752	60	2	is	be	AUX
ejpam-6752	60	3	unstable	unstable	ADJ
ejpam-6752	60	4	when	when	SCONJ
ejpam-6752	60	5	k1	k1	PROPN
ejpam-6752	60	6	<	<	X
ejpam-6752	60	7	k2	k2	PROPN
ejpam-6752	60	8	+	+	CCONJ
ejpam-6752	60	9	k3	k3	ADJ
ejpam-6752	60	10	.	.	PUNCT
ejpam-6752	61	1	proof	proof	NOUN
ejpam-6752	61	2	.	.	PUNCT
ejpam-6752	62	1	the	the	DET
ejpam-6752	62	2	jacobian	jacobian	ADJ
ejpam-6752	62	3	matrix	matrix	NOUN
ejpam-6752	62	4	of	of	ADP
ejpam-6752	62	5	system	system	NOUN
ejpam-6752	62	6	(	(	PUNCT
ejpam-6752	62	7	1	1	NUM
ejpam-6752	62	8	)	)	PUNCT
ejpam-6752	62	9	at	at	ADP
ejpam-6752	62	10	the	the	DET
ejpam-6752	62	11	equilibrium	equilibrium	NOUN
ejpam-6752	62	12	points	point	NOUN
ejpam-6752	62	13	e	e	NOUN
ejpam-6752	62	14	is	be	AUX
ejpam-6752	62	15	given	give	VERB
ejpam-6752	62	16	by	by	ADP
ejpam-6752	62	17			PROPN
ejpam-6752	62	18	0	0	NUM
ejpam-6752	63	1	−	−	NOUN
ejpam-6752	63	2	√	√	PROPN
ejpam-6752	63	3	k2k3k4	k2k3k4	PROPN
ejpam-6752	63	4	k1	k1	PROPN
ejpam-6752	63	5	√	√	PROPN
ejpam-6752	63	6	k1k3k4	k1k3k4	PROPN
ejpam-6752	63	7	k2√	k2√	PROPN
ejpam-6752	63	8	k1k2k4	k1k2k4	PROPN
ejpam-6752	63	9	k3	k3	VERB
ejpam-6752	63	10	0	0	NUM
ejpam-6752	63	11	−	−	PROPN
ejpam-6752	63	12	√	√	PROPN
ejpam-6752	63	13	k1k3k4	k1k3k4	PROPN
ejpam-6752	63	14	k2	k2	PROPN
ejpam-6752	63	15	−	−	PROPN
ejpam-6752	63	16	√	√	PROPN
ejpam-6752	63	17	k1k2k4	k1k2k4	NOUN
ejpam-6752	63	18	k3	k3	VERB
ejpam-6752	63	19	−	−	PROPN
ejpam-6752	63	20	√	√	NUM
ejpam-6752	63	21	k2k3k4	k2k3k4	PROPN
ejpam-6752	63	22	k1	k1	PROPN
ejpam-6752	63	23	−2	−2	PROPN
ejpam-6752	63	24	√	√	PROPN
ejpam-6752	63	25	k1k3k4	k1k3k4	PROPN
ejpam-6752	63	26	k2	k2	PROPN
ejpam-6752	63	27			PROPN
ejpam-6752	63	28	(	(	PUNCT
ejpam-6752	63	29	2	2	X
ejpam-6752	63	30	)	)	PUNCT
ejpam-6752	63	31	its	its	PRON
ejpam-6752	63	32	characteristic	characteristic	ADJ
ejpam-6752	63	33	equation	equation	NOUN
ejpam-6752	63	34	is	be	AUX
ejpam-6752	63	35	λ3	λ3	PROPN
ejpam-6752	63	36	−	−	PROPN
ejpam-6752	64	1	tλ2	tλ2	NOUN
ejpam-6752	64	2	−kλ−d	−kλ−d	NOUN
ejpam-6752	65	1	=	=	SYM
ejpam-6752	65	2	0	0	NUM
ejpam-6752	65	3	,	,	PUNCT
ejpam-6752	65	4	(	(	PUNCT
ejpam-6752	65	5	3	3	X
ejpam-6752	65	6	)	)	PUNCT
ejpam-6752	65	7	where	where	SCONJ
ejpam-6752	65	8	•	•	NUM
ejpam-6752	65	9	t	t	PROPN
ejpam-6752	65	10	is	be	AUX
ejpam-6752	65	11	the	the	DET
ejpam-6752	65	12	trace	trace	NOUN
ejpam-6752	65	13	of	of	ADP
ejpam-6752	65	14	(	(	PUNCT
ejpam-6752	65	15	2	2	NUM
ejpam-6752	65	16	)	)	PUNCT
ejpam-6752	65	17	and	and	CCONJ
ejpam-6752	65	18	t	t	X
ejpam-6752	65	19	=	=	SYM
ejpam-6752	65	20	−2	−2	PROPN
ejpam-6752	65	21	√	√	PROPN
ejpam-6752	65	22	k1k3k4	k1k3k4	PROPN
ejpam-6752	65	23	k2	k2	PROPN
ejpam-6752	65	24	,	,	PUNCT
ejpam-6752	65	25	•	•	CCONJ
ejpam-6752	65	26	k	k	PROPN
ejpam-6752	65	27	is	be	AUX
ejpam-6752	65	28	the	the	DET
ejpam-6752	65	29	sum	sum	NOUN
ejpam-6752	65	30	of	of	ADP
ejpam-6752	65	31	the	the	DET
ejpam-6752	65	32	diagonal	diagonal	ADJ
ejpam-6752	65	33	minors	minor	NOUN
ejpam-6752	65	34	of	of	ADP
ejpam-6752	65	35	(	(	PUNCT
ejpam-6752	65	36	2	2	NUM
ejpam-6752	65	37	)	)	PUNCT
ejpam-6752	65	38	and	and	CCONJ
ejpam-6752	65	39	k	k	PROPN
ejpam-6752	65	40	=	=	NOUN
ejpam-6752	65	41	k4	k4	PROPN
ejpam-6752	65	42	(	(	PUNCT
ejpam-6752	65	43	k3	k3	VERB
ejpam-6752	65	44	−	−	PROPN
ejpam-6752	65	45	k1	k1	NOUN
ejpam-6752	65	46	−	−	PROPN
ejpam-6752	65	47	k2	k2	PROPN
ejpam-6752	65	48	)	)	PUNCT
ejpam-6752	65	49	,	,	PUNCT
ejpam-6752	65	50	•	•	NOUN
ejpam-6752	65	51	d	d	NOUN
ejpam-6752	65	52	is	be	AUX
ejpam-6752	65	53	the	the	DET
ejpam-6752	65	54	determinant	determinant	ADJ
ejpam-6752	65	55	of	of	ADP
ejpam-6752	65	56	(	(	PUNCT
ejpam-6752	65	57	2	2	NUM
ejpam-6752	65	58	)	)	PUNCT
ejpam-6752	65	59	and	and	CCONJ
ejpam-6752	65	60	d	d	X
ejpam-6752	65	61	=	=	SYM
ejpam-6752	65	62	−4k4	−4k4	NUM
ejpam-6752	65	63	√	√	PROPN
ejpam-6752	65	64	k1k2k3k4	k1k2k3k4	PROPN
ejpam-6752	65	65	.	.	PUNCT
ejpam-6752	66	1	since	since	SCONJ
ejpam-6752	66	2	d	d	PROPN
ejpam-6752	66	3	is	be	AUX
ejpam-6752	66	4	negative	negative	ADJ
ejpam-6752	66	5	,	,	PUNCT
ejpam-6752	66	6	eq	eq	ADJ
ejpam-6752	66	7	.	.	PUNCT
ejpam-6752	67	1	(	(	PUNCT
ejpam-6752	67	2	3	3	X
ejpam-6752	67	3	)	)	PUNCT
ejpam-6752	67	4	has	have	VERB
ejpam-6752	67	5	one	one	NUM
ejpam-6752	67	6	negative	negative	ADJ
ejpam-6752	67	7	real	real	ADJ
ejpam-6752	67	8	root	root	NOUN
ejpam-6752	67	9	and	and	CCONJ
ejpam-6752	67	10	two	two	NUM
ejpam-6752	67	11	other	other	ADJ
ejpam-6752	67	12	roots	root	NOUN
ejpam-6752	67	13	that	that	PRON
ejpam-6752	67	14	have	have	VERB
ejpam-6752	67	15	the	the	DET
ejpam-6752	67	16	same	same	ADJ
ejpam-6752	67	17	sign	sign	NOUN
ejpam-6752	67	18	.	.	PUNCT
ejpam-6752	68	1	as	as	SCONJ
ejpam-6752	68	2	t	t	PROPN
ejpam-6752	68	3	is	be	AUX
ejpam-6752	68	4	negative	negative	ADJ
ejpam-6752	68	5	,	,	PUNCT
ejpam-6752	68	6	the	the	DET
ejpam-6752	68	7	sign	sign	NOUN
ejpam-6752	68	8	of	of	ADP
ejpam-6752	68	9	tk+d	tk+d	PROPN
ejpam-6752	68	10	is	be	AUX
ejpam-6752	68	11	determined	determine	VERB
ejpam-6752	68	12	by	by	ADP
ejpam-6752	68	13	(	(	PUNCT
ejpam-6752	68	14	k1−k2−k3	k1−k2−k3	PROPN
ejpam-6752	68	15	)	)	PUNCT
ejpam-6752	68	16	.	.	PUNCT
ejpam-6752	69	1	the	the	DET
ejpam-6752	69	2	sign	sign	NOUN
ejpam-6752	69	3	of	of	ADP
ejpam-6752	69	4	(	(	PUNCT
ejpam-6752	69	5	k1	k1	PROPN
ejpam-6752	69	6	−	−	PROPN
ejpam-6752	69	7	k2	k2	PROPN
ejpam-6752	69	8	−	−	PROPN
ejpam-6752	69	9	k3	k3	PROPN
ejpam-6752	69	10	)	)	PUNCT
ejpam-6752	69	11	plays	play	VERB
ejpam-6752	69	12	an	an	DET
ejpam-6752	69	13	important	important	ADJ
ejpam-6752	69	14	role	role	NOUN
ejpam-6752	69	15	in	in	ADP
ejpam-6752	69	16	determining	determine	VERB
ejpam-6752	69	17	the	the	DET
ejpam-6752	69	18	stability	stability	NOUN
ejpam-6752	69	19	of	of	ADP
ejpam-6752	69	20	the	the	DET
ejpam-6752	69	21	equilibrium	equilibrium	NOUN
ejpam-6752	69	22	point	point	NOUN
ejpam-6752	69	23	.	.	PUNCT
ejpam-6752	70	1	thus	thus	ADV
ejpam-6752	70	2	,	,	PUNCT
ejpam-6752	70	3	i.	i.	NOUN
ejpam-6752	70	4	when	when	SCONJ
ejpam-6752	70	5	k1	k1	PROPN
ejpam-6752	70	6	>	>	X
ejpam-6752	70	7	k2	k2	PROPN
ejpam-6752	70	8	+	+	CCONJ
ejpam-6752	70	9	k3	k3	PROPN
ejpam-6752	70	10	,	,	PUNCT
ejpam-6752	70	11	it	it	PRON
ejpam-6752	70	12	implies	imply	VERB
ejpam-6752	70	13	that	that	SCONJ
ejpam-6752	70	14	tk	tk	PROPN
ejpam-6752	71	1	+	+	PROPN
ejpam-6752	71	2	d	d	PROPN
ejpam-6752	71	3	>	>	X
ejpam-6752	71	4	0	0	NUM
ejpam-6752	71	5	.	.	PUNCT
ejpam-6752	72	1	according	accord	VERB
ejpam-6752	72	2	to	to	ADP
ejpam-6752	72	3	the	the	DET
ejpam-6752	72	4	routh	routh	PROPN
ejpam-6752	72	5	-	-	PUNCT
ejpam-6752	72	6	hurwitz	hurwitz	PROPN
ejpam-6752	72	7	criterion	criterion	NOUN
ejpam-6752	72	8	,	,	PUNCT
ejpam-6752	72	9	the	the	DET
ejpam-6752	72	10	real	real	ADJ
ejpam-6752	72	11	parts	part	NOUN
ejpam-6752	72	12	of	of	ADP
ejpam-6752	72	13	the	the	DET
ejpam-6752	72	14	eigenvalues	eigenvalue	NOUN
ejpam-6752	72	15	are	be	AUX
ejpam-6752	72	16	negative	negative	ADJ
ejpam-6752	72	17	.	.	PUNCT
ejpam-6752	73	1	therefore	therefore	ADV
ejpam-6752	73	2	,	,	PUNCT
ejpam-6752	73	3	the	the	DET
ejpam-6752	73	4	equilibrium	equilibrium	NOUN
ejpam-6752	73	5	point	point	NOUN
ejpam-6752	73	6	e	e	NOUN
ejpam-6752	73	7	is	be	AUX
ejpam-6752	73	8	asymptotically	asymptotically	ADV
ejpam-6752	73	9	stable	stable	ADJ
ejpam-6752	73	10	if	if	SCONJ
ejpam-6752	73	11	and	and	CCONJ
ejpam-6752	73	12	only	only	ADV
ejpam-6752	73	13	if	if	SCONJ
ejpam-6752	73	14	k1	k1	PROPN
ejpam-6752	73	15	>	>	X
ejpam-6752	73	16	k2	k2	PROPN
ejpam-6752	73	17	+	+	CCONJ
ejpam-6752	73	18	k3	k3	PROPN
ejpam-6752	73	19	,	,	PUNCT
ejpam-6752	73	20	see	see	VERB
ejpam-6752	73	21	fig.1	fig.1	PROPN
ejpam-6752	73	22	-	-	PUNCT
ejpam-6752	73	23	a.	a.	NOUN
ejpam-6752	73	24	ii	ii	PROPN
ejpam-6752	73	25	.	.	PUNCT
ejpam-6752	74	1	when	when	SCONJ
ejpam-6752	74	2	k1	k1	NOUN
ejpam-6752	74	3	=	=	SYM
ejpam-6752	74	4	k2+k3	k2+k3	PROPN
ejpam-6752	74	5	,	,	PUNCT
ejpam-6752	74	6	eq	eq	NOUN
ejpam-6752	74	7	.	.	PUNCT
ejpam-6752	74	8	(	(	PUNCT
ejpam-6752	74	9	3	3	X
ejpam-6752	74	10	)	)	PUNCT
ejpam-6752	74	11	has	have	VERB
ejpam-6752	74	12	one	one	NUM
ejpam-6752	74	13	real	real	ADJ
ejpam-6752	74	14	negative	negative	ADJ
ejpam-6752	74	15	root	root	NOUN
ejpam-6752	74	16	and	and	CCONJ
ejpam-6752	74	17	a	a	DET
ejpam-6752	74	18	pair	pair	NOUN
ejpam-6752	74	19	of	of	ADP
ejpam-6752	74	20	purely	purely	ADV
ejpam-6752	74	21	imaginary	imaginary	ADJ
ejpam-6752	74	22	roots	root	NOUN
ejpam-6752	74	23	.	.	PUNCT
ejpam-6752	75	1	in	in	ADP
ejpam-6752	75	2	reference	reference	NOUN
ejpam-6752	75	3	[	[	X
ejpam-6752	75	4	4	4	NUM
ejpam-6752	75	5	]	]	PUNCT
ejpam-6752	75	6	,	,	PUNCT
ejpam-6752	75	7	it	it	PRON
ejpam-6752	75	8	has	have	AUX
ejpam-6752	75	9	been	be	AUX
ejpam-6752	75	10	proven	prove	VERB
ejpam-6752	75	11	that	that	SCONJ
ejpam-6752	75	12	the	the	DET
ejpam-6752	75	13	equilibrium	equilibrium	NOUN
ejpam-6752	75	14	point	point	NOUN
ejpam-6752	75	15	e	e	NOUN
ejpam-6752	75	16	is	be	AUX
ejpam-6752	75	17	of	of	ADP
ejpam-6752	75	18	center	center	ADJ
ejpam-6752	75	19	type	type	NOUN
ejpam-6752	75	20	,	,	PUNCT
ejpam-6752	75	21	see	see	VERB
ejpam-6752	75	22	fig.1	fig.1	PROPN
ejpam-6752	75	23	-	-	PUNCT
ejpam-6752	75	24	b.	b.	NOUN
ejpam-6752	75	25	iii	iii	PROPN
ejpam-6752	75	26	.	.	PUNCT
ejpam-6752	76	1	when	when	SCONJ
ejpam-6752	76	2	k1	k1	PROPN
ejpam-6752	76	3	<	<	X
ejpam-6752	76	4	k2	k2	PROPN
ejpam-6752	76	5	+	+	CCONJ
ejpam-6752	76	6	k3	k3	PROPN
ejpam-6752	76	7	,	,	PUNCT
ejpam-6752	76	8	it	it	PRON
ejpam-6752	76	9	implies	imply	VERB
ejpam-6752	76	10	that	that	SCONJ
ejpam-6752	76	11	tk	tk	PROPN
ejpam-6752	77	1	+	+	NOUN
ejpam-6752	77	2	d	d	X
ejpam-6752	77	3	<	<	X
ejpam-6752	77	4	0	0	NUM
ejpam-6752	77	5	.	.	PUNCT
ejpam-6752	78	1	in	in	ADP
ejpam-6752	78	2	this	this	DET
ejpam-6752	78	3	case	case	NOUN
ejpam-6752	78	4	,	,	PUNCT
ejpam-6752	78	5	eq	eq	NOUN
ejpam-6752	78	6	.	.	PUNCT
ejpam-6752	79	1	(	(	PUNCT
ejpam-6752	79	2	3	3	X
ejpam-6752	79	3	)	)	PUNCT
ejpam-6752	79	4	has	have	VERB
ejpam-6752	79	5	two	two	NUM
ejpam-6752	79	6	roots	root	NOUN
ejpam-6752	79	7	with	with	ADP
ejpam-6752	79	8	positive	positive	ADJ
ejpam-6752	79	9	real	real	ADJ
ejpam-6752	79	10	parts	part	NOUN
ejpam-6752	79	11	,	,	PUNCT
ejpam-6752	79	12	making	make	VERB
ejpam-6752	79	13	the	the	DET
ejpam-6752	79	14	equilibrium	equilibrium	NOUN
ejpam-6752	79	15	point	point	NOUN
ejpam-6752	79	16	e	e	X
ejpam-6752	79	17	unstable	unstable	ADJ
ejpam-6752	79	18	,	,	PUNCT
ejpam-6752	79	19	see	see	VERB
ejpam-6752	79	20	fig.1	fig.1	PROPN
ejpam-6752	79	21	-	-	PUNCT
ejpam-6752	79	22	c.	c.	PROPN
ejpam-6752	79	23	r.	r.	PROPN
ejpam-6752	79	24	h.	h.	PROPN
ejpam-6752	79	25	salih	salih	PROPN
ejpam-6752	79	26	/	/	SYM
ejpam-6752	79	27	eur	eur	PROPN
ejpam-6752	79	28	.	.	PUNCT
ejpam-6752	80	1	j.	j.	PROPN
ejpam-6752	80	2	pure	pure	PROPN
ejpam-6752	80	3	appl	appl	PROPN
ejpam-6752	80	4	.	.	PROPN
ejpam-6752	80	5	math	math	PROPN
ejpam-6752	80	6	,	,	PUNCT
ejpam-6752	80	7	18	18	NUM
ejpam-6752	80	8	(	(	PUNCT
ejpam-6752	80	9	4	4	NUM
ejpam-6752	80	10	)	)	PUNCT
ejpam-6752	80	11	(	(	PUNCT
ejpam-6752	80	12	2025	2025	NUM
ejpam-6752	80	13	)	)	PUNCT
ejpam-6752	80	14	,	,	PUNCT
ejpam-6752	80	15	6752	6752	NUM
ejpam-6752	80	16	4	4	NUM
ejpam-6752	80	17	of	of	ADP
ejpam-6752	80	18	14	14	NUM
ejpam-6752	80	19	(	(	PUNCT
ejpam-6752	80	20	a	a	NOUN
ejpam-6752	80	21	)	)	PUNCT
ejpam-6752	80	22	(	(	PUNCT
ejpam-6752	80	23	b	b	X
ejpam-6752	80	24	)	)	PUNCT
ejpam-6752	80	25	(	(	PUNCT
ejpam-6752	80	26	c	c	X
ejpam-6752	80	27	)	)	PUNCT
ejpam-6752	80	28	figure	figure	NOUN
ejpam-6752	80	29	1	1	NUM
ejpam-6752	80	30	:	:	PUNCT
ejpam-6752	80	31	the	the	DET
ejpam-6752	80	32	phase	phase	NOUN
ejpam-6752	80	33	portrait	portrait	NOUN
ejpam-6752	80	34	of	of	ADP
ejpam-6752	80	35	system	system	NOUN
ejpam-6752	80	36	(	(	PUNCT
ejpam-6752	80	37	1	1	X
ejpam-6752	80	38	)	)	PUNCT
ejpam-6752	80	39	is	be	AUX
ejpam-6752	80	40	shown	show	VERB
ejpam-6752	80	41	and	and	CCONJ
ejpam-6752	80	42	the	the	DET
ejpam-6752	80	43	parameters	parameter	NOUN
ejpam-6752	80	44	k2	k2	NOUN
ejpam-6752	80	45	=	=	NOUN
ejpam-6752	80	46	1	1	NUM
ejpam-6752	80	47	2	2	NUM
ejpam-6752	80	48	,	,	PUNCT
ejpam-6752	80	49	k3	k3	VERB
ejpam-6752	80	50	=	=	SYM
ejpam-6752	80	51	k4	k4	NOUN
ejpam-6752	80	52	=	=	SYM
ejpam-6752	80	53	1	1	NUM
ejpam-6752	80	54	are	be	AUX
ejpam-6752	80	55	fixed	fix	VERB
ejpam-6752	80	56	.	.	PUNCT
ejpam-6752	81	1	(	(	PUNCT
ejpam-6752	81	2	a	a	X
ejpam-6752	81	3	)	)	PUNCT
ejpam-6752	81	4	when	when	SCONJ
ejpam-6752	81	5	k1	k1	NOUN
ejpam-6752	81	6	=	=	SYM
ejpam-6752	81	7	2	2	NUM
ejpam-6752	81	8	,	,	PUNCT
ejpam-6752	81	9	e	e	X
ejpam-6752	81	10	is	be	AUX
ejpam-6752	81	11	asymptotically	asymptotically	ADV
ejpam-6752	81	12	stable	stable	ADJ
ejpam-6752	81	13	.	.	PUNCT
ejpam-6752	82	1	(	(	PUNCT
ejpam-6752	82	2	b	b	X
ejpam-6752	82	3	)	)	PUNCT
ejpam-6752	82	4	when	when	SCONJ
ejpam-6752	82	5	k1	k1	NOUN
ejpam-6752	82	6	=	=	NOUN
ejpam-6752	82	7	3	3	NUM
ejpam-6752	82	8	2	2	NUM
ejpam-6752	82	9	,	,	PUNCT
ejpam-6752	82	10	e	e	X
ejpam-6752	82	11	is	be	AUX
ejpam-6752	82	12	a	a	DET
ejpam-6752	82	13	center	center	NOUN
ejpam-6752	82	14	.	.	PUNCT
ejpam-6752	83	1	(	(	PUNCT
ejpam-6752	83	2	c	c	X
ejpam-6752	83	3	)	)	PUNCT
ejpam-6752	83	4	when	when	SCONJ
ejpam-6752	83	5	k1	k1	NOUN
ejpam-6752	83	6	=	=	SYM
ejpam-6752	83	7	1	1	NUM
ejpam-6752	83	8	,	,	PUNCT
ejpam-6752	83	9	e	e	NOUN
ejpam-6752	83	10	is	be	AUX
ejpam-6752	83	11	unstable	unstable	ADJ
ejpam-6752	83	12	.	.	PUNCT
ejpam-6752	84	1	the	the	DET
ejpam-6752	84	2	green	green	ADJ
ejpam-6752	84	3	and	and	CCONJ
ejpam-6752	84	4	red	red	ADJ
ejpam-6752	84	5	balls	ball	NOUN
ejpam-6752	84	6	indicate	indicate	VERB
ejpam-6752	84	7	the	the	DET
ejpam-6752	84	8	equilibrium	equilibrium	NOUN
ejpam-6752	84	9	and	and	CCONJ
ejpam-6752	84	10	initial	initial	ADJ
ejpam-6752	84	11	points	point	NOUN
ejpam-6752	84	12	,	,	PUNCT
ejpam-6752	84	13	respectively	respectively	ADV
ejpam-6752	84	14	.	.	PUNCT
ejpam-6752	85	1	3	3	X
ejpam-6752	85	2	.	.	X
ejpam-6752	85	3	trajectories	trajectory	NOUN
ejpam-6752	85	4	in	in	ADP
ejpam-6752	85	5	planes	plane	NOUN
ejpam-6752	85	6	this	this	DET
ejpam-6752	85	7	section	section	NOUN
ejpam-6752	85	8	focuses	focus	VERB
ejpam-6752	85	9	on	on	ADP
ejpam-6752	85	10	the	the	DET
ejpam-6752	85	11	study	study	NOUN
ejpam-6752	85	12	of	of	ADP
ejpam-6752	85	13	the	the	DET
ejpam-6752	85	14	dynamics	dynamic	NOUN
ejpam-6752	85	15	of	of	ADP
ejpam-6752	85	16	system	system	NOUN
ejpam-6752	85	17	(	(	PUNCT
ejpam-6752	85	18	1	1	NUM
ejpam-6752	85	19	)	)	PUNCT
ejpam-6752	85	20	in	in	ADP
ejpam-6752	85	21	the	the	DET
ejpam-6752	85	22	planes	plane	NOUN
ejpam-6752	85	23	.	.	PUNCT
ejpam-6752	86	1	to	to	PART
ejpam-6752	86	2	understand	understand	VERB
ejpam-6752	86	3	the	the	DET
ejpam-6752	86	4	dynamics	dynamic	NOUN
ejpam-6752	86	5	of	of	ADP
ejpam-6752	86	6	the	the	DET
ejpam-6752	86	7	system	system	NOUN
ejpam-6752	86	8	,	,	PUNCT
ejpam-6752	86	9	the	the	DET
ejpam-6752	86	10	trajectories	trajectory	NOUN
ejpam-6752	86	11	and	and	CCONJ
ejpam-6752	86	12	their	their	PRON
ejpam-6752	86	13	evolution	evolution	NOUN
ejpam-6752	86	14	on	on	ADP
ejpam-6752	86	15	the	the	DET
ejpam-6752	86	16	planes	plane	NOUN
ejpam-6752	86	17	are	be	AUX
ejpam-6752	86	18	investigated	investigate	VERB
ejpam-6752	86	19	individually	individually	ADV
ejpam-6752	86	20	.	.	PUNCT
ejpam-6752	87	1	two	two	NUM
ejpam-6752	87	2	of	of	ADP
ejpam-6752	87	3	the	the	DET
ejpam-6752	87	4	planes	plane	NOUN
ejpam-6752	87	5	,	,	PUNCT
ejpam-6752	87	6	namely	namely	ADV
ejpam-6752	87	7	the	the	DET
ejpam-6752	87	8	x1x3−plane	x1x3−plane	PROPN
ejpam-6752	87	9	and	and	CCONJ
ejpam-6752	87	10	the	the	DET
ejpam-6752	87	11	x2x3−plane	x2x3−plane	PROPN
ejpam-6752	87	12	,	,	PUNCT
ejpam-6752	87	13	are	be	AUX
ejpam-6752	87	14	invariant	invariant	ADJ
ejpam-6752	87	15	,	,	PUNCT
ejpam-6752	87	16	meaning	mean	VERB
ejpam-6752	87	17	that	that	SCONJ
ejpam-6752	87	18	the	the	DET
ejpam-6752	87	19	trajectories	trajectory	NOUN
ejpam-6752	87	20	remain	remain	VERB
ejpam-6752	87	21	confined	confine	VERB
ejpam-6752	87	22	to	to	ADP
ejpam-6752	87	23	them	they	PRON
ejpam-6752	87	24	as	as	ADP
ejpam-6752	87	25	time	time	NOUN
ejpam-6752	87	26	approaches	approach	NOUN
ejpam-6752	87	27	infinity	infinity	NOUN
ejpam-6752	87	28	.	.	PUNCT
ejpam-6752	88	1	moreover	moreover	ADV
ejpam-6752	88	2	,	,	PUNCT
ejpam-6752	88	3	along	along	ADP
ejpam-6752	88	4	all	all	PRON
ejpam-6752	88	5	three	three	NUM
ejpam-6752	88	6	coordinate	coordinate	NOUN
ejpam-6752	88	7	axes	axis	NOUN
ejpam-6752	88	8	,	,	PUNCT
ejpam-6752	88	9	ẋ3	ẋ3	PROPN
ejpam-6752	88	10	is	be	AUX
ejpam-6752	88	11	always	always	ADV
ejpam-6752	88	12	positive	positive	ADJ
ejpam-6752	88	13	.	.	PUNCT
ejpam-6752	89	1	on	on	ADP
ejpam-6752	89	2	the	the	DET
ejpam-6752	89	3	x2x3−plane	x2x3−plane	NOUN
ejpam-6752	89	4	,	,	PUNCT
ejpam-6752	89	5	ẋ2	ẋ2	PROPN
ejpam-6752	89	6	is	be	AUX
ejpam-6752	89	7	always	always	ADV
ejpam-6752	89	8	negative	negative	ADJ
ejpam-6752	89	9	.	.	PUNCT
ejpam-6752	90	1	the	the	DET
ejpam-6752	90	2	horizontal	horizontal	ADJ
ejpam-6752	90	3	isocline	isocline	NOUN
ejpam-6752	90	4	,	,	PUNCT
ejpam-6752	90	5	x2x3	x2x3	PUNCT
ejpam-6752	91	1	=	=	SYM
ejpam-6752	91	2	2k4	2k4	NUM
ejpam-6752	91	3	k3	k3	NOUN
ejpam-6752	91	4	,	,	PUNCT
ejpam-6752	91	5	is	be	AUX
ejpam-6752	91	6	used	use	VERB
ejpam-6752	91	7	to	to	PART
ejpam-6752	91	8	determine	determine	VERB
ejpam-6752	91	9	the	the	DET
ejpam-6752	91	10	sign	sign	NOUN
ejpam-6752	91	11	of	of	ADP
ejpam-6752	91	12	ẋ3	ẋ3	PROPN
ejpam-6752	91	13	.	.	PUNCT
ejpam-6752	92	1	a	a	DET
ejpam-6752	92	2	point	point	NOUN
ejpam-6752	92	3	(	(	PUNCT
ejpam-6752	92	4	x2	x2	PROPN
ejpam-6752	92	5	,	,	PUNCT
ejpam-6752	92	6	x3	x3	ADJ
ejpam-6752	92	7	)	)	PUNCT
ejpam-6752	92	8	is	be	AUX
ejpam-6752	92	9	chosen	choose	VERB
ejpam-6752	92	10	on	on	ADP
ejpam-6752	92	11	one	one	NUM
ejpam-6752	92	12	side	side	NOUN
ejpam-6752	92	13	of	of	ADP
ejpam-6752	92	14	the	the	DET
ejpam-6752	92	15	isocline	isocline	NOUN
ejpam-6752	92	16	.	.	PUNCT
ejpam-6752	93	1	first	first	ADV
ejpam-6752	93	2	,	,	PUNCT
ejpam-6752	93	3	a	a	DET
ejpam-6752	93	4	point	point	NOUN
ejpam-6752	93	5	on	on	ADP
ejpam-6752	93	6	the	the	DET
ejpam-6752	93	7	left	left	ADJ
ejpam-6752	93	8	side	side	NOUN
ejpam-6752	93	9	is	be	AUX
ejpam-6752	93	10	selected	select	VERB
ejpam-6752	93	11	and	and	CCONJ
ejpam-6752	93	12	x2x3	x2x3	X
ejpam-6752	94	1	=	=	SYM
ejpam-6752	94	2	2k4	2k4	NUM
ejpam-6752	94	3	k3	k3	VERB
ejpam-6752	94	4	−	−	PROPN
ejpam-6752	94	5	ϵ	ϵ	NOUN
ejpam-6752	94	6	,	,	PUNCT
ejpam-6752	94	7	where	where	SCONJ
ejpam-6752	94	8	ϵ	ϵ	X
ejpam-6752	94	9	>	>	X
ejpam-6752	94	10	0	0	NUM
ejpam-6752	94	11	is	be	AUX
ejpam-6752	94	12	set	set	VERB
ejpam-6752	94	13	.	.	PUNCT
ejpam-6752	95	1	this	this	PRON
ejpam-6752	95	2	implies	imply	VERB
ejpam-6752	95	3	that	that	SCONJ
ejpam-6752	95	4	ẋ3	ẋ3	PROPN
ejpam-6752	95	5	=	=	SYM
ejpam-6752	95	6	k3ϵ	k3ϵ	PROPN
ejpam-6752	95	7	>	>	X
ejpam-6752	95	8	0	0	X
ejpam-6752	95	9	.	.	PUNCT
ejpam-6752	96	1	however	however	ADV
ejpam-6752	96	2	,	,	PUNCT
ejpam-6752	96	3	if	if	SCONJ
ejpam-6752	96	4	a	a	DET
ejpam-6752	96	5	point	point	NOUN
ejpam-6752	96	6	on	on	ADP
ejpam-6752	96	7	the	the	DET
ejpam-6752	96	8	other	other	ADJ
ejpam-6752	96	9	side	side	NOUN
ejpam-6752	96	10	is	be	AUX
ejpam-6752	96	11	chosen	choose	VERB
ejpam-6752	96	12	,	,	PUNCT
ejpam-6752	96	13	x2x3	x2x3	PUNCT
ejpam-6752	97	1	=	=	SYM
ejpam-6752	97	2	2k4	2k4	NUM
ejpam-6752	97	3	k3	k3	VERB
ejpam-6752	97	4	+	+	CCONJ
ejpam-6752	97	5	ϵ	ϵ	X
ejpam-6752	97	6	,	,	PUNCT
ejpam-6752	97	7	ϵ	ϵ	X
ejpam-6752	97	8	>	>	X
ejpam-6752	97	9	0	0	PROPN
ejpam-6752	97	10	,	,	PUNCT
ejpam-6752	97	11	then	then	ADV
ejpam-6752	97	12	ẋ3	ẋ3	X
ejpam-6752	97	13	=	=	SYM
ejpam-6752	97	14	−k3ϵ	−k3ϵ	X
ejpam-6752	97	15	<	<	X
ejpam-6752	97	16	0	0	X
ejpam-6752	97	17	.	.	PUNCT
ejpam-6752	98	1	the	the	DET
ejpam-6752	98	2	x3−axis	x3−axis	PROPN
ejpam-6752	98	3	is	be	AUX
ejpam-6752	98	4	always	always	ADV
ejpam-6752	98	5	invariant	invariant	ADJ
ejpam-6752	98	6	and	and	CCONJ
ejpam-6752	98	7	on	on	ADP
ejpam-6752	98	8	the	the	DET
ejpam-6752	98	9	x2−axis	x2−axis	PROPN
ejpam-6752	98	10	,	,	PUNCT
ejpam-6752	99	1	ẋ3	ẋ3	X
ejpam-6752	99	2	>	>	X
ejpam-6752	99	3	0	0	X
ejpam-6752	99	4	.	.	PUNCT
ejpam-6752	100	1	now	now	ADV
ejpam-6752	100	2	,	,	PUNCT
ejpam-6752	100	3	sufficient	sufficient	ADJ
ejpam-6752	100	4	information	information	NOUN
ejpam-6752	100	5	has	have	AUX
ejpam-6752	100	6	been	be	AUX
ejpam-6752	100	7	gathered	gather	VERB
ejpam-6752	100	8	to	to	PART
