id	sid	tid	token	lemma	pos
ajst-2833	1	1	academic	academic	ADJ
ajst-2833	1	2	journal	journal	NOUN
ajst-2833	1	3	of	of	ADP
ajst-2833	1	4	science	science	NOUN
ajst-2833	1	5	and	and	CCONJ
ajst-2833	1	6	technology	technology	NOUN
ajst-2833	1	7	issn	issn	NOUN
ajst-2833	1	8	:	:	PUNCT
ajst-2833	1	9	2771	2771	NUM
ajst-2833	1	10	-	-	SYM
ajst-2833	1	11	3032	3032	NUM
ajst-2833	1	12	|	|	NOUN
ajst-2833	1	13	vol	vol	NOUN
ajst-2833	1	14	.	.	PROPN
ajst-2833	2	1	3	3	NUM
ajst-2833	2	2	,	,	PUNCT
ajst-2833	2	3	no	no	INTJ
ajst-2833	2	4	.	.	NOUN
ajst-2833	2	5	3	3	NUM
ajst-2833	2	6	,	,	PUNCT
ajst-2833	2	7	2022	2022	NUM
ajst-2833	2	8	119	119	NUM
ajst-2833	2	9	complicate	complicate	NOUN
ajst-2833	2	10	dynamics	dynamic	NOUN
ajst-2833	2	11	of	of	ADP
ajst-2833	2	12	a	a	DET
ajst-2833	2	13	discrete	discrete	ADJ
ajst-2833	2	14	predator‐prey	predator‐prey	PROPN
ajst-2833	2	15	model	model	NOUN
ajst-2833	2	16	with	with	ADP
ajst-2833	2	17	competition	competition	NOUN
ajst-2833	2	18	between	between	ADP
ajst-2833	2	19	predators	predator	NOUN
ajst-2833	2	20	shaosan	shaosan	PROPN
ajst-2833	2	21	xia1	xia1	PROPN
ajst-2833	2	22	,	,	PUNCT
ajst-2833	2	23	a	a	PRON
ajst-2833	2	24	,	,	PUNCT
ajst-2833	2	25	xianyi	xianyi	PROPN
ajst-2833	2	26	li1	li1	PROPN
ajst-2833	2	27	,	,	PUNCT
ajst-2833	2	28	b	b	NOUN
ajst-2833	2	29	,	,	PUNCT
ajst-2833	2	30	*	*	PROPN
ajst-2833	2	31	1department	1department	NUM
ajst-2833	2	32	of	of	ADP
ajst-2833	2	33	big	big	ADJ
ajst-2833	2	34	data	datum	NOUN
ajst-2833	2	35	science	science	NOUN
ajst-2833	2	36	,	,	PUNCT
ajst-2833	2	37	school	school	NOUN
ajst-2833	2	38	of	of	ADP
ajst-2833	2	39	science	science	NOUN
ajst-2833	2	40	,	,	PUNCT
ajst-2833	2	41	zhejiang	zhejiang	PROPN
ajst-2833	2	42	university	university	PROPN
ajst-2833	2	43	of	of	ADP
ajst-2833	2	44	science	science	NOUN
ajst-2833	2	45	and	and	CCONJ
ajst-2833	2	46	technology	technology	NOUN
ajst-2833	2	47	,	,	PUNCT
ajst-2833	2	48	hangzhou	hangzhou	PROPN
ajst-2833	2	49	,	,	PUNCT
ajst-2833	2	50	310023	310023	NUM
ajst-2833	2	51	,	,	PUNCT
ajst-2833	2	52	china	china	PROPN
ajst-2833	2	53	ae	ae	PROPN
ajst-2833	2	54	-	-	PUNCT
ajst-2833	2	55	mail	mail	NOUN
ajst-2833	2	56	:	:	PUNCT
ajst-2833	2	57	ssxia96@163.com	ssxia96@163.com	NOUN
ajst-2833	2	58	,	,	PUNCT
ajst-2833	2	59	bmathxyli@zust.edu.cn	bmathxyli@zust.edu.cn	NOUN
ajst-2833	2	60	*	*	SYM
ajst-2833	2	61	correspondence	correspondence	NOUN
ajst-2833	2	62	author	author	NOUN
ajst-2833	2	63	:	:	PUNCT
ajst-2833	3	1	xianyi	xianyi	PROPN
ajst-2833	3	2	li	li	PROPN
ajst-2833	4	1	abstract	abstract	PROPN
ajst-2833	4	2	:	:	PUNCT
ajst-2833	4	3	we	we	PRON
ajst-2833	4	4	consider	consider	VERB
ajst-2833	4	5	a	a	DET
ajst-2833	4	6	discrete	discrete	ADJ
ajst-2833	4	7	predator	predator	NOUN
ajst-2833	4	8	-	-	PUNCT
ajst-2833	4	9	prey	prey	NOUN
ajst-2833	4	10	model	model	NOUN
ajst-2833	4	11	with	with	ADP
ajst-2833	4	12	competition	competition	NOUN
ajst-2833	4	13	between	between	ADP
ajst-2833	4	14	predators	predator	NOUN
ajst-2833	4	15	in	in	ADP
ajst-2833	4	16	this	this	DET
ajst-2833	4	17	paper	paper	NOUN
ajst-2833	4	18	.	.	PUNCT
ajst-2833	5	1	by	by	ADP
ajst-2833	5	2	simplifying	simplify	VERB
ajst-2833	5	3	the	the	DET
ajst-2833	5	4	corresponding	corresponding	ADJ
ajst-2833	5	5	continuous	continuous	ADJ
ajst-2833	5	6	predator	predator	NOUN
ajst-2833	5	7	-	-	PUNCT
ajst-2833	5	8	prey	prey	NOUN
ajst-2833	5	9	model	model	NOUN
ajst-2833	5	10	,	,	PUNCT
ajst-2833	5	11	and	and	CCONJ
ajst-2833	5	12	using	use	VERB
ajst-2833	5	13	the	the	DET
ajst-2833	5	14	semidiscretization	semidiscretization	ADJ
ajst-2833	5	15	method	method	NOUN
ajst-2833	5	16	to	to	PART
ajst-2833	5	17	obtain	obtain	VERB
ajst-2833	5	18	a	a	DET
ajst-2833	5	19	new	new	ADJ
ajst-2833	5	20	discrete	discrete	ADJ
ajst-2833	5	21	model	model	NOUN
ajst-2833	5	22	,	,	PUNCT
ajst-2833	5	23	we	we	PRON
ajst-2833	5	24	discuss	discuss	VERB
ajst-2833	5	25	the	the	DET
ajst-2833	5	26	existence	existence	NOUN
ajst-2833	5	27	and	and	CCONJ
ajst-2833	5	28	local	local	ADJ
ajst-2833	5	29	stability	stability	NOUN
ajst-2833	5	30	of	of	ADP
ajst-2833	5	31	nonnegative	nonnegative	ADJ
ajst-2833	5	32	fixed	fix	VERB
ajst-2833	5	33	points	point	NOUN
ajst-2833	5	34	of	of	ADP
ajst-2833	5	35	the	the	DET
ajst-2833	5	36	new	new	ADJ
ajst-2833	5	37	discrete	discrete	ADJ
ajst-2833	5	38	model	model	NOUN
ajst-2833	5	39	.	.	PUNCT
ajst-2833	6	1	what	what	PRON
ajst-2833	6	2	’s	’	VERB
ajst-2833	6	3	more	more	ADV
ajst-2833	6	4	important	important	ADJ
ajst-2833	6	5	,	,	PUNCT
ajst-2833	6	6	by	by	ADP
ajst-2833	6	7	using	use	VERB
ajst-2833	6	8	the	the	DET
ajst-2833	6	9	bifurcation	bifurcation	NOUN
ajst-2833	6	10	theory	theory	NOUN
ajst-2833	6	11	,	,	PUNCT
ajst-2833	6	12	we	we	PRON
ajst-2833	6	13	derive	derive	VERB
ajst-2833	6	14	the	the	DET
ajst-2833	6	15	sufficient	sufficient	ADJ
ajst-2833	6	16	conditions	condition	NOUN
ajst-2833	6	17	for	for	ADP
ajst-2833	6	18	the	the	DET
ajst-2833	6	19	occurrences	occurrence	NOUN
ajst-2833	6	20	of	of	ADP
ajst-2833	6	21	neimark	neimark	NOUN
ajst-2833	6	22	-	-	PUNCT
ajst-2833	6	23	sacker	sacker	NOUN
ajst-2833	6	24	bifurcation	bifurcation	NOUN
ajst-2833	6	25	and	and	CCONJ
ajst-2833	6	26	the	the	DET
ajst-2833	6	27	stability	stability	NOUN
ajst-2833	6	28	of	of	ADP
ajst-2833	6	29	closed	closed	ADJ
ajst-2833	6	30	orbit	orbit	NOUN
ajst-2833	6	31	bifurcated	bifurcate	VERB
ajst-2833	6	32	.	.	PUNCT
ajst-2833	7	1	finally	finally	ADV
ajst-2833	7	2	,	,	PUNCT
ajst-2833	7	3	the	the	DET
ajst-2833	7	4	numerical	numerical	PROPN
ajst-2833	7	5	simulation	simulation	PROPN
ajst-2833	7	6	are	be	AUX
ajst-2833	7	7	presented	present	VERB
ajst-2833	7	8	,	,	PUNCT
ajst-2833	7	9	which	which	PRON
ajst-2833	7	10	not	not	PART
ajst-2833	7	11	only	only	ADV
ajst-2833	7	12	illustrate	illustrate	VERB
ajst-2833	7	13	the	the	DET
ajst-2833	7	14	existence	existence	NOUN
ajst-2833	7	15	of	of	ADP
ajst-2833	7	16	neimarksacker	neimarksacker	ADJ
ajst-2833	7	17	bifurcation	bifurcation	NOUN
ajst-2833	7	18	but	but	CCONJ
ajst-2833	7	19	also	also	ADV
ajst-2833	7	20	reveal	reveal	VERB
ajst-2833	7	21	some	some	DET
ajst-2833	7	22	new	new	ADJ
ajst-2833	7	23	dynamic	dynamic	ADJ
ajst-2833	7	24	phenomena	phenomenon	NOUN
ajst-2833	7	25	of	of	ADP
ajst-2833	7	26	this	this	DET
ajst-2833	7	27	model	model	NOUN
ajst-2833	7	28	.	.	PUNCT
ajst-2833	8	1	keywords	keyword	NOUN
ajst-2833	8	2	:	:	PUNCT
ajst-2833	8	3	discrete	discrete	ADJ
ajst-2833	8	4	predator	predator	NOUN
ajst-2833	8	5	-	-	PUNCT
ajst-2833	8	6	prey	prey	NOUN
ajst-2833	8	7	system	system	NOUN
ajst-2833	8	8	with	with	ADP
ajst-2833	8	9	competition	competition	NOUN
ajst-2833	8	10	,	,	PUNCT
ajst-2833	8	11	semidiscretization	semidiscretization	NOUN
ajst-2833	8	12	method	method	NOUN
ajst-2833	8	13	,	,	PUNCT
ajst-2833	8	14	neimark	neimark	NOUN
ajst-2833	8	15	-	-	PUNCT
ajst-2833	8	16	sacker	sacker	NOUN
ajst-2833	8	17	bifurcation	bifurcation	NOUN
ajst-2833	8	18	.	.	PUNCT
ajst-2833	9	1	1	1	X
ajst-2833	9	2	.	.	X
ajst-2833	9	3	introduction	introduction	NOUN
ajst-2833	9	4	the	the	DET
ajst-2833	9	5	dynamic	dynamic	ADJ
ajst-2833	9	6	relationship	relationship	NOUN
ajst-2833	9	7	between	between	ADP
ajst-2833	9	8	predator	predator	NOUN
ajst-2833	9	9	and	and	CCONJ
ajst-2833	9	10	prey	prey	NOUN
ajst-2833	10	1	[	[	X
ajst-2833	10	2	1	1	NUM
ajst-2833	10	3	-	-	SYM
ajst-2833	10	4	4	4	NUM
ajst-2833	10	5	]	]	PUNCT
ajst-2833	10	6	is	be	AUX
ajst-2833	10	7	a	a	DET
ajst-2833	10	8	kind	kind	NOUN
ajst-2833	10	9	of	of	ADP
ajst-2833	10	10	interaction	interaction	NOUN
ajst-2833	10	11	between	between	ADP
ajst-2833	10	12	different	different	ADJ
ajst-2833	10	13	species	specie	NOUN
ajst-2833	10	14	in	in	ADP
ajst-2833	10	15	the	the	DET
ajst-2833	10	16	ecosystem	ecosystem	NOUN
ajst-2833	10	17	.	.	PUNCT
ajst-2833	11	1	in	in	ADP
ajst-2833	11	2	population	population	NOUN
ajst-2833	11	3	biology	biology	NOUN
ajst-2833	11	4	,	,	PUNCT
ajst-2833	11	5	lotka	lotka	PROPN
ajst-2833	11	6	volterra	volterra	PROPN
ajst-2833	11	7	(	(	PUNCT
ajst-2833	11	8	l	l	NOUN
ajst-2833	11	9	-	-	PUNCT
ajst-2833	11	10	v	v	NOUN
ajst-2833	11	11	)	)	PUNCT
ajst-2833	11	12	predator	predator	NOUN
ajst-2833	11	13	-	-	PUNCT
ajst-2833	11	14	prey	prey	NOUN
ajst-2833	11	15	model	model	NOUN
ajst-2833	11	16	[	[	X
ajst-2833	11	17	5,6	5,6	NUM
ajst-2833	11	18	]	]	PUNCT
ajst-2833	11	19	is	be	AUX
ajst-2833	11	20	one	one	NUM
ajst-2833	11	21	of	of	ADP
ajst-2833	11	22	the	the	DET
ajst-2833	11	23	most	most	ADV
ajst-2833	11	24	famous	famous	ADJ
ajst-2833	11	25	models	model	NOUN
ajst-2833	11	26	,	,	PUNCT
ajst-2833	11	27	which	which	PRON
ajst-2833	11	28	was	be	AUX
ajst-2833	11	29	respectively	respectively	ADV
ajst-2833	11	30	proposed	propose	VERB
ajst-2833	11	31	by	by	ADP
ajst-2833	11	32	a.	a.	PROPN
ajst-2833	11	33	lotka	lotka	PROPN
ajst-2833	11	34	in	in	ADP
ajst-2833	11	35	1925	1925	NUM
ajst-2833	11	36	and	and	CCONJ
ajst-2833	11	37	v.	v.	ADP
ajst-2833	11	38	volterra	volterra	NOUN
ajst-2833	11	39	in	in	ADP
ajst-2833	11	40	1926	1926	NUM
ajst-2833	11	41	.	.	PUNCT
ajst-2833	12	1	this	this	DET
ajst-2833	12	2	model	model	NOUN
ajst-2833	12	3	has	have	AUX
ajst-2833	12	4	become	become	VERB
ajst-2833	12	5	the	the	DET
ajst-2833	12	6	standard	standard	ADJ
ajst-2833	12	7	basis	basis	NOUN
ajst-2833	12	8	for	for	ADP
ajst-2833	12	9	many	many	ADJ
ajst-2833	12	10	subsequent	subsequent	ADJ
ajst-2833	12	11	models	model	NOUN
ajst-2833	12	12	in	in	ADP
ajst-2833	12	13	many	many	ADJ
ajst-2833	12	14	different	different	ADJ
ajst-2833	12	15	fields	field	NOUN
ajst-2833	12	16	.	.	PUNCT
ajst-2833	13	1	since	since	SCONJ
ajst-2833	13	2	lotka	lotka	PROPN
ajst-2833	13	3	and	and	CCONJ
ajst-2833	13	4	volterra	volterra	PROPN
ajst-2833	13	5	’s	’s	PART
ajst-2833	13	6	pioneering	pioneer	VERB
ajst-2833	13	7	work	work	NOUN
ajst-2833	13	8	,	,	PUNCT
ajst-2833	13	9	the	the	DET
ajst-2833	13	10	predator	predator	NOUN
ajst-2833	13	11	-	-	PUNCT
ajst-2833	13	12	prey	prey	NOUN
ajst-2833	13	13	model	model	NOUN
ajst-2833	13	14	in	in	ADP
ajst-2833	13	15	the	the	DET
ajst-2833	13	16	ecosystem	ecosystem	NOUN
ajst-2833	13	17	has	have	AUX
ajst-2833	13	18	been	be	AUX
ajst-2833	13	19	an	an	DET
ajst-2833	13	20	important	important	ADJ
ajst-2833	13	21	research	research	NOUN
ajst-2833	13	22	role	role	NOUN
ajst-2833	13	23	from	from	ADP
ajst-2833	13	24	an	an	DET
ajst-2833	13	25	ecological	ecological	ADJ
ajst-2833	13	26	point	point	NOUN
ajst-2833	13	27	of	of	ADP
ajst-2833	13	28	view	view	NOUN
ajst-2833	13	29	.	.	PUNCT
ajst-2833	14	1	in	in	ADP
ajst-2833	14	2	random	random	ADJ
ajst-2833	14	3	and	and	CCONJ
ajst-2833	14	4	deterministic	deterministic	ADJ
ajst-2833	14	5	environments	environment	NOUN
ajst-2833	14	6	,	,	PUNCT
ajst-2833	14	7	mathematical	mathematical	ADJ
ajst-2833	14	8	modeling	modeling	NOUN
ajst-2833	14	9	has	have	VERB
ajst-2833	14	10	an	an	DET
ajst-2833	14	11	increasing	increase	VERB
ajst-2833	14	12	impact	impact	NOUN
ajst-2833	14	13	on	on	ADP
ajst-2833	14	14	theoretical	theoretical	ADJ
ajst-2833	14	15	ecology	ecology	NOUN
ajst-2833	14	16	.	.	PUNCT
ajst-2833	15	1	in	in	ADP
ajst-2833	15	2	the	the	DET
ajst-2833	15	3	past	past	ADJ
ajst-2833	15	4	few	few	ADJ
ajst-2833	15	5	decades	decade	NOUN
ajst-2833	15	6	,	,	PUNCT
ajst-2833	15	7	a	a	DET
ajst-2833	15	8	lot	lot	NOUN
ajst-2833	15	9	of	of	ADP
ajst-2833	15	10	empirical	empirical	ADJ
ajst-2833	15	11	and	and	CCONJ
ajst-2833	15	12	theoretical	theoretical	ADJ
ajst-2833	15	13	work	work	NOUN
ajst-2833	15	14	on	on	ADP
ajst-2833	15	15	predator	predator	NOUN
ajst-2833	15	16	-	-	PUNCT
ajst-2833	15	17	prey	prey	NOUN
ajst-2833	15	18	models	model	NOUN
ajst-2833	15	19	has	have	AUX
ajst-2833	15	20	been	be	AUX
ajst-2833	15	21	carried	carry	VERB
ajst-2833	15	22	out	out	ADP
ajst-2833	15	23	.	.	PUNCT
ajst-2833	16	1	functional	functional	ADJ
ajst-2833	16	2	response	response	NOUN
ajst-2833	16	3	plays	play	VERB
ajst-2833	16	4	an	an	DET
ajst-2833	16	5	important	important	ADJ
ajst-2833	16	6	role	role	NOUN
ajst-2833	16	7	in	in	ADP
ajst-2833	16	8	system	system	NOUN
ajst-2833	16	9	modeling	modeling	NOUN
ajst-2833	16	10	.	.	PUNCT
ajst-2833	17	1	functional	functional	ADJ
ajst-2833	17	2	response	response	NOUN
ajst-2833	17	3	is	be	AUX
ajst-2833	17	4	a	a	DET
ajst-2833	17	5	function	function	NOUN
ajst-2833	17	6	of	of	ADP
ajst-2833	17	7	the	the	DET
ajst-2833	17	8	number	number	NOUN
ajst-2833	17	9	of	of	ADP
ajst-2833	17	10	prey	prey	NOUN
ajst-2833	17	11	consumed	consume	VERB
ajst-2833	17	12	by	by	ADP
ajst-2833	17	13	each	each	DET
ajst-2833	17	14	predator	predator	NOUN
ajst-2833	17	15	per	per	ADP
ajst-2833	17	16	unit	unit	NOUN
ajst-2833	17	17	time	time	NOUN
ajst-2833	17	18	.	.	PUNCT
ajst-2833	18	1	this	this	DET
ajst-2833	18	2	nutrient	nutrient	NOUN
ajst-2833	18	3	function	function	NOUN
ajst-2833	18	4	determines	determine	VERB
ajst-2833	18	5	the	the	DET
ajst-2833	18	6	dynamics	dynamic	NOUN
ajst-2833	18	7	of	of	ADP
ajst-2833	18	8	the	the	DET
ajst-2833	18	9	system	system	NOUN
ajst-2833	18	10	,	,	PUNCT
ajst-2833	18	11	such	such	ADJ
ajst-2833	18	12	as	as	ADP
ajst-2833	18	13	the	the	DET
ajst-2833	18	14	stability	stability	NOUN
ajst-2833	18	15	and	and	CCONJ
ajst-2833	18	16	bifurcation	bifurcation	NOUN
ajst-2833	18	17	,	,	PUNCT
ajst-2833	18	18	etc	etc	X
ajst-2833	18	19	.	.	X
ajst-2833	18	20	the	the	DET
ajst-2833	18	21	predator	predator	NOUN
ajst-2833	18	22	-	-	PUNCT
ajst-2833	18	23	prey	prey	NOUN
ajst-2833	18	24	models	model	NOUN
ajst-2833	18	25	studied	study	VERB
ajst-2833	18	26	in	in	ADP
ajst-2833	18	27	the	the	DET
ajst-2833	18	28	past	past	ADJ
ajst-2833	18	29	half	half	ADJ
ajst-2833	18	30	century	century	NOUN
ajst-2833	18	31	are	be	AUX
ajst-2833	18	32	given	give	VERB
ajst-2833	18	33	many	many	ADJ
ajst-2833	18	34	different	different	ADJ
ajst-2833	18	35	functional	functional	ADJ
ajst-2833	18	36	responses	response	NOUN
ajst-2833	18	37	.	.	PUNCT
ajst-2833	19	1	enrichment	enrichment	NOUN
ajst-2833	19	2	paradox	paradox	NOUN
ajst-2833	19	3	has	have	AUX
ajst-2833	19	4	also	also	ADV
ajst-2833	19	5	become	become	VERB
ajst-2833	19	6	one	one	NUM
ajst-2833	19	7	of	of	ADP
ajst-2833	19	8	the	the	DET
ajst-2833	19	9	important	important	ADJ
ajst-2833	19	10	topics	topic	NOUN
ajst-2833	19	11	in	in	ADP
ajst-2833	19	12	predator	predator	NOUN
ajst-2833	19	13	-	-	PUNCT
ajst-2833	19	14	prey	prey	NOUN
ajst-2833	19	15	model	model	NOUN
ajst-2833	20	1	[	[	X
ajst-2833	20	2	7	7	NUM
ajst-2833	20	3	-	-	SYM
ajst-2833	20	4	9	9	NUM
ajst-2833	20	5	]	]	PUNCT
ajst-2833	20	6	.	.	PUNCT
ajst-2833	21	1	it	it	PRON
ajst-2833	21	2	is	be	AUX
ajst-2833	21	3	pointed	point	VERB
ajst-2833	21	4	out	out	ADP
ajst-2833	21	5	that	that	SCONJ
ajst-2833	21	6	enriching	enrich	VERB
ajst-2833	21	7	the	the	DET
ajst-2833	21	8	predatorprey	predatorprey	NOUN
ajst-2833	21	9	system	system	NOUN
ajst-2833	21	10	by	by	ADP
ajst-2833	21	11	increasing	increase	VERB
ajst-2833	21	12	the	the	DET
ajst-2833	21	13	carrying	carry	VERB
ajst-2833	21	14	capacity	capacity	NOUN
ajst-2833	21	15	of	of	ADP
ajst-2833	21	16	a	a	DET
ajst-2833	21	17	predator	predator	NOUN
ajst-2833	21	18	-	-	PUNCT
ajst-2833	21	19	prey	prey	NOUN
ajst-2833	21	20	system	system	NOUN
ajst-2833	21	21	to	to	ADP
ajst-2833	21	22	prey	prey	PROPN
ajst-2833	21	23	will	will	AUX
ajst-2833	21	24	lead	lead	VERB
ajst-2833	21	25	to	to	ADP
ajst-2833	21	26	the	the	DET
ajst-2833	21	27	increase	increase	NOUN
ajst-2833	21	28	of	of	ADP
ajst-2833	21	29	predator	predator	NOUN
ajst-2833	21	30	equilibrium	equilibrium	NOUN
ajst-2833	21	31	density	density	NOUN
ajst-2833	21	32	,	,	PUNCT
ajst-2833	21	33	but	but	CCONJ
