id	sid	tid	token	lemma	pos
ejpam-4661	1	1	european	european	PROPN
ejpam-4661	1	2	journal	journal	PROPN
ejpam-4661	1	3	of	of	ADP
ejpam-4661	1	4	pure	pure	ADJ
ejpam-4661	1	5	and	and	CCONJ
ejpam-4661	1	6	applied	apply	VERB
ejpam-4661	1	7	mathematics	mathematic	NOUN
ejpam-4661	1	8	vol	vol	NOUN
ejpam-4661	1	9	.	.	PUNCT
ejpam-4661	2	1	16	16	NUM
ejpam-4661	2	2	,	,	PUNCT
ejpam-4661	2	3	no	no	INTJ
ejpam-4661	2	4	.	.	NOUN
ejpam-4661	2	5	1	1	NUM
ejpam-4661	2	6	,	,	PUNCT
ejpam-4661	2	7	2023	2023	NUM
ejpam-4661	2	8	,	,	PUNCT
ejpam-4661	2	9	71	71	NUM
ejpam-4661	2	10	-	-	SYM
ejpam-4661	2	11	83	83	NUM
ejpam-4661	2	12	issn	issn	PROPN
ejpam-4661	2	13	1307	1307	NUM
ejpam-4661	2	14	-	-	SYM
ejpam-4661	2	15	5543	5543	NUM
ejpam-4661	2	16	–	–	PUNCT
ejpam-4661	2	17	ejpam.com	ejpam.com	X
ejpam-4661	2	18	published	publish	VERB
ejpam-4661	2	19	by	by	ADP
ejpam-4661	2	20	new	new	PROPN
ejpam-4661	2	21	york	york	PROPN
ejpam-4661	2	22	business	business	PROPN
ejpam-4661	3	1	global	global	PROPN
ejpam-4661	3	2	a	a	DET
ejpam-4661	3	3	discrete	discrete	ADJ
ejpam-4661	3	4	predator	predator	NOUN
ejpam-4661	3	5	-	-	PUNCT
ejpam-4661	3	6	prey	prey	NOUN
ejpam-4661	3	7	model	model	NOUN
ejpam-4661	3	8	with	with	ADP
ejpam-4661	3	9	allee	allee	NOUN
ejpam-4661	3	10	and	and	CCONJ
ejpam-4661	3	11	refuge	refuge	NOUN
ejpam-4661	3	12	effect	effect	NOUN
ejpam-4661	3	13	sinan	sinan	PROPN
ejpam-4661	3	14	kapçak	kapçak	PROPN
ejpam-4661	3	15	college	college	PROPN
ejpam-4661	3	16	of	of	ADP
ejpam-4661	3	17	engineering	engineering	NOUN
ejpam-4661	3	18	and	and	CCONJ
ejpam-4661	3	19	technology	technology	NOUN
ejpam-4661	3	20	,	,	PUNCT
ejpam-4661	3	21	american	american	PROPN
ejpam-4661	3	22	university	university	PROPN
ejpam-4661	3	23	of	of	ADP
ejpam-4661	3	24	the	the	DET
ejpam-4661	3	25	middle	middle	PROPN
ejpam-4661	3	26	east	east	PROPN
ejpam-4661	3	27	,	,	PUNCT
ejpam-4661	3	28	kuwait	kuwait	PROPN
ejpam-4661	3	29	abstract	abstract	NOUN
ejpam-4661	3	30	.	.	PUNCT
ejpam-4661	4	1	we	we	PRON
ejpam-4661	4	2	consider	consider	VERB
ejpam-4661	4	3	a	a	DET
ejpam-4661	4	4	predator	predator	NOUN
ejpam-4661	4	5	-	-	PUNCT
ejpam-4661	4	6	prey	prey	NOUN
ejpam-4661	4	7	model	model	NOUN
ejpam-4661	4	8	,	,	PUNCT
ejpam-4661	4	9	where	where	SCONJ
ejpam-4661	4	10	some	some	DET
ejpam-4661	4	11	prey	prey	NOUN
ejpam-4661	4	12	are	be	AUX
ejpam-4661	4	13	completely	completely	ADV
ejpam-4661	4	14	free	free	ADJ
ejpam-4661	4	15	from	from	ADP
ejpam-4661	4	16	predation	predation	NOUN
ejpam-4661	4	17	within	within	ADP
ejpam-4661	4	18	a	a	DET
ejpam-4661	4	19	temporal	temporal	ADJ
ejpam-4661	4	20	or	or	CCONJ
ejpam-4661	4	21	spacial	spacial	ADJ
ejpam-4661	4	22	refuge	refuge	NOUN
ejpam-4661	4	23	and	and	CCONJ
ejpam-4661	4	24	the	the	DET
ejpam-4661	4	25	predator	predator	NOUN
ejpam-4661	4	26	population	population	NOUN
ejpam-4661	4	27	is	be	AUX
ejpam-4661	4	28	subject	subject	ADJ
ejpam-4661	4	29	to	to	ADP
ejpam-4661	4	30	allee	allee	PROPN
ejpam-4661	4	31	effect	effect	NOUN
ejpam-4661	4	32	.	.	PUNCT
ejpam-4661	5	1	we	we	PRON
ejpam-4661	5	2	study	study	VERB
ejpam-4661	5	3	the	the	DET
ejpam-4661	5	4	effect	effect	NOUN
ejpam-4661	5	5	of	of	ADP
ejpam-4661	5	6	the	the	DET
ejpam-4661	5	7	presence	presence	NOUN
ejpam-4661	5	8	of	of	ADP
ejpam-4661	5	9	refuge	refuge	NOUN
ejpam-4661	5	10	and	and	CCONJ
ejpam-4661	5	11	allee	allee	ADJ
ejpam-4661	5	12	effect	effect	NOUN
ejpam-4661	5	13	on	on	ADP
ejpam-4661	5	14	the	the	DET
ejpam-4661	5	15	stability	stability	NOUN
ejpam-4661	5	16	and	and	CCONJ
ejpam-4661	5	17	bifurcation	bifurcation	NOUN
ejpam-4661	5	18	of	of	ADP
ejpam-4661	5	19	the	the	DET
ejpam-4661	5	20	system	system	NOUN
ejpam-4661	5	21	.	.	PUNCT
ejpam-4661	6	1	we	we	PRON
ejpam-4661	6	2	investigate	investigate	VERB
ejpam-4661	6	3	the	the	DET
ejpam-4661	6	4	existence	existence	NOUN
ejpam-4661	6	5	and	and	CCONJ
ejpam-4661	6	6	stability	stability	NOUN
ejpam-4661	6	7	of	of	ADP
ejpam-4661	6	8	the	the	DET
ejpam-4661	6	9	model	model	NOUN
ejpam-4661	6	10	as	as	ADV
ejpam-4661	6	11	well	well	ADV
ejpam-4661	6	12	as	as	ADP
ejpam-4661	6	13	the	the	DET
ejpam-4661	6	14	stability	stability	NOUN
ejpam-4661	6	15	region	region	NOUN
ejpam-4661	6	16	.	.	PUNCT
ejpam-4661	7	1	we	we	PRON
ejpam-4661	7	2	also	also	ADV
ejpam-4661	7	3	obtain	obtain	VERB
ejpam-4661	7	4	the	the	DET
ejpam-4661	7	5	invariant	invariant	ADJ
ejpam-4661	7	6	manifolds	manifold	NOUN
ejpam-4661	7	7	of	of	ADP
ejpam-4661	7	8	the	the	DET
ejpam-4661	7	9	system	system	NOUN
ejpam-4661	7	10	.	.	PUNCT
ejpam-4661	8	1	2020	2020	NUM
ejpam-4661	8	2	mathematics	mathematic	NOUN
ejpam-4661	8	3	subject	subject	NOUN
ejpam-4661	8	4	classifications	classification	NOUN
ejpam-4661	8	5	:	:	PUNCT
ejpam-4661	8	6	37n25	37n25	NUM
ejpam-4661	8	7	,	,	PUNCT
ejpam-4661	8	8	37d10	37d10	NUM
ejpam-4661	8	9	,	,	PUNCT
ejpam-4661	8	10	39a28	39a28	NUM
ejpam-4661	8	11	,	,	PUNCT
ejpam-4661	8	12	39a30	39a30	NUM
ejpam-4661	8	13	,	,	PUNCT
ejpam-4661	8	14	39a60	39a60	NUM
ejpam-4661	8	15	key	key	ADJ
ejpam-4661	8	16	words	word	NOUN
ejpam-4661	8	17	and	and	CCONJ
ejpam-4661	8	18	phrases	phrase	NOUN
ejpam-4661	8	19	:	:	PUNCT
ejpam-4661	8	20	allee	allee	ADJ
ejpam-4661	8	21	effect	effect	NOUN
ejpam-4661	8	22	,	,	PUNCT
ejpam-4661	8	23	refuge	refuge	ADJ
ejpam-4661	8	24	effect	effect	NOUN
ejpam-4661	8	25	,	,	PUNCT
ejpam-4661	8	26	invariant	invariant	ADJ
ejpam-4661	8	27	manifolds	manifold	NOUN
ejpam-4661	8	28	1	1	NUM
ejpam-4661	8	29	.	.	PUNCT
ejpam-4661	8	30	introduction	introduction	NOUN
ejpam-4661	8	31	in	in	ADP
ejpam-4661	8	32	this	this	DET
ejpam-4661	8	33	paper	paper	NOUN
ejpam-4661	8	34	,	,	PUNCT
ejpam-4661	8	35	we	we	PRON
ejpam-4661	8	36	investigate	investigate	VERB
ejpam-4661	8	37	a	a	DET
ejpam-4661	8	38	predator	predator	NOUN
ejpam-4661	8	39	-	-	PUNCT
ejpam-4661	8	40	prey	prey	NOUN
ejpam-4661	8	41	model	model	NOUN
ejpam-4661	8	42	,	,	PUNCT
ejpam-4661	8	43	where	where	SCONJ
ejpam-4661	8	44	some	some	DET
ejpam-4661	8	45	prey	prey	NOUN
ejpam-4661	8	46	are	be	AUX
ejpam-4661	8	47	completely	completely	ADV
ejpam-4661	8	48	free	free	ADJ
ejpam-4661	8	49	from	from	ADP
ejpam-4661	8	50	predation	predation	NOUN
ejpam-4661	8	51	within	within	ADP
ejpam-4661	8	52	a	a	DET
ejpam-4661	8	53	temporal	temporal	ADJ
ejpam-4661	8	54	or	or	CCONJ
ejpam-4661	8	55	spacial	spacial	ADJ
ejpam-4661	8	56	refuge	refuge	NOUN
ejpam-4661	8	57	and	and	CCONJ
ejpam-4661	8	58	predator	predator	NOUN
ejpam-4661	8	59	are	be	AUX
ejpam-4661	8	60	subject	subject	ADJ
ejpam-4661	8	61	to	to	ADP
ejpam-4661	8	62	allee	allee	PROPN
ejpam-4661	8	63	effect	effect	NOUN
ejpam-4661	8	64	.	.	PUNCT
ejpam-4661	9	1	the	the	DET
ejpam-4661	9	2	most	most	ADV
ejpam-4661	9	3	common	common	ADJ
ejpam-4661	9	4	type	type	NOUN
ejpam-4661	9	5	of	of	ADP
ejpam-4661	9	6	spacial	spacial	ADJ
ejpam-4661	9	7	refuge	refuge	NOUN
ejpam-4661	9	8	,	,	PUNCT
ejpam-4661	9	9	that	that	SCONJ
ejpam-4661	9	10	we	we	PRON
ejpam-4661	9	11	investigate	investigate	VERB
ejpam-4661	9	12	here	here	ADV
ejpam-4661	9	13	,	,	PUNCT
ejpam-4661	9	14	takes	take	VERB
ejpam-4661	9	15	the	the	DET
ejpam-4661	9	16	form	form	NOUN
ejpam-4661	9	17	where	where	SCONJ
ejpam-4661	9	18	a	a	DET
ejpam-4661	9	19	constant	constant	ADJ
ejpam-4661	9	20	proportion	proportion	NOUN
ejpam-4661	9	21	of	of	ADP
ejpam-4661	9	22	the	the	DET
ejpam-4661	9	23	prey	prey	NOUN
ejpam-4661	9	24	population	population	NOUN
ejpam-4661	9	25	is	be	AUX
ejpam-4661	9	26	protected	protect	VERB
ejpam-4661	9	27	.	.	PUNCT
ejpam-4661	10	1	some	some	PRON
ejpam-4661	10	2	of	of	ADP
ejpam-4661	10	3	studies	study	NOUN
ejpam-4661	10	4	have	have	AUX
ejpam-4661	10	5	investigated	investigate	VERB
ejpam-4661	10	6	the	the	DET
ejpam-4661	10	7	influence	influence	NOUN
ejpam-4661	10	8	of	of	ADP
ejpam-4661	10	9	prey	prey	ADJ
ejpam-4661	10	10	refuge	refuge	NOUN
ejpam-4661	10	11	and	and	CCONJ
ejpam-4661	10	12	concluded	conclude	VERB
ejpam-4661	10	13	that	that	SCONJ
ejpam-4661	10	14	the	the	DET
ejpam-4661	10	15	refuge	refuge	NOUN
ejpam-4661	10	16	used	use	VERB
ejpam-4661	10	17	by	by	ADP
ejpam-4661	10	18	the	the	DET
ejpam-4661	10	19	prey	prey	NOUN
ejpam-4661	10	20	has	have	VERB
ejpam-4661	10	21	a	a	DET
ejpam-4661	10	22	stabilizing	stabilize	VERB
ejpam-4661	10	23	effect	effect	NOUN
ejpam-4661	10	24	on	on	ADP
ejpam-4661	10	25	the	the	DET
ejpam-4661	10	26	predator	predator	NOUN
ejpam-4661	10	27	-	-	PUNCT
ejpam-4661	10	28	prey	prey	NOUN
ejpam-4661	10	29	interaction	interaction	NOUN
ejpam-4661	10	30	and	and	CCONJ
ejpam-4661	10	31	also	also	ADV
ejpam-4661	10	32	that	that	SCONJ
ejpam-4661	10	33	the	the	DET
ejpam-4661	10	34	prey	prey	NOUN
ejpam-4661	10	35	species	specie	NOUN
ejpam-4661	10	36	can	can	AUX
ejpam-4661	10	37	be	be	AUX
ejpam-4661	10	38	prevented	prevent	VERB
ejpam-4661	10	39	well	well	ADV
ejpam-4661	10	40	from	from	ADP
ejpam-4661	10	41	extinction	extinction	NOUN
ejpam-4661	10	42	.	.	PUNCT
ejpam-4661	11	1	some	some	DET
ejpam-4661	11	2	studies	study	NOUN
ejpam-4661	11	3	on	on	ADP
ejpam-4661	11	4	refuge	refuge	ADJ
ejpam-4661	11	5	effect	effect	NOUN
ejpam-4661	11	6	can	can	AUX
ejpam-4661	11	7	be	be	AUX
ejpam-4661	11	8	found	find	VERB
ejpam-4661	11	9	in	in	ADP
ejpam-4661	11	10	[	[	X
ejpam-4661	11	11	3	3	NUM
ejpam-4661	11	12	,	,	PUNCT
ejpam-4661	11	13	12	12	NUM
ejpam-4661	11	14	,	,	PUNCT
ejpam-4661	11	15	13	13	NUM
ejpam-4661	11	16	]	]	PUNCT
ejpam-4661	11	17	.	.	PUNCT
ejpam-4661	12	1	the	the	DET
ejpam-4661	12	2	allee	allee	PROPN
ejpam-4661	12	3	effect	effect	NOUN
ejpam-4661	12	4	is	be	AUX
ejpam-4661	12	5	characterized	characterize	VERB
ejpam-4661	12	6	by	by	ADP
ejpam-4661	12	7	a	a	DET
ejpam-4661	12	8	positive	positive	ADJ
ejpam-4661	12	9	correlation	correlation	NOUN
ejpam-4661	12	10	between	between	ADP
ejpam-4661	12	11	population	population	NOUN
ejpam-4661	12	12	size	size	NOUN
ejpam-4661	12	13	and	and	CCONJ
ejpam-4661	12	14	the	the	DET
ejpam-4661	12	15	mean	mean	ADJ
ejpam-4661	12	16	individual	individual	ADJ
ejpam-4661	12	17	fitness	fitness	NOUN
ejpam-4661	12	18	of	of	ADP
ejpam-4661	12	19	a	a	DET
ejpam-4661	12	20	population	population	NOUN
ejpam-4661	12	21	.	.	PUNCT
ejpam-4661	13	1	when	when	SCONJ
ejpam-4661	13	2	the	the	DET
ejpam-4661	13	3	population	population	NOUN
ejpam-4661	13	4	density	density	NOUN
ejpam-4661	13	5	is	be	AUX
ejpam-4661	13	6	low	low	ADJ
ejpam-4661	13	7	,	,	PUNCT
ejpam-4661	13	8	the	the	DET
ejpam-4661	13	9	population	population	NOUN
ejpam-4661	13	10	will	will	AUX
ejpam-4661	13	11	experience	experience	VERB
ejpam-4661	13	12	a	a	DET
ejpam-4661	13	13	reduced	reduced	ADJ
ejpam-4661	13	14	overall	overall	ADJ
ejpam-4661	13	15	growth	growth	NOUN
ejpam-4661	13	16	rate	rate	NOUN
ejpam-4661	13	17	,	,	PUNCT
ejpam-4661	13	18	and	and	CCONJ
ejpam-4661	13	19	may	may	AUX
ejpam-4661	13	20	increase	increase	VERB
ejpam-4661	13	21	the	the	DET
ejpam-4661	13	22	risk	risk	NOUN
ejpam-4661	13	23	of	of	ADP
ejpam-4661	13	24	extinction	extinction	NOUN
ejpam-4661	13	25	.	.	PUNCT
ejpam-4661	14	1	if	if	SCONJ
ejpam-4661	14	2	there	there	PRON
ejpam-4661	14	3	are	be	VERB
ejpam-4661	14	4	more	more	ADJ
ejpam-4661	14	5	individuals	individual	NOUN
ejpam-4661	14	6	,	,	PUNCT
ejpam-4661	14	7	population	population	NOUN
ejpam-4661	14	8	grows	grow	VERB
ejpam-4661	14	9	more	more	ADV
ejpam-4661	14	10	rapidly	rapidly	ADV
ejpam-4661	14	11	,	,	PUNCT
ejpam-4661	14	12	and	and	CCONJ
ejpam-4661	14	13	the	the	DET
ejpam-4661	14	14	aggregation	aggregation	NOUN
ejpam-4661	14	15	can	can	AUX
ejpam-4661	14	16	improve	improve	VERB
ejpam-4661	14	17	the	the	DET
ejpam-4661	14	18	survival	survival	NOUN
ejpam-4661	14	19	rate	rate	NOUN
ejpam-4661	14	20	of	of	ADP
ejpam-4661	14	21	individuals	individual	NOUN
ejpam-4661	14	22	.	.	PUNCT
ejpam-4661	15	1	recently	recently	ADV
ejpam-4661	15	2	,	,	PUNCT
ejpam-4661	15	3	many	many	ADJ
ejpam-4661	15	4	studies	study	NOUN
ejpam-4661	15	5	have	have	AUX
ejpam-4661	15	6	been	be	AUX
ejpam-4661	15	7	done	do	VERB
ejpam-4661	15	8	on	on	ADP
ejpam-4661	15	9	predator	predator	NOUN
ejpam-4661	15	10	-	-	PUNCT
ejpam-4661	15	11	prey	prey	NOUN
ejpam-4661	15	12	models	model	NOUN
ejpam-4661	15	13	with	with	ADP
ejpam-4661	15	14	allee	allee	ADJ
ejpam-4661	15	15	effect	effect	NOUN
ejpam-4661	15	16	.	.	PUNCT
ejpam-4661	16	1	livadiotis	livadiotis	NOUN
ejpam-4661	16	2	,	,	PUNCT
ejpam-4661	16	3	assas	assa	NOUN
ejpam-4661	16	4	,	,	PUNCT
ejpam-4661	16	5	elaydi	elaydi	VERB
ejpam-4661	16	6	,	,	PUNCT
ejpam-4661	16	7	kwessi	kwessi	NOUN
ejpam-4661	16	8	,	,	PUNCT
ejpam-4661	16	9	dennis	dennis	PROPN
ejpam-4661	17	1	[	[	X
ejpam-4661	17	2	11	11	NUM
ejpam-4661	17	3	]	]	PUNCT
ejpam-4661	17	4	investigated	investigate	VERB
ejpam-4661	17	5	the	the	DET
ejpam-4661	17	6	impact	impact	NOUN
ejpam-4661	17	7	of	of	ADP
ejpam-4661	17	8	the	the	DET
ejpam-4661	17	9	allee	allee	ADJ
ejpam-4661	17	10	effect	effect	NOUN
ejpam-4661	17	11	on	on	ADP
ejpam-4661	17	12	the	the	DET
ejpam-4661	17	13	global	global	ADJ
ejpam-4661	17	14	dynamics	dynamic	NOUN
ejpam-4661	17	15	of	of	ADP
ejpam-4661	17	16	beddington	beddington	PROPN
ejpam-4661	17	17	model	model	NOUN
ejpam-4661	17	18	.	.	PUNCT
ejpam-4661	18	1	some	some	DET
ejpam-4661	18	2	other	other	ADJ
ejpam-4661	18	3	predator	predator	NOUN
ejpam-4661	18	4	-	-	PUNCT
ejpam-4661	18	5	prey	prey	NOUN
ejpam-4661	18	6	studies	study	NOUN
ejpam-4661	18	7	with	with	ADP
ejpam-4661	18	8	/	/	SYM
ejpam-4661	18	9	without	without	ADP
ejpam-4661	18	10	allee	allee	ADJ
ejpam-4661	18	11	effect	effect	NOUN
ejpam-4661	18	12	were	be	AUX
ejpam-4661	18	13	conducted	conduct	VERB
ejpam-4661	18	14	in	in	ADP
ejpam-4661	18	15	[	[	X
ejpam-4661	18	16	5–7]/[1	5–7]/[1	NUM
ejpam-4661	18	17	,	,	PUNCT
ejpam-4661	18	18	9	9	NUM
ejpam-4661	18	19	]	]	PUNCT
ejpam-4661	18	20	.	.	PUNCT
ejpam-4661	19	1	doi	doi	NOUN
ejpam-4661	19	2	:	:	PUNCT
ejpam-4661	19	3	https://doi.org/10.29020/nybg.ejpam.v16i1.4661	https://doi.org/10.29020/nybg.ejpam.v16i1.4661	VERB
ejpam-4661	19	4	email	email	NOUN
ejpam-4661	19	5	address	address	NOUN
ejpam-4661	19	6	:	:	PUNCT
ejpam-4661	19	7	sinan.kapcak@aum.edu.kw	sinan.kapcak@aum.edu.kw	PROPN
ejpam-4661	19	8	(	(	PUNCT
ejpam-4661	19	9	s.	s.	PROPN
ejpam-4661	19	10	kapçak	kapçak	PROPN
ejpam-4661	19	11	)	)	PUNCT
ejpam-4661	19	12	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4661	19	13	71	71	NUM
ejpam-4661	19	14	©	©	PROPN
ejpam-4661	19	15	2023	2023	NUM
ejpam-4661	19	16	ejpam	ejpam	NOUN
ejpam-4661	19	17	all	all	DET
ejpam-4661	19	18	rights	right	NOUN
ejpam-4661	19	19	reserved	reserve	VERB
ejpam-4661	19	20	.	.	PUNCT
ejpam-4661	20	1	s.	s.	PROPN
ejpam-4661	20	2	kapcak	kapcak	PROPN
ejpam-4661	20	3	/	/	SYM
ejpam-4661	20	4	eur	eur	PROPN
ejpam-4661	20	5	.	.	PUNCT
ejpam-4661	21	1	j.	j.	PROPN
ejpam-4661	21	2	pure	pure	PROPN
ejpam-4661	21	3	appl	appl	PROPN
ejpam-4661	21	4	.	.	PROPN
ejpam-4661	21	5	math	math	PROPN
ejpam-4661	21	6	,	,	PUNCT
ejpam-4661	21	7	16	16	NUM
ejpam-4661	21	8	(	(	PUNCT
ejpam-4661	21	9	1	1	NUM
ejpam-4661	21	10	)	)	PUNCT
ejpam-4661	21	11	(	(	PUNCT
ejpam-4661	21	12	2023	2023	NUM
ejpam-4661	21	13	)	)	PUNCT
ejpam-4661	21	14	,	,	PUNCT
ejpam-4661	21	15	71	71	NUM
ejpam-4661	21	16	-	-	SYM
ejpam-4661	21	17	83	83	NUM
ejpam-4661	21	18	72	72	NUM
ejpam-4661	21	19	maynard	maynard	NOUN
ejpam-4661	21	20	smith	smith	PROPN
ejpam-4661	22	1	[	[	X
ejpam-4661	22	2	17	17	NUM
ejpam-4661	22	3	]	]	PUNCT
ejpam-4661	22	4	proposed	propose	VERB
ejpam-4661	22	5	the	the	DET
ejpam-4661	22	6	following	follow	VERB
ejpam-4661	22	7	predator	predator	NOUN
ejpam-4661	22	8	-	-	PUNCT
ejpam-4661	22	9	prey	prey	NOUN
ejpam-4661	22	10	model	model	NOUN
ejpam-4661	22	11	:	:	PUNCT
ejpam-4661	22	12	xt+1	xt+1	X
ejpam-4661	22	13	=	=	SYM
ejpam-4661	22	14	rxt	rxt	PROPN
ejpam-4661	22	15	−	−	PROPN
ejpam-4661	22	16	r−	r−	PROPN
ejpam-4661	22	17	1	1	NUM
ejpam-4661	22	18	xe	xe	PROPN
ejpam-4661	22	19	x2	x2	PROPN
ejpam-4661	22	20	t	t	PROPN
ejpam-4661	23	1	−	−	PROPN
ejpam-4661	23	2	cxtyt	cxtyt	ADJ
ejpam-4661	23	3	,	,	PUNCT
ejpam-4661	23	4	yt+1	yt+1	NUM
ejpam-4661	24	1	=	=	SYM
ejpam-4661	24	2	r	r	NOUN
ejpam-4661	24	3	xe	xe	PROPN
ejpam-4661	24	4	xtyt	xtyt	PROPN
ejpam-4661	24	5	,	,	PUNCT
ejpam-4661	24	6	(	(	PUNCT
ejpam-4661	24	7	1	1	X
ejpam-4661	24	8	)	)	PUNCT
ejpam-4661	24	9	where	where	SCONJ