ejpam-6752	100	9	sketch	sketch	VERB
ejpam-6752	100	10	the	the	DET
ejpam-6752	100	11	trajectory	trajectory	NOUN
ejpam-6752	100	12	directions	direction	NOUN
ejpam-6752	100	13	of	of	ADP
ejpam-6752	100	14	the	the	DET
ejpam-6752	100	15	system	system	NOUN
ejpam-6752	100	16	,	,	PUNCT
ejpam-6752	100	17	as	as	SCONJ
ejpam-6752	100	18	depicted	depict	VERB
ejpam-6752	100	19	in	in	ADP
ejpam-6752	100	20	fig	fig	NOUN
ejpam-6752	100	21	.	.	PUNCT
ejpam-6752	101	1	2	2	NUM
ejpam-6752	101	2	-	-	PUNCT
ejpam-6752	101	3	a.	a.	NOUN
ejpam-6752	101	4	on	on	ADP
ejpam-6752	101	5	the	the	DET
ejpam-6752	101	6	x1x3	x1x3	NOUN
ejpam-6752	101	7	-	-	NOUN
ejpam-6752	101	8	plane	plane	NOUN
ejpam-6752	101	9	,	,	PUNCT
ejpam-6752	101	10	ẋ1	ẋ1	PROPN
ejpam-6752	101	11	is	be	AUX
ejpam-6752	101	12	always	always	ADV
ejpam-6752	101	13	positive	positive	ADJ
ejpam-6752	101	14	and	and	CCONJ
ejpam-6752	101	15	a	a	DET
ejpam-6752	101	16	horizontal	horizontal	ADJ
ejpam-6752	101	17	isocline	isocline	NOUN
ejpam-6752	101	18	,	,	PUNCT
ejpam-6752	101	19	x1x3	x1x3	PROPN
ejpam-6752	101	20	=	=	SYM
ejpam-6752	101	21	2k4	2k4	NUM
ejpam-6752	101	22	k1	k1	NOUN
ejpam-6752	101	23	,	,	PUNCT
ejpam-6752	101	24	is	be	AUX
ejpam-6752	101	25	present	present	ADJ
ejpam-6752	101	26	,	,	PUNCT
ejpam-6752	101	27	which	which	PRON
ejpam-6752	101	28	determines	determine	VERB
ejpam-6752	101	29	the	the	DET
ejpam-6752	101	30	sign	sign	NOUN
ejpam-6752	101	31	of	of	ADP
ejpam-6752	101	32	ẋ3	ẋ3	PROPN
ejpam-6752	101	33	.	.	PUNCT
ejpam-6752	102	1	it	it	PRON
ejpam-6752	102	2	can	can	AUX
ejpam-6752	102	3	be	be	AUX
ejpam-6752	102	4	easily	easily	ADV
ejpam-6752	102	5	shown	show	VERB
ejpam-6752	102	6	that	that	SCONJ
ejpam-6752	102	7	ẋ3	ẋ3	PROPN
ejpam-6752	102	8	>	>	X
ejpam-6752	102	9	0	0	PUNCT
ejpam-6752	103	1	on	on	ADP
ejpam-6752	103	2	the	the	DET
ejpam-6752	103	3	left	left	ADJ
ejpam-6752	103	4	side	side	NOUN
ejpam-6752	103	5	,	,	PUNCT
ejpam-6752	103	6	while	while	SCONJ
ejpam-6752	103	7	ẋ3	ẋ3	X
ejpam-6752	103	8	<	<	X
ejpam-6752	103	9	0	0	NUM
ejpam-6752	103	10	on	on	ADP
ejpam-6752	103	11	the	the	DET
ejpam-6752	103	12	other	other	ADJ
ejpam-6752	103	13	side	side	NOUN
ejpam-6752	103	14	of	of	ADP
ejpam-6752	103	15	the	the	DET
ejpam-6752	103	16	isocline	isocline	NOUN
ejpam-6752	103	17	.	.	PUNCT
ejpam-6752	104	1	the	the	DET
ejpam-6752	104	2	x3	x3	ADJ
ejpam-6752	104	3	-	-	PUNCT
ejpam-6752	104	4	axis	axis	NOUN
ejpam-6752	104	5	is	be	AUX
ejpam-6752	104	6	found	find	VERB
ejpam-6752	104	7	to	to	PART
ejpam-6752	104	8	be	be	AUX
ejpam-6752	104	9	invariant	invariant	ADJ
ejpam-6752	104	10	and	and	CCONJ
ejpam-6752	104	11	ẋ3	ẋ3	PROPN
ejpam-6752	104	12	is	be	AUX
ejpam-6752	104	13	positive	positive	ADJ
ejpam-6752	104	14	on	on	ADP
ejpam-6752	104	15	the	the	DET
ejpam-6752	104	16	x1	x1	PROPN
ejpam-6752	104	17	-	-	PUNCT
ejpam-6752	104	18	axis	axis	NOUN
ejpam-6752	104	19	.	.	PUNCT
ejpam-6752	105	1	by	by	ADP
ejpam-6752	105	2	combining	combine	VERB
ejpam-6752	105	3	these	these	DET
ejpam-6752	105	4	observations	observation	NOUN
ejpam-6752	105	5	,	,	PUNCT
ejpam-6752	105	6	sufficient	sufficient	ADJ
ejpam-6752	105	7	conditions	condition	NOUN
ejpam-6752	105	8	for	for	ADP
ejpam-6752	105	9	sketching	sketch	VERB
ejpam-6752	105	10	the	the	DET
ejpam-6752	105	11	trajectory	trajectory	NOUN
ejpam-6752	105	12	directions	direction	NOUN
ejpam-6752	105	13	are	be	AUX
ejpam-6752	105	14	derived	derive	VERB
ejpam-6752	105	15	and	and	CCONJ
ejpam-6752	105	16	illustrated	illustrate	VERB
ejpam-6752	105	17	in	in	ADP
ejpam-6752	105	18	fig	fig	NOUN
ejpam-6752	105	19	.	.	PUNCT
ejpam-6752	106	1	2	2	NUM
ejpam-6752	106	2	-	-	PUNCT
ejpam-6752	106	3	b.	b.	NOUN
ejpam-6752	106	4	on	on	ADP
ejpam-6752	106	5	the	the	DET
ejpam-6752	106	6	x1x2	x1x2	NOUN
ejpam-6752	106	7	-	-	NOUN
ejpam-6752	106	8	plane	plane	NOUN
ejpam-6752	106	9	,	,	PUNCT
ejpam-6752	106	10	it	it	PRON
ejpam-6752	106	11	is	be	AUX
ejpam-6752	106	12	noted	note	VERB
ejpam-6752	106	13	that	that	SCONJ
ejpam-6752	106	14	ẋ1	ẋ1	PROPN
ejpam-6752	106	15	is	be	AUX
ejpam-6752	106	16	always	always	ADV
ejpam-6752	106	17	negative	negative	ADJ
ejpam-6752	106	18	,	,	PUNCT
ejpam-6752	106	19	while	while	SCONJ
ejpam-6752	106	20	both	both	PRON
ejpam-6752	106	21	ẋ2	ẋ2	PROPN
ejpam-6752	106	22	and	and	CCONJ
ejpam-6752	106	23	ẋ3	ẋ3	PROPN
ejpam-6752	106	24	are	be	AUX
ejpam-6752	106	25	positive	positive	ADJ
ejpam-6752	106	26	.	.	PUNCT
ejpam-6752	107	1	the	the	DET
ejpam-6752	107	2	relations	relation	NOUN
ejpam-6752	107	3	ẋ1	ẋ1	PROPN
ejpam-6752	107	4	+	+	PROPN
ejpam-6752	107	5	ẋ2	ẋ2	NOUN
ejpam-6752	107	6	=	=	SYM
ejpam-6752	107	7	0	0	NUM
ejpam-6752	107	8	and	and	CCONJ
ejpam-6752	107	9	ẋ3	ẋ3	PROPN
ejpam-6752	107	10	=	=	SYM
ejpam-6752	107	11	2k4	2k4	NUM
ejpam-6752	107	12	are	be	AUX
ejpam-6752	107	13	satisfied	satisfied	ADJ
ejpam-6752	107	14	,	,	PUNCT
ejpam-6752	107	15	which	which	PRON
ejpam-6752	107	16	implies	imply	VERB
ejpam-6752	107	17	that	that	PRON
ejpam-6752	107	18	x1+x2	x1+x2	PROPN
ejpam-6752	107	19	=	=	PUNCT
ejpam-6752	107	20	c	c	X
ejpam-6752	107	21	,	,	PUNCT
ejpam-6752	107	22	where	where	SCONJ
ejpam-6752	107	23	c	c	X
ejpam-6752	107	24	∈	∈	PROPN
ejpam-6752	107	25	r	r	NOUN
ejpam-6752	107	26	,	,	PUNCT
ejpam-6752	107	27	and	and	CCONJ
ejpam-6752	107	28	x3(t	x3(t	NUM
ejpam-6752	107	29	)	)	PUNCT
ejpam-6752	107	30	=	=	PUNCT
ejpam-6752	107	31	2k4	2k4	NUM
ejpam-6752	107	32	t.	t.	NOUN
ejpam-6752	107	33	since	since	SCONJ
ejpam-6752	107	34	the	the	DET
ejpam-6752	107	35	plane	plane	NOUN
ejpam-6752	107	36	is	be	AUX
ejpam-6752	107	37	not	not	PART
ejpam-6752	107	38	invariant	invariant	ADJ
ejpam-6752	107	39	,	,	PUNCT
ejpam-6752	107	40	this	this	DET
ejpam-6752	107	41	information	information	NOUN
ejpam-6752	107	42	indicates	indicate	VERB
ejpam-6752	107	43	that	that	SCONJ
ejpam-6752	107	44	the	the	DET
ejpam-6752	107	45	trajectories	trajectory	NOUN
ejpam-6752	107	46	move	move	VERB
ejpam-6752	107	47	with	with	ADP
ejpam-6752	107	48	a	a	DET
ejpam-6752	107	49	positive	positive	ADJ
ejpam-6752	107	50	slope	slope	NOUN
ejpam-6752	107	51	.	.	PUNCT
ejpam-6752	108	1	however	however	ADV
ejpam-6752	108	2	,	,	PUNCT
ejpam-6752	108	3	on	on	ADP
ejpam-6752	108	4	each	each	DET
ejpam-6752	108	5	x1	x1	PROPN
ejpam-6752	108	6	and	and	CCONJ
ejpam-6752	108	7	x2	x2	ADJ
ejpam-6752	108	8	-	-	PUNCT
ejpam-6752	108	9	axis	axis	NOUN
ejpam-6752	108	10	,	,	PUNCT
ejpam-6752	108	11	ẋ1	ẋ1	PROPN
ejpam-6752	108	12	=	=	PUNCT
ejpam-6752	109	1	ẋ2	ẋ2	PUNCT
ejpam-6752	109	2	=	=	PUNCT
ejpam-6752	109	3	0	0	NUM
ejpam-6752	109	4	and	and	CCONJ
ejpam-6752	109	5	ẋ3	ẋ3	X
ejpam-6752	109	6	>	>	X
ejpam-6752	109	7	0	0	X
ejpam-6752	109	8	.	.	PUNCT
ejpam-6752	110	1	this	this	PRON
ejpam-6752	110	2	indicates	indicate	VERB
ejpam-6752	110	3	that	that	SCONJ
ejpam-6752	110	4	near	near	ADP
ejpam-6752	110	5	the	the	DET
ejpam-6752	110	6	axes	axis	NOUN
ejpam-6752	110	7	,	,	PUNCT
ejpam-6752	110	8	the	the	DET
ejpam-6752	110	9	trajectories	trajectory	NOUN
ejpam-6752	110	10	move	move	VERB
ejpam-6752	110	11	upward	upward	ADV
ejpam-6752	110	12	toward	toward	ADP
ejpam-6752	110	13	the	the	DET
ejpam-6752	110	14	x3	x3	ADJ
ejpam-6752	110	15	-	-	PUNCT
ejpam-6752	110	16	axis	axis	NOUN
ejpam-6752	110	17	.	.	PUNCT
ejpam-6752	111	1	this	this	DET
ejpam-6752	111	2	information	information	NOUN
ejpam-6752	111	3	helps	help	VERB
ejpam-6752	111	4	us	we	PRON
ejpam-6752	111	5	predict	predict	VERB
ejpam-6752	111	6	the	the	DET
ejpam-6752	111	7	direction	direction	NOUN
ejpam-6752	111	8	of	of	ADP
ejpam-6752	111	9	the	the	DET
ejpam-6752	111	10	trajectories	trajectory	NOUN
ejpam-6752	111	11	.	.	PUNCT
ejpam-6752	112	1	r.	r.	PROPN
ejpam-6752	112	2	h.	h.	PROPN
ejpam-6752	112	3	salih	salih	PROPN
ejpam-6752	112	4	/	/	SYM
ejpam-6752	112	5	eur	eur	PROPN
ejpam-6752	112	6	.	.	PUNCT
ejpam-6752	113	1	j.	j.	PROPN
ejpam-6752	113	2	pure	pure	PROPN
ejpam-6752	113	3	appl	appl	PROPN
ejpam-6752	113	4	.	.	PROPN
ejpam-6752	113	5	math	math	PROPN
ejpam-6752	113	6	,	,	PUNCT
ejpam-6752	113	7	18	18	NUM
ejpam-6752	113	8	(	(	PUNCT
ejpam-6752	113	9	4	4	NUM
ejpam-6752	113	10	)	)	PUNCT
ejpam-6752	113	11	(	(	PUNCT
ejpam-6752	113	12	2025	2025	NUM
ejpam-6752	113	13	)	)	PUNCT
ejpam-6752	113	14	,	,	PUNCT
ejpam-6752	113	15	6752	6752	NUM
ejpam-6752	113	16	5	5	NUM
ejpam-6752	113	17	of	of	ADP
ejpam-6752	113	18	14	14	NUM
ejpam-6752	113	19	by	by	ADP
ejpam-6752	113	20	integrating	integrate	VERB
ejpam-6752	113	21	the	the	DET
ejpam-6752	113	22	information	information	NOUN
ejpam-6752	113	23	obtained	obtain	VERB
ejpam-6752	113	24	from	from	ADP
ejpam-6752	113	25	figs	fig	NOUN
ejpam-6752	113	26	.	.	PUNCT
ejpam-6752	114	1	2	2	NUM
ejpam-6752	114	2	-	-	SYM
ejpam-6752	114	3	a	a	DET
ejpam-6752	114	4	,	,	PUNCT
ejpam-6752	114	5	2	2	NUM
ejpam-6752	114	6	-	-	SYM
ejpam-6752	114	7	b	b	NOUN
ejpam-6752	114	8	and	and	CCONJ
ejpam-6752	114	9	the	the	DET
ejpam-6752	114	10	x1x2	x1x2	NOUN
ejpam-6752	114	11	-	-	NOUN
ejpam-6752	114	12	plane	plane	NOUN
ejpam-6752	114	13	,	,	PUNCT
ejpam-6752	114	14	along	along	ADP
ejpam-6752	114	15	with	with	ADP
ejpam-6752	114	16	the	the	DET
ejpam-6752	114	17	dynamics	dynamic	NOUN
ejpam-6752	114	18	at	at	ADP
ejpam-6752	114	19	infinity	infinity	NOUN
ejpam-6752	114	20	,	,	PUNCT
ejpam-6752	114	21	the	the	DET
ejpam-6752	114	22	complete	complete	ADJ
ejpam-6752	114	23	information	information	NOUN
ejpam-6752	114	24	in	in	ADP
ejpam-6752	114	25	fig	fig	NOUN
ejpam-6752	114	26	.	.	PUNCT
ejpam-6752	115	1	3	3	NUM
ejpam-6752	115	2	is	be	AUX
ejpam-6752	115	3	derived	derive	VERB
ejpam-6752	115	4	.	.	PUNCT
ejpam-6752	116	1	this	this	DET
ejpam-6752	116	2	information	information	NOUN
ejpam-6752	116	3	is	be	AUX
ejpam-6752	116	4	useful	useful	ADJ
ejpam-6752	116	5	for	for	ADP
ejpam-6752	116	6	understanding	understand	VERB
ejpam-6752	116	7	the	the	DET
ejpam-6752	116	8	trajectory	trajectory	NOUN
ejpam-6752	116	9	directions	direction	NOUN
ejpam-6752	116	10	around	around	ADP
ejpam-6752	116	11	the	the	DET
ejpam-6752	116	12	positive	positive	ADJ
ejpam-6752	116	13	critical	critical	ADJ
ejpam-6752	116	14	point	point	NOUN
ejpam-6752	116	15	e	e	NOUN
ejpam-6752	116	16	,	,	PUNCT
ejpam-6752	116	17	which	which	PRON
ejpam-6752	116	18	can	can	AUX
ejpam-6752	116	19	be	be	AUX
ejpam-6752	116	20	stable	stable	ADJ
ejpam-6752	116	21	,	,	PUNCT
ejpam-6752	116	22	unstable	unstable	ADJ
ejpam-6752	116	23	or	or	CCONJ
ejpam-6752	116	24	a	a	DET
ejpam-6752	116	25	center	center	NOUN
ejpam-6752	116	26	in	in	ADP
ejpam-6752	116	27	different	different	ADJ
ejpam-6752	116	28	cases	case	NOUN
ejpam-6752	116	29	.	.	PUNCT
ejpam-6752	117	1	(	(	PUNCT
ejpam-6752	117	2	a	a	X
ejpam-6752	117	3	)	)	PUNCT
ejpam-6752	117	4	(	(	PUNCT
ejpam-6752	117	5	b	b	X
ejpam-6752	117	6	)	)	PUNCT
ejpam-6752	117	7	figure	figure	NOUN
ejpam-6752	117	8	2	2	NUM
ejpam-6752	117	9	:	:	PUNCT
ejpam-6752	117	10	the	the	DET
ejpam-6752	117	11	trajectory	trajectory	NOUN
ejpam-6752	117	12	directions	direction	NOUN
ejpam-6752	117	13	of	of	ADP
ejpam-6752	117	14	system	system	NOUN
ejpam-6752	117	15	(	(	PUNCT
ejpam-6752	117	16	1	1	NUM
ejpam-6752	117	17	)	)	PUNCT
ejpam-6752	117	18	on	on	ADP
ejpam-6752	117	19	the	the	DET
ejpam-6752	117	20	planes	plane	NOUN
ejpam-6752	117	21	are	be	AUX
ejpam-6752	117	22	shown	show	VERB
ejpam-6752	117	23	.	.	PUNCT
ejpam-6752	118	1	(	(	PUNCT
ejpam-6752	118	2	a	a	X
ejpam-6752	118	3	)	)	PUNCT
ejpam-6752	118	4	trajectory	trajectory	NOUN
ejpam-6752	118	5	direction	direction	NOUN
ejpam-6752	118	6	on	on	ADP
ejpam-6752	118	7	x2x3−plane	x2x3−plane	PROPN
ejpam-6752	118	8	.	.	PUNCT
ejpam-6752	119	1	(	(	PUNCT
ejpam-6752	119	2	b	b	X
ejpam-6752	119	3	)	)	PUNCT
ejpam-6752	119	4	trajectory	trajectory	NOUN
ejpam-6752	119	5	direction	direction	NOUN
ejpam-6752	119	6	on	on	ADP
ejpam-6752	119	7	x1x3−plane	x1x3−plane	PROPN
ejpam-6752	119	8	.	.	PUNCT
ejpam-6752	120	1	the	the	DET
ejpam-6752	120	2	dotted	dotted	ADJ
ejpam-6752	120	3	lines	line	NOUN
ejpam-6752	120	4	indicate	indicate	VERB
ejpam-6752	120	5	the	the	DET
ejpam-6752	120	6	isoclines	isocline	NOUN
ejpam-6752	120	7	.	.	PUNCT
ejpam-6752	121	1	figure	figure	VERB
ejpam-6752	121	2	3	3	NUM
ejpam-6752	121	3	:	:	PUNCT
ejpam-6752	121	4	directions	direction	NOUN
ejpam-6752	121	5	of	of	ADP
ejpam-6752	121	6	the	the	DET
ejpam-6752	121	7	trajectory	trajectory	NOUN
ejpam-6752	121	8	of	of	ADP
ejpam-6752	121	9	system	system	NOUN
ejpam-6752	121	10	(	(	PUNCT
ejpam-6752	121	11	1	1	NUM
ejpam-6752	121	12	)	)	PUNCT
ejpam-6752	121	13	in	in	ADP
ejpam-6752	121	14	the	the	DET
ejpam-6752	121	15	three	three	NUM
ejpam-6752	121	16	planes	plane	NOUN
ejpam-6752	121	17	.	.	PUNCT
ejpam-6752	122	1	4	4	X
ejpam-6752	122	2	.	.	X
ejpam-6752	122	3	bifurcation	bifurcation	NOUN
ejpam-6752	122	4	analysis	analysis	NOUN
ejpam-6752	122	5	bifurcations	bifurcation	NOUN
ejpam-6752	122	6	describe	describe	VERB
ejpam-6752	122	7	significant	significant	ADJ
ejpam-6752	122	8	changes	change	NOUN
ejpam-6752	122	9	in	in	ADP
ejpam-6752	122	10	the	the	DET
ejpam-6752	122	11	behavior	behavior	NOUN
ejpam-6752	122	12	of	of	ADP
ejpam-6752	122	13	solution	solution	NOUN
ejpam-6752	122	14	curves	curve	NOUN
ejpam-6752	122	15	within	within	ADP
ejpam-6752	122	16	a	a	DET
ejpam-6752	122	17	dynamical	dynamical	ADJ
ejpam-6752	122	18	system	system	NOUN
ejpam-6752	122	19	as	as	ADP
ejpam-6752	122	20	certain	certain	ADJ
ejpam-6752	122	21	parameter	parameter	NOUN
ejpam-6752	122	22	values	value	NOUN
ejpam-6752	122	23	,	,	PUNCT
ejpam-6752	122	24	called	call	VERB
ejpam-6752	122	25	bifurcation	bifurcation	NOUN
ejpam-6752	122	26	values	value	NOUN
ejpam-6752	122	27	,	,	PUNCT
ejpam-6752	122	28	are	be	AUX
ejpam-6752	122	29	varied	varied	ADJ
ejpam-6752	122	30	.	.	PUNCT
ejpam-6752	123	1	this	this	DET
ejpam-6752	123	2	section	section	NOUN
ejpam-6752	123	3	examines	examine	VERB
ejpam-6752	123	4	both	both	CCONJ
ejpam-6752	123	5	hopf	hopf	ADJ
ejpam-6752	123	6	and	and	CCONJ
ejpam-6752	123	7	center	center	ADJ
ejpam-6752	123	8	bifurcations	bifurcation	NOUN
ejpam-6752	123	9	in	in	ADP
ejpam-6752	123	10	system	system	NOUN
ejpam-6752	123	11	(	(	PUNCT
ejpam-6752	123	12	1	1	NUM
ejpam-6752	123	13	)	)	PUNCT
ejpam-6752	123	14	,	,	PUNCT
ejpam-6752	123	15	emphasizing	emphasize	VERB
ejpam-6752	123	16	the	the	DET
ejpam-6752	123	17	conditions	condition	NOUN
ejpam-6752	123	18	under	under	ADP
ejpam-6752	123	19	which	which	PRON
ejpam-6752	123	20	they	they	PRON
ejpam-6752	123	21	occur	occur	VERB
ejpam-6752	123	22	.	.	PUNCT
ejpam-6752	124	1	r.	r.	PROPN
ejpam-6752	124	2	h.	h.	PROPN
ejpam-6752	124	3	salih	salih	PROPN
ejpam-6752	124	4	/	/	SYM
ejpam-6752	124	5	eur	eur	PROPN
ejpam-6752	124	6	.	.	PUNCT
ejpam-6752	125	1	j.	j.	PROPN
ejpam-6752	125	2	pure	pure	PROPN
ejpam-6752	125	3	appl	appl	PROPN
ejpam-6752	125	4	.	.	PROPN
ejpam-6752	125	5	math	math	PROPN
ejpam-6752	125	6	,	,	PUNCT
ejpam-6752	125	7	18	18	NUM
ejpam-6752	125	8	(	(	PUNCT
ejpam-6752	125	9	4	4	NUM
ejpam-6752	125	10	)	)	PUNCT
ejpam-6752	125	11	(	(	PUNCT
ejpam-6752	125	12	2025	2025	NUM
ejpam-6752	125	13	)	)	PUNCT
ejpam-6752	125	14	,	,	PUNCT
ejpam-6752	125	15	6752	6752	NUM
ejpam-6752	125	16	6	6	NUM
ejpam-6752	125	17	of	of	ADP
ejpam-6752	125	18	14	14	NUM
ejpam-6752	125	19	4.1	4.1	NUM
ejpam-6752	125	20	.	.	PUNCT
ejpam-6752	126	1	hopf	hopf	ADJ
ejpam-6752	126	2	bifurcation	bifurcation	NOUN
ejpam-6752	126	3	consider	consider	VERB
ejpam-6752	126	4	the	the	DET
ejpam-6752	126	5	following	follow	VERB
ejpam-6752	126	6	dynamical	dynamical	ADJ
ejpam-6752	126	7	system	system	NOUN
ejpam-6752	126	8	in	in	ADP
ejpam-6752	126	9	three	three	NUM
ejpam-6752	126	10	dimensions	dimension	NOUN
ejpam-6752	126	11	:	:	PUNCT
ejpam-6752	126	12	ẋ	ẋ	PROPN
ejpam-6752	126	13	=	=	SYM
ejpam-6752	126	14	f(x,µ	f(x,µ	NOUN
ejpam-6752	126	15	)	)	PUNCT
ejpam-6752	126	16	,	,	PUNCT
ejpam-6752	126	17	(	(	PUNCT
ejpam-6752	126	18	4	4	X
ejpam-6752	126	19	)	)	PUNCT
ejpam-6752	126	20	where	where	SCONJ
ejpam-6752	126	21	x	x	PRON
ejpam-6752	126	22	is	be	AUX
ejpam-6752	126	23	an	an	DET
ejpam-6752	126	24	element	element	NOUN
ejpam-6752	126	25	of	of	ADP
ejpam-6752	126	26	r3	r3	PROPN
ejpam-6752	126	27	,	,	PUNCT
ejpam-6752	126	28	f	f	PROPN
ejpam-6752	126	29	is	be	AUX
ejpam-6752	126	30	a	a	DET
ejpam-6752	126	31	real	real	ADJ
ejpam-6752	126	32	analytic	analytic	ADJ
ejpam-6752	126	33	function	function	NOUN
ejpam-6752	126	34	and	and	CCONJ
ejpam-6752	126	35	µ	µ	NOUN
ejpam-6752	126	36	belongs	belong	VERB
ejpam-6752	126	37	to	to	ADP
ejpam-6752	126	38	rk	rk	PRON
ejpam-6752	126	39	,	,	PUNCT
ejpam-6752	126	40	serving	serve	VERB
ejpam-6752	126	41	as	as	ADP
ejpam-6752	126	42	the	the	DET
ejpam-6752	126	43	bifurcation	bifurcation	NOUN
ejpam-6752	126	44	parameter	parameter	NOUN
ejpam-6752	126	45	.	.	PUNCT
ejpam-6752	127	1	the	the	DET
ejpam-6752	127	2	essential	essential	ADJ
ejpam-6752	127	3	conditions	condition	NOUN
ejpam-6752	127	4	for	for	ADP
ejpam-6752	127	5	the	the	DET
ejpam-6752	127	6	occurrence	occurrence	NOUN
ejpam-6752	127	7	of	of	ADP
ejpam-6752	127	8	a	a	DET
ejpam-6752	127	9	hopf	hopf	ADJ
ejpam-6752	127	10	bifurcation	bifurcation	NOUN
ejpam-6752	127	11	are	be	AUX
ejpam-6752	127	12	now	now	ADV
ejpam-6752	127	13	presented	present	VERB
ejpam-6752	127	14	.	.	PUNCT
ejpam-6752	128	1	it	it	PRON
ejpam-6752	128	2	is	be	AUX
ejpam-6752	128	3	assumed	assume	VERB
ejpam-6752	128	4	that	that	SCONJ
ejpam-6752	128	5	the	the	DET
ejpam-6752	128	6	system	system	NOUN
ejpam-6752	128	7	possesses	possess	VERB
ejpam-6752	128	8	an	an	DET
ejpam-6752	128	9	equilibrium	equilibrium	NOUN
ejpam-6752	128	10	point	point	NOUN
ejpam-6752	128	11	(	(	PUNCT
ejpam-6752	128	12	e0	e0	PROPN
ejpam-6752	128	13	,	,	PUNCT
ejpam-6752	128	14	µ0	µ0	PROPN
ejpam-6752	128	15	)	)	PUNCT
ejpam-6752	128	16	at	at	ADP
ejpam-6752	128	17	which	which	PRON
ejpam-6752	128	18	the	the	DET
ejpam-6752	128	19	following	follow	VERB
ejpam-6752	128	20	criteria	criterion	NOUN
ejpam-6752	128	21	are	be	AUX
ejpam-6752	128	22	satisfied	satisfied	ADJ
ejpam-6752	128	23	:	:	PUNCT
ejpam-6752	128	24	i.	i.	NOUN
ejpam-6752	128	25	the	the	DET
ejpam-6752	128	26	jacobian	jacobian	ADJ
ejpam-6752	128	27	matrix	matrix	NOUN
ejpam-6752	128	28	j	j	PROPN
ejpam-6752	128	29	=	=	SYM
ejpam-6752	128	30	df(e0	df(e0	PROPN
ejpam-6752	128	31	,	,	PUNCT
ejpam-6752	128	32	µ0	µ0	NOUN
ejpam-6752	128	33	)	)	PUNCT
ejpam-6752	128	34	possesses	possess	VERB
ejpam-6752	128	35	a	a	DET
ejpam-6752	128	36	unique	unique	ADJ
ejpam-6752	128	37	pair	pair	NOUN
ejpam-6752	128	38	of	of	ADP
ejpam-6752	128	39	purely	purely	ADV
ejpam-6752	128	40	imaginary	imaginary	ADJ
ejpam-6752	128	41	eigenvalues	eigenvalue	NOUN
ejpam-6752	128	42	λ(µ0	λ(µ0	NOUN
ejpam-6752	128	43	)	)	PUNCT
ejpam-6752	128	44	and	and	CCONJ
ejpam-6752	128	45	λ̄(µ0	λ̄(µ0	X
ejpam-6752	128	46	)	)	PUNCT
ejpam-6752	128	47	,	,	PUNCT
ejpam-6752	128	48	while	while	SCONJ
ejpam-6752	128	49	the	the	DET
ejpam-6752	128	50	remaining	remain	VERB
ejpam-6752	128	51	eigenvalues	eigenvalue	NOUN
ejpam-6752	128	52	are	be	AUX
ejpam-6752	128	53	non	non	ADJ
ejpam-6752	128	54	-	-	ADJ
ejpam-6752	128	55	zero	zero	NUM
ejpam-6752	128	56	.	.	PUNCT
ejpam-6752	128	57	ii	ii	PROPN
ejpam-6752	128	58	.	.	PUNCT
ejpam-6752	129	1	dre(λ(µ0	dre(λ(µ0	PROPN
ejpam-6752	129	2	)	)	PUNCT
ejpam-6752	129	3	)	)	PUNCT
ejpam-6752	129	4	dµ	dµ	VERB
ejpam-6752	129	5	̸=	̸=	PROPN
ejpam-6752	129	6	0	0	NUM
ejpam-6752	129	7	.	.	PUNCT
ejpam-6752	130	1	subsequently	subsequently	ADV
ejpam-6752	130	2	,	,	PUNCT
ejpam-6752	130	3	the	the	DET
ejpam-6752	130	4	system	system	NOUN
ejpam-6752	130	5	defined	define	VERB
ejpam-6752	130	6	by	by	ADP
ejpam-6752	130	7	(	(	PUNCT
ejpam-6752	130	8	4	4	X
ejpam-6752	130	9	)	)	PUNCT
ejpam-6752	130	10	experiences	experience	NOUN
ejpam-6752	130	11	a	a	DET
ejpam-6752	130	12	hopf	hopf	ADJ
ejpam-6752	130	13	bifurcation	bifurcation	NOUN
ejpam-6752	130	14	at	at	ADP
ejpam-6752	130	15	the	the	DET
ejpam-6752	130	16	equilibrium	equilibrium	NOUN
ejpam-6752	130	17	point	point	NOUN
ejpam-6752	130	18	(	(	PUNCT
ejpam-6752	130	19	e0	e0	PROPN
ejpam-6752	130	20	,	,	PUNCT
ejpam-6752	130	21	µ0	µ0	PROPN
ejpam-6752	130	22	)	)	PUNCT
ejpam-6752	131	1	[	[	X
ejpam-6752	131	2	14	14	NUM
ejpam-6752	131	3	]	]	PUNCT
ejpam-6752	131	4	.	.	PUNCT
ejpam-6752	132	1	system	system	NOUN
ejpam-6752	132	2	(	(	PUNCT
ejpam-6752	132	3	4	4	NUM
ejpam-6752	132	4	)	)	PUNCT
ejpam-6752	132	5	,	,	PUNCT
ejpam-6752	132	6	satisfying	satisfy	VERB
ejpam-6752	132	7	the	the	DET
ejpam-6752	132	8	conditions	condition	NOUN
ejpam-6752	132	9	above	above	ADV
ejpam-6752	132	10	,	,	PUNCT
ejpam-6752	132	11	can	can	AUX