ajst-2833	21	34	not	not	PART
ajst-2833	21	35	lead	lead	VERB
ajst-2833	21	36	to	to	ADP
ajst-2833	21	37	the	the	DET
ajst-2833	21	38	increase	increase	NOUN
ajst-2833	21	39	of	of	ADP
ajst-2833	21	40	prey	prey	PROPN
ajst-2833	21	41	equilibrium	equilibrium	NOUN
ajst-2833	21	42	density	density	NOUN
ajst-2833	21	43	,	,	PUNCT
ajst-2833	21	44	and	and	CCONJ
ajst-2833	21	45	will	will	AUX
ajst-2833	21	46	eventually	eventually	ADV
ajst-2833	21	47	destroy	destroy	VERB
ajst-2833	21	48	the	the	DET
ajst-2833	21	49	positive	positive	ADJ
ajst-2833	21	50	balance	balance	NOUN
ajst-2833	21	51	.	.	PUNCT
ajst-2833	22	1	intuitively	intuitively	ADV
ajst-2833	22	2	,	,	PUNCT
ajst-2833	22	3	this	this	PRON
ajst-2833	22	4	increases	increase	VERB
ajst-2833	22	5	the	the	DET
ajst-2833	22	6	probability	probability	NOUN
ajst-2833	22	7	of	of	ADP
ajst-2833	22	8	random	random	ADJ
ajst-2833	22	9	extinction	extinction	NOUN
ajst-2833	22	10	of	of	ADP
ajst-2833	22	11	predator	predator	NOUN
ajst-2833	22	12	and	and	CCONJ
ajst-2833	22	13	prey	prey	PROPN
ajst-2833	22	14	species	specie	NOUN
ajst-2833	22	15	.	.	PUNCT
ajst-2833	23	1	the	the	DET
ajst-2833	23	2	interspecific	interspecific	NOUN
ajst-2833	23	3	and	and	CCONJ
ajst-2833	23	4	intraspecific	intraspecific	NOUN
ajst-2833	23	5	interactions	interaction	NOUN
ajst-2833	23	6	in	in	ADP
ajst-2833	23	7	a	a	DET
ajst-2833	23	8	l	l	NOUN
ajst-2833	23	9	-	-	PUNCT
ajst-2833	23	10	v	v	NOUN
ajst-2833	23	11	model	model	NOUN
ajst-2833	23	12	can	can	AUX
ajst-2833	23	13	not	not	PART
ajst-2833	23	14	reflect	reflect	VERB
ajst-2833	23	15	the	the	DET
ajst-2833	23	16	real	real	ADJ
ajst-2833	23	17	experimental	experimental	ADJ
ajst-2833	23	18	phenomena	phenomenon	NOUN
ajst-2833	23	19	or	or	CCONJ
ajst-2833	23	20	the	the	DET
ajst-2833	23	21	specific	specific	ADJ
ajst-2833	23	22	characteristics	characteristic	NOUN
ajst-2833	23	23	of	of	ADP
ajst-2833	23	24	different	different	ADJ
ajst-2833	23	25	groups	group	NOUN
ajst-2833	23	26	.	.	PUNCT
ajst-2833	24	1	therefore	therefore	ADV
ajst-2833	24	2	,	,	PUNCT
ajst-2833	24	3	the	the	DET
ajst-2833	24	4	original	original	ADJ
ajst-2833	24	5	l	l	NOUN
ajst-2833	24	6	-	-	PUNCT
ajst-2833	24	7	v	v	NOUN
ajst-2833	24	8	model	model	NOUN
ajst-2833	24	9	has	have	AUX
ajst-2833	24	10	been	be	AUX
ajst-2833	24	11	developed	develop	VERB
ajst-2833	24	12	and	and	CCONJ
ajst-2833	24	13	improved	improve	VERB
ajst-2833	24	14	by	by	ADP
ajst-2833	24	15	combining	combine	VERB
ajst-2833	24	16	more	more	ADV
ajst-2833	24	17	realistic	realistic	ADJ
ajst-2833	24	18	and	and	CCONJ
ajst-2833	24	19	important	important	ADJ
ajst-2833	24	20	biological	biological	ADJ
ajst-2833	24	21	factors	factor	NOUN
ajst-2833	24	22	and	and	CCONJ
ajst-2833	24	23	relationships	relationship	NOUN
ajst-2833	24	24	.	.	PUNCT
ajst-2833	25	1	the	the	DET
ajst-2833	25	2	following	follow	VERB
ajst-2833	25	3	improved	improve	VERB
ajst-2833	25	4	lotka	lotka	PROPN
ajst-2833	25	5	volterra	volterra	NOUN
ajst-2833	25	6	predator	predator	NOUN
ajst-2833	25	7	-	-	PUNCT
ajst-2833	25	8	prey	prey	NOUN
ajst-2833	25	9	system	system	NOUN
ajst-2833	25	10	is	be	AUX
ajst-2833	25	11	also	also	ADV
ajst-2833	25	12	called	call	VERB
ajst-2833	25	13	wangersky	wangersky	ADJ
ajst-2833	25	14	-	-	PUNCT
ajst-2833	25	15	cunningham	cunningham	PROPN
ajst-2833	25	16	model	model	NOUN
ajst-2833	26	1	[	[	X
ajst-2833	26	2	10	10	NUM
ajst-2833	26	3	]	]	X
ajst-2833	26	4	(	(	PUNCT
ajst-2833	26	5	1	1	NUM
ajst-2833	26	6	)	)	PUNCT
ajst-2833	26	7	,	,	PUNCT
ajst-2833	26	8	.	.	PUNCT
ajst-2833	27	1	du	du	PROPN
ajst-2833	27	2	u	u	PROPN
ajst-2833	27	3	u	u	NOUN
ajst-2833	27	4	muv	muv	PROPN
ajst-2833	27	5	d	d	PROPN
ajst-2833	27	6	k	k	PROPN
ajst-2833	27	7	dv	dv	PROPN
ajst-2833	27	8	emuv	emuv	VERB
ajst-2833	27	9	dv	dv	PROPN
ajst-2833	27	10	d	d	PROPN
ajst-2833	27	11			NUM
ajst-2833	27	12			PROPN
ajst-2833	27	13			NOUN
ajst-2833	27	14			ADV
ajst-2833	27	15			PROPN
ajst-2833	27	16			PROPN
ajst-2833	27	17			NOUN
ajst-2833	28	1			NOUN
ajst-2833	28	2			NUM
ajst-2833	28	3			PROPN
ajst-2833	28	4			PROPN
ajst-2833	28	5			NOUN
ajst-2833	28	6	(	(	PUNCT
ajst-2833	28	7	1	1	NUM
ajst-2833	28	8	)	)	PUNCT
ajst-2833	28	9	most	most	ADJ
ajst-2833	28	10	predator	predator	NOUN
ajst-2833	28	11	-	-	PUNCT
ajst-2833	28	12	prey	prey	NOUN
ajst-2833	28	13	models	model	NOUN
ajst-2833	28	14	are	be	AUX
ajst-2833	28	15	developed	develop	VERB
ajst-2833	28	16	on	on	ADP
ajst-2833	28	17	the	the	DET
ajst-2833	28	18	basis	basis	NOUN
ajst-2833	28	19	of	of	ADP
ajst-2833	28	20	trophic	trophic	ADJ
ajst-2833	28	21	function	function	NOUN
ajst-2833	28	22	,	,	PUNCT
ajst-2833	28	23	which	which	PRON
ajst-2833	28	24	is	be	AUX
ajst-2833	28	25	a	a	DET
ajst-2833	28	26	function	function	NOUN
ajst-2833	28	27	of	of	ADP
ajst-2833	28	28	prey	prey	PROPN
ajst-2833	28	29	density	density	NOUN
ajst-2833	28	30	.	.	PUNCT
ajst-2833	29	1	by	by	ADP
ajst-2833	29	2	introducing	introduce	VERB
ajst-2833	29	3	intraspecific	intraspecific	NOUN
ajst-2833	29	4	competition	competition	NOUN
ajst-2833	29	5	in	in	ADP
ajst-2833	29	6	the	the	DET
ajst-2833	29	7	predator	predator	NOUN
ajst-2833	29	8	population	population	NOUN
ajst-2833	29	9	,	,	PUNCT
ajst-2833	29	10	the	the	DET
ajst-2833	29	11	above	above	ADJ
ajst-2833	29	12	model	model	NOUN
ajst-2833	29	13	(	(	PUNCT
ajst-2833	29	14	1	1	NUM
ajst-2833	29	15	)	)	PUNCT
ajst-2833	29	16	is	be	AUX
ajst-2833	29	17	further	far	ADV
ajst-2833	29	18	modified	modify	VERB
ajst-2833	29	19	and	and	CCONJ
ajst-2833	29	20	studied	study	VERB
ajst-2833	29	21	;	;	PUNCT
ajst-2833	29	22	for	for	ADP
ajst-2833	29	23	instance	instance	NOUN
ajst-2833	29	24	,	,	PUNCT
ajst-2833	29	25	pielou	pielou	VERB
ajst-2833	29	26	[	[	X
ajst-2833	29	27	11	11	NUM
ajst-2833	29	28	]	]	PUNCT
ajst-2833	29	29	modified	modify	VERB
ajst-2833	29	30	it	it	PRON
ajst-2833	29	31	and	and	CCONJ
ajst-2833	29	32	took	take	VERB
ajst-2833	29	33	the	the	DET
ajst-2833	29	34	following	follow	VERB
ajst-2833	29	35	form	form	NOUN
ajst-2833	29	36	:	:	PUNCT
ajst-2833	29	37	2	2	NUM
ajst-2833	29	38	(	(	PUNCT
ajst-2833	29	39	1	1	NUM
ajst-2833	29	40	)	)	PUNCT
ajst-2833	29	41	,	,	PUNCT
ajst-2833	29	42	,	,	PUNCT
ajst-2833	29	43	du	du	PROPN
ajst-2833	29	44	u	u	PROPN
ajst-2833	29	45	u	u	NOUN
ajst-2833	29	46	muv	muv	PROPN
ajst-2833	29	47	d	d	PROPN
ajst-2833	29	48	k	k	PROPN
ajst-2833	29	49	dv	dv	PROPN
ajst-2833	29	50	emuv	emuv	VERB
ajst-2833	29	51	dv	dv	PROPN
ajst-2833	29	52	hv	hv	PROPN
ajst-2833	30	1	d	d	PROPN
ajst-2833	30	2			NUM
ajst-2833	30	3			NOUN
ajst-2833	30	4			NOUN
ajst-2833	30	5			ADV
ajst-2833	31	1			PROPN
ajst-2833	31	2			PROPN
ajst-2833	31	3			NOUN
ajst-2833	31	4			NOUN
ajst-2833	31	5			NUM
ajst-2833	31	6			PROPN
ajst-2833	31	7			PROPN
ajst-2833	31	8			PROPN
ajst-2833	31	9			NOUN
ajst-2833	31	10	(	(	PUNCT
ajst-2833	31	11	2	2	NUM
ajst-2833	31	12	)	)	PUNCT
ajst-2833	31	13	where	where	SCONJ
ajst-2833	31	14	u(τ	u(τ	ADJ
ajst-2833	31	15	)	)	PUNCT
ajst-2833	31	16	and	and	CCONJ
ajst-2833	31	17	v(τ	v(τ	PROPN
ajst-2833	31	18	)	)	PUNCT
ajst-2833	31	19	stand	stand	VERB
ajst-2833	31	20	for	for	ADP
ajst-2833	31	21	the	the	DET
ajst-2833	31	22	prey	prey	NOUN
ajst-2833	31	23	and	and	CCONJ
ajst-2833	31	24	predator	predator	NOUN
ajst-2833	31	25	density	density	NOUN
ajst-2833	31	26	,	,	PUNCT
ajst-2833	31	27	respectively	respectively	ADV
ajst-2833	31	28	,	,	PUNCT
ajst-2833	31	29	at	at	ADP
ajst-2833	31	30	time	time	NOUN
ajst-2833	31	31	τ	τ	PROPN
ajst-2833	31	32	,	,	PUNCT
ajst-2833	31	33	and	and	CCONJ
ajst-2833	31	34	the	the	DET
ajst-2833	31	35	parameters	parameter	NOUN
ajst-2833	31	36	γ	γ	X
ajst-2833	31	37	,	,	PUNCT
ajst-2833	31	38	k	k	PROPN
ajst-2833	31	39	,	,	PUNCT
ajst-2833	31	40	m	m	PROPN
ajst-2833	31	41	,	,	PUNCT
ajst-2833	31	42	e	e	NOUN
ajst-2833	31	43	,	,	PUNCT
ajst-2833	31	44	d	d	PROPN
ajst-2833	31	45	,	,	PUNCT
ajst-2833	31	46	h	h	NOUN
ajst-2833	31	47	are	be	AUX
ajst-2833	31	48	positive	positive	ADJ
ajst-2833	31	49	constants	constant	NOUN
ajst-2833	31	50	,	,	PUNCT
ajst-2833	31	51	which	which	PRON
ajst-2833	31	52	respectively	respectively	ADV
ajst-2833	31	53	stand	stand	VERB
ajst-2833	31	54	for	for	ADP
ajst-2833	31	55	prey	prey	NOUN
ajst-2833	31	56	intrinsic	intrinsic	ADJ
ajst-2833	31	57	growth	growth	NOUN
ajst-2833	31	58	rate	rate	NOUN
ajst-2833	31	59	,	,	PUNCT
ajst-2833	31	60	carrying	carry	VERB
ajst-2833	31	61	capacity	capacity	NOUN
ajst-2833	31	62	of	of	ADP
ajst-2833	31	63	the	the	DET
ajst-2833	31	64	environment	environment	NOUN
ajst-2833	31	65	to	to	PART
ajst-2833	31	66	prey	prey	VERB
ajst-2833	31	67	,	,	PUNCT
ajst-2833	31	68	consumption	consumption	NOUN
ajst-2833	31	69	rate	rate	NOUN
ajst-2833	31	70	,	,	PUNCT
ajst-2833	31	71	conversion	conversion	NOUN
ajst-2833	31	72	factor	factor	NOUN
ajst-2833	31	73	of	of	ADP
ajst-2833	31	74	biomass	biomass	NOUN
ajst-2833	31	75	due	due	ADP
ajst-2833	31	76	to	to	ADP
ajst-2833	31	77	change	change	NOUN
ajst-2833	31	78	of	of	ADP
ajst-2833	31	79	food	food	NOUN
ajst-2833	31	80	level	level	NOUN
ajst-2833	31	81	,	,	PUNCT
ajst-2833	31	82	predator	predator	NOUN
ajst-2833	31	83	death	death	NOUN
ajst-2833	31	84	rate	rate	NOUN
ajst-2833	31	85	,	,	PUNCT
ajst-2833	31	86	predator	predator	NOUN
ajst-2833	31	87	interspecies	interspecie	NOUN
ajst-2833	31	88	competition	competition	NOUN
ajst-2833	31	89	degree	degree	NOUN
ajst-2833	31	90	.	.	PUNCT
ajst-2833	32	1	in	in	ADP
ajst-2833	32	2	order	order	NOUN
ajst-2833	32	3	to	to	PART
ajst-2833	32	4	simplify	simplify	VERB
ajst-2833	32	5	the	the	DET
ajst-2833	32	6	analysis	analysis	NOUN
ajst-2833	32	7	of	of	ADP
ajst-2833	32	8	system	system	NOUN
ajst-2833	32	9	(	(	PUNCT
ajst-2833	32	10	2	2	NUM
ajst-2833	32	11	)	)	PUNCT
ajst-2833	32	12	,	,	PUNCT
ajst-2833	32	13	we	we	PRON
ajst-2833	32	14	use	use	VERB
ajst-2833	32	15	the	the	DET
ajst-2833	32	16	scaling	scaling	NOUN
ajst-2833	32	17	x	x	NOUN
ajst-2833	32	18	=	=	NOUN
ajst-2833	32	19	u	u	NOUN
ajst-2833	32	20	/	/	SYM
ajst-2833	32	21	k	k	PROPN
ajst-2833	32	22	,	,	PUNCT
ajst-2833	32	23	y	y	PROPN
ajst-2833	32	24	=	=	PUNCT
ajst-2833	32	25	mv	mv	PROPN
ajst-2833	32	26	/	/	SYM
ajst-2833	32	27	γ	γ	PROPN
ajst-2833	32	28	and	and	CCONJ
ajst-2833	32	29	t	t	PROPN
ajst-2833	32	30	=	=	PUNCT
ajst-2833	32	31	γτ	γτ	NOUN
ajst-2833	32	32	to	to	PART
ajst-2833	32	33	nondimensionalize	nondimensionalize	VERB
ajst-2833	32	34	the	the	DET
ajst-2833	32	35	system	system	NOUN
ajst-2833	32	36	(	(	PUNCT
ajst-2833	32	37	2	2	NUM
ajst-2833	32	38	)	)	PUNCT
ajst-2833	32	39	to	to	PART
ajst-2833	32	40	derive	derive	VERB
ajst-2833	32	41	the	the	DET
ajst-2833	32	42	following	follow	VERB
ajst-2833	32	43	dimensionless	dimensionless	NOUN
ajst-2833	32	44	system	system	NOUN
ajst-2833	32	45	:	:	PUNCT
ajst-2833	32	46	(	(	PUNCT
ajst-2833	32	47	1	1	X
ajst-2833	32	48	)	)	PUNCT
ajst-2833	32	49	,	,	PUNCT
ajst-2833	32	50	(	(	PUNCT
ajst-2833	32	51	)	)	PUNCT
ajst-2833	32	52	,	,	PUNCT
ajst-2833	32	53	dx	dx	PROPN
ajst-2833	32	54	x	x	PUNCT
ajst-2833	32	55	x	x	VERB
ajst-2833	32	56	y	y	NOUN
ajst-2833	32	57	dt	dt	NOUN
ajst-2833	32	58	dy	dy	X
ajst-2833	32	59	y	y	PROPN
ajst-2833	32	60	b	b	PROPN
ajst-2833	32	61	ax	ax	NOUN
ajst-2833	32	62	ry	ry	NOUN
ajst-2833	32	63	dt	dt	NOUN
ajst-2833	32	64			ADP
ajst-2833	33	1			PROPN
ajst-2833	33	2			PROPN
ajst-2833	33	3			NOUN
ajst-2833	34	1			NOUN
ajst-2833	34	2			NUM
ajst-2833	34	3			PROPN
ajst-2833	34	4			PROPN
ajst-2833	34	5			VERB
ajst-2833	34	6			PROPN
ajst-2833	34	7			NOUN
ajst-2833	34	8	(	(	PUNCT
ajst-2833	34	9	3	3	NUM
ajst-2833	34	10	)	)	PUNCT
ajst-2833	34	11	where	where	SCONJ
ajst-2833	34	12	120	120	NUM
ajst-2833	34	13	,	,	PUNCT
ajst-2833	34	14	,	,	PUNCT
ajst-2833	34	15	.	.	PUNCT
ajst-2833	35	1	emk	emk	NOUN
ajst-2833	36	1	d	d	NOUN
ajst-2833	36	2	h	h	NOUN
ajst-2833	36	3	a	a	DET
ajst-2833	36	4	b	b	NOUN
ajst-2833	36	5	r	r	NOUN
ajst-2833	36	6	m	m	NOUN
ajst-2833	36	7			NUM
ajst-2833	37	1			ADV
ajst-2833	38	1			PRON
ajst-2833	39	1			INTJ
ajst-2833	39	2	we	we	PRON
ajst-2833	39	3	now	now	ADV
ajst-2833	39	4	use	use	VERB
ajst-2833	39	5	the	the	DET
ajst-2833	39	6	semidiscretization	semidiscretization	ADJ
ajst-2833	39	7	method	method	NOUN
ajst-2833	39	8	,	,	PUNCT
ajst-2833	39	9	which	which	PRON
ajst-2833	39	10	has	have	AUX
ajst-2833	39	11	been	be	AUX
ajst-2833	39	12	applied	apply	VERB
ajst-2833	39	13	in	in	ADP
ajst-2833	39	14	many	many	ADJ
ajst-2833	39	15	studies	study	NOUN
ajst-2833	39	16	[	[	X
ajst-2833	39	17	12	12	NUM
ajst-2833	39	18	-	-	SYM
ajst-2833	39	19	15	15	NUM
ajst-2833	39	20	]	]	PUNCT
ajst-2833	39	21	,	,	PUNCT
ajst-2833	39	22	to	to	PART
ajst-2833	39	23	derive	derive	VERB
ajst-2833	39	24	the	the	DET
ajst-2833	39	25	discrete	discrete	ADJ
ajst-2833	39	26	model	model	NOUN
ajst-2833	39	27	of	of	ADP
ajst-2833	39	28	system	system	NOUN
ajst-2833	39	29	(	(	PUNCT
ajst-2833	39	30	3	3	NUM
ajst-2833	39	31	)	)	PUNCT
ajst-2833	39	32	.	.	PUNCT
ajst-2833	40	1	for	for	ADP
ajst-2833	40	2	this	this	PRON
ajst-2833	40	3	,	,	PUNCT
ajst-2833	40	4	suppose	suppose	VERB
ajst-2833	40	5	that	that	SCONJ
ajst-2833	40	6	[	[	X
ajst-2833	40	7	t	t	X
ajst-2833	40	8	]	]	PUNCT
ajst-2833	40	9	denotes	denote	VERB
ajst-2833	40	10	the	the	DET
ajst-2833	40	11	greatest	great	ADJ
ajst-2833	40	12	integer	integer	NOUN
ajst-2833	40	13	not	not	PART
ajst-2833	40	14	exceeding	exceed	VERB
ajst-2833	40	15	t.	t.	NOUN
ajst-2833	40	16	consider	consider	VERB
ajst-2833	40	17	the	the	DET
ajst-2833	40	18	following	follow	VERB
ajst-2833	40	19	semidiscretization	semidiscretization	NOUN
ajst-2833	40	20	version	version	NOUN
ajst-2833	40	21	of	of	ADP
ajst-2833	40	22	system	system	NOUN
ajst-2833	40	23	(	(	PUNCT
ajst-2833	40	24	3	3	NUM
ajst-2833	40	25	)	)	PUNCT
ajst-2833	40	26	.	.	PUNCT
ajst-2833	41	1	(	(	PUNCT
ajst-2833	41	2	4	4	X
ajst-2833	41	3	)	)	PUNCT
ajst-2833	41	4	it	it	PRON
ajst-2833	41	5	is	be	AUX
ajst-2833	41	6	easy	easy	ADJ
ajst-2833	41	7	to	to	PART
ajst-2833	41	8	see	see	VERB
ajst-2833	41	9	that	that	SCONJ
ajst-2833	41	10	the	the	DET
ajst-2833	41	11	system	system	NOUN
ajst-2833	41	12	(	(	PUNCT
ajst-2833	41	13	4	4	X
ajst-2833	41	14	)	)	PUNCT
ajst-2833	41	15	has	have	AUX
ajst-2833	41	16	piecewise	piecewise	VERB
ajst-2833	41	17	constant	constant	ADJ
ajst-2833	41	18	arguments	argument	NOUN
ajst-2833	41	19	,	,	PUNCT
ajst-2833	41	20	and	and	CCONJ
ajst-2833	41	21	that	that	SCONJ
ajst-2833	41	22	a	a	DET
ajst-2833	41	23	solution	solution	NOUN
ajst-2833	41	24	(	(	PUNCT
ajst-2833	41	25	x(t),y(t	x(t),y(t	PROPN
ajst-2833	41	26	)	)	PUNCT
ajst-2833	41	27	)	)	PUNCT
ajst-2833	41	28	of	of	ADP
ajst-2833	41	29	the	the	DET
ajst-2833	41	30	system	system	NOUN
ajst-2833	41	31	(	(	PUNCT
ajst-2833	41	32	4	4	NUM
ajst-2833	41	33	)	)	PUNCT
ajst-2833	41	34	for	for	ADP
ajst-2833	41	35	t	t	PROPN
ajst-2833	41	36	∈	∈	PROPN
ajst-2833	42	1	[	[	X
ajst-2833	42	2	0,+∞	0,+∞	NUM
ajst-2833	42	3	)	)	PUNCT
ajst-2833	42	4	possesses	possess	VERB
ajst-2833	42	5	the	the	DET
ajst-2833	42	6	following	follow	VERB
ajst-2833	42	7	natures	nature	NOUN
ajst-2833	42	8	:	:	PUNCT
ajst-2833	42	9	1	1	X
ajst-2833	42	10	.	.	X
ajst-2833	42	11	on	on	ADP
ajst-2833	42	12	the	the	DET
ajst-2833	42	13	interval	interval	NOUN
ajst-2833	42	14	[	[	X
ajst-2833	42	15	0,+∞	0,+∞	NUM
ajst-2833	42	16	)	)	PUNCT
ajst-2833	42	17	,	,	PUNCT
ajst-2833	42	18	x(t	x(t	PROPN
ajst-2833	42	19	)	)	PUNCT
ajst-2833	42	20	and	and	CCONJ
ajst-2833	42	21	y(t	y(t	NUM
ajst-2833	42	22	)	)	PUNCT
ajst-2833	42	23	are	be	AUX
ajst-2833	42	24	continuous	continuous	ADJ
ajst-2833	42	25	;	;	PUNCT
ajst-2833	43	1	2	2	X
ajst-2833	43	2	.	.	X
ajst-2833	43	3	when	when	SCONJ
ajst-2833	43	4	t	t	PROPN
