id	sid	tid	token	lemma	pos
ejpam-4716	1	1	european	european	PROPN
ejpam-4716	1	2	journal	journal	PROPN
ejpam-4716	1	3	of	of	ADP
ejpam-4716	1	4	pure	pure	ADJ
ejpam-4716	1	5	and	and	CCONJ
ejpam-4716	1	6	applied	apply	VERB
ejpam-4716	1	7	mathematics	mathematic	NOUN
ejpam-4716	1	8	vol	vol	NOUN
ejpam-4716	1	9	.	.	PUNCT
ejpam-4716	2	1	16	16	NUM
ejpam-4716	2	2	,	,	PUNCT
ejpam-4716	2	3	no	no	INTJ
ejpam-4716	2	4	.	.	NOUN
ejpam-4716	2	5	2	2	NUM
ejpam-4716	2	6	,	,	PUNCT
ejpam-4716	2	7	2023	2023	NUM
ejpam-4716	2	8	,	,	PUNCT
ejpam-4716	2	9	899	899	NUM
ejpam-4716	2	10	-	-	SYM
ejpam-4716	2	11	918	918	NUM
ejpam-4716	2	12	issn	issn	PROPN
ejpam-4716	2	13	1307	1307	NUM
ejpam-4716	2	14	-	-	SYM
ejpam-4716	2	15	5543	5543	NUM
ejpam-4716	2	16	–	–	PUNCT
ejpam-4716	2	17	ejpam.com	ejpam.com	X
ejpam-4716	2	18	published	publish	VERB
ejpam-4716	2	19	by	by	ADP
ejpam-4716	2	20	new	new	PROPN
ejpam-4716	2	21	york	york	PROPN
ejpam-4716	2	22	business	business	PROPN
ejpam-4716	2	23	global	global	ADJ
ejpam-4716	2	24	dynamical	dynamical	ADJ
ejpam-4716	2	25	behaviors	behavior	NOUN
ejpam-4716	2	26	of	of	ADP
ejpam-4716	2	27	four	four	NUM
ejpam-4716	2	28	-	-	PUNCT
ejpam-4716	2	29	dimensional	dimensional	ADJ
ejpam-4716	2	30	prey	prey	NOUN
ejpam-4716	2	31	-	-	PUNCT
ejpam-4716	2	32	predator	predator	NOUN
ejpam-4716	2	33	model	model	NOUN
ejpam-4716	2	34	a.	a.	PROPN
ejpam-4716	2	35	g.	g.	PROPN
ejpam-4716	2	36	farhan1,∗	farhan1,∗	PROPN
ejpam-4716	2	37	,	,	PUNCT
ejpam-4716	2	38	nihad	nihad	VERB
ejpam-4716	2	39	sh	sh	PROPN
ejpam-4716	2	40	.	.	PROPN
ejpam-4716	2	41	khalaf2	khalaf2	PROPN
ejpam-4716	3	1	,	,	PUNCT
ejpam-4716	3	2	talat	talat	PROPN
ejpam-4716	3	3	j.	j.	PROPN
ejpam-4716	3	4	aldhlki	aldhlki	PROPN
ejpam-4716	3	5	1	1	NUM
ejpam-4716	3	6	1	1	NUM
ejpam-4716	3	7	department	department	NOUN
ejpam-4716	3	8	of	of	ADP
ejpam-4716	3	9	mathematics	mathematic	NOUN
ejpam-4716	3	10	,	,	PUNCT
ejpam-4716	3	11	college	college	NOUN
ejpam-4716	3	12	of	of	ADP
ejpam-4716	3	13	basic	basic	ADJ
ejpam-4716	3	14	education	education	NOUN
ejpam-4716	3	15	,	,	PUNCT
ejpam-4716	3	16	mustansiriyah	mustansiriyah	NOUN
ejpam-4716	3	17	university	university	NOUN
ejpam-4716	3	18	,	,	PUNCT
ejpam-4716	3	19	baghdad	baghdad	PROPN
ejpam-4716	3	20	,	,	PUNCT
ejpam-4716	3	21	iraq	iraq	PROPN
ejpam-4716	3	22	2	2	NUM
ejpam-4716	3	23	department	department	NOUN
ejpam-4716	3	24	of	of	ADP
ejpam-4716	3	25	mathematics	mathematic	NOUN
ejpam-4716	3	26	,	,	PUNCT
ejpam-4716	3	27	college	college	NOUN
ejpam-4716	3	28	of	of	ADP
ejpam-4716	3	29	education	education	NOUN
ejpam-4716	3	30	for	for	ADP
ejpam-4716	3	31	women	woman	NOUN
ejpam-4716	3	32	,	,	PUNCT
ejpam-4716	3	33	tikrit	tikrit	NOUN
ejpam-4716	3	34	university	university	NOUN
ejpam-4716	3	35	,	,	PUNCT
ejpam-4716	3	36	tikrit	tikrit	NOUN
ejpam-4716	3	37	,	,	PUNCT
ejpam-4716	3	38	iraq	iraq	PROPN
ejpam-4716	3	39	abstract	abstract	NOUN
ejpam-4716	3	40	.	.	PUNCT
ejpam-4716	4	1	in	in	ADP
ejpam-4716	4	2	this	this	DET
ejpam-4716	4	3	paper	paper	NOUN
ejpam-4716	4	4	,	,	PUNCT
ejpam-4716	4	5	we	we	PRON
ejpam-4716	4	6	study	study	VERB
ejpam-4716	4	7	the	the	DET
ejpam-4716	4	8	dynamic	dynamic	ADJ
ejpam-4716	4	9	behavior	behavior	NOUN
ejpam-4716	4	10	of	of	ADP
ejpam-4716	4	11	a	a	DET
ejpam-4716	4	12	four	four	NUM
ejpam-4716	4	13	-	-	PUNCT
ejpam-4716	4	14	dimensional	dimensional	ADJ
ejpam-4716	4	15	prey	prey	NOUN
ejpam-4716	4	16	-	-	PUNCT
ejpam-4716	4	17	predator	predator	NOUN
ejpam-4716	4	18	suggested	suggest	VERB
ejpam-4716	4	19	model	model	NOUN
ejpam-4716	4	20	of	of	ADP
ejpam-4716	4	21	four	four	NUM
ejpam-4716	4	22	species	specie	NOUN
ejpam-4716	4	23	.	.	PUNCT
ejpam-4716	5	1	the	the	DET
ejpam-4716	5	2	four	four	NUM
ejpam-4716	5	3	species	specie	NOUN
ejpam-4716	5	4	are	be	AUX
ejpam-4716	5	5	two	two	NUM
ejpam-4716	5	6	prey	prey	NOUN
ejpam-4716	5	7	and	and	CCONJ
ejpam-4716	5	8	two	two	NUM
ejpam-4716	5	9	predator	predator	NOUN
ejpam-4716	5	10	species	specie	NOUN
ejpam-4716	5	11	,	,	PUNCT
ejpam-4716	5	12	each	each	PRON
ejpam-4716	5	13	of	of	ADP
ejpam-4716	5	14	them	they	PRON
ejpam-4716	5	15	grows	grow	VERB
ejpam-4716	5	16	logistically	logistically	ADV
ejpam-4716	5	17	.	.	PUNCT
ejpam-4716	6	1	the	the	DET
ejpam-4716	6	2	two	two	NUM
ejpam-4716	6	3	prey	prey	NOUN
ejpam-4716	6	4	live	live	VERB
ejpam-4716	6	5	in	in	ADP
ejpam-4716	6	6	diverse	diverse	ADJ
ejpam-4716	6	7	habitats	habitat	NOUN
ejpam-4716	6	8	and	and	CCONJ
ejpam-4716	6	9	have	have	VERB
ejpam-4716	6	10	the	the	DET
ejpam-4716	6	11	ability	ability	NOUN
ejpam-4716	6	12	of	of	ADP
ejpam-4716	6	13	group	group	NOUN
ejpam-4716	6	14	defense	defense	NOUN
ejpam-4716	6	15	.	.	PUNCT
ejpam-4716	7	1	in	in	ADP
ejpam-4716	7	2	the	the	DET
ejpam-4716	7	3	mentioned	mention	VERB
ejpam-4716	7	4	model	model	NOUN
ejpam-4716	7	5	,	,	PUNCT
ejpam-4716	7	6	one	one	NUM
ejpam-4716	7	7	predator	predator	NOUN
ejpam-4716	7	8	feeds	feed	VERB
ejpam-4716	7	9	on	on	ADP
ejpam-4716	7	10	the	the	DET
ejpam-4716	7	11	two	two	NUM
ejpam-4716	7	12	prey	prey	NOUN
ejpam-4716	7	13	,	,	PUNCT
ejpam-4716	7	14	the	the	DET
ejpam-4716	7	15	top	top	ADJ
ejpam-4716	7	16	predator	predator	NOUN
ejpam-4716	7	17	feeds	feed	VERB
ejpam-4716	7	18	on	on	ADP
ejpam-4716	7	19	other	other	ADJ
ejpam-4716	7	20	three	three	NUM
ejpam-4716	7	21	species	specie	NOUN
ejpam-4716	7	22	.	.	PUNCT
ejpam-4716	8	1	the	the	DET
ejpam-4716	8	2	existents	existent	NOUN
ejpam-4716	8	3	and	and	CCONJ
ejpam-4716	8	4	,	,	PUNCT
ejpam-4716	8	5	the	the	DET
ejpam-4716	8	6	boundedness	boundedness	NOUN
ejpam-4716	8	7	of	of	ADP
ejpam-4716	8	8	the	the	DET
ejpam-4716	8	9	positive	positive	ADJ
ejpam-4716	8	10	solution	solution	NOUN
ejpam-4716	8	11	,	,	PUNCT
ejpam-4716	8	12	the	the	DET
ejpam-4716	8	13	existence	existence	NOUN
ejpam-4716	8	14	and	and	CCONJ
ejpam-4716	8	15	the	the	DET
ejpam-4716	8	16	local	local	ADJ
ejpam-4716	8	17	stability	stability	NOUN
ejpam-4716	8	18	of	of	ADP
ejpam-4716	8	19	all	all	DET
ejpam-4716	8	20	possible	possible	ADJ
ejpam-4716	8	21	equilibrium	equilibrium	NOUN
ejpam-4716	8	22	points	point	NOUN
ejpam-4716	8	23	,	,	PUNCT
ejpam-4716	8	24	of	of	ADP
ejpam-4716	8	25	the	the	DET
ejpam-4716	8	26	model	model	NOUN
ejpam-4716	8	27	are	be	AUX
ejpam-4716	8	28	investigated	investigate	VERB
ejpam-4716	8	29	.	.	PUNCT
ejpam-4716	9	1	the	the	DET
ejpam-4716	9	2	model	model	NOUN
ejpam-4716	9	3	has	have	VERB
ejpam-4716	9	4	seven	seven	NUM
ejpam-4716	9	5	equilibrium	equilibrium	NOUN
ejpam-4716	9	6	points	point	NOUN
ejpam-4716	9	7	at	at	ADP
ejpam-4716	9	8	most	most	ADJ
ejpam-4716	9	9	,	,	PUNCT
ejpam-4716	9	10	four	four	NUM
ejpam-4716	9	11	of	of	ADP
ejpam-4716	9	12	them	they	PRON
ejpam-4716	9	13	always	always	ADV
ejpam-4716	9	14	exist	exist	VERB
ejpam-4716	9	15	and	and	CCONJ
ejpam-4716	9	16	the	the	DET
ejpam-4716	9	17	others	other	NOUN
ejpam-4716	9	18	exist	exist	VERB
ejpam-4716	9	19	under	under	ADP
ejpam-4716	9	20	certain	certain	ADJ
ejpam-4716	9	21	conditions	condition	NOUN
ejpam-4716	9	22	.	.	PUNCT
ejpam-4716	10	1	three	three	NUM
ejpam-4716	10	2	equilibrium	equilibrium	NOUN
ejpam-4716	10	3	points	point	NOUN
ejpam-4716	10	4	are	be	AUX
ejpam-4716	10	5	not	not	PART
ejpam-4716	10	6	stable	stable	ADJ
ejpam-4716	10	7	while	while	SCONJ
ejpam-4716	10	8	the	the	DET
ejpam-4716	10	9	others	other	NOUN
ejpam-4716	10	10	are	be	AUX
ejpam-4716	10	11	locally	locally	ADV
ejpam-4716	10	12	asymptotically	asymptotically	ADV
ejpam-4716	10	13	stable	stable	ADJ
ejpam-4716	10	14	,	,	PUNCT
ejpam-4716	10	15	under	under	ADP
ejpam-4716	10	16	given	give	VERB
ejpam-4716	10	17	conditions	condition	NOUN
ejpam-4716	10	18	.	.	PUNCT
ejpam-4716	11	1	for	for	ADP
ejpam-4716	11	2	the	the	DET
ejpam-4716	11	3	coexistence	coexistence	NOUN
ejpam-4716	11	4	point	point	NOUN
ejpam-4716	11	5	,	,	PUNCT
ejpam-4716	11	6	a	a	DET
ejpam-4716	11	7	basin	basin	NOUN
ejpam-4716	11	8	of	of	ADP
ejpam-4716	11	9	attraction	attraction	NOUN
ejpam-4716	11	10	for	for	ADP
ejpam-4716	11	11	it	it	PRON
ejpam-4716	11	12	has	have	AUX
ejpam-4716	11	13	been	be	AUX
ejpam-4716	11	14	found	find	VERB
ejpam-4716	11	15	.	.	PUNCT
ejpam-4716	12	1	the	the	DET
ejpam-4716	12	2	steady	steady	ADJ
ejpam-4716	12	3	-	-	PUNCT
ejpam-4716	12	4	state	state	NOUN
ejpam-4716	12	5	bifurcation	bifurcation	NOUN
ejpam-4716	12	6	relative	relative	ADJ
ejpam-4716	12	7	to	to	ADP
ejpam-4716	12	8	the	the	DET
ejpam-4716	12	9	mortality	mortality	NOUN
ejpam-4716	12	10	rate	rate	NOUN
ejpam-4716	12	11	of	of	ADP
ejpam-4716	12	12	the	the	DET
ejpam-4716	12	13	predators	predator	NOUN
ejpam-4716	12	14	in	in	ADP
ejpam-4716	12	15	the	the	DET
ejpam-4716	12	16	neighborhood	neighborhood	NOUN
ejpam-4716	12	17	of	of	ADP
ejpam-4716	12	18	three	three	NUM
ejpam-4716	12	19	of	of	ADP
ejpam-4716	12	20	the	the	DET
ejpam-4716	12	21	equilibrium	equilibrium	NOUN
ejpam-4716	12	22	points	point	NOUN
ejpam-4716	12	23	and	and	CCONJ
ejpam-4716	12	24	the	the	DET
ejpam-4716	12	25	hopf	hopf	ADJ
ejpam-4716	12	26	-	-	PUNCT
ejpam-4716	12	27	bifurcation	bifurcation	NOUN
ejpam-4716	12	28	relative	relative	ADJ
ejpam-4716	12	29	to	to	ADP
ejpam-4716	12	30	the	the	DET
ejpam-4716	12	31	growth	growth	NOUN
ejpam-4716	12	32	rate	rate	NOUN
ejpam-4716	12	33	of	of	ADP
ejpam-4716	12	34	the	the	DET
ejpam-4716	12	35	prey	prey	NOUN
ejpam-4716	12	36	in	in	ADP
ejpam-4716	12	37	the	the	DET
ejpam-4716	12	38	neighborhood	neighborhood	NOUN
ejpam-4716	12	39	of	of	ADP
ejpam-4716	12	40	two	two	NUM
ejpam-4716	12	41	of	of	ADP
ejpam-4716	12	42	the	the	DET
ejpam-4716	12	43	equilibrium	equilibrium	NOUN
ejpam-4716	12	44	points	point	NOUN
ejpam-4716	12	45	has	have	AUX
ejpam-4716	12	46	been	be	AUX
ejpam-4716	12	47	found	find	VERB
ejpam-4716	12	48	.	.	PUNCT
ejpam-4716	13	1	finally	finally	ADV
ejpam-4716	13	2	,	,	PUNCT
ejpam-4716	13	3	two	two	NUM
ejpam-4716	13	4	numerical	numerical	ADJ
ejpam-4716	13	5	example	example	NOUN
ejpam-4716	13	6	has	have	AUX
ejpam-4716	13	7	been	be	AUX
ejpam-4716	13	8	given	give	VERB
ejpam-4716	13	9	to	to	PART
ejpam-4716	13	10	support	support	VERB
ejpam-4716	13	11	the	the	DET
ejpam-4716	13	12	theoretical	theoretical	ADJ
ejpam-4716	13	13	results	result	NOUN
ejpam-4716	13	14	.	.	PUNCT
ejpam-4716	14	1	2020	2020	NUM
ejpam-4716	14	2	mathematics	mathematic	NOUN
ejpam-4716	14	3	subject	subject	NOUN
ejpam-4716	14	4	classifications	classification	NOUN
ejpam-4716	14	5	:	:	PUNCT
ejpam-4716	14	6	65p30	65p30	NUM
ejpam-4716	14	7	,	,	PUNCT
ejpam-4716	14	8	34c23	34c23	NUM
ejpam-4716	14	9	,	,	PUNCT
ejpam-4716	14	10	92d25	92d25	NUM
ejpam-4716	14	11	key	key	ADJ
ejpam-4716	14	12	words	word	NOUN
ejpam-4716	14	13	and	and	CCONJ
ejpam-4716	14	14	phrases	phrase	NOUN
ejpam-4716	14	15	:	:	PUNCT
ejpam-4716	14	16	basin	basin	NOUN
ejpam-4716	14	17	of	of	ADP
ejpam-4716	14	18	attraction	attraction	NOUN
ejpam-4716	14	19	,	,	PUNCT
ejpam-4716	14	20	bifurcation	bifurcation	NOUN
ejpam-4716	14	21	,	,	PUNCT
ejpam-4716	14	22	equilibrium	equilibrium	NOUN
ejpam-4716	14	23	point	point	NOUN
ejpam-4716	14	24	,	,	PUNCT
ejpam-4716	14	25	group	group	NOUN
ejpam-4716	14	26	defence	defence	NOUN
ejpam-4716	14	27	,	,	PUNCT
ejpam-4716	14	28	stability	stability	NOUN
ejpam-4716	14	29	1	1	NUM
ejpam-4716	14	30	.	.	PUNCT
ejpam-4716	15	1	introduction	introduction	NOUN
ejpam-4716	15	2	predators	predator	NOUN
ejpam-4716	15	3	feed	feed	VERB
ejpam-4716	15	4	in	in	ADP
ejpam-4716	15	5	a	a	DET
ejpam-4716	15	6	habitat	habitat	NOUN
ejpam-4716	15	7	that	that	PRON
ejpam-4716	15	8	is	be	AUX
ejpam-4716	15	9	relatively	relatively	ADV
ejpam-4716	15	10	rich	rich	ADJ
ejpam-4716	15	11	in	in	ADP
ejpam-4716	15	12	food	food	NOUN
ejpam-4716	15	13	for	for	ADP
ejpam-4716	15	14	some	some	DET
ejpam-4716	15	15	time	time	NOUN
ejpam-4716	15	16	,	,	PUNCT
ejpam-4716	15	17	which	which	PRON
ejpam-4716	15	18	means	mean	VERB
ejpam-4716	15	19	to	to	ADP
ejpam-4716	15	20	them	they	PRON
ejpam-4716	15	21	that	that	SCONJ
ejpam-4716	15	22	there	there	PRON
ejpam-4716	15	23	are	be	VERB
ejpam-4716	15	24	large	large	ADJ
ejpam-4716	15	25	numbers	number	NOUN
ejpam-4716	15	26	of	of	ADP
ejpam-4716	15	27	prey	prey	NOUN
ejpam-4716	15	28	,	,	PUNCT
ejpam-4716	15	29	or	or	CCONJ
ejpam-4716	15	30	that	that	SCONJ
ejpam-4716	15	31	such	such	ADJ
ejpam-4716	15	32	prey	prey	NOUN
ejpam-4716	15	33	is	be	AUX
ejpam-4716	15	34	easy	easy	ADJ
ejpam-4716	15	35	to	to	PART
ejpam-4716	15	36	catch	catch	VERB
ejpam-4716	15	37	.	.	PUNCT
ejpam-4716	16	1	when	when	SCONJ
ejpam-4716	16	2	food	food	NOUN
ejpam-4716	16	3	is	be	AUX
ejpam-4716	16	4	scarce	scarce	ADJ
ejpam-4716	16	5	,	,	PUNCT
ejpam-4716	16	6	or	or	CCONJ
ejpam-4716	16	7	prey	prey	NOUN
ejpam-4716	16	8	is	be	AUX
ejpam-4716	16	9	minor	minor	ADJ
ejpam-4716	16	10	in	in	ADP
ejpam-4716	16	11	the	the	DET
ejpam-4716	16	12	habitat	habitat	NOUN
ejpam-4716	16	13	,	,	PUNCT
ejpam-4716	16	14	the	the	DET
ejpam-4716	16	15	predators	predator	NOUN
ejpam-4716	16	16	look	look	VERB
ejpam-4716	16	17	for	for	ADP
ejpam-4716	16	18	another	another	DET
ejpam-4716	16	19	habitat	habitat	NOUN
ejpam-4716	16	20	with	with	ADP
ejpam-4716	16	21	enough	enough	ADJ
ejpam-4716	16	22	food	food	NOUN
ejpam-4716	16	23	to	to	PART
ejpam-4716	16	24	live	live	VERB
ejpam-4716	16	25	in	in	ADP
ejpam-4716	16	26	for	for	ADP
ejpam-4716	16	27	another	another	DET
ejpam-4716	16	28	period	period	NOUN
ejpam-4716	16	29	of	of	ADP
ejpam-4716	16	30	time	time	NOUN
ejpam-4716	16	31	,	,	PUNCT
ejpam-4716	16	32	this	this	DET
ejpam-4716	16	33	phenomenon	phenomenon	NOUN
ejpam-4716	16	34	is	be	AUX
ejpam-4716	16	35	called	call	VERB
ejpam-4716	16	36	switching	switch	VERB
ejpam-4716	16	37	,	,	PUNCT
ejpam-4716	16	38	see	see	VERB
ejpam-4716	16	39	[	[	X
ejpam-4716	16	40	8	8	NUM
ejpam-4716	16	41	,	,	PUNCT
ejpam-4716	16	42	9	9	NUM
ejpam-4716	16	43	,	,	PUNCT
ejpam-4716	16	44	13	13	NUM
ejpam-4716	16	45	]	]	PUNCT
ejpam-4716	16	46	.	.	PUNCT
ejpam-4716	17	1	group	group	PROPN
ejpam-4716	17	2	defense	defense	NOUN
ejpam-4716	17	3	means	mean	VERB
ejpam-4716	17	4	that	that	SCONJ
ejpam-4716	17	5	all	all	DET
ejpam-4716	17	6	prey	prey	NOUN
ejpam-4716	17	7	animals	animal	NOUN
ejpam-4716	17	8	attack	attack	VERB
ejpam-4716	17	9	predators	predator	NOUN
ejpam-4716	17	10	collectively	collectively	ADV
ejpam-4716	17	11	and	and	CCONJ
ejpam-4716	17	12	do	do	AUX
ejpam-4716	17	13	∗corresponding	∗corresponde	VERB
ejpam-4716	17	14	author	author	NOUN
ejpam-4716	17	15	.	.	PUNCT
ejpam-4716	18	1	doi	doi	NOUN
ejpam-4716	18	2	:	:	PUNCT
ejpam-4716	18	3	https://doi.org/10.29020/nybg.ejpam.v16i2.4716	https://doi.org/10.29020/nybg.ejpam.v16i2.4716	VERB
ejpam-4716	18	4	email	email	NOUN
ejpam-4716	18	5	addresses	address	NOUN
ejpam-4716	18	6	:	:	PUNCT
ejpam-4716	18	7	a.g.farhan.edbs@uomustansiriyah.edu.iq	a.g.farhan.edbs@uomustansiriyah.edu.iq	NOUN
ejpam-4716	18	8	(	(	PUNCT
ejpam-4716	18	9	a.	a.	NOUN
ejpam-4716	18	10	g.	g.	PROPN
ejpam-4716	18	11	farhan	farhan	PROPN
ejpam-4716	18	12	)	)	PUNCT
ejpam-4716	18	13	,	,	PUNCT
ejpam-4716	18	14	nihad.shreef16@tu.edu.iq	nihad.shreef16@tu.edu.iq	PROPN
ejpam-4716	18	15	(	(	PUNCT
ejpam-4716	18	16	n.sh	n.sh	PROPN
ejpam-4716	18	17	.	.	PUNCT
ejpam-4716	18	18	khalaf	khalaf	PROPN
ejpam-4716	18	19	)	)	PUNCT
ejpam-4716	18	20	,	,	PUNCT
ejpam-4716	18	21	dr.talatjassim.edbs@uomustansiriyah.edu.iq	dr.talatjassim.edbs@uomustansiriyah.edu.iq	NOUN
ejpam-4716	18	22	(	(	PUNCT
ejpam-4716	18	23	t.g	t.g	PROPN
ejpam-4716	18	24	.	.	PROPN
ejpam-4716	18	25	aldhlki	aldhlki	PROPN
ejpam-4716	18	26	)	)	PUNCT
ejpam-4716	18	27	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4716	18	28	899	899	NUM
ejpam-4716	19	1	©	©	PROPN
ejpam-4716	19	2	2023	2023	NUM
ejpam-4716	19	3	ejpam	ejpam	NOUN
ejpam-4716	19	4	all	all	DET
ejpam-4716	19	5	rights	right	NOUN
ejpam-4716	19	6	reserved	reserve	VERB
ejpam-4716	19	7	.	.	PUNCT
ejpam-4716	20	1	a.	a.	PROPN
ejpam-4716	20	2	g.	g.	PROPN
ejpam-4716	20	3	farhan	farhan	PROPN
ejpam-4716	20	4	,	,	PUNCT
ejpam-4716	20	5	n.	n.	PROPN
ejpam-4716	20	6	sh	sh	PROPN
ejpam-4716	20	7	.	.	PROPN
ejpam-4716	20	8	khalaf	khalaf	PROPN
ejpam-4716	20	9	,	,	PUNCT
ejpam-4716	20	10	t.	t.	PROPN
ejpam-4716	20	11	j.	j.	PROPN
ejpam-4716	20	12	aldhlki	aldhlki	PROPN
ejpam-4716	20	13	/	/	SYM
ejpam-4716	20	14	eur	eur	PROPN
ejpam-4716	20	15	.	.	PUNCT
ejpam-4716	21	1	j.	j.	PROPN
ejpam-4716	21	2	pure	pure	PROPN
ejpam-4716	21	3	appl	appl	PROPN
ejpam-4716	21	4	.	.	PROPN
ejpam-4716	21	5	math	math	PROPN
ejpam-4716	21	6	,	,	PUNCT
ejpam-4716	21	7	16	16	NUM
ejpam-4716	21	8	(	(	PUNCT
ejpam-4716	21	9	2	2	NUM
ejpam-4716	21	10	)	)	PUNCT
ejpam-4716	21	11	(	(	PUNCT
ejpam-4716	21	12	2023	2023	NUM
ejpam-4716	21	13	)	)	PUNCT
ejpam-4716	21	14	,	,	PUNCT
ejpam-4716	21	15	899	899	NUM
ejpam-4716	21	16	-	-	SYM
ejpam-4716	21	17	918	918	NUM
ejpam-4716	21	18	900	900	NUM
ejpam-4716	21	19	not	not	PART
ejpam-4716	21	20	give	give	VERB
ejpam-4716	21	21	them	they	PRON
ejpam-4716	21	22	an	an	DET
ejpam-4716	21	23	opportunity	opportunity	NOUN
ejpam-4716	21	24	to	to	PART
ejpam-4716	21	25	attack	attack	VERB
ejpam-4716	21	26	and	and	CCONJ
ejpam-4716	21	27	prey	prey	VERB
ejpam-4716	21	28	on	on	ADP
ejpam-4716	21	29	them	they	PRON
ejpam-4716	21	30	.	.	PUNCT
ejpam-4716	22	1	in	in	ADP
ejpam-4716	22	2	1920	1920	NUM
ejpam-4716	22	3	,	,	PUNCT
ejpam-4716	22	4	volterra	volterra	PROPN
ejpam-4716	22	5	introduced	introduce	VERB
ejpam-4716	22	6	a	a	DET
ejpam-4716	22	7	mathematical	mathematical	ADJ
ejpam-4716	22	8	model	model	NOUN
ejpam-4716	22	9	that	that	PRON
ejpam-4716	22	10	represents	represent	VERB
ejpam-4716	22	11	the	the	DET
ejpam-4716	22	12	interaction	interaction	NOUN
ejpam-4716	22	13	between	between	ADP
ejpam-4716	22	14	prey	prey	NOUN
ejpam-4716	22	15	and	and	CCONJ
ejpam-4716	22	16	predator	predator	NOUN
ejpam-4716	22	17	[	[	X
ejpam-4716	22	18	1	1	NUM
ejpam-4716	22	19	,	,	PUNCT
ejpam-4716	22	20	10	10	NUM
ejpam-4716	22	21	]	]	PUNCT
ejpam-4716	22	22	.	.	PUNCT
ejpam-4716	23	1	later	later	ADV
ejpam-4716	23	2	many	many	ADJ
ejpam-4716	23	3	modified	modified	ADJ
ejpam-4716	23	4	volterra	volterra	NOUN
ejpam-4716	23	5	models	model	NOUN
ejpam-4716	23	6	were	be	AUX
ejpam-4716	23	7	introduced	introduce	VERB
ejpam-4716	23	8	by	by	ADP
ejpam-4716	23	9	researchers	researcher	NOUN
ejpam-4716	23	10	interested	interested	ADJ
ejpam-4716	23	11	in	in	ADP
ejpam-4716	23	12	this	this	DET
ejpam-4716	23	13	field	field	NOUN
ejpam-4716	23	14	.	.	PUNCT
ejpam-4716	24	1	various	various	ADJ
ejpam-4716	24	2	models	model	NOUN
ejpam-4716	24	3	,	,	PUNCT
ejpam-4716	24	4	including	include	VERB
ejpam-4716	24	5	prey	prey	NOUN
ejpam-4716	24	6	with	with	ADP
ejpam-4716	24	7	one	one	NUM
ejpam-4716	24	8	predator	predator	NOUN
ejpam-4716	24	9	,	,	PUNCT
ejpam-4716	24	10	two	two	NUM
ejpam-4716	24	11	predators	predator	NOUN
ejpam-4716	24	12	with	with	ADP
ejpam-4716	24	13	one	one	NUM
ejpam-4716	24	14	prey	prey	NOUN
ejpam-4716	24	15	,	,	PUNCT
ejpam-4716	24	16	two	two	NUM
ejpam-4716	24	17	prey	prey	NOUN
ejpam-4716	24	18	with	with	ADP
ejpam-4716	24	19	two	two	NUM
ejpam-4716	24	20	predators	predator	NOUN
ejpam-4716	24	21	,	,	PUNCT
ejpam-4716	24	22	and	and	CCONJ
ejpam-4716	24	23	food	food	NOUN
ejpam-4716	24	24	chains	chain	NOUN
ejpam-4716	24	25	of	of	ADP
ejpam-4716	24	26	three	three	NUM
ejpam-4716	24	27	or	or	CCONJ
ejpam-4716	24	28	more	more	ADJ
ejpam-4716	24	29	species	specie	NOUN
ejpam-4716	24	30	have	have	AUX
ejpam-4716	24	31	been	be	AUX
ejpam-4716	24	32	studied	study	VERB
ejpam-4716	24	33	in	in	ADP
ejpam-4716	24	34	[	[	X
ejpam-4716	24	35	2–4	2–4	NUM
ejpam-4716	24	36	,	,	PUNCT
ejpam-4716	24	37	15	15	NUM
ejpam-4716	24	38	,	,	PUNCT
ejpam-4716	24	39	16	16	NUM
ejpam-4716	24	40	]	]	PUNCT
ejpam-4716	24	41	.	.	PUNCT
ejpam-4716	25	1	in	in	ADP
ejpam-4716	25	2	the	the	DET
ejpam-4716	25	3	wild	wild	NOUN
ejpam-4716	25	4	,	,	PUNCT
ejpam-4716	25	5	lions	lion	NOUN
ejpam-4716	25	6	are	be	AUX
ejpam-4716	25	7	at	at	ADP
ejpam-4716	25	8	the	the	DET
ejpam-4716	25	9	top	top	NOUN
ejpam-4716	25	10	of	of	ADP
ejpam-4716	25	11	the	the	DET
ejpam-4716	25	12	food	food	NOUN
ejpam-4716	25	13	chain	chain	NOUN
ejpam-4716	25	14	because	because	SCONJ
ejpam-4716	25	15	of	of	ADP
ejpam-4716	25	16	their	their	PRON
ejpam-4716	25	17	strength	strength	NOUN
ejpam-4716	25	18	and	and	CCONJ
ejpam-4716	25	19	ability	ability	NOUN
ejpam-4716	25	20	to	to	PART
ejpam-4716	25	21	kill	kill	VERB
ejpam-4716	25	22	all	all	DET
ejpam-4716	25	23	animals	animal	NOUN
ejpam-4716	25	24	and	and	CCONJ
ejpam-4716	25	25	prey	prey	VERB
ejpam-4716	25	26	on	on	ADP
ejpam-4716	25	27	them	they	PRON
ejpam-4716	25	28	,	,	PUNCT
ejpam-4716	25	29	but	but	CCONJ
ejpam-4716	25	30	it	it	PRON
ejpam-4716	25	31	is	be	AUX
ejpam-4716	25	32	possible	possible	ADJ
ejpam-4716	25	33	for	for	SCONJ
ejpam-4716	25	34	a	a	DET
ejpam-4716	25	35	herd	herd	NOUN
ejpam-4716	25	36	or	or	CCONJ
ejpam-4716	25	37	a	a	DET
ejpam-4716	25	38	small	small	ADJ
ejpam-4716	25	39	group	group	NOUN
ejpam-4716	25	40	of	of	ADP
ejpam-4716	25	41	hyenas	hyena	NOUN
ejpam-4716	25	42	to	to	PART
ejpam-4716	25	43	attack	attack	VERB
ejpam-4716	25	44	a	a	DET
ejpam-4716	25	45	young	young	ADJ
ejpam-4716	25	46	lion	lion	NOUN
ejpam-4716	25	47	or	or	CCONJ
ejpam-4716	25	48	an	an	DET
ejpam-4716	25	49	old	old	ADJ
ejpam-4716	25	50	lion	lion	NOUN
ejpam-4716	25	51	outside	outside	ADP
ejpam-4716	25	52	its	its	PRON
ejpam-4716	25	53	kingdom	kingdom	NOUN
ejpam-4716	25	54	.	.	PUNCT
ejpam-4716	26	1	in	in	ADP
ejpam-4716	26	2	general	general	ADJ
ejpam-4716	26	3	,	,	PUNCT
ejpam-4716	26	4	predators	predator	NOUN
ejpam-4716	26	5	such	such	ADJ
ejpam-4716	26	6	as	as	ADP
ejpam-4716	26	7	lions	lion	NOUN
ejpam-4716	26	8	,	,	PUNCT
ejpam-4716	26	9	hyenas	hyena	NOUN
ejpam-4716	26	10	,	,	PUNCT
ejpam-4716	26	11	wolves	wolf	NOUN
ejpam-4716	26	12	,	,	PUNCT
ejpam-4716	26	13	and	and	CCONJ
ejpam-4716	26	14	others	other	NOUN
ejpam-4716	26	15	attack	attack	VERB
ejpam-4716	26	16	prey	prey	NOUN
ejpam-4716	26	17	such	such	ADJ
ejpam-4716	26	18	as	as	ADP
ejpam-4716	26	19	zebra	zebra	NOUN
ejpam-4716	26	20	,	,	PUNCT
ejpam-4716	26	21	wild	wild	ADJ
ejpam-4716	26	22	buffalo	buffalo	NOUN
ejpam-4716	26	23	,	,	PUNCT
ejpam-4716	26	24	and	and	CCONJ
ejpam-4716	26	25	other	other	ADJ
ejpam-4716	26	26	prey	prey	NOUN
ejpam-4716	26	27	with	with	ADP
ejpam-4716	26	28	the	the	DET
ejpam-4716	26	29	aim	aim	NOUN
ejpam-4716	26	30	of	of	ADP
ejpam-4716	26	31	killing	kill	VERB
ejpam-4716	26	32	and	and	CCONJ
ejpam-4716	26	33	devouring	devour	VERB
ejpam-4716	26	34	them	they	PRON
ejpam-4716	26	35	.	.	PUNCT
ejpam-4716	27	1	prey	prey	NOUN
ejpam-4716	27	2	by	by	ADP
ejpam-4716	27	3	nature	nature	NOUN
ejpam-4716	27	4	has	have	VERB
ejpam-4716	27	5	the	the	DET
ejpam-4716	27	6	ability	ability	NOUN
ejpam-4716	27	7	to	to	PART
ejpam-4716	27	8	live	live	VERB
ejpam-4716	27	9	in	in	ADP
ejpam-4716	27	10	groups	group	NOUN
ejpam-4716	27	11	that	that	PRON
ejpam-4716	27	12	move	move	VERB
ejpam-4716	27	13	from	from	ADP
ejpam-4716	27	14	one	one	NUM
ejpam-4716	27	15	habitat	habitat	NOUN
ejpam-4716	27	16	to	to	ADP
ejpam-4716	27	17	another	another	PRON
ejpam-4716	27	18	in	in	ADP
ejpam-4716	27	19	search	search	NOUN
ejpam-4716	27	20	of	of	ADP
ejpam-4716	27	21	food	food	NOUN
ejpam-4716	27	22	.	.	PUNCT
ejpam-4716	28	1	some	some	DET
ejpam-4716	28	2	prey	prey	NOUN
ejpam-4716	28	3	animals	animal	NOUN
ejpam-4716	28	4	,	,	PUNCT
ejpam-4716	28	5	such	such	ADJ
ejpam-4716	28	6	as	as	ADP
ejpam-4716	28	7	buffaloes	buffalo	NOUN
ejpam-4716	28	8	and	and	CCONJ
ejpam-4716	28	9	zebras	zebra	NOUN
ejpam-4716	28	10	,	,	PUNCT
ejpam-4716	28	11	have	have	VERB
ejpam-4716	28	12	the	the	DET
ejpam-4716	28	13	ability	ability	NOUN
ejpam-4716	28	14	to	to	PART
ejpam-4716	28	15	collectively	collectively	ADV
ejpam-4716	28	16	defend	defend	VERB
ejpam-4716	28	17	and	and	CCONJ
ejpam-4716	28	18	attack	attack	VERB
ejpam-4716	28	19	predators	predator	NOUN
ejpam-4716	28	20	in	in	ADP
ejpam-4716	28	21	masse	masse	NOUN
ejpam-4716	29	1	[	[	X
ejpam-4716	29	2	3	3	NUM
ejpam-4716	29	3	]	]	PUNCT
ejpam-4716	29	4	and	and	CCONJ
ejpam-4716	29	5	[	[	X
ejpam-4716	29	6	8	8	NUM
ejpam-4716	29	7	]	]	PUNCT
ejpam-4716	29	8	.	.	PUNCT
ejpam-4716	30	1	in	in	ADP
ejpam-4716	30	2	[	[	X
ejpam-4716	30	3	3	3	NUM
ejpam-4716	30	4	]	]	PUNCT
ejpam-4716	30	5	,	,	PUNCT
ejpam-4716	30	6	two	two	NUM
ejpam-4716	30	7	prey	prey	NOUN
ejpam-4716	30	8	-	-	PUNCT
ejpam-4716	30	9	predatory	predatory	NOUN
ejpam-4716	30	10	models	model	NOUN
ejpam-4716	30	11	were	be	AUX
ejpam-4716	30	12	studied	study	VERB
ejpam-4716	30	13	,	,	PUNCT
ejpam-4716	30	14	one	one	NUM
ejpam-4716	30	15	of	of	ADP
ejpam-4716	30	16	the	the	DET
ejpam-4716	30	17	two	two	NUM
ejpam-4716	30	18	models	model	NOUN
ejpam-4716	30	19	was	be	AUX
ejpam-4716	30	20	with	with	ADP
ejpam-4716	30	21	group	group	NOUN
ejpam-4716	30	22	prey	prey	PROPN
ejpam-4716	30	23	defense	defense	PROPN
ejpam-4716	30	24	,	,	PUNCT
ejpam-4716	30	25	while	while	SCONJ
ejpam-4716	30	26	the	the	DET
ejpam-4716	30	27	other	other	ADJ
ejpam-4716	30	28	model	model	NOUN
ejpam-4716	30	29	was	be	AUX
ejpam-4716	30	30	without	without	ADP
ejpam-4716	30	31	group	group	NOUN
ejpam-4716	30	32	prey	prey	PROPN
ejpam-4716	30	33	defense	defense	PROPN
ejpam-4716	30	34	.	.	PUNCT
ejpam-4716	31	1	the	the	DET
ejpam-4716	31	2	prey	prey	NOUN
ejpam-4716	31	3	was	be	AUX
ejpam-4716	31	4	supposed	suppose	VERB
ejpam-4716	31	5	to	to	PART
ejpam-4716	31	6	live	live	VERB
ejpam-4716	31	7	in	in	ADP
ejpam-4716	31	8	two	two	NUM
ejpam-4716	31	9	different	different	ADJ
ejpam-4716	31	10	habitats	habitat	NOUN
ejpam-4716	31	11	.	.	PUNCT
ejpam-4716	32	1	both	both	DET
ejpam-4716	32	2	predatory	predatory	ADJ
ejpam-4716	32	3	species	specie	NOUN
ejpam-4716	32	4	tend	tend	VERB
ejpam-4716	32	5	to	to	PART
ejpam-4716	32	6	move	move	VERB
ejpam-4716	32	7	from	from	ADP
ejpam-4716	32	8	one	one	NUM
ejpam-4716	32	9	habitat	habitat	NOUN
ejpam-4716	32	10	to	to	ADP
ejpam-4716	32	11	another	another	PRON
ejpam-4716	32	12	in	in	ADP
ejpam-4716	32	13	search	search	NOUN
ejpam-4716	32	14	of	of	ADP
ejpam-4716	32	15	food	food	NOUN
ejpam-4716	32	16	.	.	PUNCT
ejpam-4716	33	1	the	the	DET
ejpam-4716	33	2	first	first	ADJ
ejpam-4716	33	3	model	model	NOUN
ejpam-4716	33	4	has	have	AUX
ejpam-4716	33	5	been	be	AUX
ejpam-4716	33	6	expanded	expand	VERB
ejpam-4716	33	7	into	into	ADP
ejpam-4716	33	8	the	the	DET
ejpam-4716	33	9	following	following	ADJ
ejpam-4716	33	10	mathematical	mathematical	ADJ
ejpam-4716	33	11	model	model	NOUN
ejpam-4716	33	12	that	that	PRON
ejpam-4716	33	13	proposed	propose	VERB
ejpam-4716	33	14	and	and	CCONJ
ejpam-4716	33	15	studied	study	VERB
ejpam-4716	33	16	,	,	PUNCT
ejpam-4716	33	17	in	in	ADP
ejpam-4716	33	18	[	[	X
ejpam-4716	33	19	5	5	NUM
ejpam-4716	33	20	]	]	PUNCT
ejpam-4716	33	21	and	and	CCONJ
ejpam-4716	33	22	[	[	X
ejpam-4716	33	23	7	7	X
ejpam-4716	33	24	]	]	PUNCT
ejpam-4716	33	25	with	with	ADP
ejpam-4716	33	26	switching	switch	VERB
ejpam-4716	33	27	index	index	NOUN
ejpam-4716	33	28	n	n	NOUN
ejpam-4716	33	29	=	=	SYM
ejpam-4716	33	30	1,2	1,2	NUM
ejpam-4716	33	31	,	,	PUNCT
ejpam-4716	33	32	respectively	respectively	ADV
ejpam-4716	33	33	.	.	PUNCT
ejpam-4716	34	1	the	the	DET
ejpam-4716	34	2	expanded	expand	VERB
ejpam-4716	34	3	model	model	NOUN
ejpam-4716	34	4	deals	deal	NOUN
ejpam-4716	34	5	with	with	ADP
ejpam-4716	34	6	,	,	PUNCT
ejpam-4716	34	7	two	two	NUM
ejpam-4716	34	8	prey	prey	NOUN
ejpam-4716	34	9	and	and	CCONJ
ejpam-4716	34	10	two	two	NUM
ejpam-4716	34	11	predators	predator	NOUN
ejpam-4716	34	12	,	,	PUNCT
ejpam-4716	34	13	all	all	DET
ejpam-4716	34	14	species	specie	NOUN
ejpam-4716	34	15	grow	grow	VERB
ejpam-4716	34	16	logistically	logistically	ADV
ejpam-4716	34	17	,	,	PUNCT
ejpam-4716	34	18	the	the	DET
ejpam-4716	34	19	prey	prey	NOUN
ejpam-4716	34	20	lives	live	VERB
ejpam-4716	34	21	in	in	ADP
ejpam-4716	34	22	diverse	diverse	ADJ
ejpam-4716	34	23	habitats	habitat	NOUN
ejpam-4716	34	24	with	with	ADP
ejpam-4716	34	25	prey	prey	PROPN
ejpam-4716	34	26	group	group	PROPN
ejpam-4716	34	27	defense	defense	PROPN
ejpam-4716	34	28	,	,	PUNCT
ejpam-4716	34	29	one	one	NUM
ejpam-4716	34	30	predator	predator	NOUN
ejpam-4716	34	31	tends	tend	VERB
ejpam-4716	34	32	to	to	PART
ejpam-4716	34	33	switch	switch	VERB
ejpam-4716	34	34	habitats	habitat	NOUN
ejpam-4716	34	35	and	and	CCONJ
ejpam-4716	34	36	feeds	feed	VERB
ejpam-4716	34	37	on	on	ADP
ejpam-4716	34	38	the	the	DET
ejpam-4716	34	39	prey	prey	NOUN
ejpam-4716	34	40	,	,	PUNCT
ejpam-4716	34	41	while	while	SCONJ
ejpam-4716	34	42	the	the	DET
ejpam-4716	34	43	other	other	ADJ
ejpam-4716	34	44	predator	predator	NOUN
ejpam-4716	34	45	feeds	feed	VERB
ejpam-4716	34	46	on	on	ADP
ejpam-4716	34	47	only	only	ADV
ejpam-4716	34	48	one	one	NUM
ejpam-4716	34	49	prey	prey	NOUN
ejpam-4716	34	50	.	.	PUNCT
ejpam-4716	35	1	ẋ1	ẋ1	PROPN
ejpam-4716	35	2	=	=	PUNCT
ejpam-4716	36	1	x1	x1	PROPN
ejpam-4716	36	2	(	(	PUNCT
ejpam-4716	36	3	g1	g1	PROPN
ejpam-4716	36	4	(	(	PUNCT
ejpam-4716	36	5	1−	1−	NUM
ejpam-4716	36	6	x1	x1	PROPN
ejpam-4716	36	7	k1	k1	NOUN
ejpam-4716	36	8	)	)	PUNCT
ejpam-4716	36	9	−	−	PROPN
ejpam-4716	36	10	α1x	α1x	NUM
ejpam-4716	36	11	n	n	ADP
ejpam-4716	36	12	2y1	2y1	NUM
ejpam-4716	36	13	xn1	xn1	PRON
ejpam-4716	37	1	+	+	CCONJ
ejpam-4716	37	2	xn2	xn2	PROPN
ejpam-4716	37	3	−	−	PROPN
ejpam-4716	37	4	βy2	βy2	PROPN
ejpam-4716	37	5	)	)	PUNCT
ejpam-4716	37	6	,	,	PUNCT
ejpam-4716	38	1	ẋ2	ẋ2	PROPN
ejpam-4716	38	2	=	=	SYM
ejpam-4716	38	3	x2	x2	PROPN
ejpam-4716	38	4	(	(	PUNCT
ejpam-4716	38	5	g2	g2	PROPN
ejpam-4716	38	6	(	(	PUNCT
ejpam-4716	38	7	1−	1−	NUM
ejpam-4716	38	8	x2	x2	PROPN
ejpam-4716	38	9	k2	k2	PROPN
ejpam-4716	38	10	)	)	PUNCT
ejpam-4716	38	11	−	−	PROPN
ejpam-4716	38	12	α2x	α2x	NUM
ejpam-4716	38	13	n	n	PRON
ejpam-4716	38	14	1y1	1y1	NUM
ejpam-4716	38	15	xn1	xn1	PRON
ejpam-4716	38	16	+	+	CCONJ
ejpam-4716	38	17	xn2	xn2	NUM
ejpam-4716	38	18	)	)	PUNCT
ejpam-4716	38	19	,	,	PUNCT
ejpam-4716	38	20	ẏ1	ẏ1	PROPN
ejpam-4716	38	21	=	=	SYM
ejpam-4716	38	22	y1	y1	PROPN
ejpam-4716	38	23	(	(	PUNCT
ejpam-4716	38	24	−µ1	−µ1	PROPN
ejpam-4716	38	25	+	+	NOUN
ejpam-4716	38	26	δ1x1x	δ1x1x	NUM
ejpam-4716	38	27	n	n	PRON
ejpam-4716	38	28	2	2	NUM
ejpam-4716	38	29	xn1	xn1	PRON
ejpam-4716	38	30	+	+	CCONJ
ejpam-4716	38	31	xn2	xn2	X
ejpam-4716	39	1	+	+	PUNCT
ejpam-4716	39	2	δ2x	δ2x	NOUN
ejpam-4716	39	3	n	n	NOUN
ejpam-4716	39	4	1x2	1x2	NUM
ejpam-4716	39	5	xn1	xn1	X
ejpam-4716	39	6	+	+	CCONJ
ejpam-4716	39	7	xn2	xn2	NUM
ejpam-4716	39	8	)	)	PUNCT
ejpam-4716	39	9	,	,	PUNCT
ejpam-4716	40	1	ẏ2	ẏ2	PROPN
ejpam-4716	40	2	=	=	SYM
ejpam-4716	40	3	y2(−µ2	y2(−µ2	PROPN
ejpam-4716	40	4	+	+	NUM
ejpam-4716	40	5	γx1	γx1	NOUN
ejpam-4716	40	6	)	)	PUNCT
ejpam-4716	40	7	(	(	PUNCT
ejpam-4716	40	8	1	1	X
ejpam-4716	40	9	)	)	PUNCT
ejpam-4716	40	10	the	the	DET
ejpam-4716	40	11	aim	aim	NOUN
ejpam-4716	40	12	of	of	ADP
ejpam-4716	40	13	this	this	DET
ejpam-4716	40	14	work	work	NOUN
ejpam-4716	40	15	is	be	AUX
ejpam-4716	40	16	to	to	PART
ejpam-4716	40	17	study	study	VERB
ejpam-4716	40	18	the	the	DET
ejpam-4716	40	19	local	local	ADJ
ejpam-4716	40	20	qualitative	qualitative	ADJ
ejpam-4716	40	21	behaviors	behavior	NOUN
ejpam-4716	40	22	in	in	ADP
ejpam-4716	40	23	the	the	DET
ejpam-4716	40	24	neighborhood	neighborhood	NOUN
ejpam-4716	40	25	of	of	ADP
ejpam-4716	40	26	the	the	DET
ejpam-4716	40	27	equilibrium	equilibrium	NOUN
ejpam-4716	40	28	points	point	NOUN
ejpam-4716	40	29	of	of	ADP
ejpam-4716	40	30	a	a	DET
ejpam-4716	40	31	proposed	propose	VERB
ejpam-4716	40	32	prey	prey	NOUN
ejpam-4716	40	33	-	-	PUNCT
ejpam-4716	40	34	predator	predator	NOUN
ejpam-4716	40	35	mathematical	mathematical	ADJ
ejpam-4716	40	36	model	model	NOUN
ejpam-4716	40	37	for	for	ADP
ejpam-4716	40	38	four	four	NUM
ejpam-4716	40	39	species	specie	NOUN
ejpam-4716	40	40	with	with	ADP
ejpam-4716	40	41	an	an	DET
ejpam-4716	40	42	incomplete	incomplete	ADJ
ejpam-4716	40	43	food	food	NOUN
ejpam-4716	40	44	chain	chain	NOUN
ejpam-4716	40	45	.	.	PUNCT
ejpam-4716	41	1	the	the	DET
ejpam-4716	41	2	four	four	NUM
ejpam-4716	41	3	species	specie	NOUN
ejpam-4716	41	4	,	,	PUNCT
ejpam-4716	41	5	consist	consist	VERB
ejpam-4716	41	6	of	of	ADP
ejpam-4716	41	7	two	two	NUM
ejpam-4716	41	8	prey	prey	NOUN
ejpam-4716	41	9	and	and	CCONJ
ejpam-4716	41	10	two	two	NUM
ejpam-4716	41	11	predators	predator	NOUN
ejpam-4716	41	12	,	,	PUNCT
ejpam-4716	41	13	and	and	CCONJ
ejpam-4716	41	14	each	each	PRON
ejpam-4716	41	15	of	of	ADP
ejpam-4716	41	16	them	they	PRON
ejpam-4716	41	17	grows	grow	VERB
ejpam-4716	41	18	logistically	logistically	ADV
ejpam-4716	41	19	.	.	PUNCT
ejpam-4716	42	1	the	the	DET
ejpam-4716	42	2	two	two	NUM
ejpam-4716	42	3	prey	prey	NOUN
ejpam-4716	42	4	live	live	ADV
ejpam-4716	42	5	in	in	ADP
ejpam-4716	42	6	two	two	NUM
ejpam-4716	42	7	different	different	ADJ
ejpam-4716	42	8	habitats	habitat	NOUN
ejpam-4716	42	9	and	and	CCONJ
ejpam-4716	42	10	have	have	VERB
ejpam-4716	42	11	the	the	DET
ejpam-4716	42	12	ability	ability	NOUN