ejpam-6752	132	12	be	be	AUX
ejpam-6752	132	13	transformed	transform	VERB
ejpam-6752	132	14	into	into	ADP
ejpam-6752	132	15	the	the	DET
ejpam-6752	132	16	following	follow	VERB
ejpam-6752	132	17	canonical	canonical	ADJ
ejpam-6752	132	18	form	form	NOUN
ejpam-6752	132	19	:	:	PUNCT
ejpam-6752	133	1	ẋ1	ẋ1	PROPN
ejpam-6752	133	2	=	=	PUNCT
ejpam-6752	134	1	−ωx2	−ωx2	NOUN
ejpam-6752	134	2	+	+	CCONJ
ejpam-6752	134	3	f1(x1	f1(x1	NOUN
ejpam-6752	134	4	,	,	PUNCT
ejpam-6752	134	5	x2	x2	PROPN
ejpam-6752	134	6	,	,	PUNCT
ejpam-6752	134	7	x3;µ	x3;µ	PROPN
ejpam-6752	134	8	)	)	PUNCT
ejpam-6752	134	9	,	,	PUNCT
ejpam-6752	135	1	ẋ2	ẋ2	X
ejpam-6752	135	2	=	=	PUNCT
ejpam-6752	135	3	ωx1	ωx1	NOUN
ejpam-6752	135	4	+	+	CCONJ
ejpam-6752	135	5	f2(x1	f2(x1	ADJ
ejpam-6752	135	6	,	,	PUNCT
ejpam-6752	135	7	x2	x2	PROPN
ejpam-6752	135	8	,	,	PUNCT
ejpam-6752	135	9	x3;µ	x3;µ	PROPN
ejpam-6752	135	10	)	)	PUNCT
ejpam-6752	135	11	,	,	PUNCT
ejpam-6752	135	12	(	(	PUNCT
ejpam-6752	135	13	5	5	X
ejpam-6752	135	14	)	)	PUNCT
ejpam-6752	135	15	ẋ3	ẋ3	PROPN
ejpam-6752	136	1	=	=	PUNCT
ejpam-6752	136	2	λx3	λx3	PROPN
ejpam-6752	136	3	+	+	CCONJ
ejpam-6752	136	4	f3(x1	f3(x1	ADJ
ejpam-6752	136	5	,	,	PUNCT
ejpam-6752	136	6	x2	x2	PROPN
ejpam-6752	136	7	,	,	PUNCT
ejpam-6752	136	8	x3;µ	x3;µ	PROPN
ejpam-6752	136	9	)	)	PUNCT
ejpam-6752	136	10	,	,	PUNCT
ejpam-6752	136	11	where	where	SCONJ
ejpam-6752	136	12	ω	ω	X
ejpam-6752	136	13	>	>	X
ejpam-6752	136	14	0	0	PROPN
ejpam-6752	136	15	,	,	PUNCT
ejpam-6752	136	16	λ	λ	X
ejpam-6752	136	17	̸=	̸=	PROPN
ejpam-6752	136	18	0	0	NUM
ejpam-6752	136	19	and	and	CCONJ
ejpam-6752	136	20	fi(x1	fi(x1	ADJ
ejpam-6752	136	21	,	,	PUNCT
ejpam-6752	136	22	x2	x2	PROPN
ejpam-6752	136	23	,	,	PUNCT
ejpam-6752	136	24	x3;µ	x3;µ	NOUN
ejpam-6752	136	25	)	)	PUNCT
ejpam-6752	137	1	=	=	NOUN
ejpam-6752	137	2	∑∞	∑∞	NOUN
ejpam-6752	137	3	k=2	k=2	PROPN
ejpam-6752	138	1	f	f	X
ejpam-6752	138	2	k	k	PROPN
ejpam-6752	139	1	i	i	PRON
ejpam-6752	139	2	(	(	PUNCT
ejpam-6752	139	3	x1	x1	PROPN
ejpam-6752	139	4	,	,	PUNCT
ejpam-6752	139	5	x2	x2	PROPN
ejpam-6752	139	6	,	,	PUNCT
ejpam-6752	139	7	x3;µ	x3;µ	PROPN
ejpam-6752	139	8	)	)	PUNCT
ejpam-6752	139	9	for	for	ADP
ejpam-6752	139	10	i	i	PROPN
ejpam-6752	139	11	=	=	NOUN
ejpam-6752	139	12	1	1	NUM
ejpam-6752	139	13	,	,	PUNCT
ejpam-6752	139	14	2	2	NUM
ejpam-6752	139	15	,	,	PUNCT
ejpam-6752	139	16	3	3	NUM
ejpam-6752	139	17	and	and	CCONJ
ejpam-6752	139	18	fk	fk	INTJ
ejpam-6752	139	19	i	i	INTJ
ejpam-6752	139	20	(	(	PUNCT
ejpam-6752	139	21	x1	x1	PROPN
ejpam-6752	139	22	,	,	PUNCT
ejpam-6752	139	23	x2	x2	PROPN
ejpam-6752	139	24	,	,	PUNCT
ejpam-6752	139	25	x3;µ	x3;µ	PROPN
ejpam-6752	139	26	)	)	PUNCT
ejpam-6752	139	27	are	be	AUX
ejpam-6752	139	28	homogeneous	homogeneous	ADJ
ejpam-6752	139	29	polynomials	polynomial	NOUN
ejpam-6752	139	30	of	of	ADP
ejpam-6752	139	31	degree	degree	NOUN
ejpam-6752	139	32	k.	k.	NOUN
ejpam-6752	139	33	proposition	proposition	PROPN
ejpam-6752	139	34	2	2	NUM
ejpam-6752	139	35	.	.	X
ejpam-6752	139	36	for	for	ADP
ejpam-6752	139	37	system	system	NOUN
ejpam-6752	139	38	(	(	PUNCT
ejpam-6752	139	39	1	1	NUM
ejpam-6752	139	40	)	)	PUNCT
ejpam-6752	139	41	,	,	PUNCT
ejpam-6752	139	42	the	the	DET
ejpam-6752	139	43	hopf	hopf	ADJ
ejpam-6752	139	44	bifurcation	bifurcation	NOUN
ejpam-6752	139	45	occurs	occur	VERB
ejpam-6752	139	46	at	at	ADP
ejpam-6752	139	47	the	the	DET
ejpam-6752	139	48	equilibrium	equilibrium	NOUN
ejpam-6752	139	49	point	point	NOUN
ejpam-6752	139	50	e	e	X
ejpam-6752	139	51	when	when	SCONJ
ejpam-6752	139	52	the	the	DET
ejpam-6752	139	53	parameter	parameter	NOUN
ejpam-6752	139	54	k1	k1	PROPN
ejpam-6752	139	55	passes	pass	VERB
ejpam-6752	139	56	through	through	ADP
ejpam-6752	139	57	k∗1	k∗1	NOUN
ejpam-6752	139	58	where	where	SCONJ
ejpam-6752	139	59	k∗1	k∗1	NOUN
ejpam-6752	139	60	=	=	SYM
ejpam-6752	139	61	k2	k2	PROPN
ejpam-6752	139	62	+	+	CCONJ
ejpam-6752	139	63	k3	k3	ADJ
ejpam-6752	139	64	.	.	PUNCT
ejpam-6752	140	1	proof	proof	NOUN
ejpam-6752	140	2	.	.	PUNCT
ejpam-6752	141	1	by	by	ADP
ejpam-6752	141	2	applying	apply	VERB
ejpam-6752	141	3	the	the	DET
ejpam-6752	141	4	linear	linear	ADJ
ejpam-6752	141	5	transformation	transformation	NOUN
ejpam-6752	141	6	x1	x1	PROPN
ejpam-6752	141	7	→	→	PUNCT
ejpam-6752	141	8	x1	x1	PROPN
ejpam-6752	142	1	+	+	CCONJ
ejpam-6752	142	2	√	√	INTJ
ejpam-6752	142	3	k3k4	k3k4	PROPN
ejpam-6752	142	4	k1k2	k1k2	PROPN
ejpam-6752	142	5	,	,	PUNCT
ejpam-6752	142	6	x2	x2	PROPN
ejpam-6752	142	7	→	→	PUNCT
ejpam-6752	142	8	x2	x2	PROPN
ejpam-6752	143	1	+	+	CCONJ
ejpam-6752	143	2	√	√	INTJ
ejpam-6752	143	3	k1k4	k1k4	NOUN
ejpam-6752	144	1	k2k3	k2k3	PROPN
ejpam-6752	144	2	and	and	CCONJ
ejpam-6752	144	3	x3	x3	ADJ
ejpam-6752	144	4	→	→	SYM
ejpam-6752	145	1	x3	x3	ADJ
ejpam-6752	145	2	+	+	CCONJ
ejpam-6752	145	3	√	√	ADJ
ejpam-6752	145	4	k2k4	k2k4	NOUN
ejpam-6752	145	5	k1k3	k1k3	PROPN
ejpam-6752	145	6	,	,	PUNCT
ejpam-6752	145	7	the	the	DET
ejpam-6752	145	8	equilibrium	equilibrium	NOUN
ejpam-6752	145	9	point	point	NOUN
ejpam-6752	145	10	e	e	NOUN
ejpam-6752	145	11	is	be	AUX
ejpam-6752	145	12	relocated	relocate	VERB
ejpam-6752	145	13	to	to	ADP
ejpam-6752	145	14	the	the	DET
ejpam-6752	145	15	origin	origin	NOUN
ejpam-6752	145	16	,	,	PUNCT
ejpam-6752	145	17	resulting	result	VERB
ejpam-6752	145	18	in	in	ADP
ejpam-6752	145	19	the	the	DET
ejpam-6752	145	20	transformation	transformation	NOUN
ejpam-6752	145	21	of	of	ADP
ejpam-6752	145	22	system	system	NOUN
ejpam-6752	145	23	(	(	PUNCT
ejpam-6752	145	24	1	1	NUM
ejpam-6752	145	25	)	)	PUNCT
ejpam-6752	145	26	into	into	ADP
ejpam-6752	145	27	:	:	PUNCT
ejpam-6752	145	28	ẋ1	ẋ1	PROPN
ejpam-6752	145	29	=	=	SYM
ejpam-6752	145	30	(	(	PUNCT
ejpam-6752	145	31	√	√	INTJ
ejpam-6752	145	32	k3k4	k3k4	PROPN
ejpam-6752	145	33	k1k2	k1k2	PROPN
ejpam-6752	145	34	+	+	CCONJ
ejpam-6752	145	35	x1	x1	PROPN
ejpam-6752	145	36	)	)	PUNCT
ejpam-6752	146	1	(	(	PUNCT
ejpam-6752	146	2	−k2x2	−k2x2	NOUN
ejpam-6752	146	3	+	+	NUM
ejpam-6752	146	4	k1x3	k1x3	NOUN
ejpam-6752	146	5	)	)	PUNCT
ejpam-6752	146	6	,	,	PUNCT
ejpam-6752	147	1	ẋ2	ẋ2	PROPN
ejpam-6752	147	2	=	=	PRON
ejpam-6752	147	3	(	(	PUNCT
ejpam-6752	147	4	√	√	INTJ
ejpam-6752	147	5	k1k4	k1k4	NOUN
ejpam-6752	148	1	k2k3	k2k3	PROPN
ejpam-6752	148	2	+	+	CCONJ
ejpam-6752	148	3	x2	x2	NOUN
ejpam-6752	148	4	)	)	PUNCT
ejpam-6752	148	5	(	(	PUNCT
ejpam-6752	148	6	k2x1	k2x1	INTJ
ejpam-6752	148	7	−	−	NUM
ejpam-6752	148	8	k3x3	k3x3	NOUN
ejpam-6752	148	9	)	)	PUNCT
ejpam-6752	149	1	,	,	PUNCT
ejpam-6752	149	2	(	(	PUNCT
ejpam-6752	149	3	6	6	X
ejpam-6752	149	4	)	)	PUNCT
ejpam-6752	149	5	ẋ3	ẋ3	PROPN
ejpam-6752	149	6	=	=	PUNCT
ejpam-6752	149	7	−	−	PROPN
ejpam-6752	149	8	√	√	NUM
ejpam-6752	149	9	k1k2k4	k1k2k4	NOUN
ejpam-6752	149	10	k3	k3	VERB
ejpam-6752	149	11	x1	x1	PROPN
ejpam-6752	149	12	−	−	PROPN
ejpam-6752	149	13	√	√	PROPN
ejpam-6752	149	14	k2k3k4	k2k3k4	PROPN
ejpam-6752	149	15	k1	k1	PROPN
ejpam-6752	149	16	x2	x2	PROPN
ejpam-6752	150	1	−	−	PROPN
ejpam-6752	150	2	2	2	NUM
ejpam-6752	150	3	√	√	PROPN
ejpam-6752	150	4	k1k3k4	k1k3k4	PROPN
ejpam-6752	150	5	k2	k2	PROPN
ejpam-6752	150	6	x3	x3	PROPN
ejpam-6752	150	7	−	−	PROPN
ejpam-6752	151	1	k1x1x3	k1x1x3	PROPN
ejpam-6752	151	2	−	−	PROPN
ejpam-6752	151	3	k3x2x3	k3x2x3	PROPN
ejpam-6752	151	4	.	.	PUNCT
ejpam-6752	152	1	the	the	DET
ejpam-6752	152	2	characteristic	characteristic	ADJ
ejpam-6752	152	3	equation	equation	NOUN
ejpam-6752	152	4	corresponding	correspond	VERB
ejpam-6752	152	5	to	to	ADP
ejpam-6752	152	6	the	the	DET
ejpam-6752	152	7	jacobian	jacobian	ADJ
ejpam-6752	152	8	matrix	matrix	NOUN
ejpam-6752	152	9	of	of	ADP
ejpam-6752	152	10	system	system	NOUN
ejpam-6752	152	11	(	(	PUNCT
ejpam-6752	152	12	6	6	NUM
ejpam-6752	152	13	)	)	PUNCT
ejpam-6752	152	14	evaluated	evaluate	VERB
ejpam-6752	152	15	at	at	ADP
ejpam-6752	152	16	the	the	DET
ejpam-6752	152	17	origin	origin	NOUN
ejpam-6752	152	18	is	be	AUX
ejpam-6752	152	19	λ3	λ3	PROPN
ejpam-6752	152	20	+	+	PROPN
ejpam-6752	152	21	2	2	NUM
ejpam-6752	152	22	√	√	PROPN
ejpam-6752	152	23	k1k3k4	k1k3k4	PROPN
ejpam-6752	152	24	k2	k2	PROPN
ejpam-6752	152	25	λ2	λ2	PROPN
ejpam-6752	152	26	−	−	PROPN
ejpam-6752	152	27	k4	k4	NOUN
ejpam-6752	152	28	(	(	PUNCT
ejpam-6752	152	29	k3	k3	VERB
ejpam-6752	152	30	−	−	PROPN
ejpam-6752	152	31	k1	k1	PROPN
ejpam-6752	152	32	−	−	PROPN
ejpam-6752	152	33	k2)λ+	k2)λ+	PROPN
ejpam-6752	152	34	4k4	4k4	NUM
ejpam-6752	152	35	√	√	ADP
ejpam-6752	152	36	k1k2k3k4	k1k2k3k4	PROPN
ejpam-6752	152	37	=	=	SYM
ejpam-6752	152	38	0	0	NUM
ejpam-6752	152	39	,	,	PUNCT
ejpam-6752	152	40	(	(	PUNCT
ejpam-6752	152	41	7	7	X
ejpam-6752	152	42	)	)	PUNCT
ejpam-6752	152	43	r.	r.	PROPN
ejpam-6752	152	44	h.	h.	PROPN
ejpam-6752	152	45	salih	salih	PROPN
ejpam-6752	152	46	/	/	SYM
ejpam-6752	152	47	eur	eur	PROPN
ejpam-6752	152	48	.	.	PUNCT
ejpam-6752	153	1	j.	j.	PROPN
ejpam-6752	153	2	pure	pure	PROPN
ejpam-6752	153	3	appl	appl	PROPN
ejpam-6752	153	4	.	.	PROPN
ejpam-6752	153	5	math	math	PROPN
ejpam-6752	153	6	,	,	PUNCT
ejpam-6752	153	7	18	18	NUM
ejpam-6752	153	8	(	(	PUNCT
ejpam-6752	153	9	4	4	NUM
ejpam-6752	153	10	)	)	PUNCT
ejpam-6752	153	11	(	(	PUNCT
ejpam-6752	153	12	2025	2025	NUM
ejpam-6752	153	13	)	)	PUNCT
ejpam-6752	153	14	,	,	PUNCT
ejpam-6752	153	15	6752	6752	NUM
ejpam-6752	153	16	7	7	NUM
ejpam-6752	153	17	of	of	ADP
ejpam-6752	153	18	14	14	NUM
ejpam-6752	153	19	letting	let	VERB
ejpam-6752	153	20	k1	k1	NOUN
ejpam-6752	153	21	=	=	SYM
ejpam-6752	153	22	k∗1	k∗1	NOUN
ejpam-6752	153	23	,	,	PUNCT
ejpam-6752	153	24	then	then	ADV
ejpam-6752	153	25	eq	eq	ADP
ejpam-6752	153	26	.	.	PUNCT
ejpam-6752	154	1	(	(	PUNCT
ejpam-6752	154	2	7	7	X
ejpam-6752	154	3	)	)	PUNCT
ejpam-6752	154	4	can	can	AUX
ejpam-6752	154	5	be	be	AUX
ejpam-6752	154	6	rewritten	rewrite	VERB
ejpam-6752	154	7	as	as	ADP
ejpam-6752	154	8	(	(	PUNCT
ejpam-6752	154	9	λ+	λ+	NUM
ejpam-6752	154	10	2	2	NUM
ejpam-6752	154	11	ω	ω	NUM
ejpam-6752	154	12	√	√	NUM
ejpam-6752	154	13	k3k4	k3k4	PROPN
ejpam-6752	154	14	(	(	PUNCT
ejpam-6752	154	15	ω2	ω2	ADJ
ejpam-6752	154	16	+	+	CCONJ
ejpam-6752	154	17	2k4k3	2k4k3	NUM
ejpam-6752	154	18	)	)	PUNCT
ejpam-6752	154	19	)	)	PUNCT
ejpam-6752	155	1	(	(	PUNCT
ejpam-6752	155	2	λ2	λ2	NOUN
ejpam-6752	155	3	+	+	CCONJ
ejpam-6752	155	4	ω2	ω2	ADJ
ejpam-6752	155	5	)	)	PUNCT
ejpam-6752	155	6	=	=	SYM
ejpam-6752	155	7	0	0	NUM
ejpam-6752	155	8	,	,	PUNCT
ejpam-6752	155	9	where	where	SCONJ
ejpam-6752	155	10	ω	ω	NOUN
ejpam-6752	155	11	=	=	NOUN
ejpam-6752	155	12	√	√	PROPN
ejpam-6752	155	13	2k2k4	2k2k4	NUM
ejpam-6752	155	14	.	.	PUNCT
ejpam-6752	156	1	clearly	clearly	ADV
ejpam-6752	156	2	,	,	PUNCT
ejpam-6752	156	3	eq	eq	ADJ
ejpam-6752	156	4	.	.	PUNCT
ejpam-6752	157	1	(	(	PUNCT
ejpam-6752	157	2	7	7	X
ejpam-6752	157	3	)	)	PUNCT
ejpam-6752	157	4	has	have	VERB
ejpam-6752	157	5	two	two	NUM
ejpam-6752	157	6	complex	complex	ADJ
ejpam-6752	157	7	conjugate	conjugate	ADJ
ejpam-6752	157	8	roots	root	NOUN
ejpam-6752	157	9	λ1,2	λ1,2	NOUN
ejpam-6752	157	10	=	=	SYM
ejpam-6752	157	11	±iω	±iω	PROPN
ejpam-6752	157	12	and	and	CCONJ
ejpam-6752	157	13	one	one	NUM
ejpam-6752	157	14	real	real	ADJ
ejpam-6752	157	15	root	root	NOUN
ejpam-6752	157	16	λ3	λ3	PROPN
ejpam-6752	158	1	=	=	SYM
ejpam-6752	158	2	−	−	PROPN
ejpam-6752	158	3	2	2	NUM
ejpam-6752	158	4	ω	ω	NUM
ejpam-6752	158	5	√	√	PROPN
ejpam-6752	158	6	k3k4	k3k4	PROPN
ejpam-6752	158	7	(	(	PUNCT
ejpam-6752	158	8	ω2	ω2	PROPN
ejpam-6752	158	9	+	+	CCONJ
ejpam-6752	158	10	2k4k3	2k4k3	NUM
ejpam-6752	158	11	)	)	PUNCT
ejpam-6752	158	12	.	.	PUNCT
ejpam-6752	159	1	thus	thus	ADV
ejpam-6752	159	2	,	,	PUNCT
ejpam-6752	159	3	the	the	DET
ejpam-6752	159	4	initial	initial	ADJ
ejpam-6752	159	5	requirement	requirement	NOUN
ejpam-6752	159	6	for	for	ADP
ejpam-6752	159	7	the	the	DET
ejpam-6752	159	8	hopf	hopf	ADJ
ejpam-6752	159	9	bifurcation	bifurcation	NOUN
ejpam-6752	159	10	theorem	theorem	VERB
ejpam-6752	159	11	,	,	PUNCT
ejpam-6752	159	12	which	which	PRON
ejpam-6752	159	13	is	be	AUX
ejpam-6752	159	14	the	the	DET
ejpam-6752	159	15	first	first	ADJ
ejpam-6752	159	16	condition	condition	NOUN
ejpam-6752	159	17	,	,	PUNCT
ejpam-6752	159	18	is	be	AUX
ejpam-6752	159	19	fulfilled	fulfil	VERB
ejpam-6752	159	20	.	.	PUNCT
ejpam-6752	160	1	it	it	PRON
ejpam-6752	160	2	is	be	AUX
ejpam-6752	160	3	important	important	ADJ
ejpam-6752	160	4	to	to	PART
ejpam-6752	160	5	note	note	VERB
ejpam-6752	160	6	that	that	SCONJ
ejpam-6752	160	7	,	,	PUNCT
ejpam-6752	160	8	in	in	ADP
ejpam-6752	160	9	general	general	ADJ
ejpam-6752	160	10	,	,	PUNCT
ejpam-6752	160	11	λ	λ	PROPN
ejpam-6752	160	12	=	=	SYM
ejpam-6752	160	13	λ(k1	λ(k1	NUM
ejpam-6752	160	14	)	)	PUNCT
ejpam-6752	160	15	.	.	PUNCT
ejpam-6752	161	1	from	from	ADP
ejpam-6752	161	2	eq	eq	ADP
ejpam-6752	161	3	.	.	PUNCT
ejpam-6752	162	1	(	(	PUNCT
ejpam-6752	162	2	7	7	NUM
ejpam-6752	162	3	)	)	PUNCT
ejpam-6752	162	4	,	,	PUNCT
ejpam-6752	162	5	we	we	PRON
ejpam-6752	162	6	can	can	AUX
ejpam-6752	162	7	then	then	ADV
ejpam-6752	162	8	express	express	VERB
ejpam-6752	162	9	the	the	DET
ejpam-6752	162	10	relation	relation	NOUN
ejpam-6752	162	11	as	as	SCONJ
ejpam-6752	162	12	follows	follow	VERB
ejpam-6752	162	13	:	:	PUNCT
ejpam-6752	162	14	f(λ(k1	f(λ(k1	NOUN
ejpam-6752	162	15	)	)	PUNCT
ejpam-6752	162	16	,	,	PUNCT
ejpam-6752	162	17	k1	k1	NOUN
ejpam-6752	162	18	)	)	PUNCT
ejpam-6752	163	1	=	=	SYM
ejpam-6752	163	2	(	(	PUNCT
ejpam-6752	163	3	λ(k1	λ(k1	ADV
ejpam-6752	163	4	)	)	PUNCT
ejpam-6752	163	5	+	+	CCONJ
ejpam-6752	163	6	2	2	NUM
ejpam-6752	163	7	ω	ω	NUM
ejpam-6752	163	8	√	√	NUM
ejpam-6752	163	9	k3k4	k3k4	PROPN
ejpam-6752	163	10	(	(	PUNCT
ejpam-6752	163	11	ω2	ω2	ADJ
ejpam-6752	163	12	+	+	CCONJ
ejpam-6752	163	13	2k4k3	2k4k3	NUM
ejpam-6752	163	14	)	)	PUNCT
ejpam-6752	163	15	)	)	PUNCT
ejpam-6752	164	1	(	(	PUNCT
ejpam-6752	164	2	λ2(k1	λ2(k1	X
ejpam-6752	164	3	)	)	PUNCT
ejpam-6752	164	4	+	+	NUM
ejpam-6752	164	5	ω2	ω2	ADJ
ejpam-6752	164	6	)	)	PUNCT
ejpam-6752	164	7	.	.	PUNCT
ejpam-6752	165	1	then	then	ADV
ejpam-6752	165	2	,	,	PUNCT
ejpam-6752	165	3	the	the	DET
ejpam-6752	165	4	root	root	NOUN
ejpam-6752	165	5	λ	λ	X
ejpam-6752	165	6	=	=	SYM
ejpam-6752	165	7	λ(k1	λ(k1	NUM
ejpam-6752	165	8	)	)	PUNCT
ejpam-6752	165	9	of	of	ADP
ejpam-6752	165	10	eq	eq	PROPN
ejpam-6752	165	11	.	.	PUNCT
ejpam-6752	165	12	(	(	PUNCT
ejpam-6752	165	13	7	7	X
ejpam-6752	165	14	)	)	PUNCT
ejpam-6752	165	15	satisfies	satisfy	VERB
ejpam-6752	165	16	the	the	DET
ejpam-6752	165	17	following	follow	VERB
ejpam-6752	165	18	f(λ(k1	f(λ(k1	NOUN
ejpam-6752	165	19	)	)	PUNCT
ejpam-6752	165	20	,	,	PUNCT
ejpam-6752	165	21	k1	k1	NOUN
ejpam-6752	165	22	)	)	PUNCT
ejpam-6752	165	23	=	=	SYM
ejpam-6752	166	1	0	0	X
ejpam-6752	166	2	.	.	PUNCT
ejpam-6752	167	1	(	(	PUNCT
ejpam-6752	167	2	8)	8)	NUM
ejpam-6752	167	3	differentiating	differentiate	VERB
ejpam-6752	167	4	eq	eq	NOUN
ejpam-6752	167	5	.	.	PUNCT
ejpam-6752	168	1	(	(	PUNCT
ejpam-6752	168	2	8)	8)	NUM
ejpam-6752	168	3	with	with	ADP
ejpam-6752	168	4	respect	respect	NOUN
ejpam-6752	168	5	to	to	ADP
ejpam-6752	168	6	k1	k1	NOUN
ejpam-6752	168	7	yields	yield	NOUN
ejpam-6752	168	8	∂f	∂f	PROPN
ejpam-6752	168	9	∂λ(k1	∂λ(k1	NOUN
ejpam-6752	168	10	)	)	PUNCT
ejpam-6752	168	11	dλ(k1	dλ(k1	NOUN
ejpam-6752	168	12	)	)	PUNCT
ejpam-6752	168	13	dk1	dk1	VERB
ejpam-6752	169	1	+	+	CCONJ
ejpam-6752	169	2	∂f	∂f	PROPN
ejpam-6752	169	3	∂k1	∂k1	VERB
ejpam-6752	169	4	=	=	SYM
ejpam-6752	169	5	0	0	NUM
ejpam-6752	169	6	,	,	PUNCT
ejpam-6752	169	7	this	this	PRON
ejpam-6752	169	8	implies	imply	VERB
ejpam-6752	169	9	that	that	PRON
ejpam-6752	169	10	dλ(k1	dλ(k1	NOUN
ejpam-6752	169	11	)	)	PUNCT
ejpam-6752	169	12	dk1	dk1	NOUN
ejpam-6752	170	1	=	=	PUNCT
ejpam-6752	170	2	−	−	PROPN
ejpam-6752	171	1	∂f	∂f	PROPN
ejpam-6752	171	2	∂k1	∂k1	PROPN
ejpam-6752	171	3	(	(	PUNCT
ejpam-6752	171	4	∂f	∂f	PROPN
ejpam-6752	171	5	∂λ(k1	∂λ(k1	NOUN
ejpam-6752	171	6	)	)	PUNCT
ejpam-6752	171	7	)	)	PUNCT
ejpam-6752	171	8	−1	−1	NOUN
ejpam-6752	172	1	=	=	NOUN
ejpam-6752	173	1	−	−	NOUN
ejpam-6752	174	1	k2k4	k2k4	NOUN
ejpam-6752	174	2	(	(	PUNCT
ejpam-6752	174	3	λ2	λ2	NOUN
ejpam-6752	174	4	+	+	CCONJ
ejpam-6752	174	5	√	√	ADJ
ejpam-6752	174	6	k1k2k4	k1k2k4	NOUN
ejpam-6752	174	7	k3	k3	VERB
ejpam-6752	174	8	λ+	λ+	PUNCT
ejpam-6752	174	9	2k2k4	2k2k4	NUM
ejpam-6752	174	10	)	)	PUNCT
ejpam-6752	174	11	√	√	VERB
ejpam-6752	175	1	k1k2k4	k1k2k4	NOUN
ejpam-6752	175	2	k3	k3	VERB
ejpam-6752	175	3	(	(	PUNCT
ejpam-6752	175	4	3k2λ2	3k2λ2	NUM
ejpam-6752	175	5	+	+	CCONJ
ejpam-6752	175	6	4	4	NUM
ejpam-6752	175	7	√	√	NOUN
ejpam-6752	175	8	k1k2k3k4	k1k2k3k4	PROPN
ejpam-6752	175	9	λ+	λ+	PUNCT
ejpam-6752	175	10	k2k4	k2k4	NOUN
ejpam-6752	175	11	(	(	PUNCT
ejpam-6752	175	12	k1	k1	NOUN
ejpam-6752	175	13	+	+	CCONJ
ejpam-6752	175	14	k2	k2	ADJ
ejpam-6752	175	15	−	−	PROPN
ejpam-6752	175	16	k3	k3	PROPN
ejpam-6752	175	17	)	)	PUNCT
ejpam-6752	175	18	)	)	PUNCT
ejpam-6752	175	19	.	.	PUNCT
ejpam-6752	176	1	(	(	PUNCT
ejpam-6752	176	2	9	9	NUM
ejpam-6752	176	3	)	)	PUNCT
ejpam-6752	176	4	by	by	ADP
ejpam-6752	176	5	taking	take	VERB
ejpam-6752	176	6	the	the	DET
ejpam-6752	176	7	root	root	NOUN
ejpam-6752	176	8	λ(k∗1	λ(k∗1	ADJ
ejpam-6752	176	9	)	)	PUNCT
ejpam-6752	176	10	=	=	SYM
ejpam-6752	177	1	λ1,2(k	λ1,2(k	NOUN
ejpam-6752	177	2	∗	∗	NOUN
ejpam-6752	177	3	1	1	NUM
ejpam-6752	177	4	)	)	PUNCT
ejpam-6752	177	5	,	,	PUNCT
ejpam-6752	177	6	we	we	PRON
ejpam-6752	177	7	find	find	VERB
ejpam-6752	177	8	that	that	SCONJ
ejpam-6752	177	9	λ1,2(k	λ1,2(k	NOUN
ejpam-6752	177	10	∗	∗	NOUN
ejpam-6752	177	11	1	1	NUM
ejpam-6752	177	12	)	)	PUNCT
ejpam-6752	177	13	=	=	PUNCT
ejpam-6752	178	1	±iω	±iω	PROPN
ejpam-6752	178	2	.	.	PUNCT
ejpam-6752	179	1	substituting	substitute	VERB
ejpam-6752	179	2	the	the	DET
ejpam-6752	179	3	value	value	NOUN
ejpam-6752	179	4	of	of	ADP
ejpam-6752	179	5	λ1	λ1	PROPN
ejpam-6752	179	6	into	into	ADP
ejpam-6752	179	7	eq	eq	NOUN
ejpam-6752	179	8	.	.	PUNCT
ejpam-6752	180	1	(	(	PUNCT
ejpam-6752	180	2	9	9	NUM
ejpam-6752	180	3	)	)	PUNCT
ejpam-6752	180	4	,	,	PUNCT
ejpam-6752	180	5	we	we	PRON
ejpam-6752	180	6	obtain	obtain	VERB
ejpam-6752	180	7	:	:	PUNCT
ejpam-6752	180	8	d	d	X
ejpam-6752	180	9	dk1	dk1	ADP
ejpam-6752	180	10	re(λ1,2(k1))|k1	re(λ1,2(k1))|k1	NOUN
ejpam-6752	180	11	=	=	ADJ
ejpam-6752	180	12	k∗1	k∗1	NOUN
ejpam-6752	180	13	=	=	PUNCT
ejpam-6752	181	1	−	−	PROPN
ejpam-6752	182	1	k4ω	k4ω	NOUN
ejpam-6752	182	2	√	√	NUM
ejpam-6752	182	3	k3k4	k3k4	PROPN
ejpam-6752	182	4	(	(	PUNCT
ejpam-6752	182	5	ω2	ω2	ADJ
ejpam-6752	182	6	+	+	CCONJ
ejpam-6752	182	7	2k3k4	2k3k4	NOUN
ejpam-6752	182	8	)	)	PUNCT
ejpam-6752	182	9	ω4	ω4	NOUN
ejpam-6752	182	10	+	+	NUM
ejpam-6752	182	11	4k3k4	4k3k4	NOUN
ejpam-6752	182	12	(	(	PUNCT
ejpam-6752	182	13	ω2	ω2	ADJ
ejpam-6752	182	14	+	+	CCONJ
ejpam-6752	182	15	2k3k4	2k3k4	NOUN
ejpam-6752	182	16	)	)	PUNCT
ejpam-6752	182	17	̸=	̸=	PROPN
ejpam-6752	182	18	0	0	NUM
ejpam-6752	182	19	.	.	PUNCT
ejpam-6752	183	1	thus	thus	ADV
ejpam-6752	183	2	,	,	PUNCT
ejpam-6752	183	3	the	the	DET
ejpam-6752	183	4	second	second	ADJ
ejpam-6752	183	5	condition	condition	NOUN
ejpam-6752	183	6	for	for	ADP
ejpam-6752	183	7	a	a	DET
ejpam-6752	183	8	hopf	hopf	ADJ
ejpam-6752	183	9	bifurcation	bifurcation	NOUN
ejpam-6752	183	10	is	be	AUX
ejpam-6752	183	11	met	meet	VERB
ejpam-6752	183	12	.	.	PUNCT
ejpam-6752	184	1	consequently	consequently	ADV
ejpam-6752	184	2	,	,	PUNCT
ejpam-6752	184	3	at	at	ADP
ejpam-6752	184	4	e	e	NOUN
ejpam-6752	184	5	,	,	PUNCT
ejpam-6752	184	6	system	system	NOUN
ejpam-6752	184	7	(	(	PUNCT
ejpam-6752	184	8	1	1	X
ejpam-6752	184	9	)	)	PUNCT
ejpam-6752	184	10	undergoes	undergo	VERB
ejpam-6752	184	11	a	a	DET
ejpam-6752	184	12	hopf	hopf	ADJ
ejpam-6752	184	13	bifurcation	bifurcation	NOUN
ejpam-6752	184	14	when	when	SCONJ
ejpam-6752	184	15	k1	k1	NOUN
ejpam-6752	184	16	=	=	SYM
ejpam-6752	184	17	k∗1	k∗1	NOUN
ejpam-6752	184	18	.	.	PUNCT
ejpam-6752	185	1	it	it	PRON
ejpam-6752	185	2	is	be	AUX
ejpam-6752	185	3	straightforward	straightforward	ADJ
ejpam-6752	185	4	to	to	PART
ejpam-6752	185	5	determine	determine	VERB
ejpam-6752	185	6	the	the	DET
ejpam-6752	185	7	lyapunov	lyapunov	ADJ
ejpam-6752	185	8	coefficients	coefficient	NOUN
ejpam-6752	185	9	corresponding	correspond	VERB
ejpam-6752	185	10	to	to	ADP
ejpam-6752	185	11	system	system	NOUN
ejpam-6752	185	12	(	(	PUNCT
ejpam-6752	185	13	6	6	NUM
ejpam-6752	185	14	)	)	PUNCT
ejpam-6752	185	15	at	at	ADP
ejpam-6752	185	16	k1	k1	NOUN
ejpam-6752	185	17	=	=	SYM
ejpam-6752	185	18	k∗1	k∗1	NOUN
ejpam-6752	185	19	.	.	PUNCT
ejpam-6752	186	1	since	since	SCONJ