ajst-2833	43	5	∈	∈	PROPN
ajst-2833	44	1	[	[	X
ajst-2833	44	2	0,+∞	0,+∞	NUM
ajst-2833	44	3	)	)	PUNCT
ajst-2833	44	4	except	except	SCONJ
ajst-2833	44	5	for	for	ADP
ajst-2833	44	6	the	the	DET
ajst-2833	44	7	points	point	NOUN
ajst-2833	44	8	and	and	CCONJ
ajst-2833	44	9	exist	exist	VERB
ajst-2833	44	10	everywhere	everywhere	ADV
ajst-2833	44	11	.	.	PUNCT
ajst-2833	45	1	the	the	DET
ajst-2833	45	2	following	follow	VERB
ajst-2833	45	3	system	system	NOUN
ajst-2833	45	4	can	can	AUX
ajst-2833	45	5	be	be	AUX
ajst-2833	45	6	obtained	obtain	VERB
ajst-2833	45	7	by	by	ADP
ajst-2833	45	8	integrating	integrate	VERB
ajst-2833	45	9	(	(	PUNCT
ajst-2833	45	10	4	4	NUM
ajst-2833	45	11	)	)	PUNCT
ajst-2833	45	12	over	over	ADP
ajst-2833	45	13	the	the	DET
ajst-2833	45	14	interval	interval	NOUN
ajst-2833	45	15	[	[	X
ajst-2833	45	16	n	n	CCONJ
ajst-2833	45	17	,	,	PUNCT
ajst-2833	45	18	t	t	PROPN
ajst-2833	45	19	]	]	PUNCT
ajst-2833	45	20	for	for	ADP
ajst-2833	45	21	any	any	DET
ajst-2833	45	22	t∈[n	t∈[n	NOUN
ajst-2833	45	23	,	,	PUNCT
ajst-2833	45	24	n+1	n+1	NOUN
ajst-2833	45	25	)	)	PUNCT
ajst-2833	45	26	and	and	CCONJ
ajst-2833	45	27	n	n	NOUN
ajst-2833	45	28	=	=	NOUN
ajst-2833	45	29	0,1,2	0,1,2	NUM
ajst-2833	45	30	,	,	PUNCT
ajst-2833	45	31	·	·	PUNCT
ajst-2833	45	32	·	·	PUNCT
ajst-2833	45	33	·	·	PUNCT
ajst-2833	45	34	1	1	NUM
ajst-2833	45	35	(	(	PUNCT
ajst-2833	45	36	)	)	PUNCT
ajst-2833	45	37	(	(	PUNCT
ajst-2833	45	38	)	)	PUNCT
ajst-2833	45	39	,	,	PUNCT
ajst-2833	45	40	(	(	PUNCT
ajst-2833	45	41	)	)	PUNCT
ajst-2833	45	42	(	(	PUNCT
ajst-2833	45	43	)	)	PUNCT
ajst-2833	45	44	,	,	PUNCT
ajst-2833	46	1	n	n	CCONJ
ajst-2833	46	2	n	n	CCONJ
ajst-2833	46	3	n	n	CCONJ
ajst-2833	46	4	n	n	NOUN
ajst-2833	46	5	x	x	SYM
ajst-2833	46	6	y	y	PROPN
ajst-2833	46	7	n	n	PROPN
ajst-2833	46	8	b	b	PROPN
ajst-2833	46	9	ax	ax	NOUN
ajst-2833	46	10	ry	ry	NOUN
ajst-2833	46	11	n	n	PROPN
ajst-2833	46	12	x	x	SYM
ajst-2833	46	13	t	t	NOUN
ajst-2833	46	14	x	x	PUNCT
ajst-2833	46	15	e	e	NOUN
ajst-2833	46	16	t	t	PROPN
ajst-2833	46	17	n	n	CCONJ
ajst-2833	46	18	y	y	PROPN
ajst-2833	46	19	t	t	PROPN
ajst-2833	46	20	y	y	PROPN
ajst-2833	46	21	e	e	PROPN
ajst-2833	46	22	t	t	PROPN
ajst-2833	46	23	n	n	CCONJ
ajst-2833	46	24			PROPN
ajst-2833	46	25			PROPN
ajst-2833	46	26			PROPN
ajst-2833	46	27			PUNCT
ajst-2833	46	28			NOUN
ajst-2833	46	29			ADP
ajst-2833	46	30			PROPN
ajst-2833	46	31			NOUN
ajst-2833	46	32			NUM
ajst-2833	46	33			NUM
ajst-2833	47	1			CCONJ
ajst-2833	47	2	(	(	PUNCT
ajst-2833	47	3	5	5	NUM
ajst-2833	47	4	)	)	PUNCT
ajst-2833	47	5	where	where	SCONJ
ajst-2833	47	6	xn	xn	NOUN
ajst-2833	47	7	=	=	SYM
ajst-2833	48	1	x(n	x(n	NOUN
ajst-2833	48	2	)	)	PUNCT
ajst-2833	48	3	and	and	CCONJ
ajst-2833	48	4	yn	yn	X
ajst-2833	48	5	=	=	SYM
ajst-2833	48	6	y(n	y(n	PROPN
ajst-2833	48	7	)	)	PUNCT
ajst-2833	48	8	.	.	PUNCT
ajst-2833	49	1	letting	let	VERB
ajst-2833	49	2	(	(	PUNCT
ajst-2833	49	3	1)t	1)t	PROPN
ajst-2833	49	4	n	n	PRON
ajst-2833	49	5			NOUN
ajst-2833	49	6			VERB
ajst-2833	49	7	in	in	ADP
ajst-2833	49	8	(	(	PUNCT
ajst-2833	49	9	5	5	NUM
ajst-2833	49	10	)	)	PUNCT
ajst-2833	49	11	produces	produce	VERB
ajst-2833	49	12	1	1	NUM
ajst-2833	49	13	1	1	NUM
ajst-2833	49	14	1	1	NUM
ajst-2833	49	15	,	,	PUNCT
ajst-2833	49	16	,	,	PUNCT
ajst-2833	49	17	n	n	CCONJ
ajst-2833	49	18	n	n	CCONJ
ajst-2833	49	19	n	n	CCONJ
ajst-2833	49	20	n	n	NOUN
ajst-2833	49	21	x	x	SYM
ajst-2833	49	22	y	y	PROPN
ajst-2833	49	23	n	n	PROPN
ajst-2833	49	24	n	n	PROPN
ajst-2833	49	25	b	b	PROPN
ajst-2833	49	26	ax	ax	NOUN
ajst-2833	49	27	ry	ry	NOUN
ajst-2833	49	28	n	n	CCONJ
ajst-2833	49	29	n	n	NOUN
ajst-2833	49	30	x	x	PUNCT
ajst-2833	49	31	x	x	PUNCT
ajst-2833	49	32	e	e	X
ajst-2833	49	33	y	y	PROPN
ajst-2833	49	34	y	y	PROPN
ajst-2833	49	35	e	e	PROPN
ajst-2833	49	36			PROPN
ajst-2833	49	37			PROPN
ajst-2833	49	38			PUNCT
ajst-2833	49	39			PROPN
ajst-2833	49	40			ADV
ajst-2833	49	41			PROPN
ajst-2833	49	42			VERB
ajst-2833	49	43			ADP
ajst-2833	49	44			NUM
ajst-2833	49	45			NUM
ajst-2833	49	46			NOUN
ajst-2833	49	47	(	(	PUNCT
ajst-2833	49	48	6	6	NUM
ajst-2833	49	49	)	)	PUNCT
ajst-2833	50	1	where	where	SCONJ
ajst-2833	50	2	a	a	DET
ajst-2833	50	3	,	,	PUNCT
ajst-2833	50	4	b	b	NOUN
ajst-2833	50	5	,	,	PUNCT
ajst-2833	50	6	r	r	NOUN
ajst-2833	50	7	>	>	X
ajst-2833	50	8	0	0	NUM
ajst-2833	50	9	.	.	PUNCT
ajst-2833	50	10	we	we	PRON
ajst-2833	50	11	mainly	mainly	ADV
ajst-2833	50	12	study	study	VERB
ajst-2833	50	13	the	the	DET
ajst-2833	50	14	properties	property	NOUN
ajst-2833	50	15	of	of	ADP
ajst-2833	50	16	system	system	NOUN
ajst-2833	50	17	(	(	PUNCT
ajst-2833	50	18	1.6	1.6	NUM
ajst-2833	50	19	)	)	PUNCT
ajst-2833	50	20	in	in	ADP
ajst-2833	50	21	the	the	DET
ajst-2833	50	22	sequel	sequel	NOUN
ajst-2833	50	23	.	.	PUNCT
ajst-2833	51	1	before	before	SCONJ
ajst-2833	51	2	we	we	PRON
ajst-2833	51	3	analyze	analyze	VERB
ajst-2833	51	4	the	the	DET
ajst-2833	51	5	fixed	fix	VERB
ajst-2833	51	6	points	point	NOUN
ajst-2833	51	7	of	of	ADP
ajst-2833	51	8	the	the	DET
ajst-2833	51	9	system	system	NOUN
ajst-2833	51	10	(	(	PUNCT
ajst-2833	51	11	6	6	NUM
ajst-2833	51	12	)	)	PUNCT
ajst-2833	51	13	,	,	PUNCT
ajst-2833	51	14	we	we	PRON
ajst-2833	51	15	recall	recall	VERB
ajst-2833	51	16	the	the	DET
ajst-2833	51	17	following	follow	VERB
ajst-2833	51	18	lemma	lemma	PROPN
ajst-2833	51	19	(	(	PUNCT
ajst-2833	51	20	see	see	VERB
ajst-2833	51	21	[	[	X
ajst-2833	51	22	13	13	NUM
ajst-2833	51	23	,	,	PUNCT
ajst-2833	51	24	pp1628	pp1628	NOUN
ajst-2833	51	25	]	]	X
ajst-2833	51	26	,	,	PUNCT
ajst-2833	51	27	[	[	X
ajst-2833	51	28	16	16	NUM
ajst-2833	51	29	,	,	PUNCT
ajst-2833	51	30	pp422	pp422	X
ajst-2833	51	31	]	]	PUNCT
ajst-2833	51	32	)	)	PUNCT
ajst-2833	51	33	.	.	PUNCT
ajst-2833	52	1	lemma	lemma	PROPN
ajst-2833	52	2	1.1	1.1	NUM
ajst-2833	52	3	.	.	PUNCT
ajst-2833	53	1	let	let	VERB
ajst-2833	53	2	f(λ	f(λ	NOUN
ajst-2833	53	3	)	)	PUNCT
ajst-2833	53	4	=	=	SYM
ajst-2833	53	5	λ2+pλ+q	λ2+pλ+q	PROPN
ajst-2833	53	6	,	,	PUNCT
ajst-2833	53	7	where	where	SCONJ
ajst-2833	53	8	p	p	NOUN
ajst-2833	53	9	and	and	CCONJ
ajst-2833	53	10	q	q	NOUN
ajst-2833	53	11	are	be	AUX
ajst-2833	53	12	two	two	NUM
ajst-2833	53	13	real	real	ADJ
ajst-2833	53	14	constants	constant	NOUN
ajst-2833	53	15	.	.	PUNCT
ajst-2833	54	1	suppose	suppose	VERB
ajst-2833	54	2	λ1	λ1	ADJ
ajst-2833	54	3	and	and	CCONJ
ajst-2833	54	4	λ2	λ2	NOUN
ajst-2833	54	5	are	be	AUX
ajst-2833	54	6	two	two	NUM
ajst-2833	54	7	roots	root	NOUN
ajst-2833	54	8	of	of	ADP
ajst-2833	54	9	f(λ	f(λ	NOUN
ajst-2833	54	10	)	)	PUNCT
ajst-2833	54	11	=	=	SYM
ajst-2833	55	1	0	0	X
ajst-2833	55	2	.	.	PUNCT
ajst-2833	56	1	then	then	ADV
ajst-2833	56	2	the	the	DET
ajst-2833	56	3	following	follow	VERB
ajst-2833	56	4	statements	statement	NOUN
ajst-2833	56	5	hold	hold	VERB
ajst-2833	56	6	.	.	PUNCT
ajst-2833	57	1	if	if	SCONJ
ajst-2833	57	2	f(1	f(1	PROPN
ajst-2833	57	3	)	)	PUNCT
ajst-2833	57	4	>	>	X
ajst-2833	57	5	0	0	NUM
ajst-2833	57	6	,	,	PUNCT
ajst-2833	57	7	then	then	ADV
ajst-2833	57	8	|λ1|	|λ1|	ADP
ajst-2833	57	9	<	<	X
ajst-2833	57	10	1	1	NUM
ajst-2833	57	11	and	and	CCONJ
ajst-2833	57	12	|λ2|	|λ2|	PRON
ajst-2833	57	13	<	<	X
ajst-2833	57	14	1	1	NUM
ajst-2833	57	15	if	if	SCONJ
ajst-2833	57	16	and	and	CCONJ
ajst-2833	57	17	only	only	ADV
ajst-2833	57	18	if	if	SCONJ
ajst-2833	57	19	f(−1	f(−1	PROPN
ajst-2833	57	20	)	)	PUNCT
ajst-2833	58	1	>	>	X
ajst-2833	58	2	0	0	PUNCT
ajst-2833	59	1	and	and	CCONJ
ajst-2833	59	2	q	q	ADJ
ajst-2833	59	3	<	<	X
ajst-2833	59	4	1	1	NUM
ajst-2833	59	5	;	;	PUNCT
ajst-2833	59	6	λ1	λ1	ADJ
ajst-2833	59	7	=	=	SYM
ajst-2833	59	8	−1	−1	NOUN
ajst-2833	59	9	and	and	CCONJ
ajst-2833	59	10	λ2	λ2	NOUN
ajst-2833	59	11	≠	≠	PROPN
ajst-2833	59	12	−1	−1	NOUN
ajst-2833	60	1	if	if	SCONJ
ajst-2833	60	2	and	and	CCONJ
ajst-2833	60	3	only	only	ADV
ajst-2833	60	4	if	if	SCONJ
ajst-2833	60	5	f(−1	f(−1	PROPN
ajst-2833	60	6	)	)	PUNCT
ajst-2833	60	7	=	=	SYM
ajst-2833	60	8	0	0	NUM
ajst-2833	60	9	and	and	CCONJ
ajst-2833	60	10	p	p	X
ajst-2833	60	11	≠	≠	PROPN
ajst-2833	60	12	2	2	NUM
ajst-2833	60	13	;	;	PUNCT
ajst-2833	60	14	|λ1|	|λ1|	ADP
ajst-2833	60	15	<	<	X
ajst-2833	60	16	1	1	NUM
ajst-2833	60	17	and	and	CCONJ
ajst-2833	60	18	|λ2|	|λ2|	PRON
ajst-2833	60	19	>	>	X
ajst-2833	60	20	1	1	NUM
ajst-2833	60	21	if	if	SCONJ
ajst-2833	60	22	and	and	CCONJ
ajst-2833	60	23	only	only	ADV
ajst-2833	60	24	if	if	SCONJ
ajst-2833	60	25	f(−1	f(−1	PROPN
ajst-2833	60	26	)	)	PUNCT
ajst-2833	60	27	<	<	X
ajst-2833	60	28	0	0	NUM
ajst-2833	60	29	;	;	PUNCT
ajst-2833	60	30	|λ1|	|λ1|	X
ajst-2833	60	31	>	>	X
ajst-2833	60	32	1	1	NUM
ajst-2833	60	33	and	and	CCONJ
ajst-2833	60	34	|λ2|	|λ2|	PRON
ajst-2833	60	35	>	>	X
ajst-2833	60	36	1	1	NUM
ajst-2833	60	37	if	if	SCONJ
ajst-2833	60	38	and	and	CCONJ
ajst-2833	60	39	only	only	ADV
ajst-2833	60	40	if	if	SCONJ
ajst-2833	60	41	f(−1	f(−1	PROPN
ajst-2833	60	42	)	)	PUNCT
ajst-2833	60	43	>	>	X
ajst-2833	60	44	0	0	PUNCT
ajst-2833	61	1	and	and	CCONJ
ajst-2833	61	2	q	q	ADJ
ajst-2833	61	3	>	>	X
ajst-2833	61	4	1	1	NUM
ajst-2833	61	5	;	;	PUNCT
ajst-2833	61	6	λ1	λ1	ADJ
ajst-2833	61	7	and	and	CCONJ
ajst-2833	61	8	λ2	λ2	NOUN
ajst-2833	61	9	are	be	AUX
ajst-2833	61	10	a	a	DET
ajst-2833	61	11	pair	pair	NOUN
ajst-2833	61	12	of	of	ADP
ajst-2833	61	13	conjugate	conjugate	ADJ
ajst-2833	61	14	complex	complex	ADJ
ajst-2833	61	15	roots	root	NOUN
ajst-2833	61	16	with	with	ADP
ajst-2833	61	17	|λ1|	|λ1|	NOUN
ajst-2833	61	18	=	=	NOUN
ajst-2833	61	19	|λ2|	|λ2|	NOUN
ajst-2833	61	20	=	=	NOUN
ajst-2833	61	21	1	1	NUM
ajst-2833	62	1	if	if	SCONJ
ajst-2833	62	2	and	and	CCONJ
ajst-2833	62	3	only	only	ADV
ajst-2833	62	4	if	if	SCONJ
ajst-2833	62	5	−2	−2	NOUN
ajst-2833	62	6	<	<	X
ajst-2833	62	7	p	p	X
ajst-2833	62	8	<	<	X
ajst-2833	62	9	2	2	NUM
ajst-2833	62	10	and	and	CCONJ
ajst-2833	62	11	q	q	NOUN
ajst-2833	62	12	=	=	NOUN
ajst-2833	62	13	1	1	NUM
ajst-2833	62	14	;	;	PUNCT
ajst-2833	62	15	λ1	λ1	ADJ
ajst-2833	62	16	=	=	SYM
ajst-2833	62	17	λ2	λ2	PROPN
ajst-2833	62	18	=	=	PUNCT
ajst-2833	62	19	−1	−1	NOUN
ajst-2833	62	20	if	if	SCONJ
ajst-2833	62	21	and	and	CCONJ
ajst-2833	62	22	only	only	ADV
ajst-2833	62	23	if	if	SCONJ
ajst-2833	62	24	f(−1	f(−1	PROPN
ajst-2833	62	25	)	)	PUNCT
ajst-2833	62	26	=	=	SYM
ajst-2833	62	27	0	0	NUM
ajst-2833	62	28	and	and	CCONJ
ajst-2833	62	29	p	p	X
ajst-2833	62	30	=	=	ADJ
ajst-2833	62	31	2	2	X
ajst-2833	62	32	.	.	PUNCT
ajst-2833	62	33	if	if	SCONJ
ajst-2833	62	34	f(1	f(1	PROPN
ajst-2833	62	35	)	)	PUNCT
ajst-2833	62	36	=	=	SYM
ajst-2833	62	37	0	0	NUM
ajst-2833	62	38	,	,	PUNCT
ajst-2833	62	39	namely	namely	ADV
ajst-2833	62	40	,	,	PUNCT
ajst-2833	62	41	1	1	NUM
ajst-2833	62	42	is	be	AUX
ajst-2833	62	43	one	one	NUM
ajst-2833	62	44	root	root	NOUN
ajst-2833	62	45	of	of	ADP
ajst-2833	62	46	f(λ	f(λ	NOUN
ajst-2833	62	47	)	)	PUNCT
ajst-2833	62	48	=	=	SYM
ajst-2833	62	49	0	0	NUM
ajst-2833	62	50	,	,	PUNCT
ajst-2833	62	51	then	then	ADV
ajst-2833	62	52	the	the	DET
ajst-2833	62	53	another	another	DET
ajst-2833	62	54	root	root	NOUN
ajst-2833	62	55	λ	λ	NOUN
ajst-2833	62	56	satisfies	satisfie	NOUN
ajst-2833	62	57	|λ|	|λ|	X
ajst-2833	62	58	=	=	SYM
ajst-2833	62	59	(	(	PUNCT
ajst-2833	62	60	<	<	X
ajst-2833	62	61	,	,	PUNCT
ajst-2833	62	62	>	>	PUNCT
ajst-2833	62	63	)	)	PUNCT
ajst-2833	62	64	1	1	NUM
ajst-2833	62	65	if	if	SCONJ
ajst-2833	62	66	and	and	CCONJ
ajst-2833	62	67	only	only	ADV
ajst-2833	62	68	if	if	SCONJ
ajst-2833	62	69	|q|	|q|	VERB
ajst-2833	62	70	=	=	SYM
ajst-2833	62	71	(	(	PUNCT
ajst-2833	62	72	<	<	X
ajst-2833	62	73	,	,	PUNCT
ajst-2833	62	74	>	>	PUNCT
ajst-2833	62	75	)	)	PUNCT
ajst-2833	62	76	1	1	X
ajst-2833	62	77	.	.	X
ajst-2833	63	1	if	if	SCONJ
ajst-2833	63	2	f(1	f(1	PROPN
ajst-2833	63	3	)	)	PUNCT
ajst-2833	63	4	<	<	X
ajst-2833	63	5	0	0	NUM
ajst-2833	63	6	,	,	PUNCT
ajst-2833	63	7	then	then	ADV
ajst-2833	63	8	f(λ	f(λ	NOUN
ajst-2833	63	9	)	)	PUNCT
ajst-2833	63	10	=	=	SYM
ajst-2833	63	11	0	0	PUNCT
ajst-2833	63	12	has	have	VERB
ajst-2833	63	13	one	one	NUM
ajst-2833	63	14	root	root	NOUN
ajst-2833	63	15	lying	lie	VERB
ajst-2833	63	16	in	in	ADP
ajst-2833	63	17	(	(	PUNCT
ajst-2833	63	18	1,∞	1,∞	NUM
ajst-2833	63	19	)	)	PUNCT
ajst-2833	63	20	.	.	PUNCT
ajst-2833	64	1	moreover	moreover	ADV
ajst-2833	64	2	,	,	PUNCT
ajst-2833	64	3	(	(	PUNCT
ajst-2833	64	4	iii.1	iii.1	PROPN
ajst-2833	64	5	)	)	PUNCT
ajst-2833	64	6	the	the	DET
ajst-2833	64	7	other	other	ADJ
ajst-2833	64	8	root	root	NOUN
ajst-2833	64	9	λ	λ	PROPN
ajst-2833	64	10	satisfies	satisfy	VERB
ajst-2833	64	11	λ	λ	X
ajst-2833	64	12	<	<	X
ajst-2833	64	13	(=	(=	NOUN
ajst-2833	64	14	)	)	PUNCT
ajst-2833	64	15	−1	−1	NOUN
ajst-2833	64	16	if	if	SCONJ
ajst-2833	65	1	and	and	CCONJ
ajst-2833	65	2	only	only	ADV
ajst-2833	65	3	if	if	SCONJ
ajst-2833	65	4	f(−1	f(−1	PROPN
ajst-2833	65	5	)	)	PUNCT
ajst-2833	65	6	<	<	X
ajst-2833	66	1	(=	(=	X
ajst-2833	66	2	)	)	PUNCT
ajst-2833	66	3	0	0	NUM
ajst-2833	66	4	;	;	PUNCT
ajst-2833	66	5	(	(	PUNCT
ajst-2833	66	6	iii.2	iii.2	X
ajst-2833	66	7	)	)	PUNCT
ajst-2833	67	1	the	the	DET
ajst-2833	67	2	other	other	ADJ
ajst-2833	67	3	root	root	NOUN
ajst-2833	67	4	−1	−1	NOUN
ajst-2833	67	5	<	<	X
ajst-2833	67	6	λ	λ	X
ajst-2833	67	7	<	<	X
ajst-2833	67	8	1	1	NUM
ajst-2833	67	9	if	if	SCONJ
ajst-2833	67	10	and	and	CCONJ
ajst-2833	67	11	only	only	ADV
ajst-2833	67	12	if	if	SCONJ
ajst-2833	67	13	f(−1	f(−1	PROPN
ajst-2833	67	14	)	)	PUNCT
ajst-2833	67	15	>	>	X
ajst-2833	68	1	0	0	X
ajst-2833	68	2	.	.	NOUN
ajst-2833	68	3	2	2	NUM
ajst-2833	68	4	.	.	NOUN
ajst-2833	68	5	existence	existence	NOUN
ajst-2833	68	6	and	and	CCONJ
ajst-2833	68	7	stability	stability	NOUN
ajst-2833	68	8	of	of	ADP
ajst-2833	68	9	fixed	fix	VERB
ajst-2833	68	10	points	point	NOUN
ajst-2833	68	11	in	in	ADP
ajst-2833	68	12	this	this	DET
ajst-2833	68	13	section	section	NOUN
ajst-2833	68	14	,	,	PUNCT
ajst-2833	68	15	we	we	PRON
ajst-2833	68	16	first	first	ADV
ajst-2833	68	17	consider	consider	VERB
ajst-2833	68	18	the	the	DET
ajst-2833	68	19	existence	existence	NOUN
ajst-2833	68	20	of	of	ADP
ajst-2833	68	21	fixed	fix	VERB
ajst-2833	68	22	points	point	NOUN
ajst-2833	68	23	and	and	CCONJ
ajst-2833	68	24	then	then	ADV
ajst-2833	68	25	analyze	analyze	VERB
ajst-2833	68	26	the	the	DET
ajst-2833	68	27	local	local	ADJ
ajst-2833	68	28	stability	stability	NOUN
ajst-2833	68	29	of	of	ADP
ajst-2833	68	30	each	each	DET
ajst-2833	68	31	fixed	fix	VERB
ajst-2833	68	32	point	point	NOUN
ajst-2833	68	33	of	of	ADP
ajst-2833	68	34	the	the	DET
ajst-2833	68	35	system	system	NOUN
ajst-2833	68	36	(	(	PUNCT
ajst-2833	68	37	6	6	NUM
ajst-2833	68	38	)	)	PUNCT
ajst-2833	68	39	.	.	PUNCT
ajst-2833	69	1	the	the	DET
ajst-2833	69	2	fixed	fix	VERB
ajst-2833	69	3	points	point	NOUN
ajst-2833	69	4	of	of	ADP
ajst-2833	69	5	the	the	DET
ajst-2833	69	6	system	system	NOUN
ajst-2833	69	7	(	(	PUNCT
ajst-2833	69	8	6	6	NUM
ajst-2833	69	9	)	)	PUNCT
ajst-2833	69	10	satisfy	satisfy	NOUN
ajst-2833	69	11	1	1	NUM
ajst-2833	69	12	,	,	PUNCT
ajst-2833	69	13	x	x	PROPN
ajst-2833	69	14	y	y	PROPN
ajst-2833	69	15	b	b	PROPN
ajst-2833	69	16	ax	ax	NOUN
ajst-2833	69	17	ryx	ryx	PROPN
ajst-2833	69	18	xe	xe	PROPN
ajst-2833	69	19	y	y	PROPN
ajst-2833	69	20	ye	ye	X
ajst-2833	69	21			PROPN
ajst-2833	69	22			PROPN
ajst-2833	69	23			VERB
ajst-2833	69	24			PROPN
ajst-2833	69	25			NUM
ajst-2833	69	26	considering	consider	VERB
ajst-2833	69	27	the	the	DET
ajst-2833	69	28	biological	biological	ADJ
ajst-2833	69	29	meanings	meaning	NOUN
ajst-2833	69	30	of	of	ADP
ajst-2833	69	31	the	the	DET
ajst-2833	69	32	system	system	NOUN
ajst-2833	69	33	(	(	PUNCT
ajst-2833	69	34	6	6	NUM
ajst-2833	69	35	)	)	PUNCT
