id	sid	tid	token	lemma	pos
ejpam-5397	1	1	european	european	PROPN
ejpam-5397	1	2	journal	journal	PROPN
ejpam-5397	1	3	of	of	ADP
ejpam-5397	1	4	pure	pure	ADJ
ejpam-5397	1	5	and	and	CCONJ
ejpam-5397	1	6	applied	applied	ADJ
ejpam-5397	1	7	mathematics	mathematic	NOUN
ejpam-5397	1	8	2025	2025	NUM
ejpam-5397	1	9	,	,	PUNCT
ejpam-5397	1	10	vol	vol	NOUN
ejpam-5397	1	11	.	.	PROPN
ejpam-5397	1	12	18	18	NUM
ejpam-5397	1	13	,	,	PUNCT
ejpam-5397	1	14	issue	issue	NOUN
ejpam-5397	1	15	1	1	NUM
ejpam-5397	1	16	,	,	PUNCT
ejpam-5397	1	17	article	article	NOUN
ejpam-5397	1	18	number	number	NOUN
ejpam-5397	1	19	5397	5397	NUM
ejpam-5397	1	20	issn	issn	VERB
ejpam-5397	1	21	1307	1307	NUM
ejpam-5397	1	22	-	-	SYM
ejpam-5397	1	23	5543	5543	NUM
ejpam-5397	1	24	–	–	PUNCT
ejpam-5397	1	25	ejpam.com	ejpam.com	X
ejpam-5397	1	26	published	publish	VERB
ejpam-5397	1	27	by	by	ADP
ejpam-5397	1	28	new	new	PROPN
ejpam-5397	1	29	york	york	PROPN
ejpam-5397	1	30	business	business	PROPN
ejpam-5397	1	31	global	global	ADJ
ejpam-5397	1	32	dynamical	dynamical	ADJ
ejpam-5397	1	33	analysis	analysis	NOUN
ejpam-5397	1	34	of	of	ADP
ejpam-5397	1	35	a	a	DET
ejpam-5397	1	36	three	three	NUM
ejpam-5397	1	37	species	specie	NOUN
ejpam-5397	1	38	food	food	NOUN
ejpam-5397	1	39	-	-	PUNCT
ejpam-5397	1	40	web	web	NOUN
ejpam-5397	1	41	model	model	NOUN
ejpam-5397	1	42	with	with	ADP
ejpam-5397	1	43	extended	extended	ADJ
ejpam-5397	1	44	holling	holling	NOUN
ejpam-5397	1	45	type	type	NOUN
ejpam-5397	1	46	ii	ii	NOUN
ejpam-5397	1	47	functional	functional	ADJ
ejpam-5397	1	48	response	response	NOUN
ejpam-5397	1	49	bakhan	bakhan	ADP
ejpam-5397	1	50	bahman	bahman	PROPN
ejpam-5397	1	51	kamal1	kamal1	PROPN
ejpam-5397	1	52	,	,	PUNCT
ejpam-5397	1	53	arkan	arkan	VERB
ejpam-5397	1	54	nawzad	nawzad	PROPN
ejpam-5397	1	55	mustafa1,∗	mustafa1,∗	NOUN
ejpam-5397	1	56	1	1	NUM
ejpam-5397	1	57	department	department	NOUN
ejpam-5397	1	58	of	of	ADP
ejpam-5397	1	59	mathematics	mathematic	NOUN
ejpam-5397	1	60	,	,	PUNCT
ejpam-5397	1	61	college	college	NOUN
ejpam-5397	1	62	of	of	ADP
ejpam-5397	1	63	education	education	NOUN
ejpam-5397	1	64	,	,	PUNCT
ejpam-5397	1	65	university	university	NOUN
ejpam-5397	1	66	of	of	ADP
ejpam-5397	1	67	sulaimani	sulaimani	PROPN
ejpam-5397	1	68	,	,	PUNCT
ejpam-5397	1	69	sulaymaniyah	sulaymaniyah	NOUN
ejpam-5397	1	70	46001	46001	NUM
ejpam-5397	1	71	,	,	PUNCT
ejpam-5397	1	72	iraq	iraq	PROPN
ejpam-5397	1	73	abstract	abstract	NOUN
ejpam-5397	1	74	.	.	PUNCT
ejpam-5397	2	1	this	this	DET
ejpam-5397	2	2	paper	paper	NOUN
ejpam-5397	2	3	deals	deal	NOUN
ejpam-5397	2	4	with	with	ADP
ejpam-5397	2	5	dynamical	dynamical	ADJ
ejpam-5397	2	6	analysis	analysis	NOUN
ejpam-5397	2	7	of	of	ADP
ejpam-5397	2	8	a	a	DET
ejpam-5397	2	9	food	food	NOUN
ejpam-5397	2	10	-	-	PUNCT
ejpam-5397	2	11	web	web	NOUN
ejpam-5397	2	12	including	include	VERB
ejpam-5397	2	13	three	three	NUM
ejpam-5397	2	14	logistically	logistically	ADV
ejpam-5397	2	15	growing	grow	VERB
ejpam-5397	2	16	interaction	interaction	NOUN
ejpam-5397	2	17	species	specie	NOUN
ejpam-5397	2	18	,	,	PUNCT
ejpam-5397	2	19	prey	prey	NOUN
ejpam-5397	2	20	,	,	PUNCT
ejpam-5397	2	21	intermediate	intermediate	ADJ
ejpam-5397	2	22	predators	predator	NOUN
ejpam-5397	2	23	and	and	CCONJ
ejpam-5397	2	24	apex	apex	NOUN
ejpam-5397	2	25	predators	predator	NOUN
ejpam-5397	2	26	.	.	PUNCT
ejpam-5397	3	1	the	the	DET
ejpam-5397	3	2	intermediate	intermediate	ADJ
ejpam-5397	3	3	predator	predator	NOUN
ejpam-5397	3	4	species	specie	NOUN
ejpam-5397	3	5	predate	predate	VERB
ejpam-5397	3	6	the	the	DET
ejpam-5397	3	7	prey	prey	NOUN
ejpam-5397	3	8	species	specie	NOUN
ejpam-5397	3	9	according	accord	VERB
ejpam-5397	3	10	to	to	ADP
ejpam-5397	3	11	the	the	DET
ejpam-5397	3	12	holling	holle	VERB
ejpam-5397	3	13	type	type	NOUN
ejpam-5397	3	14	-	-	PUNCT
ejpam-5397	3	15	ii	ii	NOUN
ejpam-5397	3	16	functional	functional	ADJ
ejpam-5397	3	17	response	response	NOUN
ejpam-5397	3	18	,	,	PUNCT
ejpam-5397	3	19	while	while	SCONJ
ejpam-5397	3	20	the	the	DET
ejpam-5397	3	21	apex	apex	NOUN
ejpam-5397	3	22	predator	predator	NOUN
ejpam-5397	3	23	species	specie	NOUN
ejpam-5397	3	24	predate	predate	VERB
ejpam-5397	3	25	both	both	PRON
ejpam-5397	3	26	prey	prey	VERB
ejpam-5397	3	27	species	specie	NOUN
ejpam-5397	3	28	and	and	CCONJ
ejpam-5397	3	29	intermediate	intermediate	ADJ
ejpam-5397	3	30	predator	predator	NOUN
ejpam-5397	3	31	species	specie	NOUN
ejpam-5397	3	32	according	accord	VERB
ejpam-5397	3	33	to	to	ADP
ejpam-5397	3	34	extended	extended	ADJ
ejpam-5397	3	35	holling	holling	NOUN
ejpam-5397	3	36	type	type	NOUN
ejpam-5397	3	37	ii	ii	NOUN
ejpam-5397	3	38	functional	functional	ADJ
ejpam-5397	3	39	response	response	NOUN
ejpam-5397	3	40	for	for	ADP
ejpam-5397	3	41	two	two	NUM
ejpam-5397	3	42	prey	prey	PROPN
ejpam-5397	3	43	species	specie	NOUN
ejpam-5397	3	44	.	.	PUNCT
ejpam-5397	4	1	firstly	firstly	ADV
ejpam-5397	4	2	,	,	PUNCT
ejpam-5397	4	3	we	we	PRON
ejpam-5397	4	4	conduct	conduct	VERB
ejpam-5397	4	5	a	a	DET
ejpam-5397	4	6	thorough	thorough	ADJ
ejpam-5397	4	7	analytical	analytical	ADJ
ejpam-5397	4	8	examination	examination	NOUN
ejpam-5397	4	9	of	of	ADP
ejpam-5397	4	10	the	the	DET
ejpam-5397	4	11	system	system	NOUN
ejpam-5397	4	12	,	,	PUNCT
ejpam-5397	4	13	demonstrating	demonstrate	VERB
ejpam-5397	4	14	the	the	DET
ejpam-5397	4	15	positivity	positivity	NOUN
ejpam-5397	4	16	and	and	CCONJ
ejpam-5397	4	17	boundedness	boundedness	NOUN
ejpam-5397	4	18	of	of	ADP
ejpam-5397	4	19	the	the	DET
ejpam-5397	4	20	solutions	solution	NOUN
ejpam-5397	4	21	criteria	criterion	NOUN
ejpam-5397	4	22	for	for	ADP
ejpam-5397	4	23	the	the	DET
ejpam-5397	4	24	persistence	persistence	NOUN
ejpam-5397	4	25	of	of	ADP
ejpam-5397	4	26	the	the	DET
ejpam-5397	4	27	model	model	NOUN
ejpam-5397	4	28	are	be	AUX
ejpam-5397	4	29	founded	found	VERB
ejpam-5397	4	30	,	,	PUNCT
ejpam-5397	4	31	four	four	NUM
ejpam-5397	4	32	biologically	biologically	ADV
ejpam-5397	4	33	possible	possible	ADJ
ejpam-5397	4	34	steady	steady	ADJ
ejpam-5397	4	35	states	state	NOUN
ejpam-5397	4	36	are	be	AUX
ejpam-5397	4	37	determined	determine	VERB
ejpam-5397	4	38	and	and	CCONJ
ejpam-5397	4	39	the	the	DET
ejpam-5397	4	40	local	local	ADJ
ejpam-5397	4	41	as	as	ADV
ejpam-5397	4	42	well	well	ADV
ejpam-5397	4	43	as	as	ADP
ejpam-5397	4	44	the	the	DET
ejpam-5397	4	45	dynamics	dynamic	NOUN
ejpam-5397	4	46	around	around	ADP
ejpam-5397	4	47	the	the	DET
ejpam-5397	4	48	model	model	NOUN
ejpam-5397	4	49	’	'	PUNCT
ejpam-5397	4	50	steady	steady	ADJ
ejpam-5397	4	51	states	state	NOUN
ejpam-5397	4	52	based	base	VERB
ejpam-5397	4	53	on	on	ADP
ejpam-5397	4	54	the	the	DET
ejpam-5397	4	55	parameters	parameter	NOUN
ejpam-5397	4	56	are	be	AUX
ejpam-5397	4	57	also	also	ADV
ejpam-5397	4	58	investigated	investigate	VERB
ejpam-5397	4	59	.	.	PUNCT
ejpam-5397	5	1	the	the	DET
ejpam-5397	5	2	occurrence	occurrence	NOUN
ejpam-5397	5	3	of	of	ADP
ejpam-5397	5	4	hopf	hopf	ADJ
ejpam-5397	5	5	-	-	PUNCT
ejpam-5397	5	6	bifurcation	bifurcation	NOUN
ejpam-5397	5	7	of	of	ADP
ejpam-5397	5	8	thee	thee	NOUN
ejpam-5397	5	9	model	model	NOUN
ejpam-5397	5	10	near	near	ADP
ejpam-5397	5	11	all	all	DET
ejpam-5397	5	12	steady	steady	ADJ
ejpam-5397	5	13	states	state	NOUN
ejpam-5397	5	14	,	,	PUNCT
ejpam-5397	5	15	are	be	AUX
ejpam-5397	5	16	discussed	discuss	VERB
ejpam-5397	5	17	.	.	PUNCT
ejpam-5397	6	1	finally	finally	ADV
ejpam-5397	6	2	,	,	PUNCT
ejpam-5397	6	3	with	with	ADP
ejpam-5397	6	4	the	the	DET
ejpam-5397	6	5	help	help	NOUN
ejpam-5397	6	6	of	of	ADP
ejpam-5397	6	7	matlab	matlab	PROPN
ejpam-5397	6	8	program	program	PROPN
ejpam-5397	6	9	,	,	PUNCT
ejpam-5397	6	10	it	it	PRON
ejpam-5397	6	11	is	be	AUX
ejpam-5397	6	12	performed	perform	VERB
ejpam-5397	6	13	numerical	numerical	ADJ
ejpam-5397	6	14	simulations	simulation	NOUN
ejpam-5397	6	15	to	to	PART
ejpam-5397	6	16	support	support	VERB
ejpam-5397	6	17	the	the	DET
ejpam-5397	6	18	evidence	evidence	NOUN
ejpam-5397	6	19	of	of	ADP
ejpam-5397	6	20	our	our	PRON
ejpam-5397	6	21	analytical	analytical	ADJ
ejpam-5397	6	22	results	result	NOUN
ejpam-5397	6	23	.	.	PUNCT
ejpam-5397	7	1	2020	2020	NUM
ejpam-5397	7	2	mathematics	mathematic	NOUN
ejpam-5397	7	3	subject	subject	NOUN
ejpam-5397	7	4	classifications	classification	NOUN
ejpam-5397	7	5	:	:	PUNCT
ejpam-5397	7	6	37n25	37n25	NUM
ejpam-5397	7	7	,	,	PUNCT
ejpam-5397	7	8	34d20	34d20	NUM
ejpam-5397	7	9	,	,	PUNCT
ejpam-5397	7	10	37g99	37g99	NUM
ejpam-5397	7	11	,	,	PUNCT
ejpam-5397	7	12	92d25	92d25	NUM
ejpam-5397	7	13	,	,	PUNCT
ejpam-5397	7	14	92d40	92d40	NUM
ejpam-5397	7	15	key	key	ADJ
ejpam-5397	7	16	words	word	NOUN
ejpam-5397	7	17	and	and	CCONJ
ejpam-5397	7	18	phrases	phrase	NOUN
ejpam-5397	7	19	:	:	PUNCT
ejpam-5397	7	20	food	food	NOUN
ejpam-5397	7	21	web	web	NOUN
ejpam-5397	7	22	,	,	PUNCT
ejpam-5397	7	23	functional	functional	ADJ
ejpam-5397	7	24	response	response	NOUN
ejpam-5397	7	25	,	,	PUNCT
ejpam-5397	7	26	permanence	permanence	NOUN
ejpam-5397	7	27	,	,	PUNCT
ejpam-5397	7	28	stability	stability	NOUN
ejpam-5397	7	29	analysis	analysis	NOUN
ejpam-5397	7	30	,	,	PUNCT
ejpam-5397	7	31	hopf	hopf	ADJ
ejpam-5397	7	32	-	-	PUNCT
ejpam-5397	7	33	bifurcation	bifurcation	NOUN
ejpam-5397	7	34	1	1	NUM
ejpam-5397	7	35	.	.	PUNCT
ejpam-5397	7	36	introduction	introduction	NOUN
ejpam-5397	7	37	mathematical	mathematical	ADJ
ejpam-5397	7	38	models	model	NOUN
ejpam-5397	7	39	for	for	ADP
ejpam-5397	7	40	the	the	DET
ejpam-5397	7	41	dynamics	dynamic	NOUN
ejpam-5397	7	42	of	of	ADP
ejpam-5397	7	43	interaction	interaction	NOUN
ejpam-5397	7	44	between	between	ADP
ejpam-5397	7	45	two	two	NUM
ejpam-5397	7	46	species	specie	NOUN
ejpam-5397	7	47	of	of	ADP
ejpam-5397	7	48	prey	prey	NOUN
ejpam-5397	7	49	and	and	CCONJ
ejpam-5397	7	50	predator	predator	NOUN
ejpam-5397	7	51	,	,	PUNCT
ejpam-5397	7	52	has	have	AUX
ejpam-5397	7	53	been	be	AUX
ejpam-5397	7	54	derived	derive	VERB
ejpam-5397	7	55	by	by	ADP
ejpam-5397	7	56	many	many	ADJ
ejpam-5397	7	57	mathematician	mathematician	ADJ
ejpam-5397	7	58	author	author	NOUN
ejpam-5397	7	59	[	[	X
ejpam-5397	7	60	2	2	NUM
ejpam-5397	7	61	,	,	PUNCT
ejpam-5397	7	62	3	3	NUM
ejpam-5397	7	63	,	,	PUNCT
ejpam-5397	7	64	6	6	NUM
ejpam-5397	7	65	,	,	PUNCT
ejpam-5397	7	66	9	9	NUM
ejpam-5397	7	67	]	]	PUNCT
ejpam-5397	7	68	.	.	PUNCT
ejpam-5397	8	1	food	food	NOUN
ejpam-5397	8	2	web	web	NOUN
ejpam-5397	8	3	models	model	NOUN
ejpam-5397	8	4	are	be	AUX
ejpam-5397	8	5	important	important	ADJ
ejpam-5397	8	6	conceptual	conceptual	ADJ
ejpam-5397	8	7	tool	tool	NOUN
ejpam-5397	8	8	for	for	ADP
ejpam-5397	8	9	illustrating	illustrate	VERB
ejpam-5397	8	10	the	the	DET
ejpam-5397	8	11	feeding	feeding	NOUN
ejpam-5397	8	12	relationships	relationship	NOUN
ejpam-5397	8	13	among	among	ADP
ejpam-5397	8	14	species	specie	NOUN
ejpam-5397	8	15	within	within	ADP
ejpam-5397	8	16	a	a	DET
ejpam-5397	8	17	community	community	NOUN
ejpam-5397	8	18	,	,	PUNCT
ejpam-5397	8	19	revealing	reveal	VERB
ejpam-5397	8	20	species	specie	NOUN
ejpam-5397	8	21	interactions	interaction	NOUN
ejpam-5397	8	22	and	and	CCONJ
ejpam-5397	8	23	community	community	NOUN
ejpam-5397	8	24	structure	structure	NOUN
ejpam-5397	8	25	,	,	PUNCT
ejpam-5397	8	26	and	and	CCONJ
ejpam-5397	8	27	understanding	understand	VERB
ejpam-5397	8	28	the	the	DET
ejpam-5397	8	29	dynamics	dynamic	NOUN
ejpam-5397	8	30	of	of	ADP
ejpam-5397	8	31	energy	energy	NOUN
ejpam-5397	8	32	transfer	transfer	NOUN
ejpam-5397	8	33	in	in	ADP
ejpam-5397	8	34	an	an	DET
ejpam-5397	8	35	ecosystem	ecosystem	NOUN
ejpam-5397	8	36	,	,	PUNCT
ejpam-5397	8	37	therefore	therefore	ADV
ejpam-5397	8	38	two	two	NUM
ejpam-5397	8	39	-	-	PUNCT
ejpam-5397	8	40	species	specie	NOUN
ejpam-5397	8	41	model	model	NOUN
ejpam-5397	8	42	has	have	AUX
ejpam-5397	8	43	been	be	AUX
ejpam-5397	8	44	extended	extend	VERB
ejpam-5397	8	45	to	to	ADP
ejpam-5397	8	46	the	the	DET
ejpam-5397	8	47	three	three	NUM
ejpam-5397	8	48	-	-	PUNCT
ejpam-5397	8	49	species	species	NOUN
ejpam-5397	8	50	model	model	NOUN
ejpam-5397	8	51	by	by	ADP
ejpam-5397	8	52	many	many	ADJ
ejpam-5397	8	53	authors	author	NOUN
ejpam-5397	8	54	[	[	X
ejpam-5397	8	55	5	5	NUM
ejpam-5397	8	56	,	,	PUNCT
ejpam-5397	8	57	8	8	NUM
ejpam-5397	8	58	,	,	PUNCT
ejpam-5397	8	59	10	10	NUM
ejpam-5397	8	60	,	,	PUNCT
ejpam-5397	8	61	18	18	NUM
ejpam-5397	8	62	]	]	PUNCT
ejpam-5397	8	63	.	.	PUNCT
ejpam-5397	9	1	the	the	DET
ejpam-5397	9	2	important	important	ADJ
ejpam-5397	9	3	element	element	NOUN
ejpam-5397	9	4	to	to	PART
ejpam-5397	9	5	represent	represent	VERB
ejpam-5397	9	6	the	the	DET
ejpam-5397	9	7	dynamics	dynamic	NOUN
ejpam-5397	9	8	relationship	relationship	NOUN
ejpam-5397	9	9	between	between	ADP
ejpam-5397	9	10	predator	predator	NOUN
ejpam-5397	9	11	population	population	NOUN
ejpam-5397	9	12	and	and	CCONJ
ejpam-5397	9	13	prey	prey	PROPN
ejpam-5397	9	14	population	population	NOUN
ejpam-5397	9	15	is	be	AUX
ejpam-5397	9	16	the	the	DET
ejpam-5397	9	17	functional	functional	ADJ
ejpam-5397	9	18	response	response	NOUN
ejpam-5397	9	19	for	for	ADP
ejpam-5397	9	20	the	the	DET
ejpam-5397	9	21	predator	predator	NOUN
ejpam-5397	9	22	,	,	PUNCT
ejpam-5397	9	23	which	which	PRON
ejpam-5397	9	24	defined	define	VERB
ejpam-5397	9	25	as	as	ADP
ejpam-5397	9	26	∗corresponding	∗corresponde	VERB
ejpam-5397	9	27	author	author	NOUN
ejpam-5397	9	28	.	.	PUNCT
ejpam-5397	10	1	doi	doi	NOUN
ejpam-5397	10	2	:	:	PUNCT
ejpam-5397	10	3	https://doi.org/10.29020/nybg.ejpam.v18i1.5397	https://doi.org/10.29020/nybg.ejpam.v18i1.5397	PRON
ejpam-5397	10	4	email	email	NOUN
ejpam-5397	10	5	addresses	address	NOUN
ejpam-5397	10	6	:	:	PUNCT
ejpam-5397	11	1	bakhan.kamal@univsul.edu.iq	bakhan.kamal@univsul.edu.iq	PROPN
ejpam-5397	11	2	(	(	PUNCT
ejpam-5397	11	3	b.	b.	PROPN
ejpam-5397	11	4	b.	b.	PROPN
ejpam-5397	11	5	kamal	kamal	PROPN
ejpam-5397	11	6	)	)	PUNCT
ejpam-5397	11	7	,	,	PUNCT
ejpam-5397	11	8	arkan.mustafa@univsul.edu.iq	arkan.mustafa@univsul.edu.iq	ADJ
ejpam-5397	11	9	(	(	PUNCT
ejpam-5397	11	10	a.	a.	PROPN
ejpam-5397	11	11	n.	n.	PROPN
ejpam-5397	11	12	mustafa	mustafa	PROPN
ejpam-5397	11	13	)	)	PUNCT
ejpam-5397	11	14	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5397	12	1	1	1	NUM
ejpam-5397	12	2	copyright	copyright	NOUN
ejpam-5397	12	3	:	:	PUNCT
ejpam-5397	12	4	©	©	PROPN
ejpam-5397	12	5	2025	2025	NUM
ejpam-5397	12	6	the	the	DET
ejpam-5397	12	7	author(s	author(s	NOUN
ejpam-5397	12	8	)	)	PUNCT
ejpam-5397	12	9	.	.	PUNCT
ejpam-5397	13	1	(	(	PUNCT
ejpam-5397	13	2	cc	cc	NOUN
ejpam-5397	13	3	by	by	ADP
ejpam-5397	13	4	-	-	PUNCT
ejpam-5397	13	5	nc	nc	PROPN
ejpam-5397	13	6	4.0	4.0	NUM
ejpam-5397	13	7	)	)	PUNCT
ejpam-5397	13	8	b.	b.	PROPN
ejpam-5397	13	9	b.	b.	PROPN
ejpam-5397	13	10	kamal	kamal	PROPN
ejpam-5397	13	11	,	,	PUNCT
ejpam-5397	13	12	a.	a.	PROPN
ejpam-5397	13	13	n.	n.	PROPN
ejpam-5397	13	14	mustafa	mustafa	PROPN
ejpam-5397	13	15	/	/	SYM
ejpam-5397	13	16	eur	eur	PROPN
ejpam-5397	13	17	.	.	PUNCT
ejpam-5397	14	1	j.	j.	PROPN
ejpam-5397	14	2	pure	pure	PROPN
ejpam-5397	14	3	appl	appl	PROPN
ejpam-5397	14	4	.	.	PROPN
ejpam-5397	14	5	math	math	PROPN
ejpam-5397	14	6	,	,	PUNCT
ejpam-5397	14	7	18	18	NUM
ejpam-5397	14	8	(	(	PUNCT
ejpam-5397	14	9	1	1	NUM
ejpam-5397	14	10	)	)	PUNCT
ejpam-5397	14	11	(	(	PUNCT
ejpam-5397	14	12	2025	2025	NUM
ejpam-5397	14	13	)	)	PUNCT
ejpam-5397	14	14	,	,	PUNCT
ejpam-5397	14	15	5397	5397	NUM
ejpam-5397	14	16	2	2	NUM
ejpam-5397	14	17	of	of	ADP
ejpam-5397	14	18	21	21	NUM
ejpam-5397	14	19	the	the	DET
ejpam-5397	14	20	number	number	NOUN
ejpam-5397	14	21	of	of	ADP
ejpam-5397	14	22	consumed	consume	VERB
ejpam-5397	14	23	prey	prey	NOUN
ejpam-5397	14	24	per	per	ADP
ejpam-5397	14	25	predator	predator	NOUN
ejpam-5397	14	26	per	per	ADP
ejpam-5397	14	27	unit	unit	NOUN
ejpam-5397	14	28	time	time	NOUN
ejpam-5397	14	29	[	[	X
ejpam-5397	14	30	9	9	NUM
ejpam-5397	14	31	]	]	PUNCT
ejpam-5397	14	32	.	.	PUNCT
ejpam-5397	15	1	c.s	c.s	PROPN
ejpam-5397	15	2	.	.	PROPN
ejpam-5397	15	3	holling	holling	PROPN
ejpam-5397	16	1	[	[	X
ejpam-5397	16	2	12	12	NUM
ejpam-5397	16	3	]	]	PUNCT
ejpam-5397	16	4	identified	identify	VERB
ejpam-5397	16	5	three	three	NUM
ejpam-5397	16	6	types	type	NOUN
ejpam-5397	16	7	of	of	ADP
ejpam-5397	16	8	functional	functional	ADJ
ejpam-5397	16	9	response	response	NOUN
ejpam-5397	16	10	type	type	NOUN
ejpam-5397	16	11	i	i	PRON
ejpam-5397	16	12	,	,	PUNCT
ejpam-5397	16	13	type	type	NOUN
ejpam-5397	16	14	ii	ii	NOUN
ejpam-5397	16	15	and	and	CCONJ
ejpam-5397	16	16	typeiii	typeiii	NOUN
ejpam-5397	16	17	.	.	PUNCT
ejpam-5397	17	1	the	the	DET
ejpam-5397	17	2	most	most	ADV
ejpam-5397	17	3	useful	useful	ADJ
ejpam-5397	17	4	functional	functional	ADJ
ejpam-5397	17	5	response	response	NOUN
ejpam-5397	17	6	is	be	AUX
ejpam-5397	17	7	the	the	DET
ejpam-5397	17	8	holling	holle	VERB
ejpam-5397	17	9	type	type	NOUN
ejpam-5397	17	10	ii	ii	PROPN
ejpam-5397	17	11	functional	functional	ADJ
ejpam-5397	17	12	response	response	NOUN
ejpam-5397	17	13	,	,	PUNCT
ejpam-5397	17	14	which	which	PRON
ejpam-5397	17	15	is	be	AUX
ejpam-5397	17	16	characterized	characterize	VERB
ejpam-5397	17	17	by	by	ADP
ejpam-5397	17	18	decelerating	decelerate	VERB
ejpam-5397	17	19	intake	intake	ADJ
ejpam-5397	17	20	rate	rate	NOUN
ejpam-5397	18	1	[	[	X
ejpam-5397	18	2	12	12	NUM
ejpam-5397	18	3	]	]	PUNCT
ejpam-5397	18	4	.	.	PUNCT
ejpam-5397	19	1	many	many	ADJ
ejpam-5397	19	2	authors	author	NOUN
ejpam-5397	19	3	used	use	VERB
ejpam-5397	19	4	this	this	DET
ejpam-5397	19	5	type	type	NOUN
ejpam-5397	19	6	of	of	ADP
ejpam-5397	19	7	functional	functional	ADJ
ejpam-5397	19	8	response	response	NOUN
ejpam-5397	19	9	for	for	ADP
ejpam-5397	19	10	modeling	model	VERB
ejpam-5397	19	11	the	the	DET
ejpam-5397	19	12	dynamics	dynamic	NOUN
ejpam-5397	19	13	of	of	ADP
ejpam-5397	19	14	interactions	interaction	NOUN
ejpam-5397	19	15	between	between	ADP
ejpam-5397	19	16	predator	predator	NOUN
ejpam-5397	19	17	and	and	CCONJ
ejpam-5397	19	18	prey	prey	NOUN
ejpam-5397	19	19	[	[	X
ejpam-5397	19	20	4	4	NUM
ejpam-5397	19	21	,	,	PUNCT
ejpam-5397	19	22	14	14	NUM
ejpam-5397	19	23	]	]	PUNCT
ejpam-5397	19	24	.	.	PUNCT
ejpam-5397	20	1	jha	jha	NOUN
ejpam-5397	20	2	and	and	CCONJ
ejpam-5397	20	3	ghorai	ghorai	VERB
ejpam-5397	20	4	[	[	X
ejpam-5397	20	5	14	14	NUM
ejpam-5397	20	6	]	]	PUNCT
ejpam-5397	20	7	proposed	propose	VERB
ejpam-5397	20	8	a	a	DET
ejpam-5397	20	9	prey	prey	NOUN
ejpam-5397	20	10	-	-	PUNCT
ejpam-5397	20	11	predator	predator	NOUN
ejpam-5397	20	12	model	model	NOUN
ejpam-5397	20	13	with	with	ADP
ejpam-5397	20	14	selective	selective	ADJ
ejpam-5397	20	15	harvesting	harvesting	NOUN
ejpam-5397	20	16	between	between	ADP
ejpam-5397	20	17	the	the	DET
ejpam-5397	20	18	species	specie	NOUN
ejpam-5397	20	19	using	use	VERB
ejpam-5397	20	20	a	a	DET
ejpam-5397	20	21	holling	holling	ADJ
ejpam-5397	20	22	-	-	PUNCT
ejpam-5397	20	23	type	type	NOUN
ejpam-5397	20	24	functional	functional	ADJ
ejpam-5397	20	25	response	response	NOUN
ejpam-5397	20	26	.	.	PUNCT
ejpam-5397	21	1	hastings	hastings	PROPN
ejpam-5397	22	1	[	[	X
ejpam-5397	22	2	11	11	NUM
ejpam-5397	22	3	,	,	PUNCT
ejpam-5397	22	4	16	16	NUM
ejpam-5397	22	5	]	]	PUNCT
ejpam-5397	22	6	has	have	AUX
ejpam-5397	22	7	studied	study	VERB
ejpam-5397	22	8	the	the	DET
ejpam-5397	22	9	chaotic	chaotic	ADJ
ejpam-5397	22	10	behavior	behavior	NOUN
ejpam-5397	22	11	of	of	ADP
ejpam-5397	22	12	an	an	DET
ejpam-5397	22	13	ecology	ecology	NOUN
ejpam-5397	22	14	model	model	NOUN
ejpam-5397	22	15	including	include	VERB
ejpam-5397	22	16	the	the	DET
ejpam-5397	22	17	three	three	NUM
ejpam-5397	22	18	species	specie	NOUN
ejpam-5397	22	19	.	.	PUNCT
ejpam-5397	23	1	khan	khan	PROPN
ejpam-5397	23	2	et	et	PROPN
ejpam-5397	23	3	al	al	PROPN
ejpam-5397	23	4	.	.	PUNCT
ejpam-5397	24	1	[	[	X
ejpam-5397	24	2	15	15	NUM
ejpam-5397	24	3	]	]	PUNCT
ejpam-5397	24	4	investigated	investigate	VERB
ejpam-5397	24	5	bifurcation	bifurcation	NOUN
ejpam-5397	24	6	analysis	analysis	NOUN
ejpam-5397	24	7	of	of	ADP
ejpam-5397	24	8	a	a	DET
ejpam-5397	24	9	three	three	NUM
ejpam-5397	24	10	-	-	PUNCT
ejpam-5397	24	11	species	species	NOUN
ejpam-5397	24	12	discrete	discrete	ADJ
ejpam-5397	24	13	time	time	NOUN
ejpam-5397	24	14	.	.	PUNCT
ejpam-5397	25	1	sk	sk	INTJ
ejpam-5397	25	2	et	et	PROPN
ejpam-5397	25	3	al	al	PROPN
ejpam-5397	25	4	.	.	PUNCT
ejpam-5397	26	1	[	[	X
ejpam-5397	26	2	22	22	NUM
ejpam-5397	26	3	]	]	PUNCT
ejpam-5397	26	4	explored	explore	VERB
ejpam-5397	26	5	the	the	DET
ejpam-5397	26	6	impact	impact	NOUN
ejpam-5397	26	7	of	of	ADP
ejpam-5397	26	8	the	the	DET
ejpam-5397	26	9	fear	fear	NOUN
ejpam-5397	26	10	of	of	ADP
ejpam-5397	26	11	predators	predator	NOUN
ejpam-5397	26	12	in	in	ADP
ejpam-5397	26	13	prey	prey	NOUN
ejpam-5397	26	14	and	and	CCONJ
ejpam-5397	26	15	shelter	shelter	NOUN
ejpam-5397	26	16	in	in	ADP
ejpam-5397	26	17	a	a	DET
ejpam-5397	26	18	three	three	NUM
ejpam-5397	26	19	-	-	PUNCT
ejpam-5397	26	20	species	species	NOUN
ejpam-5397	26	21	food	food	NOUN
ejpam-5397	26	22	chain	chain	NOUN
ejpam-5397	26	23	model	model	NOUN
ejpam-5397	26	24	with	with	ADP
ejpam-5397	26	25	delays	delay	NOUN
ejpam-5397	26	26	in	in	ADP
ejpam-5397	26	27	hunting	hunt	VERB
ejpam-5397	26	28	cooperation	cooperation	NOUN
ejpam-5397	26	29	.	.	PUNCT
ejpam-5397	27	1	the	the	DET
ejpam-5397	27	2	authors	author	NOUN
ejpam-5397	27	3	[	[	X
ejpam-5397	27	4	20	20	NUM
ejpam-5397	27	5	,	,	PUNCT
ejpam-5397	27	6	21	21	NUM
ejpam-5397	27	7	]	]	PUNCT
ejpam-5397	27	8	have	have	AUX
ejpam-5397	27	9	investigated	investigate	VERB
ejpam-5397	27	10	the	the	DET
ejpam-5397	27	11	dynamic	dynamic	ADJ
ejpam-5397	27	12	behavior	behavior	NOUN
ejpam-5397	27	13	of	of	ADP
ejpam-5397	27	14	a	a	DET
ejpam-5397	27	15	three	three	NUM
ejpam-5397	27	16	species	specie	NOUN
ejpam-5397	27	17	system	system	NOUN
ejpam-5397	27	18	with	with	ADP
ejpam-5397	27	19	a	a	DET
ejpam-5397	27	20	scavenger	scavenger	NOUN
ejpam-5397	27	21	.	.	PUNCT
ejpam-5397	28	1	diana	diana	PROPN
ejpam-5397	28	2	et	et	PROPN
ejpam-5397	28	3	al	al	PROPN
ejpam-5397	28	4	.	.	PUNCT
ejpam-5397	29	1	[	[	X
ejpam-5397	29	2	7	7	NUM
ejpam-5397	29	3	]	]	PUNCT
ejpam-5397	29	4	investigated	investigate	VERB
ejpam-5397	29	5	the	the	DET
ejpam-5397	29	6	three	three	NUM
ejpam-5397	29	7	species	specie	NOUN
ejpam-5397	29	8	model	model	NOUN
ejpam-5397	29	9	’s	’s	PART
ejpam-5397	29	10	dynamic	dynamic	ADJ
ejpam-5397	29	11	behavior	behavior	NOUN
ejpam-5397	29	12	with	with	ADP
ejpam-5397	29	13	logistic	logistic	ADJ
ejpam-5397	29	14	growth	growth	NOUN
ejpam-5397	29	15	in	in	ADP
ejpam-5397	29	16	which	which	PRON
ejpam-5397	29	17	disease	disease	NOUN
ejpam-5397	29	18	was	be	AUX
ejpam-5397	29	19	included	include	VERB
ejpam-5397	29	20	.	.	PUNCT
ejpam-5397	30	1	the	the	DET
ejpam-5397	30	2	behavior	behavior	NOUN
ejpam-5397	30	3	of	of	ADP
ejpam-5397	30	4	a	a	DET
ejpam-5397	30	5	three	three	NUM
ejpam-5397	30	6	-	-	PUNCT
ejpam-5397	30	7	species	species	NOUN
ejpam-5397	30	8	model	model	NOUN
ejpam-5397	30	9	with	with	ADP
ejpam-5397	30	10	time	time	NOUN
ejpam-5397	30	11	delay	delay	NOUN
ejpam-5397	30	12	and	and	CCONJ
ejpam-5397	30	13	noise	noise	NOUN
ejpam-5397	30	14	was	be	AUX
ejpam-5397	30	15	analyzed	analyze	VERB
ejpam-5397	30	16	stochastically	stochastically	ADV
ejpam-5397	30	17	by	by	ADP
ejpam-5397	30	18	danane	danane	NOUN
ejpam-5397	30	19	and	and	CCONJ
ejpam-5397	30	20	torres	torre	VERB
ejpam-5397	30	21	[	[	X
ejpam-5397	30	22	13	13	NUM
ejpam-5397	30	23	]	]	PUNCT
ejpam-5397	30	24	.	.	PUNCT
ejpam-5397	31	1	numerous	numerous	ADJ
ejpam-5397	31	2	writers	writer	NOUN
ejpam-5397	31	3	have	have	AUX
ejpam-5397	31	4	examined	examine	VERB
ejpam-5397	31	5	the	the	DET
ejpam-5397	31	6	three	three	NUM
ejpam-5397	31	7	species	specie	NOUN
ejpam-5397	31	8	model	model	NOUN
ejpam-5397	31	9	’s	’s	PART
ejpam-5397	31	10	dynamics	dynamic	NOUN
ejpam-5397	31	11	in	in	ADP
ejpam-5397	31	12	the	the	DET
ejpam-5397	31	13	presence	presence	NOUN
ejpam-5397	31	14	of	of	ADP
ejpam-5397	31	15	both	both	CCONJ
ejpam-5397	31	16	logistic	logistic	ADJ
ejpam-5397	31	17	and	and	CCONJ
ejpam-5397	31	18	non	non	ADJ
ejpam-5397	31	19	-	-	ADJ
ejpam-5397	31	20	logistic	logistic	ADJ
ejpam-5397	31	21	growth	growth	NOUN
ejpam-5397	31	22	as	as	ADP
ejpam-5397	31	23	of	of	ADP
ejpam-5397	31	24	now	now	ADV
ejpam-5397	31	25	.	.	PUNCT
ejpam-5397	32	1	it	it	PRON
ejpam-5397	32	2	has	have	AUX
ejpam-5397	32	3	been	be	AUX
ejpam-5397	32	4	explored	explore	VERB
ejpam-5397	32	5	the	the	DET
ejpam-5397	32	6	fear	fear	NOUN
ejpam-5397	32	7	effect	effect	NOUN
ejpam-5397	32	8	and	and	CCONJ
ejpam-5397	32	9	stability	stability	NOUN
ejpam-5397	32	10	analysis	analysis	NOUN
ejpam-5397	32	11	of	of	ADP
ejpam-5397	32	12	the	the	DET
ejpam-5397	32	13	food	food	NOUN
ejpam-5397	32	14	chain	chain	NOUN
ejpam-5397	32	15	model	model	NOUN
ejpam-5397	32	16	[	[	X
ejpam-5397	32	17	1	1	NUM
ejpam-5397	32	18	,	,	PUNCT
ejpam-5397	32	19	17	17	NUM
ejpam-5397	32	20	,	,	PUNCT
ejpam-5397	32	21	19	19	NUM
ejpam-5397	32	22	]	]	PUNCT
ejpam-5397	32	23	.	.	PUNCT
ejpam-5397	33	1	in	in	ADP
ejpam-5397	33	2	nature	nature	NOUN
ejpam-5397	33	3	,	,	PUNCT
ejpam-5397	33	4	there	there	PRON
ejpam-5397	33	5	are	be	VERB
ejpam-5397	33	6	many	many	ADJ
ejpam-5397	33	7	predator	predator	NOUN
ejpam-5397	33	8	species	specie	NOUN
ejpam-5397	33	9	that	that	PRON
ejpam-5397	33	10	consume	consume	VERB
ejpam-5397	33	11	more	more	ADJ
ejpam-5397	33	12	than	than	ADP
ejpam-5397	33	13	one	one	NUM
ejpam-5397	33	14	species	specie	NOUN
ejpam-5397	33	15	of	of	ADP
ejpam-5397	33	16	prey	prey	NOUN
ejpam-5397	33	17	as	as	ADV
ejpam-5397	33	18	well	well	ADV
ejpam-5397	33	19	as	as	ADP
ejpam-5397	33	20	intermediate	intermediate	ADJ
ejpam-5397	33	21	predator	predator	NOUN
ejpam-5397	33	22	.	.	PUNCT
ejpam-5397	34	1	for	for	ADP
ejpam-5397	34	2	example	example	NOUN
ejpam-5397	34	3	,	,	PUNCT
ejpam-5397	34	4	lions	lion	NOUN
ejpam-5397	34	5	usually	usually	ADV
ejpam-5397	34	6	predate	predate	VERB
ejpam-5397	34	7	a	a	DET
ejpam-5397	34	8	number	number	NOUN
ejpam-5397	34	9	of	of	ADP
ejpam-5397	34	10	large	large	ADJ
ejpam-5397	34	11	land	land	NOUN
ejpam-5397	34	12	-	-	PUNCT
ejpam-5397	34	13	based	base	VERB
ejpam-5397	34	14	animals	animal	NOUN
ejpam-5397	34	15	,	,	PUNCT
ejpam-5397	34	16	such	such	ADJ
ejpam-5397	34	17	as	as	ADP
ejpam-5397	34	18	antelopes	antelope	NOUN
ejpam-5397	34	19	,	,	PUNCT
ejpam-5397	34	20	buffaloes	buffalo	NOUN
ejpam-5397	34	21	,	,	PUNCT
ejpam-5397	34	22	crocodiles	crocodile	NOUN
ejpam-5397	34	23	,	,	PUNCT
ejpam-5397	34	24	giraffes	giraffe	NOUN
ejpam-5397	34	25	,	,	PUNCT
ejpam-5397	34	26	pigs	pig	NOUN
ejpam-5397	34	27	,	,	PUNCT
ejpam-5397	34	28	zebra	zebra	NOUN
ejpam-5397	34	29	,	,	PUNCT
ejpam-5397	34	30	wild	wild	ADJ
ejpam-5397	34	31	dogs	dog	NOUN
ejpam-5397	34	32	and	and	CCONJ
ejpam-5397	34	33	wildebeest	wildebeest	NOUN
ejpam-5397	34	34	.	.	PUNCT
ejpam-5397	35	1	in	in	ADP
ejpam-5397	35	2	2022	2022	NUM
ejpam-5397	35	3	,	,	PUNCT
ejpam-5397	35	4	the	the	DET
ejpam-5397	35	5	holling	holle	VERB
ejpam-5397	35	6	type	type	NOUN
ejpam-5397	35	7	ii	ii	PROPN
ejpam-5397	35	8	functional	functional	ADJ
ejpam-5397	35	9	response	response	NOUN
ejpam-5397	35	10	is	be	AUX
ejpam-5397	35	11	extended	extend	VERB
ejpam-5397	35	12	to	to	ADP
ejpam-5397	35	13	more	more	ADJ
ejpam-5397	35	14	than	than	ADP
ejpam-5397	35	15	one	one	NUM
ejpam-5397	35	16	prey	prey	NOUN
ejpam-5397	35	17	species	specie	NOUN
ejpam-5397	35	18	[	[	X
ejpam-5397	35	19	9	9	NUM
ejpam-5397	35	20	]	]	PUNCT
ejpam-5397	35	21	.	.	PUNCT
ejpam-5397	36	1	therefore	therefore	ADV
ejpam-5397	36	2	,	,	PUNCT
ejpam-5397	36	3	this	this	DET
ejpam-5397	36	4	current	current	ADJ
ejpam-5397	36	5	work	work	NOUN
ejpam-5397	36	6	is	be	AUX
ejpam-5397	36	7	considered	consider	VERB
ejpam-5397	36	8	and	and	CCONJ
ejpam-5397	36	9	studying	study	VERB
ejpam-5397	36	10	the	the	DET
ejpam-5397	36	11	following	follow	VERB
ejpam-5397	36	12	food	food	NOUN
ejpam-5397	36	13	web	web	NOUN
ejpam-5397	36	14	system	system	NOUN
ejpam-5397	36	15	with	with	ADP
ejpam-5397	36	16	extended	extended	ADJ
ejpam-5397	36	17	holling	holling	NOUN
ejpam-5397	36	18	type	type	NOUN
ejpam-5397	36	19	ii	ii	NOUN
ejpam-5397	36	20	functional	functional	ADJ
ejpam-5397	36	21	response	response	NOUN
ejpam-5397	36	22	to	to	ADP
ejpam-5397	36	23	two	two	NUM
ejpam-5397	36	24	preys.	preys.	NUM
ejpam-5397	36	25	dx	dx	NOUN
ejpam-5397	36	26	dt	dt	NOUN
ejpam-5397	37	1	=	=	PUNCT
ejpam-5397	37	2	x	x	PUNCT
ejpam-5397	37	3	[	[	PUNCT
ejpam-5397	37	4	r1	r1	PROPN
ejpam-5397	37	5	(	(	PUNCT
ejpam-5397	37	6	1−	1−	NUM
ejpam-5397	37	7	x	x	SYM
ejpam-5397	37	8	k	k	NOUN
ejpam-5397	37	9	)	)	PUNCT
ejpam-5397	37	10	−	−	PROPN
ejpam-5397	38	1	βy	βy	DET
ejpam-5397	38	2	1+βtx	1+βtx	PROPN
ejpam-5397	38	3	−	−	PROPN
ejpam-5397	39	1	α1z	α1z	PROPN
ejpam-5397	39	2	1+α1t1x+α2t2y	1+α1t1x+α2t2y	PROPN
ejpam-5397	39	3	]	]	PUNCT
ejpam-5397	39	4	,	,	PUNCT
ejpam-5397	39	5	dy	dy	NOUN
ejpam-5397	39	6	dt	dt	NOUN
ejpam-5397	39	7	=	=	SYM
ejpam-5397	39	8	y	y	PROPN
ejpam-5397	39	9	[	[	PUNCT
ejpam-5397	39	10	r2	r2	PROPN
ejpam-5397	39	11	(	(	PUNCT
ejpam-5397	39	12	1−	1−	NUM
ejpam-5397	39	13	y	y	NOUN
ejpam-5397	39	14	x	x	PROPN
ejpam-5397	39	15	)	)	PUNCT
ejpam-5397	39	16	−	−	PROPN
ejpam-5397	39	17	α2z	α2z	SYM
ejpam-5397	39	18	1+α1t1x+α2t2y	1+α1t1x+α2t2y	PROPN
ejpam-5397	39	19	]	]	PUNCT
ejpam-5397	39	20	,	,	PUNCT
ejpam-5397	39	21	dz	dz	ADJ
ejpam-5397	39	22	dt	dt	NOUN
ejpam-5397	39	23	=	=	PUNCT
ejpam-5397	39	24	r3z	r3z	NOUN
ejpam-5397	39	25	(	(	PUNCT
ejpam-5397	39	26	1−	1−	NUM
ejpam-5397	39	27	z	z	NOUN
ejpam-5397	39	28	x+y	x+y	NUM
ejpam-5397	39	29	)	)	PUNCT
ejpam-5397	39	30	,	,	PUNCT
ejpam-5397	39	31	(	(	PUNCT
ejpam-5397	39	32	1	1	X
ejpam-5397	39	33	)	)	PUNCT
ejpam-5397	39	34	where	where	SCONJ
ejpam-5397	39	35	x(t	x(t	PROPN
ejpam-5397	39	36	)	)	PUNCT
ejpam-5397	39	37	,	,	PUNCT
ejpam-5397	39	38	y	y	PROPN
ejpam-5397	39	39	(	(	PUNCT
ejpam-5397	39	40	t	t	PROPN
ejpam-5397	39	41	)	)	PUNCT
ejpam-5397	39	42	and	and	CCONJ
ejpam-5397	39	43	z(t	z(t	NOUN
ejpam-5397	39	44	)	)	PUNCT
ejpam-5397	39	45	represent	represent	VERB
ejpam-5397	39	46	the	the	DET
ejpam-5397	39	47	individual	individual	ADJ
ejpam-5397	39	48	numbers	number	NOUN
ejpam-5397	39	49	of	of	ADP
ejpam-5397	39	50	the	the	DET
ejpam-5397	39	51	prey	prey	NOUN
ejpam-5397	39	52	,	,	PUNCT
ejpam-5397	39	53	intermediate	intermediate	ADJ
ejpam-5397	39	54	predators	predator	NOUN
ejpam-5397	39	55	and	and	CCONJ
ejpam-5397	39	56	apex	apex	NOUN
ejpam-5397	39	57	predators	predator	NOUN
ejpam-5397	39	58	,	,	PUNCT
ejpam-5397	39	59	respectively	respectively	ADV
ejpam-5397	39	60	.	.	PUNCT
ejpam-5397	40	1	the	the	DET
ejpam-5397	40	2	parameters	parameter	NOUN
ejpam-5397	40	3	are	be	AUX
ejpam-5397	40	4	positive	positive	ADJ
ejpam-5397	40	5	and	and	CCONJ
ejpam-5397	40	6	their	their	PRON