ejpam-4661	24	10	xt	xt	PUNCT
ejpam-4661	24	11	and	and	CCONJ
ejpam-4661	24	12	yt	yt	PROPN
ejpam-4661	24	13	represent	represent	VERB
ejpam-4661	24	14	the	the	DET
ejpam-4661	24	15	prey	prey	NOUN
ejpam-4661	24	16	and	and	CCONJ
ejpam-4661	24	17	predator	predator	NOUN
ejpam-4661	24	18	population	population	NOUN
ejpam-4661	24	19	in	in	ADP
ejpam-4661	24	20	year	year	PROPN
ejpam-4661	24	21	t	t	PROPN
ejpam-4661	24	22	,	,	PUNCT
ejpam-4661	24	23	respectively	respectively	ADV
ejpam-4661	24	24	.	.	PUNCT
ejpam-4661	25	1	xe	xe	PROPN
ejpam-4661	25	2	is	be	AUX
ejpam-4661	25	3	the	the	DET
ejpam-4661	25	4	equilibrium	equilibrium	NOUN
ejpam-4661	25	5	value	value	NOUN
ejpam-4661	25	6	of	of	ADP
ejpam-4661	25	7	xt	xt	PROPN
ejpam-4661	25	8	in	in	ADP
ejpam-4661	25	9	the	the	DET
ejpam-4661	25	10	absence	absence	NOUN
ejpam-4661	25	11	of	of	ADP
ejpam-4661	25	12	predator	predator	NOUN
ejpam-4661	25	13	.	.	PUNCT
ejpam-4661	26	1	r	r	NOUN
ejpam-4661	26	2	and	and	CCONJ
ejpam-4661	26	3	r	r	NOUN
ejpam-4661	26	4	are	be	AUX
ejpam-4661	26	5	maximum	maximum	ADJ
ejpam-4661	26	6	reproductive	reproductive	ADJ
ejpam-4661	26	7	rates	rate	NOUN
ejpam-4661	26	8	of	of	ADP
ejpam-4661	26	9	prey	prey	NOUN
ejpam-4661	26	10	and	and	CCONJ
ejpam-4661	26	11	predator	predator	NOUN
ejpam-4661	26	12	,	,	PUNCT
ejpam-4661	26	13	respectively	respectively	ADV
ejpam-4661	26	14	.	.	PUNCT
ejpam-4661	27	1	in	in	ADP
ejpam-4661	27	2	[	[	X
ejpam-4661	27	3	14	14	NUM
ejpam-4661	27	4	]	]	X
ejpam-4661	27	5	,	,	PUNCT
ejpam-4661	27	6	murakami	murakami	NOUN
ejpam-4661	27	7	investigates	investigate	VERB
ejpam-4661	27	8	the	the	DET
ejpam-4661	27	9	stability	stability	NOUN
ejpam-4661	27	10	and	and	CCONJ
ejpam-4661	27	11	bifurcation	bifurcation	NOUN
ejpam-4661	27	12	,	,	PUNCT
ejpam-4661	27	13	including	include	VERB
ejpam-4661	27	14	neimark	neimark	NOUN
ejpam-4661	27	15	-	-	PUNCT
ejpam-4661	27	16	sacker	sacker	NOUN
ejpam-4661	27	17	bifurcation	bifurcation	NOUN
ejpam-4661	27	18	,	,	PUNCT
ejpam-4661	27	19	of	of	ADP
ejpam-4661	27	20	model	model	NOUN
ejpam-4661	27	21	(	(	PUNCT
ejpam-4661	27	22	1	1	NUM
ejpam-4661	27	23	)	)	PUNCT
ejpam-4661	27	24	.	.	PUNCT
ejpam-4661	28	1	in	in	ADP
ejpam-4661	28	2	this	this	DET
ejpam-4661	28	3	paper	paper	NOUN
ejpam-4661	28	4	,	,	PUNCT
ejpam-4661	28	5	we	we	PRON
ejpam-4661	28	6	study	study	VERB
ejpam-4661	28	7	model	model	NOUN
ejpam-4661	28	8	(	(	PUNCT
ejpam-4661	28	9	1	1	NUM
ejpam-4661	28	10	)	)	PUNCT
ejpam-4661	28	11	with	with	ADP
ejpam-4661	28	12	prey	prey	NOUN
ejpam-4661	28	13	and	and	CCONJ
ejpam-4661	28	14	predator	predator	NOUN
ejpam-4661	28	15	subject	subject	NOUN
ejpam-4661	28	16	to	to	ADP
ejpam-4661	28	17	a	a	DET
ejpam-4661	28	18	refuge	refuge	NOUN
ejpam-4661	28	19	and	and	CCONJ
ejpam-4661	28	20	allee	allee	ADJ
ejpam-4661	28	21	effect	effect	NOUN
ejpam-4661	28	22	,	,	PUNCT
ejpam-4661	28	23	respectively	respectively	ADV
ejpam-4661	28	24	.	.	PUNCT
ejpam-4661	29	1	regarding	regard	VERB
ejpam-4661	29	2	the	the	DET
ejpam-4661	29	3	refuge	refuge	NOUN
ejpam-4661	29	4	effect	effect	NOUN
ejpam-4661	29	5	,	,	PUNCT
ejpam-4661	29	6	we	we	PRON
ejpam-4661	29	7	assume	assume	VERB
ejpam-4661	29	8	the	the	DET
ejpam-4661	29	9	presence	presence	NOUN
ejpam-4661	29	10	of	of	ADP
ejpam-4661	29	11	spacial	spacial	ADJ
ejpam-4661	29	12	heterogeneity	heterogeneity	NOUN
ejpam-4661	29	13	.	.	PUNCT
ejpam-4661	30	1	the	the	DET
ejpam-4661	30	2	refuge	refuge	NOUN
ejpam-4661	30	3	model	model	NOUN
ejpam-4661	30	4	is	be	AUX
ejpam-4661	30	5	due	due	ADJ
ejpam-4661	30	6	to	to	ADP
ejpam-4661	30	7	hassel	hassel	PROPN
ejpam-4661	31	1	[	[	X
ejpam-4661	31	2	3	3	NUM
ejpam-4661	31	3	]	]	PUNCT
ejpam-4661	31	4	.	.	PUNCT
ejpam-4661	32	1	in	in	ADP
ejpam-4661	32	2	the	the	DET
ejpam-4661	32	3	absence	absence	NOUN
ejpam-4661	32	4	of	of	ADP
ejpam-4661	32	5	predator	predator	NOUN
ejpam-4661	32	6	,	,	PUNCT
ejpam-4661	32	7	the	the	DET
ejpam-4661	32	8	growth	growth	NOUN
ejpam-4661	32	9	of	of	ADP
ejpam-4661	32	10	the	the	DET
ejpam-4661	32	11	prey	prey	NOUN
ejpam-4661	32	12	population	population	NOUN
ejpam-4661	32	13	is	be	AUX
ejpam-4661	32	14	logistic	logistic	ADJ
ejpam-4661	32	15	.	.	PUNCT
ejpam-4661	33	1	the	the	DET
ejpam-4661	33	2	following	follow	VERB
ejpam-4661	33	3	model	model	NOUN
ejpam-4661	33	4	is	be	AUX
ejpam-4661	33	5	proposed	propose	VERB
ejpam-4661	33	6	:	:	PUNCT
ejpam-4661	33	7	xt+1	xt+1	X
ejpam-4661	34	1	=	=	SYM
ejpam-4661	34	2	r(1−	r(1−	PROPN
ejpam-4661	35	1	b)xt	b)xt	PROPN
ejpam-4661	35	2	−	−	PROPN
ejpam-4661	35	3	r−	r−	PROPN
ejpam-4661	35	4	1	1	NUM
ejpam-4661	35	5	xe	xe	PROPN
ejpam-4661	35	6	(	(	PUNCT
ejpam-4661	35	7	1−	1−	NUM
ejpam-4661	35	8	b)2x2	b)2x2	PROPN
ejpam-4661	35	9	t	t	PROPN
ejpam-4661	35	10	+	+	NOUN
ejpam-4661	35	11	rbxt	rbxt	NOUN
ejpam-4661	35	12	−	−	PROPN
ejpam-4661	35	13	(	(	PUNCT
ejpam-4661	35	14	r−	r−	PROPN
ejpam-4661	35	15	1)b2	1)b2	PROPN
ejpam-4661	35	16	xe	xe	PROPN
ejpam-4661	35	17	x2	x2	PROPN
ejpam-4661	35	18	t	t	PROPN
ejpam-4661	35	19	−	−	PROPN
ejpam-4661	35	20	cbxtyt	cbxtyt	PROPN
ejpam-4661	35	21	,	,	PUNCT
ejpam-4661	35	22	yt+1	yt+1	PROPN
ejpam-4661	35	23	=	=	PUNCT
ejpam-4661	35	24	rb	rb	PROPN
ejpam-4661	35	25	xe	xe	PROPN
ejpam-4661	35	26	xtyt	xtyt	PROPN
ejpam-4661	35	27	yt	yt	PROPN
ejpam-4661	35	28	a+	a+	PUNCT
ejpam-4661	35	29	yt	yt	PROPN
ejpam-4661	35	30	.	.	PUNCT
ejpam-4661	36	1	(	(	PUNCT
ejpam-4661	36	2	2	2	X
ejpam-4661	36	3	)	)	PUNCT
ejpam-4661	36	4	in	in	ADP
ejpam-4661	36	5	equation	equation	NOUN
ejpam-4661	36	6	(	(	PUNCT
ejpam-4661	36	7	2	2	NUM
ejpam-4661	36	8	)	)	PUNCT
ejpam-4661	36	9	,	,	PUNCT
ejpam-4661	36	10	the	the	DET
ejpam-4661	36	11	expression	expression	NOUN
ejpam-4661	36	12	(	(	PUNCT
ejpam-4661	36	13	1	1	NUM
ejpam-4661	36	14	−	−	NOUN
ejpam-4661	36	15	b)xt	b)xt	PROPN
ejpam-4661	36	16	is	be	AUX
ejpam-4661	36	17	the	the	DET
ejpam-4661	36	18	number	number	NOUN
ejpam-4661	36	19	of	of	ADP
ejpam-4661	36	20	the	the	DET
ejpam-4661	36	21	prey	prey	NOUN
ejpam-4661	36	22	in	in	ADP
ejpam-4661	36	23	a	a	DET
ejpam-4661	36	24	protective	protective	ADJ
ejpam-4661	36	25	refuge	refuge	NOUN
ejpam-4661	36	26	at	at	ADP
ejpam-4661	36	27	time	time	NOUN
ejpam-4661	36	28	t	t	PROPN
ejpam-4661	36	29	,	,	PUNCT
ejpam-4661	36	30	0	0	PUNCT
ejpam-4661	36	31	<	<	X
ejpam-4661	36	32	b	b	X
ejpam-4661	36	33	<	<	X
ejpam-4661	36	34	1	1	NUM
ejpam-4661	36	35	,	,	PUNCT
ejpam-4661	36	36	which	which	PRON
ejpam-4661	36	37	has	have	VERB
ejpam-4661	36	38	logistic	logistic	ADJ
ejpam-4661	36	39	growth	growth	NOUN
ejpam-4661	36	40	represented	represent	VERB
ejpam-4661	36	41	by	by	ADP
ejpam-4661	36	42	the	the	DET
ejpam-4661	36	43	expression	expression	NOUN
ejpam-4661	36	44	r(1−	r(1−	PUNCT
ejpam-4661	37	1	b)xt	b)xt	PROPN
ejpam-4661	37	2	−	−	PROPN
ejpam-4661	37	3	r−1	r−1	PROPN
ejpam-4661	37	4	xe	xe	PROPN
ejpam-4661	37	5	(	(	PUNCT
ejpam-4661	37	6	1−	1−	NUM
ejpam-4661	37	7	b)2x2	b)2x2	PROPN
ejpam-4661	37	8	t	t	PROPN
ejpam-4661	37	9	.	.	PUNCT
ejpam-4661	38	1	the	the	DET
ejpam-4661	38	2	rest	rest	NOUN
ejpam-4661	38	3	of	of	ADP
ejpam-4661	38	4	the	the	DET
ejpam-4661	38	5	prey	prey	NOUN
ejpam-4661	38	6	,	,	PUNCT
ejpam-4661	38	7	bxt	bxt	PROPN
ejpam-4661	38	8	,	,	PUNCT
ejpam-4661	38	9	is	be	AUX
ejpam-4661	38	10	affected	affect	VERB
ejpam-4661	38	11	by	by	ADP
ejpam-4661	38	12	the	the	DET
ejpam-4661	38	13	predator	predator	NOUN
ejpam-4661	38	14	.	.	PUNCT
ejpam-4661	39	1	the	the	DET
ejpam-4661	39	2	expression	expression	NOUN
ejpam-4661	39	3	rbxt−	rbxt−	NOUN
ejpam-4661	39	4	(	(	PUNCT
ejpam-4661	39	5	r−1)b2	r−1)b2	VERB
ejpam-4661	39	6	xe	xe	PROPN
ejpam-4661	39	7	x2	x2	PROPN
ejpam-4661	39	8	t	t	PROPN
ejpam-4661	39	9	−cbxtyt	−cbxtyt	ADV
ejpam-4661	39	10	gives	give	VERB
ejpam-4661	39	11	this	this	DET
ejpam-4661	39	12	interaction	interaction	NOUN
ejpam-4661	39	13	.	.	PUNCT
ejpam-4661	40	1	we	we	PRON
ejpam-4661	40	2	provide	provide	VERB
ejpam-4661	40	3	support	support	NOUN
ejpam-4661	40	4	for	for	ADP
ejpam-4661	40	5	the	the	DET
ejpam-4661	40	6	stabilizing	stabilize	VERB
ejpam-4661	40	7	power	power	NOUN
ejpam-4661	40	8	of	of	ADP
ejpam-4661	40	9	physical	physical	ADJ
ejpam-4661	40	10	refuge	refuge	NOUN
ejpam-4661	40	11	.	.	PUNCT
ejpam-4661	41	1	we	we	PRON
ejpam-4661	41	2	show	show	VERB
ejpam-4661	41	3	that	that	SCONJ
ejpam-4661	41	4	with	with	ADP
ejpam-4661	41	5	refuge	refuge	NOUN
ejpam-4661	41	6	present	present	ADJ
ejpam-4661	41	7	,	,	PUNCT
ejpam-4661	41	8	the	the	DET
ejpam-4661	41	9	host	host	NOUN
ejpam-4661	41	10	and	and	CCONJ
ejpam-4661	41	11	parasitoid	parasitoid	NOUN
ejpam-4661	41	12	can	can	AUX
ejpam-4661	41	13	,	,	PUNCT
ejpam-4661	41	14	apparently	apparently	ADV
ejpam-4661	41	15	,	,	PUNCT
ejpam-4661	41	16	persist	persist	VERB
ejpam-4661	41	17	together	together	ADV
ejpam-4661	41	18	indefinitely	indefinitely	ADV
ejpam-4661	41	19	.	.	PUNCT
ejpam-4661	42	1	the	the	DET
ejpam-4661	42	2	expression	expression	NOUN
ejpam-4661	42	3	yt	yt	PRON
ejpam-4661	42	4	a+yt	a+yt	PROPN
ejpam-4661	42	5	is	be	AUX
ejpam-4661	42	6	a	a	DET
ejpam-4661	42	7	mate	mate	NOUN
ejpam-4661	42	8	-	-	PUNCT
ejpam-4661	42	9	finding	find	VERB
ejpam-4661	42	10	allee	allee	ADJ
ejpam-4661	42	11	effect	effect	NOUN
ejpam-4661	42	12	on	on	ADP
ejpam-4661	42	13	predator	predator	NOUN
ejpam-4661	42	14	.	.	PUNCT
ejpam-4661	43	1	simplifying	simplify	VERB
ejpam-4661	43	2	equation	equation	NOUN
ejpam-4661	43	3	(	(	PUNCT
ejpam-4661	43	4	2	2	NUM
ejpam-4661	43	5	)	)	PUNCT
ejpam-4661	43	6	,	,	PUNCT
ejpam-4661	43	7	we	we	PRON
ejpam-4661	43	8	obtain	obtain	VERB
ejpam-4661	43	9	the	the	DET
ejpam-4661	43	10	following	follow	VERB
ejpam-4661	43	11	system	system	NOUN
ejpam-4661	43	12	:	:	PUNCT
ejpam-4661	43	13	xt+1	xt+1	PROPN
ejpam-4661	43	14	=	=	SYM
ejpam-4661	43	15	rxt	rxt	PROPN
ejpam-4661	43	16	−	−	PROPN
ejpam-4661	43	17	r−	r−	PROPN
ejpam-4661	43	18	1	1	PROPN
ejpam-4661	43	19	xe	xe	PROPN
ejpam-4661	43	20	(	(	PUNCT
ejpam-4661	43	21	2b2	2b2	NUM
ejpam-4661	43	22	−	−	PROPN
ejpam-4661	43	23	2b+	2b+	NUM
ejpam-4661	43	24	1)x2	1)x2	PROPN
ejpam-4661	43	25	t	t	PROPN
ejpam-4661	43	26	−	−	PROPN
ejpam-4661	43	27	cbxtyt	cbxtyt	PROPN
ejpam-4661	43	28	,	,	PUNCT
ejpam-4661	43	29	yt+1	yt+1	PROPN
ejpam-4661	43	30	=	=	PUNCT
ejpam-4661	43	31	rb	rb	PROPN
ejpam-4661	43	32	xe	xe	PROPN
ejpam-4661	43	33	xtyt	xtyt	PROPN
ejpam-4661	43	34	yt	yt	PROPN
ejpam-4661	43	35	a+	a+	PUNCT
ejpam-4661	43	36	yt	yt	PROPN
ejpam-4661	43	37	.	.	PUNCT
ejpam-4661	44	1	(	(	PUNCT
ejpam-4661	44	2	3	3	X
ejpam-4661	44	3	)	)	PUNCT
ejpam-4661	44	4	note	note	NOUN
ejpam-4661	44	5	that	that	SCONJ
ejpam-4661	44	6	,	,	PUNCT
ejpam-4661	44	7	in	in	ADP
ejpam-4661	44	8	equation	equation	NOUN
ejpam-4661	44	9	(	(	PUNCT
ejpam-4661	44	10	3	3	NUM
ejpam-4661	44	11	)	)	PUNCT
ejpam-4661	44	12	,	,	PUNCT
ejpam-4661	44	13	when	when	SCONJ
ejpam-4661	44	14	b	b	X
ejpam-4661	44	15	=	=	SYM
ejpam-4661	44	16	1	1	NUM
ejpam-4661	44	17	and	and	CCONJ
ejpam-4661	44	18	a	a	DET
ejpam-4661	44	19	=	=	NOUN
ejpam-4661	44	20	0	0	NUM
ejpam-4661	44	21	,	,	PUNCT
ejpam-4661	44	22	there	there	PRON
ejpam-4661	44	23	is	be	VERB
ejpam-4661	44	24	no	no	DET
ejpam-4661	44	25	prey	prey	NOUN
ejpam-4661	44	26	in	in	ADP
ejpam-4661	44	27	a	a	DET
ejpam-4661	44	28	protective	protective	ADJ
ejpam-4661	44	29	refuge	refuge	NOUN
ejpam-4661	44	30	and	and	CCONJ
ejpam-4661	44	31	no	no	DET
ejpam-4661	44	32	allee	allee	ADJ
ejpam-4661	44	33	effect	effect	NOUN
ejpam-4661	44	34	.	.	PUNCT
ejpam-4661	45	1	hence	hence	ADV
ejpam-4661	45	2	we	we	PRON
ejpam-4661	45	3	obtain	obtain	VERB
ejpam-4661	45	4	equation	equation	NOUN
ejpam-4661	45	5	(	(	PUNCT
ejpam-4661	45	6	1	1	NUM
ejpam-4661	45	7	)	)	PUNCT
ejpam-4661	45	8	for	for	ADP
ejpam-4661	45	9	this	this	DET
ejpam-4661	45	10	particular	particular	ADJ
ejpam-4661	45	11	case	case	NOUN
ejpam-4661	45	12	.	.	PUNCT
ejpam-4661	46	1	when	when	SCONJ
ejpam-4661	46	2	b	b	X
ejpam-4661	46	3	=	=	SYM
ejpam-4661	46	4	0	0	PROPN
ejpam-4661	46	5	,	,	PUNCT
ejpam-4661	46	6	all	all	DET
ejpam-4661	46	7	the	the	DET
ejpam-4661	46	8	prey	prey	NOUN
ejpam-4661	46	9	population	population	NOUN
ejpam-4661	46	10	is	be	AUX
ejpam-4661	46	11	protected	protect	VERB
ejpam-4661	46	12	and	and	CCONJ
ejpam-4661	46	13	has	have	VERB
ejpam-4661	46	14	logistic	logistic	ADJ
ejpam-4661	46	15	growth	growth	NOUN
ejpam-4661	46	16	while	while	SCONJ
ejpam-4661	46	17	the	the	DET
ejpam-4661	46	18	predator	predator	NOUN
ejpam-4661	46	19	population	population	NOUN
ejpam-4661	46	20	extincts	extinct	NOUN
ejpam-4661	46	21	in	in	ADP
ejpam-4661	46	22	the	the	DET
ejpam-4661	46	23	next	next	ADJ
ejpam-4661	46	24	generation	generation	NOUN
ejpam-4661	46	25	.	.	PUNCT
ejpam-4661	47	1	s.	s.	PROPN
ejpam-4661	47	2	kapcak	kapcak	PROPN
ejpam-4661	47	3	/	/	SYM
ejpam-4661	47	4	eur	eur	PROPN
ejpam-4661	47	5	.	.	PUNCT
ejpam-4661	48	1	j.	j.	PROPN
ejpam-4661	48	2	pure	pure	PROPN
ejpam-4661	48	3	appl	appl	PROPN
ejpam-4661	48	4	.	.	PROPN
ejpam-4661	48	5	math	math	PROPN
ejpam-4661	48	6	,	,	PUNCT
ejpam-4661	48	7	16	16	NUM
ejpam-4661	48	8	(	(	PUNCT
ejpam-4661	48	9	1	1	NUM
ejpam-4661	48	10	)	)	PUNCT
ejpam-4661	48	11	(	(	PUNCT
ejpam-4661	48	12	2023	2023	NUM
ejpam-4661	48	13	)	)	PUNCT
ejpam-4661	48	14	,	,	PUNCT
ejpam-4661	48	15	71	71	NUM
ejpam-4661	48	16	-	-	SYM
ejpam-4661	48	17	83	83	NUM
ejpam-4661	48	18	73	73	NUM
ejpam-4661	48	19	we	we	PRON
ejpam-4661	48	20	apply	apply	VERB
ejpam-4661	48	21	yt	yt	NOUN
ejpam-4661	48	22	=	=	SYM
ejpam-4661	48	23	cbyt	cbyt	X
ejpam-4661	48	24	and	and	CCONJ
ejpam-4661	48	25	xt	xt	X
ejpam-4661	48	26	=	=	PROPN
ejpam-4661	48	27	rb	rb	PROPN
ejpam-4661	48	28	xe	xe	PROPN
ejpam-4661	48	29	xt	xt	PROPN
ejpam-4661	48	30	with	with	ADP
ejpam-4661	48	31	α	α	PROPN
ejpam-4661	48	32	=	=	SYM
ejpam-4661	48	33	r	r	NOUN
ejpam-4661	48	34	,	,	PUNCT
ejpam-4661	48	35	β	β	NOUN
ejpam-4661	48	36	=	=	SYM
ejpam-4661	48	37	2b2−2b+1	2b2−2b+1	NUM
ejpam-4661	48	38	rb	rb	NOUN
ejpam-4661	48	39	,	,	PUNCT
ejpam-4661	48	40	and	and	CCONJ
ejpam-4661	48	41	γ	γ	X
ejpam-4661	48	42	=	=	SYM
ejpam-4661	48	43	acb	acb	PROPN
ejpam-4661	48	44	.	.	PUNCT
ejpam-4661	49	1	hence	hence	ADV
ejpam-4661	49	2	we	we	PRON
ejpam-4661	49	3	obtain	obtain	VERB
ejpam-4661	49	4	the	the	DET
ejpam-4661	49	5	following	follow	VERB
ejpam-4661	49	6	system	system	NOUN
ejpam-4661	49	7	:	:	PUNCT
ejpam-4661	49	8	xt+1	xt+1	X
ejpam-4661	50	1	=	=	SYM
ejpam-4661	50	2	xt(α−	xt(α−	PUNCT
ejpam-4661	50	3	β(α−	β(α−	PUNCT
ejpam-4661	50	4	1)xt)−	1)xt)−	NUM
ejpam-4661	50	5	xtyt	xtyt	ADJ
ejpam-4661	50	6	,	,	PUNCT
ejpam-4661	50	7	yt+1	yt+1	PROPN
ejpam-4661	50	8	=	=	SYM
ejpam-4661	50	9	xty	xty	PROPN
ejpam-4661	50	10	2	2	NUM
ejpam-4661	50	11	t	t	NOUN
ejpam-4661	50	12	γ	γ	X
ejpam-4661	50	13	+	+	X
ejpam-4661	50	14	yt	yt	NOUN
ejpam-4661	50	15	,	,	PUNCT
ejpam-4661	50	16	(	(	PUNCT
ejpam-4661	50	17	4	4	X
ejpam-4661	50	18	)	)	PUNCT
ejpam-4661	50	19	where	where	SCONJ
ejpam-4661	50	20	α	α	X
ejpam-4661	50	21	,	,	PUNCT
ejpam-4661	50	22	β	β	X
ejpam-4661	50	23	>	>	X
ejpam-4661	50	24	0	0	PUNCT
ejpam-4661	50	25	and	and	CCONJ
ejpam-4661	50	26	γ	γ	X
ejpam-4661	50	27	>	>	X
ejpam-4661	50	28	0	0	NUM
ejpam-4661	50	29	.	.	NOUN
ejpam-4661	50	30	2	2	NUM
ejpam-4661	50	31	.	.	X
ejpam-4661	50	32	existence	existence	NOUN
ejpam-4661	50	33	of	of	ADP
ejpam-4661	50	34	the	the	DET
ejpam-4661	50	35	fixed	fix	VERB
ejpam-4661	50	36	points	point	NOUN
ejpam-4661	50	37	in	in	ADP
ejpam-4661	50	38	this	this	DET
ejpam-4661	50	39	section	section	NOUN
ejpam-4661	50	40	,	,	PUNCT
ejpam-4661	50	41	we	we	PRON
ejpam-4661	50	42	analyse	analyse	VERB
ejpam-4661	50	43	the	the	DET
ejpam-4661	50	44	existence	existence	NOUN
ejpam-4661	50	45	of	of	ADP
ejpam-4661	50	46	fixed	fix	VERB
ejpam-4661	50	47	points	point	NOUN
ejpam-4661	50	48	of	of	ADP
ejpam-4661	50	49	discrete	discrete	ADJ
ejpam-4661	50	50	system	system	NOUN
ejpam-4661	50	51	(	(	PUNCT
ejpam-4661	50	52	4	4	NUM
ejpam-4661	50	53	)	)	PUNCT
ejpam-4661	50	54	.	.	PUNCT
ejpam-4661	51	1	firstly	firstly	ADV
ejpam-4661	51	2	,	,	PUNCT
ejpam-4661	51	3	we	we	PRON
ejpam-4661	51	4	focus	focus	VERB
ejpam-4661	51	5	on	on	ADP
ejpam-4661	51	6	the	the	DET
ejpam-4661	51	7	following	follow	VERB
ejpam-4661	51	8	isocline	isocline	ADJ
ejpam-4661	51	9	equations	equation	NOUN
ejpam-4661	51	10	:	:	PUNCT
ejpam-4661	51	11	x	x	SYM