ajst-2833	69	36	,	,	PUNCT
ajst-2833	69	37	one	one	NUM
ajst-2833	69	38	only	only	ADV
ajst-2833	69	39	takes	take	VERB
ajst-2833	69	40	into	into	ADP
ajst-2833	69	41	account	account	NOUN
ajst-2833	69	42	its	its	PRON
ajst-2833	69	43	nonnegative	nonnegative	ADJ
ajst-2833	69	44	fixed	fix	VERB
ajst-2833	69	45	points	point	NOUN
ajst-2833	69	46	.	.	PUNCT
ajst-2833	70	1	thereout	thereout	NOUN
ajst-2833	70	2	,	,	PUNCT
ajst-2833	70	3	one	one	NUM
ajst-2833	70	4	notices	notice	VERB
ajst-2833	70	5	that	that	SCONJ
ajst-2833	70	6	the	the	DET
ajst-2833	70	7	system	system	NOUN
ajst-2833	70	8	(	(	PUNCT
ajst-2833	70	9	6	6	NUM
ajst-2833	70	10	)	)	PUNCT
ajst-2833	70	11	has	have	AUX
ajst-2833	70	12	and	and	CCONJ
ajst-2833	70	13	only	only	ADV
ajst-2833	70	14	has	have	VERB
ajst-2833	70	15	three	three	NUM
ajst-2833	70	16	nonnegative	nonnegative	ADJ
ajst-2833	70	17	fixed	fix	VERB
ajst-2833	70	18	points	point	NOUN
ajst-2833	70	19	e0	e0	PROPN
ajst-2833	70	20	=	=	PUNCT
ajst-2833	70	21	(	(	PUNCT
ajst-2833	70	22	0,0),e1	0,0),e1	NOUN
ajst-2833	70	23	=(	=(	NOUN
ajst-2833	70	24	1,0	1,0	NUM
ajst-2833	70	25	)	)	PUNCT
ajst-2833	70	26	and	and	CCONJ
ajst-2833	70	27	2	2	NUM
ajst-2833	70	28	(	(	PUNCT
ajst-2833	70	29	,	,	PUNCT
ajst-2833	70	30	)	)	PUNCT
ajst-2833	70	31	b	b	X
ajst-2833	70	32	r	r	NOUN
ajst-2833	70	33	a	a	PRON
ajst-2833	70	34	b	b	NOUN
ajst-2833	70	35	e	e	NOUN
ajst-2833	70	36	a	a	DET
ajst-2833	70	37	r	r	NOUN
ajst-2833	70	38	a	a	DET
ajst-2833	70	39	r	r	NOUN
ajst-2833	70	40			ADV
ajst-2833	70	41			PROPN
ajst-2833	70	42			PROPN
ajst-2833	70	43			PRON
ajst-2833	70	44			VERB
ajst-2833	70	45	for	for	ADP
ajst-2833	70	46	a	a	DET
ajst-2833	70	47	-	-	PUNCT
ajst-2833	70	48	b>0	b>0	NOUN
ajst-2833	70	49	.	.	PUNCT
ajst-2833	71	1	the	the	DET
ajst-2833	71	2	jacobian	jacobian	ADJ
ajst-2833	71	3	matrix	matrix	NOUN
ajst-2833	71	4	of	of	ADP
ajst-2833	71	5	the	the	DET
ajst-2833	71	6	system	system	NOUN
ajst-2833	71	7	(	(	PUNCT
ajst-2833	71	8	6	6	NUM
ajst-2833	71	9	)	)	PUNCT
ajst-2833	71	10	at	at	ADP
ajst-2833	71	11	any	any	DET
ajst-2833	71	12	fixed	fix	VERB
ajst-2833	71	13	point	point	NOUN
ajst-2833	71	14	e(x	e(x	NUM
ajst-2833	71	15	,	,	PUNCT
ajst-2833	71	16	y	y	NOUN
ajst-2833	71	17	)	)	PUNCT
ajst-2833	71	18	takes	take	VERB
ajst-2833	71	19	the	the	DET
ajst-2833	71	20	following	follow	VERB
ajst-2833	71	21	form	form	NOUN
ajst-2833	71	22	.	.	PUNCT
ajst-2833	72	1	the	the	DET
ajst-2833	72	2	characteristic	characteristic	ADJ
ajst-2833	72	3	polynomial	polynomial	NOUN
ajst-2833	72	4	of	of	ADP
ajst-2833	72	5	jacobian	jacobian	ADJ
ajst-2833	72	6	matrix	matrix	NOUN
ajst-2833	72	7	j(e	j(e	PROPN
ajst-2833	72	8	)	)	PUNCT
ajst-2833	72	9	reads	read	VERB
ajst-2833	72	10	f(λ	f(λ	NOUN
ajst-2833	72	11	)	)	PUNCT
ajst-2833	72	12	=	=	SYM
ajst-2833	72	13	λ2	λ2	NOUN
ajst-2833	72	14	−	−	NOUN
ajst-2833	72	15	pλ	pλ	PROPN
ajst-2833	73	1	+	+	CCONJ
ajst-2833	73	2	q	q	ADJ
ajst-2833	73	3	,	,	PUNCT
ajst-2833	73	4	where	where	SCONJ
ajst-2833	73	5	1	1	NUM
ajst-2833	73	6	(	(	PUNCT
ajst-2833	73	7	(	(	PUNCT
ajst-2833	73	8	)	)	PUNCT
ajst-2833	73	9	)	)	PUNCT
ajst-2833	73	10	(	(	PUNCT
ajst-2833	73	11	1	1	X
ajst-2833	73	12	)	)	PUNCT
ajst-2833	73	13	(	(	PUNCT
ajst-2833	73	14	1	1	NUM
ajst-2833	73	15	)	)	PUNCT
ajst-2833	73	16	,	,	PUNCT
ajst-2833	73	17	x	x	PUNCT
ajst-2833	73	18	y	y	NOUN
ajst-2833	73	19	b	b	PROPN
ajst-2833	73	20	ax	ax	NOUN
ajst-2833	73	21	ryp	ryp	NOUN
ajst-2833	73	22	tr	tr	NOUN
ajst-2833	74	1	j	j	PROPN
ajst-2833	74	2	e	e	NOUN
ajst-2833	74	3	x	x	X
ajst-2833	74	4	e	e	VERB
ajst-2833	74	5	ry	ry	ADJ
ajst-2833	74	6	e	e	PROPN
ajst-2833	74	7			PROPN
ajst-2833	74	8			PROPN
ajst-2833	74	9			VERB
ajst-2833	74	10			ADJ
ajst-2833	74	11			PROPN
ajst-2833	74	12			PROPN
ajst-2833	74	13			CCONJ
ajst-2833	74	14			PROPN
ajst-2833	74	15	1	1	NUM
ajst-2833	74	16	(	(	PUNCT
ajst-2833	74	17	1	1	NUM
ajst-2833	74	18	)	)	PUNCT
ajst-2833	74	19	(	(	PUNCT
ajst-2833	74	20	1	1	NUM
ajst-2833	74	21	)	)	PUNCT
ajst-2833	74	22	(	(	PUNCT
ajst-2833	74	23	(	(	PUNCT
ajst-2833	74	24	)	)	PUNCT
ajst-2833	74	25	)	)	PUNCT
ajst-2833	75	1	[	[	X
ajst-2833	75	2	1	1	NUM
ajst-2833	75	3	(	(	PUNCT
ajst-2833	75	4	)	)	PUNCT
ajst-2833	75	5	]	]	PUNCT
ajst-2833	76	1	.b	.b	PROPN
ajst-2833	77	1	a	a	DET
ajst-2833	77	2	x	x	SYM
ajst-2833	77	3	r	r	NOUN
ajst-2833	77	4	yq	yq	PROPN
ajst-2833	77	5	det	det	PROPN
ajst-2833	77	6	j	j	PROPN
ajst-2833	77	7	e	e	PROPN
ajst-2833	77	8	x	x	X
ajst-2833	77	9	ry	ry	NOUN
ajst-2833	77	10	a	a	DET
ajst-2833	77	11	r	r	NOUN
ajst-2833	77	12	xy	xy	NOUN
ajst-2833	77	13	e	e	X
ajst-2833	77	14			PROPN
ajst-2833	77	15			CCONJ
ajst-2833	77	16			PROPN
ajst-2833	77	17			PROPN
ajst-2833	77	18			ADJ
ajst-2833	77	19			NUM
ajst-2833	77	20			PROPN
ajst-2833	77	21			PROPN
ajst-2833	77	22			ADV
ajst-2833	77	23			VERB
ajst-2833	77	24	for	for	ADP
ajst-2833	77	25	the	the	DET
ajst-2833	77	26	stability	stability	NOUN
ajst-2833	77	27	of	of	ADP
ajst-2833	77	28	fixed	fix	VERB
ajst-2833	77	29	points	point	NOUN
ajst-2833	77	30	e0	e0	PROPN
ajst-2833	77	31	,	,	PUNCT
ajst-2833	77	32	e1	e1	PROPN
ajst-2833	77	33	and	and	CCONJ
ajst-2833	77	34	e2	e2	PROPN
ajst-2833	77	35	,	,	PUNCT
ajst-2833	77	36	we	we	PRON
ajst-2833	77	37	can	can	AUX
ajst-2833	77	38	easily	easily	ADV
ajst-2833	77	39	get	get	VERB
ajst-2833	77	40	the	the	DET
ajst-2833	77	41	following	follow	VERB
ajst-2833	77	42	theorems	theorem	NOUN
ajst-2833	77	43	2.1	2.1	NUM
ajst-2833	77	44	-	-	SYM
ajst-2833	77	45	2.3	2.3	NUM
ajst-2833	77	46	respectively	respectively	ADV
ajst-2833	77	47	.	.	PUNCT
ajst-2833	78	1	theorem	theorem	VERB
ajst-2833	78	2	2.1	2.1	NUM
ajst-2833	78	3	.	.	PUNCT
ajst-2833	79	1	the	the	DET
ajst-2833	79	2	fixed	fixed	ADJ
ajst-2833	79	3	point	point	NOUN
ajst-2833	79	4	e0	e0	PROPN
ajst-2833	79	5	=	=	SYM
ajst-2833	79	6	(	(	PUNCT
ajst-2833	79	7	0,0	0,0	NOUN
ajst-2833	79	8	)	)	PUNCT
ajst-2833	79	9	of	of	ADP
ajst-2833	79	10	the	the	DET
ajst-2833	79	11	system	system	NOUN
ajst-2833	79	12	(	(	PUNCT
ajst-2833	79	13	6	6	NUM
ajst-2833	79	14	)	)	PUNCT
ajst-2833	79	15	is	be	AUX
ajst-2833	79	16	a	a	DET
ajst-2833	79	17	saddle	saddle	NOUN
ajst-2833	79	18	.	.	PUNCT
ajst-2833	80	1	proof	proof	NOUN
ajst-2833	80	2	.	.	PUNCT
ajst-2833	81	1	the	the	DET
ajst-2833	81	2	jacobian	jacobian	ADJ
ajst-2833	81	3	matrix	matrix	NOUN
ajst-2833	81	4	j(e0	j(e0	NOUN
ajst-2833	81	5	)	)	PUNCT
ajst-2833	81	6	of	of	ADP
ajst-2833	81	7	the	the	DET
ajst-2833	81	8	system	system	NOUN
ajst-2833	81	9	(	(	PUNCT
ajst-2833	81	10	6	6	NUM
ajst-2833	81	11	)	)	PUNCT
ajst-2833	81	12	at	at	ADP
ajst-2833	81	13	the	the	DET
ajst-2833	81	14	fixed	fix	VERB
ajst-2833	81	15	point	point	NOUN
ajst-2833	81	16	e0	e0	PROPN
ajst-2833	81	17	=	=	SYM
ajst-2833	81	18	(	(	PUNCT
ajst-2833	81	19	0,0	0,0	NOUN
ajst-2833	81	20	)	)	PUNCT
ajst-2833	81	21	is	be	AUX
ajst-2833	81	22	given	give	VERB
ajst-2833	81	23	by	by	ADP
ajst-2833	81	24	.	.	PUNCT
ajst-2833	82	1	obviously	obviously	ADV
ajst-2833	82	2	,	,	PUNCT
ajst-2833	82	3	|λ1|	|λ1|	X
ajst-2833	82	4	=	=	SYM
ajst-2833	82	5	e	e	X
ajst-2833	82	6	>	>	X
ajst-2833	82	7	1	1	NUM
ajst-2833	82	8	and	and	CCONJ
ajst-2833	82	9	|λ2|	|λ2|	PRON
ajst-2833	82	10	=	=	PUNCT
ajst-2833	82	11	e‾b	e‾b	PROPN
ajst-2833	82	12	<	<	X
ajst-2833	82	13	1	1	NUM
ajst-2833	82	14	,	,	PUNCT
ajst-2833	82	15	so	so	ADV
ajst-2833	82	16	e0	e0	PROPN
ajst-2833	82	17	=	=	SYM
ajst-2833	82	18	(	(	PUNCT
ajst-2833	82	19	0,0	0,0	NOUN
ajst-2833	82	20	)	)	PUNCT
ajst-2833	82	21	is	be	AUX
ajst-2833	82	22	a	a	DET
ajst-2833	82	23	saddle	saddle	NOUN
ajst-2833	82	24	.	.	PUNCT
ajst-2833	83	1	theorem	theorem	VERB
ajst-2833	83	2	2.2	2.2	NUM
ajst-2833	83	3	.	.	PUNCT
ajst-2833	84	1	the	the	DET
ajst-2833	84	2	following	follow	VERB
ajst-2833	84	3	statements	statement	NOUN
ajst-2833	84	4	about	about	ADP
ajst-2833	84	5	the	the	DET
ajst-2833	84	6	fixed	fix	VERB
ajst-2833	84	7	point	point	NOUN
ajst-2833	84	8	e1	e1	NOUN
ajst-2833	84	9	=	=	SYM
ajst-2833	84	10	(	(	PUNCT
ajst-2833	84	11	1,0	1,0	NUM
ajst-2833	84	12	)	)	PUNCT
ajst-2833	84	13	of	of	ADP
ajst-2833	84	14	the	the	DET
ajst-2833	84	15	system	system	NOUN
ajst-2833	84	16	(	(	PUNCT
ajst-2833	84	17	6	6	NUM
ajst-2833	84	18	)	)	PUNCT
ajst-2833	84	19	are	be	AUX
ajst-2833	84	20	true	true	ADJ
ajst-2833	84	21	.	.	PUNCT
ajst-2833	85	1	if	if	SCONJ
ajst-2833	85	2	b	b	X
ajst-2833	85	3	<	<	X
ajst-2833	85	4	a	a	X
ajst-2833	85	5	,	,	PUNCT
ajst-2833	85	6	then	then	ADV
ajst-2833	85	7	e1	e1	NOUN
ajst-2833	85	8	is	be	AUX
ajst-2833	85	9	a	a	DET
ajst-2833	85	10	saddle	saddle	NOUN
ajst-2833	85	11	.	.	PUNCT
ajst-2833	86	1	if	if	SCONJ
ajst-2833	86	2	b	b	X
ajst-2833	86	3	=	=	SYM
ajst-2833	86	4	a	a	X
ajst-2833	86	5	,	,	PUNCT
ajst-2833	86	6	then	then	ADV
ajst-2833	86	7	e1	e1	PROPN
ajst-2833	86	8	is	be	AUX
ajst-2833	86	9	non	non	ADJ
ajst-2833	86	10	-	-	ADJ
ajst-2833	86	11	hyperbolic	hyperbolic	ADJ
ajst-2833	86	12	.	.	PUNCT
ajst-2833	87	1	if	if	SCONJ
ajst-2833	87	2	b	b	X
ajst-2833	87	3	>	>	X
ajst-2833	87	4	a	a	X
ajst-2833	87	5	,	,	PUNCT
ajst-2833	87	6	then	then	ADV
ajst-2833	87	7	e1	e1	NOUN
ajst-2833	87	8	is	be	AUX
ajst-2833	87	9	a	a	DET
ajst-2833	87	10	stable	stable	ADJ
ajst-2833	87	11	node	node	NOUN
ajst-2833	87	12	.	.	PUNCT
ajst-2833	88	1	proof	proof	NOUN
ajst-2833	88	2	.	.	PUNCT
ajst-2833	89	1	the	the	DET
ajst-2833	89	2	jacobian	jacobian	ADJ
ajst-2833	89	3	matrix	matrix	NOUN
ajst-2833	89	4	of	of	ADP
ajst-2833	89	5	the	the	DET
ajst-2833	89	6	system	system	NOUN
ajst-2833	89	7	(	(	PUNCT
ajst-2833	89	8	1.6	1.6	NUM
ajst-2833	89	9	)	)	PUNCT
ajst-2833	89	10	at	at	ADP
ajst-2833	89	11	e1	e1	NOUN
ajst-2833	89	12	=	=	SYM
ajst-2833	89	13	(	(	PUNCT
ajst-2833	89	14	1,0	1,0	NUM
ajst-2833	89	15	)	)	PUNCT
ajst-2833	89	16	is	be	AUX
ajst-2833	89	17	.	.	PUNCT
ajst-2833	90	1	obviously	obviously	ADV
ajst-2833	90	2	,	,	PUNCT
ajst-2833	90	3	λ1	λ1	PROPN
ajst-2833	90	4	=	=	SYM
ajst-2833	90	5	0	0	NUM
ajst-2833	90	6	and	and	CCONJ
ajst-2833	90	7	λ2	λ2	PROPN
ajst-2833	90	8	=	=	SYM
ajst-2833	90	9	ea‾b	ea‾b	ADV
ajst-2833	90	10	.	.	PUNCT
ajst-2833	91	1	note	note	NOUN
ajst-2833	91	2	|λ1|	|λ1|	ADP
ajst-2833	91	3	<	<	X
ajst-2833	91	4	1	1	NUM
ajst-2833	91	5	is	be	AUX
ajst-2833	91	6	always	always	ADV
ajst-2833	91	7	true	true	ADJ
ajst-2833	91	8	.	.	PUNCT
ajst-2833	92	1	if	if	SCONJ
ajst-2833	92	2	b	b	X
ajst-2833	92	3	<	<	X
ajst-2833	92	4	a	a	X
ajst-2833	92	5	,	,	PUNCT
ajst-2833	92	6	then	then	ADV
ajst-2833	92	7	|λ2|	|λ2|	NOUN
ajst-2833	92	8	>	>	X
ajst-2833	92	9	1	1	NUM
ajst-2833	92	10	,	,	PUNCT
ajst-2833	92	11	so	so	ADV
ajst-2833	92	12	e1	e1	NOUN
ajst-2833	92	13	is	be	AUX
ajst-2833	92	14	a	a	DET
ajst-2833	92	15	saddle	saddle	NOUN
ajst-2833	92	16	;	;	PUNCT
ajst-2833	92	17	if	if	SCONJ
ajst-2833	92	18	b	b	X
ajst-2833	92	19	=	=	SYM
ajst-2833	92	20	a	a	NOUN
ajst-2833	92	21	,	,	PUNCT
ajst-2833	92	22	then	then	ADV
ajst-2833	92	23	|λ2|	|λ2|	NOUN
ajst-2833	92	24	=	=	SYM
ajst-2833	92	25	1	1	NUM
ajst-2833	92	26	,	,	PUNCT
ajst-2833	92	27	therefore	therefore	ADV
ajst-2833	92	28	e1	e1	PROPN
ajst-2833	92	29	is	be	AUX
ajst-2833	92	30	non	non	ADJ
ajst-2833	92	31	-	-	ADJ
ajst-2833	92	32	hyperbolic	hyperbolic	ADJ
ajst-2833	92	33	;	;	PUNCT
ajst-2833	92	34	if	if	SCONJ
ajst-2833	92	35	b	b	X
ajst-2833	92	36	>	>	X
ajst-2833	92	37	a	a	DET
ajst-2833	92	38	,	,	PUNCT
ajst-2833	92	39	implying	imply	VERB
ajst-2833	92	40	|λ2|	|λ2|	NOUN
ajst-2833	92	41	<	<	X
ajst-2833	92	42	1	1	NUM
ajst-2833	92	43	,	,	PUNCT
ajst-2833	92	44	then	then	ADV
ajst-2833	92	45	e1	e1	NOUN
ajst-2833	92	46	is	be	AUX
ajst-2833	92	47	a	a	DET
ajst-2833	92	48	stable	stable	ADJ
ajst-2833	92	49	node	node	NOUN
ajst-2833	92	50	,	,	PUNCT
ajst-2833	92	51	namely	namely	ADV
ajst-2833	92	52	,	,	PUNCT
ajst-2833	92	53	a	a	DET
ajst-2833	92	54	sink	sink	NOUN
ajst-2833	92	55	.	.	PUNCT
ajst-2833	93	1	the	the	DET
ajst-2833	93	2	proof	proof	NOUN
ajst-2833	93	3	is	be	AUX
ajst-2833	93	4	complete	complete	ADJ
ajst-2833	93	5	.	.	PUNCT
ajst-2833	94	1	theorem	theorem	VERB
ajst-2833	94	2	2.3	2.3	NUM
ajst-2833	94	3	.	.	PUNCT
ajst-2833	95	1	when	when	SCONJ
ajst-2833	95	2	0a	0a	PROPN
ajst-2833	95	3	b	b	NOUN
ajst-2833	95	4			INTJ
ajst-2833	95	5	,	,	PUNCT
ajst-2833	95	6	2	2	NUM
ajst-2833	95	7	(	(	PUNCT
ajst-2833	95	8	,	,	PUNCT
ajst-2833	95	9	)	)	PUNCT
ajst-2833	95	10	b	b	X
ajst-2833	95	11	r	r	NOUN
ajst-2833	95	12	a	a	PRON
ajst-2833	95	13	b	b	NOUN
ajst-2833	95	14	e	e	NOUN
ajst-2833	95	15	a	a	DET
ajst-2833	95	16	r	r	NOUN
ajst-2833	95	17	a	a	DET
ajst-2833	95	18	r	r	NOUN
ajst-2833	95	19			ADV
ajst-2833	95	20			PROPN
ajst-2833	95	21			PROPN
ajst-2833	95	22			PRON
ajst-2833	95	23			PRON
ajst-2833	95	24	is	be	AUX
ajst-2833	95	25	a	a	DET
ajst-2833	95	26	positive	positive	ADJ
ajst-2833	95	27	fixed	fix	VERB
ajst-2833	95	28	point	point	NOUN
ajst-2833	95	29	of	of	ADP
ajst-2833	95	30	the	the	DET
ajst-2833	95	31	system	system	NOUN
ajst-2833	95	32	(	(	PUNCT
ajst-2833	95	33	1.6	1.6	NUM
ajst-2833	95	34	)	)	PUNCT
ajst-2833	95	35	.	.	PUNCT
ajst-2833	96	1	let	let	VERB
ajst-2833	96	2	0	0	NUM
ajst-2833	96	3	2	2	NUM
ajst-2833	96	4	(	(	PUNCT
ajst-2833	96	5	2	2	NUM
ajst-2833	96	6	)	)	PUNCT
ajst-2833	96	7	(	(	PUNCT
ajst-2833	96	8	)	)	PUNCT
ajst-2833	96	9	2	2	NUM
ajst-2833	96	10	a	a	DET
ajst-2833	96	11	b	b	NOUN
ajst-2833	96	12	a	a	DET
ajst-2833	96	13	b	b	NOUN
ajst-2833	96	14	r	r	NOUN
ajst-2833	96	15	a	a	PRON
ajst-2833	96	16	b	b	NOUN
ajst-2833	96	17			X
ajst-2833	96	18			VERB
ajst-2833	96	19			PROPN
ajst-2833	96	20			PROPN
ajst-2833	96	21			PROPN
ajst-2833	96	22			NOUN
ajst-2833	96	23	for	for	ADP
ajst-2833	96	24	2a	2a	NUM
ajst-2833	96	25	b	b	PART
ajst-2833	96	26			PROPN
ajst-2833	96	27	and	and	CCONJ
ajst-2833	96	28	r1	r1	PROPN
ajst-2833	96	29	=	=	SYM
ajst-2833	96	30	b(a	b(a	PROPN
ajst-2833	96	31	−	−	PROPN
ajst-2833	96	32	b	b	PROPN
ajst-2833	96	33	−	−	PROPN
ajst-2833	96	34	1	1	NUM
ajst-2833	96	35	)	)	PUNCT
ajst-2833	96	36	,	,	PUNCT
ajst-2833	96	37	then	then	ADV
ajst-2833	96	38	the	the	DET
ajst-2833	96	39	following	follow	VERB
ajst-2833	96	40	table	table	NOUN
ajst-2833	96	41	statements	statement	NOUN
ajst-2833	96	42	are	be	AUX
ajst-2833	96	43	true	true	ADJ
ajst-2833	96	44	about	about	ADP
ajst-2833	96	45	the	the	DET
ajst-2833	96	46	positive	positive	ADJ
ajst-2833	96	47	fixed	fix	VERB
ajst-2833	96	48	point	point	NOUN
ajst-2833	96	49	e2	e2	PROPN
ajst-2833	96	50	.	.	PUNCT
ajst-2833	97	1	121	121	NUM
ajst-2833	97	2	table	table	NOUN
ajst-2833	97	3	1	1	NUM
ajst-2833	97	4	.	.	PUNCT
ajst-2833	97	5	properties	property	NOUN
ajst-2833	97	6	of	of	ADP
ajst-2833	97	7	the	the	DET
ajst-2833	97	8	fixed	fix	VERB
ajst-2833	97	9	point	point	NOUN
ajst-2833	97	10	e2	e2	PROPN
ajst-2833	97	11	.	.	PUNCT
ajst-2833	98	1	conditions	condition	NOUN
ajst-2833	98	2	eigenvalues	eigenvalue	VERB
ajst-2833	98	3	properties	property	NOUN
ajst-2833	98	4	0	0	NUM
ajst-2833	98	5	<	<	X
ajst-2833	98	6	a	a	DET
ajst-2833	98	7	−	−	PROPN
ajst-2833	98	8	b	b	SYM
ajst-2833	98	9	≤	≤	NUM
ajst-2833	98	10	1	1	NUM
ajst-2833	98	11	|λ1|	|λ1|	ADP
ajst-2833	98	12	<	<	X
ajst-2833	98	13	1,|λ2|	1,|λ2|	NUM
ajst-2833	98	14	<	<	SYM
ajst-2833	98	15	1	1	NUM
ajst-2833	98	16	sink	sink	NOUN
ajst-2833	98	17	1	1	NUM
ajst-2833	98	18	<	<	X
ajst-2833	98	19	a	a	DET
ajst-2833	98	20	−	−	PROPN
ajst-2833	98	21	b	b	SYM
ajst-2833	98	22	≤	≤	ADV
ajst-2833	98	23	2	2	NUM
ajst-2833	98	24	r	r	NOUN
ajst-2833	98	25	<	<	X
ajst-2833	98	26	r1	r1	PROPN
ajst-2833	98	27	|λ1|	|λ1|	X
ajst-2833	98	28	>	>	X
ajst-2833	98	29	1,|λ2|	1,|λ2|	NUM
ajst-2833	98	30	>	>	SYM
ajst-2833	98	31	1	1	NUM
ajst-2833	98	32	source	source	NOUN
ajst-2833	98	33	r	r	NOUN
ajst-2833	98	34	=	=	SYM
ajst-2833	98	35	r1	r1	NOUN
ajst-2833	98	36	|λ1|	|λ1|	NOUN