ejpam-5397	40	7	descriptions	description	NOUN
ejpam-5397	40	8	are	be	AUX
ejpam-5397	40	9	given	give	VERB
ejpam-5397	40	10	in	in	ADP
ejpam-5397	40	11	table	table	NOUN
ejpam-5397	40	12	.	.	PUNCT
ejpam-5397	41	1	system	system	NOUN
ejpam-5397	41	2	(	(	PUNCT
ejpam-5397	41	3	1	1	X
ejpam-5397	41	4	)	)	PUNCT
ejpam-5397	41	5	is	be	AUX
ejpam-5397	41	6	derived	derive	VERB
ejpam-5397	41	7	on	on	ADP
ejpam-5397	41	8	the	the	DET
ejpam-5397	41	9	following	follow	VERB
ejpam-5397	41	10	assumptions	assumption	NOUN
ejpam-5397	41	11	(	(	PUNCT
ejpam-5397	41	12	i	i	NOUN
ejpam-5397	41	13	)	)	PUNCT
ejpam-5397	41	14	all	all	DET
ejpam-5397	41	15	the	the	DET
ejpam-5397	41	16	species	specie	NOUN
ejpam-5397	41	17	grow	grow	VERB
ejpam-5397	41	18	logistically	logistically	ADV
ejpam-5397	41	19	.	.	PUNCT
ejpam-5397	42	1	(	(	PUNCT
ejpam-5397	42	2	ii	ii	NOUN
ejpam-5397	42	3	)	)	PUNCT
ejpam-5397	42	4	the	the	DET
ejpam-5397	42	5	apex	apex	NOUN
ejpam-5397	42	6	predators	predator	NOUN
ejpam-5397	42	7	predate	predate	VERB
ejpam-5397	42	8	both	both	PRON
ejpam-5397	42	9	prey	prey	NOUN
ejpam-5397	42	10	and	and	CCONJ
ejpam-5397	42	11	intermediate	intermediate	ADJ
ejpam-5397	42	12	predators	predator	NOUN
ejpam-5397	42	13	according	accord	VERB
ejpam-5397	42	14	to	to	ADP
ejpam-5397	42	15	extended	extended	ADJ
ejpam-5397	42	16	holling	holling	NOUN
ejpam-5397	42	17	type	type	NOUN
ejpam-5397	42	18	ii	ii	NOUN
ejpam-5397	42	19	functional	functional	ADJ
ejpam-5397	42	20	response	response	NOUN
ejpam-5397	42	21	[	[	X
ejpam-5397	42	22	8	8	NUM
ejpam-5397	42	23	]	]	PUNCT
ejpam-5397	42	24	.	.	PUNCT
ejpam-5397	43	1	(	(	PUNCT
ejpam-5397	43	2	iii	iii	X
ejpam-5397	43	3	)	)	PUNCT
ejpam-5397	43	4	the	the	DET
ejpam-5397	43	5	prey	prey	PROPN
ejpam-5397	43	6	population	population	NOUN
ejpam-5397	43	7	predated	predate	VERB
ejpam-5397	43	8	by	by	ADP
ejpam-5397	43	9	intermediate	intermediate	ADJ
ejpam-5397	43	10	predators	predator	NOUN
ejpam-5397	43	11	according	accord	VERB
ejpam-5397	43	12	to	to	ADP
ejpam-5397	43	13	holling	holle	VERB
ejpam-5397	43	14	type	type	NOUN
ejpam-5397	43	15	ii	ii	NOUN
ejpam-5397	43	16	functional	functional	ADJ
ejpam-5397	43	17	response	response	NOUN
ejpam-5397	43	18	.	.	PUNCT
ejpam-5397	44	1	the	the	DET
ejpam-5397	44	2	paper	paper	NOUN
ejpam-5397	44	3	organized	organize	VERB
ejpam-5397	44	4	as	as	SCONJ
ejpam-5397	44	5	follows	follow	VERB
ejpam-5397	44	6	:	:	PUNCT
ejpam-5397	44	7	in	in	ADP
ejpam-5397	44	8	the	the	DET
ejpam-5397	44	9	next	next	ADJ
ejpam-5397	44	10	section	section	NOUN
ejpam-5397	44	11	some	some	DET
ejpam-5397	44	12	preliminaries	preliminary	NOUN
ejpam-5397	44	13	on	on	ADP
ejpam-5397	44	14	the	the	DET
ejpam-5397	44	15	model	model	NOUN
ejpam-5397	44	16	solution	solution	NOUN
ejpam-5397	44	17	property	property	NOUN
ejpam-5397	44	18	,	,	PUNCT
ejpam-5397	44	19	which	which	PRON
ejpam-5397	44	20	are	be	AUX
ejpam-5397	44	21	also	also	ADV
ejpam-5397	44	22	needed	need	VERB
ejpam-5397	44	23	in	in	ADP
ejpam-5397	44	24	this	this	DET
ejpam-5397	44	25	work	work	NOUN
ejpam-5397	44	26	,	,	PUNCT
ejpam-5397	44	27	are	be	AUX
ejpam-5397	44	28	given	give	VERB
ejpam-5397	44	29	.	.	PUNCT
ejpam-5397	45	1	in	in	ADP
ejpam-5397	45	2	the	the	DET
ejpam-5397	45	3	third	third	ADJ
ejpam-5397	45	4	section	section	NOUN
ejpam-5397	45	5	,	,	PUNCT
ejpam-5397	45	6	the	the	DET
ejpam-5397	45	7	existence	existence	NOUN
ejpam-5397	45	8	conditions	condition	NOUN
ejpam-5397	45	9	of	of	ADP
ejpam-5397	45	10	all	all	DET
ejpam-5397	45	11	feasible	feasible	ADJ
ejpam-5397	45	12	and	and	CCONJ
ejpam-5397	45	13	possible	possible	ADJ
ejpam-5397	45	14	steady	steady	ADJ
ejpam-5397	45	15	stat	stat	NOUN
ejpam-5397	45	16	points	point	NOUN
ejpam-5397	45	17	of	of	ADP
ejpam-5397	45	18	system	system	NOUN
ejpam-5397	45	19	(	(	PUNCT
ejpam-5397	45	20	1	1	X
ejpam-5397	45	21	)	)	PUNCT
ejpam-5397	45	22	are	be	AUX
ejpam-5397	45	23	b.	b.	PROPN
ejpam-5397	45	24	b.	b.	PROPN
ejpam-5397	45	25	kamal	kamal	PROPN
ejpam-5397	45	26	,	,	PUNCT
ejpam-5397	45	27	a.	a.	PROPN
ejpam-5397	45	28	n.	n.	PROPN
ejpam-5397	45	29	mustafa	mustafa	PROPN
ejpam-5397	45	30	/	/	SYM
ejpam-5397	45	31	eur	eur	PROPN
ejpam-5397	45	32	.	.	PUNCT
ejpam-5397	46	1	j.	j.	PROPN
ejpam-5397	46	2	pure	pure	PROPN
ejpam-5397	46	3	appl	appl	PROPN
ejpam-5397	46	4	.	.	PROPN
ejpam-5397	46	5	math	math	PROPN
ejpam-5397	46	6	,	,	PUNCT
ejpam-5397	46	7	18	18	NUM
ejpam-5397	46	8	(	(	PUNCT
ejpam-5397	46	9	1	1	NUM
ejpam-5397	46	10	)	)	PUNCT
ejpam-5397	46	11	(	(	PUNCT
ejpam-5397	46	12	2025	2025	NUM
ejpam-5397	46	13	)	)	PUNCT
ejpam-5397	46	14	,	,	PUNCT
ejpam-5397	46	15	5397	5397	NUM
ejpam-5397	46	16	3	3	NUM
ejpam-5397	46	17	of	of	ADP
ejpam-5397	46	18	21	21	NUM
ejpam-5397	46	19	found	find	VERB
ejpam-5397	46	20	and	and	CCONJ
ejpam-5397	46	21	their	their	PRON
ejpam-5397	46	22	local	local	ADJ
ejpam-5397	46	23	as	as	ADV
ejpam-5397	46	24	well	well	ADV
ejpam-5397	46	25	as	as	ADP
ejpam-5397	46	26	globally	globally	ADV
ejpam-5397	46	27	stability	stability	NOUN
ejpam-5397	46	28	are	be	AUX
ejpam-5397	46	29	investigated	investigate	VERB
ejpam-5397	46	30	.	.	PUNCT
ejpam-5397	47	1	in	in	ADP
ejpam-5397	47	2	section	section	NOUN
ejpam-5397	47	3	five	five	NUM
ejpam-5397	47	4	,	,	PUNCT
ejpam-5397	47	5	the	the	DET
ejpam-5397	47	6	hopfbifurcation	hopfbifurcation	NOUN
ejpam-5397	47	7	near	near	ADV
ejpam-5397	47	8	to	to	ADP
ejpam-5397	47	9	each	each	DET
ejpam-5397	47	10	steady	steady	ADJ
ejpam-5397	47	11	state	state	NOUN
ejpam-5397	47	12	point	point	NOUN
ejpam-5397	47	13	is	be	AUX
ejpam-5397	47	14	studied	study	VERB
ejpam-5397	47	15	.	.	PUNCT
ejpam-5397	48	1	in	in	ADP
ejpam-5397	48	2	section	section	NOUN
ejpam-5397	48	3	six	six	NUM
ejpam-5397	48	4	,	,	PUNCT
ejpam-5397	48	5	system	system	NOUN
ejpam-5397	48	6	(	(	PUNCT
ejpam-5397	48	7	1	1	X
ejpam-5397	48	8	)	)	PUNCT
ejpam-5397	48	9	numerically	numerically	ADV
ejpam-5397	48	10	solved	solve	VERB
ejpam-5397	48	11	to	to	PART
ejpam-5397	48	12	observe	observe	VERB
ejpam-5397	48	13	the	the	DET
ejpam-5397	48	14	impact	impact	NOUN
ejpam-5397	48	15	of	of	ADP
ejpam-5397	48	16	parameters	parameter	NOUN
ejpam-5397	48	17	and	and	CCONJ
ejpam-5397	48	18	confirm	confirm	VERB
ejpam-5397	48	19	the	the	DET
ejpam-5397	48	20	analytical	analytical	ADJ
ejpam-5397	48	21	results	result	NOUN
ejpam-5397	48	22	in	in	ADP
ejpam-5397	48	23	this	this	DET
ejpam-5397	48	24	work	work	NOUN
ejpam-5397	48	25	.	.	PUNCT
ejpam-5397	49	1	finally	finally	ADV
ejpam-5397	49	2	in	in	ADP
ejpam-5397	49	3	section	section	NOUN
ejpam-5397	49	4	eight	eight	NUM
ejpam-5397	49	5	.	.	PUNCT
ejpam-5397	50	1	a	a	DET
ejpam-5397	50	2	brief	brief	ADJ
ejpam-5397	50	3	conclusion	conclusion	NOUN
ejpam-5397	50	4	on	on	ADP
ejpam-5397	50	5	the	the	DET
ejpam-5397	50	6	total	total	ADJ
ejpam-5397	50	7	work	work	NOUN
ejpam-5397	50	8	is	be	AUX
ejpam-5397	50	9	given	give	VERB
ejpam-5397	50	10	.	.	PUNCT
ejpam-5397	51	1	where	where	SCONJ
ejpam-5397	51	2	,	,	PUNCT
ejpam-5397	51	3	all	all	DET
ejpam-5397	51	4	other	other	ADJ
ejpam-5397	51	5	parameter	parameter	NOUN
ejpam-5397	51	6	description	description	NOUN
ejpam-5397	51	7	in	in	ADP
ejpam-5397	51	8	table	table	NOUN
ejpam-5397	51	9	1	1	NUM
ejpam-5397	51	10	.	.	PUNCT
ejpam-5397	52	1	parameters	parameter	NOUN
ejpam-5397	52	2	description	description	NOUN
ejpam-5397	52	3	r1	r1	PROPN
ejpam-5397	52	4	,	,	PUNCT
ejpam-5397	52	5	r2	r2	PROPN
ejpam-5397	52	6	,	,	PUNCT
ejpam-5397	52	7	r3	r3	PROPN
ejpam-5397	52	8	intrinsic	intrinsic	ADJ
ejpam-5397	52	9	growth	growth	NOUN
ejpam-5397	52	10	rate	rate	NOUN
ejpam-5397	52	11	for	for	ADP
ejpam-5397	52	12	prey	prey	NOUN
ejpam-5397	52	13	,	,	PUNCT
ejpam-5397	52	14	intermediate	intermediate	ADJ
ejpam-5397	52	15	predators	predator	NOUN
ejpam-5397	52	16	and	and	CCONJ
ejpam-5397	52	17	apex	apex	NOUN
ejpam-5397	52	18	predators	predator	NOUN
ejpam-5397	52	19	,	,	PUNCT
ejpam-5397	52	20	respectively	respectively	ADV
ejpam-5397	52	21	k	k	NOUN
ejpam-5397	52	22	carrying	carry	VERB
ejpam-5397	52	23	capacity	capacity	NOUN
ejpam-5397	52	24	for	for	ADP
ejpam-5397	52	25	prey	prey	PROPN
ejpam-5397	52	26	species	species	PROPN
ejpam-5397	52	27	β	β	X
ejpam-5397	52	28	by	by	ADP
ejpam-5397	52	29	intermediate	intermediate	ADJ
ejpam-5397	52	30	predators	predator	NOUN
ejpam-5397	52	31	’	'	PUNCT
ejpam-5397	52	32	predation	predation	NOUN
ejpam-5397	52	33	rate	rate	NOUN
ejpam-5397	52	34	t	t	PROPN
ejpam-5397	52	35	the	the	DET
ejpam-5397	52	36	predator	predator	NOUN
ejpam-5397	52	37	’s	’s	PART
ejpam-5397	52	38	average	average	ADJ
ejpam-5397	52	39	handling	handling	NOUN
ejpam-5397	52	40	time	time	NOUN
ejpam-5397	52	41	of	of	ADP
ejpam-5397	52	42	intermediate	intermediate	ADJ
ejpam-5397	52	43	predators	predator	NOUN
ejpam-5397	52	44	α1	α1	NOUN
ejpam-5397	52	45	,	,	PUNCT
ejpam-5397	52	46	α2	α2	ADJ
ejpam-5397	52	47	predator	predator	NOUN
ejpam-5397	52	48	’s	’s	PART
ejpam-5397	52	49	search	search	NOUN
ejpam-5397	52	50	efficiency	efficiency	NOUN
ejpam-5397	52	51	of	of	ADP
ejpam-5397	52	52	prey	prey	NOUN
ejpam-5397	52	53	,	,	PUNCT
ejpam-5397	52	54	intermediate	intermediate	ADJ
ejpam-5397	52	55	predators	predator	NOUN
ejpam-5397	52	56	,	,	PUNCT
ejpam-5397	52	57	respectively	respectively	ADV
ejpam-5397	52	58	t1	t1	NOUN
ejpam-5397	52	59	,	,	PUNCT
ejpam-5397	52	60	t2	t2	NOUN
ejpam-5397	52	61	predator	predator	NOUN
ejpam-5397	52	62	’s	’s	PART
ejpam-5397	52	63	average	average	ADJ
ejpam-5397	52	64	handling	handling	NOUN
ejpam-5397	52	65	time	time	NOUN
ejpam-5397	52	66	of	of	ADP
ejpam-5397	52	67	prey	prey	NOUN
ejpam-5397	52	68	,	,	PUNCT
ejpam-5397	52	69	intermediate	intermediate	ADJ
ejpam-5397	52	70	predators	predator	NOUN
ejpam-5397	52	71	,	,	PUNCT
ejpam-5397	52	72	respectively	respectively	ADV
ejpam-5397	52	73	table	table	NOUN
ejpam-5397	52	74	1	1	NUM
ejpam-5397	52	75	:	:	PUNCT
ejpam-5397	52	76	parameter	parameter	NOUN
ejpam-5397	52	77	description	description	NOUN
ejpam-5397	52	78	of	of	ADP
ejpam-5397	52	79	system	system	NOUN
ejpam-5397	52	80	(	(	PUNCT
ejpam-5397	52	81	1	1	NUM
ejpam-5397	52	82	)	)	PUNCT
ejpam-5397	52	83	.	.	PUNCT
ejpam-5397	53	1	2	2	X
ejpam-5397	53	2	.	.	NUM
ejpam-5397	53	3	preliminaries	preliminary	NOUN
ejpam-5397	53	4	and	and	CCONJ
ejpam-5397	53	5	permanence	permanence	NOUN
ejpam-5397	53	6	in	in	ADP
ejpam-5397	53	7	this	this	DET
ejpam-5397	53	8	section	section	NOUN
ejpam-5397	53	9	,	,	PUNCT
ejpam-5397	53	10	it	it	PRON
ejpam-5397	53	11	is	be	AUX
ejpam-5397	53	12	proved	prove	VERB
ejpam-5397	53	13	some	some	DET
ejpam-5397	53	14	lemma	lemma	PROPN
ejpam-5397	53	15	on	on	ADP
ejpam-5397	53	16	the	the	DET
ejpam-5397	53	17	model	model	NOUN
ejpam-5397	53	18	solutions	solution	NOUN
ejpam-5397	53	19	,	,	PUNCT
ejpam-5397	53	20	the	the	DET
ejpam-5397	53	21	lemmas	lemma	NOUN
ejpam-5397	53	22	are	be	AUX
ejpam-5397	53	23	also	also	ADV
ejpam-5397	53	24	needed	need	VERB
ejpam-5397	53	25	to	to	PART
ejpam-5397	53	26	obtain	obtain	VERB
ejpam-5397	53	27	the	the	DET
ejpam-5397	53	28	result	result	NOUN
ejpam-5397	53	29	in	in	ADP
ejpam-5397	53	30	this	this	DET
ejpam-5397	53	31	paper	paper	NOUN
ejpam-5397	53	32	.	.	PUNCT
ejpam-5397	54	1	a	a	DET
ejpam-5397	54	2	permanent	permanent	ADJ
ejpam-5397	54	3	ecological	ecological	ADJ
ejpam-5397	54	4	model	model	NOUN
ejpam-5397	54	5	,	,	PUNCT
ejpam-5397	54	6	imply	imply	VERB
ejpam-5397	54	7	that	that	SCONJ
ejpam-5397	54	8	all	all	DET
ejpam-5397	54	9	the	the	DET
ejpam-5397	54	10	species	specie	NOUN
ejpam-5397	54	11	in	in	ADP
ejpam-5397	54	12	an	an	DET
ejpam-5397	54	13	ecosystem	ecosystem	NOUN
ejpam-5397	54	14	continues	continue	VERB
ejpam-5397	54	15	to	to	PART
ejpam-5397	54	16	exist	exist	VERB
ejpam-5397	54	17	,	,	PUNCT
ejpam-5397	54	18	therefore	therefore	ADV
ejpam-5397	54	19	,	,	PUNCT
ejpam-5397	54	20	the	the	DET
ejpam-5397	54	21	criteria	criterion	NOUN
ejpam-5397	54	22	that	that	PRON
ejpam-5397	54	23	make	make	VERB
ejpam-5397	54	24	the	the	DET
ejpam-5397	54	25	model	model	NOUN
ejpam-5397	54	26	permanent	permanent	ADJ
ejpam-5397	54	27	is	be	AUX
ejpam-5397	54	28	important	important	ADJ
ejpam-5397	54	29	,	,	PUNCT
ejpam-5397	54	30	so	so	ADV
ejpam-5397	54	31	in	in	ADP
ejpam-5397	54	32	this	this	DET
ejpam-5397	54	33	section	section	NOUN
ejpam-5397	54	34	,	,	PUNCT
ejpam-5397	54	35	the	the	DET
ejpam-5397	54	36	definition	definition	NOUN
ejpam-5397	54	37	of	of	ADP
ejpam-5397	54	38	permanence	permanence	NOUN
ejpam-5397	54	39	is	be	AUX
ejpam-5397	54	40	reviewed	review	VERB
ejpam-5397	54	41	and	and	CCONJ
ejpam-5397	54	42	then	then	ADV
ejpam-5397	54	43	it	it	PRON
ejpam-5397	54	44	is	be	AUX
ejpam-5397	54	45	proved	prove	VERB
ejpam-5397	54	46	that	that	DET
ejpam-5397	54	47	system	system	NOUN
ejpam-5397	54	48	(	(	PUNCT
ejpam-5397	54	49	1	1	X
ejpam-5397	54	50	)	)	PUNCT
ejpam-5397	54	51	is	be	AUX
ejpam-5397	54	52	permanent	permanent	ADJ
ejpam-5397	54	53	under	under	ADP
ejpam-5397	54	54	certain	certain	ADJ
ejpam-5397	54	55	conditions	condition	NOUN
ejpam-5397	54	56	.	.	PUNCT
ejpam-5397	55	1	lemma	lemma	PROPN
ejpam-5397	55	2	2.1	2.1	NUM
ejpam-5397	55	3	.	.	PUNCT
ejpam-5397	55	4	system	system	NOUN
ejpam-5397	55	5	(	(	PUNCT
ejpam-5397	55	6	1	1	NUM
ejpam-5397	55	7	)	)	PUNCT
ejpam-5397	55	8	,	,	PUNCT
ejpam-5397	55	9	exhibits	exhibit	VERB
ejpam-5397	55	10	a	a	DET
ejpam-5397	55	11	unique	unique	ADJ
ejpam-5397	55	12	solution	solution	NOUN
ejpam-5397	55	13	that	that	PRON
ejpam-5397	55	14	is	be	AUX
ejpam-5397	55	15	non	non	ADJ
ejpam-5397	55	16	-	-	ADJ
ejpam-5397	55	17	negative	negative	ADJ
ejpam-5397	55	18	and	and	CCONJ
ejpam-5397	55	19	satisfy	satisfy	VERB
ejpam-5397	55	20	the	the	DET
ejpam-5397	55	21	following	follow	VERB
ejpam-5397	55	22	inequalities	inequality	NOUN
ejpam-5397	55	23	:	:	PUNCT
ejpam-5397	55	24	lim	lim	PROPN
ejpam-5397	55	25	t→∞	t→∞	PRON
ejpam-5397	55	26	sup(x(t	sup(x(t	PROPN
ejpam-5397	55	27	)	)	PUNCT
ejpam-5397	55	28	)	)	PUNCT
ejpam-5397	56	1	≤	≤	NUM
ejpam-5397	57	1	k	k	X
ejpam-5397	57	2	(	(	PUNCT
ejpam-5397	57	3	2	2	X
ejpam-5397	57	4	)	)	PUNCT
ejpam-5397	57	5	lim	lim	NOUN
ejpam-5397	57	6	t→∞	t→∞	X
ejpam-5397	57	7	sup(y	sup(y	PROPN
ejpam-5397	57	8	(	(	PUNCT
ejpam-5397	57	9	t	t	PROPN
ejpam-5397	57	10	)	)	PUNCT
ejpam-5397	57	11	)	)	PUNCT
ejpam-5397	57	12	≤	≤	NUM
ejpam-5397	58	1	k	k	X
ejpam-5397	58	2	(	(	PUNCT
ejpam-5397	58	3	3	3	X
ejpam-5397	58	4	)	)	PUNCT
ejpam-5397	58	5	lim	lim	PROPN
ejpam-5397	58	6	t→∞	t→∞	NUM
ejpam-5397	58	7	sup(z(t	sup(z(t	PROPN
ejpam-5397	58	8	)	)	PUNCT
ejpam-5397	58	9	)	)	PUNCT
ejpam-5397	58	10	≤	≤	ADV
ejpam-5397	58	11	2	2	NUM
ejpam-5397	58	12	k	k	X
ejpam-5397	58	13	(	(	PUNCT
ejpam-5397	58	14	4	4	X
ejpam-5397	58	15	)	)	PUNCT
ejpam-5397	58	16	proof	proof	NOUN
ejpam-5397	58	17	.	.	PUNCT
ejpam-5397	59	1	right	right	ADJ
ejpam-5397	59	2	side	side	NOUN
ejpam-5397	59	3	of	of	ADP
ejpam-5397	59	4	system	system	NOUN
ejpam-5397	59	5	(	(	PUNCT
ejpam-5397	59	6	1	1	NUM
ejpam-5397	59	7	)	)	PUNCT
ejpam-5397	59	8	,	,	PUNCT
ejpam-5397	59	9	are	be	AUX
ejpam-5397	59	10	continuous	continuous	ADJ
ejpam-5397	59	11	and	and	CCONJ
ejpam-5397	59	12	has	have	VERB
ejpam-5397	59	13	partial	partial	ADJ
ejpam-5397	59	14	derivatives	derivative	NOUN
ejpam-5397	59	15	on	on	ADP
ejpam-5397	59	16	the	the	DET
ejpam-5397	59	17	space	space	NOUN
ejpam-5397	59	18	r3	r3	NOUN
ejpam-5397	59	19	,	,	PUNCT
ejpam-5397	59	20	and	and	CCONJ
ejpam-5397	59	21	hence	hence	ADV
ejpam-5397	59	22	,	,	PUNCT
ejpam-5397	59	23	system	system	NOUN
ejpam-5397	59	24	(	(	PUNCT
ejpam-5397	59	25	1	1	X
ejpam-5397	59	26	)	)	PUNCT
ejpam-5397	59	27	satisfies	satisfy	VERB
ejpam-5397	59	28	the	the	DET
ejpam-5397	59	29	lipschitzian	lipschitzian	ADJ
ejpam-5397	59	30	condition	condition	NOUN
ejpam-5397	59	31	.	.	PUNCT
ejpam-5397	60	1	therefore	therefore	ADV
ejpam-5397	60	2	,	,	PUNCT
ejpam-5397	60	3	by	by	ADP
ejpam-5397	60	4	uniqueness	uniqueness	NOUN
ejpam-5397	60	5	theorem	theorem	VERB
ejpam-5397	60	6	,	,	PUNCT
ejpam-5397	60	7	it	it	PRON
ejpam-5397	60	8	has	have	VERB
ejpam-5397	60	9	unique	unique	ADJ
ejpam-5397	60	10	solution	solution	NOUN
ejpam-5397	60	11	.	.	PUNCT
ejpam-5397	61	1	further	far	ADV
ejpam-5397	61	2	,	,	PUNCT
ejpam-5397	61	3	the	the	DET
ejpam-5397	61	4	time	time	NOUN
ejpam-5397	61	5	derivative	derivative	NOUN
ejpam-5397	61	6	of	of	ADP
ejpam-5397	61	7	x	x	PROPN
ejpam-5397	61	8	,	,	PUNCT
ejpam-5397	61	9	y	y	PROPN
ejpam-5397	61	10	and	and	CCONJ
ejpam-5397	61	11	z	z	PROPN
ejpam-5397	61	12	are	be	AUX
ejpam-5397	61	13	zero	zero	NUM
ejpam-5397	61	14	in	in	ADP
ejpam-5397	61	15	y	y	PROPN
ejpam-5397	61	16	z	z	PROPN
ejpam-5397	61	17	plane	plane	NOUN
ejpam-5397	61	18	,	,	PUNCT
ejpam-5397	61	19	xz	xz	PROPN
ejpam-5397	61	20	plane	plane	NOUN
ejpam-5397	61	21	and	and	CCONJ
ejpam-5397	61	22	xy	xy	PROPN
ejpam-5397	61	23	plane	plane	NOUN
ejpam-5397	61	24	,	,	PUNCT
ejpam-5397	61	25	respectively	respectively	ADV
ejpam-5397	61	26	.	.	PUNCT
ejpam-5397	62	1	b.	b.	PROPN
ejpam-5397	62	2	b.	b.	PROPN
ejpam-5397	62	3	kamal	kamal	PROPN
ejpam-5397	62	4	,	,	PUNCT
ejpam-5397	62	5	a.	a.	PROPN
ejpam-5397	62	6	n.	n.	PROPN
ejpam-5397	62	7	mustafa	mustafa	PROPN
ejpam-5397	62	8	/	/	SYM
ejpam-5397	62	9	eur	eur	PROPN
ejpam-5397	62	10	.	.	PUNCT
ejpam-5397	63	1	j.	j.	PROPN
ejpam-5397	63	2	pure	pure	PROPN
ejpam-5397	63	3	appl	appl	PROPN
ejpam-5397	63	4	.	.	PROPN
ejpam-5397	63	5	math	math	PROPN
ejpam-5397	63	6	,	,	PUNCT
ejpam-5397	63	7	18	18	NUM
ejpam-5397	63	8	(	(	PUNCT
ejpam-5397	63	9	1	1	NUM
ejpam-5397	63	10	)	)	PUNCT
ejpam-5397	63	11	(	(	PUNCT
ejpam-5397	63	12	2025	2025	NUM
ejpam-5397	63	13	)	)	PUNCT
ejpam-5397	63	14	,	,	PUNCT
ejpam-5397	63	15	5397	5397	NUM
ejpam-5397	63	16	4	4	NUM
ejpam-5397	63	17	of	of	ADP
ejpam-5397	63	18	21	21	NUM
ejpam-5397	63	19	therefore	therefore	ADV
ejpam-5397	63	20	,	,	PUNCT
ejpam-5397	63	21	if	if	SCONJ
ejpam-5397	63	22	the	the	DET
ejpam-5397	63	23	solution	solution	NOUN
ejpam-5397	63	24	initiates	initiate	VERB
ejpam-5397	63	25	at	at	ADP
ejpam-5397	63	26	a	a	DET
ejpam-5397	63	27	non	non	ADJ
ejpam-5397	63	28	-	-	ADJ
ejpam-5397	63	29	negative	negative	ADJ
ejpam-5397	63	30	point	point	NOUN
ejpam-5397	63	31	,	,	PUNCT
ejpam-5397	63	32	then	then	ADV
ejpam-5397	63	33	the	the	DET
ejpam-5397	63	34	component	component	NOUN
ejpam-5397	63	35	x	x	PROPN
ejpam-5397	63	36	,	,	PUNCT
ejpam-5397	63	37	y	y	PROPN
ejpam-5397	63	38	and	and	CCONJ
ejpam-5397	63	39	z	z	PROPN
ejpam-5397	63	40	of	of	ADP
ejpam-5397	63	41	the	the	DET
ejpam-5397	63	42	solution	solution	NOUN
ejpam-5397	63	43	points	point	NOUN
ejpam-5397	63	44	of	of	ADP
ejpam-5397	63	45	system	system	NOUN
ejpam-5397	63	46	(	(	PUNCT
ejpam-5397	63	47	1	1	NUM
ejpam-5397	63	48	)	)	PUNCT
ejpam-5397	63	49	,	,	PUNCT
ejpam-5397	63	50	can	can	AUX
ejpam-5397	63	51	not	not	PART
ejpam-5397	63	52	cross	cross	VERB
ejpam-5397	63	53	any	any	DET
ejpam-5397	63	54	coordinates	coordinate	NOUN
ejpam-5397	63	55	of	of	ADP
ejpam-5397	63	56	the	the	DET
ejpam-5397	63	57	solution	solution	NOUN
ejpam-5397	63	58	points	point	NOUN
ejpam-5397	63	59	.	.	PUNCT
ejpam-5397	64	1	hence	hence	ADV
ejpam-5397	64	2	components	component	NOUN
ejpam-5397	64	3	x	x	NOUN
ejpam-5397	64	4	,	,	PUNCT
ejpam-5397	64	5	y	y	PROPN
ejpam-5397	64	6	and	and	CCONJ
ejpam-5397	64	7	z	z	PROPN
ejpam-5397	64	8	of	of	ADP
ejpam-5397	64	9	solution	solution	NOUN
ejpam-5397	64	10	points	point	NOUN
ejpam-5397	64	11	is	be	AUX
ejpam-5397	64	12	always	always	ADV
ejpam-5397	64	13	non	non	ADJ
ejpam-5397	64	14	negative	negative	ADJ
ejpam-5397	64	15	.	.	PUNCT
ejpam-5397	65	1	the	the	DET
ejpam-5397	65	2	first	first	ADJ
ejpam-5397	65	3	equation	equation	NOUN
ejpam-5397	65	4	in	in	ADP
ejpam-5397	65	5	system	system	NOUN
ejpam-5397	65	6	(	(	PUNCT
ejpam-5397	65	7	1	1	X
ejpam-5397	65	8	)	)	PUNCT
ejpam-5397	65	9	gives	give	VERB
ejpam-5397	65	10	that	that	DET
ejpam-5397	65	11	dx	dx	PROPN
ejpam-5397	65	12	dt	dt	PUNCT
ejpam-5397	65	13	≤	≤	PUNCT
ejpam-5397	65	14	r1x	r1x	NOUN
ejpam-5397	65	15	(	(	PUNCT
ejpam-5397	65	16	1−	1−	NUM
ejpam-5397	65	17	x	x	SYM
ejpam-5397	65	18	k	k	NOUN
ejpam-5397	65	19	)	)	PUNCT
ejpam-5397	65	20	.	.	PUNCT
ejpam-5397	66	1	solving	solve	VERB
ejpam-5397	66	2	above	above	ADP
ejpam-5397	66	3	differential	differential	ADJ
ejpam-5397	66	4	inequality	inequality	NOUN
ejpam-5397	66	5	,	,	PUNCT
ejpam-5397	66	6	it	it	PRON
ejpam-5397	66	7	gets	get	VERB
ejpam-5397	66	8	lim	lim	PROPN
ejpam-5397	66	9	t→∞	t→∞	PRON
ejpam-5397	66	10	sup(x(t	sup(x(t	PROPN
ejpam-5397	66	11	)	)	PUNCT
ejpam-5397	66	12	)	)	PUNCT
ejpam-5397	67	1	≤	≤	PROPN
ejpam-5397	67	2	k.	k.	PROPN
ejpam-5397	67	3	apply	apply	VERB
ejpam-5397	67	4	above	above	ADP
ejpam-5397	67	5	inequality	inequality	NOUN
ejpam-5397	67	6	at	at	ADP
ejpam-5397	67	7	the	the	DET
ejpam-5397	67	8	second	second	ADJ
ejpam-5397	67	9	equation	equation	NOUN
ejpam-5397	67	10	of	of	ADP
ejpam-5397	67	11	system	system	NOUN
ejpam-5397	67	12	(	(	PUNCT
ejpam-5397	67	13	1	1	NUM
ejpam-5397	67	14	)	)	PUNCT
ejpam-5397	67	15	,	,	PUNCT
ejpam-5397	67	16	it	it	PRON
ejpam-5397	67	17	gets	get	VERB
ejpam-5397	67	18	dy	dy	NOUN
ejpam-5397	67	19	dt	dt	NOUN
ejpam-5397	67	20	≤	≤	NOUN
ejpam-5397	67	21	r2y	r2y	ADJ
ejpam-5397	67	22	(	(	PUNCT
ejpam-5397	67	23	1−	1−	NUM
ejpam-5397	67	24	x	x	SYM
ejpam-5397	67	25	k	k	NOUN
ejpam-5397	67	26	)	)	PUNCT
ejpam-5397	67	27	.	.	PUNCT
ejpam-5397	68	1	again	again	ADV
ejpam-5397	68	2	solving	solve	VERB
ejpam-5397	68	3	above	above	ADP
ejpam-5397	68	4	differential	differential	ADJ
ejpam-5397	68	5	inequality	inequality	NOUN
ejpam-5397	68	6	,	,	PUNCT
ejpam-5397	68	7	it	it	PRON
ejpam-5397	68	8	gets	get	VERB
ejpam-5397	68	9	lim	lim	PROPN
ejpam-5397	68	10	t→∞	t→∞	PRON
ejpam-5397	68	11	sup(y	sup(y	PROPN
ejpam-5397	68	12	(	(	PUNCT
ejpam-5397	68	13	t	t	PROPN
ejpam-5397	68	14	)	)	PUNCT
ejpam-5397	68	15	)	)	PUNCT
ejpam-5397	68	16	≤	≤	PROPN
ejpam-5397	69	1	k.	k.	PROPN
ejpam-5397	70	1	so	so	ADV
ejpam-5397	70	2	,	,	PUNCT
ejpam-5397	70	3	inequalities	inequality	NOUN
ejpam-5397	70	4	(	(	PUNCT
ejpam-5397	70	5	2	2	NUM
ejpam-5397	70	6	)	)	PUNCT
ejpam-5397	70	7	and	and	CCONJ
ejpam-5397	70	8	(	(	PUNCT
ejpam-5397	70	9	3	3	X
ejpam-5397	70	10	)	)	PUNCT
ejpam-5397	70	11	are	be	AUX
ejpam-5397	70	12	guaranteed	guarantee	VERB
ejpam-5397	70	13	.	.	PUNCT
ejpam-5397	71	1	apply	apply	VERB
ejpam-5397	71	2	inequalities	inequality	NOUN
ejpam-5397	71	3	(	(	PUNCT
ejpam-5397	71	4	2	2	NUM
ejpam-5397	71	5	,	,	PUNCT
ejpam-5397	71	6	3	3	NUM
ejpam-5397	71	7	)	)	PUNCT
ejpam-5397	71	8	in	in	ADP
ejpam-5397	71	9	the	the	DET
ejpam-5397	71	10	third	third	ADJ
ejpam-5397	71	11	equation	equation	NOUN
ejpam-5397	71	12	of	of	ADP
ejpam-5397	71	13	system	system	NOUN
ejpam-5397	71	14	(	(	PUNCT
ejpam-5397	71	15	1	1	NUM
ejpam-5397	71	16	)	)	PUNCT
ejpam-5397	71	17	,	,	PUNCT
ejpam-5397	71	18	it	it	PRON
ejpam-5397	71	19	gets	get	VERB
ejpam-5397	71	20	dz	dz	ADJ
ejpam-5397	71	21	dt	dt	NOUN
ejpam-5397	71	22	≤	≤	X
ejpam-5397	71	23	r1z	r1z	NOUN
ejpam-5397	71	24	(	(	PUNCT
ejpam-5397	71	25	1−	1−	NUM
ejpam-5397	71	26	z	z	NOUN
ejpam-5397	71	27	2k	2k	NUM
ejpam-5397	71	28	)	)	PUNCT
ejpam-5397	72	1	so	so	ADV
ejpam-5397	72	2	,	,	PUNCT
ejpam-5397	72	3	lim	lim	PROPN
ejpam-5397	72	4	t→∞	t→∞	NUM
ejpam-5397	72	5	sup(z(t	sup(z(t	PROPN
ejpam-5397	72	6	)	)	PUNCT
ejpam-5397	72	7	)	)	PUNCT
ejpam-5397	72	8	≤	≤	NOUN
ejpam-5397	72	9	2k	2k	NOUN
ejpam-5397	72	10	.	.	PUNCT
ejpam-5397	73	1	this	this	PRON
ejpam-5397	73	2	completes	complete	VERB
ejpam-5397	73	3	the	the	DET
ejpam-5397	73	4	proof	proof	NOUN
ejpam-5397	73	5	.	.	PUNCT
ejpam-5397	74	1	lemma	lemma	PROPN
ejpam-5397	74	2	2.2	2.2	NUM
ejpam-5397	74	3	.	.	PUNCT
ejpam-5397	75	1	(	(	PUNCT
ejpam-5397	75	2	i	i	NOUN
ejpam-5397	75	3	)	)	PUNCT
ejpam-5397	75	4	limt→∞	limt→∞	ADP
ejpam-5397	75	5	infx(t	infx(t	PROPN
ejpam-5397	75	6	)	)	PUNCT
ejpam-5397	75	7	≥	≥	NOUN
ejpam-5397	75	8	k1	k1	NOUN
ejpam-5397	75	9	,	,	PUNCT
ejpam-5397	75	10	if	if	SCONJ
ejpam-5397	75	11	r1	r1	PROPN
ejpam-5397	75	12	>	>	X
ejpam-5397	75	13	(	(	PUNCT
ejpam-5397	75	14	β	β	X
ejpam-5397	75	15	+	+	CCONJ
ejpam-5397	75	16	2α1)k	2α1)k	NUM
ejpam-5397	75	17	(	(	PUNCT
ejpam-5397	75	18	5	5	NUM
ejpam-5397	75	19	)	)	PUNCT
ejpam-5397	75	20	(	(	PUNCT
ejpam-5397	75	21	ii	ii	NOUN
ejpam-5397	75	22	)	)	PUNCT
ejpam-5397	75	23	limt→∞	limt→∞	PROPN
ejpam-5397	75	24	inf	inf	PROPN
ejpam-5397	75	25	y	y	PROPN
ejpam-5397	75	26	(	(	PUNCT
ejpam-5397	75	27	t	t	PROPN
ejpam-5397	75	28	)	)	PUNCT
ejpam-5397	75	29	≥	≥	NOUN
ejpam-5397	75	30	k2	k2	NOUN
ejpam-5397	75	31	,	,	PUNCT
ejpam-5397	75	32	if	if	SCONJ
ejpam-5397	75	33	inq.(5	inq.(5	NOUN
ejpam-5397	75	34	)	)	PUNCT
ejpam-5397	75	35	and	and	CCONJ
ejpam-5397	75	36	the	the	DET
ejpam-5397	75	37	following	follow	VERB
ejpam-5397	75	38	inequality	inequality	NOUN
ejpam-5397	75	39	are	be	AUX
ejpam-5397	75	40	satisfied	satisfied	ADJ
ejpam-5397	75	41	r2	r2	PROPN
ejpam-5397	75	42	>	>	X
ejpam-5397	75	43	2α2	2α2	NUM
ejpam-5397	75	44	(	(	PUNCT
ejpam-5397	75	45	1	1	NUM
ejpam-5397	75	46	+	+	NUM
ejpam-5397	75	47	α1t1k1	α1t1k1	NOUN
ejpam-5397	75	48	)	)	PUNCT
ejpam-5397	76	1	k	k	NOUN
ejpam-5397	76	2	(	(	PUNCT
ejpam-5397	76	3	6	6	NUM
ejpam-5397	76	4	)	)	PUNCT
ejpam-5397	76	5	(	(	PUNCT
ejpam-5397	76	6	iii	iii	X
ejpam-5397	76	7	)	)	PUNCT
ejpam-5397	76	8	limt→∞	limt→∞	ADP
ejpam-5397	76	9	inf	inf	PROPN
ejpam-5397	76	10	z(t	z(t	PROPN
ejpam-5397	76	11	)	)	PUNCT
ejpam-5397	76	12	≥	≥	NOUN
ejpam-5397	76	13	k1	k1	NOUN
ejpam-5397	76	14	+	+	X
ejpam-5397	76	15	k2	k2	ADJ
ejpam-5397	76	16	,	,	PUNCT
ejpam-5397	76	17	if	if	SCONJ
ejpam-5397	76	18	both	both	DET
ejpam-5397	76	19	conditions	condition	NOUN
ejpam-5397	76	20	(	(	PUNCT
ejpam-5397	76	21	5	5	NUM
ejpam-5397	76	22	)	)	PUNCT
ejpam-5397	76	23	and	and	CCONJ
ejpam-5397	76	24	(	(	PUNCT
ejpam-5397	76	25	6	6	NUM
ejpam-5397	76	26	)	)	PUNCT
ejpam-5397	76	27	are	be	AUX
ejpam-5397	76	28	provided	provide	VERB
ejpam-5397	76	29	.	.	PUNCT
ejpam-5397	77	1	where	where	SCONJ
ejpam-5397	77	2	,	,	PUNCT
ejpam-5397	77	3	k1	k1	PROPN
ejpam-5397	77	4	and	and	CCONJ
ejpam-5397	77	5	k2	k2	PROPN
ejpam-5397	77	6	are	be	AUX
ejpam-5397	77	7	positive	positive	ADJ
ejpam-5397	77	8	number	number	NOUN
ejpam-5397	77	9	to	to	PART
ejpam-5397	77	10	be	be	AUX
ejpam-5397	77	11	determined	determine	VERB
ejpam-5397	77	12	in	in	ADP
ejpam-5397	77	13	the	the	DET
ejpam-5397	77	14	proof	proof	NOUN
ejpam-5397	77	15	.	.	PUNCT
ejpam-5397	78	1	proof	proof	NOUN
ejpam-5397	78	2	.	.	PUNCT
ejpam-5397	79	1	suppose	suppose	VERB
ejpam-5397	79	2	t	t	PROPN
ejpam-5397	79	3	approaches	approach	VERB
ejpam-5397	79	4	infinity	infinity	NOUN
ejpam-5397	79	5	,	,	PUNCT
ejpam-5397	79	6	then	then	ADV
ejpam-5397	79	7	b.	b.	PROPN
ejpam-5397	79	8	b.	b.	PROPN
ejpam-5397	79	9	kamal	kamal	PROPN
ejpam-5397	79	10	,	,	PUNCT
ejpam-5397	79	11	a.	a.	PROPN
ejpam-5397	79	12	n.	n.	PROPN
ejpam-5397	79	13	mustafa	mustafa	PROPN
ejpam-5397	79	14	/	/	SYM
ejpam-5397	79	15	eur	eur	PROPN
ejpam-5397	79	16	.	.	PUNCT
ejpam-5397	80	1	j.	j.	PROPN
ejpam-5397	80	2	pure	pure	PROPN
ejpam-5397	80	3	appl	appl	PROPN
ejpam-5397	80	4	.	.	PROPN
ejpam-5397	80	5	math	math	PROPN
ejpam-5397	80	6	,	,	PUNCT
ejpam-5397	80	7	18	18	NUM
ejpam-5397	80	8	(	(	PUNCT
ejpam-5397	80	9	1	1	NUM
ejpam-5397	80	10	)	)	PUNCT
ejpam-5397	80	11	(	(	PUNCT
ejpam-5397	80	12	2025	2025	NUM
ejpam-5397	80	13	)	)	PUNCT
ejpam-5397	80	14	,	,	PUNCT
ejpam-5397	80	15	5397	5397	NUM
ejpam-5397	80	16	5	5	NUM
ejpam-5397	80	17	of	of	ADP
ejpam-5397	80	18	21	21	NUM
ejpam-5397	80	19	(	(	PUNCT
ejpam-5397	80	20	i	i	NOUN
ejpam-5397	80	21	)	)	PUNCT
ejpam-5397	80	22	apply	apply	VERB
ejpam-5397	80	23	inequalities	inequality	NOUN
ejpam-5397	80	24	(	(	PUNCT
ejpam-5397	80	25	2)–(4	2)–(4	NUM
ejpam-5397	80	26	)	)	PUNCT
ejpam-5397	80	27	in	in	ADP
ejpam-5397	80	28	lemma	lemma	PROPN
ejpam-5397	80	29	2.1	2.1	NUM
ejpam-5397	80	30	,	,	PUNCT
ejpam-5397	80	31	at	at	ADP
ejpam-5397	80	32	the	the	DET
ejpam-5397	80	33	first	first	ADJ
ejpam-5397	80	34	equation	equation	NOUN
ejpam-5397	80	35	of	of	ADP
ejpam-5397	80	36	system	system	NOUN
ejpam-5397	80	37	(	(	PUNCT
ejpam-5397	80	38	1	1	NUM
ejpam-5397	80	39	)	)	PUNCT
ejpam-5397	80	40	,	,	PUNCT
ejpam-5397	80	41	it	it	PRON
ejpam-5397	80	42	gets	get	VERB
ejpam-5397	80	43	dx(t	dx(t	NOUN
ejpam-5397	80	44	)	)	PUNCT
ejpam-5397	80	45	dt	dt	PART
ejpam-5397	81	1	≥	≥	NOUN
ejpam-5397	81	2	x	x	PUNCT
ejpam-5397	81	3	[	[	PUNCT
ejpam-5397	81	4	r1	r1	PROPN
ejpam-5397	81	5	(	(	PUNCT
ejpam-5397	81	6	1−	1−	NUM
ejpam-5397	81	7	x	x	SYM
ejpam-5397	81	8	k	k	NOUN
ejpam-5397	81	9	)	)	PUNCT
ejpam-5397	81	10	−	−	PROPN
ejpam-5397	82	1	(	(	PUNCT
ejpam-5397	82	2	β	β	X
ejpam-5397	82	3	+	+	X
ejpam-5397	82	4	2α1)k	2α1)k	NUM
ejpam-5397	82	5	]	]	PUNCT
ejpam-5397	82	6	.	.	PUNCT
ejpam-5397	83	1	therefore	therefore	ADV
ejpam-5397	83	2	under	under	ADP
ejpam-5397	83	3	condition	condition	NOUN
ejpam-5397	83	4	(	(	PUNCT
ejpam-5397	83	5	5	5	NUM
ejpam-5397	83	6	)	)	PUNCT
ejpam-5397	83	7	,	,	PUNCT
ejpam-5397	83	8	it	it	PRON
ejpam-5397	83	9	gets	get	VERB
ejpam-5397	83	10	lim	lim	PROPN
ejpam-5397	83	11	t→∞	t→∞	ADP
ejpam-5397	83	12	infx(t	infx(t	PROPN
ejpam-5397	83	13	)	)	PUNCT
ejpam-5397	83	14	≥	≥	NOUN
ejpam-5397	83	15	.	.	PUNCT
ejpam-5397	84	1	[	[	X
ejpam-5397	84	2	r1	r1	NOUN
ejpam-5397	84	3	−	−	PROPN
ejpam-5397	84	4	(	(	PUNCT
ejpam-5397	84	5	β	β	X
ejpam-5397	84	6	+	+	CCONJ
ejpam-5397	84	7	2α1)k]k	2α1)k]k	NUM
ejpam-5397	84	8	r1	r1	NOUN
ejpam-5397	84	9	=	=	SYM
ejpam-5397	84	10	k1	k1	PROPN
ejpam-5397	84	11	>	>	X
ejpam-5397	84	12	0	0	PUNCT
ejpam-5397	84	13	(	(	PUNCT
ejpam-5397	84	14	ii	ii	NOUN
ejpam-5397	84	15	)	)	PUNCT
ejpam-5397	84	16	from	from	ADP
ejpam-5397	84	17	condition(4	condition(4	PROPN
ejpam-5397	84	18	)	)	PUNCT
ejpam-5397	84	19	in	in	ADP
ejpam-5397	84	20	lemma	lemma	PROPN
ejpam-5397	84	21	2.1	2.1	NUM
ejpam-5397	84	22	and	and	CCONJ
ejpam-5397	84	23	inequality	inequality	NOUN
ejpam-5397	84	24	(	(	PUNCT
ejpam-5397	84	25	7	7	NUM
ejpam-5397	84	26	)	)	PUNCT
ejpam-5397	84	27	,	,	PUNCT
ejpam-5397	84	28	it	it	PRON
ejpam-5397	84	29	follows	follow	VERB
ejpam-5397	84	30	dy	dy	PROPN
ejpam-5397	84	31	dt	dt	NOUN
ejpam-5397	84	32	≥	≥	PROPN
ejpam-5397	84	33	y	y	PROPN
ejpam-5397	84	34	[	[	PUNCT
ejpam-5397	84	35	r2	r2	PROPN
ejpam-5397	84	36	(	(	PUNCT
ejpam-5397	84	37	1−	1−	NUM
ejpam-5397	84	38	y	y	PROPN
ejpam-5397	84	39	k1	k1	PROPN
ejpam-5397	84	40	)	)	PUNCT
ejpam-5397	84	41	−	−	PROPN
ejpam-5397	85	1	2α2k	2α2k	NOUN
ejpam-5397	85	2	1	1	NUM
ejpam-5397	85	3	+	+	NUM
ejpam-5397	85	4	α1t1k1	α1t1k1	NOUN
ejpam-5397	85	5	]	]	PUNCT
ejpam-5397	85	6	,	,	PUNCT
ejpam-5397	85	7	so	so	CCONJ
ejpam-5397	85	8	under	under	ADP
ejpam-5397	85	9	condition	condition	NOUN
ejpam-5397	85	10	(	(	PUNCT
ejpam-5397	85	11	6	6	NUM
ejpam-5397	85	12	)	)	PUNCT
ejpam-5397	85	13	,	,	PUNCT
ejpam-5397	85	14	it	it	PRON
ejpam-5397	85	15	is	be	AUX
ejpam-5397	85	16	concluded	conclude	VERB
ejpam-5397	85	17	that	that	SCONJ
ejpam-5397	85	18	:	:	PUNCT