ejpam-6752	186	2	the	the	DET
ejpam-6752	186	3	equilibrium	equilibrium	NOUN
ejpam-6752	186	4	point	point	NOUN
ejpam-6752	186	5	is	be	AUX
ejpam-6752	186	6	a	a	DET
ejpam-6752	186	7	center	center	NOUN
ejpam-6752	186	8	,	,	PUNCT
ejpam-6752	186	9	the	the	DET
ejpam-6752	186	10	k−th	k−th	PROPN
ejpam-6752	186	11	lyapunov	lyapunov	PROPN
ejpam-6752	186	12	coefficients	coefficient	NOUN
ejpam-6752	186	13	vanish	vanish	VERB
ejpam-6752	186	14	for	for	ADP
ejpam-6752	186	15	all	all	DET
ejpam-6752	186	16	k	k	PROPN
ejpam-6752	186	17	at	at	ADP
ejpam-6752	186	18	k∗1	k∗1	PROPN
ejpam-6752	186	19	[	[	X
ejpam-6752	186	20	15	15	NUM
ejpam-6752	186	21	]	]	PUNCT
ejpam-6752	186	22	.	.	PUNCT
ejpam-6752	187	1	therefore	therefore	ADV
ejpam-6752	187	2	,	,	PUNCT
ejpam-6752	187	3	by	by	ADP
ejpam-6752	187	4	the	the	DET
ejpam-6752	187	5	lyapunov	lyapunov	NOUN
ejpam-6752	187	6	theorem	theorem	NOUN
ejpam-6752	187	7	,	,	PUNCT
ejpam-6752	187	8	system	system	NOUN
ejpam-6752	187	9	(	(	PUNCT
ejpam-6752	187	10	1	1	X
ejpam-6752	187	11	)	)	PUNCT
ejpam-6752	187	12	exhibits	exhibit	VERB
ejpam-6752	187	13	a	a	DET
ejpam-6752	187	14	vertical	vertical	ADJ
ejpam-6752	187	15	andronov	andronov	NOUN
ejpam-6752	187	16	-	-	PUNCT
ejpam-6752	187	17	hopf	hopf	ADJ
ejpam-6752	187	18	bifurcation	bifurcation	NOUN
ejpam-6752	187	19	as	as	SCONJ
ejpam-6752	187	20	k1	k1	NOUN
ejpam-6752	187	21	passes	pass	VERB
ejpam-6752	187	22	through	through	ADP
ejpam-6752	187	23	k∗1	k∗1	NOUN
ejpam-6752	187	24	.	.	PUNCT
ejpam-6752	188	1	4.2	4.2	NUM
ejpam-6752	188	2	.	.	PUNCT
ejpam-6752	188	3	center	center	NOUN
ejpam-6752	188	4	bifurcation	bifurcation	NOUN
ejpam-6752	188	5	research	research	NOUN
ejpam-6752	188	6	in	in	ADP
ejpam-6752	188	7	bifurcation	bifurcation	NOUN
ejpam-6752	188	8	theory	theory	NOUN
ejpam-6752	188	9	currently	currently	ADV
ejpam-6752	188	10	focuses	focus	VERB
ejpam-6752	188	11	on	on	ADP
ejpam-6752	188	12	the	the	DET
ejpam-6752	188	13	bifurcation	bifurcation	NOUN
ejpam-6752	188	14	of	of	ADP
ejpam-6752	188	15	limit	limit	NOUN
ejpam-6752	188	16	cycles	cycle	NOUN
ejpam-6752	188	17	from	from	ADP
ejpam-6752	188	18	critical	critical	ADJ
ejpam-6752	188	19	points	point	NOUN
ejpam-6752	188	20	.	.	PUNCT
ejpam-6752	189	1	a	a	DET
ejpam-6752	189	2	limit	limit	NOUN
ejpam-6752	189	3	cycle	cycle	NOUN
ejpam-6752	189	4	can	can	AUX
ejpam-6752	189	5	be	be	AUX
ejpam-6752	189	6	achieved	achieve	VERB
ejpam-6752	189	7	by	by	ADP
ejpam-6752	189	8	perturbing	perturb	VERB
ejpam-6752	189	9	a	a	DET
ejpam-6752	189	10	focus	focus	NOUN
ejpam-6752	189	11	or	or	CCONJ
ejpam-6752	189	12	center	center	NOUN
ejpam-6752	189	13	.	.	PUNCT
ejpam-6752	190	1	a	a	DET
ejpam-6752	190	2	widely	widely	ADV
ejpam-6752	190	3	used	use	VERB
ejpam-6752	190	4	method	method	NOUN
ejpam-6752	190	5	is	be	AUX
ejpam-6752	190	6	center	center	NOUN
ejpam-6752	190	7	bifurcation	bifurcation	NOUN
ejpam-6752	190	8	,	,	PUNCT
ejpam-6752	190	9	which	which	PRON
ejpam-6752	190	10	helps	help	VERB
ejpam-6752	190	11	estimate	estimate	VERB
ejpam-6752	190	12	cyclicity	cyclicity	NOUN
ejpam-6752	190	13	and	and	CCONJ
ejpam-6752	190	14	examine	examine	VERB
ejpam-6752	190	15	the	the	DET
ejpam-6752	190	16	bifurcation	bifurcation	NOUN
ejpam-6752	190	17	of	of	ADP
ejpam-6752	190	18	limit	limit	NOUN
ejpam-6752	190	19	cycles	cycle	NOUN
ejpam-6752	190	20	from	from	ADP
ejpam-6752	190	21	the	the	DET
ejpam-6752	190	22	center	center	NOUN
ejpam-6752	190	23	(	(	PUNCT
ejpam-6752	190	24	see	see	VERB
ejpam-6752	190	25	[	[	X
ejpam-6752	190	26	16	16	NUM
ejpam-6752	190	27	]	]	PUNCT
ejpam-6752	190	28	and	and	CCONJ
ejpam-6752	190	29	[	[	X
ejpam-6752	190	30	17	17	NUM
ejpam-6752	190	31	]	]	NUM
ejpam-6752	190	32	)	)	PUNCT
ejpam-6752	190	33	.	.	PUNCT
ejpam-6752	191	1	here	here	ADV
ejpam-6752	191	2	,	,	PUNCT
ejpam-6752	191	3	we	we	PRON
ejpam-6752	191	4	consider	consider	VERB
ejpam-6752	191	5	system	system	NOUN
ejpam-6752	191	6	(	(	PUNCT
ejpam-6752	191	7	5	5	NUM
ejpam-6752	191	8	)	)	PUNCT
ejpam-6752	191	9	.	.	PUNCT
ejpam-6752	192	1	the	the	DET
ejpam-6752	192	2	set	set	NOUN
ejpam-6752	192	3	of	of	ADP
ejpam-6752	192	4	all	all	DET
ejpam-6752	192	5	parameters	parameter	NOUN
ejpam-6752	192	6	in	in	ADP
ejpam-6752	192	7	fi(x1	fi(x1	ADJ
ejpam-6752	192	8	,	,	PUNCT
ejpam-6752	192	9	x2	x2	PROPN
ejpam-6752	192	10	,	,	PUNCT
ejpam-6752	192	11	x3	x3	ADJ
ejpam-6752	192	12	)	)	PUNCT
ejpam-6752	192	13	for	for	ADP
ejpam-6752	192	14	i	i	PROPN
ejpam-6752	192	15	=	=	SYM
ejpam-6752	192	16	1	1	NUM
ejpam-6752	192	17	,	,	PUNCT
ejpam-6752	192	18	2	2	NUM
ejpam-6752	192	19	,	,	PUNCT
ejpam-6752	192	20	3	3	NUM
ejpam-6752	192	21	is	be	AUX
ejpam-6752	192	22	denoted	denote	VERB
ejpam-6752	192	23	by	by	ADP
ejpam-6752	192	24	λ	λ	PROPN
ejpam-6752	192	25	and	and	CCONJ
ejpam-6752	192	26	k	k	PROPN
ejpam-6752	192	27	is	be	AUX
ejpam-6752	192	28	the	the	DET
ejpam-6752	192	29	corresponding	corresponding	ADJ
ejpam-6752	192	30	parameter	parameter	NOUN
ejpam-6752	192	31	space	space	NOUN
ejpam-6752	192	32	.	.	PUNCT
ejpam-6752	193	1	r.	r.	PROPN
ejpam-6752	193	2	h.	h.	PROPN
ejpam-6752	193	3	salih	salih	PROPN
ejpam-6752	193	4	/	/	SYM
ejpam-6752	193	5	eur	eur	PROPN
ejpam-6752	193	6	.	.	PUNCT
ejpam-6752	194	1	j.	j.	PROPN
ejpam-6752	194	2	pure	pure	PROPN
ejpam-6752	194	3	appl	appl	PROPN
ejpam-6752	194	4	.	.	PROPN
ejpam-6752	194	5	math	math	PROPN
ejpam-6752	194	6	,	,	PUNCT
ejpam-6752	194	7	18	18	NUM
ejpam-6752	194	8	(	(	PUNCT
ejpam-6752	194	9	4	4	NUM
ejpam-6752	194	10	)	)	PUNCT
ejpam-6752	194	11	(	(	PUNCT
ejpam-6752	194	12	2025	2025	NUM
ejpam-6752	194	13	)	)	PUNCT
ejpam-6752	194	14	,	,	PUNCT
ejpam-6752	194	15	6752	6752	NUM
ejpam-6752	194	16	8	8	NUM
ejpam-6752	194	17	of	of	ADP
ejpam-6752	194	18	14	14	NUM
ejpam-6752	194	19	4.2.1	4.2.1	NUM
ejpam-6752	194	20	.	.	PUNCT
ejpam-6752	195	1	a	a	DET
ejpam-6752	195	2	technique	technique	NOUN
ejpam-6752	195	3	to	to	PART
ejpam-6752	195	4	examine	examine	VERB
ejpam-6752	195	5	the	the	DET
ejpam-6752	195	6	cyclicity	cyclicity	NOUN
ejpam-6752	195	7	this	this	DET
ejpam-6752	195	8	subsection	subsection	NOUN
ejpam-6752	195	9	describes	describe	VERB
ejpam-6752	195	10	a	a	DET
ejpam-6752	195	11	technique	technique	NOUN
ejpam-6752	195	12	used	use	VERB
ejpam-6752	195	13	for	for	ADP
ejpam-6752	195	14	analyzing	analyze	VERB
ejpam-6752	195	15	cyclicity	cyclicity	NOUN
ejpam-6752	195	16	.	.	PUNCT
ejpam-6752	196	1	as	as	SCONJ
ejpam-6752	196	2	previously	previously	ADV
ejpam-6752	196	3	noted	note	VERB
ejpam-6752	196	4	,	,	PUNCT
ejpam-6752	196	5	christopher	christopher	PROPN
ejpam-6752	197	1	[	[	X
ejpam-6752	197	2	18	18	NUM
ejpam-6752	197	3	]	]	PUNCT
ejpam-6752	197	4	explored	explore	VERB
ejpam-6752	197	5	a	a	DET
ejpam-6752	197	6	method	method	NOUN
ejpam-6752	197	7	for	for	ADP
ejpam-6752	197	8	analyzing	analyze	VERB
ejpam-6752	197	9	cyclicity	cyclicity	NOUN
ejpam-6752	197	10	bifurcating	bifurcate	VERB
ejpam-6752	197	11	from	from	ADP
ejpam-6752	197	12	a	a	DET
ejpam-6752	197	13	center	center	NOUN
ejpam-6752	197	14	in	in	ADP
ejpam-6752	197	15	two	two	NUM
ejpam-6752	197	16	-	-	PUNCT
ejpam-6752	197	17	dimensional	dimensional	ADJ
ejpam-6752	197	18	systems	system	NOUN
ejpam-6752	197	19	by	by	ADP
ejpam-6752	197	20	linearizing	linearize	VERB
ejpam-6752	197	21	the	the	DET
ejpam-6752	197	22	lyapunov	lyapunov	ADJ
ejpam-6752	197	23	quantities	quantity	NOUN
ejpam-6752	197	24	.	.	PUNCT
ejpam-6752	198	1	salih	salih	PROPN
ejpam-6752	199	1	[	[	X
ejpam-6752	199	2	11	11	NUM
ejpam-6752	199	3	]	]	PUNCT
ejpam-6752	199	4	extended	extend	VERB
ejpam-6752	199	5	this	this	DET
ejpam-6752	199	6	approach	approach	NOUN
ejpam-6752	199	7	to	to	ADP
ejpam-6752	199	8	three	three	NUM
ejpam-6752	199	9	-	-	PUNCT
ejpam-6752	199	10	dimensional	dimensional	ADJ
ejpam-6752	199	11	systems	system	NOUN
ejpam-6752	199	12	to	to	PART
ejpam-6752	199	13	estimate	estimate	VERB
ejpam-6752	199	14	the	the	DET
ejpam-6752	199	15	cyclicity	cyclicity	NOUN
ejpam-6752	199	16	of	of	ADP
ejpam-6752	199	17	the	the	DET
ejpam-6752	199	18	center	center	NOUN
ejpam-6752	199	19	,	,	PUNCT
ejpam-6752	199	20	applying	apply	VERB
ejpam-6752	199	21	it	it	PRON
ejpam-6752	199	22	for	for	ADP
ejpam-6752	199	23	the	the	DET
ejpam-6752	199	24	first	first	ADJ
ejpam-6752	199	25	time	time	NOUN
ejpam-6752	199	26	to	to	ADP
ejpam-6752	199	27	three	three	NUM
ejpam-6752	199	28	-	-	PUNCT
ejpam-6752	199	29	dimensional	dimensional	ADJ
ejpam-6752	199	30	lotka	lotka	PROPN
ejpam-6752	199	31	-	-	PUNCT
ejpam-6752	199	32	volterra	volterra	NOUN
ejpam-6752	199	33	systems	system	NOUN
ejpam-6752	199	34	.	.	PUNCT
ejpam-6752	200	1	the	the	DET
ejpam-6752	200	2	technique	technique	NOUN
ejpam-6752	200	3	used	use	VERB
ejpam-6752	200	4	to	to	PART
ejpam-6752	200	5	estimate	estimate	VERB
ejpam-6752	200	6	cyclicity	cyclicity	NOUN
ejpam-6752	200	7	in	in	ADP
ejpam-6752	200	8	three	three	NUM
ejpam-6752	200	9	-	-	PUNCT
ejpam-6752	200	10	dimensional	dimensional	ADJ
ejpam-6752	200	11	differential	differential	NOUN
ejpam-6752	200	12	systems	system	NOUN
ejpam-6752	200	13	can	can	AUX
ejpam-6752	200	14	be	be	AUX
ejpam-6752	200	15	summarized	summarize	VERB
ejpam-6752	200	16	in	in	ADP
ejpam-6752	200	17	the	the	DET
ejpam-6752	200	18	following	follow	VERB
ejpam-6752	200	19	steps	step	NOUN
ejpam-6752	200	20	:	:	PUNCT
ejpam-6752	200	21	(	(	PUNCT
ejpam-6752	200	22	i	i	NOUN
ejpam-6752	200	23	)	)	PUNCT
ejpam-6752	200	24	select	select	VERB
ejpam-6752	200	25	a	a	DET
ejpam-6752	200	26	point	point	NOUN
ejpam-6752	200	27	on	on	ADP
ejpam-6752	200	28	a	a	DET
ejpam-6752	200	29	center	center	ADJ
ejpam-6752	200	30	variety	variety	NOUN
ejpam-6752	200	31	.	.	PUNCT
ejpam-6752	201	1	(	(	PUNCT
ejpam-6752	201	2	ii	ii	X
ejpam-6752	201	3	)	)	PUNCT
ejpam-6752	201	4	linearize	linearize	NOUN
ejpam-6752	201	5	the	the	DET
ejpam-6752	201	6	lyapunov	lyapunov	ADJ
ejpam-6752	201	7	quantities	quantity	NOUN
ejpam-6752	201	8	around	around	ADP
ejpam-6752	201	9	this	this	DET
ejpam-6752	201	10	point	point	NOUN
ejpam-6752	201	11	.	.	PUNCT
ejpam-6752	202	1	(	(	PUNCT
ejpam-6752	202	2	iii	iii	X
ejpam-6752	202	3	)	)	PUNCT
ejpam-6752	202	4	determine	determine	VERB
ejpam-6752	202	5	the	the	DET
ejpam-6752	202	6	codimension	codimension	NOUN
ejpam-6752	202	7	of	of	ADP
ejpam-6752	202	8	the	the	DET
ejpam-6752	202	9	point	point	NOUN
ejpam-6752	202	10	.	.	PUNCT
ejpam-6752	203	1	if	if	SCONJ
ejpam-6752	203	2	the	the	DET
ejpam-6752	203	3	codimension	codimension	NOUN
ejpam-6752	203	4	of	of	ADP
ejpam-6752	203	5	the	the	DET
ejpam-6752	203	6	selected	select	VERB
ejpam-6752	203	7	point	point	NOUN
ejpam-6752	203	8	on	on	ADP
ejpam-6752	203	9	the	the	DET
ejpam-6752	203	10	center	center	ADJ
ejpam-6752	203	11	variety	variety	NOUN
ejpam-6752	203	12	is	be	AUX
ejpam-6752	203	13	r	r	NOUN
ejpam-6752	203	14	and	and	CCONJ
ejpam-6752	203	15	the	the	DET
ejpam-6752	203	16	first	first	ADJ
ejpam-6752	203	17	r	r	NOUN
ejpam-6752	203	18	linear	linear	NOUN
ejpam-6752	203	19	terms	term	NOUN
ejpam-6752	203	20	of	of	ADP
ejpam-6752	203	21	the	the	DET
ejpam-6752	203	22	lyapunov	lyapunov	ADJ
ejpam-6752	203	23	quantities	quantity	NOUN
ejpam-6752	203	24	are	be	AUX
ejpam-6752	203	25	linearly	linearly	ADV
ejpam-6752	203	26	independent	independent	ADJ
ejpam-6752	203	27	,	,	PUNCT
ejpam-6752	203	28	then	then	ADV
ejpam-6752	203	29	the	the	DET
ejpam-6752	203	30	cyclicity	cyclicity	NOUN
ejpam-6752	203	31	is	be	AUX
ejpam-6752	203	32	r	r	NOUN
ejpam-6752	203	33	−	−	NOUN
ejpam-6752	203	34	1	1	NUM
ejpam-6752	203	35	.	.	PUNCT
ejpam-6752	204	1	this	this	PRON
ejpam-6752	204	2	means	mean	VERB
ejpam-6752	204	3	that	that	SCONJ
ejpam-6752	204	4	r	r	NOUN
ejpam-6752	204	5	−	−	NUM
ejpam-6752	204	6	1	1	NUM
ejpam-6752	204	7	limit	limit	NOUN
ejpam-6752	204	8	cycles	cycle	NOUN
ejpam-6752	204	9	can	can	AUX
ejpam-6752	204	10	bifurcate	bifurcate	VERB
ejpam-6752	204	11	from	from	ADP
ejpam-6752	204	12	a	a	DET
ejpam-6752	204	13	small	small	ADJ
ejpam-6752	204	14	perturbation	perturbation	NOUN
ejpam-6752	204	15	.	.	PUNCT
ejpam-6752	205	1	defining	define	VERB
ejpam-6752	205	2	the	the	DET
ejpam-6752	205	3	lyapunov	lyapunov	ADJ
ejpam-6752	205	4	function	function	NOUN
ejpam-6752	205	5	and	and	CCONJ
ejpam-6752	205	6	computing	compute	VERB
ejpam-6752	205	7	its	its	PRON
ejpam-6752	205	8	focal	focal	ADJ
ejpam-6752	205	9	values	value	NOUN
ejpam-6752	205	10	is	be	AUX
ejpam-6752	205	11	a	a	DET
ejpam-6752	205	12	traditional	traditional	ADJ
ejpam-6752	205	13	approach	approach	NOUN
ejpam-6752	205	14	to	to	PART
ejpam-6752	205	15	assess	assess	VERB
ejpam-6752	205	16	the	the	DET
ejpam-6752	205	17	number	number	NOUN
ejpam-6752	205	18	of	of	ADP
ejpam-6752	205	19	limit	limit	NOUN
ejpam-6752	205	20	cycles	cycle	NOUN
ejpam-6752	205	21	and	and	CCONJ
ejpam-6752	205	22	their	their	PRON
ejpam-6752	205	23	stability	stability	NOUN
ejpam-6752	205	24	.	.	PUNCT
ejpam-6752	206	1	this	this	DET
ejpam-6752	206	2	method	method	NOUN
ejpam-6752	206	3	involves	involve	VERB
ejpam-6752	206	4	looking	look	VERB
ejpam-6752	206	5	for	for	ADP
ejpam-6752	206	6	a	a	DET
ejpam-6752	206	7	function	function	NOUN
ejpam-6752	206	8	of	of	ADP
ejpam-6752	206	9	the	the	DET
ejpam-6752	206	10	following	follow	VERB
ejpam-6752	206	11	form	form	NOUN
ejpam-6752	206	12	:	:	PUNCT
ejpam-6752	206	13	f	f	PROPN
ejpam-6752	206	14	(	(	PUNCT
ejpam-6752	206	15	x1	x1	PROPN
ejpam-6752	206	16	,	,	PUNCT
ejpam-6752	206	17	x2	x2	PROPN
ejpam-6752	206	18	,	,	PUNCT
ejpam-6752	206	19	x3	x3	ADJ
ejpam-6752	206	20	)	)	PUNCT
ejpam-6752	207	1	=	=	SYM
ejpam-6752	207	2	x21	x21	PROPN
ejpam-6752	208	1	+	+	NUM
ejpam-6752	208	2	x22	x22	NOUN
ejpam-6752	209	1	+	+	CCONJ
ejpam-6752	209	2	∞∑	∞∑	NUM
ejpam-6752	209	3	k=3	k=3	ADJ
ejpam-6752	209	4	fk(x1	fk(x1	PROPN
ejpam-6752	209	5	,	,	PUNCT
ejpam-6752	209	6	x2	x2	PROPN
ejpam-6752	209	7	,	,	PUNCT
ejpam-6752	209	8	x3	x3	ADJ
ejpam-6752	209	9	)	)	PUNCT
ejpam-6752	209	10	,	,	PUNCT
ejpam-6752	209	11	(	(	PUNCT
ejpam-6752	209	12	10	10	NUM
ejpam-6752	209	13	)	)	PUNCT
ejpam-6752	209	14	where	where	SCONJ
ejpam-6752	209	15	fk	fk	INTJ
ejpam-6752	209	16	=	=	PUNCT
ejpam-6752	210	1	∑k	∑k	PROPN
ejpam-6752	210	2	i=0	i=0	PROPN
ejpam-6752	210	3	∑i	∑i	PROPN
ejpam-6752	210	4	j=0ck−i	j=0ck−i	PROPN
ejpam-6752	210	5	,	,	PUNCT
ejpam-6752	210	6	i−j	i−j	PROPN
ejpam-6752	210	7	,	,	PUNCT
ejpam-6752	210	8	jx	jx	PROPN
ejpam-6752	210	9	k−i	k−i	VERB
ejpam-6752	210	10	1	1	NUM
ejpam-6752	210	11	xi−j	xi−j	PROPN
ejpam-6752	210	12	2	2	NUM
ejpam-6752	210	13	xj3	xj3	NOUN
ejpam-6752	210	14	for	for	ADP
ejpam-6752	210	15	system	system	NOUN
ejpam-6752	210	16	(	(	PUNCT
ejpam-6752	210	17	5	5	NUM
ejpam-6752	210	18	)	)	PUNCT
ejpam-6752	210	19	and	and	CCONJ
ejpam-6752	210	20	the	the	DET
ejpam-6752	210	21	coefficients	coefficient	NOUN
ejpam-6752	210	22	of	of	ADP
ejpam-6752	210	23	fk	fk	INTJ
ejpam-6752	210	24	satisfy	satisfy	NOUN
ejpam-6752	210	25	x	x	PUNCT
ejpam-6752	210	26	(	(	PUNCT
ejpam-6752	210	27	f	f	X
ejpam-6752	210	28	)	)	PUNCT
ejpam-6752	211	1	=	=	SYM
ejpam-6752	211	2	l1(x	l1(x	NOUN
ejpam-6752	211	3	2	2	NUM
ejpam-6752	211	4	1	1	NUM
ejpam-6752	211	5	+	+	NUM
ejpam-6752	211	6	x22	x22	NUM
ejpam-6752	211	7	)	)	PUNCT
ejpam-6752	212	1	+	+	CCONJ
ejpam-6752	212	2	l2(x	l2(x	PROPN
ejpam-6752	212	3	2	2	NUM
ejpam-6752	212	4	1	1	NUM
ejpam-6752	212	5	+	+	NUM
ejpam-6752	212	6	x22	x22	NUM
ejpam-6752	212	7	)	)	PUNCT
ejpam-6752	212	8	2	2	NUM
ejpam-6752	213	1	+	+	CCONJ
ejpam-6752	213	2	l3(x	l3(x	NUM
ejpam-6752	213	3	2	2	NUM
ejpam-6752	213	4	1	1	NUM
ejpam-6752	213	5	+	+	NUM
ejpam-6752	213	6	x22	x22	NUM
ejpam-6752	213	7	)	)	PUNCT
ejpam-6752	213	8	3	3	NUM
ejpam-6752	213	9	+	+	CCONJ
ejpam-6752	213	10	...	...	PUNCT
ejpam-6752	213	11	,	,	PUNCT
ejpam-6752	213	12	(	(	PUNCT
ejpam-6752	213	13	11	11	NUM
ejpam-6752	213	14	)	)	PUNCT
ejpam-6752	213	15	where	where	SCONJ
ejpam-6752	213	16	li	li	PROPN
ejpam-6752	213	17	,	,	PUNCT
ejpam-6752	213	18	i	i	NOUN
ejpam-6752	213	19	=	=	NOUN
ejpam-6752	213	20	1	1	NUM
ejpam-6752	213	21	,	,	PUNCT
ejpam-6752	213	22	2	2	NUM
ejpam-6752	213	23	,	,	PUNCT
ejpam-6752	213	24	..	..	PUNCT
ejpam-6752	213	25	are	be	AUX
ejpam-6752	213	26	polynomials	polynomial	NOUN
ejpam-6752	213	27	in	in	ADP
ejpam-6752	213	28	the	the	DET
ejpam-6752	213	29	parameters	parameter	NOUN
ejpam-6752	213	30	of	of	ADP
ejpam-6752	213	31	the	the	DET
ejpam-6752	213	32	system	system	NOUN
ejpam-6752	213	33	and	and	CCONJ
ejpam-6752	213	34	the	the	DET
ejpam-6752	213	35	li	li	PROPN
ejpam-6752	213	36	is	be	AUX
ejpam-6752	213	37	called	call	VERB
ejpam-6752	213	38	the	the	DET
ejpam-6752	213	39	i−th	i−th	PROPN
ejpam-6752	213	40	lyapunov	lyapunov	ADJ
ejpam-6752	213	41	constant	constant	ADJ
ejpam-6752	213	42	(	(	PUNCT
ejpam-6752	213	43	focal	focal	ADJ
ejpam-6752	213	44	value	value	NOUN
ejpam-6752	213	45	)	)	PUNCT
ejpam-6752	213	46	.	.	PUNCT
ejpam-6752	214	1	to	to	PART
ejpam-6752	214	2	explain	explain	VERB
ejpam-6752	214	3	the	the	DET
ejpam-6752	214	4	technique	technique	NOUN
ejpam-6752	214	5	in	in	ADP
ejpam-6752	214	6	greater	great	ADJ
ejpam-6752	214	7	detail	detail	NOUN
ejpam-6752	214	8	,	,	PUNCT
ejpam-6752	214	9	it	it	PRON
ejpam-6752	214	10	is	be	AUX
ejpam-6752	214	11	assumed	assume	VERB
ejpam-6752	214	12	that	that	SCONJ
ejpam-6752	214	13	the	the	DET
ejpam-6752	214	14	center	center	NOUN
ejpam-6752	214	15	critical	critical	ADJ
ejpam-6752	214	16	point	point	NOUN
ejpam-6752	214	17	of	of	ADP
ejpam-6752	214	18	(	(	PUNCT
ejpam-6752	214	19	5	5	NUM
ejpam-6752	214	20	)	)	PUNCT
ejpam-6752	214	21	corresponds	correspond	VERB
ejpam-6752	214	22	to	to	ADP
ejpam-6752	214	23	0	0	NUM
ejpam-6752	214	24	∈	∈	PROPN
ejpam-6752	214	25	k	k	NOUN
ejpam-6752	214	26	,	,	PUNCT
ejpam-6752	214	27	using	use	VERB
ejpam-6752	214	28	a	a	DET
ejpam-6752	214	29	perturbation	perturbation	NOUN
ejpam-6752	214	30	method	method	NOUN
ejpam-6752	214	31	in	in	ADP
ejpam-6752	214	32	the	the	DET
ejpam-6752	214	33	parameters	parameter	NOUN
ejpam-6752	214	34	.	.	PUNCT
ejpam-6752	215	1	this	this	PRON
ejpam-6752	215	2	can	can	AUX
ejpam-6752	215	3	be	be	AUX
ejpam-6752	215	4	written	write	VERB
ejpam-6752	215	5	:	:	PUNCT
ejpam-6752	215	6	x	x	PUNCT
ejpam-6752	215	7	=	=	PUNCT
ejpam-6752	215	8	x0	x0	PROPN
ejpam-6752	216	1	+	+	CCONJ
ejpam-6752	217	1	x1	x1	PROPN
ejpam-6752	218	1	+	+	CCONJ
ejpam-6752	218	2	x2	x2	PROPN
ejpam-6752	219	1	+	+	CCONJ
ejpam-6752	219	2	...	...	PUNCT
ejpam-6752	219	3	,	,	PUNCT
ejpam-6752	219	4	f	f	X
ejpam-6752	219	5	=	=	SYM
ejpam-6752	219	6	f0	f0	PROPN
ejpam-6752	219	7	+	+	CCONJ
ejpam-6752	219	8	f1	f1	NOUN
ejpam-6752	219	9	+	+	CCONJ
ejpam-6752	219	10	f2	f2	PROPN
ejpam-6752	219	11	+	+	X
ejpam-6752	219	12	...	...	PUNCT
ejpam-6752	219	13	,	,	PUNCT
ejpam-6752	219	14	(	(	PUNCT
ejpam-6752	219	15	12	12	NUM
ejpam-6752	219	16	)	)	PUNCT
ejpam-6752	219	17	li	li	NOUN
ejpam-6752	219	18	=	=	SYM
ejpam-6752	219	19	li0	li0	PROPN
ejpam-6752	219	20	+	+	CCONJ
ejpam-6752	219	21	li1	li1	X
ejpam-6752	219	22	+	+	CCONJ
ejpam-6752	219	23	li2	li2	PROPN
ejpam-6752	219	24	+	+	CCONJ
ejpam-6752	219	25	...	...	PUNCT
ejpam-6752	219	26	,	,	PUNCT
ejpam-6752	219	27	i	i	PRON
ejpam-6752	219	28	=	=	NOUN
ejpam-6752	219	29	1	1	NUM
ejpam-6752	219	30	,	,	PUNCT
ejpam-6752	219	31	2	2	NUM
ejpam-6752	219	32	,	,	PUNCT
ejpam-6752	219	33	...	...	PUNCT
ejpam-6752	219	34	,	,	PUNCT
ejpam-6752	219	35	where	where	SCONJ
ejpam-6752	219	36	x0	x0	PROPN
ejpam-6752	219	37	,	,	PUNCT
ejpam-6752	219	38	f0	f0	PROPN
ejpam-6752	219	39	and	and	CCONJ
ejpam-6752	219	40	li0	li0	NOUN
ejpam-6752	219	41	are	be	AUX
ejpam-6752	219	42	calculated	calculate	VERB
ejpam-6752	219	43	at	at	ADP
ejpam-6752	219	44	the	the	DET
ejpam-6752	219	45	unperturbed	unperturbed	ADJ
ejpam-6752	219	46	parameters	parameter	NOUN
ejpam-6752	219	47	,	,	PUNCT
ejpam-6752	219	48	x1	x1	PROPN
ejpam-6752	219	49	,	,	PUNCT
ejpam-6752	219	50	f1	f1	NOUN
ejpam-6752	219	51	and	and	CCONJ
ejpam-6752	219	52	l1i	l1i	PROPN
ejpam-6752	219	53	are	be	AUX
ejpam-6752	219	54	obtained	obtain	VERB
ejpam-6752	219	55	at	at	ADP
ejpam-6752	219	56	a	a	DET
ejpam-6752	219	57	perturbed	perturb	VERB
ejpam-6752	219	58	parameters	parameter	NOUN
ejpam-6752	219	59	of	of	ADP
ejpam-6752	219	60	first	first	ADJ
ejpam-6752	219	61	order	order	NOUN
ejpam-6752	219	62	(	(	PUNCT
ejpam-6752	219	63	they	they	PRON
ejpam-6752	219	64	contain	contain	VERB
ejpam-6752	219	65	the	the	DET
ejpam-6752	219	66	terms	term	NOUN
ejpam-6752	219	67	of	of	ADP
ejpam-6752	219	68	degree	degree	NOUN
ejpam-6752	219	69	one	one	NUM
ejpam-6752	219	70	in	in	ADP
ejpam-6752	219	71	λ	λ	NOUN
ejpam-6752	219	72	)	)	PUNCT
ejpam-6752	219	73	,	,	PUNCT