ejpam-4661	51	12	=	=	SYM
ejpam-4661	51	13	x(α−	x(α−	PROPN
ejpam-4661	51	14	β(α−	β(α−	NUM
ejpam-4661	51	15	1)x)−	1)x)−	NUM
ejpam-4661	51	16	xy	xy	PROPN
ejpam-4661	51	17	,	,	PUNCT
ejpam-4661	51	18	y	y	PROPN
ejpam-4661	51	19	=	=	PUNCT
ejpam-4661	51	20	xy2	xy2	PROPN
ejpam-4661	51	21	γ	γ	X
ejpam-4661	51	22	+	+	X
ejpam-4661	51	23	y	y	PROPN
ejpam-4661	51	24	.	.	PUNCT
ejpam-4661	52	1	(	(	PUNCT
ejpam-4661	52	2	5	5	NUM
ejpam-4661	52	3	)	)	PUNCT
ejpam-4661	52	4	2.1	2.1	NUM
ejpam-4661	52	5	.	.	PUNCT
ejpam-4661	53	1	extinction	extinction	NOUN
ejpam-4661	53	2	and	and	CCONJ
ejpam-4661	53	3	exclusion	exclusion	NOUN
ejpam-4661	53	4	fixed	fix	VERB
ejpam-4661	53	5	points	point	NOUN
ejpam-4661	53	6	in	in	ADP
ejpam-4661	53	7	equation	equation	NOUN
ejpam-4661	53	8	(	(	PUNCT
ejpam-4661	53	9	5	5	NUM
ejpam-4661	53	10	)	)	PUNCT
ejpam-4661	53	11	,	,	PUNCT
ejpam-4661	53	12	if	if	SCONJ
ejpam-4661	53	13	x	x	ADP
ejpam-4661	53	14	=	=	SYM
ejpam-4661	53	15	0	0	NUM
ejpam-4661	53	16	,	,	PUNCT
ejpam-4661	53	17	we	we	PRON
ejpam-4661	53	18	have	have	VERB
ejpam-4661	53	19	the	the	DET
ejpam-4661	53	20	extinction	extinction	NOUN
ejpam-4661	53	21	fixed	fix	VERB
ejpam-4661	53	22	point	point	NOUN
ejpam-4661	53	23	p0	p0	NOUN
ejpam-4661	53	24	=	=	SYM
ejpam-4661	53	25	(	(	PUNCT
ejpam-4661	53	26	0	0	NUM
ejpam-4661	53	27	,	,	PUNCT
ejpam-4661	53	28	0	0	NUM
ejpam-4661	53	29	)	)	PUNCT
ejpam-4661	53	30	for	for	ADP
ejpam-4661	53	31	any	any	DET
ejpam-4661	53	32	parameter	parameter	NOUN
ejpam-4661	53	33	values	value	NOUN
ejpam-4661	53	34	.	.	PUNCT
ejpam-4661	54	1	if	if	SCONJ
ejpam-4661	54	2	x	x	PROPN
ejpam-4661	54	3	̸=	̸=	PROPN
ejpam-4661	54	4	0	0	NUM
ejpam-4661	54	5	and	and	CCONJ
ejpam-4661	54	6	y	y	PROPN
ejpam-4661	54	7	=	=	SYM
ejpam-4661	54	8	0	0	PROPN
ejpam-4661	54	9	,	,	PUNCT
ejpam-4661	54	10	we	we	PRON
ejpam-4661	54	11	obtain	obtain	VERB
ejpam-4661	54	12	the	the	DET
ejpam-4661	54	13	exclusion	exclusion	NOUN
ejpam-4661	54	14	fixed	fix	VERB
ejpam-4661	54	15	point	point	NOUN
ejpam-4661	54	16	p1	p1	NOUN
ejpam-4661	54	17	=	=	SYM
ejpam-4661	54	18	(	(	PUNCT
ejpam-4661	54	19	1β	1β	NUM
ejpam-4661	54	20	,	,	PUNCT
ejpam-4661	54	21	0	0	NUM
ejpam-4661	54	22	)	)	PUNCT
ejpam-4661	54	23	.	.	PUNCT
ejpam-4661	55	1	2.2	2.2	NUM
ejpam-4661	55	2	.	.	PUNCT
ejpam-4661	55	3	coexistence	coexistence	NOUN
ejpam-4661	55	4	fixed	fix	VERB
ejpam-4661	55	5	points	point	NOUN
ejpam-4661	55	6	if	if	SCONJ
ejpam-4661	55	7	x	x	PROPN
ejpam-4661	55	8	̸=	̸=	PROPN
ejpam-4661	55	9	0	0	NUM
ejpam-4661	55	10	and	and	CCONJ
ejpam-4661	55	11	y	y	PROPN
ejpam-4661	55	12	̸=	̸=	PROPN
ejpam-4661	55	13	0	0	NUM
ejpam-4661	55	14	,	,	PUNCT
ejpam-4661	55	15	the	the	DET
ejpam-4661	55	16	isoclines	isocline	NOUN
ejpam-4661	55	17	become	become	VERB
ejpam-4661	55	18	y	y	NOUN
ejpam-4661	55	19	=	=	PUNCT
ejpam-4661	55	20	−β(α−	−β(α−	X
ejpam-4661	55	21	1)x+	1)x+	NUM
ejpam-4661	55	22	α−	α−	ADP
ejpam-4661	55	23	1	1	NUM
ejpam-4661	55	24	,	,	PUNCT
ejpam-4661	55	25	y	y	PROPN
ejpam-4661	55	26	=	=	SYM
ejpam-4661	55	27	γ	γ	X
ejpam-4661	55	28	x−	x−	PROPN
ejpam-4661	55	29	1	1	NUM
ejpam-4661	55	30	.	.	PUNCT
ejpam-4661	56	1	(	(	PUNCT
ejpam-4661	56	2	6	6	X
ejpam-4661	56	3	)	)	PUNCT
ejpam-4661	56	4	the	the	DET
ejpam-4661	56	5	intersection	intersection	NOUN
ejpam-4661	56	6	points	point	NOUN
ejpam-4661	56	7	of	of	ADP
ejpam-4661	56	8	the	the	DET
ejpam-4661	56	9	isoclines	isocline	NOUN
ejpam-4661	56	10	in	in	ADP
ejpam-4661	56	11	equation	equation	NOUN
ejpam-4661	56	12	(	(	PUNCT
ejpam-4661	56	13	6	6	X
ejpam-4661	56	14	)	)	PUNCT
ejpam-4661	56	15	give	give	VERB
ejpam-4661	56	16	us	we	PRON
ejpam-4661	56	17	the	the	DET
ejpam-4661	56	18	candidates	candidate	NOUN
ejpam-4661	56	19	for	for	ADP
ejpam-4661	56	20	coexistence	coexistence	NOUN
ejpam-4661	56	21	fixed	fix	VERB
ejpam-4661	56	22	points	point	NOUN
ejpam-4661	56	23	which	which	PRON
ejpam-4661	56	24	can	can	AUX
ejpam-4661	56	25	be	be	AUX
ejpam-4661	56	26	found	find	VERB
ejpam-4661	56	27	by	by	ADP
ejpam-4661	56	28	solving	solve	VERB
ejpam-4661	56	29	the	the	DET
ejpam-4661	56	30	following	follow	VERB
ejpam-4661	56	31	quadratic	quadratic	ADJ
ejpam-4661	56	32	equation	equation	NOUN
ejpam-4661	56	33	:	:	PUNCT
ejpam-4661	56	34	β(α−	β(α−	SYM
ejpam-4661	56	35	1)x2	1)x2	NUM
ejpam-4661	56	36	−	−	PROPN
ejpam-4661	56	37	(	(	PUNCT
ejpam-4661	56	38	α−	α−	ADP
ejpam-4661	56	39	1)(β	1)(β	NUM
ejpam-4661	56	40	+	+	NOUN
ejpam-4661	56	41	1)x+	1)x+	NUM
ejpam-4661	56	42	(	(	PUNCT
ejpam-4661	56	43	α+	α+	NOUN
ejpam-4661	56	44	γ	γ	NOUN
ejpam-4661	56	45	−	−	PROPN
ejpam-4661	56	46	1	1	NUM
ejpam-4661	56	47	)	)	PUNCT
ejpam-4661	56	48	=	=	SYM
ejpam-4661	56	49	0	0	X
ejpam-4661	56	50	.	.	PUNCT
ejpam-4661	57	1	(	(	PUNCT
ejpam-4661	57	2	7	7	X
ejpam-4661	57	3	)	)	PUNCT
ejpam-4661	57	4	note	note	NOUN
ejpam-4661	57	5	that	that	SCONJ
ejpam-4661	57	6	in	in	ADP
ejpam-4661	57	7	order	order	NOUN
ejpam-4661	57	8	to	to	PART
ejpam-4661	57	9	have	have	AUX
ejpam-4661	57	10	a	a	DET
ejpam-4661	57	11	positive	positive	ADJ
ejpam-4661	57	12	fixed	fix	VERB
ejpam-4661	57	13	point	point	NOUN
ejpam-4661	57	14	,	,	PUNCT
ejpam-4661	57	15	by	by	ADP
ejpam-4661	57	16	the	the	DET
ejpam-4661	57	17	second	second	ADJ
ejpam-4661	57	18	equation	equation	NOUN
ejpam-4661	57	19	of	of	ADP
ejpam-4661	57	20	system	system	NOUN
ejpam-4661	57	21	(	(	PUNCT
ejpam-4661	57	22	6	6	NUM
ejpam-4661	57	23	)	)	PUNCT
ejpam-4661	57	24	,	,	PUNCT
ejpam-4661	57	25	it	it	PRON
ejpam-4661	57	26	is	be	AUX
ejpam-4661	57	27	necessary	necessary	ADJ
ejpam-4661	57	28	that	that	SCONJ
ejpam-4661	57	29	x	x	NOUN
ejpam-4661	57	30	-	-	NOUN
ejpam-4661	57	31	component	component	NOUN
ejpam-4661	57	32	of	of	ADP
ejpam-4661	57	33	the	the	DET
ejpam-4661	57	34	fixed	fix	VERB
ejpam-4661	57	35	point	point	NOUN
ejpam-4661	57	36	is	be	AUX
ejpam-4661	57	37	bigger	big	ADJ
ejpam-4661	57	38	than	than	ADP
ejpam-4661	57	39	1	1	NUM
ejpam-4661	57	40	.	.	PUNCT
ejpam-4661	58	1	therefore	therefore	ADV
ejpam-4661	58	2	,	,	PUNCT
ejpam-4661	58	3	we	we	PRON
ejpam-4661	58	4	have	have	VERB
ejpam-4661	58	5	a	a	DET
ejpam-4661	58	6	coexistence	coexistence	NOUN
ejpam-4661	58	7	fixed	fix	VERB
ejpam-4661	58	8	point	point	NOUN
ejpam-4661	58	9	if	if	SCONJ
ejpam-4661	58	10	and	and	CCONJ
ejpam-4661	58	11	only	only	ADV
ejpam-4661	58	12	if	if	SCONJ
ejpam-4661	58	13	x∗	x∗	PROPN
ejpam-4661	58	14	is	be	AUX
ejpam-4661	58	15	a	a	DET
ejpam-4661	58	16	real	real	ADJ
ejpam-4661	58	17	root	root	NOUN
ejpam-4661	58	18	of	of	ADP
ejpam-4661	58	19	equation	equation	NOUN
ejpam-4661	58	20	(	(	PUNCT
ejpam-4661	58	21	7	7	NUM
ejpam-4661	58	22	)	)	PUNCT
ejpam-4661	58	23	and	and	CCONJ
ejpam-4661	58	24	x∗	x∗	X
ejpam-4661	58	25	>	>	X
ejpam-4661	59	1	1	1	X
ejpam-4661	59	2	.	.	PUNCT
ejpam-4661	60	1	the	the	DET
ejpam-4661	60	2	possible	possible	ADJ
ejpam-4661	60	3	roots	root	NOUN
ejpam-4661	60	4	of	of	ADP
ejpam-4661	60	5	the	the	DET
ejpam-4661	60	6	equation	equation	NOUN
ejpam-4661	60	7	(	(	PUNCT
ejpam-4661	60	8	7	7	X
ejpam-4661	60	9	)	)	PUNCT
ejpam-4661	60	10	are	be	AUX
ejpam-4661	60	11	the	the	DET
ejpam-4661	60	12	following	follow	VERB
ejpam-4661	60	13	:	:	PUNCT
ejpam-4661	61	1	x∗1,2	x∗1,2	PROPN
ejpam-4661	61	2	=	=	PUNCT
ejpam-4661	62	1	(	(	PUNCT
ejpam-4661	62	2	α−	α−	ADP
ejpam-4661	62	3	1)(β	1)(β	NUM
ejpam-4661	62	4	+	+	SYM
ejpam-4661	62	5	1)±	1)±	NUM
ejpam-4661	62	6	√	√	NUM
ejpam-4661	62	7	∆	∆	PROPN
ejpam-4661	62	8	2β(α−	2β(α−	NUM
ejpam-4661	62	9	1	1	NUM
ejpam-4661	62	10	)	)	PUNCT
ejpam-4661	62	11	,	,	PUNCT
ejpam-4661	62	12	(	(	PUNCT
ejpam-4661	62	13	8)	8)	NUM
ejpam-4661	62	14	where	where	SCONJ
ejpam-4661	62	15	∆	∆	PUNCT
ejpam-4661	62	16	=	=	PRON
ejpam-4661	62	17	(	(	PUNCT
ejpam-4661	62	18	α−	α−	ADP
ejpam-4661	62	19	1)2(β	1)2(β	PRON
ejpam-4661	62	20	−	−	PROPN
ejpam-4661	62	21	1)2	1)2	NUM
ejpam-4661	62	22	−	−	NOUN
ejpam-4661	62	23	4β(α−	4β(α−	NUM
ejpam-4661	62	24	1)γ	1)γ	NOUN
ejpam-4661	62	25	.	.	PUNCT
ejpam-4661	63	1	in	in	ADP
ejpam-4661	63	2	order	order	NOUN
ejpam-4661	63	3	to	to	PART
ejpam-4661	63	4	have	have	AUX
ejpam-4661	63	5	positive	positive	ADJ
ejpam-4661	63	6	fixed	fix	VERB
ejpam-4661	63	7	points	point	NOUN
ejpam-4661	63	8	,	,	PUNCT
ejpam-4661	63	9	we	we	PRON
ejpam-4661	63	10	must	must	AUX
ejpam-4661	63	11	have	have	VERB
ejpam-4661	63	12	∆	∆	PROPN
ejpam-4661	63	13	≥	≥	X
ejpam-4661	63	14	0	0	NUM
ejpam-4661	63	15	and	and	CCONJ
ejpam-4661	63	16	x∗i	x∗i	PROPN
ejpam-4661	63	17	>	>	SYM
ejpam-4661	63	18	1	1	NUM
ejpam-4661	63	19	for	for	ADP
ejpam-4661	63	20	some	some	DET
ejpam-4661	63	21	i	i	PRON
ejpam-4661	63	22	∈	∈	PROPN
ejpam-4661	63	23	{	{	PUNCT
ejpam-4661	63	24	1	1	NUM
ejpam-4661	63	25	,	,	PUNCT
ejpam-4661	63	26	2	2	NUM
ejpam-4661	63	27	}	}	PUNCT
ejpam-4661	63	28	.	.	PUNCT
ejpam-4661	64	1	under	under	ADP
ejpam-4661	64	2	the	the	DET
ejpam-4661	64	3	condition	condition	NOUN
ejpam-4661	64	4	∆	∆	PROPN
ejpam-4661	64	5	>	>	X
ejpam-4661	64	6	0	0	NUM
ejpam-4661	64	7	,	,	PUNCT
ejpam-4661	64	8	we	we	PRON
ejpam-4661	64	9	obtain	obtain	VERB
ejpam-4661	64	10	two	two	NUM
ejpam-4661	64	11	s.	s.	PROPN
ejpam-4661	64	12	kapcak	kapcak	PROPN
ejpam-4661	64	13	/	/	SYM
ejpam-4661	64	14	eur	eur	PROPN
ejpam-4661	64	15	.	.	PUNCT
ejpam-4661	65	1	j.	j.	PROPN
ejpam-4661	65	2	pure	pure	PROPN
ejpam-4661	65	3	appl	appl	PROPN
ejpam-4661	65	4	.	.	PROPN
ejpam-4661	65	5	math	math	PROPN
ejpam-4661	65	6	,	,	PUNCT
ejpam-4661	65	7	16	16	NUM
ejpam-4661	65	8	(	(	PUNCT
ejpam-4661	65	9	1	1	NUM
ejpam-4661	65	10	)	)	PUNCT
ejpam-4661	65	11	(	(	PUNCT
ejpam-4661	65	12	2023	2023	NUM
ejpam-4661	65	13	)	)	PUNCT
ejpam-4661	65	14	,	,	PUNCT
ejpam-4661	65	15	71	71	NUM
ejpam-4661	65	16	-	-	SYM
ejpam-4661	65	17	83	83	NUM
ejpam-4661	65	18	74	74	NUM
ejpam-4661	65	19	different	different	ADJ
ejpam-4661	65	20	scenario	scenario	NOUN
ejpam-4661	65	21	:	:	PUNCT
ejpam-4661	65	22	(	(	PUNCT
ejpam-4661	65	23	a	a	X
ejpam-4661	65	24	)	)	PUNCT
ejpam-4661	65	25	there	there	PRON
ejpam-4661	65	26	exist	exist	VERB
ejpam-4661	65	27	two	two	NUM
ejpam-4661	65	28	coexistence	coexistence	NOUN
ejpam-4661	65	29	fixed	fix	VERB
ejpam-4661	65	30	points	point	NOUN
ejpam-4661	65	31	if	if	SCONJ
ejpam-4661	65	32	α	α	PROPN
ejpam-4661	65	33	>	>	X
ejpam-4661	65	34	1	1	NUM
ejpam-4661	65	35	and	and	CCONJ
ejpam-4661	65	36	β	β	X
ejpam-4661	65	37	<	<	X
ejpam-4661	65	38	1	1	NUM
ejpam-4661	65	39	.	.	PUNCT
ejpam-4661	66	1	(	(	PUNCT
ejpam-4661	66	2	b	b	X
ejpam-4661	66	3	)	)	PUNCT
ejpam-4661	66	4	there	there	PRON
ejpam-4661	66	5	exists	exist	VERB
ejpam-4661	66	6	one	one	NUM
ejpam-4661	66	7	coexistence	coexistence	NOUN
ejpam-4661	66	8	fixed	fix	VERB
ejpam-4661	66	9	point	point	NOUN
ejpam-4661	66	10	if	if	SCONJ
ejpam-4661	66	11	α	α	PRON
ejpam-4661	66	12	<	<	X
ejpam-4661	66	13	1	1	NUM
ejpam-4661	66	14	.	.	PUNCT
ejpam-4661	67	1	for	for	ADP
ejpam-4661	67	2	the	the	DET
ejpam-4661	67	3	case	case	NOUN
ejpam-4661	67	4	when	when	SCONJ
ejpam-4661	67	5	∆	∆	PROPN
ejpam-4661	67	6	=	=	SYM
ejpam-4661	67	7	0	0	NUM
ejpam-4661	67	8	,	,	PUNCT
ejpam-4661	67	9	the	the	DET
ejpam-4661	67	10	condition	condition	NOUN
ejpam-4661	67	11	that	that	SCONJ
ejpam-4661	67	12	a	a	DET
ejpam-4661	67	13	coexistence	coexistence	NOUN
ejpam-4661	67	14	fixed	fix	VERB
ejpam-4661	67	15	point	point	NOUN
ejpam-4661	67	16	exists	exist	VERB
ejpam-4661	67	17	is	be	AUX
ejpam-4661	67	18	β	β	X
ejpam-4661	67	19	<	<	X
ejpam-4661	67	20	1	1	NUM
ejpam-4661	67	21	.	.	PUNCT
ejpam-4661	68	1	we	we	PRON
ejpam-4661	68	2	obtain	obtain	VERB
ejpam-4661	68	3	the	the	DET
ejpam-4661	68	4	following	following	NOUN
ejpam-4661	68	5	theorem	theorem	NOUN
ejpam-4661	68	6	for	for	ADP
ejpam-4661	68	7	the	the	DET
ejpam-4661	68	8	condition	condition	NOUN
ejpam-4661	68	9	of	of	ADP
ejpam-4661	68	10	existence	existence	NOUN
ejpam-4661	68	11	and	and	CCONJ
ejpam-4661	68	12	the	the	DET
ejpam-4661	68	13	corresponding	corresponding	ADJ
ejpam-4661	68	14	fixed	fix	VERB
ejpam-4661	68	15	points	point	NOUN
ejpam-4661	68	16	of	of	ADP
ejpam-4661	68	17	system	system	NOUN
ejpam-4661	68	18	(	(	PUNCT
ejpam-4661	68	19	4	4	NUM
ejpam-4661	68	20	)	)	PUNCT
ejpam-4661	68	21	.	.	PUNCT
ejpam-4661	69	1	(	(	PUNCT
ejpam-4661	69	2	a	a	X
ejpam-4661	69	3	)	)	PUNCT
ejpam-4661	69	4	fixed	fixed	ADJ
ejpam-4661	69	5	points	point	NOUN
ejpam-4661	69	6	:	:	PUNCT
ejpam-4661	70	1	p0	p0	NOUN
ejpam-4661	70	2	,	,	PUNCT
ejpam-4661	70	3	p1	p1	NOUN
ejpam-4661	70	4	(	(	PUNCT
ejpam-4661	70	5	b	b	NOUN
ejpam-4661	70	6	)	)	PUNCT
ejpam-4661	70	7	fixed	fix	VERB
ejpam-4661	70	8	points	point	NOUN
ejpam-4661	70	9	:	:	PUNCT
ejpam-4661	70	10	p0	p0	NOUN
ejpam-4661	70	11	,	,	PUNCT
ejpam-4661	70	12	p1	p1	NOUN
ejpam-4661	70	13	,	,	PUNCT
ejpam-4661	70	14	p	p	X
ejpam-4661	70	15	+	+	NOUN
ejpam-4661	70	16	1	1	NUM
ejpam-4661	70	17	(	(	PUNCT
ejpam-4661	70	18	c	c	NOUN
ejpam-4661	70	19	)	)	PUNCT
ejpam-4661	70	20	fixed	fix	VERB
ejpam-4661	70	21	points	point	NOUN
ejpam-4661	70	22	:	:	PUNCT
ejpam-4661	70	23	p0	p0	NOUN
ejpam-4661	70	24	,	,	PUNCT
ejpam-4661	70	25	p1	p1	NOUN
ejpam-4661	70	26	,	,	PUNCT
ejpam-4661	70	27	p	p	X
ejpam-4661	70	28	+	+	NOUN
ejpam-4661	70	29	0	0	NUM
ejpam-4661	70	30	(	(	PUNCT
ejpam-4661	70	31	d	d	NOUN
ejpam-4661	70	32	)	)	PUNCT
ejpam-4661	70	33	fixed	fix	VERB
ejpam-4661	70	34	points	point	NOUN
ejpam-4661	70	35	:	:	PUNCT
ejpam-4661	70	36	p0	p0	NOUN
ejpam-4661	70	37	,	,	PUNCT
ejpam-4661	70	38	p1	p1	NOUN
ejpam-4661	70	39	,	,	PUNCT
ejpam-4661	70	40	p	p	X
ejpam-4661	70	41	+	+	ADJ
ejpam-4661	70	42	2	2	NUM
ejpam-4661	70	43	,	,	PUNCT
ejpam-4661	70	44	p+	p+	VERB
ejpam-4661	70	45	3	3	NUM
ejpam-4661	70	46	figure	figure	NOUN
ejpam-4661	70	47	1	1	NUM
ejpam-4661	70	48	:	:	SYM
ejpam-4661	70	49	four	four	NUM
ejpam-4661	70	50	possible	possible	ADJ
ejpam-4661	70	51	cases	case	NOUN
ejpam-4661	70	52	for	for	ADP
ejpam-4661	70	53	existence	existence	NOUN
ejpam-4661	70	54	of	of	ADP
ejpam-4661	70	55	the	the	DET
ejpam-4661	70	56	fixed	fix	VERB
ejpam-4661	70	57	points	point	NOUN
ejpam-4661	70	58	.	.	PUNCT
ejpam-4661	71	1	the	the	DET
ejpam-4661	71	2	dashed	dash	VERB
ejpam-4661	71	3	line	line	NOUN
ejpam-4661	71	4	is	be	AUX
ejpam-4661	71	5	the	the	DET
ejpam-4661	71	6	isocline	isocline	NOUN
ejpam-4661	71	7	x	x	PUNCT
ejpam-4661	71	8	=	=	SYM
ejpam-4661	71	9	x(α−	x(α−	PROPN
ejpam-4661	71	10	β(α−	β(α−	NUM
ejpam-4661	71	11	1)x)−	1)x)−	NUM
ejpam-4661	71	12	xy	xy	VERB
ejpam-4661	71	13	whereas	whereas	SCONJ
ejpam-4661	71	14	the	the	DET
ejpam-4661	71	15	solid	solid	ADJ
ejpam-4661	71	16	graph	graph	NOUN
ejpam-4661	71	17	is	be	AUX
ejpam-4661	71	18	the	the	DET
ejpam-4661	71	19	isocline	isocline	ADJ
ejpam-4661	71	20	y	y	PROPN
ejpam-4661	71	21	=	=	PUNCT
ejpam-4661	71	22	xy2	xy2	PROPN
ejpam-4661	72	1	γ+y	γ+y	NUM
ejpam-4661	72	2	.	.	PUNCT
ejpam-4661	73	1	theorem	theorem	VERB
ejpam-4661	73	2	1	1	NUM
ejpam-4661	73	3	.	.	PUNCT
ejpam-4661	74	1	the	the	DET
ejpam-4661	74	2	following	follow	VERB
ejpam-4661	74	3	table	table	NOUN
ejpam-4661	74	4	gives	give	VERB
ejpam-4661	74	5	the	the	DET
ejpam-4661	74	6	existence	existence	NOUN
ejpam-4661	74	7	condition	condition	NOUN
ejpam-4661	74	8	for	for	ADP
ejpam-4661	74	9	the	the	DET
ejpam-4661	74	10	fixed	fix	VERB
ejpam-4661	74	11	points	point	NOUN
ejpam-4661	74	12	of	of	ADP
ejpam-4661	74	13	system	system	NOUN
ejpam-4661	74	14	(	(	PUNCT
ejpam-4661	74	15	4	4	NUM
ejpam-4661	74	16	)	)	PUNCT
ejpam-4661	74	17	.	.	PUNCT
ejpam-4661	75	1	s.	s.	PROPN
ejpam-4661	75	2	kapcak	kapcak	PROPN
ejpam-4661	75	3	/	/	SYM
ejpam-4661	75	4	eur	eur	PROPN
ejpam-4661	75	5	.	.	PUNCT
ejpam-4661	76	1	j.	j.	PROPN
ejpam-4661	76	2	pure	pure	PROPN
ejpam-4661	76	3	appl	appl	PROPN
ejpam-4661	76	4	.	.	PROPN
ejpam-4661	76	5	math	math	PROPN
ejpam-4661	76	6	,	,	PUNCT
ejpam-4661	76	7	16	16	NUM
ejpam-4661	76	8	(	(	PUNCT
ejpam-4661	76	9	1	1	NUM
ejpam-4661	76	10	)	)	PUNCT
ejpam-4661	76	11	(	(	PUNCT
ejpam-4661	76	12	2023	2023	NUM
ejpam-4661	76	13	)	)	PUNCT
ejpam-4661	76	14	,	,	PUNCT
ejpam-4661	76	15	71	71	NUM
ejpam-4661	76	16	-	-	SYM
ejpam-4661	76	17	83	83	NUM
ejpam-4661	76	18	75	75	NUM
ejpam-4661	76	19	fixed	fix	VERB
ejpam-4661	76	20	point	point	NOUN
ejpam-4661	76	21	condition	condition	NOUN
ejpam-4661	76	22	for	for	ADP
ejpam-4661	76	23	existence	existence	NOUN
ejpam-4661	76	24	p0	p0	NOUN
ejpam-4661	76	25	=	=	SYM
ejpam-4661	76	26	(	(	PUNCT