ejpam-5397	85	19	lim	lim	PROPN
ejpam-5397	85	20	t→∞	t→∞	X
ejpam-5397	85	21	inf	inf	PROPN
ejpam-5397	85	22	y	y	PROPN
ejpam-5397	85	23	(	(	PUNCT
ejpam-5397	85	24	t	t	PROPN
ejpam-5397	85	25	)	)	PUNCT
ejpam-5397	85	26	≥	≥	NOUN
ejpam-5397	85	27	[	[	PUNCT
ejpam-5397	85	28	1−	1−	NUM
ejpam-5397	85	29	2α2k	2α2k	NUM
ejpam-5397	85	30	r2	r2	NOUN
ejpam-5397	85	31	(	(	PUNCT
ejpam-5397	85	32	1	1	NUM
ejpam-5397	85	33	+	+	NUM
ejpam-5397	85	34	α1t1k1	α1t1k1	NOUN
ejpam-5397	85	35	)	)	PUNCT
ejpam-5397	85	36	]	]	PUNCT
ejpam-5397	85	37	k1	k1	NOUN
ejpam-5397	85	38	=	=	SYM
ejpam-5397	85	39	k2	k2	PROPN
ejpam-5397	85	40	>	>	X
ejpam-5397	85	41	0	0	PUNCT
ejpam-5397	85	42	(	(	PUNCT
ejpam-5397	85	43	iii	iii	NOUN
ejpam-5397	85	44	)	)	PUNCT
ejpam-5397	85	45	from	from	ADP
ejpam-5397	85	46	(	(	PUNCT
ejpam-5397	85	47	7	7	NUM
ejpam-5397	85	48	)	)	PUNCT
ejpam-5397	85	49	and	and	CCONJ
ejpam-5397	85	50	(	(	PUNCT
ejpam-5397	85	51	8)	8)	NUM
ejpam-5397	85	52	,	,	PUNCT
ejpam-5397	85	53	it	it	PRON
ejpam-5397	85	54	follows	follow	VERB
ejpam-5397	85	55	dz	dz	PROPN
ejpam-5397	85	56	dt	dt	ADP
ejpam-5397	85	57	≥	≥	NOUN
ejpam-5397	85	58	r3z	r3z	NOUN
ejpam-5397	85	59	(	(	PUNCT
ejpam-5397	85	60	1−	1−	NUM
ejpam-5397	85	61	z	z	NOUN
ejpam-5397	85	62	k1	k1	NOUN
ejpam-5397	86	1	+	+	NOUN
ejpam-5397	86	2	k2	k2	NOUN
ejpam-5397	86	3	)	)	PUNCT
ejpam-5397	86	4	,	,	PUNCT
ejpam-5397	86	5	and	and	CCONJ
ejpam-5397	86	6	hence	hence	ADV
ejpam-5397	86	7	lim	lim	PROPN
ejpam-5397	86	8	t→∞	t→∞	X
ejpam-5397	86	9	inf	inf	PROPN
ejpam-5397	86	10	z(t	z(t	PROPN
ejpam-5397	86	11	)	)	PUNCT
ejpam-5397	86	12	≥	≥	NOUN
ejpam-5397	86	13	k1	k1	NOUN
ejpam-5397	87	1	+	+	NOUN
ejpam-5397	88	1	k2	k2	ADJ
ejpam-5397	88	2	.	.	PUNCT
ejpam-5397	89	1	definition	definition	NOUN
ejpam-5397	89	2	2.1	2.1	NUM
ejpam-5397	89	3	.	.	PUNCT
ejpam-5397	90	1	[	[	X
ejpam-5397	90	2	5	5	NUM
ejpam-5397	90	3	]	]	X
ejpam-5397	90	4	system	system	NOUN
ejpam-5397	90	5	(	(	PUNCT
ejpam-5397	90	6	1	1	X
ejpam-5397	90	7	)	)	PUNCT
ejpam-5397	90	8	is	be	AUX
ejpam-5397	90	9	said	say	VERB
ejpam-5397	90	10	to	to	PART
ejpam-5397	90	11	be	be	AUX
ejpam-5397	90	12	permanent	permanent	ADJ
ejpam-5397	90	13	if	if	SCONJ
ejpam-5397	90	14	there	there	PRON
ejpam-5397	90	15	exist	exist	VERB
ejpam-5397	90	16	positive	positive	ADJ
ejpam-5397	90	17	constants	constant	NOUN
ejpam-5397	90	18	a	a	PRON
ejpam-5397	90	19	and	and	CCONJ
ejpam-5397	90	20	b	b	NOUN
ejpam-5397	90	21	such	such	ADJ
ejpam-5397	90	22	that	that	DET
ejpam-5397	90	23	b	b	PROPN
ejpam-5397	90	24	≥	≥	NUM
ejpam-5397	90	25	max	max	PROPN
ejpam-5397	90	26	{	{	PUNCT
ejpam-5397	90	27	lim	lim	PROPN
ejpam-5397	90	28	t→∞	t→∞	NUM
ejpam-5397	90	29	sup(x(t	sup(x(t	PROPN
ejpam-5397	90	30	)	)	PUNCT
ejpam-5397	90	31	)	)	PUNCT
ejpam-5397	90	32	,	,	PUNCT
ejpam-5397	90	33	lim	lim	PROPN
ejpam-5397	90	34	t→∞	t→∞	PRON
ejpam-5397	90	35	sup(y	sup(y	PROPN
ejpam-5397	90	36	(	(	PUNCT
ejpam-5397	90	37	t	t	PROPN
ejpam-5397	90	38	)	)	PUNCT
ejpam-5397	90	39	)	)	PUNCT
ejpam-5397	90	40	,	,	PUNCT
ejpam-5397	90	41	lim	lim	PROPN
ejpam-5397	90	42	t→∞	t→∞	NUM
ejpam-5397	90	43	sup(z(t	sup(z(t	PROPN
ejpam-5397	90	44	)	)	PUNCT
ejpam-5397	90	45	)	)	PUNCT
ejpam-5397	90	46	}	}	PUNCT
ejpam-5397	90	47	≥	≥	PROPN
ejpam-5397	90	48	min	min	NOUN
ejpam-5397	90	49	{	{	PUNCT
ejpam-5397	90	50	lim	lim	PROPN
ejpam-5397	90	51	t→∞	t→∞	PART
ejpam-5397	90	52	inf(x(t	inf(x(t	PROPN
ejpam-5397	90	53	)	)	PUNCT
ejpam-5397	90	54	)	)	PUNCT
ejpam-5397	90	55	,	,	PUNCT
ejpam-5397	90	56	lim	lim	PROPN
ejpam-5397	90	57	t→∞	t→∞	NUM
ejpam-5397	90	58	inf(y	inf(y	PROPN
ejpam-5397	90	59	(	(	PUNCT
ejpam-5397	90	60	t	t	PROPN
ejpam-5397	90	61	)	)	PUNCT
ejpam-5397	90	62	)	)	PUNCT
ejpam-5397	90	63	,	,	PUNCT
ejpam-5397	90	64	lim	lim	PROPN
ejpam-5397	90	65	t→∞	t→∞	NUM
ejpam-5397	90	66	inf(z(t	inf(z(t	PROPN
ejpam-5397	90	67	)	)	PUNCT
ejpam-5397	90	68	)	)	PUNCT
ejpam-5397	90	69	}	}	PUNCT
ejpam-5397	90	70	≥	≥	PROPN
ejpam-5397	90	71	a.	a.	NOUN
ejpam-5397	90	72	theorem	theorem	NOUN
ejpam-5397	90	73	2.1	2.1	NUM
ejpam-5397	90	74	.	.	PUNCT
ejpam-5397	91	1	if	if	SCONJ
ejpam-5397	91	2	the	the	DET
ejpam-5397	91	3	following	follow	VERB
ejpam-5397	91	4	conditions	condition	NOUN
ejpam-5397	91	5	(	(	PUNCT
ejpam-5397	91	6	5	5	NUM
ejpam-5397	91	7	)	)	PUNCT
ejpam-5397	91	8	and	and	CCONJ
ejpam-5397	91	9	(	(	PUNCT
ejpam-5397	91	10	6	6	NUM
ejpam-5397	91	11	)	)	PUNCT
ejpam-5397	91	12	in	in	ADP
ejpam-5397	91	13	lemma	lemma	PROPN
ejpam-5397	91	14	2.2	2.2	NUM
ejpam-5397	91	15	are	be	AUX
ejpam-5397	91	16	provided	provide	VERB
ejpam-5397	91	17	,	,	PUNCT
ejpam-5397	91	18	then	then	ADV
ejpam-5397	91	19	system	system	NOUN
ejpam-5397	91	20	(	(	PUNCT
ejpam-5397	91	21	1	1	NUM
ejpam-5397	91	22	)	)	PUNCT
ejpam-5397	91	23	,	,	PUNCT
ejpam-5397	91	24	is	be	AUX
ejpam-5397	91	25	permanent	permanent	ADJ
ejpam-5397	91	26	.	.	PUNCT
ejpam-5397	92	1	b.	b.	PROPN
ejpam-5397	92	2	b.	b.	PROPN
ejpam-5397	92	3	kamal	kamal	PROPN
ejpam-5397	92	4	,	,	PUNCT
ejpam-5397	92	5	a.	a.	PROPN
ejpam-5397	92	6	n.	n.	PROPN
ejpam-5397	92	7	mustafa	mustafa	PROPN
ejpam-5397	92	8	/	/	SYM
ejpam-5397	92	9	eur	eur	PROPN
ejpam-5397	92	10	.	.	PUNCT
ejpam-5397	93	1	j.	j.	PROPN
ejpam-5397	93	2	pure	pure	PROPN
ejpam-5397	93	3	appl	appl	PROPN
ejpam-5397	93	4	.	.	PROPN
ejpam-5397	93	5	math	math	PROPN
ejpam-5397	93	6	,	,	PUNCT
ejpam-5397	93	7	18	18	NUM
ejpam-5397	93	8	(	(	PUNCT
ejpam-5397	93	9	1	1	NUM
ejpam-5397	93	10	)	)	PUNCT
ejpam-5397	93	11	(	(	PUNCT
ejpam-5397	93	12	2025	2025	NUM
ejpam-5397	93	13	)	)	PUNCT
ejpam-5397	93	14	,	,	PUNCT
ejpam-5397	93	15	5397	5397	NUM
ejpam-5397	93	16	6	6	NUM
ejpam-5397	93	17	of	of	ADP
ejpam-5397	93	18	21	21	NUM
ejpam-5397	93	19	proof	proof	NOUN
ejpam-5397	93	20	.	.	PUNCT
ejpam-5397	94	1	from	from	ADP
ejpam-5397	94	2	lemma	lemma	PROPN
ejpam-5397	94	3	2.1	2.1	NUM
ejpam-5397	94	4	,	,	PUNCT
ejpam-5397	94	5	it	it	PRON
ejpam-5397	94	6	is	be	AUX
ejpam-5397	94	7	obtained	obtain	VERB
ejpam-5397	94	8	that	that	DET
ejpam-5397	94	9	min	min	PROPN
ejpam-5397	94	10	{	{	PUNCT
ejpam-5397	94	11	lim	lim	PROPN
ejpam-5397	94	12	t→∞	t→∞	PART
ejpam-5397	94	13	inf(x(t	inf(x(t	PROPN
ejpam-5397	94	14	)	)	PUNCT
ejpam-5397	94	15	)	)	PUNCT
ejpam-5397	94	16	,	,	PUNCT
ejpam-5397	94	17	lim	lim	PROPN
ejpam-5397	94	18	t→∞	t→∞	NUM
ejpam-5397	94	19	inf(y	inf(y	PROPN
ejpam-5397	94	20	(	(	PUNCT
ejpam-5397	94	21	t	t	PROPN
ejpam-5397	94	22	)	)	PUNCT
ejpam-5397	94	23	)	)	PUNCT
ejpam-5397	94	24	,	,	PUNCT
ejpam-5397	94	25	lim	lim	PROPN
ejpam-5397	94	26	t→∞	t→∞	NUM
ejpam-5397	94	27	inf(z(t	inf(z(t	PROPN
ejpam-5397	94	28	)	)	PUNCT
ejpam-5397	94	29	)	)	PUNCT
ejpam-5397	94	30	}	}	PUNCT
ejpam-5397	94	31	≥	≥	PROPN
ejpam-5397	94	32	min	min	NOUN
ejpam-5397	94	33	{	{	PUNCT
ejpam-5397	94	34	k1,k2	k1,k2	PROPN
ejpam-5397	94	35	}	}	PUNCT
ejpam-5397	94	36	.	.	PUNCT
ejpam-5397	95	1	from	from	ADP
ejpam-5397	95	2	lemma	lemma	PROPN
ejpam-5397	95	3	2.2	2.2	NUM
ejpam-5397	95	4	,	,	PUNCT
ejpam-5397	95	5	it	it	PRON
ejpam-5397	95	6	follows	follow	VERB
ejpam-5397	95	7	2k	2k	PROPN
ejpam-5397	95	8	≥	≥	PROPN
ejpam-5397	95	9	max	max	PROPN
ejpam-5397	95	10	{	{	PUNCT
ejpam-5397	95	11	lim	lim	PROPN
ejpam-5397	95	12	t→∞	t→∞	NUM
ejpam-5397	95	13	sup(x(t	sup(x(t	PROPN
ejpam-5397	95	14	)	)	PUNCT
ejpam-5397	95	15	)	)	PUNCT
ejpam-5397	95	16	,	,	PUNCT
ejpam-5397	95	17	lim	lim	PROPN
ejpam-5397	95	18	t→∞	t→∞	PRON
ejpam-5397	95	19	sup(y	sup(y	PROPN
ejpam-5397	95	20	(	(	PUNCT
ejpam-5397	95	21	t	t	PROPN
ejpam-5397	95	22	)	)	PUNCT
ejpam-5397	95	23	)	)	PUNCT
ejpam-5397	95	24	,	,	PUNCT
ejpam-5397	95	25	lim	lim	PROPN
ejpam-5397	95	26	t→∞	t→∞	NUM
ejpam-5397	95	27	sup(z(t	sup(z(t	PROPN
ejpam-5397	95	28	)	)	PUNCT
ejpam-5397	95	29	)	)	PUNCT
ejpam-5397	95	30	}	}	PUNCT
ejpam-5397	95	31	.	.	PUNCT
ejpam-5397	96	1	the	the	DET
ejpam-5397	96	2	proof	proof	NOUN
ejpam-5397	96	3	is	be	AUX
ejpam-5397	96	4	completed	complete	VERB
ejpam-5397	96	5	.	.	PUNCT
ejpam-5397	97	1	3	3	X
ejpam-5397	97	2	.	.	X
ejpam-5397	97	3	stability	stability	NOUN
ejpam-5397	97	4	analysis	analysis	NOUN
ejpam-5397	97	5	this	this	DET
ejpam-5397	97	6	section	section	NOUN
ejpam-5397	97	7	including	include	VERB
ejpam-5397	97	8	three	three	NUM
ejpam-5397	97	9	subsections	subsection	NOUN
ejpam-5397	97	10	.	.	PUNCT
ejpam-5397	98	1	in	in	ADP
ejpam-5397	98	2	the	the	DET
ejpam-5397	98	3	first	first	ADJ
ejpam-5397	98	4	subsection	subsection	NOUN
ejpam-5397	98	5	,	,	PUNCT
ejpam-5397	98	6	the	the	DET
ejpam-5397	98	7	existence	existence	NOUN
ejpam-5397	98	8	conditions	condition	NOUN
ejpam-5397	98	9	of	of	ADP
ejpam-5397	98	10	all	all	DET
ejpam-5397	98	11	feasible	feasible	ADJ
ejpam-5397	98	12	and	and	CCONJ
ejpam-5397	98	13	possible	possible	ADJ
ejpam-5397	98	14	steady	steady	ADJ
ejpam-5397	98	15	stat	stat	NOUN
ejpam-5397	98	16	points	point	NOUN
ejpam-5397	98	17	of	of	ADP
ejpam-5397	98	18	system	system	NOUN
ejpam-5397	98	19	(	(	PUNCT
ejpam-5397	98	20	1	1	X
ejpam-5397	98	21	)	)	PUNCT
ejpam-5397	98	22	are	be	AUX
ejpam-5397	98	23	determined	determine	VERB
ejpam-5397	98	24	and	and	CCONJ
ejpam-5397	98	25	their	their	PRON
ejpam-5397	98	26	local	local	ADJ
ejpam-5397	98	27	and	and	CCONJ
ejpam-5397	98	28	globally	globally	ADV
ejpam-5397	98	29	stability	stability	NOUN
ejpam-5397	98	30	are	be	AUX
ejpam-5397	98	31	investigated	investigate	VERB
ejpam-5397	98	32	in	in	ADP
ejpam-5397	98	33	the	the	DET
ejpam-5397	98	34	second	second	ADJ
ejpam-5397	98	35	and	and	CCONJ
ejpam-5397	98	36	third	third	ADJ
ejpam-5397	98	37	subsection	subsection	NOUN
ejpam-5397	98	38	,	,	PUNCT
ejpam-5397	98	39	respectively	respectively	ADV
ejpam-5397	98	40	.	.	PUNCT
ejpam-5397	99	1	3.1	3.1	NUM
ejpam-5397	99	2	.	.	PUNCT
ejpam-5397	99	3	existence	existence	NOUN
ejpam-5397	99	4	of	of	ADP
ejpam-5397	99	5	steady	steady	ADJ
ejpam-5397	99	6	states	state	NOUN
ejpam-5397	99	7	system	system	NOUN
ejpam-5397	99	8	(	(	PUNCT
ejpam-5397	99	9	1	1	X
ejpam-5397	99	10	)	)	PUNCT
ejpam-5397	99	11	has	have	VERB
ejpam-5397	99	12	at	at	ADP
ejpam-5397	99	13	most	most	ADJ
ejpam-5397	99	14	four	four	NUM
ejpam-5397	99	15	steady	steady	ADJ
ejpam-5397	99	16	states	state	NOUN
ejpam-5397	99	17	,	,	PUNCT
ejpam-5397	99	18	they	they	PRON
ejpam-5397	99	19	are	be	AUX
ejpam-5397	99	20	the	the	DET
ejpam-5397	99	21	only	only	ADJ
ejpam-5397	99	22	prey	prey	PROPN
ejpam-5397	99	23	existence	existence	PROPN
ejpam-5397	99	24	steady	steady	ADJ
ejpam-5397	99	25	state	state	NOUN
ejpam-5397	99	26	s1	s1	NOUN
ejpam-5397	99	27	=	=	SYM
ejpam-5397	99	28	(	(	PUNCT
ejpam-5397	99	29	k	k	X
ejpam-5397	99	30	,	,	PUNCT
ejpam-5397	99	31	0	0	NUM
ejpam-5397	99	32	,	,	PUNCT
ejpam-5397	99	33	0	0	NUM
ejpam-5397	99	34	)	)	PUNCT
ejpam-5397	99	35	,	,	PUNCT
ejpam-5397	99	36	apex	apex	VERB
ejpam-5397	99	37	predatorfree	predatorfree	NOUN
ejpam-5397	99	38	steady	steady	ADJ
ejpam-5397	99	39	state	state	NOUN
ejpam-5397	99	40	s2	s2	NOUN
ejpam-5397	99	41	=	=	SYM
ejpam-5397	99	42	(	(	PUNCT
ejpam-5397	99	43	s̄	s̄	NOUN
ejpam-5397	99	44	,	,	PUNCT
ejpam-5397	99	45	s̄	s̄	NOUN
ejpam-5397	99	46	,	,	PUNCT
ejpam-5397	99	47	0	0	NUM
ejpam-5397	99	48	)	)	PUNCT
ejpam-5397	99	49	,	,	PUNCT
ejpam-5397	99	50	intermediate	intermediate	ADJ
ejpam-5397	99	51	predators	predator	NOUN
ejpam-5397	99	52	-	-	PUNCT
ejpam-5397	99	53	free	free	ADJ
ejpam-5397	99	54	steady	steady	ADJ
ejpam-5397	99	55	state	state	NOUN
ejpam-5397	99	56	s3	s3	NOUN
ejpam-5397	99	57	=	=	SYM
ejpam-5397	99	58	(	(	PUNCT
ejpam-5397	99	59	s̄	s̄	NOUN
ejpam-5397	99	60	,	,	PUNCT
ejpam-5397	99	61	0	0	NUM
ejpam-5397	99	62	,	,	PUNCT
ejpam-5397	99	63	s̄	s̄	NOUN
ejpam-5397	99	64	)	)	PUNCT
ejpam-5397	99	65	and	and	CCONJ
ejpam-5397	99	66	coexistence	coexistence	VERB
ejpam-5397	99	67	steady	steady	ADJ
ejpam-5397	99	68	state	state	NOUN
ejpam-5397	99	69	is	be	AUX
ejpam-5397	99	70	s4	s4	NOUN
ejpam-5397	99	71	=	=	SYM
ejpam-5397	99	72	(	(	PUNCT
ejpam-5397	99	73	x∗	x∗	PROPN
ejpam-5397	99	74	,	,	PUNCT
ejpam-5397	99	75	y	y	PROPN
ejpam-5397	99	76	∗	∗	NOUN
ejpam-5397	99	77	,	,	PUNCT
ejpam-5397	99	78	z∗	z∗	NOUN
ejpam-5397	99	79	)	)	PUNCT
ejpam-5397	99	80	always	always	ADV
ejpam-5397	99	81	exist	exist	VERB
ejpam-5397	99	82	,	,	PUNCT
ejpam-5397	99	83	where	where	SCONJ
ejpam-5397	99	84	s̄	s̄	NOUN
ejpam-5397	99	85	=	=	SYM
ejpam-5397	99	86	r1βtk	r1βtk	NUM
ejpam-5397	99	87	−	−	PROPN
ejpam-5397	99	88	r1	r1	PROPN
ejpam-5397	99	89	−	−	PROPN
ejpam-5397	99	90	βk	βk	ADV
ejpam-5397	99	91	+	+	CCONJ
ejpam-5397	99	92	√	√	INTJ
ejpam-5397	99	93	(	(	PUNCT
ejpam-5397	99	94	r1βtk	r1βtk	ADJ
ejpam-5397	99	95	−	−	PROPN
ejpam-5397	99	96	r1	r1	PROPN
ejpam-5397	99	97	−	−	PROPN
ejpam-5397	99	98	βk)2	βk)2	PROPN
ejpam-5397	99	99	+	+	CCONJ
ejpam-5397	99	100	4r21βtk	4r21βtk	NUM
ejpam-5397	99	101	2r1βt	2r1βt	NUM
ejpam-5397	99	102	,	,	PUNCT
ejpam-5397	99	103	s̄	s̄	NOUN
ejpam-5397	99	104	=	=	SYM
ejpam-5397	99	105	r1α1t1k	r1α1t1k	PROPN
ejpam-5397	99	106	−	−	PROPN
ejpam-5397	99	107	r1	r1	PROPN
ejpam-5397	99	108	−	−	PROPN
ejpam-5397	99	109	α1k	α1k	NOUN
ejpam-5397	99	110	+	+	CCONJ
ejpam-5397	99	111	√	√	PROPN
ejpam-5397	99	112	(	(	PUNCT
ejpam-5397	99	113	r1α1t1k	r1α1t1k	PROPN
ejpam-5397	99	114	−	−	PROPN
ejpam-5397	99	115	r1	r1	PROPN
ejpam-5397	99	116	−	−	PROPN
ejpam-5397	99	117	α1k)2	α1k)2	PROPN
ejpam-5397	99	118	+	+	CCONJ
ejpam-5397	99	119	4r21α1t1k	4r21α1t1k	NUM
ejpam-5397	99	120	2r1α1t1	2r1α1t1	NUM
ejpam-5397	99	121	,	,	PUNCT
ejpam-5397	99	122	z∗	z∗	NOUN
ejpam-5397	99	123	=	=	SYM
ejpam-5397	99	124	x∗	x∗	PROPN
ejpam-5397	100	1	+	+	CCONJ
ejpam-5397	100	2	y	y	PROPN
ejpam-5397	100	3	∗	∗	NOUN
ejpam-5397	100	4	,	,	PUNCT
ejpam-5397	100	5	y	y	PROPN
ejpam-5397	100	6	∗	∗	NOUN
ejpam-5397	100	7	=	=	PUNCT
ejpam-5397	100	8	a1x	a1x	NOUN
ejpam-5397	100	9	∗	∗	NOUN
ejpam-5397	100	10	+	+	CCONJ
ejpam-5397	100	11	a2x	a2x	ADP
ejpam-5397	100	12	∗2	∗2	PROPN
ejpam-5397	100	13	+	+	CCONJ
ejpam-5397	100	14	a3x	a3x	VERB
ejpam-5397	100	15	∗3	∗3	PROPN
ejpam-5397	100	16	and	and	CCONJ
ejpam-5397	100	17	x∗	x∗	PROPN
ejpam-5397	100	18	is	be	AUX
ejpam-5397	100	19	root	root	NOUN
ejpam-5397	100	20	for	for	ADP
ejpam-5397	100	21	the	the	DET
ejpam-5397	100	22	following	follow	VERB
ejpam-5397	100	23	function	function	NOUN
ejpam-5397	100	24	f	f	PROPN
ejpam-5397	100	25	(	(	PUNCT
ejpam-5397	100	26	x	x	X
ejpam-5397	100	27	)	)	PUNCT
ejpam-5397	100	28	=	=	SYM
ejpam-5397	100	29	r1	r1	PROPN
ejpam-5397	100	30	(	(	PUNCT
ejpam-5397	100	31	1−	1−	NUM
ejpam-5397	100	32	x	x	SYM
ejpam-5397	100	33	k	k	NOUN
ejpam-5397	100	34	)	)	PUNCT
ejpam-5397	100	35	−	−	PROPN
ejpam-5397	100	36	βy	βy	INTJ
ejpam-5397	100	37	(	(	PUNCT
ejpam-5397	100	38	x	x	X
ejpam-5397	100	39	)	)	PUNCT
ejpam-5397	100	40	1	1	NUM
ejpam-5397	100	41	+	+	NUM
ejpam-5397	100	42	βtx	βtx	NOUN
ejpam-5397	100	43	−	−	PROPN
ejpam-5397	100	44	α1(x	α1(x	NUM
ejpam-5397	101	1	+	+	CCONJ
ejpam-5397	101	2	y	y	PROPN
ejpam-5397	101	3	(	(	PUNCT
ejpam-5397	101	4	x	x	NOUN
ejpam-5397	101	5	)	)	PUNCT
ejpam-5397	101	6	)	)	PUNCT
ejpam-5397	101	7	1	1	NUM
ejpam-5397	102	1	+	+	CCONJ
ejpam-5397	102	2	α1t1x	α1t1x	NUM
ejpam-5397	102	3	+	+	NUM
ejpam-5397	102	4	α2t2y	α2t2y	NUM
ejpam-5397	102	5	(	(	PUNCT
ejpam-5397	102	6	x	x	X
ejpam-5397	102	7	)	)	PUNCT
ejpam-5397	102	8	,	,	PUNCT
ejpam-5397	102	9	(	(	PUNCT
ejpam-5397	102	10	10	10	NUM
ejpam-5397	102	11	)	)	PUNCT
ejpam-5397	102	12	with	with	ADP
ejpam-5397	102	13	a1	a1	NOUN
ejpam-5397	102	14	=	=	SYM
ejpam-5397	102	15	r1α2βt	r1α2βt	X
ejpam-5397	102	16	r2α1k	r2α1k	PUNCT
ejpam-5397	102	17	,	,	PUNCT
ejpam-5397	102	18	a2	a2	PROPN
ejpam-5397	102	19	=	=	SYM
ejpam-5397	102	20	r1α2	r1α2	NOUN
ejpam-5397	102	21	r2α1k	r2α1k	PUNCT
ejpam-5397	102	22	−	−	VERB
ejpam-5397	102	23	r1α2βt	r1α2βt	ADV
ejpam-5397	102	24	r2α1	r2α1	VERB
ejpam-5397	102	25	and	and	CCONJ
ejpam-5397	102	26	a3	a3	NOUN
ejpam-5397	102	27	=	=	SYM
ejpam-5397	103	1	r2β	r2β	PROPN
ejpam-5397	103	2	r2α1	r2α1	NOUN
ejpam-5397	103	3	+	+	NOUN
ejpam-5397	103	4	1	1	NUM
ejpam-5397	103	5	−	−	NOUN
ejpam-5397	103	6	r1α2	r1α2	NOUN
ejpam-5397	103	7	r2α1	r2α1	VERB
ejpam-5397	103	8	and	and	CCONJ
ejpam-5397	103	9	y	y	PROPN
ejpam-5397	103	10	(	(	PUNCT
ejpam-5397	103	11	x	x	X
ejpam-5397	103	12	)	)	PUNCT
ejpam-5397	103	13	=	=	PUNCT
ejpam-5397	103	14	a1x	a1x	NOUN
ejpam-5397	104	1	+	+	CCONJ
ejpam-5397	104	2	a2x	a2x	PROPN
ejpam-5397	104	3	2	2	NUM
ejpam-5397	104	4	+	+	CCONJ
ejpam-5397	104	5	a3x	a3x	PROPN
ejpam-5397	104	6	3	3	NUM
ejpam-5397	104	7	.	.	PUNCT
ejpam-5397	104	8	note	note	VERB
ejpam-5397	104	9	the	the	DET
ejpam-5397	104	10	steady	steady	ADJ
ejpam-5397	104	11	states	state	NOUN
ejpam-5397	104	12	s1	s1	NOUN
ejpam-5397	104	13	,	,	PUNCT
ejpam-5397	104	14	s2	s2	NOUN
ejpam-5397	104	15	and	and	CCONJ
ejpam-5397	104	16	s3	s3	PROPN
ejpam-5397	104	17	are	be	AUX
ejpam-5397	104	18	always	always	ADV
ejpam-5397	104	19	uniquely	uniquely	ADV
ejpam-5397	104	20	exists	exist	VERB
ejpam-5397	104	21	.	.	PUNCT
ejpam-5397	105	1	but	but	CCONJ
ejpam-5397	105	2	the	the	DET
ejpam-5397	105	3	existence	existence	NOUN
ejpam-5397	105	4	criteria	criterion	NOUN
ejpam-5397	105	5	for	for	ADP
ejpam-5397	105	6	the	the	DET
ejpam-5397	105	7	coexistence	coexistence	NOUN
ejpam-5397	105	8	steady	steady	ADJ
ejpam-5397	105	9	state	state	NOUN
ejpam-5397	105	10	s4	s4	PROPN
ejpam-5397	105	11	is	be	AUX
ejpam-5397	105	12	determined	determine	VERB
ejpam-5397	105	13	in	in	ADP
ejpam-5397	105	14	the	the	DET
ejpam-5397	105	15	following	follow	VERB
ejpam-5397	105	16	theorem	theorem	NOUN
ejpam-5397	105	17	theorem	theorem	VERB
ejpam-5397	105	18	3.1	3.1	NUM
ejpam-5397	105	19	.	.	PUNCT
ejpam-5397	106	1	the	the	DET
ejpam-5397	106	2	coexistence	coexistence	NOUN
ejpam-5397	106	3	steady	steady	ADJ
ejpam-5397	106	4	state	state	NOUN
ejpam-5397	106	5	s4	s4	NOUN
ejpam-5397	106	6	=	=	SYM
ejpam-5397	106	7	(	(	PUNCT
ejpam-5397	106	8	x∗	x∗	PROPN
ejpam-5397	106	9	,	,	PUNCT
ejpam-5397	106	10	y	y	PROPN
ejpam-5397	106	11	∗	∗	NOUN
ejpam-5397	106	12	,	,	PUNCT
ejpam-5397	106	13	z∗	z∗	NOUN
ejpam-5397	106	14	)	)	PUNCT
ejpam-5397	106	15	exist	exist	VERB
ejpam-5397	106	16	uniquely	uniquely	ADV
ejpam-5397	106	17	,	,	PUNCT
ejpam-5397	106	18	if	if	SCONJ
ejpam-5397	106	19	ai	ai	VERB
ejpam-5397	106	20	≥	≥	NOUN
ejpam-5397	106	21	0	0	NUM
ejpam-5397	106	22	,	,	PUNCT
ejpam-5397	106	23	i	i	PRON
ejpam-5397	106	24	=	=	NOUN
ejpam-5397	106	25	2	2	NUM
ejpam-5397	106	26	,	,	PUNCT
ejpam-5397	106	27	3	3	NUM
ejpam-5397	106	28	(	(	PUNCT
ejpam-5397	106	29	11	11	NUM
ejpam-5397	106	30	)	)	PUNCT
ejpam-5397	106	31	b.	b.	PROPN
ejpam-5397	106	32	b.	b.	PROPN
ejpam-5397	106	33	kamal	kamal	PROPN
ejpam-5397	106	34	,	,	PUNCT
ejpam-5397	106	35	a.	a.	PROPN
ejpam-5397	106	36	n.	n.	PROPN
ejpam-5397	106	37	mustafa	mustafa	PROPN
ejpam-5397	106	38	/	/	SYM
ejpam-5397	106	39	eur	eur	PROPN
ejpam-5397	106	40	.	.	PUNCT
ejpam-5397	107	1	j.	j.	PROPN
ejpam-5397	107	2	pure	pure	PROPN
ejpam-5397	107	3	appl	appl	PROPN
ejpam-5397	107	4	.	.	PROPN
ejpam-5397	107	5	math	math	PROPN
ejpam-5397	107	6	,	,	PUNCT
ejpam-5397	107	7	18	18	NUM
ejpam-5397	107	8	(	(	PUNCT
ejpam-5397	107	9	1	1	NUM
ejpam-5397	107	10	)	)	PUNCT
ejpam-5397	107	11	(	(	PUNCT
ejpam-5397	107	12	2025	2025	NUM
ejpam-5397	107	13	)	)	PUNCT
ejpam-5397	107	14	,	,	PUNCT
ejpam-5397	107	15	5397	5397	NUM
ejpam-5397	107	16	7	7	NUM
ejpam-5397	107	17	of	of	ADP
ejpam-5397	107	18	21	21	NUM
ejpam-5397	107	19	proof	proof	NOUN
ejpam-5397	107	20	.	.	PUNCT
ejpam-5397	108	1	from	from	ADP
ejpam-5397	108	2	(	(	PUNCT
ejpam-5397	108	3	10	10	NUM
ejpam-5397	108	4	)	)	PUNCT
ejpam-5397	108	5	,	,	PUNCT
ejpam-5397	108	6	it	it	PRON
ejpam-5397	108	7	gets	get	VERB
ejpam-5397	108	8	f	f	X
ejpam-5397	108	9	(	(	PUNCT
ejpam-5397	108	10	0	0	NUM
ejpam-5397	108	11	)	)	PUNCT
ejpam-5397	108	12	=	=	SYM
ejpam-5397	109	1	r1	r1	PROPN
ejpam-5397	109	2	>	>	X
ejpam-5397	109	3	0	0	PUNCT
ejpam-5397	110	1	and	and	CCONJ
ejpam-5397	110	2	f	f	PROPN
ejpam-5397	110	3	(	(	PUNCT
ejpam-5397	110	4	k	k	NOUN
ejpam-5397	110	5	)	)	PUNCT
ejpam-5397	110	6	=	=	SYM
ejpam-5397	111	1	−	−	PROPN
ejpam-5397	111	2	βy	βy	INTJ
ejpam-5397	111	3	(	(	PUNCT
ejpam-5397	111	4	k	k	NOUN
ejpam-5397	111	5	)	)	PUNCT
ejpam-5397	111	6	1	1	NUM
ejpam-5397	112	1	+	+	CCONJ
ejpam-5397	112	2	βtk	βtk	VERB
ejpam-5397	112	3	−	−	PROPN
ejpam-5397	112	4	α1(k	α1(k	PROPN
ejpam-5397	113	1	+	+	NUM
ejpam-5397	113	2	y	y	PROPN
ejpam-5397	113	3	(	(	PUNCT
ejpam-5397	113	4	k	k	NOUN
ejpam-5397	113	5	)	)	PUNCT
ejpam-5397	113	6	)	)	PUNCT
ejpam-5397	113	7	1	1	NUM
ejpam-5397	114	1	+	+	CCONJ
ejpam-5397	114	2	α1t1k	α1t1k	NUM
ejpam-5397	114	3	+	+	X
ejpam-5397	114	4	α2t2y	α2t2y	X
ejpam-5397	114	5	(	(	PUNCT
ejpam-5397	114	6	k	k	NOUN
ejpam-5397	114	7	)	)	PUNCT
ejpam-5397	114	8	<	<	X
ejpam-5397	115	1	0	0	X
ejpam-5397	115	2	.	.	PUNCT
ejpam-5397	115	3	intermediate	intermediate	ADJ
ejpam-5397	115	4	value	value	NOUN
ejpam-5397	115	5	theorem	theorem	VERB
ejpam-5397	115	6	,	,	PUNCT
ejpam-5397	115	7	guarantees	guarantee	VERB
ejpam-5397	115	8	that	that	SCONJ
ejpam-5397	115	9	f	f	PROPN
ejpam-5397	115	10	(	(	PUNCT
ejpam-5397	115	11	x	x	X
ejpam-5397	115	12	)	)	PUNCT
ejpam-5397	115	13	has	have	VERB
ejpam-5397	115	14	a	a	DET
ejpam-5397	115	15	root	root	NOUN
ejpam-5397	115	16	,	,	PUNCT
ejpam-5397	115	17	namely	namely	ADV
ejpam-5397	115	18	x∗	x∗	PROPN
ejpam-5397	115	19	in	in	ADP
ejpam-5397	115	20	(	(	PUNCT
ejpam-5397	115	21	0,k	0,k	NUM
ejpam-5397	115	22	)	)	PUNCT
ejpam-5397	115	23	.	.	PUNCT
ejpam-5397	116	1	further	further	ADJ
ejpam-5397	116	2	df	df	PROPN
ejpam-5397	116	3	(	(	PUNCT
ejpam-5397	116	4	x	x	X
ejpam-5397	116	5	)	)	PUNCT
ejpam-5397	116	6	dx	dx	PROPN
ejpam-5397	116	7	<	<	X
ejpam-5397	116	8	0	0	NUM
ejpam-5397	116	9	,	,	PUNCT
ejpam-5397	116	10	for	for	ADP
ejpam-5397	116	11	all	all	DET
ejpam-5397	116	12	x	x	PRON
ejpam-5397	116	13	≥	≥	NOUN
ejpam-5397	116	14	0	0	NUM
ejpam-5397	116	15	,	,	PUNCT
ejpam-5397	116	16	due	due	ADP
ejpam-5397	116	17	to	to	ADP
ejpam-5397	116	18	condition	condition	NOUN
ejpam-5397	116	19	(	(	PUNCT
ejpam-5397	116	20	11	11	NUM
ejpam-5397	116	21	)	)	PUNCT
ejpam-5397	116	22	,	,	PUNCT
ejpam-5397	116	23	that	that	PRON
ejpam-5397	116	24	is	is	ADV
ejpam-5397	116	25	f	f	PROPN
ejpam-5397	116	26	(	(	PUNCT
ejpam-5397	116	27	x	x	X
ejpam-5397	116	28	)	)	PUNCT
ejpam-5397	116	29	is	be	AUX
ejpam-5397	116	30	decreasing	decrease	VERB
ejpam-5397	116	31	on	on	ADP
ejpam-5397	116	32	the	the	DET
ejpam-5397	116	33	positive	positive	ADJ
ejpam-5397	116	34	real	real	ADJ
ejpam-5397	116	35	line	line	NOUN
ejpam-5397	116	36	,	,	PUNCT
ejpam-5397	116	37	and	and	CCONJ
ejpam-5397	116	38	hence	hence	ADV
ejpam-5397	116	39	x∗	x∗	PROPN
ejpam-5397	116	40	is	be	AUX
ejpam-5397	116	41	unique	unique	ADJ
ejpam-5397	116	42	root	root	NOUN
ejpam-5397	116	43	of	of	ADP
ejpam-5397	116	44	f	f	PROPN
ejpam-5397	116	45	(	(	PUNCT
ejpam-5397	116	46	x	x	NOUN
ejpam-5397	116	47	)	)	PUNCT
ejpam-5397	116	48	,	,	PUNCT
ejpam-5397	116	49	and	and	CCONJ
ejpam-5397	116	50	this	this	PRON
ejpam-5397	116	51	completes	complete	VERB
ejpam-5397	116	52	the	the	DET
ejpam-5397	116	53	proof	proof	NOUN
ejpam-5397	116	54	.	.	PUNCT
ejpam-5397	117	1	3.2	3.2	NUM
ejpam-5397	117	2	.	.	PUNCT
ejpam-5397	117	3	local	local	ADJ
ejpam-5397	117	4	stability	stability	NOUN
ejpam-5397	117	5	here	here	ADV
ejpam-5397	117	6	,	,	PUNCT
ejpam-5397	117	7	local	local	ADJ
ejpam-5397	117	8	asymptotical	asymptotical	ADJ
ejpam-5397	117	9	stability	stability	NOUN
ejpam-5397	117	10	(	(	PUNCT
ejpam-5397	117	11	las	las	NOUN
ejpam-5397	117	12	)	)	PUNCT
ejpam-5397	117	13	of	of	ADP
ejpam-5397	117	14	all	all	DET
ejpam-5397	117	15	the	the	DET
ejpam-5397	117	16	steady	steady	ADJ
ejpam-5397	117	17	states	state	NOUN
ejpam-5397	117	18	of	of	ADP
ejpam-5397	117	19	system	system	NOUN
ejpam-5397	117	20	(	(	PUNCT
ejpam-5397	117	21	1	1	X
ejpam-5397	117	22	)	)	PUNCT
ejpam-5397	117	23	is	be	AUX
ejpam-5397	117	24	studied	study	VERB
ejpam-5397	117	25	.	.	PUNCT
ejpam-5397	118	1	suppose	suppose	VERB
ejpam-5397	118	2	λix	λix	NOUN
ejpam-5397	118	3	,	,	PUNCT
ejpam-5397	118	4	λiy	λiy	PRON
ejpam-5397	118	5	and	and	CCONJ
ejpam-5397	118	6	λiz	λiz	AUX
ejpam-5397	118	7	represent	represent	VERB
ejpam-5397	118	8	the	the	DET
ejpam-5397	118	9	eigenvalues	eigenvalue	NOUN
ejpam-5397	118	10	of	of	ADP
ejpam-5397	118	11	the	the	DET
ejpam-5397	118	12	variational	variational	ADJ
ejpam-5397	118	13	matrix	matrix	NOUN
ejpam-5397	118	14	at	at	ADP
ejpam-5397	118	15	si	si	PROPN
ejpam-5397	118	16	,	,	PUNCT
ejpam-5397	118	17	in	in	ADP
ejpam-5397	118	18	the	the	DET
ejpam-5397	118	19	x-	x-	PROPN
ejpam-5397	118	20	,	,	PUNCT
ejpam-5397	118	21	y	y	PROPN
ejpam-5397	118	22	-	-	PUNCT
ejpam-5397	118	23	,	,	PUNCT
ejpam-5397	118	24	and	and	CCONJ
ejpam-5397	118	25	z	z	NOUN
ejpam-5397	118	26	-	-	PUNCT
ejpam-5397	118	27	directions	direction	NOUN
ejpam-5397	118	28	,	,	PUNCT
ejpam-5397	118	29	respectively	respectively	ADV
ejpam-5397	118	30	;	;	PUNCT
ejpam-5397	118	31	i	i	PROPN
ejpam-5397	118	32	=	=	NOUN
ejpam-5397	118	33	1	1	NUM
ejpam-5397	118	34	,	,	PUNCT
ejpam-5397	118	35	2	2	NUM
ejpam-5397	118	36	,	,	PUNCT
ejpam-5397	118	37	3	3	NUM
ejpam-5397	118	38	,	,	PUNCT
ejpam-5397	118	39	4	4	NUM
ejpam-5397	118	40	.	.	PUNCT
ejpam-5397	119	1	then	then	ADV
ejpam-5397	119	2	,	,	PUNCT
ejpam-5397	119	3	(	(	PUNCT
ejpam-5397	119	4	i	i	NOUN
ejpam-5397	119	5	)	)	PUNCT
ejpam-5397	119	6	λ1x	λ1x	X
ejpam-5397	119	7	=	=	SYM
ejpam-5397	119	8	−r1	−r1	PROPN
ejpam-5397	119	9	,	,	PUNCT
ejpam-5397	119	10	λ0y	λ0y	NOUN
ejpam-5397	119	11	=	=	PUNCT
ejpam-5397	119	12	r2	r2	PROPN
ejpam-5397	119	13	and	and	CCONJ
ejpam-5397	119	14	λ1z	λ1z	NOUN
ejpam-5397	119	15	=	=	SYM
ejpam-5397	119	16	r3	r3	PROPN
ejpam-5397	119	17	(	(	PUNCT
ejpam-5397	119	18	ii	ii	NOUN
ejpam-5397	119	19	)	)	PUNCT
ejpam-5397	120	1	λ2z	λ2z	PROPN
ejpam-5397	120	2	=	=	SYM
ejpam-5397	120	3	r3	r3	PROPN
ejpam-5397	120	4	and	and	CCONJ
ejpam-5397	120	5	λ2x	λ2x	PROPN
ejpam-5397	120	6	and	and	CCONJ
ejpam-5397	120	7	λ2x	λ2x	PRON
ejpam-5397	120	8	are	be	AUX
ejpam-5397	120	9	roots	root	NOUN
ejpam-5397	120	10	of	of	ADP
ejpam-5397	120	11	the	the	DET
ejpam-5397	120	12	equation	equation	NOUN
ejpam-5397	120	13	λ2	λ2	NOUN
ejpam-5397	120	14	+	+	NOUN
ejpam-5397	120	15	a1λ+b1	a1λ+b1	NOUN
ejpam-5397	120	16	=	=	SYM
ejpam-5397	120	17	0	0	NUM
ejpam-5397	120	18	,	,	PUNCT
ejpam-5397	120	19	where	where	SCONJ
ejpam-5397	120	20	,	,	PUNCT
ejpam-5397	120	21	a1	a1	NOUN
ejpam-5397	120	22	=	=	SYM
ejpam-5397	120	23	r1	r1	PROPN
ejpam-5397	120	24	k	k	PROPN
ejpam-5397	120	25	s̄	s̄	PROPN
ejpam-5397	120	26	+	+	CCONJ
ejpam-5397	120	27	r2	r2	PROPN
ejpam-5397	120	28	−	−	PROPN
ejpam-5397	120	29	(	(	PUNCT
ejpam-5397	120	30	β2	β2	PROPN
ejpam-5397	120	31	t	t	PROPN
ejpam-5397	120	32	s̄2	s̄2	NUM
ejpam-5397	120	33	)	)	PUNCT
ejpam-5397	120	34	/(1	/(1	PUNCT
ejpam-5397	121	1	+	+	CCONJ
ejpam-5397	121	2	βt	βt	VERB
ejpam-5397	121	3	s̄)2	s̄)2	NOUN
ejpam-5397	121	4	and	and	CCONJ
ejpam-5397	121	5	b1	b1	NOUN
ejpam-5397	121	6	=	=	PUNCT
ejpam-5397	121	7	r2r1	r2r1	NOUN
ejpam-5397	121	8	k	k	X
ejpam-5397	121	9	s̄	s̄	PROPN
ejpam-5397	121	10	+	+	CCONJ
ejpam-5397	121	11	(	(	PUNCT
ejpam-5397	121	12	r2βs̄	r2βs̄	PROPN
ejpam-5397	121	13	)	)	PUNCT
ejpam-5397	121	14	/(1	/(1	PUNCT
ejpam-5397	122	1	+	+	CCONJ
ejpam-5397	122	2	βt	βt	VERB
ejpam-5397	122	3	s̄)2	s̄)2	PROPN
ejpam-5397	122	4	(	(	PUNCT
ejpam-5397	122	5	iii	iii	NOUN
ejpam-5397	122	6	)	)	PUNCT
ejpam-5397	122	7	λ3x	λ3x	NOUN
ejpam-5397	122	8	,	,	PUNCT
ejpam-5397	122	9	λ3y	λ3y	PROPN
ejpam-5397	122	10	and	and	CCONJ
ejpam-5397	122	11	λ3z	λ3z	PROPN
ejpam-5397	122	12	are	be	AUX
ejpam-5397	122	13	roots	root	NOUN
ejpam-5397	122	14	of	of	ADP
ejpam-5397	122	15	the	the	DET
ejpam-5397	122	16	equation	equation	NOUN
ejpam-5397	123	1	λ3	λ3	PROPN
ejpam-5397	123	2	+	+	PROPN
ejpam-5397	123	3	a2λ	a2λ	NOUN
ejpam-5397	123	4	2	2	NUM
ejpam-5397	123	5	+	+	NOUN
ejpam-5397	123	6	b2λ+	b2λ+	NOUN
ejpam-5397	123	7	r3c2	r3c2	NOUN
ejpam-5397	123	8	=	=	SYM
ejpam-5397	123	9	0	0	NUM
ejpam-5397	123	10	,	,	PUNCT
ejpam-5397	123	11	where	where	SCONJ
ejpam-5397	123	12	,	,	PUNCT
ejpam-5397	123	13	a2	a2	PROPN
ejpam-5397	123	14	=	=	SYM
ejpam-5397	123	15	−	−	PROPN
ejpam-5397	123	16	(	(	PUNCT
ejpam-5397	123	17	r1	r1	PROPN
ejpam-5397	123	18	+	+	PROPN
ejpam-5397	123	19	r5	r5	PROPN
ejpam-5397	123	20	)	)	PUNCT
ejpam-5397	123	21	,	,	PUNCT
ejpam-5397	123	22	b2	b2	NOUN
ejpam-5397	123	23	=	=	SYM
ejpam-5397	123	24	r1r5−r2r4−r3	r1r5−r2r4−r3	PROPN
ejpam-5397	123	25	(	(	PUNCT
ejpam-5397	123	26	r1	r1	PROPN
ejpam-5397	123	27	+	+	PROPN
ejpam-5397	123	28	r3	r3	PROPN
ejpam-5397	123	29	+	+	NOUN
ejpam-5397	123	30	r5	r5	PROPN
ejpam-5397	123	31	)	)	PUNCT
ejpam-5397	123	32	and	and	CCONJ
ejpam-5397	123	33	c2	c2	PROPN
ejpam-5397	123	34	=	=	SYM
ejpam-5397	123	35	r1r5−r2r4−r3r4+r3r5	r1r5−r2r4−r3r4+r3r5	PROPN
ejpam-5397	123	36	with	with	ADP
ejpam-5397	123	37	r1	r1	PROPN
ejpam-5397	123	38	=	=	PUNCT
ejpam-5397	123	39	−r1	−r1	PROPN
ejpam-5397	123	40	k	k	PROPN
ejpam-5397	123	41	s̄	s̄	PROPN
ejpam-5397	123	42	+	+	CCONJ
ejpam-5397	123	43	(	(	PUNCT
ejpam-5397	123	44	α2	α2	ADV
ejpam-5397	123	45	1t1s̄	1t1s̄	NUM
ejpam-5397	123	46	2	2	NUM
ejpam-5397	123	47	)	)	PUNCT
ejpam-5397	123	48	/	/	PUNCT
ejpam-5397	123	49	(	(	PUNCT
ejpam-5397	123	50	1	1	NUM
ejpam-5397	123	51	+	+	CCONJ
ejpam-5397	123	52	α1t1s̄	α1t1s̄	ADJ
ejpam-5397	123	53	)	)	PUNCT
ejpam-5397	123	54	2	2	NUM
ejpam-5397	123	55	,	,	PUNCT
ejpam-5397	123	56	r2	r2	NOUN
ejpam-5397	123	57	=	=	SYM
ejpam-5397	124	1	−	−	PROPN
ejpam-5397	124	2	βs̄	βs̄	NOUN
ejpam-5397	124	3	(	(	PUNCT
ejpam-5397	124	4	1	1	NUM
ejpam-5397	124	5	+	+	CCONJ
ejpam-5397	124	6	βt	βt	NOUN
ejpam-5397	124	7	s̄	s̄	NOUN
ejpam-5397	124	8	)	)	PUNCT
ejpam-5397	124	9	−	−	PROPN
ejpam-5397	125	1	α1s̄/	α1s̄/	NOUN
ejpam-5397	125	2	(	(	PUNCT
ejpam-5397	125	3	1	1	NUM
ejpam-5397	125	4	+	+	CCONJ
ejpam-5397	125	5	α1t1s̄	α1t1s̄	ADJ
ejpam-5397	125	6	)	)	PUNCT
ejpam-5397	125	7	,	,	PUNCT
ejpam-5397	125	8	r3	r3	PROPN
ejpam-5397	125	9	=	=	SYM
ejpam-5397	125	10	−α2s̄/	−α2s̄/	PROPN
ejpam-5397	125	11	(	(	PUNCT
ejpam-5397	125	12	1	1	NUM
ejpam-5397	125	13	+	+	CCONJ
ejpam-5397	125	14	α1t1s̄	α1t1s̄	ADJ
ejpam-5397	125	15	)	)	PUNCT
ejpam-5397	125	16	,	,	PUNCT
ejpam-5397	125	17	r4	r4	NOUN
ejpam-5397	125	18	=	=	PUNCT
ejpam-5397	125	19	−α2s̄/	−α2s̄/	NOUN
ejpam-5397	125	20	(	(	PUNCT
ejpam-5397	125	21	1	1	NUM
ejpam-5397	125	22	+	+	CCONJ
ejpam-5397	125	23	α1t1s̄	α1t1s̄	ADJ
ejpam-5397	125	24	)	)	PUNCT
ejpam-5397	125	25	2	2	NUM
ejpam-5397	125	26	and	and	CCONJ
ejpam-5397	125	27	r5	r5	PROPN
ejpam-5397	125	28	=	=	SYM
ejpam-5397	125	29	r2	r2	PROPN
ejpam-5397	125	30	−	−	PROPN
ejpam-5397	125	31	(	(	PUNCT
ejpam-5397	125	32	α2s̄	α2s̄	NUM
ejpam-5397	125	33	)	)	PUNCT
ejpam-5397	125	34	/	/	PUNCT
ejpam-5397	126	1	(	(	PUNCT
ejpam-5397	126	2	1	1	NUM
ejpam-5397	126	3	+	+	CCONJ
ejpam-5397	126	4	α1t1s̄	α1t1s̄	ADJ
ejpam-5397	126	5	)	)	PUNCT
ejpam-5397	126	6	(	(	PUNCT
ejpam-5397	126	7	iv	iv	X
ejpam-5397	126	8	)	)	PUNCT
ejpam-5397	126	9	λ4x	λ4x	NOUN
ejpam-5397	126	10	,	,	PUNCT