ejpam-6752	219	74	x2	x2	PROPN
ejpam-6752	219	75	,	,	PUNCT
ejpam-6752	219	76	f2	f2	PROPN
ejpam-6752	219	77	and	and	CCONJ
ejpam-6752	219	78	l2i	l2i	NOUN
ejpam-6752	219	79	are	be	AUX
ejpam-6752	219	80	obtained	obtain	VERB
ejpam-6752	219	81	at	at	ADP
ejpam-6752	219	82	a	a	DET
ejpam-6752	219	83	perturbed	perturb	VERB
ejpam-6752	219	84	parameters	parameter	NOUN
ejpam-6752	219	85	of	of	ADP
ejpam-6752	219	86	second	second	ADJ
ejpam-6752	219	87	order	order	NOUN
ejpam-6752	219	88	(	(	PUNCT
ejpam-6752	219	89	they	they	PRON
ejpam-6752	219	90	contain	contain	VERB
ejpam-6752	219	91	the	the	DET
ejpam-6752	219	92	terms	term	NOUN
ejpam-6752	219	93	of	of	ADP
ejpam-6752	219	94	degree	degree	NOUN
ejpam-6752	219	95	two	two	NUM
ejpam-6752	219	96	in	in	ADP
ejpam-6752	219	97	λ	λ	NOUN
ejpam-6752	219	98	)	)	PUNCT
ejpam-6752	219	99	and	and	CCONJ
ejpam-6752	219	100	so	so	ADV
ejpam-6752	219	101	forth	forth	ADV
ejpam-6752	219	102	.	.	PUNCT
ejpam-6752	220	1	the	the	DET
ejpam-6752	220	2	lyapunov	lyapunov	ADJ
ejpam-6752	220	3	function	function	NOUN
ejpam-6752	220	4	fi	fi	NOUN
ejpam-6752	220	5	and	and	CCONJ
ejpam-6752	220	6	the	the	DET
ejpam-6752	220	7	lyapunov	lyapunov	PROPN
ejpam-6752	220	8	r.	r.	PROPN
ejpam-6752	220	9	h.	h.	PROPN
ejpam-6752	220	10	salih	salih	PROPN
ejpam-6752	220	11	/	/	SYM
ejpam-6752	220	12	eur	eur	PROPN
ejpam-6752	220	13	.	.	PUNCT
ejpam-6752	221	1	j.	j.	PROPN
ejpam-6752	221	2	pure	pure	PROPN
ejpam-6752	221	3	appl	appl	PROPN
ejpam-6752	221	4	.	.	PROPN
ejpam-6752	221	5	math	math	PROPN
ejpam-6752	221	6	,	,	PUNCT
ejpam-6752	221	7	18	18	NUM
ejpam-6752	221	8	(	(	PUNCT
ejpam-6752	221	9	4	4	NUM
ejpam-6752	221	10	)	)	PUNCT
ejpam-6752	221	11	(	(	PUNCT
ejpam-6752	221	12	2025	2025	NUM
ejpam-6752	221	13	)	)	PUNCT
ejpam-6752	221	14	,	,	PUNCT
ejpam-6752	221	15	6752	6752	NUM
ejpam-6752	221	16	9	9	NUM
ejpam-6752	221	17	of	of	ADP
ejpam-6752	221	18	14	14	NUM
ejpam-6752	221	19	quantity	quantity	NOUN
ejpam-6752	221	20	li	li	NOUN
ejpam-6752	221	21	are	be	AUX
ejpam-6752	221	22	both	both	PRON
ejpam-6752	221	23	of	of	ADP
ejpam-6752	221	24	degree	degree	NOUN
ejpam-6752	221	25	i	i	PRON
ejpam-6752	221	26	in	in	ADP
ejpam-6752	221	27	terms	term	NOUN
ejpam-6752	221	28	of	of	ADP
ejpam-6752	221	29	parameters	parameter	NOUN
ejpam-6752	221	30	.	.	PUNCT
ejpam-6752	222	1	by	by	ADP
ejpam-6752	222	2	substituting	substitute	VERB
ejpam-6752	222	3	eq	eq	PROPN
ejpam-6752	222	4	.	.	PUNCT
ejpam-6752	223	1	(	(	PUNCT
ejpam-6752	223	2	12	12	NUM
ejpam-6752	223	3	)	)	PUNCT
ejpam-6752	223	4	into	into	ADP
ejpam-6752	223	5	eq.(11	eq.(11	PROPN
ejpam-6752	223	6	)	)	PUNCT
ejpam-6752	223	7	,	,	PUNCT
ejpam-6752	223	8	we	we	PRON
ejpam-6752	223	9	obtain	obtain	VERB
ejpam-6752	223	10	:	:	PUNCT
ejpam-6752	223	11	x0f0	x0f0	SYM
ejpam-6752	223	12	=	=	SYM
ejpam-6752	223	13	0	0	PROPN
ejpam-6752	223	14	,	,	PUNCT
ejpam-6752	223	15	x0f1	x0f1	PUNCT
ejpam-6752	224	1	+	+	CCONJ
ejpam-6752	224	2	x1f0	x1f0	PUNCT
ejpam-6752	225	1	=	=	SYM
ejpam-6752	225	2	l11(x	l11(x	NOUN
ejpam-6752	225	3	2	2	NUM
ejpam-6752	225	4	1	1	NUM
ejpam-6752	225	5	+	+	NUM
ejpam-6752	225	6	x22	x22	NUM
ejpam-6752	225	7	)	)	PUNCT
ejpam-6752	225	8	+	+	NUM
ejpam-6752	225	9	l21(x	l21(x	NOUN
ejpam-6752	225	10	2	2	NUM
ejpam-6752	225	11	1	1	NUM
ejpam-6752	225	12	+	+	NUM
ejpam-6752	225	13	x22	x22	NUM
ejpam-6752	225	14	)	)	PUNCT
ejpam-6752	225	15	2	2	NUM
ejpam-6752	225	16	+	+	CCONJ
ejpam-6752	225	17	...	...	PUNCT
ejpam-6752	225	18	,	,	PUNCT
ejpam-6752	225	19	x0f2	x0f2	PUNCT
ejpam-6752	226	1	+	+	PUNCT
ejpam-6752	226	2	x1f1	x1f1	PUNCT
ejpam-6752	227	1	+	+	CCONJ
ejpam-6752	227	2	x2f0	x2f0	PRON
ejpam-6752	227	3	=	=	NOUN
ejpam-6752	227	4	l12(x	l12(x	ADJ
ejpam-6752	227	5	2	2	NUM
ejpam-6752	227	6	1	1	NUM
ejpam-6752	227	7	+	+	NUM
ejpam-6752	227	8	x22	x22	NUM
ejpam-6752	227	9	)	)	PUNCT
ejpam-6752	228	1	+	+	CCONJ
ejpam-6752	228	2	l22(x	l22(x	NOUN
ejpam-6752	228	3	2	2	NUM
ejpam-6752	228	4	1	1	NUM
ejpam-6752	228	5	+	+	NUM
ejpam-6752	228	6	x22	x22	NUM
ejpam-6752	228	7	)	)	PUNCT
ejpam-6752	228	8	2	2	NUM
ejpam-6752	229	1	+	+	CCONJ
ejpam-6752	229	2	...	...	PUNCT
ejpam-6752	229	3	(	(	PUNCT
ejpam-6752	229	4	13	13	NUM
ejpam-6752	229	5	)	)	PUNCT
ejpam-6752	229	6	and	and	CCONJ
ejpam-6752	229	7	more	more	ADV
ejpam-6752	229	8	general	general	ADJ
ejpam-6752	229	9	,	,	PUNCT
ejpam-6752	229	10	x0fi	x0fi	PUNCT
ejpam-6752	230	1	+	+	CCONJ
ejpam-6752	230	2	...	...	PUNCT
ejpam-6752	231	1	+	+	NUM
ejpam-6752	231	2	xif0	xif0	NOUN
ejpam-6752	231	3	=	=	SYM
ejpam-6752	231	4	l1i(x	l1i(x	PROPN
ejpam-6752	231	5	2	2	NUM
ejpam-6752	231	6	1	1	NUM
ejpam-6752	231	7	+	+	NUM
ejpam-6752	231	8	x22	x22	NUM
ejpam-6752	231	9	)	)	PUNCT
ejpam-6752	232	1	+	+	CCONJ
ejpam-6752	232	2	l2i(x	l2i(x	NOUN
ejpam-6752	232	3	2	2	NUM
ejpam-6752	232	4	1	1	NUM
ejpam-6752	232	5	+	+	NUM
ejpam-6752	232	6	x22	x22	NUM
ejpam-6752	232	7	)	)	PUNCT
ejpam-6752	232	8	2	2	NUM
ejpam-6752	233	1	+	+	CCONJ
ejpam-6752	233	2	...	...	PUNCT
ejpam-6752	233	3	,	,	PUNCT
ejpam-6752	233	4	i	i	PRON
ejpam-6752	233	5	=	=	NOUN
ejpam-6752	233	6	1	1	NUM
ejpam-6752	233	7	,	,	PUNCT
ejpam-6752	233	8	2	2	NUM
ejpam-6752	233	9	,	,	PUNCT
ejpam-6752	233	10	3	3	NUM
ejpam-6752	233	11	,	,	PUNCT
ejpam-6752	233	12	...	...	PUNCT
ejpam-6752	233	13	(	(	PUNCT
ejpam-6752	233	14	14	14	NUM
ejpam-6752	233	15	)	)	PUNCT
ejpam-6752	233	16	the	the	DET
ejpam-6752	233	17	linear	linear	ADJ
ejpam-6752	233	18	terms	term	NOUN
ejpam-6752	233	19	of	of	ADP
ejpam-6752	233	20	the	the	DET
ejpam-6752	233	21	lyapunov	lyapunov	ADJ
ejpam-6752	233	22	quantities	quantity	NOUN
ejpam-6752	233	23	lk	lk	INTJ
ejpam-6752	233	24	(	(	PUNCT
ejpam-6752	233	25	modulo	modulo	PROPN
ejpam-6752	233	26	the	the	DET
ejpam-6752	233	27	li	li	PROPN
ejpam-6752	233	28	,	,	PUNCT
ejpam-6752	233	29	i	i	PRON
ejpam-6752	233	30	<	<	X
ejpam-6752	233	31	k	k	X
ejpam-6752	233	32	)	)	PUNCT
ejpam-6752	233	33	can	can	AUX
ejpam-6752	233	34	be	be	AUX
ejpam-6752	233	35	obtained	obtain	VERB
ejpam-6752	233	36	by	by	ADP
ejpam-6752	233	37	simultaneously	simultaneously	ADV
ejpam-6752	233	38	solving	solve	VERB
ejpam-6752	233	39	the	the	DET
ejpam-6752	233	40	two	two	NUM
ejpam-6752	233	41	equations	equation	NOUN
ejpam-6752	233	42	in	in	ADP
ejpam-6752	233	43	(	(	PUNCT
ejpam-6752	233	44	13	13	NUM
ejpam-6752	233	45	)	)	PUNCT
ejpam-6752	233	46	using	use	VERB
ejpam-6752	233	47	linear	linear	ADJ
ejpam-6752	233	48	algebra	algebra	NOUN
ejpam-6752	233	49	.	.	PUNCT
ejpam-6752	234	1	eq	eq	ADJ
ejpam-6752	234	2	.	.	PUNCT
ejpam-6752	235	1	(	(	PUNCT
ejpam-6752	235	2	14	14	NUM
ejpam-6752	235	3	)	)	PUNCT
ejpam-6752	235	4	is	be	AUX
ejpam-6752	235	5	then	then	ADV
ejpam-6752	235	6	used	use	VERB
ejpam-6752	235	7	to	to	PART
ejpam-6752	235	8	derive	derive	VERB
ejpam-6752	235	9	the	the	DET
ejpam-6752	235	10	higher	high	ADJ
ejpam-6752	235	11	-	-	PUNCT
ejpam-6752	235	12	order	order	NOUN
ejpam-6752	235	13	terms	term	NOUN
ejpam-6752	235	14	of	of	ADP
ejpam-6752	235	15	the	the	DET
ejpam-6752	235	16	lyapunov	lyapunov	ADJ
ejpam-6752	235	17	quantities	quantity	NOUN
ejpam-6752	235	18	.	.	PUNCT
ejpam-6752	236	1	4.2.2	4.2.2	X
ejpam-6752	236	2	.	.	PUNCT
ejpam-6752	237	1	cyclicities	cyclicity	NOUN
ejpam-6752	237	2	bifurcated	bifurcate	VERB
ejpam-6752	237	3	from	from	ADP
ejpam-6752	237	4	the	the	DET
ejpam-6752	237	5	center	center	ADJ
ejpam-6752	237	6	equilibrium	equilibrium	NOUN
ejpam-6752	237	7	point	point	NOUN
ejpam-6752	237	8	to	to	PART
ejpam-6752	237	9	apply	apply	VERB
ejpam-6752	237	10	the	the	DET
ejpam-6752	237	11	above	above	ADJ
ejpam-6752	237	12	technique	technique	NOUN
ejpam-6752	237	13	,	,	PUNCT
ejpam-6752	237	14	we	we	PRON
ejpam-6752	237	15	choose	choose	VERB
ejpam-6752	237	16	point	point	NOUN
ejpam-6752	237	17	(	(	PUNCT
ejpam-6752	237	18	k1	k1	NOUN
ejpam-6752	237	19	,	,	PUNCT
ejpam-6752	237	20	k2	k2	NOUN
ejpam-6752	237	21	,	,	PUNCT
ejpam-6752	237	22	k3	k3	PROPN
ejpam-6752	237	23	,	,	PUNCT
ejpam-6752	237	24	k4	k4	NOUN
ejpam-6752	237	25	)	)	PUNCT
ejpam-6752	237	26	=	=	PUNCT
ejpam-6752	238	1	(	(	PUNCT
ejpam-6752	238	2	32	32	NUM
ejpam-6752	238	3	,	,	PUNCT
ejpam-6752	238	4	1	1	NUM
ejpam-6752	238	5	2	2	NUM
ejpam-6752	238	6	,	,	PUNCT
ejpam-6752	238	7	1	1	NUM
ejpam-6752	238	8	,	,	PUNCT
ejpam-6752	238	9	1	1	NUM
ejpam-6752	238	10	)	)	PUNCT
ejpam-6752	238	11	on	on	ADP
ejpam-6752	238	12	center	center	ADJ
ejpam-6752	238	13	variety	variety	NOUN
ejpam-6752	238	14	and	and	CCONJ
ejpam-6752	238	15	let	let	VERB
ejpam-6752	238	16	k1	k1	NOUN
ejpam-6752	238	17	=	=	NOUN
ejpam-6752	238	18	3	3	NUM
ejpam-6752	238	19	2	2	NUM
ejpam-6752	238	20	+	+	CCONJ
ejpam-6752	238	21	a1	a1	NOUN
ejpam-6752	238	22	+	+	CCONJ
ejpam-6752	238	23	a2	a2	PROPN
ejpam-6752	238	24	,	,	PUNCT
ejpam-6752	238	25	k2	k2	NOUN
ejpam-6752	238	26	=	=	SYM
ejpam-6752	238	27	1	1	NUM
ejpam-6752	238	28	2	2	NUM
ejpam-6752	238	29	+	+	CCONJ
ejpam-6752	238	30	b1	b1	NOUN
ejpam-6752	238	31	+	+	CCONJ
ejpam-6752	238	32	b2	b2	NOUN
ejpam-6752	238	33	,	,	PUNCT
ejpam-6752	238	34	k3	k3	VERB
ejpam-6752	238	35	=	=	NOUN
ejpam-6752	238	36	1	1	NUM
ejpam-6752	238	37	+	+	NUM
ejpam-6752	238	38	c1	c1	NOUN
ejpam-6752	238	39	+	+	CCONJ
ejpam-6752	238	40	c2	c2	PROPN
ejpam-6752	238	41	and	and	CCONJ
ejpam-6752	238	42	(	(	PUNCT
ejpam-6752	238	43	15	15	NUM
ejpam-6752	238	44	)	)	PUNCT
ejpam-6752	238	45	k4	k4	NOUN
ejpam-6752	238	46	=	=	NOUN
ejpam-6752	238	47	1	1	NUM
ejpam-6752	238	48	+	+	CCONJ
ejpam-6752	238	49	d1	d1	PROPN
ejpam-6752	238	50	+	+	CCONJ
ejpam-6752	238	51	d2	d2	PROPN
ejpam-6752	238	52	are	be	AUX
ejpam-6752	238	53	defined	define	VERB
ejpam-6752	238	54	where	where	SCONJ
ejpam-6752	238	55	a1	a1	NOUN
ejpam-6752	238	56	,	,	PUNCT
ejpam-6752	238	57	b1	b1	NOUN
ejpam-6752	238	58	,	,	PUNCT
ejpam-6752	238	59	c1	c1	NOUN
ejpam-6752	238	60	,	,	PUNCT
ejpam-6752	238	61	d1	d1	PROPN
ejpam-6752	238	62	and	and	CCONJ
ejpam-6752	238	63	a2	a2	PROPN
ejpam-6752	238	64	,	,	PUNCT
ejpam-6752	238	65	b2	b2	NOUN
ejpam-6752	238	66	,	,	PUNCT
ejpam-6752	238	67	c2	c2	PROPN
ejpam-6752	238	68	,	,	PUNCT
ejpam-6752	238	69	d2	d2	PROPN
ejpam-6752	238	70	are	be	AUX
ejpam-6752	238	71	parameters	parameter	NOUN
ejpam-6752	238	72	introduced	introduce	VERB
ejpam-6752	238	73	by	by	ADP
ejpam-6752	238	74	perturbation	perturbation	NOUN
ejpam-6752	238	75	in	in	ADP
ejpam-6752	238	76	the	the	DET
ejpam-6752	238	77	system	system	NOUN
ejpam-6752	238	78	of	of	ADP
ejpam-6752	238	79	first	first	ADJ
ejpam-6752	238	80	and	and	CCONJ
ejpam-6752	238	81	second	second	ADJ
ejpam-6752	238	82	order	order	NOUN
ejpam-6752	238	83	,	,	PUNCT
ejpam-6752	238	84	respectively	respectively	ADV
ejpam-6752	238	85	.	.	PUNCT
ejpam-6752	239	1	therefore	therefore	ADV
ejpam-6752	239	2	,	,	PUNCT
ejpam-6752	239	3	the	the	DET
ejpam-6752	239	4	unperturbed	unperturbed	ADJ
ejpam-6752	239	5	vector	vector	NOUN
ejpam-6752	239	6	field	field	NOUN
ejpam-6752	239	7	x0	x0	PROPN
ejpam-6752	239	8	,	,	PUNCT
ejpam-6752	239	9	the	the	DET
ejpam-6752	239	10	first	first	ADJ
ejpam-6752	239	11	-	-	PUNCT
ejpam-6752	239	12	order	order	NOUN
ejpam-6752	239	13	perturbed	perturb	VERB
ejpam-6752	239	14	vector	vector	NOUN
ejpam-6752	239	15	field	field	NOUN
ejpam-6752	239	16	x1	x1	PROPN
ejpam-6752	239	17	and	and	CCONJ
ejpam-6752	239	18	the	the	DET
ejpam-6752	239	19	second	second	ADJ
ejpam-6752	239	20	-	-	PUNCT
ejpam-6752	239	21	order	order	NOUN
ejpam-6752	239	22	perturbed	perturb	VERB
ejpam-6752	239	23	vector	vector	NOUN
ejpam-6752	239	24	field	field	NOUN
ejpam-6752	239	25	x2	x2	PRON
ejpam-6752	239	26	are	be	AUX
ejpam-6752	239	27	defined	define	VERB
ejpam-6752	239	28	as	as	SCONJ
ejpam-6752	239	29	follows	follow	VERB
ejpam-6752	239	30	:	:	PUNCT
ejpam-6752	240	1	x0	x0	PROPN
ejpam-6752	240	2	=	=	NOUN
ejpam-6752	240	3	1	1	NUM
ejpam-6752	240	4	6	6	NUM
ejpam-6752	240	5	(	(	PUNCT
ejpam-6752	240	6	2	2	NUM
ejpam-6752	240	7	√	√	NUM
ejpam-6752	240	8	3	3	NUM
ejpam-6752	240	9	+	+	SYM
ejpam-6752	240	10	3x1	3x1	NUM
ejpam-6752	240	11	)	)	PUNCT
ejpam-6752	240	12	(	(	PUNCT
ejpam-6752	240	13	3x3	3x3	NUM
ejpam-6752	240	14	−	−	NUM
ejpam-6752	240	15	x2	x2	PROPN
ejpam-6752	240	16	)	)	PUNCT
ejpam-6752	240	17	∂	∂	PUNCT
ejpam-6752	240	18	∂x1	∂x1	NOUN
ejpam-6752	240	19	+	+	CCONJ
ejpam-6752	240	20	1	1	NUM
ejpam-6752	240	21	2	2	NUM
ejpam-6752	240	22	(	(	PUNCT
ejpam-6752	240	23	x1	x1	PROPN
ejpam-6752	240	24	−	−	PROPN
ejpam-6752	240	25	2x3	2x3	NUM
ejpam-6752	240	26	)	)	PUNCT
ejpam-6752	240	27	(	(	PUNCT
ejpam-6752	240	28	x2	x2	PROPN
ejpam-6752	240	29	+	+	CCONJ
ejpam-6752	240	30	√	√	NUM
ejpam-6752	240	31	3	3	NUM
ejpam-6752	240	32	)	)	PUNCT
ejpam-6752	240	33	∂	∂	NUM
ejpam-6752	240	34	∂x2	∂x2	NOUN
ejpam-6752	240	35	−	−	NOUN
ejpam-6752	240	36	1	1	NUM
ejpam-6752	240	37	6	6	NUM
ejpam-6752	240	38	(	(	PUNCT
ejpam-6752	240	39	3	3	NUM
ejpam-6752	240	40	√	√	NUM
ejpam-6752	240	41	3	3	NUM
ejpam-6752	240	42	x1	x1	NOUN
ejpam-6752	241	1	+	+	CCONJ
ejpam-6752	241	2	2	2	NUM
ejpam-6752	241	3	√	√	NUM
ejpam-6752	241	4	3x2	3x2	NUM
ejpam-6752	241	5	+	+	CCONJ
ejpam-6752	241	6	12	12	NUM
ejpam-6752	241	7	√	√	NUM
ejpam-6752	241	8	3x3	3x3	NUM
ejpam-6752	242	1	+	+	CCONJ
ejpam-6752	242	2	9x1x3	9x1x3	NUM
ejpam-6752	242	3	+	+	CCONJ
ejpam-6752	242	4	6x2x3	6x2x3	NUM
ejpam-6752	242	5	)	)	PUNCT
ejpam-6752	242	6	∂	∂	NOUN
ejpam-6752	242	7	∂x3	∂x3	ADV
ejpam-6752	242	8	,	,	PUNCT
ejpam-6752	242	9	x1	x1	PROPN
ejpam-6752	242	10	=	=	PUNCT
ejpam-6752	242	11	(	(	PUNCT
ejpam-6752	242	12	e2x2	e2x2	X
ejpam-6752	242	13	+	+	CCONJ
ejpam-6752	242	14	e3x3	e3x3	NUM
ejpam-6752	242	15	−	−	NOUN
ejpam-6752	242	16	b1x1x2	b1x1x2	NOUN
ejpam-6752	242	17	+	+	CCONJ
ejpam-6752	242	18	a1x1x3	a1x1x3	PROPN
ejpam-6752	242	19	)	)	PUNCT
ejpam-6752	242	20	∂	∂	PUNCT
ejpam-6752	243	1	∂x1	∂x1	NOUN
ejpam-6752	243	2	+	+	CCONJ
ejpam-6752	243	3	(	(	PUNCT
ejpam-6752	243	4	e1x1	e1x1	NOUN
ejpam-6752	243	5	−	−	PROPN
ejpam-6752	243	6	e3x3	e3x3	SYM
ejpam-6752	243	7	+	+	NUM
ejpam-6752	243	8	b1x1x2	b1x1x2	NOUN
ejpam-6752	243	9	−	−	PROPN
ejpam-6752	243	10	c1x2x3	c1x2x3	PROPN
ejpam-6752	243	11	)	)	PUNCT
ejpam-6752	243	12	∂	∂	NUM
ejpam-6752	243	13	∂x2	∂x2	NOUN
ejpam-6752	243	14	+	+	CCONJ
ejpam-6752	243	15	(	(	PUNCT
ejpam-6752	243	16	e2x2	e2x2	NUM
ejpam-6752	243	17	−	−	NUM
ejpam-6752	243	18	2e3x3	2e3x3	NUM
ejpam-6752	243	19	−	−	PROPN
ejpam-6752	243	20	a1x1x3	a1x1x3	PROPN
ejpam-6752	243	21	−	−	PROPN
ejpam-6752	243	22	c1x2x3	c1x2x3	PROPN
ejpam-6752	243	23	)	)	PUNCT
ejpam-6752	243	24	∂	∂	NUM
ejpam-6752	243	25	∂x3	∂x3	ADV
ejpam-6752	243	26	,	,	PUNCT
ejpam-6752	243	27	x2	x2	PROPN
ejpam-6752	244	1	=	=	PUNCT
ejpam-6752	244	2	(	(	PUNCT
ejpam-6752	244	3	f2x2	f2x2	X
ejpam-6752	244	4	+	+	CCONJ
ejpam-6752	244	5	f3x3	f3x3	X
ejpam-6752	244	6	+	+	X
ejpam-6752	244	7	a2x1x3	a2x1x3	NOUN
ejpam-6752	244	8	−	−	NOUN
ejpam-6752	244	9	b2x1x2	b2x1x2	NOUN
ejpam-6752	244	10	)	)	PUNCT
ejpam-6752	244	11	∂	∂	NUM
ejpam-6752	245	1	∂x1	∂x1	NOUN
ejpam-6752	245	2	+	+	CCONJ
ejpam-6752	245	3	(	(	PUNCT
ejpam-6752	245	4	f1x1	f1x1	NOUN
ejpam-6752	245	5	−	−	NOUN
ejpam-6752	245	6	f3x3	f3x3	AUX
ejpam-6752	245	7	+	+	CCONJ
ejpam-6752	245	8	b2x1x2	b2x1x2	VERB
ejpam-6752	245	9	−	−	PROPN
ejpam-6752	245	10	c2x2x3	c2x2x3	PROPN
ejpam-6752	245	11	)	)	PUNCT
ejpam-6752	245	12	∂	∂	NUM
ejpam-6752	245	13	∂x2	∂x2	NOUN
ejpam-6752	245	14	+	+	CCONJ
ejpam-6752	245	15	(	(	PUNCT
ejpam-6752	245	16	f2x2	f2x2	X
ejpam-6752	245	17	−	−	NUM
ejpam-6752	245	18	2f3x3	2f3x3	NUM
ejpam-6752	245	19	−	−	PROPN
ejpam-6752	245	20	a2x1x3	a2x1x3	PROPN
ejpam-6752	245	21	−	−	PROPN
ejpam-6752	245	22	c2x2x3	c2x2x3	PROPN
ejpam-6752	245	23	)	)	PUNCT
ejpam-6752	245	24	∂	∂	NUM
ejpam-6752	245	25	∂x3	∂x3	ADV
ejpam-6752	245	26	,	,	PUNCT
ejpam-6752	245	27	(	(	PUNCT
ejpam-6752	245	28	16	16	NUM
ejpam-6752	245	29	)	)	PUNCT
ejpam-6752	245	30	where	where	SCONJ
ejpam-6752	245	31	e1	e1	NOUN
ejpam-6752	245	32	=	=	NOUN
ejpam-6752	245	33	√	√	PROPN
ejpam-6752	245	34	3	3	NUM
ejpam-6752	245	35	12	12	NUM
ejpam-6752	245	36	(	(	PUNCT
ejpam-6752	245	37	2a1	2a1	NUM
ejpam-6752	245	38	+	+	CCONJ
ejpam-6752	245	39	6b1	6b1	NUM
ejpam-6752	245	40	−	−	NOUN
ejpam-6752	245	41	3c1	3c1	NUM
ejpam-6752	245	42	+	+	CCONJ
ejpam-6752	245	43	3d1	3d1	NUM
ejpam-6752	245	44	)	)	PUNCT
ejpam-6752	245	45	,	,	PUNCT
ejpam-6752	245	46	e2	e2	PROPN
ejpam-6752	245	47	=	=	PUNCT
ejpam-6752	246	1	√	√	PROPN
ejpam-6752	246	2	3	3	NUM
ejpam-6752	246	3	18	18	NUM
ejpam-6752	246	4	(	(	PUNCT
ejpam-6752	246	5	2a1	2a1	NUM
ejpam-6752	246	6	−	−	ADP
ejpam-6752	246	7	6b1	6b1	NUM
ejpam-6752	246	8	−	−	PROPN
ejpam-6752	246	9	3c1	3c1	NUM
ejpam-6752	246	10	−	−	PROPN
ejpam-6752	246	11	3d1	3d1	NUM
ejpam-6752	246	12	)	)	PUNCT
ejpam-6752	246	13	,	,	PUNCT
ejpam-6752	246	14	e3	e3	NOUN
ejpam-6752	246	15	=	=	SYM
ejpam-6752	247	1	√	√	NUM
ejpam-6752	247	2	3	3	NUM
ejpam-6752	247	3	6	6	NUM
ejpam-6752	247	4	(	(	PUNCT
ejpam-6752	247	5	2a1	2a1	NUM
ejpam-6752	247	6	−	−	ADP
ejpam-6752	247	7	6b1	6b1	NUM
ejpam-6752	247	8	+	+	NUM
ejpam-6752	247	9	3c1	3c1	NUM
ejpam-6752	247	10	+	+	CCONJ
ejpam-6752	247	11	3d1	3d1	NUM
ejpam-6752	247	12	)	)	PUNCT
ejpam-6752	247	13	,	,	PUNCT
ejpam-6752	247	14	r.	r.	PROPN
ejpam-6752	247	15	h.	h.	PROPN
ejpam-6752	247	16	salih	salih	PROPN
ejpam-6752	247	17	/	/	SYM
ejpam-6752	247	18	eur	eur	PROPN
ejpam-6752	247	19	.	.	PUNCT
ejpam-6752	248	1	j.	j.	PROPN
ejpam-6752	248	2	pure	pure	PROPN
ejpam-6752	248	3	appl	appl	PROPN
ejpam-6752	248	4	.	.	PROPN
ejpam-6752	248	5	math	math	PROPN
ejpam-6752	248	6	,	,	PUNCT
ejpam-6752	248	7	18	18	NUM
ejpam-6752	248	8	(	(	PUNCT
ejpam-6752	248	9	4	4	NUM
ejpam-6752	248	10	)	)	PUNCT
ejpam-6752	248	11	(	(	PUNCT
ejpam-6752	248	12	2025	2025	NUM
ejpam-6752	248	13	)	)	PUNCT
ejpam-6752	248	14	,	,	PUNCT
ejpam-6752	248	15	6752	6752	NUM
ejpam-6752	248	16	10	10	NUM
ejpam-6752	248	17	of	of	ADP
ejpam-6752	248	18	14	14	NUM
ejpam-6752	248	19	f1	f1	NOUN
ejpam-6752	248	20	=	=	SYM
ejpam-6752	248	21	√	√	PROPN
ejpam-6752	248	22	3	3	NUM
ejpam-6752	248	23	144	144	NUM
ejpam-6752	248	24	(	(	PUNCT
ejpam-6752	248	25	−4a21	−4a21	PROPN
ejpam-6752	248	26	+	+	CCONJ
ejpam-6752	248	27	24b1a1	24b1a1	NUM
ejpam-6752	248	28	−	−	ADP
ejpam-6752	248	29	12a1c1	12a1c1	NOUN
ejpam-6752	248	30	+	+	CCONJ
ejpam-6752	248	31	12a1d1	12a1d1	NOUN
ejpam-6752	248	32	−	−	NOUN
ejpam-6752	248	33	36b21	36b21	NUM
ejpam-6752	248	34	−	−	NUM
ejpam-6752	248	35	36b1c1	36b1c1	NOUN
ejpam-6752	248	36	+	+	CCONJ
ejpam-6752	248	37	36b1d1	36b1d1	NOUN
ejpam-6752	248	38	+	+	CCONJ
ejpam-6752	248	39	27c21	27c21	NUM
ejpam-6752	248	40	−	−	NUM
ejpam-6752	248	41	18c1d1	18c1d1	NOUN
ejpam-6752	248	42	−	−	NOUN
ejpam-6752	248	43	9d21	9d21	NOUN
ejpam-6752	249	1	+	+	CCONJ
ejpam-6752	249	2	24a2	24a2	NUM
ejpam-6752	250	1	+	+	CCONJ
ejpam-6752	250	2	72b2	72b2	NUM
ejpam-6752	250	3	−	−	NUM
ejpam-6752	251	1	36c2	36c2	NUM
ejpam-6752	251	2	+	+	NUM
ejpam-6752	251	3	36d2	36d2	NUM
ejpam-6752	251	4	)	)	PUNCT
ejpam-6752	251	5	,	,	PUNCT
ejpam-6752	251	6	f2	f2	PROPN
ejpam-6752	251	7	=	=	NOUN
ejpam-6752	251	8	√	√	NUM
ejpam-6752	251	9	3	3	NUM
ejpam-6752	251	10	72	72	NUM
ejpam-6752	251	11	(	(	PUNCT
ejpam-6752	251	12	−4a21	−4a21	PROPN
ejpam-6752	251	13	+	+	NOUN
ejpam-6752	251	14	8b1a1	8b1a1	NUM
ejpam-6752	252	1	+	+	CCONJ
ejpam-6752	252	2	4a1c1	4a1c1	NOUN
ejpam-6752	252	3	+	+	NUM
ejpam-6752	252	4	4a1d1	4a1d1	NOUN
ejpam-6752	252	5	+	+	CCONJ
ejpam-6752	252	6	12b21	12b21	NUM
ejpam-6752	252	7	−	−	NOUN
ejpam-6752	252	8	12b1c1	12b1c1	NOUN
ejpam-6752	252	9	−	−	PROPN
ejpam-6752	252	10	12b1d1	12b1d1	NOUN
ejpam-6752	252	11	+	+	SYM
ejpam-6752	252	12	3c21	3c21	NUM
ejpam-6752	252	13	−	−	NOUN
ejpam-6752	252	14	6c1d1	6c1d1	NOUN
ejpam-6752	252	15	+	+	CCONJ
ejpam-6752	252	16	3d21	3d21	ADJ
ejpam-6752	252	17	+	+	CCONJ
ejpam-6752	252	18	8a2	8a2	NUM
ejpam-6752	252	19	−	−	ADP
ejpam-6752	252	20	24b2	24b2	NUM
ejpam-6752	252	21	−	−	NUM
ejpam-6752	252	22	12c2	12c2	NUM
ejpam-6752	252	23	−	−	NOUN
ejpam-6752	252	24	12d2	12d2	NUM
ejpam-6752	252	25	)	)	PUNCT
ejpam-6752	252	26	and	and	CCONJ
ejpam-6752	252	27	f3	f3	PROPN
ejpam-6752	252	28	=	=	SYM
ejpam-6752	252	29	√	√	PROPN
ejpam-6752	252	30	3	3	NUM
ejpam-6752	252	31	72	72	NUM
ejpam-6752	252	32	(	(	PUNCT
ejpam-6752	252	33	−4a21	−4a21	PROPN
ejpam-6752	252	34	−	−	PROPN
ejpam-6752	252	35	24b1a1	24b1a1	NOUN
ejpam-6752	252	36	+	+	CCONJ
ejpam-6752	252	37	12a1c1	12a1c1	NOUN
ejpam-6752	252	38	+	+	CCONJ
ejpam-6752	252	39	12a1d1	12a1d1	NOUN
ejpam-6752	252	40	+	+	CCONJ
ejpam-6752	252	41	108b21c−	108b21c−	NUM
ejpam-6752	252	42	36b1c1	36b1c1	NUM
ejpam-6752	252	43	−	−	PROPN
ejpam-6752	252	44	36b1d1	36b1d1	NOUN
ejpam-6752	252	45	−	−	PROPN
ejpam-6752	252	46	9c21	9c21	NOUN
ejpam-6752	253	1	+	+	CCONJ
ejpam-6752	253	2	18c1d1	18c1d1	NOUN