ejpam-4661	76	27	0	0	NUM
ejpam-4661	76	28	,	,	PUNCT
ejpam-4661	76	29	0	0	NUM
ejpam-4661	76	30	)	)	PUNCT
ejpam-4661	76	31	always	always	ADV
ejpam-4661	76	32	exists	exist	VERB
ejpam-4661	76	33	p1	p1	NOUN
ejpam-4661	76	34	=	=	SYM
ejpam-4661	76	35	(	(	PUNCT
ejpam-4661	76	36	1	1	NUM
ejpam-4661	76	37	β	β	X
ejpam-4661	76	38	,	,	PUNCT
ejpam-4661	76	39	0	0	NUM
ejpam-4661	76	40	)	)	PUNCT
ejpam-4661	76	41	always	always	ADV
ejpam-4661	76	42	exists	exist	VERB
ejpam-4661	76	43	p+	p+	VERB
ejpam-4661	76	44	0	0	NUM
ejpam-4661	76	45	=	=	SYM
ejpam-4661	76	46	(	(	PUNCT
ejpam-4661	76	47	β+1	β+1	ADJ
ejpam-4661	76	48	2β	2β	NOUN
ejpam-4661	76	49	,	,	PUNCT
ejpam-4661	76	50	2γβ	2γβ	NOUN
ejpam-4661	76	51	1−β	1−β	NUM
ejpam-4661	76	52	)	)	PUNCT
ejpam-4661	77	1	β	β	X
ejpam-4661	77	2	<	<	X
ejpam-4661	77	3	1	1	NUM
ejpam-4661	77	4	and	and	CCONJ
ejpam-4661	77	5	(	(	PUNCT
ejpam-4661	77	6	β	β	X
ejpam-4661	77	7	−	−	PROPN
ejpam-4661	77	8	1)2	1)2	NUM
ejpam-4661	77	9	=	=	SYM
ejpam-4661	77	10	4βγ	4βγ	PROPN
ejpam-4661	77	11	α−1	α−1	PROPN
ejpam-4661	77	12	p+	p+	VERB
ejpam-4661	77	13	1	1	NUM
ejpam-4661	77	14	=	=	SYM
ejpam-4661	77	15	(	(	PUNCT
ejpam-4661	77	16	(	(	PUNCT
ejpam-4661	77	17	α−1)(β+1)−	α−1)(β+1)−	NOUN
ejpam-4661	77	18	√	√	NOUN
ejpam-4661	77	19	∆	∆	PROPN
ejpam-4661	77	20	2β(α−1	2β(α−1	NUM
ejpam-4661	77	21	)	)	PUNCT
ejpam-4661	77	22	,	,	PUNCT
ejpam-4661	77	23	−(α−1)(β−1)+	−(α−1)(β−1)+	VERB
ejpam-4661	77	24	√	√	PROPN
ejpam-4661	77	25	∆	∆	PROPN
ejpam-4661	77	26	2	2	X
ejpam-4661	77	27	)	)	PUNCT
ejpam-4661	77	28	α	α	PRON
ejpam-4661	77	29	<	<	X
ejpam-4661	77	30	1	1	NUM
ejpam-4661	77	31	p+	p+	NOUN
ejpam-4661	77	32	2	2	NUM
ejpam-4661	77	33	=	=	SYM
ejpam-4661	77	34	(	(	PUNCT
ejpam-4661	77	35	(	(	PUNCT
ejpam-4661	77	36	α−1)(β+1)+	α−1)(β+1)+	NOUN
ejpam-4661	77	37	√	√	NOUN
ejpam-4661	77	38	∆	∆	PROPN
ejpam-4661	77	39	2β(α−1	2β(α−1	NUM
ejpam-4661	77	40	)	)	PUNCT
ejpam-4661	77	41	,	,	PUNCT
ejpam-4661	78	1	−(α−1)(β−1)−	−(α−1)(β−1)−	VERB
ejpam-4661	78	2	√	√	PRON
ejpam-4661	78	3	∆	∆	X
ejpam-4661	78	4	2	2	X
ejpam-4661	78	5	)	)	PUNCT
ejpam-4661	78	6	β	β	X
ejpam-4661	78	7	<	<	X
ejpam-4661	78	8	1	1	NUM
ejpam-4661	78	9	,	,	PUNCT
ejpam-4661	78	10	α	α	PROPN
ejpam-4661	78	11	>	>	X
ejpam-4661	78	12	1	1	NUM
ejpam-4661	78	13	,	,	PUNCT
ejpam-4661	78	14	and	and	CCONJ
ejpam-4661	78	15	(	(	PUNCT
ejpam-4661	78	16	β	β	X
ejpam-4661	78	17	−	−	PROPN
ejpam-4661	78	18	1)2	1)2	NUM
ejpam-4661	78	19	>	>	PUNCT
ejpam-4661	78	20	4βγ	4βγ	PROPN
ejpam-4661	79	1	α−1	α−1	PROPN
ejpam-4661	79	2	p+	p+	VERB
ejpam-4661	79	3	3	3	NUM
ejpam-4661	79	4	=	=	SYM
ejpam-4661	79	5	(	(	PUNCT
ejpam-4661	79	6	(	(	PUNCT
ejpam-4661	79	7	α−1)(β+1)−	α−1)(β+1)−	NOUN
ejpam-4661	79	8	√	√	NOUN
ejpam-4661	79	9	∆	∆	PROPN
ejpam-4661	79	10	2β(α−1	2β(α−1	NUM
ejpam-4661	79	11	)	)	PUNCT
ejpam-4661	79	12	,	,	PUNCT
ejpam-4661	79	13	−(α−1)(β−1)+	−(α−1)(β−1)+	VERB
ejpam-4661	79	14	√	√	PROPN
ejpam-4661	79	15	∆	∆	PROPN
ejpam-4661	79	16	2	2	NUM
ejpam-4661	79	17	)	)	PUNCT
ejpam-4661	79	18	β	β	X
ejpam-4661	79	19	<	<	X
ejpam-4661	79	20	1	1	NUM
ejpam-4661	79	21	,	,	PUNCT
ejpam-4661	79	22	α	α	PROPN
ejpam-4661	79	23	>	>	X
ejpam-4661	79	24	1	1	NUM
ejpam-4661	79	25	,	,	PUNCT
ejpam-4661	79	26	and	and	CCONJ
ejpam-4661	79	27	(	(	PUNCT
ejpam-4661	79	28	β	β	X
ejpam-4661	79	29	−	−	PROPN
ejpam-4661	79	30	1)2	1)2	NUM
ejpam-4661	79	31	>	>	PUNCT
ejpam-4661	79	32	4βγ	4βγ	ADJ
ejpam-4661	79	33	α−1	α−1	PROPN
ejpam-4661	79	34	figure	figure	NOUN
ejpam-4661	79	35	2	2	NUM
ejpam-4661	79	36	:	:	PUNCT
ejpam-4661	79	37	existence	existence	NOUN
ejpam-4661	79	38	regions	region	NOUN
ejpam-4661	79	39	for	for	ADP
ejpam-4661	79	40	system	system	NOUN
ejpam-4661	79	41	(	(	PUNCT
ejpam-4661	79	42	4	4	NUM
ejpam-4661	79	43	)	)	PUNCT
ejpam-4661	79	44	in	in	ADP
ejpam-4661	79	45	α	α	PROPN
ejpam-4661	79	46	-	-	PUNCT
ejpam-4661	79	47	β	β	PRON
ejpam-4661	79	48	plane	plane	NOUN
ejpam-4661	79	49	.	.	PUNCT
ejpam-4661	80	1	figure	figure	NOUN
ejpam-4661	80	2	2	2	NUM
ejpam-4661	80	3	represents	represent	VERB
ejpam-4661	80	4	the	the	DET
ejpam-4661	80	5	existence	existence	NOUN
ejpam-4661	80	6	regions	region	NOUN
ejpam-4661	80	7	for	for	ADP
ejpam-4661	80	8	fixed	fix	VERB
ejpam-4661	80	9	points	point	NOUN
ejpam-4661	80	10	in	in	ADP
ejpam-4661	80	11	α	α	PROPN
ejpam-4661	80	12	-	-	PUNCT
ejpam-4661	80	13	β	β	NUM
ejpam-4661	80	14	plane	plane	NOUN
ejpam-4661	80	15	.	.	PUNCT
ejpam-4661	81	1	by	by	ADP
ejpam-4661	81	2	theorem	theorem	NOUN
ejpam-4661	81	3	1	1	NUM
ejpam-4661	81	4	,	,	PUNCT
ejpam-4661	81	5	extinction	extinction	NOUN
ejpam-4661	81	6	fixed	fix	VERB
ejpam-4661	81	7	point	point	NOUN
ejpam-4661	81	8	p0	p0	NOUN
ejpam-4661	81	9	and	and	CCONJ
ejpam-4661	81	10	exclusion	exclusion	NOUN
ejpam-4661	81	11	fixed	fix	VERB
ejpam-4661	81	12	point	point	NOUN
ejpam-4661	81	13	p1	p1	NOUN
ejpam-4661	81	14	exist	exist	VERB
ejpam-4661	81	15	for	for	ADP
ejpam-4661	81	16	any	any	DET
ejpam-4661	81	17	parameter	parameter	NOUN
ejpam-4661	81	18	values	value	NOUN
ejpam-4661	81	19	.	.	PUNCT
ejpam-4661	82	1	p+	p+	NOUN
ejpam-4661	82	2	0	0	NUM
ejpam-4661	82	3	exists	exist	VERB
ejpam-4661	82	4	only	only	ADV
ejpam-4661	82	5	on	on	ADP
ejpam-4661	82	6	the	the	DET
ejpam-4661	82	7	borderline	borderline	NOUN
ejpam-4661	82	8	of	of	ADP
ejpam-4661	82	9	e2	e2	PROPN
ejpam-4661	82	10	and	and	CCONJ
ejpam-4661	82	11	e3	e3	NOUN
ejpam-4661	82	12	.	.	PUNCT
ejpam-4661	83	1	this	this	PRON
ejpam-4661	83	2	is	be	AUX
ejpam-4661	83	3	the	the	DET
ejpam-4661	83	4	curve	curve	NOUN
ejpam-4661	83	5	where	where	SCONJ
ejpam-4661	83	6	∆	∆	VERB
ejpam-4661	83	7	=	=	SYM
ejpam-4661	83	8	0	0	X
ejpam-4661	83	9	.	.	PUNCT
ejpam-4661	84	1	region	region	NOUN
ejpam-4661	84	2	e1	e1	PROPN
ejpam-4661	84	3	is	be	AUX
ejpam-4661	84	4	the	the	DET
ejpam-4661	84	5	region	region	NOUN
ejpam-4661	84	6	for	for	ADP
ejpam-4661	84	7	existence	existence	NOUN
ejpam-4661	84	8	of	of	ADP
ejpam-4661	84	9	p+	p+	PROPN
ejpam-4661	84	10	1	1	NUM
ejpam-4661	84	11	.	.	PUNCT
ejpam-4661	85	1	e2	e2	PROPN
ejpam-4661	85	2	is	be	AUX
ejpam-4661	85	3	the	the	DET
ejpam-4661	85	4	region	region	NOUN
ejpam-4661	85	5	where	where	SCONJ
ejpam-4661	85	6	∆	∆	PROPN
ejpam-4661	85	7	>	>	X
ejpam-4661	85	8	0	0	PUNCT
ejpam-4661	86	1	and	and	CCONJ
ejpam-4661	86	2	we	we	PRON
ejpam-4661	86	3	have	have	VERB
ejpam-4661	86	4	two	two	NUM
ejpam-4661	86	5	distinct	distinct	ADJ
ejpam-4661	86	6	positive	positive	ADJ
ejpam-4661	86	7	fixed	fix	VERB
ejpam-4661	86	8	points	point	NOUN
ejpam-4661	86	9	p+	p+	VERB
ejpam-4661	86	10	2,3	2,3	NUM
ejpam-4661	86	11	.	.	PUNCT
ejpam-4661	87	1	s.	s.	PROPN
ejpam-4661	87	2	kapcak	kapcak	PROPN
ejpam-4661	87	3	/	/	SYM
ejpam-4661	87	4	eur	eur	PROPN
ejpam-4661	87	5	.	.	PUNCT
ejpam-4661	88	1	j.	j.	PROPN
ejpam-4661	88	2	pure	pure	PROPN
ejpam-4661	88	3	appl	appl	PROPN
ejpam-4661	88	4	.	.	PROPN
ejpam-4661	88	5	math	math	PROPN
ejpam-4661	88	6	,	,	PUNCT
ejpam-4661	88	7	16	16	NUM
ejpam-4661	88	8	(	(	PUNCT
ejpam-4661	88	9	1	1	NUM
ejpam-4661	88	10	)	)	PUNCT
ejpam-4661	88	11	(	(	PUNCT
ejpam-4661	88	12	2023	2023	NUM
ejpam-4661	88	13	)	)	PUNCT
ejpam-4661	88	14	,	,	PUNCT
ejpam-4661	88	15	71	71	NUM
ejpam-4661	88	16	-	-	SYM
ejpam-4661	88	17	83	83	NUM
ejpam-4661	88	18	76	76	NUM
ejpam-4661	88	19	3	3	NUM
ejpam-4661	88	20	.	.	PUNCT
ejpam-4661	89	1	stability	stability	NOUN
ejpam-4661	89	2	analysis	analysis	NOUN
ejpam-4661	89	3	of	of	ADP
ejpam-4661	89	4	system	system	NOUN
ejpam-4661	89	5	(	(	PUNCT
ejpam-4661	89	6	4	4	NUM
ejpam-4661	89	7	)	)	PUNCT
ejpam-4661	89	8	in	in	ADP
ejpam-4661	89	9	this	this	DET
ejpam-4661	89	10	section	section	NOUN
ejpam-4661	90	1	,	,	PUNCT
ejpam-4661	90	2	we	we	PRON
ejpam-4661	90	3	analyse	analyse	VERB
ejpam-4661	90	4	the	the	DET
ejpam-4661	90	5	stability	stability	NOUN
ejpam-4661	90	6	of	of	ADP
ejpam-4661	90	7	system	system	NOUN
ejpam-4661	90	8	(	(	PUNCT
ejpam-4661	90	9	4	4	NUM
ejpam-4661	90	10	)	)	PUNCT
ejpam-4661	90	11	.	.	PUNCT
ejpam-4661	91	1	the	the	DET
ejpam-4661	91	2	jacobian	jacobian	ADJ
ejpam-4661	91	3	matrix	matrix	NOUN
ejpam-4661	91	4	of	of	ADP
ejpam-4661	91	5	the	the	DET
ejpam-4661	91	6	system	system	NOUN
ejpam-4661	91	7	is	be	AUX
ejpam-4661	91	8	j(x	j(x	PROPN
ejpam-4661	91	9	,	,	PUNCT
ejpam-4661	91	10	y	y	PROPN
ejpam-4661	91	11	)	)	PUNCT
ejpam-4661	91	12	=	=	NOUN
ejpam-4661	92	1	(	(	PUNCT
ejpam-4661	92	2	α−	α−	ADP
ejpam-4661	92	3	2β(α−	2β(α−	NUM
ejpam-4661	92	4	1)x−	1)x−	NUM
ejpam-4661	92	5	y	y	PROPN
ejpam-4661	92	6	−x	−x	PROPN
ejpam-4661	92	7	y2	y2	PROPN
ejpam-4661	92	8	γ+y	γ+y	ADV
ejpam-4661	92	9	xy(2γ+y	xy(2γ+y	NOUN
ejpam-4661	92	10	)	)	PUNCT
ejpam-4661	92	11	(	(	PUNCT
ejpam-4661	92	12	γ+y)2	γ+y)2	ADV
ejpam-4661	92	13	)	)	PUNCT
ejpam-4661	92	14	.	.	PUNCT
ejpam-4661	93	1	3.1	3.1	NUM
ejpam-4661	93	2	.	.	PUNCT
ejpam-4661	93	3	stability	stability	NOUN
ejpam-4661	93	4	of	of	ADP
ejpam-4661	93	5	the	the	DET
ejpam-4661	93	6	extinction	extinction	NOUN
ejpam-4661	93	7	fixed	fix	VERB
ejpam-4661	93	8	point	point	NOUN
ejpam-4661	93	9	for	for	ADP
ejpam-4661	93	10	the	the	DET
ejpam-4661	93	11	extinction	extinction	NOUN
ejpam-4661	93	12	fixed	fix	VERB
ejpam-4661	93	13	point	point	NOUN
ejpam-4661	93	14	p0	p0	NOUN
ejpam-4661	93	15	=	=	SYM
ejpam-4661	93	16	(	(	PUNCT
ejpam-4661	93	17	0	0	NUM
ejpam-4661	93	18	,	,	PUNCT
ejpam-4661	93	19	0	0	NUM
ejpam-4661	93	20	)	)	PUNCT
ejpam-4661	93	21	,	,	PUNCT
ejpam-4661	93	22	the	the	DET
ejpam-4661	93	23	jacobian	jacobian	ADJ
ejpam-4661	93	24	matrix	matrix	NOUN
ejpam-4661	93	25	j	j	PROPN
ejpam-4661	93	26	is	be	AUX
ejpam-4661	93	27	given	give	VERB
ejpam-4661	93	28	by	by	ADP
ejpam-4661	93	29	j0	j0	PROPN
ejpam-4661	93	30	=	=	SYM
ejpam-4661	93	31	(	(	PUNCT
ejpam-4661	93	32	α	α	NOUN
ejpam-4661	93	33	0	0	NUM
ejpam-4661	93	34	0	0	NUM
ejpam-4661	93	35	0	0	NUM
ejpam-4661	93	36	)	)	PUNCT
ejpam-4661	93	37	.	.	PUNCT
ejpam-4661	94	1	the	the	DET
ejpam-4661	94	2	eigenvalues	eigenvalue	NOUN
ejpam-4661	94	3	of	of	ADP
ejpam-4661	94	4	the	the	DET
ejpam-4661	94	5	matrix	matrix	NOUN
ejpam-4661	94	6	are	be	AUX
ejpam-4661	94	7	λ1	λ1	ADJ
ejpam-4661	94	8	=	=	SYM
ejpam-4661	94	9	α	α	NOUN
ejpam-4661	94	10	and	and	CCONJ
ejpam-4661	94	11	λ2	λ2	NOUN
ejpam-4661	94	12	=	=	SYM
ejpam-4661	94	13	0	0	NUM
ejpam-4661	94	14	.	.	PUNCT
ejpam-4661	95	1	hence	hence	ADV
ejpam-4661	95	2	the	the	DET
ejpam-4661	95	3	fixed	fix	VERB
ejpam-4661	95	4	point	point	NOUN
ejpam-4661	95	5	p0	p0	NOUN
ejpam-4661	95	6	is	be	AUX
ejpam-4661	95	7	locally	locally	ADV
ejpam-4661	95	8	asymptotically	asymptotically	ADV
ejpam-4661	95	9	stable	stable	ADJ
ejpam-4661	95	10	if	if	SCONJ
ejpam-4661	95	11	α	α	NOUN
ejpam-4661	95	12	<	<	X
ejpam-4661	95	13	1	1	NUM
ejpam-4661	95	14	.	.	NOUN
ejpam-4661	95	15	3.2	3.2	NUM
ejpam-4661	95	16	.	.	PUNCT
ejpam-4661	96	1	stability	stability	NOUN
ejpam-4661	96	2	of	of	ADP
ejpam-4661	96	3	the	the	DET
ejpam-4661	96	4	exclusion	exclusion	NOUN
ejpam-4661	96	5	fixed	fix	VERB
ejpam-4661	96	6	point	point	NOUN
ejpam-4661	96	7	for	for	ADP
ejpam-4661	96	8	the	the	DET
ejpam-4661	96	9	exclusion	exclusion	NOUN
ejpam-4661	96	10	fixed	fix	VERB
ejpam-4661	96	11	point	point	NOUN
ejpam-4661	96	12	p1	p1	NOUN
ejpam-4661	96	13	=	=	SYM
ejpam-4661	96	14	(	(	PUNCT
ejpam-4661	96	15	1	1	NUM
ejpam-4661	96	16	β	β	X
ejpam-4661	96	17	,	,	PUNCT
ejpam-4661	96	18	0	0	NUM
ejpam-4661	96	19	)	)	PUNCT
ejpam-4661	96	20	,	,	PUNCT
ejpam-4661	96	21	we	we	PRON
ejpam-4661	96	22	have	have	VERB
ejpam-4661	96	23	the	the	DET
ejpam-4661	96	24	following	follow	VERB
ejpam-4661	96	25	jacobian	jacobian	ADJ
ejpam-4661	96	26	matrix	matrix	NOUN
ejpam-4661	96	27	:	:	PUNCT
ejpam-4661	96	28	j1	j1	PROPN
ejpam-4661	96	29	=	=	PUNCT
ejpam-4661	96	30	(	(	PUNCT
ejpam-4661	96	31	2−	2−	NUM
ejpam-4661	96	32	α	α	NOUN
ejpam-4661	96	33	−	−	PROPN
ejpam-4661	96	34	1	1	NUM
ejpam-4661	96	35	β	β	NOUN
ejpam-4661	96	36	0	0	NUM
ejpam-4661	96	37	0	0	NUM
ejpam-4661	96	38	)	)	PUNCT
ejpam-4661	96	39	.	.	PUNCT
ejpam-4661	97	1	the	the	DET
ejpam-4661	97	2	eigenvalues	eigenvalue	NOUN
ejpam-4661	97	3	of	of	ADP
ejpam-4661	97	4	the	the	DET
ejpam-4661	97	5	jacobian	jacobian	ADJ
ejpam-4661	97	6	matrix	matrix	NOUN
ejpam-4661	97	7	are	be	AUX
ejpam-4661	97	8	λ1	λ1	ADJ
ejpam-4661	97	9	=	=	SYM
ejpam-4661	97	10	2	2	NUM
ejpam-4661	97	11	−	−	PROPN
ejpam-4661	97	12	α	α	NOUN
ejpam-4661	97	13	and	and	CCONJ
ejpam-4661	97	14	λ2	λ2	NOUN
ejpam-4661	97	15	=	=	SYM
ejpam-4661	97	16	0	0	NUM
ejpam-4661	97	17	.	.	PUNCT
ejpam-4661	98	1	hence	hence	ADV
ejpam-4661	98	2	the	the	DET
ejpam-4661	98	3	fixed	fix	VERB
ejpam-4661	98	4	point	point	NOUN
ejpam-4661	98	5	p1	p1	NOUN
ejpam-4661	98	6	is	be	AUX
ejpam-4661	98	7	locally	locally	ADV
ejpam-4661	98	8	asymptotically	asymptotically	ADV
ejpam-4661	98	9	stable	stable	ADJ
ejpam-4661	98	10	if	if	SCONJ
ejpam-4661	98	11	1	1	NUM
ejpam-4661	98	12	<	<	X
ejpam-4661	98	13	α	α	X
ejpam-4661	98	14	<	<	X
ejpam-4661	98	15	3	3	NUM
ejpam-4661	98	16	.	.	PROPN
ejpam-4661	98	17	3.3	3.3	NUM
ejpam-4661	98	18	.	.	PUNCT
ejpam-4661	99	1	stability	stability	NOUN
ejpam-4661	99	2	of	of	ADP
ejpam-4661	99	3	the	the	DET
ejpam-4661	99	4	coexistence	coexistence	NOUN
ejpam-4661	99	5	fixed	fix	VERB
ejpam-4661	99	6	points	point	NOUN
ejpam-4661	99	7	by	by	ADP
ejpam-4661	99	8	theorem	theorem	NOUN
ejpam-4661	99	9	1	1	NUM
ejpam-4661	99	10	,	,	PUNCT
ejpam-4661	99	11	the	the	DET
ejpam-4661	99	12	coexistence	coexistence	NOUN
ejpam-4661	99	13	fixed	fix	VERB
ejpam-4661	99	14	points	point	NOUN
ejpam-4661	99	15	exist	exist	VERB
ejpam-4661	99	16	if	if	SCONJ
ejpam-4661	99	17	∆	∆	PROPN
ejpam-4661	99	18	≥	≥	X
ejpam-4661	99	19	0	0	NUM
ejpam-4661	99	20	.	.	PUNCT
ejpam-4661	100	1	we	we	PRON
ejpam-4661	100	2	start	start	VERB
ejpam-4661	100	3	with	with	ADP
ejpam-4661	100	4	the	the	DET
ejpam-4661	100	5	following	follow	VERB
ejpam-4661	100	6	case	case	NOUN
ejpam-4661	100	7	:	:	PUNCT
ejpam-4661	100	8	3.3.1	3.3.1	X
ejpam-4661	100	9	.	.	PUNCT
ejpam-4661	100	10	stability	stability	NOUN
ejpam-4661	100	11	of	of	ADP
ejpam-4661	100	12	p+	p+	PROPN
ejpam-4661	100	13	1	1	NUM
ejpam-4661	100	14	,	,	PUNCT
ejpam-4661	100	15	p+	p+	VERB
ejpam-4661	100	16	2	2	NUM
ejpam-4661	100	17	,	,	PUNCT
ejpam-4661	100	18	and	and	CCONJ
ejpam-4661	100	19	p+	p+	VERB
ejpam-4661	100	20	3	3	NUM
ejpam-4661	100	21	:	:	PUNCT
ejpam-4661	100	22	if	if	SCONJ
ejpam-4661	100	23	∆	∆	PROPN
ejpam-4661	100	24	>	>	X
ejpam-4661	100	25	0	0	PUNCT
ejpam-4661	101	1	for	for	ADP
ejpam-4661	101	2	the	the	DET
ejpam-4661	101	3	case	case	NOUN
ejpam-4661	101	4	when	when	SCONJ
ejpam-4661	101	5	∆	∆	PROPN
ejpam-4661	101	6	>	>	X
ejpam-4661	101	7	0	0	NUM
ejpam-4661	101	8	,	,	PUNCT
ejpam-4661	101	9	we	we	PRON
ejpam-4661	101	10	investigate	investigate	VERB
ejpam-4661	101	11	three	three	NUM
ejpam-4661	101	12	possible	possible	ADJ
ejpam-4661	101	13	fixed	fix	VERB
ejpam-4661	101	14	points	point	NOUN
ejpam-4661	101	15	p+	p+	VERB
ejpam-4661	101	16	1	1	NUM
ejpam-4661	101	17	,	,	PUNCT
ejpam-4661	101	18	p+	p+	NOUN
ejpam-4661	101	19	2	2	NUM
ejpam-4661	101	20	,	,	PUNCT
ejpam-4661	101	21	p+	p+	VERB
ejpam-4661	101	22	3	3	NUM
ejpam-4661	101	23	.	.	PUNCT
ejpam-4661	101	24	trace	trace	NOUN
ejpam-4661	101	25	and	and	CCONJ
ejpam-4661	101	26	determinant	determinant	ADJ
ejpam-4661	101	27	of	of	ADP
ejpam-4661	101	28	the	the	DET
ejpam-4661	101	29	jacobian	jacobian	ADJ
ejpam-4661	101	30	matrices	matrix	NOUN
ejpam-4661	101	31	j+	j+	NUM
ejpam-4661	101	32	1	1	NUM
ejpam-4661	101	33	,	,	PUNCT
ejpam-4661	101	34	j+	j+	NUM
ejpam-4661	101	35	2	2	NUM
ejpam-4661	101	36	,	,	PUNCT
ejpam-4661	101	37	j+	j+	NUM
ejpam-4661	101	38	3	3	NUM
ejpam-4661	101	39	,	,	PUNCT
ejpam-4661	101	40	respectively	respectively	ADV
ejpam-4661	101	41	,	,	PUNCT
ejpam-4661	101	42	at	at	ADP
ejpam-4661	101	43	these	these	DET
ejpam-4661	101	44	fixed	fix	VERB
ejpam-4661	101	45	points	point	NOUN
ejpam-4661	101	46	are	be	AUX
ejpam-4661	101	47	given	give	VERB
ejpam-4661	101	48	by	by	ADP
ejpam-4661	101	49	tr(j+	tr(j+	PROPN
ejpam-4661	101	50	1,2,3	1,2,3	NUM
ejpam-4661	101	51	)	)	PUNCT
ejpam-4661	101	52	=	=	SYM
ejpam-4661	101	53	1	1	NUM
ejpam-4661	101	54	2	2	NUM
ejpam-4661	101	55	(	(	PUNCT
ejpam-4661	101	56	βγ	βγ	NOUN
ejpam-4661	101	57	+	+	NUM
ejpam-4661	101	58	γ	γ	PROPN
ejpam-4661	101	59	±	±	NUM
ejpam-4661	101	60	√	√	PROPN
ejpam-4661	101	61	∆	∆	PROPN