ejpam-4716	42	13	to	to	PART
ejpam-4716	42	14	group	group	NOUN
ejpam-4716	42	15	defense	defense	NOUN
ejpam-4716	42	16	.	.	PUNCT
ejpam-4716	43	1	one	one	NUM
ejpam-4716	43	2	predator	predator	NOUN
ejpam-4716	43	3	or	or	CCONJ
ejpam-4716	43	4	the	the	DET
ejpam-4716	43	5	top	top	ADJ
ejpam-4716	43	6	feeds	feed	VERB
ejpam-4716	43	7	on	on	ADP
ejpam-4716	43	8	the	the	DET
ejpam-4716	43	9	other	other	ADJ
ejpam-4716	43	10	predator	predator	NOUN
ejpam-4716	43	11	,	,	PUNCT
ejpam-4716	43	12	in	in	ADP
ejpam-4716	43	13	addition	addition	NOUN
ejpam-4716	43	14	to	to	ADP
ejpam-4716	43	15	the	the	DET
ejpam-4716	43	16	two	two	NUM
ejpam-4716	43	17	prey	prey	NOUN
ejpam-4716	43	18	indicated	indicate	VERB
ejpam-4716	43	19	in	in	ADP
ejpam-4716	43	20	the	the	DET
ejpam-4716	43	21	model	model	NOUN
ejpam-4716	43	22	.	.	PUNCT
ejpam-4716	44	1	we	we	PRON
ejpam-4716	44	2	show	show	VERB
ejpam-4716	44	3	that	that	SCONJ
ejpam-4716	44	4	all	all	DET
ejpam-4716	44	5	positive	positive	ADJ
ejpam-4716	44	6	solutions	solution	NOUN
ejpam-4716	44	7	are	be	AUX
ejpam-4716	44	8	bounded	bound	VERB
ejpam-4716	44	9	under	under	ADP
ejpam-4716	44	10	some	some	DET
ejpam-4716	44	11	conditions	condition	NOUN
ejpam-4716	44	12	.	.	PUNCT
ejpam-4716	45	1	in	in	ADP
ejpam-4716	45	2	the	the	DET
ejpam-4716	45	3	third	third	ADJ
ejpam-4716	45	4	section	section	NOUN
ejpam-4716	45	5	,	,	PUNCT
ejpam-4716	45	6	it	it	PRON
ejpam-4716	45	7	was	be	AUX
ejpam-4716	45	8	found	find	VERB
ejpam-4716	45	9	that	that	SCONJ
ejpam-4716	45	10	the	the	DET
ejpam-4716	45	11	model	model	NOUN
ejpam-4716	45	12	has	have	VERB
ejpam-4716	45	13	,	,	PUNCT
ejpam-4716	45	14	at	at	ADP
ejpam-4716	45	15	most	most	ADJ
ejpam-4716	45	16	seven	seven	NUM
ejpam-4716	45	17	equilibrium	equilibrium	NOUN
ejpam-4716	45	18	points	point	NOUN
ejpam-4716	45	19	.	.	PUNCT
ejpam-4716	46	1	local	local	ADJ
ejpam-4716	46	2	stability	stability	NOUN
ejpam-4716	46	3	and	and	CCONJ
ejpam-4716	46	4	local	local	ADJ
ejpam-4716	46	5	bifurcation	bifurcation	NOUN
ejpam-4716	46	6	of	of	ADP
ejpam-4716	46	7	the	the	DET
ejpam-4716	46	8	equilibrium	equilibrium	NOUN
ejpam-4716	46	9	points	point	NOUN
ejpam-4716	46	10	have	have	AUX
ejpam-4716	46	11	been	be	AUX
ejpam-4716	46	12	analyzed	analyze	VERB
ejpam-4716	46	13	in	in	ADP
ejpam-4716	46	14	section4	section4	PROPN
ejpam-4716	46	15	and	and	CCONJ
ejpam-4716	46	16	section5	section5	NOUN
ejpam-4716	46	17	respectively	respectively	ADV
ejpam-4716	46	18	.	.	PUNCT
ejpam-4716	47	1	two	two	NUM
ejpam-4716	47	2	sets	set	NOUN
ejpam-4716	47	3	of	of	ADP
ejpam-4716	47	4	parameters	parameter	NOUN
ejpam-4716	47	5	form	form	VERB
ejpam-4716	47	6	two	two	NUM
ejpam-4716	47	7	systems	system	NOUN
ejpam-4716	47	8	of	of	ADP
ejpam-4716	47	9	4	4	NUM
ejpam-4716	47	10	-	-	PUNCT
ejpam-4716	47	11	dimensional	dimensional	ADJ
ejpam-4716	47	12	differential	differential	ADJ
ejpam-4716	47	13	equations	equation	NOUN
ejpam-4716	47	14	,	,	PUNCT
ejpam-4716	47	15	each	each	PRON
ejpam-4716	47	16	of	of	ADP
ejpam-4716	47	17	them	they	PRON
ejpam-4716	47	18	is	be	AUX
ejpam-4716	47	19	an	an	DET
ejpam-4716	47	20	example	example	NOUN
ejpam-4716	47	21	of	of	ADP
ejpam-4716	47	22	the	the	DET
ejpam-4716	47	23	model	model	NOUN
ejpam-4716	47	24	(	(	PUNCT
ejpam-4716	47	25	2	2	X
ejpam-4716	47	26	)	)	PUNCT
ejpam-4716	47	27	presented	present	VERB
ejpam-4716	47	28	in	in	ADP
ejpam-4716	47	29	the	the	DET
ejpam-4716	47	30	sixth	sixth	ADJ
ejpam-4716	47	31	section	section	NOUN
ejpam-4716	47	32	of	of	ADP
ejpam-4716	47	33	this	this	DET
ejpam-4716	47	34	paper	paper	NOUN
ejpam-4716	47	35	to	to	PART
ejpam-4716	47	36	simulate	simulate	VERB
ejpam-4716	47	37	the	the	DET
ejpam-4716	47	38	theoretical	theoretical	ADJ
ejpam-4716	47	39	results	result	NOUN
ejpam-4716	47	40	obtained	obtain	VERB
ejpam-4716	47	41	in	in	ADP
ejpam-4716	47	42	the	the	DET
ejpam-4716	47	43	previous	previous	ADJ
ejpam-4716	47	44	sections	section	NOUN
ejpam-4716	47	45	.	.	PUNCT
ejpam-4716	48	1	finally	finally	ADV
ejpam-4716	48	2	a	a	DET
ejpam-4716	48	3	brave	brave	ADJ
ejpam-4716	48	4	conclusion	conclusion	NOUN
ejpam-4716	48	5	of	of	ADP
ejpam-4716	48	6	this	this	DET
ejpam-4716	48	7	paper	paper	NOUN
ejpam-4716	48	8	is	be	AUX
ejpam-4716	48	9	given	give	VERB
ejpam-4716	48	10	in	in	ADP
ejpam-4716	48	11	the	the	DET
ejpam-4716	48	12	last	last	ADJ
ejpam-4716	48	13	section	section	NOUN
ejpam-4716	48	14	.	.	PUNCT
ejpam-4716	49	1	a.	a.	PROPN
ejpam-4716	49	2	g.	g.	PROPN
ejpam-4716	49	3	farhan	farhan	PROPN
ejpam-4716	49	4	,	,	PUNCT
ejpam-4716	49	5	n.	n.	PROPN
ejpam-4716	49	6	sh	sh	PROPN
ejpam-4716	49	7	.	.	PROPN
ejpam-4716	49	8	khalaf	khalaf	PROPN
ejpam-4716	49	9	,	,	PUNCT
ejpam-4716	49	10	t.	t.	PROPN
ejpam-4716	49	11	j.	j.	PROPN
ejpam-4716	49	12	aldhlki	aldhlki	PROPN
ejpam-4716	49	13	/	/	SYM
ejpam-4716	49	14	eur	eur	PROPN
ejpam-4716	49	15	.	.	PUNCT
ejpam-4716	50	1	j.	j.	PROPN
ejpam-4716	50	2	pure	pure	PROPN
ejpam-4716	50	3	appl	appl	PROPN
ejpam-4716	50	4	.	.	PROPN
ejpam-4716	50	5	math	math	PROPN
ejpam-4716	50	6	,	,	PUNCT
ejpam-4716	50	7	16	16	NUM
ejpam-4716	50	8	(	(	PUNCT
ejpam-4716	50	9	2	2	NUM
ejpam-4716	50	10	)	)	PUNCT
ejpam-4716	50	11	(	(	PUNCT
ejpam-4716	50	12	2023	2023	NUM
ejpam-4716	50	13	)	)	PUNCT
ejpam-4716	50	14	,	,	PUNCT
ejpam-4716	50	15	899	899	NUM
ejpam-4716	50	16	-	-	SYM
ejpam-4716	50	17	918	918	NUM
ejpam-4716	50	18	901	901	NUM
ejpam-4716	50	19	2	2	NUM
ejpam-4716	50	20	.	.	PUNCT
ejpam-4716	51	1	the	the	DET
ejpam-4716	51	2	mathematical	mathematical	ADJ
ejpam-4716	51	3	model	model	NOUN
ejpam-4716	51	4	in	in	ADP
ejpam-4716	51	5	this	this	DET
ejpam-4716	51	6	work	work	NOUN
ejpam-4716	51	7	,	,	PUNCT
ejpam-4716	51	8	the	the	DET
ejpam-4716	51	9	following	follow	VERB
ejpam-4716	51	10	model	model	NOUN
ejpam-4716	51	11	was	be	AUX
ejpam-4716	51	12	proposed	propose	VERB
ejpam-4716	51	13	,	,	PUNCT
ejpam-4716	51	14	which	which	PRON
ejpam-4716	51	15	is	be	AUX
ejpam-4716	51	16	a	a	DET
ejpam-4716	51	17	modification	modification	NOUN
ejpam-4716	51	18	of	of	ADP
ejpam-4716	51	19	model	model	NOUN
ejpam-4716	51	20	(	(	PUNCT
ejpam-4716	51	21	1	1	NUM
ejpam-4716	51	22	)	)	PUNCT
ejpam-4716	51	23	ẋ1	ẋ1	PROPN
ejpam-4716	51	24	=	=	SYM
ejpam-4716	52	1	x1	x1	PROPN
ejpam-4716	52	2	(	(	PUNCT
ejpam-4716	52	3	g1	g1	PROPN
ejpam-4716	52	4	(	(	PUNCT
ejpam-4716	52	5	1−	1−	NUM
ejpam-4716	52	6	x1	x1	PROPN
ejpam-4716	52	7	k1	k1	NOUN
ejpam-4716	52	8	)	)	PUNCT
ejpam-4716	52	9	−	−	PROPN
ejpam-4716	53	1	α1x2y1	α1x2y1	NOUN
ejpam-4716	53	2	x1	x1	PROPN
ejpam-4716	54	1	+	+	CCONJ
ejpam-4716	54	2	x2	x2	PROPN
ejpam-4716	54	3	−	−	PROPN
ejpam-4716	54	4	α2x2y2	α2x2y2	X
ejpam-4716	54	5	x1	x1	PROPN
ejpam-4716	55	1	+	+	CCONJ
ejpam-4716	55	2	x2	x2	ADJ
ejpam-4716	55	3	)	)	PUNCT
ejpam-4716	55	4	,	,	PUNCT
ejpam-4716	56	1	ẋ2	ẋ2	PROPN
ejpam-4716	56	2	=	=	SYM
ejpam-4716	56	3	x2	x2	PROPN
ejpam-4716	56	4	(	(	PUNCT
ejpam-4716	56	5	g2	g2	PROPN
ejpam-4716	56	6	(	(	PUNCT
ejpam-4716	56	7	1−	1−	NUM
ejpam-4716	56	8	x2	x2	PROPN
ejpam-4716	56	9	k2	k2	PROPN
ejpam-4716	56	10	)	)	PUNCT
ejpam-4716	56	11	−	−	PROPN
ejpam-4716	57	1	β1x1y1	β1x1y1	NOUN
ejpam-4716	57	2	x1	x1	PROPN
ejpam-4716	58	1	+	+	CCONJ
ejpam-4716	58	2	x2	x2	PROPN
ejpam-4716	58	3	−	−	PROPN
ejpam-4716	58	4	β2x1y2	β2x1y2	PROPN
ejpam-4716	59	1	x1	x1	PROPN
ejpam-4716	59	2	+	+	NUM
ejpam-4716	59	3	x2	x2	ADJ
ejpam-4716	59	4	)	)	PUNCT
ejpam-4716	59	5	,	,	PUNCT
ejpam-4716	60	1	ẏ1	ẏ1	PROPN
ejpam-4716	60	2	=	=	SYM
ejpam-4716	60	3	y1	y1	PROPN
ejpam-4716	60	4	(	(	PUNCT
ejpam-4716	60	5	−µ1	−µ1	PROPN
ejpam-4716	60	6	+	+	CCONJ
ejpam-4716	60	7	ϵ1x1x2	ϵ1x1x2	NOUN
ejpam-4716	60	8	x1	x1	PROPN
ejpam-4716	61	1	+	+	CCONJ
ejpam-4716	61	2	x2	x2	PROPN
ejpam-4716	61	3	−	−	PROPN
ejpam-4716	61	4	ρ2y2	ρ2y2	NOUN
ejpam-4716	61	5	)	)	PUNCT
ejpam-4716	61	6	,	,	PUNCT
ejpam-4716	62	1	ẏ2	ẏ2	PROPN
ejpam-4716	62	2	=	=	PUNCT
ejpam-4716	62	3	y2	y2	PROPN
ejpam-4716	62	4	(	(	PUNCT
ejpam-4716	62	5	−µ2	−µ2	NOUN
ejpam-4716	63	1	+	+	CCONJ
ejpam-4716	63	2	ϵ2x1x2	ϵ2x1x2	X
ejpam-4716	63	3	x1	x1	PROPN
ejpam-4716	64	1	+	+	CCONJ
ejpam-4716	64	2	x2	x2	PROPN
ejpam-4716	65	1	+	+	CCONJ
ejpam-4716	65	2	ρ1y1	ρ1y1	X
ejpam-4716	65	3	)	)	PUNCT
ejpam-4716	65	4	(	(	PUNCT
ejpam-4716	65	5	2	2	X
ejpam-4716	65	6	)	)	PUNCT
ejpam-4716	65	7	where	where	SCONJ
ejpam-4716	65	8	xi	xi	X
ejpam-4716	65	9	denote	denote	VERB
ejpam-4716	65	10	the	the	DET
ejpam-4716	65	11	density	density	NOUN
ejpam-4716	65	12	of	of	ADP
ejpam-4716	65	13	the	the	DET
ejpam-4716	65	14	prey	prey	NOUN
ejpam-4716	66	1	i	i	NOUN
ejpam-4716	66	2	=	=	NOUN
ejpam-4716	66	3	1	1	NUM
ejpam-4716	66	4	,	,	PUNCT
ejpam-4716	66	5	2	2	NUM
ejpam-4716	66	6	;	;	PUNCT
ejpam-4716	66	7	y1	y1	NOUN
ejpam-4716	66	8	denote	denote	VERB
ejpam-4716	66	9	the	the	DET
ejpam-4716	66	10	density	density	NOUN
ejpam-4716	66	11	of	of	ADP
ejpam-4716	66	12	the	the	DET
ejpam-4716	66	13	predator	predator	NOUN
ejpam-4716	66	14	that	that	PRON
ejpam-4716	66	15	fed	feed	VERB
ejpam-4716	66	16	on	on	ADP
ejpam-4716	66	17	the	the	DET
ejpam-4716	66	18	two	two	NUM
ejpam-4716	66	19	prey	prey	NOUN
ejpam-4716	66	20	;	;	PUNCT
ejpam-4716	66	21	y2	y2	PROPN
ejpam-4716	66	22	denote	denote	VERB
ejpam-4716	66	23	the	the	DET
ejpam-4716	66	24	density	density	NOUN
ejpam-4716	66	25	of	of	ADP
ejpam-4716	66	26	the	the	DET
ejpam-4716	66	27	predator	predator	NOUN
ejpam-4716	66	28	that	that	PRON
ejpam-4716	66	29	fed	feed	VERB
ejpam-4716	66	30	on	on	ADP
ejpam-4716	66	31	the	the	DET
ejpam-4716	66	32	other	other	ADJ
ejpam-4716	66	33	three	three	NUM
ejpam-4716	66	34	species	specie	NOUN
ejpam-4716	66	35	(	(	PUNCT
ejpam-4716	66	36	top	top	ADJ
ejpam-4716	66	37	predator	predator	NOUN
ejpam-4716	66	38	)	)	PUNCT
ejpam-4716	66	39	.	.	PUNCT
ejpam-4716	67	1	gi	gi	INTJ
ejpam-4716	67	2	,	,	PUNCT
ejpam-4716	67	3	i	i	PRON
ejpam-4716	67	4	=	=	NOUN
ejpam-4716	67	5	1	1	NUM
ejpam-4716	67	6	,	,	PUNCT
ejpam-4716	67	7	2	2	NUM
ejpam-4716	67	8	is	be	AUX
ejpam-4716	67	9	the	the	DET
ejpam-4716	67	10	growth	growth	NOUN
ejpam-4716	67	11	rate	rate	NOUN
ejpam-4716	67	12	of	of	ADP
ejpam-4716	67	13	xi	xi	PROPN
ejpam-4716	67	14	,	,	PUNCT
ejpam-4716	67	15	i	i	PRON
ejpam-4716	67	16	=	=	NOUN
ejpam-4716	67	17	1	1	NUM
ejpam-4716	67	18	,	,	PUNCT
ejpam-4716	67	19	2	2	NUM
ejpam-4716	67	20	;	;	PUNCT
ejpam-4716	67	21	ki	ki	PROPN
ejpam-4716	67	22	,	,	PUNCT
ejpam-4716	67	23	i	i	PRON
ejpam-4716	67	24	=	=	NOUN
ejpam-4716	67	25	1	1	NUM
ejpam-4716	67	26	,	,	PUNCT
ejpam-4716	67	27	2	2	NUM
ejpam-4716	67	28	,	,	PUNCT
ejpam-4716	67	29	is	be	AUX
ejpam-4716	67	30	the	the	DET
ejpam-4716	67	31	carrying	carry	VERB
ejpam-4716	67	32	environmental	environmental	ADJ
ejpam-4716	67	33	capacity	capacity	NOUN
ejpam-4716	67	34	to	to	ADP
ejpam-4716	67	35	xi	xi	PROPN
ejpam-4716	67	36	,	,	PUNCT
ejpam-4716	67	37	i	i	PRON
ejpam-4716	67	38	=	=	NOUN
ejpam-4716	67	39	1	1	NUM
ejpam-4716	67	40	,	,	PUNCT
ejpam-4716	67	41	2	2	NUM
ejpam-4716	67	42	;	;	PUNCT
ejpam-4716	67	43	αi	αi	NOUN
ejpam-4716	67	44	,	,	PUNCT
ejpam-4716	67	45	i	i	PRON
ejpam-4716	67	46	=	=	NOUN
ejpam-4716	67	47	1	1	NUM
ejpam-4716	67	48	,	,	PUNCT
ejpam-4716	67	49	2	2	NUM
ejpam-4716	67	50	,	,	PUNCT
ejpam-4716	67	51	is	be	AUX
ejpam-4716	67	52	the	the	DET
ejpam-4716	67	53	rate	rate	NOUN
ejpam-4716	67	54	of	of	ADP
ejpam-4716	67	55	predation	predation	NOUN
ejpam-4716	67	56	by	by	ADP
ejpam-4716	67	57	the	the	DET
ejpam-4716	67	58	predatoryi	predatoryi	NOUN
ejpam-4716	67	59	,	,	PUNCT
ejpam-4716	67	60	i	i	PRON
ejpam-4716	67	61	=	=	NOUN
ejpam-4716	67	62	1	1	NUM
ejpam-4716	67	63	,	,	PUNCT
ejpam-4716	67	64	2	2	NUM
ejpam-4716	67	65	with	with	ADP
ejpam-4716	67	66	the	the	DET
ejpam-4716	67	67	prey	prey	PROPN
ejpam-4716	67	68	x1;βi	x1;βi	PROPN
ejpam-4716	67	69	,	,	PUNCT
ejpam-4716	67	70	i	i	PRON
ejpam-4716	67	71	=	=	NOUN
ejpam-4716	67	72	1	1	NUM
ejpam-4716	67	73	,	,	PUNCT
ejpam-4716	67	74	2	2	NUM
ejpam-4716	67	75	is	be	AUX
ejpam-4716	67	76	the	the	DET
ejpam-4716	67	77	rate	rate	NOUN
ejpam-4716	67	78	of	of	ADP
ejpam-4716	67	79	predation	predation	NOUN
ejpam-4716	67	80	by	by	ADP
ejpam-4716	67	81	the	the	DET
ejpam-4716	67	82	predator	predator	NOUN
ejpam-4716	67	83	yi	yi	NOUN
ejpam-4716	67	84	,	,	PUNCT
ejpam-4716	67	85	i	i	PRON
ejpam-4716	67	86	=	=	NOUN
ejpam-4716	67	87	1	1	NUM
ejpam-4716	67	88	,	,	PUNCT
ejpam-4716	67	89	2	2	NUM
ejpam-4716	67	90	on	on	ADP
ejpam-4716	67	91	prey	prey	PROPN
ejpam-4716	67	92	x2	x2	PROPN
ejpam-4716	67	93	;	;	PUNCT
ejpam-4716	67	94	µi	µi	PROPN
ejpam-4716	67	95	,	,	PUNCT
ejpam-4716	67	96	i	i	PRON
ejpam-4716	67	97	=	=	NOUN
ejpam-4716	67	98	1	1	NUM
ejpam-4716	67	99	,	,	PUNCT
ejpam-4716	67	100	2	2	NUM
ejpam-4716	67	101	,	,	PUNCT
ejpam-4716	67	102	is	be	AUX
ejpam-4716	67	103	the	the	DET
ejpam-4716	67	104	mortality	mortality	NOUN
ejpam-4716	67	105	rate	rate	NOUN
ejpam-4716	67	106	of	of	ADP
ejpam-4716	67	107	predatorsyi	predatorsyi	ADJ
ejpam-4716	67	108	,	,	PUNCT
ejpam-4716	67	109	i	i	PRON
ejpam-4716	67	110	=	=	NOUN
ejpam-4716	67	111	1	1	NUM
ejpam-4716	67	112	,	,	PUNCT
ejpam-4716	67	113	2	2	NUM
ejpam-4716	67	114	;	;	PUNCT
ejpam-4716	67	115	εi	εi	VERB
ejpam-4716	67	116	,	,	PUNCT
ejpam-4716	67	117	i	i	PRON
ejpam-4716	67	118	=	=	NOUN
ejpam-4716	67	119	1	1	NUM
ejpam-4716	67	120	,	,	PUNCT
ejpam-4716	67	121	2	2	NUM
ejpam-4716	67	122	,	,	PUNCT
ejpam-4716	67	123	is	be	AUX
ejpam-4716	67	124	the	the	DET
ejpam-4716	67	125	corresponding	correspond	VERB
ejpam-4716	67	126	conversion	conversion	NOUN
ejpam-4716	67	127	rates	rate	NOUN
ejpam-4716	67	128	to	to	ADP
ejpam-4716	67	129	µi	µi	PROPN
ejpam-4716	67	130	,	,	PUNCT
ejpam-4716	67	131	i	i	PRON
ejpam-4716	67	132	=	=	NOUN
ejpam-4716	67	133	1	1	NUM
ejpam-4716	67	134	,	,	PUNCT
ejpam-4716	67	135	2	2	NUM
ejpam-4716	67	136	;	;	PUNCT
ejpam-4716	67	137	ρ1	ρ1	NOUN
ejpam-4716	67	138	,	,	PUNCT
ejpam-4716	67	139	is	be	AUX
ejpam-4716	67	140	the	the	DET
ejpam-4716	67	141	rate	rate	NOUN
ejpam-4716	67	142	of	of	ADP
ejpam-4716	67	143	change	change	NOUN
ejpam-4716	67	144	of	of	ADP
ejpam-4716	67	145	y2	y2	PROPN
ejpam-4716	67	146	due	due	ADP
ejpam-4716	67	147	to	to	ADP
ejpam-4716	67	148	the	the	DET
ejpam-4716	67	149	presence	presence	NOUN
ejpam-4716	67	150	of	of	ADP
ejpam-4716	67	151	y1	y1	PROPN
ejpam-4716	67	152	,	,	PUNCT
ejpam-4716	67	153	;	;	PUNCT
ejpam-4716	67	154	and	and	CCONJ
ejpam-4716	67	155	ρ2	ρ2	NOUN
ejpam-4716	67	156	,	,	PUNCT
ejpam-4716	67	157	is	be	AUX
ejpam-4716	67	158	the	the	DET
ejpam-4716	67	159	rate	rate	NOUN
ejpam-4716	67	160	of	of	ADP
ejpam-4716	67	161	change	change	NOUN
ejpam-4716	67	162	of	of	ADP
ejpam-4716	67	163	y1	y1	NOUN
ejpam-4716	67	164	due	due	ADP
ejpam-4716	67	165	to	to	ADP
ejpam-4716	67	166	the	the	DET
ejpam-4716	67	167	presence	presence	NOUN
ejpam-4716	67	168	of	of	ADP
ejpam-4716	67	169	y2	y2	PROPN
ejpam-4716	67	170	.	.	PUNCT
ejpam-4716	68	1	the	the	DET
ejpam-4716	68	2	switching	switch	VERB
ejpam-4716	68	3	behavior	behavior	NOUN
ejpam-4716	68	4	of	of	ADP
ejpam-4716	68	5	predators	predator	NOUN
ejpam-4716	68	6	y1	y1	VERB
ejpam-4716	68	7	and	and	CCONJ
ejpam-4716	68	8	y2	y2	PROPN
ejpam-4716	68	9	is	be	AUX
ejpam-4716	68	10	shown	show	VERB
ejpam-4716	68	11	by	by	ADP
ejpam-4716	68	12	,	,	PUNCT
ejpam-4716	69	1	the	the	DET
ejpam-4716	69	2	functions	function	NOUN
ejpam-4716	69	3	α1x2y1(x1	α1x2y1(x1	NOUN
ejpam-4716	69	4	+	+	CCONJ
ejpam-4716	69	5	x2	x2	ADJ
ejpam-4716	69	6	)	)	PUNCT
ejpam-4716	69	7	−1	−1	NOUN
ejpam-4716	69	8	,	,	PUNCT
ejpam-4716	69	9	β1x1y1(x1	β1x1y1(x1	ADJ
ejpam-4716	69	10	+	+	CCONJ
ejpam-4716	69	11	x2	x2	ADJ
ejpam-4716	69	12	)	)	PUNCT
ejpam-4716	69	13	−1	−1	NOUN
ejpam-4716	69	14	and	and	CCONJ
ejpam-4716	69	15	,	,	PUNCT
ejpam-4716	69	16	the	the	DET
ejpam-4716	69	17	functions	function	NOUN
ejpam-4716	69	18	α2x2y2(x1	α2x2y2(x1	VERB
ejpam-4716	69	19	+	+	CCONJ
ejpam-4716	69	20	x2	x2	ADJ
ejpam-4716	69	21	)	)	PUNCT
ejpam-4716	69	22	−1	−1	NOUN
ejpam-4716	69	23	,	,	PUNCT
ejpam-4716	69	24	β2x1y2(x1	β2x1y2(x1	PROPN
ejpam-4716	69	25	+	+	CCONJ
ejpam-4716	69	26	x2	x2	ADJ
ejpam-4716	69	27	)	)	PUNCT
ejpam-4716	69	28	−1	−1	NOUN
ejpam-4716	69	29	respectively	respectively	ADV
ejpam-4716	69	30	.	.	PUNCT
ejpam-4716	70	1	it	it	PRON
ejpam-4716	70	2	is	be	AUX
ejpam-4716	70	3	easy	easy	ADJ
ejpam-4716	70	4	to	to	PART
ejpam-4716	70	5	show	show	VERB
ejpam-4716	70	6	that	that	SCONJ
ejpam-4716	70	7	all	all	DET
ejpam-4716	70	8	functions	function	NOUN
ejpam-4716	70	9	of	of	ADP
ejpam-4716	70	10	the	the	DET
ejpam-4716	70	11	model	model	NOUN
ejpam-4716	70	12	(	(	PUNCT
ejpam-4716	70	13	2	2	NUM
ejpam-4716	70	14	)	)	PUNCT
ejpam-4716	70	15	and	and	CCONJ
ejpam-4716	70	16	their	their	PRON
ejpam-4716	70	17	partial	partial	ADJ
ejpam-4716	70	18	derivatives	derivative	NOUN
ejpam-4716	70	19	are	be	AUX
ejpam-4716	70	20	continuous	continuous	ADJ
ejpam-4716	70	21	,	,	PUNCT
ejpam-4716	70	22	so	so	SCONJ
ejpam-4716	70	23	that	that	SCONJ
ejpam-4716	70	24	these	these	DET
ejpam-4716	70	25	functions	function	NOUN
ejpam-4716	70	26	are	be	AUX
ejpam-4716	70	27	lipschitizion	lipschitizion	NOUN
ejpam-4716	70	28	functions	function	NOUN
ejpam-4716	70	29	on	on	ADP
ejpam-4716	70	30	r+4	r+4	NOUN
ejpam-4716	71	1	=	=	SYM
ejpam-4716	71	2	{	{	PUNCT
ejpam-4716	71	3	(	(	PUNCT
ejpam-4716	71	4	x1	x1	PROPN
ejpam-4716	71	5	,	,	PUNCT
ejpam-4716	71	6	x2	x2	PROPN
ejpam-4716	71	7	,	,	PUNCT
ejpam-4716	71	8	y1	y1	NOUN
ejpam-4716	71	9	,	,	PUNCT
ejpam-4716	71	10	y2	y2	NOUN
ejpam-4716	71	11	)	)	PUNCT
ejpam-4716	71	12	∈	∈	PROPN
ejpam-4716	71	13	r4	r4	NOUN
ejpam-4716	71	14	:	:	PUNCT
ejpam-4716	71	15	xi(0	xi(0	X
ejpam-4716	71	16	)	)	PUNCT
ejpam-4716	71	17	≥	≥	NOUN
ejpam-4716	71	18	0	0	NUM
ejpam-4716	71	19	,	,	PUNCT
ejpam-4716	71	20	yi(0	yi(0	PROPN
ejpam-4716	71	21	)	)	PUNCT
ejpam-4716	71	22	≥	≥	NOUN
ejpam-4716	71	23	0	0	NUM
ejpam-4716	71	24	,	,	PUNCT
ejpam-4716	71	25	i	i	PRON
ejpam-4716	71	26	=	=	NOUN
ejpam-4716	71	27	1	1	NUM
ejpam-4716	71	28	,	,	PUNCT
ejpam-4716	71	29	2	2	NUM
ejpam-4716	71	30	,	,	PUNCT
ejpam-4716	71	31	x1	x1	PROPN
ejpam-4716	72	1	+	+	CCONJ
ejpam-4716	72	2	x2	x2	PROPN
ejpam-4716	72	3	>	>	X
ejpam-4716	72	4	0	0	NUM
ejpam-4716	72	5	}	}	PUNCT
ejpam-4716	72	6	.	.	PUNCT
ejpam-4716	73	1	hence	hence	ADV
ejpam-4716	73	2	,	,	PUNCT
ejpam-4716	73	3	the	the	DET
ejpam-4716	73	4	existence	existence	NOUN
ejpam-4716	73	5	and	and	CCONJ
ejpam-4716	73	6	the	the	DET
ejpam-4716	73	7	uniqueness	uniqueness	NOUN
ejpam-4716	73	8	of	of	ADP
ejpam-4716	73	9	the	the	DET
ejpam-4716	73	10	solution	solution	NOUN
ejpam-4716	73	11	of	of	ADP
ejpam-4716	73	12	model	model	NOUN
ejpam-4716	73	13	(	(	PUNCT
ejpam-4716	73	14	2	2	NUM
ejpam-4716	73	15	)	)	PUNCT
ejpam-4716	73	16	is	be	AUX
ejpam-4716	73	17	guaranteed	guarantee	VERB
ejpam-4716	73	18	.	.	PUNCT
ejpam-4716	74	1	now	now	ADV
ejpam-4716	74	2	,	,	PUNCT
ejpam-4716	74	3	we	we	PRON
ejpam-4716	74	4	will	will	AUX
ejpam-4716	74	5	show	show	VERB
ejpam-4716	74	6	that	that	SCONJ
ejpam-4716	74	7	the	the	DET
ejpam-4716	74	8	trajectories	trajectory	NOUN
ejpam-4716	74	9	of	of	ADP
ejpam-4716	74	10	all	all	DET
ejpam-4716	74	11	the	the	DET
ejpam-4716	74	12	positive	positive	ADJ
ejpam-4716	74	13	solutions	solution	NOUN
ejpam-4716	74	14	of	of	ADP
ejpam-4716	74	15	the	the	DET
ejpam-4716	74	16	system	system	NOUN
ejpam-4716	74	17	(	(	PUNCT
ejpam-4716	74	18	2	2	X
ejpam-4716	74	19	)	)	PUNCT
ejpam-4716	74	20	whose	whose	DET
ejpam-4716	74	21	initial	initial	ADJ
ejpam-4716	74	22	conditions	condition	NOUN
ejpam-4716	74	23	lie	lie	VERB
ejpam-4716	74	24	within	within	ADP
ejpam-4716	74	25	the	the	DET
ejpam-4716	74	26	following	follow	VERB
ejpam-4716	74	27	region	region	NOUN
ejpam-4716	74	28	d	d	NOUN
ejpam-4716	74	29	are	be	AUX
ejpam-4716	74	30	bounded	bound	VERB
ejpam-4716	75	1	d	d	X
ejpam-4716	75	2	:	:	PUNCT
ejpam-4716	75	3	=	=	SYM
ejpam-4716	75	4	{	{	PUNCT
ejpam-4716	75	5	(	(	PUNCT
ejpam-4716	75	6	x1	x1	PROPN
ejpam-4716	75	7	,	,	PUNCT
ejpam-4716	75	8	x2	x2	PROPN
ejpam-4716	75	9	,	,	PUNCT
ejpam-4716	75	10	y1	y1	NOUN
ejpam-4716	75	11	,	,	PUNCT
ejpam-4716	75	12	y2	y2	NOUN
ejpam-4716	75	13	)	)	PUNCT
ejpam-4716	75	14	∈	∈	PROPN
ejpam-4716	75	15	r4	r4	NOUN
ejpam-4716	75	16	,	,	PUNCT
ejpam-4716	75	17	0	0	PUNCT
ejpam-4716	75	18	<	<	X
ejpam-4716	75	19	xi	xi	X
ejpam-4716	75	20	<	<	X
ejpam-4716	75	21	ki	ki	PROPN
ejpam-4716	75	22	,	,	PUNCT
ejpam-4716	75	23	yi	yi	PROPN
ejpam-4716	75	24	>	>	X
ejpam-4716	75	25	0	0	PROPN
ejpam-4716	75	26	,	,	PUNCT
ejpam-4716	75	27	i	i	PRON
ejpam-4716	75	28	=	=	NOUN
ejpam-4716	75	29	1	1	NUM
ejpam-4716	75	30	,	,	PUNCT
ejpam-4716	75	31	2	2	NUM
ejpam-4716	75	32	}	}	PUNCT
ejpam-4716	75	33	.	.	PUNCT
ejpam-4716	76	1	(	(	PUNCT
ejpam-4716	76	2	3	3	X
ejpam-4716	76	3	)	)	PUNCT
ejpam-4716	76	4	theorem	theorem	NOUN
ejpam-4716	76	5	1	1	NUM
ejpam-4716	76	6	.	.	PUNCT
ejpam-4716	77	1	if	if	SCONJ
ejpam-4716	77	2	εi	εi	NOUN
ejpam-4716	77	3	≤	≤	NOUN
ejpam-4716	77	4	αi	αi	ADV
ejpam-4716	78	1	+	+	CCONJ
ejpam-4716	78	2	βi	βi	X
ejpam-4716	78	3	,	,	PUNCT
ejpam-4716	78	4	i	i	PRON
ejpam-4716	78	5	=	=	NOUN
ejpam-4716	78	6	1	1	NUM
ejpam-4716	78	7	,	,	PUNCT
ejpam-4716	78	8	2	2	NUM
ejpam-4716	78	9	,	,	PUNCT
ejpam-4716	78	10	ρ1	ρ1	NOUN
ejpam-4716	78	11	≤	≤	ADJ
ejpam-4716	78	12	ρ2	ρ2	NOUN
ejpam-4716	78	13	,	,	PUNCT
ejpam-4716	78	14	then	then	ADV
ejpam-4716	78	15	the	the	DET
ejpam-4716	78	16	trajectories	trajectory	NOUN
ejpam-4716	78	17	of	of	ADP
ejpam-4716	78	18	all	all	DET
ejpam-4716	78	19	the	the	DET
ejpam-4716	78	20	positive	positive	ADJ
ejpam-4716	78	21	solutions	solution	NOUN
ejpam-4716	78	22	of	of	ADP
ejpam-4716	78	23	the	the	DET
ejpam-4716	78	24	system	system	NOUN
ejpam-4716	78	25	(	(	PUNCT
ejpam-4716	78	26	2	2	X
ejpam-4716	78	27	)	)	PUNCT
ejpam-4716	78	28	whose	whose	DET
ejpam-4716	78	29	initial	initial	ADJ
ejpam-4716	78	30	conditions	condition	NOUN
ejpam-4716	78	31	belong	belong	VERB
ejpam-4716	78	32	to	to	ADP
ejpam-4716	78	33	d	d	PROPN
ejpam-4716	78	34	are	be	AUX
ejpam-4716	78	35	bounded	bound	VERB
ejpam-4716	78	36	.	.	PUNCT
ejpam-4716	79	1	proof	proof	NOUN
ejpam-4716	79	2	.	.	PUNCT
ejpam-4716	80	1	the	the	DET
ejpam-4716	80	2	following	follow	VERB
ejpam-4716	80	3	real	real	ADJ
ejpam-4716	80	4	valued	value	VERB
ejpam-4716	80	5	function	function	NOUN
ejpam-4716	80	6	:	:	PUNCT
ejpam-4716	80	7	z(t	z(t	X
ejpam-4716	80	8	)	)	PUNCT
ejpam-4716	80	9	=	=	SYM
ejpam-4716	80	10	x1(t	x1(t	PROPN
ejpam-4716	80	11	)	)	PUNCT
ejpam-4716	80	12	+	+	NUM
ejpam-4716	80	13	x2(t	x2(t	X
ejpam-4716	80	14	)	)	PUNCT
ejpam-4716	80	15	+	+	CCONJ
ejpam-4716	80	16	y1(t	y1(t	X
ejpam-4716	80	17	)	)	PUNCT
ejpam-4716	80	18	+	+	CCONJ
ejpam-4716	80	19	y2(t	y2(t	PROPN
ejpam-4716	80	20	)	)	PUNCT
ejpam-4716	80	21	,	,	PUNCT
ejpam-4716	80	22	is	be	AUX
ejpam-4716	80	23	a	a	DET
ejpam-4716	80	24	positive	positive	ADJ
ejpam-4716	80	25	definitive	definitive	NOUN
ejpam-4716	80	26	on	on	ADP
ejpam-4716	80	27	d.	d.	PROPN
ejpam-4716	80	28	therefore	therefore	ADV
ejpam-4716	80	29	,	,	PUNCT
ejpam-4716	80	30	we	we	PRON
ejpam-4716	80	31	get	get	VERB
ejpam-4716	80	32	ż	ż	NOUN
ejpam-4716	80	33	=	=	PUNCT
ejpam-4716	80	34	2∑	2∑	NUM
ejpam-4716	80	35	i=1	i=1	PROPN
ejpam-4716	80	36	(	(	PUNCT
ejpam-4716	80	37	xigi	xigi	PROPN
ejpam-4716	80	38	(	(	PUNCT
ejpam-4716	80	39	1−	1−	NUM
ejpam-4716	80	40	xi	xi	INTJ
ejpam-4716	80	41	ki	ki	PROPN
ejpam-4716	80	42	)	)	PUNCT
ejpam-4716	81	1	−	−	PROPN
ejpam-4716	81	2	µiyi	µiyi	ADV
ejpam-4716	81	3	−	−	PROPN
ejpam-4716	82	1	(	(	PUNCT
ejpam-4716	82	2	ρ2	ρ2	NOUN
ejpam-4716	82	3	−	−	PROPN
ejpam-4716	82	4	ρ1	ρ1	NOUN
ejpam-4716	82	5	)	)	PUNCT
ejpam-4716	82	6	2	2	NUM
ejpam-4716	82	7	y	y	SYM
ejpam-4716	82	8	1	1	NUM
ejpam-4716	82	9	y2	y2	NOUN
ejpam-4716	82	10	−	−	PROPN
ejpam-4716	82	11	x1x2yi	x1x2yi	PUNCT
ejpam-4716	83	1	x1	x1	PROPN
ejpam-4716	84	1	+	+	NUM
ejpam-4716	84	2	x2	x2	PROPN
ejpam-4716	84	3	(	(	PUNCT
ejpam-4716	84	4	αi	αi	X
ejpam-4716	84	5	+	+	CCONJ
ejpam-4716	84	6	βi−εi	βi−εi	ADJ
ejpam-4716	84	7	)	)	PUNCT
ejpam-4716	84	8	)	)	PUNCT
ejpam-4716	84	9	a.	a.	NOUN
ejpam-4716	84	10	g.	g.	PROPN
ejpam-4716	84	11	farhan	farhan	PROPN
ejpam-4716	84	12	,	,	PUNCT
ejpam-4716	84	13	n.	n.	PROPN
ejpam-4716	84	14	sh	sh	PROPN
ejpam-4716	84	15	.	.	PROPN
ejpam-4716	84	16	khalaf	khalaf	PROPN
ejpam-4716	84	17	,	,	PUNCT
ejpam-4716	84	18	t.	t.	PROPN
ejpam-4716	84	19	j.	j.	PROPN
ejpam-4716	84	20	aldhlki	aldhlki	PROPN
ejpam-4716	84	21	/	/	SYM
ejpam-4716	84	22	eur	eur	PROPN
ejpam-4716	84	23	.	.	PUNCT
ejpam-4716	85	1	j.	j.	PROPN
ejpam-4716	85	2	pure	pure	PROPN
ejpam-4716	85	3	appl	appl	PROPN
ejpam-4716	85	4	.	.	PROPN
ejpam-4716	85	5	math	math	PROPN
ejpam-4716	85	6	,	,	PUNCT
ejpam-4716	85	7	16	16	NUM
ejpam-4716	85	8	(	(	PUNCT
ejpam-4716	85	9	2	2	NUM
ejpam-4716	85	10	)	)	PUNCT
ejpam-4716	85	11	(	(	PUNCT
ejpam-4716	85	12	2023	2023	NUM
ejpam-4716	85	13	)	)	PUNCT
ejpam-4716	85	14	,	,	PUNCT
ejpam-4716	85	15	899	899	NUM
ejpam-4716	85	16	-	-	SYM
ejpam-4716	85	17	918	918	NUM
ejpam-4716	85	18	902	902	NUM
ejpam-4716	85	19	if	if	SCONJ
ejpam-4716	85	20	0	0	NUM
ejpam-4716	85	21	<	<	X
ejpam-4716	85	22	ρ	ρ	PROPN
ejpam-4716	85	23	≤	≤	PROPN
ejpam-4716	85	24	max	max	PROPN
ejpam-4716	85	25	{	{	PUNCT
ejpam-4716	85	26	µ1	µ1	PROPN
ejpam-4716	85	27	,	,	PUNCT
ejpam-4716	85	28	µ2	µ2	PROPN
ejpam-4716	85	29	}	}	PUNCT
ejpam-4716	85	30	,	,	PUNCT
ejpam-4716	85	31	then	then	ADV
ejpam-4716	85	32	we	we	PRON
ejpam-4716	85	33	obtain	obtain	VERB
ejpam-4716	85	34	:	:	PUNCT
ejpam-4716	85	35	ż	ż	NOUN
ejpam-4716	86	1	+	+	NOUN
ejpam-4716	86	2	ρu	ρu	NOUN
ejpam-4716	86	3	=	=	SYM
ejpam-4716	86	4	2∑	2∑	NUM
ejpam-4716	86	5	i=1	i=1	PROPN
ejpam-4716	86	6	(	(	PUNCT
ejpam-4716	86	7	xigi	xigi	PROPN
ejpam-4716	86	8	(	(	PUNCT
ejpam-4716	86	9	1−	1−	NUM
ejpam-4716	86	10	xi	xi	INTJ
ejpam-4716	86	11	ki	ki	PROPN
ejpam-4716	87	1	+	+	CCONJ
ejpam-4716	87	2	ρ	ρ	PROPN
ejpam-4716	87	3	gi	gi	NOUN
ejpam-4716	87	4	)	)	PUNCT
ejpam-4716	88	1	+	+	PROPN
ejpam-4716	88	2	(	(	PUNCT
ejpam-4716	88	3	ρ−µi)yi−	ρ−µi)yi−	X
ejpam-4716	88	4	(	(	PUNCT
ejpam-4716	88	5	ρ2	ρ2	NOUN
ejpam-4716	88	6	−	−	PROPN
ejpam-4716	88	7	ρ1	ρ1	NOUN
ejpam-4716	88	8	)	)	PUNCT
ejpam-4716	88	9	2	2	NUM
ejpam-4716	88	10	y1y2	y1y2	NOUN
ejpam-4716	88	11	−	−	NOUN
ejpam-4716	88	12	x1x2yi	x1x2yi	PUNCT
ejpam-4716	89	1	x1	x1	PROPN
ejpam-4716	90	1	+	+	NUM
ejpam-4716	90	2	x2	x2	PROPN
ejpam-4716	90	3	(	(	PUNCT
ejpam-4716	90	4	αi	αi	VERB
ejpam-4716	90	5	+	+	CCONJ
ejpam-4716	90	6	βi	βi	PRON
ejpam-4716	90	7	−	−	NUM
ejpam-4716	90	8	εi	εi	VERB
ejpam-4716	90	9	)	)	PUNCT
ejpam-4716	90	10	)	)	PUNCT
ejpam-4716	90	11	.	.	PUNCT
ejpam-4716	91	1	it	it	PRON
ejpam-4716	91	2	is	be	AUX
ejpam-4716	91	3	obvious	obvious	ADJ
ejpam-4716	91	4	that	that	SCONJ
ejpam-4716	91	5	ż	ż	NOUN
ejpam-4716	92	1	+	+	CCONJ
ejpam-4716	92	2	ρz	ρz	NOUN
ejpam-4716	92	3	<	<	X
ejpam-4716	92	4	2∑	2∑	NUM
ejpam-4716	92	5	i=1	i=1	PROPN
ejpam-4716	92	6	xigi	xigi	PROPN
ejpam-4716	92	7	(	(	PUNCT
ejpam-4716	92	8	1−	1−	NUM
ejpam-4716	92	9	xi	xi	INTJ
ejpam-4716	93	1	ki	ki	PROPN
ejpam-4716	94	1	+	+	CCONJ
ejpam-4716	94	2	ρ	ρ	PROPN
ejpam-4716	94	3	gi	gi	NOUN
ejpam-4716	94	4	)	)	PUNCT
ejpam-4716	95	1	=	=	PUNCT
ejpam-4716	96	1	2∑	2∑	X
ejpam-4716	96	2	i=1	i=1	X
ejpam-4716	96	3	xi	xi	X
ejpam-4716	97	1	ki	ki	PROPN
ejpam-4716	97	2	(	(	PUNCT
ejpam-4716	97	3	kigi	kigi	PROPN
ejpam-4716	97	4	−	−	PROPN
ejpam-4716	97	5	gixi	gixi	PROPN
ejpam-4716	97	6	+	+	CCONJ
ejpam-4716	97	7	kiρ	kiρ	NOUN
ejpam-4716	97	8	)	)	PUNCT
ejpam-4716	97	9	<	<	X
ejpam-4716	97	10	2∑	2∑	X
ejpam-4716	97	11	i=1	i=1	X
ejpam-4716	97	12	xi	xi	X
ejpam-4716	98	1	ki	ki	PROPN
ejpam-4716	98	2	(	(	PUNCT
ejpam-4716	98	3	kigi	kigi	X
ejpam-4716	98	4	+	+	CCONJ
ejpam-4716	98	5	kiρ	kiρ	NOUN
ejpam-4716	98	6	)	)	PUNCT
ejpam-4716	98	7	<	<	X
ejpam-4716	99	1	2∑	2∑	NUM
ejpam-4716	99	2	i=1	i=1	PROPN
ejpam-4716	99	3	ki(gi	ki(gi	PROPN
ejpam-4716	99	4	+	+	CCONJ
ejpam-4716	99	5	ρ	ρ	PROPN
ejpam-4716	99	6	)	)	PUNCT
ejpam-4716	99	7	.	.	PUNCT
ejpam-4716	100	1	put	put	VERB
ejpam-4716	100	2	α	α	NOUN
ejpam-4716	100	3	=	=	NOUN
ejpam-4716	100	4	:	:	PUNCT
ejpam-4716	100	5	∑2	∑2	PROPN
ejpam-4716	101	1	i=1	i=1	X
ejpam-4716	102	1	ki	ki	PROPN
ejpam-4716	103	1	(	(	PUNCT
ejpam-4716	103	2	gi	gi	X
ejpam-4716	103	3	+	+	CCONJ
ejpam-4716	103	4	ρ	ρ	NOUN
ejpam-4716	103	5	)	)	PUNCT
ejpam-4716	103	6	.	.	PUNCT
ejpam-4716	104	1	so	so	ADV
ejpam-4716	104	2	it	it	PRON
ejpam-4716	104	3	is	be	AUX
ejpam-4716	104	4	clear	clear	ADJ
ejpam-4716	104	5	that	that	SCONJ
ejpam-4716	104	6	:	:	PUNCT
ejpam-4716	104	7	0	0	NUM
ejpam-4716	104	8	≤	≤	NUM
ejpam-4716	104	9	z	z	NOUN
ejpam-4716	104	10	(	(	PUNCT
ejpam-4716	104	11	t	t	PROPN
ejpam-4716	104	12	)	)	PUNCT
ejpam-4716	104	13	≤	≤	NUM
ejpam-4716	105	1	α	α	X
ejpam-4716	105	2	ρ	ρ	PROPN
ejpam-4716	106	1	+	+	X
ejpam-4716	106	2	z	z	X
ejpam-4716	106	3	(	(	PUNCT
ejpam-4716	106	4	0	0	NUM
ejpam-4716	106	5	)	)	PUNCT
ejpam-4716	106	6	e−ρt	e−ρt	PROPN
ejpam-4716	106	7	,	,	PUNCT
ejpam-4716	106	8	and	and	CCONJ
ejpam-4716	106	9	when	when	SCONJ
ejpam-4716	106	10	t	t	PROPN
ejpam-4716	106	11	→	→	SYM
ejpam-4716	106	12	∞	∞	PROPN
ejpam-4716	106	13	,	,	PUNCT
ejpam-4716	106	14	0	0	NUM
ejpam-4716	106	15	≤	≤	NUM
ejpam-4716	106	16	z(t	z(t	NOUN
ejpam-4716	106	17	)	)	PUNCT
ejpam-4716	106	18	≤	≤	NUM
ejpam-4716	106	19	α	α	PROPN
ejpam-4716	106	20	ρ	ρ	NOUN
ejpam-4716	106	21	.	.	PUNCT
ejpam-4716	107	1	(	(	PUNCT
ejpam-4716	107	2	4	4	NUM
ejpam-4716	107	3	)	)	PUNCT
ejpam-4716	107	4	so	so	SCONJ
ejpam-4716	107	5	that	that	SCONJ
ejpam-4716	107	6	,	,	PUNCT
ejpam-4716	107	7	from	from	ADP
ejpam-4716	107	8	(	(	PUNCT
ejpam-4716	107	9	4	4	NUM
ejpam-4716	107	10	)	)	PUNCT
ejpam-4716	107	11	,	,	PUNCT
ejpam-4716	107	12	the	the	DET
ejpam-4716	107	13	trajectories	trajectory	NOUN
ejpam-4716	107	14	of	of	ADP
ejpam-4716	107	15	all	all	DET
ejpam-4716	107	16	the	the	DET
ejpam-4716	107	17	positive	positive	ADJ
ejpam-4716	107	18	solutions	solution	NOUN
ejpam-4716	107	19	of	of	ADP
ejpam-4716	107	20	the	the	DET
ejpam-4716	107	21	system	system	NOUN
ejpam-4716	107	22	(	(	PUNCT
ejpam-4716	107	23	2	2	NUM
ejpam-4716	107	24	)	)	PUNCT
ejpam-4716	107	25	with	with	ADP
ejpam-4716	107	26	initial	initial	ADJ
ejpam-4716	107	27	conditions	condition	NOUN
ejpam-4716	107	28	lie	lie	VERB
ejpam-4716	107	29	within	within	ADP
ejpam-4716	107	30	the	the	DET
ejpam-4716	107	31	region	region	NOUN
ejpam-4716	107	32	d	d	PROPN
ejpam-4716	107	33	defined	define	VERB
ejpam-4716	107	34	above	above	ADV
ejpam-4716	107	35	and	and	CCONJ
ejpam-4716	107	36	satisfy	satisfy	VERB
ejpam-4716	107	37	εi	εi	VERB
ejpam-4716	107	38	≤	≤	NUM
ejpam-4716	107	39	αi+βi	αi+βi	SYM
ejpam-4716	107	40	,	,	PUNCT
ejpam-4716	107	41	i	i	PRON
ejpam-4716	107	42	=	=	NOUN
ejpam-4716	107	43	1	1	NUM
ejpam-4716	107	44	,	,	PUNCT
ejpam-4716	107	45	2	2	NUM
ejpam-4716	107	46	,	,	PUNCT
ejpam-4716	107	47	ρ1	ρ1	NOUN
ejpam-4716	107	48	≤	≤	NUM
ejpam-4716	107	49	ρ2	ρ2	NOUN
ejpam-4716	107	50	are	be	AUX
ejpam-4716	107	51	bounded	bound	VERB
ejpam-4716	107	52	.	.	PUNCT
ejpam-4716	108	1	and	and	CCONJ
ejpam-4716	108	2	with	with	ADP
ejpam-4716	108	3	this	this	PRON
ejpam-4716	108	4	,	,	PUNCT
ejpam-4716	108	5	we	we	PRON
ejpam-4716	108	6	have	have	AUX
ejpam-4716	108	7	completed	complete	VERB
ejpam-4716	108	8	the	the	DET
ejpam-4716	108	9	proof	proof	NOUN
ejpam-4716	108	10	.	.	PUNCT
ejpam-4716	109	1	3	3	X
ejpam-4716	109	2	.	.	X
ejpam-4716	109	3	existence	existence	NOUN
ejpam-4716	109	4	of	of	ADP
ejpam-4716	109	5	equilibrium	equilibrium	NOUN
ejpam-4716	109	6	points	point	NOUN
ejpam-4716	109	7	the	the	DET
ejpam-4716	109	8	system	system	NOUN
ejpam-4716	109	9	has	have	VERB
ejpam-4716	109	10	four	four	NUM
ejpam-4716	109	11	equilibrium	equilibrium	NOUN
ejpam-4716	109	12	points	point	NOUN
ejpam-4716	109	13	always	always	ADV
ejpam-4716	109	14	exist	exist	VERB
ejpam-4716	109	15	,	,	PUNCT
ejpam-4716	109	16	regardless	regardless	ADV
ejpam-4716	109	17	of	of	ADP
ejpam-4716	109	18	the	the	DET
ejpam-4716	109	19	values	value	NOUN
ejpam-4716	109	20	of	of	ADP
ejpam-4716	109	21	the	the	DET
ejpam-4716	109	22	system	system	NOUN
ejpam-4716	109	23	parameters	parameter	NOUN
ejpam-4716	109	24	plus	plus	CCONJ
ejpam-4716	109	25	three	three	NUM
ejpam-4716	109	26	others	other	NOUN
ejpam-4716	109	27	,	,	PUNCT
ejpam-4716	109	28	whose	whose	DET
ejpam-4716	109	29	existence	existence	NOUN
ejpam-4716	109	30	depends	depend	VERB
ejpam-4716	109	31	on	on	ADP
ejpam-4716	109	32	the	the	DET
ejpam-4716	109	33	change	change	NOUN
ejpam-4716	109	34	in	in	ADP
ejpam-4716	109	35	the	the	DET
ejpam-4716	109	36	values	value	NOUN
ejpam-4716	109	37	of	of	ADP
ejpam-4716	109	38	the	the	DET
ejpam-4716	109	39	system	system	NOUN
ejpam-4716	109	40	parameters	parameter	NOUN
ejpam-4716	109	41	.	.	PUNCT
ejpam-4716	110	1	the	the	DET
ejpam-4716	110	2	equilibrium	equilibrium	NOUN
ejpam-4716	110	3	point	point	NOUN
ejpam-4716	110	4	are	be	AUX
ejpam-4716	110	5	given	give	VERB
ejpam-4716	110	6	as	as	SCONJ
ejpam-4716	110	7	follows	follow	VERB
ejpam-4716	110	8	:	:	PUNCT
ejpam-4716	110	9	(	(	PUNCT
ejpam-4716	110	10	i	i	NOUN
ejpam-4716	110	11	)	)	PUNCT
ejpam-4716	110	12	the	the	DET