ejpam-5397	126	11	λ4y	λ4y	PROPN
ejpam-5397	126	12	and	and	CCONJ
ejpam-5397	126	13	λ4z	λ4z	PROPN
ejpam-5397	126	14	are	be	AUX
ejpam-5397	126	15	roots	root	NOUN
ejpam-5397	126	16	of	of	ADP
ejpam-5397	126	17	the	the	DET
ejpam-5397	126	18	equation	equation	NOUN
ejpam-5397	126	19	λ3	λ3	PROPN
ejpam-5397	127	1	+	+	PROPN
ejpam-5397	127	2	a3λ	a3λ	NOUN
ejpam-5397	127	3	2	2	NUM
ejpam-5397	127	4	+	+	NOUN
ejpam-5397	127	5	b3λ+	b3λ+	X
ejpam-5397	127	6	r3c3	r3c3	NOUN
ejpam-5397	127	7	=	=	SYM
ejpam-5397	127	8	0	0	NUM
ejpam-5397	127	9	,	,	PUNCT
ejpam-5397	127	10	where	where	SCONJ
ejpam-5397	127	11	a3	a3	NOUN
ejpam-5397	127	12	=	=	PUNCT
ejpam-5397	127	13	−	−	PROPN
ejpam-5397	127	14	(	(	PUNCT
ejpam-5397	127	15	e1	e1	PROPN
ejpam-5397	127	16	+	+	CCONJ
ejpam-5397	127	17	e5	e5	PROPN
ejpam-5397	127	18	)	)	PUNCT
ejpam-5397	127	19	,	,	PUNCT
ejpam-5397	127	20	b2	b2	NOUN
ejpam-5397	127	21	=	=	SYM
ejpam-5397	127	22	e1e5	e1e5	PUNCT
ejpam-5397	127	23	−	−	PROPN
ejpam-5397	127	24	e2e4	e2e4	NOUN
ejpam-5397	127	25	−	−	PROPN
ejpam-5397	127	26	r3	r3	PROPN
ejpam-5397	127	27	(	(	PUNCT
ejpam-5397	127	28	e1	e1	VERB
ejpam-5397	127	29	+	+	CCONJ
ejpam-5397	127	30	e3	e3	NOUN
ejpam-5397	127	31	+	+	CCONJ
ejpam-5397	127	32	e5	e5	PROPN
ejpam-5397	127	33	+	+	CCONJ
ejpam-5397	127	34	e6	e6	PROPN
ejpam-5397	127	35	)	)	PUNCT
ejpam-5397	127	36	and	and	CCONJ
ejpam-5397	127	37	c3	c3	NOUN
ejpam-5397	127	38	=	=	PUNCT
ejpam-5397	128	1	e1e5	e1e5	PUNCT
ejpam-5397	128	2	+	+	NUM
ejpam-5397	128	3	e1e6	e1e6	PROPN
ejpam-5397	128	4	−	−	PROPN
ejpam-5397	128	5	e2e4	e2e4	NOUN
ejpam-5397	128	6	−	−	NOUN
ejpam-5397	128	7	e2e6	e2e6	INTJ
ejpam-5397	128	8	−	−	NOUN
ejpam-5397	128	9	e3e4	e3e4	X
ejpam-5397	128	10	+	+	CCONJ
ejpam-5397	128	11	e3e5	e3e5	PROPN
ejpam-5397	128	12	b.	b.	PROPN
ejpam-5397	128	13	b.	b.	PROPN
ejpam-5397	128	14	kamal	kamal	PROPN
ejpam-5397	128	15	,	,	PUNCT
ejpam-5397	128	16	a.	a.	PROPN
ejpam-5397	128	17	n.	n.	PROPN
ejpam-5397	128	18	mustafa	mustafa	PROPN
ejpam-5397	128	19	/	/	SYM
ejpam-5397	128	20	eur	eur	PROPN
ejpam-5397	128	21	.	.	PUNCT
ejpam-5397	129	1	j.	j.	PROPN
ejpam-5397	129	2	pure	pure	PROPN
ejpam-5397	129	3	appl	appl	PROPN
ejpam-5397	129	4	.	.	PROPN
ejpam-5397	129	5	math	math	PROPN
ejpam-5397	129	6	,	,	PUNCT
ejpam-5397	129	7	18	18	NUM
ejpam-5397	129	8	(	(	PUNCT
ejpam-5397	129	9	1	1	NUM
ejpam-5397	129	10	)	)	PUNCT
ejpam-5397	129	11	(	(	PUNCT
ejpam-5397	129	12	2025	2025	NUM
ejpam-5397	129	13	)	)	PUNCT
ejpam-5397	129	14	,	,	PUNCT
ejpam-5397	129	15	5397	5397	NUM
ejpam-5397	129	16	8	8	NUM
ejpam-5397	129	17	of	of	ADP
ejpam-5397	129	18	21	21	NUM
ejpam-5397	129	19	with	with	ADP
ejpam-5397	129	20	e1	e1	NOUN
ejpam-5397	129	21	=	=	SYM
ejpam-5397	129	22	r1	r1	NOUN
ejpam-5397	129	23	−	−	PROPN
ejpam-5397	129	24	2	2	NUM
ejpam-5397	129	25	r1	r1	PROPN
ejpam-5397	129	26	k	k	PROPN
ejpam-5397	129	27	x∗	x∗	PROPN
ejpam-5397	129	28	−	−	PROPN
ejpam-5397	130	1	βy	βy	ADP
ejpam-5397	130	2	∗	∗	NOUN
ejpam-5397	130	3	(	(	PUNCT
ejpam-5397	130	4	1	1	NUM
ejpam-5397	130	5	+	+	NUM
ejpam-5397	130	6	βtx∗)2	βtx∗)2	ADJ
ejpam-5397	130	7	−	−	PROPN
ejpam-5397	130	8	α1	α1	PROPN
ejpam-5397	130	9	(	(	PUNCT
ejpam-5397	130	10	1	1	NUM
ejpam-5397	130	11	+	+	NOUN
ejpam-5397	130	12	α2t2y	α2t2y	NUM
ejpam-5397	130	13	∗)z∗	∗)z∗	ADJ
ejpam-5397	130	14	(	(	PUNCT
ejpam-5397	130	15	1	1	NUM
ejpam-5397	130	16	+	+	NUM
ejpam-5397	130	17	α1t1x∗	α1t1x∗	X
ejpam-5397	130	18	+	+	CCONJ
ejpam-5397	130	19	α2t2y	α2t2y	NUM
ejpam-5397	130	20	∗)2	∗)2	PROPN
ejpam-5397	130	21	,	,	PUNCT
ejpam-5397	130	22	e2	e2	PROPN
ejpam-5397	130	23	=	=	PUNCT
ejpam-5397	130	24	−	−	PROPN
ejpam-5397	130	25	βx∗	βx∗	NOUN
ejpam-5397	130	26	1	1	NUM
ejpam-5397	131	1	+	+	CCONJ
ejpam-5397	131	2	βtx∗	βtx∗	ADJ
ejpam-5397	131	3	−	−	PROPN
ejpam-5397	131	4	α1	α1	PROPN
ejpam-5397	131	5	(	(	PUNCT
ejpam-5397	131	6	1	1	NUM
ejpam-5397	131	7	+	+	NOUN
ejpam-5397	131	8	α1t1x	α1t1x	NUM
ejpam-5397	131	9	∗)z∗	∗)z∗	X
ejpam-5397	131	10	(	(	PUNCT
ejpam-5397	131	11	1	1	NUM
ejpam-5397	131	12	+	+	NUM
ejpam-5397	131	13	α1t1x∗	α1t1x∗	X
ejpam-5397	131	14	+	+	CCONJ
ejpam-5397	131	15	α2t2y	α2t2y	NUM
ejpam-5397	131	16	∗)2	∗)2	PROPN
ejpam-5397	131	17	,	,	PUNCT
ejpam-5397	131	18	e3	e3	VERB
ejpam-5397	131	19	=	=	SYM
ejpam-5397	131	20	−	−	PROPN
ejpam-5397	131	21	α1x	α1x	NUM
ejpam-5397	131	22	∗	∗	NOUN
ejpam-5397	131	23	1	1	NUM
ejpam-5397	131	24	+	+	CCONJ
ejpam-5397	131	25	α1t1x∗	α1t1x∗	X
ejpam-5397	131	26	+	+	CCONJ
ejpam-5397	131	27	α2t2y	α2t2y	NUM
ejpam-5397	131	28	∗	∗	NOUN
ejpam-5397	131	29	e4	e4	NOUN
ejpam-5397	131	30	=	=	PROPN
ejpam-5397	131	31	r2	r2	PROPN
ejpam-5397	131	32	(	(	PUNCT
ejpam-5397	131	33	y	y	NOUN
ejpam-5397	131	34	∗	∗	X
ejpam-5397	131	35	x∗	x∗	PROPN
ejpam-5397	131	36	)	)	PUNCT
ejpam-5397	131	37	2	2	NUM
ejpam-5397	131	38	−	−	NOUN
ejpam-5397	131	39	α2	α2	ADJ
ejpam-5397	131	40	(	(	PUNCT
ejpam-5397	131	41	1	1	NUM
ejpam-5397	131	42	+	+	NOUN
ejpam-5397	131	43	α2t2y	α2t2y	NUM
ejpam-5397	131	44	∗)z∗	∗)z∗	ADJ
ejpam-5397	131	45	(	(	PUNCT
ejpam-5397	131	46	1	1	NUM
ejpam-5397	131	47	+	+	NUM
ejpam-5397	131	48	α1t1x∗	α1t1x∗	X
ejpam-5397	131	49	+	+	CCONJ
ejpam-5397	131	50	α2t2y	α2t2y	NUM
ejpam-5397	131	51	∗)2	∗)2	PROPN
ejpam-5397	131	52	,	,	PUNCT
ejpam-5397	131	53	e5	e5	PROPN
ejpam-5397	131	54	=	=	PROPN
ejpam-5397	131	55	r2	r2	PROPN
ejpam-5397	131	56	−	−	PROPN
ejpam-5397	131	57	2r2	2r2	NUM
ejpam-5397	131	58	y	y	PROPN
ejpam-5397	131	59	∗	∗	X
ejpam-5397	131	60	x∗	x∗	PROPN
ejpam-5397	132	1	−	−	PROPN
ejpam-5397	132	2	α2	α2	ADJ
ejpam-5397	132	3	(	(	PUNCT
ejpam-5397	132	4	1	1	NUM
ejpam-5397	132	5	+	+	CCONJ
ejpam-5397	132	6	a1t1x	a1t1x	NUM
ejpam-5397	132	7	∗)z∗	∗)z∗	X
ejpam-5397	132	8	(	(	PUNCT
ejpam-5397	132	9	1	1	NUM
ejpam-5397	132	10	+	+	NUM
ejpam-5397	132	11	α1t1x∗	α1t1x∗	X
ejpam-5397	132	12	+	+	CCONJ
ejpam-5397	132	13	α2t2y	α2t2y	ADV
ejpam-5397	132	14	∗)2	∗)2	PROPN
ejpam-5397	132	15	and	and	CCONJ
ejpam-5397	132	16	e6	e6	PROPN
ejpam-5397	132	17	=	=	PUNCT
ejpam-5397	132	18	−	−	PROPN
ejpam-5397	132	19	α2y	α2y	NUM
ejpam-5397	132	20	∗	∗	NOUN
ejpam-5397	132	21	1	1	NUM
ejpam-5397	132	22	+	+	CCONJ
ejpam-5397	132	23	α1t1x∗	α1t1x∗	X
ejpam-5397	132	24	+	+	CCONJ
ejpam-5397	132	25	α2t2y	α2t2y	NUM
ejpam-5397	132	26	∗	∗	NOUN
ejpam-5397	132	27	therefore	therefore	ADV
ejpam-5397	132	28	,	,	PUNCT
ejpam-5397	132	29	the	the	DET
ejpam-5397	132	30	following	follow	VERB
ejpam-5397	132	31	theorem	theorem	NOUN
ejpam-5397	132	32	can	can	AUX
ejpam-5397	132	33	be	be	AUX
ejpam-5397	132	34	derived	derive	VERB
ejpam-5397	132	35	based	base	VERB
ejpam-5397	132	36	on	on	ADP
ejpam-5397	132	37	the	the	DET
ejpam-5397	132	38	above	above	ADJ
ejpam-5397	132	39	argument	argument	NOUN
ejpam-5397	132	40	.	.	PUNCT
ejpam-5397	133	1	theorem	theorem	VERB
ejpam-5397	133	2	3.2	3.2	NUM
ejpam-5397	133	3	.	.	PUNCT
ejpam-5397	134	1	(	(	PUNCT
ejpam-5397	134	2	i	i	NOUN
ejpam-5397	134	3	)	)	PUNCT
ejpam-5397	134	4	the	the	DET
ejpam-5397	134	5	only	only	ADJ
ejpam-5397	134	6	prey	prey	PROPN
ejpam-5397	134	7	existence	existence	PROPN
ejpam-5397	134	8	steady	steady	ADJ
ejpam-5397	134	9	state	state	NOUN
ejpam-5397	134	10	and	and	CCONJ
ejpam-5397	134	11	the	the	DET
ejpam-5397	134	12	apex	apex	NOUN
ejpam-5397	134	13	predator	predator	NOUN
ejpam-5397	134	14	-	-	PUNCT
ejpam-5397	134	15	free	free	ADJ
ejpam-5397	134	16	steady	steady	ADJ
ejpam-5397	134	17	state	state	NOUN
ejpam-5397	134	18	are	be	AUX
ejpam-5397	134	19	unstable	unstable	ADJ
ejpam-5397	134	20	.	.	PUNCT
ejpam-5397	135	1	(	(	PUNCT
ejpam-5397	135	2	ii	ii	NOUN
ejpam-5397	135	3	)	)	PUNCT
ejpam-5397	135	4	the	the	DET
ejpam-5397	135	5	intermediate	intermediate	ADJ
ejpam-5397	135	6	predators	predator	NOUN
ejpam-5397	135	7	-	-	PUNCT
ejpam-5397	135	8	free	free	ADJ
ejpam-5397	135	9	steady	steady	ADJ
ejpam-5397	135	10	state	state	NOUN
ejpam-5397	135	11	is	be	AUX
ejpam-5397	135	12	las	las	PROPN
ejpam-5397	135	13	if	if	SCONJ
ejpam-5397	135	14	and	and	CCONJ
ejpam-5397	135	15	only	only	ADV
ejpam-5397	135	16	if	if	SCONJ
ejpam-5397	135	17	,	,	PUNCT
ejpam-5397	135	18	all	all	DET
ejpam-5397	135	19	the	the	DET
ejpam-5397	135	20	following	follow	VERB
ejpam-5397	135	21	routh	routh	PROPN
ejpam-5397	135	22	-	-	PUNCT
ejpam-5397	135	23	hurwize	hurwize	PROPN
ejpam-5397	135	24	criteria	criterion	NOUN
ejpam-5397	135	25	hold	hold	VERB
ejpam-5397	135	26	.	.	PUNCT
ejpam-5397	136	1	a2	a2	PROPN
ejpam-5397	136	2	>	>	X
ejpam-5397	136	3	0	0	PROPN
ejpam-5397	136	4	,	,	PUNCT
ejpam-5397	136	5	c2	c2	PROPN
ejpam-5397	136	6	>	>	X
ejpam-5397	136	7	0	0	PUNCT
ejpam-5397	137	1	and	and	CCONJ
ejpam-5397	137	2	a2b2	a2b2	X
ejpam-5397	137	3	>	>	X
ejpam-5397	137	4	r3c2	r3c2	X
ejpam-5397	137	5	(	(	PUNCT
ejpam-5397	137	6	12	12	NUM
ejpam-5397	137	7	)	)	PUNCT
ejpam-5397	137	8	(	(	PUNCT
ejpam-5397	137	9	iii	iii	X
ejpam-5397	137	10	)	)	PUNCT
ejpam-5397	137	11	the	the	DET
ejpam-5397	137	12	coexistence	coexistence	NOUN
ejpam-5397	137	13	steady	steady	ADJ
ejpam-5397	137	14	state	state	NOUN
ejpam-5397	137	15	it	it	PRON
ejpam-5397	137	16	is	be	AUX
ejpam-5397	137	17	las	las	PROPN
ejpam-5397	137	18	if	if	SCONJ
ejpam-5397	137	19	and	and	CCONJ
ejpam-5397	137	20	only	only	ADV
ejpam-5397	137	21	if	if	SCONJ
ejpam-5397	137	22	,	,	PUNCT
ejpam-5397	137	23	all	all	DET
ejpam-5397	137	24	the	the	DET
ejpam-5397	137	25	following	follow	VERB
ejpam-5397	137	26	routh	routh	PROPN
ejpam-5397	137	27	-	-	PUNCT
ejpam-5397	137	28	hurwize	hurwize	PROPN
ejpam-5397	137	29	criteria	criterion	NOUN
ejpam-5397	137	30	hold	hold	VERB
ejpam-5397	137	31	.	.	PUNCT
ejpam-5397	138	1	a3	a3	PROPN
ejpam-5397	138	2	>	>	X
ejpam-5397	138	3	0	0	PROPN
ejpam-5397	138	4	,	,	PUNCT
ejpam-5397	138	5	c3	c3	X
ejpam-5397	138	6	>	>	X
ejpam-5397	138	7	0	0	PUNCT
ejpam-5397	139	1	and	and	CCONJ
ejpam-5397	139	2	a3b3	a3b3	ADJ
ejpam-5397	139	3	>	>	X
ejpam-5397	139	4	r3c3	r3c3	X
ejpam-5397	139	5	(	(	PUNCT
ejpam-5397	139	6	13	13	NUM
ejpam-5397	139	7	)	)	PUNCT
ejpam-5397	139	8	3.3	3.3	NUM
ejpam-5397	139	9	.	.	PUNCT
ejpam-5397	140	1	global	global	ADJ
ejpam-5397	140	2	stability	stability	NOUN
ejpam-5397	140	3	global	global	ADJ
ejpam-5397	140	4	stability	stability	NOUN
ejpam-5397	140	5	(	(	PUNCT
ejpam-5397	140	6	or	or	CCONJ
ejpam-5397	140	7	globally	globally	ADV
ejpam-5397	140	8	asymptotically	asymptotically	ADV
ejpam-5397	140	9	stable	stable	ADJ
ejpam-5397	140	10	gas	gas	NOUN
ejpam-5397	140	11	)	)	PUNCT
ejpam-5397	140	12	means	mean	VERB
ejpam-5397	140	13	that	that	SCONJ
ejpam-5397	140	14	any	any	DET
ejpam-5397	140	15	trajectories	trajectory	NOUN
ejpam-5397	140	16	finally	finally	ADV
ejpam-5397	140	17	tend	tend	VERB
ejpam-5397	140	18	to	to	ADP
ejpam-5397	140	19	the	the	DET
ejpam-5397	140	20	attractor	attractor	NOUN
ejpam-5397	140	21	of	of	ADP
ejpam-5397	140	22	the	the	DET
ejpam-5397	140	23	system	system	NOUN
ejpam-5397	140	24	,	,	PUNCT
ejpam-5397	140	25	regardless	regardless	ADV
ejpam-5397	140	26	of	of	ADP
ejpam-5397	140	27	initial	initial	ADJ
ejpam-5397	140	28	conditions	condition	NOUN
ejpam-5397	140	29	.	.	PUNCT
ejpam-5397	141	1	therefore	therefore	ADV
ejpam-5397	141	2	,	,	PUNCT
ejpam-5397	141	3	most	most	ADJ
ejpam-5397	141	4	of	of	ADP
ejpam-5397	141	5	biological	biological	ADJ
ejpam-5397	141	6	systems	system	NOUN
ejpam-5397	141	7	,	,	PUNCT
ejpam-5397	141	8	especially	especially	ADV
ejpam-5397	141	9	prey	prey	VERB
ejpam-5397	141	10	predator	predator	NOUN
ejpam-5397	141	11	system	system	NOUN
ejpam-5397	141	12	,	,	PUNCT
ejpam-5397	141	13	are	be	AUX
ejpam-5397	141	14	needed	need	VERB
ejpam-5397	141	15	to	to	PART
ejpam-5397	141	16	be	be	AUX
ejpam-5397	141	17	globally	globally	ADV
ejpam-5397	141	18	stable	stable	ADJ
ejpam-5397	141	19	.	.	PUNCT
ejpam-5397	142	1	since	since	SCONJ
ejpam-5397	142	2	s1	s1	NOUN
ejpam-5397	142	3	and	and	CCONJ
ejpam-5397	142	4	s2	s2	NOUN
ejpam-5397	142	5	are	be	AUX
ejpam-5397	142	6	not	not	PART
ejpam-5397	142	7	las	las	NOUN
ejpam-5397	142	8	,	,	PUNCT
ejpam-5397	142	9	so	so	SCONJ
ejpam-5397	142	10	they	they	PRON
ejpam-5397	142	11	can	can	AUX
ejpam-5397	142	12	not	not	PART
ejpam-5397	142	13	be	be	AUX
ejpam-5397	142	14	gas	gas	NOUN
ejpam-5397	142	15	.	.	PUNCT
ejpam-5397	143	1	however	however	ADV
ejpam-5397	143	2	gas	gas	NOUN
ejpam-5397	143	3	for	for	ADP
ejpam-5397	143	4	both	both	DET
ejpam-5397	143	5	s3	s3	PROPN
ejpam-5397	143	6	and	and	CCONJ
ejpam-5397	143	7	s4	s4	PROPN
ejpam-5397	143	8	of	of	ADP
ejpam-5397	143	9	the	the	DET
ejpam-5397	143	10	system	system	NOUN
ejpam-5397	143	11	(	(	PUNCT
ejpam-5397	143	12	1	1	X
ejpam-5397	143	13	)	)	PUNCT
ejpam-5397	143	14	is	be	AUX
ejpam-5397	143	15	established	establish	VERB
ejpam-5397	143	16	in	in	ADP
ejpam-5397	143	17	theorem	theorem	ADJ
ejpam-5397	143	18	3.3	3.3	NUM
ejpam-5397	143	19	and	and	CCONJ
ejpam-5397	143	20	theorem	theorem	VERB
ejpam-5397	143	21	3.4	3.4	NUM
ejpam-5397	143	22	,	,	PUNCT
ejpam-5397	143	23	respectively	respectively	ADV
ejpam-5397	143	24	.	.	PUNCT
ejpam-5397	144	1	theorem	theorem	VERB
ejpam-5397	144	2	3.3	3.3	NUM
ejpam-5397	144	3	.	.	PUNCT
ejpam-5397	145	1	suppose	suppose	VERB
ejpam-5397	145	2	that	that	SCONJ
ejpam-5397	145	3	condition	condition	NOUN
ejpam-5397	145	4	5	5	NUM
ejpam-5397	145	5	holds	hold	NOUN
ejpam-5397	145	6	,	,	PUNCT
ejpam-5397	145	7	and	and	CCONJ
ejpam-5397	145	8	then	then	ADV
ejpam-5397	145	9	s3	s3	PROPN
ejpam-5397	145	10	=	=	SYM
ejpam-5397	145	11	(	(	PUNCT
ejpam-5397	145	12	s̄	s̄	NOUN
ejpam-5397	145	13	,	,	PUNCT
ejpam-5397	145	14	0	0	NUM
ejpam-5397	145	15	,	,	PUNCT
ejpam-5397	145	16	s̄	s̄	NOUN
ejpam-5397	145	17	)	)	PUNCT
ejpam-5397	145	18	is	be	AUX
ejpam-5397	145	19	gas	gas	NOUN
ejpam-5397	145	20	,	,	PUNCT
ejpam-5397	145	21	if	if	SCONJ
ejpam-5397	145	22	the	the	DET
ejpam-5397	145	23	following	follow	VERB
ejpam-5397	145	24	inequality	inequality	NOUN
ejpam-5397	145	25	holds	hold	VERB
ejpam-5397	145	26	:	:	PUNCT
ejpam-5397	146	1	r2	r2	PROPN
ejpam-5397	146	2	<	<	X
ejpam-5397	146	3	α2k1	α2k1	X
ejpam-5397	146	4	1	1	NUM
ejpam-5397	146	5	+	+	NUM
ejpam-5397	146	6	α1t1k	α1t1k	NUM
ejpam-5397	146	7	+	+	CCONJ
ejpam-5397	146	8	α2t2k	α2t2k	NUM
ejpam-5397	146	9	(	(	PUNCT
ejpam-5397	146	10	14	14	NUM
ejpam-5397	146	11	)	)	PUNCT
ejpam-5397	146	12	r1	r1	NOUN
ejpam-5397	146	13	+	+	CCONJ
ejpam-5397	146	14	r3	r3	PROPN
ejpam-5397	146	15	k2	k2	PROPN
ejpam-5397	146	16	>	>	X
ejpam-5397	146	17	α1	α1	PROPN
ejpam-5397	146	18	(	(	PUNCT
ejpam-5397	146	19	1	1	NUM
ejpam-5397	146	20	+	+	NUM
ejpam-5397	146	21	α1t1k1	α1t1k1	NOUN
ejpam-5397	146	22	)	)	PUNCT
ejpam-5397	146	23	2	2	NUM
ejpam-5397	146	24	(	(	PUNCT
ejpam-5397	146	25	15	15	NUM
ejpam-5397	146	26	)	)	PUNCT
ejpam-5397	146	27	b.	b.	PROPN
ejpam-5397	146	28	b.	b.	PROPN
ejpam-5397	146	29	kamal	kamal	PROPN
ejpam-5397	146	30	,	,	PUNCT
ejpam-5397	146	31	a.	a.	PROPN
ejpam-5397	146	32	n.	n.	PROPN
ejpam-5397	146	33	mustafa	mustafa	PROPN
ejpam-5397	146	34	/	/	SYM
ejpam-5397	146	35	eur	eur	PROPN
ejpam-5397	146	36	.	.	PUNCT
ejpam-5397	147	1	j.	j.	PROPN
ejpam-5397	147	2	pure	pure	PROPN
ejpam-5397	147	3	appl	appl	PROPN
ejpam-5397	147	4	.	.	PROPN
ejpam-5397	147	5	math	math	PROPN
ejpam-5397	147	6	,	,	PUNCT
ejpam-5397	147	7	18	18	NUM
ejpam-5397	147	8	(	(	PUNCT
ejpam-5397	147	9	1	1	NUM
ejpam-5397	147	10	)	)	PUNCT
ejpam-5397	147	11	(	(	PUNCT
ejpam-5397	147	12	2025	2025	NUM
ejpam-5397	147	13	)	)	PUNCT
ejpam-5397	147	14	,	,	PUNCT
ejpam-5397	147	15	5397	5397	NUM
ejpam-5397	147	16	9	9	NUM
ejpam-5397	147	17	of	of	ADP
ejpam-5397	147	18	21	21	NUM
ejpam-5397	147	19	proof	proof	NOUN
ejpam-5397	147	20	.	.	PUNCT
ejpam-5397	148	1	from	from	ADP
ejpam-5397	148	2	lemma	lemma	PROPN
ejpam-5397	148	3	2.1	2.1	NUM
ejpam-5397	148	4	,	,	PUNCT
ejpam-5397	148	5	limt→∞	limt→∞	NOUN
ejpam-5397	148	6	supx(t	supx(t	NOUN
ejpam-5397	148	7	)	)	PUNCT
ejpam-5397	148	8	≤	≤	PUNCT
ejpam-5397	149	1	k	k	PROPN
ejpam-5397	149	2	and	and	CCONJ
ejpam-5397	149	3	limt→∞	limt→∞	PROPN
ejpam-5397	149	4	supy	supy	NOUN
ejpam-5397	149	5	(	(	PUNCT
ejpam-5397	149	6	t	t	NOUN
ejpam-5397	149	7	)	)	PUNCT
ejpam-5397	149	8	≤	≤	PROPN
ejpam-5397	150	1	k.	k.	ADV
ejpam-5397	150	2	from	from	ADP
ejpam-5397	150	3	lemma	lemma	PROPN
ejpam-5397	150	4	2.2	2.2	NUM
ejpam-5397	150	5	limt→∞	limt→∞	NOUN
ejpam-5397	150	6	infx(t	infx(t	PROPN
ejpam-5397	150	7	)	)	PUNCT
ejpam-5397	150	8	≥	≥	NOUN
ejpam-5397	150	9	k1	k1	NOUN
ejpam-5397	150	10	,	,	PUNCT
ejpam-5397	150	11	if	if	SCONJ
ejpam-5397	150	12	condition	condition	NOUN
ejpam-5397	150	13	5	5	NUM
ejpam-5397	150	14	,	,	PUNCT
ejpam-5397	150	15	holds	hold	VERB
ejpam-5397	150	16	.	.	PUNCT
ejpam-5397	151	1	therefore	therefore	ADV
ejpam-5397	151	2	,	,	PUNCT
ejpam-5397	151	3	the	the	DET
ejpam-5397	151	4	third	third	ADJ
ejpam-5397	151	5	equation	equation	NOUN
ejpam-5397	151	6	f	f	PROPN
ejpam-5397	151	7	system	system	NOUN
ejpam-5397	151	8	(	(	PUNCT
ejpam-5397	151	9	1	1	X
ejpam-5397	151	10	)	)	PUNCT
ejpam-5397	151	11	gives	give	VERB
ejpam-5397	151	12	that	that	DET
ejpam-5397	151	13	lim	lim	PROPN
ejpam-5397	151	14	t→∞	t→∞	ADP
ejpam-5397	151	15	infx(t	infx(t	PROPN
ejpam-5397	151	16	)	)	PUNCT
ejpam-5397	151	17	≥	≥	NOUN
ejpam-5397	151	18	k1	k1	NOUN
ejpam-5397	151	19	and	and	CCONJ
ejpam-5397	151	20	lim	lim	PROPN
ejpam-5397	151	21	t→∞	t→∞	DET
ejpam-5397	151	22	inf	inf	PROPN
ejpam-5397	151	23	y	y	PROPN
ejpam-5397	151	24	(	(	PUNCT
ejpam-5397	151	25	t	t	PROPN
ejpam-5397	151	26	)	)	PUNCT
ejpam-5397	151	27	≥	≥	NOUN
ejpam-5397	151	28	k1	k1	NOUN
ejpam-5397	151	29	.	.	PUNCT
ejpam-5397	152	1	and	and	CCONJ
ejpam-5397	152	2	hence	hence	ADV
ejpam-5397	152	3	,	,	PUNCT
ejpam-5397	152	4	from	from	ADP
ejpam-5397	152	5	the	the	DET
ejpam-5397	152	6	second	second	ADJ
ejpam-5397	152	7	equation	equation	NOUN
ejpam-5397	152	8	of	of	ADP
ejpam-5397	152	9	system	system	NOUN
ejpam-5397	152	10	(	(	PUNCT
ejpam-5397	152	11	1	1	NUM
ejpam-5397	152	12	)	)	PUNCT
ejpam-5397	152	13	,	,	PUNCT
ejpam-5397	152	14	it	it	PRON
ejpam-5397	152	15	is	be	AUX
ejpam-5397	152	16	obtained	obtain	VERB
ejpam-5397	152	17	that	that	SCONJ
ejpam-5397	152	18	dy	dy	NOUN
ejpam-5397	152	19	dt	dt	NOUN
ejpam-5397	152	20	≤	≤	PROPN
ejpam-5397	152	21	y	y	PROPN
ejpam-5397	152	22	[	[	PUNCT
ejpam-5397	152	23	r2	r2	PROPN
ejpam-5397	152	24	−	−	PROPN
ejpam-5397	152	25	α2k1	α2k1	INTJ
ejpam-5397	152	26	1	1	NUM
ejpam-5397	152	27	+	+	NUM
ejpam-5397	152	28	α1t1k	α1t1k	NUM
ejpam-5397	152	29	+	+	CCONJ
ejpam-5397	152	30	α2t2k	α2t2k	NUM
ejpam-5397	152	31	−	−	PROPN
ejpam-5397	152	32	r2y	r2y	NOUN
ejpam-5397	152	33	k	k	X
ejpam-5397	152	34	]	]	PUNCT
ejpam-5397	152	35	.	.	PUNCT
ejpam-5397	153	1	so	so	ADV
ejpam-5397	153	2	,	,	PUNCT
ejpam-5397	153	3	dy	dy	NOUN
ejpam-5397	153	4	dt	dt	NOUN
ejpam-5397	153	5	is	be	AUX
ejpam-5397	153	6	negative	negative	ADJ
ejpam-5397	153	7	due	due	ADJ
ejpam-5397	153	8	to	to	ADP
ejpam-5397	153	9	condition	condition	NOUN
ejpam-5397	153	10	14	14	NUM
ejpam-5397	153	11	,	,	PUNCT
ejpam-5397	153	12	consequently	consequently	ADV
ejpam-5397	153	13	limt→∞	limt→∞	ADP
ejpam-5397	153	14	y	y	PROPN
ejpam-5397	153	15	(	(	PUNCT
ejpam-5397	153	16	t	t	PROPN
ejpam-5397	153	17	)	)	PUNCT
ejpam-5397	153	18	=	=	SYM
ejpam-5397	154	1	0	0	X
ejpam-5397	154	2	.	.	PUNCT
ejpam-5397	154	3	therefore	therefore	ADV
ejpam-5397	154	4	as	as	SCONJ
ejpam-5397	154	5	time	time	NOUN
ejpam-5397	154	6	approaches	approach	NOUN
ejpam-5397	154	7	infinity	infinity	NOUN
ejpam-5397	154	8	,	,	PUNCT
ejpam-5397	154	9	system	system	NOUN
ejpam-5397	154	10	(	(	PUNCT
ejpam-5397	154	11	1	1	X
ejpam-5397	154	12	)	)	PUNCT
ejpam-5397	154	13	reduced	reduce	VERB
ejpam-5397	154	14	to	to	ADP
ejpam-5397	154	15	the	the	DET
ejpam-5397	154	16	following	follow	VERB
ejpam-5397	154	17	subsystem	subsystem	NOUN
ejpam-5397	154	18	{	{	PUNCT
ejpam-5397	154	19	dx	dx	PROPN
ejpam-5397	154	20	dt	dt	NOUN
ejpam-5397	155	1	=	=	PUNCT
ejpam-5397	155	2	x	x	PUNCT
ejpam-5397	155	3	[	[	PUNCT
ejpam-5397	155	4	r1	r1	PROPN
ejpam-5397	155	5	(	(	PUNCT
ejpam-5397	155	6	1−	1−	NUM
ejpam-5397	155	7	x	x	SYM
ejpam-5397	155	8	k	k	NOUN
ejpam-5397	155	9	)	)	PUNCT
ejpam-5397	155	10	−	−	PROPN
ejpam-5397	156	1	α1z	α1z	PRON
ejpam-5397	156	2	1+α1t1x	1+α1t1x	NUM
ejpam-5397	156	3	]	]	X
ejpam-5397	156	4	=	=	SYM
ejpam-5397	156	5	f	f	X
ejpam-5397	156	6	(	(	PUNCT
ejpam-5397	156	7	x	x	X
ejpam-5397	156	8	,	,	PUNCT
ejpam-5397	156	9	z	z	NOUN
ejpam-5397	156	10	)	)	PUNCT
ejpam-5397	156	11	dz	dz	ADJ
ejpam-5397	156	12	dt	dt	NOUN
ejpam-5397	156	13	=	=	PUNCT
ejpam-5397	156	14	r3z	r3z	NOUN
ejpam-5397	156	15	(	(	PUNCT
ejpam-5397	156	16	1−	1−	NUM
ejpam-5397	156	17	z	z	NOUN
ejpam-5397	156	18	x	x	SYM
ejpam-5397	156	19	)	)	PUNCT
ejpam-5397	157	1	=	=	SYM
ejpam-5397	157	2	g(x	g(x	NOUN
ejpam-5397	157	3	,	,	PUNCT
ejpam-5397	157	4	z	z	NOUN
ejpam-5397	157	5	)	)	PUNCT
ejpam-5397	157	6	(	(	PUNCT
ejpam-5397	157	7	16	16	NUM
ejpam-5397	157	8	)	)	PUNCT
ejpam-5397	157	9	consider	consider	VERB
ejpam-5397	157	10	now	now	ADV
ejpam-5397	157	11	the	the	DET
ejpam-5397	157	12	function	function	NOUN
ejpam-5397	157	13	h(x	h(x	PROPN
ejpam-5397	157	14	,	,	PUNCT
ejpam-5397	157	15	z	z	NOUN
ejpam-5397	157	16	)	)	PUNCT
ejpam-5397	157	17	=	=	SYM
ejpam-5397	157	18	1	1	NUM
ejpam-5397	157	19	/	/	SYM
ejpam-5397	157	20	xz	xz	PROPN
ejpam-5397	157	21	,	,	PUNCT
ejpam-5397	157	22	clearly	clearly	ADV
ejpam-5397	157	23	h	h	NOUN
ejpam-5397	157	24	is	be	AUX
ejpam-5397	157	25	a	a	DET
ejpam-5397	157	26	continuously	continuously	ADV
ejpam-5397	157	27	differentiable	differentiable	ADJ
ejpam-5397	157	28	function	function	NOUN
ejpam-5397	157	29	.	.	PUNCT
ejpam-5397	158	1	further	far	ADV
ejpam-5397	158	2	,	,	PUNCT
ejpam-5397	158	3	∂(hf	∂(hf	NOUN
ejpam-5397	158	4	)	)	PUNCT
ejpam-5397	158	5	∂x	∂x	PROPN
ejpam-5397	158	6	+	+	NUM
ejpam-5397	158	7	∂(hg	∂(hg	ADJ
ejpam-5397	158	8	)	)	PUNCT
ejpam-5397	159	1	∂z	∂z	PROPN
ejpam-5397	159	2	=	=	PUNCT
ejpam-5397	159	3	−	−	PROPN
ejpam-5397	159	4	r1	r1	PROPN
ejpam-5397	159	5	kz	kz	PROPN
ejpam-5397	159	6	+	+	PROPN
ejpam-5397	159	7	α1	α1	PROPN
ejpam-5397	159	8	(	(	PUNCT
ejpam-5397	159	9	1	1	NUM
ejpam-5397	159	10	+	+	NUM
ejpam-5397	159	11	α1t1x)2	α1t1x)2	NOUN
ejpam-5397	159	12	−	−	PROPN
ejpam-5397	159	13	r3	r3	PROPN
ejpam-5397	160	1	x2	x2	PROPN
ejpam-5397	160	2	<	<	X
ejpam-5397	160	3	α1	α1	PROPN
ejpam-5397	160	4	(	(	PUNCT
ejpam-5397	160	5	1	1	NUM
ejpam-5397	160	6	+	+	NUM
ejpam-5397	160	7	α1t1k1	α1t1k1	NOUN
ejpam-5397	160	8	)	)	PUNCT
ejpam-5397	160	9	2	2	NUM
ejpam-5397	160	10	−	−	NOUN
ejpam-5397	160	11	r1	r1	PROPN
ejpam-5397	160	12	+	+	CCONJ
ejpam-5397	160	13	r3	r3	PROPN
ejpam-5397	160	14	k2	k2	NOUN
ejpam-5397	160	15	.	.	PUNCT
ejpam-5397	161	1	under	under	ADP
ejpam-5397	161	2	the	the	DET
ejpam-5397	161	3	condition	condition	NOUN
ejpam-5397	161	4	(	(	PUNCT
ejpam-5397	161	5	15	15	NUM
ejpam-5397	161	6	)	)	PUNCT
ejpam-5397	161	7	,	,	PUNCT
ejpam-5397	161	8	it	it	PRON
ejpam-5397	161	9	is	be	AUX
ejpam-5397	161	10	clear	clear	ADJ
ejpam-5397	161	11	that	that	SCONJ
ejpam-5397	161	12	∂(hf	∂(hf	NOUN
ejpam-5397	161	13	)	)	PUNCT
ejpam-5397	162	1	∂x	∂x	PROPN
ejpam-5397	162	2	+	+	NUM
ejpam-5397	162	3	∂(hg	∂(hg	ADJ
ejpam-5397	162	4	)	)	PUNCT
ejpam-5397	163	1	∂z	∂z	PROPN
ejpam-5397	163	2	does	do	AUX
ejpam-5397	163	3	not	not	PART
ejpam-5397	163	4	change	change	VERB
ejpam-5397	163	5	sign	sign	NOUN
ejpam-5397	163	6	and	and	CCONJ
ejpam-5397	163	7	is	be	AUX
ejpam-5397	163	8	not	not	PART
ejpam-5397	163	9	identically	identically	ADV
ejpam-5397	163	10	zero	zero	NUM
ejpam-5397	163	11	.	.	PUNCT
ejpam-5397	164	1	so	so	ADV
ejpam-5397	164	2	,	,	PUNCT
ejpam-5397	164	3	by	by	ADP
ejpam-5397	164	4	bendixsondulac	bendixsondulac	NOUN
ejpam-5397	164	5	criterion	criterion	NOUN
ejpam-5397	164	6	,	,	PUNCT
ejpam-5397	164	7	there	there	PRON
ejpam-5397	164	8	is	be	VERB
ejpam-5397	164	9	no	no	DET
ejpam-5397	164	10	periodic	periodic	ADJ
ejpam-5397	164	11	curve	curve	NOUN
ejpam-5397	164	12	in	in	ADP
ejpam-5397	164	13	of	of	ADP
ejpam-5397	164	14	the	the	DET
ejpam-5397	164	15	xz	xz	NOUN
ejpam-5397	164	16	-	-	PUNCT
ejpam-5397	164	17	plane	plane	NOUN
ejpam-5397	164	18	.	.	PUNCT
ejpam-5397	165	1	since	since	SCONJ
ejpam-5397	165	2	(	(	PUNCT
ejpam-5397	165	3	s̄	s̄	NOUN
ejpam-5397	165	4	,	,	PUNCT
ejpam-5397	165	5	s̄	s̄	NOUN
ejpam-5397	165	6	)	)	PUNCT
ejpam-5397	165	7	represent	represent	VERB
ejpam-5397	165	8	unique	unique	ADJ
ejpam-5397	165	9	positive	positive	ADJ
ejpam-5397	165	10	equilibrium	equilibrium	NOUN
ejpam-5397	165	11	point	point	NOUN
ejpam-5397	165	12	of	of	ADP
ejpam-5397	165	13	the	the	DET
ejpam-5397	165	14	subsystem	subsystem	NOUN
ejpam-5397	165	15	(	(	PUNCT
ejpam-5397	165	16	16	16	NUM
ejpam-5397	165	17	)	)	PUNCT
ejpam-5397	165	18	,	,	PUNCT
ejpam-5397	165	19	so	so	ADV
ejpam-5397	165	20	lim	lim	PROPN
ejpam-5397	165	21	t→∞	t→∞	ADP
ejpam-5397	165	22	x(t	x(t	PROPN
ejpam-5397	165	23	)	)	PUNCT
ejpam-5397	166	1	=	=	PROPN
ejpam-5397	166	2	lim	lim	PROPN
ejpam-5397	166	3	t→∞	t→∞	X
ejpam-5397	166	4	z(t	z(t	NOUN
ejpam-5397	166	5	)	)	PUNCT
ejpam-5397	166	6	=	=	SYM
ejpam-5397	166	7	s̄.	s̄.	PUNCT
ejpam-5397	166	8	this	this	PRON
ejpam-5397	166	9	completes	complete	VERB
ejpam-5397	166	10	the	the	DET
ejpam-5397	166	11	proof	proof	NOUN
ejpam-5397	166	12	.	.	PUNCT
ejpam-5397	167	1	theorem	theorem	VERB
ejpam-5397	167	2	3.4	3.4	NUM
ejpam-5397	167	3	.	.	PUNCT
ejpam-5397	168	1	suppose	suppose	VERB
ejpam-5397	168	2	that	that	SCONJ
ejpam-5397	168	3	s4	s4	PROPN
ejpam-5397	168	4	=	=	SYM
ejpam-5397	168	5	(	(	PUNCT
ejpam-5397	168	6	x∗	x∗	PROPN
ejpam-5397	168	7	,	,	PUNCT
ejpam-5397	168	8	y	y	PROPN
ejpam-5397	168	9	∗	∗	NOUN
ejpam-5397	168	10	,	,	PUNCT
ejpam-5397	168	11	z∗	z∗	NOUN
ejpam-5397	168	12	)	)	PUNCT
ejpam-5397	168	13	is	be	AUX
ejpam-5397	168	14	exist	exist	ADJ
ejpam-5397	168	15	,	,	PUNCT
ejpam-5397	168	16	then	then	ADV
ejpam-5397	168	17	it	it	PRON
ejpam-5397	168	18	is	be	AUX
ejpam-5397	168	19	gas	gas	NOUN
ejpam-5397	168	20	,	,	PUNCT
ejpam-5397	168	21	if	if	SCONJ
ejpam-5397	168	22	in	in	ADP
ejpam-5397	168	23	addition	addition	NOUN
ejpam-5397	168	24	of	of	ADP
ejpam-5397	168	25	conditions	condition	NOUN
ejpam-5397	168	26	(	(	PUNCT
ejpam-5397	168	27	5	5	NUM
ejpam-5397	168	28	)	)	PUNCT
ejpam-5397	168	29	,	,	PUNCT
ejpam-5397	168	30	(	(	PUNCT
ejpam-5397	168	31	6	6	NUM
ejpam-5397	168	32	)	)	PUNCT
ejpam-5397	168	33	,	,	PUNCT
ejpam-5397	168	34	the	the	DET
ejpam-5397	168	35	following	follow	VERB
ejpam-5397	168	36	inequalities	inequality	NOUN
ejpam-5397	168	37	hold	hold	VERB
ejpam-5397	168	38	:	:	PUNCT
ejpam-5397	168	39	[	[	PUNCT
ejpam-5397	168	40	2α1α2z	2α1α2z	NUM
ejpam-5397	168	41	∗	∗	NOUN
ejpam-5397	168	42	(	(	PUNCT
ejpam-5397	168	43	t2	t2	NOUN
ejpam-5397	168	44	+	+	CCONJ
ejpam-5397	168	45	t1	t1	NOUN
ejpam-5397	168	46	)	)	PUNCT
ejpam-5397	168	47	g2(x	g2(x	PROPN
ejpam-5397	168	48	,	,	PUNCT
ejpam-5397	168	49	y	y	PROPN
ejpam-5397	168	50	)	)	PUNCT
ejpam-5397	169	1	+	+	CCONJ
ejpam-5397	169	2	2r2y	2r2y	NUM
ejpam-5397	169	3	∗	∗	NOUN
ejpam-5397	169	4	xx∗	xx∗	VERB
ejpam-5397	170	1	−	−	NOUN
ejpam-5397	170	2	2	2	NUM
ejpam-5397	170	3	(	(	PUNCT
ejpam-5397	170	4	β	β	X
ejpam-5397	170	5	+	+	CCONJ
ejpam-5397	170	6	β2tx∗	β2tx∗	PROPN
ejpam-5397	170	7	)	)	PUNCT
ejpam-5397	171	1	f2(x	f2(x	PROPN
ejpam-5397	171	2	)	)	PUNCT
ejpam-5397	171	3	]	]	PUNCT
ejpam-5397	171	4	2	2	NUM
ejpam-5397	171	5	<	<	SYM
ejpam-5397	171	6	4	4	NUM
ejpam-5397	171	7	[	[	PUNCT
ejpam-5397	171	8	r1	r1	NOUN
ejpam-5397	171	9	k	k	PROPN
ejpam-5397	171	10	−	−	PROPN
ejpam-5397	171	11	β2ty	β2ty	PUNCT
ejpam-5397	171	12	∗	∗	NOUN
ejpam-5397	171	13	f2	f2	PROPN
ejpam-5397	171	14	(	(	PUNCT
ejpam-5397	171	15	k1	k1	NOUN
ejpam-5397	171	16	)	)	PUNCT
ejpam-5397	171	17	−	−	PROPN
ejpam-5397	171	18	α2	α2	PROPN
ejpam-5397	172	1	1t1z	1t1z	PROPN
ejpam-5397	172	2	∗	∗	PROPN
ejpam-5397	172	3	g2	g2	PROPN
ejpam-5397	172	4	(	(	PUNCT
ejpam-5397	172	5	k1,k2	k1,k2	PROPN
ejpam-5397	172	6	)	)	PUNCT
ejpam-5397	172	7	]	]	PUNCT
ejpam-5397	173	1	[	[	PUNCT
ejpam-5397	173	2	r2	r2	PROPN
ejpam-5397	173	3	k	k	PROPN
ejpam-5397	173	4	−	−	PROPN
ejpam-5397	173	5	α2	α2	ADJ
ejpam-5397	173	6	2t2z	2t2z	NOUN
ejpam-5397	173	7	∗	∗	NOUN
ejpam-5397	173	8	g2	g2	PROPN
ejpam-5397	173	9	(	(	PUNCT
ejpam-5397	173	10	k1,k2	k1,k2	PROPN
ejpam-5397	173	11	)	)	PUNCT
ejpam-5397	173	12	]	]	PUNCT
ejpam-5397	174	1	(	(	PUNCT
ejpam-5397	174	2	17	17	NUM
ejpam-5397	174	3	)	)	PUNCT
ejpam-5397	174	4	[	[	PUNCT
ejpam-5397	174	5	2	2	NUM
ejpam-5397	174	6	(	(	PUNCT
ejpam-5397	174	7	α1	α1	PROPN
ejpam-5397	174	8	+	+	CCONJ
ejpam-5397	174	9	α2	α2	ADJ
ejpam-5397	174	10	1t1x	1t1x	NUM
ejpam-5397	174	11	∗	∗	NOUN
ejpam-5397	174	12	+	+	CCONJ
ejpam-5397	174	13	α1α2t2y	α1α2t2y	PROPN
ejpam-5397	174	14	∗	∗	NOUN
ejpam-5397	174	15	)	)	PUNCT
ejpam-5397	174	16	g2(x	g2(x	X
ejpam-5397	174	17	,	,	PUNCT
ejpam-5397	174	18	y	y	PROPN
ejpam-5397	174	19	)	)	PUNCT
ejpam-5397	174	20	−	−	PROPN
ejpam-5397	175	1	2r3	2r3	NUM
ejpam-5397	175	2	(	(	PUNCT
ejpam-5397	175	3	x	x	PROPN
ejpam-5397	175	4	+	+	NUM
ejpam-5397	175	5	y	y	PROPN
ejpam-5397	175	6	)	)	PUNCT
ejpam-5397	176	1	]	]	PUNCT
ejpam-5397	176	2	2	2	NUM
ejpam-5397	176	3	<	<	X
ejpam-5397	176	4	2r3	2r3	NUM
ejpam-5397	176	5	k	k	NOUN
ejpam-5397	176	6	[	[	PUNCT
ejpam-5397	176	7	r1	r1	PROPN
ejpam-5397	176	8	k	k	PROPN
ejpam-5397	176	9	−	−	PROPN
ejpam-5397	176	10	β2ty	β2ty	PUNCT
ejpam-5397	176	11	∗	∗	NOUN
ejpam-5397	176	12	f2	f2	PROPN
ejpam-5397	176	13	(	(	PUNCT
ejpam-5397	176	14	k1	k1	NOUN
ejpam-5397	176	15	)	)	PUNCT
ejpam-5397	176	16	−	−	PROPN
ejpam-5397	176	17	α2	α2	PROPN
ejpam-5397	176	18	1t1z	1t1z	PROPN
ejpam-5397	176	19	∗	∗	PROPN
ejpam-5397	176	20	g2	g2	PROPN
ejpam-5397	176	21	(	(	PUNCT
ejpam-5397	176	22	k1,k2	k1,k2	PROPN
ejpam-5397	176	23	)	)	PUNCT
ejpam-5397	176	24	]	]	PUNCT
ejpam-5397	176	25	b.	b.	PROPN
ejpam-5397	176	26	b.	b.	PROPN
ejpam-5397	176	27	kamal	kamal	PROPN
ejpam-5397	176	28	,	,	PUNCT
ejpam-5397	176	29	a.	a.	PROPN
ejpam-5397	176	30	n.	n.	PROPN
ejpam-5397	176	31	mustafa	mustafa	PROPN
ejpam-5397	176	32	/	/	SYM
ejpam-5397	176	33	eur	eur	PROPN
ejpam-5397	176	34	.	.	PUNCT
ejpam-5397	177	1	j.	j.	PROPN
ejpam-5397	177	2	pure	pure	PROPN
ejpam-5397	177	3	appl	appl	PROPN
ejpam-5397	177	4	.	.	PROPN
ejpam-5397	177	5	math	math	PROPN
ejpam-5397	177	6	,	,	PUNCT
ejpam-5397	177	7	18	18	NUM
ejpam-5397	177	8	(	(	PUNCT
ejpam-5397	177	9	1	1	NUM
ejpam-5397	177	10	)	)	PUNCT
ejpam-5397	177	11	(	(	PUNCT
ejpam-5397	177	12	2025	2025	NUM
ejpam-5397	177	13	)	)	PUNCT
ejpam-5397	177	14	,	,	PUNCT
ejpam-5397	177	15	5397	5397	NUM
ejpam-5397	177	16	10	10	NUM
ejpam-5397	177	17	of	of	ADP
ejpam-5397	177	18	21	21	NUM
ejpam-5397	177	19	[	[	PUNCT
ejpam-5397	177	20	2	2	NUM
ejpam-5397	177	21	(	(	PUNCT
ejpam-5397	177	22	α2	α2	ADJ
ejpam-5397	177	23	+	+	CCONJ
ejpam-5397	177	24	α1α2t1x	α1α2t1x	PROPN
ejpam-5397	177	25	∗	∗	NOUN
ejpam-5397	177	26	+	+	X
ejpam-5397	177	27	α2	α2	ADJ
ejpam-5397	177	28	2t2y	2t2y	ADJ
ejpam-5397	177	29	∗	∗	NOUN
ejpam-5397	177	30	)	)	PUNCT
ejpam-5397	178	1	g2(x	g2(x	X
ejpam-5397	178	2	,	,	PUNCT
ejpam-5397	178	3	y	y	PROPN