ajst-2833	98	37	=	=	NOUN
ajst-2833	98	38	|λ2|	|λ2|	NOUN
ajst-2833	98	39	=	=	SYM
ajst-2833	98	40	1	1	NUM
ajst-2833	98	41	non	non	ADJ
ajst-2833	98	42	-	-	ADJ
ajst-2833	98	43	hyperbolic	hyperbolic	ADJ
ajst-2833	98	44	r	r	NOUN
ajst-2833	98	45	>	>	X
ajst-2833	98	46	r1	r1	PROPN
ajst-2833	98	47	|λ1|	|λ1|	ADP
ajst-2833	98	48	<	<	X
ajst-2833	98	49	1,|λ2|	1,|λ2|	NUM
ajst-2833	98	50	<	<	SYM
ajst-2833	98	51	1	1	NUM
ajst-2833	98	52	sink	sink	NOUN
ajst-2833	98	53	2	2	NUM
ajst-2833	98	54	<	<	X
ajst-2833	98	55	a	a	DET
ajst-2833	98	56	–	–	PUNCT
ajst-2833	98	57	b	b	NOUN
ajst-2833	98	58	0	0	PUNCT
ajst-2833	98	59	<	<	X
ajst-2833	98	60	r	r	X
ajst-2833	98	61	<	<	X
ajst-2833	98	62	r1	r1	PROPN
ajst-2833	98	63	|λ1|	|λ1|	X
ajst-2833	98	64	>	>	X
ajst-2833	98	65	1,|λ2|	1,|λ2|	NUM
ajst-2833	98	66	>	>	SYM
ajst-2833	98	67	1	1	NUM
ajst-2833	98	68	source	source	NOUN
ajst-2833	98	69	r	r	NOUN
ajst-2833	98	70	=	=	SYM
ajst-2833	98	71	r1	r1	NOUN
ajst-2833	98	72	|λ1|	|λ1|	NOUN
ajst-2833	98	73	=	=	NOUN
ajst-2833	98	74	|λ2|	|λ2|	NOUN
ajst-2833	98	75	=	=	SYM
ajst-2833	98	76	1	1	NUM
ajst-2833	98	77	non	non	ADJ
ajst-2833	98	78	-	-	ADJ
ajst-2833	98	79	hyperbolic	hyperbolic	ADJ
ajst-2833	98	80	r1	r1	NOUN
ajst-2833	98	81	<	<	X
ajst-2833	98	82	r	r	NOUN
ajst-2833	98	83	<	<	X
ajst-2833	98	84	r0	r0	NOUN
ajst-2833	98	85	|λ1|	|λ1|	X
ajst-2833	98	86	<	<	X
ajst-2833	98	87	1,|λ2|	1,|λ2|	NUM
ajst-2833	98	88	<	<	SYM
ajst-2833	98	89	1	1	NUM
ajst-2833	98	90	sink	sink	NOUN
ajst-2833	98	91	r	r	NOUN
ajst-2833	98	92	=	=	SYM
ajst-2833	98	93	r0	r0	NOUN
ajst-2833	98	94	λ1	λ1	NOUN
ajst-2833	98	95	=	=	PUNCT
ajst-2833	98	96	−1,λ2	−1,λ2	PROPN
ajst-2833	98	97	≠−1	≠−1	PROPN
ajst-2833	98	98	non	non	ADJ
ajst-2833	98	99	-	-	ADJ
ajst-2833	98	100	hyperbolic	hyperbolic	ADJ
ajst-2833	98	101	r	r	NOUN
ajst-2833	98	102	>	>	X
ajst-2833	98	103	r0	r0	NOUN
ajst-2833	98	104	|λ1|	|λ1|	ADP
ajst-2833	98	105	<	<	X
ajst-2833	98	106	1,|λ2|	1,|λ2|	NUM
ajst-2833	98	107	>	>	SYM
ajst-2833	98	108	1	1	NUM
ajst-2833	98	109	saddle	saddle	NOUN
ajst-2833	98	110	0	0	NUM
ajst-2833	98	111	<	<	X
ajst-2833	98	112	r	r	X
ajst-2833	98	113	<	<	X
ajst-2833	98	114	r1	r1	PROPN
ajst-2833	98	115	|λ1|	|λ1|	X
ajst-2833	98	116	>	>	X
ajst-2833	98	117	1,|λ2|	1,|λ2|	NUM
ajst-2833	98	118	>	>	SYM
ajst-2833	98	119	1	1	NUM
ajst-2833	98	120	source	source	NOUN
ajst-2833	98	121	r	r	NOUN
ajst-2833	98	122	=	=	SYM
ajst-2833	98	123	r1	r1	NOUN
ajst-2833	98	124	λ1	λ1	NOUN
ajst-2833	98	125	=	=	SYM
ajst-2833	98	126	λ2	λ2	PROPN
ajst-2833	98	127	=	=	SYM
ajst-2833	98	128	−1	−1	NOUN
ajst-2833	98	129	non	non	ADJ
ajst-2833	98	130	-	-	ADJ
ajst-2833	98	131	hyperbolic	hyperbolic	ADJ
ajst-2833	98	132	r	r	NOUN
ajst-2833	98	133	>	>	X
ajst-2833	98	134	r1	r1	PROPN
ajst-2833	98	135	|λ1|	|λ1|	ADP
ajst-2833	98	136	<	<	X
ajst-2833	98	137	1,|λ2|	1,|λ2|	NUM
ajst-2833	98	138	>	>	SYM
ajst-2833	98	139	1	1	NUM
ajst-2833	98	140	saddle	saddle	NOUN
ajst-2833	98	141	2	2	NUM
ajst-2833	98	142	(	(	PUNCT
ajst-2833	98	143	2)b	2)b	NUM
ajst-2833	98	144	a	a	DET
ajst-2833	98	145	b	b	NOUN
ajst-2833	98	146			X
ajst-2833	98	147			X
ajst-2833	98	148	0	0	PUNCT
ajst-2833	99	1	<	<	X
ajst-2833	99	2	r	r	X
ajst-2833	99	3	<	<	X
ajst-2833	99	4	r0	r0	NOUN
ajst-2833	99	5	|λ1|	|λ1|	X
ajst-2833	99	6	>	>	X
ajst-2833	99	7	1,|λ2|	1,|λ2|	NUM
ajst-2833	99	8	>	>	SYM
ajst-2833	99	9	1	1	NUM
ajst-2833	99	10	source	source	NOUN
ajst-2833	99	11	r	r	NOUN
ajst-2833	99	12	=	=	SYM
ajst-2833	99	13	r0	r0	NOUN
ajst-2833	99	14	λ1	λ1	NOUN
ajst-2833	99	15	=	=	SYM
ajst-2833	99	16	−1,λ2	−1,λ2	NOUN
ajst-2833	99	17	≠	≠	PROPN
ajst-2833	99	18	−1	−1	NOUN
ajst-2833	99	19	non	non	ADJ
ajst-2833	99	20	-	-	ADJ
ajst-2833	99	21	hyperbolic	hyperbolic	ADJ
ajst-2833	99	22	r	r	NOUN
ajst-2833	99	23	>	>	X
ajst-2833	99	24	r0	r0	NOUN
ajst-2833	99	25	|λ1|	|λ1|	ADP
ajst-2833	99	26	<	<	X
ajst-2833	99	27	1	1	NUM
ajst-2833	99	28	,	,	PUNCT
ajst-2833	99	29	|λ2|	|λ2|	NOUN
ajst-2833	99	30	>	>	X
ajst-2833	99	31	1	1	NUM
ajst-2833	99	32	saddle	saddle	NOUN
ajst-2833	99	33	3	3	NUM
ajst-2833	99	34	.	.	PUNCT
ajst-2833	100	1	bifurcation	bifurcation	NOUN
ajst-2833	100	2	analysis	analysis	NOUN
ajst-2833	100	3	in	in	ADP
ajst-2833	100	4	this	this	DET
ajst-2833	100	5	section	section	NOUN
ajst-2833	100	6	,	,	PUNCT
ajst-2833	100	7	we	we	PRON
ajst-2833	100	8	are	be	AUX
ajst-2833	100	9	in	in	ADP
ajst-2833	100	10	a	a	DET
ajst-2833	100	11	position	position	NOUN
ajst-2833	100	12	to	to	PART
ajst-2833	100	13	use	use	VERB
ajst-2833	100	14	the	the	DET
ajst-2833	100	15	bifurcation	bifurcation	NOUN
ajst-2833	100	16	theorem	theorem	VERB
ajst-2833	100	17	to	to	PART
ajst-2833	100	18	analyze	analyze	VERB
ajst-2833	100	19	the	the	DET
ajst-2833	100	20	local	local	ADJ
ajst-2833	100	21	bifurcation	bifurcation	NOUN
ajst-2833	100	22	problems	problem	NOUN
ajst-2833	100	23	of	of	ADP
ajst-2833	100	24	the	the	DET
ajst-2833	100	25	fixed	fix	VERB
ajst-2833	100	26	points	point	NOUN
ajst-2833	100	27	e2	e2	PROPN
ajst-2833	100	28	.	.	PUNCT
ajst-2833	101	1	for	for	ADP
ajst-2833	101	2	related	related	ADJ
ajst-2833	101	3	work	work	NOUN
ajst-2833	101	4	,	,	PUNCT
ajst-2833	101	5	refer	refer	VERB
ajst-2833	101	6	to	to	ADP
ajst-2833	101	7	[	[	PUNCT
ajst-2833	101	8	17	17	NUM
ajst-2833	101	9	-	-	SYM
ajst-2833	101	10	21	21	NUM
ajst-2833	101	11	]	]	PUNCT
ajst-2833	101	12	.	.	PUNCT
ajst-2833	102	1	3.1	3.1	NUM
ajst-2833	102	2	.	.	PUNCT
ajst-2833	103	1	for	for	ADP
ajst-2833	103	2	fixed	fix	VERB
ajst-2833	103	3	point	point	NOUN
ajst-2833	103	4	2	2	NUM
ajst-2833	103	5	(	(	PUNCT
ajst-2833	103	6	,	,	PUNCT
ajst-2833	103	7	)	)	PUNCT
ajst-2833	103	8	b	b	X
ajst-2833	103	9	r	r	NOUN
ajst-2833	103	10	a	a	PRON
ajst-2833	103	11	b	b	NOUN
ajst-2833	103	12	e	e	NOUN
ajst-2833	103	13	a	a	DET
ajst-2833	103	14	r	r	NOUN
ajst-2833	103	15	a	a	DET
ajst-2833	103	16	r	r	NOUN
ajst-2833	103	17			ADV
ajst-2833	103	18			PROPN
ajst-2833	103	19			PROPN
ajst-2833	103	20			ADV
ajst-2833	103	21			PUNCT
ajst-2833	103	22	when	when	SCONJ
ajst-2833	103	23	r	r	NOUN
ajst-2833	103	24	=	=	SYM
ajst-2833	103	25	r1	r1	NOUN
ajst-2833	103	26	=	=	SYM
ajst-2833	103	27	b(a	b(a	PROPN
ajst-2833	103	28	−	−	PROPN
ajst-2833	103	29	b	b	PROPN
ajst-2833	103	30	−	−	PROPN
ajst-2833	103	31	1	1	NUM
ajst-2833	103	32	)	)	PUNCT
ajst-2833	103	33	,	,	PUNCT
ajst-2833	103	34	theorem	theorem	VERB
ajst-2833	103	35	2.4	2.4	NUM
ajst-2833	103	36	with	with	ADP
ajst-2833	103	37	lemma	lemma	PROPN
ajst-2833	103	38	1.1	1.1	NUM
ajst-2833	103	39	(	(	PUNCT
ajst-2833	103	40	i.5	i.5	NOUN
ajst-2833	103	41	)	)	PUNCT
ajst-2833	103	42	shows	show	VERB
ajst-2833	103	43	that	that	SCONJ
ajst-2833	103	44	f(1	f(1	PROPN
ajst-2833	103	45	)	)	PUNCT
ajst-2833	103	46	>	>	X
ajst-2833	104	1	0	0	NUM
ajst-2833	104	2	,	,	PUNCT
ajst-2833	104	3	f(−1	f(−1	PROPN
ajst-2833	104	4	)	)	PUNCT
ajst-2833	104	5	>	>	X
ajst-2833	104	6	0	0	NUM
ajst-2833	104	7	,	,	PUNCT
ajst-2833	104	8	−2	−2	NOUN
ajst-2833	104	9	<	<	X
ajst-2833	104	10	p	p	X
ajst-2833	104	11	<	<	X
ajst-2833	104	12	2	2	NUM
ajst-2833	104	13	and	and	CCONJ
ajst-2833	104	14	q	q	NOUN
ajst-2833	105	1	=	=	NOUN
ajst-2833	105	2	1	1	NUM
ajst-2833	105	3	,	,	PUNCT
ajst-2833	105	4	so	so	ADV
ajst-2833	105	5	λ1	λ1	ADJ
ajst-2833	105	6	and	and	CCONJ
ajst-2833	105	7	λ2	λ2	NOUN
ajst-2833	105	8	are	be	AUX
ajst-2833	105	9	a	a	DET
ajst-2833	105	10	pair	pair	NOUN
ajst-2833	105	11	of	of	ADP
ajst-2833	105	12	conjugate	conjugate	ADJ
ajst-2833	105	13	complex	complex	ADJ
ajst-2833	105	14	roots	root	NOUN
ajst-2833	105	15	with	with	ADP
ajst-2833	105	16	|λ1|	|λ1|	NOUN
ajst-2833	105	17	=	=	NOUN
ajst-2833	105	18	|λ2|	|λ2|	NOUN
ajst-2833	105	19	=	=	NOUN
ajst-2833	105	20	1	1	X
ajst-2833	105	21	.	.	PUNCT
ajst-2833	106	1	at	at	ADP
ajst-2833	106	2	this	this	DET
ajst-2833	106	3	time	time	NOUN
ajst-2833	106	4	we	we	PRON
ajst-2833	106	5	derive	derive	VERB
ajst-2833	106	6	that	that	SCONJ
ajst-2833	106	7	the	the	DET
ajst-2833	106	8	system	system	NOUN
ajst-2833	106	9	(	(	PUNCT
ajst-2833	106	10	6	6	NUM
ajst-2833	106	11	)	)	PUNCT
ajst-2833	106	12	at	at	ADP
ajst-2833	106	13	the	the	DET
ajst-2833	106	14	fixed	fix	VERB
ajst-2833	106	15	point	point	NOUN
ajst-2833	106	16	e2	e2	PROPN
ajst-2833	106	17	can	can	AUX
ajst-2833	106	18	undergo	undergo	VERB
ajst-2833	106	19	a	a	DET
ajst-2833	106	20	neimark	neimark	NOUN
ajst-2833	106	21	-	-	PUNCT
ajst-2833	106	22	sacker	sacker	NOUN
ajst-2833	106	23	bifurcation	bifurcation	NOUN
ajst-2833	106	24	in	in	ADP
ajst-2833	106	25	the	the	DET
ajst-2833	106	26	space	space	NOUN
ajst-2833	106	27	of	of	ADP
ajst-2833	106	28	parameters	parameter	NOUN
ajst-2833	106	29	3	3	NUM
ajst-2833	106	30	(	(	PUNCT
ajst-2833	106	31	,	,	PUNCT
ajst-2833	106	32	,	,	PUNCT
ajst-2833	106	33	)	)	PUNCT
ajst-2833	106	34	{	{	PUNCT
ajst-2833	106	35	(	(	PUNCT
ajst-2833	106	36	,	,	PUNCT
ajst-2833	106	37	,	,	PUNCT
ajst-2833	106	38	)	)	PUNCT
ajst-2833	106	39	|1	|1	PRON
ajst-2833	107	1	2	2	NUM
ajst-2833	107	2	,	,	PUNCT
ajst-2833	107	3	0}ea	0}ea	NOUN
ajst-2833	107	4	b	b	NOUN
ajst-2833	107	5	r	r	NOUN
ajst-2833	107	6	s	s	PROPN
ajst-2833	107	7	a	a	DET
ajst-2833	107	8	b	b	NOUN
ajst-2833	107	9	r	r	NOUN
ajst-2833	107	10	r	r	NOUN
ajst-2833	107	11	a	a	DET
ajst-2833	107	12	b	b	NOUN
ajst-2833	108	1	r	r	NOUN
ajst-2833	108	2			X
ajst-2833	108	3			PROPN
ajst-2833	108	4			PROPN
ajst-2833	108	5			NOUN
ajst-2833	108	6			PROPN
ajst-2833	108	7			VERB
ajst-2833	108	8			NOUN
ajst-2833	108	9			INTJ
ajst-2833	108	10	.	.	PUNCT
ajst-2833	109	1	in	in	ADP
ajst-2833	109	2	order	order	NOUN
ajst-2833	109	3	to	to	PART
ajst-2833	109	4	show	show	VERB
ajst-2833	109	5	the	the	DET
ajst-2833	109	6	process	process	NOUN
ajst-2833	109	7	clearly	clearly	ADV
ajst-2833	109	8	,	,	PUNCT
ajst-2833	109	9	we	we	PRON
ajst-2833	109	10	carry	carry	VERB
ajst-2833	109	11	out	out	ADP
ajst-2833	109	12	the	the	DET
ajst-2833	109	13	following	follow	VERB
ajst-2833	109	14	steps	step	NOUN
ajst-2833	109	15	.	.	PUNCT
ajst-2833	110	1	the	the	DET
ajst-2833	110	2	first	first	ADJ
ajst-2833	110	3	step	step	NOUN
ajst-2833	110	4	.	.	PUNCT
ajst-2833	111	1	take	take	VERB
ajst-2833	111	2	the	the	DET
ajst-2833	111	3	changes	change	NOUN
ajst-2833	111	4	of	of	ADP
ajst-2833	111	5	variables	variable	NOUN
ajst-2833	111	6	un	un	PROPN
ajst-2833	112	1	=	=	PROPN
ajst-2833	112	2	xn	xn	PROPN
ajst-2833	112	3	−	−	NOUN
ajst-2833	112	4	x0,vn	x0,vn	PUNCT
ajst-2833	112	5	=	=	SYM
ajst-2833	112	6	yn	yn	PROPN
ajst-2833	112	7	−y0	−y0	PROPN
ajst-2833	112	8	,	,	PUNCT
ajst-2833	112	9	which	which	PRON
ajst-2833	112	10	transform	transform	VERB
ajst-2833	112	11	fixed	fix	VERB
ajst-2833	112	12	point	point	NOUN
ajst-2833	112	13	e2	e2	PROPN
ajst-2833	112	14	=	=	SYM
ajst-2833	112	15	(	(	PUNCT
ajst-2833	112	16	x0,y0	x0,y0	PROPN
ajst-2833	112	17	)	)	PUNCT
ajst-2833	112	18	to	to	ADP
ajst-2833	112	19	the	the	DET
ajst-2833	112	20	origin	origin	NOUN
ajst-2833	112	21	o(0,0	o(0,0	NOUN
ajst-2833	112	22	)	)	PUNCT
ajst-2833	112	23	,	,	PUNCT
ajst-2833	112	24	and	and	CCONJ
ajst-2833	112	25	the	the	DET
ajst-2833	112	26	system	system	NOUN
ajst-2833	112	27	(	(	PUNCT
ajst-2833	112	28	1.6	1.6	NUM
ajst-2833	112	29	)	)	PUNCT
ajst-2833	112	30	into	into	ADP
ajst-2833	112	31	0	0	NUM
ajst-2833	112	32	0	0	NUM
ajst-2833	112	33	0	0	NUM
ajst-2833	112	34	0	0	NUM
ajst-2833	112	35	1	1	NUM
ajst-2833	112	36	1	1	NUM
ajst-2833	112	37	0	0	NUM
ajst-2833	112	38	0	0	NUM
ajst-2833	112	39	(	(	PUNCT
ajst-2833	112	40	)	)	PUNCT
ajst-2833	112	41	(	(	PUNCT
ajst-2833	112	42	)	)	PUNCT
ajst-2833	112	43	1	1	NUM
ajst-2833	112	44	0	0	NUM
ajst-2833	112	45	0	0	NUM
ajst-2833	112	46	(	(	PUNCT
ajst-2833	112	47	)	)	PUNCT
ajst-2833	112	48	,	,	PUNCT
ajst-2833	112	49	(	(	PUNCT
ajst-2833	112	50	)	)	PUNCT
ajst-2833	112	51	.	.	PUNCT
ajst-2833	113	1	n	n	CCONJ
ajst-2833	113	2	n	n	CCONJ
ajst-2833	113	3	n	n	CCONJ
ajst-2833	113	4	n	n	CCONJ
ajst-2833	113	5	u	u	NOUN
ajst-2833	113	6	x	x	PROPN
ajst-2833	113	7	v	v	ADP
ajst-2833	113	8	y	y	PROPN
ajst-2833	113	9	n	n	PROPN
ajst-2833	113	10	n	n	PROPN
ajst-2833	113	11	b	b	PROPN
ajst-2833	113	12	a	a	DET
ajst-2833	113	13	u	u	NOUN
ajst-2833	113	14	x	x	NOUN
ajst-2833	113	15	r	r	NOUN
ajst-2833	113	16	v	v	NUM
ajst-2833	113	17	y	y	PROPN
ajst-2833	113	18	n	n	CCONJ
ajst-2833	113	19	n	n	CCONJ
ajst-2833	113	20	u	u	X
ajst-2833	113	21	u	u	X
ajst-2833	113	22	x	x	X
ajst-2833	113	23	e	e	NOUN
ajst-2833	113	24	x	x	PROPN
ajst-2833	113	25	v	v	ADP
ajst-2833	113	26	v	v	ADP
ajst-2833	113	27	y	y	PROPN
ajst-2833	113	28	e	e	PROPN
ajst-2833	113	29	y	y	PROPN
ajst-2833	113	30			PROPN
ajst-2833	113	31			PROPN
ajst-2833	113	32			PROPN
ajst-2833	113	33			PROPN
ajst-2833	113	34			PUNCT
ajst-2833	113	35			PROPN
ajst-2833	113	36			PUNCT
ajst-2833	113	37			PUNCT
ajst-2833	113	38			PROPN
ajst-2833	113	39			ADV
ajst-2833	113	40			VERB
ajst-2833	113	41			ADP
ajst-2833	113	42			PROPN
ajst-2833	113	43			PUNCT
ajst-2833	113	44			X
ajst-2833	113	45			NUM
ajst-2833	113	46			NOUN
ajst-2833	113	47			PUNCT
ajst-2833	113	48			CCONJ
ajst-2833	113	49	(	(	PUNCT
ajst-2833	113	50	7	7	X
ajst-2833	113	51	)	)	PUNCT
ajst-2833	113	52	the	the	DET
ajst-2833	113	53	second	second	ADJ
ajst-2833	113	54	step	step	NOUN
ajst-2833	113	55	.	.	PUNCT
ajst-2833	114	1	give	give	VERB
ajst-2833	114	2	a	a	DET
ajst-2833	114	3	small	small	ADJ
ajst-2833	114	4	perturbation	perturbation	NOUN
ajst-2833	114	5	r	r	NOUN
ajst-2833	114	6	*	*	PUNCT
ajst-2833	114	7	of	of	ADP
ajst-2833	114	8	the	the	DET
ajst-2833	114	9	parameter	parameter	NOUN
ajst-2833	114	10	r	r	NOUN
ajst-2833	114	11	,	,	PUNCT
ajst-2833	114	12	i.e.	i.e.	X
ajst-2833	114	13	,	,	PUNCT
ajst-2833	114	14	r	r	NOUN
ajst-2833	114	15	*	*	SYM
ajst-2833	114	16	=	=	PUNCT
ajst-2833	114	17	r	r	NOUN
ajst-2833	114	18	−	−	PROPN
ajst-2833	114	19	r1	r1	NOUN
ajst-2833	114	20	,	,	PUNCT
ajst-2833	114	21	then	then	ADV
ajst-2833	114	22	the	the	DET
ajst-2833	114	23	perturbation	perturbation	NOUN
ajst-2833	114	24	of	of	ADP
ajst-2833	114	25	the	the	DET
ajst-2833	114	26	system	system	NOUN
ajst-2833	114	27	(	(	PUNCT
ajst-2833	114	28	3.1	3.1	NUM
ajst-2833	114	29	)	)	PUNCT
ajst-2833	114	30	can	can	AUX
ajst-2833	114	31	be	be	AUX
ajst-2833	114	32	regarded	regard	VERB
ajst-2833	114	33	as	as	SCONJ
ajst-2833	114	34	follows	follow	VERB
ajst-2833	114	35	0	0	NUM
ajst-2833	114	36	0	0	NUM
ajst-2833	115	1	*	*	SYM
ajst-2833	115	2	0	0	NUM
ajst-2833	116	1	1	1	NUM
ajst-2833	116	2	0	0	NUM
ajst-2833	116	3	1	1	NUM
ajst-2833	116	4	1	1	NUM
ajst-2833	116	5	0	0	NUM
ajst-2833	116	6	0	0	NUM
ajst-2833	116	7	(	(	PUNCT
ajst-2833	116	8	)	)	PUNCT
ajst-2833	116	9	(	(	PUNCT
ajst-2833	116	10	)	)	PUNCT
ajst-2833	116	11	(	(	PUNCT
ajst-2833	116	12	)	)	PUNCT
ajst-2833	117	1	1	1	NUM
ajst-2833	117	2	0	0	NUM
ajst-2833	117	3	0	0	NUM
ajst-2833	117	4	(	(	PUNCT
ajst-2833	117	5	)	)	PUNCT
ajst-2833	117	6	,	,	PUNCT
ajst-2833	117	7	(	(	PUNCT
ajst-2833	117	8	)	)	PUNCT
ajst-2833	117	9	.	.	PUNCT
ajst-2833	118	1	n	n	CCONJ
ajst-2833	118	2	n	n	CCONJ
ajst-2833	118	3	n	n	CCONJ
ajst-2833	118	4	n	n	CCONJ
ajst-2833	118	5	u	u	NOUN
ajst-2833	118	6	x	x	PROPN
ajst-2833	118	7	v	v	ADP
ajst-2833	118	8	y	y	PROPN
ajst-2833	118	9	n	n	PROPN
ajst-2833	118	10	n	n	PROPN
ajst-2833	118	11	b	b	PROPN
ajst-2833	118	12	a	a	DET
ajst-2833	118	13	u	u	NOUN
ajst-2833	119	1	x	x	NOUN
ajst-2833	119	2	r	r	NOUN
ajst-2833	119	3	r	r	NOUN
ajst-2833	119	4	v	v	NOUN
ajst-2833	119	5	y	y	PROPN
ajst-2833	119	6	n	n	CCONJ
ajst-2833	119	7	n	n	CCONJ
ajst-2833	119	8	u	u	X
ajst-2833	119	9	u	u	X
ajst-2833	119	10	x	x	X
ajst-2833	119	11	e	e	NOUN
ajst-2833	119	12	x	x	PROPN
ajst-2833	119	13	v	v	ADP
ajst-2833	119	14	v	v	ADP
ajst-2833	119	15	y	y	PROPN
ajst-2833	119	16	e	e	PROPN
ajst-2833	119	17	y	y	PROPN