ejpam-4716	110	13	equilibrium	equilibrium	NOUN
ejpam-4716	110	14	points	point	NOUN
ejpam-4716	110	15	p0	p0	NOUN
ejpam-4716	110	16	=	=	SYM
ejpam-4716	110	17	(	(	PUNCT
ejpam-4716	110	18	0	0	NUM
ejpam-4716	110	19	,	,	PUNCT
ejpam-4716	110	20	0	0	NUM
ejpam-4716	110	21	,	,	PUNCT
ejpam-4716	110	22	0	0	NUM
ejpam-4716	110	23	,	,	PUNCT
ejpam-4716	110	24	0	0	NUM
ejpam-4716	110	25	)	)	PUNCT
ejpam-4716	110	26	,	,	PUNCT
ejpam-4716	110	27	p1	p1	NOUN
ejpam-4716	110	28	=	=	SYM
ejpam-4716	110	29	(	(	PUNCT
ejpam-4716	110	30	k1	k1	PROPN
ejpam-4716	110	31	,	,	PUNCT
ejpam-4716	110	32	0	0	NUM
ejpam-4716	110	33	,	,	PUNCT
ejpam-4716	110	34	0	0	NUM
ejpam-4716	110	35	,	,	PUNCT
ejpam-4716	110	36	0	0	NUM
ejpam-4716	110	37	)	)	PUNCT
ejpam-4716	110	38	,	,	PUNCT
ejpam-4716	110	39	p2	p2	X
ejpam-4716	110	40	=	=	SYM
ejpam-4716	110	41	(	(	PUNCT
ejpam-4716	110	42	0	0	NUM
ejpam-4716	110	43	,	,	PUNCT
ejpam-4716	110	44	k2	k2	NOUN
ejpam-4716	110	45	,	,	PUNCT
ejpam-4716	110	46	0	0	NUM
ejpam-4716	110	47	,	,	PUNCT
ejpam-4716	110	48	0	0	NUM
ejpam-4716	110	49	)	)	PUNCT
ejpam-4716	110	50	and	and	CCONJ
ejpam-4716	110	51	p3	p3	PROPN
ejpam-4716	110	52	=	=	SYM
ejpam-4716	110	53	(	(	PUNCT
ejpam-4716	110	54	k1	k1	PROPN
ejpam-4716	110	55	,	,	PUNCT
ejpam-4716	110	56	k2	k2	NOUN
ejpam-4716	110	57	,	,	PUNCT
ejpam-4716	110	58	0	0	NUM
ejpam-4716	110	59	,	,	PUNCT
ejpam-4716	110	60	0	0	NUM
ejpam-4716	110	61	)	)	PUNCT
ejpam-4716	110	62	always	always	ADV
ejpam-4716	110	63	exist	exist	VERB
ejpam-4716	110	64	.	.	PUNCT
ejpam-4716	111	1	(	(	PUNCT
ejpam-4716	111	2	ii	ii	X
ejpam-4716	111	3	)	)	PUNCT
ejpam-4716	111	4	the	the	DET
ejpam-4716	111	5	equilibrium	equilibrium	NOUN
ejpam-4716	111	6	point	point	NOUN
ejpam-4716	111	7	p4	p4	ADJ
ejpam-4716	111	8	=	=	SYM
ejpam-4716	111	9	(	(	PUNCT
ejpam-4716	111	10	x̃1	x̃1	PROPN
ejpam-4716	111	11	,	,	PUNCT
ejpam-4716	111	12	x̃2	x̃2	PROPN
ejpam-4716	111	13	,	,	PUNCT
ejpam-4716	111	14	ỹ1	ỹ1	PROPN
ejpam-4716	111	15	,	,	PUNCT
ejpam-4716	111	16	0	0	NUM
ejpam-4716	111	17	)	)	PUNCT
ejpam-4716	111	18	,	,	PUNCT
ejpam-4716	111	19	where	where	SCONJ
ejpam-4716	111	20	:	:	PUNCT
ejpam-4716	111	21	x̃1	x̃1	PROPN
ejpam-4716	111	22	=	=	PROPN
ejpam-4716	111	23	µ1(1	µ1(1	VERB
ejpam-4716	111	24	+	+	PROPN
ejpam-4716	111	25	x̃	x̃	PROPN
ejpam-4716	111	26	)	)	PUNCT
ejpam-4716	111	27	ϵ1	ϵ1	PROPN
ejpam-4716	111	28	,	,	PUNCT
ejpam-4716	111	29	x̃2	x̃2	PROPN
ejpam-4716	112	1	=	=	PUNCT
ejpam-4716	112	2	x̃1	x̃1	PROPN
ejpam-4716	112	3	x̌	x̌	PROPN
ejpam-4716	112	4	,	,	PUNCT
ejpam-4716	112	5	ỹ1	ỹ1	PROPN
ejpam-4716	112	6	=	=	SYM
ejpam-4716	112	7	g1	g1	PROPN
ejpam-4716	112	8	(	(	PUNCT
ejpam-4716	112	9	1−	1−	NUM
ejpam-4716	112	10	x̃1	x̃1	PROPN
ejpam-4716	112	11	k1	k1	PROPN
ejpam-4716	112	12	)	)	PUNCT
ejpam-4716	112	13	(	(	PUNCT
ejpam-4716	112	14	1	1	X
ejpam-4716	112	15	+	+	CCONJ
ejpam-4716	112	16	x̃	x̃	PROPN
ejpam-4716	112	17	)	)	PUNCT
ejpam-4716	112	18	α1	α1	PROPN
ejpam-4716	112	19	(	(	PUNCT
ejpam-4716	112	20	5	5	NUM
ejpam-4716	112	21	)	)	PUNCT
ejpam-4716	112	22	and	and	CCONJ
ejpam-4716	112	23	x̃	x̃	PROPN
ejpam-4716	112	24	is	be	AUX
ejpam-4716	112	25	a	a	DET
ejpam-4716	112	26	positive	positive	ADJ
ejpam-4716	112	27	root	root	NOUN
ejpam-4716	112	28	of	of	ADP
ejpam-4716	112	29	the	the	DET
ejpam-4716	112	30	equation	equation	NOUN
ejpam-4716	112	31	(	(	PUNCT
ejpam-4716	112	32	7	7	NUM
ejpam-4716	112	33	)	)	PUNCT
ejpam-4716	112	34	below	below	ADV
ejpam-4716	112	35	,	,	PUNCT
ejpam-4716	112	36	provided	provide	VERB
ejpam-4716	112	37	that	that	SCONJ
ejpam-4716	112	38	x̃	x̃	PROPN
ejpam-4716	112	39	<	<	X
ejpam-4716	112	40	ε1k1	ε1k1	PRON
ejpam-4716	112	41	−	−	PROPN
ejpam-4716	112	42	µ1	µ1	PROPN
ejpam-4716	112	43	µ1	µ1	PROPN
ejpam-4716	112	44	(	(	PUNCT
ejpam-4716	112	45	6	6	NUM
ejpam-4716	112	46	)	)	PUNCT
ejpam-4716	112	47	a1x̃	a1x̃	NOUN
ejpam-4716	112	48	3	3	NUM
ejpam-4716	112	49	+	+	CCONJ
ejpam-4716	112	50	a2x̃	a2x̃	VERB
ejpam-4716	112	51	2	2	NUM
ejpam-4716	113	1	+	+	CCONJ
ejpam-4716	113	2	a3x̃+	a3x̃+	ADJ
ejpam-4716	113	3	a4	a4	NOUN
ejpam-4716	113	4	=	=	SYM
ejpam-4716	113	5	0	0	NUM
ejpam-4716	113	6	,	,	PUNCT
ejpam-4716	113	7	(	(	PUNCT
ejpam-4716	113	8	7	7	X
ejpam-4716	113	9	)	)	PUNCT
ejpam-4716	113	10	such	such	ADJ
ejpam-4716	113	11	that	that	DET
ejpam-4716	113	12	a1	a1	NOUN
ejpam-4716	113	13	=	=	SYM
ejpam-4716	113	14	g1β1k2µ1	g1β1k2µ1	PROPN
ejpam-4716	113	15	>	>	SYM
ejpam-4716	113	16	0	0	NUM
ejpam-4716	113	17	,	,	PUNCT
ejpam-4716	113	18	a2	a2	PROPN
ejpam-4716	113	19	=	=	PUNCT
ejpam-4716	113	20	g1β1k2(µ1	g1β1k2(µ1	PROPN
ejpam-4716	113	21	−	−	PROPN
ejpam-4716	113	22	k1ε1	k1ε1	PROPN
ejpam-4716	113	23	)	)	PUNCT
ejpam-4716	113	24	<	<	X
ejpam-4716	113	25	0	0	NUM
ejpam-4716	113	26	,	,	PUNCT
ejpam-4716	113	27	a.	a.	NOUN
ejpam-4716	113	28	g.	g.	PROPN
ejpam-4716	113	29	farhan	farhan	PROPN
ejpam-4716	113	30	,	,	PUNCT
ejpam-4716	113	31	n.	n.	PROPN
ejpam-4716	113	32	sh	sh	PROPN
ejpam-4716	113	33	.	.	PROPN
ejpam-4716	113	34	khalaf	khalaf	PROPN
ejpam-4716	113	35	,	,	PUNCT
ejpam-4716	113	36	t.	t.	PROPN
ejpam-4716	113	37	j.	j.	PROPN
ejpam-4716	113	38	aldhlki	aldhlki	PROPN
ejpam-4716	113	39	/	/	SYM
ejpam-4716	113	40	eur	eur	PROPN
ejpam-4716	113	41	.	.	PUNCT
ejpam-4716	114	1	j.	j.	PROPN
ejpam-4716	114	2	pure	pure	PROPN
ejpam-4716	114	3	appl	appl	PROPN
ejpam-4716	114	4	.	.	PROPN
ejpam-4716	114	5	math	math	PROPN
ejpam-4716	114	6	,	,	PUNCT
ejpam-4716	114	7	16	16	NUM
ejpam-4716	114	8	(	(	PUNCT
ejpam-4716	114	9	2	2	NUM
ejpam-4716	114	10	)	)	PUNCT
ejpam-4716	114	11	(	(	PUNCT
ejpam-4716	114	12	2023	2023	NUM
ejpam-4716	114	13	)	)	PUNCT
ejpam-4716	114	14	,	,	PUNCT
ejpam-4716	114	15	899	899	NUM
ejpam-4716	114	16	-	-	SYM
ejpam-4716	114	17	918	918	NUM
ejpam-4716	114	18	903	903	NUM
ejpam-4716	114	19	a3	a3	NOUN
ejpam-4716	114	20	=	=	PUNCT
ejpam-4716	115	1	g2α1k1(k2ε1	g2α1k1(k2ε1	PART
ejpam-4716	115	2	−	−	PROPN
ejpam-4716	115	3	µ1	µ1	PROPN
ejpam-4716	115	4	)	)	PUNCT
ejpam-4716	115	5	,	,	PUNCT
ejpam-4716	115	6	a4	a4	NOUN
ejpam-4716	116	1	=	=	SYM
ejpam-4716	116	2	−g2α1k1µ1	−g2α1k1µ1	NOUN
ejpam-4716	116	3	<	<	X
ejpam-4716	116	4	0	0	NUM
ejpam-4716	116	5	.	.	PUNCT
ejpam-4716	117	1	the	the	DET
ejpam-4716	117	2	number	number	NOUN
ejpam-4716	117	3	of	of	ADP
ejpam-4716	117	4	sign	sign	NOUN
ejpam-4716	117	5	changes	change	NOUN
ejpam-4716	117	6	between	between	ADP
ejpam-4716	117	7	a1,a2,a3	a1,a2,a3	ADJ
ejpam-4716	117	8	,	,	PUNCT
ejpam-4716	117	9	and	and	CCONJ
ejpam-4716	117	10	a4	a4	NOUN
ejpam-4716	117	11	is	be	AUX
ejpam-4716	117	12	one	one	NUM
ejpam-4716	117	13	if	if	SCONJ
ejpam-4716	117	14	a3	a3	VERB
ejpam-4716	117	15	<	<	X
ejpam-4716	117	16	0	0	NUM
ejpam-4716	117	17	,	,	PUNCT
ejpam-4716	117	18	and	and	CCONJ
ejpam-4716	117	19	three	three	NUM
ejpam-4716	117	20	if	if	SCONJ
ejpam-4716	117	21	a3	a3	PROPN
ejpam-4716	117	22	>	>	X
ejpam-4716	117	23	0	0	X
ejpam-4716	117	24	.	.	PUNCT
ejpam-4716	118	1	according	accord	VERB
ejpam-4716	118	2	to	to	ADP
ejpam-4716	118	3	descartes	descartes	PROPN
ejpam-4716	118	4	’	'	PUNCT
ejpam-4716	118	5	rule	rule	NOUN
ejpam-4716	118	6	of	of	ADP
ejpam-4716	118	7	sign	sign	NOUN
ejpam-4716	118	8	,	,	PUNCT
ejpam-4716	118	9	equation	equation	NOUN
ejpam-4716	118	10	(	(	PUNCT
ejpam-4716	118	11	7	7	X
ejpam-4716	118	12	)	)	PUNCT
ejpam-4716	118	13	has	have	VERB
ejpam-4716	118	14	at	at	ADP
ejpam-4716	118	15	most	most	ADV
ejpam-4716	118	16	one	one	NUM
ejpam-4716	118	17	positive	positive	ADJ
ejpam-4716	118	18	root	root	NOUN
ejpam-4716	118	19	if	if	SCONJ
ejpam-4716	118	20	a3	a3	VERB
ejpam-4716	118	21	<	<	X
ejpam-4716	118	22	0	0	NUM
ejpam-4716	118	23	,	,	PUNCT
ejpam-4716	118	24	and	and	CCONJ
ejpam-4716	118	25	at	at	ADP
ejpam-4716	118	26	most	most	ADV
ejpam-4716	118	27	three	three	NUM
ejpam-4716	118	28	positive	positive	ADJ
ejpam-4716	118	29	root	root	NOUN
ejpam-4716	118	30	if	if	SCONJ
ejpam-4716	118	31	a3	a3	PROPN
ejpam-4716	118	32	>	>	X
ejpam-4716	118	33	0	0	X
ejpam-4716	118	34	.	.	PUNCT
ejpam-4716	119	1	therefore	therefore	ADV
ejpam-4716	119	2	,	,	PUNCT
ejpam-4716	119	3	the	the	DET
ejpam-4716	119	4	existence	existence	NOUN
ejpam-4716	119	5	of	of	ADP
ejpam-4716	119	6	p4	p4	ADJ
ejpam-4716	119	7	depends	depend	VERB
ejpam-4716	119	8	on	on	ADP
ejpam-4716	119	9	the	the	DET
ejpam-4716	119	10	existence	existence	NOUN
ejpam-4716	119	11	of	of	ADP
ejpam-4716	119	12	the	the	DET
ejpam-4716	119	13	positive	positive	ADJ
ejpam-4716	119	14	root	root	NOUN
ejpam-4716	119	15	x̃	x̃	PROPN
ejpam-4716	119	16	achieves	achieve	VERB
ejpam-4716	119	17	the	the	DET
ejpam-4716	119	18	two	two	NUM
ejpam-4716	119	19	equations	equation	NOUN
ejpam-4716	119	20	(	(	PUNCT
ejpam-4716	119	21	6	6	NUM
ejpam-4716	119	22	)	)	PUNCT
ejpam-4716	119	23	and	and	CCONJ
ejpam-4716	119	24	(	(	PUNCT
ejpam-4716	119	25	7	7	NUM
ejpam-4716	119	26	)	)	PUNCT
ejpam-4716	119	27	.	.	PUNCT
ejpam-4716	120	1	(	(	PUNCT
ejpam-4716	120	2	iii	iii	X
ejpam-4716	120	3	)	)	PUNCT
ejpam-4716	120	4	the	the	DET
ejpam-4716	120	5	equilibrium	equilibrium	NOUN
ejpam-4716	120	6	point	point	NOUN
ejpam-4716	120	7	p5	p5	PROPN
ejpam-4716	120	8	=	=	PUNCT
ejpam-4716	120	9	(	(	PUNCT
ejpam-4716	120	10	x̌1	x̌1	NUM
ejpam-4716	120	11	,	,	PUNCT
ejpam-4716	120	12	x̌2	x̌2	NUM
ejpam-4716	120	13	,	,	PUNCT
ejpam-4716	120	14	0	0	NUM
ejpam-4716	120	15	,	,	PUNCT
ejpam-4716	120	16	y̌2	y̌2	PRON
ejpam-4716	120	17	)	)	PUNCT
ejpam-4716	120	18	,	,	PUNCT
ejpam-4716	120	19	where	where	SCONJ
ejpam-4716	120	20	:	:	PUNCT
ejpam-4716	120	21	x̌1	x̌1	X
ejpam-4716	120	22	=	=	X
ejpam-4716	120	23	µ2	µ2	PROPN
ejpam-4716	120	24	(	(	PUNCT
ejpam-4716	120	25	1	1	NUM
ejpam-4716	120	26	+	+	CCONJ
ejpam-4716	120	27	x̌	x̌	X
ejpam-4716	120	28	)	)	PUNCT
ejpam-4716	120	29	ε2	ε2	ADV
ejpam-4716	120	30	,	,	PUNCT
ejpam-4716	120	31	x̌2	x̌2	NOUN
ejpam-4716	120	32	=	=	SYM
ejpam-4716	120	33	x̌1	x̌1	X
ejpam-4716	120	34	x̌	x̌	PROPN
ejpam-4716	120	35	,	,	PUNCT
ejpam-4716	120	36	y̌2	y̌2	PRON
ejpam-4716	120	37	=	=	PUNCT
ejpam-4716	120	38	g1	g1	PROPN
ejpam-4716	120	39	(	(	PUNCT
ejpam-4716	120	40	1−	1−	NUM
ejpam-4716	120	41	µ2	µ2	PROPN
ejpam-4716	120	42	(	(	PUNCT
ejpam-4716	120	43	1	1	NUM
ejpam-4716	120	44	+	+	CCONJ
ejpam-4716	120	45	x̌	x̌	X
ejpam-4716	120	46	)	)	PUNCT
ejpam-4716	120	47	ε2k1	ε2k1	NOUN
ejpam-4716	120	48	)	)	PUNCT
ejpam-4716	120	49	(	(	PUNCT
ejpam-4716	120	50	1	1	NUM
ejpam-4716	120	51	+	+	CCONJ
ejpam-4716	120	52	x̌	x̌	X
ejpam-4716	120	53	)	)	PUNCT
ejpam-4716	120	54	α2	α2	NOUN
ejpam-4716	120	55	(	(	PUNCT
ejpam-4716	120	56	8)	8)	NUM
ejpam-4716	120	57	and	and	CCONJ
ejpam-4716	120	58	x̌	x̌	PROPN
ejpam-4716	120	59	is	be	AUX
ejpam-4716	120	60	a	a	DET
ejpam-4716	120	61	positive	positive	ADJ
ejpam-4716	120	62	root	root	NOUN
ejpam-4716	120	63	of	of	ADP
ejpam-4716	120	64	equation	equation	NOUN
ejpam-4716	120	65	(	(	PUNCT
ejpam-4716	120	66	10	10	NUM
ejpam-4716	120	67	)	)	PUNCT
ejpam-4716	120	68	below	below	ADV
ejpam-4716	120	69	,	,	PUNCT
ejpam-4716	120	70	provided	provide	VERB
ejpam-4716	120	71	that	that	SCONJ
ejpam-4716	120	72	:	:	PUNCT
ejpam-4716	121	1	x̌	x̌	PROPN
ejpam-4716	121	2	<	<	X
ejpam-4716	121	3	ε2k1	ε2k1	X
ejpam-4716	121	4	−	−	PROPN
ejpam-4716	121	5	µ2	µ2	PROPN
ejpam-4716	121	6	µ2	µ2	PROPN
ejpam-4716	121	7	,	,	PUNCT
ejpam-4716	121	8	(	(	PUNCT
ejpam-4716	121	9	9	9	X
ejpam-4716	121	10	)	)	PUNCT
ejpam-4716	121	11	b1x̌	b1x̌	NOUN
ejpam-4716	121	12	3	3	NUM
ejpam-4716	121	13	+	+	CCONJ
ejpam-4716	121	14	b2x̌	b2x̌	PROPN
ejpam-4716	121	15	2	2	NUM
ejpam-4716	121	16	+	+	NUM
ejpam-4716	121	17	b3x̌+	b3x̌+	NOUN
ejpam-4716	121	18	b4	b4	NOUN
ejpam-4716	121	19	=	=	SYM
ejpam-4716	121	20	0	0	NUM
ejpam-4716	121	21	,	,	PUNCT
ejpam-4716	121	22	(	(	PUNCT
ejpam-4716	121	23	10	10	NUM
ejpam-4716	121	24	)	)	PUNCT
ejpam-4716	121	25	such	such	ADJ
ejpam-4716	121	26	that	that	SCONJ
ejpam-4716	121	27	:	:	PUNCT
ejpam-4716	121	28	b1	b1	PROPN
ejpam-4716	121	29	=	=	SYM
ejpam-4716	121	30	g1β2k2µ2	g1β2k2µ2	PROPN
ejpam-4716	121	31	,	,	PUNCT
ejpam-4716	121	32	b2	b2	NOUN
ejpam-4716	121	33	=	=	SYM
ejpam-4716	121	34	g1β2k2	g1β2k2	PROPN
ejpam-4716	121	35	(	(	PUNCT
ejpam-4716	121	36	µ2	µ2	PROPN
ejpam-4716	121	37	−	−	PROPN
ejpam-4716	121	38	k1ε2	k1ε2	NOUN
ejpam-4716	121	39	)	)	PUNCT
ejpam-4716	121	40	<	<	X
ejpam-4716	121	41	0	0	NUM
ejpam-4716	121	42	,	,	PUNCT
ejpam-4716	121	43	b3	b3	PROPN
ejpam-4716	121	44	=	=	SYM
ejpam-4716	121	45	g2α2k1	g2α2k1	PROPN
ejpam-4716	121	46	(	(	PUNCT
ejpam-4716	121	47	k2ε2	k2ε2	NOUN
ejpam-4716	121	48	−	−	PROPN
ejpam-4716	121	49	µ2	µ2	PROPN
ejpam-4716	121	50	)	)	PUNCT
ejpam-4716	121	51	,	,	PUNCT
ejpam-4716	121	52	b4	b4	NOUN
ejpam-4716	121	53	=	=	PUNCT
ejpam-4716	121	54	−g2α2k1µ2	−g2α2k1µ2	PROPN
ejpam-4716	121	55	.	.	PUNCT
ejpam-4716	122	1	the	the	DET
ejpam-4716	122	2	number	number	NOUN
ejpam-4716	122	3	of	of	ADP
ejpam-4716	122	4	sign	sign	NOUN
ejpam-4716	122	5	changes	change	NOUN
ejpam-4716	122	6	between	between	ADP
ejpam-4716	122	7	b1,b2,b3	b1,b2,b3	PROPN
ejpam-4716	122	8	,	,	PUNCT
ejpam-4716	122	9	and	and	CCONJ
ejpam-4716	122	10	b4	b4	NOUN
ejpam-4716	122	11	is	be	AUX
ejpam-4716	122	12	one	one	NUM
ejpam-4716	122	13	if	if	SCONJ
ejpam-4716	122	14	b3	b3	PROPN
ejpam-4716	122	15	<	<	X
ejpam-4716	122	16	0	0	NUM
ejpam-4716	122	17	,	,	PUNCT
ejpam-4716	122	18	and	and	CCONJ
ejpam-4716	122	19	,	,	PUNCT
ejpam-4716	122	20	three	three	NUM
ejpam-4716	122	21	if	if	SCONJ
ejpam-4716	122	22	b3	b3	PROPN
ejpam-4716	122	23	>	>	X
ejpam-4716	122	24	0	0	X
ejpam-4716	122	25	.	.	PUNCT
ejpam-4716	123	1	based	base	VERB
ejpam-4716	123	2	on	on	ADP
ejpam-4716	123	3	descartes	descarte	NOUN
ejpam-4716	123	4	’	'	PUNCT
ejpam-4716	123	5	rule	rule	NOUN
ejpam-4716	123	6	of	of	ADP
ejpam-4716	123	7	sign	sign	NOUN
ejpam-4716	123	8	.	.	PUNCT
ejpam-4716	124	1	,	,	PUNCT
ejpam-4716	124	2	eq.(10	eq.(10	NOUN
ejpam-4716	124	3	)	)	PUNCT
ejpam-4716	124	4	has	have	VERB
ejpam-4716	124	5	at	at	ADP
ejpam-4716	124	6	most	most	ADV
ejpam-4716	124	7	one	one	NUM
ejpam-4716	124	8	positive	positive	ADJ
ejpam-4716	124	9	root	root	NOUN
ejpam-4716	124	10	if	if	SCONJ
ejpam-4716	124	11	b3	b3	PROPN
ejpam-4716	124	12	<	<	X
ejpam-4716	124	13	0	0	NUM
ejpam-4716	124	14	,	,	PUNCT
ejpam-4716	124	15	and	and	CCONJ
ejpam-4716	124	16	at	at	ADP
ejpam-4716	124	17	most	most	ADV
ejpam-4716	124	18	three	three	NUM
ejpam-4716	124	19	positive	positive	ADJ
ejpam-4716	124	20	root	root	NOUN
ejpam-4716	124	21	if	if	SCONJ
ejpam-4716	124	22	b3	b3	PROPN
ejpam-4716	124	23	>	>	X
ejpam-4716	124	24	0	0	X
ejpam-4716	124	25	.	.	PUNCT
ejpam-4716	125	1	therefore	therefore	ADV
ejpam-4716	125	2	,	,	PUNCT
ejpam-4716	125	3	the	the	DET
ejpam-4716	125	4	existence	existence	NOUN
ejpam-4716	125	5	of	of	ADP
ejpam-4716	125	6	p5	p5	PROPN
ejpam-4716	125	7	depends	depend	VERB
ejpam-4716	125	8	on	on	ADP
ejpam-4716	125	9	the	the	DET
ejpam-4716	125	10	existence	existence	NOUN
ejpam-4716	125	11	of	of	ADP
ejpam-4716	125	12	the	the	DET
ejpam-4716	125	13	positive	positive	ADJ
ejpam-4716	125	14	root	root	NOUN
ejpam-4716	125	15	x̌	x̌	PROPN
ejpam-4716	125	16	achieves	achieve	VERB
ejpam-4716	125	17	the	the	DET
ejpam-4716	125	18	two	two	NUM
ejpam-4716	125	19	equations	equation	NOUN
ejpam-4716	125	20	(	(	PUNCT
ejpam-4716	125	21	9	9	NUM
ejpam-4716	125	22	)	)	PUNCT
ejpam-4716	125	23	and	and	CCONJ
ejpam-4716	125	24	(	(	PUNCT
ejpam-4716	125	25	10	10	NUM
ejpam-4716	125	26	)	)	PUNCT
ejpam-4716	125	27	.	.	PUNCT
ejpam-4716	126	1	(	(	PUNCT
ejpam-4716	126	2	iv	iv	X
ejpam-4716	126	3	)	)	PUNCT
ejpam-4716	126	4	the	the	DET
ejpam-4716	126	5	interior	interior	ADJ
ejpam-4716	126	6	equilibrium	equilibrium	NOUN
ejpam-4716	126	7	point	point	NOUN
ejpam-4716	126	8	or	or	CCONJ
ejpam-4716	126	9	the	the	DET
ejpam-4716	126	10	coexistence	coexistence	NOUN
ejpam-4716	126	11	point	point	NOUN
ejpam-4716	126	12	p	p	NOUN
ejpam-4716	126	13	6	6	NUM
ejpam-4716	126	14	=	=	SYM
ejpam-4716	126	15	(	(	PUNCT
ejpam-4716	126	16	x1	x1	PROPN
ejpam-4716	126	17	,	,	PUNCT
ejpam-4716	126	18	x2	x2	PROPN
ejpam-4716	126	19	,	,	PUNCT
ejpam-4716	126	20	y1	y1	NOUN
ejpam-4716	126	21	,	,	PUNCT
ejpam-4716	126	22	y2	y2	PROPN
ejpam-4716	126	23	)	)	PUNCT
ejpam-4716	126	24	,	,	PUNCT
ejpam-4716	126	25	where	where	SCONJ
ejpam-4716	126	26	x1	x1	PROPN
ejpam-4716	126	27	=	=	PUNCT
ejpam-4716	126	28	k1k2(1	k1k2(1	NOUN
ejpam-4716	126	29	+	+	NUM
ejpam-4716	126	30	h	h	NOUN
ejpam-4716	126	31	)	)	PUNCT
ejpam-4716	126	32	(	(	PUNCT
ejpam-4716	126	33	(	(	PUNCT
ejpam-4716	126	34	α1β2	α1β2	ADP
ejpam-4716	126	35	−	−	X
ejpam-4716	126	36	α2β1)hµ2	α2β1)hµ2	X
ejpam-4716	127	1	+	+	CCONJ
ejpam-4716	127	2	ρ1(1	ρ1(1	PROPN
ejpam-4716	127	3	+	+	CCONJ
ejpam-4716	127	4	h)(α2g2h−	h)(α2g2h−	ADJ
ejpam-4716	127	5	β2g1	β2g1	NOUN
ejpam-4716	127	6	)	)	PUNCT
ejpam-4716	127	7	)	)	PUNCT
ejpam-4716	128	1	ρ1(1	ρ1(1	PROPN
ejpam-4716	128	2	+	+	NUM
ejpam-4716	128	3	h)2	h)2	NOUN
ejpam-4716	128	4	(	(	PUNCT
ejpam-4716	128	5	k1	k1	X
ejpam-4716	128	6	α2g2h	α2g2h	NUM
ejpam-4716	128	7	2	2	NUM
ejpam-4716	128	8	−	−	PROPN
ejpam-4716	128	9	k2β2g1	k2β2g1	PROPN
ejpam-4716	128	10	)	)	PUNCT
ejpam-4716	128	11	+	+	CCONJ
ejpam-4716	128	12	k1k2ε2h2	k1k2ε2h2	PROPN
ejpam-4716	128	13	(	(	PUNCT
ejpam-4716	128	14	α1β2	α1β2	ADP
ejpam-4716	128	15	−	−	PROPN
ejpam-4716	128	16	α2β1	α2β1	NOUN
ejpam-4716	128	17	)	)	PUNCT
ejpam-4716	128	18	,	,	PUNCT
ejpam-4716	128	19	x2	x2	NOUN
ejpam-4716	128	20	=	=	PUNCT
ejpam-4716	128	21	hx1	hx1	PROPN
ejpam-4716	128	22	,	,	PUNCT
ejpam-4716	128	23	y1	y1	NOUN
ejpam-4716	128	24	=	=	PUNCT
ejpam-4716	128	25	(	(	PUNCT
ejpam-4716	128	26	1	1	NUM
ejpam-4716	128	27	+	+	CCONJ
ejpam-4716	128	28	h)µ2	h)µ2	PROPN
ejpam-4716	128	29	−	−	PROPN
ejpam-4716	128	30	hε2	hε2	NOUN
ejpam-4716	128	31	ρ1	ρ1	NOUN
ejpam-4716	128	32	(	(	PUNCT
ejpam-4716	128	33	1	1	NUM
ejpam-4716	128	34	+	+	NUM
ejpam-4716	128	35	h	h	NOUN
ejpam-4716	128	36	)	)	PUNCT
ejpam-4716	128	37	,	,	PUNCT
ejpam-4716	128	38	y2	y2	NOUN
ejpam-4716	128	39	=	=	PUNCT
ejpam-4716	129	1	hε1	hε1	INTJ
ejpam-4716	129	2	−	−	PROPN
ejpam-4716	129	3	(	(	PUNCT
ejpam-4716	129	4	1	1	NUM
ejpam-4716	129	5	+	+	CCONJ
ejpam-4716	129	6	h)µ1	h)µ1	ADJ
ejpam-4716	129	7	ρ2	ρ2	NOUN
ejpam-4716	129	8	(	(	PUNCT
ejpam-4716	129	9	1	1	NUM
ejpam-4716	129	10	+	+	NUM
ejpam-4716	130	1	h	h	NOUN
ejpam-4716	130	2	)	)	PUNCT
ejpam-4716	131	1	,	,	PUNCT
ejpam-4716	131	2	(	(	PUNCT
ejpam-4716	131	3	11	11	NUM
ejpam-4716	131	4	)	)	PUNCT
ejpam-4716	131	5	and	and	CCONJ
ejpam-4716	131	6	h	h	NOUN
ejpam-4716	131	7	=	=	SYM
ejpam-4716	131	8	x2x	x2x	PUNCT
ejpam-4716	131	9	−1	−1	NOUN
ejpam-4716	131	10	1	1	NUM
ejpam-4716	131	11	,	,	PUNCT
ejpam-4716	131	12	is	be	AUX
ejpam-4716	131	13	a	a	DET
ejpam-4716	131	14	positive	positive	ADJ
ejpam-4716	131	15	real	real	ADJ
ejpam-4716	131	16	root	root	NOUN
ejpam-4716	131	17	of	of	ADP
ejpam-4716	131	18	the	the	DET
ejpam-4716	131	19	following	follow	VERB
ejpam-4716	131	20	equation	equation	NOUN
ejpam-4716	131	21	:	:	PUNCT
ejpam-4716	131	22	ah4	ah4	NOUN
ejpam-4716	131	23	+	+	CCONJ
ejpam-4716	131	24	bh3	bh3	ADJ
ejpam-4716	131	25	+	+	CCONJ
ejpam-4716	131	26	ch2	ch2	NOUN
ejpam-4716	131	27	+	+	CCONJ
ejpam-4716	131	28	dh+	dh+	ADJ
ejpam-4716	131	29	e	e	NOUN
ejpam-4716	131	30	=	=	SYM
ejpam-4716	131	31	0	0	NUM
ejpam-4716	131	32	,	,	PUNCT
ejpam-4716	131	33	(	(	PUNCT
ejpam-4716	131	34	12	12	NUM
ejpam-4716	131	35	)	)	PUNCT
ejpam-4716	131	36	where	where	SCONJ
ejpam-4716	131	37	:	:	PUNCT
ejpam-4716	131	38	a	a	PRON
ejpam-4716	131	39	=	=	PUNCT
ejpam-4716	131	40	k1g2(α2µ1ρ1	k1g2(α2µ1ρ1	PROPN
ejpam-4716	131	41	−	−	ADP
ejpam-4716	131	42	α1µ2ρ2	α1µ2ρ2	ADJ
ejpam-4716	131	43	+	+	CCONJ
ejpam-4716	131	44	ρ1ρ2g1	ρ1ρ2g1	PROPN
ejpam-4716	131	45	)	)	PUNCT
ejpam-4716	131	46	,	,	PUNCT
ejpam-4716	132	1	b	b	X
ejpam-4716	132	2	=	=	SYM
ejpam-4716	133	1	2k1g2(α2µ1ρ1	2k1g2(α2µ1ρ1	NUM
ejpam-4716	133	2	−	−	NOUN
ejpam-4716	133	3	α1µ2ρ2	α1µ2ρ2	ADJ
ejpam-4716	133	4	)	)	PUNCT
ejpam-4716	134	1	+	+	CCONJ
ejpam-4716	134	2	3ρ1ρ2g1g2k1	3ρ1ρ2g1g2k1	NUM
ejpam-4716	134	3	−	−	NOUN
ejpam-4716	134	4	k2ρ1ρ2g1g2	k2ρ1ρ2g1g2	NUM
ejpam-4716	134	5	a.	a.	NOUN
ejpam-4716	134	6	g.	g.	PROPN
ejpam-4716	134	7	farhan	farhan	PROPN
ejpam-4716	134	8	,	,	PUNCT
ejpam-4716	134	9	n.	n.	PROPN
ejpam-4716	134	10	sh	sh	PROPN
ejpam-4716	134	11	.	.	PROPN
ejpam-4716	134	12	khalaf	khalaf	PROPN
ejpam-4716	134	13	,	,	PUNCT
ejpam-4716	134	14	t.	t.	PROPN
ejpam-4716	134	15	j.	j.	PROPN
ejpam-4716	134	16	aldhlki	aldhlki	PROPN
ejpam-4716	134	17	/	/	SYM
ejpam-4716	134	18	eur	eur	PROPN
ejpam-4716	134	19	.	.	PUNCT
ejpam-4716	135	1	j.	j.	PROPN
ejpam-4716	135	2	pure	pure	PROPN
ejpam-4716	135	3	appl	appl	PROPN
ejpam-4716	135	4	.	.	PROPN
ejpam-4716	135	5	math	math	PROPN
ejpam-4716	135	6	,	,	PUNCT
ejpam-4716	135	7	16	16	NUM
ejpam-4716	135	8	(	(	PUNCT
ejpam-4716	135	9	2	2	NUM
ejpam-4716	135	10	)	)	PUNCT
ejpam-4716	135	11	(	(	PUNCT
ejpam-4716	135	12	2023	2023	NUM
ejpam-4716	135	13	)	)	PUNCT
ejpam-4716	135	14	,	,	PUNCT
ejpam-4716	135	15	899	899	NUM
ejpam-4716	135	16	-	-	SYM
ejpam-4716	135	17	918	918	NUM
ejpam-4716	135	18	904	904	NUM
ejpam-4716	135	19	+	+	CCONJ
ejpam-4716	135	20	k1k2g2(α1ϵ2ρ2	k1k2g2(α1ϵ2ρ2	PROPN
ejpam-4716	135	21	−	−	PROPN
ejpam-4716	135	22	α2ϵ1ρ1	α2ϵ1ρ1	PROPN
ejpam-4716	135	23	)	)	PUNCT
ejpam-4716	135	24	,	,	PUNCT
ejpam-4716	135	25	c	c	NOUN
ejpam-4716	135	26	=	=	PUNCT
ejpam-4716	136	1	k1g2(α2µ1ρ1	k1g2(α2µ1ρ1	PROPN
ejpam-4716	136	2	−	−	PROPN
ejpam-4716	136	3	α1µ2ρ2	α1µ2ρ2	VERB
ejpam-4716	136	4	)	)	PUNCT
ejpam-4716	137	1	+	+	CCONJ
ejpam-4716	137	2	k2g1(β1µ2ρ2	k2g1(β1µ2ρ2	PROPN
ejpam-4716	137	3	−	−	PROPN
ejpam-4716	137	4	β2µ1ρ1	β2µ1ρ1	PROPN
ejpam-4716	137	5	)	)	PUNCT
ejpam-4716	137	6	−	−	NOUN
ejpam-4716	138	1	k1k2g2(α2ϵ1ρ1	k1k2g2(α2ϵ1ρ1	PROPN
ejpam-4716	138	2	−	−	PROPN
ejpam-4716	138	3	α1ϵ2ρ2	α1ϵ2ρ2	PROPN
ejpam-4716	138	4	)	)	PUNCT
ejpam-4716	139	1	+	+	CCONJ
ejpam-4716	139	2	k1k2g1(β2ϵ1ρ1	k1k2g1(β2ϵ1ρ1	PROPN
ejpam-4716	139	3	−	−	PROPN
ejpam-4716	139	4	β1ϵ2ρ2	β1ϵ2ρ2	NOUN
ejpam-4716	139	5	)	)	PUNCT
ejpam-4716	139	6	+	+	CCONJ
ejpam-4716	139	7	k1k2(α1β2	k1k2(α1β2	PROPN
ejpam-4716	139	8	−	−	PROPN
ejpam-4716	139	9	α2β1)(µ1ϵ2	α2β1)(µ1ϵ2	PROPN
ejpam-4716	139	10	−	−	NOUN
ejpam-4716	139	11	µ2ϵ1	µ2ϵ1	NOUN
ejpam-4716	139	12	)	)	PUNCT
ejpam-4716	139	13	+	+	NUM
ejpam-4716	139	14	3ρ1ρ2g1g2(k1	3ρ1ρ2g1g2(k1	NUM
ejpam-4716	139	15	−	−	PROPN
ejpam-4716	139	16	k2	k2	PROPN
ejpam-4716	139	17	)	)	PUNCT
ejpam-4716	139	18	,	,	PUNCT
ejpam-4716	140	1	d	d	NOUN
ejpam-4716	140	2	=	=	SYM
ejpam-4716	141	1	2k2g1(β1µ2ρ2	2k2g1(β1µ2ρ2	NUM
ejpam-4716	142	1	−	−	NUM
ejpam-4716	142	2	β2µ1ρ1)−	β2µ1ρ1)−	INTJ
ejpam-4716	142	3	3k2ρ1ρ2g1g2	3k2ρ1ρ2g1g2	NUM
ejpam-4716	142	4	+	+	CCONJ
ejpam-4716	142	5	ρ1ρ2g1g2k1	ρ1ρ2g1g2k1	PROPN
ejpam-4716	143	1	+	+	CCONJ
ejpam-4716	143	2	k1k2g1(β2ϵ1ρ1	k1k2g1(β2ϵ1ρ1	PROPN
ejpam-4716	143	3	−	−	PROPN
ejpam-4716	143	4	β1ϵ2ρ2	β1ϵ2ρ2	NOUN
ejpam-4716	143	5	)	)	PUNCT
ejpam-4716	144	1	,	,	PUNCT
ejpam-4716	144	2	e	e	X
ejpam-4716	144	3	=	=	SYM
ejpam-4716	144	4	k2g1(β1µ2ρ2	k2g1(β1µ2ρ2	PROPN
ejpam-4716	144	5	−	−	PROPN
ejpam-4716	144	6	β2µ1ρ1	β2µ1ρ1	ADJ
ejpam-4716	144	7	−	−	PROPN
ejpam-4716	144	8	ρ1ρ2g2	ρ1ρ2g2	NOUN
ejpam-4716	144	9	)	)	PUNCT
ejpam-4716	144	10	.	.	PUNCT
ejpam-4716	145	1	if	if	SCONJ
ejpam-4716	145	2	the	the	DET
ejpam-4716	145	3	signs	sign	NOUN
ejpam-4716	145	4	of	of	ADP
ejpam-4716	145	5	the	the	DET
ejpam-4716	145	6	coefficients	coefficient	NOUN
ejpam-4716	145	7	a	a	DET
ejpam-4716	145	8	,	,	PUNCT
ejpam-4716	145	9	b	b	NOUN
ejpam-4716	145	10	,	,	PUNCT
ejpam-4716	145	11	c	c	NOUN
ejpam-4716	145	12	,	,	PUNCT
ejpam-4716	145	13	d	d	NOUN
ejpam-4716	145	14	,	,	PUNCT
ejpam-4716	145	15	and	and	CCONJ
ejpam-4716	145	16	e	e	NOUN
ejpam-4716	145	17	are	be	AUX
ejpam-4716	145	18	positive	positive	ADJ
ejpam-4716	145	19	,	,	PUNCT
ejpam-4716	145	20	a	a	DET
ejpam-4716	145	21	positive	positive	ADJ
ejpam-4716	145	22	root	root	NOUN
ejpam-4716	145	23	can	can	AUX
ejpam-4716	145	24	not	not	PART
ejpam-4716	145	25	be	be	AUX
ejpam-4716	145	26	obtained	obtain	VERB
ejpam-4716	145	27	,	,	PUNCT
ejpam-4716	145	28	and	and	CCONJ
ejpam-4716	145	29	this	this	PRON
ejpam-4716	145	30	means	mean	VERB
ejpam-4716	145	31	that	that	SCONJ
ejpam-4716	145	32	there	there	PRON
ejpam-4716	145	33	is	be	VERB
ejpam-4716	145	34	no	no	DET
ejpam-4716	145	35	interior	interior	ADJ
ejpam-4716	145	36	equilibrium	equilibrium	NOUN
ejpam-4716	145	37	point	point	NOUN
ejpam-4716	145	38	.	.	PUNCT
ejpam-4716	146	1	otherwise	otherwise	ADV
ejpam-4716	146	2	,	,	PUNCT
ejpam-4716	146	3	there	there	PRON
ejpam-4716	146	4	is	be	VERB
ejpam-4716	146	5	a	a	DET
ejpam-4716	146	6	possibility	possibility	NOUN
ejpam-4716	146	7	of	of	ADP
ejpam-4716	146	8	finding	find	VERB
ejpam-4716	146	9	one	one	NUM
ejpam-4716	146	10	positive	positive	ADJ
ejpam-4716	146	11	root	root	NOUN
ejpam-4716	146	12	,	,	PUNCT
ejpam-4716	146	13	two	two	NUM
ejpam-4716	146	14	positive	positive	ADJ
ejpam-4716	146	15	roots	root	NOUN
ejpam-4716	146	16	,	,	PUNCT
ejpam-4716	146	17	three	three	NUM
ejpam-4716	146	18	positive	positive	ADJ
ejpam-4716	146	19	roots	root	NOUN
ejpam-4716	146	20	,	,	PUNCT
ejpam-4716	146	21	or	or	CCONJ
ejpam-4716	146	22	four	four	NUM
ejpam-4716	146	23	at	at	ADV
ejpam-4716	146	24	most	most	ADJ
ejpam-4716	146	25	,	,	PUNCT
ejpam-4716	146	26	according	accord	VERB
ejpam-4716	146	27	to	to	ADP
ejpam-4716	146	28	descartes	descarte	NOUN
ejpam-4716	146	29	’	'	PUNCT
ejpam-4716	146	30	rule	rule	NOUN
ejpam-4716	146	31	of	of	ADP
ejpam-4716	146	32	signs	sign	NOUN
ejpam-4716	146	33	.	.	PUNCT
ejpam-4716	147	1	4	4	X
ejpam-4716	147	2	.	.	X
ejpam-4716	147	3	local	local	ADJ
ejpam-4716	147	4	stability	stability	NOUN
ejpam-4716	147	5	of	of	ADP
ejpam-4716	147	6	equilibrium	equilibrium	NOUN
ejpam-4716	147	7	points	point	NOUN
ejpam-4716	147	8	in	in	ADP
ejpam-4716	147	9	this	this	DET
ejpam-4716	147	10	section	section	NOUN
ejpam-4716	147	11	,	,	PUNCT
ejpam-4716	147	12	the	the	DET
ejpam-4716	147	13	local	local	ADJ
ejpam-4716	147	14	stability	stability	NOUN
ejpam-4716	147	15	of	of	ADP
ejpam-4716	147	16	the	the	DET
ejpam-4716	147	17	equilibrium	equilibrium	NOUN
ejpam-4716	147	18	points	point	NOUN
ejpam-4716	147	19	of	of	ADP
ejpam-4716	147	20	the	the	DET
ejpam-4716	147	21	system	system	NOUN
ejpam-4716	147	22	is	be	AUX
ejpam-4716	147	23	studied	study	VERB
ejpam-4716	147	24	,	,	PUNCT
ejpam-4716	147	25	by	by	ADP
ejpam-4716	147	26	using	use	VERB
ejpam-4716	147	27	the	the	DET
ejpam-4716	147	28	following	following	ADJ
ejpam-4716	147	29	jacobian	jacobian	ADJ
ejpam-4716	147	30	matrix	matrix	NOUN
ejpam-4716	147	31	j	j	PROPN
ejpam-4716	147	32	(	(	PUNCT
ejpam-4716	147	33	x1	x1	PROPN
ejpam-4716	147	34	,	,	PUNCT
ejpam-4716	147	35	x2	x2	PROPN
ejpam-4716	147	36	,	,	PUNCT
ejpam-4716	147	37	y1	y1	NOUN
ejpam-4716	147	38	,	,	PUNCT
ejpam-4716	147	39	y2	y2	PROPN
ejpam-4716	147	40	)	)	PUNCT
ejpam-4716	147	41	of	of	ADP
ejpam-4716	147	42	the	the	DET
ejpam-4716	147	43	system	system	NOUN
ejpam-4716	147	44	(	(	PUNCT
ejpam-4716	147	45	2	2	NUM
ejpam-4716	147	46	)	)	PUNCT
ejpam-4716	147	47	at	at	ADP
ejpam-4716	147	48	each	each	DET
ejpam-4716	147	49	equilibrium	equilibrium	NOUN
ejpam-4716	147	50	point	point	NOUN
ejpam-4716	147	51	[	[	X
ejpam-4716	147	52	6	6	NUM
ejpam-4716	147	53	]	]	PUNCT
ejpam-4716	147	54	,	,	PUNCT
ejpam-4716	148	1	[	[	X
ejpam-4716	148	2	11	11	NUM
ejpam-4716	148	3	]	]	PUNCT
ejpam-4716	148	4	,	,	PUNCT
ejpam-4716	148	5	[	[	X
ejpam-4716	148	6	12	12	NUM
ejpam-4716	148	7	]	]	PUNCT
ejpam-4716	148	8	.	.	PUNCT
ejpam-4716	149	1	j(x1	j(x1	PROPN
ejpam-4716	149	2	,	,	PUNCT
ejpam-4716	149	3	x2	x2	PROPN
ejpam-4716	149	4	,	,	PUNCT
ejpam-4716	149	5	y1	y1	NOUN
ejpam-4716	149	6	,	,	PUNCT
ejpam-4716	149	7	y2	y2	NOUN
ejpam-4716	149	8	)	)	PUNCT
ejpam-4716	149	9	=	=	PUNCT
ejpam-4716	149	10			PROPN
ejpam-4716	149	11	∂ẋ1	∂ẋ1	PROPN
ejpam-4716	149	12	∂x1	∂x1	PROPN
ejpam-4716	149	13	∂ẋ1	∂ẋ1	PROPN
ejpam-4716	149	14	∂x2	∂x2	PROPN
ejpam-4716	149	15	∂ẋ1	∂ẋ1	PROPN
ejpam-4716	149	16	∂y1	∂y1	PROPN
ejpam-4716	149	17	∂ẋ1	∂ẋ1	PROPN
ejpam-4716	149	18	∂y2	∂y2	ADJ
ejpam-4716	149	19	∂ẋ2	∂ẋ2	PROPN
ejpam-4716	149	20	∂x1	∂x1	NOUN
ejpam-4716	149	21	∂ẋ2	∂ẋ2	PROPN
ejpam-4716	149	22	∂x2	∂x2	NOUN
ejpam-4716	149	23	∂ẋ2	∂ẋ2	PROPN
ejpam-4716	149	24	∂y1	∂y1	PROPN
ejpam-4716	149	25	∂ẋ2	∂ẋ2	PROPN
ejpam-4716	149	26	∂y2	∂y2	VERB
ejpam-4716	149	27	∂ẏ1	∂ẏ1	PROPN
ejpam-4716	149	28	∂x1	∂x1	PROPN
ejpam-4716	149	29	∂ẏ1	∂ẏ1	PROPN
ejpam-4716	149	30	∂x2	∂x2	NOUN
ejpam-4716	149	31	∂ẏ1	∂ẏ1	PROPN
ejpam-4716	149	32	∂y1	∂y1	PROPN
ejpam-4716	149	33	∂ẏ1	∂ẏ1	PROPN
ejpam-4716	149	34	∂y2	∂y2	ADJ
ejpam-4716	149	35	∂ẏ2	∂ẏ2	PROPN
ejpam-4716	149	36	∂x1	∂x1	PROPN
ejpam-4716	149	37	∂ẏ2	∂ẏ2	PROPN
ejpam-4716	149	38	∂x2	∂x2	PROPN
ejpam-4716	149	39	∂ẏ2	∂ẏ2	PROPN
ejpam-4716	149	40	∂y1	∂y1	PROPN
ejpam-4716	149	41	∂ẏ2	∂ẏ2	PROPN
ejpam-4716	149	42	∂y2	∂y2	NUM
ejpam-4716	149	43			VERB
ejpam-4716	149	44	where	where	SCONJ
ejpam-4716	149	45	,	,	PUNCT
ejpam-4716	149	46	∂ẋ1	∂ẋ1	PROPN
ejpam-4716	149	47	∂x1	∂x1	PROPN
ejpam-4716	149	48	=	=	SYM
ejpam-4716	149	49	g1	g1	PROPN
ejpam-4716	149	50	(	(	PUNCT
ejpam-4716	149	51	1−	1−	NUM
ejpam-4716	149	52	2x1	2x1	NUM
ejpam-4716	149	53	k1	k1	NOUN
ejpam-4716	149	54	)	)	PUNCT
ejpam-4716	149	55	−	−	PROPN
ejpam-4716	149	56	(	(	PUNCT
ejpam-4716	149	57	α1y1+α2y2)x	α1y1+α2y2)x	NOUN
ejpam-4716	149	58	2	2	NUM
ejpam-4716	149	59	2	2	NUM
ejpam-4716	149	60	(	(	PUNCT
ejpam-4716	149	61	x1	x1	PROPN
ejpam-4716	149	62	+	+	NUM
ejpam-4716	149	63	x2	x2	ADJ
ejpam-4716	149	64	)	)	PUNCT
ejpam-4716	149	65	2	2	NUM
ejpam-4716	149	66	,	,	PUNCT
ejpam-4716	149	67	∂ẋ1	∂ẋ1	PROPN
ejpam-4716	149	68	∂x2	∂x2	NOUN
ejpam-4716	149	69	=	=	SYM
ejpam-4716	149	70	−	−	PROPN
ejpam-4716	149	71	(	(	PUNCT
ejpam-4716	149	72	α1y1+α2y2)x	α1y1+α2y2)x	NOUN
ejpam-4716	149	73	2	2	NUM
ejpam-4716	149	74	1	1	NUM
ejpam-4716	149	75	(	(	PUNCT
ejpam-4716	149	76	x1	x1	PROPN
ejpam-4716	149	77	+	+	NUM
ejpam-4716	149	78	x2	x2	ADJ
ejpam-4716	149	79	)	)	PUNCT
ejpam-4716	149	80	2	2	NUM
ejpam-4716	149	81	,	,	PUNCT
ejpam-4716	149	82	∂ẋ1	∂ẋ1	PROPN
ejpam-4716	149	83	∂y1	∂y1	PROPN
ejpam-4716	149	84	=	=	PUNCT
ejpam-4716	149	85	−α1x1x2	−α1x1x2	X
ejpam-4716	150	1	x1	x1	NOUN
ejpam-4716	151	1	+	+	CCONJ
ejpam-4716	151	2	x2	x2	PROPN
ejpam-4716	151	3	,	,	PUNCT
ejpam-4716	151	4	∂ẋ1	∂ẋ1	PROPN
ejpam-4716	151	5	∂y2	∂y2	NOUN
ejpam-4716	151	6	=	=	PUNCT
ejpam-4716	151	7	−α2x1x2	−α2x1x2	X
ejpam-4716	151	8	x1	x1	PROPN
ejpam-4716	152	1	+	+	CCONJ
ejpam-4716	152	2	x2	x2	PROPN
ejpam-4716	152	3	,	,	PUNCT
ejpam-4716	152	4	∂ẋ2	∂ẋ2	PROPN
ejpam-4716	152	5	∂x1	∂x1	X
ejpam-4716	152	6	=	=	PUNCT
ejpam-4716	152	7	−	−	PROPN
ejpam-4716	152	8	(	(	PUNCT
ejpam-4716	152	9	β1y1+β2y2)x	β1y1+β2y2)x	NOUN
ejpam-4716	152	10	2	2	NUM
ejpam-4716	152	11	2	2	NUM
ejpam-4716	152	12	(	(	PUNCT
ejpam-4716	152	13	x1	x1	PROPN
ejpam-4716	153	1	+	+	NUM
ejpam-4716	153	2	x2	x2	ADJ
ejpam-4716	153	3	)	)	PUNCT
ejpam-4716	153	4	2	2	NUM
ejpam-4716	153	5	,	,	PUNCT
ejpam-4716	153	6	∂ẋ2	∂ẋ2	PROPN
ejpam-4716	153	7	∂x2	∂x2	PROPN
ejpam-4716	153	8	=	=	SYM
ejpam-4716	153	9	g2	g2	PROPN
ejpam-4716	153	10	(	(	PUNCT
ejpam-4716	153	11	1−	1−	NUM
ejpam-4716	153	12	2x2	2x2	NUM
ejpam-4716	153	13	k2	k2	NOUN
ejpam-4716	153	14	)	)	PUNCT
ejpam-4716	153	15	−	−	PROPN
ejpam-4716	153	16	(	(	PUNCT
ejpam-4716	153	17	β1y1+β2y2)x	β1y1+β2y2)x	NOUN
ejpam-4716	153	18	2	2	NUM
ejpam-4716	153	19	1	1	NUM
ejpam-4716	153	20	(	(	PUNCT
ejpam-4716	153	21	x1	x1	PROPN
ejpam-4716	153	22	+	+	NUM
ejpam-4716	153	23	x2	x2	ADJ
ejpam-4716	153	24	)	)	PUNCT
ejpam-4716	153	25	2	2	NUM
ejpam-4716	153	26	,	,	PUNCT
ejpam-4716	153	27	∂ẋ2	∂ẋ2	PROPN
ejpam-4716	153	28	∂y1	∂y1	PROPN
ejpam-4716	153	29	=	=	SYM
ejpam-4716	153	30	−	−	PROPN
ejpam-4716	153	31	β1x1x2	β1x1x2	NOUN
ejpam-4716	154	1	x1	x1	PROPN
ejpam-4716	155	1	+	+	NUM
ejpam-4716	155	2	x2	x2	PROPN
ejpam-4716	155	3	,	,	PUNCT
ejpam-4716	155	4	∂ẋ2	∂ẋ2	PROPN
ejpam-4716	155	5	∂y2	∂y2	NUM
ejpam-4716	155	6	=	=	PUNCT
ejpam-4716	155	7	−	−	NOUN
ejpam-4716	155	8	β2x1x2	β2x1x2	NOUN
ejpam-4716	155	9	x1	x1	NOUN
ejpam-4716	156	1	+	+	CCONJ
ejpam-4716	156	2	x2	x2	PROPN
ejpam-4716	156	3	,	,	PUNCT
ejpam-4716	156	4	∂ẏ1	∂ẏ1	PROPN
ejpam-4716	156	5	∂x1	∂x1	NOUN
ejpam-4716	156	6	=	=	PUNCT
ejpam-4716	156	7	ε1x	ε1x	PROPN
ejpam-4716	156	8	2	2	NUM
ejpam-4716	156	9	2y1	2y1	NUM
ejpam-4716	156	10	(	(	PUNCT
ejpam-4716	156	11	x1	x1	PROPN
ejpam-4716	156	12	+	+	NUM
ejpam-4716	156	13	x2	x2	ADJ
ejpam-4716	156	14	)	)	PUNCT
ejpam-4716	156	15	2	2	NUM
ejpam-4716	156	16	,	,	PUNCT
ejpam-4716	156	17	∂ẏ1	∂ẏ1	PROPN
ejpam-4716	156	18	∂x2	∂x2	NOUN
ejpam-4716	156	19	=	=	SYM
ejpam-4716	156	20	ε1x	ε1x	PROPN
ejpam-4716	156	21	2	2	NUM
ejpam-4716	156	22	1y1	1y1	NUM
ejpam-4716	156	23	(	(	PUNCT
ejpam-4716	156	24	x1	x1	PROPN
ejpam-4716	156	25	+	+	NUM
ejpam-4716	156	26	x2	x2	ADJ
ejpam-4716	156	27	)	)	PUNCT
ejpam-4716	156	28	2	2	NUM
ejpam-4716	156	29	,	,	PUNCT
ejpam-4716	156	30	∂ẏ1	∂ẏ1	PROPN
ejpam-4716	156	31	∂y1	∂y1	PROPN
ejpam-4716	156	32	=	=	SYM
ejpam-4716	156	33	−µ1	−µ1	PROPN
ejpam-4716	156	34	+	+	NUM
ejpam-4716	156	35	ε1x1x2	ε1x1x2	NOUN
ejpam-4716	156	36	x1	x1	PROPN
ejpam-4716	157	1	+	+	CCONJ
ejpam-4716	157	2	x2	x2	PROPN