ejpam-6752	253	3	−	−	NOUN
ejpam-6752	253	4	9d21	9d21	NOUN
ejpam-6752	254	1	+	+	NOUN
ejpam-6752	255	1	24a2	24a2	NUM
ejpam-6752	255	2	−	−	NOUN
ejpam-6752	255	3	72b2	72b2	NUM
ejpam-6752	256	1	+	+	CCONJ
ejpam-6752	256	2	36c2	36c2	NUM
ejpam-6752	256	3	+	+	NUM
ejpam-6752	256	4	36d2	36d2	NUM
ejpam-6752	256	5	)	)	PUNCT
ejpam-6752	256	6	.	.	PUNCT
ejpam-6752	257	1	the	the	DET
ejpam-6752	257	2	main	main	ADJ
ejpam-6752	257	3	result	result	NOUN
ejpam-6752	257	4	regarding	regard	VERB
ejpam-6752	257	5	the	the	DET
ejpam-6752	257	6	bifurcated	bifurcated	ADJ
ejpam-6752	257	7	limit	limit	NOUN
ejpam-6752	257	8	cycle	cycle	NOUN
ejpam-6752	257	9	from	from	ADP
ejpam-6752	257	10	the	the	DET
ejpam-6752	257	11	center	center	ADJ
ejpam-6752	257	12	equilibrium	equilibrium	NOUN
ejpam-6752	257	13	point	point	NOUN
ejpam-6752	257	14	,	,	PUNCT
ejpam-6752	257	15	using	use	VERB
ejpam-6752	257	16	the	the	DET
ejpam-6752	257	17	technique	technique	NOUN
ejpam-6752	257	18	described	describe	VERB
ejpam-6752	257	19	above	above	ADV
ejpam-6752	257	20	,	,	PUNCT
ejpam-6752	257	21	is	be	AUX
ejpam-6752	257	22	the	the	DET
ejpam-6752	257	23	following	follow	VERB
ejpam-6752	257	24	theorem	theorem	NOUN
ejpam-6752	257	25	.	.	PUNCT
ejpam-6752	257	26	theorem	theorem	NOUN
ejpam-6752	257	27	1	1	NUM
ejpam-6752	257	28	.	.	X
ejpam-6752	257	29	for	for	ADP
ejpam-6752	257	30	system	system	NOUN
ejpam-6752	257	31	(	(	PUNCT
ejpam-6752	257	32	1	1	NUM
ejpam-6752	257	33	)	)	PUNCT
ejpam-6752	257	34	,	,	PUNCT
ejpam-6752	257	35	when	when	SCONJ
ejpam-6752	257	36	k1	k1	PROPN
ejpam-6752	257	37	=	=	SYM
ejpam-6752	257	38	k2	k2	PROPN
ejpam-6752	257	39	+	+	CCONJ
ejpam-6752	257	40	k3	k3	PROPN
ejpam-6752	257	41	,	,	PUNCT
ejpam-6752	257	42	using	use	VERB
ejpam-6752	257	43	first	first	ADJ
ejpam-6752	257	44	-	-	PUNCT
ejpam-6752	257	45	order	order	NOUN
ejpam-6752	257	46	perturbation	perturbation	NOUN
ejpam-6752	257	47	,	,	PUNCT
ejpam-6752	257	48	only	only	ADV
ejpam-6752	257	49	a	a	DET
ejpam-6752	257	50	single	single	ADJ
ejpam-6752	257	51	limit	limit	NOUN
ejpam-6752	257	52	cycle	cycle	NOUN
ejpam-6752	257	53	can	can	AUX
ejpam-6752	257	54	bifurcate	bifurcate	VERB
ejpam-6752	257	55	from	from	ADP
ejpam-6752	257	56	the	the	DET
ejpam-6752	257	57	equilibrium	equilibrium	NOUN
ejpam-6752	257	58	point	point	NOUN
ejpam-6752	257	59	at	at	ADP
ejpam-6752	257	60	e.	e.	PROPN
ejpam-6752	257	61	proof	proof	PROPN
ejpam-6752	257	62	.	.	PUNCT
ejpam-6752	258	1	instead	instead	ADV
ejpam-6752	258	2	of	of	ADP
ejpam-6752	258	3	analysing	analyse	VERB
ejpam-6752	258	4	system	system	NOUN
ejpam-6752	258	5	(	(	PUNCT
ejpam-6752	258	6	1	1	NUM
ejpam-6752	258	7	)	)	PUNCT
ejpam-6752	258	8	at	at	ADP
ejpam-6752	258	9	e	e	NOUN
ejpam-6752	258	10	,	,	PUNCT
ejpam-6752	258	11	system	system	NOUN
ejpam-6752	258	12	(	(	PUNCT
ejpam-6752	258	13	6	6	NUM
ejpam-6752	258	14	)	)	PUNCT
ejpam-6752	258	15	is	be	AUX
ejpam-6752	258	16	examined	examine	VERB
ejpam-6752	258	17	at	at	ADP
ejpam-6752	258	18	the	the	DET
ejpam-6752	258	19	origin	origin	NOUN
ejpam-6752	258	20	.	.	PUNCT
ejpam-6752	259	1	using	use	VERB
ejpam-6752	259	2	the	the	DET
ejpam-6752	259	3	linear	linear	ADJ
ejpam-6752	259	4	transformation	transformation	NOUN
ejpam-6752	259	5	x	x	PUNCT
ejpam-6752	259	6	=	=	SYM
ejpam-6752	259	7	py	py	PROPN
ejpam-6752	259	8	,	,	PUNCT
ejpam-6752	259	9	p	p	NOUN
ejpam-6752	259	10	=	=	NOUN
ejpam-6752	259	11	−2	−2	VERB
ejpam-6752	259	12	√	√	VERB
ejpam-6752	259	13	3	3	NUM
ejpam-6752	259	14	−2	−2	NOUN
ejpam-6752	259	15	−1/6	−1/6	NOUN
ejpam-6752	259	16	2	2	NUM
ejpam-6752	259	17	√	√	NUM
ejpam-6752	259	18	3	3	NUM
ejpam-6752	259	19	−3	−3	NOUN
ejpam-6752	259	20	1/4	1/4	NUM
ejpam-6752	259	21	0	0	NUM
ejpam-6752	259	22	1	1	NUM
ejpam-6752	259	23	5/12	5/12	NUM
ejpam-6752	259	24			NOUN
ejpam-6752	259	25	,	,	PUNCT
ejpam-6752	259	26	(	(	PUNCT
ejpam-6752	259	27	17	17	NUM
ejpam-6752	259	28	)	)	PUNCT
ejpam-6752	260	1	where	where	SCONJ
ejpam-6752	260	2	x	x	SYM
ejpam-6752	260	3	=	=	PRON
ejpam-6752	260	4	(	(	PUNCT
ejpam-6752	260	5	x1	x1	PROPN
ejpam-6752	260	6	,	,	PUNCT
ejpam-6752	260	7	x2	x2	PROPN
ejpam-6752	260	8	,	,	PUNCT
ejpam-6752	260	9	x3	x3	ADJ
ejpam-6752	260	10	)	)	PUNCT
ejpam-6752	260	11	,	,	PUNCT
ejpam-6752	260	12	y	y	PROPN
ejpam-6752	260	13	=	=	SYM
ejpam-6752	260	14	(	(	PUNCT
ejpam-6752	260	15	x	x	X
ejpam-6752	260	16	,	,	PUNCT
ejpam-6752	260	17	y	y	PROPN
ejpam-6752	260	18	,	,	PUNCT
ejpam-6752	260	19	z	z	PROPN
ejpam-6752	260	20	)	)	PUNCT
ejpam-6752	260	21	,	,	PUNCT
ejpam-6752	260	22	the	the	DET
ejpam-6752	260	23	linear	linear	ADJ
ejpam-6752	260	24	part	part	NOUN
ejpam-6752	260	25	of	of	ADP
ejpam-6752	260	26	system	system	NOUN
ejpam-6752	260	27	(	(	PUNCT
ejpam-6752	260	28	6	6	NUM
ejpam-6752	260	29	)	)	PUNCT
ejpam-6752	260	30	at	at	ADP
ejpam-6752	260	31	the	the	DET
ejpam-6752	260	32	origin	origin	NOUN
ejpam-6752	260	33	can	can	AUX
ejpam-6752	260	34	be	be	AUX
ejpam-6752	260	35	written	write	VERB
ejpam-6752	260	36	in	in	ADP
ejpam-6752	260	37	the	the	DET
ejpam-6752	260	38	real	real	ADJ
ejpam-6752	260	39	canonical	canonical	ADJ
ejpam-6752	260	40	form	form	NOUN
ejpam-6752	260	41	as0	as0	ADP
ejpam-6752	260	42	−1	−1	NOUN
ejpam-6752	260	43	0	0	NUM
ejpam-6752	260	44	1	1	NUM
ejpam-6752	260	45	0	0	NUM
ejpam-6752	260	46	0	0	NUM
ejpam-6752	260	47	0	0	NUM
ejpam-6752	260	48	0	0	NUM
ejpam-6752	260	49	−2	−2	NOUN
ejpam-6752	260	50	√	√	NOUN
ejpam-6752	260	51	3	3	NUM
ejpam-6752	260	52			NOUN
ejpam-6752	260	53	,	,	PUNCT
ejpam-6752	260	54	and	and	CCONJ
ejpam-6752	260	55	the	the	DET
ejpam-6752	260	56	new	new	ADJ
ejpam-6752	260	57	system	system	NOUN
ejpam-6752	260	58	is	be	AUX
ejpam-6752	260	59	given	give	VERB
ejpam-6752	260	60	by	by	ADP
ejpam-6752	260	61	ẋ	ẋ	PROPN
ejpam-6752	260	62	=	=	PUNCT
ejpam-6752	260	63	−y	−y	VERB
ejpam-6752	261	1	−	−	NOUN
ejpam-6752	261	2	√	√	NUM
ejpam-6752	261	3	3x2	3x2	NUM
ejpam-6752	262	1	+	+	CCONJ
ejpam-6752	262	2	xy	xy	PROPN
ejpam-6752	262	3	+	+	CCONJ
ejpam-6752	262	4	7	7	NUM
ejpam-6752	262	5	√	√	NUM
ejpam-6752	262	6	3	3	NUM
ejpam-6752	262	7	13	13	NUM
ejpam-6752	262	8	y2	y2	NOUN
ejpam-6752	263	1	+	+	CCONJ
ejpam-6752	263	2	5	5	NUM
ejpam-6752	263	3	√	√	NUM
ejpam-6752	263	4	3	3	NUM
ejpam-6752	263	5	156	156	NUM
ejpam-6752	263	6	yz	yz	NOUN
ejpam-6752	264	1	+	+	CCONJ
ejpam-6752	264	2	√	√	NUM
ejpam-6752	264	3	3	3	NUM
ejpam-6752	264	4	312	312	NUM
ejpam-6752	264	5	z2	z2	NUM
ejpam-6752	264	6	,	,	PUNCT
ejpam-6752	264	7	ẏ	ẏ	NOUN
ejpam-6752	264	8	=	=	PUNCT
ejpam-6752	264	9	x+	x+	PROPN
ejpam-6752	264	10	√	√	NUM
ejpam-6752	264	11	3xy	3xy	NOUN
ejpam-6752	265	1	+	+	CCONJ
ejpam-6752	265	2	5	5	NUM
ejpam-6752	265	3	√	√	NUM
ejpam-6752	265	4	3	3	NUM
ejpam-6752	265	5	12	12	NUM
ejpam-6752	265	6	xz	xz	NOUN
ejpam-6752	266	1	+	+	CCONJ
ejpam-6752	266	2	3	3	NUM
ejpam-6752	266	3	13	13	NUM
ejpam-6752	266	4	y2	y2	NOUN
ejpam-6752	267	1	+	+	CCONJ
ejpam-6752	267	2	5	5	NUM
ejpam-6752	267	3	26	26	NUM
ejpam-6752	267	4	yz	yz	NOUN
ejpam-6752	267	5	+	+	CCONJ
ejpam-6752	267	6	25	25	NUM
ejpam-6752	267	7	624	624	NUM
ejpam-6752	267	8	z2	z2	NUM
ejpam-6752	267	9	,	,	PUNCT
ejpam-6752	267	10	(	(	PUNCT
ejpam-6752	267	11	18	18	NUM
ejpam-6752	267	12	)	)	PUNCT
ejpam-6752	267	13	ż	ż	NOUN
ejpam-6752	267	14	=	=	PUNCT
ejpam-6752	267	15	−2	−2	NOUN
ejpam-6752	267	16	√	√	PROPN
ejpam-6752	268	1	3z	3z	NUM
ejpam-6752	268	2	+	+	CCONJ
ejpam-6752	268	3	180	180	NUM
ejpam-6752	268	4	13	13	NUM
ejpam-6752	268	5	y2	y2	NOUN
ejpam-6752	269	1	+	+	CCONJ
ejpam-6752	269	2	72	72	NUM
ejpam-6752	269	3	13	13	NUM
ejpam-6752	269	4	yz	yz	NOUN
ejpam-6752	269	5	−	−	NUM
ejpam-6752	269	6	5	5	NUM
ejpam-6752	270	1	52	52	NUM
ejpam-6752	270	2	z2	z2	PROPN
ejpam-6752	270	3	.	.	PUNCT
ejpam-6752	271	1	the	the	DET
ejpam-6752	271	2	transformation	transformation	NOUN
ejpam-6752	271	3	described	describe	VERB
ejpam-6752	271	4	in	in	ADP
ejpam-6752	271	5	eq	eq	PROPN
ejpam-6752	271	6	.	.	PUNCT
ejpam-6752	272	1	(	(	PUNCT
ejpam-6752	272	2	17	17	NUM
ejpam-6752	272	3	)	)	PUNCT
ejpam-6752	272	4	is	be	AUX
ejpam-6752	272	5	applied	apply	VERB
ejpam-6752	272	6	to	to	ADP
ejpam-6752	272	7	the	the	DET
ejpam-6752	272	8	first	first	ADJ
ejpam-6752	272	9	order	order	NOUN
ejpam-6752	272	10	perturbed	perturb	VERB
ejpam-6752	272	11	vector	vector	NOUN
ejpam-6752	272	12	field	field	NOUN
ejpam-6752	272	13	component	component	NOUN
ejpam-6752	272	14	of	of	ADP
ejpam-6752	272	15	system	system	NOUN
ejpam-6752	272	16	(	(	PUNCT
ejpam-6752	272	17	6	6	NUM
ejpam-6752	272	18	)	)	PUNCT
ejpam-6752	272	19	,	,	PUNCT
ejpam-6752	272	20	leading	lead	VERB
ejpam-6752	272	21	to	to	ADP
ejpam-6752	272	22	the	the	DET
ejpam-6752	272	23	following	follow	VERB
ejpam-6752	272	24	results	result	NOUN
ejpam-6752	272	25	:	:	PUNCT
ejpam-6752	272	26	ẋ	ẋ	PROPN
ejpam-6752	273	1	=	=	PRON
ejpam-6752	273	2	−	−	PROPN
ejpam-6752	273	3	1	1	NUM
ejpam-6752	273	4	13	13	NUM
ejpam-6752	273	5	(	(	PUNCT
ejpam-6752	273	6	4e1	4e1	NUM
ejpam-6752	274	1	+	+	NOUN
ejpam-6752	274	2	15e2)x−	15e2)x−	NUM
ejpam-6752	274	3	√	√	NUM
ejpam-6752	274	4	3	3	NUM
ejpam-6752	274	5	78	78	NUM
ejpam-6752	274	6	(	(	PUNCT
ejpam-6752	274	7	8e1	8e1	NUM
ejpam-6752	274	8	−	−	PROPN
ejpam-6752	274	9	45e2	45e2	NUM
ejpam-6752	274	10	+	+	CCONJ
ejpam-6752	274	11	e3)y	e3)y	VERB
ejpam-6752	274	12	−	−	PROPN
ejpam-6752	274	13	√	√	PROPN
ejpam-6752	274	14	3	3	NUM
ejpam-6752	274	15	936	936	NUM
ejpam-6752	274	16	(	(	PUNCT
ejpam-6752	274	17	8e1	8e1	NUM
ejpam-6752	274	18	+	+	CCONJ
ejpam-6752	275	1	45e2	45e2	NUM
ejpam-6752	275	2	+	+	CCONJ
ejpam-6752	275	3	5e3)z	5e3)z	NUM
ejpam-6752	275	4	+	+	CCONJ
ejpam-6752	275	5	1	1	NUM
ejpam-6752	275	6	13	13	NUM
ejpam-6752	275	7	(	(	PUNCT
ejpam-6752	275	8	3a1	3a1	NUM
ejpam-6752	275	9	+	+	PUNCT
ejpam-6752	275	10	13b1	13b1	NUM
ejpam-6752	275	11	+	+	SYM
ejpam-6752	275	12	2c1)xy	2c1)xy	NUM
ejpam-6752	275	13	+	+	CCONJ
ejpam-6752	275	14	1	1	NUM
ejpam-6752	275	15	156	156	NUM
ejpam-6752	275	16	(	(	PUNCT
ejpam-6752	275	17	15a1	15a1	NUM
ejpam-6752	275	18	−	−	NOUN
ejpam-6752	275	19	65b1	65b1	NUM
ejpam-6752	275	20	+	+	NUM
ejpam-6752	275	21	10c1)xz	10c1)xz	NUM
ejpam-6752	276	1	+	+	CCONJ
ejpam-6752	276	2	√	√	NUM
ejpam-6752	276	3	3	3	NUM
ejpam-6752	276	4	78	78	NUM
ejpam-6752	276	5	(	(	PUNCT
ejpam-6752	276	6	3a1	3a1	NUM
ejpam-6752	276	7	−	−	NOUN
ejpam-6752	276	8	2c1)yz	2c1)yz	NUM
ejpam-6752	276	9	−	−	NOUN
ejpam-6752	276	10	2	2	NUM
ejpam-6752	276	11	√	√	NUM
ejpam-6752	276	12	3b1x	3b1x	NOUN
ejpam-6752	276	13	2	2	NUM
ejpam-6752	276	14	+	+	CCONJ
ejpam-6752	276	15	√	√	NUM
ejpam-6752	276	16	3	3	NUM
ejpam-6752	276	17	13	13	NUM
ejpam-6752	276	18	(	(	PUNCT
ejpam-6752	276	19	a1	a1	NOUN
ejpam-6752	276	20	+	+	CCONJ
ejpam-6752	276	21	13b1	13b1	NUM
ejpam-6752	276	22	−	−	PROPN
ejpam-6752	276	23	c1)y	c1)y	PROPN
ejpam-6752	276	24	2	2	PROPN
ejpam-6752	276	25	r.	r.	PROPN
ejpam-6752	276	26	h.	h.	PROPN
ejpam-6752	276	27	salih	salih	PROPN
ejpam-6752	276	28	/	/	SYM
ejpam-6752	276	29	eur	eur	PROPN
ejpam-6752	276	30	.	.	PUNCT
ejpam-6752	277	1	j.	j.	PROPN
ejpam-6752	277	2	pure	pure	PROPN
ejpam-6752	277	3	appl	appl	PROPN
ejpam-6752	277	4	.	.	PROPN
ejpam-6752	277	5	math	math	PROPN
ejpam-6752	277	6	,	,	PUNCT
ejpam-6752	277	7	18	18	NUM
ejpam-6752	277	8	(	(	PUNCT
ejpam-6752	277	9	4	4	NUM
ejpam-6752	277	10	)	)	PUNCT
ejpam-6752	277	11	(	(	PUNCT
ejpam-6752	277	12	2025	2025	NUM
ejpam-6752	277	13	)	)	PUNCT
ejpam-6752	277	14	,	,	PUNCT
ejpam-6752	277	15	6752	6752	NUM
ejpam-6752	277	16	11	11	NUM
ejpam-6752	277	17	of	of	ADP
ejpam-6752	277	18	14	14	NUM
ejpam-6752	277	19	+	+	CCONJ
ejpam-6752	277	20	√	√	NUM
ejpam-6752	277	21	3	3	NUM
ejpam-6752	277	22	1872	1872	NUM
ejpam-6752	277	23	(	(	PUNCT
ejpam-6752	277	24	5a1	5a1	NUM
ejpam-6752	277	25	−	−	NOUN
ejpam-6752	277	26	13b1	13b1	NUM
ejpam-6752	277	27	+	+	CCONJ
ejpam-6752	277	28	5c1)z	5c1)z	NUM
ejpam-6752	277	29	2	2	NUM
ejpam-6752	277	30	,	,	PUNCT
ejpam-6752	277	31	ẏ	ẏ	NOUN
ejpam-6752	277	32	=	=	PUNCT
ejpam-6752	277	33	√	√	PROPN
ejpam-6752	278	1	3	3	NUM
ejpam-6752	278	2	13	13	NUM
ejpam-6752	278	3	(	(	PUNCT
ejpam-6752	278	4	5e1	5e1	NUM
ejpam-6752	278	5	−	−	PROPN
ejpam-6752	278	6	4e2)x+	4e2)x+	NOUN
ejpam-6752	278	7	1	1	NUM
ejpam-6752	278	8	13	13	NUM
ejpam-6752	278	9	(	(	PUNCT
ejpam-6752	278	10	5e1	5e1	NOUN
ejpam-6752	278	11	+	+	NUM
ejpam-6752	278	12	6e2	6e2	NUM
ejpam-6752	278	13	−	−	NOUN
ejpam-6752	278	14	e3)y	e3)y	NOUN
ejpam-6752	278	15	+	+	CCONJ
ejpam-6752	278	16	1	1	NUM
ejpam-6752	278	17	156	156	NUM
ejpam-6752	278	18	(	(	PUNCT
ejpam-6752	278	19	5e1	5e1	NUM
ejpam-6752	278	20	−	−	PROPN
ejpam-6752	278	21	6e2	6e2	NUM
ejpam-6752	278	22	−	−	NUM
ejpam-6752	278	23	5e3)z	5e3)z	NUM
ejpam-6752	278	24	+	+	CCONJ
ejpam-6752	278	25	2	2	NUM
ejpam-6752	278	26	√	√	NUM
ejpam-6752	278	27	3	3	NUM
ejpam-6752	278	28	13	13	NUM
ejpam-6752	278	29	(	(	PUNCT
ejpam-6752	278	30	3a1	3a1	NUM
ejpam-6752	278	31	+	+	CCONJ
ejpam-6752	278	32	2c1)xy	2c1)xy	NUM
ejpam-6752	279	1	+	+	CCONJ
ejpam-6752	279	2	5	5	NUM
ejpam-6752	279	3	√	√	NUM
ejpam-6752	279	4	3	3	NUM
ejpam-6752	279	5	78	78	NUM
ejpam-6752	279	6	(	(	PUNCT
ejpam-6752	279	7	3a1	3a1	NUM
ejpam-6752	279	8	+	+	CCONJ
ejpam-6752	279	9	2c1)xz	2c1)xz	NUM
ejpam-6752	279	10	+	+	SYM
ejpam-6752	279	11	1	1	NUM
ejpam-6752	279	12	13	13	NUM
ejpam-6752	279	13	(	(	PUNCT
ejpam-6752	279	14	3a1	3a1	NUM
ejpam-6752	279	15	−	−	NOUN
ejpam-6752	279	16	2c1)yz	2c1)yz	NUM
ejpam-6752	279	17	+	+	CCONJ
ejpam-6752	279	18	6	6	NUM
ejpam-6752	279	19	13	13	NUM
ejpam-6752	279	20	(	(	PUNCT
ejpam-6752	279	21	a1	a1	NOUN
ejpam-6752	279	22	−	−	PROPN
ejpam-6752	279	23	c1)y	c1)y	PROPN
ejpam-6752	279	24	2	2	NUM
ejpam-6752	279	25	+	+	CCONJ
ejpam-6752	279	26	5	5	NUM
ejpam-6752	279	27	312	312	NUM
ejpam-6752	279	28	(	(	PUNCT
ejpam-6752	279	29	a1	a1	NOUN
ejpam-6752	279	30	+	+	CCONJ
ejpam-6752	279	31	c1)z	c1)z	ADJ
ejpam-6752	279	32	2	2	NUM
ejpam-6752	279	33	,	,	PUNCT
ejpam-6752	279	34	ż	ż	NOUN
ejpam-6752	279	35	=	=	PUNCT
ejpam-6752	280	1	−12	−12	NOUN
ejpam-6752	280	2	√	√	ADJ
ejpam-6752	280	3	3	3	NUM
ejpam-6752	280	4	13	13	NUM
ejpam-6752	280	5	(	(	PUNCT
ejpam-6752	280	6	e1	e1	NOUN
ejpam-6752	280	7	−	−	PROPN
ejpam-6752	280	8	6e2)x−	6e2)x−	NUM
ejpam-6752	280	9	1	1	NUM
ejpam-6752	280	10	13	13	NUM
ejpam-6752	280	11	(	(	PUNCT
ejpam-6752	281	1	12e1	12e1	NUM
ejpam-6752	281	2	+	+	NUM
ejpam-6752	281	3	108e2	108e2	NUM
ejpam-6752	281	4	+	+	CCONJ
ejpam-6752	281	5	60e3)y	60e3)y	NUM
ejpam-6752	281	6	−	−	NOUN
ejpam-6752	281	7	1	1	NUM
ejpam-6752	281	8	13	13	NUM
ejpam-6752	281	9	(	(	PUNCT
ejpam-6752	281	10	e1	e1	VERB
ejpam-6752	281	11	−	−	PROPN
ejpam-6752	281	12	9e2	9e2	NUM
ejpam-6752	282	1	+	+	CCONJ
ejpam-6752	282	2	25e3)z	25e3)z	NOUN
ejpam-6752	282	3	+	+	CCONJ
ejpam-6752	282	4	24	24	NUM
ejpam-6752	282	5	√	√	NUM
ejpam-6752	282	6	3	3	NUM
ejpam-6752	282	7	13	13	NUM
ejpam-6752	282	8	(	(	PUNCT
ejpam-6752	282	9	2a1	2a1	NUM
ejpam-6752	282	10	−	−	ADP
ejpam-6752	282	11	3c1)xy	3c1)xy	NUM
ejpam-6752	282	12	+	+	CCONJ
ejpam-6752	282	13	10	10	NUM
ejpam-6752	282	14	√	√	NUM
ejpam-6752	282	15	3	3	NUM
ejpam-6752	282	16	13	13	NUM
ejpam-6752	282	17	(	(	PUNCT
ejpam-6752	282	18	2a1	2a1	NUM
ejpam-6752	282	19	−	−	ADP
ejpam-6752	282	20	3c1)xz	3c1)xz	NUM
ejpam-6752	283	1	+	+	CCONJ
ejpam-6752	283	2	12	12	NUM
ejpam-6752	283	3	13	13	NUM
ejpam-6752	283	4	(	(	PUNCT
ejpam-6752	283	5	2a1	2a1	NUM
ejpam-6752	283	6	+	+	CCONJ
ejpam-6752	283	7	3c1)yz	3c1)yz	NUM
ejpam-6752	283	8	+	+	CCONJ
ejpam-6752	283	9	12	12	NUM
ejpam-6752	283	10	13	13	NUM
ejpam-6752	283	11	(	(	PUNCT
ejpam-6752	283	12	4a1	4a1	NUM
ejpam-6752	283	13	+	+	CCONJ
ejpam-6752	283	14	9c1)y	9c1)y	NUM
ejpam-6752	283	15	2	2	NUM
ejpam-6752	283	16	+	+	CCONJ
ejpam-6752	283	17	5	5	NUM
ejpam-6752	283	18	156	156	NUM
ejpam-6752	283	19	(	(	PUNCT
ejpam-6752	283	20	4a1	4a1	NUM
ejpam-6752	283	21	−	−	NOUN
ejpam-6752	283	22	9c1)z	9c1)z	NUM
ejpam-6752	283	23	2	2	NUM
ejpam-6752	283	24	.	.	PUNCT
ejpam-6752	284	1	(	(	PUNCT
ejpam-6752	284	2	19	19	NUM
ejpam-6752	284	3	)	)	PUNCT
ejpam-6752	284	4	now	now	ADV
ejpam-6752	284	5	,	,	PUNCT
ejpam-6752	284	6	the	the	DET
ejpam-6752	284	7	unperturbed	unperturbed	ADJ
ejpam-6752	284	8	lyapunov	lyapunov	ADJ
ejpam-6752	284	9	function	function	NOUN
ejpam-6752	284	10	,	,	PUNCT
ejpam-6752	284	11	f0	f0	PROPN
ejpam-6752	284	12	,	,	PUNCT
ejpam-6752	284	13	and	and	CCONJ
ejpam-6752	284	14	the	the	DET
ejpam-6752	284	15	first	first	ADJ
ejpam-6752	284	16	-	-	PUNCT
ejpam-6752	284	17	order	order	NOUN
ejpam-6752	284	18	perturbed	perturb	VERB
ejpam-6752	284	19	lyapunov	lyapunov	ADJ
ejpam-6752	284	20	function	function	NOUN
ejpam-6752	284	21	,	,	PUNCT
ejpam-6752	284	22	f1	f1	NOUN
ejpam-6752	284	23	,	,	PUNCT
ejpam-6752	284	24	are	be	AUX
ejpam-6752	284	25	defined	define	VERB
ejpam-6752	284	26	by	by	ADP
ejpam-6752	284	27	:	:	PUNCT
ejpam-6752	284	28	f0	f0	PROPN
ejpam-6752	284	29	=	=	SYM
ejpam-6752	284	30	x2	x2	PROPN
ejpam-6752	285	1	+	+	CCONJ
ejpam-6752	285	2	y2	y2	PROPN
ejpam-6752	286	1	+	+	CCONJ
ejpam-6752	287	1	n∑	n∑	ADJ
ejpam-6752	287	2	k=3	k=3	PROPN
ejpam-6752	287	3	k∑	k∑	PROPN
ejpam-6752	287	4	i=0	i=0	PROPN
ejpam-6752	287	5	i∑	i∑	PROPN
ejpam-6752	287	6	j=0	j=0	PROPN
ejpam-6752	287	7	ck−i	ck−i	NOUN
ejpam-6752	287	8	,	,	PUNCT
ejpam-6752	287	9	i−j	i−j	PROPN
ejpam-6752	287	10	,	,	PUNCT
ejpam-6752	287	11	jx	jx	PROPN
ejpam-6752	287	12	k−iyi−jzj	k−iyi−jzj	PROPN
ejpam-6752	287	13	,	,	PUNCT
ejpam-6752	287	14	f1	f1	PROPN
ejpam-6752	287	15	=	=	SYM
ejpam-6752	287	16	n∑	n∑	PROPN
ejpam-6752	287	17	k=3	k=3	PROPN
ejpam-6752	287	18	k∑	k∑	VERB
ejpam-6752	287	19	i=0	i=0	PROPN
ejpam-6752	287	20	i∑	i∑	NUM
ejpam-6752	287	21	j=0	j=0	PROPN
ejpam-6752	287	22	dk−i	dk−i	NOUN
ejpam-6752	287	23	,	,	PUNCT
ejpam-6752	287	24	i−j	i−j	PROPN
ejpam-6752	287	25	,	,	PUNCT
ejpam-6752	287	26	jx	jx	PROPN
ejpam-6752	287	27	k−iyi−jzj	k−iyi−jzj	PROPN
ejpam-6752	287	28	,	,	PUNCT
ejpam-6752	287	29	(	(	PUNCT
ejpam-6752	287	30	20	20	NUM
ejpam-6752	287	31	)	)	PUNCT
ejpam-6752	287	32	where	where	SCONJ
ejpam-6752	287	33	n	n	PRON
ejpam-6752	287	34	≥	≥	NOUN
ejpam-6752	287	35	3	3	X
ejpam-6752	287	36	.	.	PUNCT
ejpam-6752	288	1	it	it	PRON
ejpam-6752	288	2	is	be	AUX
ejpam-6752	288	3	easy	easy	ADJ
ejpam-6752	288	4	to	to	PART
ejpam-6752	288	5	show	show	VERB
ejpam-6752	288	6	that	that	SCONJ
ejpam-6752	288	7	the	the	DET
ejpam-6752	288	8	lyapunov	lyapunov	ADJ
ejpam-6752	288	9	function	function	NOUN
ejpam-6752	288	10	,	,	PUNCT
ejpam-6752	288	11	f0	f0	PROPN
ejpam-6752	288	12	,	,	PUNCT
ejpam-6752	288	13	of	of	ADP
ejpam-6752	288	14	eq	eq	NOUN
ejpam-6752	288	15	.	.	PUNCT
ejpam-6752	288	16	(	(	PUNCT
ejpam-6752	288	17	18	18	NUM
ejpam-6752	288	18	)	)	PUNCT
ejpam-6752	288	19	is	be	AUX
ejpam-6752	288	20	satisfied	satisfy	VERB
ejpam-6752	288	21	by	by	ADP
ejpam-6752	288	22	x0f0	x0f0	X
ejpam-6752	288	23	=	=	SYM
ejpam-6752	288	24	0	0	PROPN
ejpam-6752	288	25	.	.	PUNCT
ejpam-6752	289	1	using	use	VERB
ejpam-6752	289	2	the	the	DET
ejpam-6752	289	3	computer	computer	NOUN
ejpam-6752	289	4	algebra	algebra	NOUN
ejpam-6752	289	5	package	package	NOUN
ejpam-6752	289	6	maple	maple	NOUN
ejpam-6752	289	7	,	,	PUNCT
ejpam-6752	289	8	the	the	DET
ejpam-6752	289	9	following	follow	VERB
ejpam-6752	289	10	linearly	linearly	ADV
ejpam-6752	289	11	independent	independent	ADJ
ejpam-6752	289	12	terms	term	NOUN
ejpam-6752	289	13	of	of	ADP
ejpam-6752	289	14	lyapunov	lyapunov	ADJ
ejpam-6752	289	15	quantities	quantity	NOUN
ejpam-6752	289	16	are	be	AUX
ejpam-6752	289	17	given	give	VERB
ejpam-6752	289	18	by	by	ADP
ejpam-6752	289	19	eq	eq	PROPN
ejpam-6752	289	20	.	.	PUNCT
ejpam-6752	290	1	(	(	PUNCT
ejpam-6752	290	2	13	13	NUM
ejpam-6752	290	3	):	):	PUNCT
ejpam-6752	290	4	(	(	PUNCT
ejpam-6752	290	5	i	i	NOUN
ejpam-6752	290	6	)	)	PUNCT
ejpam-6752	290	7	l11	l11	PROPN
ejpam-6752	290	8	=	=	PUNCT
ejpam-6752	291	1	−	−	PROPN
ejpam-6752	291	2	√	√	NUM
ejpam-6752	291	3	3	3	NUM
ejpam-6752	291	4	156(14a1	156(14a1	NUM
ejpam-6752	292	1	−	−	NUM
ejpam-6752	292	2	54b1	54b1	NUM
ejpam-6752	292	3	−	−	PROPN
ejpam-6752	292	4	9c1	9c1	NOUN
ejpam-6752	293	1	−	−	NOUN
ejpam-6752	293	2	15d1	15d1	NUM
ejpam-6752	293	3	)	)	PUNCT
ejpam-6752	293	4	.	.	PUNCT
ejpam-6752	294	1	(	(	PUNCT
ejpam-6752	294	2	ii	ii	NOUN
ejpam-6752	294	3	)	)	PUNCT
ejpam-6752	294	4	l21	l21	NOUN
ejpam-6752	294	5	=	=	PUNCT
ejpam-6752	295	1	3	3	NUM
ejpam-6752	295	2	√	√	NUM
ejpam-6752	295	3	3	3	NUM
ejpam-6752	295	4	21632(2254a1	21632(2254a1	NUM
ejpam-6752	295	5	−	−	NOUN
ejpam-6752	295	6	4534b1	4534b1	ADV
ejpam-6752	295	7	−	−	PROPN
ejpam-6752	295	8	1969c1	1969c1	NOUN
ejpam-6752	295	9	−	−	NOUN
ejpam-6752	295	10	855d1	855d1	NUM
ejpam-6752	295	11	)	)	PUNCT