ejpam-5397	178	4	)	)	PUNCT
ejpam-5397	178	5	−	−	PROPN
ejpam-5397	179	1	2r3	2r3	NUM
ejpam-5397	179	2	(	(	PUNCT
ejpam-5397	179	3	x	x	PROPN
ejpam-5397	179	4	+	+	NUM
ejpam-5397	179	5	y	y	PROPN
ejpam-5397	179	6	)	)	PUNCT
ejpam-5397	180	1	]	]	PUNCT
ejpam-5397	180	2	2	2	NUM
ejpam-5397	180	3	<	<	X
ejpam-5397	180	4	2r3	2r3	NUM
ejpam-5397	180	5	k	k	X
ejpam-5397	180	6	[	[	PUNCT
ejpam-5397	180	7	r2	r2	PROPN
ejpam-5397	180	8	k	k	PROPN
ejpam-5397	180	9	−	−	PROPN
ejpam-5397	180	10	α2	α2	ADJ
ejpam-5397	180	11	2t2z	2t2z	NOUN
ejpam-5397	180	12	∗	∗	NOUN
ejpam-5397	180	13	g2	g2	PROPN
ejpam-5397	180	14	(	(	PUNCT
ejpam-5397	180	15	k1,k2	k1,k2	PROPN
ejpam-5397	180	16	)	)	PUNCT
ejpam-5397	180	17	]	]	PUNCT
ejpam-5397	181	1	,	,	PUNCT
ejpam-5397	181	2	where	where	SCONJ
ejpam-5397	181	3	,	,	PUNCT
ejpam-5397	181	4	f2(x	f2(x	PROPN
ejpam-5397	181	5	)	)	PUNCT
ejpam-5397	181	6	=	=	NOUN
ejpam-5397	181	7	(	(	PUNCT
ejpam-5397	181	8	1	1	NUM
ejpam-5397	181	9	+	+	NUM
ejpam-5397	181	10	βtx	βtx	NOUN
ejpam-5397	181	11	)	)	PUNCT
ejpam-5397	181	12	(	(	PUNCT
ejpam-5397	181	13	1	1	NUM
ejpam-5397	181	14	+	+	CCONJ
ejpam-5397	181	15	βtx∗	βtx∗	ADJ
ejpam-5397	181	16	)	)	PUNCT
ejpam-5397	181	17	and	and	CCONJ
ejpam-5397	181	18	g2(x	g2(x	PROPN
ejpam-5397	181	19	,	,	PUNCT
ejpam-5397	181	20	y	y	PROPN
ejpam-5397	181	21	)	)	PUNCT
ejpam-5397	181	22	=	=	PUNCT
ejpam-5397	182	1	(	(	PUNCT
ejpam-5397	182	2	1	1	NUM
ejpam-5397	182	3	+	+	CCONJ
ejpam-5397	182	4	α1t1x	α1t1x	NUM
ejpam-5397	182	5	+	+	NUM
ejpam-5397	182	6	α2t2y	α2t2y	NUM
ejpam-5397	182	7	)	)	PUNCT
ejpam-5397	182	8	(	(	PUNCT
ejpam-5397	182	9	1	1	NUM
ejpam-5397	182	10	+	+	NUM
ejpam-5397	182	11	α1t1x	α1t1x	NUM
ejpam-5397	182	12	∗	∗	NOUN
ejpam-5397	182	13	+	+	NUM
ejpam-5397	182	14	α2t2y	α2t2y	NUM
ejpam-5397	182	15	∗	∗	NOUN
ejpam-5397	182	16	)	)	PUNCT
ejpam-5397	182	17	(	(	PUNCT
ejpam-5397	182	18	19	19	NUM
ejpam-5397	182	19	)	)	PUNCT
ejpam-5397	182	20	proof	proof	NOUN
ejpam-5397	182	21	.	.	PUNCT
ejpam-5397	183	1	consider	consider	VERB
ejpam-5397	183	2	the	the	DET
ejpam-5397	183	3	function	function	NOUN
ejpam-5397	183	4	l(x	l(x	PROPN
ejpam-5397	183	5	,	,	PUNCT
ejpam-5397	183	6	y	y	PROPN
ejpam-5397	183	7	,	,	PUNCT
ejpam-5397	183	8	z	z	NOUN
ejpam-5397	183	9	)	)	PUNCT
ejpam-5397	183	10	=	=	SYM
ejpam-5397	183	11	2	2	NUM
ejpam-5397	183	12	[	[	PUNCT
ejpam-5397	183	13	x	x	SYM
ejpam-5397	183	14	−x∗	−x∗	PRON
ejpam-5397	183	15	−x∗	−x∗	PRON
ejpam-5397	183	16	ln	ln	NOUN
ejpam-5397	183	17	(	(	PUNCT
ejpam-5397	183	18	x	x	X
ejpam-5397	183	19	x∗	x∗	X
ejpam-5397	183	20	)	)	PUNCT
ejpam-5397	183	21	]	]	PUNCT
ejpam-5397	184	1	+	+	CCONJ
ejpam-5397	184	2	2	2	NUM
ejpam-5397	184	3	[	[	PUNCT
ejpam-5397	184	4	y	y	NOUN
ejpam-5397	184	5	−	−	PROPN
ejpam-5397	184	6	y	y	PROPN
ejpam-5397	184	7	∗	∗	VERB
ejpam-5397	184	8	−	−	PROPN
ejpam-5397	185	1	y	y	PROPN
ejpam-5397	185	2	∗	∗	NOUN
ejpam-5397	185	3	ln	ln	NOUN
ejpam-5397	185	4	(	(	PUNCT
ejpam-5397	185	5	y	y	PROPN
ejpam-5397	185	6	y	y	PROPN
ejpam-5397	185	7	∗	∗	NOUN
ejpam-5397	185	8	)	)	PUNCT
ejpam-5397	185	9	]	]	PUNCT
ejpam-5397	186	1	+	+	CCONJ
ejpam-5397	186	2	2	2	NUM
ejpam-5397	186	3	[	[	PUNCT
ejpam-5397	186	4	z	z	NOUN
ejpam-5397	186	5	−	−	NOUN
ejpam-5397	186	6	z∗	z∗	NOUN
ejpam-5397	186	7	−	−	NOUN
ejpam-5397	186	8	z∗	z∗	NOUN
ejpam-5397	186	9	ln	ln	NOUN
ejpam-5397	186	10	(	(	PUNCT
ejpam-5397	186	11	y	y	PROPN
ejpam-5397	186	12	z∗	z∗	PROPN
ejpam-5397	186	13	)	)	PUNCT
ejpam-5397	186	14	]	]	PUNCT
ejpam-5397	186	15	.	.	PUNCT
ejpam-5397	187	1	clearly	clearly	ADV
ejpam-5397	187	2	,	,	PUNCT
ejpam-5397	187	3	l(x	l(x	PROPN
ejpam-5397	187	4	,	,	PUNCT
ejpam-5397	187	5	y	y	PROPN
ejpam-5397	187	6	,	,	PUNCT
ejpam-5397	187	7	z	z	NOUN
ejpam-5397	187	8	)	)	PUNCT
ejpam-5397	187	9	∈	∈	PROPN
ejpam-5397	187	10	c1	c1	NOUN
ejpam-5397	187	11	(	(	PUNCT
ejpam-5397	187	12	r3	r3	PROPN
ejpam-5397	188	1	+	+	PROPN
ejpam-5397	188	2	,	,	PUNCT
ejpam-5397	188	3	r	r	NOUN
ejpam-5397	188	4	)	)	PUNCT
ejpam-5397	188	5	with	with	ADP
ejpam-5397	188	6	l	l	NOUN
ejpam-5397	188	7	(	(	PUNCT
ejpam-5397	188	8	x∗	x∗	PROPN
ejpam-5397	188	9	,	,	PUNCT
ejpam-5397	188	10	y6	y6	NOUN
ejpam-5397	188	11	,	,	PUNCT
ejpam-5397	188	12	z6	z6	PROPN
ejpam-5397	188	13	)	)	PUNCT
ejpam-5397	188	14	=	=	SYM
ejpam-5397	188	15	0	0	NUM
ejpam-5397	188	16	and	and	CCONJ
ejpam-5397	188	17	l(x	l(x	PROPN
ejpam-5397	188	18	,	,	PUNCT
ejpam-5397	188	19	y	y	PROPN
ejpam-5397	188	20	,	,	PUNCT
ejpam-5397	188	21	z	z	NOUN
ejpam-5397	188	22	)	)	PUNCT
ejpam-5397	188	23	>	>	X
ejpam-5397	189	1	0,for	0,for	NUM
ejpam-5397	189	2	all	all	DET
ejpam-5397	189	3	(	(	PUNCT
ejpam-5397	189	4	x	x	NOUN
ejpam-5397	189	5	,	,	PUNCT
ejpam-5397	189	6	y	y	PROPN
ejpam-5397	189	7	,	,	PUNCT
ejpam-5397	189	8	z	z	NOUN
ejpam-5397	189	9	)	)	PUNCT
ejpam-5397	189	10	∈	∈	PROPN
ejpam-5397	189	11	r3	r3	PROPN
ejpam-5397	189	12	+	+	CCONJ
ejpam-5397	189	13	with	with	ADP
ejpam-5397	189	14	(	(	PUNCT
ejpam-5397	189	15	x	x	NOUN
ejpam-5397	189	16	,	,	PUNCT
ejpam-5397	189	17	y	y	PROPN
ejpam-5397	189	18	,	,	PUNCT
ejpam-5397	189	19	z	z	NOUN
ejpam-5397	189	20	)	)	PUNCT
ejpam-5397	189	21	̸=	̸=	PROPN
ejpam-5397	189	22	(	(	PUNCT
ejpam-5397	189	23	x∗	x∗	PROPN
ejpam-5397	189	24	,	,	PUNCT
ejpam-5397	189	25	y6	y6	NOUN
ejpam-5397	189	26	,	,	PUNCT
ejpam-5397	189	27	z6	z6	PROPN
ejpam-5397	189	28	)	)	PUNCT
ejpam-5397	189	29	.	.	PUNCT
ejpam-5397	190	1	further	far	ADV
ejpam-5397	190	2	,	,	PUNCT
ejpam-5397	190	3	dl	dl	PROPN
ejpam-5397	190	4	dt	dt	PROPN
ejpam-5397	191	1	=	=	AUX
ejpam-5397	191	2	−	−	X
ejpam-5397	191	3	[	[	PUNCT
ejpam-5397	191	4	r1	r1	NOUN
ejpam-5397	191	5	k	k	PROPN
ejpam-5397	191	6	−	−	PROPN
ejpam-5397	191	7	β2ty	β2ty	PUNCT
ejpam-5397	191	8	∗	∗	PROPN
ejpam-5397	191	9	f2(x	f2(x	NOUN
ejpam-5397	191	10	)	)	PUNCT
ejpam-5397	191	11	−	−	ADP
ejpam-5397	191	12	α2	α2	PROPN
ejpam-5397	191	13	1t1z	1t1z	PROPN
ejpam-5397	192	1	∗	∗	PROPN
ejpam-5397	192	2	g2(x	g2(x	PROPN
ejpam-5397	192	3	,	,	PUNCT
ejpam-5397	192	4	y	y	PROPN
ejpam-5397	192	5	)	)	PUNCT
ejpam-5397	192	6	]	]	PUNCT
ejpam-5397	193	1	(	(	PUNCT
ejpam-5397	193	2	x	x	SYM
ejpam-5397	193	3	−x∗)2	−x∗)2	PROPN
ejpam-5397	193	4	−	−	PROPN
ejpam-5397	194	1	[	[	PUNCT
ejpam-5397	194	2	r2	r2	NOUN
ejpam-5397	194	3	x	x	X
ejpam-5397	194	4	−	−	NOUN
ejpam-5397	194	5	α2	α2	ADJ
ejpam-5397	194	6	2t2z	2t2z	NOUN
ejpam-5397	194	7	∗	∗	NOUN
ejpam-5397	194	8	g2(x	g2(x	PROPN
ejpam-5397	194	9	,	,	PUNCT
ejpam-5397	194	10	y	y	PROPN
ejpam-5397	194	11	)	)	PUNCT
ejpam-5397	194	12	]	]	PUNCT
ejpam-5397	195	1	(	(	PUNCT
ejpam-5397	195	2	y	y	PROPN
ejpam-5397	195	3	−	−	PROPN
ejpam-5397	195	4	y	y	PROPN
ejpam-5397	195	5	∗)2	∗)2	PROPN
ejpam-5397	195	6	+	+	CCONJ
ejpam-5397	195	7	[	[	PUNCT
ejpam-5397	195	8	221α2z	221α2z	NUM
ejpam-5397	195	9	∗	∗	NOUN
ejpam-5397	195	10	(	(	PUNCT
ejpam-5397	195	11	t2	t2	NOUN
ejpam-5397	195	12	+	+	CCONJ
ejpam-5397	195	13	t1	t1	NOUN
ejpam-5397	195	14	)	)	PUNCT
ejpam-5397	196	1	g2(x	g2(x	PROPN
ejpam-5397	196	2	,	,	PUNCT
ejpam-5397	196	3	y	y	PROPN
ejpam-5397	196	4	)	)	PUNCT
ejpam-5397	197	1	+	+	CCONJ
ejpam-5397	197	2	2r2y	2r2y	NUM
ejpam-5397	197	3	∗	∗	NOUN
ejpam-5397	197	4	xx∗	xx∗	VERB
ejpam-5397	198	1	−	−	NOUN
ejpam-5397	198	2	2	2	NUM
ejpam-5397	198	3	(	(	PUNCT
ejpam-5397	198	4	β	β	X
ejpam-5397	198	5	+	+	CCONJ
ejpam-5397	198	6	β2tx∗	β2tx∗	PROPN
ejpam-5397	198	7	)	)	PUNCT
ejpam-5397	199	1	f2(x	f2(x	PROPN
ejpam-5397	199	2	)	)	PUNCT
ejpam-5397	199	3	]	]	PUNCT
ejpam-5397	200	1	(	(	PUNCT
ejpam-5397	200	2	y	y	PROPN
ejpam-5397	200	3	−	−	PROPN
ejpam-5397	200	4	y	y	PROPN
ejpam-5397	200	5	∗	∗	PROPN
ejpam-5397	200	6	)	)	PUNCT
ejpam-5397	200	7	(	(	PUNCT
ejpam-5397	200	8	x	x	SYM
ejpam-5397	200	9	−x∗	−x∗	X
ejpam-5397	200	10	)	)	PUNCT
ejpam-5397	200	11	−	−	PROPN
ejpam-5397	201	1	[	[	PUNCT
ejpam-5397	201	2	r1	r1	NOUN
ejpam-5397	201	3	k	k	PROPN
ejpam-5397	201	4	−	−	PROPN
ejpam-5397	201	5	β2ty	β2ty	PUNCT
ejpam-5397	201	6	∗	∗	PROPN
ejpam-5397	201	7	f2(x	f2(x	NOUN
ejpam-5397	201	8	)	)	PUNCT
ejpam-5397	201	9	−	−	ADP
ejpam-5397	202	1	α2	α2	PROPN
ejpam-5397	202	2	1t1z	1t1z	PROPN
ejpam-5397	203	1	∗	∗	PROPN
ejpam-5397	203	2	g2(x	g2(x	PROPN
ejpam-5397	203	3	,	,	PUNCT
ejpam-5397	203	4	y	y	PROPN
ejpam-5397	203	5	)	)	PUNCT
ejpam-5397	203	6	]	]	PUNCT
ejpam-5397	204	1	(	(	PUNCT
ejpam-5397	204	2	x	x	X
ejpam-5397	204	3	−x∗)2	−x∗)2	PROPN
ejpam-5397	204	4	−	−	PROPN
ejpam-5397	204	5	r3	r3	PROPN
ejpam-5397	204	6	(	(	PUNCT
ejpam-5397	204	7	x	x	PROPN
ejpam-5397	204	8	+	+	NUM
ejpam-5397	204	9	y	y	PROPN
ejpam-5397	204	10	)	)	PUNCT
ejpam-5397	204	11	(	(	PUNCT
ejpam-5397	204	12	z	z	NOUN
ejpam-5397	204	13	−	−	PROPN
ejpam-5397	204	14	z∗)2	z∗)2	NUM
ejpam-5397	204	15	−	−	PROPN
ejpam-5397	205	1	[	[	PUNCT
ejpam-5397	205	2	2	2	NUM
ejpam-5397	205	3	(	(	PUNCT
ejpam-5397	205	4	α1	α1	PROPN
ejpam-5397	205	5	+	+	CCONJ
ejpam-5397	205	6	α2	α2	ADJ
ejpam-5397	205	7	1t1x	1t1x	NUM
ejpam-5397	205	8	∗	∗	NOUN
ejpam-5397	205	9	+	+	CCONJ
ejpam-5397	205	10	α1α2t2y	α1α2t2y	PROPN
ejpam-5397	205	11	∗	∗	NOUN
ejpam-5397	205	12	)	)	PUNCT
ejpam-5397	205	13	g2(x	g2(x	X
ejpam-5397	205	14	,	,	PUNCT
ejpam-5397	205	15	y	y	PROPN
ejpam-5397	205	16	)	)	PUNCT
ejpam-5397	205	17	−	−	PROPN
ejpam-5397	206	1	2r3	2r3	NUM
ejpam-5397	206	2	(	(	PUNCT
ejpam-5397	206	3	x	x	PROPN
ejpam-5397	206	4	+	+	NUM
ejpam-5397	206	5	y	y	PROPN
ejpam-5397	206	6	)	)	PUNCT
ejpam-5397	206	7	]	]	PUNCT
ejpam-5397	207	1	(	(	PUNCT
ejpam-5397	207	2	x	x	SYM
ejpam-5397	207	3	−x∗	−x∗	NUM
ejpam-5397	207	4	)	)	PUNCT
ejpam-5397	207	5	(	(	PUNCT
ejpam-5397	207	6	z	z	NOUN
ejpam-5397	207	7	−	−	PROPN
ejpam-5397	207	8	z∗	z∗	NOUN
ejpam-5397	207	9	)	)	PUNCT
ejpam-5397	207	10	−	−	PROPN
ejpam-5397	208	1	[	[	PUNCT
ejpam-5397	208	2	r2	r2	NOUN
ejpam-5397	208	3	x	x	X
ejpam-5397	208	4	−	−	NOUN
ejpam-5397	208	5	α2	α2	ADJ
ejpam-5397	208	6	2t2z	2t2z	NOUN
ejpam-5397	208	7	∗	∗	NOUN
ejpam-5397	208	8	g2(x	g2(x	PROPN
ejpam-5397	208	9	,	,	PUNCT
ejpam-5397	208	10	y	y	PROPN
ejpam-5397	208	11	)	)	PUNCT
ejpam-5397	208	12	]	]	PUNCT
ejpam-5397	209	1	(	(	PUNCT
ejpam-5397	209	2	y	y	PROPN
ejpam-5397	209	3	−	−	PROPN
ejpam-5397	209	4	y	y	PROPN
ejpam-5397	209	5	∗)2	∗)2	ADV
ejpam-5397	210	1	−	−	PROPN
ejpam-5397	211	1	r3	r3	PROPN
ejpam-5397	211	2	(	(	PUNCT
ejpam-5397	211	3	x	x	PROPN
ejpam-5397	211	4	+	+	NUM
ejpam-5397	211	5	y	y	PROPN
ejpam-5397	211	6	)	)	PUNCT
ejpam-5397	211	7	(	(	PUNCT
ejpam-5397	211	8	z	z	NOUN
ejpam-5397	211	9	−	−	PROPN
ejpam-5397	211	10	z∗)2	z∗)2	NUM
ejpam-5397	211	11	−	−	PROPN
ejpam-5397	212	1	[	[	PUNCT
ejpam-5397	212	2	2	2	NUM
ejpam-5397	212	3	(	(	PUNCT
ejpam-5397	212	4	α2	α2	ADJ
ejpam-5397	212	5	+	+	CCONJ
ejpam-5397	212	6	α1α2t1x	α1α2t1x	PROPN
ejpam-5397	212	7	∗	∗	NOUN
ejpam-5397	212	8	+	+	X
ejpam-5397	212	9	α2	α2	ADJ
ejpam-5397	212	10	2t2y	2t2y	ADJ
ejpam-5397	212	11	∗	∗	NOUN
ejpam-5397	212	12	)	)	PUNCT
ejpam-5397	213	1	g2(x	g2(x	X
ejpam-5397	213	2	,	,	PUNCT
ejpam-5397	213	3	y	y	PROPN
ejpam-5397	213	4	)	)	PUNCT
ejpam-5397	213	5	−	−	PROPN
ejpam-5397	214	1	2r3	2r3	NUM
ejpam-5397	214	2	(	(	PUNCT
ejpam-5397	214	3	x	x	PROPN
ejpam-5397	214	4	+	+	NUM
ejpam-5397	214	5	y	y	PROPN
ejpam-5397	214	6	)	)	PUNCT
ejpam-5397	214	7	]	]	PUNCT
ejpam-5397	215	1	(	(	PUNCT
ejpam-5397	215	2	y	y	PROPN
ejpam-5397	215	3	−	−	PROPN
ejpam-5397	215	4	y	y	PROPN
ejpam-5397	215	5	∗	∗	PROPN
ejpam-5397	215	6	)	)	PUNCT
ejpam-5397	215	7	(	(	PUNCT
ejpam-5397	215	8	z	z	NOUN
ejpam-5397	215	9	−	−	PROPN
ejpam-5397	215	10	z∗	z∗	NOUN
ejpam-5397	215	11	)	)	PUNCT
ejpam-5397	215	12	.	.	PUNCT
ejpam-5397	216	1	condition	condition	NOUN
ejpam-5397	216	2	(	(	PUNCT
ejpam-5397	216	3	5	5	NUM
ejpam-5397	216	4	,	,	PUNCT
ejpam-5397	216	5	6	6	X
ejpam-5397	216	6	)	)	PUNCT
ejpam-5397	216	7	guaranteeing	guarantee	VERB
ejpam-5397	216	8	that	that	SCONJ
ejpam-5397	216	9	:	:	PUNCT
ejpam-5397	216	10	limt→∞	limt→∞	PROPN
ejpam-5397	216	11	infx(t	infx(t	PROPN
ejpam-5397	216	12	)	)	PUNCT
ejpam-5397	216	13	≥	≥	NOUN
ejpam-5397	216	14	k1	k1	NOUN
ejpam-5397	216	15	and	and	CCONJ
ejpam-5397	216	16	limt→∞	limt→∞	PROPN
ejpam-5397	216	17	inf	inf	PROPN
ejpam-5397	216	18	y	y	PROPN
ejpam-5397	216	19	(	(	PUNCT
ejpam-5397	216	20	t	t	PROPN
ejpam-5397	216	21	)	)	PUNCT
ejpam-5397	216	22	≥	≥	NOUN
ejpam-5397	216	23	k2	k2	PROPN
ejpam-5397	216	24	.	.	PUNCT
ejpam-5397	217	1	therfore	therfore	PROPN
ejpam-5397	217	2	,	,	PUNCT
ejpam-5397	217	3	b.	b.	PROPN
ejpam-5397	217	4	b.	b.	PROPN
ejpam-5397	217	5	kamal	kamal	PROPN
ejpam-5397	217	6	,	,	PUNCT
ejpam-5397	217	7	a.	a.	PROPN
ejpam-5397	217	8	n.	n.	PROPN
ejpam-5397	217	9	mustafa	mustafa	PROPN
ejpam-5397	217	10	/	/	SYM
ejpam-5397	217	11	eur	eur	PROPN
ejpam-5397	217	12	.	.	PUNCT
ejpam-5397	218	1	j.	j.	PROPN
ejpam-5397	218	2	pure	pure	PROPN
ejpam-5397	218	3	appl	appl	PROPN
ejpam-5397	218	4	.	.	PROPN
ejpam-5397	218	5	math	math	PROPN
ejpam-5397	218	6	,	,	PUNCT
ejpam-5397	218	7	18	18	NUM
ejpam-5397	218	8	(	(	PUNCT
ejpam-5397	218	9	1	1	NUM
ejpam-5397	218	10	)	)	PUNCT
ejpam-5397	218	11	(	(	PUNCT
ejpam-5397	218	12	2025	2025	NUM
ejpam-5397	218	13	)	)	PUNCT
ejpam-5397	218	14	,	,	PUNCT
ejpam-5397	218	15	5397	5397	NUM
ejpam-5397	218	16	11	11	NUM
ejpam-5397	218	17	of	of	ADP
ejpam-5397	218	18	21	21	NUM
ejpam-5397	218	19	dl	dl	NOUN
ejpam-5397	218	20	dt	dt	NOUN
ejpam-5397	218	21	<	<	X
ejpam-5397	218	22	−	−	X
ejpam-5397	218	23	[	[	PUNCT
ejpam-5397	218	24	r1	r1	NOUN
ejpam-5397	218	25	k	k	PROPN
ejpam-5397	218	26	−	−	PROPN
ejpam-5397	218	27	β2ty	β2ty	PUNCT
ejpam-5397	218	28	∗	∗	NOUN
ejpam-5397	218	29	f2	f2	PROPN
ejpam-5397	218	30	(	(	PUNCT
ejpam-5397	218	31	k1	k1	NOUN
ejpam-5397	218	32	)	)	PUNCT
ejpam-5397	218	33	−	−	PROPN
ejpam-5397	218	34	α2	α2	PROPN
ejpam-5397	218	35	1t1z	1t1z	PROPN
ejpam-5397	218	36	∗	∗	PROPN
ejpam-5397	218	37	g2	g2	PROPN
ejpam-5397	218	38	(	(	PUNCT
ejpam-5397	218	39	k1,k2	k1,k2	PROPN
ejpam-5397	218	40	)	)	PUNCT
ejpam-5397	218	41	]	]	PUNCT
ejpam-5397	219	1	(	(	PUNCT
ejpam-5397	219	2	x	x	SYM
ejpam-5397	219	3	−x∗)2	−x∗)2	PROPN
ejpam-5397	219	4	−	−	PROPN
ejpam-5397	220	1	[	[	PUNCT
ejpam-5397	220	2	r2	r2	PROPN
ejpam-5397	220	3	k	k	PROPN
ejpam-5397	220	4	−	−	PROPN
ejpam-5397	220	5	α2	α2	ADJ
ejpam-5397	220	6	2t2z	2t2z	NOUN
ejpam-5397	220	7	∗	∗	NOUN
ejpam-5397	220	8	g2	g2	PROPN
ejpam-5397	220	9	(	(	PUNCT
ejpam-5397	220	10	k1,k2	k1,k2	PROPN
ejpam-5397	220	11	)	)	PUNCT
ejpam-5397	220	12	]	]	PUNCT
ejpam-5397	220	13	(	(	PUNCT
ejpam-5397	220	14	y	y	PROPN
ejpam-5397	220	15	−	−	PROPN
ejpam-5397	220	16	y	y	PROPN
ejpam-5397	220	17	∗)2	∗)2	PROPN
ejpam-5397	220	18	+	+	CCONJ
ejpam-5397	220	19	[	[	PUNCT
ejpam-5397	220	20	2α1α2z	2α1α2z	NUM
ejpam-5397	220	21	∗	∗	NOUN
ejpam-5397	220	22	(	(	PUNCT
ejpam-5397	220	23	t2	t2	NOUN
ejpam-5397	220	24	+	+	CCONJ
ejpam-5397	220	25	t1	t1	NOUN
ejpam-5397	220	26	)	)	PUNCT
ejpam-5397	221	1	g2(x	g2(x	PROPN
ejpam-5397	221	2	,	,	PUNCT
ejpam-5397	221	3	y	y	PROPN
ejpam-5397	221	4	)	)	PUNCT
ejpam-5397	222	1	+	+	CCONJ
ejpam-5397	222	2	2r2y	2r2y	NUM
ejpam-5397	222	3	∗	∗	NOUN
ejpam-5397	222	4	xx∗	xx∗	VERB
ejpam-5397	223	1	−	−	NOUN
ejpam-5397	223	2	2	2	NUM
ejpam-5397	223	3	(	(	PUNCT
ejpam-5397	223	4	β	β	X
ejpam-5397	223	5	+	+	CCONJ
ejpam-5397	223	6	β2tx∗	β2tx∗	PROPN
ejpam-5397	223	7	)	)	PUNCT
ejpam-5397	224	1	f2(x	f2(x	PROPN
ejpam-5397	224	2	)	)	PUNCT
ejpam-5397	224	3	]	]	PUNCT
ejpam-5397	225	1	(	(	PUNCT
ejpam-5397	225	2	y	y	PROPN
ejpam-5397	225	3	−	−	PROPN
ejpam-5397	225	4	y	y	PROPN
ejpam-5397	225	5	∗	∗	PROPN
ejpam-5397	225	6	)	)	PUNCT
ejpam-5397	225	7	(	(	PUNCT
ejpam-5397	225	8	x	x	SYM
ejpam-5397	225	9	−x∗	−x∗	X
ejpam-5397	225	10	)	)	PUNCT
ejpam-5397	225	11	−	−	PROPN
ejpam-5397	226	1	[	[	PUNCT
ejpam-5397	226	2	r1	r1	NOUN
ejpam-5397	226	3	k	k	PROPN
ejpam-5397	226	4	−	−	PROPN
ejpam-5397	226	5	β2ty	β2ty	PUNCT
ejpam-5397	226	6	∗	∗	NOUN
ejpam-5397	226	7	f2	f2	PROPN
ejpam-5397	226	8	(	(	PUNCT
ejpam-5397	226	9	k1	k1	NOUN
ejpam-5397	226	10	)	)	PUNCT
ejpam-5397	226	11	−	−	PROPN
ejpam-5397	226	12	α2	α2	PROPN
ejpam-5397	226	13	1t1z	1t1z	PROPN
ejpam-5397	226	14	∗	∗	PROPN
ejpam-5397	226	15	g2	g2	PROPN
ejpam-5397	226	16	(	(	PUNCT
ejpam-5397	226	17	k1,k2	k1,k2	PROPN
ejpam-5397	226	18	)	)	PUNCT
ejpam-5397	226	19	]	]	PUNCT
ejpam-5397	227	1	(	(	PUNCT
ejpam-5397	227	2	x	x	X
ejpam-5397	227	3	−x∗)2	−x∗)2	PROPN
ejpam-5397	227	4	−	−	PROPN
ejpam-5397	227	5	r3	r3	PROPN
ejpam-5397	227	6	2k	2k	NOUN
ejpam-5397	227	7	(	(	PUNCT
ejpam-5397	227	8	z	z	NOUN
ejpam-5397	227	9	−	−	PROPN
ejpam-5397	227	10	z∗)2	z∗)2	NUM
ejpam-5397	227	11	−	−	PROPN
ejpam-5397	227	12	[	[	PUNCT
ejpam-5397	227	13	2	2	NUM
ejpam-5397	227	14	(	(	PUNCT
ejpam-5397	227	15	α1	α1	PROPN
ejpam-5397	227	16	+	+	CCONJ
ejpam-5397	227	17	α2	α2	ADJ
ejpam-5397	227	18	1t1x	1t1x	NUM
ejpam-5397	227	19	∗	∗	NOUN
ejpam-5397	227	20	+	+	CCONJ
ejpam-5397	227	21	α1α2t2y	α1α2t2y	PROPN
ejpam-5397	227	22	∗	∗	NOUN
ejpam-5397	227	23	)	)	PUNCT
ejpam-5397	227	24	g2(xy	g2(xy	PROPN
ejpam-5397	227	25	)	)	PUNCT
ejpam-5397	227	26	−	−	PROPN
ejpam-5397	228	1	2r3	2r3	NUM
ejpam-5397	228	2	(	(	PUNCT
ejpam-5397	228	3	x	x	PROPN
ejpam-5397	228	4	+	+	NUM
ejpam-5397	228	5	y	y	PROPN
ejpam-5397	228	6	)	)	PUNCT
ejpam-5397	228	7	]	]	PUNCT
ejpam-5397	229	1	(	(	PUNCT
ejpam-5397	229	2	x	x	SYM
ejpam-5397	229	3	−x∗	−x∗	NUM
ejpam-5397	229	4	)	)	PUNCT
ejpam-5397	229	5	(	(	PUNCT
ejpam-5397	229	6	z	z	NOUN
ejpam-5397	229	7	−	−	PROPN
ejpam-5397	229	8	z∗	z∗	NOUN
ejpam-5397	229	9	)	)	PUNCT
ejpam-5397	229	10	−	−	PROPN
ejpam-5397	230	1	[	[	PUNCT
ejpam-5397	230	2	r2	r2	PROPN
ejpam-5397	230	3	k	k	PROPN
ejpam-5397	230	4	−	−	PROPN
ejpam-5397	230	5	α2	α2	ADJ
ejpam-5397	230	6	2t2z	2t2z	NOUN
ejpam-5397	230	7	∗	∗	NOUN
ejpam-5397	230	8	g2	g2	PROPN
ejpam-5397	230	9	(	(	PUNCT
ejpam-5397	230	10	k1,k2	k1,k2	PROPN
ejpam-5397	230	11	)	)	PUNCT
ejpam-5397	230	12	]	]	PUNCT
ejpam-5397	230	13	(	(	PUNCT
ejpam-5397	230	14	y	y	PROPN
ejpam-5397	230	15	−	−	PROPN
ejpam-5397	230	16	y	y	PROPN
ejpam-5397	230	17	∗)2	∗)2	ADV
ejpam-5397	230	18	−	−	PROPN
ejpam-5397	230	19	r3	r3	PROPN
ejpam-5397	230	20	2k	2k	NOUN
ejpam-5397	230	21	(	(	PUNCT
ejpam-5397	230	22	z	z	NOUN
ejpam-5397	230	23	−	−	PROPN
ejpam-5397	230	24	z∗)2	z∗)2	NUM
ejpam-5397	230	25	−	−	PROPN
ejpam-5397	230	26	[	[	PUNCT
ejpam-5397	230	27	2	2	NUM
ejpam-5397	230	28	(	(	PUNCT
ejpam-5397	230	29	α2	α2	ADJ
ejpam-5397	230	30	+	+	CCONJ
ejpam-5397	230	31	α1α2t1x	α1α2t1x	PROPN
ejpam-5397	230	32	∗	∗	NOUN
ejpam-5397	230	33	+	+	X
ejpam-5397	230	34	α2	α2	ADJ
ejpam-5397	230	35	2t2y	2t2y	ADJ
ejpam-5397	230	36	∗	∗	NOUN
ejpam-5397	230	37	)	)	PUNCT
ejpam-5397	230	38	g2(x	g2(x	X
ejpam-5397	230	39	,	,	PUNCT
ejpam-5397	230	40	y	y	PROPN
ejpam-5397	230	41	)	)	PUNCT
ejpam-5397	230	42	−	−	PROPN
ejpam-5397	231	1	2r3	2r3	NUM
ejpam-5397	231	2	(	(	PUNCT
ejpam-5397	231	3	x	x	PROPN
ejpam-5397	231	4	+	+	NUM
ejpam-5397	231	5	y	y	PROPN
ejpam-5397	231	6	)	)	PUNCT
ejpam-5397	231	7	]	]	PUNCT
ejpam-5397	232	1	(	(	PUNCT
ejpam-5397	232	2	y	y	PROPN
ejpam-5397	232	3	−	−	PROPN
ejpam-5397	232	4	y	y	PROPN
ejpam-5397	232	5	∗	∗	PROPN
ejpam-5397	232	6	)	)	PUNCT
ejpam-5397	232	7	(	(	PUNCT
ejpam-5397	232	8	z	z	NOUN
ejpam-5397	232	9	−	−	PROPN
ejpam-5397	232	10	z∗	z∗	NOUN
ejpam-5397	232	11	)	)	PUNCT
ejpam-5397	232	12	.	.	PUNCT
ejpam-5397	233	1	provide	provide	VERB
ejpam-5397	233	2	both	both	DET
ejpam-5397	233	3	inequalities	inequality	NOUN
ejpam-5397	233	4	(	(	PUNCT
ejpam-5397	233	5	17	17	NUM
ejpam-5397	233	6	-	-	SYM
ejpam-5397	233	7	19	19	NUM
ejpam-5397	233	8	)	)	PUNCT
ejpam-5397	233	9	,	,	PUNCT
ejpam-5397	233	10	it	it	PRON
ejpam-5397	233	11	gets	get	VERB
ejpam-5397	233	12	dl	dl	PROPN
ejpam-5397	233	13	dt	dt	NOUN
ejpam-5397	233	14	<	<	X
ejpam-5397	233	15	−	−	PROPN
ejpam-5397	234	1	[	[	X
ejpam-5397	234	2	√	√	X
ejpam-5397	234	3	r1	r1	PROPN
ejpam-5397	234	4	k	k	PROPN
ejpam-5397	234	5	−	−	PROPN
ejpam-5397	234	6	β2ty	β2ty	PUNCT
ejpam-5397	234	7	∗	∗	NOUN
ejpam-5397	234	8	f2	f2	PROPN
ejpam-5397	234	9	(	(	PUNCT
ejpam-5397	234	10	k1	k1	NOUN
ejpam-5397	234	11	)	)	PUNCT
ejpam-5397	234	12	−	−	PROPN
ejpam-5397	234	13	α2	α2	PROPN
ejpam-5397	234	14	1t1z∗	1t1z∗	PROPN
ejpam-5397	234	15	g2	g2	PROPN
ejpam-5397	234	16	(	(	PUNCT
ejpam-5397	234	17	k1,k2	k1,k2	PROPN
ejpam-5397	234	18	)	)	PUNCT
ejpam-5397	235	1	+	+	CCONJ
ejpam-5397	235	2	√	√	NUM
ejpam-5397	235	3	r2	r2	PROPN
ejpam-5397	235	4	k	k	PROPN
ejpam-5397	235	5	−	−	PROPN
ejpam-5397	235	6	α2	α2	PROPN
ejpam-5397	235	7	2t2z∗	2t2z∗	PROPN
ejpam-5397	235	8	g2	g2	PROPN
ejpam-5397	235	9	(	(	PUNCT
ejpam-5397	235	10	k1,k2	k1,k2	PROPN
ejpam-5397	235	11	)	)	PUNCT
ejpam-5397	235	12	]	]	PUNCT
ejpam-5397	235	13	2	2	NUM
ejpam-5397	235	14	−	−	PROPN
ejpam-5397	236	1	[	[	X
ejpam-5397	236	2	√	√	X
ejpam-5397	236	3	r3	r3	PROPN
ejpam-5397	236	4	2k	2k	NOUN
ejpam-5397	236	5	−	−	ADP
ejpam-5397	236	6	√	√	NUM
ejpam-5397	236	7	r2	r2	PROPN
ejpam-5397	236	8	k	k	PROPN
ejpam-5397	237	1	−	−	PROPN
ejpam-5397	237	2	α2	α2	PROPN
ejpam-5397	237	3	2t2z∗	2t2z∗	PROPN
ejpam-5397	237	4	g2	g2	PROPN
ejpam-5397	237	5	(	(	PUNCT
ejpam-5397	237	6	k1,k2	k1,k2	PROPN
ejpam-5397	237	7	)	)	PUNCT
ejpam-5397	237	8	]	]	PUNCT
ejpam-5397	238	1	2	2	NUM
ejpam-5397	238	2	−	−	NOUN
ejpam-5397	239	1	[	[	X
ejpam-5397	239	2	√	√	X
ejpam-5397	239	3	r1	r1	PROPN
ejpam-5397	239	4	k	k	PROPN
ejpam-5397	239	5	−	−	PROPN
ejpam-5397	239	6	β2ty	β2ty	PUNCT
ejpam-5397	239	7	∗	∗	NOUN
ejpam-5397	239	8	f2	f2	PROPN
ejpam-5397	239	9	(	(	PUNCT
ejpam-5397	239	10	k1	k1	NOUN
ejpam-5397	239	11	)	)	PUNCT
ejpam-5397	239	12	−	−	PROPN
ejpam-5397	239	13	α2	α2	PROPN
ejpam-5397	239	14	1t1z∗	1t1z∗	PROPN
ejpam-5397	239	15	g2	g2	PROPN
ejpam-5397	239	16	(	(	PUNCT
ejpam-5397	239	17	k1,k2	k1,k2	PROPN
ejpam-5397	239	18	)	)	PUNCT
ejpam-5397	239	19	−	−	ADP
ejpam-5397	239	20	√	√	NUM
ejpam-5397	239	21	r3	r3	PROPN
ejpam-5397	239	22	2k	2k	NOUN
ejpam-5397	239	23	]	]	SYM
ejpam-5397	239	24	2	2	NUM
ejpam-5397	239	25	.	.	PUNCT
ejpam-5397	240	1	so	so	ADV
ejpam-5397	240	2	,	,	PUNCT
ejpam-5397	240	3	dl	dl	PROPN
ejpam-5397	240	4	dt	dt	PROPN
ejpam-5397	240	5	is	be	AUX
ejpam-5397	240	6	negative	negative	ADJ
ejpam-5397	240	7	,	,	PUNCT
ejpam-5397	240	8	and	and	CCONJ
ejpam-5397	240	9	hence	hence	ADV
ejpam-5397	240	10	l2	l2	NOUN
ejpam-5397	240	11	is	be	AUX
ejpam-5397	240	12	lyapunov	lyapunov	ADJ
ejpam-5397	240	13	function	function	NOUN
ejpam-5397	240	14	with	with	ADP
ejpam-5397	240	15	respect	respect	NOUN
ejpam-5397	240	16	to	to	ADP
ejpam-5397	240	17	s4	s4	VERB
ejpam-5397	240	18	=	=	SYM
ejpam-5397	240	19	(	(	PUNCT
ejpam-5397	240	20	x∗	x∗	PROPN
ejpam-5397	240	21	,	,	PUNCT
ejpam-5397	240	22	y	y	PROPN
ejpam-5397	240	23	∗	∗	NOUN
ejpam-5397	240	24	,	,	PUNCT
ejpam-5397	240	25	z∗	z∗	PROPN
ejpam-5397	240	26	)	)	PUNCT
ejpam-5397	240	27	,	,	PUNCT
ejpam-5397	240	28	this	this	PRON
ejpam-5397	240	29	proves	prove	VERB
ejpam-5397	240	30	the	the	DET
ejpam-5397	240	31	theorem	theorem	NOUN
ejpam-5397	240	32	.	.	PROPN
ejpam-5397	240	33	4	4	NUM
ejpam-5397	240	34	.	.	X
ejpam-5397	241	1	hopf	hopf	ADJ
ejpam-5397	241	2	-	-	PUNCT
ejpam-5397	241	3	bifurcation	bifurcation	NOUN
ejpam-5397	241	4	here	here	ADV
ejpam-5397	241	5	,	,	PUNCT
ejpam-5397	241	6	the	the	DET
ejpam-5397	241	7	occurrence	occurrence	NOUN
ejpam-5397	241	8	of	of	ADP
ejpam-5397	241	9	hopf	hopf	ADJ
ejpam-5397	241	10	bifurcation	bifurcation	NOUN
ejpam-5397	241	11	in	in	ADP
ejpam-5397	241	12	system1	system1	NOUN
ejpam-5397	241	13	near	near	ADP
ejpam-5397	241	14	all	all	DET
ejpam-5397	241	15	steady	steady	ADJ
ejpam-5397	241	16	states	state	NOUN
ejpam-5397	241	17	,	,	PUNCT
ejpam-5397	241	18	are	be	AUX
ejpam-5397	241	19	discussed	discuss	VERB
ejpam-5397	241	20	as	as	SCONJ
ejpam-5397	241	21	follows	follow	VERB
ejpam-5397	241	22	:	:	PUNCT
ejpam-5397	241	23	from	from	ADP
ejpam-5397	241	24	theorem	theorem	NOUN
ejpam-5397	241	25	(	(	PUNCT
ejpam-5397	241	26	3	3	X
ejpam-5397	241	27	)	)	PUNCT
ejpam-5397	241	28	it	it	PRON
ejpam-5397	241	29	is	be	AUX
ejpam-5397	241	30	observed	observe	VERB
ejpam-5397	241	31	that	that	SCONJ
ejpam-5397	241	32	the	the	DET
ejpam-5397	241	33	only	only	ADJ
ejpam-5397	241	34	prey	prey	PROPN
ejpam-5397	241	35	existence	existence	PROPN
ejpam-5397	241	36	steady	steady	ADJ
ejpam-5397	241	37	state	state	NOUN
ejpam-5397	241	38	s1	s1	NOUN
ejpam-5397	241	39	=	=	SYM
ejpam-5397	241	40	(	(	PUNCT
ejpam-5397	241	41	k	k	X
ejpam-5397	241	42	,	,	PUNCT
ejpam-5397	241	43	0	0	NUM
ejpam-5397	241	44	,	,	PUNCT
ejpam-5397	241	45	0	0	NUM
ejpam-5397	241	46	)	)	PUNCT
ejpam-5397	241	47	,	,	PUNCT
ejpam-5397	241	48	apex	apex	VERB
ejpam-5397	241	49	predator	predator	NOUN
ejpam-5397	241	50	-	-	PUNCT
ejpam-5397	241	51	free	free	ADJ
ejpam-5397	241	52	steady	steady	ADJ
ejpam-5397	241	53	state	state	NOUN
ejpam-5397	241	54	s2	s2	NOUN
ejpam-5397	241	55	=	=	SYM
ejpam-5397	241	56	(	(	PUNCT
ejpam-5397	241	57	s̄	s̄	NOUN
ejpam-5397	241	58	,	,	PUNCT
ejpam-5397	241	59	s̄	s̄	NOUN
ejpam-5397	241	60	,	,	PUNCT
ejpam-5397	241	61	0	0	NUM
ejpam-5397	241	62	)	)	PUNCT
ejpam-5397	241	63	,	,	PUNCT
ejpam-5397	241	64	are	be	AUX
ejpam-5397	241	65	not	not	PART
ejpam-5397	241	66	las	las	NOUN
ejpam-5397	241	67	,	,	PUNCT
ejpam-5397	241	68	therefore	therefore	ADV
ejpam-5397	241	69	there	there	PRON
ejpam-5397	241	70	is	be	VERB
ejpam-5397	241	71	no	no	DET
ejpam-5397	241	72	possibility	possibility	NOUN
ejpam-5397	241	73	to	to	PART
ejpam-5397	241	74	have	have	AUX
ejpam-5397	241	75	a	a	DET
ejpam-5397	241	76	hopf	hopf	ADJ
ejpam-5397	241	77	bifurcation	bifurcation	NOUN
ejpam-5397	241	78	near	near	ADP
ejpam-5397	241	79	s1	s1	PROPN
ejpam-5397	241	80	and	and	CCONJ
ejpam-5397	241	81	s2	s2	PROPN
ejpam-5397	241	82	.	.	PUNCT
ejpam-5397	242	1	the	the	DET
ejpam-5397	242	2	conditions	condition	NOUN
ejpam-5397	242	3	that	that	PRON
ejpam-5397	242	4	guarantee	guarantee	VERB
ejpam-5397	242	5	the	the	DET
ejpam-5397	242	6	occurring	occurring	NOUN
ejpam-5397	242	7	of	of	ADP
ejpam-5397	242	8	hopf	hopf	ADJ
ejpam-5397	242	9	bifurcation	bifurcation	NOUN
ejpam-5397	242	10	near	near	ADP
ejpam-5397	242	11	,	,	PUNCT
ejpam-5397	242	12	intermediate	intermediate	ADJ
ejpam-5397	242	13	predators	predator	NOUN
ejpam-5397	242	14	-	-	PUNCT
ejpam-5397	242	15	free	free	ADJ
ejpam-5397	242	16	steady	steady	ADJ
ejpam-5397	242	17	state	state	NOUN
ejpam-5397	242	18	s3	s3	PROPN
ejpam-5397	242	19	=(	=(	NOUN
ejpam-5397	242	20	s̄	s̄	NOUN
ejpam-5397	242	21	,	,	PUNCT
ejpam-5397	242	22	0	0	NUM
ejpam-5397	242	23	,	,	PUNCT
ejpam-5397	242	24	s̄	s̄	NOUN
ejpam-5397	242	25	)	)	PUNCT
ejpam-5397	242	26	and	and	CCONJ
ejpam-5397	242	27	coexistence	coexistence	VERB
ejpam-5397	242	28	steady	steady	ADJ
ejpam-5397	242	29	state	state	NOUN
ejpam-5397	242	30	s4	s4	NOUN
ejpam-5397	242	31	=	=	SYM
ejpam-5397	242	32	(	(	PUNCT
ejpam-5397	242	33	x∗	x∗	PROPN
ejpam-5397	242	34	,	,	PUNCT
ejpam-5397	242	35	y	y	PROPN
ejpam-5397	242	36	∗	∗	NOUN
ejpam-5397	242	37	,	,	PUNCT
ejpam-5397	242	38	z∗	z∗	NOUN
ejpam-5397	242	39	)	)	PUNCT
ejpam-5397	242	40	are	be	AUX
ejpam-5397	242	41	established	establish	VERB
ejpam-5397	242	42	in	in	ADP
ejpam-5397	242	43	theorem	theorem	ADJ
ejpam-5397	242	44	4.1	4.1	NUM
ejpam-5397	242	45	and	and	CCONJ
ejpam-5397	242	46	theorem	theorem	VERB
ejpam-5397	242	47	4.2	4.2	NUM
ejpam-5397	242	48	,	,	PUNCT
ejpam-5397	242	49	respectively	respectively	ADV
ejpam-5397	242	50	.	.	PUNCT
ejpam-5397	243	1	theorem	theorem	VERB
ejpam-5397	243	2	4.1	4.1	NUM
ejpam-5397	243	3	.	.	PUNCT
ejpam-5397	243	4	system	system	NOUN
ejpam-5397	243	5	(	(	PUNCT
ejpam-5397	243	6	1	1	X
ejpam-5397	243	7	)	)	PUNCT
ejpam-5397	243	8	exhibits	exhibit	VERB
ejpam-5397	243	9	a	a	DET
ejpam-5397	243	10	hopf	hopf	ADJ
ejpam-5397	243	11	bifurcation	bifurcation	NOUN
ejpam-5397	243	12	near	near	ADP
ejpam-5397	243	13	intermediate	intermediate	ADJ
ejpam-5397	243	14	predators	predator	NOUN
ejpam-5397	243	15	-	-	PUNCT
ejpam-5397	243	16	free	free	ADJ
ejpam-5397	243	17	steady	steady	ADJ
ejpam-5397	243	18	state	state	NOUN
ejpam-5397	243	19	as	as	SCONJ
ejpam-5397	243	20	the	the	DET
ejpam-5397	243	21	parameter	parameter	PROPN
ejpam-5397	243	22	r3	r3	PROPN
ejpam-5397	243	23	passes	pass	VERB
ejpam-5397	243	24	through	through	ADP
ejpam-5397	243	25	the	the	DET
ejpam-5397	243	26	value	value	NOUN
ejpam-5397	243	27	.	.	PUNCT
ejpam-5397	244	1	b.	b.	PROPN
ejpam-5397	244	2	b.	b.	PROPN
ejpam-5397	244	3	kamal	kamal	PROPN
ejpam-5397	244	4	,	,	PUNCT
ejpam-5397	244	5	a.	a.	PROPN
ejpam-5397	244	6	n.	n.	PROPN
ejpam-5397	244	7	mustafa	mustafa	PROPN
ejpam-5397	244	8	/	/	SYM
ejpam-5397	244	9	eur	eur	PROPN
ejpam-5397	244	10	.	.	PUNCT
ejpam-5397	245	1	j.	j.	PROPN
ejpam-5397	245	2	pure	pure	PROPN
ejpam-5397	245	3	appl	appl	PROPN
ejpam-5397	245	4	.	.	PROPN
ejpam-5397	245	5	math	math	PROPN
ejpam-5397	245	6	,	,	PUNCT
ejpam-5397	245	7	18	18	NUM
ejpam-5397	245	8	(	(	PUNCT
ejpam-5397	245	9	1	1	NUM
ejpam-5397	245	10	)	)	PUNCT
ejpam-5397	245	11	(	(	PUNCT
ejpam-5397	245	12	2025	2025	NUM
ejpam-5397	245	13	)	)	PUNCT
ejpam-5397	245	14	,	,	PUNCT
ejpam-5397	245	15	5397	5397	NUM
ejpam-5397	245	16	12	12	NUM
ejpam-5397	245	17	of	of	ADP
ejpam-5397	245	18	21	21	NUM
ejpam-5397	245	19	r3	r3	PROPN
ejpam-5397	245	20	=	=	SYM
ejpam-5397	245	21	a2	a2	PROPN
ejpam-5397	245	22	(	(	PUNCT
ejpam-5397	245	23	r1r5	r1r5	PROPN
ejpam-5397	245	24	−r2r4	−r2r4	NOUN
ejpam-5397	245	25	)	)	PUNCT
ejpam-5397	245	26	c2	c2	PROPN
ejpam-5397	245	27	+	+	PROPN
ejpam-5397	245	28	a2	a2	PROPN
ejpam-5397	245	29	(	(	PUNCT
ejpam-5397	245	30	r1	r1	PROPN
ejpam-5397	245	31	+	+	PROPN
ejpam-5397	245	32	r3	r3	PROPN
ejpam-5397	245	33	+	+	NOUN
ejpam-5397	245	34	r5	r5	PROPN
ejpam-5397	245	35	)	)	PUNCT
ejpam-5397	245	36	.	.	PUNCT
ejpam-5397	246	1	(	(	PUNCT
ejpam-5397	246	2	20	20	NUM
ejpam-5397	246	3	)	)	PUNCT
ejpam-5397	246	4	if	if	SCONJ
ejpam-5397	246	5	one	one	NUM
ejpam-5397	246	6	of	of	ADP
ejpam-5397	246	7	the	the	DET
ejpam-5397	246	8	following	follow	VERB
ejpam-5397	246	9	conditions	condition	NOUN
ejpam-5397	246	10	holds	hold	VERB
ejpam-5397	246	11	r1	r1	PROPN
ejpam-5397	246	12	+	+	PROPN
ejpam-5397	246	13	r5	r5	PROPN
ejpam-5397	246	14	<	<	X
ejpam-5397	246	15	0	0	NUM
ejpam-5397	246	16	,	,	PUNCT
ejpam-5397	246	17	r1r5	r1r5	PROPN
ejpam-5397	246	18	>	>	X
ejpam-5397	246	19	r2r4	r2r4	X
ejpam-5397	246	20	and	and	CCONJ
ejpam-5397	246	21	r1	r1	PROPN
ejpam-5397	246	22	+	+	PROPN
ejpam-5397	246	23	r3	r3	PROPN
ejpam-5397	246	24	+	+	PROPN
ejpam-5397	246	25	r5	r5	PROPN
ejpam-5397	246	26	>	>	X
ejpam-5397	246	27	−c2	−c2	PROPN
ejpam-5397	246	28	a2	a2	PROPN
ejpam-5397	246	29	,	,	PUNCT
ejpam-5397	246	30	r1	r1	PROPN
ejpam-5397	246	31	+	+	PROPN
ejpam-5397	246	32	r5	r5	PROPN
ejpam-5397	246	33	<	<	X
ejpam-5397	246	34	0	0	NUM
ejpam-5397	246	35	,	,	PUNCT
ejpam-5397	246	36	r1r5	r1r5	PRON
ejpam-5397	246	37	<	<	X
ejpam-5397	246	38	r2r4	r2r4	X
ejpam-5397	246	39	and	and	CCONJ
ejpam-5397	246	40	r1+r3+r5	r1+r3+r5	NOUN
ejpam-5397	246	41	<	<	X
ejpam-5397	246	42	−c2	−c2	PROPN
ejpam-5397	246	43	a2	a2	PROPN
ejpam-5397	246	44	,	,	PUNCT
ejpam-5397	246	45	where	where	SCONJ
ejpam-5397	246	46	a2	a2	PROPN
ejpam-5397	246	47	,	,	PUNCT