ejpam-4716	157	3	−	−	PROPN
ejpam-4716	158	1	ρ2y2	ρ2y2	X
ejpam-4716	158	2	,	,	PUNCT
ejpam-4716	158	3	∂ẏ1	∂ẏ1	PROPN
ejpam-4716	158	4	∂y2	∂y2	NOUN
ejpam-4716	158	5	=	=	SYM
ejpam-4716	158	6	−ρ2y1	−ρ2y1	ADV
ejpam-4716	158	7	,	,	PUNCT
ejpam-4716	158	8	∂ẏ2	∂ẏ2	PROPN
ejpam-4716	158	9	∂x1	∂x1	VERB
ejpam-4716	158	10	=	=	PUNCT
ejpam-4716	158	11	ε2x	ε2x	X
ejpam-4716	158	12	2	2	NUM
ejpam-4716	158	13	2y2	2y2	NUM
ejpam-4716	158	14	(	(	PUNCT
ejpam-4716	158	15	x1	x1	PROPN
ejpam-4716	158	16	+	+	NUM
ejpam-4716	158	17	x2	x2	ADJ
ejpam-4716	158	18	)	)	PUNCT
ejpam-4716	158	19	2	2	NUM
ejpam-4716	158	20	,	,	PUNCT
ejpam-4716	158	21	∂ẏ2	∂ẏ2	PROPN
ejpam-4716	158	22	∂x2	∂x2	NOUN
ejpam-4716	158	23	=	=	SYM
ejpam-4716	158	24	ε2x	ε2x	X
ejpam-4716	158	25	2	2	NUM
ejpam-4716	158	26	1y2	1y2	NUM
ejpam-4716	158	27	(	(	PUNCT
ejpam-4716	158	28	x1	x1	PROPN
ejpam-4716	158	29	+	+	NUM
ejpam-4716	158	30	x2	x2	ADJ
ejpam-4716	158	31	)	)	PUNCT
ejpam-4716	158	32	2	2	NUM
ejpam-4716	158	33	,	,	PUNCT
ejpam-4716	158	34	∂ẏ2	∂ẏ2	PROPN
ejpam-4716	158	35	∂y1	∂y1	PROPN
ejpam-4716	158	36	=	=	SYM
ejpam-4716	158	37	ρ1y2	ρ1y2	PROPN
ejpam-4716	158	38	,	,	PUNCT
ejpam-4716	158	39	∂ẏ2	∂ẏ2	PROPN
ejpam-4716	158	40	∂y2	∂y2	NUM
ejpam-4716	158	41	=	=	PUNCT
ejpam-4716	158	42	−µ2	−µ2	NOUN
ejpam-4716	158	43	+	+	NUM
ejpam-4716	158	44	ε1x1x2	ε1x1x2	NOUN
ejpam-4716	158	45	x1	x1	PROPN
ejpam-4716	159	1	+	+	CCONJ
ejpam-4716	159	2	x2	x2	PROPN
ejpam-4716	159	3	+	+	CCONJ
ejpam-4716	159	4	ρ1y1	ρ1y1	X
ejpam-4716	159	5	,	,	PUNCT
ejpam-4716	159	6	a.	a.	NOUN
ejpam-4716	159	7	g.	g.	PROPN
ejpam-4716	159	8	farhan	farhan	PROPN
ejpam-4716	159	9	,	,	PUNCT
ejpam-4716	159	10	n.	n.	PROPN
ejpam-4716	159	11	sh	sh	PROPN
ejpam-4716	159	12	.	.	PROPN
ejpam-4716	159	13	khalaf	khalaf	PROPN
ejpam-4716	159	14	,	,	PUNCT
ejpam-4716	159	15	t.	t.	PROPN
ejpam-4716	159	16	j.	j.	PROPN
ejpam-4716	159	17	aldhlki	aldhlki	PROPN
ejpam-4716	159	18	/	/	SYM
ejpam-4716	159	19	eur	eur	PROPN
ejpam-4716	159	20	.	.	PUNCT
ejpam-4716	160	1	j.	j.	PROPN
ejpam-4716	160	2	pure	pure	PROPN
ejpam-4716	160	3	appl	appl	PROPN
ejpam-4716	160	4	.	.	PROPN
ejpam-4716	160	5	math	math	PROPN
ejpam-4716	160	6	,	,	PUNCT
ejpam-4716	160	7	16	16	NUM
ejpam-4716	160	8	(	(	PUNCT
ejpam-4716	160	9	2	2	NUM
ejpam-4716	160	10	)	)	PUNCT
ejpam-4716	160	11	(	(	PUNCT
ejpam-4716	160	12	2023	2023	NUM
ejpam-4716	160	13	)	)	PUNCT
ejpam-4716	160	14	,	,	PUNCT
ejpam-4716	160	15	899	899	NUM
ejpam-4716	160	16	-	-	SYM
ejpam-4716	160	17	918	918	NUM
ejpam-4716	160	18	905	905	NUM
ejpam-4716	160	19	in	in	ADP
ejpam-4716	160	20	theorems	theorem	NOUN
ejpam-4716	160	21	2	2	NUM
ejpam-4716	160	22	,	,	PUNCT
ejpam-4716	160	23	3	3	NUM
ejpam-4716	160	24	and	and	CCONJ
ejpam-4716	160	25	4	4	NUM
ejpam-4716	161	1	,	,	PUNCT
ejpam-4716	161	2	we	we	PRON
ejpam-4716	161	3	will	will	AUX
ejpam-4716	161	4	prove	prove	VERB
ejpam-4716	161	5	that	that	SCONJ
ejpam-4716	161	6	the	the	DET
ejpam-4716	161	7	points	point	NOUN
ejpam-4716	161	8	p0	p0	NOUN
ejpam-4716	161	9	,	,	PUNCT
ejpam-4716	161	10	p1	p1	NOUN
ejpam-4716	161	11	,	,	PUNCT
ejpam-4716	161	12	and	and	CCONJ
ejpam-4716	161	13	p2	p2	PROPN
ejpam-4716	161	14	are	be	AUX
ejpam-4716	161	15	unstable	unstable	ADJ
ejpam-4716	161	16	point	point	NOUN
ejpam-4716	161	17	while	while	SCONJ
ejpam-4716	161	18	the	the	DET
ejpam-4716	161	19	remaining	remain	VERB
ejpam-4716	161	20	points	point	NOUN
ejpam-4716	161	21	are	be	AUX
ejpam-4716	161	22	locally	locally	ADV
ejpam-4716	161	23	asymptoticaly	asymptoticaly	ADJ
ejpam-4716	161	24	stable	stable	ADJ
ejpam-4716	161	25	points	point	NOUN
ejpam-4716	161	26	if	if	SCONJ
ejpam-4716	161	27	they	they	PRON
ejpam-4716	161	28	meet	meet	VERB
ejpam-4716	161	29	certain	certain	ADJ
ejpam-4716	161	30	conditions	condition	NOUN
ejpam-4716	161	31	.	.	PUNCT
ejpam-4716	162	1	theorem	theorem	NOUN
ejpam-4716	162	2	2	2	NUM
ejpam-4716	162	3	.	.	X
ejpam-4716	162	4	consider	consider	VERB
ejpam-4716	162	5	the	the	DET
ejpam-4716	162	6	system	system	NOUN
ejpam-4716	162	7	(	(	PUNCT
ejpam-4716	162	8	2	2	NUM
ejpam-4716	162	9	)	)	PUNCT
ejpam-4716	162	10	,	,	PUNCT
ejpam-4716	162	11	then	then	ADV
ejpam-4716	162	12	the	the	DET
ejpam-4716	162	13	equilibrium	equilibrium	NOUN
ejpam-4716	162	14	points	point	NOUN
ejpam-4716	162	15	(	(	PUNCT
ejpam-4716	162	16	i	i	NOUN
ejpam-4716	162	17	)	)	PUNCT
ejpam-4716	162	18	p0	p0	NOUN
ejpam-4716	162	19	=	=	SYM
ejpam-4716	162	20	(	(	PUNCT
ejpam-4716	162	21	0	0	NUM
ejpam-4716	162	22	,	,	PUNCT
ejpam-4716	162	23	0	0	NUM
ejpam-4716	162	24	,	,	PUNCT
ejpam-4716	162	25	0	0	NUM
ejpam-4716	162	26	,	,	PUNCT
ejpam-4716	162	27	0	0	NUM
ejpam-4716	162	28	)	)	PUNCT
ejpam-4716	162	29	,	,	PUNCT
ejpam-4716	162	30	p1	p1	NOUN
ejpam-4716	162	31	=	=	SYM
ejpam-4716	162	32	(	(	PUNCT
ejpam-4716	162	33	k1	k1	PROPN
ejpam-4716	162	34	,	,	PUNCT
ejpam-4716	162	35	0	0	NUM
ejpam-4716	162	36	,	,	PUNCT
ejpam-4716	162	37	0	0	NUM
ejpam-4716	162	38	,	,	PUNCT
ejpam-4716	162	39	0	0	NUM
ejpam-4716	162	40	)	)	PUNCT
ejpam-4716	162	41	and	and	CCONJ
ejpam-4716	162	42	p2	p2	PROPN
ejpam-4716	162	43	=	=	SYM
ejpam-4716	162	44	(	(	PUNCT
ejpam-4716	162	45	0	0	NUM
ejpam-4716	162	46	,	,	PUNCT
ejpam-4716	162	47	k2	k2	NOUN
ejpam-4716	162	48	,	,	PUNCT
ejpam-4716	162	49	0	0	NUM
ejpam-4716	162	50	,	,	PUNCT
ejpam-4716	162	51	0	0	NUM
ejpam-4716	162	52	)	)	PUNCT
ejpam-4716	162	53	are	be	AUX
ejpam-4716	162	54	unstable	unstable	ADJ
ejpam-4716	162	55	equilibrium	equilibrium	NOUN
ejpam-4716	162	56	points	point	NOUN
ejpam-4716	162	57	.	.	PUNCT
ejpam-4716	163	1	(	(	PUNCT
ejpam-4716	163	2	ii	ii	X
ejpam-4716	163	3	)	)	PUNCT
ejpam-4716	163	4	p3	p3	PROPN
ejpam-4716	163	5	=	=	SYM
ejpam-4716	163	6	(	(	PUNCT
ejpam-4716	163	7	k1	k1	PROPN
ejpam-4716	163	8	,	,	PUNCT
ejpam-4716	163	9	k2	k2	NOUN
ejpam-4716	163	10	,	,	PUNCT
ejpam-4716	163	11	0	0	NUM
ejpam-4716	163	12	,	,	PUNCT
ejpam-4716	163	13	0	0	NUM
ejpam-4716	163	14	)	)	PUNCT
ejpam-4716	163	15	locally	locally	ADV
ejpam-4716	163	16	asymptotically	asymptotically	ADV
ejpam-4716	163	17	stable	stable	ADJ
ejpam-4716	163	18	point	point	NOUN
ejpam-4716	163	19	if	if	SCONJ
ejpam-4716	163	20	k1k2εi	k1k2εi	NOUN
ejpam-4716	163	21	<	<	X
ejpam-4716	163	22	(	(	PUNCT
ejpam-4716	163	23	k1+k2	k1+k2	PROPN
ejpam-4716	163	24	)	)	PUNCT
ejpam-4716	163	25	µi	µi	PROPN
ejpam-4716	163	26	,	,	PUNCT
ejpam-4716	163	27	i	i	PRON
ejpam-4716	163	28	=	=	NOUN
ejpam-4716	163	29	1	1	NUM
ejpam-4716	163	30	,	,	PUNCT
ejpam-4716	163	31	2	2	NUM
ejpam-4716	163	32	.	.	PUNCT
ejpam-4716	163	33	proof	proof	NOUN
ejpam-4716	163	34	.	.	PUNCT
ejpam-4716	164	1	(	(	PUNCT
ejpam-4716	164	2	i	i	NOUN
ejpam-4716	164	3	)	)	PUNCT
ejpam-4716	164	4	suppose	suppose	VERB
ejpam-4716	164	5	that	that	SCONJ
ejpam-4716	164	6	p0	p0	NOUN
ejpam-4716	164	7	=	=	SYM
ejpam-4716	164	8	(	(	PUNCT
ejpam-4716	164	9	0	0	NUM
ejpam-4716	164	10	,	,	PUNCT
ejpam-4716	164	11	0	0	NUM
ejpam-4716	164	12	,	,	PUNCT
ejpam-4716	164	13	0	0	NUM
ejpam-4716	164	14	,	,	PUNCT
ejpam-4716	164	15	0	0	NUM
ejpam-4716	164	16	)	)	PUNCT
ejpam-4716	164	17	is	be	AUX
ejpam-4716	164	18	locally	locally	ADV
ejpam-4716	164	19	asymptotically	asymptotically	ADV
ejpam-4716	164	20	stable	stable	ADJ
ejpam-4716	164	21	.	.	PUNCT
ejpam-4716	165	1	so	so	ADV
ejpam-4716	165	2	that	that	SCONJ
ejpam-4716	165	3	all	all	DET
ejpam-4716	165	4	the	the	DET
ejpam-4716	165	5	trajectories	trajectory	NOUN
ejpam-4716	165	6	(	(	PUNCT
ejpam-4716	165	7	x1	x1	PROPN
ejpam-4716	165	8	,	,	PUNCT
ejpam-4716	165	9	x2	x2	PROPN
ejpam-4716	165	10	,	,	PUNCT
ejpam-4716	165	11	y1	y1	NOUN
ejpam-4716	165	12	,	,	PUNCT
ejpam-4716	165	13	y2	y2	PROPN
ejpam-4716	165	14	)	)	PUNCT
ejpam-4716	165	15	of	of	ADP
ejpam-4716	165	16	the	the	DET
ejpam-4716	165	17	system	system	NOUN
ejpam-4716	165	18	(	(	PUNCT
ejpam-4716	165	19	2	2	X
ejpam-4716	165	20	)	)	PUNCT
ejpam-4716	165	21	converge	converge	VERB
ejpam-4716	165	22	to	to	ADP
ejpam-4716	165	23	(	(	PUNCT
ejpam-4716	165	24	0	0	NUM
ejpam-4716	165	25	,	,	PUNCT
ejpam-4716	165	26	0	0	NUM
ejpam-4716	165	27	,	,	PUNCT
ejpam-4716	165	28	0	0	NUM
ejpam-4716	165	29	,	,	PUNCT
ejpam-4716	165	30	0	0	NUM
ejpam-4716	165	31	)	)	PUNCT
ejpam-4716	165	32	as	as	ADP
ejpam-4716	165	33	t	t	PROPN
ejpam-4716	165	34	→	→	SYM
ejpam-4716	165	35	∞.	∞.	PROPN
ejpam-4716	165	36	then	then	ADV
ejpam-4716	165	37	since	since	SCONJ
ejpam-4716	165	38	x1	x1	PROPN
ejpam-4716	165	39	>	>	X
ejpam-4716	165	40	0	0	NUM
ejpam-4716	165	41	,	,	PUNCT
ejpam-4716	165	42	we	we	PRON
ejpam-4716	165	43	have	have	VERB
ejpam-4716	165	44	that	that	PRON
ejpam-4716	165	45	d	d	PROPN
ejpam-4716	165	46	dt	dt	X
ejpam-4716	165	47	(	(	PUNCT
ejpam-4716	165	48	lnx1	lnx1	PROPN
ejpam-4716	165	49	)	)	PUNCT
ejpam-4716	165	50	→	→	SYM
ejpam-4716	165	51	g1	g1	NOUN
ejpam-4716	165	52	,	,	PUNCT
ejpam-4716	165	53	as	as	ADP
ejpam-4716	165	54	t	t	PROPN
ejpam-4716	165	55	→	→	SYM
ejpam-4716	165	56	∞.	∞.	PROPN
ejpam-4716	165	57	it	it	PRON
ejpam-4716	165	58	is	be	AUX
ejpam-4716	165	59	possible	possible	ADJ
ejpam-4716	165	60	to	to	PART
ejpam-4716	165	61	find	find	VERB
ejpam-4716	165	62	a	a	DET
ejpam-4716	165	63	small	small	ADJ
ejpam-4716	165	64	ball	ball	NOUN
ejpam-4716	165	65	with	with	ADP
ejpam-4716	165	66	center	center	NOUN
ejpam-4716	165	67	p0	p0	NOUN
ejpam-4716	165	68	and	and	CCONJ
ejpam-4716	165	69	radius	radius	NOUN
ejpam-4716	165	70	g1	g1	NOUN
ejpam-4716	165	71	,	,	PUNCT
ejpam-4716	165	72	such	such	ADJ
ejpam-4716	165	73	that	that	SCONJ
ejpam-4716	165	74	inside	inside	ADP
ejpam-4716	165	75	it	it	PRON
ejpam-4716	165	76	we	we	PRON
ejpam-4716	165	77	have	have	VERB
ejpam-4716	165	78	d	d	NOUN
ejpam-4716	165	79	dt	dt	X
ejpam-4716	165	80	(	(	PUNCT
ejpam-4716	165	81	lnx1	lnx1	PROPN
ejpam-4716	165	82	)	)	PUNCT
ejpam-4716	165	83	≥	≥	PROPN
ejpam-4716	165	84	g1	g1	NOUN
ejpam-4716	165	85	2	2	NUM
ejpam-4716	165	86	.	.	PUNCT
ejpam-4716	166	1	if	if	SCONJ
ejpam-4716	166	2	(	(	PUNCT
ejpam-4716	166	3	x1	x1	ADJ
ejpam-4716	166	4	,	,	PUNCT
ejpam-4716	166	5	x2	x2	PROPN
ejpam-4716	166	6	,	,	PUNCT
ejpam-4716	166	7	y1	y1	NOUN
ejpam-4716	166	8	,	,	PUNCT
ejpam-4716	166	9	y2	y2	PROPN
ejpam-4716	166	10	)	)	PUNCT
ejpam-4716	166	11	converges	converge	VERB
ejpam-4716	166	12	to	to	ADP
ejpam-4716	166	13	(	(	PUNCT
ejpam-4716	166	14	0	0	NUM
ejpam-4716	166	15	,	,	PUNCT
ejpam-4716	166	16	0	0	NUM
ejpam-4716	166	17	,	,	PUNCT
ejpam-4716	166	18	0	0	NUM
ejpam-4716	166	19	,	,	PUNCT
ejpam-4716	166	20	0	0	NUM
ejpam-4716	166	21	)	)	PUNCT
ejpam-4716	166	22	,	,	PUNCT
ejpam-4716	166	23	when	when	SCONJ
ejpam-4716	166	24	t	t	PROPN
ejpam-4716	166	25	converges	converge	VERB
ejpam-4716	166	26	to	to	ADP
ejpam-4716	166	27	∞	∞	PROPN
ejpam-4716	166	28	,	,	PUNCT
ejpam-4716	166	29	then	then	ADV
ejpam-4716	166	30	there	there	PRON
ejpam-4716	166	31	exists	exist	VERB
ejpam-4716	166	32	t0	t0	PROPN
ejpam-4716	166	33	>	>	X
ejpam-4716	166	34	0	0	PROPN
ejpam-4716	166	35	,	,	PUNCT
ejpam-4716	166	36	such	such	ADJ
ejpam-4716	166	37	that	that	SCONJ
ejpam-4716	166	38	;	;	PUNCT
ejpam-4716	166	39	x1(t0	x1(t0	NUM
ejpam-4716	166	40	)	)	PUNCT
ejpam-4716	166	41	>	>	X
ejpam-4716	166	42	0	0	NUM
ejpam-4716	166	43	,	,	PUNCT
ejpam-4716	166	44	x1(t	x1(t	NUM
ejpam-4716	166	45	)	)	PUNCT
ejpam-4716	166	46	≥	≥	NOUN
ejpam-4716	166	47	x1(t0)exp	x1(t0)exp	PROPN
ejpam-4716	166	48	(	(	PUNCT
ejpam-4716	166	49	g1(t−t0	g1(t−t0	PROPN
ejpam-4716	166	50	)	)	PUNCT
ejpam-4716	166	51	2	2	NUM
ejpam-4716	166	52	)	)	PUNCT
ejpam-4716	166	53	→	→	SYM
ejpam-4716	166	54	∞	∞	PROPN
ejpam-4716	166	55	,	,	PUNCT
ejpam-4716	166	56	as	as	ADP
ejpam-4716	166	57	t	t	PROPN
ejpam-4716	166	58	→	→	SYM
ejpam-4716	166	59	∞.	∞.	PROPN
ejpam-4716	166	60	so	so	ADV
ejpam-4716	166	61	x1	x1	PROPN
ejpam-4716	166	62	→	→	SYM
ejpam-4716	166	63	∞.	∞.	PROPN
ejpam-4716	166	64	similarly	similarly	ADV
ejpam-4716	166	65	,	,	PUNCT
ejpam-4716	166	66	if	if	SCONJ
ejpam-4716	166	67	x2(0	x2(0	PROPN
ejpam-4716	166	68	)	)	PUNCT
ejpam-4716	166	69	>	>	X
ejpam-4716	167	1	0	0	NUM
ejpam-4716	167	2	,	,	PUNCT
ejpam-4716	167	3	x1	x1	PROPN
ejpam-4716	167	4	→	→	SYM
ejpam-4716	167	5	∞	∞	PROPN
ejpam-4716	167	6	,	,	PUNCT
ejpam-4716	167	7	there	there	PRON
ejpam-4716	167	8	is	be	VERB
ejpam-4716	167	9	no	no	DET
ejpam-4716	167	10	a	a	DET
ejpam-4716	167	11	trajectory	trajectory	NOUN
ejpam-4716	167	12	to	to	ADP
ejpam-4716	167	13	the	the	DET
ejpam-4716	167	14	system	system	NOUN
ejpam-4716	167	15	(	(	PUNCT
ejpam-4716	167	16	2	2	X
ejpam-4716	167	17	)	)	PUNCT
ejpam-4716	167	18	converges	converge	NOUN
ejpam-4716	167	19	to	to	ADP
ejpam-4716	167	20	(	(	PUNCT
ejpam-4716	167	21	0	0	NUM
ejpam-4716	167	22	,	,	PUNCT
ejpam-4716	167	23	0	0	NUM
ejpam-4716	167	24	,	,	PUNCT
ejpam-4716	167	25	0	0	NUM
ejpam-4716	167	26	,	,	PUNCT
ejpam-4716	167	27	0	0	NUM
ejpam-4716	167	28	)	)	PUNCT
ejpam-4716	167	29	.	.	PUNCT
ejpam-4716	168	1	hence	hence	ADV
ejpam-4716	168	2	p0	p0	NOUN
ejpam-4716	168	3	=	=	SYM
ejpam-4716	168	4	(	(	PUNCT
ejpam-4716	168	5	0	0	NUM
ejpam-4716	168	6	,	,	PUNCT
ejpam-4716	168	7	0	0	NUM
ejpam-4716	168	8	,	,	PUNCT
ejpam-4716	168	9	0	0	NUM
ejpam-4716	168	10	,	,	PUNCT
ejpam-4716	168	11	0	0	NUM
ejpam-4716	168	12	)	)	PUNCT
ejpam-4716	168	13	is	be	AUX
ejpam-4716	168	14	unstable	unstable	ADJ
ejpam-4716	168	15	point	point	NOUN
ejpam-4716	168	16	.	.	PUNCT
ejpam-4716	169	1	the	the	DET
ejpam-4716	169	2	jacobian	jacobian	ADJ
ejpam-4716	169	3	matrices	matrix	NOUN
ejpam-4716	169	4	of	of	ADP
ejpam-4716	169	5	the	the	DET
ejpam-4716	169	6	system	system	NOUN
ejpam-4716	169	7	(	(	PUNCT
ejpam-4716	169	8	2	2	NUM
ejpam-4716	169	9	)	)	PUNCT
ejpam-4716	169	10	at	at	ADP
ejpam-4716	169	11	the	the	DET
ejpam-4716	169	12	equilibrium	equilibrium	NOUN
ejpam-4716	169	13	points	point	NOUN
ejpam-4716	169	14	p1	p1	NOUN
ejpam-4716	169	15	and	and	CCONJ
ejpam-4716	169	16	p2	p2	PROPN
ejpam-4716	169	17	are	be	AUX
ejpam-4716	169	18	j(p1	j(p1	ADJ
ejpam-4716	169	19	)	)	PUNCT
ejpam-4716	170	1	=	=	SYM
ejpam-4716	170	2			NOUN
ejpam-4716	170	3	−g1	−g1	VERB
ejpam-4716	170	4	0	0	NUM
ejpam-4716	170	5	0	0	NUM
ejpam-4716	170	6	0	0	NUM
ejpam-4716	170	7	0	0	NUM
ejpam-4716	171	1	g2	g2	PROPN
ejpam-4716	171	2	0	0	NUM
ejpam-4716	171	3	0	0	NUM
ejpam-4716	171	4	0	0	NUM
ejpam-4716	171	5	0	0	NUM
ejpam-4716	172	1	−µ1	−µ1	ADJ
ejpam-4716	172	2	0	0	NUM
ejpam-4716	172	3	0	0	NUM
ejpam-4716	172	4	0	0	NUM
ejpam-4716	172	5	0	0	NUM
ejpam-4716	172	6	−µ2	−µ2	NOUN
ejpam-4716	172	7			PROPN
ejpam-4716	172	8	and	and	CCONJ
ejpam-4716	172	9	j(p2	j(p2	NUM
ejpam-4716	172	10	)	)	PUNCT
ejpam-4716	172	11	=	=	SYM
ejpam-4716	172	12			NOUN
ejpam-4716	172	13	g1	g1	NOUN
ejpam-4716	172	14	0	0	NUM
ejpam-4716	172	15	0	0	NUM
ejpam-4716	172	16	0	0	SYM
ejpam-4716	172	17	0	0	NUM
ejpam-4716	173	1	−g2	−g2	ADJ
ejpam-4716	173	2	0	0	NUM
ejpam-4716	173	3	0	0	NUM
ejpam-4716	173	4	0	0	NUM
ejpam-4716	173	5	0	0	NUM
ejpam-4716	173	6	−µ1	−µ1	ADJ
ejpam-4716	173	7	0	0	NUM
ejpam-4716	173	8	0	0	NUM
ejpam-4716	173	9	0	0	NUM
ejpam-4716	173	10	0	0	NUM
ejpam-4716	173	11	−µ2	−µ2	NOUN
ejpam-4716	173	12			PROPN
ejpam-4716	173	13	,	,	PUNCT
ejpam-4716	173	14	respectively	respectively	ADV
ejpam-4716	173	15	.	.	PUNCT
ejpam-4716	174	1	the	the	DET
ejpam-4716	174	2	eigenvalues	eigenvalue	NOUN
ejpam-4716	174	3	of	of	ADP
ejpam-4716	174	4	the	the	DET
ejpam-4716	174	5	two	two	NUM
ejpam-4716	174	6	matrices	matrix	NOUN
ejpam-4716	174	7	j	j	PROPN
ejpam-4716	174	8	(	(	PUNCT
ejpam-4716	174	9	p1	p1	PROPN
ejpam-4716	174	10	)	)	PUNCT
ejpam-4716	174	11	and	and	CCONJ
ejpam-4716	174	12	j	j	PROPN
ejpam-4716	174	13	(	(	PUNCT
ejpam-4716	174	14	p2	p2	PROPN
ejpam-4716	174	15	)	)	PUNCT
ejpam-4716	174	16	are	be	AUX
ejpam-4716	174	17	:	:	PUNCT
ejpam-4716	174	18	λ1	λ1	ADJ
ejpam-4716	174	19	=	=	PUNCT
ejpam-4716	174	20	−g1	−g1	VERB
ejpam-4716	174	21	<	<	X
ejpam-4716	174	22	0	0	NUM
ejpam-4716	174	23	,	,	PUNCT
ejpam-4716	174	24	λ2	λ2	NOUN
ejpam-4716	174	25	=	=	SYM
ejpam-4716	174	26	g2	g2	PROPN
ejpam-4716	174	27	>	>	X
ejpam-4716	175	1	0	0	PROPN
ejpam-4716	175	2	,	,	PUNCT
ejpam-4716	175	3	λ3	λ3	PROPN
ejpam-4716	175	4	=	=	SYM
ejpam-4716	175	5	−µ1	−µ1	PROPN
ejpam-4716	175	6	<	<	X
ejpam-4716	175	7	0	0	NUM
ejpam-4716	175	8	,	,	PUNCT
ejpam-4716	175	9	λ4	λ4	PROPN
ejpam-4716	175	10	=	=	PUNCT
ejpam-4716	175	11	−µ2	−µ2	PROPN
ejpam-4716	175	12	<	<	X
ejpam-4716	175	13	0	0	PUNCT
ejpam-4716	175	14	and	and	CCONJ
ejpam-4716	175	15	λ1	λ1	PROPN
ejpam-4716	175	16	=	=	PUNCT
ejpam-4716	175	17	g1	g1	PROPN
ejpam-4716	175	18	>	>	X
ejpam-4716	175	19	0	0	NUM
ejpam-4716	175	20	,	,	PUNCT
ejpam-4716	175	21	λ2	λ2	NOUN
ejpam-4716	175	22	=	=	SYM
ejpam-4716	175	23	−g2	−g2	ADJ
ejpam-4716	175	24	<	<	X
ejpam-4716	175	25	0	0	NUM
ejpam-4716	175	26	,	,	PUNCT
ejpam-4716	175	27	λ3	λ3	PROPN
ejpam-4716	175	28	=	=	SYM
ejpam-4716	175	29	−µ1	−µ1	PROPN
ejpam-4716	175	30	<	<	X
ejpam-4716	175	31	0	0	NUM
ejpam-4716	175	32	,	,	PUNCT
ejpam-4716	175	33	λ4	λ4	PROPN
ejpam-4716	175	34	=	=	PUNCT
ejpam-4716	175	35	−µ2	−µ2	PROPN
ejpam-4716	175	36	<	<	X
ejpam-4716	175	37	0	0	NUM
ejpam-4716	175	38	,	,	PUNCT
ejpam-4716	175	39	respectively	respectively	ADV
ejpam-4716	175	40	.	.	PUNCT
ejpam-4716	176	1	it	it	PRON
ejpam-4716	176	2	is	be	AUX
ejpam-4716	176	3	clear	clear	ADJ
ejpam-4716	176	4	that	that	SCONJ
ejpam-4716	176	5	,	,	PUNCT
ejpam-4716	176	6	we	we	PRON
ejpam-4716	176	7	have	have	VERB
ejpam-4716	176	8	one	one	NUM
ejpam-4716	176	9	positive	positive	ADJ
ejpam-4716	176	10	eigenvalue	eigenvalue	NOUN
ejpam-4716	176	11	in	in	ADP
ejpam-4716	176	12	both	both	DET
ejpam-4716	176	13	cases	case	NOUN
ejpam-4716	176	14	.	.	PUNCT
ejpam-4716	177	1	therefore	therefore	ADV
ejpam-4716	177	2	,	,	PUNCT
ejpam-4716	177	3	the	the	DET
ejpam-4716	177	4	two	two	NUM
ejpam-4716	177	5	points	point	NOUN
ejpam-4716	177	6	p1	p1	NOUN
ejpam-4716	177	7	and	and	CCONJ
ejpam-4716	177	8	p2	p2	PROPN
ejpam-4716	177	9	are	be	AUX
ejpam-4716	177	10	saddle	saddle	NOUN
ejpam-4716	177	11	points	point	NOUN
ejpam-4716	177	12	and	and	CCONJ
ejpam-4716	177	13	this	this	PRON
ejpam-4716	177	14	means	mean	VERB
ejpam-4716	177	15	that	that	SCONJ
ejpam-4716	177	16	they	they	PRON
ejpam-4716	177	17	are	be	AUX
ejpam-4716	177	18	not	not	PART
ejpam-4716	177	19	stable	stable	ADJ
ejpam-4716	177	20	.	.	PUNCT
ejpam-4716	178	1	(	(	PUNCT
ejpam-4716	178	2	ii	ii	X
ejpam-4716	178	3	)	)	PUNCT
ejpam-4716	178	4	the	the	DET
ejpam-4716	178	5	jacobian	jacobian	ADJ
ejpam-4716	178	6	matrix	matrix	NOUN
ejpam-4716	178	7	of	of	ADP
ejpam-4716	178	8	the	the	DET
ejpam-4716	178	9	system	system	NOUN
ejpam-4716	178	10	(	(	PUNCT
ejpam-4716	178	11	2	2	NUM
ejpam-4716	178	12	)	)	PUNCT
ejpam-4716	178	13	at	at	ADP
ejpam-4716	178	14	the	the	DET
ejpam-4716	178	15	equilibrium	equilibrium	NOUN
ejpam-4716	178	16	point	point	NOUN
ejpam-4716	178	17	p3	p3	PROPN
ejpam-4716	178	18	=	=	SYM
ejpam-4716	178	19	(	(	PUNCT
ejpam-4716	178	20	k1	k1	PROPN
ejpam-4716	178	21	,	,	PUNCT
ejpam-4716	178	22	k2	k2	NOUN
ejpam-4716	178	23	,	,	PUNCT
ejpam-4716	178	24	0	0	NUM
ejpam-4716	178	25	,	,	PUNCT
ejpam-4716	178	26	0	0	NUM
ejpam-4716	178	27	)	)	PUNCT
ejpam-4716	178	28	is	be	AUX
ejpam-4716	178	29	j(p3	j(p3	PROPN
ejpam-4716	178	30	)	)	PUNCT
ejpam-4716	179	1	=	=	SYM
ejpam-4716	179	2			NOUN
ejpam-4716	179	3	−g1	−g1	VERB
ejpam-4716	179	4	0	0	NUM
ejpam-4716	179	5	−α1k1k2(k1	−α1k1k2(k1	PROPN
ejpam-4716	180	1	+	+	CCONJ
ejpam-4716	180	2	k2	k2	ADJ
ejpam-4716	180	3	)	)	PUNCT
ejpam-4716	180	4	−1	−1	NOUN
ejpam-4716	180	5	−α2k1k2(k1	−α2k1k2(k1	NOUN
ejpam-4716	181	1	+	+	X
ejpam-4716	181	2	k2	k2	ADJ
ejpam-4716	181	3	)	)	PUNCT
ejpam-4716	181	4	−1	−1	NOUN
ejpam-4716	181	5	0	0	NUM
ejpam-4716	181	6	−g2	−g2	ADJ
ejpam-4716	181	7	−β2k1k2(k1	−β2k1k2(k1	PUNCT
ejpam-4716	182	1	+	+	CCONJ
ejpam-4716	182	2	k2	k2	ADJ
ejpam-4716	182	3	)	)	PUNCT
ejpam-4716	182	4	−1	−1	NOUN
ejpam-4716	182	5	−β2k1k2(k1	−β2k1k2(k1	NOUN
ejpam-4716	183	1	+	+	CCONJ
ejpam-4716	183	2	k2	k2	ADJ
ejpam-4716	183	3	)	)	PUNCT
ejpam-4716	183	4	−1	−1	NOUN
ejpam-4716	183	5	0	0	NUM
ejpam-4716	183	6	0	0	NUM
ejpam-4716	183	7	ε1k1k2(k1	ε1k1k2(k1	NOUN
ejpam-4716	183	8	+	+	CCONJ
ejpam-4716	183	9	k2	k2	ADJ
ejpam-4716	183	10	)	)	PUNCT
ejpam-4716	183	11	−1	−1	NOUN
ejpam-4716	183	12	−	−	PROPN
ejpam-4716	183	13	µ1	µ1	PROPN
ejpam-4716	183	14	0	0	NUM
ejpam-4716	183	15	0	0	NUM
ejpam-4716	183	16	0	0	NUM
ejpam-4716	183	17	0	0	NUM
ejpam-4716	183	18	ε2k1k2(k1	ε2k1k2(k1	NOUN
ejpam-4716	183	19	+	+	CCONJ
ejpam-4716	183	20	k2	k2	ADJ
ejpam-4716	183	21	)	)	PUNCT
ejpam-4716	183	22	−1	−1	NOUN
ejpam-4716	183	23	−	−	PROPN
ejpam-4716	184	1	µ2	µ2	PROPN
ejpam-4716	184	2			PROPN
ejpam-4716	184	3	a.	a.	NOUN
ejpam-4716	184	4	g.	g.	PROPN
ejpam-4716	184	5	farhan	farhan	PROPN
ejpam-4716	184	6	,	,	PUNCT
ejpam-4716	184	7	n.	n.	PROPN
ejpam-4716	184	8	sh	sh	PROPN
ejpam-4716	184	9	.	.	PROPN
ejpam-4716	184	10	khalaf	khalaf	PROPN
ejpam-4716	184	11	,	,	PUNCT
ejpam-4716	184	12	t.	t.	PROPN
ejpam-4716	184	13	j.	j.	PROPN
ejpam-4716	184	14	aldhlki	aldhlki	PROPN
ejpam-4716	184	15	/	/	SYM
ejpam-4716	184	16	eur	eur	PROPN
ejpam-4716	184	17	.	.	PUNCT
ejpam-4716	185	1	j.	j.	PROPN
ejpam-4716	185	2	pure	pure	PROPN
ejpam-4716	185	3	appl	appl	PROPN
ejpam-4716	185	4	.	.	PROPN
ejpam-4716	185	5	math	math	PROPN
ejpam-4716	185	6	,	,	PUNCT
ejpam-4716	185	7	16	16	NUM
ejpam-4716	185	8	(	(	PUNCT
ejpam-4716	185	9	2	2	NUM
ejpam-4716	185	10	)	)	PUNCT
ejpam-4716	185	11	(	(	PUNCT
ejpam-4716	185	12	2023	2023	NUM
ejpam-4716	185	13	)	)	PUNCT
ejpam-4716	185	14	,	,	PUNCT
ejpam-4716	185	15	899	899	NUM
ejpam-4716	185	16	-	-	SYM
ejpam-4716	185	17	918	918	NUM
ejpam-4716	185	18	906	906	NUM
ejpam-4716	185	19	the	the	DET
ejpam-4716	185	20	solutions	solution	NOUN
ejpam-4716	185	21	of	of	ADP
ejpam-4716	185	22	the	the	DET
ejpam-4716	185	23	following	follow	VERB
ejpam-4716	185	24	characteristic	characteristic	ADJ
ejpam-4716	185	25	equations	equation	NOUN
ejpam-4716	185	26	|j	|j	NOUN
ejpam-4716	185	27	(	(	PUNCT
ejpam-4716	185	28	p3)−	p3)−	X
ejpam-4716	185	29	λi4×4|	λi4×4|	X
ejpam-4716	185	30	=	=	SYM
ejpam-4716	185	31	0	0	NUM
ejpam-4716	185	32	,	,	PUNCT
ejpam-4716	185	33	where	where	SCONJ
ejpam-4716	185	34	i4×4	i4×4	PROPN
ejpam-4716	185	35	is	be	AUX
ejpam-4716	185	36	the	the	DET
ejpam-4716	185	37	identity	identity	NOUN
ejpam-4716	185	38	matrix	matrix	NOUN
ejpam-4716	185	39	,	,	PUNCT
ejpam-4716	185	40	are	be	AUX
ejpam-4716	185	41	:	:	PUNCT
ejpam-4716	185	42	λ1	λ1	ADJ
ejpam-4716	185	43	=	=	PUNCT
ejpam-4716	185	44	−g1	−g1	VERB
ejpam-4716	185	45	<	<	X
ejpam-4716	185	46	0	0	NUM
ejpam-4716	185	47	,	,	PUNCT
ejpam-4716	185	48	λ2	λ2	NOUN
ejpam-4716	185	49	=	=	SYM
ejpam-4716	185	50	−g2	−g2	ADJ
ejpam-4716	185	51	<	<	X
ejpam-4716	185	52	0	0	NUM
ejpam-4716	185	53	,	,	PUNCT
ejpam-4716	185	54	λ3	λ3	PROPN
ejpam-4716	186	1	=	=	SYM
ejpam-4716	187	1	ε1k1k2	ε1k1k2	NOUN
ejpam-4716	187	2	k1	k1	NOUN
ejpam-4716	187	3	+	+	CCONJ
ejpam-4716	187	4	k2	k2	ADJ
ejpam-4716	187	5	−	−	PROPN
ejpam-4716	187	6	µ1	µ1	PROPN
ejpam-4716	187	7	,	,	PUNCT
ejpam-4716	187	8	λ4	λ4	PROPN
ejpam-4716	187	9	=	=	PROPN
ejpam-4716	187	10	ε2k1k2	ε2k1k2	PROPN
ejpam-4716	187	11	k1	k1	PROPN
ejpam-4716	187	12	+	+	CCONJ
ejpam-4716	187	13	k2	k2	PROPN
ejpam-4716	187	14	−	−	PROPN
ejpam-4716	187	15	µ2	µ2	PROPN
ejpam-4716	187	16	.	.	PUNCT
ejpam-4716	188	1	so	so	SCONJ
ejpam-4716	188	2	that	that	SCONJ
ejpam-4716	188	3	,	,	PUNCT
ejpam-4716	188	4	p3	p3	PROPN
ejpam-4716	188	5	=	=	SYM
ejpam-4716	188	6	(	(	PUNCT
ejpam-4716	188	7	k1	k1	PROPN
ejpam-4716	188	8	,	,	PUNCT
ejpam-4716	188	9	k2	k2	NOUN
ejpam-4716	188	10	,	,	PUNCT
ejpam-4716	188	11	0	0	NUM
ejpam-4716	188	12	,	,	PUNCT
ejpam-4716	188	13	0	0	NUM
ejpam-4716	188	14	)	)	PUNCT
ejpam-4716	188	15	is	be	AUX
ejpam-4716	188	16	locally	locally	ADV
ejpam-4716	188	17	asymptotically	asymptotically	ADV
ejpam-4716	188	18	stable	stable	ADJ
ejpam-4716	188	19	if	if	SCONJ
ejpam-4716	188	20	the	the	DET
ejpam-4716	188	21	following	follow	VERB
ejpam-4716	188	22	conditions	condition	NOUN
ejpam-4716	188	23	are	be	AUX
ejpam-4716	188	24	met	meet	VERB
ejpam-4716	188	25	k1k2εi	k1k2εi	NOUN
ejpam-4716	188	26	<	<	X
ejpam-4716	188	27	(	(	PUNCT
ejpam-4716	188	28	k1	k1	PROPN
ejpam-4716	188	29	+	+	CCONJ
ejpam-4716	188	30	k2)µi	k2)µi	PROPN
ejpam-4716	188	31	,	,	PUNCT
ejpam-4716	188	32	i	i	PRON
ejpam-4716	188	33	=	=	NOUN
ejpam-4716	188	34	1	1	NUM
ejpam-4716	188	35	,	,	PUNCT
ejpam-4716	188	36	2	2	NUM
ejpam-4716	188	37	.	.	PUNCT
ejpam-4716	188	38	(	(	PUNCT
ejpam-4716	188	39	13	13	NUM
ejpam-4716	188	40	)	)	PUNCT
ejpam-4716	188	41	theorem	theorem	NOUN
ejpam-4716	188	42	3	3	X
ejpam-4716	188	43	.	.	PUNCT
ejpam-4716	188	44	consider	consider	VERB
ejpam-4716	188	45	the	the	DET
ejpam-4716	188	46	system	system	NOUN
ejpam-4716	188	47	(	(	PUNCT
ejpam-4716	188	48	2	2	NUM
ejpam-4716	188	49	)	)	PUNCT
ejpam-4716	188	50	,	,	PUNCT
ejpam-4716	188	51	then	then	ADV
ejpam-4716	188	52	(	(	PUNCT
ejpam-4716	188	53	i	i	NOUN
ejpam-4716	188	54	)	)	PUNCT
ejpam-4716	188	55	the	the	DET
ejpam-4716	188	56	equilibrium	equilibrium	NOUN
ejpam-4716	188	57	point	point	NOUN
ejpam-4716	188	58	p4	p4	ADJ
ejpam-4716	188	59	=	=	SYM
ejpam-4716	188	60	(	(	PUNCT
ejpam-4716	188	61	x̃1	x̃1	PROPN
ejpam-4716	188	62	,	,	PUNCT
ejpam-4716	188	63	x̃2	x̃2	PROPN
ejpam-4716	188	64	,	,	PUNCT
ejpam-4716	188	65	ỹ1	ỹ1	PROPN
ejpam-4716	188	66	,	,	PUNCT
ejpam-4716	188	67	0	0	NUM
ejpam-4716	188	68	)	)	PUNCT
ejpam-4716	188	69	is	be	AUX
ejpam-4716	188	70	locally	locally	ADV
ejpam-4716	188	71	asymptotically	asymptotically	ADV
ejpam-4716	188	72	stable	stable	ADJ
ejpam-4716	188	73	if	if	SCONJ
ejpam-4716	188	74	γ̃ε2x̃1	γ̃ε2x̃1	PROPN
ejpam-4716	189	1	+	+	CCONJ
ejpam-4716	189	2	ρ1ỹ1	ρ1ỹ1	NUM
ejpam-4716	189	3	−	−	NOUN
ejpam-4716	189	4	µ2	µ2	VERB
ejpam-4716	189	5	<	<	X
ejpam-4716	189	6	0	0	NUM
ejpam-4716	189	7	,	,	PUNCT
ejpam-4716	189	8	trm̃	trm̃	NOUN
ejpam-4716	189	9	<	<	X
ejpam-4716	189	10	0,detm̃	0,detm̃	NUM
ejpam-4716	189	11	<	<	X
ejpam-4716	189	12	0	0	NUM
ejpam-4716	189	13	,	,	PUNCT
ejpam-4716	189	14	and	and	CCONJ
ejpam-4716	189	15	3∑	3∑	NOUN
ejpam-4716	189	16	i=1	i=1	PRON
ejpam-4716	189	17	trm̃m̃ii	trm̃m̃ii	VERB
ejpam-4716	189	18	<	<	X
ejpam-4716	189	19	detm̃.	detm̃.	PROPN
ejpam-4716	189	20	(	(	PUNCT
ejpam-4716	189	21	14	14	NUM
ejpam-4716	189	22	)	)	PUNCT
ejpam-4716	189	23	where	where	SCONJ
ejpam-4716	189	24	m̃	m̃	NOUN
ejpam-4716	189	25	=	=	SYM
ejpam-4716	189	26	γ̃2α1x̃ỹ1	γ̃2α1x̃ỹ1	PUNCT
ejpam-4716	189	27	−	−	NOUN
ejpam-4716	189	28	k−1	k−1	PROPN
ejpam-4716	189	29	1	1	NUM
ejpam-4716	189	30	x̃1g1	x̃1g1	PROPN
ejpam-4716	189	31	−γ̃2α1x̃	−γ̃2α1x̃	ADJ
ejpam-4716	189	32	2ỹ1	2ỹ1	NUM
ejpam-4716	189	33	−γ̃α1x̃1	−γ̃α1x̃1	PROPN
ejpam-4716	189	34	−γ̃2β1ỹ1	−γ̃2β1ỹ1	VERB
ejpam-4716	189	35	γ̃2β1x̃ỹ1	γ̃2β1x̃ỹ1	NOUN
ejpam-4716	189	36	−	−	PROPN
ejpam-4716	189	37	k−1	k−1	PROPN
ejpam-4716	189	38	2	2	NUM
ejpam-4716	189	39	x̃2g2	x̃2g2	PROPN
ejpam-4716	189	40	−γ̃β2x̃1	−γ̃β2x̃1	PROPN
ejpam-4716	189	41	γ̃ε1ỹ1	γ̃ε1ỹ1	NOUN
ejpam-4716	189	42	γ̃ε1x̃	γ̃ε1x̃	PRON
ejpam-4716	189	43	2ỹ1	2ỹ1	NUM
ejpam-4716	189	44	γ̃ε1x̃1	γ̃ε1x̃1	NOUN
ejpam-4716	189	45	−	−	PROPN
ejpam-4716	189	46	µ1	µ1	NOUN
ejpam-4716	189	47			PRON
ejpam-4716	189	48	and	and	CCONJ
ejpam-4716	189	49	γ̃	γ̃	PROPN
ejpam-4716	189	50	=	=	NOUN
ejpam-4716	190	1	1	1	NUM
ejpam-4716	190	2	1+x̃	1+x̃	NUM
ejpam-4716	190	3	.	.	PUNCT
ejpam-4716	191	1	(	(	PUNCT
ejpam-4716	191	2	ii	ii	X
ejpam-4716	191	3	)	)	PUNCT
ejpam-4716	191	4	the	the	DET
ejpam-4716	191	5	equilibrium	equilibrium	NOUN
ejpam-4716	191	6	point	point	NOUN
ejpam-4716	191	7	p5	p5	PROPN
ejpam-4716	191	8	=	=	PUNCT
ejpam-4716	191	9	(	(	PUNCT
ejpam-4716	191	10	x̌1	x̌1	NUM
ejpam-4716	191	11	,	,	PUNCT
ejpam-4716	191	12	x̌2	x̌2	NUM
ejpam-4716	191	13	,	,	PUNCT
ejpam-4716	191	14	0	0	NUM
ejpam-4716	191	15	,	,	PUNCT
ejpam-4716	191	16	y̌2	y̌2	PRON
ejpam-4716	191	17	)	)	PUNCT
ejpam-4716	191	18	is	be	AUX
ejpam-4716	191	19	locally	locally	ADV
ejpam-4716	191	20	asymptotically	asymptotically	ADV
ejpam-4716	191	21	stable	stable	ADJ
ejpam-4716	191	22	point	point	NOUN
ejpam-4716	192	1	if	if	SCONJ
ejpam-4716	192	2	γ̌ε1x̌1	γ̌ε1x̌1	ADJ
ejpam-4716	192	3	−	−	NOUN
ejpam-4716	192	4	ρ2y̌2	ρ2y̌2	NOUN
ejpam-4716	192	5	−	−	PROPN
ejpam-4716	192	6	µ1	µ1	PROPN
ejpam-4716	192	7	<	<	X
ejpam-4716	192	8	0	0	NUM
ejpam-4716	192	9	,	,	PUNCT
ejpam-4716	192	10	trm̌	trm̌	PUNCT
ejpam-4716	192	11	<	<	X
ejpam-4716	192	12	0	0	NUM
ejpam-4716	192	13	,	,	PUNCT
ejpam-4716	192	14	detm̌	detm̌	NOUN
ejpam-4716	192	15	<	<	X
ejpam-4716	192	16	0	0	NUM
ejpam-4716	192	17	,	,	PUNCT
ejpam-4716	192	18	and	and	CCONJ
ejpam-4716	192	19	3∑	3∑	NOUN
ejpam-4716	192	20	i=1	i=1	NUM
ejpam-4716	193	1	trm̌m̌ii	trm̌m̌ii	PROPN
ejpam-4716	193	2	<	<	X
ejpam-4716	193	3	detm̌.	detm̌.	PROPN
ejpam-4716	193	4	(	(	PUNCT
ejpam-4716	193	5	15	15	NUM
ejpam-4716	193	6	)	)	PUNCT
ejpam-4716	194	1	where	where	SCONJ
ejpam-4716	194	2	m̌	m̌	PROPN
ejpam-4716	194	3	=	=	PRON
ejpam-4716	194	4	γ̌2α1x̌y̌2	γ̌2α1x̌y̌2	NOUN
ejpam-4716	194	5	−	−	PROPN
ejpam-4716	194	6	k−1	k−1	PROPN
ejpam-4716	194	7	1	1	NUM
ejpam-4716	194	8	x̌1g1	x̌1g1	NOUN
ejpam-4716	194	9	−γ̌2α1x̌	−γ̌2α1x̌	VERB
ejpam-4716	194	10	2y̌2	2y̌2	NUM
ejpam-4716	194	11	−	−	NUM
ejpam-4716	194	12	γ̌α1x̌1	γ̌α1x̌1	NOUN
ejpam-4716	194	13	−γ̌2β2y̌2	−γ̌2β2y̌2	NOUN
ejpam-4716	194	14	γ̌2β2x̌y̌2	γ̌2β2x̌y̌2	NOUN
ejpam-4716	195	1	−	−	PROPN
ejpam-4716	195	2	k−1	k−1	PROPN
ejpam-4716	195	3	2	2	NUM
ejpam-4716	195	4	x̌2g2	x̌2g2	PROPN
ejpam-4716	195	5	γ̌β2x̌1	γ̌β2x̌1	PROPN
ejpam-4716	195	6	γ̌2ε2y̌2	γ̌2ε2y̌2	VERB
ejpam-4716	196	1	γ̌2ε2x̌	γ̌2ε2x̌	DET
ejpam-4716	196	2	2y̌2	2y̌2	NUM
ejpam-4716	196	3	γ̌ε1x̌1	γ̌ε1x̌1	NOUN
ejpam-4716	196	4	−	−	NOUN
ejpam-4716	196	5	µ2	µ2	NOUN
ejpam-4716	196	6			NOUN
ejpam-4716	196	7	and	and	CCONJ
ejpam-4716	196	8	γ̌	γ̌	PROPN
ejpam-4716	196	9	=	=	SYM
ejpam-4716	196	10	1	1	NUM
ejpam-4716	196	11	1+x̌	1+x̌	NUM
ejpam-4716	196	12	proof	proof	NOUN
ejpam-4716	196	13	.	.	PUNCT
ejpam-4716	197	1	(	(	PUNCT
ejpam-4716	197	2	i	i	NOUN
ejpam-4716	197	3	)	)	PUNCT
ejpam-4716	197	4	the	the	DET
ejpam-4716	197	5	jacobian	jacobian	ADJ
ejpam-4716	197	6	matrix	matrix	NOUN
ejpam-4716	197	7	of	of	ADP
ejpam-4716	197	8	the	the	DET
ejpam-4716	197	9	system	system	NOUN
ejpam-4716	197	10	(	(	PUNCT
ejpam-4716	197	11	2	2	NUM
ejpam-4716	197	12	)	)	PUNCT
ejpam-4716	197	13	at	at	ADP
ejpam-4716	197	14	equilibrium	equilibrium	NOUN
ejpam-4716	197	15	points	point	NOUN
ejpam-4716	197	16	p4	p4	ADJ
ejpam-4716	197	17	=	=	SYM
ejpam-4716	197	18	(	(	PUNCT
ejpam-4716	197	19	x̃1	x̃1	PROPN
ejpam-4716	197	20	,	,	PUNCT
ejpam-4716	197	21	x̃2	x̃2	PROPN
ejpam-4716	197	22	,	,	PUNCT
ejpam-4716	197	23	ỹ1	ỹ1	PROPN
ejpam-4716	197	24	,	,	PUNCT
ejpam-4716	197	25	0	0	NUM
ejpam-4716	197	26	)	)	PUNCT
ejpam-4716	197	27	,	,	PUNCT
ejpam-4716	197	28	is	be	AUX
ejpam-4716	197	29	j	j	PROPN
ejpam-4716	197	30	(	(	PUNCT
ejpam-4716	197	31	p4	p4	ADJ
ejpam-4716	197	32	)	)	PUNCT
ejpam-4716	198	1	=	=	SYM
ejpam-4716	198	2			NOUN
ejpam-4716	198	3	γ̃2α1x̃ỹ1	γ̃2α1x̃ỹ1	NOUN
ejpam-4716	198	4	−	−	PROPN
ejpam-4716	198	5	k−1	k−1	PROPN
ejpam-4716	198	6	1	1	NUM
ejpam-4716	198	7	x̃1g1	x̃1g1	PROPN
ejpam-4716	198	8	−γ̃2α1x̃	−γ̃2α1x̃	ADJ
ejpam-4716	198	9	2ỹ1	2ỹ1	NUM
ejpam-4716	198	10	−γ̃α1x̃1	−γ̃α1x̃1	PRON
ejpam-4716	198	11	−γ̃α2x̃1	−γ̃α2x̃1	PROPN
ejpam-4716	198	12	−γ̃2β1ỹ1	−γ̃2β1ỹ1	VERB
ejpam-4716	198	13	γ̃2β1x̃ỹ1	γ̃2β1x̃ỹ1	NOUN
ejpam-4716	198	14	−	−	PROPN
ejpam-4716	198	15	k−1	k−1	PROPN
ejpam-4716	198	16	2	2	NUM
ejpam-4716	198	17	x̃2g2	x̃2g2	PROPN
ejpam-4716	198	18	−γ̃β1x̃1	−γ̃β1x̃1	PROPN
ejpam-4716	198	19	−γ̃β2x̃1	−γ̃β2x̃1	PROPN
ejpam-4716	198	20	γ̃2ε1ỹ1	γ̃2ε1ỹ1	SYM
ejpam-4716	198	21	γ̃2ε1x̃	γ̃2ε1x̃	PROPN
ejpam-4716	199	1	2ỹ1	2ỹ1	NUM
ejpam-4716	199	2	γ̃ε1x̃1	γ̃ε1x̃1	NOUN
ejpam-4716	199	3	−	−	PROPN
ejpam-4716	199	4	µ1	µ1	PROPN
ejpam-4716	199	5	−ρ2ỹ1	−ρ2ỹ1	NOUN
ejpam-4716	199	6	0	0	NUM
ejpam-4716	199	7	0	0	NUM
ejpam-4716	199	8	0	0	NUM
ejpam-4716	199	9	γ̃ε2x̃1	γ̃ε2x̃1	PROPN
ejpam-4716	199	10	+	+	CCONJ
ejpam-4716	199	11	ρ1ỹ1	ρ1ỹ1	PUNCT
ejpam-4716	199	12	−	−	NOUN
ejpam-4716	199	13	µ2	µ2	PROPN
ejpam-4716	199	14			VERB
ejpam-4716	199	15	such	such	ADJ
ejpam-4716	199	16	that	that	SCONJ
ejpam-4716	199	17	γ̃	γ̃	PROPN
ejpam-4716	199	18	=	=	NOUN
ejpam-4716	199	19	1	1	NUM
ejpam-4716	199	20	1+x̃	1+x̃	NUM
ejpam-4716	199	21	.	.	PUNCT
ejpam-4716	200	1	the	the	DET
ejpam-4716	200	2	characteristic	characteristic	ADJ
ejpam-4716	200	3	equation	equation	NOUN
ejpam-4716	200	4	for	for	ADP
ejpam-4716	200	5	the	the	DET
ejpam-4716	200	6	matrix	matrix	NOUN
ejpam-4716	200	7	j	j	PROPN
ejpam-4716	200	8	(	(	PUNCT
ejpam-4716	200	9	p4	p4	ADJ
ejpam-4716	200	10	)	)	PUNCT
ejpam-4716	200	11	is	be	AUX
ejpam-4716	200	12	as	as	SCONJ
ejpam-4716	200	13	follows	follow	VERB
ejpam-4716	200	14	:	:	PUNCT
ejpam-4716	200	15	(	(	PUNCT
ejpam-4716	200	16	λ−	λ−	PROPN
ejpam-4716	200	17	γ̃ε2x̃1	γ̃ε2x̃1	PROPN
ejpam-4716	201	1	−	−	PROPN
ejpam-4716	201	2	ρ1ỹ1	ρ1ỹ1	PUNCT
ejpam-4716	202	1	+	+	CCONJ
ejpam-4716	202	2	µ2	µ2	NOUN
ejpam-4716	202	3	)	)	PUNCT
ejpam-4716	202	4	(	(	PUNCT
ejpam-4716	202	5	λ3	λ3	PROPN
ejpam-4716	202	6	−	−	PROPN
ejpam-4716	202	7	trm̃	trm̃	NOUN