ajst-2833	119	18			PROPN
ajst-2833	119	19			PROPN
ajst-2833	119	20			PROPN
ajst-2833	119	21			PROPN
ajst-2833	119	22			PUNCT
ajst-2833	119	23			PROPN
ajst-2833	119	24			PUNCT
ajst-2833	119	25			PUNCT
ajst-2833	119	26			PROPN
ajst-2833	119	27			ADV
ajst-2833	119	28			CCONJ
ajst-2833	119	29			VERB
ajst-2833	119	30			ADP
ajst-2833	119	31			NOUN
ajst-2833	119	32			PUNCT
ajst-2833	119	33			VERB
ajst-2833	119	34			NUM
ajst-2833	119	35			NOUN
ajst-2833	119	36			ADJ
ajst-2833	119	37			PROPN
ajst-2833	119	38	(	(	PUNCT
ajst-2833	119	39	8)	8)	NUM
ajst-2833	119	40	the	the	DET
ajst-2833	119	41	corresponding	corresponding	ADJ
ajst-2833	119	42	characteristic	characteristic	ADJ
ajst-2833	119	43	equation	equation	NOUN
ajst-2833	119	44	of	of	ADP
ajst-2833	119	45	the	the	DET
ajst-2833	119	46	linearized	linearize	VERB
ajst-2833	119	47	equation	equation	NOUN
ajst-2833	119	48	of	of	ADP
ajst-2833	119	49	the	the	DET
ajst-2833	119	50	system	system	NOUN
ajst-2833	119	51	(	(	PUNCT
ajst-2833	119	52	7	7	NUM
ajst-2833	119	53	)	)	PUNCT
ajst-2833	119	54	at	at	ADP
ajst-2833	119	55	the	the	DET
ajst-2833	119	56	equilibrium	equilibrium	NOUN
ajst-2833	119	57	point	point	NOUN
ajst-2833	119	58	(	(	PUNCT
ajst-2833	119	59	0,0	0,0	NOUN
ajst-2833	119	60	)	)	PUNCT
ajst-2833	119	61	can	can	AUX
ajst-2833	119	62	be	be	AUX
ajst-2833	119	63	expressed	express	VERB
ajst-2833	119	64	as	as	ADP
ajst-2833	119	65	f(λ	f(λ	NOUN
ajst-2833	119	66	)	)	PUNCT
ajst-2833	119	67	=	=	SYM
ajst-2833	119	68	λ2	λ2	NOUN
ajst-2833	119	69	−	−	PROPN
ajst-2833	119	70	p(r*)λ	p(r*)λ	PROPN
ajst-2833	119	71	+	+	CCONJ
ajst-2833	119	72	q(r	q(r	PROPN
ajst-2833	119	73	*	*	PUNCT
ajst-2833	119	74	)	)	PUNCT
ajst-2833	120	1	=	=	SYM
ajst-2833	120	2	0	0	NUM
ajst-2833	120	3	,	,	PUNCT
ajst-2833	120	4	where	where	SCONJ
ajst-2833	120	5	,	,	PUNCT
ajst-2833	120	6	and	and	CCONJ
ajst-2833	120	7	.	.	PUNCT
ajst-2833	121	1	it	it	PRON
ajst-2833	121	2	is	be	AUX
ajst-2833	121	3	easy	easy	ADJ
ajst-2833	121	4	to	to	PART
ajst-2833	121	5	derive	derive	VERB
ajst-2833	121	6	p2(r	p2(r	NOUN
ajst-2833	121	7	*	*	NOUN
ajst-2833	121	8	)	)	PUNCT
ajst-2833	121	9	−	−	PROPN
ajst-2833	122	1	4q(r	4q(r	NOUN
ajst-2833	122	2	*	*	PUNCT
ajst-2833	122	3	)	)	PUNCT
ajst-2833	123	1	<	<	X
ajst-2833	123	2	0	0	PUNCT
ajst-2833	123	3	when	when	SCONJ
ajst-2833	123	4	r	r	X
ajst-2833	123	5	*	*	SYM
ajst-2833	123	6	=	=	SYM
ajst-2833	123	7	0	0	NUM
ajst-2833	123	8	,	,	PUNCT
ajst-2833	123	9	then	then	ADV
ajst-2833	123	10	the	the	DET
ajst-2833	123	11	two	two	NUM
ajst-2833	123	12	roots	root	NOUN
ajst-2833	123	13	of	of	ADP
ajst-2833	123	14	f(λ	f(λ	NOUN
ajst-2833	123	15	)	)	PUNCT
ajst-2833	124	1	=	=	SYM
ajst-2833	124	2	0	0	NUM
ajst-2833	124	3	are	be	AUX
ajst-2833	124	4	as	as	SCONJ
ajst-2833	124	5	follows	follow	VERB
ajst-2833	124	6	,	,	PUNCT
ajst-2833	124	7	moreover	moreover	ADV
ajst-2833	124	8	which	which	PRON
ajst-2833	124	9	implies	imply	VERB
ajst-2833	124	10	the	the	DET
ajst-2833	124	11	occurrence	occurrence	NOUN
ajst-2833	124	12	of	of	ADP
ajst-2833	124	13	neimark	neimark	NOUN
ajst-2833	124	14	-	-	PUNCT
ajst-2833	124	15	sacker	sacker	NOUN
ajst-2833	124	16	bifurcation	bifurcation	NOUN
ajst-2833	124	17	requires	require	VERB
ajst-2833	124	18	the	the	DET
ajst-2833	124	19	following	follow	VERB
ajst-2833	124	20	conditions	condition	NOUN
ajst-2833	124	21	to	to	PART
ajst-2833	124	22	be	be	AUX
ajst-2833	124	23	satisfied	satisfied	ADJ
ajst-2833	124	24	*	*	PUNCT
ajst-2833	124	25	*	*	PUNCT
ajst-2833	124	26	1,2	1,2	NUM
ajst-2833	124	27	*	*	SYM
ajst-2833	124	28	0	0	NUM
ajst-2833	125	1	|	|	ADV
ajst-2833	125	2	(	(	PUNCT
ajst-2833	125	3	)	)	PUNCT
ajst-2833	125	4	|	|	ADV
ajst-2833	125	5	(	(	PUNCT
ajst-2833	125	6	.1	.1	NUM
ajst-2833	125	7	)	)	PUNCT
ajst-2833	125	8	0	0	NUM
ajst-2833	125	9	;	;	PUNCT
ajst-2833	125	10	(	(	PUNCT
ajst-2833	125	11	)	)	PUNCT
ajst-2833	126	1	|	|	ADV
ajst-2833	126	2	r	r	NOUN
ajst-2833	126	3	d	d	NOUN
ajst-2833	126	4	r	r	NOUN
ajst-2833	126	5	h	h	PROPN
ajst-2833	126	6	dr	dr	PROPN
ajst-2833	126	7			PROPN
ajst-2833	126	8			PROPN
ajst-2833	126	9			NOUN
ajst-2833	126	10	1,2	1,2	NUM
ajst-2833	126	11	(	(	PUNCT
ajst-2833	126	12	.2	.2	NUM
ajst-2833	126	13	)	)	PUNCT
ajst-2833	126	14	(	(	PUNCT
ajst-2833	126	15	0	0	NUM
ajst-2833	126	16	)	)	PUNCT
ajst-2833	126	17	1	1	NUM
ajst-2833	126	18	,	,	PUNCT
ajst-2833	126	19	1,2,3,4.ih	1,2,3,4.ih	NUM
ajst-2833	126	20	i	i	PROPN
ajst-2833	126	21			VERB
ajst-2833	126	22			NOUN
ajst-2833	126	23	since	since	SCONJ
ajst-2833	126	24	*	*	PROPN
ajst-2833	127	1	*	*	PUNCT
ajst-2833	127	2	0	0	NUM
ajst-2833	127	3	1	1	NUM
ajst-2833	127	4	(	(	PUNCT
ajst-2833	127	5	1	1	NUM
ajst-2833	127	6	)	)	PUNCT
ajst-2833	127	7	(	(	PUNCT
ajst-2833	127	8	)	)	PUNCT
ajst-2833	127	9	1	1	NUM
ajst-2833	127	10	1	1	NUM
ajst-2833	127	11	|	|	ADV
ajst-2833	127	12	r	r	NOUN
ajst-2833	127	13	b	b	PROPN
ajst-2833	127	14	a	a	DET
ajst-2833	127	15	b	b	NOUN
ajst-2833	127	16	p	p	NOUN
ajst-2833	127	17	r	r	NOUN
ajst-2833	127	18	b	b	NOUN
ajst-2833	127	19			PROPN
ajst-2833	127	20			PROPN
ajst-2833	127	21			PROPN
ajst-2833	127	22			PRON
ajst-2833	127	23			PRON
ajst-2833	127	24			PUNCT
ajst-2833	127	25	and	and	CCONJ
ajst-2833	127	26	*	*	PUNCT
ajst-2833	127	27	*	*	PUNCT
ajst-2833	127	28	0	0	PUNCT
ajst-2833	127	29	(	(	PUNCT
ajst-2833	127	30	)	)	PUNCT
ajst-2833	127	31	1|	1|	NUM
ajst-2833	127	32	r	r	NOUN
ajst-2833	127	33	q	q	NOUN
ajst-2833	127	34	r	r	NOUN
ajst-2833	127	35			NOUN
ajst-2833	127	36			NOUN
ajst-2833	127	37	,	,	PUNCT
ajst-2833	127	38	we	we	PRON
ajst-2833	127	39	have	have	VERB
ajst-2833	127	40	2	2	NUM
ajst-2833	127	41	2	2	NUM
ajst-2833	127	42	1,2	1,2	NUM
ajst-2833	127	43	2	2	NUM
ajst-2833	127	44	(	(	PUNCT
ajst-2833	127	45	2	2	NUM
ajst-2833	127	46	)	)	PUNCT
ajst-2833	127	47	4	4	NUM
ajst-2833	127	48	(	(	PUNCT
ajst-2833	127	49	2	2	NUM
ajst-2833	127	50	)	)	PUNCT
ajst-2833	127	51	(	(	PUNCT
ajst-2833	127	52	0	0	NUM
ajst-2833	127	53	)	)	PUNCT
ajst-2833	127	54	2(1	2(1	NUM
ajst-2833	127	55	)	)	PUNCT
ajst-2833	128	1	b	b	NOUN
ajst-2833	128	2	a	a	DET
ajst-2833	128	3	b	b	NOUN
ajst-2833	129	1	i	i	NOUN
ajst-2833	129	2	ab	ab	PROPN
ajst-2833	129	3	b	b	PROPN
ajst-2833	129	4	a	a	DET
ajst-2833	129	5	b	b	PROPN
ajst-2833	129	6	b	b	X
ajst-2833	129	7			X
ajst-2833	129	8			PROPN
ajst-2833	129	9			PROPN
ajst-2833	129	10			PROPN
ajst-2833	129	11			PROPN
ajst-2833	129	12			PROPN
ajst-2833	129	13			PROPN
ajst-2833	129	14			PROPN
ajst-2833	129	15			PRON
ajst-2833	129	16			PRON
ajst-2833	129	17	,	,	PUNCT
ajst-2833	129	18	then	then	ADV
ajst-2833	129	19	it	it	PRON
ajst-2833	129	20	is	be	AUX
ajst-2833	129	21	easy	easy	ADJ
ajst-2833	129	22	to	to	PART
ajst-2833	129	23	derive	derive	VERB
ajst-2833	129	24	1,2	1,2	NUM
ajst-2833	129	25	(	(	PUNCT
ajst-2833	129	26	0	0	NUM
ajst-2833	129	27	)	)	PUNCT
ajst-2833	129	28	1m	1m	NUM
ajst-2833	129	29			NOUN
ajst-2833	129	30	for	for	ADP
ajst-2833	129	31	all	all	DET
ajst-2833	129	32	m	m	NOUN
ajst-2833	129	33	=	=	NOUN
ajst-2833	129	34	1,2,3,4	1,2,3,4	NUM
ajst-2833	129	35	.	.	PUNCT
ajst-2833	130	1	according	accord	VERB
ajst-2833	130	2	to	to	ADP
ajst-2833	130	3	[	[	X
ajst-2833	130	4	22	22	NUM
ajst-2833	130	5	,	,	PUNCT
ajst-2833	130	6	pp517	pp517	PROPN
ajst-2833	130	7	-	-	PUNCT
ajst-2833	130	8	522	522	NUM
ajst-2833	130	9	]	]	PUNCT
ajst-2833	130	10	,	,	PUNCT
ajst-2833	130	11	they	they	PRON
ajst-2833	130	12	satisfy	satisfy	VERB
ajst-2833	130	13	all	all	PRON
ajst-2833	130	14	of	of	ADP
ajst-2833	130	15	the	the	DET
ajst-2833	130	16	conditions	condition	NOUN
ajst-2833	130	17	for	for	ADP
ajst-2833	130	18	neimark	neimark	NOUN
ajst-2833	130	19	-	-	PUNCT
ajst-2833	130	20	sacker	sacker	NOUN
ajst-2833	130	21	bifurcation	bifurcation	NOUN
ajst-2833	130	22	to	to	PART
ajst-2833	130	23	occur	occur	VERB
ajst-2833	130	24	.	.	PUNCT
ajst-2833	131	1	122	122	NUM
ajst-2833	131	2	4	4	NUM
ajst-2833	131	3	.	.	PUNCT
ajst-2833	131	4	numerical	numerical	PROPN
ajst-2833	131	5	simulation	simulation	PROPN
ajst-2833	131	6	in	in	ADP
ajst-2833	131	7	this	this	DET
ajst-2833	131	8	section	section	NOUN
ajst-2833	131	9	,	,	PUNCT
ajst-2833	131	10	we	we	PRON
ajst-2833	131	11	use	use	VERB
ajst-2833	131	12	the	the	DET
ajst-2833	131	13	bifurcation	bifurcation	NOUN
ajst-2833	131	14	diagrams	diagram	NOUN
ajst-2833	131	15	and	and	CCONJ
ajst-2833	131	16	lyapunov	lyapunov	ADJ
ajst-2833	131	17	exponents	exponent	NOUN
ajst-2833	131	18	of	of	ADP
ajst-2833	131	19	the	the	DET
ajst-2833	131	20	system	system	NOUN
ajst-2833	131	21	(	(	PUNCT
ajst-2833	131	22	6	6	NUM
ajst-2833	131	23	)	)	PUNCT
ajst-2833	131	24	to	to	PART
ajst-2833	131	25	illustrate	illustrate	VERB
ajst-2833	131	26	our	our	PRON
ajst-2833	131	27	theoretical	theoretical	ADJ
ajst-2833	131	28	results	result	NOUN
ajst-2833	131	29	and	and	CCONJ
ajst-2833	131	30	further	far	ADV
ajst-2833	131	31	reveal	reveal	VERB
ajst-2833	131	32	some	some	DET
ajst-2833	131	33	new	new	ADJ
ajst-2833	131	34	dynamical	dynamical	ADJ
ajst-2833	131	35	behaviors	behavior	NOUN
ajst-2833	131	36	to	to	PART
ajst-2833	131	37	occur	occur	VERB
ajst-2833	131	38	as	as	SCONJ
ajst-2833	131	39	the	the	DET
ajst-2833	131	40	parameters	parameter	NOUN
ajst-2833	131	41	vary	vary	VERB
ajst-2833	131	42	by	by	ADP
ajst-2833	131	43	matlab	matlab	PROPN
ajst-2833	131	44	software	software	NOUN
ajst-2833	131	45	.	.	PUNCT
ajst-2833	132	1	fix	fix	VERB
ajst-2833	132	2	the	the	DET
ajst-2833	132	3	parameter	parameter	NOUN
ajst-2833	132	4	values	value	VERB
ajst-2833	132	5	a	a	DET
ajst-2833	132	6	=	=	SYM
ajst-2833	132	7	1.5,b	1.5,b	NUM
ajst-2833	132	8	=	=	SYM
ajst-2833	132	9	0.2	0.2	NUM
ajst-2833	132	10	,	,	PUNCT
ajst-2833	132	11	let	let	VERB
ajst-2833	132	12	r	r	PRON
ajst-2833	132	13	∈	∈	PROPN
ajst-2833	132	14	(	(	PUNCT
ajst-2833	132	15	0,0.3	0,0.3	NUM
ajst-2833	132	16	)	)	PUNCT
ajst-2833	132	17	.	.	PUNCT
ajst-2833	133	1	figure	figure	VERB
ajst-2833	133	2	1(a	1(a	NUM
ajst-2833	133	3	)	)	PUNCT
ajst-2833	133	4	shows	show	VERB
ajst-2833	133	5	the	the	DET
ajst-2833	133	6	bifurcation	bifurcation	NOUN
ajst-2833	133	7	diagram	diagram	NOUN
ajst-2833	133	8	of	of	ADP
ajst-2833	133	9	(	(	PUNCT
ajst-2833	133	10	r	r	NOUN
ajst-2833	133	11	,	,	PUNCT
ajst-2833	133	12	x)-plane	x)-plane	PROPN
ajst-2833	133	13	,	,	PUNCT
ajst-2833	133	14	from	from	ADP
ajst-2833	133	15	which	which	PRON
ajst-2833	133	16	the	the	DET
ajst-2833	133	17	fixed	fix	VERB
ajst-2833	133	18	point	point	NOUN
ajst-2833	133	19	e2	e2	PROPN
ajst-2833	133	20	is	be	AUX
ajst-2833	133	21	unstable	unstable	ADJ
ajst-2833	133	22	when	when	SCONJ
ajst-2833	133	23	r	r	NOUN
ajst-2833	133	24	<	<	X
ajst-2833	133	25	r1	r1	PROPN
ajst-2833	133	26	=	=	PROPN
ajst-2833	133	27	0.06	0.06	NUM
ajst-2833	133	28	whlie	whlie	PROPN
ajst-2833	133	29	stable	stable	ADJ
ajst-2833	133	30	when	when	SCONJ
ajst-2833	133	31	b	b	X
ajst-2833	133	32	>	>	X
ajst-2833	133	33	b0	b0	NOUN
ajst-2833	133	34	.	.	PUNCT
ajst-2833	134	1	hence	hence	ADV
ajst-2833	134	2	,	,	PUNCT
ajst-2833	134	3	the	the	DET
ajst-2833	134	4	neimark	neimark	NOUN
ajst-2833	134	5	-	-	PUNCT
ajst-2833	134	6	sacker	sacker	NOUN
ajst-2833	134	7	bifurcation	bifurcation	NOUN
ajst-2833	134	8	occurs	occur	VERB
ajst-2833	134	9	at	at	ADP
ajst-2833	134	10	the	the	DET
ajst-2833	134	11	fixed	fix	VERB
ajst-2833	134	12	point	point	NOUN
ajst-2833	134	13	e2	e2	PROPN
ajst-2833	134	14	=	=	SYM
ajst-2833	134	15	(	(	PUNCT
ajst-2833	134	16	0.167,0.833	0.167,0.833	PROPN
ajst-2833	134	17	)	)	PUNCT
ajst-2833	134	18	when	when	SCONJ
ajst-2833	134	19	r	r	NOUN
ajst-2833	134	20	=	=	SYM
ajst-2833	134	21	r1	r1	PROPN
ajst-2833	134	22	,	,	PUNCT
ajst-2833	134	23	whose	whose	DET
ajst-2833	134	24	multipliers	multiplier	NOUN
ajst-2833	134	25	are	be	AUX
ajst-2833	134	26	λ1,2	λ1,2	ADJ
ajst-2833	134	27	=	=	SYM
ajst-2833	134	28	0.892±0.453i	0.892±0.453i	NUM
ajst-2833	134	29	with	with	ADP
ajst-2833	134	30	|λ1,2|	|λ1,2|	NOUN
ajst-2833	134	31	=	=	PUNCT
ajst-2833	134	32	1.the	1.the	DET
ajst-2833	134	33	corresponding	correspond	VERB
ajst-2833	134	34	maximum	maximum	PROPN
ajst-2833	134	35	lyapunov	lyapunov	ADJ
ajst-2833	134	36	exponent	exponent	NOUN
ajst-2833	134	37	diagram	diagram	NOUN
ajst-2833	134	38	of	of	ADP
ajst-2833	134	39	the	the	DET
ajst-2833	134	40	system	system	NOUN
ajst-2833	134	41	(	(	PUNCT
ajst-2833	134	42	1.6	1.6	NUM
ajst-2833	134	43	)	)	PUNCT
ajst-2833	134	44	is	be	AUX
ajst-2833	134	45	plotted	plot	VERB
ajst-2833	134	46	in	in	ADP
ajst-2833	134	47	figure	figure	NOUN
ajst-2833	134	48	1(b	1(b	NUM
ajst-2833	134	49	)	)	PUNCT
ajst-2833	134	50	.	.	PUNCT
ajst-2833	135	1	(	(	PUNCT
ajst-2833	135	2	a	a	X
ajst-2833	135	3	)	)	PUNCT
ajst-2833	135	4	r	r	NOUN
ajst-2833	135	5	∈	∈	PROPN
ajst-2833	135	6	(	(	PUNCT
ajst-2833	135	7	0,0.3)(b	0,0.3)(b	NOUN
ajst-2833	135	8	)	)	PUNCT
ajst-2833	135	9	r	r	NOUN
ajst-2833	135	10	∈	∈	PROPN
ajst-2833	135	11	(	(	PUNCT
ajst-2833	135	12	0,0.3	0,0.3	NOUN
ajst-2833	135	13	)	)	PUNCT
ajst-2833	135	14	figure	figure	NOUN
ajst-2833	135	15	1	1	NUM
ajst-2833	135	16	.	.	PUNCT
ajst-2833	135	17	bifurcation	bifurcation	NOUN
ajst-2833	135	18	of	of	ADP
ajst-2833	135	19	the	the	DET
ajst-2833	135	20	system	system	NOUN
ajst-2833	135	21	(	(	PUNCT
ajst-2833	135	22	1.6	1.6	NUM
ajst-2833	135	23	)	)	PUNCT
ajst-2833	135	24	in	in	ADP
ajst-2833	135	25	(	(	PUNCT
ajst-2833	135	26	r	r	NOUN
ajst-2833	135	27	,	,	PUNCT
ajst-2833	135	28	x)-plane	x)-plane	NOUN
ajst-2833	135	29	and	and	CCONJ
ajst-2833	135	30	maximal	maximal	ADJ
ajst-2833	135	31	lyapunov	lyapunov	ADJ
ajst-2833	135	32	exponent	exponent	NOUN
ajst-2833	135	33	.	.	PUNCT
ajst-2833	136	1	5	5	X
ajst-2833	136	2	.	.	X
ajst-2833	136	3	discussion	discussion	NOUN
ajst-2833	136	4	and	and	CCONJ
ajst-2833	136	5	conclusion	conclusion	NOUN
ajst-2833	136	6	in	in	ADP
ajst-2833	136	7	this	this	DET
ajst-2833	136	8	paper	paper	NOUN
ajst-2833	136	9	,	,	PUNCT
ajst-2833	136	10	we	we	PRON
ajst-2833	136	11	discuss	discuss	VERB
ajst-2833	136	12	the	the	DET
ajst-2833	136	13	dynamical	dynamical	ADJ
ajst-2833	136	14	behaviors	behavior	NOUN
ajst-2833	136	15	of	of	ADP
ajst-2833	136	16	a	a	DET
ajst-2833	136	17	predator	predator	NOUN
ajst-2833	136	18	-	-	PUNCT
ajst-2833	136	19	prey	prey	NOUN
ajst-2833	136	20	model	model	NOUN
ajst-2833	136	21	(	(	PUNCT
ajst-2833	136	22	1.6	1.6	NUM
ajst-2833	136	23	)	)	PUNCT
ajst-2833	136	24	with	with	ADP
ajst-2833	136	25	competition	competition	NOUN
ajst-2833	136	26	between	between	ADP
ajst-2833	136	27	predators	predator	NOUN
ajst-2833	136	28	.	.	PUNCT
ajst-2833	137	1	under	under	ADP
ajst-2833	137	2	the	the	DET
ajst-2833	137	3	given	give	VERB
ajst-2833	137	4	parametric	parametric	ADJ
ajst-2833	137	5	conditions	condition	NOUN
ajst-2833	137	6	,	,	PUNCT
ajst-2833	137	7	we	we	PRON
ajst-2833	137	8	completely	completely	ADV
ajst-2833	137	9	show	show	VERB
ajst-2833	137	10	the	the	DET
ajst-2833	137	11	existence	existence	NOUN
ajst-2833	137	12	and	and	CCONJ
ajst-2833	137	13	stability	stability	NOUN
ajst-2833	137	14	of	of	ADP
ajst-2833	137	15	three	three	NUM
ajst-2833	137	16	nonnegative	nonnegative	ADJ
ajst-2833	137	17	equilibria	equilibrium	NOUN
ajst-2833	137	18	e0	e0	PROPN
ajst-2833	137	19	=	=	SYM
ajst-2833	137	20	(	(	PUNCT
ajst-2833	137	21	0,0	0,0	NOUN
ajst-2833	137	22	)	)	PUNCT
ajst-2833	137	23	,	,	PUNCT
ajst-2833	137	24	e1	e1	NOUN
ajst-2833	137	25	=	=	SYM
ajst-2833	137	26	(	(	PUNCT
ajst-2833	137	27	1,0	1,0	NUM
ajst-2833	137	28	)	)	PUNCT
ajst-2833	137	29	and	and	CCONJ
ajst-2833	137	30	2	2	NUM
ajst-2833	137	31	(	(	PUNCT
ajst-2833	137	32	,	,	PUNCT
ajst-2833	137	33	)	)	PUNCT
ajst-2833	137	34	b	b	X
ajst-2833	137	35	r	r	NOUN
ajst-2833	137	36	a	a	PRON