ejpam-6752	295	12	.	.	PUNCT
ejpam-6752	296	1	the	the	DET
ejpam-6752	296	2	origin	origin	NOUN
ejpam-6752	296	3	of	of	ADP
ejpam-6752	296	4	system	system	NOUN
ejpam-6752	296	5	(	(	PUNCT
ejpam-6752	296	6	6	6	NUM
ejpam-6752	296	7	)	)	PUNCT
ejpam-6752	296	8	is	be	AUX
ejpam-6752	296	9	weak	weak	ADJ
ejpam-6752	296	10	focus	focus	NOUN
ejpam-6752	296	11	of	of	ADP
ejpam-6752	296	12	order	order	NOUN
ejpam-6752	296	13	one	one	NOUN
ejpam-6752	296	14	if	if	SCONJ
ejpam-6752	296	15	and	and	CCONJ
ejpam-6752	296	16	only	only	ADV
ejpam-6752	296	17	if	if	SCONJ
ejpam-6752	296	18	a1	a1	NOUN
ejpam-6752	296	19	=	=	SYM
ejpam-6752	296	20	1	1	NUM
ejpam-6752	296	21	14	14	NUM
ejpam-6752	296	22	(	(	PUNCT
ejpam-6752	296	23	54b1	54b1	NUM
ejpam-6752	296	24	+	+	NUM
ejpam-6752	296	25	9c1	9c1	NUM
ejpam-6752	296	26	+	+	CCONJ
ejpam-6752	296	27	15d1	15d1	NUM
ejpam-6752	296	28	)	)	PUNCT
ejpam-6752	296	29	.	.	PUNCT
ejpam-6752	297	1	(	(	PUNCT
ejpam-6752	297	2	21	21	NUM
ejpam-6752	297	3	)	)	PUNCT
ejpam-6752	297	4	since	since	SCONJ
ejpam-6752	297	5	the	the	DET
ejpam-6752	297	6	jacobian	jacobian	NOUN
ejpam-6752	297	7	of	of	ADP
ejpam-6752	297	8	l11	l11	PROPN
ejpam-6752	297	9	and	and	CCONJ
ejpam-6752	297	10	l21	l21	NOUN
ejpam-6752	297	11	with	with	ADP
ejpam-6752	297	12	respect	respect	NOUN
ejpam-6752	297	13	to	to	ADP
ejpam-6752	297	14	a1	a1	NOUN
ejpam-6752	297	15	and	and	CCONJ
ejpam-6752	297	16	b1	b1	NOUN
ejpam-6752	297	17	is	be	AUX
ejpam-6752	297	18	non	non	ADJ
ejpam-6752	297	19	-	-	ADJ
ejpam-6752	297	20	zero	zero	NUM
ejpam-6752	297	21	,	,	PUNCT
ejpam-6752	297	22	it	it	PRON
ejpam-6752	297	23	indicates	indicate	VERB
ejpam-6752	297	24	that	that	SCONJ
ejpam-6752	297	25	,	,	PUNCT
ejpam-6752	297	26	by	by	ADP
ejpam-6752	297	27	suitable	suitable	ADJ
ejpam-6752	297	28	perturbation	perturbation	NOUN
ejpam-6752	297	29	of	of	ADP
ejpam-6752	297	30	the	the	DET
ejpam-6752	297	31	coefficients	coefficient	NOUN
ejpam-6752	297	32	of	of	ADP
ejpam-6752	297	33	the	the	DET
ejpam-6752	297	34	lyapunov	lyapunov	ADJ
ejpam-6752	297	35	quantities	quantity	NOUN
ejpam-6752	297	36	,	,	PUNCT
ejpam-6752	297	37	only	only	ADV
ejpam-6752	297	38	one	one	NUM
ejpam-6752	297	39	limit	limit	NOUN
ejpam-6752	297	40	cycle	cycle	NOUN
ejpam-6752	297	41	can	can	AUX
ejpam-6752	297	42	be	be	AUX
ejpam-6752	297	43	bifurcated	bifurcate	VERB
ejpam-6752	297	44	from	from	ADP
ejpam-6752	297	45	the	the	DET
ejpam-6752	297	46	equilibrium	equilibrium	NOUN
ejpam-6752	297	47	point	point	NOUN
ejpam-6752	297	48	e	e	NOUN
ejpam-6752	297	49	of	of	ADP
ejpam-6752	297	50	system	system	NOUN
ejpam-6752	297	51	(	(	PUNCT
ejpam-6752	297	52	1	1	NUM
ejpam-6752	297	53	)	)	PUNCT
ejpam-6752	297	54	in	in	ADP
ejpam-6752	297	55	the	the	DET
ejpam-6752	297	56	neighborhood	neighborhood	NOUN
ejpam-6752	297	57	of	of	ADP
ejpam-6752	297	58	that	that	DET
ejpam-6752	297	59	point	point	NOUN
ejpam-6752	297	60	.	.	PUNCT
ejpam-6752	298	1	if	if	SCONJ
ejpam-6752	298	2	we	we	PRON
ejpam-6752	298	3	take	take	VERB
ejpam-6752	298	4	b1	b1	NOUN
ejpam-6752	298	5	=	=	SYM
ejpam-6752	298	6	c1	c1	PROPN
ejpam-6752	298	7	=	=	PUNCT
ejpam-6752	298	8	d1	d1	PROPN
ejpam-6752	298	9	=	=	SYM
ejpam-6752	298	10	0.1	0.1	NUM
ejpam-6752	298	11	as	as	ADP
ejpam-6752	298	12	a	a	DET
ejpam-6752	298	13	numerical	numerical	ADJ
ejpam-6752	298	14	example	example	NOUN
ejpam-6752	298	15	,	,	PUNCT
ejpam-6752	298	16	then	then	ADV
ejpam-6752	298	17	from	from	ADP
ejpam-6752	298	18	equation	equation	NOUN
ejpam-6752	298	19	(	(	PUNCT
ejpam-6752	298	20	21	21	NUM
ejpam-6752	298	21	)	)	PUNCT
ejpam-6752	298	22	,	,	PUNCT
ejpam-6752	298	23	we	we	PRON
ejpam-6752	298	24	obtain	obtain	VERB
ejpam-6752	298	25	a1	a1	NOUN
ejpam-6752	298	26	=	=	NOUN
ejpam-6752	298	27	39	39	NUM
ejpam-6752	298	28	70	70	NUM
ejpam-6752	298	29	and	and	CCONJ
ejpam-6752	298	30	a	a	DET
ejpam-6752	298	31	limit	limit	NOUN
ejpam-6752	298	32	cycle	cycle	NOUN
ejpam-6752	298	33	is	be	AUX
ejpam-6752	298	34	observed	observe	VERB
ejpam-6752	298	35	from	from	ADP
ejpam-6752	298	36	the	the	DET
ejpam-6752	298	37	first	first	ADJ
ejpam-6752	298	38	-	-	PUNCT
ejpam-6752	298	39	order	order	NOUN
ejpam-6752	298	40	perturbation	perturbation	NOUN
ejpam-6752	298	41	.	.	PUNCT
ejpam-6752	299	1	from	from	ADP
ejpam-6752	299	2	fig	fig	NOUN
ejpam-6752	299	3	.	.	PUNCT
ejpam-6752	300	1	4	4	NUM
ejpam-6752	300	2	,	,	PUNCT
ejpam-6752	300	3	we	we	PRON
ejpam-6752	300	4	note	note	VERB
ejpam-6752	300	5	that	that	SCONJ
ejpam-6752	300	6	the	the	DET
ejpam-6752	300	7	blue	blue	ADJ
ejpam-6752	300	8	trajectory	trajectory	NOUN
ejpam-6752	300	9	moves	move	VERB
ejpam-6752	300	10	inward	inward	ADV
ejpam-6752	300	11	toward	toward	ADP
ejpam-6752	300	12	the	the	DET
ejpam-6752	300	13	equilibrium	equilibrium	NOUN
ejpam-6752	300	14	point	point	NOUN
ejpam-6752	300	15	,	,	PUNCT
ejpam-6752	300	16	while	while	SCONJ
ejpam-6752	300	17	the	the	DET
ejpam-6752	300	18	red	red	ADJ
ejpam-6752	300	19	trajectory	trajectory	NOUN
ejpam-6752	300	20	moves	move	VERB
ejpam-6752	300	21	outward	outward	ADV
ejpam-6752	300	22	.	.	PUNCT
ejpam-6752	301	1	this	this	PRON
ejpam-6752	301	2	predicts	predict	VERB
ejpam-6752	301	3	that	that	SCONJ
ejpam-6752	301	4	there	there	PRON
ejpam-6752	301	5	may	may	AUX
ejpam-6752	301	6	be	be	AUX
ejpam-6752	301	7	a	a	DET
ejpam-6752	301	8	limit	limit	NOUN
ejpam-6752	301	9	cycle	cycle	NOUN
ejpam-6752	301	10	located	locate	VERB
ejpam-6752	301	11	in	in	ADP
ejpam-6752	301	12	a	a	DET
ejpam-6752	301	13	region	region	NOUN
ejpam-6752	301	14	between	between	ADP
ejpam-6752	301	15	the	the	DET
ejpam-6752	301	16	two	two	NUM
ejpam-6752	301	17	initial	initial	ADJ
ejpam-6752	301	18	points	point	NOUN
ejpam-6752	301	19	,	,	PUNCT
ejpam-6752	301	20	although	although	SCONJ
ejpam-6752	301	21	determining	determine	VERB
ejpam-6752	301	22	the	the	DET
ejpam-6752	301	23	existence	existence	NOUN
ejpam-6752	301	24	of	of	ADP
ejpam-6752	301	25	the	the	DET
ejpam-6752	301	26	limit	limit	NOUN
ejpam-6752	301	27	cycle	cycle	NOUN
ejpam-6752	301	28	is	be	AUX
ejpam-6752	301	29	not	not	PART
ejpam-6752	301	30	an	an	DET
ejpam-6752	301	31	easy	easy	ADJ
ejpam-6752	301	32	task	task	NOUN
ejpam-6752	301	33	.	.	PUNCT
ejpam-6752	302	1	r.	r.	PROPN
ejpam-6752	302	2	h.	h.	PROPN
ejpam-6752	302	3	salih	salih	PROPN
ejpam-6752	302	4	/	/	SYM
ejpam-6752	302	5	eur	eur	PROPN
ejpam-6752	302	6	.	.	PUNCT
ejpam-6752	303	1	j.	j.	PROPN
ejpam-6752	303	2	pure	pure	PROPN
ejpam-6752	303	3	appl	appl	PROPN
ejpam-6752	303	4	.	.	PROPN
ejpam-6752	303	5	math	math	PROPN
ejpam-6752	303	6	,	,	PUNCT
ejpam-6752	303	7	18	18	NUM
ejpam-6752	303	8	(	(	PUNCT
ejpam-6752	303	9	4	4	NUM
ejpam-6752	303	10	)	)	PUNCT
ejpam-6752	303	11	(	(	PUNCT
ejpam-6752	303	12	2025	2025	NUM
ejpam-6752	303	13	)	)	PUNCT
ejpam-6752	303	14	,	,	PUNCT
ejpam-6752	303	15	6752	6752	NUM
ejpam-6752	303	16	12	12	NUM
ejpam-6752	303	17	of	of	ADP
ejpam-6752	303	18	14	14	NUM
ejpam-6752	303	19	figure	figure	NOUN
ejpam-6752	303	20	4	4	NUM
ejpam-6752	303	21	:	:	PUNCT
ejpam-6752	303	22	the	the	DET
ejpam-6752	303	23	phase	phase	NOUN
ejpam-6752	303	24	portrait	portrait	NOUN
ejpam-6752	303	25	of	of	ADP
ejpam-6752	303	26	system	system	NOUN
ejpam-6752	303	27	(	(	PUNCT
ejpam-6752	303	28	1	1	NUM
ejpam-6752	303	29	)	)	PUNCT
ejpam-6752	303	30	around	around	ADP
ejpam-6752	303	31	the	the	DET
ejpam-6752	303	32	positive	positive	ADJ
ejpam-6752	303	33	equilibrium	equilibrium	NOUN
ejpam-6752	303	34	point	point	NOUN
ejpam-6752	303	35	is	be	AUX
ejpam-6752	303	36	shown	show	VERB
ejpam-6752	303	37	.	.	PUNCT
ejpam-6752	304	1	the	the	DET
ejpam-6752	304	2	red	red	ADJ
ejpam-6752	304	3	and	and	CCONJ
ejpam-6752	304	4	green	green	ADJ
ejpam-6752	304	5	balls	ball	NOUN
ejpam-6752	304	6	indicate	indicate	VERB
ejpam-6752	304	7	the	the	DET
ejpam-6752	304	8	equilibrium	equilibrium	NOUN
ejpam-6752	304	9	point	point	NOUN
ejpam-6752	304	10	and	and	CCONJ
ejpam-6752	304	11	the	the	DET
ejpam-6752	304	12	initial	initial	ADJ
ejpam-6752	304	13	points	point	NOUN
ejpam-6752	304	14	,	,	PUNCT
ejpam-6752	304	15	respectively	respectively	ADV
ejpam-6752	304	16	.	.	PUNCT
ejpam-6752	305	1	it	it	PRON
ejpam-6752	305	2	is	be	AUX
ejpam-6752	305	3	also	also	ADV
ejpam-6752	305	4	observed	observe	VERB
ejpam-6752	305	5	that	that	SCONJ
ejpam-6752	305	6	applying	apply	VERB
ejpam-6752	305	7	the	the	DET
ejpam-6752	305	8	second	second	ADJ
ejpam-6752	305	9	-	-	PUNCT
ejpam-6752	305	10	order	order	NOUN
ejpam-6752	305	11	perturbation	perturbation	NOUN
ejpam-6752	305	12	in	in	ADP
ejpam-6752	305	13	eq	eq	ADP
ejpam-6752	305	14	.	.	PUNCT
ejpam-6752	306	1	(	(	PUNCT
ejpam-6752	306	2	14	14	NUM
ejpam-6752	306	3	)	)	PUNCT
ejpam-6752	306	4	does	do	AUX
ejpam-6752	306	5	not	not	PART
ejpam-6752	306	6	change	change	VERB
ejpam-6752	306	7	the	the	DET
ejpam-6752	306	8	outcome	outcome	NOUN
ejpam-6752	306	9	regarding	regard	VERB
ejpam-6752	306	10	the	the	DET
ejpam-6752	306	11	number	number	NOUN
ejpam-6752	306	12	of	of	ADP
ejpam-6752	306	13	perturbed	perturb	VERB
ejpam-6752	306	14	limit	limit	NOUN
ejpam-6752	306	15	cycles	cycle	NOUN
ejpam-6752	306	16	,	,	PUNCT
ejpam-6752	306	17	which	which	PRON
ejpam-6752	306	18	remains	remain	VERB
ejpam-6752	306	19	one	one	NUM
ejpam-6752	306	20	.	.	PUNCT
ejpam-6752	307	1	understanding	understand	VERB
ejpam-6752	307	2	the	the	DET
ejpam-6752	307	3	uniqueness	uniqueness	NOUN
ejpam-6752	307	4	of	of	ADP
ejpam-6752	307	5	the	the	DET
ejpam-6752	307	6	limit	limit	NOUN
ejpam-6752	307	7	cycle	cycle	NOUN
ejpam-6752	307	8	in	in	ADP
ejpam-6752	307	9	bimolecular	bimolecular	ADJ
ejpam-6752	307	10	mass	mass	ADJ
ejpam-6752	307	11	-	-	PUNCT
ejpam-6752	307	12	action	action	NOUN
ejpam-6752	307	13	systems	system	NOUN
ejpam-6752	307	14	has	have	VERB
ejpam-6752	307	15	important	important	ADJ
ejpam-6752	307	16	implications	implication	NOUN
ejpam-6752	307	17	for	for	ADP
ejpam-6752	307	18	chemical	chemical	NOUN
ejpam-6752	307	19	reaction	reaction	NOUN
ejpam-6752	307	20	dynamics	dynamic	NOUN
ejpam-6752	307	21	and	and	CCONJ
ejpam-6752	307	22	computational	computational	ADJ
ejpam-6752	307	23	chemistry	chemistry	NOUN
ejpam-6752	307	24	.	.	PUNCT
ejpam-6752	308	1	this	this	DET
ejpam-6752	308	2	framework	framework	NOUN
ejpam-6752	308	3	enhances	enhance	VERB
ejpam-6752	308	4	our	our	PRON
ejpam-6752	308	5	comprehension	comprehension	NOUN
ejpam-6752	308	6	of	of	ADP
ejpam-6752	308	7	chemical	chemical	NOUN
ejpam-6752	308	8	behavior	behavior	NOUN
ejpam-6752	308	9	under	under	ADP
ejpam-6752	308	10	varying	vary	VERB
ejpam-6752	308	11	conditions	condition	NOUN
ejpam-6752	308	12	,	,	PUNCT
ejpam-6752	308	13	aiding	aid	VERB
ejpam-6752	308	14	in	in	ADP
ejpam-6752	308	15	the	the	DET
ejpam-6752	308	16	prediction	prediction	NOUN
ejpam-6752	308	17	of	of	ADP
ejpam-6752	308	18	real	real	ADJ
ejpam-6752	308	19	-	-	PUNCT
ejpam-6752	308	20	world	world	NOUN
ejpam-6752	308	21	reaction	reaction	NOUN
ejpam-6752	308	22	outcomes	outcome	NOUN
ejpam-6752	308	23	.	.	PUNCT
ejpam-6752	309	1	additionally	additionally	ADV
ejpam-6752	309	2	,	,	PUNCT
ejpam-6752	309	3	these	these	DET
ejpam-6752	309	4	findings	finding	NOUN
ejpam-6752	309	5	can	can	AUX
ejpam-6752	309	6	improve	improve	VERB
ejpam-6752	309	7	computational	computational	ADJ
ejpam-6752	309	8	models	model	NOUN
ejpam-6752	309	9	,	,	PUNCT
ejpam-6752	309	10	enhancing	enhance	VERB
ejpam-6752	309	11	the	the	DET
ejpam-6752	309	12	accuracy	accuracy	NOUN
ejpam-6752	309	13	of	of	ADP
ejpam-6752	309	14	simulations	simulation	NOUN
ejpam-6752	309	15	for	for	ADP
ejpam-6752	309	16	complex	complex	ADJ
ejpam-6752	309	17	chemical	chemical	NOUN
ejpam-6752	309	18	networks	network	NOUN
ejpam-6752	309	19	.	.	PUNCT
ejpam-6752	310	1	by	by	ADP
ejpam-6752	310	2	connecting	connect	VERB
ejpam-6752	310	3	theory	theory	NOUN
ejpam-6752	310	4	with	with	ADP
ejpam-6752	310	5	practical	practical	ADJ
ejpam-6752	310	6	applications	application	NOUN
ejpam-6752	310	7	,	,	PUNCT
ejpam-6752	310	8	this	this	DET
ejpam-6752	310	9	research	research	NOUN
ejpam-6752	310	10	fosters	foster	VERB
ejpam-6752	310	11	a	a	DET
ejpam-6752	310	12	deeper	deep	ADJ
ejpam-6752	310	13	understanding	understanding	NOUN
ejpam-6752	310	14	of	of	ADP
ejpam-6752	310	15	chemical	chemical	NOUN
ejpam-6752	310	16	systems	system	NOUN
ejpam-6752	310	17	and	and	CCONJ
ejpam-6752	310	18	supports	support	VERB
ejpam-6752	310	19	future	future	ADJ
ejpam-6752	310	20	advancements	advancement	NOUN
ejpam-6752	310	21	in	in	ADP
ejpam-6752	310	22	the	the	DET
ejpam-6752	310	23	field	field	NOUN
ejpam-6752	310	24	.	.	PUNCT
ejpam-6752	311	1	5	5	X
ejpam-6752	311	2	.	.	X
ejpam-6752	311	3	conclusions	conclusion	NOUN
ejpam-6752	311	4	in	in	ADP
ejpam-6752	311	5	this	this	DET
ejpam-6752	311	6	paper	paper	NOUN
ejpam-6752	311	7	,	,	PUNCT
ejpam-6752	311	8	the	the	DET
ejpam-6752	311	9	smallest	small	ADJ
ejpam-6752	311	10	bimolecular	bimolecular	ADJ
ejpam-6752	311	11	mass	mass	ADJ
ejpam-6752	311	12	-	-	PUNCT
ejpam-6752	311	13	action	action	NOUN
ejpam-6752	311	14	system	system	NOUN
ejpam-6752	311	15	exhibiting	exhibit	VERB
ejpam-6752	311	16	a	a	DET
ejpam-6752	311	17	center	center	ADJ
ejpam-6752	311	18	equilibrium	equilibrium	NOUN
ejpam-6752	311	19	point	point	NOUN
ejpam-6752	311	20	is	be	AUX
ejpam-6752	311	21	studied	study	VERB
ejpam-6752	311	22	.	.	PUNCT
ejpam-6752	312	1	it	it	PRON
ejpam-6752	312	2	has	have	AUX
ejpam-6752	312	3	previously	previously	ADV
ejpam-6752	312	4	been	be	AUX
ejpam-6752	312	5	shown	show	VERB
ejpam-6752	312	6	that	that	SCONJ
ejpam-6752	312	7	when	when	SCONJ
ejpam-6752	312	8	a	a	DET
ejpam-6752	312	9	key	key	ADJ
ejpam-6752	312	10	reaction	reaction	NOUN
ejpam-6752	312	11	rate	rate	NOUN
ejpam-6752	312	12	parameter	parameter	PROPN
ejpam-6752	312	13	k1	k1	PROPN
ejpam-6752	312	14	satisfies	satisfie	NOUN
ejpam-6752	312	15	k1	k1	PROPN
ejpam-6752	312	16	=	=	SYM
ejpam-6752	312	17	k2	k2	PROPN
ejpam-6752	312	18	+	+	CCONJ
ejpam-6752	312	19	k3	k3	PROPN
ejpam-6752	312	20	,	,	PUNCT
ejpam-6752	312	21	the	the	DET
ejpam-6752	312	22	positive	positive	ADJ
ejpam-6752	312	23	equilibrium	equilibrium	NOUN
ejpam-6752	312	24	point	point	NOUN
ejpam-6752	312	25	was	be	AUX
ejpam-6752	312	26	classified	classify	VERB
ejpam-6752	312	27	as	as	ADP
ejpam-6752	312	28	a	a	DET
ejpam-6752	312	29	center	center	NOUN
ejpam-6752	312	30	and	and	CCONJ
ejpam-6752	312	31	a	a	DET
ejpam-6752	312	32	vertical	vertical	ADJ
ejpam-6752	312	33	andronov	andronov	NOUN
ejpam-6752	312	34	-	-	PUNCT
ejpam-6752	312	35	hopf	hopf	ADJ
ejpam-6752	312	36	bifurcation	bifurcation	NOUN
ejpam-6752	312	37	was	be	AUX
ejpam-6752	312	38	observed	observe	VERB
ejpam-6752	312	39	.	.	PUNCT
ejpam-6752	313	1	the	the	DET
ejpam-6752	313	2	novelty	novelty	NOUN
ejpam-6752	313	3	of	of	ADP
ejpam-6752	313	4	this	this	DET
ejpam-6752	313	5	research	research	NOUN
ejpam-6752	313	6	lies	lie	VERB
ejpam-6752	313	7	in	in	ADP
ejpam-6752	313	8	determining	determine	VERB
ejpam-6752	313	9	how	how	SCONJ
ejpam-6752	313	10	many	many	ADJ
ejpam-6752	313	11	limit	limit	NOUN
ejpam-6752	313	12	cycles	cycle	NOUN
ejpam-6752	313	13	can	can	AUX
ejpam-6752	313	14	bifurcate	bifurcate	VERB
ejpam-6752	313	15	from	from	ADP
ejpam-6752	313	16	the	the	DET
ejpam-6752	313	17	center	center	ADJ
ejpam-6752	313	18	equilibrium	equilibrium	NOUN
ejpam-6752	313	19	point	point	NOUN
ejpam-6752	313	20	.	.	PUNCT
ejpam-6752	314	1	using	use	VERB
ejpam-6752	314	2	a	a	DET
ejpam-6752	314	3	perturbation	perturbation	NOUN
ejpam-6752	314	4	technique	technique	NOUN
ejpam-6752	314	5	,	,	PUNCT
ejpam-6752	314	6	the	the	DET
ejpam-6752	314	7	number	number	NOUN
ejpam-6752	314	8	of	of	ADP
ejpam-6752	314	9	limit	limit	NOUN
ejpam-6752	314	10	cycles	cycle	NOUN
ejpam-6752	314	11	bifurcating	bifurcate	VERB
ejpam-6752	314	12	from	from	ADP
ejpam-6752	314	13	the	the	DET
ejpam-6752	314	14	center	center	ADJ
ejpam-6752	314	15	equilibrium	equilibrium	NOUN
ejpam-6752	314	16	point	point	NOUN
ejpam-6752	314	17	is	be	AUX
ejpam-6752	314	18	estimated	estimate	VERB
ejpam-6752	314	19	and	and	CCONJ
ejpam-6752	314	20	it	it	PRON
ejpam-6752	314	21	is	be	AUX
ejpam-6752	314	22	concluded	conclude	VERB
ejpam-6752	314	23	that	that	SCONJ
ejpam-6752	314	24	only	only	ADV
ejpam-6752	314	25	one	one	NUM
ejpam-6752	314	26	limit	limit	NOUN
ejpam-6752	314	27	cycle	cycle	NOUN
ejpam-6752	314	28	can	can	AUX
ejpam-6752	314	29	emerge	emerge	VERB
ejpam-6752	314	30	.	.	PUNCT
ejpam-6752	315	1	these	these	DET
ejpam-6752	315	2	findings	finding	NOUN
ejpam-6752	315	3	enhance	enhance	VERB
ejpam-6752	315	4	the	the	DET
ejpam-6752	315	5	understanding	understanding	NOUN
ejpam-6752	315	6	of	of	ADP
ejpam-6752	315	7	the	the	DET
ejpam-6752	315	8	dynamics	dynamic	NOUN
ejpam-6752	315	9	of	of	ADP
ejpam-6752	315	10	bimolecular	bimolecular	ADJ
ejpam-6752	315	11	reaction	reaction	NOUN
ejpam-6752	315	12	networks	network	NOUN
ejpam-6752	315	13	and	and	CCONJ
ejpam-6752	315	14	provide	provide	VERB
ejpam-6752	315	15	a	a	DET
ejpam-6752	315	16	foundation	foundation	NOUN
ejpam-6752	315	17	for	for	ADP
ejpam-6752	315	18	further	further	ADJ
ejpam-6752	315	19	research	research	NOUN
ejpam-6752	315	20	on	on	ADP
ejpam-6752	315	21	the	the	DET
ejpam-6752	315	22	bifurcation	bifurcation	NOUN
ejpam-6752	315	23	behavior	behavior	NOUN
ejpam-6752	315	24	of	of	ADP
ejpam-6752	315	25	r.	r.	PROPN
ejpam-6752	315	26	h.	h.	PROPN
ejpam-6752	315	27	salih	salih	PROPN
ejpam-6752	315	28	/	/	SYM
ejpam-6752	315	29	eur	eur	PROPN
ejpam-6752	315	30	.	.	PUNCT
ejpam-6752	316	1	j.	j.	PROPN
ejpam-6752	316	2	pure	pure	PROPN
ejpam-6752	316	3	appl	appl	PROPN
ejpam-6752	316	4	.	.	PROPN
ejpam-6752	316	5	math	math	PROPN
ejpam-6752	316	6	,	,	PUNCT
ejpam-6752	316	7	18	18	NUM
ejpam-6752	316	8	(	(	PUNCT
ejpam-6752	316	9	4	4	NUM
ejpam-6752	316	10	)	)	PUNCT
ejpam-6752	316	11	(	(	PUNCT
ejpam-6752	316	12	2025	2025	NUM
ejpam-6752	316	13	)	)	PUNCT
ejpam-6752	316	14	,	,	PUNCT
ejpam-6752	316	15	6752	6752	NUM
ejpam-6752	316	16	13	13	NUM
ejpam-6752	316	17	of	of	ADP
ejpam-6752	316	18	14	14	NUM
ejpam-6752	316	19	complex	complex	ADJ
ejpam-6752	316	20	chemical	chemical	NOUN
ejpam-6752	316	21	systems	system	NOUN
ejpam-6752	316	22	.	.	PUNCT
ejpam-6752	317	1	the	the	DET
ejpam-6752	317	2	presence	presence	NOUN
ejpam-6752	317	3	of	of	ADP
ejpam-6752	317	4	the	the	DET
ejpam-6752	317	5	limit	limit	NOUN
ejpam-6752	317	6	cycle	cycle	NOUN
ejpam-6752	317	7	is	be	AUX
ejpam-6752	317	8	important	important	ADJ
ejpam-6752	317	9	because	because	SCONJ
ejpam-6752	317	10	it	it	PRON
ejpam-6752	317	11	offers	offer	VERB
ejpam-6752	317	12	valuable	valuable	ADJ
ejpam-6752	317	13	insights	insight	NOUN
ejpam-6752	317	14	into	into	ADP
ejpam-6752	317	15	the	the	DET
ejpam-6752	317	16	stability	stability	NOUN
ejpam-6752	317	17	and	and	CCONJ
ejpam-6752	317	18	behavior	behavior	NOUN
ejpam-6752	317	19	of	of	ADP
ejpam-6752	317	20	chemical	chemical	ADJ
ejpam-6752	317	21	reaction	reaction	NOUN
ejpam-6752	317	22	networks	network	NOUN
ejpam-6752	317	23	,	,	PUNCT
ejpam-6752	317	24	forming	form	VERB
ejpam-6752	317	25	a	a	DET
ejpam-6752	317	26	foundation	foundation	NOUN
ejpam-6752	317	27	for	for	ADP
ejpam-6752	317	28	comprehending	comprehend	VERB
ejpam-6752	317	29	more	more	ADJ
ejpam-6752	317	30	complex	complex	ADJ
ejpam-6752	317	31	systems	system	NOUN
ejpam-6752	317	32	.	.	PUNCT
ejpam-6752	318	1	future	future	ADJ
ejpam-6752	318	2	studies	study	NOUN
ejpam-6752	318	3	could	could	AUX
ejpam-6752	318	4	focus	focus	VERB
ejpam-6752	318	5	on	on	ADP
ejpam-6752	318	6	higher	higher	ADV
ejpam-6752	318	7	-	-	PUNCT
ejpam-6752	318	8	dimensional	dimensional	ADJ
ejpam-6752	318	9	mass	mass	ADJ
ejpam-6752	318	10	-	-	PUNCT
ejpam-6752	318	11	action	action	NOUN
ejpam-6752	318	12	systems	system	NOUN
ejpam-6752	318	13	,	,	PUNCT
ejpam-6752	318	14	which	which	PRON
ejpam-6752	318	15	might	might	AUX
ejpam-6752	318	16	display	display	VERB
ejpam-6752	318	17	more	more	ADV
ejpam-6752	318	18	complex	complex	ADJ
ejpam-6752	318	19	bifurcation	bifurcation	NOUN
ejpam-6752	318	20	patterns	pattern	NOUN
ejpam-6752	318	21	.	.	PUNCT
ejpam-6752	319	1	furthermore	furthermore	ADV
ejpam-6752	319	2	,	,	PUNCT
ejpam-6752	319	3	examining	examine	VERB
ejpam-6752	319	4	the	the	DET
ejpam-6752	319	5	implications	implication	NOUN
ejpam-6752	319	6	of	of	ADP
ejpam-6752	319	7	these	these	DET
ejpam-6752	319	8	results	result	NOUN
ejpam-6752	319	9	in	in	ADP
ejpam-6752	319	10	practical	practical	ADJ
ejpam-6752	319	11	chemical	chemical	NOUN
ejpam-6752	319	12	processes	process	NOUN
ejpam-6752	319	13	and	and	CCONJ
ejpam-6752	319	14	integrating	integrate	VERB