ejpam-4716	202	8	λ2	λ2	NOUN
ejpam-4716	202	9	+	+	CCONJ
ejpam-4716	202	10	3∑	3∑	NUM
ejpam-4716	202	11	i=1	i=1	NOUN
ejpam-4716	202	12	m̃iiλ−detm̃	m̃iiλ−detm̃	X
ejpam-4716	202	13	)	)	PUNCT
ejpam-4716	202	14	=	=	SYM
ejpam-4716	202	15	0	0	NUM
ejpam-4716	202	16	,	,	PUNCT
ejpam-4716	202	17	a.	a.	NOUN
ejpam-4716	202	18	g.	g.	PROPN
ejpam-4716	202	19	farhan	farhan	PROPN
ejpam-4716	202	20	,	,	PUNCT
ejpam-4716	202	21	n.	n.	PROPN
ejpam-4716	202	22	sh	sh	PROPN
ejpam-4716	202	23	.	.	PROPN
ejpam-4716	202	24	khalaf	khalaf	PROPN
ejpam-4716	202	25	,	,	PUNCT
ejpam-4716	202	26	t.	t.	PROPN
ejpam-4716	202	27	j.	j.	PROPN
ejpam-4716	202	28	aldhlki	aldhlki	PROPN
ejpam-4716	202	29	/	/	SYM
ejpam-4716	202	30	eur	eur	PROPN
ejpam-4716	202	31	.	.	PUNCT
ejpam-4716	203	1	j.	j.	PROPN
ejpam-4716	203	2	pure	pure	PROPN
ejpam-4716	203	3	appl	appl	PROPN
ejpam-4716	203	4	.	.	PROPN
ejpam-4716	203	5	math	math	PROPN
ejpam-4716	203	6	,	,	PUNCT
ejpam-4716	203	7	16	16	NUM
ejpam-4716	203	8	(	(	PUNCT
ejpam-4716	203	9	2	2	NUM
ejpam-4716	203	10	)	)	PUNCT
ejpam-4716	203	11	(	(	PUNCT
ejpam-4716	203	12	2023	2023	NUM
ejpam-4716	203	13	)	)	PUNCT
ejpam-4716	203	14	,	,	PUNCT
ejpam-4716	203	15	899	899	NUM
ejpam-4716	203	16	-	-	SYM
ejpam-4716	203	17	918	918	NUM
ejpam-4716	203	18	907	907	NUM
ejpam-4716	203	19	where	where	SCONJ
ejpam-4716	203	20	,	,	PUNCT
ejpam-4716	203	21	m̃	m̃	PROPN
ejpam-4716	203	22	=	=	SYM
ejpam-4716	203	23	γ̃2α1x̃ỹ1	γ̃2α1x̃ỹ1	PUNCT
ejpam-4716	203	24	−	−	NOUN
ejpam-4716	203	25	k−1	k−1	PROPN
ejpam-4716	203	26	1	1	NUM
ejpam-4716	203	27	x̃1g1	x̃1g1	PROPN
ejpam-4716	203	28	−γ̃2α1x̃	−γ̃2α1x̃	ADJ
ejpam-4716	203	29	2ỹ1	2ỹ1	NUM
ejpam-4716	203	30	−γ̃α1x̃1	−γ̃α1x̃1	PROPN
ejpam-4716	203	31	−γ̃2β1ỹ1	−γ̃2β1ỹ1	VERB
ejpam-4716	203	32	γ̃2β1x̃ỹ1	γ̃2β1x̃ỹ1	NOUN
ejpam-4716	203	33	−	−	PROPN
ejpam-4716	203	34	k−1	k−1	PROPN
ejpam-4716	203	35	2	2	NUM
ejpam-4716	204	1	x̃2g2	x̃2g2	PROPN
ejpam-4716	204	2	−γ̃β2x̃1	−γ̃β2x̃1	PROPN
ejpam-4716	204	3	γ̃2ε1ỹ1	γ̃2ε1ỹ1	SYM
ejpam-4716	204	4	γ̃2ε1x̃	γ̃2ε1x̃	PROPN
ejpam-4716	204	5	2ỹ1	2ỹ1	NUM
ejpam-4716	204	6	γ̃ε1x̃1	γ̃ε1x̃1	NOUN
ejpam-4716	204	7	−	−	PROPN
ejpam-4716	204	8	µ1	µ1	NOUN
ejpam-4716	204	9			NUM
ejpam-4716	204	10	and	and	CCONJ
ejpam-4716	204	11	m̃ii	m̃ii	PROPN
ejpam-4716	204	12	,	,	PUNCT
ejpam-4716	204	13	i	i	NOUN
ejpam-4716	204	14	=	=	NOUN
ejpam-4716	204	15	1	1	NUM
ejpam-4716	204	16	,	,	PUNCT
ejpam-4716	204	17	2	2	NUM
ejpam-4716	204	18	,	,	PUNCT
ejpam-4716	204	19	3	3	NUM
ejpam-4716	204	20	is	be	AUX
ejpam-4716	204	21	the	the	DET
ejpam-4716	204	22	diagonal	diagonal	ADJ
ejpam-4716	204	23	minor	minor	NOUN
ejpam-4716	204	24	’s	’s	NOUN
ejpam-4716	204	25	of	of	ADP
ejpam-4716	204	26	the	the	DET
ejpam-4716	204	27	matrix	matrix	NOUN
ejpam-4716	204	28	m̃	m̃	PROPN
ejpam-4716	204	29	.	.	PUNCT
ejpam-4716	205	1	according	accord	VERB
ejpam-4716	205	2	to	to	ADP
ejpam-4716	205	3	the	the	DET
ejpam-4716	205	4	criteria	criterion	NOUN
ejpam-4716	205	5	of	of	ADP
ejpam-4716	205	6	routh	routh	PROPN
ejpam-4716	205	7	-	-	PUNCT
ejpam-4716	205	8	hurwitz	hurwitz	PROPN
ejpam-4716	205	9	,	,	PUNCT
ejpam-4716	205	10	p4	p4	NOUN
ejpam-4716	205	11	=	=	SYM
ejpam-4716	205	12	(	(	PUNCT
ejpam-4716	205	13	x̃1	x̃1	PROPN
ejpam-4716	205	14	,	,	PUNCT
ejpam-4716	205	15	x̃2	x̃2	PROPN
ejpam-4716	205	16	,	,	PUNCT
ejpam-4716	205	17	ỹ1	ỹ1	PROPN
ejpam-4716	205	18	,	,	PUNCT
ejpam-4716	205	19	0	0	NUM
ejpam-4716	205	20	)	)	PUNCT
ejpam-4716	205	21	,	,	PUNCT
ejpam-4716	205	22	is	be	AUX
ejpam-4716	205	23	a	a	DET
ejpam-4716	205	24	locally	locally	ADV
ejpam-4716	205	25	asymptotically	asymptotically	ADV
ejpam-4716	205	26	stable	stable	ADJ
ejpam-4716	205	27	point	point	NOUN
ejpam-4716	205	28	provided	provide	VERB
ejpam-4716	205	29	that	that	SCONJ
ejpam-4716	205	30	(	(	PUNCT
ejpam-4716	205	31	14	14	NUM
ejpam-4716	205	32	)	)	PUNCT
ejpam-4716	205	33	are	be	AUX
ejpam-4716	205	34	satisfied	satisfied	ADJ
ejpam-4716	205	35	.	.	PUNCT
ejpam-4716	206	1	(	(	PUNCT
ejpam-4716	206	2	ii	ii	X
ejpam-4716	206	3	)	)	PUNCT
ejpam-4716	206	4	the	the	DET
ejpam-4716	206	5	jacobi	jacobi	PROPN
ejpam-4716	206	6	’s	’s	PART
ejpam-4716	206	7	matrix	matrix	NOUN
ejpam-4716	206	8	of	of	ADP
ejpam-4716	206	9	the	the	DET
ejpam-4716	206	10	system	system	NOUN
ejpam-4716	206	11	(	(	PUNCT
ejpam-4716	206	12	2	2	NUM
ejpam-4716	206	13	)	)	PUNCT
ejpam-4716	206	14	at	at	ADP
ejpam-4716	206	15	p5	p5	PROPN
ejpam-4716	206	16	=	=	SYM
ejpam-4716	206	17	(	(	PUNCT
ejpam-4716	206	18	x̌1	x̌1	NUM
ejpam-4716	206	19	,	,	PUNCT
ejpam-4716	206	20	x̌2	x̌2	NUM
ejpam-4716	206	21	,	,	PUNCT
ejpam-4716	206	22	0	0	NUM
ejpam-4716	206	23	,	,	PUNCT
ejpam-4716	206	24	y̌2	y̌2	PRON
ejpam-4716	206	25	)	)	PUNCT
ejpam-4716	206	26	is	be	AUX
ejpam-4716	206	27	j	j	PROPN
ejpam-4716	206	28	(	(	PUNCT
ejpam-4716	206	29	p5	p5	PROPN
ejpam-4716	206	30	)	)	PUNCT
ejpam-4716	206	31	=	=	SYM
ejpam-4716	206	32			NOUN
ejpam-4716	206	33	γ̌2α1x̌y̌2	γ̌2α1x̌y̌2	NOUN
ejpam-4716	206	34	−	−	PROPN
ejpam-4716	206	35	k−1	k−1	PROPN
ejpam-4716	206	36	1	1	NUM
ejpam-4716	207	1	x̌1g1	x̌1g1	NOUN
ejpam-4716	207	2	−γ̌2α2x̌	−γ̌2α2x̌	ADJ
ejpam-4716	207	3	2y̌2	2y̌2	NUM
ejpam-4716	208	1	−γ̌α1x̌1	−γ̌α1x̌1	ADP
ejpam-4716	208	2	−γ̌α2x̌1	−γ̌α2x̌1	PROPN
ejpam-4716	208	3	−γ̌2β2y2	−γ̌2β2y2	PUNCT
ejpam-4716	208	4	γ̌2β2x̌y̌2	γ̌2β2x̌y̌2	NOUN
ejpam-4716	208	5	−	−	PROPN
ejpam-4716	208	6	k−1	k−1	PROPN
ejpam-4716	208	7	2	2	NUM
ejpam-4716	208	8	x̌2g2	x̌2g2	NOUN
ejpam-4716	208	9	−γ̌β1x̌1	−γ̌β1x̌1	PUNCT
ejpam-4716	208	10	−γ̌β2x̌1	−γ̌β2x̌1	SYM
ejpam-4716	208	11	0	0	NUM
ejpam-4716	208	12	0	0	NUM
ejpam-4716	208	13	γ̌ε1x̌1	γ̌ε1x̌1	NOUN
ejpam-4716	208	14	−	−	NOUN
ejpam-4716	208	15	ρ2y̌2	ρ2y̌2	NOUN
ejpam-4716	208	16	−	−	PROPN
ejpam-4716	208	17	µ1	µ1	NOUN
ejpam-4716	208	18	0	0	NUM
ejpam-4716	208	19	γ̌2ε2y̌2	γ̌2ε2y̌2	NOUN
ejpam-4716	208	20	γ̌2ε2x̌	γ̌2ε2x̌	PRON
ejpam-4716	208	21	2y̌2	2y̌2	NUM
ejpam-4716	208	22	ρ1y̌2	ρ1y̌2	NOUN
ejpam-4716	208	23	γ̌ε1x̌1	γ̌ε1x̌1	PROPN
ejpam-4716	209	1	−	−	PROPN
ejpam-4716	210	1	µ2	µ2	PROPN
ejpam-4716	210	2			NOUN
ejpam-4716	210	3	such	such	ADJ
ejpam-4716	210	4	that	that	SCONJ
ejpam-4716	210	5	γ̌	γ̌	PROPN
ejpam-4716	210	6	=	=	SYM
ejpam-4716	210	7	1	1	NUM
ejpam-4716	210	8	1+x̌	1+x̌	NUM
ejpam-4716	210	9	.	.	PUNCT
ejpam-4716	211	1	simple	simple	ADJ
ejpam-4716	211	2	calculations	calculation	NOUN
ejpam-4716	211	3	yield	yield	VERB
ejpam-4716	211	4	that	that	SCONJ
ejpam-4716	211	5	the	the	DET
ejpam-4716	211	6	characteristic	characteristic	ADJ
ejpam-4716	211	7	equation	equation	NOUN
ejpam-4716	211	8	of	of	ADP
ejpam-4716	211	9	the	the	DET
ejpam-4716	211	10	matrixj	matrixj	NOUN
ejpam-4716	211	11	(	(	PUNCT
ejpam-4716	211	12	p5	p5	PROPN
ejpam-4716	211	13	)	)	PUNCT
ejpam-4716	211	14	is	be	AUX
ejpam-4716	211	15	:	:	PUNCT
ejpam-4716	211	16	(	(	PUNCT
ejpam-4716	211	17	γ̌ε1x̌1	γ̌ε1x̌1	INTJ
ejpam-4716	211	18	−	−	NOUN
ejpam-4716	212	1	ρ2y2	ρ2y2	INTJ
ejpam-4716	212	2	−	−	PROPN
ejpam-4716	212	3	µ1	µ1	PROPN
ejpam-4716	212	4	−	−	PROPN
ejpam-4716	212	5	λ	λ	PROPN
ejpam-4716	212	6	)	)	PUNCT
ejpam-4716	212	7	(	(	PUNCT
ejpam-4716	212	8	λ3	λ3	PROPN
ejpam-4716	212	9	−	−	PROPN
ejpam-4716	212	10	trm̌	trm̌	PUNCT
ejpam-4716	212	11	λ2	λ2	NOUN
ejpam-4716	213	1	+	+	CCONJ
ejpam-4716	214	1	3∑	3∑	NUM
ejpam-4716	214	2	i=1	i=1	NOUN
ejpam-4716	214	3	m̌ii	m̌ii	NOUN
ejpam-4716	214	4	λ−detm̌	λ−detm̌	PROPN
ejpam-4716	214	5	)	)	PUNCT
ejpam-4716	215	1	=	=	PUNCT
ejpam-4716	215	2	0	0	NUM
ejpam-4716	215	3	,	,	PUNCT
ejpam-4716	215	4	where	where	SCONJ
ejpam-4716	215	5	m̌	m̌	PROPN
ejpam-4716	215	6	=	=	PRON
ejpam-4716	215	7	γ̌2α1x̌y̌2	γ̌2α1x̌y̌2	NOUN
ejpam-4716	215	8	−	−	PROPN
ejpam-4716	215	9	k−1	k−1	PROPN
ejpam-4716	215	10	1	1	NUM
ejpam-4716	215	11	x̌1g1	x̌1g1	NOUN
ejpam-4716	215	12	−γ̌2α1x̌	−γ̌2α1x̌	VERB
ejpam-4716	215	13	2y̌2	2y̌2	NUM
ejpam-4716	215	14	−γ̌α1x̌1	−γ̌α1x̌1	DET
ejpam-4716	215	15	−γ̌2β2y̌2	−γ̌2β2y̌2	NOUN
ejpam-4716	215	16	γ̌2β2x̌y̌2	γ̌2β2x̌y̌2	NOUN
ejpam-4716	215	17	−	−	NOUN
ejpam-4716	215	18	k−1	k−1	PROPN
ejpam-4716	215	19	2	2	NUM
ejpam-4716	215	20	x̌2g2	x̌2g2	PROPN
ejpam-4716	215	21	γ̌β2x̌1	γ̌β2x̌1	PROPN
ejpam-4716	215	22	γ̌2ε2y̌2	γ̌2ε2y̌2	VERB
ejpam-4716	216	1	γ̌2ε2x̌	γ̌2ε2x̌	DET
ejpam-4716	216	2	2y̌2	2y̌2	NUM
ejpam-4716	216	3	γ̌ε1x̌1	γ̌ε1x̌1	NOUN
ejpam-4716	216	4	−	−	NOUN
ejpam-4716	216	5	µ2	µ2	NOUN
ejpam-4716	216	6			NOUN
ejpam-4716	216	7	and	and	CCONJ
ejpam-4716	216	8	m̌ii	m̌ii	PRON
ejpam-4716	216	9	,	,	PUNCT
ejpam-4716	216	10	i	i	PRON
ejpam-4716	216	11	=	=	NOUN
ejpam-4716	216	12	1	1	NUM
ejpam-4716	216	13	,	,	PUNCT
ejpam-4716	216	14	2	2	NUM
ejpam-4716	216	15	,	,	PUNCT
ejpam-4716	216	16	3	3	NUM
ejpam-4716	216	17	is	be	AUX
ejpam-4716	216	18	the	the	DET
ejpam-4716	216	19	diagonal	diagonal	ADJ
ejpam-4716	216	20	minor	minor	ADJ
ejpam-4716	216	21	’s	’s	PART
ejpam-4716	216	22	matrix	matrix	NOUN
ejpam-4716	216	23	m̌.	m̌.	NOUN
ejpam-4716	216	24	according	accord	VERB
ejpam-4716	216	25	to	to	ADP
ejpam-4716	216	26	the	the	DET
ejpam-4716	216	27	criteria	criterion	NOUN
ejpam-4716	216	28	of	of	ADP
ejpam-4716	216	29	routh	routh	PROPN
ejpam-4716	216	30	-	-	PUNCT
ejpam-4716	216	31	hurwitz	hurwitz	PROPN
ejpam-4716	216	32	,	,	PUNCT
ejpam-4716	216	33	any	any	PRON
ejpam-4716	216	34	of	of	ADP
ejpam-4716	216	35	the	the	DET
ejpam-4716	216	36	equilibrium	equilibrium	NOUN
ejpam-4716	216	37	points	point	VERB
ejpam-4716	216	38	p5	p5	PROPN
ejpam-4716	216	39	=	=	PUNCT
ejpam-4716	216	40	(	(	PUNCT
ejpam-4716	216	41	x̌1	x̌1	NUM
ejpam-4716	216	42	,	,	PUNCT
ejpam-4716	216	43	x̌2	x̌2	NUM
ejpam-4716	216	44	,	,	PUNCT
ejpam-4716	216	45	0	0	NUM
ejpam-4716	216	46	,	,	PUNCT
ejpam-4716	216	47	y̌2	y̌2	PRON
ejpam-4716	216	48	)	)	PUNCT
ejpam-4716	216	49	,	,	PUNCT
ejpam-4716	216	50	is	be	AUX
ejpam-4716	216	51	locally	locally	ADV
ejpam-4716	216	52	asymptotically	asymptotically	ADV
ejpam-4716	216	53	provided	provide	VERB
ejpam-4716	216	54	that	that	SCONJ
ejpam-4716	216	55	(	(	PUNCT
ejpam-4716	216	56	15	15	NUM
ejpam-4716	216	57	)	)	PUNCT
ejpam-4716	216	58	are	be	AUX
ejpam-4716	216	59	satisfied	satisfied	ADJ
ejpam-4716	216	60	.	.	PUNCT
ejpam-4716	217	1	and	and	CCONJ
ejpam-4716	217	2	with	with	ADP
ejpam-4716	217	3	this	this	PRON
ejpam-4716	217	4	,	,	PUNCT
ejpam-4716	217	5	we	we	PRON
ejpam-4716	217	6	have	have	AUX
ejpam-4716	217	7	completed	complete	VERB
ejpam-4716	217	8	the	the	DET
ejpam-4716	217	9	proof	proof	NOUN
ejpam-4716	217	10	.	.	PUNCT
ejpam-4716	218	1	theorem	theorem	ADJ
ejpam-4716	218	2	4	4	NUM
ejpam-4716	218	3	.	.	PUNCT
ejpam-4716	218	4	consider	consider	VERB
ejpam-4716	218	5	the	the	DET
ejpam-4716	218	6	system	system	NOUN
ejpam-4716	218	7	(	(	PUNCT
ejpam-4716	218	8	2	2	NUM
ejpam-4716	218	9	)	)	PUNCT
ejpam-4716	218	10	,	,	PUNCT
ejpam-4716	218	11	then	then	ADV
ejpam-4716	218	12	p6	p6	PROPN
ejpam-4716	218	13	=	=	PUNCT
ejpam-4716	218	14	(	(	PUNCT
ejpam-4716	218	15	x1	x1	PROPN
ejpam-4716	218	16	,	,	PUNCT
ejpam-4716	218	17	x2	x2	PROPN
ejpam-4716	218	18	,	,	PUNCT
ejpam-4716	218	19	y1	y1	NOUN
ejpam-4716	218	20	,	,	PUNCT
ejpam-4716	218	21	y2	y2	PROPN
ejpam-4716	218	22	)	)	PUNCT
ejpam-4716	218	23	is	be	AUX
ejpam-4716	218	24	a	a	DET
ejpam-4716	218	25	locally	locally	ADV
ejpam-4716	218	26	asymptotically	asymptotically	ADV
ejpam-4716	218	27	stable	stable	ADJ
ejpam-4716	218	28	point	point	NOUN
ejpam-4716	218	29	if	if	SCONJ
ejpam-4716	218	30			PROPN
ejpam-4716	218	31	trm	trm	VERB
ejpam-4716	218	32	>	>	X
ejpam-4716	218	33	0	0	PROPN
ejpam-4716	218	34	,	,	PUNCT
ejpam-4716	218	35	trm	trm	NOUN
ejpam-4716	218	36	∆−	∆−	VERB
ejpam-4716	218	37	4∑	4∑	NOUN
ejpam-4716	219	1	i=1	i=1	PROPN
ejpam-4716	219	2	mii	mii	PROPN
ejpam-4716	219	3	>	>	X
ejpam-4716	219	4	0	0	PROPN
ejpam-4716	219	5	,	,	PUNCT
ejpam-4716	219	6	4∑	4∑	NUM
ejpam-4716	219	7	i=1	i=1	PROPN
ejpam-4716	219	8	mii	mii	PROPN
ejpam-4716	219	9	(	(	PUNCT
ejpam-4716	219	10	trm	trm	PROPN
ejpam-4716	219	11	∆−	∆−	VERB
ejpam-4716	219	12	4∑	4∑	NOUN
ejpam-4716	219	13	i=1	i=1	PROPN
ejpam-4716	219	14	mii	mii	PROPN
ejpam-4716	219	15	)	)	PUNCT
ejpam-4716	220	1	−detm	−detm	PROPN
ejpam-4716	220	2	trm2	trm2	PROPN
ejpam-4716	220	3	>	>	X
ejpam-4716	220	4	0	0	NUM
ejpam-4716	220	5	,	,	PUNCT
ejpam-4716	220	6	(	(	PUNCT
ejpam-4716	220	7	16	16	NUM
ejpam-4716	220	8	)	)	PUNCT
ejpam-4716	221	1	where	where	SCONJ
ejpam-4716	221	2	,	,	PUNCT
ejpam-4716	221	3	for	for	ADP
ejpam-4716	221	4	i	i	PROPN
ejpam-4716	221	5	=	=	SYM
ejpam-4716	221	6	1	1	NUM
ejpam-4716	221	7	,	,	PUNCT
ejpam-4716	221	8	2	2	NUM
ejpam-4716	221	9	,	,	PUNCT
ejpam-4716	221	10	3	3	NUM
ejpam-4716	221	11	,	,	PUNCT
ejpam-4716	221	12	4	4	NUM
ejpam-4716	221	13	,	,	PUNCT
ejpam-4716	221	14	mii	mii	PROPN
ejpam-4716	221	15	is	be	AUX
ejpam-4716	221	16	the	the	DET
ejpam-4716	221	17	diagonal	diagonal	ADJ
ejpam-4716	221	18	minor	minor	NOUN
ejpam-4716	221	19	’s	’s	NOUN
ejpam-4716	221	20	of	of	ADP
ejpam-4716	221	21	the	the	DET
ejpam-4716	221	22	matrix	matrix	NOUN
ejpam-4716	221	23	m	m	NOUN
ejpam-4716	221	24	=	=	PUNCT
ejpam-4716	221	25	j(p6	j(p6	NOUN
ejpam-4716	221	26	)	)	PUNCT
ejpam-4716	221	27	a.	a.	NOUN
ejpam-4716	221	28	g.	g.	PROPN
ejpam-4716	221	29	farhan	farhan	PROPN
ejpam-4716	221	30	,	,	PUNCT
ejpam-4716	221	31	n.	n.	PROPN
ejpam-4716	221	32	sh	sh	PROPN
ejpam-4716	221	33	.	.	PROPN
ejpam-4716	222	1	khalaf	khalaf	PROPN
ejpam-4716	222	2	,	,	PUNCT
ejpam-4716	222	3	t.	t.	PROPN
ejpam-4716	222	4	j.	j.	PROPN
ejpam-4716	222	5	aldhlki	aldhlki	PROPN
ejpam-4716	222	6	/	/	SYM
ejpam-4716	222	7	eur	eur	PROPN
ejpam-4716	222	8	.	.	PUNCT
ejpam-4716	223	1	j.	j.	PROPN
ejpam-4716	223	2	pure	pure	PROPN
ejpam-4716	223	3	appl	appl	PROPN
ejpam-4716	223	4	.	.	PROPN
ejpam-4716	223	5	math	math	PROPN
ejpam-4716	223	6	,	,	PUNCT
ejpam-4716	223	7	16	16	NUM
ejpam-4716	223	8	(	(	PUNCT
ejpam-4716	223	9	2	2	NUM
ejpam-4716	223	10	)	)	PUNCT
ejpam-4716	223	11	(	(	PUNCT
ejpam-4716	223	12	2023	2023	NUM
ejpam-4716	223	13	)	)	PUNCT
ejpam-4716	223	14	,	,	PUNCT
ejpam-4716	223	15	899	899	NUM
ejpam-4716	223	16	-	-	SYM
ejpam-4716	223	17	918	918	NUM
ejpam-4716	223	18	908	908	NUM
ejpam-4716	223	19	proof	proof	NOUN
ejpam-4716	223	20	.	.	PUNCT
ejpam-4716	224	1	the	the	DET
ejpam-4716	224	2	jacobian	jacobian	ADJ
ejpam-4716	224	3	matrix	matrix	NOUN
ejpam-4716	224	4	of	of	ADP
ejpam-4716	224	5	the	the	DET
ejpam-4716	224	6	system	system	NOUN
ejpam-4716	224	7	(	(	PUNCT
ejpam-4716	224	8	2	2	NUM
ejpam-4716	224	9	)	)	PUNCT
ejpam-4716	224	10	at	at	ADP
ejpam-4716	224	11	equilibrium	equilibrium	NOUN
ejpam-4716	224	12	points	point	NOUN
ejpam-4716	224	13	p6	p6	NOUN
ejpam-4716	224	14	=	=	PUNCT
ejpam-4716	224	15	(	(	PUNCT
ejpam-4716	224	16	x1	x1	PROPN
ejpam-4716	224	17	,	,	PUNCT
ejpam-4716	224	18	x2	x2	PROPN
ejpam-4716	224	19	,	,	PUNCT
ejpam-4716	224	20	y1	y1	NOUN
ejpam-4716	224	21	,	,	PUNCT
ejpam-4716	224	22	y2	y2	PROPN
ejpam-4716	224	23	)	)	PUNCT
ejpam-4716	224	24	is	be	AUX
ejpam-4716	224	25	as	as	SCONJ
ejpam-4716	224	26	follows	follow	VERB
ejpam-4716	224	27	j	j	PROPN
ejpam-4716	224	28	(	(	PUNCT
ejpam-4716	224	29	p6	p6	PROPN
ejpam-4716	224	30	)	)	PUNCT
ejpam-4716	224	31	=	=	SYM
ejpam-4716	224	32			PROPN
ejpam-4716	224	33	q1	q1	NOUN
ejpam-4716	224	34	−	−	NOUN
ejpam-4716	224	35	g1x1	g1x1	NOUN
ejpam-4716	224	36	k1	k1	NOUN
ejpam-4716	224	37	−q1	−q1	PROPN
ejpam-4716	224	38	h	h	PROPN
ejpam-4716	224	39	α1e	α1e	PROPN
ejpam-4716	224	40	α2e	α2e	PROPN
ejpam-4716	224	41	−h2q2	−h2q2	PROPN
ejpam-4716	224	42	hq2	hq2	ADJ
ejpam-4716	224	43	−	−	PROPN
ejpam-4716	224	44	g2x2	g2x2	PROPN
ejpam-4716	224	45	k2	k2	ADJ
ejpam-4716	224	46	β1e	β1e	NOUN
ejpam-4716	224	47	β2e	β2e	PUNCT
ejpam-4716	224	48	h2f	h2f	PROPN
ejpam-4716	224	49	1	1	NUM
ejpam-4716	224	50	f1	f1	NOUN
ejpam-4716	224	51	0	0	PUNCT
ejpam-4716	225	1	−ρ2y1	−ρ2y1	NOUN
ejpam-4716	225	2	h2f2	h2f2	X
ejpam-4716	225	3	f2	f2	PROPN
ejpam-4716	225	4	ρ1y2	ρ1y2	PUNCT
ejpam-4716	225	5	0	0	NUM
ejpam-4716	225	6			ADJ
ejpam-4716	225	7	=	=	NOUN
ejpam-4716	225	8	:	:	PUNCT
ejpam-4716	225	9	m	m	ADJ
ejpam-4716	225	10	,	,	PUNCT
ejpam-4716	225	11	such	such	ADJ
ejpam-4716	225	12	that	that	SCONJ
ejpam-4716	225	13	,	,	PUNCT
ejpam-4716	225	14	for	for	ADP
ejpam-4716	225	15	i	i	PROPN
ejpam-4716	225	16	=	=	SYM
ejpam-4716	225	17	1	1	NUM
ejpam-4716	225	18	,	,	PUNCT
ejpam-4716	225	19	2	2	NUM
ejpam-4716	225	20	,	,	PUNCT
ejpam-4716	225	21	qi	qi	NOUN
ejpam-4716	225	22	=	=	SYM
ejpam-4716	225	23	gi	gi	X
ejpam-4716	225	24	(	(	PUNCT
ejpam-4716	225	25	1−	1−	NUM
ejpam-4716	225	26	xi	xi	NUM
ejpam-4716	225	27	ki	ki	PROPN
ejpam-4716	225	28	)	)	PUNCT
ejpam-4716	225	29	1	1	NUM
ejpam-4716	225	30	1+h	1+h	NUM
ejpam-4716	225	31	,	,	PUNCT
ejpam-4716	225	32	e	e	X
ejpam-4716	225	33	=	=	PUNCT
ejpam-4716	225	34	−x2	−x2	PROPN
ejpam-4716	225	35	1+h	1+h	NUM
ejpam-4716	225	36	,	,	PUNCT
ejpam-4716	225	37	and	and	CCONJ
ejpam-4716	225	38	fi	fi	NOUN
ejpam-4716	225	39	=	=	NOUN
ejpam-4716	225	40	εiyi	εiyi	NOUN
ejpam-4716	225	41	(	(	PUNCT
ejpam-4716	225	42	1+h)2	1+h)2	NUM
ejpam-4716	225	43	,	,	PUNCT
ejpam-4716	225	44	further	far	ADV
ejpam-4716	225	45	,	,	PUNCT
ejpam-4716	225	46	the	the	DET
ejpam-4716	225	47	characteristic	characteristic	ADJ
ejpam-4716	225	48	equation	equation	NOUN
ejpam-4716	225	49	of	of	ADP
ejpam-4716	225	50	the	the	DET
ejpam-4716	225	51	matrix	matrix	NOUN
ejpam-4716	225	52	m	m	VERB
ejpam-4716	225	53	is	be	AUX
ejpam-4716	225	54	λ4	λ4	ADJ
ejpam-4716	225	55	−	−	PROPN
ejpam-4716	225	56	trm	trm	VERB
ejpam-4716	225	57	λ3	λ3	PROPN
ejpam-4716	225	58	+	+	PROPN
ejpam-4716	225	59	∆	∆	ADJ
ejpam-4716	225	60	λ2	λ2	NOUN
ejpam-4716	225	61	−	−	PROPN
ejpam-4716	225	62	4∑	4∑	NOUN
ejpam-4716	225	63	i=1	i=1	PROPN
ejpam-4716	225	64	mii	mii	PROPN
ejpam-4716	225	65	λ+	λ+	PUNCT
ejpam-4716	225	66	detm	detm	NOUN
ejpam-4716	225	67	=	=	SYM
ejpam-4716	225	68	0	0	NUM
ejpam-4716	225	69	,	,	PUNCT
ejpam-4716	225	70	where	where	SCONJ
ejpam-4716	225	71	,	,	PUNCT
ejpam-4716	225	72	mii	mii	PROPN
ejpam-4716	225	73	,	,	PUNCT
ejpam-4716	225	74	i	i	PRON
ejpam-4716	225	75	=	=	NOUN
ejpam-4716	225	76	1	1	NUM
ejpam-4716	225	77	,	,	PUNCT
ejpam-4716	225	78	2	2	NUM
ejpam-4716	225	79	,	,	PUNCT
ejpam-4716	225	80	3	3	NUM
ejpam-4716	225	81	,	,	PUNCT
ejpam-4716	225	82	4	4	NUM
ejpam-4716	225	83	is	be	AUX
ejpam-4716	225	84	the	the	DET
ejpam-4716	225	85	diagonal	diagonal	ADJ
ejpam-4716	225	86	minor	minor	NOUN
ejpam-4716	225	87	’s	’s	NOUN
ejpam-4716	225	88	of	of	ADP
ejpam-4716	225	89	the	the	DET
ejpam-4716	225	90	matrix	matrix	NOUN
ejpam-4716	225	91	m	m	NOUN
ejpam-4716	225	92	,	,	PUNCT
ejpam-4716	225	93	and	and	CCONJ
ejpam-4716	225	94	∆	∆	X
ejpam-4716	225	95	=	=	SYM
ejpam-4716	225	96	g1x1g2x2	g1x1g2x2	PROPN
ejpam-4716	225	97	k1k2	k1k2	PROPN
ejpam-4716	226	1	+	+	CCONJ
ejpam-4716	226	2	ρ1ρ2y1y2	ρ1ρ2y1y2	PROPN
ejpam-4716	227	1	−	−	PROPN
ejpam-4716	227	2	2∑	2∑	NUM
ejpam-4716	227	3	i=1	i=1	PROPN
ejpam-4716	227	4	(	(	PUNCT
ejpam-4716	227	5	efi	efi	PROPN
ejpam-4716	227	6	(	(	PUNCT
ejpam-4716	227	7	h2αi	h2αi	X
ejpam-4716	227	8	+	+	X
ejpam-4716	227	9	βi	βi	X
ejpam-4716	227	10	)	)	PUNCT
ejpam-4716	228	1	+	+	CCONJ
ejpam-4716	228	2	xi	xi	ADP
ejpam-4716	228	3	giq(i−(−1)i	giq(i−(−1)i	NOUN
ejpam-4716	228	4	)	)	PUNCT
ejpam-4716	228	5	ki	ki	PROPN
ejpam-4716	228	6	)	)	PUNCT
ejpam-4716	228	7	.	.	PUNCT
ejpam-4716	229	1	according	accord	VERB
ejpam-4716	229	2	to	to	ADP
ejpam-4716	229	3	the	the	DET
ejpam-4716	229	4	criteria	criterion	NOUN
ejpam-4716	229	5	of	of	ADP
ejpam-4716	229	6	routh	routh	PROPN
ejpam-4716	229	7	-	-	PUNCT
ejpam-4716	229	8	hurwitz	hurwitz	PROPN
ejpam-4716	229	9	,	,	PUNCT
ejpam-4716	229	10	p6	p6	NOUN
ejpam-4716	229	11	=	=	PUNCT
ejpam-4716	229	12	(	(	PUNCT
ejpam-4716	229	13	x1	x1	PROPN
ejpam-4716	229	14	,	,	PUNCT
ejpam-4716	229	15	x2	x2	PROPN
ejpam-4716	229	16	,	,	PUNCT
ejpam-4716	229	17	y1	y1	NOUN
ejpam-4716	229	18	,	,	PUNCT
ejpam-4716	229	19	y2	y2	PROPN
ejpam-4716	229	20	)	)	PUNCT
ejpam-4716	229	21	is	be	AUX
ejpam-4716	229	22	locally	locally	ADV
ejpam-4716	229	23	asymptotically	asymptotically	ADV
ejpam-4716	229	24	stable	stable	ADJ
ejpam-4716	229	25	point	point	NOUN
ejpam-4716	229	26	if	if	SCONJ
ejpam-4716	229	27	the	the	DET
ejpam-4716	229	28	(	(	PUNCT
ejpam-4716	229	29	16	16	NUM
ejpam-4716	229	30	)	)	PUNCT
ejpam-4716	229	31	is	be	AUX
ejpam-4716	229	32	satisfied	satisfied	ADJ
ejpam-4716	229	33	.	.	PUNCT
ejpam-4716	230	1	and	and	CCONJ
ejpam-4716	230	2	with	with	ADP
ejpam-4716	230	3	this	this	PRON
ejpam-4716	230	4	,	,	PUNCT
ejpam-4716	230	5	we	we	PRON
ejpam-4716	230	6	have	have	AUX
ejpam-4716	230	7	completed	complete	VERB
ejpam-4716	230	8	the	the	DET
ejpam-4716	230	9	proof	proof	NOUN
ejpam-4716	230	10	.	.	PUNCT
ejpam-4716	231	1	in	in	ADP
ejpam-4716	231	2	the	the	DET
ejpam-4716	231	3	following	following	NOUN
ejpam-4716	231	4	theorem	theorem	NOUN
ejpam-4716	231	5	,	,	PUNCT
ejpam-4716	231	6	we	we	PRON
ejpam-4716	231	7	give	give	VERB
ejpam-4716	231	8	conditions	condition	NOUN
ejpam-4716	231	9	through	through	ADP
ejpam-4716	231	10	which	which	PRON
ejpam-4716	231	11	the	the	DET
ejpam-4716	231	12	stability	stability	NOUN
ejpam-4716	231	13	region	region	NOUN
ejpam-4716	231	14	of	of	ADP
ejpam-4716	231	15	the	the	DET
ejpam-4716	231	16	coexistence	coexistence	NOUN
ejpam-4716	231	17	point	point	NOUN
ejpam-4716	231	18	be	be	AUX
ejpam-4716	231	19	asymptotically	asymptotically	ADV
ejpam-4716	231	20	stable	stable	ADJ
ejpam-4716	231	21	.	.	PUNCT
ejpam-4716	232	1	theorem	theorem	NOUN
ejpam-4716	232	2	5	5	NUM
ejpam-4716	232	3	.	.	PUNCT
ejpam-4716	232	4	assume	assume	VERB
ejpam-4716	232	5	that	that	SCONJ
ejpam-4716	232	6	p6	p6	PROPN
ejpam-4716	232	7	=	=	PUNCT
ejpam-4716	232	8	(	(	PUNCT
ejpam-4716	232	9	x1	x1	PROPN
ejpam-4716	232	10	,	,	PUNCT
ejpam-4716	232	11	x2	x2	PROPN
ejpam-4716	232	12	,	,	PUNCT
ejpam-4716	232	13	y1	y1	NOUN
ejpam-4716	232	14	,	,	PUNCT
ejpam-4716	232	15	y2	y2	PROPN
ejpam-4716	232	16	)	)	PUNCT
ejpam-4716	232	17	is	be	AUX
ejpam-4716	232	18	locally	locally	ADV
ejpam-4716	232	19	asymptotically	asymptotically	ADV
ejpam-4716	232	20	stable	stable	ADJ
ejpam-4716	232	21	point	point	NOUN
ejpam-4716	232	22	,	,	PUNCT
ejpam-4716	232	23	and	and	CCONJ
ejpam-4716	233	1	xi	xi	NUM
ejpam-4716	233	2	≥	≥	NUM
ejpam-4716	234	1	ki	ki	INTJ
ejpam-4716	234	2	,	,	PUNCT
ejpam-4716	234	3	i	i	PRON
ejpam-4716	234	4	=	=	NOUN
ejpam-4716	234	5	1	1	NUM
ejpam-4716	234	6	,	,	PUNCT
ejpam-4716	234	7	2.then	2.then	NUM
ejpam-4716	234	8	,	,	PUNCT
ejpam-4716	234	9	the	the	DET
ejpam-4716	234	10	set	set	PROPN
ejpam-4716	234	11	b	b	NOUN
ejpam-4716	234	12	,	,	PUNCT
ejpam-4716	234	13	which	which	PRON
ejpam-4716	234	14	is	be	AUX
ejpam-4716	234	15	defined	define	VERB
ejpam-4716	234	16	below	below	ADV
ejpam-4716	234	17	represents	represent	VERB
ejpam-4716	234	18	an	an	DET
ejpam-4716	234	19	attraction	attraction	NOUN
ejpam-4716	234	20	basin	basin	NOUN
ejpam-4716	234	21	for	for	ADP
ejpam-4716	234	22	p6	p6	PROPN
ejpam-4716	234	23	.	.	PUNCT
ejpam-4716	235	1	b	b	X
ejpam-4716	235	2	=	=	PRON
ejpam-4716	235	3	{	{	PUNCT
ejpam-4716	235	4	(	(	PUNCT
ejpam-4716	235	5	x1	x1	PROPN
ejpam-4716	235	6	,	,	PUNCT
ejpam-4716	235	7	x2	x2	PROPN
ejpam-4716	235	8	,	,	PUNCT
ejpam-4716	235	9	y1	y1	NOUN
ejpam-4716	235	10	,	,	PUNCT
ejpam-4716	235	11	y2	y2	PROPN
ejpam-4716	235	12	)	)	PUNCT
ejpam-4716	235	13	:	:	PUNCT
ejpam-4716	235	14	xi	xi	X
ejpam-4716	235	15	≥	≥	PROPN
ejpam-4716	235	16	xi	xi	PROPN
ejpam-4716	235	17	,	,	PUNCT
ejpam-4716	235	18	y1	y1	PROPN
ejpam-4716	235	19	≤	≤	NUM
ejpam-4716	235	20	y1	y1	NOUN
ejpam-4716	235	21	,	,	PUNCT
ejpam-4716	235	22	y2	y2	PROPN
ejpam-4716	235	23	=	=	PUNCT
ejpam-4716	235	24	y2	y2	PROPN
ejpam-4716	235	25	}	}	PUNCT
ejpam-4716	235	26	.	.	PUNCT
ejpam-4716	236	1	proof	proof	NOUN
ejpam-4716	236	2	.	.	PUNCT
ejpam-4716	237	1	the	the	DET
ejpam-4716	237	2	function	function	NOUN
ejpam-4716	237	3	v	v	NOUN
ejpam-4716	237	4	(	(	PUNCT
ejpam-4716	237	5	x1	x1	PROPN
ejpam-4716	237	6	,	,	PUNCT
ejpam-4716	237	7	x2	x2	PROPN
ejpam-4716	237	8	,	,	PUNCT
ejpam-4716	237	9	y1	y1	NOUN
ejpam-4716	237	10	,	,	PUNCT
ejpam-4716	237	11	y2	y2	NOUN
ejpam-4716	237	12	)	)	PUNCT
ejpam-4716	237	13	=	=	PUNCT
ejpam-4716	238	1	2∑	2∑	X
ejpam-4716	238	2	i=1	i=1	PROPN
ejpam-4716	238	3	(	(	PUNCT
ejpam-4716	238	4	xi	xi	ADP
ejpam-4716	238	5	−	−	PROPN
ejpam-4716	238	6	xi	xi	INTJ
ejpam-4716	238	7	−	−	PROPN
ejpam-4716	239	1	xiln	xiln	PROPN
ejpam-4716	240	1	xi	xi	INTJ
ejpam-4716	240	2	xi	xi	PROPN
ejpam-4716	241	1	+	+	CCONJ
ejpam-4716	241	2	yi	yi	PROPN
ejpam-4716	241	3	−	−	PROPN
ejpam-4716	241	4	yi	yi	PROPN
ejpam-4716	241	5	−	−	PROPN
ejpam-4716	241	6	yiln	yiln	PROPN
ejpam-4716	241	7	yi	yi	PROPN
ejpam-4716	241	8	yi	yi	PROPN
ejpam-4716	241	9	)	)	PUNCT
ejpam-4716	241	10	is	be	AUX
ejpam-4716	241	11	positive	positive	ADJ
ejpam-4716	241	12	definite	definite	ADJ
ejpam-4716	241	13	.	.	PUNCT
ejpam-4716	242	1	v̇	v̇	NOUN
ejpam-4716	242	2	(	(	PUNCT
ejpam-4716	242	3	x1	x1	PROPN
ejpam-4716	242	4	,	,	PUNCT
ejpam-4716	242	5	x2	x2	PROPN
ejpam-4716	242	6	,	,	PUNCT
ejpam-4716	242	7	y1	y1	NOUN
ejpam-4716	242	8	,	,	PUNCT
ejpam-4716	242	9	y2	y2	NOUN
ejpam-4716	242	10	)	)	PUNCT
ejpam-4716	243	1	=	=	PUNCT
ejpam-4716	244	1	2∑	2∑	X
ejpam-4716	244	2	i=1	i=1	X
ejpam-4716	244	3	(	(	PUNCT
ejpam-4716	244	4	ẋi	ẋi	PROPN
ejpam-4716	244	5	(	(	PUNCT
ejpam-4716	244	6	1−	1−	NUM
ejpam-4716	244	7	k1	k1	NOUN
ejpam-4716	244	8	xi	xi	X
ejpam-4716	244	9	)	)	PUNCT
ejpam-4716	245	1	+	+	CCONJ
ejpam-4716	245	2	ẏi	ẏi	ADJ
ejpam-4716	245	3	(	(	PUNCT
ejpam-4716	245	4	1−	1−	NUM
ejpam-4716	245	5	yi	yi	NOUN
ejpam-4716	245	6	yi	yi	PROPN
ejpam-4716	245	7	)	)	PUNCT
ejpam-4716	245	8	)	)	PUNCT
ejpam-4716	246	1	=	=	PUNCT
ejpam-4716	247	1	2∑	2∑	X
ejpam-4716	247	2	i=1	i=1	X
ejpam-4716	247	3	(	(	PUNCT
ejpam-4716	247	4	xi	xi	ADP
ejpam-4716	247	5	−	−	PROPN
ejpam-4716	247	6	xi)gi	xi)gi	PUNCT
ejpam-4716	247	7	(	(	PUNCT
ejpam-4716	247	8	x1	x1	PROPN
ejpam-4716	247	9	,	,	PUNCT
ejpam-4716	247	10	x2	x2	PROPN
ejpam-4716	247	11	)	)	PUNCT
ejpam-4716	247	12	+	+	CCONJ
ejpam-4716	247	13	(	(	PUNCT
ejpam-4716	247	14	yi	yi	NOUN
ejpam-4716	247	15	−	−	PROPN
ejpam-4716	247	16	yi)g3	yi)g3	PROPN
ejpam-4716	247	17	(	(	PUNCT
ejpam-4716	247	18	x1	x1	PROPN
ejpam-4716	247	19	,	,	PUNCT
ejpam-4716	247	20	x2	x2	PROPN
ejpam-4716	247	21	)	)	PUNCT
ejpam-4716	247	22	,	,	PUNCT
ejpam-4716	247	23	such	such	ADJ
ejpam-4716	247	24	that	that	SCONJ
ejpam-4716	247	25	g1	g1	PROPN
ejpam-4716	247	26	(	(	PUNCT
ejpam-4716	247	27	x1	x1	PROPN
ejpam-4716	247	28	,	,	PUNCT
ejpam-4716	247	29	x2	x2	PROPN
ejpam-4716	247	30	)	)	PUNCT
ejpam-4716	247	31	=	=	PRON
ejpam-4716	247	32	(	(	PUNCT
ejpam-4716	247	33	g1	g1	PROPN
ejpam-4716	247	34	(	(	PUNCT
ejpam-4716	247	35	1−	1−	NUM
ejpam-4716	247	36	x1	x1	PROPN
ejpam-4716	247	37	k1	k1	NOUN
ejpam-4716	247	38	)	)	PUNCT
ejpam-4716	247	39	−	−	PROPN
ejpam-4716	248	1	α1x2y1	α1x2y1	NOUN
ejpam-4716	248	2	x1	x1	PROPN
ejpam-4716	249	1	+	+	CCONJ
ejpam-4716	249	2	x2	x2	PROPN
ejpam-4716	249	3	−	−	PROPN
ejpam-4716	249	4	α2x2y2	α2x2y2	X
ejpam-4716	249	5	x1	x1	PROPN
ejpam-4716	250	1	+	+	CCONJ
ejpam-4716	250	2	x2	x2	PROPN
ejpam-4716	250	3	)	)	PUNCT
ejpam-4716	250	4	,	,	PUNCT
ejpam-4716	251	1	a.	a.	NOUN
ejpam-4716	251	2	g.	g.	PROPN
ejpam-4716	251	3	farhan	farhan	PROPN
ejpam-4716	251	4	,	,	PUNCT
ejpam-4716	251	5	n.	n.	PROPN
ejpam-4716	251	6	sh	sh	PROPN
ejpam-4716	251	7	.	.	PROPN
ejpam-4716	251	8	khalaf	khalaf	PROPN
ejpam-4716	251	9	,	,	PUNCT
ejpam-4716	251	10	t.	t.	PROPN
ejpam-4716	251	11	j.	j.	PROPN
ejpam-4716	251	12	aldhlki	aldhlki	PROPN
ejpam-4716	251	13	/	/	SYM
ejpam-4716	251	14	eur	eur	PROPN
ejpam-4716	251	15	.	.	PUNCT
ejpam-4716	252	1	j.	j.	PROPN
ejpam-4716	252	2	pure	pure	PROPN
ejpam-4716	252	3	appl	appl	PROPN
ejpam-4716	252	4	.	.	PROPN
ejpam-4716	252	5	math	math	PROPN
ejpam-4716	252	6	,	,	PUNCT
ejpam-4716	252	7	16	16	NUM
ejpam-4716	252	8	(	(	PUNCT
ejpam-4716	252	9	2	2	NUM
ejpam-4716	252	10	)	)	PUNCT
ejpam-4716	252	11	(	(	PUNCT
ejpam-4716	252	12	2023	2023	NUM
ejpam-4716	252	13	)	)	PUNCT
ejpam-4716	252	14	,	,	PUNCT
ejpam-4716	252	15	899	899	NUM
ejpam-4716	252	16	-	-	SYM
ejpam-4716	252	17	918	918	NUM
ejpam-4716	252	18	909	909	NUM
ejpam-4716	252	19	g2	g2	PROPN
ejpam-4716	252	20	(	(	PUNCT
ejpam-4716	252	21	x1	x1	PROPN
ejpam-4716	252	22	,	,	PUNCT
ejpam-4716	252	23	x2	x2	PROPN
ejpam-4716	252	24	)	)	PUNCT
ejpam-4716	252	25	=	=	SYM
ejpam-4716	252	26	(	(	PUNCT
ejpam-4716	252	27	g2	g2	PROPN
ejpam-4716	252	28	(	(	PUNCT
ejpam-4716	252	29	1−	1−	NUM
ejpam-4716	252	30	x2	x2	PROPN
ejpam-4716	252	31	k2	k2	PROPN
ejpam-4716	252	32	)	)	PUNCT
ejpam-4716	252	33	−	−	PROPN
ejpam-4716	253	1	α2x1y1	α2x1y1	INTJ
ejpam-4716	253	2	x1	x1	PROPN
ejpam-4716	254	1	+	+	CCONJ
ejpam-4716	254	2	x2	x2	PROPN
ejpam-4716	254	3	)	)	PUNCT
ejpam-4716	254	4	,	,	PUNCT
ejpam-4716	255	1	g3	g3	PROPN
ejpam-4716	255	2	(	(	PUNCT
ejpam-4716	255	3	x1	x1	PROPN
ejpam-4716	255	4	,	,	PUNCT
ejpam-4716	255	5	x2	x2	PROPN
ejpam-4716	255	6	)	)	PUNCT
ejpam-4716	255	7	=	=	SYM
ejpam-4716	255	8	(	(	PUNCT
ejpam-4716	255	9	−µ1	−µ1	PROPN
ejpam-4716	255	10	+	+	CCONJ
ejpam-4716	255	11	ε1x1x2	ε1x1x2	NOUN
ejpam-4716	255	12	x1	x1	PROPN
ejpam-4716	256	1	+	+	CCONJ
ejpam-4716	256	2	x2	x2	PROPN
ejpam-4716	256	3	−	−	NOUN
ejpam-4716	256	4	ρ2y2	ρ2y2	NOUN
ejpam-4716	256	5	)	)	PUNCT
ejpam-4716	256	6	.	.	PUNCT
ejpam-4716	257	1	it	it	PRON
ejpam-4716	257	2	is	be	AUX
ejpam-4716	257	3	obvious	obvious	ADJ
ejpam-4716	257	4	that	that	SCONJ
ejpam-4716	257	5	(	(	PUNCT
ejpam-4716	257	6	x1	x1	PROPN
ejpam-4716	257	7	−	−	PROPN
ejpam-4716	257	8	x1	x1	PROPN
ejpam-4716	257	9	)	)	PUNCT
ejpam-4716	257	10	>	>	X
ejpam-4716	257	11	0	0	NUM
ejpam-4716	257	12	,	,	PUNCT
ejpam-4716	257	13	(	(	PUNCT
ejpam-4716	257	14	x2	x2	INTJ
ejpam-4716	257	15	−	−	PROPN
ejpam-4716	257	16	2	2	NUM
ejpam-4716	257	17	)	)	PUNCT
ejpam-4716	257	18	>	>	X
ejpam-4716	258	1	0,g1	0,g1	PUNCT
ejpam-4716	258	2	(	(	PUNCT
ejpam-4716	258	3	x1	x1	PROPN
ejpam-4716	258	4	,	,	PUNCT
ejpam-4716	258	5	x2	x2	PROPN
ejpam-4716	258	6	)	)	PUNCT
ejpam-4716	258	7	<	<	X
ejpam-4716	258	8	0	0	PROPN
ejpam-4716	258	9	and	and	CCONJ
ejpam-4716	258	10	g2	g2	PROPN
ejpam-4716	258	11	(	(	PUNCT
ejpam-4716	258	12	x1	x1	PROPN
ejpam-4716	258	13	,	,	PUNCT
ejpam-4716	258	14	x2	x2	PROPN
ejpam-4716	258	15	)	)	PUNCT
ejpam-4716	258	16	<	<	X
ejpam-4716	258	17	0	0	NUM
ejpam-4716	258	18	,	,	PUNCT
ejpam-4716	258	19	so	so	SCONJ
ejpam-4716	258	20	that	that	SCONJ
ejpam-4716	258	21	,	,	PUNCT
ejpam-4716	258	22	2∑	2∑	X
ejpam-4716	258	23	i=1	i=1	X
ejpam-4716	258	24	(	(	PUNCT
ejpam-4716	258	25	xi	xi	ADP
ejpam-4716	258	26	−	−	PROPN
ejpam-4716	258	27	xi)gi	xi)gi	PUNCT
ejpam-4716	259	1	(	(	PUNCT
ejpam-4716	259	2	x1	x1	PROPN
ejpam-4716	259	3	,	,	PUNCT
ejpam-4716	259	4	x2	x2	PROPN
ejpam-4716	259	5	)	)	PUNCT
ejpam-4716	259	6	<	<	X
ejpam-4716	259	7	0	0	X
ejpam-4716	259	8	.	.	PUNCT
ejpam-4716	260	1	the	the	DET
ejpam-4716	260	2	function	function	PROPN
ejpam-4716	260	3	g3	g3	PROPN
ejpam-4716	260	4	(	(	PUNCT
ejpam-4716	260	5	x1	x1	PROPN
ejpam-4716	260	6	,	,	PUNCT
ejpam-4716	260	7	x2	x2	PROPN
ejpam-4716	260	8	)	)	PUNCT
ejpam-4716	260	9	is	be	AUX
ejpam-4716	260	10	increasing	increase	VERB
ejpam-4716	260	11	with	with	ADP
ejpam-4716	260	12	respect	respect	NOUN
ejpam-4716	260	13	to	to	ADP
ejpam-4716	260	14	xi	xi	PROPN
ejpam-4716	260	15	,	,	PUNCT
ejpam-4716	260	16	i	i	PRON
ejpam-4716	260	17	=	=	NOUN
ejpam-4716	260	18	1	1	NUM
ejpam-4716	260	19	,	,	PUNCT
ejpam-4716	260	20	2	2	NUM
ejpam-4716	260	21	,	,	PUNCT
ejpam-4716	260	22	because	because	SCONJ
ejpam-4716	260	23	of	of	ADP
ejpam-4716	260	24	the	the	DET
ejpam-4716	260	25	positivity	positivity	NOUN
ejpam-4716	260	26	of	of	ADP
ejpam-4716	260	27	it	it	PRON
ejpam-4716	260	28	derivative	derivative	ADJ
ejpam-4716	260	29	with	with	ADP
ejpam-4716	260	30	respect	respect	NOUN
ejpam-4716	260	31	to	to	ADP
ejpam-4716	260	32	xi	xi	PROPN
ejpam-4716	260	33	for	for	ADP
ejpam-4716	260	34	xi	xi	PROPN
ejpam-4716	260	35	≥	≥	PROPN
ejpam-4716	260	36	xi	xi	PROPN
ejpam-4716	260	37	,	,	PUNCT
ejpam-4716	260	38	i	i	PRON
ejpam-4716	260	39	=	=	NOUN
ejpam-4716	260	40	1	1	NUM
ejpam-4716	260	41	,	,	PUNCT
ejpam-4716	260	42	2	2	NUM
ejpam-4716	260	43	as	as	SCONJ
ejpam-4716	260	44	shown	show	VERB
ejpam-4716	260	45	below	below	ADP
ejpam-4716	260	46	:	:	PUNCT
ejpam-4716	260	47	∂g3	∂g3	NOUN
ejpam-4716	260	48	(	(	PUNCT
ejpam-4716	260	49	x1	x1	PROPN
ejpam-4716	260	50	,	,	PUNCT
ejpam-4716	260	51	x2	x2	PROPN
ejpam-4716	260	52	)	)	PUNCT
ejpam-4716	260	53	∂x1	∂x1	NOUN
ejpam-4716	260	54	=	=	PUNCT
ejpam-4716	261	1	ε1x	ε1x	PROPN
ejpam-4716	261	2	2	2	NUM
ejpam-4716	261	3	2	2	NUM
ejpam-4716	261	4	(	(	PUNCT
ejpam-4716	261	5	x1	x1	PROPN
ejpam-4716	261	6	+	+	NUM
ejpam-4716	261	7	x2	x2	ADJ
ejpam-4716	261	8	)	)	PUNCT
ejpam-4716	261	9	2	2	NUM
ejpam-4716	261	10	>	>	SYM
ejpam-4716	261	11	0	0	NUM
ejpam-4716	261	12	,	,	PUNCT
ejpam-4716	261	13	∂g3	∂g3	NOUN
ejpam-4716	261	14	(	(	PUNCT
ejpam-4716	261	15	x1	x1	PROPN
ejpam-4716	261	16	,	,	PUNCT
ejpam-4716	261	17	x2	x2	ADJ
ejpam-4716	261	18	)	)	PUNCT
ejpam-4716	261	19	∂x2	∂x2	NOUN
ejpam-4716	261	20	=	=	SYM
ejpam-4716	261	21	ε1x	ε1x	PROPN