ejpam-4661	102	1	α+	α+	PUNCT
ejpam-4661	102	2	γ	γ	NOUN
ejpam-4661	102	3	−	−	PROPN
ejpam-4661	102	4	1	1	NUM
ejpam-4661	102	5	−	−	PROPN
ejpam-4661	102	6	α(β	α(β	PROPN
ejpam-4661	102	7	+	+	CCONJ
ejpam-4661	102	8	1)±	1)±	NUM
ejpam-4661	102	9	√	√	NUM
ejpam-4661	102	10	∆+	∆+	NUM
ejpam-4661	102	11	6	6	NUM
ejpam-4661	102	12	)	)	PUNCT
ejpam-4661	102	13	,	,	PUNCT
ejpam-4661	102	14	det(j+	det(j+	NOUN
ejpam-4661	102	15	1,2,3	1,2,3	NUM
ejpam-4661	102	16	)	)	PUNCT
ejpam-4661	102	17	=	=	SYM
ejpam-4661	102	18	1	1	NUM
ejpam-4661	102	19	2	2	NUM
ejpam-4661	102	20	(	(	PUNCT
ejpam-4661	102	21	βγ	βγ	NOUN
ejpam-4661	102	22	+	+	NUM
ejpam-4661	102	23	γ	γ	PROPN
ejpam-4661	102	24	±	±	NUM
ejpam-4661	102	25	√	√	PROPN
ejpam-4661	102	26	∆	∆	PROPN
ejpam-4661	102	27	α+	α+	PUNCT
ejpam-4661	102	28	γ	γ	NOUN
ejpam-4661	102	29	−	−	PROPN
ejpam-4661	102	30	1	1	NUM
ejpam-4661	102	31	−	−	PROPN
ejpam-4661	102	32	α(β	α(β	PROPN
ejpam-4661	102	33	+	+	CCONJ
ejpam-4661	102	34	1)±	1)±	NUM
ejpam-4661	102	35	3	3	NUM
ejpam-4661	102	36	√	√	NUM
ejpam-4661	102	37	∆+	∆+	NUM
ejpam-4661	102	38	4	4	NUM
ejpam-4661	102	39	)	)	PUNCT
ejpam-4661	102	40	,	,	PUNCT
ejpam-4661	102	41	s.	s.	PROPN
ejpam-4661	102	42	kapcak	kapcak	PROPN
ejpam-4661	102	43	/	/	SYM
ejpam-4661	102	44	eur	eur	PROPN
ejpam-4661	102	45	.	.	PUNCT
ejpam-4661	103	1	j.	j.	PROPN
ejpam-4661	103	2	pure	pure	PROPN
ejpam-4661	103	3	appl	appl	PROPN
ejpam-4661	103	4	.	.	PROPN
ejpam-4661	103	5	math	math	PROPN
ejpam-4661	103	6	,	,	PUNCT
ejpam-4661	103	7	16	16	NUM
ejpam-4661	103	8	(	(	PUNCT
ejpam-4661	103	9	1	1	NUM
ejpam-4661	103	10	)	)	PUNCT
ejpam-4661	103	11	(	(	PUNCT
ejpam-4661	103	12	2023	2023	NUM
ejpam-4661	103	13	)	)	PUNCT
ejpam-4661	103	14	,	,	PUNCT
ejpam-4661	103	15	71	71	NUM
ejpam-4661	103	16	-	-	SYM
ejpam-4661	103	17	83	83	NUM
ejpam-4661	103	18	77	77	NUM
ejpam-4661	103	19	where	where	SCONJ
ejpam-4661	103	20	∆	∆	PUNCT
ejpam-4661	103	21	=	=	PRON
ejpam-4661	104	1	(	(	PUNCT
ejpam-4661	104	2	α−	α−	ADP
ejpam-4661	104	3	1)2(β	1)2(β	PRON
ejpam-4661	104	4	−	−	PROPN
ejpam-4661	104	5	1)2	1)2	NUM
ejpam-4661	104	6	−	−	NOUN
ejpam-4661	104	7	4β(α−	4β(α−	NUM
ejpam-4661	104	8	1)γ	1)γ	NOUN
ejpam-4661	104	9	.	.	PUNCT
ejpam-4661	105	1	we	we	PRON
ejpam-4661	105	2	obtained	obtain	VERB
ejpam-4661	105	3	the	the	DET
ejpam-4661	105	4	stability	stability	NOUN
ejpam-4661	105	5	conditions	condition	NOUN
ejpam-4661	105	6	applying	apply	VERB
ejpam-4661	105	7	the	the	DET
ejpam-4661	105	8	tr	tr	VERB
ejpam-4661	105	9	-	-	PUNCT
ejpam-4661	105	10	det	det	NOUN
ejpam-4661	105	11	formula	formula	NOUN
ejpam-4661	105	12	|tr(j)|	|tr(j)|	NOUN
ejpam-4661	105	13	−	−	PROPN
ejpam-4661	105	14	1	1	NUM
ejpam-4661	105	15	<	<	X
ejpam-4661	105	16	det(j	det(j	PROPN
ejpam-4661	105	17	)	)	PUNCT
ejpam-4661	105	18	<	<	X
ejpam-4661	105	19	1	1	X
ejpam-4661	105	20	.	.	PUNCT
ejpam-4661	105	21	theorem	theorem	NOUN
ejpam-4661	105	22	2	2	NUM
ejpam-4661	105	23	.	.	X
ejpam-4661	105	24	for	for	ADP
ejpam-4661	105	25	system	system	NOUN
ejpam-4661	105	26	(	(	PUNCT
ejpam-4661	105	27	4	4	NUM
ejpam-4661	105	28	)	)	PUNCT
ejpam-4661	105	29	,	,	PUNCT
ejpam-4661	105	30	i.	i.	PROPN
ejpam-4661	105	31	p+	p+	PROPN
ejpam-4661	105	32	1	1	NUM
ejpam-4661	105	33	is	be	AUX
ejpam-4661	105	34	unstable	unstable	ADJ
ejpam-4661	105	35	.	.	PUNCT
ejpam-4661	106	1	ii	ii	PROPN
ejpam-4661	106	2	.	.	PUNCT
ejpam-4661	106	3	p+	p+	PROPN
ejpam-4661	106	4	2	2	NUM
ejpam-4661	106	5	is	be	AUX
ejpam-4661	106	6	unstable	unstable	ADJ
ejpam-4661	106	7	.	.	PUNCT
ejpam-4661	107	1	iii	iii	X
ejpam-4661	107	2	.	.	PROPN
ejpam-4661	107	3	p+	p+	PROPN
ejpam-4661	107	4	3	3	NUM
ejpam-4661	107	5	is	be	AUX
ejpam-4661	107	6	locally	locally	ADV
ejpam-4661	107	7	asymptotically	asymptotically	ADV
ejpam-4661	107	8	stable	stable	ADJ
ejpam-4661	107	9	if	if	SCONJ
ejpam-4661	107	10	2	2	NUM
ejpam-4661	107	11	+	+	SYM
ejpam-4661	107	12	3	3	NUM
ejpam-4661	107	13	√	√	NOUN
ejpam-4661	107	14	∆	∆	PROPN
ejpam-4661	107	15	<	<	X
ejpam-4661	107	16	α(α+	α(α+	PUNCT
ejpam-4661	107	17	β)−k	β)−k	PRON
ejpam-4661	107	18	<	<	X
ejpam-4661	107	19	6	6	NUM
ejpam-4661	107	20	+	+	SYM
ejpam-4661	107	21	2	2	NUM
ejpam-4661	107	22	√	√	NOUN
ejpam-4661	107	23	∆	∆	PROPN
ejpam-4661	107	24	,	,	PUNCT
ejpam-4661	107	25	where	where	SCONJ
ejpam-4661	107	26	k	k	PROPN
ejpam-4661	107	27	=	=	PUNCT
ejpam-4661	107	28	βγ+γ−	βγ+γ−	ADJ
ejpam-4661	107	29	√	√	PROPN
ejpam-4661	107	30	∆	∆	PROPN
ejpam-4661	107	31	α+γ−1	α+γ−1	PROPN
ejpam-4661	107	32	and	and	CCONJ
ejpam-4661	107	33	∆	∆	PROPN
ejpam-4661	107	34	=	=	SYM
ejpam-4661	108	1	(	(	PUNCT
ejpam-4661	108	2	α−	α−	ADP
ejpam-4661	108	3	1)2(β	1)2(β	PRON
ejpam-4661	108	4	−	−	PROPN
ejpam-4661	108	5	1)2	1)2	NUM
ejpam-4661	108	6	−	−	PROPN
ejpam-4661	108	7	4β(α−	4β(α−	NUM
ejpam-4661	108	8	1)γ	1)γ	NOUN
ejpam-4661	108	9	.	.	PUNCT
ejpam-4661	108	10	neimark	neimark	NOUN
ejpam-4661	108	11	-	-	PUNCT
ejpam-4661	108	12	sacker	sacker	NOUN
ejpam-4661	108	13	bifurcation	bifurcation	NOUN
ejpam-4661	108	14	saddle	saddle	NOUN
ejpam-4661	108	15	-	-	PUNCT
ejpam-4661	108	16	node	node	NOUN
ejpam-4661	108	17	bifurcation	bifurcation	NOUN
ejpam-4661	108	18	flip	flip	NOUN
ejpam-4661	108	19	bifurcation	bifurcation	NOUN
ejpam-4661	108	20	0	0	NUM
ejpam-4661	108	21	2	2	NUM
ejpam-4661	108	22	4	4	NUM
ejpam-4661	108	23	6	6	NUM
ejpam-4661	108	24	8	8	NUM
ejpam-4661	108	25	10	10	NUM
ejpam-4661	108	26	α	α	NOUN
ejpam-4661	108	27	0.2	0.2	NUM
ejpam-4661	108	28	0.4	0.4	NUM
ejpam-4661	108	29	0.6	0.6	NUM
ejpam-4661	108	30	0.8	0.8	NUM
ejpam-4661	108	31	1.0	1.0	NUM
ejpam-4661	108	32	1.2	1.2	NUM
ejpam-4661	108	33	1.4	1.4	NUM
ejpam-4661	108	34	β	β	NOUN
ejpam-4661	108	35	figure	figure	NOUN
ejpam-4661	108	36	3	3	NUM
ejpam-4661	108	37	:	:	PUNCT
ejpam-4661	108	38	(	(	PUNCT
ejpam-4661	108	39	γ	γ	X
ejpam-4661	108	40	=	=	NOUN
ejpam-4661	108	41	0.26	0.26	NUM
ejpam-4661	108	42	)	)	PUNCT
ejpam-4661	108	43	stability	stability	NOUN
ejpam-4661	108	44	region	region	NOUN
ejpam-4661	108	45	of	of	ADP
ejpam-4661	108	46	coexistence	coexistence	NOUN
ejpam-4661	108	47	fixed	fix	VERB
ejpam-4661	108	48	point	point	NOUN
ejpam-4661	108	49	p+	p+	VERB
ejpam-4661	108	50	3	3	NUM
ejpam-4661	108	51	figure	figure	NOUN
ejpam-4661	108	52	3	3	NUM
ejpam-4661	108	53	represents	represent	VERB
ejpam-4661	108	54	the	the	DET
ejpam-4661	108	55	stability	stability	NOUN
ejpam-4661	108	56	region	region	NOUN
ejpam-4661	108	57	of	of	ADP
ejpam-4661	108	58	the	the	DET
ejpam-4661	108	59	coexistence	coexistence	NOUN
ejpam-4661	108	60	fixed	fix	VERB
ejpam-4661	108	61	point	point	NOUN
ejpam-4661	108	62	p+	p+	VERB
ejpam-4661	108	63	3	3	NUM
ejpam-4661	108	64	in	in	ADP
ejpam-4661	108	65	the	the	DET
ejpam-4661	108	66	parameter	parameter	NOUN
ejpam-4661	108	67	plane	plane	NOUN
ejpam-4661	108	68	α	α	PROPN
ejpam-4661	108	69	-	-	PUNCT
ejpam-4661	108	70	β	β	NOUN
ejpam-4661	108	71	.	.	PUNCT
ejpam-4661	108	72	types	type	NOUN
ejpam-4661	108	73	of	of	ADP
ejpam-4661	108	74	bifurcations	bifurcation	NOUN
ejpam-4661	108	75	are	be	AUX
ejpam-4661	108	76	also	also	ADV
ejpam-4661	108	77	given	give	VERB
ejpam-4661	108	78	.	.	PUNCT
ejpam-4661	109	1	in	in	ADP
ejpam-4661	109	2	table	table	NOUN
ejpam-4661	109	3	1	1	NUM
ejpam-4661	109	4	and	and	CCONJ
ejpam-4661	109	5	2	2	NUM
ejpam-4661	109	6	,	,	PUNCT
ejpam-4661	109	7	we	we	PRON
ejpam-4661	109	8	give	give	VERB
ejpam-4661	109	9	several	several	ADJ
ejpam-4661	109	10	parameter	parameter	NOUN
ejpam-4661	109	11	values	value	NOUN
ejpam-4661	109	12	and	and	CCONJ
ejpam-4661	109	13	corresponding	corresponding	ADJ
ejpam-4661	109	14	phase	phase	NOUN
ejpam-4661	109	15	diagrams	diagram	NOUN
ejpam-4661	109	16	.	.	PUNCT
ejpam-4661	110	1	one	one	PRON
ejpam-4661	110	2	can	can	AUX
ejpam-4661	110	3	see	see	VERB
ejpam-4661	110	4	in	in	ADP
ejpam-4661	110	5	the	the	DET
ejpam-4661	110	6	table	table	NOUN
ejpam-4661	110	7	that	that	SCONJ
ejpam-4661	110	8	the	the	DET
ejpam-4661	110	9	system	system	NOUN
ejpam-4661	110	10	also	also	ADV
ejpam-4661	110	11	exhibits	exhibit	VERB
ejpam-4661	110	12	neimark	neimark	NOUN
ejpam-4661	110	13	-	-	PUNCT
ejpam-4661	110	14	sacker	sacker	NOUN
ejpam-4661	110	15	bifurcation	bifurcation	NOUN
ejpam-4661	110	16	(	(	PUNCT
ejpam-4661	110	17	see	see	VERB
ejpam-4661	110	18	[	[	X
ejpam-4661	110	19	4	4	NUM
ejpam-4661	110	20	,	,	PUNCT
ejpam-4661	110	21	8	8	NUM
ejpam-4661	110	22	,	,	PUNCT
ejpam-4661	110	23	10	10	NUM
ejpam-4661	110	24	,	,	PUNCT
ejpam-4661	110	25	15	15	NUM
ejpam-4661	110	26	,	,	PUNCT
ejpam-4661	110	27	16	16	NUM
ejpam-4661	110	28	]	]	PUNCT
ejpam-4661	110	29	)	)	PUNCT
ejpam-4661	110	30	for	for	ADP
ejpam-4661	110	31	some	some	DET
ejpam-4661	110	32	values	value	NOUN
ejpam-4661	110	33	of	of	ADP
ejpam-4661	110	34	parameters	parameter	NOUN
ejpam-4661	110	35	.	.	PUNCT
ejpam-4661	111	1	this	this	PRON
ejpam-4661	111	2	is	be	AUX
ejpam-4661	111	3	the	the	DET
ejpam-4661	111	4	case	case	NOUN
ejpam-4661	111	5	when	when	SCONJ
ejpam-4661	111	6	det(j+	det(j+	PROPN
ejpam-4661	111	7	3	3	NUM
ejpam-4661	111	8	)	)	PUNCT
ejpam-4661	111	9	=	=	SYM
ejpam-4661	111	10	1	1	NUM
ejpam-4661	111	11	and	and	CCONJ
ejpam-4661	111	12	|tr(j+	|tr(j+	NOUN
ejpam-4661	111	13	3	3	X
ejpam-4661	111	14	)	)	PUNCT
ejpam-4661	112	1	|	|	ADV
ejpam-4661	112	2	<	<	X
ejpam-4661	112	3	2	2	X
ejpam-4661	112	4	.	.	PUNCT
ejpam-4661	112	5	when	when	SCONJ
ejpam-4661	112	6	the	the	DET
ejpam-4661	112	7	parameter	parameter	NOUN
ejpam-4661	112	8	point	point	NOUN
ejpam-4661	112	9	is	be	AUX
ejpam-4661	112	10	in	in	ADP
ejpam-4661	112	11	the	the	DET
ejpam-4661	112	12	stability	stability	NOUN
ejpam-4661	112	13	region	region	NOUN
ejpam-4661	112	14	and	and	CCONJ
ejpam-4661	112	15	close	close	ADJ
ejpam-4661	112	16	to	to	ADP
ejpam-4661	112	17	the	the	DET
ejpam-4661	112	18	neimark	neimark	NOUN
ejpam-4661	112	19	-	-	PUNCT
ejpam-4661	112	20	sacker	sacker	NOUN
ejpam-4661	112	21	borderline	borderline	NOUN
ejpam-4661	112	22	,	,	PUNCT
ejpam-4661	112	23	the	the	DET
ejpam-4661	112	24	orbit	orbit	NOUN
ejpam-4661	112	25	is	be	AUX
ejpam-4661	112	26	spiraling	spiral	VERB
ejpam-4661	112	27	and	and	CCONJ
ejpam-4661	112	28	just	just	ADV
ejpam-4661	112	29	after	after	SCONJ
ejpam-4661	112	30	the	the	DET
ejpam-4661	112	31	parameter	parameter	NOUN
ejpam-4661	112	32	point	point	NOUN
ejpam-4661	112	33	(	(	PUNCT
ejpam-4661	112	34	α	α	X
ejpam-4661	112	35	,	,	PUNCT
ejpam-4661	112	36	β	β	NOUN
ejpam-4661	112	37	)	)	PUNCT
ejpam-4661	112	38	crosses	cross	VERB
ejpam-4661	112	39	the	the	DET
ejpam-4661	112	40	n	n	CCONJ
ejpam-4661	112	41	-	-	PUNCT
ejpam-4661	112	42	s	s	NOUN
ejpam-4661	112	43	curve	curve	NOUN
ejpam-4661	112	44	,	,	PUNCT
ejpam-4661	112	45	orbits	orbit	NOUN
ejpam-4661	112	46	converge	converge	VERB
ejpam-4661	112	47	to	to	ADP
ejpam-4661	112	48	a	a	DET
ejpam-4661	112	49	closed	close	VERB
ejpam-4661	112	50	invariant	invariant	ADJ
ejpam-4661	112	51	curve	curve	NOUN
ejpam-4661	112	52	in	in	ADP
ejpam-4661	112	53	the	the	DET
ejpam-4661	112	54	phase	phase	NOUN
ejpam-4661	112	55	diagram	diagram	NOUN
ejpam-4661	112	56	.	.	PUNCT
ejpam-4661	113	1	s.	s.	PROPN
ejpam-4661	113	2	kapcak	kapcak	PROPN
ejpam-4661	113	3	/	/	SYM
ejpam-4661	113	4	eur	eur	PROPN
ejpam-4661	113	5	.	.	PUNCT
ejpam-4661	114	1	j.	j.	PROPN
ejpam-4661	114	2	pure	pure	PROPN
ejpam-4661	114	3	appl	appl	PROPN
ejpam-4661	114	4	.	.	PROPN
ejpam-4661	114	5	math	math	PROPN
ejpam-4661	114	6	,	,	PUNCT
ejpam-4661	114	7	16	16	NUM
ejpam-4661	114	8	(	(	PUNCT
ejpam-4661	114	9	1	1	NUM
ejpam-4661	114	10	)	)	PUNCT
ejpam-4661	114	11	(	(	PUNCT
ejpam-4661	114	12	2023	2023	NUM
ejpam-4661	114	13	)	)	PUNCT
ejpam-4661	114	14	,	,	PUNCT
ejpam-4661	114	15	71	71	NUM
ejpam-4661	114	16	-	-	SYM
ejpam-4661	114	17	83	83	NUM
ejpam-4661	114	18	78	78	NUM
ejpam-4661	114	19	table	table	NOUN
ejpam-4661	114	20	1	1	NUM
ejpam-4661	114	21	:	:	PUNCT
ejpam-4661	114	22	(	(	PUNCT
ejpam-4661	114	23	γ	γ	X
ejpam-4661	114	24	=	=	NOUN
ejpam-4661	114	25	0.26	0.26	NUM
ejpam-4661	114	26	)	)	PUNCT
ejpam-4661	114	27	stability	stability	NOUN
ejpam-4661	114	28	of	of	ADP
ejpam-4661	114	29	the	the	DET
ejpam-4661	114	30	coexistence	coexistence	NOUN
ejpam-4661	114	31	fixed	fix	VERB
ejpam-4661	114	32	point	point	NOUN
ejpam-4661	114	33	.	.	PUNCT
ejpam-4661	115	1	α	α	X
ejpam-4661	115	2	-	-	PUNCT
ejpam-4661	115	3	β	β	NOUN
ejpam-4661	115	4	plane	plane	NOUN
ejpam-4661	115	5	phase	phase	NOUN
ejpam-4661	115	6	diagram	diagram	NOUN
ejpam-4661	115	7	3.3.2	3.3.2	NUM
ejpam-4661	115	8	.	.	PUNCT
ejpam-4661	116	1	stability	stability	NOUN
ejpam-4661	116	2	of	of	ADP
ejpam-4661	116	3	p+	p+	PROPN
ejpam-4661	116	4	0	0	NUM
ejpam-4661	116	5	:	:	PUNCT
ejpam-4661	116	6	non	non	ADJ
ejpam-4661	116	7	-	-	ADJ
ejpam-4661	116	8	hyperbolic	hyperbolic	ADJ
ejpam-4661	116	9	case	case	NOUN
ejpam-4661	116	10	or	or	CCONJ
ejpam-4661	116	11	the	the	DET
ejpam-4661	116	12	case	case	NOUN
ejpam-4661	116	13	∆	∆	PUNCT
ejpam-4661	117	1	=	=	SYM
ejpam-4661	117	2	0	0	X
ejpam-4661	118	1	there	there	PRON
ejpam-4661	118	2	is	be	VERB
ejpam-4661	118	3	only	only	ADV
ejpam-4661	118	4	one	one	NUM
ejpam-4661	118	5	positive	positive	ADJ
ejpam-4661	118	6	fixed	fix	VERB
ejpam-4661	118	7	point	point	NOUN
ejpam-4661	118	8	when	when	SCONJ
ejpam-4661	118	9	∆	∆	PROPN
ejpam-4661	118	10	=	=	SYM
ejpam-4661	118	11	0	0	NUM
ejpam-4661	118	12	and	and	CCONJ
ejpam-4661	118	13	β	β	X
ejpam-4661	118	14	<	<	X
ejpam-4661	118	15	1	1	NUM
ejpam-4661	118	16	by	by	ADP
ejpam-4661	118	17	theorem	theorem	NOUN
ejpam-4661	118	18	1	1	NUM
ejpam-4661	118	19	:	:	PUNCT
ejpam-4661	118	20	p+	p+	X
ejpam-4661	118	21	0	0	NUM
ejpam-4661	118	22	=(	=(	NOUN
ejpam-4661	118	23	β+1	β+1	ADJ
ejpam-4661	118	24	2β	2β	NOUN
ejpam-4661	118	25	,	,	PUNCT
ejpam-4661	118	26	2γβ	2γβ	NOUN
ejpam-4661	118	27	1−β	1−β	NUM
ejpam-4661	118	28	)	)	PUNCT
ejpam-4661	118	29	.	.	PUNCT
ejpam-4661	119	1	applying	apply	VERB
ejpam-4661	119	2	this	this	DET
ejpam-4661	119	3	point	point	NOUN
ejpam-4661	119	4	to	to	ADP
ejpam-4661	119	5	jacobian	jacobian	ADJ
ejpam-4661	119	6	matrix	matrix	NOUN
ejpam-4661	119	7	and	and	CCONJ
ejpam-4661	119	8	eliminating	eliminate	VERB
ejpam-4661	119	9	γ	γ	NOUN
ejpam-4661	119	10	using	use	VERB
ejpam-4661	119	11	the	the	DET
ejpam-4661	119	12	equation	equation	NOUN
ejpam-4661	119	13	∆	∆	X
ejpam-4661	119	14	=	=	SYM
ejpam-4661	119	15	0	0	NUM
ejpam-4661	119	16	,	,	PUNCT
ejpam-4661	119	17	we	we	PRON
ejpam-4661	119	18	obtain	obtain	VERB
ejpam-4661	119	19	j+	j+	NUM
ejpam-4661	119	20	0	0	NUM
ejpam-4661	120	1	=	=	SYM
ejpam-4661	120	2	(	(	PUNCT
ejpam-4661	120	3	1	1	NUM
ejpam-4661	120	4	2(β	2(β	NUM
ejpam-4661	120	5	−	−	NOUN
ejpam-4661	120	6	α(β	α(β	PROPN
ejpam-4661	120	7	+	+	CCONJ
ejpam-4661	120	8	1	1	NUM
ejpam-4661	120	9	)	)	PUNCT
ejpam-4661	120	10	+	+	CCONJ
ejpam-4661	120	11	3	3	X
ejpam-4661	120	12	)	)	PUNCT
ejpam-4661	120	13	−β+1	−β+1	ADJ
ejpam-4661	120	14	2β	2β	NOUN
ejpam-4661	120	15	−	−	NOUN
ejpam-4661	120	16	(	(	PUNCT
ejpam-4661	120	17	α−1)(β−1)β	α−1)(β−1)β	NOUN
ejpam-4661	120	18	β+1	β+1	NUM
ejpam-4661	120	19	2	2	NUM
ejpam-4661	120	20	β+1	β+1	NUM
ejpam-4661	120	21	)	)	PUNCT
ejpam-4661	120	22	.	.	PUNCT
ejpam-4661	121	1	the	the	DET
ejpam-4661	121	2	eigenvalues	eigenvalue	NOUN
ejpam-4661	121	3	of	of	ADP
ejpam-4661	121	4	the	the	DET
ejpam-4661	121	5	jacobian	jacobian	ADJ
ejpam-4661	121	6	matrix	matrix	NOUN
ejpam-4661	121	7	are	be	AUX
ejpam-4661	121	8	λ1	λ1	ADJ
ejpam-4661	121	9	=	=	SYM
ejpam-4661	121	10	1	1	NUM
ejpam-4661	121	11	and	and	CCONJ
ejpam-4661	121	12	λ2	λ2	NOUN
ejpam-4661	121	13	=	=	PUNCT
ejpam-4661	122	1	−α(β+1)2+β2	−α(β+1)2+β2	NOUN
ejpam-4661	122	2	+	+	ADJ
ejpam-4661	122	3	2β+5	2β+5	PROPN
ejpam-4661	122	4	2(β+1	2(β+1	NUM
ejpam-4661	122	5	)	)	PUNCT
ejpam-4661	122	6	.	.	PUNCT
ejpam-4661	123	1	the	the	DET
ejpam-4661	123	2	fixed	fixed	ADJ
ejpam-4661	123	3	point	point	NOUN
ejpam-4661	123	4	p+	p+	X
ejpam-4661	123	5	0	0	NUM
ejpam-4661	123	6	is	be	AUX
ejpam-4661	123	7	non	non	ADJ
ejpam-4661	123	8	-	-	ADJ
ejpam-4661	123	9	hyperbolic	hyperbolic	ADJ
ejpam-4661	123	10	.	.	PUNCT
ejpam-4661	124	1	if	if	SCONJ
ejpam-4661	124	2	|λ2|	|λ2|	VERB
ejpam-4661	124	3	>	>	X
ejpam-4661	124	4	1	1	NUM
ejpam-4661	124	5	,	,	PUNCT
ejpam-4661	124	6	then	then	ADV
ejpam-4661	124	7	it	it	PRON
ejpam-4661	124	8	is	be	AUX