ajst-2833	137	37	b	b	NOUN
ajst-2833	137	38	e	e	NOUN
ajst-2833	137	39	a	a	DET
ajst-2833	137	40	r	r	NOUN
ajst-2833	137	41	a	a	DET
ajst-2833	137	42	r	r	NOUN
ajst-2833	137	43			ADV
ajst-2833	137	44			PROPN
ajst-2833	137	45			PROPN
ajst-2833	137	46			PRON
ajst-2833	137	47			ADJ
ajst-2833	137	48	.	.	PUNCT
ajst-2833	138	1	then	then	ADV
ajst-2833	138	2	we	we	PRON
ajst-2833	138	3	derive	derive	VERB
ajst-2833	138	4	the	the	DET
ajst-2833	138	5	sufficient	sufficient	ADJ
ajst-2833	138	6	conditions	condition	NOUN
ajst-2833	138	7	for	for	SCONJ
ajst-2833	138	8	its	its	PRON
ajst-2833	138	9	neimark	neimark	NOUN
ajst-2833	138	10	-	-	PUNCT
ajst-2833	138	11	sacker	sacker	NOUN
ajst-2833	138	12	bifurcation	bifurcation	NOUN
ajst-2833	138	13	to	to	PART
ajst-2833	138	14	occur	occur	VERB
ajst-2833	138	15	.	.	PUNCT
ajst-2833	139	1	meanwhile	meanwhile	ADV
ajst-2833	139	2	,	,	PUNCT
ajst-2833	139	3	it	it	PRON
ajst-2833	139	4	is	be	AUX
ajst-2833	139	5	clear	clear	ADJ
ajst-2833	139	6	that	that	SCONJ
ajst-2833	139	7	the	the	DET
ajst-2833	139	8	positive	positive	ADJ
ajst-2833	139	9	equilibrium	equilibrium	NOUN
ajst-2833	139	10	e2	e2	PROPN
ajst-2833	139	11	=	=	SYM
ajst-2833	139	12	(	(	PUNCT
ajst-2833	139	13	x0,y0	x0,y0	PROPN
ajst-2833	139	14	)	)	PUNCT
ajst-2833	139	15	is	be	AUX
ajst-2833	139	16	asymptotically	asymptotically	ADV
ajst-2833	139	17	stable	stable	ADJ
ajst-2833	139	18	when	when	SCONJ
ajst-2833	139	19	r	r	NOUN
ajst-2833	139	20	>	>	X
ajst-2833	139	21	r1	r1	PROPN
ajst-2833	139	22	=	=	SYM
ajst-2833	139	23	b(a	b(a	PROPN
ajst-2833	139	24	−	−	PROPN
ajst-2833	139	25	b	b	PROPN
ajst-2833	139	26	−	−	PROPN
ajst-2833	139	27	1	1	NUM
ajst-2833	139	28	)	)	PUNCT
ajst-2833	139	29	and	and	CCONJ
ajst-2833	139	30	unstable	unstable	ADJ
ajst-2833	139	31	when	when	SCONJ
ajst-2833	139	32	r	r	NOUN
ajst-2833	139	33	<	<	X
ajst-2833	139	34	r1	r1	PROPN
ajst-2833	139	35	under	under	ADP
ajst-2833	139	36	the	the	DET
ajst-2833	139	37	condition	condition	NOUN
ajst-2833	139	38	1	1	NUM
ajst-2833	139	39	<	<	X
ajst-2833	139	40	a	a	DET
ajst-2833	139	41	−	−	PROPN
ajst-2833	139	42	b	b	SYM
ajst-2833	139	43	≤	≤	ADV
ajst-2833	139	44	2	2	NUM
ajst-2833	139	45	.	.	PUNCT
ajst-2833	140	1	hence	hence	ADV
ajst-2833	140	2	,	,	PUNCT
ajst-2833	140	3	the	the	DET
ajst-2833	140	4	system	system	NOUN
ajst-2833	140	5	(	(	PUNCT
ajst-2833	140	6	1.6	1.6	NUM
ajst-2833	140	7	)	)	PUNCT
ajst-2833	140	8	undergoes	undergo	VERB
ajst-2833	140	9	a	a	DET
ajst-2833	140	10	bifurcation	bifurcation	NOUN
ajst-2833	140	11	which	which	PRON
ajst-2833	140	12	has	have	AUX
ajst-2833	140	13	been	be	AUX
ajst-2833	140	14	shown	show	VERB
ajst-2833	140	15	to	to	PART
ajst-2833	140	16	be	be	AUX
ajst-2833	140	17	a	a	DET
ajst-2833	140	18	neimark	neimark	NOUN
ajst-2833	140	19	-	-	PUNCT
ajst-2833	140	20	sacker	sacker	NOUN
ajst-2833	140	21	bifurcation	bifurcation	NOUN
ajst-2833	140	22	when	when	SCONJ
ajst-2833	140	23	the	the	DET
ajst-2833	140	24	parameter	parameter	NOUN
ajst-2833	140	25	r	r	NOUN
ajst-2833	140	26	goes	go	VERB
ajst-2833	140	27	through	through	ADP
ajst-2833	140	28	the	the	DET
ajst-2833	140	29	critical	critical	ADJ
ajst-2833	140	30	value	value	NOUN
ajst-2833	140	31	r1	r1	NOUN
ajst-2833	140	32	.	.	PUNCT
ajst-2833	141	1	finally	finally	ADV
ajst-2833	141	2	,	,	PUNCT
ajst-2833	141	3	numerical	numerical	ADJ
ajst-2833	141	4	simulations	simulation	NOUN
ajst-2833	141	5	confirm	confirm	VERB
ajst-2833	141	6	the	the	DET
ajst-2833	141	7	theoretical	theoretical	ADJ
ajst-2833	141	8	analysis	analysis	NOUN
ajst-2833	141	9	results	result	NOUN
ajst-2833	141	10	of	of	ADP
ajst-2833	141	11	the	the	DET
ajst-2833	141	12	system	system	NOUN
ajst-2833	141	13	(	(	PUNCT
ajst-2833	141	14	1.6	1.6	NUM
ajst-2833	141	15	)	)	PUNCT
ajst-2833	141	16	.	.	PUNCT
ajst-2833	142	1	acknowledgment	acknowledgment	NOUN
ajst-2833	142	2	this	this	DET
ajst-2833	142	3	work	work	NOUN
ajst-2833	142	4	is	be	AUX
ajst-2833	142	5	partly	partly	ADV
ajst-2833	142	6	supported	support	VERB
ajst-2833	142	7	by	by	ADP
ajst-2833	142	8	the	the	DET
ajst-2833	142	9	national	national	ADJ
ajst-2833	142	10	natural	natural	PROPN
ajst-2833	142	11	science	science	PROPN
ajst-2833	142	12	foundation	foundation	PROPN
ajst-2833	142	13	of	of	ADP
ajst-2833	142	14	china	china	PROPN
ajst-2833	142	15	(	(	PUNCT
ajst-2833	142	16	61473340	61473340	NUM
ajst-2833	142	17	)	)	PUNCT
ajst-2833	142	18	,	,	PUNCT
ajst-2833	142	19	the	the	DET
ajst-2833	142	20	distinguished	distinguished	ADJ
ajst-2833	142	21	professor	professor	NOUN
ajst-2833	142	22	foundation	foundation	PROPN
ajst-2833	142	23	of	of	ADP
ajst-2833	142	24	qianjiang	qianjiang	PROPN
ajst-2833	142	25	scholar	scholar	NOUN
ajst-2833	142	26	in	in	ADP
ajst-2833	142	27	zhejiang	zhejiang	PROPN
ajst-2833	142	28	province	province	PROPN
ajst-2833	142	29	(	(	PUNCT
ajst-2833	142	30	f703108l02	f703108l02	NOUN
ajst-2833	142	31	)	)	PUNCT
ajst-2833	142	32	,	,	PUNCT
ajst-2833	142	33	and	and	CCONJ
ajst-2833	142	34	the	the	DET
ajst-2833	142	35	natural	natural	ADJ
ajst-2833	142	36	science	science	NOUN
ajst-2833	142	37	foundation	foundation	PROPN
ajst-2833	142	38	of	of	ADP
ajst-2833	142	39	zhejiang	zhejiang	PROPN
ajst-2833	142	40	university	university	PROPN
ajst-2833	142	41	of	of	ADP
ajst-2833	142	42	science	science	NOUN
ajst-2833	142	43	and	and	CCONJ
ajst-2833	142	44	technology	technology	NOUN
ajst-2833	142	45	(	(	PUNCT
ajst-2833	142	46	f701108g14	f701108g14	ADJ
ajst-2833	142	47	)	)	PUNCT
ajst-2833	142	48	.	.	PUNCT
ajst-2833	143	1	references	reference	NOUN
ajst-2833	143	2	[	[	X
ajst-2833	143	3	1	1	NUM
ajst-2833	143	4	]	]	X
ajst-2833	143	5	md	md	PROPN
ajst-2833	143	6	,	,	PUNCT
ajst-2833	143	7	s.	s.	PROPN
ajst-2833	143	8	&	&	CCONJ
ajst-2833	143	9	rana	rana	PROPN
ajst-2833	143	10	,	,	PUNCT
ajst-2833	143	11	s.	s.	PROPN
ajst-2833	144	1	[	[	X
ajst-2833	144	2	2019	2019	NUM
ajst-2833	144	3	]	]	PUNCT
ajst-2833	144	4	“	"	PUNCT
ajst-2833	144	5	dynamics	dynamic	NOUN
ajst-2833	144	6	and	and	CCONJ
ajst-2833	144	7	chaos	chaos	NOUN
ajst-2833	144	8	control	control	NOUN
ajst-2833	144	9	in	in	ADP
ajst-2833	144	10	a	a	DET
ajst-2833	144	11	discrete	discrete	ADJ
ajst-2833	144	12	-	-	PUNCT
ajst-2833	144	13	time	time	NOUN
ajst-2833	144	14	ratio	ratio	NOUN
ajst-2833	144	15	-	-	PUNCT
ajst-2833	144	16	dependent	dependent	ADJ
ajst-2833	144	17	holling	holling	NOUN
ajst-2833	144	18	-	-	PUNCT
ajst-2833	144	19	tanner	tanner	NOUN
ajst-2833	144	20	model	model	NOUN
ajst-2833	144	21	,	,	PUNCT
ajst-2833	144	22	”	"	PUNCT
ajst-2833	144	23	j.egypt.math.soc	j.egypt.math.soc	NOUN
ajst-2833	144	24	.	.	PROPN
ajst-2833	144	25	2019	2019	NUM
ajst-2833	144	26	,	,	PUNCT
ajst-2833	144	27	doi:10.1186	doi:10.1186	NOUN
ajst-2833	144	28	/	/	SYM
ajst-2833	144	29	s42787	s42787	NOUN
ajst-2833	144	30	-	-	PUNCT
ajst-2833	144	31	019	019	NUM
ajst-2833	144	32	-	-	PUNCT
ajst-2833	144	33	0055	0055	NUM
ajst-2833	144	34	-	-	PUNCT
ajst-2833	144	35	4	4	NUM
ajst-2833	144	36	.	.	PUNCT
ajst-2833	145	1	[	[	X
ajst-2833	145	2	2	2	NUM
ajst-2833	145	3	]	]	X
ajst-2833	145	4	khan	khan	PROPN
ajst-2833	145	5	,	,	PUNCT
ajst-2833	145	6	a.	a.	PROPN
ajst-2833	145	7	q.	q.	PROPN
ajst-2833	146	1	[	[	X
ajst-2833	146	2	2016	2016	NUM
ajst-2833	146	3	]	]	PUNCT
ajst-2833	146	4	“	"	PUNCT
ajst-2833	146	5	neimark	neimark	NOUN
ajst-2833	146	6	-	-	PUNCT
ajst-2833	146	7	sacker	sacker	NOUN
ajst-2833	146	8	bifurcation	bifurcation	NOUN
ajst-2833	146	9	of	of	ADP
ajst-2833	146	10	a	a	DET
ajst-2833	146	11	twodimensional	twodimensional	ADJ
ajst-2833	146	12	discrete	discrete	ADJ
ajst-2833	146	13	-	-	PUNCT
ajst-2833	146	14	time	time	NOUN
ajst-2833	146	15	predator	predator	NOUN
ajst-2833	146	16	-	-	PUNCT
ajst-2833	146	17	prey	prey	NOUN
ajst-2833	146	18	model	model	NOUN
ajst-2833	146	19	,	,	PUNCT
ajst-2833	146	20	”	"	PUNCT
ajst-2833	146	21	adv.differ.equ	adv.differ.equ	NOUN
ajst-2833	146	22	.	.	PROPN
ajst-2833	146	23	2016	2016	NUM
ajst-2833	146	24	,	,	PUNCT
ajst-2833	146	25	doi:10.1186	doi:10.1186	PROPN
ajst-2833	146	26	/	/	SYM
ajst-2833	146	27	s40064	s40064	PROPN
ajst-2833	146	28	-	-	PUNCT
ajst-2833	146	29	015	015	NUM
ajst-2833	146	30	-	-	PUNCT
ajst-2833	146	31	1618	1618	NUM
ajst-2833	146	32	-	-	PUNCT
ajst-2833	146	33	y.	y.	NOUN
ajst-2833	147	1	[	[	X
ajst-2833	147	2	3	3	NUM
ajst-2833	147	3	]	]	X
ajst-2833	147	4	rodrigo	rodrigo	PROPN
ajst-2833	147	5	,	,	PUNCT
ajst-2833	147	6	c.	c.	PROPN
ajst-2833	147	7	,	,	PUNCT
ajst-2833	147	8	willy	willy	ADV
ajst-2833	147	9	,	,	PUNCT
ajst-2833	147	10	s.	s.	PROPN
ajst-2833	147	11	&	&	CCONJ
ajst-2833	147	12	eduardo	eduardo	PROPN
ajst-2833	147	13	,	,	PUNCT
ajst-2833	147	14	s.	s.	PROPN
ajst-2833	148	1	[	[	X
ajst-2833	148	2	2017	2017	NUM
ajst-2833	148	3	]	]	PUNCT
ajst-2833	148	4	“	"	PUNCT
ajst-2833	148	5	bifurcations	bifurcation	NOUN
ajst-2833	148	6	in	in	ADP
ajst-2833	148	7	a	a	DET
ajst-2833	148	8	predatorprey	predatorprey	NOUN
ajst-2833	148	9	model	model	NOUN
ajst-2833	148	10	with	with	ADP
ajst-2833	148	11	general	general	ADJ
ajst-2833	148	12	logistic	logistic	ADJ
ajst-2833	148	13	growth	growth	NOUN
ajst-2833	148	14	and	and	CCONJ
ajst-2833	148	15	exponential	exponential	ADJ
ajst-2833	148	16	fading	fade	VERB
ajst-2833	148	17	memory	memory	NOUN
ajst-2833	148	18	,	,	PUNCT
ajst-2833	148	19	”	"	PUNCT
ajst-2833	148	20	appl.math.model	appl.math.model	NOUN
ajst-2833	148	21	.	.	PROPN
ajst-2833	148	22	45	45	NUM
ajst-2833	148	23	,	,	PUNCT
ajst-2833	148	24	134–147	134–147	NUM
ajst-2833	148	25	.	.	PUNCT
ajst-2833	149	1	[	[	X
ajst-2833	149	2	4	4	NUM
ajst-2833	149	3	]	]	SYM
ajst-2833	149	4	holling	holling	NOUN
ajst-2833	149	5	,	,	PUNCT
ajst-2833	149	6	c.	c.	PROPN
ajst-2833	150	1	[	[	X
ajst-2833	150	2	1959	1959	NUM
ajst-2833	150	3	]	]	PUNCT
ajst-2833	150	4	“	"	PUNCT
ajst-2833	150	5	the	the	DET
ajst-2833	150	6	functional	functional	ADJ
ajst-2833	150	7	response	response	NOUN
ajst-2833	150	8	of	of	ADP
ajst-2833	150	9	predator	predator	NOUN
ajst-2833	150	10	to	to	PART
ajst-2833	150	11	prey	prey	VERB
ajst-2833	150	12	density	density	NOUN
ajst-2833	150	13	and	and	CCONJ
ajst-2833	150	14	its	its	PRON
ajst-2833	150	15	role	role	NOUN
ajst-2833	150	16	in	in	ADP
ajst-2833	150	17	mimicry	mimicry	ADJ
ajst-2833	150	18	and	and	CCONJ
ajst-2833	150	19	population	population	NOUN
ajst-2833	150	20	regulation	regulation	NOUN
ajst-2833	150	21	,	,	PUNCT
ajst-2833	150	22	”	"	PUNCT
ajst-2833	150	23	mem.entomol.soc.can	mem.entomol.soc.can	NOUN
ajst-2833	150	24	.	.	PROPN
ajst-2833	151	1	91	91	NUM
ajst-2833	151	2	,	,	PUNCT
ajst-2833	151	3	385	385	NUM
ajst-2833	151	4	-	-	SYM
ajst-2833	151	5	398	398	NUM
ajst-2833	151	6	.	.	PUNCT
ajst-2833	152	1	[	[	X
ajst-2833	152	2	5	5	NUM
ajst-2833	152	3	]	]	X
ajst-2833	152	4	berryman	berryman	NOUN
ajst-2833	152	5	,	,	PUNCT
ajst-2833	152	6	a.	a.	NOUN
ajst-2833	152	7	a.	a.	PROPN
ajst-2833	152	8	,	,	PUNCT
ajst-2833	152	9	gutierrez	gutierrez	PROPN
ajst-2833	152	10	,	,	PUNCT
ajst-2833	152	11	a.	a.	NOUN
ajst-2833	152	12	p.	p.	PROPN
ajst-2833	152	13	&	&	CCONJ
ajst-2833	152	14	arditi	arditi	PROPN
ajst-2833	152	15	,	,	PUNCT
ajst-2833	152	16	r.	r.	PROPN
ajst-2833	153	1	[	[	X
ajst-2833	153	2	1995	1995	NUM
ajst-2833	153	3	]	]	PUNCT
ajst-2833	153	4	“	"	PUNCT
ajst-2833	153	5	credible	credible	ADJ
ajst-2833	153	6	,	,	PUNCT
ajst-2833	153	7	parsimonious	parsimonious	ADJ
ajst-2833	153	8	and	and	CCONJ
ajst-2833	153	9	useful	useful	ADJ
ajst-2833	153	10	predator	predator	NOUN
ajst-2833	153	11	–	–	PUNCT
ajst-2833	153	12	prey	prey	NOUN
ajst-2833	153	13	models	model	VERB
ajst-2833	153	14	a	a	DET
ajst-2833	153	15	reply	reply	NOUN
ajst-2833	153	16	to	to	ADP
ajst-2833	153	17	abrams	abrams	PROPN
ajst-2833	153	18	,	,	PUNCT
ajst-2833	153	19	gleeson	gleeson	NOUN
ajst-2833	153	20	,	,	PUNCT
ajst-2833	153	21	and	and	CCONJ
ajst-2833	153	22	sarnelle	sarnelle	PROPN
ajst-2833	153	23	,	,	PUNCT
ajst-2833	153	24	”	"	PUNCT
ajst-2833	153	25	entomological	entomological	ADJ
ajst-2833	153	26	society	society	NOUN
ajst-2833	153	27	of	of	ADP
ajst-2833	153	28	america	america	PROPN
ajst-2833	153	29	.	.	PUNCT
ajst-2833	154	1	76	76	NUM
ajst-2833	154	2	,	,	PUNCT
ajst-2833	154	3	1980–1985	1980–1985	NUM
ajst-2833	154	4	.	.	PUNCT
ajst-2833	155	1	[	[	X
ajst-2833	155	2	6	6	NUM
ajst-2833	155	3	]	]	PUNCT
ajst-2833	155	4	saunders	saunder	NOUN
ajst-2833	155	5	,	,	PUNCT
ajst-2833	155	6	m.	m.	NOUN
ajst-2833	155	7	c.	c.	PROPN
ajst-2833	156	1	[	[	X
ajst-2833	156	2	2006	2006	NUM
ajst-2833	156	3	]	]	PUNCT
ajst-2833	156	4	“	"	PUNCT
ajst-2833	156	5	complex	complex	ADJ
ajst-2833	156	6	population	population	NOUN
ajst-2833	156	7	dynamics	dynamic	NOUN
ajst-2833	156	8	:	:	PUNCT
ajst-2833	156	9	a	a	DET
ajst-2833	156	10	theoretical	theoretical	ADJ
ajst-2833	156	11	/	/	SYM
ajst-2833	156	12	empirical	empirical	ADJ
ajst-2833	156	13	synthesis	synthesis	NOUN
ajst-2833	156	14	,	,	PUNCT
ajst-2833	156	15	”	"	PUNCT
ajst-2833	156	16	entomological	entomological	ADJ
ajst-2833	156	17	society	society	NOUN
ajst-2833	156	18	of	of	ADP
ajst-2833	156	19	america	america	PROPN
ajst-2833	156	20	.	.	PUNCT
ajst-2833	157	1	35	35	NUM
ajst-2833	157	2	,	,	PUNCT
ajst-2833	157	3	1139	1139	NUM
ajst-2833	157	4	-	-	SYM
ajst-2833	157	5	1139	1139	NUM
ajst-2833	157	6	.	.	PUNCT
ajst-2833	158	1	[	[	X
ajst-2833	158	2	7	7	NUM
ajst-2833	158	3	]	]	X
ajst-2833	158	4	akcakaya	akcakaya	NOUN
ajst-2833	158	5	,	,	PUNCT
ajst-2833	158	6	hr	hr	PROPN
ajst-2833	158	7	.	.	PROPN
ajst-2833	158	8	,	,	PUNCT
ajst-2833	158	9	et	et	PROPN
ajst-2833	158	10	al	al	PROPN
ajst-2833	158	11	.	.	PUNCT
ajst-2833	159	1	[	[	X
ajst-2833	159	2	1995	1995	NUM
ajst-2833	159	3	]	]	PUNCT
ajst-2833	159	4	“	"	PUNCT
ajst-2833	159	5	ratio	ratio	NOUN
ajst-2833	159	6	-	-	PUNCT
ajst-2833	159	7	dependent	dependent	ADJ
ajst-2833	159	8	predation	predation	NOUN
ajst-2833	159	9	:	:	PUNCT
ajst-2833	159	10	an	an	DET
ajst-2833	159	11	abstraction	abstraction	NOUN
ajst-2833	159	12	that	that	PRON
ajst-2833	159	13	works	work	VERB
ajst-2833	159	14	,	,	PUNCT
ajst-2833	159	15	”	"	PUNCT
ajst-2833	159	16	ecology	ecology	NOUN
ajst-2833	159	17	.	.	PUNCT
ajst-2833	160	1	76	76	NUM
ajst-2833	160	2	,	,	PUNCT
ajst-2833	160	3	995–1004	995–1004	NUM
ajst-2833	160	4	.	.	PUNCT
ajst-2833	161	1	[	[	X
ajst-2833	161	2	8	8	NUM
ajst-2833	161	3	]	]	SYM
ajst-2833	161	4	cosner	cosner	NOUN
ajst-2833	161	5	,	,	PUNCT
ajst-2833	161	6	c.	c.	PROPN
ajst-2833	161	7	,	,	PUNCT
ajst-2833	161	8	et	et	PROPN
ajst-2833	161	9	al	al	PROPN
ajst-2833	161	10	.	.	PUNCT
ajst-2833	162	1	[	[	X
ajst-2833	162	2	1999	1999	NUM
ajst-2833	162	3	]	]	PUNCT
ajst-2833	162	4	“	"	PUNCT
ajst-2833	162	5	effects	effect	NOUN
ajst-2833	162	6	of	of	ADP
ajst-2833	162	7	spatial	spatial	ADJ
ajst-2833	162	8	grouping	grouping	NOUN
ajst-2833	162	9	on	on	ADP
ajst-2833	162	10	the	the	DET
ajst-2833	162	11	functional	functional	ADJ
ajst-2833	162	12	response	response	NOUN
ajst-2833	162	13	of	of	ADP
ajst-2833	162	14	predators	predator	NOUN
ajst-2833	162	15	,	,	PUNCT
ajst-2833	162	16	”	"	PUNCT
ajst-2833	162	17	theor.popul.biol	theor.popul.biol	PROPN
ajst-2833	162	18	.	.	PUNCT
ajst-2833	163	1	56	56	NUM
ajst-2833	163	2	,	,	PUNCT
ajst-2833	163	3	65–75	65–75	NUM
ajst-2833	163	4	.	.	PUNCT
ajst-2833	164	1	[	[	X
ajst-2833	164	2	9	9	NUM
ajst-2833	164	3	]	]	PUNCT
ajst-2833	164	4	gutierrez	gutierrez	PROPN
ajst-2833	164	5	,	,	PUNCT
ajst-2833	164	6	ap	ap	PROPN
ajst-2833	164	7	.	.	PUNCT
ajst-2833	165	1	[	[	X
ajst-2833	165	2	1992	1992	NUM
ajst-2833	165	3	]	]	PUNCT
ajst-2833	165	4	“	"	PUNCT
ajst-2833	165	5	physiological	physiological	ADJ
ajst-2833	165	6	basis	basis	NOUN
ajst-2833	165	7	of	of	ADP
ajst-2833	165	8	ratio	ratio	NOUN