ejpam-5397	246	48	c2	c2	PROPN
ejpam-5397	246	49	and	and	CCONJ
ejpam-5397	246	50	ri	ri	PROPN
ejpam-5397	246	51	;	;	PUNCT
ejpam-5397	246	52	i	i	NOUN
ejpam-5397	246	53	=	=	NOUN
ejpam-5397	246	54	1	1	NUM
ejpam-5397	246	55	,	,	PUNCT
ejpam-5397	246	56	2	2	NUM
ejpam-5397	246	57	,	,	PUNCT
ejpam-5397	246	58	3	3	NUM
ejpam-5397	246	59	,	,	PUNCT
ejpam-5397	246	60	4	4	NUM
ejpam-5397	246	61	,	,	PUNCT
ejpam-5397	246	62	5	5	NUM
ejpam-5397	246	63	are	be	AUX
ejpam-5397	246	64	given	give	VERB
ejpam-5397	246	65	in	in	ADP
ejpam-5397	246	66	previous	previous	ADJ
ejpam-5397	246	67	section	section	NOUN
ejpam-5397	246	68	.	.	PUNCT
ejpam-5397	247	1	proof	proof	NOUN
ejpam-5397	247	2	.	.	PUNCT
ejpam-5397	248	1	recall	recall	VERB
ejpam-5397	248	2	that	that	SCONJ
ejpam-5397	248	3	the	the	DET
ejpam-5397	248	4	eigenvalues	eigenvalue	NOUN
ejpam-5397	248	5	of	of	ADP
ejpam-5397	248	6	variational	variational	ADJ
ejpam-5397	248	7	matrix	matrix	NOUN
ejpam-5397	248	8	at	at	ADP
ejpam-5397	248	9	s3	s3	PROPN
ejpam-5397	248	10	=	=	SYM
ejpam-5397	248	11	(	(	PUNCT
ejpam-5397	248	12	s̄	s̄	NOUN
ejpam-5397	248	13	,	,	PUNCT
ejpam-5397	248	14	0	0	NUM
ejpam-5397	248	15	,	,	PUNCT
ejpam-5397	248	16	s̄	s̄	NOUN
ejpam-5397	248	17	)	)	PUNCT
ejpam-5397	248	18	satisfy	satisfy	NOUN
ejpam-5397	248	19	λ3	λ3	PROPN
ejpam-5397	249	1	+	+	PROPN
ejpam-5397	249	2	a2λ	a2λ	NOUN
ejpam-5397	249	3	2	2	NUM
ejpam-5397	249	4	+	+	NOUN
ejpam-5397	249	5	b2λ+	b2λ+	NOUN
ejpam-5397	249	6	r3c2	r3c2	NOUN
ejpam-5397	250	1	=	=	NOUN
ejpam-5397	250	2	0	0	X
ejpam-5397	250	3	.	.	PUNCT
ejpam-5397	251	1	(	(	PUNCT
ejpam-5397	251	2	22	22	NUM
ejpam-5397	251	3	)	)	PUNCT
ejpam-5397	251	4	the	the	DET
ejpam-5397	251	5	hopf	hopf	ADJ
ejpam-5397	251	6	bifurcation	bifurcation	NOUN
ejpam-5397	251	7	near	near	ADP
ejpam-5397	251	8	intermediate	intermediate	ADJ
ejpam-5397	251	9	predators	predator	NOUN
ejpam-5397	251	10	-	-	PUNCT
ejpam-5397	251	11	free	free	ADJ
ejpam-5397	251	12	steady	steady	ADJ
ejpam-5397	251	13	state	state	NOUN
ejpam-5397	251	14	of	of	ADP
ejpam-5397	251	15	system	system	NOUN
ejpam-5397	251	16	(	(	PUNCT
ejpam-5397	251	17	1	1	X
ejpam-5397	251	18	)	)	PUNCT
ejpam-5397	251	19	occurs	occur	VERB
ejpam-5397	251	20	if	if	SCONJ
ejpam-5397	251	21	and	and	CCONJ
ejpam-5397	251	22	only	only	ADV
ejpam-5397	251	23	if	if	SCONJ
ejpam-5397	251	24	two	two	NUM
ejpam-5397	251	25	roots	root	NOUN
ejpam-5397	251	26	of	of	ADP
ejpam-5397	251	27	eq	eq	NOUN
ejpam-5397	251	28	.	.	PUNCT
ejpam-5397	252	1	(	(	PUNCT
ejpam-5397	252	2	22	22	NUM
ejpam-5397	252	3	)	)	PUNCT
ejpam-5397	252	4	have	have	VERB
ejpam-5397	252	5	two	two	NUM
ejpam-5397	252	6	complex	complex	ADJ
ejpam-5397	252	7	conjugate	conjugate	NOUN
ejpam-5397	252	8	eigenvalues	eigenvalue	NOUN
ejpam-5397	252	9	with	with	ADP
ejpam-5397	252	10	the	the	DET
ejpam-5397	252	11	third	third	ADJ
ejpam-5397	252	12	eigenvalue	eigenvalue	ADJ
ejpam-5397	252	13	real	real	ADJ
ejpam-5397	252	14	and	and	CCONJ
ejpam-5397	252	15	negative	negative	ADJ
ejpam-5397	252	16	such	such	ADJ
ejpam-5397	252	17	that	that	SCONJ
ejpam-5397	252	18	there	there	PRON
ejpam-5397	252	19	exists	exist	VERB
ejpam-5397	252	20	a	a	DET
ejpam-5397	252	21	constant	constant	ADJ
ejpam-5397	252	22	parameter	parameter	NOUN
ejpam-5397	252	23	value	value	NOUN
ejpam-5397	252	24	,	,	PUNCT
ejpam-5397	252	25	say	say	VERB
ejpam-5397	252	26	r3	r3	PROPN
ejpam-5397	252	27	satisfying	satisfying	NOUN
ejpam-5397	252	28	:	:	PUNCT
ejpam-5397	252	29	ree	ree	NOUN
ejpam-5397	252	30	(	(	PUNCT
ejpam-5397	252	31	λ	λ	X
ejpam-5397	252	32	(	(	PUNCT
ejpam-5397	252	33	r3))r3	r3))r3	PROPN
ejpam-5397	252	34	=	=	SYM
ejpam-5397	252	35	r3	r3	PROPN
ejpam-5397	252	36	=	=	SYM
ejpam-5397	252	37	0	0	PROPN
ejpam-5397	252	38	and	and	CCONJ
ejpam-5397	252	39	[	[	PUNCT
ejpam-5397	252	40	dre	dre	X
ejpam-5397	252	41	e	e	PROPN
ejpam-5397	252	42	(	(	PUNCT
ejpam-5397	252	43	λ	λ	PROPN
ejpam-5397	252	44	(	(	PUNCT
ejpam-5397	252	45	r3	r3	PROPN
ejpam-5397	252	46	)	)	PUNCT
ejpam-5397	252	47	)	)	PUNCT
ejpam-5397	253	1	dr3	dr3	PROPN
ejpam-5397	253	2	]	]	PUNCT
ejpam-5397	253	3	r3	r3	PROPN
ejpam-5397	253	4	=	=	SYM
ejpam-5397	253	5	r3	r3	PROPN
ejpam-5397	253	6	̸=	̸=	PROPN
ejpam-5397	253	7	0	0	NUM
ejpam-5397	253	8	where	where	SCONJ
ejpam-5397	253	9	λ	λ	PROPN
ejpam-5397	253	10	is	be	AUX
ejpam-5397	253	11	a	a	DET
ejpam-5397	253	12	complex	complex	ADJ
ejpam-5397	253	13	root	root	NOUN
ejpam-5397	253	14	of	of	ADP
ejpam-5397	253	15	eq	eq	PROPN
ejpam-5397	253	16	.	.	PUNCT
ejpam-5397	254	1	(	(	PUNCT
ejpam-5397	254	2	22	22	NUM
ejpam-5397	254	3	)	)	PUNCT
ejpam-5397	254	4	if	if	SCONJ
ejpam-5397	254	5	r3	r3	PROPN
ejpam-5397	254	6	=	=	SYM
ejpam-5397	254	7	r̄3	r̄3	PROPN
ejpam-5397	254	8	,	,	PUNCT
ejpam-5397	254	9	then	then	ADV
ejpam-5397	254	10	a2b2	a2b2	PROPN
ejpam-5397	254	11	=	=	SYM
ejpam-5397	254	12	r3c2	r3c2	NOUN
ejpam-5397	254	13	and	and	CCONJ
ejpam-5397	254	14	hence	hence	ADV
ejpam-5397	254	15	equation	equation	NOUN
ejpam-5397	254	16	(	(	PUNCT
ejpam-5397	254	17	)	)	PUNCT
ejpam-5397	254	18	can	can	AUX
ejpam-5397	254	19	be	be	AUX
ejpam-5397	254	20	written	write	VERB
ejpam-5397	254	21	(	(	PUNCT
ejpam-5397	254	22	λ2	λ2	NOUN
ejpam-5397	254	23	+	+	NOUN
ejpam-5397	254	24	b2	b2	NOUN
ejpam-5397	254	25	)	)	PUNCT
ejpam-5397	254	26	(	(	PUNCT
ejpam-5397	254	27	λ+a2	λ+a2	PROPN
ejpam-5397	254	28	)	)	PUNCT
ejpam-5397	254	29	=	=	SYM
ejpam-5397	254	30	0	0	NUM
ejpam-5397	255	1	(	(	PUNCT
ejpam-5397	255	2	23	23	NUM
ejpam-5397	255	3	)	)	PUNCT
ejpam-5397	255	4	clearly	clearly	ADV
ejpam-5397	255	5	,	,	PUNCT
ejpam-5397	255	6	equation	equation	NOUN
ejpam-5397	255	7	(	(	PUNCT
ejpam-5397	255	8	23	23	NUM
ejpam-5397	255	9	)	)	PUNCT
ejpam-5397	255	10	has	have	VERB
ejpam-5397	255	11	the	the	DET
ejpam-5397	255	12	following	follow	VERB
ejpam-5397	255	13	three	three	NUM
ejpam-5397	255	14	roots	root	NOUN
ejpam-5397	255	15	:	:	PUNCT
ejpam-5397	255	16	λ1	λ1	PROPN
ejpam-5397	255	17	=	=	PUNCT
ejpam-5397	255	18	i	i	NOUN
ejpam-5397	255	19	√	√	PROPN
ejpam-5397	255	20	b2	b2	NOUN
ejpam-5397	255	21	,	,	PUNCT
ejpam-5397	255	22	λ2	λ2	NOUN
ejpam-5397	255	23	=	=	SYM
ejpam-5397	255	24	−i	−i	ADJ
ejpam-5397	255	25	√	√	NUM
ejpam-5397	255	26	b2	b2	NOUN
ejpam-5397	255	27	and	and	CCONJ
ejpam-5397	255	28	dλ3	dλ3	NOUN
ejpam-5397	255	29	=	=	PROPN
ejpam-5397	255	30	−a2	−a2	PROPN
ejpam-5397	255	31	.	.	PUNCT
ejpam-5397	256	1	however	however	ADV
ejpam-5397	256	2	,	,	PUNCT
ejpam-5397	256	3	for	for	ADP
ejpam-5397	256	4	all	all	DET
ejpam-5397	256	5	values	value	NOUN
ejpam-5397	256	6	of	of	ADP
ejpam-5397	256	7	r3	r3	PROPN
ejpam-5397	256	8	in	in	ADP
ejpam-5397	256	9	the	the	DET
ejpam-5397	256	10	neighborhood	neighborhood	NOUN
ejpam-5397	256	11	of	of	ADP
ejpam-5397	256	12	r3	r3	PROPN
ejpam-5397	256	13	,	,	PUNCT
ejpam-5397	256	14	these	these	DET
ejpam-5397	256	15	roots	root	NOUN
ejpam-5397	256	16	can	can	AUX
ejpam-5397	256	17	be	be	AUX
ejpam-5397	256	18	written	write	VERB
ejpam-5397	256	19	in	in	ADP
ejpam-5397	256	20	general	general	ADJ
ejpam-5397	256	21	as	as	ADP
ejpam-5397	256	22	λ1	λ1	PROPN
ejpam-5397	256	23	=	=	PUNCT
ejpam-5397	256	24	a	a	DET
ejpam-5397	256	25	(	(	PUNCT
ejpam-5397	256	26	r3	r3	PROPN
ejpam-5397	256	27	)	)	PUNCT
ejpam-5397	256	28	+	+	NUM
ejpam-5397	256	29	ib	ib	INTJ
ejpam-5397	256	30	(	(	PUNCT
ejpam-5397	256	31	r3	r3	PROPN
ejpam-5397	256	32	)	)	PUNCT
ejpam-5397	256	33	,	,	PUNCT
ejpam-5397	256	34	λ2	λ2	NOUN
ejpam-5397	256	35	=	=	SYM
ejpam-5397	256	36	a	a	DET
ejpam-5397	256	37	(	(	PUNCT
ejpam-5397	256	38	r3)−	r3)−	PROPN
ejpam-5397	256	39	ib	ib	PROPN
ejpam-5397	256	40	(	(	PUNCT
ejpam-5397	256	41	r3	r3	PROPN
ejpam-5397	256	42	)	)	PUNCT
ejpam-5397	256	43	and	and	CCONJ
ejpam-5397	256	44	λ3	λ3	PROPN
ejpam-5397	256	45	=	=	PROPN
ejpam-5397	256	46	−a2	−a2	PROPN
ejpam-5397	256	47	(	(	PUNCT
ejpam-5397	256	48	r3	r3	PROPN
ejpam-5397	256	49	)	)	PUNCT
ejpam-5397	256	50	.	.	PUNCT
ejpam-5397	257	1	clearly	clearly	ADV
ejpam-5397	257	2	,	,	PUNCT
ejpam-5397	257	3	a	a	DET
ejpam-5397	257	4	(	(	PUNCT
ejpam-5397	257	5	r3	r3	PROPN
ejpam-5397	257	6	)	)	PUNCT
ejpam-5397	257	7	=	=	SYM
ejpam-5397	257	8	0	0	NUM
ejpam-5397	257	9	which	which	PRON
ejpam-5397	257	10	means	mean	VERB
ejpam-5397	257	11	that	that	SCONJ
ejpam-5397	257	12	the	the	DET
ejpam-5397	257	13	first	first	ADJ
ejpam-5397	257	14	condition	condition	NOUN
ejpam-5397	257	15	of	of	ADP
ejpam-5397	257	16	hopf	hopf	ADJ
ejpam-5397	257	17	bifurcation	bifurcation	NOUN
ejpam-5397	257	18	holds	hold	VERB
ejpam-5397	257	19	.	.	PUNCT
ejpam-5397	258	1	now	now	ADV
ejpam-5397	258	2	,	,	PUNCT
ejpam-5397	258	3	the	the	DET
ejpam-5397	258	4	proof	proof	NOUN
ejpam-5397	258	5	will	will	AUX
ejpam-5397	258	6	follows	follow	VERB
ejpam-5397	258	7	,	,	PUNCT
ejpam-5397	258	8	if	if	SCONJ
ejpam-5397	258	9	we	we	PRON
ejpam-5397	258	10	can	can	AUX
ejpam-5397	258	11	verify	verify	VERB
ejpam-5397	258	12	the	the	DET
ejpam-5397	258	13	above	above	ADJ
ejpam-5397	258	14	second	second	ADJ
ejpam-5397	258	15	condition	condition	NOUN
ejpam-5397	258	16	(	(	PUNCT
ejpam-5397	258	17	known	know	VERB
ejpam-5397	258	18	as	as	ADP
ejpam-5397	258	19	transversality	transversality	NOUN
ejpam-5397	258	20	condition	condition	NOUN
ejpam-5397	258	21	)	)	PUNCT
ejpam-5397	258	22	of	of	ADP
ejpam-5397	258	23	hopf	hopf	ADJ
ejpam-5397	258	24	bifurcation	bifurcation	NOUN
ejpam-5397	258	25	when	when	SCONJ
ejpam-5397	258	26	ree	ree	NOUN
ejpam-5397	258	27	(	(	PUNCT
ejpam-5397	258	28	λ	λ	PROPN
ejpam-5397	258	29	(	(	PUNCT
ejpam-5397	258	30	r3	r3	PROPN
ejpam-5397	258	31	)	)	PUNCT
ejpam-5397	258	32	)	)	PUNCT
ejpam-5397	259	1	=	=	SYM
ejpam-5397	259	2	a	a	PRON
ejpam-5397	259	3	(	(	PUNCT
ejpam-5397	259	4	r3	r3	PROPN
ejpam-5397	259	5	)	)	PUNCT
ejpam-5397	259	6	.	.	PUNCT
ejpam-5397	260	1	thus	thus	ADV
ejpam-5397	260	2	,	,	PUNCT
ejpam-5397	260	3	by	by	ADP
ejpam-5397	260	4	substituting	substitute	VERB
ejpam-5397	260	5	λ1	λ1	PROPN
ejpam-5397	260	6	=	=	PUNCT
ejpam-5397	260	7	a	a	DET
ejpam-5397	260	8	(	(	PUNCT
ejpam-5397	260	9	r3	r3	PROPN
ejpam-5397	260	10	)	)	PUNCT
ejpam-5397	260	11	+	+	NUM
ejpam-5397	260	12	ib	ib	INTJ
ejpam-5397	260	13	(	(	PUNCT
ejpam-5397	260	14	r3	r3	PROPN
ejpam-5397	260	15	)	)	PUNCT
ejpam-5397	260	16	in	in	ADP
ejpam-5397	260	17	(	(	PUNCT
ejpam-5397	260	18	22	22	NUM
ejpam-5397	260	19	)	)	PUNCT
ejpam-5397	260	20	and	and	CCONJ
ejpam-5397	260	21	calculating	calculate	VERB
ejpam-5397	260	22	the	the	DET
ejpam-5397	260	23	derivative	derivative	NOUN
ejpam-5397	260	24	with	with	ADP
ejpam-5397	260	25	respect	respect	NOUN
ejpam-5397	260	26	to	to	ADP
ejpam-5397	260	27	the	the	DET
ejpam-5397	260	28	r3	r3	PROPN
ejpam-5397	260	29	,	,	PUNCT
ejpam-5397	260	30	it	it	PRON
ejpam-5397	260	31	is	be	AUX
ejpam-5397	260	32	obtained	obtain	VERB
ejpam-5397	260	33	that	that	SCONJ
ejpam-5397	260	34	{	{	PUNCT
ejpam-5397	260	35	d1	d1	PROPN
ejpam-5397	260	36	(	(	PUNCT
ejpam-5397	260	37	r3	r3	PROPN
ejpam-5397	260	38	)	)	PUNCT
ejpam-5397	260	39	da(r3	da(r3	NOUN
ejpam-5397	260	40	)	)	PUNCT
ejpam-5397	260	41	dr3	dr3	PROPN
ejpam-5397	260	42	−d2	−d2	PROPN
ejpam-5397	260	43	(	(	PUNCT
ejpam-5397	260	44	r3	r3	PROPN
ejpam-5397	260	45	)	)	PUNCT
ejpam-5397	260	46	db(r3	db(r3	PROPN
ejpam-5397	260	47	)	)	PUNCT
ejpam-5397	261	1	dr3	dr3	PROPN
ejpam-5397	262	1	+	+	PROPN
ejpam-5397	262	2	d3	d3	PROPN
ejpam-5397	262	3	(	(	PUNCT
ejpam-5397	262	4	r3	r3	PROPN
ejpam-5397	262	5	)	)	PUNCT
ejpam-5397	262	6	=	=	SYM
ejpam-5397	262	7	0	0	NUM
ejpam-5397	262	8	d1	d1	PROPN
ejpam-5397	262	9	(	(	PUNCT
ejpam-5397	262	10	r3	r3	PROPN
ejpam-5397	262	11	)	)	PUNCT
ejpam-5397	262	12	db(r3	db(r3	PROPN
ejpam-5397	262	13	)	)	PUNCT
ejpam-5397	263	1	dr3	dr3	PROPN
ejpam-5397	263	2	+	+	PROPN
ejpam-5397	263	3	d2	d2	PROPN
ejpam-5397	263	4	(	(	PUNCT
ejpam-5397	263	5	r3	r3	PROPN
ejpam-5397	263	6	)	)	PUNCT
ejpam-5397	263	7	da(r3	da(r3	PUNCT
ejpam-5397	263	8	)	)	PUNCT
ejpam-5397	264	1	dr3	dr3	PROPN
ejpam-5397	264	2	+	+	PROPN
ejpam-5397	264	3	d4	d4	PROPN
ejpam-5397	264	4	(	(	PUNCT
ejpam-5397	264	5	r3	r3	PROPN
ejpam-5397	264	6	)	)	PUNCT
ejpam-5397	264	7	=	=	SYM
ejpam-5397	264	8	0	0	PUNCT
ejpam-5397	264	9	(	(	PUNCT
ejpam-5397	264	10	24	24	NUM
ejpam-5397	264	11	)	)	PUNCT
ejpam-5397	264	12	where	where	SCONJ
ejpam-5397	264	13	d1	d1	PROPN
ejpam-5397	264	14	(	(	PUNCT
ejpam-5397	264	15	r3	r3	PROPN
ejpam-5397	264	16	)	)	PUNCT
ejpam-5397	264	17	=	=	PUNCT
ejpam-5397	265	1	3	3	NUM
ejpam-5397	265	2	[	[	X
ejpam-5397	265	3	a	a	DET
ejpam-5397	265	4	(	(	PUNCT
ejpam-5397	265	5	r3	r3	PROPN
ejpam-5397	265	6	)	)	PUNCT
ejpam-5397	265	7	]	]	PUNCT
ejpam-5397	266	1	2	2	NUM
ejpam-5397	266	2	+	+	NUM
ejpam-5397	266	3	2a2	2a2	NUM
ejpam-5397	266	4	(	(	PUNCT
ejpam-5397	266	5	r3	r3	PROPN
ejpam-5397	266	6	)	)	PUNCT
ejpam-5397	266	7	a	a	DET
ejpam-5397	266	8	(	(	PUNCT
ejpam-5397	266	9	r3	r3	PROPN
ejpam-5397	266	10	)	)	PUNCT
ejpam-5397	267	1	+	+	NOUN
ejpam-5397	267	2	b2	b2	NOUN
ejpam-5397	267	3	(	(	PUNCT
ejpam-5397	267	4	r3)−	r3)−	NOUN
ejpam-5397	267	5	3	3	NUM
ejpam-5397	267	6	[	[	X
ejpam-5397	267	7	b	b	X
ejpam-5397	267	8	(	(	PUNCT
ejpam-5397	267	9	r3	r3	PROPN
ejpam-5397	267	10	)	)	PUNCT
ejpam-5397	267	11	]	]	PUNCT
ejpam-5397	268	1	2	2	NUM
ejpam-5397	268	2	b.	b.	PROPN
ejpam-5397	268	3	b.	b.	PROPN
ejpam-5397	268	4	kamal	kamal	PROPN
ejpam-5397	268	5	,	,	PUNCT
ejpam-5397	268	6	a.	a.	PROPN
ejpam-5397	268	7	n.	n.	PROPN
ejpam-5397	268	8	mustafa	mustafa	PROPN
ejpam-5397	268	9	/	/	SYM
ejpam-5397	268	10	eur	eur	PROPN
ejpam-5397	268	11	.	.	PUNCT
ejpam-5397	269	1	j.	j.	PROPN
ejpam-5397	269	2	pure	pure	PROPN
ejpam-5397	269	3	appl	appl	PROPN
ejpam-5397	269	4	.	.	PROPN
ejpam-5397	269	5	math	math	PROPN
ejpam-5397	269	6	,	,	PUNCT
ejpam-5397	269	7	18	18	NUM
ejpam-5397	269	8	(	(	PUNCT
ejpam-5397	269	9	1	1	NUM
ejpam-5397	269	10	)	)	PUNCT
ejpam-5397	269	11	(	(	PUNCT
ejpam-5397	269	12	2025	2025	NUM
ejpam-5397	269	13	)	)	PUNCT
ejpam-5397	269	14	,	,	PUNCT
ejpam-5397	269	15	5397	5397	NUM
ejpam-5397	269	16	13	13	NUM
ejpam-5397	269	17	of	of	ADP
ejpam-5397	269	18	21	21	NUM
ejpam-5397	269	19	d2	d2	PROPN
ejpam-5397	269	20	(	(	PUNCT
ejpam-5397	269	21	r3	r3	PROPN
ejpam-5397	269	22	)	)	PUNCT
ejpam-5397	269	23	=	=	SYM
ejpam-5397	269	24	6a	6a	NOUN
ejpam-5397	269	25	(	(	PUNCT
ejpam-5397	269	26	r3	r3	PROPN
ejpam-5397	269	27	)	)	PUNCT
ejpam-5397	269	28	b	b	PROPN
ejpam-5397	269	29	(	(	PUNCT
ejpam-5397	269	30	r3	r3	PROPN
ejpam-5397	269	31	)	)	PUNCT
ejpam-5397	269	32	+	+	NUM
ejpam-5397	269	33	2a2	2a2	NUM
ejpam-5397	269	34	(	(	PUNCT
ejpam-5397	269	35	r3	r3	PROPN
ejpam-5397	269	36	)	)	PUNCT
ejpam-5397	269	37	b	b	PROPN
ejpam-5397	269	38	(	(	PUNCT
ejpam-5397	269	39	r3	r3	PROPN
ejpam-5397	269	40	)	)	PUNCT
ejpam-5397	269	41	d3	d3	PROPN
ejpam-5397	269	42	(	(	PUNCT
ejpam-5397	269	43	r3	r3	PROPN
ejpam-5397	269	44	)	)	PUNCT
ejpam-5397	269	45	=	=	SYM
ejpam-5397	270	1	a	a	DET
ejpam-5397	270	2	(	(	PUNCT
ejpam-5397	270	3	r3	r3	PROPN
ejpam-5397	270	4	)	)	PUNCT
ejpam-5397	270	5	db2	db2	PROPN
ejpam-5397	270	6	(	(	PUNCT
ejpam-5397	270	7	r3	r3	PROPN
ejpam-5397	270	8	)	)	PUNCT
ejpam-5397	270	9	dr3	dr3	PROPN
ejpam-5397	271	1	+	+	PROPN
ejpam-5397	271	2	c2	c2	PROPN
ejpam-5397	271	3	d4	d4	PROPN
ejpam-5397	271	4	(	(	PUNCT
ejpam-5397	271	5	r3	r3	PROPN
ejpam-5397	271	6	)	)	PUNCT
ejpam-5397	271	7	=	=	SYM
ejpam-5397	272	1	b	b	PROPN
ejpam-5397	272	2	(	(	PUNCT
ejpam-5397	272	3	r3	r3	PROPN
ejpam-5397	272	4	)	)	PUNCT
ejpam-5397	272	5	db2	db2	PROPN
ejpam-5397	272	6	(	(	PUNCT
ejpam-5397	272	7	r3	r3	PROPN
ejpam-5397	272	8	)	)	PUNCT
ejpam-5397	272	9	dr3	dr3	PROPN
ejpam-5397	272	10	thus	thus	ADV
ejpam-5397	272	11	,	,	PUNCT
ejpam-5397	272	12	by	by	ADP
ejpam-5397	272	13	solving	solve	VERB
ejpam-5397	272	14	the	the	DET
ejpam-5397	272	15	linear	linear	ADJ
ejpam-5397	272	16	system	system	NOUN
ejpam-5397	272	17	(	(	PUNCT
ejpam-5397	272	18	24	24	NUM
ejpam-5397	272	19	)	)	PUNCT
ejpam-5397	272	20	for	for	ADP
ejpam-5397	272	21	the	the	DET
ejpam-5397	272	22	unknown	unknown	ADJ
ejpam-5397	272	23	da(r3	da(r3	NOUN
ejpam-5397	272	24	)	)	PUNCT
ejpam-5397	272	25	dr3	dr3	PROPN
ejpam-5397	272	26	,	,	PUNCT
ejpam-5397	272	27	it	it	PRON
ejpam-5397	272	28	gets	get	VERB
ejpam-5397	272	29	da	da	NOUN
ejpam-5397	272	30	(	(	PUNCT
ejpam-5397	272	31	r3	r3	PROPN
ejpam-5397	272	32	)	)	PUNCT
ejpam-5397	272	33	dr3	dr3	PROPN
ejpam-5397	272	34	=	=	PROPN
ejpam-5397	272	35	dree	dree	PROPN
ejpam-5397	272	36	(	(	PUNCT
ejpam-5397	272	37	λ	λ	PROPN
ejpam-5397	272	38	(	(	PUNCT
ejpam-5397	272	39	r3	r3	PROPN
ejpam-5397	272	40	)	)	PUNCT
ejpam-5397	272	41	)	)	PUNCT
ejpam-5397	273	1	dr3	dr3	PROPN
ejpam-5397	273	2	=	=	PROPN
ejpam-5397	274	1	−d2	−d2	X
ejpam-5397	274	2	(	(	PUNCT
ejpam-5397	274	3	r3)d4	r3)d4	X
ejpam-5397	274	4	(	(	PUNCT
ejpam-5397	274	5	r3	r3	PROPN
ejpam-5397	274	6	)	)	PUNCT
ejpam-5397	275	1	+	+	NUM
ejpam-5397	275	2	d1	d1	PROPN
ejpam-5397	275	3	(	(	PUNCT
ejpam-5397	275	4	r3)d3	r3)d3	NOUN
ejpam-5397	275	5	(	(	PUNCT
ejpam-5397	275	6	r3	r3	PROPN
ejpam-5397	275	7	)	)	PUNCT
ejpam-5397	276	1	[	[	X
ejpam-5397	276	2	d1	d1	NOUN
ejpam-5397	276	3	(	(	PUNCT
ejpam-5397	276	4	r3	r3	PROPN
ejpam-5397	276	5	)	)	PUNCT
ejpam-5397	276	6	]	]	PUNCT
ejpam-5397	276	7	2	2	NUM
ejpam-5397	276	8	+	+	CCONJ
ejpam-5397	276	9	[	[	X
ejpam-5397	276	10	d2	d2	PROPN
ejpam-5397	276	11	(	(	PUNCT
ejpam-5397	276	12	r3	r3	PROPN
ejpam-5397	276	13	)	)	PUNCT
ejpam-5397	276	14	]	]	PUNCT
ejpam-5397	276	15	2	2	NUM
ejpam-5397	276	16	so	so	ADV
ejpam-5397	276	17	for	for	ADP
ejpam-5397	276	18	r3	r3	PROPN
ejpam-5397	276	19	=	=	SYM
ejpam-5397	276	20	r3	r3	PROPN
ejpam-5397	276	21	,	,	PUNCT
ejpam-5397	276	22	it	it	PRON
ejpam-5397	276	23	is	be	AUX
ejpam-5397	276	24	easy	easy	ADJ
ejpam-5397	276	25	to	to	PART
ejpam-5397	276	26	verify	verify	VERB
ejpam-5397	276	27	that	that	SCONJ
ejpam-5397	276	28	[	[	PUNCT
ejpam-5397	276	29	dree	dree	X
ejpam-5397	276	30	(	(	PUNCT
ejpam-5397	276	31	λ	λ	PROPN
ejpam-5397	276	32	(	(	PUNCT
ejpam-5397	276	33	r3	r3	PROPN
ejpam-5397	276	34	)	)	PUNCT
ejpam-5397	276	35	)	)	PUNCT
ejpam-5397	277	1	dr3	dr3	PROPN
ejpam-5397	277	2	]	]	PUNCT
ejpam-5397	277	3	r3	r3	PROPN
ejpam-5397	277	4	=	=	SYM
ejpam-5397	277	5	r3	r3	PROPN
ejpam-5397	277	6	̸=	̸=	PROPN
ejpam-5397	277	7	0	0	NUM
ejpam-5397	277	8	also	also	ADV
ejpam-5397	277	9	,	,	PUNCT
ejpam-5397	277	10	condition	condition	NOUN
ejpam-5397	277	11	(	(	PUNCT
ejpam-5397	277	12	20	20	NUM
ejpam-5397	277	13	)	)	PUNCT
ejpam-5397	277	14	or	or	CCONJ
ejpam-5397	277	15	(	(	PUNCT
ejpam-5397	277	16	21	21	NUM
ejpam-5397	277	17	)	)	PUNCT
ejpam-5397	277	18	guarantee	guarantee	VERB
ejpam-5397	277	19	that	that	SCONJ
ejpam-5397	277	20	a2	a2	PROPN
ejpam-5397	277	21	is	be	AUX
ejpam-5397	277	22	positive	positive	ADJ
ejpam-5397	277	23	for	for	ADP
ejpam-5397	277	24	all	all	DET
ejpam-5397	277	25	values	value	NOUN
ejpam-5397	277	26	of	of	ADP
ejpam-5397	277	27	r3	r3	NOUN
ejpam-5397	277	28	,	,	PUNCT
ejpam-5397	277	29	and	and	CCONJ
ejpam-5397	277	30	hence	hence	ADV
ejpam-5397	277	31	λ3	λ3	PROPN
ejpam-5397	277	32	=	=	PROPN
ejpam-5397	277	33	−a2	−a2	PROPN
ejpam-5397	277	34	(	(	PUNCT
ejpam-5397	277	35	r3	r3	PROPN
ejpam-5397	277	36	)	)	PUNCT
ejpam-5397	277	37	<	<	X
ejpam-5397	277	38	0	0	X
ejpam-5397	277	39	.	.	PUNCT
ejpam-5397	278	1	the	the	DET
ejpam-5397	278	2	proof	proof	NOUN
ejpam-5397	278	3	is	be	AUX
ejpam-5397	278	4	completed	complete	VERB
ejpam-5397	278	5	.	.	PUNCT
ejpam-5397	279	1	in	in	ADP
ejpam-5397	279	2	similar	similar	ADJ
ejpam-5397	279	3	ways	way	NOUN
ejpam-5397	279	4	of	of	ADP
ejpam-5397	279	5	proving	prove	VERB
ejpam-5397	279	6	above	above	ADP
ejpam-5397	279	7	theorem	theorem	NOUN
ejpam-5397	279	8	we	we	PRON
ejpam-5397	279	9	can	can	AUX
ejpam-5397	279	10	get	get	VERB
ejpam-5397	279	11	the	the	DET
ejpam-5397	279	12	following	follow	VERB
ejpam-5397	279	13	theorem	theorem	VERB
ejpam-5397	279	14	.	.	PUNCT
ejpam-5397	279	15	theorem	theorem	VERB
ejpam-5397	279	16	4.2	4.2	NUM
ejpam-5397	279	17	.	.	PUNCT
ejpam-5397	280	1	system	system	NOUN
ejpam-5397	280	2	(	(	PUNCT
ejpam-5397	280	3	1	1	X
ejpam-5397	280	4	)	)	PUNCT
ejpam-5397	280	5	exhibits	exhibit	VERB
ejpam-5397	280	6	a	a	DET
ejpam-5397	280	7	hopf	hopf	ADJ
ejpam-5397	280	8	bifurcation	bifurcation	NOUN
ejpam-5397	280	9	coexistence	coexistence	NOUN
ejpam-5397	280	10	steady	steady	ADJ
ejpam-5397	280	11	state	state	NOUN
ejpam-5397	280	12	as	as	SCONJ
ejpam-5397	280	13	the	the	DET
ejpam-5397	280	14	parameter	parameter	PROPN
ejpam-5397	280	15	r3	r3	PROPN
ejpam-5397	280	16	passes	pass	VERB
ejpam-5397	280	17	through	through	ADP
ejpam-5397	280	18	the	the	DET
ejpam-5397	280	19	value	value	NOUN
ejpam-5397	280	20	r3	r3	PROPN
ejpam-5397	280	21	=	=	SYM
ejpam-5397	280	22	a3	a3	NOUN
ejpam-5397	280	23	(	(	PUNCT
ejpam-5397	280	24	e1e5	e1e5	PUNCT
ejpam-5397	280	25	−	−	NUM
ejpam-5397	280	26	e2e4	e2e4	NOUN
ejpam-5397	280	27	)	)	PUNCT
ejpam-5397	280	28	c3	c3	PROPN
ejpam-5397	280	29	+	+	PROPN
ejpam-5397	280	30	a3	a3	PROPN
ejpam-5397	280	31	(	(	PUNCT
ejpam-5397	280	32	e1	e1	NOUN
ejpam-5397	280	33	+	+	CCONJ
ejpam-5397	280	34	e3	e3	NOUN
ejpam-5397	280	35	+	+	X
ejpam-5397	280	36	e5	e5	NOUN
ejpam-5397	280	37	)	)	PUNCT
ejpam-5397	280	38	(	(	PUNCT
ejpam-5397	280	39	25	25	NUM
ejpam-5397	280	40	)	)	PUNCT
ejpam-5397	280	41	if	if	SCONJ
ejpam-5397	280	42	one	one	NUM
ejpam-5397	280	43	of	of	ADP
ejpam-5397	280	44	the	the	DET
ejpam-5397	280	45	following	follow	VERB
ejpam-5397	280	46	condition	condition	NOUN
ejpam-5397	280	47	holds	hold	VERB
ejpam-5397	280	48	e1	e1	PROPN
ejpam-5397	280	49	+	+	CCONJ
ejpam-5397	280	50	e5	e5	PROPN
ejpam-5397	280	51	<	<	X
ejpam-5397	280	52	0	0	PROPN
ejpam-5397	280	53	,	,	PUNCT
ejpam-5397	280	54	e1e5	e1e5	PUNCT
ejpam-5397	280	55	>	>	X
ejpam-5397	280	56	e2e4	e2e4	PROPN
ejpam-5397	280	57	and	and	CCONJ
ejpam-5397	280	58	e1	e1	VERB
ejpam-5397	280	59	+	+	CCONJ
ejpam-5397	280	60	e3	e3	NOUN
ejpam-5397	280	61	+	+	X
ejpam-5397	280	62	e5	e5	NOUN
ejpam-5397	280	63	+	+	CCONJ
ejpam-5397	280	64	e6	e6	PROPN
ejpam-5397	280	65	>	>	X
ejpam-5397	280	66	−c3	−c3	PROPN
ejpam-5397	280	67	a3	a3	PROPN
ejpam-5397	280	68	e1	e1	PROPN
ejpam-5397	280	69	+	+	CCONJ
ejpam-5397	280	70	e5	e5	PROPN
ejpam-5397	280	71	<	<	X
ejpam-5397	280	72	0	0	PROPN
ejpam-5397	280	73	,	,	PUNCT
ejpam-5397	280	74	e1e5	e1e5	PUNCT
ejpam-5397	280	75	<	<	X
ejpam-5397	280	76	e2e4	e2e4	PROPN
ejpam-5397	280	77	and	and	CCONJ
ejpam-5397	280	78	e1	e1	VERB
ejpam-5397	280	79	+	+	CCONJ
ejpam-5397	280	80	e3	e3	NOUN
ejpam-5397	280	81	+	+	X
ejpam-5397	280	82	e5	e5	NOUN
ejpam-5397	280	83	+	+	CCONJ
ejpam-5397	280	84	e6	e6	PROPN
ejpam-5397	280	85	<	<	X
ejpam-5397	280	86	−c3	−c3	PROPN
ejpam-5397	280	87	a3	a3	PROPN
ejpam-5397	281	1	where	where	SCONJ
ejpam-5397	281	2	a3	a3	NOUN
ejpam-5397	281	3	,	,	PUNCT
ejpam-5397	281	4	c3	c3	PROPN
ejpam-5397	281	5	and	and	CCONJ
ejpam-5397	281	6	ei	ei	NOUN
ejpam-5397	281	7	;	;	PUNCT
ejpam-5397	281	8	i	i	NOUN
ejpam-5397	281	9	=	=	NOUN
ejpam-5397	281	10	1	1	NUM
ejpam-5397	281	11	,	,	PUNCT
ejpam-5397	281	12	2	2	NUM
ejpam-5397	281	13	,	,	PUNCT
ejpam-5397	281	14	3	3	NUM
ejpam-5397	281	15	,	,	PUNCT
ejpam-5397	281	16	4	4	NUM
ejpam-5397	281	17	,	,	PUNCT
ejpam-5397	281	18	5	5	NUM
ejpam-5397	281	19	,	,	PUNCT
ejpam-5397	281	20	6	6	NUM
ejpam-5397	281	21	are	be	AUX
ejpam-5397	281	22	given	give	VERB
ejpam-5397	281	23	in	in	ADP
ejpam-5397	281	24	previous	previous	ADJ
ejpam-5397	281	25	section	section	NOUN
ejpam-5397	281	26	5	5	NUM
ejpam-5397	281	27	.	.	PUNCT
ejpam-5397	281	28	numerical	numerical	PROPN
ejpam-5397	281	29	simulation	simulation	PROPN
ejpam-5397	281	30	in	in	ADP
ejpam-5397	281	31	order	order	NOUN
ejpam-5397	281	32	to	to	PART
ejpam-5397	281	33	support	support	VERB
ejpam-5397	281	34	the	the	DET
ejpam-5397	281	35	analytical	analytical	ADJ
ejpam-5397	281	36	finding	finding	NOUN
ejpam-5397	281	37	in	in	ADP
ejpam-5397	281	38	this	this	DET
ejpam-5397	281	39	paper	paper	NOUN
ejpam-5397	281	40	via	via	ADP
ejpam-5397	281	41	the	the	DET
ejpam-5397	281	42	phase	phase	NOUN
ejpam-5397	281	43	portrait	portrait	NOUN
ejpam-5397	281	44	and	and	CCONJ
ejpam-5397	281	45	time	time	NOUN
ejpam-5397	281	46	series[22	series[22	PROPN
ejpam-5397	281	47	]	]	X
ejpam-5397	281	48	,	,	PUNCT
ejpam-5397	281	49	some	some	DET
ejpam-5397	281	50	numerical	numerical	ADJ
ejpam-5397	281	51	simulations	simulation	NOUN
ejpam-5397	281	52	are	be	AUX
ejpam-5397	281	53	performed	perform	VERB
ejpam-5397	281	54	;	;	PUNCT
ejpam-5397	281	55	all	all	DET
ejpam-5397	281	56	the	the	DET
ejpam-5397	281	57	simulations	simulation	NOUN
ejpam-5397	281	58	are	be	AUX
ejpam-5397	281	59	carried	carry	VERB
ejpam-5397	281	60	out	out	ADP
ejpam-5397	281	61	through	through	ADP
ejpam-5397	281	62	runga	runga	PROPN
ejpam-5397	281	63	kutta	kutta	PROPN
ejpam-5397	281	64	method	method	NOUN
ejpam-5397	281	65	of	of	ADP
ejpam-5397	281	66	order	order	NOUN
ejpam-5397	281	67	six	six	NUM
ejpam-5397	281	68	method	method	NOUN
ejpam-5397	281	69	,	,	PUNCT
ejpam-5397	281	70	using	use	VERB
ejpam-5397	281	71	matlab	matlab	PROPN
ejpam-5397	281	72	.	.	PUNCT
ejpam-5397	282	1	first	first	ADV
ejpam-5397	282	2	,	,	PUNCT
ejpam-5397	282	3	we	we	PRON
ejpam-5397	282	4	assume	assume	VERB
ejpam-5397	282	5	two	two	NUM
ejpam-5397	282	6	set	set	NOUN
ejpam-5397	282	7	of	of	ADP
ejpam-5397	282	8	parameter	parameter	NOUN
ejpam-5397	282	9	values	value	NOUN
ejpam-5397	282	10	as	as	SCONJ
ejpam-5397	282	11	given	give	VERB
ejpam-5397	282	12	in	in	ADP
ejpam-5397	282	13	(	(	PUNCT
ejpam-5397	282	14	27	27	NUM
ejpam-5397	282	15	)	)	PUNCT
ejpam-5397	282	16	and	and	CCONJ
ejpam-5397	282	17	(	(	PUNCT
ejpam-5397	282	18	28	28	NUM
ejpam-5397	282	19	)	)	PUNCT
ejpam-5397	282	20	.	.	PUNCT
ejpam-5397	283	1	r1	r1	PROPN
ejpam-5397	283	2	=	=	NOUN
ejpam-5397	283	3	0.5	0.5	NUM
ejpam-5397	283	4	,	,	PUNCT
ejpam-5397	283	5	r2	r2	PROPN
ejpam-5397	283	6	=	=	PUNCT
ejpam-5397	283	7	0.3	0.3	NUM
ejpam-5397	283	8	,	,	PUNCT
ejpam-5397	283	9	r3	r3	PROPN
ejpam-5397	283	10	=	=	SYM
ejpam-5397	283	11	0.15	0.15	NUM
ejpam-5397	283	12	,	,	PUNCT
ejpam-5397	283	13	k	k	X
ejpam-5397	283	14	=	=	SYM
ejpam-5397	283	15	1000	1000	NUM
ejpam-5397	283	16	,	,	PUNCT
ejpam-5397	283	17	β	β	X
ejpam-5397	283	18	=	=	SYM
ejpam-5397	283	19	0.001	0.001	NUM
ejpam-5397	283	20	t	t	NOUN
ejpam-5397	283	21	=	=	SYM
ejpam-5397	283	22	1	1	NUM
ejpam-5397	283	23	,	,	PUNCT
ejpam-5397	283	24	α1	α1	PROPN
ejpam-5397	283	25	=	=	SYM
ejpam-5397	283	26	0.005	0.005	NUM
ejpam-5397	283	27	,	,	PUNCT
ejpam-5397	283	28	α2	α2	NOUN
ejpam-5397	283	29	=	=	SYM
ejpam-5397	283	30	0.004	0.004	NUM
ejpam-5397	283	31	,	,	PUNCT
ejpam-5397	283	32	t1	t1	NOUN
ejpam-5397	283	33	=	=	SYM
ejpam-5397	283	34	1	1	NUM
ejpam-5397	283	35	and	and	CCONJ
ejpam-5397	283	36	t2	t2	NOUN
ejpam-5397	283	37	=	=	SYM
ejpam-5397	283	38	1	1	NUM
ejpam-5397	283	39	(	(	PUNCT
ejpam-5397	283	40	27	27	NUM
ejpam-5397	283	41	)	)	PUNCT
ejpam-5397	283	42	b.	b.	PROPN
ejpam-5397	283	43	b.	b.	PROPN
ejpam-5397	283	44	kamal	kamal	PROPN
ejpam-5397	283	45	,	,	PUNCT
ejpam-5397	283	46	a.	a.	PROPN
ejpam-5397	283	47	n.	n.	PROPN
ejpam-5397	283	48	mustafa	mustafa	PROPN
ejpam-5397	283	49	/	/	SYM
ejpam-5397	283	50	eur	eur	PROPN
ejpam-5397	283	51	.	.	PUNCT
ejpam-5397	284	1	j.	j.	PROPN
ejpam-5397	284	2	pure	pure	PROPN
ejpam-5397	284	3	appl	appl	PROPN
ejpam-5397	284	4	.	.	PROPN
ejpam-5397	284	5	math	math	PROPN
ejpam-5397	284	6	,	,	PUNCT
ejpam-5397	284	7	18	18	NUM
ejpam-5397	284	8	(	(	PUNCT
ejpam-5397	284	9	1	1	NUM
ejpam-5397	284	10	)	)	PUNCT
ejpam-5397	284	11	(	(	PUNCT
ejpam-5397	284	12	2025	2025	NUM
ejpam-5397	284	13	)	)	PUNCT
ejpam-5397	284	14	,	,	PUNCT
ejpam-5397	284	15	5397	5397	NUM
ejpam-5397	284	16	14	14	NUM
ejpam-5397	284	17	of	of	ADP
ejpam-5397	284	18	21	21	NUM
ejpam-5397	284	19	r1	r1	NOUN
ejpam-5397	284	20	=	=	SYM
ejpam-5397	284	21	1.2	1.2	NUM
ejpam-5397	284	22	,	,	PUNCT
ejpam-5397	284	23	r2	r2	PROPN
ejpam-5397	284	24	=	=	SYM
ejpam-5397	284	25	0.9	0.9	NUM
ejpam-5397	284	26	,	,	PUNCT
ejpam-5397	284	27	r3	r3	PROPN
ejpam-5397	284	28	=	=	SYM
ejpam-5397	284	29	0.15	0.15	NUM
ejpam-5397	284	30	,	,	PUNCT
ejpam-5397	284	31	k	k	X
ejpam-5397	284	32	=	=	SYM
ejpam-5397	284	33	1000	1000	NUM
ejpam-5397	284	34	,	,	PUNCT
ejpam-5397	284	35	β	β	X
ejpam-5397	284	36	=	=	SYM
ejpam-5397	284	37	0.001	0.001	NUM
ejpam-5397	284	38	t	t	NOUN
ejpam-5397	284	39	=	=	SYM
ejpam-5397	284	40	1	1	NUM
ejpam-5397	284	41	,	,	PUNCT
ejpam-5397	284	42	α1	α1	PROPN
ejpam-5397	284	43	=	=	SYM
ejpam-5397	284	44	0.005	0.005	NUM
ejpam-5397	284	45	,	,	PUNCT
ejpam-5397	284	46	α2	α2	NOUN
ejpam-5397	284	47	=	=	SYM
ejpam-5397	284	48	0.004	0.004	NUM
ejpam-5397	284	49	,	,	PUNCT
ejpam-5397	284	50	t1	t1	NOUN
ejpam-5397	284	51	=	=	SYM
ejpam-5397	284	52	1	1	NUM
ejpam-5397	284	53	and	and	CCONJ
ejpam-5397	284	54	t2	t2	NOUN
ejpam-5397	284	55	=	=	SYM
ejpam-5397	284	56	1	1	NUM
ejpam-5397	284	57	(	(	PUNCT
ejpam-5397	284	58	28	28	NUM
ejpam-5397	284	59	)	)	PUNCT
ejpam-5397	284	60	the	the	DET
ejpam-5397	284	61	parameter	parameter	NOUN
ejpam-5397	284	62	values	value	NOUN
ejpam-5397	284	63	in	in	ADP
ejpam-5397	284	64	(	(	PUNCT
ejpam-5397	284	65	27	27	NUM
ejpam-5397	284	66	)	)	PUNCT
ejpam-5397	284	67	and	and	CCONJ
ejpam-5397	284	68	(	(	PUNCT
ejpam-5397	284	69	28	28	NUM
ejpam-5397	284	70	)	)	PUNCT
ejpam-5397	284	71	,	,	PUNCT
ejpam-5397	284	72	satisfy	satisfy	VERB
ejpam-5397	284	73	the	the	DET
ejpam-5397	284	74	condition	condition	NOUN
ejpam-5397	284	75	for	for	ADP
ejpam-5397	284	76	global	global	ADJ
ejpam-5397	284	77	stability	stability	NOUN
ejpam-5397	284	78	of	of	ADP
ejpam-5397	284	79	the	the	DET
ejpam-5397	284	80	intermediate	intermediate	ADJ
ejpam-5397	284	81	predator	predator	NOUN
ejpam-5397	284	82	-	-	PUNCT
ejpam-5397	284	83	free	free	ADJ
ejpam-5397	284	84	steady	steady	ADJ
ejpam-5397	284	85	state	state	NOUN
ejpam-5397	284	86	and	and	CCONJ
ejpam-5397	284	87	coexistence	coexistence	VERB
ejpam-5397	284	88	steady	steady	ADJ
ejpam-5397	284	89	state	state	NOUN
ejpam-5397	284	90	,	,	PUNCT
ejpam-5397	284	91	respectively	respectively	ADV
ejpam-5397	284	92	.	.	PUNCT
ejpam-5397	285	1	figure	figure	NOUN
ejpam-5397	285	2	1	1	NUM
ejpam-5397	285	3	:	:	PUNCT
ejpam-5397	285	4	both	both	CCONJ
ejpam-5397	285	5	the	the	DET
ejpam-5397	285	6	time	time	NOUN
ejpam-5397	285	7	series	series	NOUN
ejpam-5397	285	8	and	and	CCONJ
ejpam-5397	285	9	the	the	DET
ejpam-5397	285	10	phase	phase	NOUN
ejpam-5397	285	11	portrait	portrait	NOUN
ejpam-5397	285	12	shows	show	VERB
ejpam-5397	285	13	that	that	SCONJ
ejpam-5397	285	14	model	model	NOUN
ejpam-5397	285	15	1	1	NUM
ejpam-5397	285	16	approaches	approach	NOUN
ejpam-5397	285	17	intermediate	intermediate	ADJ
ejpam-5397	285	18	predator	predator	NOUN
ejpam-5397	285	19	free	free	ADJ
ejpam-5397	285	20	steady	steady	ADJ
ejpam-5397	285	21	state	state	NOUN
ejpam-5397	285	22	,	,	PUNCT
ejpam-5397	285	23	when	when	SCONJ
ejpam-5397	285	24	the	the	DET
ejpam-5397	285	25	parameter	parameter	NOUN