ejpam-4661	124	9	unstable	unstable	ADJ
ejpam-4661	124	10	.	.	PUNCT
ejpam-4661	125	1	if	if	SCONJ
ejpam-4661	125	2	|λ2|	|λ2|	VERB
ejpam-4661	125	3	<	<	X
ejpam-4661	125	4	1	1	NUM
ejpam-4661	125	5	,	,	PUNCT
ejpam-4661	125	6	we	we	PRON
ejpam-4661	125	7	have	have	VERB
ejpam-4661	125	8	to	to	PART
ejpam-4661	125	9	apply	apply	VERB
ejpam-4661	125	10	the	the	DET
ejpam-4661	125	11	center	center	ADJ
ejpam-4661	125	12	manifold	manifold	ADJ
ejpam-4661	125	13	theory	theory	NOUN
ejpam-4661	125	14	[	[	X
ejpam-4661	125	15	2	2	NUM
ejpam-4661	125	16	]	]	PUNCT
ejpam-4661	125	17	.	.	PUNCT
ejpam-4661	126	1	it	it	PRON
ejpam-4661	126	2	is	be	AUX
ejpam-4661	126	3	more	more	ADV
ejpam-4661	126	4	convenient	convenient	ADJ
ejpam-4661	126	5	to	to	PART
ejpam-4661	126	6	make	make	VERB
ejpam-4661	126	7	a	a	DET
ejpam-4661	126	8	change	change	NOUN
ejpam-4661	126	9	of	of	ADP
ejpam-4661	126	10	variables	variable	NOUN
ejpam-4661	126	11	in	in	ADP
ejpam-4661	126	12	system	system	NOUN
ejpam-4661	126	13	(	(	PUNCT
ejpam-4661	126	14	4	4	NUM
ejpam-4661	126	15	)	)	PUNCT
ejpam-4661	126	16	so	so	SCONJ
ejpam-4661	126	17	we	we	PRON
ejpam-4661	126	18	can	can	AUX
ejpam-4661	126	19	have	have	VERB
ejpam-4661	126	20	a	a	DET
ejpam-4661	126	21	shift	shift	NOUN
ejpam-4661	126	22	from	from	ADP
ejpam-4661	126	23	the	the	DET
ejpam-4661	126	24	point	point	NOUN
ejpam-4661	126	25	p+	p+	NOUN
ejpam-4661	126	26	0	0	NUM
ejpam-4661	126	27	to	to	PART
ejpam-4661	126	28	(	(	PUNCT
ejpam-4661	126	29	0	0	NUM
ejpam-4661	126	30	,	,	PUNCT
ejpam-4661	126	31	0	0	NUM
ejpam-4661	126	32	)	)	PUNCT
ejpam-4661	126	33	.	.	PUNCT
ejpam-4661	127	1	let	let	VERB
ejpam-4661	127	2	u	u	PRON
ejpam-4661	127	3	=	=	PUNCT
ejpam-4661	127	4	x−	x−	PROPN
ejpam-4661	127	5	β+1	β+1	NUM
ejpam-4661	127	6	2β	2β	NOUN
ejpam-4661	127	7	and	and	CCONJ
ejpam-4661	127	8	v	v	NOUN
ejpam-4661	127	9	=	=	SYM
ejpam-4661	127	10	y−	y−	NOUN
ejpam-4661	127	11	2γβ	2γβ	NOUN
ejpam-4661	127	12	1−β	1−β	NUM
ejpam-4661	127	13	.	.	PUNCT
ejpam-4661	128	1	then	then	ADV
ejpam-4661	128	2	the	the	DET
ejpam-4661	128	3	new	new	ADJ
ejpam-4661	128	4	system	system	NOUN
ejpam-4661	128	5	s.	s.	PROPN
ejpam-4661	128	6	kapcak	kapcak	PROPN
ejpam-4661	128	7	/	/	SYM
ejpam-4661	128	8	eur	eur	PROPN
ejpam-4661	128	9	.	.	PUNCT
ejpam-4661	129	1	j.	j.	PROPN
ejpam-4661	129	2	pure	pure	PROPN
ejpam-4661	129	3	appl	appl	PROPN
ejpam-4661	129	4	.	.	PROPN
ejpam-4661	129	5	math	math	PROPN
ejpam-4661	129	6	,	,	PUNCT
ejpam-4661	129	7	16	16	NUM
ejpam-4661	129	8	(	(	PUNCT
ejpam-4661	129	9	1	1	NUM
ejpam-4661	129	10	)	)	PUNCT
ejpam-4661	129	11	(	(	PUNCT
ejpam-4661	129	12	2023	2023	NUM
ejpam-4661	129	13	)	)	PUNCT
ejpam-4661	129	14	,	,	PUNCT
ejpam-4661	129	15	71	71	NUM
ejpam-4661	129	16	-	-	SYM
ejpam-4661	129	17	83	83	NUM
ejpam-4661	129	18	79	79	NUM
ejpam-4661	129	19	table	table	NOUN
ejpam-4661	129	20	2	2	NUM
ejpam-4661	129	21	:	:	PUNCT
ejpam-4661	129	22	(	(	PUNCT
ejpam-4661	129	23	γ	γ	X
ejpam-4661	129	24	=	=	NOUN
ejpam-4661	129	25	0.26	0.26	NUM
ejpam-4661	129	26	)	)	PUNCT
ejpam-4661	129	27	stability	stability	NOUN
ejpam-4661	129	28	of	of	ADP
ejpam-4661	129	29	the	the	DET
ejpam-4661	129	30	coexistence	coexistence	NOUN
ejpam-4661	129	31	fixed	fix	VERB
ejpam-4661	129	32	point	point	NOUN
ejpam-4661	129	33	.	.	PUNCT
ejpam-4661	130	1	α	α	X
ejpam-4661	130	2	-	-	PUNCT
ejpam-4661	130	3	β	β	NOUN
ejpam-4661	130	4	plane	plane	NOUN
ejpam-4661	130	5	phase	phase	NOUN
ejpam-4661	130	6	diagram	diagram	NOUN
ejpam-4661	130	7	is	be	AUX
ejpam-4661	130	8	ut+1	ut+1	X
ejpam-4661	130	9	=	=	SYM
ejpam-4661	130	10	(	(	PUNCT
ejpam-4661	130	11	β	β	X
ejpam-4661	130	12	+	+	NOUN
ejpam-4661	130	13	1	1	NUM
ejpam-4661	130	14	2β	2β	NOUN
ejpam-4661	130	15	+	+	CCONJ
ejpam-4661	130	16	ut	ut	PROPN
ejpam-4661	130	17	)	)	PUNCT
ejpam-4661	130	18	(	(	PUNCT
ejpam-4661	130	19	α−	α−	ADP
ejpam-4661	130	20	(	(	PUNCT
ejpam-4661	130	21	α−	α−	ADP
ejpam-4661	130	22	1)β	1)β	NUM
ejpam-4661	130	23	(	(	PUNCT
ejpam-4661	130	24	β	β	X
ejpam-4661	130	25	+	+	NOUN
ejpam-4661	130	26	1	1	NUM
ejpam-4661	130	27	2β	2β	NOUN
ejpam-4661	130	28	+	+	CCONJ
ejpam-4661	130	29	ut	ut	PROPN
ejpam-4661	130	30	)	)	PUNCT
ejpam-4661	130	31	)	)	PUNCT
ejpam-4661	131	1	−	−	PROPN
ejpam-4661	131	2	(	(	PUNCT
ejpam-4661	131	3	β	β	X
ejpam-4661	131	4	+	+	NOUN
ejpam-4661	131	5	1	1	NUM
ejpam-4661	131	6	2β	2β	NOUN
ejpam-4661	131	7	+	+	CCONJ
ejpam-4661	131	8	ut	ut	PROPN
ejpam-4661	131	9	)	)	PUNCT
ejpam-4661	131	10	(	(	PUNCT
ejpam-4661	131	11	2βγ	2βγ	NOUN
ejpam-4661	131	12	1−	1−	NUM
ejpam-4661	131	13	β	β	X
ejpam-4661	131	14	+	+	NUM
ejpam-4661	131	15	vt	vt	PROPN
ejpam-4661	131	16	)	)	PUNCT
ejpam-4661	132	1	−	−	PROPN
ejpam-4661	132	2	β	β	NOUN
ejpam-4661	132	3	+	+	CCONJ
ejpam-4661	132	4	1	1	NUM
ejpam-4661	132	5	2β	2β	NOUN
ejpam-4661	132	6	,	,	PUNCT
ejpam-4661	132	7	vt+1	vt+1	X
ejpam-4661	132	8	=	=	PUNCT
ejpam-4661	132	9	(	(	PUNCT
ejpam-4661	132	10	β+1	β+1	NUM
ejpam-4661	132	11	2β	2β	NOUN
ejpam-4661	132	12	+	+	CCONJ
ejpam-4661	132	13	ut	ut	PROPN
ejpam-4661	132	14	)	)	PUNCT
ejpam-4661	132	15	(	(	PUNCT
ejpam-4661	132	16	2βγ	2βγ	NOUN
ejpam-4661	132	17	1−β	1−β	NUM
ejpam-4661	132	18	+	+	NUM
ejpam-4661	132	19	vt	vt	PROPN
ejpam-4661	132	20	)	)	PUNCT
ejpam-4661	132	21	2	2	NUM
ejpam-4661	132	22	(	(	PUNCT
ejpam-4661	132	23	2βγ	2βγ	NOUN
ejpam-4661	132	24	1−β	1−β	NUM
ejpam-4661	132	25	+	+	NUM
ejpam-4661	132	26	vt	vt	PROPN
ejpam-4661	132	27	)	)	PUNCT
ejpam-4661	133	1	+	+	CCONJ
ejpam-4661	133	2	γ	γ	PROPN
ejpam-4661	133	3	−	−	NOUN
ejpam-4661	133	4	2βγ	2βγ	NOUN
ejpam-4661	133	5	1−	1−	NUM
ejpam-4661	133	6	β	β	X
ejpam-4661	133	7	.	.	PUNCT
ejpam-4661	134	1	(	(	PUNCT
ejpam-4661	134	2	9	9	X
ejpam-4661	134	3	)	)	PUNCT
ejpam-4661	134	4	s.	s.	PROPN
ejpam-4661	134	5	kapcak	kapcak	PROPN
ejpam-4661	134	6	/	/	SYM
ejpam-4661	134	7	eur	eur	PROPN
ejpam-4661	134	8	.	.	PUNCT
ejpam-4661	135	1	j.	j.	PROPN
ejpam-4661	135	2	pure	pure	PROPN
ejpam-4661	135	3	appl	appl	PROPN
ejpam-4661	135	4	.	.	PROPN
ejpam-4661	135	5	math	math	PROPN
ejpam-4661	135	6	,	,	PUNCT
ejpam-4661	135	7	16	16	NUM
ejpam-4661	135	8	(	(	PUNCT
ejpam-4661	135	9	1	1	NUM
ejpam-4661	135	10	)	)	PUNCT
ejpam-4661	135	11	(	(	PUNCT
ejpam-4661	135	12	2023	2023	NUM
ejpam-4661	135	13	)	)	PUNCT
ejpam-4661	135	14	,	,	PUNCT
ejpam-4661	135	15	71	71	NUM
ejpam-4661	135	16	-	-	SYM
ejpam-4661	135	17	83	83	NUM
ejpam-4661	135	18	80	80	NUM
ejpam-4661	135	19	the	the	DET
ejpam-4661	135	20	jacobian	jacobian	ADJ
ejpam-4661	135	21	matrix	matrix	NOUN
ejpam-4661	135	22	of	of	ADP
ejpam-4661	135	23	the	the	DET
ejpam-4661	135	24	system	system	NOUN
ejpam-4661	135	25	(	(	PUNCT
ejpam-4661	135	26	9	9	NUM
ejpam-4661	135	27	)	)	PUNCT
ejpam-4661	135	28	at	at	ADP
ejpam-4661	135	29	(	(	PUNCT
ejpam-4661	135	30	0	0	NUM
ejpam-4661	135	31	,	,	PUNCT
ejpam-4661	135	32	0	0	NUM
ejpam-4661	135	33	)	)	PUNCT
ejpam-4661	135	34	is	be	AUX
ejpam-4661	135	35	j̃+	j̃+	PROPN
ejpam-4661	135	36	0	0	PUNCT
ejpam-4661	136	1	=	=	SYM
ejpam-4661	136	2	(	(	PUNCT
ejpam-4661	136	3	a	a	DET
ejpam-4661	136	4	b	b	NOUN
ejpam-4661	136	5	c	c	NOUN
ejpam-4661	136	6	d	d	NOUN
ejpam-4661	136	7	)	)	PUNCT
ejpam-4661	136	8	=	=	PUNCT
ejpam-4661	136	9	(	(	PUNCT
ejpam-4661	136	10	1	1	NUM
ejpam-4661	136	11	2(β	2(β	NUM
ejpam-4661	136	12	−	−	NOUN
ejpam-4661	136	13	α(β	α(β	PROPN
ejpam-4661	136	14	+	+	CCONJ
ejpam-4661	136	15	1	1	NUM
ejpam-4661	136	16	)	)	PUNCT
ejpam-4661	136	17	+	+	CCONJ
ejpam-4661	136	18	3	3	X
ejpam-4661	136	19	)	)	PUNCT
ejpam-4661	136	20	−β+1	−β+1	ADJ
ejpam-4661	136	21	2β	2β	NOUN
ejpam-4661	136	22	−	−	NOUN
ejpam-4661	136	23	(	(	PUNCT
ejpam-4661	136	24	α−1)(β−1)β	α−1)(β−1)β	NOUN
ejpam-4661	136	25	β+1	β+1	NUM
ejpam-4661	136	26	2	2	NUM
ejpam-4661	136	27	β+1	β+1	NUM
ejpam-4661	136	28	)	)	PUNCT
ejpam-4661	136	29	.	.	PUNCT
ejpam-4661	137	1	now	now	ADV
ejpam-4661	137	2	we	we	PRON
ejpam-4661	137	3	can	can	AUX
ejpam-4661	137	4	write	write	VERB
ejpam-4661	137	5	the	the	DET
ejpam-4661	137	6	equations	equation	NOUN
ejpam-4661	137	7	in	in	ADP
ejpam-4661	137	8	system	system	NOUN
ejpam-4661	137	9	(	(	PUNCT
ejpam-4661	137	10	9	9	NUM
ejpam-4661	137	11	)	)	PUNCT
ejpam-4661	137	12	as	as	ADP
ejpam-4661	137	13	ut+1	ut+1	X
ejpam-4661	137	14	=	=	PUNCT
ejpam-4661	137	15	aut	aut	PROPN
ejpam-4661	138	1	+	+	PROPN
ejpam-4661	138	2	bvt	bvt	PROPN
ejpam-4661	138	3	+	+	CCONJ
ejpam-4661	138	4	f̃(ut	f̃(ut	PROPN
ejpam-4661	138	5	,	,	PUNCT
ejpam-4661	138	6	vt	vt	PROPN
ejpam-4661	138	7	)	)	PUNCT
ejpam-4661	138	8	,	,	PUNCT
ejpam-4661	138	9	vt+1	vt+1	PROPN
ejpam-4661	138	10	=	=	PRON
ejpam-4661	138	11	cut	cut	VERB
ejpam-4661	138	12	+	+	PROPN
ejpam-4661	138	13	dvt	dvt	PROPN
ejpam-4661	138	14	+	+	ADJ
ejpam-4661	138	15	g̃(ut	g̃(ut	NOUN
ejpam-4661	138	16	,	,	PUNCT
ejpam-4661	138	17	vt	vt	PROPN
ejpam-4661	138	18	)	)	PUNCT
ejpam-4661	138	19	,	,	PUNCT
ejpam-4661	138	20	(	(	PUNCT
ejpam-4661	138	21	10	10	NUM
ejpam-4661	138	22	)	)	PUNCT
ejpam-4661	138	23	where	where	SCONJ
ejpam-4661	138	24	f̃(ut	f̃(ut	PROPN
ejpam-4661	138	25	,	,	PUNCT
ejpam-4661	138	26	vt	vt	PROPN
ejpam-4661	138	27	)	)	PUNCT
ejpam-4661	138	28	and	and	CCONJ
ejpam-4661	138	29	g̃(ut	g̃(ut	PROPN
ejpam-4661	138	30	,	,	PUNCT
ejpam-4661	138	31	vt	vt	PROPN
ejpam-4661	138	32	)	)	PUNCT
ejpam-4661	138	33	are	be	AUX
ejpam-4661	138	34	the	the	DET
ejpam-4661	138	35	rest	rest	NOUN
ejpam-4661	138	36	of	of	ADP
ejpam-4661	138	37	the	the	DET
ejpam-4661	138	38	expressions	expression	NOUN
ejpam-4661	138	39	.	.	PUNCT
ejpam-4661	139	1	let	let	VERB
ejpam-4661	139	2	us	we	PRON
ejpam-4661	139	3	assume	assume	VERB
ejpam-4661	139	4	that	that	SCONJ
ejpam-4661	139	5	the	the	DET
ejpam-4661	139	6	map	map	NOUN
ejpam-4661	139	7	h	h	NOUN
ejpam-4661	139	8	,	,	PUNCT
ejpam-4661	139	9	which	which	PRON
ejpam-4661	139	10	represents	represent	VERB
ejpam-4661	139	11	a	a	DET
ejpam-4661	139	12	center	center	NOUN
ejpam-4661	139	13	manifold	manifold	NOUN
ejpam-4661	139	14	,	,	PUNCT
ejpam-4661	139	15	takes	take	VERB
ejpam-4661	139	16	the	the	DET
ejpam-4661	139	17	form	form	NOUN
ejpam-4661	139	18	h(u	h(u	PROPN
ejpam-4661	139	19	)	)	PUNCT
ejpam-4661	140	1	=	=	PUNCT
ejpam-4661	140	2	(	(	PUNCT
ejpam-4661	140	3	β	β	X
ejpam-4661	140	4	−	−	PROPN
ejpam-4661	140	5	αβ)u+	αβ)u+	NOUN
ejpam-4661	140	6	au2	au2	NOUN
ejpam-4661	140	7	+	+	CCONJ
ejpam-4661	140	8	bu3	bu3	NOUN
ejpam-4661	140	9	+	+	NOUN
ejpam-4661	140	10	o(u4	o(u4	NOUN
ejpam-4661	140	11	)	)	PUNCT
ejpam-4661	140	12	,	,	PUNCT
ejpam-4661	140	13	a	a	DET
ejpam-4661	140	14	,	,	PUNCT
ejpam-4661	140	15	b	b	PROPN
ejpam-4661	140	16	∈	∈	PROPN
ejpam-4661	140	17	r.	r.	NOUN
ejpam-4661	140	18	now	now	ADV
ejpam-4661	140	19	we	we	PRON
ejpam-4661	140	20	have	have	VERB
ejpam-4661	140	21	to	to	PART
ejpam-4661	140	22	compute	compute	VERB
ejpam-4661	140	23	the	the	DET
ejpam-4661	140	24	constants	constant	NOUN
ejpam-4661	140	25	a	a	PRON
ejpam-4661	140	26	and	and	CCONJ
ejpam-4661	140	27	b.	b.	X
ejpam-4661	141	1	the	the	DET
ejpam-4661	141	2	function	function	NOUN
ejpam-4661	141	3	h	h	NOUN
ejpam-4661	141	4	must	must	AUX
ejpam-4661	141	5	satisfy	satisfy	VERB
ejpam-4661	141	6	the	the	DET
ejpam-4661	141	7	center	center	NOUN
ejpam-4661	141	8	manifold	manifold	ADJ
ejpam-4661	141	9	equation	equation	NOUN
ejpam-4661	141	10	h(au+bh(u	h(au+bh(u	PROPN
ejpam-4661	141	11	)	)	PUNCT
ejpam-4661	142	1	+	+	CCONJ
ejpam-4661	142	2	f̃(u	f̃(u	PROPN
ejpam-4661	142	3	,	,	PUNCT
ejpam-4661	142	4	h(u)))−	h(u)))−	PROPN
ejpam-4661	142	5	cu−dh(u)−	cu−dh(u)−	PROPN
ejpam-4661	142	6	g̃(u	g̃(u	PROPN
ejpam-4661	142	7	,	,	PUNCT
ejpam-4661	142	8	h(u	h(u	PROPN
ejpam-4661	142	9	)	)	PUNCT
ejpam-4661	142	10	)	)	PUNCT
ejpam-4661	143	1	=	=	PUNCT
ejpam-4661	143	2	0	0	X
ejpam-4661	143	3	.	.	PUNCT
ejpam-4661	144	1	(	(	PUNCT
ejpam-4661	144	2	11	11	NUM
ejpam-4661	144	3	)	)	PUNCT
ejpam-4661	144	4	the	the	DET
ejpam-4661	144	5	taylor	taylor	PROPN
ejpam-4661	144	6	series	series	PROPN
ejpam-4661	144	7	expansions	expansion	NOUN
ejpam-4661	144	8	,	,	PUNCT
ejpam-4661	144	9	at	at	ADP
ejpam-4661	144	10	the	the	DET
ejpam-4661	144	11	point	point	NOUN
ejpam-4661	144	12	u	u	NOUN
ejpam-4661	144	13	=	=	NOUN
ejpam-4661	144	14	0	0	NUM
ejpam-4661	144	15	,	,	PUNCT
ejpam-4661	144	16	are	be	AUX
ejpam-4661	144	17	evaluated	evaluate	VERB
ejpam-4661	144	18	for	for	ADP
ejpam-4661	144	19	the	the	DET
ejpam-4661	144	20	equation	equation	NOUN
ejpam-4661	144	21	above	above	ADV
ejpam-4661	144	22	.	.	PUNCT
ejpam-4661	145	1	equating	equate	VERB
ejpam-4661	145	2	the	the	DET
ejpam-4661	145	3	coefficients	coefficient	NOUN
ejpam-4661	145	4	of	of	ADP
ejpam-4661	145	5	the	the	DET
ejpam-4661	145	6	series	series	NOUN
ejpam-4661	145	7	and	and	CCONJ
ejpam-4661	145	8	using	use	VERB
ejpam-4661	145	9	the	the	DET
ejpam-4661	145	10	equation	equation	NOUN
ejpam-4661	145	11	∆	∆	X
ejpam-4661	145	12	=	=	SYM
ejpam-4661	145	13	0	0	NUM
ejpam-4661	145	14	,	,	PUNCT
ejpam-4661	145	15	after	after	ADP
ejpam-4661	145	16	some	some	DET
ejpam-4661	145	17	manipulations	manipulation	NOUN
ejpam-4661	145	18	,	,	PUNCT
ejpam-4661	145	19	we	we	PRON
ejpam-4661	145	20	obtain	obtain	VERB
ejpam-4661	145	21	a	a	DET
ejpam-4661	145	22	=	=	SYM
ejpam-4661	145	23	−	−	PROPN
ejpam-4661	145	24	4(α−	4(α−	NUM
ejpam-4661	145	25	1)β2	1)β2	NUM
ejpam-4661	145	26	α(β	α(β	PROPN
ejpam-4661	145	27	+	+	CCONJ
ejpam-4661	145	28	1)2	1)2	NUM
ejpam-4661	145	29	−	−	NOUN
ejpam-4661	145	30	β2	β2	NOUN
ejpam-4661	145	31	−	−	PROPN
ejpam-4661	145	32	3	3	NUM
ejpam-4661	145	33	b	b	NOUN
ejpam-4661	145	34	=	=	SYM
ejpam-4661	145	35	16β3	16β3	NUM
ejpam-4661	145	36	(	(	PUNCT
ejpam-4661	145	37	α3(β	α3(β	PROPN
ejpam-4661	145	38	+	+	NUM
ejpam-4661	145	39	1)3	1)3	NUM
ejpam-4661	145	40	−	−	PROPN
ejpam-4661	145	41	α2(β	α2(β	PROPN
ejpam-4661	146	1	+	+	CCONJ
ejpam-4661	147	1	1)(3β(β	1)(3β(β	NUM
ejpam-4661	148	1	+	+	CCONJ
ejpam-4661	148	2	1	1	X
ejpam-4661	148	3	)	)	PUNCT
ejpam-4661	148	4	+	+	CCONJ
ejpam-4661	148	5	4	4	X
ejpam-4661	148	6	)	)	PUNCT
ejpam-4661	148	7	+	+	CCONJ
ejpam-4661	148	8	α	α	PROPN
ejpam-4661	148	9	(	(	PUNCT
ejpam-4661	148	10	3β	3β	NUM
ejpam-4661	148	11	(	(	PUNCT
ejpam-4661	148	12	β2	β2	NOUN
ejpam-4661	148	13	+	+	NOUN
ejpam-4661	148	14	β	β	X
ejpam-4661	149	1	+	+	CCONJ
ejpam-4661	149	2	1	1	NUM
ejpam-4661	149	3	)	)	PUNCT
ejpam-4661	149	4	+	+	CCONJ
ejpam-4661	149	5	7	7	X
ejpam-4661	149	6	)	)	PUNCT
ejpam-4661	149	7	−	−	NOUN
ejpam-4661	149	8	β3	β3	PROPN
ejpam-4661	149	9	+	+	NUM
ejpam-4661	149	10	β	β	X
ejpam-4661	149	11	−	−	NOUN
ejpam-4661	149	12	4	4	NUM
ejpam-4661	149	13	)	)	PUNCT
ejpam-4661	149	14	(	(	PUNCT
ejpam-4661	149	15	α(β	α(β	PROPN
ejpam-4661	149	16	+	+	CCONJ
ejpam-4661	149	17	1)2	1)2	NUM
ejpam-4661	149	18	−	−	NOUN
ejpam-4661	149	19	β2	β2	NOUN
ejpam-4661	149	20	−	−	PROPN
ejpam-4661	149	21	3)3	3)3	NUM
ejpam-4661	149	22	.	.	PUNCT
ejpam-4661	150	1	thus	thus	ADV
ejpam-4661	150	2	on	on	ADP
ejpam-4661	150	3	the	the	DET
ejpam-4661	150	4	center	center	NOUN
ejpam-4661	150	5	manifold	manifold	ADJ
ejpam-4661	150	6	v	v	ADP
ejpam-4661	150	7	=	=	SYM
ejpam-4661	150	8	h(u	h(u	PROPN
ejpam-4661	150	9	)	)	PUNCT
ejpam-4661	150	10	we	we	PRON
ejpam-4661	150	11	find	find	VERB
ejpam-4661	150	12	the	the	DET
ejpam-4661	150	13	map	map	NOUN
ejpam-4661	150	14	p	p	X
ejpam-4661	150	15	(	(	PUNCT
ejpam-4661	150	16	u	u	NOUN
ejpam-4661	150	17	)	)	PUNCT
ejpam-4661	150	18	.	.	PUNCT
ejpam-4661	151	1	because	because	SCONJ
ejpam-4661	151	2	of	of	ADP
ejpam-4661	151	3	the	the	DET
ejpam-4661	151	4	lengthy	lengthy	ADJ
ejpam-4661	151	5	expressions	expression	NOUN
ejpam-4661	151	6	we	we	PRON
ejpam-4661	151	7	omit	omit	VERB
ejpam-4661	151	8	it	it	PRON
ejpam-4661	151	9	here	here	ADV
ejpam-4661	151	10	.	.	PUNCT
ejpam-4661	152	1	calculations	calculation	NOUN
ejpam-4661	152	2	show	show	VERB
ejpam-4661	152	3	that	that	SCONJ
ejpam-4661	152	4	p	p	PROPN
ejpam-4661	152	5	′(0	′(0	PROPN
ejpam-4661	152	6	)	)	PUNCT
ejpam-4661	152	7	=	=	SYM
ejpam-4661	153	1	1	1	X
ejpam-4661	153	2	.	.	PUNCT
ejpam-4661	154	1	since	since	SCONJ
ejpam-4661	154	2	0	0	NUM
ejpam-4661	154	3	<	<	X
ejpam-4661	154	4	β	β	X
ejpam-4661	154	5	<	<	X
ejpam-4661	154	6	1	1	NUM
ejpam-4661	154	7	and	and	CCONJ
ejpam-4661	154	8	|λ2|	|λ2|	PRON
ejpam-4661	154	9	<	<	X
ejpam-4661	154	10	1	1	NUM
ejpam-4661	154	11	,	,	PUNCT
ejpam-4661	154	12	we	we	PRON
ejpam-4661	154	13	have	have	VERB