ejpam-4716	261	22	2	2	NUM
ejpam-4716	261	23	1	1	NUM
ejpam-4716	261	24	(	(	PUNCT
ejpam-4716	261	25	x1	x1	PROPN
ejpam-4716	261	26	+	+	NUM
ejpam-4716	261	27	x2	x2	ADJ
ejpam-4716	261	28	)	)	PUNCT
ejpam-4716	261	29	2	2	NUM
ejpam-4716	261	30	>	>	SYM
ejpam-4716	261	31	0	0	NUM
ejpam-4716	261	32	,	,	PUNCT
ejpam-4716	261	33	for	for	ADP
ejpam-4716	261	34	xi	xi	PROPN
ejpam-4716	261	35	≥	≥	PROPN
ejpam-4716	261	36	xi	xi	PROPN
ejpam-4716	261	37	,	,	PUNCT
ejpam-4716	261	38	i	i	PRON
ejpam-4716	261	39	=	=	NOUN
ejpam-4716	261	40	1	1	NUM
ejpam-4716	261	41	,	,	PUNCT
ejpam-4716	261	42	2	2	NUM
ejpam-4716	261	43	.	.	PUNCT
ejpam-4716	262	1	now	now	ADV
ejpam-4716	262	2	,	,	PUNCT
ejpam-4716	262	3	since	since	SCONJ
ejpam-4716	262	4	g3	g3	PROPN
ejpam-4716	262	5	(	(	PUNCT
ejpam-4716	262	6	x1	x1	PROPN
ejpam-4716	262	7	,	,	PUNCT
ejpam-4716	262	8	x2	x2	PROPN
ejpam-4716	262	9	)	)	PUNCT
ejpam-4716	262	10	=	=	SYM
ejpam-4716	262	11	0	0	NUM
ejpam-4716	262	12	,	,	PUNCT
ejpam-4716	262	13	then	then	ADV
ejpam-4716	262	14	it	it	PRON
ejpam-4716	262	15	is	be	AUX
ejpam-4716	262	16	obtained	obtain	VERB
ejpam-4716	262	17	that	that	DET
ejpam-4716	262	18	g3	g3	PROPN
ejpam-4716	262	19	(	(	PUNCT
ejpam-4716	262	20	x1	x1	PROPN
ejpam-4716	262	21	,	,	PUNCT
ejpam-4716	262	22	x2	x2	PROPN
ejpam-4716	262	23	)	)	PUNCT
ejpam-4716	262	24	>	>	X
ejpam-4716	262	25	0	0	NUM
ejpam-4716	262	26	,	,	PUNCT
ejpam-4716	262	27	for	for	ADP
ejpam-4716	262	28	xi	xi	PROPN
ejpam-4716	262	29	≥	≥	PROPN
ejpam-4716	262	30	xi	xi	PROPN
ejpam-4716	262	31	,	,	PUNCT
ejpam-4716	262	32	i	i	PRON
ejpam-4716	262	33	=	=	NOUN
ejpam-4716	262	34	1	1	NUM
ejpam-4716	262	35	,	,	PUNCT
ejpam-4716	262	36	2	2	NUM
ejpam-4716	262	37	.	.	PUNCT
ejpam-4716	262	38	hence	hence	ADV
ejpam-4716	262	39	,	,	PUNCT
ejpam-4716	262	40	(	(	PUNCT
ejpam-4716	262	41	y1	y1	INTJ
ejpam-4716	262	42	−	−	PROPN
ejpam-4716	262	43	y1)g3	y1)g3	NOUN
ejpam-4716	262	44	(	(	PUNCT
ejpam-4716	262	45	x1	x1	PROPN
ejpam-4716	262	46	,	,	PUNCT
ejpam-4716	262	47	x2	x2	PROPN
ejpam-4716	262	48	)	)	PUNCT
ejpam-4716	262	49	<	<	X
ejpam-4716	262	50	0	0	X
ejpam-4716	262	51	.	.	PUNCT
ejpam-4716	263	1	so	so	ADV
ejpam-4716	263	2	that	that	SCONJ
ejpam-4716	263	3	,	,	PUNCT
ejpam-4716	263	4	2∑	2∑	X
ejpam-4716	263	5	i=1	i=1	X
ejpam-4716	263	6	(	(	PUNCT
ejpam-4716	263	7	xi	xi	ADP
ejpam-4716	263	8	−	−	PROPN
ejpam-4716	263	9	xi)gi	xi)gi	PUNCT
ejpam-4716	264	1	(	(	PUNCT
ejpam-4716	264	2	x1	x1	PROPN
ejpam-4716	264	3	,	,	PUNCT
ejpam-4716	264	4	x2	x2	PROPN
ejpam-4716	264	5	)	)	PUNCT
ejpam-4716	265	1	+	+	CCONJ
ejpam-4716	265	2	(	(	PUNCT
ejpam-4716	265	3	yi	yi	NOUN
ejpam-4716	265	4	−	−	PROPN
ejpam-4716	265	5	yi)g3	yi)g3	PROPN
ejpam-4716	265	6	(	(	PUNCT
ejpam-4716	265	7	x1	x1	PROPN
ejpam-4716	265	8	,	,	PUNCT
ejpam-4716	265	9	x2	x2	PROPN
ejpam-4716	265	10	)	)	PUNCT
ejpam-4716	265	11	<	<	X
ejpam-4716	265	12	0	0	NUM
ejpam-4716	265	13	,	,	PUNCT
ejpam-4716	265	14	v̇	v̇	PROPN
ejpam-4716	265	15	(	(	PUNCT
ejpam-4716	265	16	x1	x1	PROPN
ejpam-4716	265	17	,	,	PUNCT
ejpam-4716	265	18	x2	x2	PROPN
ejpam-4716	265	19	,	,	PUNCT
ejpam-4716	265	20	y1	y1	NOUN
ejpam-4716	265	21	,	,	PUNCT
ejpam-4716	265	22	y2	y2	PROPN
ejpam-4716	265	23	)	)	PUNCT
ejpam-4716	265	24	<	<	X
ejpam-4716	265	25	0	0	NUM
ejpam-4716	265	26	,	,	PUNCT
ejpam-4716	265	27	∀	∀	X
ejpam-4716	265	28	(	(	PUNCT
ejpam-4716	265	29	x1	x1	PROPN
ejpam-4716	265	30	,	,	PUNCT
ejpam-4716	265	31	x2	x2	PROPN
ejpam-4716	265	32	,	,	PUNCT
ejpam-4716	265	33	y1	y1	NOUN
ejpam-4716	265	34	,	,	PUNCT
ejpam-4716	265	35	y2	y2	NOUN
ejpam-4716	265	36	)	)	PUNCT
ejpam-4716	265	37	∈	∈	PROPN
ejpam-4716	265	38	b	b	PROPN
ejpam-4716	265	39	−	−	PROPN
ejpam-4716	265	40	{	{	PUNCT
ejpam-4716	265	41	(	(	PUNCT
ejpam-4716	265	42	x1	x1	PROPN
ejpam-4716	265	43	,	,	PUNCT
ejpam-4716	265	44	x2	x2	PROPN
ejpam-4716	265	45	,	,	PUNCT
ejpam-4716	265	46	y1	y1	NOUN
ejpam-4716	265	47	,	,	PUNCT
ejpam-4716	265	48	y2	y2	PROPN
ejpam-4716	265	49	)	)	PUNCT
ejpam-4716	265	50	}	}	PUNCT
ejpam-4716	265	51	,	,	PUNCT
ejpam-4716	265	52	and	and	CCONJ
ejpam-4716	265	53	v̇	v̇	NOUN
ejpam-4716	265	54	(	(	PUNCT
ejpam-4716	265	55	x1	x1	PROPN
ejpam-4716	265	56	,	,	PUNCT
ejpam-4716	265	57	x2	x2	PROPN
ejpam-4716	265	58	,	,	PUNCT
ejpam-4716	265	59	y1	y1	NOUN
ejpam-4716	265	60	,	,	PUNCT
ejpam-4716	265	61	y2	y2	NOUN
ejpam-4716	265	62	)	)	PUNCT
ejpam-4716	265	63	=	=	PUNCT
ejpam-4716	266	1	0	0	X
ejpam-4716	266	2	.	.	PUNCT
ejpam-4716	267	1	so	so	ADV
ejpam-4716	267	2	that	that	SCONJ
ejpam-4716	267	3	,	,	PUNCT
ejpam-4716	267	4	b	b	PROPN
ejpam-4716	267	5	is	be	AUX
ejpam-4716	267	6	an	an	DET
ejpam-4716	267	7	attraction	attraction	NOUN
ejpam-4716	267	8	basin	basin	NOUN
ejpam-4716	267	9	for	for	ADP
ejpam-4716	267	10	p6	p6	NOUN
ejpam-4716	267	11	=	=	SYM
ejpam-4716	267	12	(	(	PUNCT
ejpam-4716	267	13	x1	x1	PROPN
ejpam-4716	267	14	,	,	PUNCT
ejpam-4716	267	15	x2	x2	PROPN
ejpam-4716	267	16	,	,	PUNCT
ejpam-4716	267	17	y1	y1	NOUN
ejpam-4716	267	18	,	,	PUNCT
ejpam-4716	267	19	y2	y2	PROPN
ejpam-4716	267	20	)	)	PUNCT
ejpam-4716	267	21	and	and	CCONJ
ejpam-4716	267	22	with	with	ADP
ejpam-4716	267	23	this	this	PRON
ejpam-4716	267	24	,	,	PUNCT
ejpam-4716	267	25	we	we	PRON
ejpam-4716	267	26	have	have	AUX
ejpam-4716	267	27	completed	complete	VERB
ejpam-4716	267	28	the	the	DET
ejpam-4716	267	29	proof	proof	NOUN
ejpam-4716	267	30	.	.	PUNCT
ejpam-4716	268	1	5	5	X
ejpam-4716	268	2	.	.	X
ejpam-4716	268	3	local	local	ADJ
ejpam-4716	268	4	bifurcation	bifurcation	NOUN
ejpam-4716	268	5	this	this	DET
ejpam-4716	268	6	section	section	NOUN
ejpam-4716	268	7	is	be	AUX
ejpam-4716	268	8	dedicated	dedicate	VERB
ejpam-4716	268	9	to	to	ADP
ejpam-4716	268	10	the	the	DET
ejpam-4716	268	11	study	study	NOUN
ejpam-4716	268	12	of	of	ADP
ejpam-4716	268	13	the	the	DET
ejpam-4716	268	14	local	local	ADJ
ejpam-4716	268	15	bifurcation	bifurcation	NOUN
ejpam-4716	268	16	of	of	ADP
ejpam-4716	268	17	the	the	DET
ejpam-4716	268	18	three	three	NUM
ejpam-4716	268	19	equilibrium	equilibrium	NOUN
ejpam-4716	268	20	points	point	NOUN
ejpam-4716	268	21	.	.	PUNCT
ejpam-4716	269	1	local	local	ADJ
ejpam-4716	269	2	bifurcation	bifurcation	NOUN
ejpam-4716	269	3	occurs	occur	VERB
ejpam-4716	269	4	when	when	SCONJ
ejpam-4716	269	5	a	a	DET
ejpam-4716	269	6	small	small	ADJ
ejpam-4716	269	7	change	change	NOUN
ejpam-4716	269	8	in	in	ADP
ejpam-4716	269	9	the	the	DET
ejpam-4716	269	10	parameter	parameter	NOUN
ejpam-4716	269	11	value	value	NOUN
ejpam-4716	269	12	changes	change	VERB
ejpam-4716	269	13	the	the	DET
ejpam-4716	269	14	behavior	behavior	NOUN
ejpam-4716	269	15	of	of	ADP
ejpam-4716	269	16	the	the	DET
ejpam-4716	269	17	equilibrium	equilibrium	NOUN
ejpam-4716	269	18	.	.	PUNCT
ejpam-4716	270	1	if	if	SCONJ
ejpam-4716	270	2	the	the	DET
ejpam-4716	270	3	corresponding	corresponding	ADJ
ejpam-4716	270	4	real	real	ADJ
ejpam-4716	270	5	part	part	NOUN
ejpam-4716	270	6	of	of	ADP
ejpam-4716	270	7	one	one	NUM
ejpam-4716	270	8	eigenvalue	eigenvalue	NOUN
ejpam-4716	270	9	of	of	ADP
ejpam-4716	270	10	the	the	DET
ejpam-4716	270	11	equilibrium	equilibrium	NOUN
ejpam-4716	270	12	passes	pass	VERB
ejpam-4716	270	13	through	through	ADP
ejpam-4716	270	14	zero	zero	NUM
ejpam-4716	270	15	,	,	PUNCT
ejpam-4716	270	16	a	a	DET
ejpam-4716	270	17	steady	steady	ADJ
ejpam-4716	270	18	-	-	PUNCT
ejpam-4716	270	19	state	state	NOUN
ejpam-4716	270	20	bifurcation	bifurcation	NOUN
ejpam-4716	270	21	occurs	occur	VERB
ejpam-4716	270	22	,	,	PUNCT
ejpam-4716	270	23	and	and	CCONJ
ejpam-4716	270	24	in	in	ADP
ejpam-4716	270	25	the	the	DET
ejpam-4716	270	26	case	case	NOUN
ejpam-4716	270	27	that	that	SCONJ
ejpam-4716	270	28	the	the	DET
ejpam-4716	270	29	eigenvalues	eigenvalue	NOUN
ejpam-4716	270	30	is	be	AUX
ejpam-4716	270	31	not	not	PART
ejpam-4716	270	32	zeros	zero	NOUN
ejpam-4716	270	33	but	but	CCONJ
ejpam-4716	270	34	is	be	AUX
ejpam-4716	270	35	purely	purely	ADV
ejpam-4716	270	36	imaginary	imaginary	ADJ
ejpam-4716	270	37	,	,	PUNCT
ejpam-4716	270	38	then	then	ADV
ejpam-4716	270	39	this	this	PRON
ejpam-4716	270	40	is	be	AUX
ejpam-4716	270	41	a	a	DET
ejpam-4716	270	42	hopf	hopf	ADJ
ejpam-4716	270	43	-	-	PUNCT
ejpam-4716	270	44	bifurcation	bifurcation	NOUN
ejpam-4716	270	45	[	[	X
ejpam-4716	270	46	12	12	NUM
ejpam-4716	270	47	,	,	PUNCT
ejpam-4716	270	48	14	14	NUM
ejpam-4716	270	49	]	]	PUNCT
ejpam-4716	270	50	.	.	PUNCT
ejpam-4716	271	1	(	(	PUNCT
ejpam-4716	271	2	i	i	NOUN
ejpam-4716	271	3	)	)	PUNCT
ejpam-4716	271	4	if	if	SCONJ
ejpam-4716	271	5	the	the	DET
ejpam-4716	271	6	equilibrium	equilibrium	NOUN
ejpam-4716	271	7	point	point	NOUN
ejpam-4716	271	8	p	p	X
ejpam-4716	271	9	(	(	PUNCT
ejpam-4716	271	10	ϑ	ϑ	NOUN
ejpam-4716	271	11	)	)	PUNCT
ejpam-4716	271	12	is	be	AUX
ejpam-4716	271	13	locally	locally	ADV
ejpam-4716	271	14	asymptotically	asymptotically	ADV
ejpam-4716	271	15	stable	stable	ADJ
ejpam-4716	271	16	and	and	CCONJ
ejpam-4716	271	17	for	for	ADP
ejpam-4716	271	18	ϑ	ϑ	X
ejpam-4716	271	19	=	=	SYM
ejpam-4716	271	20	ϑ∗	ϑ∗	PROPN
ejpam-4716	271	21	we	we	PRON
ejpam-4716	271	22	have	have	VERB
ejpam-4716	271	23	one	one	NUM
ejpam-4716	271	24	eigenvalue	eigenvalue	PROPN
ejpam-4716	271	25	λ	λ	PROPN
ejpam-4716	271	26	(	(	PUNCT
ejpam-4716	271	27	ϑ∗	ϑ∗	PROPN
ejpam-4716	271	28	)	)	PUNCT
ejpam-4716	271	29	=	=	SYM
ejpam-4716	271	30	0	0	NUM
ejpam-4716	271	31	,	,	PUNCT
ejpam-4716	271	32	the	the	DET
ejpam-4716	271	33	bifurcation	bifurcation	NOUN
ejpam-4716	271	34	that	that	PRON
ejpam-4716	271	35	occurs	occur	VERB
ejpam-4716	271	36	is	be	AUX
ejpam-4716	271	37	a	a	DET
ejpam-4716	271	38	steady	steady	ADJ
ejpam-4716	271	39	state	state	NOUN
ejpam-4716	271	40	bifurcation	bifurcation	NOUN
ejpam-4716	272	1	[	[	X
ejpam-4716	272	2	6	6	NUM
ejpam-4716	272	3	]	]	PUNCT
ejpam-4716	272	4	.	.	PUNCT
ejpam-4716	273	1	the	the	DET
ejpam-4716	273	2	following	follow	VERB
ejpam-4716	273	3	theorems	theorem	NOUN
ejpam-4716	273	4	show	show	VERB
ejpam-4716	273	5	that	that	SCONJ
ejpam-4716	273	6	steady	steady	ADJ
ejpam-4716	273	7	-	-	PUNCT
ejpam-4716	273	8	state	state	NOUN
ejpam-4716	273	9	bifurcation	bifurcation	NOUN
ejpam-4716	273	10	occurs	occur	VERB
ejpam-4716	273	11	at	at	ADP
ejpam-4716	273	12	points	point	NOUN
ejpam-4716	273	13	p3	p3	PROPN
ejpam-4716	273	14	=	=	SYM
ejpam-4716	273	15	(	(	PUNCT
ejpam-4716	273	16	k1	k1	PROPN
ejpam-4716	273	17	,	,	PUNCT
ejpam-4716	273	18	k2.0	k2.0	PROPN
ejpam-4716	273	19	,	,	PUNCT
ejpam-4716	273	20	0	0	NUM
ejpam-4716	273	21	)	)	PUNCT
ejpam-4716	273	22	,	,	PUNCT
ejpam-4716	273	23	p4	p4	NOUN
ejpam-4716	273	24	=	=	SYM
ejpam-4716	273	25	(	(	PUNCT
ejpam-4716	273	26	x̃1	x̃1	PROPN
ejpam-4716	273	27	,	,	PUNCT
ejpam-4716	273	28	x̃2	x̃2	PROPN
ejpam-4716	273	29	,	,	PUNCT
ejpam-4716	273	30	ỹ1	ỹ1	PROPN
ejpam-4716	273	31	,	,	PUNCT
ejpam-4716	273	32	0	0	NUM
ejpam-4716	273	33	)	)	PUNCT
ejpam-4716	273	34	,	,	PUNCT
ejpam-4716	273	35	and	and	CCONJ
ejpam-4716	273	36	p5	p5	ADJ
ejpam-4716	273	37	=	=	SYM
ejpam-4716	273	38	(	(	PUNCT
ejpam-4716	273	39	x̌1	x̌1	NUM
ejpam-4716	273	40	,	,	PUNCT
ejpam-4716	273	41	x̌2	x̌2	NUM
ejpam-4716	273	42	,	,	PUNCT
ejpam-4716	273	43	0	0	NUM
ejpam-4716	273	44	,	,	PUNCT
ejpam-4716	273	45	y̌2	y̌2	PRON
ejpam-4716	273	46	)	)	PUNCT
ejpam-4716	273	47	for	for	ADP
ejpam-4716	273	48	the	the	DET
ejpam-4716	273	49	parameters	parameter	NOUN
ejpam-4716	273	50	µi	µi	ADP
ejpam-4716	273	51	,	,	PUNCT
ejpam-4716	273	52	i	i	PRON
ejpam-4716	273	53	=	=	NOUN
ejpam-4716	273	54	1	1	NUM
ejpam-4716	273	55	or	or	CCONJ
ejpam-4716	273	56	2	2	NUM
ejpam-4716	273	57	,	,	PUNCT
ejpam-4716	273	58	µ1	µ1	PROPN
ejpam-4716	273	59	,	,	PUNCT
ejpam-4716	273	60	and	and	CCONJ
ejpam-4716	273	61	µ2	µ2	PROPN
ejpam-4716	273	62	,	,	PUNCT
ejpam-4716	273	63	respectively	respectively	ADV
ejpam-4716	273	64	.	.	PUNCT
ejpam-4716	274	1	theorem	theorem	VERB
ejpam-4716	274	2	6	6	NUM
ejpam-4716	274	3	.	.	PUNCT
ejpam-4716	274	4	suppose	suppose	VERB
ejpam-4716	274	5	that	that	SCONJ
ejpam-4716	274	6	,	,	PUNCT
ejpam-4716	274	7	the	the	DET
ejpam-4716	274	8	equilibrium	equilibrium	NOUN
ejpam-4716	274	9	point	point	NOUN
ejpam-4716	274	10	p3	p3	PROPN
ejpam-4716	274	11	=	=	SYM
ejpam-4716	274	12	(	(	PUNCT
ejpam-4716	274	13	k1	k1	PROPN
ejpam-4716	274	14	,	,	PUNCT
ejpam-4716	274	15	k2.0	k2.0	PROPN
ejpam-4716	274	16	,	,	PUNCT
ejpam-4716	274	17	0	0	NUM
ejpam-4716	274	18	)	)	PUNCT
ejpam-4716	274	19	of	of	ADP
ejpam-4716	274	20	the	the	DET
ejpam-4716	274	21	system	system	NOUN
ejpam-4716	274	22	(	(	PUNCT
ejpam-4716	274	23	2	2	X
ejpam-4716	274	24	)	)	PUNCT
ejpam-4716	274	25	is	be	AUX
ejpam-4716	274	26	locally	locally	ADV
ejpam-4716	274	27	asymptotically	asymptotically	ADV
ejpam-4716	274	28	stable	stable	ADJ
ejpam-4716	274	29	point	point	NOUN
ejpam-4716	274	30	,	,	PUNCT
ejpam-4716	274	31	then	then	ADV
ejpam-4716	274	32	(	(	PUNCT
ejpam-4716	274	33	i	i	NOUN
ejpam-4716	274	34	)	)	PUNCT
ejpam-4716	274	35	a	a	DET
ejpam-4716	274	36	steady	steady	ADJ
ejpam-4716	274	37	state	state	NOUN
ejpam-4716	274	38	bifurcation	bifurcation	NOUN
ejpam-4716	274	39	occurs	occur	VERB
ejpam-4716	274	40	as	as	SCONJ
ejpam-4716	274	41	µ1	µ1	PROPN
ejpam-4716	274	42	pass	pass	NOUN
ejpam-4716	274	43	through	through	ADP
ejpam-4716	274	44	µ∗	µ∗	NOUN
ejpam-4716	274	45	1	1	NUM
ejpam-4716	274	46	=	=	SYM
ejpam-4716	274	47	k1k2ε1	k1k2ε1	PROPN
ejpam-4716	274	48	k1+k2	k1+k2	PROPN
ejpam-4716	274	49	,	,	PUNCT
ejpam-4716	274	50	(	(	PUNCT
ejpam-4716	274	51	ii	ii	NOUN
ejpam-4716	274	52	)	)	PUNCT
ejpam-4716	274	53	a	a	DET
ejpam-4716	274	54	steady	steady	ADJ
ejpam-4716	274	55	state	state	NOUN
ejpam-4716	274	56	bifurcation	bifurcation	NOUN
ejpam-4716	274	57	occurs	occur	VERB
ejpam-4716	274	58	as	as	SCONJ
ejpam-4716	274	59	µ1	µ1	PROPN
ejpam-4716	274	60	pass	pass	NOUN
ejpam-4716	274	61	through	through	ADP
ejpam-4716	274	62	µ∗	µ∗	NOUN
ejpam-4716	274	63	2	2	NUM
ejpam-4716	274	64	=	=	SYM
ejpam-4716	274	65	k1k2ε2	k1k2ε2	PROPN
ejpam-4716	274	66	k1+k2	k1+k2	PROPN
ejpam-4716	274	67	.	.	PUNCT
ejpam-4716	275	1	a.	a.	PROPN
ejpam-4716	275	2	g.	g.	PROPN
ejpam-4716	275	3	farhan	farhan	PROPN
ejpam-4716	275	4	,	,	PUNCT
ejpam-4716	275	5	n.	n.	PROPN
ejpam-4716	275	6	sh	sh	PROPN
ejpam-4716	275	7	.	.	PROPN
ejpam-4716	275	8	khalaf	khalaf	PROPN
ejpam-4716	275	9	,	,	PUNCT
ejpam-4716	275	10	t.	t.	PROPN
ejpam-4716	275	11	j.	j.	PROPN
ejpam-4716	275	12	aldhlki	aldhlki	PROPN
ejpam-4716	275	13	/	/	SYM
ejpam-4716	275	14	eur	eur	PROPN
ejpam-4716	275	15	.	.	PUNCT
ejpam-4716	276	1	j.	j.	PROPN
ejpam-4716	276	2	pure	pure	PROPN
ejpam-4716	276	3	appl	appl	PROPN
ejpam-4716	276	4	.	.	PROPN
ejpam-4716	276	5	math	math	PROPN
ejpam-4716	276	6	,	,	PUNCT
ejpam-4716	276	7	16	16	NUM
ejpam-4716	276	8	(	(	PUNCT
ejpam-4716	276	9	2	2	NUM
ejpam-4716	276	10	)	)	PUNCT
ejpam-4716	276	11	(	(	PUNCT
ejpam-4716	276	12	2023	2023	NUM
ejpam-4716	276	13	)	)	PUNCT
ejpam-4716	276	14	,	,	PUNCT
ejpam-4716	276	15	899	899	NUM
ejpam-4716	276	16	-	-	SYM
ejpam-4716	276	17	918	918	NUM
ejpam-4716	276	18	910	910	NUM
ejpam-4716	276	19	proof	proof	NOUN
ejpam-4716	276	20	.	.	PUNCT
ejpam-4716	277	1	(	(	PUNCT
ejpam-4716	277	2	i	i	NOUN
ejpam-4716	277	3	)	)	PUNCT
ejpam-4716	277	4	from	from	ADP
ejpam-4716	277	5	theorem	theorem	ADJ
ejpam-4716	277	6	2	2	NUM
ejpam-4716	277	7	and	and	CCONJ
ejpam-4716	277	8	the	the	DET
ejpam-4716	277	9	assumption	assumption	NOUN
ejpam-4716	277	10	or	or	CCONJ
ejpam-4716	277	11	the	the	DET
ejpam-4716	277	12	theorem	theorem	NOUN
ejpam-4716	277	13	that	that	PRON
ejpam-4716	277	14	we	we	PRON
ejpam-4716	277	15	have	have	VERB
ejpam-4716	277	16	that	that	SCONJ
ejpam-4716	277	17	the	the	DET
ejpam-4716	277	18	eigenvalues	eigenvalue	NOUN
ejpam-4716	277	19	of	of	ADP
ejpam-4716	277	20	the	the	DET
ejpam-4716	277	21	characteristic	characteristic	ADJ
ejpam-4716	277	22	equation	equation	NOUN
ejpam-4716	277	23	of	of	ADP
ejpam-4716	277	24	j(p3	j(p3	PROPN
ejpam-4716	277	25	)	)	PUNCT
ejpam-4716	277	26	are	be	AUX
ejpam-4716	277	27	λ1	λ1	ADJ
ejpam-4716	277	28	=	=	PUNCT
ejpam-4716	277	29	−g1	−g1	VERB
ejpam-4716	277	30	,	,	PUNCT
ejpam-4716	277	31	λ2	λ2	NOUN
ejpam-4716	277	32	=	=	SYM
ejpam-4716	277	33	−g2	−g2	ADJ
ejpam-4716	277	34	,	,	PUNCT
ejpam-4716	277	35	λ3	λ3	PROPN
ejpam-4716	277	36	=	=	SYM
ejpam-4716	277	37	ε1k1k2	ε1k1k2	NOUN
ejpam-4716	277	38	k1	k1	NOUN
ejpam-4716	277	39	+	+	CCONJ
ejpam-4716	277	40	k2	k2	ADJ
ejpam-4716	277	41	−	−	PROPN
ejpam-4716	277	42	µ1	µ1	PROPN
ejpam-4716	277	43	<	<	X
ejpam-4716	277	44	0	0	NUM
ejpam-4716	277	45	,	,	PUNCT
ejpam-4716	277	46	λ4	λ4	PROPN
ejpam-4716	277	47	=	=	SYM
ejpam-4716	277	48	ε2k1k2	ε2k1k2	PROPN
ejpam-4716	277	49	k1	k1	PROPN
ejpam-4716	277	50	+	+	CCONJ
ejpam-4716	277	51	k2	k2	PROPN
ejpam-4716	277	52	−	−	PROPN
ejpam-4716	277	53	µ2	µ2	PROPN
ejpam-4716	277	54	<	<	X
ejpam-4716	277	55	0	0	NUM
ejpam-4716	277	56	.	.	PUNCT
ejpam-4716	278	1	it	it	PRON
ejpam-4716	278	2	obvious	obvious	ADJ
ejpam-4716	278	3	that	that	SCONJ
ejpam-4716	278	4	p3	p3	PROPN
ejpam-4716	278	5	=	=	SYM
ejpam-4716	278	6	(	(	PUNCT
ejpam-4716	278	7	k1	k1	PROPN
ejpam-4716	278	8	,	,	PUNCT
ejpam-4716	278	9	k2.0	k2.0	PROPN
ejpam-4716	278	10	,	,	PUNCT
ejpam-4716	278	11	0	0	NUM
ejpam-4716	278	12	)	)	PUNCT
ejpam-4716	278	13	do	do	AUX
ejpam-4716	278	14	not	not	PART
ejpam-4716	278	15	depends	depend	VERB
ejpam-4716	278	16	on	on	ADP
ejpam-4716	278	17	the	the	DET
ejpam-4716	278	18	parameter	parameter	NOUN
ejpam-4716	278	19	µ1	µ1	PROPN
ejpam-4716	278	20	,	,	PUNCT
ejpam-4716	278	21	which	which	PRON
ejpam-4716	278	22	means	mean	VERB
ejpam-4716	278	23	that	that	SCONJ
ejpam-4716	278	24	p3	p3	PROPN
ejpam-4716	278	25	do	do	AUX
ejpam-4716	278	26	not	not	PART
ejpam-4716	278	27	change	change	VERB
ejpam-4716	278	28	with	with	ADP
ejpam-4716	278	29	the	the	DET
ejpam-4716	278	30	change	change	NOUN
ejpam-4716	278	31	of	of	ADP
ejpam-4716	278	32	the	the	DET
ejpam-4716	278	33	value	value	NOUN
ejpam-4716	278	34	of	of	ADP
ejpam-4716	278	35	µ1	µ1	PROPN
ejpam-4716	278	36	.	.	PUNCT
ejpam-4716	279	1	hence	hence	ADV
ejpam-4716	279	2	,	,	PUNCT
ejpam-4716	279	3	if	if	SCONJ
ejpam-4716	279	4	µ1	µ1	PROPN
ejpam-4716	279	5	>	>	SYM
ejpam-4716	279	6	µ∗	µ∗	PROPN
ejpam-4716	279	7	1	1	NUM
ejpam-4716	279	8	then	then	ADV
ejpam-4716	279	9	p3	p3	PROPN
ejpam-4716	279	10	of	of	ADP
ejpam-4716	279	11	the	the	DET
ejpam-4716	279	12	system	system	NOUN
ejpam-4716	279	13	(	(	PUNCT
ejpam-4716	279	14	2	2	X
ejpam-4716	279	15	)	)	PUNCT
ejpam-4716	279	16	is	be	AUX
ejpam-4716	279	17	locally	locally	ADV
ejpam-4716	279	18	asymptotically	asymptotically	ADV
ejpam-4716	279	19	stable	stable	ADJ
ejpam-4716	279	20	point	point	NOUN
ejpam-4716	279	21	(	(	PUNCT
ejpam-4716	279	22	nod	nod	NOUN
ejpam-4716	279	23	point	point	NOUN
ejpam-4716	279	24	)	)	PUNCT
ejpam-4716	279	25	and	and	CCONJ
ejpam-4716	279	26	if	if	SCONJ
ejpam-4716	279	27	µ1	µ1	PROPN
ejpam-4716	279	28	<	<	X
ejpam-4716	279	29	µ∗	µ∗	PROPN
ejpam-4716	279	30	1	1	NUM
ejpam-4716	279	31	then	then	ADV
ejpam-4716	279	32	p3	p3	PROPN
ejpam-4716	279	33	of	of	ADP
ejpam-4716	279	34	the	the	DET
ejpam-4716	279	35	system	system	NOUN
ejpam-4716	279	36	(	(	PUNCT
ejpam-4716	279	37	2	2	X
ejpam-4716	279	38	)	)	PUNCT
ejpam-4716	279	39	is	be	AUX
ejpam-4716	279	40	unstable	unstable	ADJ
ejpam-4716	279	41	point	point	NOUN
ejpam-4716	279	42	(	(	PUNCT
ejpam-4716	279	43	saddle	saddle	NOUN
ejpam-4716	279	44	point	point	NOUN
ejpam-4716	279	45	)	)	PUNCT
ejpam-4716	279	46	.	.	PUNCT
ejpam-4716	280	1	(	(	PUNCT
ejpam-4716	280	2	ii	ii	X
ejpam-4716	280	3	)	)	PUNCT
ejpam-4716	280	4	the	the	DET
ejpam-4716	280	5	proof	proof	NOUN
ejpam-4716	280	6	is	be	AUX
ejpam-4716	280	7	the	the	DET
ejpam-4716	280	8	same	same	ADJ
ejpam-4716	280	9	as	as	ADP
ejpam-4716	280	10	the	the	DET
ejpam-4716	280	11	proof	proof	NOUN
ejpam-4716	280	12	of	of	ADP
ejpam-4716	280	13	the	the	DET
ejpam-4716	280	14	first	first	ADJ
ejpam-4716	280	15	part	part	NOUN
ejpam-4716	280	16	of	of	ADP
ejpam-4716	280	17	this	this	DET
ejpam-4716	280	18	theorem	theorem	NOUN
ejpam-4716	280	19	,	,	PUNCT
ejpam-4716	280	20	and	and	CCONJ
ejpam-4716	280	21	with	with	ADP
ejpam-4716	280	22	this	this	PRON
ejpam-4716	280	23	,	,	PUNCT
ejpam-4716	280	24	we	we	PRON
ejpam-4716	280	25	have	have	AUX
ejpam-4716	280	26	completed	complete	VERB
ejpam-4716	280	27	the	the	DET
ejpam-4716	280	28	proof	proof	NOUN
ejpam-4716	280	29	.	.	PUNCT
ejpam-4716	281	1	theorem	theorem	ADJ
ejpam-4716	281	2	7	7	NUM
ejpam-4716	281	3	.	.	PUNCT
ejpam-4716	282	1	(	(	PUNCT
ejpam-4716	282	2	i	i	NOUN
ejpam-4716	282	3	)	)	PUNCT
ejpam-4716	282	4	suppose	suppose	VERB
ejpam-4716	282	5	that	that	SCONJ
ejpam-4716	282	6	,	,	PUNCT
ejpam-4716	282	7	the	the	DET
ejpam-4716	282	8	equilibrium	equilibrium	NOUN
ejpam-4716	282	9	point	point	NOUN
ejpam-4716	282	10	p4	p4	ADJ
ejpam-4716	282	11	=	=	PUNCT
ejpam-4716	282	12	(	(	PUNCT
ejpam-4716	282	13	x̌1	x̌1	NUM
ejpam-4716	282	14	,	,	PUNCT
ejpam-4716	282	15	x̌2	x̌2	NUM
ejpam-4716	282	16	,	,	PUNCT
ejpam-4716	282	17	0	0	NUM
ejpam-4716	282	18	,	,	PUNCT
ejpam-4716	282	19	y̌2	y̌2	PRON
ejpam-4716	282	20	)	)	PUNCT
ejpam-4716	282	21	of	of	ADP
ejpam-4716	282	22	the	the	DET
ejpam-4716	282	23	system	system	NOUN
ejpam-4716	282	24	(	(	PUNCT
ejpam-4716	282	25	2	2	X
ejpam-4716	282	26	)	)	PUNCT
ejpam-4716	282	27	exists	exist	VERB
ejpam-4716	282	28	and	and	CCONJ
ejpam-4716	282	29	is	be	AUX
ejpam-4716	282	30	locally	locally	ADV
ejpam-4716	282	31	asymptotically	asymptotically	ADV
ejpam-4716	282	32	stable	stable	ADJ
ejpam-4716	282	33	point	point	NOUN
ejpam-4716	282	34	then	then	ADV
ejpam-4716	282	35	a	a	DET
ejpam-4716	282	36	steady	steady	ADJ
ejpam-4716	282	37	state	state	NOUN
ejpam-4716	282	38	bifurcation	bifurcation	NOUN
ejpam-4716	282	39	occurs	occur	VERB
ejpam-4716	282	40	as	as	SCONJ
ejpam-4716	282	41	µ2	µ2	PROPN
ejpam-4716	282	42	pass	pass	VERB
ejpam-4716	282	43	through	through	ADP
ejpam-4716	282	44	µ∗	µ∗	PROPN
ejpam-4716	282	45	2	2	NUM
ejpam-4716	282	46	=	=	SYM
ejpam-4716	282	47	ε2x̌1	ε2x̌1	NOUN
ejpam-4716	282	48	1+x̌	1+x̌	NUM
ejpam-4716	282	49	+	+	CCONJ
ejpam-4716	282	50	ρ1y̌1	ρ1y̌1	NUM
ejpam-4716	282	51	.	.	PUNCT
ejpam-4716	283	1	(	(	PUNCT
ejpam-4716	283	2	ii	ii	NOUN
ejpam-4716	283	3	)	)	PUNCT
ejpam-4716	283	4	suppose	suppose	VERB
ejpam-4716	283	5	that	that	SCONJ
ejpam-4716	283	6	,	,	PUNCT
ejpam-4716	283	7	the	the	DET
ejpam-4716	283	8	equilibrium	equilibrium	NOUN
ejpam-4716	283	9	point	point	NOUN
ejpam-4716	283	10	p5	p5	ADJ
ejpam-4716	283	11	of	of	ADP
ejpam-4716	283	12	the	the	DET
ejpam-4716	283	13	system	system	NOUN
ejpam-4716	283	14	(	(	PUNCT
ejpam-4716	283	15	2	2	X
ejpam-4716	283	16	)	)	PUNCT
ejpam-4716	283	17	exist	exist	VERB
ejpam-4716	283	18	and	and	CCONJ
ejpam-4716	283	19	is	be	AUX
ejpam-4716	283	20	locally	locally	ADV
ejpam-4716	283	21	asymptotically	asymptotically	ADV
ejpam-4716	283	22	stable	stable	ADJ
ejpam-4716	283	23	point	point	NOUN
ejpam-4716	283	24	then	then	ADV
ejpam-4716	283	25	a	a	DET
ejpam-4716	283	26	steady	steady	ADJ
ejpam-4716	283	27	state	state	NOUN
ejpam-4716	283	28	bifurcation	bifurcation	NOUN
ejpam-4716	283	29	occurs	occur	VERB
ejpam-4716	283	30	as	as	SCONJ
ejpam-4716	283	31	µ1	µ1	PROPN
ejpam-4716	283	32	pass	pass	NOUN
ejpam-4716	283	33	through	through	ADP
ejpam-4716	283	34	µ∗	µ∗	NOUN
ejpam-4716	283	35	1	1	NUM
ejpam-4716	283	36	=	=	NOUN
ejpam-4716	283	37	ε1x̃1	ε1x̃1	NOUN
ejpam-4716	284	1	1+x̃	1+x̃	NUM
ejpam-4716	284	2	−	−	NOUN
ejpam-4716	285	1	ρ2ỹ2	ρ2ỹ2	X
ejpam-4716	285	2	.	.	PUNCT
ejpam-4716	286	1	proof	proof	NOUN
ejpam-4716	286	2	.	.	PUNCT
ejpam-4716	287	1	(	(	PUNCT
ejpam-4716	287	2	i	i	NOUN
ejpam-4716	287	3	)	)	PUNCT
ejpam-4716	287	4	from	from	ADP
ejpam-4716	287	5	theorem	theorem	ADJ
ejpam-4716	287	6	3	3	NUM
ejpam-4716	287	7	,	,	PUNCT
ejpam-4716	287	8	the	the	DET
ejpam-4716	287	9	characteristic	characteristic	ADJ
ejpam-4716	287	10	equation	equation	NOUN
ejpam-4716	287	11	of	of	ADP
ejpam-4716	287	12	j(p4	j(p4	NOUN
ejpam-4716	287	13	)	)	PUNCT
ejpam-4716	287	14	is	be	AUX
ejpam-4716	287	15	(	(	PUNCT
ejpam-4716	287	16	λ−	λ−	PROPN
ejpam-4716	287	17	γ̃ε2x̃1	γ̃ε2x̃1	PROPN
ejpam-4716	287	18	−	−	PROPN
ejpam-4716	287	19	ρ1ỹ1	ρ1ỹ1	PUNCT
ejpam-4716	288	1	+	+	CCONJ
ejpam-4716	288	2	µ2	µ2	NOUN
ejpam-4716	288	3	)	)	PUNCT
ejpam-4716	288	4	(	(	PUNCT
ejpam-4716	288	5	λ3	λ3	PROPN
ejpam-4716	288	6	−	−	PROPN
ejpam-4716	288	7	trm̃	trm̃	NOUN
ejpam-4716	288	8	λ2	λ2	NOUN
ejpam-4716	288	9	+	+	CCONJ
ejpam-4716	288	10	3∑	3∑	NUM
ejpam-4716	288	11	i=1	i=1	X
ejpam-4716	288	12	m̃ii	m̃ii	PROPN
ejpam-4716	288	13	λ−detm̃	λ−detm̃	PUNCT
ejpam-4716	288	14	)	)	PUNCT
ejpam-4716	289	1	=	=	SYM
ejpam-4716	289	2	0	0	X
ejpam-4716	289	3	.	.	PUNCT
ejpam-4716	290	1	as	as	SCONJ
ejpam-4716	290	2	it	it	PRON
ejpam-4716	290	3	is	be	AUX
ejpam-4716	290	4	clear	clear	ADJ
ejpam-4716	290	5	from	from	ADP
ejpam-4716	290	6	the	the	DET
ejpam-4716	290	7	equation	equation	NOUN
ejpam-4716	290	8	that	that	PRON
ejpam-4716	290	9	second	second	ADJ
ejpam-4716	290	10	algebraic	algebraic	ADJ
ejpam-4716	290	11	expression	expression	NOUN
ejpam-4716	290	12	(	(	PUNCT
ejpam-4716	290	13	λ3	λ3	PROPN
ejpam-4716	290	14	−	−	PROPN
ejpam-4716	290	15	trm̃λ2	trm̃λ2	NOUN
ejpam-4716	291	1	+	+	CCONJ
ejpam-4716	291	2	∑3	∑3	PROPN
ejpam-4716	291	3	i=1	i=1	PROPN
ejpam-4716	291	4	m̃iiλ−detm̃	m̃iiλ−detm̃	X
ejpam-4716	291	5	)	)	PUNCT
ejpam-4716	291	6	of	of	ADP
ejpam-4716	291	7	the	the	DET
ejpam-4716	291	8	left	left	ADJ
ejpam-4716	291	9	side	side	NOUN
ejpam-4716	291	10	the	the	DET
ejpam-4716	291	11	characteristic	characteristic	ADJ
ejpam-4716	291	12	equation	equation	NOUN
ejpam-4716	291	13	does	do	AUX
ejpam-4716	291	14	not	not	PART
ejpam-4716	291	15	depend	depend	VERB
ejpam-4716	291	16	on	on	ADP
ejpam-4716	291	17	the	the	DET
ejpam-4716	291	18	parameter	parameter	NOUN
ejpam-4716	291	19	µ2	µ2	PROPN
ejpam-4716	291	20	.	.	PUNCT
ejpam-4716	292	1	the	the	DET
ejpam-4716	292	2	equations	equation	NOUN
ejpam-4716	292	3	(	(	PUNCT
ejpam-4716	292	4	5	5	NUM
ejpam-4716	292	5	)	)	PUNCT
ejpam-4716	292	6	,	,	PUNCT
ejpam-4716	292	7	(	(	PUNCT
ejpam-4716	292	8	6	6	NUM
ejpam-4716	292	9	)	)	PUNCT
ejpam-4716	292	10	and	and	CCONJ
ejpam-4716	292	11	(	(	PUNCT
ejpam-4716	292	12	8)	8)	NUM
ejpam-4716	292	13	,	,	PUNCT
ejpam-4716	292	14	show	show	VERB
ejpam-4716	292	15	that	that	SCONJ
ejpam-4716	292	16	the	the	DET
ejpam-4716	292	17	existence	existence	NOUN
ejpam-4716	292	18	of	of	ADP
ejpam-4716	292	19	p4	p4	NOUN
ejpam-4716	292	20	does	do	AUX
ejpam-4716	292	21	not	not	PART
ejpam-4716	292	22	depends	depend	VERB
ejpam-4716	292	23	on	on	ADP
ejpam-4716	292	24	µ2	µ2	PROPN
ejpam-4716	292	25	.	.	PUNCT
ejpam-4716	293	1	hence	hence	ADV
ejpam-4716	293	2	,	,	PUNCT
ejpam-4716	293	3	if	if	SCONJ
ejpam-4716	293	4	µ2	µ2	PROPN
ejpam-4716	293	5	>	>	PUNCT
ejpam-4716	293	6	µ∗	µ∗	PROPN
ejpam-4716	293	7	2	2	NUM
ejpam-4716	293	8	the	the	DET
ejpam-4716	293	9	p3	p3	PROPN
ejpam-4716	293	10	of	of	ADP
ejpam-4716	293	11	the	the	DET
ejpam-4716	293	12	system	system	NOUN
ejpam-4716	293	13	(	(	PUNCT
ejpam-4716	293	14	2	2	X
ejpam-4716	293	15	)	)	PUNCT
ejpam-4716	293	16	is	be	AUX
ejpam-4716	293	17	locally	locally	ADV
ejpam-4716	293	18	asymptotically	asymptotically	ADV
ejpam-4716	293	19	stable	stable	ADJ
ejpam-4716	293	20	point	point	NOUN
ejpam-4716	293	21	(	(	PUNCT
ejpam-4716	293	22	nod	nod	NOUN
ejpam-4716	293	23	point	point	NOUN
ejpam-4716	293	24	)	)	PUNCT
ejpam-4716	293	25	and	and	CCONJ
ejpam-4716	293	26	if	if	SCONJ
ejpam-4716	293	27	µ2	µ2	PROPN
ejpam-4716	293	28	<	<	X
ejpam-4716	293	29	µ∗	µ∗	PROPN
ejpam-4716	293	30	2	2	NUM
ejpam-4716	293	31	the	the	DET
ejpam-4716	293	32	p4	p4	NOUN
ejpam-4716	293	33	of	of	ADP
ejpam-4716	293	34	the	the	DET
ejpam-4716	293	35	system	system	NOUN
ejpam-4716	293	36	(	(	PUNCT
ejpam-4716	293	37	2	2	X
ejpam-4716	293	38	)	)	PUNCT
ejpam-4716	293	39	is	be	AUX
ejpam-4716	293	40	unstable	unstable	ADJ
ejpam-4716	293	41	point	point	NOUN
ejpam-4716	293	42	(	(	PUNCT
ejpam-4716	293	43	saddle	saddle	NOUN
ejpam-4716	293	44	point	point	NOUN
ejpam-4716	293	45	)	)	PUNCT
ejpam-4716	293	46	.	.	PUNCT
ejpam-4716	294	1	(	(	PUNCT
ejpam-4716	294	2	ii	ii	X
ejpam-4716	294	3	)	)	PUNCT
ejpam-4716	294	4	the	the	DET
ejpam-4716	294	5	proof	proof	NOUN
ejpam-4716	294	6	is	be	AUX
ejpam-4716	294	7	the	the	DET
ejpam-4716	294	8	same	same	ADJ
ejpam-4716	294	9	as	as	ADP
ejpam-4716	294	10	the	the	DET
ejpam-4716	294	11	proof	proof	NOUN
ejpam-4716	294	12	of	of	ADP
ejpam-4716	294	13	first	first	ADJ
ejpam-4716	294	14	part	part	NOUN
ejpam-4716	294	15	of	of	ADP
ejpam-4716	294	16	this	this	DET
ejpam-4716	294	17	theorem	theorem	NOUN
ejpam-4716	294	18	.	.	PUNCT
ejpam-4716	294	19	and	and	CCONJ
ejpam-4716	294	20	with	with	ADP
ejpam-4716	294	21	this	this	PRON
ejpam-4716	294	22	,	,	PUNCT
ejpam-4716	294	23	we	we	PRON
ejpam-4716	294	24	have	have	AUX
ejpam-4716	294	25	completed	complete	VERB
ejpam-4716	294	26	the	the	DET
ejpam-4716	294	27	proof	proof	NOUN
ejpam-4716	294	28	.	.	PUNCT
ejpam-4716	295	1	(	(	PUNCT
ejpam-4716	295	2	ii	ii	X
ejpam-4716	295	3	)	)	PUNCT
ejpam-4716	295	4	the	the	DET
ejpam-4716	295	5	local	local	ADJ
ejpam-4716	295	6	birth	birth	NOUN
ejpam-4716	295	7	or	or	CCONJ
ejpam-4716	295	8	death	death	NOUN
ejpam-4716	295	9	of	of	ADP
ejpam-4716	295	10	a	a	DET
ejpam-4716	295	11	periodic	periodic	ADJ
ejpam-4716	295	12	solution	solution	NOUN
ejpam-4716	295	13	from	from	ADP
ejpam-4716	295	14	equilibrium	equilibrium	NOUN
ejpam-4716	295	15	as	as	ADP
ejpam-4716	295	16	a	a	DET
ejpam-4716	295	17	parameter	parameter	NOUN
ejpam-4716	295	18	ϑ	ϑ	PROPN
ejpam-4716	295	19	passes	pass	VERB
ejpam-4716	295	20	through	through	ADP
ejpam-4716	295	21	a	a	DET
ejpam-4716	295	22	critical	critical	ADJ
ejpam-4716	295	23	value	value	NOUN
ejpam-4716	295	24	ϑ∗	ϑ∗	NOUN
ejpam-4716	295	25	is	be	AUX
ejpam-4716	295	26	called	call	VERB
ejpam-4716	295	27	hopf	hopf	ADJ
ejpam-4716	295	28	bifurcation	bifurcation	NOUN
ejpam-4716	295	29	.	.	PUNCT
ejpam-4716	296	1	for	for	ADP
ejpam-4716	296	2	the	the	DET
ejpam-4716	296	3	parameter	parameter	NOUN
ejpam-4716	296	4	g	g	PROPN
ejpam-4716	296	5	=	=	PROPN
ejpam-4716	296	6	g1	g1	PROPN
ejpam-4716	296	7	=	=	SYM
ejpam-4716	296	8	g2	g2	PROPN
ejpam-4716	296	9	,	,	PUNCT
ejpam-4716	296	10	let	let	VERB
ejpam-4716	296	11	p4	p4	ADJ
ejpam-4716	296	12	be	be	AUX
ejpam-4716	296	13	a	a	DET
ejpam-4716	296	14	locally	locally	ADV
ejpam-4716	296	15	asymptotically	asymptotically	ADV
ejpam-4716	296	16	stable	stable	ADJ
ejpam-4716	296	17	equilibrium	equilibrium	NOUN
ejpam-4716	296	18	point	point	NOUN
ejpam-4716	296	19	and	and	CCONJ
ejpam-4716	296	20	trm̃	trm̃	NOUN
ejpam-4716	296	21	3∑	3∑	NOUN
ejpam-4716	296	22	i=1	i=1	PROPN
ejpam-4716	297	1	m̃ii	m̃ii	PROPN
ejpam-4716	297	2	=	=	SYM
ejpam-4716	297	3	detm̃	detm̃	PROPN
ejpam-4716	297	4	,	,	PUNCT
ejpam-4716	297	5	(	(	PUNCT
ejpam-4716	297	6	17	17	NUM
ejpam-4716	297	7	)	)	PUNCT
ejpam-4716	297	8	g∗	g∗	NOUN
ejpam-4716	297	9	=	=	SYM
ejpam-4716	297	10	s2∓	s2∓	NOUN
ejpam-4716	297	11	√	√	NUM
ejpam-4716	297	12	s2	s2	VERB
ejpam-4716	297	13	2−4s1s3	2−4s1s3	NUM
ejpam-4716	297	14	2s1	2s1	NUM
ejpam-4716	297	15	,	,	PUNCT
ejpam-4716	297	16	is	be	AUX
ejpam-4716	297	17	the	the	DET
ejpam-4716	297	18	positive	positive	ADJ
ejpam-4716	297	19	root	root	NOUN
ejpam-4716	297	20	of	of	ADP
ejpam-4716	297	21	the	the	DET
ejpam-4716	297	22	equation	equation	NOUN
ejpam-4716	297	23	(	(	PUNCT
ejpam-4716	297	24	17	17	NUM
ejpam-4716	297	25	)	)	PUNCT
ejpam-4716	298	1	where	where	SCONJ
ejpam-4716	298	2	,	,	PUNCT
ejpam-4716	298	3	s1	s1	PROPN
ejpam-4716	298	4	=	=	SYM
ejpam-4716	298	5	ãñ22	ãñ22	PROPN
ejpam-4716	298	6	,	,	PUNCT
ejpam-4716	298	7	s2	s2	NOUN
ejpam-4716	298	8	=	=	PUNCT
ejpam-4716	298	9	detñ	detñ	NOUN
ejpam-4716	299	1	−	−	PROPN
ejpam-4716	300	1	ã	ã	PROPN
ejpam-4716	300	2	(	(	PUNCT
ejpam-4716	300	3	ñ11	ñ11	PROPN
ejpam-4716	300	4	+	+	CCONJ
ejpam-4716	300	5	ñ22	ñ22	PROPN
ejpam-4716	300	6	)	)	PUNCT
ejpam-4716	301	1	−	−	ADP
ejpam-4716	301	2	b̃ñ33	b̃ñ33	PROPN
ejpam-4716	301	3	,	,	PUNCT
ejpam-4716	301	4	s3	s3	PROPN
ejpam-4716	301	5	=	=	PROPN
ejpam-4716	301	6	b̃	b̃	PROPN
ejpam-4716	301	7	(	(	PUNCT
ejpam-4716	301	8	ñ11	ñ11	PROPN
ejpam-4716	301	9	+	+	CCONJ
ejpam-4716	301	10	ñ22	ñ22	PROPN
ejpam-4716	301	11	)	)	PUNCT
ejpam-4716	301	12	,	,	PUNCT
ejpam-4716	301	13	a.	a.	NOUN
ejpam-4716	301	14	g.	g.	PROPN
ejpam-4716	301	15	farhan	farhan	PROPN
ejpam-4716	301	16	,	,	PUNCT
ejpam-4716	301	17	n.	n.	PROPN
ejpam-4716	301	18	sh	sh	PROPN
ejpam-4716	301	19	.	.	PROPN
ejpam-4716	301	20	khalaf	khalaf	PROPN
ejpam-4716	301	21	,	,	PUNCT
ejpam-4716	301	22	t.	t.	PROPN
ejpam-4716	301	23	j.	j.	PROPN
ejpam-4716	301	24	aldhlki	aldhlki	PROPN
ejpam-4716	301	25	/	/	SYM
ejpam-4716	301	26	eur	eur	PROPN
ejpam-4716	301	27	.	.	PUNCT
ejpam-4716	302	1	j.	j.	PROPN
ejpam-4716	302	2	pure	pure	PROPN
ejpam-4716	302	3	appl	appl	PROPN
ejpam-4716	302	4	.	.	PROPN
ejpam-4716	302	5	math	math	PROPN
ejpam-4716	302	6	,	,	PUNCT
ejpam-4716	302	7	16	16	NUM
ejpam-4716	302	8	(	(	PUNCT
ejpam-4716	302	9	2	2	NUM
ejpam-4716	302	10	)	)	PUNCT