ejpam-6752	319	15	them	they	PRON
ejpam-6752	319	16	into	into	ADP
ejpam-6752	319	17	computational	computational	ADJ
ejpam-6752	319	18	models	model	NOUN
ejpam-6752	319	19	could	could	AUX
ejpam-6752	319	20	deepen	deepen	VERB
ejpam-6752	319	21	our	our	PRON
ejpam-6752	319	22	understanding	understanding	NOUN
ejpam-6752	319	23	and	and	CCONJ
ejpam-6752	319	24	application	application	NOUN
ejpam-6752	319	25	of	of	ADP
ejpam-6752	319	26	dynamical	dynamical	ADJ
ejpam-6752	319	27	systems	system	NOUN
ejpam-6752	319	28	in	in	ADP
ejpam-6752	319	29	chemistry	chemistry	NOUN
ejpam-6752	319	30	.	.	PUNCT
ejpam-6752	320	1	references	reference	NOUN
ejpam-6752	320	2	[	[	X
ejpam-6752	320	3	1	1	X
ejpam-6752	320	4	]	]	PUNCT
ejpam-6752	320	5	rachel	rachel	PROPN
ejpam-6752	320	6	s	s	PROPN
ejpam-6752	321	1	lawrence	lawrence	PROPN
ejpam-6752	321	2	.	.	PUNCT
ejpam-6752	321	3	simplicial	simplicial	PROPN
ejpam-6752	321	4	reaction	reaction	NOUN
ejpam-6752	321	5	networks	network	NOUN
ejpam-6752	321	6	and	and	CCONJ
ejpam-6752	321	7	dynamics	dynamic	NOUN
ejpam-6752	321	8	on	on	ADP
ejpam-6752	321	9	graphs	graph	NOUN
ejpam-6752	321	10	.	.	PUNCT
ejpam-6752	322	1	phd	phd	NOUN
ejpam-6752	322	2	thesis	thesis	PROPN
ejpam-6752	322	3	,	,	PUNCT
ejpam-6752	322	4	university	university	PROPN
ejpam-6752	322	5	of	of	ADP
ejpam-6752	322	6	california	california	PROPN
ejpam-6752	322	7	,	,	PUNCT
ejpam-6752	322	8	berkeley	berkeley	PROPN
ejpam-6752	322	9	,	,	PUNCT
ejpam-6752	322	10	2023	2023	NUM
ejpam-6752	322	11	.	.	PUNCT
ejpam-6752	323	1	[	[	X
ejpam-6752	323	2	2	2	NUM
ejpam-6752	323	3	]	]	PUNCT
ejpam-6752	323	4	thomas	thomas	PROPN
ejpam-6752	323	5	wilhelm	wilhelm	PROPN
ejpam-6752	323	6	.	.	PUNCT
ejpam-6752	324	1	the	the	DET
ejpam-6752	324	2	smallest	small	ADJ
ejpam-6752	324	3	chemical	chemical	NOUN
ejpam-6752	324	4	reaction	reaction	NOUN
ejpam-6752	324	5	system	system	NOUN
ejpam-6752	324	6	with	with	ADP
ejpam-6752	324	7	bistability	bistability	NOUN
ejpam-6752	324	8	.	.	PUNCT
ejpam-6752	325	1	bmc	bmc	NOUN
ejpam-6752	325	2	systems	system	NOUN
ejpam-6752	325	3	biology	biology	NOUN
ejpam-6752	325	4	,	,	PUNCT
ejpam-6752	325	5	3:1–9	3:1–9	NUM
ejpam-6752	325	6	,	,	PUNCT
ejpam-6752	325	7	2009	2009	NUM
ejpam-6752	325	8	.	.	PUNCT
ejpam-6752	326	1	[	[	X
ejpam-6752	326	2	3	3	NUM
ejpam-6752	326	3	]	]	SYM
ejpam-6752	326	4	murad	murad	NOUN
ejpam-6752	326	5	banaji	banaji	PROPN
ejpam-6752	326	6	and	and	CCONJ
ejpam-6752	326	7	balázs	balázs	PROPN
ejpam-6752	326	8	boros	boros	PROPN
ejpam-6752	326	9	.	.	PUNCT
ejpam-6752	327	1	the	the	DET
ejpam-6752	327	2	smallest	small	ADJ
ejpam-6752	327	3	bimolecular	bimolecular	ADJ
ejpam-6752	327	4	mass	mass	NOUN
ejpam-6752	327	5	action	action	NOUN
ejpam-6752	327	6	reaction	reaction	NOUN
ejpam-6752	327	7	networks	network	NOUN
ejpam-6752	327	8	admitting	admit	VERB
ejpam-6752	327	9	andronov	andronov	ADJ
ejpam-6752	327	10	–	–	PUNCT
ejpam-6752	327	11	hopf	hopf	ADJ
ejpam-6752	327	12	bifurcation	bifurcation	NOUN
ejpam-6752	327	13	.	.	PUNCT
ejpam-6752	328	1	nonlinearity	nonlinearity	NOUN
ejpam-6752	328	2	,	,	PUNCT
ejpam-6752	328	3	36(2):1398	36(2):1398	NUM
ejpam-6752	328	4	,	,	PUNCT
ejpam-6752	328	5	2023	2023	NUM
ejpam-6752	328	6	.	.	PUNCT
ejpam-6752	329	1	[	[	X
ejpam-6752	329	2	4	4	NUM
ejpam-6752	329	3	]	]	SYM
ejpam-6752	329	4	murad	murad	NOUN
ejpam-6752	329	5	banaji	banaji	NOUN
ejpam-6752	329	6	,	,	PUNCT
ejpam-6752	329	7	balázs	balázs	PROPN
ejpam-6752	329	8	boros	boro	NOUN
ejpam-6752	329	9	,	,	PUNCT
ejpam-6752	329	10	and	and	CCONJ
ejpam-6752	329	11	josef	josef	PROPN
ejpam-6752	329	12	hofbauer	hofbauer	PROPN
ejpam-6752	329	13	.	.	PUNCT
ejpam-6752	330	1	the	the	DET
ejpam-6752	330	2	smallest	small	ADJ
ejpam-6752	330	3	bimolecular	bimolecular	ADJ
ejpam-6752	330	4	massaction	massaction	NOUN
ejpam-6752	330	5	system	system	NOUN
ejpam-6752	330	6	with	with	ADP
ejpam-6752	330	7	a	a	DET
ejpam-6752	330	8	vertical	vertical	ADJ
ejpam-6752	330	9	andronov	andronov	NOUN
ejpam-6752	330	10	–	–	PUNCT
ejpam-6752	330	11	hopf	hopf	ADJ
ejpam-6752	330	12	bifurcation	bifurcation	NOUN
ejpam-6752	330	13	.	.	PUNCT
ejpam-6752	331	1	applied	apply	VERB
ejpam-6752	331	2	mathematics	mathematics	NOUN
ejpam-6752	331	3	letters	letter	NOUN
ejpam-6752	331	4	,	,	PUNCT
ejpam-6752	331	5	143:108671	143:108671	NUM
ejpam-6752	331	6	,	,	PUNCT
ejpam-6752	331	7	2023	2023	NUM
ejpam-6752	331	8	.	.	PUNCT
ejpam-6752	332	1	[	[	X
ejpam-6752	332	2	5	5	NUM
ejpam-6752	332	3	]	]	X
ejpam-6752	332	4	balázs	balázs	PROPN
ejpam-6752	332	5	boros	boros	PROPN
ejpam-6752	332	6	and	and	CCONJ
ejpam-6752	332	7	josef	josef	PROPN
ejpam-6752	332	8	hofbauer	hofbauer	PROPN
ejpam-6752	332	9	.	.	PUNCT
ejpam-6752	333	1	limit	limit	NOUN
ejpam-6752	333	2	cycles	cycle	NOUN
ejpam-6752	333	3	in	in	ADP
ejpam-6752	333	4	mass	mass	NOUN
ejpam-6752	333	5	-	-	PUNCT
ejpam-6752	333	6	conserving	conserve	VERB
ejpam-6752	333	7	deficiency	deficiency	NOUN
ejpam-6752	333	8	-	-	PUNCT
ejpam-6752	333	9	one	one	NUM
ejpam-6752	333	10	mass	mass	ADJ
ejpam-6752	333	11	-	-	PUNCT
ejpam-6752	333	12	action	action	NOUN
ejpam-6752	333	13	systems	system	NOUN
ejpam-6752	333	14	.	.	PUNCT
ejpam-6752	334	1	electron	electron	PROPN
ejpam-6752	334	2	.	.	PUNCT
ejpam-6752	335	1	j.	j.	PROPN
ejpam-6752	335	2	qual	qual	PROPN
ejpam-6752	335	3	.	.	PROPN
ejpam-6752	335	4	theory	theory	NOUN
ejpam-6752	335	5	differ	differ	VERB
ejpam-6752	335	6	.	.	PUNCT
ejpam-6752	336	1	equ	equ	PROPN
ejpam-6752	336	2	.	.	PROPN
ejpam-6752	336	3	,	,	PUNCT
ejpam-6752	336	4	(	(	PUNCT
ejpam-6752	336	5	42):1–18	42):1–18	NUM
ejpam-6752	336	6	,	,	PUNCT
ejpam-6752	336	7	2022	2022	NUM
ejpam-6752	336	8	.	.	PUNCT
ejpam-6752	337	1	[	[	X
ejpam-6752	337	2	6	6	NUM
ejpam-6752	337	3	]	]	X
ejpam-6752	337	4	péter	péter	NOUN
ejpam-6752	337	5	érdi	érdi	PROPN
ejpam-6752	337	6	and	and	CCONJ
ejpam-6752	337	7	jános	jános	PROPN
ejpam-6752	337	8	tóth	tóth	PROPN
ejpam-6752	337	9	.	.	PUNCT
ejpam-6752	337	10	mathematical	mathematical	ADJ
ejpam-6752	337	11	models	model	NOUN
ejpam-6752	337	12	of	of	ADP
ejpam-6752	337	13	chemical	chemical	ADJ
ejpam-6752	337	14	reactions	reaction	NOUN
ejpam-6752	337	15	:	:	PUNCT
ejpam-6752	337	16	theory	theory	NOUN
ejpam-6752	337	17	and	and	CCONJ
ejpam-6752	337	18	applications	application	NOUN
ejpam-6752	337	19	of	of	ADP
ejpam-6752	337	20	deterministic	deterministic	ADJ
ejpam-6752	337	21	and	and	CCONJ
ejpam-6752	337	22	stochastic	stochastic	ADJ
ejpam-6752	337	23	models	model	NOUN
ejpam-6752	337	24	.	.	PUNCT
ejpam-6752	338	1	manchester	manchester	PROPN
ejpam-6752	338	2	university	university	PROPN
ejpam-6752	338	3	press	press	NOUN
ejpam-6752	338	4	,	,	PUNCT
ejpam-6752	338	5	1989	1989	NUM
ejpam-6752	338	6	.	.	PUNCT
ejpam-6752	339	1	[	[	X
ejpam-6752	339	2	7	7	X
ejpam-6752	339	3	]	]	X
ejpam-6752	339	4	gy	gy	NOUN
ejpam-6752	339	5	póta	póta	ADJ
ejpam-6752	339	6	.	.	PUNCT
ejpam-6752	340	1	two	two	NUM
ejpam-6752	340	2	-	-	PUNCT
ejpam-6752	340	3	component	component	NOUN
ejpam-6752	340	4	bimolecular	bimolecular	ADJ
ejpam-6752	340	5	systems	system	NOUN
ejpam-6752	340	6	can	can	AUX
ejpam-6752	340	7	not	not	PART
ejpam-6752	340	8	have	have	AUX
ejpam-6752	340	9	limit	limit	NOUN
ejpam-6752	340	10	cycles	cycle	NOUN
ejpam-6752	340	11	:	:	PUNCT
ejpam-6752	340	12	a	a	DET
ejpam-6752	340	13	complete	complete	ADJ
ejpam-6752	340	14	proof	proof	NOUN
ejpam-6752	340	15	.	.	PUNCT
ejpam-6752	341	1	the	the	DET
ejpam-6752	341	2	journal	journal	PROPN
ejpam-6752	341	3	of	of	ADP
ejpam-6752	341	4	chemical	chemical	PROPN
ejpam-6752	341	5	physics	physics	PROPN
ejpam-6752	341	6	,	,	PUNCT
ejpam-6752	341	7	78(3):1621–1622	78(3):1621–1622	NUM
ejpam-6752	341	8	,	,	PUNCT
ejpam-6752	341	9	1983	1983	NUM
ejpam-6752	341	10	.	.	PUNCT
ejpam-6752	342	1	[	[	X
ejpam-6752	342	2	8	8	X
ejpam-6752	342	3	]	]	PUNCT
ejpam-6752	342	4	györgy	györgy	NOUN
ejpam-6752	342	5	póta	póta	ADV
ejpam-6752	342	6	.	.	PUNCT
ejpam-6752	343	1	irregular	irregular	ADJ
ejpam-6752	343	2	behaviour	behaviour	NOUN
ejpam-6752	343	3	of	of	ADP
ejpam-6752	343	4	kinetic	kinetic	ADJ
ejpam-6752	343	5	equations	equation	NOUN
ejpam-6752	343	6	in	in	ADP
ejpam-6752	343	7	closed	closed	ADJ
ejpam-6752	343	8	chemical	chemical	NOUN
ejpam-6752	343	9	systems	system	NOUN
ejpam-6752	343	10	.	.	PUNCT
ejpam-6752	344	1	oscillatory	oscillatory	ADJ
ejpam-6752	344	2	effects	effect	NOUN
ejpam-6752	344	3	.	.	PUNCT
ejpam-6752	345	1	journal	journal	NOUN
ejpam-6752	345	2	of	of	ADP
ejpam-6752	345	3	the	the	DET
ejpam-6752	345	4	chemical	chemical	NOUN
ejpam-6752	345	5	society	society	NOUN
ejpam-6752	345	6	,	,	PUNCT
ejpam-6752	345	7	faraday	faraday	PROPN
ejpam-6752	345	8	transactions	transaction	NOUN
ejpam-6752	345	9	2	2	NUM
ejpam-6752	345	10	:	:	PUNCT
ejpam-6752	345	11	molecular	molecular	ADJ
ejpam-6752	345	12	and	and	CCONJ
ejpam-6752	345	13	chemical	chemical	NOUN
ejpam-6752	345	14	physics	physic	NOUN
ejpam-6752	345	15	,	,	PUNCT
ejpam-6752	345	16	81(1):115–121	81(1):115–121	NUM
ejpam-6752	345	17	,	,	PUNCT
ejpam-6752	345	18	1985	1985	NUM
ejpam-6752	345	19	.	.	PUNCT
ejpam-6752	346	1	[	[	X
ejpam-6752	346	2	9	9	NUM
ejpam-6752	346	3	]	]	PUNCT
ejpam-6752	346	4	thomas	thomas	PROPN
ejpam-6752	346	5	wilhelm	wilhelm	PROPN
ejpam-6752	346	6	and	and	CCONJ
ejpam-6752	346	7	reinhart	reinhart	PROPN
ejpam-6752	346	8	heinrich	heinrich	PROPN
ejpam-6752	346	9	.	.	PUNCT
ejpam-6752	347	1	smallest	small	ADJ
ejpam-6752	347	2	chemical	chemical	ADJ
ejpam-6752	347	3	reaction	reaction	NOUN
ejpam-6752	347	4	system	system	NOUN
ejpam-6752	347	5	with	with	ADP
ejpam-6752	347	6	hopf	hopf	ADJ
ejpam-6752	347	7	bifurcation	bifurcation	NOUN
ejpam-6752	347	8	.	.	PUNCT
ejpam-6752	348	1	journal	journal	PROPN
ejpam-6752	348	2	of	of	ADP
ejpam-6752	348	3	mathematical	mathematical	ADJ
ejpam-6752	348	4	chemistry	chemistry	NOUN
ejpam-6752	348	5	,	,	PUNCT
ejpam-6752	348	6	17(1):1–14	17(1):1–14	NUM
ejpam-6752	348	7	,	,	PUNCT
ejpam-6752	348	8	1995	1995	NUM
ejpam-6752	348	9	.	.	PUNCT
ejpam-6752	349	1	[	[	X
ejpam-6752	349	2	10	10	NUM
ejpam-6752	349	3	]	]	X
ejpam-6752	349	4	thomas	thomas	PROPN
ejpam-6752	349	5	wilhelm	wilhelm	PROPN
ejpam-6752	349	6	and	and	CCONJ
ejpam-6752	349	7	reinhart	reinhart	PROPN
ejpam-6752	349	8	heinrich	heinrich	PROPN
ejpam-6752	349	9	.	.	PUNCT
ejpam-6752	350	1	mathematical	mathematical	ADJ
ejpam-6752	350	2	analysis	analysis	NOUN
ejpam-6752	350	3	of	of	ADP
ejpam-6752	350	4	the	the	DET
ejpam-6752	350	5	smallest	small	ADJ
ejpam-6752	350	6	chemical	chemical	NOUN
ejpam-6752	350	7	reaction	reaction	NOUN
ejpam-6752	350	8	system	system	NOUN
ejpam-6752	350	9	with	with	ADP
ejpam-6752	350	10	hopf	hopf	ADJ
ejpam-6752	350	11	bifurcation	bifurcation	NOUN
ejpam-6752	350	12	.	.	PUNCT
ejpam-6752	351	1	journal	journal	PROPN
ejpam-6752	351	2	of	of	ADP
ejpam-6752	351	3	mathematical	mathematical	ADJ
ejpam-6752	351	4	chemistry	chemistry	NOUN
ejpam-6752	351	5	,	,	PUNCT
ejpam-6752	351	6	19(2):111–130	19(2):111–130	NOUN
ejpam-6752	351	7	,	,	PUNCT
ejpam-6752	351	8	1996	1996	NUM
ejpam-6752	351	9	.	.	PUNCT
ejpam-6752	352	1	[	[	X
ejpam-6752	352	2	11	11	NUM
ejpam-6752	352	3	]	]	PUNCT
ejpam-6752	352	4	rizgar	rizgar	PROPN
ejpam-6752	352	5	salih	salih	PROPN
ejpam-6752	352	6	.	.	PUNCT
ejpam-6752	353	1	hopf	hopf	ADJ
ejpam-6752	353	2	bifurcation	bifurcation	NOUN
ejpam-6752	353	3	and	and	CCONJ
ejpam-6752	353	4	centre	centre	NOUN
ejpam-6752	353	5	bifurcation	bifurcation	NOUN
ejpam-6752	353	6	in	in	ADP
ejpam-6752	353	7	three	three	NUM
ejpam-6752	353	8	dimensional	dimensional	ADJ
ejpam-6752	353	9	lotkavolterra	lotkavolterra	NOUN
ejpam-6752	353	10	systems	system	NOUN
ejpam-6752	353	11	.	.	PUNCT
ejpam-6752	354	1	phd	phd	NOUN
ejpam-6752	354	2	thesis	thesis	PROPN
ejpam-6752	354	3	,	,	PUNCT
ejpam-6752	354	4	plymouth	plymouth	PROPN
ejpam-6752	354	5	university	university	NOUN
ejpam-6752	354	6	,	,	PUNCT
ejpam-6752	354	7	2015	2015	NUM
ejpam-6752	354	8	.	.	PUNCT
ejpam-6752	355	1	[	[	X
ejpam-6752	355	2	12	12	NUM
ejpam-6752	355	3	]	]	PUNCT
ejpam-6752	355	4	rizgar	rizgar	NOUN
ejpam-6752	355	5	salih	salih	PROPN
ejpam-6752	355	6	and	and	CCONJ
ejpam-6752	355	7	mohammad	mohammad	PROPN
ejpam-6752	355	8	hasso	hasso	PROPN
ejpam-6752	355	9	.	.	PUNCT
ejpam-6752	356	1	centre	centre	NOUN
ejpam-6752	356	2	bifurcations	bifurcation	NOUN
ejpam-6752	356	3	of	of	ADP
ejpam-6752	356	4	periodic	periodic	ADJ
ejpam-6752	356	5	orbits	orbit	NOUN
ejpam-6752	356	6	for	for	ADP
ejpam-6752	356	7	some	some	DET
ejpam-6752	356	8	special	special	ADJ
ejpam-6752	356	9	three	three	NUM
ejpam-6752	356	10	dimensional	dimensional	ADJ
ejpam-6752	356	11	systems	system	NOUN
ejpam-6752	356	12	.	.	PUNCT
ejpam-6752	357	1	electronic	electronic	ADJ
ejpam-6752	357	2	journal	journal	NOUN
ejpam-6752	357	3	of	of	ADP
ejpam-6752	357	4	qualitative	qualitative	ADJ
ejpam-6752	357	5	theory	theory	NOUN
ejpam-6752	357	6	of	of	ADP
ejpam-6752	357	7	differential	differential	ADJ
ejpam-6752	357	8	equations	equation	NOUN
ejpam-6752	357	9	,	,	PUNCT
ejpam-6752	357	10	2017(19):1–10	2017(19):1–10	NUM
ejpam-6752	357	11	,	,	PUNCT
ejpam-6752	357	12	2017	2017	NUM
ejpam-6752	357	13	.	.	PUNCT
ejpam-6752	358	1	[	[	X
ejpam-6752	358	2	13	13	NUM
ejpam-6752	358	3	]	]	PUNCT
ejpam-6752	358	4	rizgar	rizgar	PROPN
ejpam-6752	358	5	salih	salih	PROPN
ejpam-6752	358	6	,	,	PUNCT
ejpam-6752	358	7	mohammad	mohammad	PROPN
ejpam-6752	358	8	hasso	hasso	PROPN
ejpam-6752	358	9	,	,	PUNCT
ejpam-6752	358	10	and	and	CCONJ
ejpam-6752	358	11	surma	surma	VERB
ejpam-6752	358	12	ibrahim	ibrahim	PROPN
ejpam-6752	358	13	.	.	PUNCT
ejpam-6752	359	1	centre	centre	NOUN
ejpam-6752	359	2	bifurcations	bifurcation	NOUN
ejpam-6752	359	3	for	for	ADP
ejpam-6752	359	4	a	a	DET
ejpam-6752	359	5	three	three	NUM
ejpam-6752	359	6	dimensional	dimensional	ADJ
ejpam-6752	359	7	system	system	NOUN
ejpam-6752	359	8	with	with	ADP
ejpam-6752	359	9	quadratic	quadratic	ADJ
ejpam-6752	359	10	terms	term	NOUN
ejpam-6752	359	11	.	.	PUNCT
ejpam-6752	360	1	zanco	zanco	PROPN
ejpam-6752	360	2	journal	journal	PROPN
ejpam-6752	360	3	of	of	ADP
ejpam-6752	360	4	pure	pure	ADJ
ejpam-6752	360	5	and	and	CCONJ
ejpam-6752	360	6	applied	applied	ADJ
ejpam-6752	360	7	sciences	science	NOUN
ejpam-6752	360	8	,	,	PUNCT
ejpam-6752	360	9	32(2):62–71	32(2):62–71	NUM
ejpam-6752	360	10	,	,	PUNCT
ejpam-6752	360	11	2020	2020	NUM
ejpam-6752	360	12	.	.	PUNCT
ejpam-6752	361	1	r.	r.	PROPN
ejpam-6752	361	2	h.	h.	PROPN
ejpam-6752	361	3	salih	salih	PROPN
ejpam-6752	361	4	/	/	SYM
ejpam-6752	361	5	eur	eur	PROPN
ejpam-6752	361	6	.	.	PUNCT
ejpam-6752	362	1	j.	j.	PROPN
ejpam-6752	362	2	pure	pure	PROPN
ejpam-6752	362	3	appl	appl	PROPN
ejpam-6752	362	4	.	.	PROPN
ejpam-6752	362	5	math	math	PROPN
ejpam-6752	362	6	,	,	PUNCT
ejpam-6752	362	7	18	18	NUM
ejpam-6752	362	8	(	(	PUNCT
ejpam-6752	362	9	4	4	NUM
ejpam-6752	362	10	)	)	PUNCT
ejpam-6752	362	11	(	(	PUNCT
ejpam-6752	362	12	2025	2025	NUM
ejpam-6752	362	13	)	)	PUNCT
ejpam-6752	362	14	,	,	PUNCT
ejpam-6752	362	15	6752	6752	NUM
ejpam-6752	362	16	14	14	NUM
ejpam-6752	362	17	of	of	ADP
ejpam-6752	362	18	14	14	NUM
ejpam-6752	362	19	[	[	X
ejpam-6752	362	20	14	14	NUM
ejpam-6752	362	21	]	]	X
ejpam-6752	362	22	john	john	PROPN
ejpam-6752	362	23	guckenheimer	guckenheimer	PROPN
ejpam-6752	362	24	and	and	CCONJ
ejpam-6752	362	25	philip	philip	PROPN
ejpam-6752	362	26	holmes	holmes	PROPN
ejpam-6752	362	27	.	.	PUNCT
ejpam-6752	363	1	nonlinear	nonlinear	ADJ
ejpam-6752	363	2	oscillations	oscillation	NOUN
ejpam-6752	363	3	,	,	PUNCT
ejpam-6752	363	4	dynamical	dynamical	ADJ
ejpam-6752	363	5	systems	system	NOUN
ejpam-6752	363	6	,	,	PUNCT
ejpam-6752	363	7	and	and	CCONJ
ejpam-6752	363	8	bifurcations	bifurcation	NOUN
ejpam-6752	363	9	of	of	ADP
ejpam-6752	363	10	vector	vector	NOUN
ejpam-6752	363	11	fields	field	NOUN
ejpam-6752	363	12	,	,	PUNCT
ejpam-6752	363	13	volume	volume	NOUN
ejpam-6752	363	14	42	42	NUM
ejpam-6752	363	15	.	.	PUNCT
ejpam-6752	364	1	springer	springer	PROPN
ejpam-6752	364	2	science	science	PROPN
ejpam-6752	364	3	&	&	CCONJ
ejpam-6752	364	4	business	business	NOUN
ejpam-6752	364	5	media	medium	NOUN
ejpam-6752	364	6	,	,	PUNCT
ejpam-6752	364	7	2013	2013	NUM
ejpam-6752	364	8	.	.	PUNCT
ejpam-6752	365	1	[	[	X
ejpam-6752	365	2	15	15	NUM
ejpam-6752	365	3	]	]	X
ejpam-6752	365	4	valery	valery	NOUN
ejpam-6752	365	5	romanovski	romanovski	PROPN
ejpam-6752	365	6	and	and	CCONJ
ejpam-6752	365	7	douglas	douglas	PROPN
ejpam-6752	365	8	shafer	shafer	PROPN
ejpam-6752	365	9	.	.	PUNCT
ejpam-6752	366	1	the	the	DET
ejpam-6752	366	2	center	center	NOUN
ejpam-6752	366	3	and	and	CCONJ
ejpam-6752	366	4	cyclicity	cyclicity	NOUN
ejpam-6752	366	5	problems	problem	NOUN
ejpam-6752	366	6	:	:	PUNCT
ejpam-6752	366	7	a	a	DET
ejpam-6752	366	8	computational	computational	ADJ
ejpam-6752	366	9	algebra	algebra	NOUN
ejpam-6752	366	10	approach	approach	NOUN
ejpam-6752	366	11	.	.	PUNCT
ejpam-6752	367	1	springer	springer	NOUN
ejpam-6752	367	2	science	science	PROPN
ejpam-6752	367	3	&	&	CCONJ
ejpam-6752	367	4	business	business	NOUN
ejpam-6752	367	5	media	medium	NOUN
ejpam-6752	367	6	,	,	PUNCT
ejpam-6752	367	7	2009	2009	NUM
ejpam-6752	367	8	.	.	PUNCT
ejpam-6752	368	1	[	[	X
ejpam-6752	368	2	16	16	NUM
ejpam-6752	368	3	]	]	X
ejpam-6752	368	4	nikolai	nikolai	PROPN
ejpam-6752	368	5	nikolaevich	nikolaevich	PROPN
ejpam-6752	368	6	bautin	bautin	PROPN
ejpam-6752	368	7	.	.	PUNCT
ejpam-6752	369	1	on	on	ADP
ejpam-6752	369	2	the	the	DET
ejpam-6752	369	3	number	number	NOUN
ejpam-6752	369	4	of	of	ADP
ejpam-6752	369	5	limit	limit	NOUN
ejpam-6752	369	6	cycles	cycle	NOUN
ejpam-6752	369	7	appearing	appear	VERB
ejpam-6752	369	8	with	with	ADP
ejpam-6752	369	9	variation	variation	NOUN
ejpam-6752	369	10	of	of	ADP
ejpam-6752	369	11	the	the	DET
ejpam-6752	369	12	coefficients	coefficient	NOUN
ejpam-6752	369	13	from	from	ADP
ejpam-6752	369	14	an	an	DET
ejpam-6752	369	15	equilibrium	equilibrium	NOUN
ejpam-6752	369	16	state	state	NOUN
ejpam-6752	369	17	of	of	ADP
ejpam-6752	369	18	the	the	DET
ejpam-6752	369	19	type	type	NOUN
ejpam-6752	369	20	of	of	ADP
ejpam-6752	369	21	a	a	DET
ejpam-6752	369	22	focus	focus	NOUN
ejpam-6752	369	23	or	or	CCONJ
ejpam-6752	369	24	a	a	DET
ejpam-6752	369	25	center	center	NOUN
ejpam-6752	369	26	.	.	PUNCT
ejpam-6752	370	1	matematicheskii	matematicheskii	PROPN
ejpam-6752	370	2	sbornik	sbornik	PROPN
ejpam-6752	370	3	,	,	PUNCT
ejpam-6752	370	4	72(1):181–196	72(1):181–196	NUM
ejpam-6752	370	5	,	,	PUNCT
ejpam-6752	370	6	1952	1952	NUM
ejpam-6752	370	7	.	.	PUNCT
ejpam-6752	371	1	[	[	X
ejpam-6752	371	2	17	17	NUM
ejpam-6752	371	3	]	]	X
ejpam-6752	371	4	p	p	X
ejpam-6752	371	5	yu	yu	PROPN
ejpam-6752	371	6	and	and	CCONJ
ejpam-6752	371	7	m	m	PROPN
ejpam-6752	371	8	han	han	PROPN
ejpam-6752	371	9	.	.	PROPN
ejpam-6752	371	10	twelve	twelve	NUM
ejpam-6752	371	11	limit	limit	NOUN
ejpam-6752	371	12	cycles	cycle	NOUN
ejpam-6752	371	13	in	in	ADP
ejpam-6752	371	14	a	a	DET
ejpam-6752	371	15	cubic	cubic	ADJ
ejpam-6752	371	16	order	order	NOUN
ejpam-6752	371	17	planar	planar	ADJ
ejpam-6752	371	18	system	system	NOUN
ejpam-6752	371	19	with	with	ADP
ejpam-6752	371	20	z˜	z˜	SYM
ejpam-6752	371	21	2	2	NUM
ejpam-6752	371	22	symmetry	symmetry	NOUN
ejpam-6752	371	23	.	.	PUNCT
ejpam-6752	372	1	communications	communication	NOUN
ejpam-6752	372	2	on	on	ADP
ejpam-6752	372	3	pure	pure	ADJ
ejpam-6752	372	4	and	and	CCONJ
ejpam-6752	372	5	applied	apply	VERB
ejpam-6752	372	6	analysis	analysis	NOUN
ejpam-6752	372	7	,	,	PUNCT
ejpam-6752	372	8	3:515–526	3:515–526	NUM
ejpam-6752	372	9	,	,	PUNCT
ejpam-6752	372	10	2004	2004	NUM
ejpam-6752	372	11	.	.	PUNCT
ejpam-6752	373	1	[	[	X
ejpam-6752	373	2	18	18	NUM
ejpam-6752	373	3	]	]	X
ejpam-6752	373	4	colin	colin	PROPN
ejpam-6752	373	5	christopher	christopher	PROPN
ejpam-6752	373	6	.	.	PUNCT
ejpam-6752	374	1	estimating	estimate	VERB
ejpam-6752	374	2	limit	limit	NOUN
ejpam-6752	374	3	cycle	cycle	NOUN
ejpam-6752	374	4	bifurcations	bifurcation	NOUN
ejpam-6752	374	5	from	from	ADP
ejpam-6752	374	6	centers	center	NOUN
ejpam-6752	374	7	.	.	PUNCT
ejpam-6752	375	1	in	in	ADP
ejpam-6752	375	2	differential	differential	ADJ
ejpam-6752	375	3	equations	equation	NOUN
ejpam-6752	375	4	with	with	ADP
ejpam-6752	375	5	symbolic	symbolic	ADJ
ejpam-6752	375	6	computation	computation	NOUN
ejpam-6752	375	7	,	,	PUNCT
ejpam-6752	375	8	pages	page	NOUN
ejpam-6752	375	9	23–35	23–35	NUM
ejpam-6752	375	10	.	.	PUNCT
ejpam-6752	375	11	springer	springer	NOUN
ejpam-6752	375	12	,	,	PUNCT
ejpam-6752	375	13	2005	2005	NUM
ejpam-6752	375	14	.	.	PUNCT