ejpam-5397	285	26	values	value	NOUN
ejpam-5397	285	27	are	be	AUX
ejpam-5397	285	28	as	as	SCONJ
ejpam-5397	285	29	given	give	VERB
ejpam-5397	285	30	in	in	ADP
ejpam-5397	285	31	(	(	PUNCT
ejpam-5397	285	32	27	27	NUM
ejpam-5397	285	33	)	)	PUNCT
ejpam-5397	285	34	.	.	PUNCT
ejpam-5397	286	1	b.	b.	PROPN
ejpam-5397	286	2	b.	b.	PROPN
ejpam-5397	286	3	kamal	kamal	PROPN
ejpam-5397	286	4	,	,	PUNCT
ejpam-5397	286	5	a.	a.	PROPN
ejpam-5397	286	6	n.	n.	PROPN
ejpam-5397	286	7	mustafa	mustafa	PROPN
ejpam-5397	286	8	/	/	SYM
ejpam-5397	286	9	eur	eur	PROPN
ejpam-5397	286	10	.	.	PUNCT
ejpam-5397	287	1	j.	j.	PROPN
ejpam-5397	287	2	pure	pure	PROPN
ejpam-5397	287	3	appl	appl	PROPN
ejpam-5397	287	4	.	.	PROPN
ejpam-5397	287	5	math	math	PROPN
ejpam-5397	287	6	,	,	PUNCT
ejpam-5397	287	7	18	18	NUM
ejpam-5397	287	8	(	(	PUNCT
ejpam-5397	287	9	1	1	NUM
ejpam-5397	287	10	)	)	PUNCT
ejpam-5397	287	11	(	(	PUNCT
ejpam-5397	287	12	2025	2025	NUM
ejpam-5397	287	13	)	)	PUNCT
ejpam-5397	287	14	,	,	PUNCT
ejpam-5397	287	15	5397	5397	NUM
ejpam-5397	287	16	15	15	NUM
ejpam-5397	287	17	of	of	ADP
ejpam-5397	287	18	21	21	NUM
ejpam-5397	287	19	figure	figure	NOUN
ejpam-5397	287	20	2	2	NUM
ejpam-5397	287	21	:	:	PUNCT
ejpam-5397	287	22	both	both	CCONJ
ejpam-5397	287	23	the	the	DET
ejpam-5397	287	24	time	time	NOUN
ejpam-5397	287	25	series	series	NOUN
ejpam-5397	287	26	and	and	CCONJ
ejpam-5397	287	27	the	the	DET
ejpam-5397	287	28	phase	phase	NOUN
ejpam-5397	287	29	portrait	portrait	NOUN
ejpam-5397	287	30	shows	show	VERB
ejpam-5397	287	31	that	that	SCONJ
ejpam-5397	287	32	model	model	NOUN
ejpam-5397	287	33	1	1	NUM
ejpam-5397	287	34	approaches	approach	NOUN
ejpam-5397	287	35	coexistence	coexistence	VERB
ejpam-5397	287	36	steady	steady	ADJ
ejpam-5397	287	37	state	state	NOUN
ejpam-5397	287	38	,	,	PUNCT
ejpam-5397	287	39	when	when	SCONJ
ejpam-5397	287	40	the	the	DET
ejpam-5397	287	41	parameter	parameter	NOUN
ejpam-5397	287	42	values	value	NOUN
ejpam-5397	287	43	are	be	AUX
ejpam-5397	287	44	as	as	SCONJ
ejpam-5397	287	45	given	give	VERB
ejpam-5397	287	46	in	in	ADP
ejpam-5397	287	47	(	(	PUNCT
ejpam-5397	287	48	28	28	NUM
ejpam-5397	287	49	)	)	PUNCT
ejpam-5397	287	50	therefore	therefore	ADV
ejpam-5397	287	51	,	,	PUNCT
ejpam-5397	287	52	fig	fig	NOUN
ejpam-5397	287	53	.	.	NOUN
ejpam-5397	287	54	1	1	NUM
ejpam-5397	287	55	and	and	CCONJ
ejpam-5397	287	56	fig	fig	NOUN
ejpam-5397	287	57	.	.	PUNCT
ejpam-5397	288	1	2	2	NUM
ejpam-5397	288	2	confirm	confirm	VERB
ejpam-5397	288	3	the	the	DET
ejpam-5397	288	4	analytical	analytical	ADJ
ejpam-5397	288	5	results	result	NOUN
ejpam-5397	288	6	regarding	regard	VERB
ejpam-5397	288	7	to	to	ADP
ejpam-5397	288	8	global	global	ADJ
ejpam-5397	288	9	stability	stability	NOUN
ejpam-5397	288	10	of	of	ADP
ejpam-5397	288	11	intermediate	intermediate	ADJ
ejpam-5397	288	12	predator	predator	NOUN
ejpam-5397	288	13	-	-	PUNCT
ejpam-5397	288	14	free	free	ADJ
ejpam-5397	288	15	steady	steady	ADJ
ejpam-5397	288	16	state	state	NOUN
ejpam-5397	288	17	and	and	CCONJ
ejpam-5397	288	18	coexistence	coexistence	VERB
ejpam-5397	288	19	steady	steady	ADJ
ejpam-5397	288	20	state	state	NOUN
ejpam-5397	288	21	,	,	PUNCT
ejpam-5397	288	22	respectively	respectively	ADV
ejpam-5397	288	23	.	.	PUNCT
ejpam-5397	289	1	the	the	DET
ejpam-5397	289	2	critical	critical	ADJ
ejpam-5397	289	3	values	value	NOUN
ejpam-5397	289	4	r3	r3	PROPN
ejpam-5397	289	5	≈	≈	PROPN
ejpam-5397	289	6	0.11	0.11	NUM
ejpam-5397	289	7	and	and	CCONJ
ejpam-5397	289	8	r3	r3	PROPN
ejpam-5397	290	1	≈	≈	PROPN
ejpam-5397	290	2	0.95	0.95	NUM
ejpam-5397	290	3	for	for	ADP
ejpam-5397	290	4	the	the	DET
ejpam-5397	290	5	parameters	parameter	NOUN
ejpam-5397	290	6	given	give	VERB
ejpam-5397	290	7	in	in	ADP
ejpam-5397	290	8	(	(	PUNCT
ejpam-5397	290	9	27	27	NUM
ejpam-5397	290	10	)	)	PUNCT
ejpam-5397	290	11	and	and	CCONJ
ejpam-5397	290	12	(	(	PUNCT
ejpam-5397	290	13	28	28	NUM
ejpam-5397	290	14	)	)	PUNCT
ejpam-5397	290	15	,	,	PUNCT
ejpam-5397	290	16	respectively	respectively	ADV
ejpam-5397	290	17	.	.	PUNCT
ejpam-5397	291	1	first	first	ADV
ejpam-5397	291	2	let	let	VERB
ejpam-5397	291	3	decrease	decrease	VERB
ejpam-5397	291	4	the	the	DET
ejpam-5397	291	5	value	value	NOUN
ejpam-5397	291	6	of	of	ADP
ejpam-5397	291	7	r3	r3	PROPN
ejpam-5397	291	8	to	to	ADP
ejpam-5397	291	9	0.1	0.1	NUM
ejpam-5397	291	10	and	and	CCONJ
ejpam-5397	291	11	fixed	fix	VERB
ejpam-5397	291	12	another	another	DET
ejpam-5397	291	13	parameter	parameter	NOUN
ejpam-5397	291	14	as	as	SCONJ
ejpam-5397	291	15	given	give	VERB
ejpam-5397	291	16	in	in	ADP
ejpam-5397	291	17	(	(	PUNCT
ejpam-5397	291	18	27	27	NUM
ejpam-5397	291	19	)	)	PUNCT
ejpam-5397	291	20	,	,	PUNCT
ejpam-5397	291	21	then	then	ADV
ejpam-5397	291	22	it	it	PRON
ejpam-5397	291	23	is	be	AUX
ejpam-5397	291	24	observed	observe	VERB
ejpam-5397	291	25	that	that	SCONJ
ejpam-5397	291	26	,	,	PUNCT
ejpam-5397	291	27	the	the	DET
ejpam-5397	291	28	dynamics	dynamic	NOUN
ejpam-5397	291	29	of	of	ADP
ejpam-5397	291	30	the	the	DET
ejpam-5397	291	31	system	system	NOUN
ejpam-5397	291	32	(	(	PUNCT
ejpam-5397	291	33	1	1	X
ejpam-5397	291	34	)	)	PUNCT
ejpam-5397	291	35	induced	induce	VERB
ejpam-5397	291	36	a	a	DET
ejpam-5397	291	37	transition	transition	NOUN
ejpam-5397	291	38	from	from	ADP
ejpam-5397	291	39	the	the	DET
ejpam-5397	291	40	a	a	DET
ejpam-5397	291	41	stability	stability	NOUN
ejpam-5397	291	42	situation	situation	NOUN
ejpam-5397	291	43	to	to	ADP
ejpam-5397	291	44	the	the	DET
ejpam-5397	291	45	state	state	NOUN
ejpam-5397	291	46	where	where	SCONJ
ejpam-5397	291	47	the	the	DET
ejpam-5397	291	48	prey	prey	NOUN
ejpam-5397	291	49	species	specie	NOUN
ejpam-5397	291	50	and	and	CCONJ
ejpam-5397	291	51	apex	apex	NOUN
ejpam-5397	291	52	predators	predator	NOUN
ejpam-5397	291	53	oscillate	oscillate	VERB
ejpam-5397	291	54	periodically	periodically	ADV
ejpam-5397	291	55	oscillate	oscillate	VERB
ejpam-5397	291	56	periodically	periodically	ADV
ejpam-5397	291	57	as	as	SCONJ
ejpam-5397	291	58	illustrated	illustrate	VERB
ejpam-5397	291	59	in	in	ADP
ejpam-5397	291	60	fig.3	fig.3	PROPN
ejpam-5397	291	61	.	.	PUNCT
ejpam-5397	292	1	further	far	ADV
ejpam-5397	292	2	,	,	PUNCT
ejpam-5397	292	3	for	for	ADP
ejpam-5397	292	4	a	a	DET
ejpam-5397	292	5	range	range	NOUN
ejpam-5397	292	6	of	of	ADP
ejpam-5397	292	7	values	value	NOUN
ejpam-5397	292	8	r3	r3	PROPN
ejpam-5397	292	9	∈	∈	PROPN
ejpam-5397	292	10	[	[	X
ejpam-5397	292	11	004,0.12	004,0.12	X
ejpam-5397	292	12	]	]	X
ejpam-5397	292	13	,	,	PUNCT
ejpam-5397	292	14	in	in	ADP
ejpam-5397	292	15	fig.4	fig.4	PROPN
ejpam-5397	292	16	,	,	PUNCT
ejpam-5397	292	17	bifurcation	bifurcation	NOUN
ejpam-5397	292	18	diagram	diagram	NOUN
ejpam-5397	292	19	with	with	ADP
ejpam-5397	292	20	respect	respect	NOUN
ejpam-5397	292	21	to	to	ADP
ejpam-5397	292	22	r3	r3	PROPN
ejpam-5397	292	23	is	be	AUX
ejpam-5397	292	24	drawn	draw	VERB
ejpam-5397	292	25	.	.	PUNCT
ejpam-5397	293	1	from	from	ADP
ejpam-5397	293	2	fig	fig	NOUN
ejpam-5397	293	3	.	.	PUNCT
ejpam-5397	294	1	4	4	NUM
ejpam-5397	294	2	,	,	PUNCT
ejpam-5397	294	3	the	the	DET
ejpam-5397	294	4	prey	prey	NOUN
ejpam-5397	294	5	and	and	CCONJ
ejpam-5397	294	6	apex	apex	VERB
ejpam-5397	294	7	predator	predator	NOUN
ejpam-5397	294	8	populations	population	NOUN
ejpam-5397	294	9	show	show	VERB
ejpam-5397	294	10	oscillatory	oscillatory	ADJ
ejpam-5397	294	11	for	for	ADP
ejpam-5397	294	12	the	the	DET
ejpam-5397	294	13	further	further	ADJ
ejpam-5397	294	14	smaller	small	ADJ
ejpam-5397	294	15	values	value	NOUN
ejpam-5397	294	16	of	of	ADP
ejpam-5397	294	17	r3	r3	NOUN
ejpam-5397	294	18	;	;	PUNCT
ejpam-5397	294	19	this	this	PRON
ejpam-5397	294	20	indicates	indicate	VERB
ejpam-5397	294	21	that	that	SCONJ
ejpam-5397	294	22	decreasing	decrease	VERB
ejpam-5397	294	23	r3	r3	PROPN
ejpam-5397	294	24	may	may	AUX
ejpam-5397	294	25	induce	induce	VERB
ejpam-5397	294	26	a	a	DET
ejpam-5397	294	27	transition	transition	NOUN
ejpam-5397	294	28	from	from	ADP
ejpam-5397	294	29	the	the	DET
ejpam-5397	294	30	a	a	DET
ejpam-5397	294	31	stability	stability	NOUN
ejpam-5397	294	32	situation	situation	NOUN
ejpam-5397	294	33	to	to	ADP
ejpam-5397	294	34	the	the	DET
ejpam-5397	294	35	state	state	NOUN
ejpam-5397	294	36	where	where	SCONJ
ejpam-5397	294	37	the	the	DET
ejpam-5397	294	38	populations	population	NOUN
ejpam-5397	294	39	oscillate	oscillate	VERB
ejpam-5397	294	40	periodically	periodically	ADV
ejpam-5397	294	41	.	.	PUNCT
ejpam-5397	295	1	b.	b.	PROPN
ejpam-5397	295	2	b.	b.	PROPN
ejpam-5397	295	3	kamal	kamal	PROPN
ejpam-5397	295	4	,	,	PUNCT
ejpam-5397	295	5	a.	a.	PROPN
ejpam-5397	295	6	n.	n.	PROPN
ejpam-5397	295	7	mustafa	mustafa	PROPN
ejpam-5397	295	8	/	/	SYM
ejpam-5397	295	9	eur	eur	PROPN
ejpam-5397	295	10	.	.	PUNCT
ejpam-5397	296	1	j.	j.	PROPN
ejpam-5397	296	2	pure	pure	PROPN
ejpam-5397	296	3	appl	appl	PROPN
ejpam-5397	296	4	.	.	PROPN
ejpam-5397	296	5	math	math	PROPN
ejpam-5397	296	6	,	,	PUNCT
ejpam-5397	296	7	18	18	NUM
ejpam-5397	296	8	(	(	PUNCT
ejpam-5397	296	9	1	1	NUM
ejpam-5397	296	10	)	)	PUNCT
ejpam-5397	296	11	(	(	PUNCT
ejpam-5397	296	12	2025	2025	NUM
ejpam-5397	296	13	)	)	PUNCT
ejpam-5397	296	14	,	,	PUNCT
ejpam-5397	296	15	5397	5397	NUM
ejpam-5397	296	16	16	16	NUM
ejpam-5397	296	17	of	of	ADP
ejpam-5397	296	18	21	21	NUM
ejpam-5397	296	19	figure	figure	NOUN
ejpam-5397	296	20	3	3	NUM
ejpam-5397	296	21	:	:	PUNCT
ejpam-5397	296	22	both	both	CCONJ
ejpam-5397	296	23	the	the	DET
ejpam-5397	296	24	time	time	NOUN
ejpam-5397	296	25	series	series	NOUN
ejpam-5397	296	26	and	and	CCONJ
ejpam-5397	296	27	the	the	DET
ejpam-5397	296	28	phase	phase	NOUN
ejpam-5397	296	29	portrait	portrait	NOUN
ejpam-5397	296	30	show	show	VERB
ejpam-5397	296	31	periodic	periodic	ADJ
ejpam-5397	296	32	oscillations	oscillation	NOUN
ejpam-5397	296	33	around	around	ADP
ejpam-5397	296	34	intermediate	intermediate	ADJ
ejpam-5397	296	35	predatorsfree	predatorsfree	ADJ
ejpam-5397	296	36	steady	steady	ADJ
ejpam-5397	296	37	state	state	NOUN
ejpam-5397	296	38	,	,	PUNCT
ejpam-5397	296	39	when	when	SCONJ
ejpam-5397	296	40	r3	r3	PROPN
ejpam-5397	296	41	=	=	SYM
ejpam-5397	296	42	0.1	0.1	NUM
ejpam-5397	296	43	and	and	CCONJ
ejpam-5397	296	44	other	other	ADJ
ejpam-5397	296	45	parameter	parameter	NOUN
ejpam-5397	296	46	values	value	NOUN
ejpam-5397	296	47	are	be	AUX
ejpam-5397	296	48	as	as	SCONJ
ejpam-5397	296	49	given	give	VERB
ejpam-5397	296	50	in	in	ADP
ejpam-5397	296	51	(	(	PUNCT
ejpam-5397	296	52	27	27	NUM
ejpam-5397	296	53	)	)	PUNCT
ejpam-5397	296	54	.	.	PUNCT
ejpam-5397	297	1	b.	b.	PROPN
ejpam-5397	297	2	b.	b.	PROPN
ejpam-5397	297	3	kamal	kamal	PROPN
ejpam-5397	297	4	,	,	PUNCT
ejpam-5397	297	5	a.	a.	PROPN
ejpam-5397	297	6	n.	n.	PROPN
ejpam-5397	297	7	mustafa	mustafa	PROPN
ejpam-5397	297	8	/	/	SYM
ejpam-5397	297	9	eur	eur	PROPN
ejpam-5397	297	10	.	.	PUNCT
ejpam-5397	298	1	j.	j.	PROPN
ejpam-5397	298	2	pure	pure	PROPN
ejpam-5397	298	3	appl	appl	PROPN
ejpam-5397	298	4	.	.	PROPN
ejpam-5397	298	5	math	math	PROPN
ejpam-5397	298	6	,	,	PUNCT
ejpam-5397	298	7	18	18	NUM
ejpam-5397	298	8	(	(	PUNCT
ejpam-5397	298	9	1	1	NUM
ejpam-5397	298	10	)	)	PUNCT
ejpam-5397	298	11	(	(	PUNCT
ejpam-5397	298	12	2025	2025	NUM
ejpam-5397	298	13	)	)	PUNCT
ejpam-5397	298	14	,	,	PUNCT
ejpam-5397	298	15	5397	5397	NUM
ejpam-5397	298	16	17	17	NUM
ejpam-5397	298	17	of	of	ADP
ejpam-5397	298	18	21	21	NUM
ejpam-5397	298	19	figure	figure	NOUN
ejpam-5397	298	20	4	4	NUM
ejpam-5397	298	21	:	:	PUNCT
ejpam-5397	298	22	the	the	DET
ejpam-5397	298	23	figure	figure	NOUN
ejpam-5397	298	24	shows	show	VERB
ejpam-5397	298	25	the	the	DET
ejpam-5397	298	26	bifurcation	bifurcation	NOUN
ejpam-5397	298	27	diagrams	diagram	NOUN
ejpam-5397	298	28	of	of	ADP
ejpam-5397	298	29	system	system	NOUN
ejpam-5397	298	30	(	(	PUNCT
ejpam-5397	298	31	1	1	NUM
ejpam-5397	298	32	)	)	PUNCT
ejpam-5397	298	33	,	,	PUNCT
ejpam-5397	298	34	which	which	PRON
ejpam-5397	298	35	indicates	indicate	VERB
ejpam-5397	298	36	the	the	DET
ejpam-5397	298	37	emergence	emergence	NOUN
ejpam-5397	298	38	of	of	ADP
ejpam-5397	298	39	hopf	hopf	ADJ
ejpam-5397	298	40	bifurcations	bifurcation	NOUN
ejpam-5397	298	41	as	as	ADP
ejpam-5397	298	42	parameter	parameter	PROPN
ejpam-5397	298	43	r3	r3	PROPN
ejpam-5397	298	44	decreases	decrease	VERB
ejpam-5397	298	45	,	,	PUNCT
ejpam-5397	298	46	and	and	CCONJ
ejpam-5397	298	47	other	other	ADJ
ejpam-5397	298	48	parameters	parameter	NOUN
ejpam-5397	298	49	are	be	AUX
ejpam-5397	298	50	fixed	fix	VERB
ejpam-5397	298	51	as	as	ADP
ejpam-5397	298	52	in(27	in(27	PROPN
ejpam-5397	298	53	)	)	PUNCT
ejpam-5397	298	54	.	.	PUNCT
ejpam-5397	299	1	again	again	ADV
ejpam-5397	299	2	let	let	AUX
ejpam-5397	299	3	further	far	ADV
ejpam-5397	299	4	decrease	decrease	VERB
ejpam-5397	299	5	the	the	DET
ejpam-5397	299	6	value	value	NOUN
ejpam-5397	299	7	of	of	ADP
ejpam-5397	299	8	r3	r3	PROPN
ejpam-5397	299	9	to	to	ADP
ejpam-5397	299	10	0.07	0.07	NUM
ejpam-5397	299	11	and	and	CCONJ
ejpam-5397	299	12	fixed	fix	VERB
ejpam-5397	299	13	other	other	ADJ
ejpam-5397	299	14	parameters	parameter	NOUN
ejpam-5397	299	15	given	give	VERB
ejpam-5397	299	16	in	in	ADP
ejpam-5397	299	17	(	(	PUNCT
ejpam-5397	299	18	28	28	NUM
ejpam-5397	299	19	)	)	PUNCT
ejpam-5397	299	20	,	,	PUNCT
ejpam-5397	299	21	then	then	ADV
ejpam-5397	299	22	it	it	PRON
ejpam-5397	299	23	is	be	AUX
ejpam-5397	299	24	observed	observe	VERB
ejpam-5397	299	25	that	that	SCONJ
ejpam-5397	299	26	,	,	PUNCT
ejpam-5397	299	27	the	the	DET
ejpam-5397	299	28	dynamics	dynamic	NOUN
ejpam-5397	299	29	of	of	ADP
ejpam-5397	299	30	the	the	DET
ejpam-5397	299	31	system	system	NOUN
ejpam-5397	299	32	(	(	PUNCT
ejpam-5397	299	33	1	1	X
ejpam-5397	299	34	)	)	PUNCT
ejpam-5397	299	35	induced	induce	VERB
ejpam-5397	299	36	a	a	DET
ejpam-5397	299	37	transition	transition	NOUN
ejpam-5397	299	38	from	from	ADP
ejpam-5397	299	39	the	the	DET
ejpam-5397	299	40	a	a	DET
ejpam-5397	299	41	stability	stability	NOUN
ejpam-5397	299	42	situation	situation	NOUN
ejpam-5397	299	43	to	to	ADP
ejpam-5397	299	44	the	the	DET
ejpam-5397	299	45	state	state	NOUN
ejpam-5397	299	46	where	where	SCONJ
ejpam-5397	299	47	the	the	DET
ejpam-5397	299	48	population	population	NOUN
ejpam-5397	299	49	oscillate	oscillate	VERB
ejpam-5397	299	50	periodically	periodically	ADV
ejpam-5397	299	51	oscillate	oscillate	VERB
ejpam-5397	299	52	periodically	periodically	ADV
ejpam-5397	299	53	as	as	SCONJ
ejpam-5397	299	54	illustrated	illustrate	VERB
ejpam-5397	299	55	in	in	ADP
ejpam-5397	299	56	fig.5	fig.5	PROPN
ejpam-5397	299	57	.	.	PUNCT
ejpam-5397	300	1	further	far	ADV
ejpam-5397	300	2	,	,	PUNCT
ejpam-5397	300	3	for	for	ADP
ejpam-5397	300	4	a	a	DET
ejpam-5397	300	5	range	range	NOUN
ejpam-5397	300	6	of	of	ADP
ejpam-5397	300	7	values	value	NOUN
ejpam-5397	300	8	r3	r3	PROPN
ejpam-5397	300	9	∈	∈	PROPN
ejpam-5397	301	1	[	[	X
ejpam-5397	301	2	0	0	NUM
ejpam-5397	301	3	,	,	PUNCT
ejpam-5397	301	4	0.2	0.2	NUM
ejpam-5397	301	5	]	]	PUNCT
ejpam-5397	301	6	,	,	PUNCT
ejpam-5397	301	7	in	in	ADP
ejpam-5397	301	8	fig.6	fig.6	PROPN
ejpam-5397	301	9	,	,	PUNCT
ejpam-5397	301	10	bifurcation	bifurcation	NOUN
ejpam-5397	301	11	diagram	diagram	NOUN
ejpam-5397	301	12	with	with	ADP
ejpam-5397	301	13	respect	respect	NOUN
ejpam-5397	301	14	to	to	ADP
ejpam-5397	301	15	r3	r3	PROPN
ejpam-5397	301	16	is	be	AUX
ejpam-5397	301	17	drawn	draw	VERB
ejpam-5397	301	18	.	.	PUNCT
ejpam-5397	302	1	from	from	ADP
ejpam-5397	302	2	fig	fig	NOUN
ejpam-5397	302	3	.	.	PUNCT
ejpam-5397	303	1	6	6	NUM
ejpam-5397	303	2	,	,	PUNCT
ejpam-5397	303	3	all	all	DET
ejpam-5397	303	4	the	the	DET
ejpam-5397	303	5	species	specie	NOUN
ejpam-5397	303	6	show	show	VERB
ejpam-5397	303	7	oscillatory	oscillatory	ADJ
ejpam-5397	303	8	for	for	ADP
ejpam-5397	303	9	the	the	DET
ejpam-5397	303	10	further	further	ADJ
ejpam-5397	303	11	smaller	small	ADJ
ejpam-5397	303	12	values	value	NOUN
ejpam-5397	303	13	of	of	ADP
ejpam-5397	303	14	r3	r3	NOUN
ejpam-5397	303	15	;	;	PUNCT
ejpam-5397	303	16	this	this	PRON
ejpam-5397	303	17	indicates	indicate	VERB
ejpam-5397	303	18	that	that	SCONJ
ejpam-5397	303	19	decreasing	decrease	VERB
ejpam-5397	303	20	r3	r3	PROPN
ejpam-5397	303	21	may	may	AUX
ejpam-5397	303	22	induce	induce	VERB
ejpam-5397	303	23	a	a	DET
ejpam-5397	303	24	transition	transition	NOUN
ejpam-5397	303	25	from	from	ADP
ejpam-5397	303	26	the	the	DET
ejpam-5397	303	27	a	a	DET
ejpam-5397	303	28	stability	stability	NOUN
ejpam-5397	303	29	situation	situation	NOUN
ejpam-5397	303	30	to	to	ADP
ejpam-5397	303	31	the	the	DET
ejpam-5397	303	32	state	state	NOUN
ejpam-5397	303	33	where	where	SCONJ
ejpam-5397	303	34	the	the	DET
ejpam-5397	303	35	populations	population	NOUN
ejpam-5397	303	36	oscillate	oscillate	VERB
ejpam-5397	303	37	periodically	periodically	ADV
ejpam-5397	303	38	.	.	PUNCT
ejpam-5397	304	1	b.	b.	PROPN
ejpam-5397	304	2	b.	b.	PROPN
ejpam-5397	304	3	kamal	kamal	PROPN
ejpam-5397	304	4	,	,	PUNCT
ejpam-5397	304	5	a.	a.	PROPN
ejpam-5397	304	6	n.	n.	PROPN
ejpam-5397	304	7	mustafa	mustafa	PROPN
ejpam-5397	304	8	/	/	SYM
ejpam-5397	304	9	eur	eur	PROPN
ejpam-5397	304	10	.	.	PUNCT
ejpam-5397	305	1	j.	j.	PROPN
ejpam-5397	305	2	pure	pure	PROPN
ejpam-5397	305	3	appl	appl	PROPN
ejpam-5397	305	4	.	.	PROPN
ejpam-5397	305	5	math	math	PROPN
ejpam-5397	305	6	,	,	PUNCT
ejpam-5397	305	7	18	18	NUM
ejpam-5397	305	8	(	(	PUNCT
ejpam-5397	305	9	1	1	NUM
ejpam-5397	305	10	)	)	PUNCT
ejpam-5397	305	11	(	(	PUNCT
ejpam-5397	305	12	2025	2025	NUM
ejpam-5397	305	13	)	)	PUNCT
ejpam-5397	305	14	,	,	PUNCT
ejpam-5397	305	15	5397	5397	NUM
ejpam-5397	305	16	18	18	NUM
ejpam-5397	305	17	of	of	ADP
ejpam-5397	305	18	21	21	NUM
ejpam-5397	305	19	figure	figure	NOUN
ejpam-5397	305	20	5	5	NUM
ejpam-5397	305	21	:	:	PUNCT
ejpam-5397	305	22	both	both	CCONJ
ejpam-5397	305	23	the	the	DET
ejpam-5397	305	24	time	time	NOUN
ejpam-5397	305	25	series	series	NOUN
ejpam-5397	305	26	and	and	CCONJ
ejpam-5397	305	27	the	the	DET
ejpam-5397	305	28	phase	phase	NOUN
ejpam-5397	305	29	portrait	portrait	NOUN
ejpam-5397	305	30	shows	show	VERB
ejpam-5397	305	31	periodic	periodic	ADJ
ejpam-5397	305	32	oscillations	oscillation	NOUN
ejpam-5397	305	33	around	around	ADP
ejpam-5397	305	34	coexistence	coexistence	NOUN
ejpam-5397	305	35	steady	steady	ADJ
ejpam-5397	305	36	state	state	NOUN
ejpam-5397	305	37	,	,	PUNCT
ejpam-5397	305	38	when	when	SCONJ
ejpam-5397	305	39	r3	r3	PROPN
ejpam-5397	305	40	=	=	SYM
ejpam-5397	305	41	0.07	0.07	NUM
ejpam-5397	305	42	and	and	CCONJ
ejpam-5397	305	43	other	other	ADJ
ejpam-5397	305	44	parameter	parameter	NOUN
ejpam-5397	305	45	values	value	NOUN
ejpam-5397	305	46	are	be	AUX
ejpam-5397	305	47	as	as	SCONJ
ejpam-5397	305	48	given	give	VERB
ejpam-5397	305	49	in	in	ADP
ejpam-5397	305	50	(	(	PUNCT
ejpam-5397	305	51	28	28	NUM
ejpam-5397	305	52	)	)	PUNCT
ejpam-5397	305	53	.	.	PUNCT
ejpam-5397	306	1	note	note	VERB
ejpam-5397	306	2	that	that	DET
ejpam-5397	306	3	fig	fig	NOUN
ejpam-5397	306	4	.	.	PUNCT
ejpam-5397	307	1	3	3	NUM
ejpam-5397	307	2	and	and	CCONJ
ejpam-5397	307	3	fig	fig	NOUN
ejpam-5397	307	4	.	.	PUNCT
ejpam-5397	308	1	5	5	NUM
ejpam-5397	308	2	confirms	confirm	VERB
ejpam-5397	308	3	the	the	DET
ejpam-5397	308	4	analytical	analytical	ADJ
ejpam-5397	308	5	finding	finding	NOUN
ejpam-5397	308	6	in	in	ADP
ejpam-5397	308	7	theorem	theorem	ADJ
ejpam-5397	308	8	6	6	NUM
ejpam-5397	308	9	and	and	CCONJ
ejpam-5397	308	10	theorem	theorem	VERB
ejpam-5397	308	11	7	7	NUM
ejpam-5397	308	12	,	,	PUNCT
ejpam-5397	308	13	respectively	respectively	ADV
ejpam-5397	308	14	.	.	PUNCT
ejpam-5397	309	1	b.	b.	PROPN
ejpam-5397	309	2	b.	b.	PROPN
ejpam-5397	309	3	kamal	kamal	PROPN
ejpam-5397	309	4	,	,	PUNCT
ejpam-5397	309	5	a.	a.	PROPN
ejpam-5397	309	6	n.	n.	PROPN
ejpam-5397	309	7	mustafa	mustafa	PROPN
ejpam-5397	309	8	/	/	SYM
ejpam-5397	309	9	eur	eur	PROPN
ejpam-5397	309	10	.	.	PUNCT
ejpam-5397	310	1	j.	j.	PROPN
ejpam-5397	310	2	pure	pure	PROPN
ejpam-5397	310	3	appl	appl	PROPN
ejpam-5397	310	4	.	.	PROPN
ejpam-5397	310	5	math	math	PROPN
ejpam-5397	310	6	,	,	PUNCT
ejpam-5397	310	7	18	18	NUM
ejpam-5397	310	8	(	(	PUNCT
ejpam-5397	310	9	1	1	NUM
ejpam-5397	310	10	)	)	PUNCT
ejpam-5397	310	11	(	(	PUNCT
ejpam-5397	310	12	2025	2025	NUM
ejpam-5397	310	13	)	)	PUNCT
ejpam-5397	310	14	,	,	PUNCT
ejpam-5397	310	15	5397	5397	NUM
ejpam-5397	310	16	19	19	NUM
ejpam-5397	310	17	of	of	ADP
ejpam-5397	310	18	21	21	NUM
ejpam-5397	310	19	figure	figure	NOUN
ejpam-5397	310	20	6	6	NUM
ejpam-5397	310	21	:	:	PUNCT
ejpam-5397	310	22	the	the	DET
ejpam-5397	310	23	figure	figure	NOUN
ejpam-5397	310	24	shows	show	VERB
ejpam-5397	310	25	the	the	DET
ejpam-5397	310	26	bifurcation	bifurcation	NOUN
ejpam-5397	310	27	diagrams	diagram	NOUN
ejpam-5397	310	28	of	of	ADP
ejpam-5397	310	29	system	system	NOUN
ejpam-5397	310	30	(	(	PUNCT
ejpam-5397	310	31	1	1	NUM
ejpam-5397	310	32	)	)	PUNCT
ejpam-5397	310	33	,	,	PUNCT
ejpam-5397	310	34	which	which	PRON
ejpam-5397	310	35	indicates	indicate	VERB
ejpam-5397	310	36	the	the	DET
ejpam-5397	310	37	emergence	emergence	NOUN
ejpam-5397	310	38	of	of	ADP
ejpam-5397	310	39	hopf	hopf	ADJ
ejpam-5397	310	40	bifurcations	bifurcation	NOUN
ejpam-5397	310	41	as	as	ADP
ejpam-5397	310	42	parameter	parameter	PROPN
ejpam-5397	310	43	r3	r3	PROPN
ejpam-5397	310	44	decreases	decrease	VERB
ejpam-5397	310	45	,	,	PUNCT
ejpam-5397	310	46	and	and	CCONJ
ejpam-5397	310	47	other	other	ADJ
ejpam-5397	310	48	parameters	parameter	NOUN
ejpam-5397	310	49	are	be	AUX
ejpam-5397	310	50	fixed	fix	VERB
ejpam-5397	310	51	as	as	ADP
ejpam-5397	310	52	in(28	in(28	PROPN
ejpam-5397	310	53	)	)	PUNCT
ejpam-5397	310	54	.	.	PUNCT
ejpam-5397	311	1	6	6	X
ejpam-5397	311	2	.	.	X
ejpam-5397	311	3	conclusion	conclusion	NOUN
ejpam-5397	311	4	a	a	DET
ejpam-5397	311	5	three	three	NUM
ejpam-5397	311	6	species	specie	NOUN
ejpam-5397	311	7	food	food	NOUN
ejpam-5397	311	8	-	-	PUNCT
ejpam-5397	311	9	web	web	NOUN
ejpam-5397	311	10	is	be	AUX
ejpam-5397	311	11	considered	consider	VERB
ejpam-5397	311	12	in	in	ADP
ejpam-5397	311	13	this	this	DET
ejpam-5397	311	14	paper	paper	NOUN
ejpam-5397	311	15	,	,	PUNCT
ejpam-5397	311	16	the	the	DET
ejpam-5397	311	17	species	specie	NOUN
ejpam-5397	311	18	are	be	AUX
ejpam-5397	311	19	,	,	PUNCT
ejpam-5397	311	20	prey	prey	NOUN
ejpam-5397	311	21	,	,	PUNCT
ejpam-5397	311	22	intermediate	intermediate	ADJ
ejpam-5397	311	23	predators	predator	NOUN
ejpam-5397	311	24	and	and	CCONJ
ejpam-5397	311	25	apex	apex	NOUN
ejpam-5397	311	26	predators	predator	NOUN
ejpam-5397	311	27	,	,	PUNCT
ejpam-5397	311	28	the	the	DET
ejpam-5397	311	29	intermediate	intermediate	ADJ
ejpam-5397	311	30	predators	predator	NOUN
ejpam-5397	311	31	predating	predate	VERB
ejpam-5397	311	32	the	the	DET
ejpam-5397	311	33	prey	prey	NOUN
ejpam-5397	311	34	with	with	ADP
ejpam-5397	311	35	the	the	DET
ejpam-5397	311	36	holling	holle	VERB
ejpam-5397	311	37	type	type	NOUN
ejpam-5397	311	38	-	-	PUNCT
ejpam-5397	311	39	ii	ii	NOUN
ejpam-5397	311	40	functional	functional	ADJ
ejpam-5397	311	41	response	response	NOUN
ejpam-5397	311	42	,	,	PUNCT
ejpam-5397	311	43	while	while	SCONJ
ejpam-5397	311	44	the	the	DET
ejpam-5397	311	45	apex	apex	NOUN
ejpam-5397	311	46	predators	predator	NOUN
ejpam-5397	311	47	predating	predate	VERB
ejpam-5397	311	48	both	both	CCONJ
ejpam-5397	311	49	prey	prey	NOUN
ejpam-5397	311	50	and	and	CCONJ
ejpam-5397	311	51	intermediate	intermediate	ADJ
ejpam-5397	311	52	predators	predator	NOUN
ejpam-5397	311	53	according	accord	VERB
ejpam-5397	311	54	to	to	ADP
ejpam-5397	311	55	extended	extended	ADJ
ejpam-5397	311	56	holling	holling	NOUN
ejpam-5397	311	57	type	type	NOUN
ejpam-5397	311	58	ii	ii	NOUN
ejpam-5397	311	59	functional	functional	ADJ
ejpam-5397	311	60	response	response	NOUN
ejpam-5397	311	61	for	for	ADP
ejpam-5397	311	62	two	two	NUM
ejpam-5397	311	63	prey	prey	PROPN
ejpam-5397	311	64	species	specie	NOUN
ejpam-5397	311	65	.	.	PUNCT
ejpam-5397	312	1	it	it	PRON
ejpam-5397	312	2	is	be	AUX
ejpam-5397	312	3	proved	prove	VERB
ejpam-5397	312	4	that	that	SCONJ
ejpam-5397	312	5	under	under	ADP
ejpam-5397	312	6	condition	condition	NOUN
ejpam-5397	312	7	(	(	PUNCT
ejpam-5397	312	8	5)and(6	5)and(6	NUM
ejpam-5397	312	9	)	)	PUNCT
ejpam-5397	312	10	,	,	PUNCT
ejpam-5397	312	11	the	the	DET
ejpam-5397	312	12	model	model	NOUN
ejpam-5397	312	13	is	be	AUX
ejpam-5397	312	14	permanent	permanent	ADJ
ejpam-5397	312	15	,	,	PUNCT
ejpam-5397	312	16	it	it	PRON
ejpam-5397	312	17	is	be	AUX
ejpam-5397	312	18	explored	explore	VERB
ejpam-5397	312	19	that	that	SCONJ
ejpam-5397	312	20	the	the	DET
ejpam-5397	312	21	model	model	NOUN
ejpam-5397	312	22	has	have	VERB
ejpam-5397	312	23	biologically	biologically	ADV
ejpam-5397	312	24	possible	possible	ADJ
ejpam-5397	312	25	steady	steady	ADJ
ejpam-5397	312	26	states	state	NOUN
ejpam-5397	312	27	,	,	PUNCT
ejpam-5397	312	28	they	they	PRON
ejpam-5397	312	29	are	be	AUX
ejpam-5397	312	30	s1	s1	NOUN
ejpam-5397	312	31	=	=	SYM
ejpam-5397	312	32	(	(	PUNCT
ejpam-5397	312	33	k	k	X
ejpam-5397	312	34	,	,	PUNCT
ejpam-5397	312	35	0	0	NUM
ejpam-5397	312	36	,	,	PUNCT
ejpam-5397	312	37	0	0	NUM
ejpam-5397	312	38	)	)	PUNCT
ejpam-5397	312	39	,	,	PUNCT
ejpam-5397	312	40	s2	s2	NOUN
ejpam-5397	312	41	=	=	SYM
ejpam-5397	312	42	(	(	PUNCT
ejpam-5397	312	43	s̄	s̄	NOUN
ejpam-5397	312	44	,	,	PUNCT
ejpam-5397	312	45	s̄	s̄	NOUN
ejpam-5397	312	46	,	,	PUNCT
ejpam-5397	312	47	0	0	NUM
ejpam-5397	312	48	)	)	PUNCT
ejpam-5397	312	49	,	,	PUNCT
ejpam-5397	312	50	s3	s3	PROPN
ejpam-5397	312	51	=	=	SYM
ejpam-5397	312	52	(	(	PUNCT
ejpam-5397	312	53	s̄	s̄	NOUN
ejpam-5397	312	54	,	,	PUNCT
ejpam-5397	312	55	0	0	NUM
ejpam-5397	312	56	,	,	PUNCT
ejpam-5397	312	57	s̄	s̄	NOUN
ejpam-5397	312	58	)	)	PUNCT
ejpam-5397	312	59	and	and	CCONJ
ejpam-5397	312	60	s4	s4	PROPN
ejpam-5397	312	61	=	=	SYM
ejpam-5397	312	62	(	(	PUNCT
ejpam-5397	312	63	x∗	x∗	PROPN
ejpam-5397	312	64	,	,	PUNCT
ejpam-5397	312	65	y	y	PROPN
ejpam-5397	312	66	∗	∗	NOUN
ejpam-5397	312	67	,	,	PUNCT
ejpam-5397	312	68	z∗	z∗	NOUN
ejpam-5397	312	69	)	)	PUNCT
ejpam-5397	312	70	,	,	PUNCT
ejpam-5397	312	71	and	and	CCONJ
ejpam-5397	312	72	also	also	ADV
ejpam-5397	312	73	it	it	PRON
ejpam-5397	312	74	is	be	AUX
ejpam-5397	312	75	discovered	discover	VERB
ejpam-5397	312	76	that	that	SCONJ
ejpam-5397	312	77	both	both	PRON
ejpam-5397	312	78	s1	s1	NOUN
ejpam-5397	312	79	=	=	SYM
ejpam-5397	312	80	(	(	PUNCT
ejpam-5397	312	81	k	k	NOUN
ejpam-5397	312	82	,	,	PUNCT
ejpam-5397	312	83	0	0	NUM
ejpam-5397	312	84	,	,	PUNCT
ejpam-5397	312	85	0	0	NUM
ejpam-5397	312	86	)	)	PUNCT
ejpam-5397	312	87	,	,	PUNCT
ejpam-5397	312	88	s2	s2	NOUN
ejpam-5397	312	89	=	=	SYM
ejpam-5397	312	90	(	(	PUNCT
ejpam-5397	312	91	s̄	s̄	NOUN
ejpam-5397	312	92	,	,	PUNCT
ejpam-5397	312	93	s̄	s̄	NOUN
ejpam-5397	312	94	,	,	PUNCT
ejpam-5397	312	95	0	0	NUM
ejpam-5397	312	96	)	)	PUNCT
ejpam-5397	312	97	are	be	AUX
ejpam-5397	312	98	unstable	unstable	ADJ
ejpam-5397	312	99	,	,	PUNCT
ejpam-5397	312	100	but	but	CCONJ
ejpam-5397	312	101	stability	stability	NOUN
ejpam-5397	312	102	as	as	ADV
ejpam-5397	312	103	well	well	ADV
ejpam-5397	312	104	as	as	ADP
ejpam-5397	312	105	global	global	ADJ
ejpam-5397	312	106	stability	stability	NOUN
ejpam-5397	312	107	for	for	ADP
ejpam-5397	312	108	both	both	DET
ejpam-5397	312	109	s3	s3	NOUN
ejpam-5397	312	110	=	=	SYM
ejpam-5397	312	111	(	(	PUNCT
ejpam-5397	312	112	s̄	s̄	NOUN
ejpam-5397	312	113	,	,	PUNCT
ejpam-5397	312	114	0	0	NUM
ejpam-5397	312	115	,	,	PUNCT
ejpam-5397	312	116	s̄	s̄	NOUN
ejpam-5397	312	117	)	)	PUNCT
ejpam-5397	312	118	and	and	CCONJ
ejpam-5397	312	119	s4	s4	PROPN
ejpam-5397	312	120	=	=	SYM
ejpam-5397	312	121	(	(	PUNCT
ejpam-5397	312	122	x∗	x∗	PROPN
ejpam-5397	312	123	,	,	PUNCT
ejpam-5397	312	124	y	y	PROPN
ejpam-5397	312	125	∗	∗	NOUN
ejpam-5397	312	126	,	,	PUNCT
ejpam-5397	312	127	z∗	z∗	NOUN
ejpam-5397	312	128	)	)	PUNCT
ejpam-5397	312	129	based	base	VERB
ejpam-5397	312	130	on	on	ADP
ejpam-5397	312	131	the	the	DET
ejpam-5397	312	132	sample	sample	NOUN
ejpam-5397	312	133	parameters	parameter	NOUN
ejpam-5397	312	134	are	be	AUX
ejpam-5397	312	135	given	give	VERB
ejpam-5397	312	136	.	.	PUNCT
ejpam-5397	313	1	and	and	CCONJ
ejpam-5397	313	2	also	also	ADV
ejpam-5397	313	3	it	it	PRON
ejpam-5397	313	4	is	be	AUX
ejpam-5397	313	5	proved	prove	VERB
ejpam-5397	313	6	that	that	SCONJ
ejpam-5397	313	7	critical	critical	ADJ
ejpam-5397	313	8	values	value	NOUN
ejpam-5397	313	9	r3	r3	PROPN
ejpam-5397	313	10	and	and	CCONJ
ejpam-5397	313	11	r3	r3	PROPN
ejpam-5397	313	12	,	,	PUNCT
ejpam-5397	313	13	make	make	VERB
ejpam-5397	313	14	the	the	DET
ejpam-5397	313	15	occurrence	occurrence	NOUN
ejpam-5397	313	16	of	of	ADP
ejpam-5397	313	17	hopf	hopf	ADJ
ejpam-5397	313	18	-	-	PUNCT
ejpam-5397	313	19	bifurcation	bifurcation	NOUN
ejpam-5397	313	20	of	of	ADP
ejpam-5397	313	21	thee	thee	NOUN
ejpam-5397	313	22	model	model	NOUN
ejpam-5397	313	23	near	near	ADP
ejpam-5397	313	24	s3	s3	PROPN
ejpam-5397	313	25	=	=	SYM
ejpam-5397	313	26	(	(	PUNCT
ejpam-5397	313	27	s̄	s̄	NOUN
ejpam-5397	313	28	,	,	PUNCT
ejpam-5397	313	29	0	0	NUM
ejpam-5397	313	30	,	,	PUNCT
ejpam-5397	313	31	s̄	s̄	NOUN
ejpam-5397	313	32	)	)	PUNCT
ejpam-5397	313	33	and	and	CCONJ
ejpam-5397	313	34	s4	s4	PROPN
ejpam-5397	313	35	=	=	SYM
ejpam-5397	313	36	(	(	PUNCT
ejpam-5397	313	37	x∗	x∗	PROPN
ejpam-5397	313	38	,	,	PUNCT
ejpam-5397	313	39	y	y	PROPN
ejpam-5397	313	40	∗	∗	NOUN
ejpam-5397	313	41	,	,	PUNCT
ejpam-5397	313	42	z∗	z∗	PROPN
ejpam-5397	313	43	)	)	PUNCT
ejpam-5397	313	44	,	,	PUNCT
ejpam-5397	313	45	respectively	respectively	ADV
ejpam-5397	313	46	.	.	PUNCT
ejpam-5397	314	1	the	the	DET
ejpam-5397	314	2	model	model	NOUN
ejpam-5397	314	3	solved	solve	VERB
ejpam-5397	314	4	numerically	numerically	ADV
ejpam-5397	314	5	by	by	ADP
ejpam-5397	314	6	choosing	choose	VERB
ejpam-5397	314	7	suitable	suitable	ADJ
ejpam-5397	314	8	value	value	NOUN
ejpam-5397	314	9	of	of	ADP
ejpam-5397	314	10	the	the	DET
ejpam-5397	314	11	model	model	NOUN
ejpam-5397	314	12	parameters	parameter	NOUN
ejpam-5397	314	13	as	as	SCONJ
ejpam-5397	314	14	given	give	VERB
ejpam-5397	314	15	in	in	ADP
ejpam-5397	314	16	(	(	PUNCT
ejpam-5397	314	17	27	27	NUM
ejpam-5397	314	18	)	)	PUNCT
ejpam-5397	314	19	and	and	CCONJ
ejpam-5397	314	20	(	(	PUNCT
ejpam-5397	314	21	28	28	NUM
ejpam-5397	314	22	)	)	PUNCT
ejpam-5397	314	23	,	,	PUNCT
ejpam-5397	314	24	the	the	DET
ejpam-5397	314	25	numerical	numerical	ADJ
ejpam-5397	314	26	solutions	solution	NOUN
ejpam-5397	314	27	insulated	insulate	VERB
ejpam-5397	314	28	in	in	ADP
ejpam-5397	314	29	fig	fig	NOUN
ejpam-5397	314	30	.	.	PUNCT
ejpam-5397	315	1	1	1	NUM
ejpam-5397	315	2	and	and	CCONJ
ejpam-5397	315	3	fig.2	fig.2	PROPN
ejpam-5397	315	4	,	,	PUNCT
ejpam-5397	315	5	it	it	PRON