ejpam-4716	302	11	(	(	PUNCT
ejpam-4716	302	12	2023	2023	NUM
ejpam-4716	302	13	)	)	PUNCT
ejpam-4716	302	14	,	,	PUNCT
ejpam-4716	302	15	899	899	NUM
ejpam-4716	302	16	-	-	SYM
ejpam-4716	302	17	918	918	NUM
ejpam-4716	302	18	911	911	NUM
ejpam-4716	302	19	ã	ã	PROPN
ejpam-4716	302	20	=	=	SYM
ejpam-4716	302	21	2∑	2∑	NUM
ejpam-4716	302	22	i=1	i=1	PROPN
ejpam-4716	302	23	(	(	PUNCT
ejpam-4716	302	24	k−1	k−1	PROPN
ejpam-4716	302	25	i	i	PRON
ejpam-4716	302	26	x̃i	x̃i	PUNCT
ejpam-4716	302	27	)	)	PUNCT
ejpam-4716	303	1	−	−	PROPN
ejpam-4716	303	2	γ̃2x̃ỹ	γ̃2x̃ỹ	ADJ
ejpam-4716	303	3	(	(	PUNCT
ejpam-4716	303	4	α1	α1	PROPN
ejpam-4716	303	5	+	+	CCONJ
ejpam-4716	303	6	β1	β1	PROPN
ejpam-4716	303	7	)	)	PUNCT
ejpam-4716	303	8	,	,	PUNCT
ejpam-4716	303	9	b̃	b̃	PROPN
ejpam-4716	303	10	=	=	PRON
ejpam-4716	303	11	(	(	PUNCT
ejpam-4716	303	12	µ1	µ1	PROPN
ejpam-4716	303	13	−	−	PROPN
ejpam-4716	303	14	γ̃ε1x̃1	γ̃ε1x̃1	PROPN
ejpam-4716	303	15	)	)	PUNCT
ejpam-4716	303	16	,	,	PUNCT
ejpam-4716	303	17	ñ	ñ	PROPN
ejpam-4716	303	18	=	=	SYM
ejpam-4716	303	19	k−1	k−1	NUM
ejpam-4716	303	20	1	1	NUM
ejpam-4716	303	21	x̃1	x̃1	PROPN
ejpam-4716	303	22	−	−	PROPN
ejpam-4716	303	23	γ̃2α1x̃ỹ	γ̃2α1x̃ỹ	VERB
ejpam-4716	303	24	γ̃2α1x̃	γ̃2α1x̃	PRON
ejpam-4716	303	25	2ỹ	2ỹ	NUM
ejpam-4716	303	26	γ̃α1x̃1	γ̃α1x̃1	PROPN
ejpam-4716	303	27	γ̃2β1ỹ	γ̃2β1ỹ	PROPN
ejpam-4716	303	28	k−1	k−1	PROPN
ejpam-4716	303	29	2	2	NUM
ejpam-4716	303	30	x̃2	x̃2	PROPN
ejpam-4716	303	31	−	−	PROPN
ejpam-4716	303	32	γ̃2β1x̃ỹ	γ̃2β1x̃ỹ	VERB
ejpam-4716	303	33	γ̃β2x̃1	γ̃β2x̃1	PROPN
ejpam-4716	303	34	−γ̃ε1x̃	−γ̃ε1x̃	ADP
ejpam-4716	303	35	−1	−1	NOUN
ejpam-4716	303	36	2	2	X
ejpam-4716	303	37	ỹ	ỹ	PRON
ejpam-4716	303	38	−γ̃ε1x̃x̃	−γ̃ε1x̃x̃	NOUN
ejpam-4716	303	39	−1	−1	NOUN
ejpam-4716	303	40	2	2	NUM
ejpam-4716	303	41	ỹ	ỹ	PROPN
ejpam-4716	303	42	µ1	µ1	NOUN
ejpam-4716	303	43	−	−	NOUN
ejpam-4716	303	44	γ̃ε1x̃1	γ̃ε1x̃1	PROPN
ejpam-4716	303	45			NOUN
ejpam-4716	303	46	,	,	PUNCT
ejpam-4716	303	47	ỹ	ỹ	PROPN
ejpam-4716	303	48	=	=	SYM
ejpam-4716	303	49	(	(	PUNCT
ejpam-4716	303	50	1−	1−	NUM
ejpam-4716	303	51	x̃1	x̃1	PROPN
ejpam-4716	303	52	k1	k1	PROPN
ejpam-4716	303	53	)	)	PUNCT
ejpam-4716	303	54	(	(	PUNCT
ejpam-4716	303	55	1	1	X
ejpam-4716	303	56	+	+	CCONJ
ejpam-4716	303	57	x̃	x̃	PROPN
ejpam-4716	303	58	)	)	PUNCT
ejpam-4716	303	59	α1	α1	PROPN
ejpam-4716	303	60	.	.	PUNCT
ejpam-4716	304	1	from	from	ADP
ejpam-4716	304	2	(	(	PUNCT
ejpam-4716	304	3	17	17	NUM
ejpam-4716	304	4	)	)	PUNCT
ejpam-4716	304	5	,	,	PUNCT
ejpam-4716	304	6	eigenvalues	eigenvalue	VERB
ejpam-4716	304	7	of	of	ADP
ejpam-4716	304	8	(	(	PUNCT
ejpam-4716	304	9	p4(g	p4(g	NOUN
ejpam-4716	304	10	∗	∗	NOUN
ejpam-4716	304	11	)	)	PUNCT
ejpam-4716	304	12	)	)	PUNCT
ejpam-4716	304	13	are	be	AUX
ejpam-4716	304	14	λ1,2	λ1,2	X
ejpam-4716	304	15	(	(	PUNCT
ejpam-4716	304	16	g	g	NOUN
ejpam-4716	304	17	∗	∗	NOUN
ejpam-4716	304	18	)	)	PUNCT
ejpam-4716	305	1	=	=	PUNCT
ejpam-4716	305	2	±i	±i	DET
ejpam-4716	305	3	√√√√	√√√√	PRON
ejpam-4716	305	4	3∑	3∑	NOUN
ejpam-4716	305	5	i=1	i=1	NOUN
ejpam-4716	305	6	m̌ii	m̌ii	PROPN
ejpam-4716	305	7	,	,	PUNCT
ejpam-4716	305	8	λ3	λ3	PROPN
ejpam-4716	305	9	(	(	PUNCT
ejpam-4716	305	10	g	g	NOUN
ejpam-4716	305	11	∗	∗	NOUN
ejpam-4716	305	12	)	)	PUNCT
ejpam-4716	305	13	=	=	SYM
ejpam-4716	306	1	trm̃(g	trm̃(g	PROPN
ejpam-4716	306	2	)	)	PUNCT
ejpam-4716	306	3	,	,	PUNCT
ejpam-4716	306	4	λ4(g	λ4(g	NOUN
ejpam-4716	306	5	∗	∗	NOUN
ejpam-4716	306	6	)	)	PUNCT
ejpam-4716	306	7	=	=	SYM
ejpam-4716	306	8	γ̃ε2x̃1	γ̃ε2x̃1	PROPN
ejpam-4716	307	1	+	+	CCONJ
ejpam-4716	307	2	ρ1ỹ1	ρ1ỹ1	NUM
ejpam-4716	308	1	−	−	NOUN
ejpam-4716	308	2	µ2	µ2	PROPN
ejpam-4716	308	3	.	.	PUNCT
ejpam-4716	308	4	theorem	theorem	VERB
ejpam-4716	308	5	8	8	NUM
ejpam-4716	308	6	.	.	PUNCT
ejpam-4716	308	7	suppose	suppose	VERB
ejpam-4716	308	8	that	that	SCONJ
ejpam-4716	308	9	the	the	DET
ejpam-4716	308	10	equilibrium	equilibrium	NOUN
ejpam-4716	308	11	point	point	NOUN
ejpam-4716	308	12	p4	p4	ADJ
ejpam-4716	308	13	=	=	SYM
ejpam-4716	308	14	(	(	PUNCT
ejpam-4716	308	15	x̃1	x̃1	PROPN
ejpam-4716	308	16	,	,	PUNCT
ejpam-4716	308	17	x̃2	x̃2	PROPN
ejpam-4716	308	18	,	,	PUNCT
ejpam-4716	308	19	ỹ1	ỹ1	PROPN
ejpam-4716	308	20	,	,	PUNCT
ejpam-4716	308	21	0	0	NUM
ejpam-4716	308	22	)	)	PUNCT
ejpam-4716	308	23	,	,	PUNCT
ejpam-4716	308	24	of	of	ADP
ejpam-4716	308	25	the	the	DET
ejpam-4716	308	26	system	system	NOUN
ejpam-4716	308	27	(	(	PUNCT
ejpam-4716	308	28	2	2	X
ejpam-4716	308	29	)	)	PUNCT
ejpam-4716	308	30	exists	exist	VERB
ejpam-4716	308	31	and	and	CCONJ
ejpam-4716	308	32	is	be	AUX
ejpam-4716	308	33	locally	locally	ADV
ejpam-4716	308	34	asymptotically	asymptotically	ADV
ejpam-4716	308	35	stable	stable	ADJ
ejpam-4716	308	36	for	for	ADP
ejpam-4716	308	37	the	the	DET
ejpam-4716	308	38	parameter	parameter	NOUN
ejpam-4716	308	39	g	g	PROPN
ejpam-4716	308	40	=	=	PROPN
ejpam-4716	308	41	g1	g1	PROPN
ejpam-4716	308	42	=	=	SYM
ejpam-4716	308	43	g2	g2	PROPN
ejpam-4716	308	44	,	,	PUNCT
ejpam-4716	308	45	and	and	CCONJ
ejpam-4716	308	46	g∗	g∗	PROPN
ejpam-4716	308	47	be	be	VERB
ejpam-4716	308	48	the	the	DET
ejpam-4716	308	49	positive	positive	ADJ
ejpam-4716	308	50	root	root	NOUN
ejpam-4716	308	51	of	of	ADP
ejpam-4716	308	52	the	the	DET
ejpam-4716	308	53	equation	equation	NOUN
ejpam-4716	308	54	(	(	PUNCT
ejpam-4716	308	55	17	17	NUM
ejpam-4716	308	56	)	)	PUNCT
ejpam-4716	308	57	,	,	PUNCT
ejpam-4716	308	58	then	then	ADV
ejpam-4716	308	59	a	a	DET
ejpam-4716	308	60	simple	simple	ADJ
ejpam-4716	308	61	hopf	hopf	ADJ
ejpam-4716	308	62	bifurcation	bifurcation	NOUN
ejpam-4716	308	63	occurs	occur	VERB
ejpam-4716	308	64	as	as	SCONJ
ejpam-4716	308	65	g	g	PROPN
ejpam-4716	308	66	passes	pass	VERB
ejpam-4716	308	67	through	through	ADP
ejpam-4716	308	68	g∗	g∗	PROPN
ejpam-4716	308	69	provided	provide	VERB
ejpam-4716	308	70	that	that	SCONJ
ejpam-4716	308	71	(	(	PUNCT
ejpam-4716	308	72	m̃11	m̃11	X
ejpam-4716	309	1	+	+	CCONJ
ejpam-4716	309	2	m̃22	m̃22	NUM
ejpam-4716	309	3	)	)	PUNCT
ejpam-4716	309	4	(	(	PUNCT
ejpam-4716	309	5	µ1	µ1	PROPN
ejpam-4716	309	6	−	−	PROPN
ejpam-4716	309	7	γ̃ε1x̃1	γ̃ε1x̃1	PROPN
ejpam-4716	309	8	)	)	PUNCT
ejpam-4716	310	1	g−1	g−1	PROPN
ejpam-4716	310	2	−	−	NOUN
ejpam-4716	311	1	m̃33	m̃33	PROPN
ejpam-4716	311	2	(	(	PUNCT
ejpam-4716	311	3	k−1	k−1	PROPN
ejpam-4716	311	4	1	1	NUM
ejpam-4716	311	5	x̃1−γ̃2α1x̃ỹ	x̃1−γ̃2α1x̃ỹ	VERB
ejpam-4716	311	6	+	+	CCONJ
ejpam-4716	311	7	k−1	k−1	PROPN
ejpam-4716	311	8	2	2	NUM
ejpam-4716	311	9	x̃2	x̃2	PROPN
ejpam-4716	311	10	−	−	PROPN
ejpam-4716	311	11	γ̃2β1x̃ỹ	γ̃2β1x̃ỹ	NOUN
ejpam-4716	311	12	)	)	PUNCT
ejpam-4716	312	1	̸=0	̸=0	ADV
ejpam-4716	312	2	.	.	PUNCT
ejpam-4716	313	1	proof	proof	NOUN
ejpam-4716	313	2	.	.	PUNCT
ejpam-4716	314	1	since	since	SCONJ
ejpam-4716	314	2	∂x̃1	∂x̃1	NOUN
ejpam-4716	314	3	∂g	∂g	PROPN
ejpam-4716	314	4	=	=	PUNCT
ejpam-4716	314	5	∂x̃2	∂x̃2	PROPN
ejpam-4716	315	1	∂g	∂g	PROPN
ejpam-4716	316	1	=	=	PUNCT
ejpam-4716	316	2	∂ỹ2	∂ỹ2	NOUN
ejpam-4716	317	1	∂g	∂g	X
ejpam-4716	317	2	=	=	SYM
ejpam-4716	317	3	0	0	NUM
ejpam-4716	317	4	,	,	PUNCT
ejpam-4716	317	5	∂ỹ1∂g	∂ỹ1∂g	VERB
ejpam-4716	317	6	=	=	PUNCT
ejpam-4716	317	7	ỹ1	ỹ1	NOUN
ejpam-4716	317	8	g	g	NOUN
ejpam-4716	317	9	=	=	SYM
ejpam-4716	317	10	ỹ	ỹ	PROPN
ejpam-4716	317	11	,	,	PUNCT
ejpam-4716	317	12	then	then	ADV
ejpam-4716	317	13	the	the	DET
ejpam-4716	317	14	point	point	NOUN
ejpam-4716	317	15	p4	p4	NOUN
ejpam-4716	317	16	=	=	SYM
ejpam-4716	317	17	(	(	PUNCT
ejpam-4716	317	18	x̃1	x̃1	PROPN
ejpam-4716	317	19	,	,	PUNCT
ejpam-4716	317	20	x̃2	x̃2	PROPN
ejpam-4716	317	21	,	,	PUNCT
ejpam-4716	317	22	ỹ1	ỹ1	PROPN
ejpam-4716	317	23	,	,	PUNCT
ejpam-4716	317	24	0	0	NUM
ejpam-4716	317	25	)	)	PUNCT
ejpam-4716	317	26	,	,	PUNCT
ejpam-4716	317	27	depends	depend	VERB
ejpam-4716	317	28	smoothly	smoothly	ADV
ejpam-4716	317	29	on	on	ADP
ejpam-4716	317	30	the	the	DET
ejpam-4716	317	31	parameter	parameter	NOUN
ejpam-4716	317	32	g.	g.	PROPN
ejpam-4716	318	1	if	if	SCONJ
ejpam-4716	318	2	there	there	PRON
ejpam-4716	318	3	is	be	VERB
ejpam-4716	318	4	a	a	DET
ejpam-4716	318	5	simple	simple	ADJ
ejpam-4716	318	6	pair	pair	NOUN
ejpam-4716	318	7	of	of	ADP
ejpam-4716	318	8	complex	complex	ADJ
ejpam-4716	318	9	eigenvalues	eigenvalue	NOUN
ejpam-4716	318	10	λ1,2	λ1,2	PROPN
ejpam-4716	318	11	(	(	PUNCT
ejpam-4716	318	12	g	g	NOUN
ejpam-4716	318	13	)	)	PUNCT
ejpam-4716	318	14	=	=	SYM
ejpam-4716	318	15	u±	u±	PROPN
ejpam-4716	318	16	iv	iv	NOUN
ejpam-4716	318	17	of	of	ADP
ejpam-4716	318	18	the	the	DET
ejpam-4716	318	19	jacobian	jacobian	ADJ
ejpam-4716	318	20	matrix	matrix	NOUN
ejpam-4716	318	21	(	(	PUNCT
ejpam-4716	318	22	j	j	PROPN
ejpam-4716	318	23	(	(	PUNCT
ejpam-4716	318	24	p4(g	p4(g	PROPN
ejpam-4716	318	25	)	)	PUNCT
ejpam-4716	318	26	)	)	PUNCT
ejpam-4716	318	27	)	)	PUNCT
ejpam-4716	318	28	at	at	ADP
ejpam-4716	318	29	the	the	DET
ejpam-4716	318	30	equilibrium	equilibrium	NOUN
ejpam-4716	318	31	point	point	NOUN
ejpam-4716	318	32	p4	p4	ADJ
ejpam-4716	318	33	(	(	PUNCT
ejpam-4716	318	34	g	g	NOUN
ejpam-4716	318	35	)	)	PUNCT
ejpam-4716	318	36	,	,	PUNCT
ejpam-4716	318	37	such	such	ADJ
ejpam-4716	318	38	that	that	SCONJ
ejpam-4716	318	39	,	,	PUNCT
ejpam-4716	318	40	it	it	PRON
ejpam-4716	318	41	becomes	become	VERB
ejpam-4716	318	42	a	a	DET
ejpam-4716	318	43	purely	purely	ADV
ejpam-4716	318	44	imaginary	imaginary	ADJ
ejpam-4716	318	45	at	at	ADP
ejpam-4716	318	46	g	g	PROPN
ejpam-4716	318	47	=	=	SYM
ejpam-4716	318	48	g∗	g∗	PROPN
ejpam-4716	318	49	,	,	PUNCT
ejpam-4716	318	50	while	while	SCONJ
ejpam-4716	318	51	all	all	DET
ejpam-4716	318	52	other	other	ADJ
ejpam-4716	318	53	eigenvalues	eigenvalue	NOUN
ejpam-4716	318	54	are	be	AUX
ejpam-4716	318	55	real	real	ADJ
ejpam-4716	318	56	and	and	CCONJ
ejpam-4716	318	57	negative	negative	ADJ
ejpam-4716	318	58	;	;	PUNCT
ejpam-4716	318	59	and	and	CCONJ
ejpam-4716	318	60	du(g∗	du(g∗	NOUN
ejpam-4716	318	61	)	)	PUNCT
ejpam-4716	318	62	dg	dg	PROPN
ejpam-4716	318	63	̸=	̸=	PROPN
ejpam-4716	318	64	0	0	NUM
ejpam-4716	318	65	,	,	PUNCT
ejpam-4716	318	66	then	then	ADV
ejpam-4716	318	67	at	at	ADP
ejpam-4716	318	68	g∗we	g∗we	PROPN
ejpam-4716	318	69	have	have	VERB
ejpam-4716	318	70	a	a	DET
ejpam-4716	318	71	simple	simple	ADJ
ejpam-4716	318	72	hopf	hopf	ADJ
ejpam-4716	318	73	bifurcation	bifurcation	NOUN
ejpam-4716	318	74	,	,	PUNCT
ejpam-4716	318	75	[	[	X
ejpam-4716	318	76	5	5	NUM
ejpam-4716	318	77	]	]	PUNCT
ejpam-4716	318	78	.	.	PUNCT
ejpam-4716	319	1	it	it	PRON
ejpam-4716	319	2	is	be	AUX
ejpam-4716	319	3	easy	easy	ADJ
ejpam-4716	319	4	to	to	PART
ejpam-4716	319	5	deduce	deduce	VERB
ejpam-4716	319	6	,	,	PUNCT
ejpam-4716	319	7	du	du	PROPN
ejpam-4716	319	8	(	(	PUNCT
ejpam-4716	319	9	g∗	g∗	PROPN
ejpam-4716	319	10	)	)	PUNCT
ejpam-4716	319	11	dg	dg	PROPN
ejpam-4716	319	12	=	=	SYM
ejpam-4716	319	13	(	(	PUNCT
ejpam-4716	319	14	d(detm̃	d(detm̃	NOUN
ejpam-4716	319	15	)	)	PUNCT
ejpam-4716	319	16	dg	dg	VERB
ejpam-4716	319	17	−	−	PROPN
ejpam-4716	319	18	∑3	∑3	PROPN
ejpam-4716	320	1	i=1	i=1	PROPN
ejpam-4716	321	1	m̃ii	m̃ii	PROPN
ejpam-4716	321	2	dtrm̃	dtrm̃	PROPN
ejpam-4716	321	3	dg	dg	VERB
ejpam-4716	321	4	−	−	PROPN
ejpam-4716	321	5	trm̃	trm̃	NOUN
ejpam-4716	321	6	db	db	NOUN
ejpam-4716	321	7	dg	dg	NOUN
ejpam-4716	321	8	)	)	PUNCT
ejpam-4716	321	9	2	2	NUM
ejpam-4716	321	10	∑3	∑3	PROPN
ejpam-4716	321	11	i=1	i=1	PROPN
ejpam-4716	322	1	m̃ii	m̃ii	PROPN
ejpam-4716	323	1	+	+	CCONJ
ejpam-4716	323	2	2	2	NUM
ejpam-4716	323	3	(	(	PUNCT
ejpam-4716	323	4	trm̃	trm̃	NOUN
ejpam-4716	323	5	)	)	PUNCT
ejpam-4716	323	6	2	2	NUM
ejpam-4716	323	7	.	.	PUNCT
ejpam-4716	324	1	because	because	SCONJ
ejpam-4716	324	2	2	2	NUM
ejpam-4716	324	3	∑3	∑3	PROPN
ejpam-4716	324	4	i=1	i=1	PROPN
ejpam-4716	324	5	m̃ii	m̃ii	PROPN
ejpam-4716	324	6	+	+	CCONJ
ejpam-4716	324	7	2	2	NUM
ejpam-4716	324	8	(	(	PUNCT
ejpam-4716	324	9	trm̃	trm̃	NOUN
ejpam-4716	324	10	)	)	PUNCT
ejpam-4716	324	11	2	2	NUM
ejpam-4716	324	12	is	be	AUX
ejpam-4716	324	13	positive	positive	ADJ
ejpam-4716	324	14	,	,	PUNCT
ejpam-4716	324	15	so	so	CCONJ
ejpam-4716	324	16	it	it	PRON
ejpam-4716	324	17	is	be	AUX
ejpam-4716	324	18	sufficient	sufficient	ADJ
ejpam-4716	324	19	to	to	PART
ejpam-4716	324	20	prove	prove	VERB
ejpam-4716	324	21	that	that	PRON
ejpam-4716	324	22	w	w	ADP
ejpam-4716	324	23	:	:	PUNCT
ejpam-4716	324	24	=	=	SYM
ejpam-4716	324	25	d(detm̃	d(detm̃	NOUN
ejpam-4716	324	26	)	)	PUNCT
ejpam-4716	324	27	dg	dg	VERB
ejpam-4716	324	28	−	−	PROPN
ejpam-4716	324	29	trm̃	trm̃	NOUN
ejpam-4716	325	1	d	d	NOUN
ejpam-4716	325	2	∑3	∑3	PROPN
ejpam-4716	325	3	i=1	i=1	PROPN
ejpam-4716	326	1	m̃ii	m̃ii	PROPN
ejpam-4716	326	2	dg	dg	VERB
ejpam-4716	326	3	−	−	PROPN
ejpam-4716	326	4	3∑	3∑	NOUN
ejpam-4716	326	5	i=1	i=1	PROPN
ejpam-4716	327	1	m̃ii	m̃ii	PROPN
ejpam-4716	328	1	d	d	PROPN
ejpam-4716	328	2	trm̃	trm̃	NOUN
ejpam-4716	328	3	dg	dg	NOUN
ejpam-4716	328	4	̸=	̸=	PROPN
ejpam-4716	328	5	0	0	NUM
ejpam-4716	328	6	.	.	PUNCT
ejpam-4716	329	1	simple	simple	ADJ
ejpam-4716	329	2	calculation	calculation	NOUN
ejpam-4716	329	3	show	show	VERB
ejpam-4716	329	4	that	that	SCONJ
ejpam-4716	329	5	w	w	NOUN
ejpam-4716	329	6	=	=	SYM
ejpam-4716	329	7	d(detm̃	d(detm̃	X
ejpam-4716	329	8	)	)	PUNCT
ejpam-4716	329	9	dg	dg	VERB
ejpam-4716	330	1	−	−	PROPN
ejpam-4716	330	2	3∑	3∑	NOUN
ejpam-4716	330	3	i=1	i=1	PROPN
ejpam-4716	331	1	m̃ii	m̃ii	PROPN
ejpam-4716	331	2	d	d	PROPN
ejpam-4716	331	3	trm̃	trm̃	NOUN
ejpam-4716	331	4	dg	dg	NOUN
ejpam-4716	331	5	−	−	NOUN
ejpam-4716	331	6	trm̃	trm̃	NOUN
ejpam-4716	331	7	d	d	NOUN
ejpam-4716	331	8	(	(	PUNCT
ejpam-4716	331	9	∑3	∑3	PROPN
ejpam-4716	331	10	i=1	i=1	PROPN
ejpam-4716	331	11	m̃ii	m̃ii	PROPN
ejpam-4716	331	12	)	)	PUNCT
ejpam-4716	331	13	dg	dg	PROPN
ejpam-4716	331	14	=	=	SYM
ejpam-4716	331	15	(	(	PUNCT
ejpam-4716	331	16	2	2	NUM
ejpam-4716	331	17	g	g	NOUN
ejpam-4716	331	18	)	)	PUNCT
ejpam-4716	331	19	det	det	NOUN
ejpam-4716	331	20	ñ	ñ	VERB
ejpam-4716	331	21	−	−	PROPN
ejpam-4716	331	22	trm̃	trm̃	NOUN
ejpam-4716	331	23	(	(	PUNCT
ejpam-4716	331	24	ñ11	ñ11	PROPN
ejpam-4716	331	25	+	+	CCONJ
ejpam-4716	331	26	ñ22	ñ22	PUNCT
ejpam-4716	332	1	+	+	CCONJ
ejpam-4716	332	2	2gñ33	2gñ33	NUM
ejpam-4716	332	3	)	)	PUNCT
ejpam-4716	332	4	−	−	NOUN
ejpam-4716	333	1	3∑	3∑	NOUN
ejpam-4716	333	2	i=1	i=1	PROPN
ejpam-4716	334	1	m̃ii	m̃ii	PROPN
ejpam-4716	334	2	(	(	PUNCT
ejpam-4716	334	3	k−1	k−1	PROPN
ejpam-4716	334	4	1	1	NUM
ejpam-4716	334	5	x̃1	x̃1	PROPN
ejpam-4716	334	6	−	−	PROPN
ejpam-4716	334	7	γ̃2α1x̃ỹ	γ̃2α1x̃ỹ	VERB
ejpam-4716	334	8	+	+	CCONJ
ejpam-4716	334	9	k−1	k−1	PROPN
ejpam-4716	334	10	2	2	NUM
ejpam-4716	334	11	x̃2	x̃2	PROPN
ejpam-4716	334	12	−	−	PROPN
ejpam-4716	334	13	γ̃2β1x̃ỹ	γ̃2β1x̃ỹ	PROPN
ejpam-4716	334	14	)	)	PUNCT
ejpam-4716	335	1	a.	a.	NOUN
ejpam-4716	335	2	g.	g.	PROPN
ejpam-4716	335	3	farhan	farhan	PROPN
ejpam-4716	335	4	,	,	PUNCT
ejpam-4716	335	5	n.	n.	PROPN
ejpam-4716	335	6	sh	sh	PROPN
ejpam-4716	335	7	.	.	PROPN
ejpam-4716	335	8	khalaf	khalaf	PROPN
ejpam-4716	335	9	,	,	PUNCT
ejpam-4716	335	10	t.	t.	PROPN
ejpam-4716	335	11	j.	j.	PROPN
ejpam-4716	335	12	aldhlki	aldhlki	PROPN
ejpam-4716	335	13	/	/	SYM
ejpam-4716	335	14	eur	eur	PROPN
ejpam-4716	335	15	.	.	PUNCT
ejpam-4716	336	1	j.	j.	PROPN
ejpam-4716	336	2	pure	pure	PROPN
ejpam-4716	336	3	appl	appl	PROPN
ejpam-4716	336	4	.	.	PROPN
ejpam-4716	336	5	math	math	PROPN
ejpam-4716	336	6	,	,	PUNCT
ejpam-4716	336	7	16	16	NUM
ejpam-4716	336	8	(	(	PUNCT
ejpam-4716	336	9	2	2	NUM
ejpam-4716	336	10	)	)	PUNCT
ejpam-4716	336	11	(	(	PUNCT
ejpam-4716	336	12	2023	2023	NUM
ejpam-4716	336	13	)	)	PUNCT
ejpam-4716	336	14	,	,	PUNCT
ejpam-4716	336	15	899	899	NUM
ejpam-4716	336	16	-	-	SYM
ejpam-4716	336	17	918	918	NUM
ejpam-4716	336	18	912	912	NUM
ejpam-4716	336	19	=	=	SYM
ejpam-4716	336	20	trm̃	trm̃	NOUN
ejpam-4716	336	21	(	(	PUNCT
ejpam-4716	336	22	ñ11	ñ11	PROPN
ejpam-4716	336	23	+	+	CCONJ
ejpam-4716	336	24	ñ22	ñ22	PROPN
ejpam-4716	336	25	)	)	PUNCT
ejpam-4716	337	1	−	−	PROPN
ejpam-4716	337	2	(	(	PUNCT
ejpam-4716	337	3	gñ11	gñ11	NOUN
ejpam-4716	337	4	+	+	CCONJ
ejpam-4716	337	5	gñ22+g2ñ33	gñ22+g2ñ33	NOUN
ejpam-4716	337	6	)	)	PUNCT
ejpam-4716	338	1	(	(	PUNCT
ejpam-4716	338	2	k−1	k−1	PROPN
ejpam-4716	338	3	1	1	NUM
ejpam-4716	338	4	x̃1−γ̃2α1x̃ỹ	x̃1−γ̃2α1x̃ỹ	VERB
ejpam-4716	338	5	+	+	CCONJ
ejpam-4716	338	6	k−1	k−1	PROPN
ejpam-4716	338	7	2	2	NUM
ejpam-4716	338	8	x̃2	x̃2	PROPN
ejpam-4716	338	9	−	−	PROPN
ejpam-4716	338	10	γ̃2β1x̃ỹ	γ̃2β1x̃ỹ	PROPN
ejpam-4716	338	11	)	)	PUNCT
ejpam-4716	338	12	=	=	PUNCT
ejpam-4716	339	1	(	(	PUNCT
ejpam-4716	339	2	m̃11	m̃11	NOUN
ejpam-4716	339	3	+	+	CCONJ
ejpam-4716	339	4	m̃22	m̃22	NUM
ejpam-4716	339	5	)	)	PUNCT
ejpam-4716	340	1	(	(	PUNCT
ejpam-4716	340	2	µ1	µ1	NOUN
ejpam-4716	340	3	−	−	PROPN
ejpam-4716	340	4	γ̃ε1x̃1)g	γ̃ε1x̃1)g	PROPN
ejpam-4716	340	5	−1	−1	NOUN
ejpam-4716	340	6	−	−	PROPN
ejpam-4716	341	1	m̃33	m̃33	PROPN
ejpam-4716	341	2	(	(	PUNCT
ejpam-4716	341	3	k−1	k−1	PROPN
ejpam-4716	341	4	1	1	NUM
ejpam-4716	341	5	x̃1	x̃1	PROPN
ejpam-4716	341	6	−	−	PROPN
ejpam-4716	341	7	γ̃2α1x̃ỹ	γ̃2α1x̃ỹ	VERB
ejpam-4716	341	8	+	+	CCONJ
ejpam-4716	341	9	k−1	k−1	PROPN
ejpam-4716	341	10	2	2	NUM
ejpam-4716	341	11	x̃2	x̃2	PROPN
ejpam-4716	341	12	−	−	PROPN
ejpam-4716	341	13	γ̃2β1x̃ỹ.	γ̃2β1x̃ỹ.	PROPN
ejpam-4716	341	14	)	)	PUNCT
ejpam-4716	341	15	and	and	CCONJ
ejpam-4716	341	16	with	with	ADP
ejpam-4716	341	17	this	this	PRON
ejpam-4716	341	18	,	,	PUNCT
ejpam-4716	341	19	we	we	PRON
ejpam-4716	341	20	have	have	AUX
ejpam-4716	341	21	completed	complete	VERB
ejpam-4716	341	22	the	the	DET
ejpam-4716	341	23	proof	proof	NOUN
ejpam-4716	341	24	.	.	PUNCT
ejpam-4716	342	1	now	now	ADV
ejpam-4716	342	2	consider	consider	VERB
ejpam-4716	342	3	the	the	DET
ejpam-4716	342	4	following	follow	VERB
ejpam-4716	342	5	equation	equation	NOUN
ejpam-4716	342	6	trm̌	trm̌	VERB
ejpam-4716	342	7	3∑	3∑	NOUN
ejpam-4716	342	8	i=1	i=1	NOUN
ejpam-4716	342	9	m̌ii	m̌ii	NOUN
ejpam-4716	342	10	=	=	NOUN
ejpam-4716	342	11	detm̌	detm̌	NOUN
ejpam-4716	342	12	(	(	PUNCT
ejpam-4716	342	13	18	18	NUM
ejpam-4716	342	14	)	)	PUNCT
ejpam-4716	342	15	g∗∗	g∗∗	NOUN
ejpam-4716	343	1	=	=	PUNCT
ejpam-4716	343	2	r2∓	r2∓	NOUN
ejpam-4716	343	3	√	√	NUM
ejpam-4716	343	4	r22−4r1r3	r22−4r1r3	NOUN
ejpam-4716	343	5	2r1	2r1	NUM
ejpam-4716	343	6	is	be	AUX
ejpam-4716	343	7	the	the	DET
ejpam-4716	343	8	positive	positive	ADJ
ejpam-4716	343	9	root	root	NOUN
ejpam-4716	343	10	of	of	ADP
ejpam-4716	343	11	the	the	DET
ejpam-4716	343	12	(	(	PUNCT
ejpam-4716	343	13	18	18	NUM
ejpam-4716	343	14	)	)	PUNCT
ejpam-4716	343	15	where	where	SCONJ
ejpam-4716	343	16	r1	r1	PROPN
ejpam-4716	343	17	=	=	SYM
ejpam-4716	343	18	ǎň22	ǎň22	PROPN
ejpam-4716	343	19	,	,	PUNCT
ejpam-4716	343	20	r2	r2	PROPN
ejpam-4716	343	21	=	=	PUNCT
ejpam-4716	343	22	detň	detň	PROPN
ejpam-4716	343	23	−	−	PROPN
ejpam-4716	343	24	ǎ	ǎ	PROPN
ejpam-4716	343	25	(	(	PUNCT
ejpam-4716	343	26	ň11	ň11	NOUN
ejpam-4716	343	27	+	+	CCONJ
ejpam-4716	343	28	ň22	ň22	ADJ
ejpam-4716	343	29	)	)	PUNCT
ejpam-4716	344	1	−	−	PROPN
ejpam-4716	344	2	b̌ň33	b̌ň33	PROPN
ejpam-4716	344	3	,	,	PUNCT
ejpam-4716	344	4	r3	r3	PROPN
ejpam-4716	344	5	=	=	SYM
ejpam-4716	344	6	b̌	b̌	PROPN
ejpam-4716	344	7	(	(	PUNCT
ejpam-4716	344	8	ň11	ň11	NOUN
ejpam-4716	344	9	+	+	CCONJ
ejpam-4716	344	10	ň22	ň22	PROPN
ejpam-4716	344	11	)	)	PUNCT
ejpam-4716	344	12	,	,	PUNCT
ejpam-4716	344	13	ǎ	ǎ	X
ejpam-4716	345	1	=	=	PUNCT
ejpam-4716	345	2	2∑	2∑	X
ejpam-4716	345	3	i=1	i=1	PROPN
ejpam-4716	345	4	(	(	PUNCT
ejpam-4716	345	5	k−1	k−1	PROPN
ejpam-4716	345	6	i	i	PRON
ejpam-4716	345	7	x̃i	x̃i	PUNCT
ejpam-4716	345	8	)	)	PUNCT
ejpam-4716	346	1	−	−	PROPN
ejpam-4716	346	2	γ̃2x̃ỹ	γ̃2x̃ỹ	ADJ
ejpam-4716	346	3	(	(	PUNCT
ejpam-4716	346	4	α1	α1	PROPN
ejpam-4716	346	5	+	+	CCONJ
ejpam-4716	346	6	β1	β1	PROPN
ejpam-4716	346	7	)	)	PUNCT
ejpam-4716	346	8	,	,	PUNCT
ejpam-4716	346	9	b̌	b̌	PROPN
ejpam-4716	346	10	=	=	SYM
ejpam-4716	346	11	(	(	PUNCT
ejpam-4716	346	12	µ1	µ1	PROPN
ejpam-4716	346	13	−	−	PROPN
ejpam-4716	346	14	γ̃ε1x̃1	γ̃ε1x̃1	PROPN
ejpam-4716	346	15	)	)	PUNCT
ejpam-4716	346	16	,	,	PUNCT
ejpam-4716	346	17	ň	ň	NOUN
ejpam-4716	346	18	=	=	SYM
ejpam-4716	346	19	γ̌2α1x̌y̌	γ̌2α1x̌y̌	PROPN
ejpam-4716	347	1	−	−	PROPN
ejpam-4716	348	1	k−1	k−1	PROPN
ejpam-4716	348	2	1	1	NUM
ejpam-4716	348	3	−γ̌2α1x̌	−γ̌2α1x̌	VERB
ejpam-4716	348	4	2y̌	2y̌	NUM
ejpam-4716	349	1	−γ̌α1x̌1	−γ̌α1x̌1	ADJ
ejpam-4716	349	2	−γ̌2β2y̌	−γ̌2β2y̌	PRON
ejpam-4716	349	3	γ̌2β2x̌y̌	γ̌2β2x̌y̌	ADP
ejpam-4716	349	4	−	−	PROPN
ejpam-4716	349	5	k−1	k−1	PROPN
ejpam-4716	349	6	2	2	NUM
ejpam-4716	349	7	x̌2	x̌2	NUM
ejpam-4716	349	8	γ̌β2x̌1	γ̌β2x̌1	PROPN
ejpam-4716	349	9	γ̌2ε2y̌	γ̌2ε2y̌	PROPN
ejpam-4716	350	1	γ̌2ε2x̌	γ̌2ε2x̌	PROPN
ejpam-4716	350	2	2y̌	2y̌	NUM
ejpam-4716	350	3	γ̌ε2x̌1	γ̌ε2x̌1	NOUN
ejpam-4716	350	4	−	−	NOUN
ejpam-4716	350	5	µ2	µ2	NOUN
ejpam-4716	350	6			NOUN
ejpam-4716	350	7	and	and	CCONJ
ejpam-4716	350	8	γ̌	γ̌	PROPN
ejpam-4716	350	9	=	=	SYM
ejpam-4716	350	10	1	1	NUM
ejpam-4716	350	11	1	1	NUM
ejpam-4716	350	12	+	+	CCONJ
ejpam-4716	350	13	x̌	x̌	NOUN
ejpam-4716	350	14	theorem	theorem	NOUN
ejpam-4716	350	15	9	9	NUM
ejpam-4716	350	16	.	.	PUNCT
ejpam-4716	350	17	suppose	suppose	VERB
ejpam-4716	350	18	that	that	SCONJ
ejpam-4716	350	19	the	the	DET
ejpam-4716	350	20	equilibrium	equilibrium	NOUN
ejpam-4716	350	21	point	point	NOUN
ejpam-4716	350	22	p5	p5	PROPN
ejpam-4716	350	23	=	=	PUNCT
ejpam-4716	350	24	(	(	PUNCT
ejpam-4716	350	25	x̌1	x̌1	NUM
ejpam-4716	350	26	,	,	PUNCT
ejpam-4716	350	27	x̌2	x̌2	NUM
ejpam-4716	350	28	,	,	PUNCT
ejpam-4716	350	29	0	0	NUM
ejpam-4716	350	30	,	,	PUNCT
ejpam-4716	350	31	y̌2	y̌2	PRON
ejpam-4716	350	32	)	)	PUNCT
ejpam-4716	350	33	of	of	ADP
ejpam-4716	350	34	the	the	DET
ejpam-4716	350	35	system	system	NOUN
ejpam-4716	350	36	(	(	PUNCT
ejpam-4716	350	37	2	2	X
ejpam-4716	350	38	)	)	PUNCT
ejpam-4716	350	39	exists	exist	VERB
ejpam-4716	350	40	and	and	CCONJ
ejpam-4716	350	41	is	be	AUX
ejpam-4716	350	42	locally	locally	ADV
ejpam-4716	350	43	asymptotically	asymptotically	ADV
ejpam-4716	350	44	stable	stable	ADJ
ejpam-4716	350	45	for	for	ADP
ejpam-4716	350	46	the	the	DET
ejpam-4716	350	47	parameter	parameter	NOUN
ejpam-4716	350	48	g	g	PROPN
ejpam-4716	350	49	=	=	PROPN
ejpam-4716	350	50	g1	g1	PROPN
ejpam-4716	350	51	=	=	SYM
ejpam-4716	350	52	g2	g2	PROPN
ejpam-4716	350	53	,	,	PUNCT
ejpam-4716	350	54	and	and	CCONJ
ejpam-4716	350	55	g∗∗	g∗∗	PROPN
ejpam-4716	350	56	be	be	AUX
ejpam-4716	350	57	the	the	DET
ejpam-4716	350	58	positive	positive	ADJ
ejpam-4716	350	59	root	root	NOUN
ejpam-4716	350	60	of	of	ADP
ejpam-4716	350	61	the	the	DET
ejpam-4716	350	62	equation	equation	NOUN
ejpam-4716	350	63	(	(	PUNCT
ejpam-4716	350	64	17	17	NUM
ejpam-4716	350	65	)	)	PUNCT
ejpam-4716	350	66	,	,	PUNCT
ejpam-4716	350	67	then	then	ADV
ejpam-4716	350	68	a	a	DET
ejpam-4716	350	69	simple	simple	ADJ
ejpam-4716	350	70	hopf	hopf	ADJ
ejpam-4716	350	71	bifurcation	bifurcation	NOUN
ejpam-4716	350	72	occurs	occur	VERB
ejpam-4716	350	73	as	as	SCONJ
ejpam-4716	350	74	g	g	PROPN
ejpam-4716	350	75	passes	pass	VERB
ejpam-4716	350	76	through	through	ADP
ejpam-4716	350	77	g∗∗	g∗∗	PROPN
ejpam-4716	350	78	provided	provide	VERB
ejpam-4716	350	79	that	that	SCONJ
ejpam-4716	350	80	(	(	PUNCT
ejpam-4716	350	81	m̌11	m̌11	PROPN
ejpam-4716	350	82	+	+	PROPN
ejpam-4716	350	83	m̌22	m̌22	PROPN
ejpam-4716	350	84	)	)	PUNCT
ejpam-4716	350	85	(	(	PUNCT
ejpam-4716	350	86	µ2	µ2	NOUN
ejpam-4716	350	87	−	−	PROPN
ejpam-4716	350	88	γ̌ε1x̌1)g	γ̌ε1x̌1)g	PROPN
ejpam-4716	350	89	−1	−1	NOUN
ejpam-4716	350	90	−	−	PROPN
ejpam-4716	350	91	m̌33	m̌33	PROPN
ejpam-4716	350	92	(	(	PUNCT
ejpam-4716	350	93	k−1	k−1	PROPN
ejpam-4716	350	94	1	1	NUM
ejpam-4716	350	95	x̌1	x̌1	NUM
ejpam-4716	350	96	−	−	PROPN
ejpam-4716	351	1	γ̌2α1x̌y̌	γ̌2α1x̌y̌	PROPN
ejpam-4716	352	1	+	+	CCONJ
ejpam-4716	352	2	k−1	k−1	PROPN
ejpam-4716	352	3	2	2	NUM
ejpam-4716	352	4	x̌2	x̌2	NUM
ejpam-4716	352	5	−	−	PROPN
ejpam-4716	352	6	γ̌2β2x̌y̌.	γ̌2β2x̌y̌.	PROPN
ejpam-4716	352	7	)	)	PUNCT
ejpam-4716	352	8	̸=0	̸=0	ADV
ejpam-4716	352	9	,	,	PUNCT
ejpam-4716	352	10	where	where	SCONJ
ejpam-4716	352	11	y̌	y̌	PROPN
ejpam-4716	352	12	=	=	SYM
ejpam-4716	352	13	g−1y̌2	g−1y̌2	NOUN
ejpam-4716	352	14	,	,	PUNCT
ejpam-4716	352	15	and	and	CCONJ
ejpam-4716	352	16	g∗∗	g∗∗	PROPN
ejpam-4716	352	17	is	be	AUX
ejpam-4716	352	18	the	the	DET
ejpam-4716	352	19	positive	positive	ADJ
ejpam-4716	352	20	root	root	NOUN
ejpam-4716	352	21	of	of	ADP
ejpam-4716	352	22	the	the	DET
ejpam-4716	352	23	(	(	PUNCT
ejpam-4716	352	24	17	17	NUM
ejpam-4716	352	25	)	)	PUNCT
ejpam-4716	352	26	given	give	VERB
ejpam-4716	352	27	above	above	ADV
ejpam-4716	352	28	.	.	PUNCT
ejpam-4716	353	1	proof	proof	NOUN
ejpam-4716	353	2	.	.	PUNCT
ejpam-4716	354	1	the	the	DET
ejpam-4716	354	2	proof	proof	NOUN
ejpam-4716	354	3	is	be	AUX
ejpam-4716	354	4	the	the	DET
ejpam-4716	354	5	same	same	ADJ
ejpam-4716	354	6	as	as	ADP
ejpam-4716	354	7	the	the	DET
ejpam-4716	354	8	proof	proof	NOUN
ejpam-4716	354	9	of	of	ADP
ejpam-4716	354	10	theorem	theorem	ADJ
ejpam-4716	354	11	8	8	NUM
ejpam-4716	354	12	.	.	NOUN
ejpam-4716	354	13	6	6	NUM
ejpam-4716	354	14	.	.	X
ejpam-4716	354	15	numerical	numerical	ADJ
ejpam-4716	354	16	example	example	NOUN
ejpam-4716	354	17	in	in	ADP
ejpam-4716	354	18	this	this	DET
ejpam-4716	354	19	section	section	NOUN
ejpam-4716	354	20	,	,	PUNCT
ejpam-4716	354	21	two	two	NUM
ejpam-4716	354	22	numerical	numerical	ADJ
ejpam-4716	354	23	examples	example	NOUN
ejpam-4716	354	24	are	be	AUX
ejpam-4716	354	25	given	give	VERB
ejpam-4716	354	26	to	to	PART
ejpam-4716	354	27	confirm	confirm	VERB
ejpam-4716	354	28	the	the	DET
ejpam-4716	354	29	obtained	obtain	VERB
ejpam-4716	354	30	theoretical	theoretical	ADJ
ejpam-4716	354	31	results	result	NOUN
ejpam-4716	354	32	in	in	ADP
ejpam-4716	354	33	the	the	DET
ejpam-4716	354	34	above	above	ADJ
ejpam-4716	354	35	sections	section	NOUN
ejpam-4716	354	36	.	.	PUNCT
ejpam-4716	355	1	consider	consider	VERB
ejpam-4716	355	2	is	be	AUX
ejpam-4716	355	3	the	the	DET
ejpam-4716	355	4	set	set	NOUN
ejpam-4716	355	5	of	of	ADP
ejpam-4716	355	6	parameters	parameter	NOUN
ejpam-4716	355	7	in	in	ADP
ejpam-4716	355	8	the	the	DET
ejpam-4716	355	9	following	follow	VERB
ejpam-4716	355	10	table	table	NOUN
ejpam-4716	355	11	table	table	NOUN
ejpam-4716	355	12	1	1	NUM
ejpam-4716	356	1	:	:	PUNCT
ejpam-4716	356	2	model	model	NOUN
ejpam-4716	356	3	parameters1	parameters1	NOUN
ejpam-4716	357	1	i	i	PRON
ejpam-4716	357	2	gi	gi	VERB
ejpam-4716	357	3	ki	ki	PROPN
ejpam-4716	357	4	αi	αi	VERB
ejpam-4716	357	5	βi	βi	PUNCT
ejpam-4716	358	1	µi	µi	INTJ
ejpam-4716	358	2	ϵi	ϵi	X
ejpam-4716	358	3	ρi	ρi	DET
ejpam-4716	358	4	1	1	NUM
ejpam-4716	358	5	0.5	0.5	NUM
ejpam-4716	358	6	1.9	1.9	NUM
ejpam-4716	358	7	0.2	0.2	NUM
ejpam-4716	358	8	0.49	0.49	NUM
ejpam-4716	358	9	0.12	0.12	NUM
ejpam-4716	358	10	0.19	0.19	NUM
ejpam-4716	358	11	0.1	0.1	NUM
ejpam-4716	358	12	2	2	NUM
ejpam-4716	358	13	0.51	0.51	NUM
ejpam-4716	358	14	1.8	1.8	NUM
ejpam-4716	358	15	0.21	0.21	NUM
ejpam-4716	358	16	0.5	0.5	NUM
ejpam-4716	358	17	0.19	0.19	NUM
ejpam-4716	358	18	0.2	0.2	NUM
ejpam-4716	358	19	0.12	0.12	NUM
ejpam-4716	358	20	the	the	DET
ejpam-4716	358	21	point	point	NOUN
ejpam-4716	358	22	p3	p3	NOUN
ejpam-4716	358	23	=	=	SYM
ejpam-4716	358	24	(	(	PUNCT
ejpam-4716	358	25	k1	k1	PROPN
ejpam-4716	358	26	,	,	PUNCT
ejpam-4716	358	27	k1	k1	NOUN
ejpam-4716	358	28	,	,	PUNCT
ejpam-4716	358	29	0	0	NUM
ejpam-4716	358	30	,	,	PUNCT
ejpam-4716	358	31	0	0	NUM
ejpam-4716	358	32	)	)	PUNCT
ejpam-4716	358	33	is	be	AUX
ejpam-4716	358	34	unstable	unstable	ADJ
ejpam-4716	358	35	,	,	PUNCT
ejpam-4716	358	36	but	but	CCONJ
ejpam-4716	358	37	with	with	ADP
ejpam-4716	358	38	µ1	µ1	PROPN
ejpam-4716	358	39	>	>	SYM
ejpam-4716	358	40	µ∗	µ∗	PROPN
ejpam-4716	358	41	1	1	NUM
ejpam-4716	358	42	=	=	SYM
ejpam-4716	358	43	0.1756	0.1756	NUM
ejpam-4716	358	44	is	be	AUX
ejpam-4716	358	45	locally	locally	ADV
ejpam-4716	358	46	asymptotically	asymptotically	ADV
ejpam-4716	358	47	stable	stable	ADJ
ejpam-4716	358	48	as	as	SCONJ
ejpam-4716	358	49	shown	show	VERB
ejpam-4716	358	50	in	in	ADP
ejpam-4716	358	51	figure	figure	NOUN
ejpam-4716	358	52	1	1	NUM
ejpam-4716	358	53	,	,	PUNCT
ejpam-4716	358	54	this	this	PRON
ejpam-4716	358	55	means	mean	VERB
ejpam-4716	358	56	p3	p3	PROPN
ejpam-4716	358	57	has	have	VERB
ejpam-4716	358	58	a	a	DET
ejpam-4716	358	59	steady	steady	ADJ
ejpam-4716	358	60	state	state	NOUN
ejpam-4716	358	61	bifurcation	bifurcation	NOUN
ejpam-4716	358	62	when	when	SCONJ
ejpam-4716	358	63	µ1	µ1	PROPN
ejpam-4716	358	64	pass	pass	AUX
ejpam-4716	358	65	throw	throw	VERB
ejpam-4716	358	66	µ∗	µ∗	NOUN
ejpam-4716	358	67	1	1	NUM
ejpam-4716	358	68	=	=	SYM
ejpam-4716	358	69	0.1756	0.1756	NUM
ejpam-4716	358	70	.	.	PUNCT
ejpam-4716	359	1	the	the	DET
ejpam-4716	359	2	point	point	NOUN
ejpam-4716	359	3	p4	p4	NOUN
ejpam-4716	359	4	=	=	PUNCT
ejpam-4716	359	5	(	(	PUNCT
ejpam-4716	359	6	1.6927	1.6927	NUM
ejpam-4716	359	7	,	,	PUNCT
ejpam-4716	359	8	1.0075	1.0075	NUM
ejpam-4716	359	9	,	,	PUNCT
ejpam-4716	359	10	0.731	0.731	NUM
ejpam-4716	359	11	,	,	PUNCT
ejpam-4716	359	12	0	0	NUM
ejpam-4716	359	13	)	)	PUNCT
ejpam-4716	359	14	,	,	PUNCT
ejpam-4716	359	15	is	be	AUX
ejpam-4716	359	16	unstable	unstable	ADJ
ejpam-4716	359	17	,	,	PUNCT
ejpam-4716	359	18	see	see	VERB
ejpam-4716	359	19	figure	figure	NOUN
ejpam-4716	359	20	a.	a.	NOUN
ejpam-4716	359	21	g.	g.	PROPN
ejpam-4716	359	22	farhan	farhan	PROPN
ejpam-4716	359	23	,	,	PUNCT
ejpam-4716	359	24	n.	n.	PROPN
ejpam-4716	359	25	sh	sh	PROPN
ejpam-4716	360	1	.	.	PROPN
ejpam-4716	360	2	khalaf	khalaf	PROPN
ejpam-4716	360	3	,	,	PUNCT
ejpam-4716	360	4	t.	t.	PROPN
ejpam-4716	360	5	j.	j.	PROPN
ejpam-4716	360	6	aldhlki	aldhlki	PROPN
ejpam-4716	360	7	/	/	SYM
ejpam-4716	360	8	eur	eur	PROPN
ejpam-4716	360	9	.	.	PUNCT
ejpam-4716	361	1	j.	j.	PROPN
ejpam-4716	361	2	pure	pure	PROPN
ejpam-4716	361	3	appl	appl	PROPN
ejpam-4716	361	4	.	.	PROPN
ejpam-4716	361	5	math	math	PROPN
ejpam-4716	361	6	,	,	PUNCT
ejpam-4716	361	7	16	16	NUM
ejpam-4716	361	8	(	(	PUNCT
ejpam-4716	361	9	2	2	NUM
ejpam-4716	361	10	)	)	PUNCT
ejpam-4716	361	11	(	(	PUNCT
ejpam-4716	361	12	2023	2023	NUM
ejpam-4716	361	13	)	)	PUNCT
ejpam-4716	361	14	,	,	PUNCT
ejpam-4716	361	15	899	899	NUM
ejpam-4716	361	16	-	-	SYM
ejpam-4716	361	17	918	918	NUM
ejpam-4716	361	18	913	913	NUM
ejpam-4716	361	19	2	2	NUM
ejpam-4716	361	20	,	,	PUNCT
ejpam-4716	361	21	whether	whether	SCONJ
ejpam-4716	361	22	the	the	DET
ejpam-4716	361	23	equilibrium	equilibrium	NOUN
ejpam-4716	361	24	point	point	NOUN
ejpam-4716	361	25	p5	p5	ADJ
ejpam-4716	361	26	=	=	PUNCT
ejpam-4716	361	27	(	(	PUNCT
ejpam-4716	361	28	1.6934	1.6934	NUM
ejpam-4716	361	29	,	,	PUNCT
ejpam-4716	361	30	0.7095	0.7095	NUM
ejpam-4716	361	31	,	,	PUNCT
ejpam-4716	361	32	0	0	NUM
ejpam-4716	361	33	,	,	PUNCT
ejpam-4716	361	34	0.87686	0.87686	NUM
ejpam-4716	361	35	)	)	PUNCT
ejpam-4716	361	36	,	,	PUNCT
ejpam-4716	361	37	exist	exist	VERB
ejpam-4716	361	38	when	when	SCONJ
ejpam-4716	361	39	µ2	µ2	PROPN
ejpam-4716	361	40	=	=	PROPN
ejpam-4716	361	41	0.1	0.1	NUM
ejpam-4716	361	42	,	,	PUNCT
ejpam-4716	361	43	and	and	CCONJ
ejpam-4716	361	44	is	be	AUX
ejpam-4716	361	45	locally	locally	ADV
ejpam-4716	361	46	asymptotically	asymptotically	ADV
ejpam-4716	361	47	stable	stable	ADJ
ejpam-4716	361	48	as	as	SCONJ
ejpam-4716	361	49	shown	show	VERB
ejpam-4716	361	50	in	in	ADP
ejpam-4716	361	51	figure	figure	NOUN
ejpam-4716	361	52	3	3	NUM
ejpam-4716	361	53	.	.	PUNCT
ejpam-4716	362	1	the	the	DET
ejpam-4716	362	2	point	point	NOUN
ejpam-4716	362	3	p6	p6	NOUN
ejpam-4716	362	4	=	=	PUNCT
ejpam-4716	362	5	(	(	PUNCT
ejpam-4716	362	6	1.7098	1.7098	NUM
ejpam-4716	362	7	,	,	PUNCT
ejpam-4716	362	8	1.1715	1.1715	NUM
ejpam-4716	362	9	,	,	PUNCT
ejpam-4716	362	10	0.5096	0.5096	NUM
ejpam-4716	362	11	,	,	PUNCT
ejpam-4716	362	12	0.1007	0.1007	NUM
ejpam-4716	362	13	)	)	PUNCT
ejpam-4716	362	14	,	,	PUNCT
ejpam-4716	362	15	exist	exist	VERB
ejpam-4716	362	16	and	and	CCONJ
ejpam-4716	362	17	is	be	AUX
ejpam-4716	362	18	locally	locally	ADV
ejpam-4716	362	19	asymptotically	asymptotically	ADV
ejpam-4716	362	20	stable	stable	ADJ
ejpam-4716	362	21	as	as	SCONJ
ejpam-4716	362	22	shown	show	VERB
ejpam-4716	362	23	in	in	ADP
ejpam-4716	362	24	figure	figure	NOUN
ejpam-4716	362	25	4	4	NUM
ejpam-4716	362	26	.	.	PUNCT
ejpam-4716	362	27	now	now	ADV
ejpam-4716	362	28	consider	consider	VERB
ejpam-4716	362	29	the	the	DET
ejpam-4716	362	30	table	table	NOUN
ejpam-4716	362	31	bellow	bellow	ADJ
ejpam-4716	362	32	table	table	NOUN
ejpam-4716	362	33	2	2	NUM
ejpam-4716	362	34	:	:	PUNCT
ejpam-4716	362	35	model	model	NOUN
ejpam-4716	362	36	parameters	parameter	NOUN
ejpam-4716	363	1	2	2	NUM
ejpam-4716	364	1	i	i	PRON
ejpam-4716	364	2	gi	gi	VERB
ejpam-4716	364	3	ki	ki	PROPN
ejpam-4716	364	4	αi	αi	VERB
ejpam-4716	364	5	βi	βi	PUNCT
ejpam-4716	365	1	µi	µi	INTJ