ejpam-4661	154	14	α	α	NOUN
ejpam-4661	154	15	>	>	X
ejpam-4661	154	16	1	1	NUM
ejpam-4661	154	17	and	and	CCONJ
ejpam-4661	154	18	α(β	α(β	PROPN
ejpam-4661	154	19	+	+	CCONJ
ejpam-4661	155	1	1)2	1)2	NUM
ejpam-4661	155	2	>	>	X
ejpam-4661	155	3	β2	β2	NOUN
ejpam-4661	155	4	+	+	CCONJ
ejpam-4661	155	5	3	3	X
ejpam-4661	155	6	.	.	X
ejpam-4661	156	1	therefore	therefore	ADV
ejpam-4661	156	2	,	,	PUNCT
ejpam-4661	156	3	p	p	NOUN
ejpam-4661	156	4	′′(0	′′(0	X
ejpam-4661	156	5	)	)	PUNCT
ejpam-4661	156	6	=	=	SYM
ejpam-4661	156	7	4(α−	4(α−	NUM
ejpam-4661	157	1	1)β(β	1)β(β	NUM
ejpam-4661	157	2	+	+	CCONJ
ejpam-4661	157	3	1	1	X
ejpam-4661	157	4	)	)	PUNCT
ejpam-4661	157	5	α(β	α(β	PROPN
ejpam-4661	157	6	+	+	CCONJ
ejpam-4661	157	7	1)2	1)2	NUM
ejpam-4661	157	8	−	−	NOUN
ejpam-4661	157	9	β2	β2	NOUN
ejpam-4661	157	10	−	−	PROPN
ejpam-4661	157	11	3	3	NUM
ejpam-4661	157	12	>	>	X
ejpam-4661	157	13	0	0	NUM
ejpam-4661	157	14	.	.	PUNCT
ejpam-4661	158	1	hence	hence	ADV
ejpam-4661	158	2	,	,	PUNCT
ejpam-4661	158	3	for	for	ADP
ejpam-4661	158	4	the	the	DET
ejpam-4661	158	5	map	map	NOUN
ejpam-4661	158	6	p	p	NOUN
ejpam-4661	158	7	,	,	PUNCT
ejpam-4661	158	8	the	the	DET
ejpam-4661	158	9	origin	origin	NOUN
ejpam-4661	158	10	is	be	AUX
ejpam-4661	158	11	semistable	semistable	ADJ
ejpam-4661	158	12	from	from	ADP
ejpam-4661	158	13	the	the	DET
ejpam-4661	158	14	left	left	NOUN
ejpam-4661	158	15	.	.	PUNCT
ejpam-4661	159	1	now	now	ADV
ejpam-4661	159	2	,	,	PUNCT
ejpam-4661	159	3	we	we	PRON
ejpam-4661	159	4	are	be	AUX
ejpam-4661	159	5	going	go	VERB
ejpam-4661	159	6	to	to	PART
ejpam-4661	159	7	find	find	VERB
ejpam-4661	159	8	the	the	DET
ejpam-4661	159	9	stable	stable	ADJ
ejpam-4661	159	10	manifold	manifold	NOUN
ejpam-4661	159	11	,	,	PUNCT
ejpam-4661	159	12	which	which	PRON
ejpam-4661	159	13	exists	exist	VERB
ejpam-4661	159	14	when	when	SCONJ
ejpam-4661	159	15	|λ2|	|λ2|	NOUN
ejpam-4661	159	16	<	<	X
ejpam-4661	159	17	1	1	NUM
ejpam-4661	159	18	or	or	CCONJ
ejpam-4661	159	19	−α(β	−α(β	NOUN
ejpam-4661	160	1	+	+	CCONJ
ejpam-4661	160	2	1)2	1)2	NUM
ejpam-4661	160	3	+	+	CCONJ
ejpam-4661	160	4	β2	β2	NOUN
ejpam-4661	160	5	+	+	CCONJ
ejpam-4661	160	6	2β	2β	NOUN
ejpam-4661	160	7	+	+	CCONJ
ejpam-4661	160	8	5	5	NUM
ejpam-4661	160	9	<	<	NOUN
ejpam-4661	160	10	2(β	2(β	NUM
ejpam-4661	160	11	+	+	CCONJ
ejpam-4661	160	12	1	1	NUM
ejpam-4661	160	13	)	)	PUNCT
ejpam-4661	160	14	.	.	PUNCT
ejpam-4661	161	1	s.	s.	PROPN
ejpam-4661	161	2	kapcak	kapcak	PROPN
ejpam-4661	161	3	/	/	SYM
ejpam-4661	161	4	eur	eur	PROPN
ejpam-4661	161	5	.	.	PUNCT
ejpam-4661	162	1	j.	j.	PROPN
ejpam-4661	162	2	pure	pure	PROPN
ejpam-4661	162	3	appl	appl	PROPN
ejpam-4661	162	4	.	.	PROPN
ejpam-4661	162	5	math	math	PROPN
ejpam-4661	162	6	,	,	PUNCT
ejpam-4661	162	7	16	16	NUM
ejpam-4661	162	8	(	(	PUNCT
ejpam-4661	162	9	1	1	NUM
ejpam-4661	162	10	)	)	PUNCT
ejpam-4661	162	11	(	(	PUNCT
ejpam-4661	162	12	2023	2023	NUM
ejpam-4661	162	13	)	)	PUNCT
ejpam-4661	162	14	,	,	PUNCT
ejpam-4661	162	15	71	71	NUM
ejpam-4661	162	16	-	-	SYM
ejpam-4661	162	17	83	83	NUM
ejpam-4661	162	18	81	81	NUM
ejpam-4661	162	19	since	since	SCONJ
ejpam-4661	162	20	the	the	DET
ejpam-4661	162	21	stable	stable	ADJ
ejpam-4661	162	22	manifold	manifold	NOUN
ejpam-4661	162	23	is	be	AUX
ejpam-4661	162	24	tangent	tangent	NOUN
ejpam-4661	162	25	to	to	ADP
ejpam-4661	162	26	the	the	DET
ejpam-4661	162	27	eigenvector	eigenvector	NOUN
ejpam-4661	162	28	at	at	ADP
ejpam-4661	162	29	the	the	DET
ejpam-4661	162	30	point	point	NOUN
ejpam-4661	162	31	,	,	PUNCT
ejpam-4661	162	32	let	let	VERB
ejpam-4661	162	33	us	we	PRON
ejpam-4661	162	34	take	take	VERB
ejpam-4661	162	35	h(u	h(u	NOUN
ejpam-4661	162	36	)	)	PUNCT
ejpam-4661	163	1	=	=	PUNCT
ejpam-4661	164	1	2(β	2(β	NUM
ejpam-4661	164	2	−	−	NUM
ejpam-4661	164	3	1)β	1)β	NUM
ejpam-4661	164	4	(	(	PUNCT
ejpam-4661	164	5	β	β	X
ejpam-4661	164	6	+	+	X
ejpam-4661	164	7	1)2	1)2	NUM
ejpam-4661	164	8	u+	u+	NOUN
ejpam-4661	164	9	au2	au2	NOUN
ejpam-4661	164	10	+	+	CCONJ
ejpam-4661	164	11	bu3	bu3	NOUN
ejpam-4661	164	12	+	+	NOUN
ejpam-4661	164	13	o(u4	o(u4	NOUN
ejpam-4661	164	14	)	)	PUNCT
ejpam-4661	164	15	,	,	PUNCT
ejpam-4661	164	16	a	a	DET
ejpam-4661	164	17	,	,	PUNCT
ejpam-4661	164	18	b	b	PROPN
ejpam-4661	164	19	∈	∈	PROPN
ejpam-4661	164	20	r.	r.	NOUN
ejpam-4661	164	21	this	this	DET
ejpam-4661	164	22	map	map	NOUN
ejpam-4661	164	23	must	must	AUX
ejpam-4661	164	24	satisfy	satisfy	VERB
ejpam-4661	164	25	the	the	DET
ejpam-4661	164	26	centre	centre	NOUN
ejpam-4661	164	27	manifold	manifold	ADJ
ejpam-4661	164	28	equation	equation	NOUN
ejpam-4661	164	29	(	(	PUNCT
ejpam-4661	164	30	11	11	NUM
ejpam-4661	164	31	)	)	PUNCT
ejpam-4661	164	32	.	.	PUNCT
ejpam-4661	165	1	we	we	PRON
ejpam-4661	165	2	calculate	calculate	VERB
ejpam-4661	165	3	map	map	VERB
ejpam-4661	165	4	q	q	PROPN
ejpam-4661	165	5	on	on	ADP
ejpam-4661	165	6	the	the	DET
ejpam-4661	165	7	stable	stable	ADJ
ejpam-4661	165	8	manifold	manifold	NOUN
ejpam-4661	165	9	and	and	CCONJ
ejpam-4661	165	10	found	find	VERB
ejpam-4661	165	11	that	that	SCONJ
ejpam-4661	165	12	q′(0	q′(0	PROPN
ejpam-4661	165	13	)	)	PUNCT
ejpam-4661	165	14	=	=	SYM
ejpam-4661	165	15	−α(β	−α(β	NOUN
ejpam-4661	165	16	+	+	X
ejpam-4661	165	17	1)2	1)2	NUM
ejpam-4661	165	18	+	+	CCONJ
ejpam-4661	165	19	β2	β2	NOUN
ejpam-4661	165	20	+	+	CCONJ
ejpam-4661	165	21	2β	2β	NOUN
ejpam-4661	165	22	+	+	CCONJ
ejpam-4661	165	23	5	5	NUM
ejpam-4661	165	24	2(β	2(β	NUM
ejpam-4661	165	25	+	+	CCONJ
ejpam-4661	165	26	1	1	NUM
ejpam-4661	165	27	)	)	PUNCT
ejpam-4661	165	28	.	.	PUNCT
ejpam-4661	166	1	because	because	SCONJ
ejpam-4661	166	2	of	of	ADP
ejpam-4661	166	3	the	the	DET
ejpam-4661	166	4	long	long	ADJ
ejpam-4661	166	5	output	output	NOUN
ejpam-4661	166	6	of	of	ADP
ejpam-4661	166	7	the	the	DET
ejpam-4661	166	8	computations	computation	NOUN
ejpam-4661	166	9	we	we	PRON
ejpam-4661	166	10	omit	omit	VERB
ejpam-4661	166	11	them	they	PRON
ejpam-4661	166	12	here	here	ADV
ejpam-4661	166	13	.	.	PUNCT
ejpam-4661	167	1	stable	stable	ADJ
ejpam-4661	167	2	manifold	manifold	ADJ
ejpam-4661	167	3	center	center	NOUN
ejpam-4661	167	4	m	m	PROPN
ejpam-4661	167	5	anifold	anifold	VERB
ejpam-4661	167	6	1.6	1.6	NUM
ejpam-4661	167	7	1.7	1.7	NUM
ejpam-4661	167	8	1.8	1.8	NUM
ejpam-4661	167	9	1.9	1.9	NUM
ejpam-4661	167	10	2.0	2.0	NUM
ejpam-4661	167	11	x	x	SYM
ejpam-4661	167	12	0.45	0.45	NUM
ejpam-4661	167	13	0.50	0.50	NUM
ejpam-4661	167	14	0.55	0.55	NUM
ejpam-4661	167	15	0.60	0.60	NUM
ejpam-4661	167	16	0.65	0.65	NUM
ejpam-4661	167	17	0.70	0.70	NUM
ejpam-4661	167	18	0.75	0.75	NUM
ejpam-4661	167	19	y	y	PROPN
ejpam-4661	167	20	figure	figure	NOUN
ejpam-4661	167	21	4	4	NUM
ejpam-4661	167	22	:	:	PUNCT
ejpam-4661	167	23	(	(	PUNCT
ejpam-4661	167	24	α	α	X
ejpam-4661	167	25	=	=	SYM
ejpam-4661	167	26	2.75	2.75	NUM
ejpam-4661	167	27	and	and	CCONJ
ejpam-4661	167	28	β	β	X
ejpam-4661	167	29	=	=	SYM
ejpam-4661	167	30	0.4	0.4	NUM
ejpam-4661	167	31	)	)	PUNCT
ejpam-4661	167	32	phase	phase	NOUN
ejpam-4661	167	33	diagram	diagram	NOUN
ejpam-4661	167	34	of	of	ADP
ejpam-4661	167	35	system	system	NOUN
ejpam-4661	167	36	(	(	PUNCT
ejpam-4661	167	37	4	4	NUM
ejpam-4661	167	38	)	)	PUNCT
ejpam-4661	167	39	with	with	ADP
ejpam-4661	167	40	the	the	DET
ejpam-4661	167	41	invariant	invariant	ADJ
ejpam-4661	167	42	manifolds	manifold	NOUN
ejpam-4661	167	43	.	.	PUNCT
ejpam-4661	168	1	stable	stable	ADJ
ejpam-4661	168	2	and	and	CCONJ
ejpam-4661	168	3	centre	centre	NOUN
ejpam-4661	168	4	manifolds	manifold	NOUN
ejpam-4661	168	5	are	be	AUX
ejpam-4661	168	6	given	give	VERB
ejpam-4661	168	7	in	in	ADP
ejpam-4661	168	8	the	the	DET
ejpam-4661	168	9	phase	phase	NOUN
ejpam-4661	168	10	diagram	diagram	NOUN
ejpam-4661	168	11	in	in	ADP
ejpam-4661	168	12	figure	figure	NOUN
ejpam-4661	168	13	4	4	NUM
ejpam-4661	168	14	for	for	ADP
ejpam-4661	168	15	the	the	DET
ejpam-4661	168	16	case	case	NOUN
ejpam-4661	168	17	∆	∆	PUNCT
ejpam-4661	169	1	=	=	SYM
ejpam-4661	170	1	0	0	X
ejpam-4661	170	2	.	.	PUNCT
ejpam-4661	171	1	the	the	DET
ejpam-4661	171	2	dashed	dash	VERB
ejpam-4661	171	3	curve	curve	NOUN
ejpam-4661	171	4	is	be	AUX
ejpam-4661	171	5	the	the	DET
ejpam-4661	171	6	centre	centre	NOUN
ejpam-4661	171	7	manifold	manifold	ADJ
ejpam-4661	171	8	for	for	ADP
ejpam-4661	171	9	which	which	PRON
ejpam-4661	171	10	the	the	DET
ejpam-4661	171	11	fixed	fix	VERB
ejpam-4661	171	12	point	point	NOUN
ejpam-4661	171	13	is	be	AUX
ejpam-4661	171	14	semi	semi	ADJ
ejpam-4661	171	15	-	-	ADJ
ejpam-4661	171	16	stable	stable	ADJ
ejpam-4661	171	17	.	.	PUNCT
ejpam-4661	172	1	the	the	DET
ejpam-4661	172	2	solid	solid	ADJ
ejpam-4661	172	3	curve	curve	NOUN
ejpam-4661	172	4	is	be	AUX
ejpam-4661	172	5	the	the	DET
ejpam-4661	172	6	stable	stable	ADJ
ejpam-4661	172	7	manifold	manifold	NOUN
ejpam-4661	172	8	.	.	PUNCT
ejpam-4661	173	1	an	an	DET
ejpam-4661	173	2	orbit	orbit	NOUN
ejpam-4661	173	3	approaching	approach	VERB
ejpam-4661	173	4	the	the	DET
ejpam-4661	173	5	fixed	fix	VERB
ejpam-4661	173	6	point	point	NOUN
ejpam-4661	173	7	is	be	AUX
ejpam-4661	173	8	also	also	ADV
ejpam-4661	173	9	shown	show	VERB
ejpam-4661	173	10	.	.	PUNCT
ejpam-4661	174	1	4	4	X
ejpam-4661	174	2	.	.	X
ejpam-4661	174	3	conclusions	conclusion	NOUN
ejpam-4661	174	4	in	in	ADP
ejpam-4661	174	5	this	this	DET
ejpam-4661	174	6	paper	paper	NOUN
ejpam-4661	174	7	,	,	PUNCT
ejpam-4661	174	8	we	we	PRON
ejpam-4661	174	9	investigated	investigate	VERB
ejpam-4661	174	10	the	the	DET
ejpam-4661	174	11	stability	stability	NOUN
ejpam-4661	174	12	of	of	ADP
ejpam-4661	174	13	a	a	DET
ejpam-4661	174	14	predator	predator	NOUN
ejpam-4661	174	15	-	-	PUNCT
ejpam-4661	174	16	prey	prey	NOUN
ejpam-4661	174	17	model	model	NOUN
ejpam-4661	174	18	with	with	ADP
ejpam-4661	174	19	refuge	refuge	NOUN
ejpam-4661	174	20	and	and	CCONJ
ejpam-4661	174	21	allee	allee	ADJ
ejpam-4661	174	22	effect	effect	NOUN
ejpam-4661	174	23	.	.	PUNCT
ejpam-4661	175	1	we	we	PRON
ejpam-4661	175	2	showed	show	VERB
ejpam-4661	175	3	that	that	SCONJ
ejpam-4661	175	4	the	the	DET
ejpam-4661	175	5	presence	presence	NOUN
ejpam-4661	175	6	of	of	ADP
ejpam-4661	175	7	a	a	DET
ejpam-4661	175	8	safe	safe	ADJ
ejpam-4661	175	9	refuge	refuge	NOUN
ejpam-4661	175	10	,	,	PUNCT
ejpam-4661	175	11	where	where	SCONJ
ejpam-4661	175	12	a	a	DET
ejpam-4661	175	13	portion	portion	NOUN
ejpam-4661	175	14	of	of	ADP
ejpam-4661	175	15	the	the	DET
ejpam-4661	175	16	host	host	NOUN
ejpam-4661	175	17	is	be	AUX
ejpam-4661	175	18	in	in	ADP
ejpam-4661	175	19	a	a	DET
ejpam-4661	175	20	safe	safe	ADJ
ejpam-4661	175	21	refuge	refuge	NOUN
ejpam-4661	175	22	from	from	ADP
ejpam-4661	175	23	predation	predation	NOUN
ejpam-4661	175	24	has	have	VERB
ejpam-4661	175	25	a	a	DET
ejpam-4661	175	26	stabilizing	stabilize	VERB
ejpam-4661	175	27	effect	effect	NOUN
ejpam-4661	175	28	on	on	ADP
ejpam-4661	175	29	the	the	DET
ejpam-4661	175	30	model	model	NOUN
ejpam-4661	175	31	.	.	PUNCT
ejpam-4661	176	1	the	the	DET
ejpam-4661	176	2	conditions	condition	NOUN
ejpam-4661	176	3	references	reference	VERB
ejpam-4661	176	4	82	82	NUM
ejpam-4661	176	5	for	for	ADP
ejpam-4661	176	6	the	the	DET
ejpam-4661	176	7	existence	existence	NOUN
ejpam-4661	176	8	of	of	ADP
ejpam-4661	176	9	the	the	DET
ejpam-4661	176	10	fixed	fix	VERB
ejpam-4661	176	11	points	point	NOUN
ejpam-4661	176	12	are	be	AUX
ejpam-4661	176	13	found	find	VERB
ejpam-4661	176	14	.	.	PUNCT
ejpam-4661	177	1	we	we	PRON
ejpam-4661	177	2	also	also	ADV
ejpam-4661	177	3	obtained	obtain	VERB
ejpam-4661	177	4	the	the	DET
ejpam-4661	177	5	invariant	invariant	ADJ
ejpam-4661	177	6	manifolds	manifold	NOUN
ejpam-4661	177	7	for	for	ADP
ejpam-4661	177	8	the	the	DET
ejpam-4661	177	9	positive	positive	ADJ
ejpam-4661	177	10	fixed	fix	VERB
ejpam-4661	177	11	point	point	NOUN
ejpam-4661	177	12	p+	p+	NOUN
ejpam-4661	177	13	0	0	NUM
ejpam-4661	177	14	.	.	PUNCT
ejpam-4661	178	1	furthermore	furthermore	ADV
ejpam-4661	178	2	,	,	PUNCT
ejpam-4661	178	3	we	we	PRON
ejpam-4661	178	4	obtained	obtain	VERB
ejpam-4661	178	5	the	the	DET
ejpam-4661	178	6	stability	stability	NOUN
ejpam-4661	178	7	region	region	NOUN
ejpam-4661	178	8	for	for	ADP
ejpam-4661	178	9	the	the	DET
ejpam-4661	178	10	coexistence	coexistence	NOUN
ejpam-4661	178	11	fixed	fix	VERB
ejpam-4661	178	12	point	point	NOUN
ejpam-4661	178	13	p+	p+	VERB
ejpam-4661	178	14	3	3	NUM
ejpam-4661	178	15	.	.	PUNCT
ejpam-4661	179	1	by	by	ADP
ejpam-4661	179	2	numerical	numerical	ADJ
ejpam-4661	179	3	computations	computation	NOUN
ejpam-4661	179	4	,	,	PUNCT
ejpam-4661	179	5	we	we	PRON
ejpam-4661	179	6	confirm	confirm	VERB
ejpam-4661	179	7	our	our	PRON
ejpam-4661	179	8	analytic	analytic	ADJ
ejpam-4661	179	9	results	result	NOUN
ejpam-4661	179	10	.	.	PUNCT
ejpam-4661	180	1	the	the	DET
ejpam-4661	180	2	mathematica	mathematica	PROPN
ejpam-4661	180	3	codes	code	NOUN
ejpam-4661	180	4	displaying	display	VERB
ejpam-4661	180	5	phase	phase	NOUN
ejpam-4661	180	6	diagram	diagram	NOUN
ejpam-4661	180	7	can	can	AUX
ejpam-4661	180	8	be	be	AUX
ejpam-4661	180	9	found	find	VERB
ejpam-4661	180	10	in	in	ADP
ejpam-4661	180	11	[	[	X
ejpam-4661	180	12	18	18	NUM
ejpam-4661	180	13	]	]	PUNCT
ejpam-4661	180	14	.	.	PUNCT
ejpam-4661	181	1	references	reference	NOUN
ejpam-4661	181	2	[	[	X
ejpam-4661	181	3	1	1	NUM
ejpam-4661	181	4	]	]	X
ejpam-4661	181	5	r	r	NOUN
ejpam-4661	181	6	asheghi	asheghi	NOUN
ejpam-4661	181	7	.	.	PUNCT
ejpam-4661	182	1	bifurcations	bifurcation	NOUN
ejpam-4661	182	2	and	and	CCONJ
ejpam-4661	182	3	dynamics	dynamic	NOUN
ejpam-4661	182	4	of	of	ADP
ejpam-4661	182	5	a	a	DET
ejpam-4661	182	6	discrete	discrete	ADJ
ejpam-4661	182	7	predator	predator	NOUN
ejpam-4661	182	8	–	–	PUNCT
ejpam-4661	182	9	prey	prey	NOUN
ejpam-4661	182	10	system	system	NOUN
ejpam-4661	182	11	.	.	PUNCT
ejpam-4661	183	1	journal	journal	NOUN
ejpam-4661	183	2	of	of	ADP
ejpam-4661	183	3	biological	biological	ADJ
ejpam-4661	183	4	dynamics	dynamic	NOUN
ejpam-4661	183	5	,	,	PUNCT
ejpam-4661	183	6	8(1):161–186	8(1):161–186	NUM
ejpam-4661	183	7	,	,	PUNCT
ejpam-4661	183	8	2014	2014	NUM
ejpam-4661	183	9	.	.	PUNCT
ejpam-4661	184	1	[	[	X
ejpam-4661	184	2	2	2	NUM
ejpam-4661	184	3	]	]	X
ejpam-4661	184	4	s	s	PART
ejpam-4661	184	5	elaydi	elaydi	VERB
ejpam-4661	184	6	.	.	PUNCT
ejpam-4661	185	1	discrete	discrete	ADJ
ejpam-4661	185	2	chaos	chaos	NOUN
ejpam-4661	185	3	:	:	PUNCT
ejpam-4661	185	4	with	with	ADP
ejpam-4661	185	5	applications	application	NOUN
ejpam-4661	185	6	in	in	ADP
ejpam-4661	185	7	science	science	NOUN
ejpam-4661	185	8	and	and	CCONJ
ejpam-4661	185	9	engineering	engineering	NOUN
ejpam-4661	185	10	,	,	PUNCT
ejpam-4661	185	11	second	second	ADJ
ejpam-4661	185	12	edition	edition	NOUN
ejpam-4661	185	13	.	.	PUNCT
ejpam-4661	186	1	chapman	chapman	PROPN
ejpam-4661	186	2	&	&	CCONJ
ejpam-4661	186	3	hall	hall	PROPN
ejpam-4661	186	4	/	/	SYM
ejpam-4661	186	5	crc	crc	PROPN
ejpam-4661	186	6	,	,	PUNCT
ejpam-4661	186	7	2008	2008	NUM
ejpam-4661	186	8	.	.	PUNCT
ejpam-4661	187	1	[	[	X
ejpam-4661	187	2	3	3	X
ejpam-4661	187	3	]	]	PUNCT
ejpam-4661	187	4	m	m	VERB
ejpam-4661	187	5	p	p	NOUN
ejpam-4661	187	6	hassell	hassell	NOUN
ejpam-4661	187	7	.	.	PUNCT
ejpam-4661	188	1	the	the	DET
ejpam-4661	188	2	dynamics	dynamic	NOUN
ejpam-4661	188	3	of	of	ADP
ejpam-4661	188	4	arthropod	arthropod	ADJ
ejpam-4661	188	5	predator	predator	NOUN
ejpam-4661	188	6	-	-	PUNCT
ejpam-4661	188	7	prey	prey	NOUN
ejpam-4661	188	8	systems	system	NOUN
ejpam-4661	188	9	,	,	PUNCT
ejpam-4661	188	10	volume	volume	NOUN
ejpam-4661	188	11	111	111	NUM
ejpam-4661	188	12	.	.	PUNCT
ejpam-4661	189	1	princeton	princeton	PROPN
ejpam-4661	189	2	university	university	PROPN
ejpam-4661	189	3	press	press	NOUN
ejpam-4661	189	4	,	,	PUNCT
ejpam-4661	189	5	2020	2020	NUM
ejpam-4661	189	6	.	.	PUNCT
ejpam-4661	190	1	[	[	X
ejpam-4661	190	2	4	4	X
ejpam-4661	190	3	]	]	X
ejpam-4661	190	4	anw	anw	PROPN
ejpam-4661	190	5	hone	hone	NOUN
ejpam-4661	190	6	,	,	PUNCT
ejpam-4661	190	7	mv	mv	PROPN
ejpam-4661	190	8	irle	irle	PROPN
ejpam-4661	190	9	,	,	PUNCT
ejpam-4661	190	10	and	and	CCONJ
ejpam-4661	190	11	gw	gw	PROPN
ejpam-4661	190	12	thurura	thurura	NOUN
ejpam-4661	190	13	.	.	PUNCT
ejpam-4661	191	1	on	on	ADP
ejpam-4661	191	2	the	the	DET