ejpam-5397	315	6	is	be	AUX
ejpam-5397	315	7	explained	explain	VERB
ejpam-5397	315	8	that	that	SCONJ
ejpam-5397	315	9	both	both	DET
ejpam-5397	315	10	figures	figure	NOUN
ejpam-5397	315	11	confirms	confirm	VERB
ejpam-5397	315	12	analytical	analytical	ADJ
ejpam-5397	315	13	results	result	NOUN
ejpam-5397	315	14	regarding	regard	VERB
ejpam-5397	315	15	to	to	ADP
ejpam-5397	315	16	the	the	DET
ejpam-5397	315	17	stability	stability	NOUN
ejpam-5397	315	18	of	of	ADP
ejpam-5397	315	19	both	both	DET
ejpam-5397	315	20	s3	s3	NOUN
ejpam-5397	315	21	=	=	SYM
ejpam-5397	315	22	(	(	PUNCT
ejpam-5397	315	23	s̄	s̄	NOUN
ejpam-5397	315	24	,	,	PUNCT
ejpam-5397	315	25	0	0	NUM
ejpam-5397	315	26	,	,	PUNCT
ejpam-5397	315	27	s̄	s̄	NOUN
ejpam-5397	315	28	)	)	PUNCT
ejpam-5397	315	29	and	and	CCONJ
ejpam-5397	315	30	s4	s4	PROPN
ejpam-5397	315	31	=	=	SYM
ejpam-5397	315	32	(	(	PUNCT
ejpam-5397	315	33	x∗	x∗	PROPN
ejpam-5397	315	34	,	,	PUNCT
ejpam-5397	315	35	y	y	PROPN
ejpam-5397	315	36	∗	∗	NOUN
ejpam-5397	315	37	,	,	PUNCT
ejpam-5397	315	38	z∗	z∗	PROPN
ejpam-5397	315	39	)	)	PUNCT
ejpam-5397	315	40	,	,	PUNCT
ejpam-5397	315	41	respectively	respectively	ADV
ejpam-5397	315	42	.	.	PUNCT
ejpam-5397	316	1	also	also	ADV
ejpam-5397	316	2	we	we	PRON
ejpam-5397	316	3	have	have	AUX
ejpam-5397	316	4	shown	show	VERB
ejpam-5397	316	5	that	that	DET
ejpam-5397	316	6	fig	fig	NOUN
ejpam-5397	316	7	3	3	NUM
ejpam-5397	316	8	,	,	PUNCT
ejpam-5397	316	9	and	and	CCONJ
ejpam-5397	316	10	fig.4	fig.4	PROPN
ejpam-5397	316	11	,	,	PUNCT
ejpam-5397	316	12	confirm	confirm	VERB
ejpam-5397	316	13	analytical	analytical	ADJ
ejpam-5397	316	14	results	result	NOUN
ejpam-5397	316	15	regard	regard	VERB
ejpam-5397	316	16	to	to	ADP
ejpam-5397	316	17	hopf	hopf	ADJ
ejpam-5397	316	18	-	-	PUNCT
ejpam-5397	316	19	bifurcation	bifurcation	NOUN
ejpam-5397	316	20	near	near	ADP
ejpam-5397	316	21	s3	s3	PROPN
ejpam-5397	316	22	=	=	SYM
ejpam-5397	316	23	(	(	PUNCT
ejpam-5397	316	24	s̄	s̄	NOUN
ejpam-5397	316	25	,	,	PUNCT
ejpam-5397	316	26	0	0	NUM
ejpam-5397	316	27	,	,	PUNCT
ejpam-5397	316	28	s̄	s̄	NOUN
ejpam-5397	316	29	)	)	PUNCT
ejpam-5397	316	30	and	and	CCONJ
ejpam-5397	316	31	s4	s4	PROPN
ejpam-5397	316	32	=	=	SYM
ejpam-5397	316	33	(	(	PUNCT
ejpam-5397	316	34	x∗	x∗	PROPN
ejpam-5397	316	35	,	,	PUNCT
ejpam-5397	316	36	y	y	PROPN
ejpam-5397	316	37	∗	∗	NOUN
ejpam-5397	316	38	,	,	PUNCT
ejpam-5397	316	39	z∗	z∗	PROPN
ejpam-5397	316	40	)	)	PUNCT
ejpam-5397	316	41	,	,	PUNCT
ejpam-5397	316	42	respectively	respectively	ADV
ejpam-5397	316	43	.	.	PUNCT
ejpam-5397	317	1	because	because	SCONJ
ejpam-5397	317	2	they	they	PRON
ejpam-5397	317	3	show	show	VERB
ejpam-5397	317	4	periodic	periodic	ADJ
ejpam-5397	317	5	solution	solution	NOUN
ejpam-5397	317	6	of	of	ADP
ejpam-5397	317	7	the	the	DET
ejpam-5397	317	8	model	model	NOUN
ejpam-5397	317	9	.	.	PUNCT
ejpam-5397	318	1	b.	b.	PROPN
ejpam-5397	318	2	b.	b.	PROPN
ejpam-5397	318	3	kamal	kamal	PROPN
ejpam-5397	318	4	,	,	PUNCT
ejpam-5397	318	5	a.	a.	PROPN
ejpam-5397	318	6	n.	n.	PROPN
ejpam-5397	318	7	mustafa	mustafa	PROPN
ejpam-5397	318	8	/	/	SYM
ejpam-5397	318	9	eur	eur	PROPN
ejpam-5397	318	10	.	.	PUNCT
ejpam-5397	319	1	j.	j.	PROPN
ejpam-5397	319	2	pure	pure	PROPN
ejpam-5397	319	3	appl	appl	PROPN
ejpam-5397	319	4	.	.	PROPN
ejpam-5397	319	5	math	math	PROPN
ejpam-5397	319	6	,	,	PUNCT
ejpam-5397	319	7	18	18	NUM
ejpam-5397	319	8	(	(	PUNCT
ejpam-5397	319	9	1	1	NUM
ejpam-5397	319	10	)	)	PUNCT
ejpam-5397	319	11	(	(	PUNCT
ejpam-5397	319	12	2025	2025	NUM
ejpam-5397	319	13	)	)	PUNCT
ejpam-5397	319	14	,	,	PUNCT
ejpam-5397	319	15	5397	5397	NUM
ejpam-5397	319	16	20	20	NUM
ejpam-5397	319	17	of	of	ADP
ejpam-5397	319	18	21	21	NUM
ejpam-5397	319	19	references	reference	NOUN
ejpam-5397	319	20	[	[	X
ejpam-5397	319	21	1	1	NUM
ejpam-5397	319	22	]	]	PUNCT
ejpam-5397	319	23	dakhil	dakhil	VERB
ejpam-5397	319	24	r.	r.	PROPN
ejpam-5397	319	25	a.	a.	PROPN
ejpam-5397	319	26	and	and	CCONJ
ejpam-5397	319	27	majeed	majeed	PROPN
ejpam-5397	319	28	s.	s.	PROPN
ejpam-5397	319	29	j.	j.	PROPN
ejpam-5397	319	30	three	three	NUM
ejpam-5397	319	31	-	-	PUNCT
ejpam-5397	319	32	species	species	NOUN
ejpam-5397	319	33	lotka	lotka	PROPN
ejpam-5397	319	34	-	-	PUNCT
ejpam-5397	319	35	volterra	volterra	PROPN
ejpam-5397	319	36	food	food	NOUN
ejpam-5397	319	37	chain	chain	NOUN
ejpam-5397	319	38	model	model	NOUN
ejpam-5397	319	39	with	with	ADP
ejpam-5397	319	40	fear	fear	NOUN
ejpam-5397	319	41	effect	effect	NOUN
ejpam-5397	319	42	and	and	CCONJ
ejpam-5397	319	43	hunting	hunt	VERB
ejpam-5397	319	44	cooperation	cooperation	NOUN
ejpam-5397	319	45	.	.	PUNCT
ejpam-5397	320	1	university	university	NOUN
ejpam-5397	320	2	of	of	ADP
ejpam-5397	320	3	thi	thi	PROPN
ejpam-5397	320	4	-	-	PUNCT
ejpam-5397	320	5	qar	qar	PROPN
ejpam-5397	320	6	journal	journal	NOUN
ejpam-5397	320	7	,	,	PUNCT
ejpam-5397	320	8	18(1	18(1	NUM
ejpam-5397	320	9	)	)	PUNCT
ejpam-5397	320	10	,	,	PUNCT
ejpam-5397	320	11	2023	2023	NUM
ejpam-5397	320	12	.	.	PUNCT
ejpam-5397	321	1	[	[	X
ejpam-5397	321	2	2	2	NUM
ejpam-5397	321	3	]	]	PUNCT
ejpam-5397	321	4	i.	i.	PROPN
ejpam-5397	321	5	al	al	PROPN
ejpam-5397	321	6	-	-	PUNCT
ejpam-5397	321	7	darabsah	darabsah	PROPN
ejpam-5397	321	8	,	,	PUNCT
ejpam-5397	321	9	x.	x.	NOUN
ejpam-5397	321	10	tang	tang	PROPN
ejpam-5397	321	11	,	,	PUNCT
ejpam-5397	321	12	and	and	CCONJ
ejpam-5397	321	13	y.	y.	PROPN
ejpam-5397	321	14	yuan	yuan	PROPN
ejpam-5397	321	15	.	.	PUNCT
ejpam-5397	322	1	a	a	DET
ejpam-5397	322	2	prey	prey	NOUN
ejpam-5397	322	3	-	-	PUNCT
ejpam-5397	322	4	predator	predator	NOUN
ejpam-5397	322	5	model	model	NOUN
ejpam-5397	322	6	with	with	ADP
ejpam-5397	322	7	migrations	migration	NOUN
ejpam-5397	322	8	and	and	CCONJ
ejpam-5397	322	9	delays	delay	NOUN
ejpam-5397	322	10	.	.	PUNCT
ejpam-5397	323	1	discrete	discrete	ADJ
ejpam-5397	323	2	cont	cont	NOUN
ejpam-5397	323	3	.	.	PUNCT
ejpam-5397	324	1	dyn	dyn	NOUN
ejpam-5397	324	2	.	.	PUNCT
ejpam-5397	325	1	syst.-b	syst.-b	PROPN
ejpam-5397	325	2	,	,	PUNCT
ejpam-5397	325	3	21:737–761	21:737–761	NUM
ejpam-5397	325	4	,	,	PUNCT
ejpam-5397	325	5	2016	2016	NUM
ejpam-5397	325	6	.	.	PUNCT
ejpam-5397	326	1	[	[	X
ejpam-5397	326	2	3	3	X
ejpam-5397	326	3	]	]	X
ejpam-5397	326	4	g.	g.	PROPN
ejpam-5397	326	5	e.	e.	PROPN
ejpam-5397	326	6	arif	arif	PROPN
ejpam-5397	326	7	,	,	PUNCT
ejpam-5397	326	8	j.	j.	PROPN
ejpam-5397	326	9	alebraheem	alebraheem	PROPN
ejpam-5397	326	10	,	,	PUNCT
ejpam-5397	326	11	and	and	CCONJ
ejpam-5397	326	12	w.	w.	PROPN
ejpam-5397	326	13	b.	b.	PROPN
ejpam-5397	326	14	yahia	yahia	PROPN
ejpam-5397	326	15	.	.	PUNCT
ejpam-5397	327	1	dynamics	dynamic	NOUN
ejpam-5397	327	2	of	of	ADP
ejpam-5397	327	3	predator	predator	NOUN
ejpam-5397	327	4	-	-	PUNCT
ejpam-5397	327	5	prey	prey	NOUN
ejpam-5397	327	6	model	model	NOUN
ejpam-5397	327	7	under	under	ADP
ejpam-5397	327	8	fluctuation	fluctuation	NOUN
ejpam-5397	327	9	rescue	rescue	NOUN
ejpam-5397	327	10	effect	effect	NOUN
ejpam-5397	327	11	.	.	PUNCT
ejpam-5397	328	1	baghdad	baghdad	PROPN
ejpam-5397	328	2	sci	sci	PROPN
ejpam-5397	328	3	.	.	PUNCT
ejpam-5397	329	1	j.	j.	PROPN
ejpam-5397	329	2	,	,	PUNCT
ejpam-5397	329	3	20:1742–1750	20:1742–1750	NUM
ejpam-5397	329	4	,	,	PUNCT
ejpam-5397	329	5	2023	2023	NUM
ejpam-5397	329	6	.	.	PUNCT
ejpam-5397	330	1	[	[	X
ejpam-5397	330	2	4	4	NUM
ejpam-5397	330	3	]	]	X
ejpam-5397	330	4	b.	b.	PROPN
ejpam-5397	330	5	divya	divya	PROPN
ejpam-5397	330	6	and	and	CCONJ
ejpam-5397	330	7	k.	k.	PROPN
ejpam-5397	330	8	kavitha	kavitha	PROPN
ejpam-5397	330	9	.	.	PUNCT
ejpam-5397	331	1	dynamical	dynamical	ADJ
ejpam-5397	331	2	behavior	behavior	NOUN
ejpam-5397	331	3	of	of	ADP
ejpam-5397	331	4	three	three	NUM
ejpam-5397	331	5	species	specie	NOUN
ejpam-5397	331	6	model	model	NOUN
ejpam-5397	331	7	with	with	ADP
ejpam-5397	331	8	holling	holle	VERB
ejpam-5397	331	9	type	type	NOUN
ejpam-5397	331	10	functional	functional	ADJ
ejpam-5397	331	11	response	response	NOUN
ejpam-5397	331	12	in	in	ADP
ejpam-5397	331	13	the	the	DET
ejpam-5397	331	14	presence	presence	NOUN
ejpam-5397	331	15	of	of	ADP
ejpam-5397	331	16	logistic	logistic	ADJ
ejpam-5397	331	17	growth	growth	NOUN
ejpam-5397	331	18	.	.	PUNCT
ejpam-5397	332	1	j.	j.	PROPN
ejpam-5397	332	2	appl	appl	PROPN
ejpam-5397	332	3	.	.	PUNCT
ejpam-5397	333	1	sci	sci	PROPN
ejpam-5397	333	2	.	.	PUNCT
ejpam-5397	334	1	eng	eng	PROPN
ejpam-5397	334	2	.	.	PROPN
ejpam-5397	334	3	,	,	PUNCT
ejpam-5397	334	4	28(1):101	28(1):101	PROPN
ejpam-5397	334	5	–	–	PUNCT
ejpam-5397	334	6	108	108	NUM
ejpam-5397	334	7	,	,	PUNCT
ejpam-5397	334	8	2025	2025	NUM
ejpam-5397	334	9	.	.	PUNCT
ejpam-5397	335	1	[	[	X
ejpam-5397	335	2	5	5	X
ejpam-5397	335	3	]	]	PUNCT
ejpam-5397	335	4	s.	s.	PROPN
ejpam-5397	335	5	djilali	djilali	PROPN
ejpam-5397	335	6	and	and	CCONJ
ejpam-5397	335	7	b.	b.	PROPN
ejpam-5397	335	8	ghanbari	ghanbari	PROPN
ejpam-5397	335	9	.	.	PUNCT
ejpam-5397	336	1	dynamical	dynamical	ADJ
ejpam-5397	336	2	behavior	behavior	NOUN
ejpam-5397	336	3	of	of	ADP
ejpam-5397	336	4	two	two	NUM
ejpam-5397	336	5	predators	predator	NOUN
ejpam-5397	336	6	-	-	PUNCT
ejpam-5397	336	7	one	one	NUM
ejpam-5397	336	8	prey	prey	NOUN
ejpam-5397	336	9	model	model	NOUN
ejpam-5397	336	10	with	with	ADP
ejpam-5397	336	11	generalized	generalized	ADJ
ejpam-5397	336	12	functional	functional	ADJ
ejpam-5397	336	13	response	response	NOUN
ejpam-5397	336	14	and	and	CCONJ
ejpam-5397	336	15	time	time	NOUN
ejpam-5397	336	16	-	-	PUNCT
ejpam-5397	336	17	fractional	fractional	ADJ
ejpam-5397	336	18	derivative	derivative	NOUN
ejpam-5397	336	19	.	.	PUNCT
ejpam-5397	337	1	adv	adv	PROPN
ejpam-5397	337	2	.	.	PROPN
ejpam-5397	337	3	differ	differ	VERB
ejpam-5397	337	4	.	.	PUNCT
ejpam-5397	338	1	equations	equation	NOUN
ejpam-5397	338	2	,	,	PUNCT
ejpam-5397	338	3	2021(1):1–19	2021(1):1–19	NOUN
ejpam-5397	338	4	,	,	PUNCT
ejpam-5397	338	5	2021	2021	NUM
ejpam-5397	338	6	.	.	PUNCT
ejpam-5397	339	1	[	[	X
ejpam-5397	339	2	6	6	NUM
ejpam-5397	339	3	]	]	PUNCT
ejpam-5397	339	4	m.	m.	PROPN
ejpam-5397	339	5	f.	f.	PROPN
ejpam-5397	339	6	elettreby	elettreby	PROPN
ejpam-5397	339	7	.	.	PUNCT
ejpam-5397	340	1	two	two	NUM
ejpam-5397	340	2	-	-	PUNCT
ejpam-5397	340	3	prey	prey	NOUN
ejpam-5397	340	4	one	one	NUM
ejpam-5397	340	5	-	-	PUNCT
ejpam-5397	340	6	predator	predator	NOUN
ejpam-5397	340	7	model	model	NOUN
ejpam-5397	340	8	.	.	PUNCT
ejpam-5397	341	1	chaos	chaos	NOUN
ejpam-5397	341	2	,	,	PUNCT
ejpam-5397	341	3	solitons	soliton	NOUN
ejpam-5397	341	4	fractals	fractal	NOUN
ejpam-5397	341	5	,	,	PUNCT
ejpam-5397	341	6	39:2018	39:2018	NUM
ejpam-5397	341	7	–	–	PUNCT
ejpam-5397	341	8	2027	2027	NUM
ejpam-5397	341	9	,	,	PUNCT
ejpam-5397	341	10	2009	2009	NUM
ejpam-5397	341	11	.	.	PUNCT
ejpam-5397	342	1	[	[	X
ejpam-5397	342	2	7	7	X
ejpam-5397	342	3	]	]	X
ejpam-5397	342	4	diana	diana	PROPN
ejpam-5397	342	5	a.	a.	PROPN
ejpam-5397	342	6	f.	f.	PROPN
ejpam-5397	342	7	,	,	PUNCT
ejpam-5397	342	8	widowati	widowati	ADV
ejpam-5397	342	9	w.	w.	PROPN
ejpam-5397	342	10	,	,	PUNCT
ejpam-5397	342	11	and	and	CCONJ
ejpam-5397	342	12	tjahjana	tjahjana	PROPN
ejpam-5397	342	13	r.	r.	PROPN
ejpam-5397	342	14	h.	h.	PROPN
ejpam-5397	342	15	stability	stability	PROPN
ejpam-5397	342	16	analysis	analysis	NOUN
ejpam-5397	342	17	of	of	ADP
ejpam-5397	342	18	lotka	lotka	PROPN
ejpam-5397	342	19	-	-	PUNCT
ejpam-5397	342	20	volterra	volterra	PROPN
ejpam-5397	342	21	model	model	NOUN
ejpam-5397	342	22	for	for	ADP
ejpam-5397	342	23	three	three	NUM
ejpam-5397	342	24	species	specie	NOUN
ejpam-5397	342	25	with	with	ADP
ejpam-5397	342	26	disease	disease	NOUN
ejpam-5397	342	27	.	.	PUNCT
ejpam-5397	343	1	aip	aip	PROPN
ejpam-5397	343	2	conference	conference	NOUN
ejpam-5397	343	3	proceedings	proceeding	NOUN
ejpam-5397	343	4	,	,	PUNCT
ejpam-5397	343	5	2738(1	2738(1	NOUN
ejpam-5397	343	6	)	)	PUNCT
ejpam-5397	343	7	,	,	PUNCT
ejpam-5397	343	8	2023	2023	NUM
ejpam-5397	343	9	.	.	PUNCT
ejpam-5397	344	1	[	[	X
ejpam-5397	344	2	8	8	NUM
ejpam-5397	344	3	]	]	PUNCT
ejpam-5397	344	4	a.	a.	NOUN
ejpam-5397	344	5	g.	g.	PROPN
ejpam-5397	344	6	farhan	farhan	PROPN
ejpam-5397	344	7	,	,	PUNCT
ejpam-5397	344	8	n.	n.	PROPN
ejpam-5397	344	9	khalaf	khalaf	PROPN
ejpam-5397	344	10	,	,	PUNCT
ejpam-5397	344	11	and	and	CCONJ
ejpam-5397	344	12	t.	t.	PROPN
ejpam-5397	344	13	aldhlki	aldhlki	NOUN
ejpam-5397	344	14	.	.	PUNCT
ejpam-5397	345	1	dynamical	dynamical	ADJ
ejpam-5397	345	2	behaviors	behavior	NOUN
ejpam-5397	345	3	of	of	ADP
ejpam-5397	345	4	four	four	NUM
ejpam-5397	345	5	-	-	PUNCT
ejpam-5397	345	6	dimensional	dimensional	ADJ
ejpam-5397	345	7	prey	prey	NOUN
ejpam-5397	345	8	-	-	PUNCT
ejpam-5397	345	9	predator	predator	NOUN
ejpam-5397	345	10	model	model	NOUN
ejpam-5397	345	11	.	.	PUNCT
ejpam-5397	346	1	eur	eur	PROPN
ejpam-5397	346	2	.	.	PUNCT
ejpam-5397	347	1	j.	j.	PROPN
ejpam-5397	347	2	pure	pure	PROPN
ejpam-5397	347	3	appl	appl	PROPN
ejpam-5397	347	4	.	.	PUNCT
ejpam-5397	347	5	math	math	PROPN
ejpam-5397	347	6	.	.	PUNCT
ejpam-5397	347	7	,	,	PUNCT
ejpam-5397	347	8	16(2):899–918	16(2):899–918	PROPN
ejpam-5397	347	9	,	,	PUNCT
ejpam-5397	347	10	2023	2023	NUM
ejpam-5397	347	11	.	.	PUNCT
ejpam-5397	348	1	[	[	X
ejpam-5397	348	2	9	9	NUM
ejpam-5397	348	3	]	]	PUNCT
ejpam-5397	348	4	s.	s.	PROPN
ejpam-5397	348	5	fatah	fatah	PROPN
ejpam-5397	348	6	,	,	PUNCT
ejpam-5397	348	7	a.	a.	PROPN
ejpam-5397	348	8	mustafa	mustafa	PROPN
ejpam-5397	348	9	,	,	PUNCT
ejpam-5397	348	10	and	and	CCONJ
ejpam-5397	348	11	a.	a.	NOUN
ejpam-5397	348	12	shilan	shilan	NOUN
ejpam-5397	348	13	.	.	PUNCT
ejpam-5397	349	1	predator	predator	NOUN
ejpam-5397	349	2	and	and	CCONJ
ejpam-5397	349	3	n	n	CCONJ
ejpam-5397	349	4	-	-	PUNCT
ejpam-5397	349	5	classes	class	NOUN
ejpam-5397	349	6	-	-	PUNCT
ejpam-5397	349	7	of	of	ADP
ejpam-5397	349	8	-	-	PUNCT
ejpam-5397	349	9	prey	prey	NOUN
ejpam-5397	349	10	model	model	NOUN
ejpam-5397	349	11	incorporating	incorporate	VERB
ejpam-5397	349	12	extended	extended	ADJ
ejpam-5397	349	13	holling	holling	NOUN
ejpam-5397	349	14	type	type	NOUN
ejpam-5397	349	15	ii	ii	NOUN
ejpam-5397	349	16	functional	functional	ADJ
ejpam-5397	349	17	response	response	NOUN
ejpam-5397	349	18	for	for	ADP
ejpam-5397	349	19	n	n	CCONJ
ejpam-5397	349	20	different	different	ADJ
ejpam-5397	349	21	prey	prey	NOUN
ejpam-5397	349	22	species	specie	NOUN
ejpam-5397	349	23	.	.	PUNCT
ejpam-5397	350	1	aims	aim	VERB
ejpam-5397	350	2	mathematics	mathematic	NOUN
ejpam-5397	350	3	,	,	PUNCT
ejpam-5397	350	4	8:5779–5788	8:5779–5788	NUM
ejpam-5397	350	5	,	,	PUNCT
ejpam-5397	350	6	2022	2022	NUM
ejpam-5397	350	7	.	.	PUNCT
ejpam-5397	351	1	[	[	X
ejpam-5397	351	2	10	10	NUM
ejpam-5397	351	3	]	]	X
ejpam-5397	351	4	u.	u.	PROPN
ejpam-5397	351	5	ghosh	ghosh	PROPN
ejpam-5397	351	6	,	,	PUNCT
ejpam-5397	351	7	s.	s.	PROPN
ejpam-5397	351	8	sarkar	sarkar	PROPN
ejpam-5397	351	9	,	,	PUNCT
ejpam-5397	351	10	and	and	CCONJ
ejpam-5397	351	11	b.	b.	PROPN
ejpam-5397	351	12	mondal	mondal	PROPN
ejpam-5397	351	13	.	.	PUNCT
ejpam-5397	352	1	study	study	NOUN
ejpam-5397	352	2	of	of	ADP
ejpam-5397	352	3	stability	stability	NOUN
ejpam-5397	352	4	and	and	CCONJ
ejpam-5397	352	5	bifurcation	bifurcation	NOUN
ejpam-5397	352	6	of	of	ADP
ejpam-5397	352	7	three	three	NUM
ejpam-5397	352	8	species	specie	NOUN
ejpam-5397	352	9	food	food	NOUN
ejpam-5397	352	10	chain	chain	NOUN
ejpam-5397	352	11	model	model	NOUN
ejpam-5397	352	12	with	with	ADP
ejpam-5397	352	13	nonmonotone	nonmonotone	NOUN
ejpam-5397	352	14	functional	functional	ADJ
ejpam-5397	352	15	response	response	NOUN
ejpam-5397	352	16	.	.	PUNCT
ejpam-5397	353	1	int	int	NOUN
ejpam-5397	353	2	.	.	PUNCT
ejpam-5397	354	1	j.	j.	PROPN
ejpam-5397	354	2	appl	appl	PROPN
ejpam-5397	354	3	.	.	PUNCT
ejpam-5397	355	1	comput	comput	PROPN
ejpam-5397	355	2	.	.	PUNCT
ejpam-5397	356	1	math	math	NOUN
ejpam-5397	356	2	.	.	PUNCT
ejpam-5397	356	3	,	,	PUNCT
ejpam-5397	356	4	7:1–24	7:1–24	NUM
ejpam-5397	356	5	,	,	PUNCT
ejpam-5397	356	6	2021	2021	NUM
ejpam-5397	356	7	.	.	PUNCT
ejpam-5397	357	1	[	[	X
ejpam-5397	357	2	11	11	NUM
ejpam-5397	357	3	]	]	PUNCT
ejpam-5397	357	4	a.	a.	NOUN
ejpam-5397	357	5	hastings	hastings	PROPN
ejpam-5397	357	6	and	and	CCONJ
ejpam-5397	357	7	t.	t.	PROPN
ejpam-5397	357	8	powell	powell	PROPN
ejpam-5397	357	9	.	.	PUNCT
ejpam-5397	358	1	chaos	chaos	NOUN
ejpam-5397	358	2	in	in	ADP
ejpam-5397	358	3	a	a	DET
ejpam-5397	358	4	three	three	NUM
ejpam-5397	358	5	-	-	PUNCT
ejpam-5397	358	6	species	species	NOUN
ejpam-5397	358	7	food	food	NOUN
ejpam-5397	358	8	chain	chain	NOUN
ejpam-5397	358	9	.	.	PUNCT
ejpam-5397	359	1	ecology	ecology	NOUN
ejpam-5397	359	2	,	,	PUNCT
ejpam-5397	359	3	72(3):896	72(3):896	NOUN
ejpam-5397	359	4	–	–	PUNCT
ejpam-5397	359	5	903	903	NUM
ejpam-5397	359	6	,	,	PUNCT
ejpam-5397	359	7	1991	1991	NUM
ejpam-5397	359	8	.	.	PUNCT
ejpam-5397	360	1	[	[	X
ejpam-5397	360	2	12	12	NUM
ejpam-5397	360	3	]	]	X
ejpam-5397	360	4	c.	c.	PROPN
ejpam-5397	360	5	s.	s.	PROPN
ejpam-5397	360	6	holling	holling	PROPN
ejpam-5397	360	7	.	.	PUNCT
ejpam-5397	361	1	some	some	DET
ejpam-5397	361	2	characteristics	characteristic	NOUN
ejpam-5397	361	3	of	of	ADP
ejpam-5397	361	4	simple	simple	ADJ
ejpam-5397	361	5	types	type	NOUN
ejpam-5397	361	6	of	of	ADP
ejpam-5397	361	7	predation	predation	NOUN
ejpam-5397	361	8	and	and	CCONJ
ejpam-5397	361	9	parasitism	parasitism	NOUN
ejpam-5397	361	10	.	.	PUNCT
ejpam-5397	362	1	can	can	AUX
ejpam-5397	362	2	.	.	PUNCT
ejpam-5397	363	1	entomol	entomol	PROPN
ejpam-5397	363	2	.	.	PUNCT
ejpam-5397	363	3	,	,	PUNCT
ejpam-5397	363	4	91(7):385–398	91(7):385–398	PROPN
ejpam-5397	363	5	,	,	PUNCT
ejpam-5397	363	6	1959	1959	NUM
ejpam-5397	363	7	.	.	PUNCT
ejpam-5397	364	1	[	[	X
ejpam-5397	364	2	13	13	NUM
ejpam-5397	364	3	]	]	SYM
ejpam-5397	364	4	danane	danane	NOUN
ejpam-5397	364	5	j.	j.	PROPN
ejpam-5397	364	6	and	and	CCONJ
ejpam-5397	364	7	torres	torre	VERB
ejpam-5397	364	8	d.	d.	PROPN
ejpam-5397	364	9	f.	f.	PROPN
ejpam-5397	364	10	three	three	NUM
ejpam-5397	364	11	-	-	PUNCT
ejpam-5397	364	12	species	species	NOUN
ejpam-5397	364	13	predator	predator	NOUN
ejpam-5397	364	14	-	-	PUNCT
ejpam-5397	364	15	prey	prey	NOUN
ejpam-5397	364	16	stochastic	stochastic	ADJ
ejpam-5397	364	17	delayed	delay	VERB
ejpam-5397	364	18	model	model	NOUN
ejpam-5397	364	19	driven	drive	VERB
ejpam-5397	364	20	by	by	ADP
ejpam-5397	364	21	lévy	lévy	NOUN
ejpam-5397	364	22	jumps	jump	NOUN
ejpam-5397	364	23	and	and	CCONJ
ejpam-5397	364	24	with	with	ADP
ejpam-5397	364	25	cooperation	cooperation	NOUN
ejpam-5397	364	26	among	among	ADP
ejpam-5397	364	27	prey	prey	PROPN
ejpam-5397	364	28	species	specie	NOUN
ejpam-5397	364	29	.	.	PUNCT
ejpam-5397	365	1	mathematics	mathematic	NOUN
ejpam-5397	365	2	,	,	PUNCT
ejpam-5397	365	3	11(7):1595	11(7):1595	NUM
ejpam-5397	365	4	,	,	PUNCT
ejpam-5397	365	5	2023	2023	NUM
ejpam-5397	365	6	.	.	PUNCT
ejpam-5397	366	1	[	[	X
ejpam-5397	366	2	14	14	NUM
ejpam-5397	366	3	]	]	PUNCT
ejpam-5397	366	4	p.	p.	PROPN
ejpam-5397	366	5	jha	jha	PROPN
ejpam-5397	366	6	and	and	CCONJ
ejpam-5397	366	7	s.	s.	PROPN
ejpam-5397	366	8	ghorai	ghorai	PROPN
ejpam-5397	366	9	.	.	PUNCT
ejpam-5397	367	1	stability	stability	NOUN
ejpam-5397	367	2	of	of	ADP
ejpam-5397	367	3	prey	prey	NOUN
ejpam-5397	367	4	-	-	PUNCT
ejpam-5397	367	5	predator	predator	NOUN
ejpam-5397	367	6	model	model	NOUN
ejpam-5397	367	7	with	with	ADP
ejpam-5397	367	8	holling	holle	VERB
ejpam-5397	367	9	type	type	NOUN
ejpam-5397	367	10	response	response	NOUN
ejpam-5397	367	11	function	function	NOUN
ejpam-5397	367	12	and	and	CCONJ
ejpam-5397	367	13	selective	selective	ADJ
ejpam-5397	367	14	harvesting	harvesting	NOUN
ejpam-5397	367	15	.	.	PUNCT
ejpam-5397	368	1	j.	j.	PROPN
ejpam-5397	368	2	appl	appl	PROPN
ejpam-5397	368	3	.	.	PUNCT
ejpam-5397	369	1	comput	comput	PROPN
ejpam-5397	369	2	.	.	PUNCT
ejpam-5397	370	1	math	math	NOUN
ejpam-5397	370	2	.	.	PUNCT
ejpam-5397	370	3	,	,	PUNCT
ejpam-5397	370	4	6(3):1–7	6(3):1–7	NOUN
ejpam-5397	370	5	,	,	PUNCT
ejpam-5397	370	6	2017	2017	NUM
ejpam-5397	370	7	.	.	PUNCT
ejpam-5397	371	1	[	[	X
ejpam-5397	371	2	15	15	NUM
ejpam-5397	371	3	]	]	X
ejpam-5397	371	4	a.	a.	NOUN
ejpam-5397	371	5	khan	khan	PROPN
ejpam-5397	371	6	,	,	PUNCT
ejpam-5397	371	7	s.	s.	PROPN
ejpam-5397	371	8	qureshi	qureshi	PROPN
ejpam-5397	371	9	,	,	PUNCT
ejpam-5397	371	10	and	and	CCONJ
ejpam-5397	371	11	a.	a.	NOUN
ejpam-5397	371	12	alotaibi	alotaibi	NOUN
ejpam-5397	371	13	.	.	PUNCT
ejpam-5397	372	1	bifurcation	bifurcation	NOUN
ejpam-5397	372	2	analysis	analysis	NOUN
ejpam-5397	372	3	of	of	ADP
ejpam-5397	372	4	a	a	DET
ejpam-5397	372	5	three	three	NUM
ejpam-5397	372	6	-	-	PUNCT
ejpam-5397	372	7	species	species	NOUN
ejpam-5397	372	8	discretetime	discretetime	NOUN
ejpam-5397	372	9	predator	predator	NOUN
ejpam-5397	372	10	-	-	PUNCT
ejpam-5397	372	11	prey	prey	NOUN
ejpam-5397	372	12	model	model	NOUN
ejpam-5397	372	13	.	.	PUNCT
ejpam-5397	373	1	alexandria	alexandria	PROPN
ejpam-5397	373	2	eng	eng	PROPN
ejpam-5397	373	3	.	.	PUNCT
ejpam-5397	374	1	j.	j.	PROPN
ejpam-5397	374	2	,	,	PUNCT
ejpam-5397	374	3	61(10):7853–7875	61(10):7853–7875	NUM
ejpam-5397	374	4	,	,	PUNCT
ejpam-5397	374	5	2022	2022	NUM
ejpam-5397	374	6	.	.	PUNCT
ejpam-5397	375	1	[	[	X
ejpam-5397	375	2	16	16	NUM
ejpam-5397	375	3	]	]	PUNCT
ejpam-5397	375	4	a.	a.	NOUN
ejpam-5397	375	5	klebanoff	klebanoff	NOUN
ejpam-5397	375	6	and	and	CCONJ
ejpam-5397	375	7	a.	a.	PROPN
ejpam-5397	375	8	hastings	hastings	PROPN
ejpam-5397	375	9	.	.	PUNCT
ejpam-5397	376	1	chaos	chaos	NOUN
ejpam-5397	376	2	in	in	ADP
ejpam-5397	376	3	three	three	NUM
ejpam-5397	376	4	-	-	PUNCT
ejpam-5397	376	5	species	species	NOUN
ejpam-5397	376	6	food	food	NOUN
ejpam-5397	376	7	chains	chain	NOUN
ejpam-5397	376	8	.	.	PUNCT
ejpam-5397	377	1	j.	j.	PROPN
ejpam-5397	377	2	math	math	PROPN
ejpam-5397	377	3	.	.	PUNCT
ejpam-5397	378	1	biol	biol	PROPN
ejpam-5397	378	2	.	.	PUNCT
ejpam-5397	378	3	,	,	PUNCT
ejpam-5397	378	4	32:427–451	32:427–451	NUM
ejpam-5397	378	5	,	,	PUNCT
ejpam-5397	378	6	1994	1994	NUM
ejpam-5397	378	7	.	.	PUNCT
ejpam-5397	379	1	[	[	X
ejpam-5397	379	2	17	17	NUM
ejpam-5397	379	3	]	]	X
ejpam-5397	379	4	faraj	faraj	PROPN
ejpam-5397	379	5	b.	b.	PROPN
ejpam-5397	379	6	m.	m.	PROPN
ejpam-5397	379	7	,	,	PUNCT
ejpam-5397	379	8	sabir	sabir	PROPN
ejpam-5397	379	9	p.	p.	PROPN
ejpam-5397	379	10	o.	o.	PROPN
ejpam-5397	379	11	,	,	PUNCT
ejpam-5397	379	12	salih	salih	PROPN
ejpam-5397	379	13	d.	d.	PROPN
ejpam-5397	379	14	t.	t.	PROPN
ejpam-5397	379	15	m.	m.	PROPN
ejpam-5397	379	16	,	,	PUNCT
ejpam-5397	379	17	and	and	CCONJ
ejpam-5397	379	18	hilmi	hilmi	PROPN
ejpam-5397	379	19	h.	h.	PROPN
ejpam-5397	379	20	comment	comment	NOUN
ejpam-5397	379	21	on	on	ADP
ejpam-5397	379	22	the	the	DET
ejpam-5397	379	23	paper	paper	NOUN
ejpam-5397	379	24	by	by	ADP
ejpam-5397	379	25	jalal	jalal	PROPN
ejpam-5397	379	26	et	et	PROPN
ejpam-5397	379	27	al	al	PROPN
ejpam-5397	379	28	.	.	PUNCT
ejpam-5397	380	1	[	[	X
ejpam-5397	380	2	chaos	chaos	NOUN
ejpam-5397	380	3	,	,	PUNCT
ejpam-5397	380	4	solitons	soliton	NOUN
ejpam-5397	380	5	and	and	CCONJ
ejpam-5397	380	6	fractals	fractal	NOUN
ejpam-5397	380	7	135	135	NUM
ejpam-5397	380	8	(	(	PUNCT
ejpam-5397	380	9	2020	2020	NUM
ejpam-5397	380	10	)	)	PUNCT
ejpam-5397	380	11	109712	109712	NUM
ejpam-5397	380	12	]	]	PUNCT
ejpam-5397	380	13	.	.	PUNCT
ejpam-5397	381	1	chaos	chaos	NOUN
ejpam-5397	381	2	,	,	PUNCT
ejpam-5397	381	3	solitons	soliton	NOUN
ejpam-5397	381	4	&	&	CCONJ
ejpam-5397	381	5	fractals	fractal	NOUN
ejpam-5397	381	6	,	,	PUNCT
ejpam-5397	381	7	187:115428	187:115428	NUM
ejpam-5397	381	8	,	,	PUNCT
ejpam-5397	381	9	2024	2024	NUM
ejpam-5397	381	10	.	.	PUNCT
ejpam-5397	382	1	[	[	X
ejpam-5397	382	2	18	18	NUM
ejpam-5397	382	3	]	]	X
ejpam-5397	382	4	s.	s.	PROPN
ejpam-5397	382	5	mishra	mishra	PROPN
ejpam-5397	382	6	and	and	CCONJ
ejpam-5397	382	7	r.	r.	PROPN
ejpam-5397	382	8	k.	k.	PROPN
ejpam-5397	382	9	upadhyay	upadhyay	PROPN
ejpam-5397	382	10	.	.	PUNCT
ejpam-5397	382	11	exploring	explore	VERB
ejpam-5397	382	12	the	the	DET
ejpam-5397	382	13	cascading	cascade	VERB
ejpam-5397	382	14	effect	effect	NOUN
ejpam-5397	382	15	of	of	ADP
ejpam-5397	382	16	fear	fear	NOUN
ejpam-5397	382	17	on	on	ADP
ejpam-5397	382	18	the	the	DET
ejpam-5397	382	19	foraging	foraging	PROPN
ejpam-5397	382	20	b.	b.	PROPN
ejpam-5397	382	21	b.	b.	PROPN
ejpam-5397	382	22	kamal	kamal	PROPN
ejpam-5397	382	23	,	,	PUNCT
ejpam-5397	382	24	a.	a.	PROPN
ejpam-5397	382	25	n.	n.	PROPN
ejpam-5397	382	26	mustafa	mustafa	PROPN
ejpam-5397	382	27	/	/	SYM
ejpam-5397	382	28	eur	eur	PROPN
ejpam-5397	382	29	.	.	PUNCT
ejpam-5397	383	1	j.	j.	PROPN
ejpam-5397	383	2	pure	pure	PROPN
ejpam-5397	383	3	appl	appl	PROPN
ejpam-5397	383	4	.	.	PROPN
ejpam-5397	383	5	math	math	PROPN
ejpam-5397	383	6	,	,	PUNCT
ejpam-5397	383	7	18	18	NUM
ejpam-5397	383	8	(	(	PUNCT
ejpam-5397	383	9	1	1	NUM
ejpam-5397	383	10	)	)	PUNCT
ejpam-5397	383	11	(	(	PUNCT
ejpam-5397	383	12	2025	2025	NUM
ejpam-5397	383	13	)	)	PUNCT
ejpam-5397	383	14	,	,	PUNCT
ejpam-5397	383	15	5397	5397	NUM
ejpam-5397	383	16	21	21	NUM
ejpam-5397	383	17	of	of	ADP
ejpam-5397	383	18	21	21	NUM
ejpam-5397	383	19	activities	activity	NOUN
ejpam-5397	383	20	of	of	ADP
ejpam-5397	383	21	prey	prey	NOUN
ejpam-5397	383	22	in	in	ADP
ejpam-5397	383	23	a	a	DET
ejpam-5397	383	24	three	three	NUM
ejpam-5397	383	25	-	-	PUNCT
ejpam-5397	383	26	species	species	NOUN
ejpam-5397	383	27	agroecosystem	agroecosystem	NOUN
ejpam-5397	383	28	.	.	PUNCT
ejpam-5397	384	1	eur	eur	NOUN
ejpam-5397	384	2	.	.	PUNCT
ejpam-5397	385	1	phys	phy	NOUN
ejpam-5397	385	2	.	.	PUNCT
ejpam-5397	386	1	j.	j.	PROPN
ejpam-5397	386	2	plus	plus	PROPN
ejpam-5397	386	3	,	,	PUNCT
ejpam-5397	386	4	136:1–36	136:1–36	NUM
ejpam-5397	386	5	,	,	PUNCT
ejpam-5397	386	6	2021	2021	NUM
ejpam-5397	386	7	.	.	PUNCT
ejpam-5397	387	1	[	[	X
ejpam-5397	387	2	19	19	NUM
ejpam-5397	387	3	]	]	X
ejpam-5397	387	4	soumitra	soumitra	PROPN
ejpam-5397	387	5	p.	p.	PROPN
ejpam-5397	387	6	,	,	PUNCT
ejpam-5397	387	7	tiwari	tiwari	PROPN
ejpam-5397	387	8	p.	p.	PROPN
ejpam-5397	387	9	k.	k.	PROPN
ejpam-5397	387	10	,	,	PUNCT
ejpam-5397	387	11	mishra	mishra	PROPN
ejpam-5397	387	12	a.	a.	PROPN
ejpam-5397	387	13	k.	k.	PROPN
ejpam-5397	387	14	,	,	PUNCT
ejpam-5397	387	15	and	and	CCONJ
ejpam-5397	387	16	wang	wang	PROPN
ejpam-5397	387	17	h.	h.	PROPN
ejpam-5397	387	18	fear	fear	PROPN
ejpam-5397	387	19	effect	effect	NOUN
ejpam-5397	387	20	in	in	ADP
ejpam-5397	387	21	a	a	DET
ejpam-5397	387	22	threespecies	threespecie	NOUN
ejpam-5397	387	23	food	food	NOUN
ejpam-5397	387	24	chain	chain	NOUN
ejpam-5397	387	25	model	model	NOUN
ejpam-5397	387	26	with	with	ADP
ejpam-5397	387	27	generalist	generalist	ADJ
ejpam-5397	387	28	predator	predator	NOUN
ejpam-5397	387	29	.	.	PUNCT
ejpam-5397	388	1	mathematical	mathematical	ADJ
ejpam-5397	388	2	biosciences	bioscience	NOUN
ejpam-5397	388	3	and	and	CCONJ
ejpam-5397	388	4	engineering	engineering	NOUN
ejpam-5397	388	5	,	,	PUNCT
ejpam-5397	388	6	21:1–33	21:1–33	NUM
ejpam-5397	388	7	,	,	PUNCT
ejpam-5397	388	8	2023	2023	NUM
ejpam-5397	388	9	.	.	PUNCT
ejpam-5397	389	1	[	[	X
ejpam-5397	389	2	20	20	NUM
ejpam-5397	389	3	]	]	X
ejpam-5397	389	4	khan	khan	PROPN
ejpam-5397	389	5	a.	a.	PROPN
ejpam-5397	389	6	q.	q.	PROPN
ejpam-5397	389	7	and	and	CCONJ
ejpam-5397	389	8	kazmi	kazmi	PROPN
ejpam-5397	389	9	s.	s.	PROPN
ejpam-5397	389	10	s.	s.	PROPN
ejpam-5397	389	11	bifurcations	bifurcations	PROPN
ejpam-5397	389	12	of	of	ADP
ejpam-5397	389	13	a	a	DET
ejpam-5397	389	14	three	three	NUM
ejpam-5397	389	15	-	-	PUNCT
ejpam-5397	389	16	species	species	NOUN
ejpam-5397	389	17	prey	prey	NOUN
ejpam-5397	389	18	-	-	PUNCT
ejpam-5397	389	19	predator	predator	NOUN
ejpam-5397	389	20	system	system	NOUN
ejpam-5397	389	21	with	with	ADP
ejpam-5397	389	22	scavenger	scavenger	NOUN
ejpam-5397	389	23	.	.	PUNCT
ejpam-5397	390	1	ain	ain	PROPN
ejpam-5397	390	2	shams	sham	VERB
ejpam-5397	390	3	engineering	engineering	NOUN
ejpam-5397	390	4	journal	journal	NOUN
ejpam-5397	390	5	,	,	PUNCT
ejpam-5397	390	6	14(11):102514	14(11):102514	NUM
ejpam-5397	390	7	,	,	PUNCT
ejpam-5397	390	8	2022	2022	NUM
ejpam-5397	390	9	.	.	PUNCT
ejpam-5397	391	1	[	[	X
ejpam-5397	391	2	21	21	NUM
ejpam-5397	391	3	]	]	X
ejpam-5397	391	4	khan	khan	PROPN
ejpam-5397	391	5	a.	a.	PROPN
ejpam-5397	391	6	q.	q.	PROPN
ejpam-5397	391	7	and	and	CCONJ
ejpam-5397	391	8	kazmi	kazmi	PROPN
ejpam-5397	391	9	s.	s.	PROPN
ejpam-5397	391	10	s.	s.	PROPN
ejpam-5397	392	1	dynamical	dynamical	ADJ
ejpam-5397	392	2	analysis	analysis	NOUN
ejpam-5397	392	3	of	of	ADP
ejpam-5397	392	4	a	a	DET
ejpam-5397	392	5	three	three	NUM
ejpam-5397	392	6	-	-	PUNCT
ejpam-5397	392	7	species	species	NOUN
ejpam-5397	392	8	discrete	discrete	ADJ
ejpam-5397	392	9	biological	biological	ADJ
ejpam-5397	392	10	system	system	NOUN
ejpam-5397	392	11	with	with	ADP
ejpam-5397	392	12	scavenger	scavenger	NOUN
ejpam-5397	392	13	.	.	PUNCT
ejpam-5397	393	1	journal	journal	NOUN
ejpam-5397	393	2	of	of	ADP
ejpam-5397	393	3	computational	computational	ADJ
ejpam-5397	393	4	and	and	CCONJ
ejpam-5397	393	5	applied	applied	ADJ
ejpam-5397	393	6	mathematics	mathematic	NOUN
ejpam-5397	393	7	,	,	PUNCT
ejpam-5397	393	8	440:115644	440:115644	NUM
ejpam-5397	393	9	,	,	PUNCT
ejpam-5397	393	10	2024	2024	NUM
ejpam-5397	393	11	.	.	PUNCT
ejpam-5397	394	1	[	[	X
ejpam-5397	394	2	22	22	NUM
ejpam-5397	394	3	]	]	PUNCT
ejpam-5397	394	4	sk	sk	PROPN
ejpam-5397	394	5	n.	n.	PROPN
ejpam-5397	394	6	tiwari	tiwari	PROPN
ejpam-5397	394	7	and	and	CCONJ
ejpam-5397	394	8	p.	p.	PROPN
ejpam-5397	394	9	k.	k.	PROPN
ejpam-5397	395	1	pal	pal	PROPN
ejpam-5397	395	2	.	.	PUNCT
ejpam-5397	396	1	a	a	DET
ejpam-5397	396	2	delay	delay	NOUN
ejpam-5397	396	3	nonautonomous	nonautonomous	ADJ
ejpam-5397	396	4	model	model	NOUN
ejpam-5397	396	5	for	for	ADP
ejpam-5397	396	6	the	the	DET
ejpam-5397	396	7	impacts	impact	NOUN
ejpam-5397	396	8	of	of	ADP
ejpam-5397	396	9	fear	fear	NOUN
ejpam-5397	396	10	and	and	CCONJ
ejpam-5397	396	11	refuge	refuge	NOUN
ejpam-5397	396	12	in	in	ADP
ejpam-5397	396	13	a	a	DET
ejpam-5397	396	14	three	three	NUM
ejpam-5397	396	15	-	-	PUNCT
ejpam-5397	396	16	species	species	NOUN
ejpam-5397	396	17	food	food	NOUN
ejpam-5397	396	18	chain	chain	NOUN
ejpam-5397	396	19	model	model	NOUN
ejpam-5397	396	20	with	with	ADP
ejpam-5397	396	21	hunting	hunt	VERB
ejpam-5397	396	22	cooperation	cooperation	NOUN
ejpam-5397	396	23	.	.	PUNCT
ejpam-5397	397	1	mathematics	mathematic	NOUN
ejpam-5397	397	2	and	and	CCONJ
ejpam-5397	397	3	computers	computer	NOUN
ejpam-5397	397	4	in	in	ADP
ejpam-5397	397	5	simulation	simulation	NOUN
ejpam-5397	397	6	,	,	PUNCT
ejpam-5397	397	7	192:136–166	192:136–166	NUM
ejpam-5397	397	8	,	,	PUNCT
ejpam-5397	397	9	2022	2022	NUM
ejpam-5397	397	10	.	.	PUNCT