ajst-2833	165	9	-	-	PUNCT
ajst-2833	165	10	dependent	dependent	ADJ
ajst-2833	165	11	predatorprey	predatorprey	NOUN
ajst-2833	165	12	theory	theory	NOUN
ajst-2833	165	13	:	:	PUNCT
ajst-2833	165	14	the	the	DET
ajst-2833	165	15	metabolic	metabolic	NOUN
ajst-2833	165	16	pool	pool	NOUN
ajst-2833	165	17	model	model	NOUN
ajst-2833	165	18	as	as	ADP
ajst-2833	165	19	a	a	DET
ajst-2833	165	20	paradigm	paradigm	NOUN
ajst-2833	165	21	,	,	PUNCT
ajst-2833	165	22	”	"	PUNCT
ajst-2833	165	23	ecology	ecology	NOUN
ajst-2833	165	24	.	.	PUNCT
ajst-2833	166	1	73	73	NUM
ajst-2833	166	2	,	,	PUNCT
ajst-2833	166	3	1552–1563	1552–1563	NUM
ajst-2833	166	4	.	.	PUNCT
ajst-2833	167	1	[	[	X
ajst-2833	167	2	10	10	NUM
ajst-2833	167	3	]	]	X
ajst-2833	167	4	may	may	AUX
ajst-2833	167	5	,	,	PUNCT
ajst-2833	167	6	r.	r.	PROPN
ajst-2833	168	1	[	[	X
ajst-2833	168	2	1973	1973	NUM
ajst-2833	168	3	]	]	PUNCT
ajst-2833	168	4	“	"	PUNCT
ajst-2833	168	5	stability	stability	NOUN
ajst-2833	168	6	and	and	CCONJ
ajst-2833	168	7	complexity	complexity	NOUN
ajst-2833	168	8	in	in	ADP
ajst-2833	168	9	model	model	NOUN
ajst-2833	168	10	ecosystems	ecosystem	NOUN
ajst-2833	168	11	with	with	ADP
ajst-2833	168	12	a	a	DET
ajst-2833	168	13	new	new	ADJ
ajst-2833	168	14	introduction	introduction	NOUN
ajst-2833	168	15	by	by	ADP
ajst-2833	168	16	the	the	DET
ajst-2833	168	17	author	author	NOUN
ajst-2833	168	18	,	,	PUNCT
ajst-2833	168	19	”	"	PUNCT
ajst-2833	168	20	princeton	princeton	PROPN
ajst-2833	168	21	university	university	PROPN
ajst-2833	168	22	press	press	NOUN
ajst-2833	168	23	.	.	PUNCT
ajst-2833	169	1	[	[	X
ajst-2833	169	2	11	11	NUM
ajst-2833	169	3	]	]	SYM
ajst-2833	169	4	pielou	pielou	NOUN
ajst-2833	169	5	,	,	PUNCT
ajst-2833	169	6	ec	ec	PROPN
ajst-2833	169	7	.	.	PUNCT
ajst-2833	170	1	[	[	X
ajst-2833	170	2	1969	1969	NUM
ajst-2833	170	3	]	]	PUNCT
ajst-2833	170	4	“	"	PUNCT
ajst-2833	170	5	an	an	DET
ajst-2833	170	6	introduction	introduction	NOUN
ajst-2833	170	7	to	to	ADP
ajst-2833	170	8	mathematical	mathematical	ADJ
ajst-2833	170	9	ecology	ecology	NOUN
ajst-2833	170	10	,	,	PUNCT
ajst-2833	170	11	”	"	PUNCT
ajst-2833	170	12	biometrical	biometrical	ADJ
ajst-2833	170	13	journal	journal	NOUN
ajst-2833	170	14	.	.	PUNCT
ajst-2833	171	1	13	13	NUM
ajst-2833	171	2	,	,	PUNCT
ajst-2833	171	3	doi:10.1002	doi:10.1002	NOUN
ajst-2833	171	4	/	/	SYM
ajst-2833	171	5	bimj.19710130308	bimj.19710130308	PROPN
ajst-2833	171	6	.	.	PUNCT
ajst-2833	172	1	[	[	X
ajst-2833	172	2	12	12	NUM
ajst-2833	172	3	]	]	X
ajst-2833	172	4	din	din	PROPN
ajst-2833	172	5	,	,	PUNCT
ajst-2833	172	6	q.	q.	PROPN
ajst-2833	173	1	[	[	X
ajst-2833	173	2	2017	2017	NUM
ajst-2833	173	3	]	]	PUNCT
ajst-2833	173	4	“	"	PUNCT
ajst-2833	173	5	complexity	complexity	NOUN
ajst-2833	173	6	and	and	CCONJ
ajst-2833	173	7	chaos	chaos	NOUN
ajst-2833	173	8	control	control	NOUN
ajst-2833	173	9	in	in	ADP
ajst-2833	173	10	a	a	DET
ajst-2833	173	11	discretetime	discretetime	ADJ
ajst-2833	173	12	prey	prey	NOUN
ajst-2833	173	13	-	-	PUNCT
ajst-2833	173	14	predator	predator	NOUN
ajst-2833	173	15	model	model	NOUN
ajst-2833	173	16	,	,	PUNCT
ajst-2833	173	17	”	"	PUNCT
ajst-2833	173	18	commun.nonliner.sci.numer	commun.nonliner.sci.numer	PROPN
ajst-2833	173	19	.	.	PUNCT
ajst-2833	173	20	simul	simul	PROPN
ajst-2833	173	21	.	.	PROPN
ajst-2833	174	1	49	49	NUM
ajst-2833	174	2	,	,	PUNCT
ajst-2833	174	3	113	113	NUM
ajst-2833	174	4	-	-	SYM
ajst-2833	174	5	134	134	NUM
ajst-2833	174	6	.	.	PUNCT
ajst-2833	175	1	[	[	X
ajst-2833	175	2	13	13	NUM
ajst-2833	175	3	]	]	SYM
ajst-2833	175	4	li	li	PROPN
ajst-2833	175	5	,	,	PUNCT
ajst-2833	175	6	w.	w.	PROPN
ajst-2833	175	7	&	&	CCONJ
ajst-2833	175	8	li	li	PROPN
ajst-2833	175	9	,	,	PUNCT
ajst-2833	175	10	x.	x.	PROPN
ajst-2833	175	11	y.	y.	PROPN
ajst-2833	176	1	[	[	X
ajst-2833	176	2	2018	2018	NUM
ajst-2833	176	3	]	]	PUNCT
ajst-2833	176	4	“	"	PUNCT
ajst-2833	176	5	neimark	neimark	ADJ
ajst-2833	176	6	–	–	PUNCT
ajst-2833	176	7	sacker	sacker	NOUN
ajst-2833	176	8	bifurcation	bifurcation	NOUN
ajst-2833	176	9	of	of	ADP
ajst-2833	176	10	a	a	DET
ajst-2833	176	11	semi	semi	ADJ
ajst-2833	176	12	-	-	ADJ
ajst-2833	176	13	discrete	discrete	ADJ
ajst-2833	176	14	hematopoiesis	hematopoiesis	NOUN
ajst-2833	176	15	model	model	NOUN
ajst-2833	176	16	,	,	PUNCT
ajst-2833	176	17	”	"	PUNCT
ajst-2833	176	18	j.appl.anal.comput	j.appl.anal.comput	NOUN
ajst-2833	176	19	.	.	PUNCT
ajst-2833	177	1	8	8	NUM
ajst-2833	177	2	,	,	PUNCT
ajst-2833	177	3	1679–1693	1679–1693	NUM
ajst-2833	177	4	.	.	PUNCT
ajst-2833	178	1	[	[	X
ajst-2833	178	2	14	14	NUM
ajst-2833	178	3	]	]	SYM
ajst-2833	178	4	hu	hu	PROPN
ajst-2833	178	5	,	,	PUNCT
ajst-2833	178	6	z.	z.	PROPN
ajst-2833	178	7	y.	y.	PROPN
ajst-2833	178	8	,	,	PUNCT
ajst-2833	178	9	teng	teng	PROPN
ajst-2833	178	10	,	,	PUNCT
ajst-2833	178	11	z.	z.	PROPN
ajst-2833	178	12	d.	d.	PROPN
ajst-2833	178	13	&	&	CCONJ
ajst-2833	178	14	zhang	zhang	PROPN
ajst-2833	178	15	,	,	PUNCT
ajst-2833	178	16	l.	l.	PROPN
ajst-2833	179	1	[	[	X
ajst-2833	179	2	2011	2011	NUM
ajst-2833	179	3	]	]	PUNCT
ajst-2833	179	4	“	"	PUNCT
ajst-2833	179	5	stability	stability	NOUN
ajst-2833	179	6	and	and	CCONJ
ajst-2833	179	7	bifurcation	bifurcation	NOUN
ajst-2833	179	8	analysis	analysis	NOUN
ajst-2833	179	9	of	of	ADP
ajst-2833	179	10	a	a	DET
ajst-2833	179	11	discrete	discrete	ADJ
ajst-2833	179	12	predator	predator	NOUN
ajst-2833	179	13	-	-	PUNCT
ajst-2833	179	14	prey	prey	NOUN
ajst-2833	179	15	model	model	NOUN
ajst-2833	179	16	with	with	ADP
ajst-2833	179	17	nonmonotonic	nonmonotonic	ADJ
ajst-2833	179	18	func	func	PROPN
ajst-2833	179	19	-	-	PUNCT
ajst-2833	179	20	tional	tional	ADJ
ajst-2833	179	21	response	response	NOUN
ajst-2833	179	22	,	,	PUNCT
ajst-2833	179	23	”	"	PUNCT
ajst-2833	179	24	nonlinear	nonlinear	ADJ
ajst-2833	179	25	.	.	PUNCT
ajst-2833	180	1	anal	anal	ADJ
ajst-2833	180	2	.	.	PUNCT
ajst-2833	181	1	real	real	ADJ
ajst-2833	181	2	.	.	PUNCT
ajst-2833	182	1	world	world	NOUN
ajst-2833	182	2	.	.	PUNCT
ajst-2833	183	1	appl	appl	PROPN
ajst-2833	183	2	.	.	PROPN
ajst-2833	184	1	12	12	NUM
ajst-2833	184	2	,	,	PUNCT
ajst-2833	184	3	2356–2377	2356–2377	NUM
ajst-2833	184	4	.	.	PUNCT
ajst-2833	185	1	[	[	X
ajst-2833	185	2	15	15	NUM
ajst-2833	185	3	]	]	X
ajst-2833	185	4	wang	wang	PROPN
ajst-2833	185	5	,	,	PUNCT
ajst-2833	185	6	c.	c.	PROPN
ajst-2833	185	7	&	&	CCONJ
ajst-2833	185	8	li	li	PROPN
ajst-2833	185	9	,	,	PUNCT
ajst-2833	185	10	x.	x.	PROPN
ajst-2833	185	11	y.	y.	PROPN
ajst-2833	186	1	[	[	X
ajst-2833	186	2	2015	2015	NUM
ajst-2833	186	3	]	]	PUNCT
ajst-2833	186	4	“	"	PUNCT
ajst-2833	186	5	further	further	ADJ
ajst-2833	186	6	investigations	investigation	NOUN
ajst-2833	186	7	into	into	ADP
ajst-2833	186	8	the	the	DET
ajst-2833	186	9	stability	stability	NOUN
ajst-2833	186	10	and	and	CCONJ
ajst-2833	186	11	bifurcation	bifurcation	NOUN
ajst-2833	186	12	of	of	ADP
ajst-2833	186	13	a	a	DET
ajst-2833	186	14	discrete	discrete	ADJ
ajst-2833	186	15	predator	predator	NOUN
ajst-2833	186	16	-	-	PUNCT
ajst-2833	186	17	prey	prey	NOUN
ajst-2833	186	18	model	model	NOUN
ajst-2833	186	19	,	,	PUNCT
ajst-2833	186	20	”	"	PUNCT
ajst-2833	186	21	j.math.anal.appl	j.math.anal.appl	NOUN
ajst-2833	186	22	.	.	PUNCT
ajst-2833	187	1	422	422	NUM
ajst-2833	187	2	,	,	PUNCT
ajst-2833	187	3	920–939	920–939	NUM
ajst-2833	187	4	.	.	PUNCT
ajst-2833	188	1	[	[	X
ajst-2833	188	2	16	16	NUM
ajst-2833	188	3	]	]	X
ajst-2833	188	4	wang	wang	PROPN
ajst-2833	188	5	,	,	PUNCT
ajst-2833	188	6	c.	c.	PROPN
ajst-2833	188	7	&	&	CCONJ
ajst-2833	188	8	li	li	PROPN
ajst-2833	188	9	,	,	PUNCT
ajst-2833	188	10	x.	x.	PROPN
ajst-2833	188	11	y.	y.	PROPN
ajst-2833	189	1	[	[	X
ajst-2833	189	2	2014	2014	NUM
ajst-2833	189	3	]	]	PUNCT
ajst-2833	189	4	“	"	PUNCT
ajst-2833	189	5	stability	stability	NOUN
ajst-2833	189	6	and	and	CCONJ
ajst-2833	189	7	neimark	neimark	ADJ
ajst-2833	189	8	–	–	PUNCT
ajst-2833	189	9	sacker	sacker	NOUN
ajst-2833	189	10	bifurcation	bifurcation	NOUN
ajst-2833	189	11	of	of	ADP
ajst-2833	189	12	a	a	DET
ajst-2833	189	13	semi	semi	ADJ
ajst-2833	189	14	-	-	ADJ
ajst-2833	189	15	discrete	discrete	ADJ
ajst-2833	189	16	population	population	NOUN
ajst-2833	189	17	model	model	NOUN
ajst-2833	189	18	,	,	PUNCT
ajst-2833	189	19	”	"	PUNCT
ajst-2833	189	20	j.appl.anal.comput	j.appl.anal.comput	NOUN
ajst-2833	189	21	.	.	PUNCT
ajst-2833	190	1	4	4	NUM
ajst-2833	190	2	,	,	PUNCT
ajst-2833	190	3	419–435	419–435	NUM
ajst-2833	190	4	.	.	PUNCT
ajst-2833	191	1	123	123	NUM
ajst-2833	191	2	[	[	X
ajst-2833	191	3	17	17	NUM
ajst-2833	191	4	]	]	SYM
ajst-2833	191	5	li	li	PROPN
ajst-2833	191	6	,	,	PUNCT
ajst-2833	191	7	m.	m.	PROPN
ajst-2833	191	8	s.	s.	PROPN
ajst-2833	191	9	,	,	PUNCT
ajst-2833	191	10	zhou	zhou	PROPN
ajst-2833	191	11	,	,	PUNCT
ajst-2833	191	12	x.	x.	PROPN
ajst-2833	191	13	l.	l.	PROPN
ajst-2833	191	14	&	&	CCONJ
ajst-2833	191	15	xu	xu	PROPN
ajst-2833	191	16	,	,	PUNCT
ajst-2833	191	17	j.	j.	PROPN
ajst-2833	191	18	m.	m.	PROPN
ajst-2833	192	1	[	[	X
ajst-2833	192	2	2020	2020	NUM
ajst-2833	192	3	]	]	PUNCT
ajst-2833	192	4	“	"	PUNCT
ajst-2833	192	5	dynamic	dynamic	ADJ
ajst-2833	192	6	properties	property	NOUN
ajst-2833	192	7	of	of	ADP
ajst-2833	192	8	a	a	DET
ajst-2833	192	9	discrete	discrete	ADJ
ajst-2833	192	10	population	population	NOUN
ajst-2833	192	11	model	model	NOUN
ajst-2833	192	12	with	with	ADP
ajst-2833	192	13	diffusion	diffusion	NOUN
ajst-2833	192	14	,	,	PUNCT
ajst-2833	192	15	”	"	PUNCT
ajst-2833	192	16	adv.differ.equ	adv.differ.equ	NOUN
ajst-2833	192	17	.	.	PUNCT
ajst-2833	192	18	2020	2020	NUM
ajst-2833	192	19	,	,	PUNCT
ajst-2833	192	20	doi:10.1186	doi:10.1186	PROPN
ajst-2833	192	21	/	/	SYM
ajst-2833	192	22	s13662	s13662	PROPN
ajst-2833	192	23	-	-	PUNCT
ajst-2833	192	24	020	020	NUM
ajst-2833	192	25	-	-	PUNCT
ajst-2833	192	26	03033	03033	NUM
ajst-2833	192	27	-	-	PUNCT
ajst-2833	192	28	w.	w.	NOUN
ajst-2833	192	29	[	[	X
ajst-2833	192	30	18	18	NUM
ajst-2833	192	31	]	]	PUNCT
ajst-2833	192	32	gallay	gallay	NOUN
ajst-2833	192	33	,	,	PUNCT
ajst-2833	192	34	t.	t.	PROPN
ajst-2833	193	1	[	[	X
ajst-2833	193	2	1993	1993	NUM
ajst-2833	193	3	]	]	PUNCT
ajst-2833	193	4	“	"	PUNCT
ajst-2833	193	5	a	a	DET
ajst-2833	193	6	center	center	ADJ
ajst-2833	193	7	-	-	PUNCT
ajst-2833	193	8	stable	stable	ADJ
ajst-2833	193	9	manifold	manifold	ADJ
ajst-2833	193	10	theorem	theorem	NOUN
ajst-2833	193	11	for	for	ADP
ajst-2833	193	12	differential	differential	ADJ
ajst-2833	193	13	equations	equation	NOUN
ajst-2833	193	14	in	in	ADP
ajst-2833	193	15	banach	banach	NOUN
ajst-2833	193	16	spaces	space	NOUN
ajst-2833	193	17	,	,	PUNCT
ajst-2833	193	18	”	"	PUNCT
ajst-2833	193	19	commun.math.phys	commun.math.phys	PROPN
ajst-2833	193	20	.	.	PUNCT
ajst-2833	194	1	152	152	NUM
ajst-2833	194	2	,	,	PUNCT
ajst-2833	194	3	249–268	249–268	NUM
ajst-2833	194	4	.	.	PUNCT
ajst-2833	195	1	[	[	X
ajst-2833	195	2	19	19	NUM
ajst-2833	195	3	]	]	X
ajst-2833	195	4	liu	liu	PROPN
ajst-2833	195	5	,	,	PUNCT
ajst-2833	195	6	w.	w.	PROPN
ajst-2833	195	7	,	,	PUNCT
ajst-2833	195	8	cai	cai	PROPN
ajst-2833	195	9	,	,	PUNCT
ajst-2833	195	10	d.	d.	PROPN
ajst-2833	195	11	&	&	CCONJ
ajst-2833	195	12	shi	shi	PROPN
ajst-2833	195	13	,	,	PUNCT
ajst-2833	195	14	j.	j.	PROPN
ajst-2833	196	1	[	[	X
ajst-2833	196	2	2018	2018	NUM
ajst-2833	196	3	]	]	PUNCT
ajst-2833	196	4	“	"	PUNCT
ajst-2833	196	5	dynamic	dynamic	ADJ
ajst-2833	196	6	behaviors	behavior	NOUN
ajst-2833	196	7	of	of	ADP
ajst-2833	196	8	a	a	DET
ajst-2833	196	9	discretetime	discretetime	ADJ
ajst-2833	196	10	predator	predator	NOUN
ajst-2833	196	11	–	–	PUNCT
ajst-2833	196	12	prey	prey	NOUN
ajst-2833	196	13	bioeconomic	bioeconomic	ADJ
ajst-2833	196	14	system	system	NOUN
ajst-2833	196	15	,	,	PUNCT
ajst-2833	196	16	”	"	PUNCT
ajst-2833	196	17	adv.differ.equ	adv.differ.equ	NOUN
ajst-2833	196	18	.	.	PROPN
ajst-2833	196	19	2018	2018	NUM
ajst-2833	196	20	,	,	PUNCT
ajst-2833	196	21	doi:10.1186	doi:10.1186	NOUN
ajst-2833	196	22	/	/	SYM
ajst-2833	196	23	s13662	s13662	PROPN
ajst-2833	196	24	-	-	PUNCT
ajst-2833	196	25	018	018	NUM
ajst-2833	196	26	-	-	PUNCT
ajst-2833	196	27	1592	1592	NUM
ajst-2833	196	28	-	-	SYM
ajst-2833	196	29	0	0	NUM
ajst-2833	196	30	.	.	PUNCT
ajst-2833	197	1	[	[	X
ajst-2833	197	2	20	20	NUM
ajst-2833	197	3	]	]	SYM
ajst-2833	197	4	jorba	jorba	NOUN
ajst-2833	197	5	,	,	PUNCT
ajst-2833	197	6	a.	a.	NOUN
ajst-2833	197	7	&	&	CCONJ
ajst-2833	197	8	masdemont	masdemont	PROPN
ajst-2833	197	9	,	,	PUNCT
ajst-2833	197	10	j.	j.	PROPN
ajst-2833	198	1	[	[	X
ajst-2833	198	2	1999	1999	NUM
ajst-2833	198	3	]	]	PUNCT
ajst-2833	198	4	“	"	PUNCT
ajst-2833	198	5	dynamics	dynamic	NOUN
ajst-2833	198	6	in	in	ADP
ajst-2833	198	7	the	the	DET
ajst-2833	198	8	center	center	NOUN
ajst-2833	198	9	manifold	manifold	ADJ
ajst-2833	198	10	of	of	ADP
ajst-2833	198	11	the	the	DET
ajst-2833	198	12	collinear	collinear	ADJ
ajst-2833	198	13	points	point	NOUN
ajst-2833	198	14	of	of	ADP
ajst-2833	198	15	the	the	DET
ajst-2833	198	16	restricted	restricted	ADJ
ajst-2833	198	17	three	three	NUM
ajst-2833	198	18	body	body	NOUN
ajst-2833	198	19	problem	problem	NOUN
ajst-2833	198	20	,	,	PUNCT
ajst-2833	198	21	”	"	PUNCT
ajst-2833	198	22	physica	physica	NOUN
ajst-2833	198	23	d	d	PROPN
ajst-2833	198	24	:	:	PUNCT
ajst-2833	198	25	nonlinear	nonlinear	ADJ
ajst-2833	198	26	phenomena	phenomenon	NOUN
ajst-2833	198	27	.	.	PUNCT
ajst-2833	199	1	132	132	NUM
ajst-2833	199	2	,	,	PUNCT
ajst-2833	199	3	189–213	189–213	NUM
ajst-2833	199	4	.	.	PUNCT
ajst-2833	200	1	[	[	X
ajst-2833	200	2	21	21	NUM
ajst-2833	200	3	]	]	X
ajst-2833	200	4	zhao	zhao	X
ajst-2833	200	5	,	,	PUNCT
ajst-2833	200	6	m.	m.	NOUN
ajst-2833	200	7	,	,	PUNCT
ajst-2833	200	8	xuan	xuan	PROPN
ajst-2833	200	9	,	,	PUNCT
ajst-2833	200	10	z.	z.	PROPN
ajst-2833	200	11	&	&	CCONJ
ajst-2833	200	12	li	li	PROPN
ajst-2833	200	13	,	,	PUNCT
ajst-2833	200	14	c.	c.	PROPN
ajst-2833	201	1	[	[	X
ajst-2833	201	2	2016	2016	NUM
ajst-2833	201	3	]	]	PUNCT
ajst-2833	201	4	“	"	PUNCT
ajst-2833	201	5	dynamics	dynamic	NOUN
ajst-2833	201	6	of	of	ADP
ajst-2833	201	7	a	a	DET
ajst-2833	201	8	discretetime	discretetime	ADJ
ajst-2833	201	9	predator	predator	NOUN
ajst-2833	201	10	-	-	PUNCT
ajst-2833	201	11	prey	prey	NOUN
ajst-2833	201	12	system	system	NOUN
ajst-2833	201	13	,	,	PUNCT
ajst-2833	201	14	”	"	PUNCT
ajst-2833	201	15	adv.differ.equ	adv.differ.equ	NOUN
ajst-2833	201	16	.	.	PROPN
ajst-2833	201	17	2016	2016	NUM
ajst-2833	201	18	,	,	PUNCT
ajst-2833	201	19	doi:10.1186	doi:10.1186	NOUN
ajst-2833	201	20	/	/	SYM
ajst-2833	201	21	s13662016	s13662016	PROPN
ajst-2833	201	22	-	-	PUNCT
ajst-2833	201	23	0903	0903	NUM
ajst-2833	201	24	-	-	PUNCT
ajst-2833	201	25	6	6	NUM
ajst-2833	201	26	.	.	PUNCT
ajst-2833	202	1	[	[	X
ajst-2833	202	2	22	22	NUM
ajst-2833	202	3	]	]	PUNCT
ajst-2833	202	4	winggins	winggin	NOUN
ajst-2833	202	5	,	,	PUNCT
ajst-2833	202	6	s.	s.	PROPN
ajst-2833	203	1	[	[	X
ajst-2833	203	2	2003	2003	NUM
ajst-2833	203	3	]	]	PUNCT
ajst-2833	203	4	“	"	PUNCT
ajst-2833	203	5	introduction	introduction	NOUN
ajst-2833	203	6	to	to	PART
ajst-2833	203	7	applied	apply	VERB
ajst-2833	203	8	nonlinear	nonlinear	ADJ
ajst-2833	203	9	dynamical	dynamical	ADJ
ajst-2833	203	10	systems	system	NOUN
ajst-2833	203	11	and	and	CCONJ
ajst-2833	203	12	chaos	chaos	NOUN
ajst-2833	203	13	,	,	PUNCT
ajst-2833	203	14	”	"	PUNCT
ajst-2833	203	15	springer	springer	NOUN
ajst-2833	203	16	-	-	PUNCT
ajst-2833	203	17	verlag	verlag	PROPN
ajst-2833	203	18	,	,	PUNCT
ajst-2833	203	19	new	new	PROPN
ajst-2833	203	20	york	york	PROPN
ajst-2833	203	21	.	.	PUNCT