ejpam-4661	191	3	neimark	neimark	ADJ
ejpam-4661	191	4	–	–	PUNCT
ejpam-4661	191	5	sacker	sacker	NOUN
ejpam-4661	191	6	bifurcation	bifurcation	NOUN
ejpam-4661	191	7	in	in	ADP
ejpam-4661	191	8	a	a	DET
ejpam-4661	191	9	discrete	discrete	ADJ
ejpam-4661	191	10	predator	predator	NOUN
ejpam-4661	191	11	-	-	PUNCT
ejpam-4661	191	12	prey	prey	NOUN
ejpam-4661	191	13	system	system	NOUN
ejpam-4661	191	14	.	.	PUNCT
ejpam-4661	192	1	journal	journal	NOUN
ejpam-4661	192	2	of	of	ADP
ejpam-4661	192	3	biological	biological	ADJ
ejpam-4661	192	4	dynamics	dynamic	NOUN
ejpam-4661	192	5	,	,	PUNCT
ejpam-4661	192	6	4(6):594–606	4(6):594–606	NUM
ejpam-4661	192	7	,	,	PUNCT
ejpam-4661	192	8	2010	2010	NUM
ejpam-4661	192	9	.	.	PUNCT
ejpam-4661	193	1	[	[	X
ejpam-4661	193	2	5	5	NUM
ejpam-4661	193	3	]	]	SYM
ejpam-4661	193	4	s	s	PART
ejpam-4661	193	5	r	r	PROPN
ejpam-4661	193	6	-	-	PUNCT
ejpam-4661	193	7	j	j	PROPN
ejpam-4661	193	8	jang	jang	PROPN
ejpam-4661	193	9	.	.	PUNCT
ejpam-4661	194	1	allee	allee	PROPN
ejpam-4661	194	2	effects	effect	NOUN
ejpam-4661	194	3	in	in	ADP
ejpam-4661	194	4	a	a	DET
ejpam-4661	194	5	discrete	discrete	ADJ
ejpam-4661	194	6	-	-	PUNCT
ejpam-4661	194	7	time	time	NOUN
ejpam-4661	194	8	host	host	NOUN
ejpam-4661	194	9	-	-	PUNCT
ejpam-4661	194	10	parasitoid	parasitoid	NOUN
ejpam-4661	194	11	model	model	NOUN
ejpam-4661	194	12	.	.	PUNCT
ejpam-4661	195	1	journal	journal	PROPN
ejpam-4661	195	2	of	of	ADP
ejpam-4661	195	3	difference	difference	NOUN
ejpam-4661	195	4	equations	equation	NOUN
ejpam-4661	195	5	and	and	CCONJ
ejpam-4661	195	6	applications	application	NOUN
ejpam-4661	195	7	,	,	PUNCT
ejpam-4661	195	8	12(2):165–181	12(2):165–181	NUM
ejpam-4661	195	9	,	,	PUNCT
ejpam-4661	195	10	2006	2006	NUM
ejpam-4661	195	11	.	.	PUNCT
ejpam-4661	196	1	[	[	X
ejpam-4661	196	2	6	6	NUM
ejpam-4661	196	3	]	]	SYM
ejpam-4661	196	4	s	s	PART
ejpam-4661	196	5	r	r	PROPN
ejpam-4661	196	6	-	-	PUNCT
ejpam-4661	196	7	j	j	PROPN
ejpam-4661	196	8	jang	jang	PROPN
ejpam-4661	196	9	.	.	PUNCT
ejpam-4661	196	10	discrete	discrete	ADJ
ejpam-4661	196	11	-	-	PUNCT
ejpam-4661	196	12	time	time	NOUN
ejpam-4661	196	13	host	host	NOUN
ejpam-4661	196	14	–	–	PUNCT
ejpam-4661	196	15	parasitoid	parasitoid	NOUN
ejpam-4661	196	16	models	model	NOUN
ejpam-4661	196	17	with	with	ADP
ejpam-4661	196	18	allee	allee	PROPN
ejpam-4661	196	19	effects	effect	NOUN
ejpam-4661	196	20	:	:	PUNCT
ejpam-4661	196	21	density	density	NOUN
ejpam-4661	196	22	dependence	dependence	NOUN
ejpam-4661	196	23	versus	versus	ADP
ejpam-4661	196	24	parasitism	parasitism	NOUN
ejpam-4661	196	25	.	.	PUNCT
ejpam-4661	197	1	journal	journal	NOUN
ejpam-4661	197	2	of	of	ADP
ejpam-4661	197	3	difference	difference	NOUN
ejpam-4661	197	4	equations	equation	NOUN
ejpam-4661	197	5	and	and	CCONJ
ejpam-4661	197	6	applications	application	NOUN
ejpam-4661	197	7	,	,	PUNCT
ejpam-4661	197	8	17(04):525–539	17(04):525–539	NUM
ejpam-4661	197	9	,	,	PUNCT
ejpam-4661	197	10	2011	2011	NUM
ejpam-4661	197	11	.	.	PUNCT
ejpam-4661	198	1	[	[	X
ejpam-4661	198	2	7	7	X
ejpam-4661	198	3	]	]	X
ejpam-4661	198	4	sr	sr	PROPN
ejpam-4661	198	5	-	-	PUNCT
ejpam-4661	198	6	j	j	PROPN
ejpam-4661	198	7	jang	jang	PROPN
ejpam-4661	198	8	and	and	CCONJ
ejpam-4661	198	9	s.l	s.l	PROPN
ejpam-4661	198	10	.	.	PROPN
ejpam-4661	198	11	diamond	diamond	PROPN
ejpam-4661	198	12	.	.	PUNCT
ejpam-4661	199	1	a	a	DET
ejpam-4661	199	2	host	host	NOUN
ejpam-4661	199	3	-	-	PUNCT
ejpam-4661	199	4	parasitoid	parasitoid	NOUN
ejpam-4661	199	5	interaction	interaction	NOUN
ejpam-4661	199	6	with	with	ADP
ejpam-4661	199	7	allee	allee	PROPN
ejpam-4661	199	8	effects	effect	NOUN
ejpam-4661	199	9	on	on	ADP
ejpam-4661	199	10	the	the	DET
ejpam-4661	199	11	host	host	NOUN
ejpam-4661	199	12	.	.	PUNCT
ejpam-4661	200	1	computers	computer	NOUN
ejpam-4661	200	2	and	and	CCONJ
ejpam-4661	200	3	mathematics	mathematic	NOUN
ejpam-4661	200	4	with	with	ADP
ejpam-4661	200	5	applications	application	NOUN
ejpam-4661	200	6	,	,	PUNCT
ejpam-4661	200	7	53:89–103	53:89–103	NUM
ejpam-4661	200	8	,	,	PUNCT
ejpam-4661	200	9	2007	2007	NUM
ejpam-4661	200	10	.	.	PUNCT
ejpam-4661	201	1	[	[	X
ejpam-4661	201	2	8	8	NUM
ejpam-4661	201	3	]	]	X
ejpam-4661	201	4	s	s	X
ejpam-4661	201	5	kapçak	kapçak	NOUN
ejpam-4661	201	6	,	,	PUNCT
ejpam-4661	201	7	s	s	X
ejpam-4661	201	8	elaydi	elaydi	NOUN
ejpam-4661	201	9	,	,	PUNCT
ejpam-4661	201	10	and	and	CCONJ
ejpam-4661	201	11	ü	ü	VERB
ejpam-4661	201	12	ufuktepe	ufuktepe	NOUN
ejpam-4661	201	13	.	.	PUNCT
ejpam-4661	202	1	stability	stability	NOUN
ejpam-4661	202	2	of	of	ADP
ejpam-4661	202	3	a	a	DET
ejpam-4661	202	4	predator	predator	NOUN
ejpam-4661	202	5	–	–	PUNCT
ejpam-4661	202	6	prey	prey	NOUN
ejpam-4661	202	7	model	model	NOUN
ejpam-4661	202	8	with	with	ADP
ejpam-4661	202	9	refuge	refuge	NOUN
ejpam-4661	202	10	effect	effect	NOUN
ejpam-4661	202	11	.	.	PUNCT
ejpam-4661	203	1	journal	journal	NOUN
ejpam-4661	203	2	of	of	ADP
ejpam-4661	203	3	difference	difference	NOUN
ejpam-4661	203	4	equations	equation	NOUN
ejpam-4661	203	5	and	and	CCONJ
ejpam-4661	203	6	applications	application	NOUN
ejpam-4661	203	7	,	,	PUNCT
ejpam-4661	203	8	22(7):989–1004	22(7):989–1004	NUM
ejpam-4661	203	9	,	,	PUNCT
ejpam-4661	203	10	2016	2016	NUM
ejpam-4661	203	11	.	.	PUNCT
ejpam-4661	204	1	[	[	X
ejpam-4661	204	2	9	9	NUM
ejpam-4661	204	3	]	]	X
ejpam-4661	204	4	s	s	X
ejpam-4661	204	5	kapçak	kapçak	NOUN
ejpam-4661	204	6	,	,	PUNCT
ejpam-4661	204	7	ü	ü	NOUN
ejpam-4661	204	8	ufuktepe	ufuktepe	NOUN
ejpam-4661	204	9	,	,	PUNCT
ejpam-4661	204	10	and	and	CCONJ
ejpam-4661	204	11	s	s	AUX
ejpam-4661	204	12	elaydi	elaydi	NOUN
ejpam-4661	204	13	.	.	PUNCT
ejpam-4661	205	1	stability	stability	NOUN
ejpam-4661	205	2	and	and	CCONJ
ejpam-4661	205	3	invariant	invariant	ADJ
ejpam-4661	205	4	manifolds	manifold	NOUN
ejpam-4661	205	5	of	of	ADP
ejpam-4661	205	6	a	a	DET
ejpam-4661	205	7	generalized	generalized	ADJ
ejpam-4661	205	8	beddington	beddington	NOUN
ejpam-4661	205	9	host	host	NOUN
ejpam-4661	205	10	-	-	PUNCT
ejpam-4661	205	11	parasitoid	parasitoid	NOUN
ejpam-4661	205	12	model	model	NOUN
ejpam-4661	205	13	.	.	PUNCT
ejpam-4661	206	1	journal	journal	PROPN
ejpam-4661	206	2	of	of	ADP
ejpam-4661	206	3	biological	biological	ADJ
ejpam-4661	206	4	dynamics	dynamic	NOUN
ejpam-4661	206	5	,	,	PUNCT
ejpam-4661	206	6	7(1):233–253	7(1):233–253	ADJ
ejpam-4661	206	7	,	,	PUNCT
ejpam-4661	206	8	2013	2013	NUM
ejpam-4661	206	9	.	.	PUNCT
ejpam-4661	207	1	[	[	X
ejpam-4661	207	2	10	10	NUM
ejpam-4661	207	3	]	]	X
ejpam-4661	207	4	mrs	mrs	PROPN
ejpam-4661	207	5	kulenovic	kulenovic	PROPN
ejpam-4661	207	6	,	,	PUNCT
ejpam-4661	207	7	e	e	NOUN
ejpam-4661	207	8	pilav	pilav	NOUN
ejpam-4661	207	9	,	,	PUNCT
ejpam-4661	207	10	and	and	CCONJ
ejpam-4661	207	11	e	e	X
ejpam-4661	207	12	silic	silic	NOUN
ejpam-4661	207	13	.	.	PUNCT
ejpam-4661	208	1	naimark	naimark	ADJ
ejpam-4661	208	2	-	-	PUNCT
ejpam-4661	208	3	sacker	sacker	NOUN
ejpam-4661	208	4	bifurcation	bifurcation	NOUN
ejpam-4661	208	5	of	of	ADP
ejpam-4661	208	6	a	a	DET
ejpam-4661	208	7	certain	certain	ADJ
ejpam-4661	208	8	second	second	ADJ
ejpam-4661	208	9	order	order	NOUN
ejpam-4661	208	10	quadratic	quadratic	ADJ
ejpam-4661	208	11	fractional	fractional	ADJ
ejpam-4661	208	12	difference	difference	NOUN
ejpam-4661	208	13	equation	equation	NOUN
ejpam-4661	208	14	.	.	PUNCT
ejpam-4661	209	1	journal	journal	PROPN
ejpam-4661	209	2	of	of	ADP
ejpam-4661	209	3	mathematical	mathematical	ADJ
ejpam-4661	209	4	and	and	CCONJ
ejpam-4661	209	5	computational	computational	ADJ
ejpam-4661	209	6	science	science	NOUN
ejpam-4661	209	7	,	,	PUNCT
ejpam-4661	209	8	4(6):1025–1043	4(6):1025–1043	PROPN
ejpam-4661	209	9	,	,	PUNCT
ejpam-4661	209	10	2014	2014	NUM
ejpam-4661	209	11	.	.	PUNCT
ejpam-4661	210	1	[	[	X
ejpam-4661	210	2	11	11	NUM
ejpam-4661	210	3	]	]	X
ejpam-4661	210	4	g	g	PROPN
ejpam-4661	210	5	livadiotis	livadiotis	PROPN
ejpam-4661	210	6	,	,	PUNCT
ejpam-4661	210	7	l	l	NOUN
ejpam-4661	210	8	assas	assas	NOUN
ejpam-4661	210	9	,	,	PUNCT
ejpam-4661	210	10	b	b	PROPN
ejpam-4661	210	11	dennis	dennis	PROPN
ejpam-4661	210	12	,	,	PUNCT
ejpam-4661	210	13	s	s	PART
ejpam-4661	210	14	elaydi	elaydi	NOUN
ejpam-4661	210	15	,	,	PUNCT
ejpam-4661	210	16	and	and	CCONJ
ejpam-4661	210	17	e	e	NOUN
ejpam-4661	210	18	kwessi	kwessi	PROPN
ejpam-4661	210	19	.	.	PUNCT
ejpam-4661	211	1	a	a	DET
ejpam-4661	211	2	discrete	discrete	ADJ
ejpam-4661	211	3	-	-	PUNCT
ejpam-4661	211	4	time	time	NOUN
ejpam-4661	211	5	host	host	NOUN
ejpam-4661	211	6	–	–	PUNCT
ejpam-4661	211	7	parasitoid	parasitoid	NOUN
ejpam-4661	211	8	model	model	NOUN
ejpam-4661	211	9	with	with	ADP
ejpam-4661	211	10	an	an	DET
ejpam-4661	211	11	allee	allee	ADJ
ejpam-4661	211	12	effect	effect	NOUN
ejpam-4661	211	13	.	.	PUNCT
ejpam-4661	212	1	journal	journal	NOUN
ejpam-4661	212	2	of	of	ADP
ejpam-4661	212	3	biological	biological	ADJ
ejpam-4661	212	4	dynamics	dynamic	NOUN
ejpam-4661	212	5	,	,	PUNCT
ejpam-4661	212	6	9(1):34–51	9(1):34–51	NUM
ejpam-4661	212	7	,	,	PUNCT
ejpam-4661	212	8	2015	2015	NUM
ejpam-4661	212	9	.	.	PUNCT
ejpam-4661	213	1	[	[	X
ejpam-4661	213	2	12	12	NUM
ejpam-4661	213	3	]	]	X
ejpam-4661	213	4	r	r	NOUN
ejpam-4661	213	5	m	m	VERB
ejpam-4661	213	6	may	may	AUX
ejpam-4661	213	7	.	.	PUNCT
ejpam-4661	214	1	host	host	NOUN
ejpam-4661	214	2	-	-	PUNCT
ejpam-4661	214	3	parasitoid	parasitoid	NOUN
ejpam-4661	214	4	systems	system	NOUN
ejpam-4661	214	5	in	in	ADP
ejpam-4661	214	6	patchy	patchy	ADJ
ejpam-4661	214	7	environments	environment	NOUN
ejpam-4661	214	8	:	:	PUNCT
ejpam-4661	214	9	a	a	DET
ejpam-4661	214	10	phenomenological	phenomenological	ADJ
ejpam-4661	214	11	model	model	NOUN
ejpam-4661	214	12	.	.	PUNCT
ejpam-4661	215	1	the	the	DET
ejpam-4661	215	2	journal	journal	NOUN
ejpam-4661	215	3	of	of	ADP
ejpam-4661	215	4	animal	animal	NOUN
ejpam-4661	215	5	ecology	ecology	NOUN
ejpam-4661	215	6	,	,	PUNCT
ejpam-4661	215	7	pages	page	NOUN
ejpam-4661	215	8	833–844	833–844	NUM
ejpam-4661	215	9	,	,	PUNCT
ejpam-4661	215	10	1978	1978	NUM
ejpam-4661	215	11	.	.	PUNCT
ejpam-4661	216	1	references	reference	NOUN
ejpam-4661	216	2	83	83	NUM
ejpam-4661	217	1	[	[	X
ejpam-4661	217	2	13	13	NUM
ejpam-4661	217	3	]	]	X
ejpam-4661	217	4	r	r	NOUN
ejpam-4661	217	5	m	m	VERB
ejpam-4661	217	6	may	may	AUX
ejpam-4661	217	7	,	,	PUNCT
ejpam-4661	217	8	mp	mp	PROPN
ejpam-4661	217	9	hassell	hassell	PROPN
ejpam-4661	217	10	,	,	PUNCT
ejpam-4661	217	11	rm	rm	PROPN
ejpam-4661	217	12	anderson	anderson	PROPN
ejpam-4661	217	13	,	,	PUNCT
ejpam-4661	217	14	and	and	CCONJ
ejpam-4661	217	15	dw	dw	PROPN
ejpam-4661	217	16	tonkyn	tonkyn	PROPN
ejpam-4661	217	17	.	.	PUNCT
ejpam-4661	218	1	density	density	NOUN
ejpam-4661	218	2	dependence	dependence	NOUN
ejpam-4661	218	3	in	in	ADP
ejpam-4661	218	4	host	host	NOUN
ejpam-4661	218	5	-	-	PUNCT
ejpam-4661	218	6	parasitiod	parasitiod	NOUN
ejpam-4661	218	7	models	model	NOUN
ejpam-4661	218	8	.	.	PUNCT
ejpam-4661	219	1	journal	journal	NOUN
ejpam-4661	219	2	of	of	ADP
ejpam-4661	219	3	animal	animal	NOUN
ejpam-4661	219	4	ecology	ecology	NOUN
ejpam-4661	219	5	,	,	PUNCT
ejpam-4661	219	6	50:855–865	50:855–865	NUM
ejpam-4661	219	7	,	,	PUNCT
ejpam-4661	219	8	1981	1981	NUM
ejpam-4661	219	9	.	.	PUNCT
ejpam-4661	220	1	[	[	X
ejpam-4661	220	2	14	14	NUM
ejpam-4661	220	3	]	]	X
ejpam-4661	220	4	k	k	PROPN
ejpam-4661	220	5	murakami	murakami	NOUN
ejpam-4661	220	6	.	.	PUNCT
ejpam-4661	221	1	stability	stability	NOUN
ejpam-4661	221	2	and	and	CCONJ
ejpam-4661	221	3	bifurcation	bifurcation	NOUN
ejpam-4661	221	4	in	in	ADP
ejpam-4661	221	5	a	a	DET
ejpam-4661	221	6	discrete	discrete	ADJ
ejpam-4661	221	7	-	-	PUNCT
ejpam-4661	221	8	time	time	NOUN
ejpam-4661	221	9	predator	predator	NOUN
ejpam-4661	221	10	–	–	PUNCT
ejpam-4661	221	11	prey	prey	PROPN
ejpam-4661	221	12	model	model	NOUN
ejpam-4661	221	13	.	.	PUNCT
ejpam-4661	222	1	journal	journal	PROPN
ejpam-4661	222	2	of	of	ADP
ejpam-4661	222	3	difference	difference	NOUN
ejpam-4661	222	4	equations	equation	NOUN
ejpam-4661	222	5	and	and	CCONJ
ejpam-4661	222	6	applications	application	NOUN
ejpam-4661	222	7	,	,	PUNCT
ejpam-4661	222	8	13(10):911–925	13(10):911–925	NUM
ejpam-4661	222	9	,	,	PUNCT
ejpam-4661	222	10	2007	2007	NUM
ejpam-4661	222	11	.	.	PUNCT
ejpam-4661	223	1	[	[	X
ejpam-4661	223	2	15	15	NUM
ejpam-4661	223	3	]	]	X
ejpam-4661	223	4	r	r	NOUN
ejpam-4661	223	5	j	j	PROPN
ejpam-4661	223	6	sacker	sacker	NOUN
ejpam-4661	223	7	.	.	PUNCT
ejpam-4661	224	1	introduction	introduction	NOUN
ejpam-4661	224	2	to	to	ADP
ejpam-4661	224	3	the	the	DET
ejpam-4661	224	4	2009	2009	NUM
ejpam-4661	224	5	re	re	NOUN
ejpam-4661	224	6	-	-	NOUN
ejpam-4661	224	7	publication	publication	NOUN
ejpam-4661	224	8	of	of	ADP
ejpam-4661	224	9	the	the	DET
ejpam-4661	224	10	‘	'	PUNCT
ejpam-4661	224	11	neimark	neimark	ADJ
ejpam-4661	224	12	–	–	PUNCT
ejpam-4661	224	13	sacker	sacker	NOUN
ejpam-4661	224	14	bifurcation	bifurcation	NOUN
ejpam-4661	224	15	theorem	theorem	VERB
ejpam-4661	224	16	’	'	PUNCT
ejpam-4661	224	17	.	.	PUNCT
ejpam-4661	225	1	journal	journal	PROPN
ejpam-4661	225	2	of	of	ADP
ejpam-4661	225	3	difference	difference	NOUN
ejpam-4661	225	4	equations	equation	NOUN
ejpam-4661	225	5	and	and	CCONJ
ejpam-4661	225	6	applications	application	NOUN
ejpam-4661	225	7	,	,	PUNCT
ejpam-4661	225	8	15(8	15(8	NOUN
ejpam-4661	225	9	-	-	SYM
ejpam-4661	225	10	9):753–758	9):753–758	NUM
ejpam-4661	225	11	,	,	PUNCT
ejpam-4661	225	12	2009	2009	NUM
ejpam-4661	225	13	.	.	PUNCT
ejpam-4661	226	1	[	[	X
ejpam-4661	226	2	16	16	NUM
ejpam-4661	226	3	]	]	X
ejpam-4661	226	4	r	r	NOUN
ejpam-4661	226	5	john	john	PROPN
ejpam-4661	226	6	sacker	sacker	NOUN
ejpam-4661	226	7	.	.	PUNCT
ejpam-4661	227	1	on	on	ADP
ejpam-4661	227	2	invariant	invariant	ADJ
ejpam-4661	227	3	surfaces	surface	NOUN
ejpam-4661	227	4	and	and	CCONJ
ejpam-4661	227	5	bifurcation	bifurcation	NOUN
ejpam-4661	227	6	of	of	ADP
ejpam-4661	227	7	periodic	periodic	ADJ
ejpam-4661	227	8	solutions	solution	NOUN
ejpam-4661	227	9	of	of	ADP
ejpam-4661	227	10	ordinary	ordinary	ADJ
ejpam-4661	227	11	differential	differential	ADJ
ejpam-4661	227	12	equations	equation	NOUN
ejpam-4661	227	13	.	.	PUNCT
ejpam-4661	228	1	new	new	PROPN
ejpam-4661	228	2	york	york	PROPN
ejpam-4661	228	3	university	university	PROPN
ejpam-4661	228	4	,	,	PUNCT
ejpam-4661	228	5	1964	1964	NUM
ejpam-4661	228	6	.	.	PUNCT
ejpam-4661	229	1	[	[	X
ejpam-4661	229	2	17	17	NUM
ejpam-4661	229	3	]	]	X
ejpam-4661	229	4	j	j	PROPN
ejpam-4661	229	5	m	m	PROPN
ejpam-4661	229	6	smith	smith	PROPN
ejpam-4661	229	7	.	.	PUNCT
ejpam-4661	230	1	mathematical	mathematical	ADJ
ejpam-4661	230	2	ideas	idea	NOUN
ejpam-4661	230	3	in	in	ADP
ejpam-4661	230	4	biology	biology	NOUN
ejpam-4661	230	5	.	.	PUNCT
ejpam-4661	231	1	cup	cup	NOUN
ejpam-4661	231	2	archive	archive	NOUN
ejpam-4661	231	3	,	,	PUNCT
ejpam-4661	231	4	1968	1968	NUM
ejpam-4661	231	5	.	.	PUNCT
ejpam-4661	232	1	[	[	X
ejpam-4661	232	2	18	18	NUM
ejpam-4661	232	3	]	]	PUNCT
ejpam-4661	232	4	ü	ü	VERB
ejpam-4661	232	5	ufuktepe	ufuktepe	NOUN
ejpam-4661	232	6	and	and	CCONJ
ejpam-4661	232	7	s	s	NOUN
ejpam-4661	232	8	kapçak	kapçak	X
ejpam-4661	232	9	.	.	PUNCT
ejpam-4661	233	1	applications	application	NOUN
ejpam-4661	233	2	of	of	ADP
ejpam-4661	233	3	discrete	discrete	ADJ
ejpam-4661	233	4	dynamical	dynamical	ADJ
ejpam-4661	233	5	systems	system	NOUN
ejpam-4661	233	6	with	with	ADP
ejpam-4661	233	7	mathematica	mathematica	PROPN
ejpam-4661	233	8	(	(	PUNCT
ejpam-4661	233	9	study	study	NOUN
ejpam-4661	233	10	of	of	ADP
ejpam-4661	233	11	mathematical	mathematical	ADJ
ejpam-4661	233	12	software	software	NOUN
ejpam-4661	233	13	and	and	CCONJ
ejpam-4661	233	14	its	its	PRON
ejpam-4661	233	15	effective	effective	ADJ
ejpam-4661	233	16	use	use	NOUN
ejpam-4661	233	17	for	for	ADP
ejpam-4661	233	18	mathematics	mathematics	NOUN
ejpam-4661	233	19	education	education	NOUN
ejpam-4661	233	20	)	)	PUNCT
ejpam-4661	233	21	.	.	PUNCT
ejpam-4661	234	1	rims	rims	PROPN
ejpam-4661	234	2	kyoto	kyoto	PROPN
ejpam-4661	234	3	university	university	PROPN
ejpam-4661	234	4	,	,	PUNCT
ejpam-4661	234	5	1909:207–216	1909:207–216	NUM
ejpam-4661	234	6	,	,	PUNCT
ejpam-4661	234	7	2014	2014	NUM
ejpam-4661	234	8	.	.	PUNCT