ejpam-4716	365	2	ϵi	ϵi	X
ejpam-4716	365	3	ρi	ρi	ADP
ejpam-4716	365	4	1	1	NUM
ejpam-4716	365	5	0.3	0.3	NUM
ejpam-4716	365	6	2	2	NUM
ejpam-4716	365	7	0.1	0.1	NUM
ejpam-4716	365	8	0.4	0.4	NUM
ejpam-4716	365	9	0.12	0.12	NUM
ejpam-4716	365	10	0.1	0.1	NUM
ejpam-4716	365	11	0.1	0.1	NUM
ejpam-4716	365	12	2	2	NUM
ejpam-4716	365	13	0.4	0.4	NUM
ejpam-4716	365	14	3.2	3.2	NUM
ejpam-4716	365	15	0.2	0.2	NUM
ejpam-4716	365	16	0.5	0.5	NUM
ejpam-4716	365	17	0.13	0.13	NUM
ejpam-4716	365	18	0.2	0.2	NUM
ejpam-4716	365	19	0.11	0.11	NUM
ejpam-4716	365	20	the	the	DET
ejpam-4716	365	21	point	point	NOUN
ejpam-4716	365	22	p3	p3	NOUN
ejpam-4716	365	23	=	=	SYM
ejpam-4716	365	24	(	(	PUNCT
ejpam-4716	365	25	k1	k1	PROPN
ejpam-4716	365	26	,	,	PUNCT
ejpam-4716	365	27	k1	k1	NOUN
ejpam-4716	365	28	,	,	PUNCT
ejpam-4716	365	29	0	0	NUM
ejpam-4716	365	30	,	,	PUNCT
ejpam-4716	365	31	0	0	NUM
ejpam-4716	365	32	)	)	PUNCT
ejpam-4716	365	33	is	be	AUX
ejpam-4716	365	34	unstable	unstable	ADJ
ejpam-4716	365	35	,	,	PUNCT
ejpam-4716	365	36	but	but	CCONJ
ejpam-4716	365	37	with	with	ADP
ejpam-4716	365	38	µ1	µ1	PROPN
ejpam-4716	365	39	>	>	SYM
ejpam-4716	365	40	µ∗	µ∗	PROPN
ejpam-4716	365	41	1	1	NUM
ejpam-4716	365	42	=	=	SYM
ejpam-4716	365	43	0.12308	0.12308	NUM
ejpam-4716	365	44	and	and	CCONJ
ejpam-4716	365	45	µ2	µ2	PROPN
ejpam-4716	365	46	>	>	PUNCT
ejpam-4716	365	47	µ∗	µ∗	PROPN
ejpam-4716	365	48	2	2	NUM
ejpam-4716	365	49	=	=	SYM
ejpam-4716	365	50	0.24615	0.24615	NUM
ejpam-4716	365	51	is	be	AUX
ejpam-4716	365	52	locally	locally	ADV
ejpam-4716	365	53	asymptotically	asymptotically	ADV
ejpam-4716	365	54	stable	stable	ADJ
ejpam-4716	365	55	as	as	SCONJ
ejpam-4716	365	56	shown	show	VERB
ejpam-4716	365	57	in	in	ADP
ejpam-4716	365	58	figure	figure	NOUN
ejpam-4716	365	59	6	6	NUM
ejpam-4716	365	60	this	this	PRON
ejpam-4716	365	61	means	mean	VERB
ejpam-4716	365	62	p3	p3	PROPN
ejpam-4716	365	63	has	have	VERB
ejpam-4716	365	64	a	a	DET
ejpam-4716	365	65	steady	steady	ADJ
ejpam-4716	365	66	bifurcation	bifurcation	NOUN
ejpam-4716	365	67	when	when	SCONJ
ejpam-4716	365	68	µ1	µ1	PROPN
ejpam-4716	365	69	pass	pass	NOUN
ejpam-4716	365	70	throw	throw	VERB
ejpam-4716	365	71	µ∗	µ∗	NOUN
ejpam-4716	365	72	1	1	NUM
ejpam-4716	365	73	=	=	SYM
ejpam-4716	365	74	0.12308	0.12308	NUM
ejpam-4716	365	75	,	,	PUNCT
ejpam-4716	365	76	and	and	CCONJ
ejpam-4716	365	77	µ2	µ2	AUX
ejpam-4716	365	78	pass	pass	NOUN
ejpam-4716	365	79	throw	throw	VERB
ejpam-4716	365	80	µ∗	µ∗	NOUN
ejpam-4716	365	81	2	2	NUM
ejpam-4716	365	82	=	=	SYM
ejpam-4716	365	83	0.24615	0.24615	NUM
ejpam-4716	365	84	.	.	PUNCT
ejpam-4716	366	1	the	the	DET
ejpam-4716	366	2	point	point	NOUN
ejpam-4716	366	3	p4	p4	NOUN
ejpam-4716	366	4	=	=	SYM
ejpam-4716	366	5	(	(	PUNCT
ejpam-4716	366	6	1.9630	1.9630	NUM
ejpam-4716	366	7	,	,	PUNCT
ejpam-4716	366	8	3.0872	3.0872	NUM
ejpam-4716	366	9	,	,	PUNCT
ejpam-4716	366	10	0.0907	0.0907	NUM
ejpam-4716	366	11	,	,	PUNCT
ejpam-4716	366	12	0	0	NUM
ejpam-4716	366	13	)	)	PUNCT
ejpam-4716	366	14	,	,	PUNCT
ejpam-4716	366	15	is	be	AUX
ejpam-4716	366	16	unstable	unstable	ADJ
ejpam-4716	366	17	,	,	PUNCT
ejpam-4716	366	18	see	see	VERB
ejpam-4716	366	19	figure	figure	NOUN
ejpam-4716	366	20	7	7	NUM
ejpam-4716	366	21	,	,	PUNCT
ejpam-4716	366	22	whether	whether	SCONJ
ejpam-4716	366	23	the	the	DET
ejpam-4716	366	24	equilibrium	equilibrium	NOUN
ejpam-4716	366	25	point	point	NOUN
ejpam-4716	366	26	p5	p5	PROPN
ejpam-4716	366	27	=	=	PUNCT
ejpam-4716	366	28	(	(	PUNCT
ejpam-4716	366	29	1.4549	1.4549	NUM
ejpam-4716	366	30	,	,	PUNCT
ejpam-4716	366	31	1.1749	1.1749	NUM
ejpam-4716	366	32	,	,	PUNCT
ejpam-4716	366	33	0	0	NUM
ejpam-4716	366	34	,	,	PUNCT
ejpam-4716	366	35	0.9151	0.9151	NUM
ejpam-4716	366	36	)	)	PUNCT
ejpam-4716	366	37	,	,	PUNCT
ejpam-4716	366	38	exist	exist	VERB
ejpam-4716	366	39	and	and	CCONJ
ejpam-4716	366	40	is	be	AUX
ejpam-4716	366	41	locally	locally	ADV
ejpam-4716	366	42	asymptotically	asymptotically	ADV
ejpam-4716	366	43	stable	stable	ADJ
ejpam-4716	366	44	as	as	SCONJ
ejpam-4716	366	45	shown	show	VERB
ejpam-4716	366	46	in	in	ADP
ejpam-4716	366	47	figure	figure	NOUN
ejpam-4716	366	48	8	8	NUM
ejpam-4716	366	49	.	.	PUNCT
ejpam-4716	367	1	the	the	DET
ejpam-4716	367	2	point	point	NOUN
ejpam-4716	367	3	p6	p6	NOUN
ejpam-4716	367	4	=	=	PRON
ejpam-4716	367	5	does	do	AUX
ejpam-4716	367	6	not	not	PART
ejpam-4716	367	7	exist	exist	VERB
ejpam-4716	367	8	.	.	PUNCT
ejpam-4716	368	1	figure	figure	VERB
ejpam-4716	368	2	1	1	NUM
ejpam-4716	368	3	:	:	PUNCT
ejpam-4716	368	4	the	the	DET
ejpam-4716	368	5	trajectory	trajectory	NOUN
ejpam-4716	368	6	of	of	ADP
ejpam-4716	368	7	system	system	NOUN
ejpam-4716	368	8	(	(	PUNCT
ejpam-4716	368	9	2	2	NUM
ejpam-4716	368	10	)	)	PUNCT
ejpam-4716	368	11	,	,	PUNCT
ejpam-4716	368	12	according	accord	VERB
ejpam-4716	368	13	to	to	ADP
ejpam-4716	368	14	the	the	DET
ejpam-4716	368	15	parameters	parameter	NOUN
ejpam-4716	368	16	listed	list	VERB
ejpam-4716	368	17	in	in	ADP
ejpam-4716	368	18	table	table	NOUN
ejpam-4716	368	19	1	1	NUM
ejpam-4716	368	20	and	and	CCONJ
ejpam-4716	368	21	µ1	µ1	PROPN
ejpam-4716	368	22	>	>	SYM
ejpam-4716	368	23	µ∗	µ∗	PROPN
ejpam-4716	368	24	1	1	NUM
ejpam-4716	368	25	=	=	SYM
ejpam-4716	368	26	0.1756	0.1756	NUM
ejpam-4716	368	27	,	,	PUNCT
ejpam-4716	368	28	starts	start	VERB
ejpam-4716	368	29	in	in	ADP
ejpam-4716	368	30	(	(	PUNCT
ejpam-4716	368	31	1.7,1.6,0.05,0.08	1.7,1.6,0.05,0.08	NUM
ejpam-4716	368	32	)	)	PUNCT
ejpam-4716	368	33	,	,	PUNCT
ejpam-4716	368	34	which	which	PRON
ejpam-4716	368	35	located	locate	VERB
ejpam-4716	368	36	close	close	ADV
ejpam-4716	368	37	to	to	ADP
ejpam-4716	368	38	p3	p3	PROPN
ejpam-4716	368	39	tend	tend	VERB
ejpam-4716	368	40	to	to	PART
ejpam-4716	368	41	p3	p3	PROPN
ejpam-4716	368	42	.	.	PUNCT
ejpam-4716	369	1	a.	a.	PROPN
ejpam-4716	369	2	g.	g.	PROPN
ejpam-4716	369	3	farhan	farhan	PROPN
ejpam-4716	369	4	,	,	PUNCT
ejpam-4716	369	5	n.	n.	PROPN
ejpam-4716	369	6	sh	sh	PROPN
ejpam-4716	369	7	.	.	PROPN
ejpam-4716	369	8	khalaf	khalaf	PROPN
ejpam-4716	369	9	,	,	PUNCT
ejpam-4716	369	10	t.	t.	PROPN
ejpam-4716	369	11	j.	j.	PROPN
ejpam-4716	369	12	aldhlki	aldhlki	PROPN
ejpam-4716	369	13	/	/	SYM
ejpam-4716	369	14	eur	eur	PROPN
ejpam-4716	369	15	.	.	PUNCT
ejpam-4716	370	1	j.	j.	PROPN
ejpam-4716	370	2	pure	pure	PROPN
ejpam-4716	370	3	appl	appl	PROPN
ejpam-4716	370	4	.	.	PROPN
ejpam-4716	370	5	math	math	PROPN
ejpam-4716	370	6	,	,	PUNCT
ejpam-4716	370	7	16	16	NUM
ejpam-4716	370	8	(	(	PUNCT
ejpam-4716	370	9	2	2	NUM
ejpam-4716	370	10	)	)	PUNCT
ejpam-4716	370	11	(	(	PUNCT
ejpam-4716	370	12	2023	2023	NUM
ejpam-4716	370	13	)	)	PUNCT
ejpam-4716	370	14	,	,	PUNCT
ejpam-4716	370	15	899	899	NUM
ejpam-4716	370	16	-	-	SYM
ejpam-4716	370	17	918	918	NUM
ejpam-4716	370	18	914	914	NUM
ejpam-4716	370	19	figure	figure	NOUN
ejpam-4716	370	20	2	2	NUM
ejpam-4716	370	21	:	:	PUNCT
ejpam-4716	370	22	the	the	DET
ejpam-4716	370	23	trajectory	trajectory	NOUN
ejpam-4716	370	24	of	of	ADP
ejpam-4716	370	25	system	system	NOUN
ejpam-4716	370	26	(	(	PUNCT
ejpam-4716	370	27	2	2	NUM
ejpam-4716	370	28	)	)	PUNCT
ejpam-4716	370	29	,	,	PUNCT
ejpam-4716	370	30	according	accord	VERB
ejpam-4716	370	31	to	to	ADP
ejpam-4716	370	32	the	the	DET
ejpam-4716	370	33	parameters	parameter	NOUN
ejpam-4716	370	34	listed	list	VERB
ejpam-4716	370	35	in	in	ADP
ejpam-4716	370	36	table	table	NOUN
ejpam-4716	370	37	1	1	NUM
ejpam-4716	370	38	,	,	PUNCT
ejpam-4716	370	39	starts	start	VERB
ejpam-4716	370	40	in	in	ADP
ejpam-4716	370	41	the	the	DET
ejpam-4716	370	42	initial	initial	ADJ
ejpam-4716	370	43	point	point	NOUN
ejpam-4716	370	44	(	(	PUNCT
ejpam-4716	370	45	1.6	1.6	NUM
ejpam-4716	370	46	,	,	PUNCT
ejpam-4716	370	47	,	,	PUNCT
ejpam-4716	370	48	1	1	NUM
ejpam-4716	370	49	,	,	PUNCT
ejpam-4716	370	50	0.7	0.7	NUM
ejpam-4716	370	51	,	,	PUNCT
ejpam-4716	370	52	0.01	0.01	NUM
ejpam-4716	370	53	)	)	PUNCT
ejpam-4716	370	54	,	,	PUNCT
ejpam-4716	370	55	which	which	PRON
ejpam-4716	370	56	located	locate	VERB
ejpam-4716	370	57	close	close	ADV
ejpam-4716	370	58	to	to	ADP
ejpam-4716	370	59	p4	p4	ADJ
ejpam-4716	370	60	and	and	CCONJ
ejpam-4716	370	61	it	it	PRON
ejpam-4716	370	62	is	be	AUX
ejpam-4716	370	63	moving	move	VERB
ejpam-4716	370	64	away	away	ADV
ejpam-4716	370	65	from	from	ADP
ejpam-4716	370	66	p4	p4	ADJ
ejpam-4716	370	67	and	and	CCONJ
ejpam-4716	370	68	approaching	approach	VERB
ejpam-4716	370	69	p6	p6	PROPN
ejpam-4716	370	70	.	.	PUNCT
ejpam-4716	371	1	figure	figure	VERB
ejpam-4716	371	2	3	3	NUM
ejpam-4716	371	3	:	:	PUNCT
ejpam-4716	371	4	the	the	DET
ejpam-4716	371	5	trajectory	trajectory	NOUN
ejpam-4716	371	6	of	of	ADP
ejpam-4716	371	7	system	system	NOUN
ejpam-4716	371	8	(	(	PUNCT
ejpam-4716	371	9	2	2	NUM
ejpam-4716	371	10	)	)	PUNCT
ejpam-4716	371	11	,	,	PUNCT
ejpam-4716	371	12	according	accord	VERB
ejpam-4716	371	13	to	to	ADP
ejpam-4716	371	14	the	the	DET
ejpam-4716	371	15	parameters	parameter	NOUN
ejpam-4716	371	16	listed	list	VERB
ejpam-4716	371	17	in	in	ADP
ejpam-4716	371	18	table	table	NOUN
ejpam-4716	371	19	1	1	NUM
ejpam-4716	371	20	,	,	PUNCT
ejpam-4716	371	21	starts	start	VERB
ejpam-4716	371	22	in	in	ADP
ejpam-4716	371	23	the	the	DET
ejpam-4716	371	24	initial	initial	ADJ
ejpam-4716	371	25	point	point	NOUN
ejpam-4716	371	26	(	(	PUNCT
ejpam-4716	371	27	1.6	1.6	NUM
ejpam-4716	371	28	,	,	PUNCT
ejpam-4716	371	29	0.7	0.7	NUM
ejpam-4716	371	30	,	,	PUNCT
ejpam-4716	371	31	0.02	0.02	NUM
ejpam-4716	371	32	,	,	PUNCT
ejpam-4716	371	33	0.8	0.8	NUM
ejpam-4716	371	34	)	)	PUNCT
ejpam-4716	371	35	,	,	PUNCT
ejpam-4716	371	36	which	which	PRON
ejpam-4716	371	37	located	locate	VERB
ejpam-4716	371	38	close	close	ADV
ejpam-4716	371	39	to	to	PART
ejpam-4716	371	40	p5	p5	VERB
ejpam-4716	371	41	,	,	PUNCT
ejpam-4716	371	42	is	be	AUX
ejpam-4716	371	43	approaching	approach	VERB
ejpam-4716	371	44	p5	p5	ADJ
ejpam-4716	371	45	.	.	PUNCT
ejpam-4716	372	1	a.	a.	NOUN
ejpam-4716	372	2	g.	g.	PROPN
ejpam-4716	372	3	farhan	farhan	PROPN
ejpam-4716	372	4	,	,	PUNCT
ejpam-4716	372	5	n.	n.	PROPN
ejpam-4716	372	6	sh	sh	PROPN
ejpam-4716	372	7	.	.	PROPN
ejpam-4716	372	8	khalaf	khalaf	PROPN
ejpam-4716	372	9	,	,	PUNCT
ejpam-4716	372	10	t.	t.	PROPN
ejpam-4716	372	11	j.	j.	PROPN
ejpam-4716	372	12	aldhlki	aldhlki	PROPN
ejpam-4716	372	13	/	/	SYM
ejpam-4716	372	14	eur	eur	PROPN
ejpam-4716	372	15	.	.	PUNCT
ejpam-4716	373	1	j.	j.	PROPN
ejpam-4716	373	2	pure	pure	PROPN
ejpam-4716	373	3	appl	appl	PROPN
ejpam-4716	373	4	.	.	PROPN
ejpam-4716	373	5	math	math	PROPN
ejpam-4716	373	6	,	,	PUNCT
ejpam-4716	373	7	16	16	NUM
ejpam-4716	373	8	(	(	PUNCT
ejpam-4716	373	9	2	2	NUM
ejpam-4716	373	10	)	)	PUNCT
ejpam-4716	373	11	(	(	PUNCT
ejpam-4716	373	12	2023	2023	NUM
ejpam-4716	373	13	)	)	PUNCT
ejpam-4716	373	14	,	,	PUNCT
ejpam-4716	373	15	899	899	NUM
ejpam-4716	373	16	-	-	SYM
ejpam-4716	373	17	918	918	NUM
ejpam-4716	373	18	915	915	NUM
ejpam-4716	373	19	figure	figure	NOUN
ejpam-4716	373	20	4	4	NUM
ejpam-4716	373	21	:	:	PUNCT
ejpam-4716	373	22	the	the	DET
ejpam-4716	373	23	trajectory	trajectory	NOUN
ejpam-4716	373	24	of	of	ADP
ejpam-4716	373	25	system	system	NOUN
ejpam-4716	373	26	(	(	PUNCT
ejpam-4716	373	27	2	2	NUM
ejpam-4716	373	28	)	)	PUNCT
ejpam-4716	373	29	,	,	PUNCT
ejpam-4716	373	30	according	accord	VERB
ejpam-4716	373	31	to	to	ADP
ejpam-4716	373	32	the	the	DET
ejpam-4716	373	33	parameters	parameter	NOUN
ejpam-4716	373	34	listed	list	VERB
ejpam-4716	373	35	in	in	ADP
ejpam-4716	373	36	table	table	NOUN
ejpam-4716	373	37	1	1	NUM
ejpam-4716	373	38	,	,	PUNCT
ejpam-4716	373	39	starts	start	VERB
ejpam-4716	373	40	in	in	ADP
ejpam-4716	373	41	the	the	DET
ejpam-4716	373	42	initial	initial	ADJ
ejpam-4716	373	43	point	point	NOUN
ejpam-4716	373	44	(	(	PUNCT
ejpam-4716	373	45	1.4	1.4	NUM
ejpam-4716	373	46	,	,	PUNCT
ejpam-4716	373	47	1.3	1.3	NUM
ejpam-4716	373	48	,	,	PUNCT
ejpam-4716	373	49	0.3	0.3	NUM
ejpam-4716	373	50	,	,	PUNCT
ejpam-4716	373	51	0.05	0.05	NUM
ejpam-4716	373	52	)	)	PUNCT
ejpam-4716	373	53	,	,	PUNCT
ejpam-4716	373	54	which	which	PRON
ejpam-4716	373	55	located	locate	VERB
ejpam-4716	373	56	close	close	ADV
ejpam-4716	373	57	to	to	ADP
ejpam-4716	373	58	p6	p6	PROPN
ejpam-4716	373	59	is	be	AUX
ejpam-4716	373	60	approaching	approach	VERB
ejpam-4716	373	61	p6	p6	PROPN
ejpam-4716	373	62	.	.	PUNCT
ejpam-4716	374	1	figure	figure	NOUN
ejpam-4716	374	2	5	5	NUM
ejpam-4716	374	3	:	:	PUNCT
ejpam-4716	374	4	the	the	DET
ejpam-4716	374	5	trajectory	trajectory	NOUN
ejpam-4716	374	6	of	of	ADP
ejpam-4716	374	7	system	system	NOUN
ejpam-4716	374	8	(	(	PUNCT
ejpam-4716	374	9	2	2	NUM
ejpam-4716	374	10	)	)	PUNCT
ejpam-4716	374	11	,	,	PUNCT
ejpam-4716	374	12	according	accord	VERB
ejpam-4716	374	13	to	to	ADP
ejpam-4716	374	14	the	the	DET
ejpam-4716	374	15	parameters	parameter	NOUN
ejpam-4716	374	16	listed	list	VERB
ejpam-4716	374	17	in	in	ADP
ejpam-4716	374	18	table	table	NOUN
ejpam-4716	374	19	1	1	NUM
ejpam-4716	374	20	,	,	PUNCT
ejpam-4716	374	21	starts	start	VERB
ejpam-4716	374	22	in	in	ADP
ejpam-4716	374	23	the	the	DET
ejpam-4716	374	24	initial	initial	ADJ
ejpam-4716	374	25	point	point	NOUN
ejpam-4716	374	26	(	(	PUNCT
ejpam-4716	374	27	1.4	1.4	NUM
ejpam-4716	374	28	,	,	PUNCT
ejpam-4716	374	29	1.3	1.3	NUM
ejpam-4716	374	30	,	,	PUNCT
ejpam-4716	374	31	0.3	0.3	NUM
ejpam-4716	374	32	,	,	PUNCT
ejpam-4716	374	33	0.05	0.05	NUM
ejpam-4716	374	34	)	)	PUNCT
ejpam-4716	374	35	,	,	PUNCT
ejpam-4716	374	36	which	which	PRON
ejpam-4716	374	37	located	locate	VERB
ejpam-4716	374	38	close	close	ADV
ejpam-4716	374	39	to	to	ADP
ejpam-4716	374	40	p6	p6	PROPN
ejpam-4716	374	41	is	be	AUX
ejpam-4716	374	42	approaching	approach	VERB
ejpam-4716	374	43	p6	p6	PROPN
ejpam-4716	374	44	.	.	PUNCT
ejpam-4716	375	1	a.	a.	PROPN
ejpam-4716	375	2	g.	g.	PROPN
ejpam-4716	375	3	farhan	farhan	PROPN
ejpam-4716	375	4	,	,	PUNCT
ejpam-4716	375	5	n.	n.	PROPN
ejpam-4716	375	6	sh	sh	PROPN
ejpam-4716	375	7	.	.	PROPN
ejpam-4716	375	8	khalaf	khalaf	PROPN
ejpam-4716	375	9	,	,	PUNCT
ejpam-4716	375	10	t.	t.	PROPN
ejpam-4716	375	11	j.	j.	PROPN
ejpam-4716	375	12	aldhlki	aldhlki	PROPN
ejpam-4716	375	13	/	/	SYM
ejpam-4716	375	14	eur	eur	PROPN
ejpam-4716	375	15	.	.	PUNCT
ejpam-4716	376	1	j.	j.	PROPN
ejpam-4716	376	2	pure	pure	PROPN
ejpam-4716	376	3	appl	appl	PROPN
ejpam-4716	376	4	.	.	PROPN
ejpam-4716	376	5	math	math	PROPN
ejpam-4716	376	6	,	,	PUNCT
ejpam-4716	376	7	16	16	NUM
ejpam-4716	376	8	(	(	PUNCT
ejpam-4716	376	9	2	2	NUM
ejpam-4716	376	10	)	)	PUNCT
ejpam-4716	376	11	(	(	PUNCT
ejpam-4716	376	12	2023	2023	NUM
ejpam-4716	376	13	)	)	PUNCT
ejpam-4716	376	14	,	,	PUNCT
ejpam-4716	376	15	899	899	NUM
ejpam-4716	376	16	-	-	SYM
ejpam-4716	376	17	918	918	NUM
ejpam-4716	376	18	916	916	NUM
ejpam-4716	376	19	figure	figure	NOUN
ejpam-4716	376	20	6	6	NUM
ejpam-4716	376	21	:	:	PUNCT
ejpam-4716	376	22	the	the	DET
ejpam-4716	376	23	trajectory	trajectory	NOUN
ejpam-4716	376	24	of	of	ADP
ejpam-4716	376	25	system	system	NOUN
ejpam-4716	376	26	(	(	PUNCT
ejpam-4716	376	27	2	2	NUM
ejpam-4716	376	28	)	)	PUNCT
ejpam-4716	376	29	,	,	PUNCT
ejpam-4716	376	30	according	accord	VERB
ejpam-4716	376	31	to	to	ADP
ejpam-4716	376	32	the	the	DET
ejpam-4716	376	33	parameters	parameter	NOUN
ejpam-4716	376	34	listed	list	VERB
ejpam-4716	376	35	in	in	ADP
ejpam-4716	376	36	table	table	NOUN
ejpam-4716	376	37	2	2	NUM
ejpam-4716	376	38	and	and	CCONJ
ejpam-4716	376	39	µ1	µ1	PROPN
ejpam-4716	376	40	>	>	SYM
ejpam-4716	376	41	µ∗	µ∗	PROPN
ejpam-4716	376	42	1	1	NUM
ejpam-4716	376	43	=	=	SYM
ejpam-4716	376	44	0.12308	0.12308	NUM
ejpam-4716	376	45	,	,	PUNCT
ejpam-4716	376	46	and	and	CCONJ
ejpam-4716	376	47	µ2	µ2	PROPN
ejpam-4716	376	48	>	>	PUNCT
ejpam-4716	376	49	µ∗	µ∗	PROPN
ejpam-4716	376	50	2	2	NUM
ejpam-4716	376	51	=	=	SYM
ejpam-4716	376	52	0.24615	0.24615	NUM
ejpam-4716	376	53	starts	start	VERB
ejpam-4716	376	54	in	in	ADP
ejpam-4716	376	55	the	the	DET
ejpam-4716	376	56	initial	initial	ADJ
ejpam-4716	376	57	point	point	NOUN
ejpam-4716	376	58	(	(	PUNCT
ejpam-4716	376	59	1.8,2.9,0.3,0.1	1.8,2.9,0.3,0.1	NOUN
ejpam-4716	376	60	)	)	PUNCT
ejpam-4716	376	61	that	that	PRON
ejpam-4716	376	62	located	locate	VERB
ejpam-4716	376	63	close	close	ADV
ejpam-4716	376	64	to	to	ADP
ejpam-4716	376	65	p3	p3	PROPN
ejpam-4716	376	66	tends	tend	VERB
ejpam-4716	376	67	to	to	ADP
ejpam-4716	376	68	p3	p3	PROPN
ejpam-4716	376	69	.	.	PUNCT
ejpam-4716	377	1	figure	figure	VERB
ejpam-4716	377	2	7	7	NUM
ejpam-4716	377	3	:	:	PUNCT
ejpam-4716	377	4	the	the	DET
ejpam-4716	377	5	trajectory	trajectory	NOUN
ejpam-4716	377	6	of	of	ADP
ejpam-4716	377	7	system	system	NOUN
ejpam-4716	377	8	(	(	PUNCT
ejpam-4716	377	9	2	2	NUM
ejpam-4716	377	10	)	)	PUNCT
ejpam-4716	377	11	,	,	PUNCT
ejpam-4716	377	12	according	accord	VERB
ejpam-4716	377	13	to	to	ADP
ejpam-4716	377	14	the	the	DET
ejpam-4716	377	15	parameters	parameter	NOUN
ejpam-4716	377	16	listed	list	VERB
ejpam-4716	377	17	in	in	ADP
ejpam-4716	377	18	table	table	NOUN
ejpam-4716	377	19	2	2	NUM
ejpam-4716	377	20	starts	start	NOUN
ejpam-4716	377	21	in	in	ADP
ejpam-4716	377	22	the	the	DET
ejpam-4716	377	23	initial	initial	ADJ
ejpam-4716	377	24	point	point	NOUN
ejpam-4716	377	25	(	(	PUNCT
ejpam-4716	377	26	1.7	1.7	NUM
ejpam-4716	377	27	,	,	PUNCT
ejpam-4716	377	28	2.9	2.9	NUM
ejpam-4716	377	29	,	,	PUNCT
ejpam-4716	377	30	0.07	0.07	NUM
ejpam-4716	377	31	,	,	PUNCT
ejpam-4716	377	32	0.03	0.03	NUM
ejpam-4716	377	33	)	)	PUNCT
ejpam-4716	377	34	that	that	PRON
ejpam-4716	377	35	located	locate	VERB
ejpam-4716	377	36	close	close	ADV
ejpam-4716	377	37	to	to	ADP
ejpam-4716	377	38	p4	p4	ADJ
ejpam-4716	377	39	tends	tend	VERB
ejpam-4716	377	40	to	to	PART
ejpam-4716	377	41	p5	p5	VERB
ejpam-4716	377	42	references	reference	NOUN
ejpam-4716	377	43	917	917	NUM
ejpam-4716	377	44	figure	figure	NOUN
ejpam-4716	377	45	8	8	NUM
ejpam-4716	377	46	:	:	PUNCT
ejpam-4716	377	47	the	the	DET
ejpam-4716	377	48	trajectory	trajectory	NOUN
ejpam-4716	377	49	of	of	ADP
ejpam-4716	377	50	system	system	NOUN
ejpam-4716	377	51	(	(	PUNCT
ejpam-4716	377	52	2	2	NUM
ejpam-4716	377	53	)	)	PUNCT
ejpam-4716	377	54	,	,	PUNCT
ejpam-4716	377	55	according	accord	VERB
ejpam-4716	377	56	to	to	ADP
ejpam-4716	377	57	the	the	DET
ejpam-4716	377	58	parameters	parameter	NOUN
ejpam-4716	377	59	listed	list	VERB
ejpam-4716	377	60	in	in	ADP
ejpam-4716	377	61	table	table	NOUN
ejpam-4716	377	62	2	2	NUM
ejpam-4716	377	63	starts	start	NOUN
ejpam-4716	377	64	in	in	ADP
ejpam-4716	377	65	the	the	DET
ejpam-4716	377	66	initial	initial	ADJ
ejpam-4716	377	67	point	point	NOUN
ejpam-4716	377	68	(	(	PUNCT
ejpam-4716	377	69	1.3	1.3	NUM
ejpam-4716	377	70	,	,	PUNCT
ejpam-4716	377	71	1	1	NUM
ejpam-4716	377	72	,	,	PUNCT
ejpam-4716	377	73	0.3	0.3	NUM
ejpam-4716	377	74	,	,	PUNCT
ejpam-4716	377	75	0.8	0.8	NUM
ejpam-4716	377	76	)	)	PUNCT
ejpam-4716	377	77	is	be	AUX
ejpam-4716	377	78	located	locate	VERB
ejpam-4716	377	79	close	close	ADV
ejpam-4716	377	80	to	to	ADP
ejpam-4716	377	81	p5	p5	ADJ
ejpam-4716	377	82	tends	tend	VERB
ejpam-4716	377	83	to	to	PART
ejpam-4716	377	84	p5	p5	VERB
ejpam-4716	377	85	7	7	NUM
ejpam-4716	377	86	.	.	PUNCT
ejpam-4716	377	87	conclusion	conclusion	NOUN
ejpam-4716	377	88	in	in	ADP
ejpam-4716	377	89	this	this	DET
ejpam-4716	377	90	paper	paper	NOUN
ejpam-4716	377	91	,	,	PUNCT
ejpam-4716	377	92	the	the	DET
ejpam-4716	377	93	dynamical	dynamical	ADJ
ejpam-4716	377	94	behavior	behavior	NOUN
ejpam-4716	377	95	of	of	ADP
ejpam-4716	377	96	a	a	DET
ejpam-4716	377	97	four	four	NUM
ejpam-4716	377	98	-	-	PUNCT
ejpam-4716	377	99	dimensional	dimensional	ADJ
ejpam-4716	377	100	prey	prey	NOUN
ejpam-4716	377	101	-	-	PUNCT
ejpam-4716	377	102	predator	predator	NOUN
ejpam-4716	377	103	model	model	NOUN
ejpam-4716	377	104	for	for	ADP
ejpam-4716	377	105	four	four	NUM
ejpam-4716	377	106	species	specie	NOUN
ejpam-4716	377	107	was	be	AUX
ejpam-4716	377	108	presented	present	VERB
ejpam-4716	377	109	.	.	PUNCT
ejpam-4716	378	1	the	the	DET
ejpam-4716	378	2	model	model	NOUN
ejpam-4716	378	3	has	have	VERB
ejpam-4716	378	4	seven	seven	NUM
ejpam-4716	378	5	equilibrium	equilibrium	NOUN
ejpam-4716	378	6	points	point	NOUN
ejpam-4716	378	7	,	,	PUNCT
ejpam-4716	378	8	four	four	NUM
ejpam-4716	378	9	of	of	ADP
ejpam-4716	378	10	them	they	PRON
ejpam-4716	378	11	always	always	ADV
ejpam-4716	378	12	exist	exist	VERB
ejpam-4716	378	13	,	,	PUNCT
ejpam-4716	378	14	whatever	whatever	PRON
ejpam-4716	378	15	the	the	DET
ejpam-4716	378	16	values	value	NOUN
ejpam-4716	378	17	of	of	ADP
ejpam-4716	378	18	the	the	DET
ejpam-4716	378	19	model	model	NOUN
ejpam-4716	378	20	parameters	parameter	NOUN
ejpam-4716	378	21	.	.	PUNCT
ejpam-4716	379	1	the	the	DET
ejpam-4716	379	2	positive	positive	ADJ
ejpam-4716	379	3	trajectory	trajectory	NOUN
ejpam-4716	379	4	of	of	ADP
ejpam-4716	379	5	the	the	DET
ejpam-4716	379	6	model	model	NOUN
ejpam-4716	379	7	are	be	AUX
ejpam-4716	379	8	bounded	bound	VERB
ejpam-4716	379	9	under	under	ADP
ejpam-4716	379	10	some	some	DET
ejpam-4716	379	11	certain	certain	ADJ
ejpam-4716	379	12	conditions	condition	NOUN
ejpam-4716	379	13	.	.	PUNCT
ejpam-4716	380	1	the	the	DET
ejpam-4716	380	2	system	system	NOUN
ejpam-4716	380	3	has	have	VERB
ejpam-4716	380	4	three	three	NUM
ejpam-4716	380	5	,	,	PUNCT
ejpam-4716	380	6	unstable	unstable	ADJ
ejpam-4716	380	7	equilibrium	equilibrium	NOUN
ejpam-4716	380	8	points	point	NOUN
ejpam-4716	380	9	and	and	CCONJ
ejpam-4716	380	10	four	four	NUM
ejpam-4716	380	11	equilibrium	equilibrium	NOUN
ejpam-4716	380	12	points	point	NOUN
ejpam-4716	380	13	that	that	PRON
ejpam-4716	380	14	are	be	AUX
ejpam-4716	380	15	asymptotically	asymptotically	ADV
ejpam-4716	380	16	locally	locally	ADV
ejpam-4716	380	17	stable	stable	ADJ
ejpam-4716	380	18	under	under	ADP
ejpam-4716	380	19	some	some	DET
ejpam-4716	380	20	conditions	condition	NOUN
ejpam-4716	380	21	.	.	PUNCT
ejpam-4716	381	1	the	the	DET
ejpam-4716	381	2	appearance	appearance	NOUN
ejpam-4716	381	3	of	of	ADP
ejpam-4716	381	4	steady	steady	ADJ
ejpam-4716	381	5	-	-	PUNCT
ejpam-4716	381	6	state	state	NOUN
ejpam-4716	381	7	and	and	CCONJ
ejpam-4716	381	8	,	,	PUNCT
ejpam-4716	381	9	hopf	hopf	ADJ
ejpam-4716	381	10	bifurcation	bifurcation	NOUN
ejpam-4716	381	11	near	near	ADP
ejpam-4716	381	12	the	the	DET
ejpam-4716	381	13	equilibrium	equilibrium	NOUN
ejpam-4716	381	14	points	point	NOUN
ejpam-4716	381	15	has	have	AUX
ejpam-4716	381	16	been	be	AUX
ejpam-4716	381	17	discussed	discuss	VERB
ejpam-4716	381	18	.	.	PUNCT
ejpam-4716	382	1	in	in	ADP
ejpam-4716	382	2	the	the	DET
ejpam-4716	382	3	numerical	numerical	ADJ
ejpam-4716	382	4	example	example	NOUN
ejpam-4716	382	5	represented	represent	VERB
ejpam-4716	382	6	by	by	ADP
ejpam-4716	382	7	table	table	NOUN
ejpam-4716	382	8	1	1	NUM
ejpam-4716	382	9	,	,	PUNCT
ejpam-4716	382	10	all	all	DET
ejpam-4716	382	11	the	the	DET
ejpam-4716	382	12	possible	possible	ADJ
ejpam-4716	382	13	equilibrium	equilibrium	NOUN
ejpam-4716	382	14	points	point	NOUN
ejpam-4716	382	15	exist	exist	VERB
ejpam-4716	382	16	,	,	PUNCT
ejpam-4716	382	17	and	and	CCONJ
ejpam-4716	382	18	in	in	ADP
ejpam-4716	382	19	the	the	DET
ejpam-4716	382	20	example	example	NOUN
ejpam-4716	382	21	represented	represent	VERB
ejpam-4716	382	22	by	by	ADP
ejpam-4716	382	23	table	table	NOUN
ejpam-4716	382	24	2	2	NUM
ejpam-4716	382	25	,	,	PUNCT
ejpam-4716	382	26	the	the	DET
ejpam-4716	382	27	coexistence	coexistence	NOUN
ejpam-4716	382	28	point	point	NOUN
ejpam-4716	382	29	disappeared	disappear	VERB
ejpam-4716	382	30	.	.	PUNCT
ejpam-4716	383	1	in	in	ADP
ejpam-4716	383	2	both	both	DET
ejpam-4716	383	3	examples	example	NOUN
ejpam-4716	383	4	,	,	PUNCT
ejpam-4716	383	5	the	the	DET
ejpam-4716	383	6	steady	steady	ADJ
ejpam-4716	383	7	-	-	PUNCT
ejpam-4716	383	8	state	state	NOUN
ejpam-4716	383	9	bifurcation	bifurcation	NOUN
ejpam-4716	383	10	was	be	AUX
ejpam-4716	383	11	present	present	ADJ
ejpam-4716	383	12	in	in	ADP
ejpam-4716	383	13	the	the	DET
ejpam-4716	383	14	neighborhood	neighborhood	NOUN
ejpam-4716	383	15	of	of	ADP
ejpam-4716	383	16	p3	p3	PROPN
ejpam-4716	383	17	;	;	PUNCT
ejpam-4716	383	18	p4	p4	NOUN
ejpam-4716	383	19	is	be	AUX
ejpam-4716	383	20	not	not	PART
ejpam-4716	383	21	stable	stable	ADJ
ejpam-4716	383	22	while	while	SCONJ
ejpam-4716	383	23	p5	p5	ADJ
ejpam-4716	383	24	is	be	AUX
ejpam-4716	383	25	locally	locally	ADV
ejpam-4716	383	26	asymptotically	asymptotically	ADV
ejpam-4716	383	27	stable	stable	ADJ
ejpam-4716	383	28	.	.	PUNCT
ejpam-4716	384	1	references	reference	NOUN
ejpam-4716	384	2	[	[	X
ejpam-4716	384	3	1	1	X
ejpam-4716	384	4	]	]	PUNCT
ejpam-4716	384	5	a	a	DET
ejpam-4716	384	6	h	h	NOUN
ejpam-4716	384	7	adamu	adamu	PROPN
ejpam-4716	384	8	.	.	PUNCT
ejpam-4716	385	1	mathematical	mathematical	ADJ
ejpam-4716	385	2	analysis	analysis	NOUN
ejpam-4716	385	3	of	of	ADP
ejpam-4716	385	4	predator	predator	NOUN
ejpam-4716	385	5	-	-	PUNCT
ejpam-4716	385	6	prey	prey	NOUN
ejpam-4716	385	7	model	model	NOUN
ejpam-4716	385	8	with	with	ADP
ejpam-4716	385	9	two	two	NUM
ejpam-4716	385	10	preys	prey	NOUN
ejpam-4716	385	11	and	and	CCONJ
ejpam-4716	385	12	one	one	NUM
ejpam-4716	385	13	predator	predator	NOUN
ejpam-4716	385	14	.	.	PUNCT
ejpam-4716	386	1	international	international	ADJ
ejpam-4716	386	2	journal	journal	PROPN
ejpam-4716	386	3	of	of	ADP
ejpam-4716	386	4	engineering	engineering	NOUN
ejpam-4716	386	5	and	and	CCONJ
ejpam-4716	386	6	applied	apply	VERB
ejpam-4716	386	7	sciences	science	NOUN
ejpam-4716	386	8	,	,	PUNCT
ejpam-4716	386	9	5:17–23	5:17–23	NUM
ejpam-4716	386	10	,	,	PUNCT
ejpam-4716	386	11	2018	2018	NUM
ejpam-4716	386	12	.	.	PUNCT
ejpam-4716	387	1	[	[	X
ejpam-4716	387	2	2	2	NUM
ejpam-4716	387	3	]	]	SYM
ejpam-4716	387	4	s	s	PART
ejpam-4716	387	5	antipova	antipova	PROPN
ejpam-4716	387	6	.	.	PUNCT
ejpam-4716	387	7	mathematical	mathematical	ADJ
ejpam-4716	387	8	modeling	modeling	NOUN
ejpam-4716	387	9	of	of	ADP
ejpam-4716	387	10	competition	competition	NOUN
ejpam-4716	387	11	two	two	NUM
ejpam-4716	387	12	ideologies	ideology	NOUN
ejpam-4716	387	13	with	with	ADP
ejpam-4716	387	14	internal	internal	ADJ
ejpam-4716	387	15	conflicts	conflict	NOUN
ejpam-4716	387	16	.	.	PUNCT
ejpam-4716	388	1	bulletin	bulletin	NOUN
ejpam-4716	388	2	of	of	ADP
ejpam-4716	388	3	sib	sib	PROPN
ejpam-4716	388	4	guti	guti	PROPN
ejpam-4716	388	5	,	,	PUNCT
ejpam-4716	388	6	4:27–42	4:27–42	NUM
ejpam-4716	388	7	,	,	PUNCT
ejpam-4716	388	8	2022	2022	NUM
ejpam-4716	388	9	.	.	PUNCT
ejpam-4716	389	1	[	[	X
ejpam-4716	389	2	3	3	NUM
ejpam-4716	389	3	]	]	X
ejpam-4716	389	4	r	r	NOUN
ejpam-4716	389	5	bhattacharyya	bhattacharyya	ADJ
ejpam-4716	389	6	and	and	CCONJ
ejpam-4716	389	7	b	b	NOUN
ejpam-4716	389	8	mukhopadhyay	mukhopadhyay	NOUN
ejpam-4716	389	9	.	.	PUNCT
ejpam-4716	390	1	spatial	spatial	ADJ
ejpam-4716	390	2	dynamics	dynamic	NOUN
ejpam-4716	390	3	of	of	ADP
ejpam-4716	390	4	nonlinear	nonlinear	ADJ
ejpam-4716	390	5	prey	prey	NOUN
ejpam-4716	390	6	-	-	PUNCT
ejpam-4716	390	7	predator	predator	NOUN
ejpam-4716	390	8	models	model	NOUN
ejpam-4716	390	9	with	with	ADP
ejpam-4716	390	10	pry	pry	NOUN
ejpam-4716	390	11	migration	migration	NOUN
ejpam-4716	390	12	and	and	CCONJ
ejpam-4716	390	13	predator	predator	NOUN
ejpam-4716	390	14	switching	switching	NOUN
ejpam-4716	390	15	.	.	PUNCT
ejpam-4716	391	1	ecological	ecological	ADJ
ejpam-4716	391	2	complexity	complexity	NOUN
ejpam-4716	391	3	,	,	PUNCT
ejpam-4716	391	4	3:160–169	3:160–169	NUM
ejpam-4716	391	5	,	,	PUNCT
ejpam-4716	391	6	2006	2006	NUM
ejpam-4716	391	7	.	.	PUNCT
ejpam-4716	392	1	references	reference	NOUN
ejpam-4716	392	2	918	918	NUM
ejpam-4716	393	1	[	[	X
ejpam-4716	393	2	4	4	NUM
ejpam-4716	393	3	]	]	X
ejpam-4716	393	4	a	a	DET
ejpam-4716	393	5	chatterjee	chatterjee	NOUN
ejpam-4716	393	6	and	and	CCONJ
ejpam-4716	393	7	s	s	NOUN
ejpam-4716	393	8	pal	pal	NOUN
ejpam-4716	393	9	.	.	PUNCT
ejpam-4716	394	1	switching	switch	VERB
ejpam-4716	394	2	effects	effect	NOUN
ejpam-4716	394	3	driven	drive	VERB
ejpam-4716	394	4	by	by	ADP
ejpam-4716	394	5	predation	predation	NOUN
ejpam-4716	394	6	on	on	ADP
ejpam-4716	394	7	diffusive	diffusive	ADJ
ejpam-4716	394	8	predator	predator	NOUN
ejpam-4716	394	9	prey	prey	NOUN
ejpam-4716	394	10	system	system	NOUN
ejpam-4716	394	11	.	.	PUNCT
ejpam-4716	395	1	applications	application	NOUN
ejpam-4716	395	2	and	and	CCONJ
ejpam-4716	395	3	applied	apply	VERB
ejpam-4716	395	4	mathematics	mathematic	NOUN
ejpam-4716	395	5	:	:	PUNCT
ejpam-4716	395	6	an	an	DET
ejpam-4716	395	7	international	international	ADJ
ejpam-4716	395	8	journal	journal	NOUN
ejpam-4716	395	9	,	,	PUNCT
ejpam-4716	395	10	16:682–704	16:682–704	NUM
ejpam-4716	395	11	,	,	PUNCT
ejpam-4716	395	12	2021	2021	NUM
ejpam-4716	395	13	.	.	PUNCT
ejpam-4716	396	1	[	[	X
ejpam-4716	396	2	5	5	NUM
ejpam-4716	396	3	]	]	PUNCT
ejpam-4716	396	4	a	a	DET
ejpam-4716	396	5	g	g	PROPN
ejpam-4716	396	6	farhan	farhan	NOUN
ejpam-4716	396	7	.	.	PUNCT
ejpam-4716	397	1	study	study	NOUN
ejpam-4716	397	2	of	of	ADP
ejpam-4716	397	3	a	a	DET
ejpam-4716	397	4	nonlinear	nonlinear	ADJ
ejpam-4716	397	5	model	model	NOUN
ejpam-4716	397	6	for	for	ADP
ejpam-4716	397	7	two	two	NUM
ejpam-4716	397	8	prey	prey	NOUN
ejpam-4716	397	9	and	and	CCONJ
ejpam-4716	397	10	two	two	NUM
ejpam-4716	397	11	predators	predator	NOUN
ejpam-4716	397	12	species	specie	NOUN
ejpam-4716	397	13	.	.	PUNCT
ejpam-4716	398	1	journal	journal	NOUN
ejpam-4716	398	2	of	of	ADP
ejpam-4716	398	3	the	the	DET
ejpam-4716	398	4	college	college	NOUN
ejpam-4716	398	5	of	of	ADP
ejpam-4716	398	6	basic	basic	ADJ
ejpam-4716	398	7	education	education	NOUN
ejpam-4716	398	8	,	,	PUNCT
ejpam-4716	398	9	mustansiriyah	mustansiriyah	NOUN
ejpam-4716	398	10	university	university	NOUN
ejpam-4716	398	11	,	,	PUNCT
ejpam-4716	398	12	100:73–86	100:73–86	NUM
ejpam-4716	398	13	,	,	PUNCT
ejpam-4716	398	14	2018	2018	NUM
ejpam-4716	398	15	.	.	PUNCT
ejpam-4716	399	1	[	[	X
ejpam-4716	399	2	6	6	NUM
ejpam-4716	399	3	]	]	PUNCT
ejpam-4716	399	4	a	a	DET
ejpam-4716	399	5	g	g	PROPN
ejpam-4716	399	6	farhan	farhan	PROPN
ejpam-4716	399	7	.	.	PUNCT
ejpam-4716	400	1	lotka	lotka	PROPN
ejpam-4716	400	2	-	-	PUNCT
ejpam-4716	400	3	volterra	volterra	PROPN
ejpam-4716	400	4	model	model	NOUN
ejpam-4716	400	5	with	with	ADP
ejpam-4716	400	6	prey	prey	NOUN
ejpam-4716	400	7	-	-	PUNCT
ejpam-4716	400	8	predators	predator	NOUN
ejpam-4716	400	9	food	food	NOUN
ejpam-4716	400	10	chain	chain	NOUN
ejpam-4716	400	11	.	.	PUNCT
ejpam-4716	401	1	iraqi	iraqi	ADJ
ejpam-4716	401	2	journal	journal	PROPN
ejpam-4716	401	3	of	of	ADP
ejpam-4716	401	4	science	science	NOUN
ejpam-4716	401	5	,	,	PUNCT
ejpam-4716	401	6	0:56–63	0:56–63	NUM
ejpam-4716	401	7	,	,	PUNCT
ejpam-4716	401	8	2020	2020	NUM
ejpam-4716	401	9	.	.	PUNCT
ejpam-4716	402	1	[	[	X
ejpam-4716	402	2	7	7	X
ejpam-4716	402	3	]	]	X
ejpam-4716	402	4	a	a	DET
ejpam-4716	402	5	g	g	NOUN
ejpam-4716	402	6	farhan	farhan	NOUN
ejpam-4716	402	7	.	.	PUNCT
ejpam-4716	403	1	on	on	ADP
ejpam-4716	403	2	the	the	DET
ejpam-4716	403	3	mathematical	mathematical	ADJ
ejpam-4716	403	4	model	model	NOUN
ejpam-4716	403	5	of	of	ADP
ejpam-4716	403	6	two	two	NUM
ejpam-4716	403	7	-	-	PUNCT
ejpam-4716	403	8	prey	prey	NOUN
ejpam-4716	403	9	and	and	CCONJ
ejpam-4716	403	10	two	two	NUM
ejpam-4716	403	11	-	-	PUNCT
ejpam-4716	403	12	predator	predator	NOUN
ejpam-4716	403	13	species	specie	NOUN
ejpam-4716	403	14	.	.	PUNCT
ejpam-4716	404	1	iraqi	iraqi	ADJ
ejpam-4716	404	2	journal	journal	PROPN
ejpam-4716	404	3	of	of	ADP
ejpam-4716	404	4	science	science	NOUN
ejpam-4716	404	5	,	,	PUNCT
ejpam-4716	404	6	3:608–619	3:608–619	NUM
ejpam-4716	404	7	,	,	PUNCT
ejpam-4716	404	8	2020	2020	NUM
ejpam-4716	404	9	.	.	PUNCT
ejpam-4716	405	1	[	[	X
ejpam-4716	405	2	8	8	NUM
ejpam-4716	405	3	]	]	X
ejpam-4716	405	4	a	a	DET
ejpam-4716	405	5	g	g	NOUN
ejpam-4716	405	6	farhan	farhan	NOUN
ejpam-4716	405	7	and	and	CCONJ
ejpam-4716	405	8	m	m	VERB
ejpam-4716	405	9	a	a	DET
ejpam-4716	405	10	rasheed	rasheed	NOUN
ejpam-4716	405	11	.	.	PUNCT
ejpam-4716	406	1	on	on	ADP
ejpam-4716	406	2	dynamics	dynamic	NOUN
ejpam-4716	406	3	of	of	ADP
ejpam-4716	406	4	nonlinear	nonlinear	ADJ
ejpam-4716	406	5	prey	prey	NOUN
ejpam-4716	406	6	–	–	PUNCT
ejpam-4716	406	7	predator	predator	NOUN
ejpam-4716	406	8	model	model	NOUN
ejpam-4716	406	9	involving	involve	VERB
ejpam-4716	406	10	group	group	NOUN
ejpam-4716	406	11	defense	defense	NOUN
ejpam-4716	406	12	.	.	PUNCT
ejpam-4716	407	1	j.	j.	PROPN
ejpam-4716	407	2	of	of	ADP
ejpam-4716	407	3	college	college	PROPN
ejpam-4716	407	4	of	of	ADP
ejpam-4716	407	5	education	education	NOUN
ejpam-4716	407	6	,	,	PUNCT
ejpam-4716	407	7	mustansiriyah	mustansiriyah	NOUN
ejpam-4716	407	8	university	university	NOUN
ejpam-4716	407	9	,	,	PUNCT
ejpam-4716	407	10	5:249	5:249	NUM
ejpam-4716	407	11	–	–	PUNCT
ejpam-4716	407	12	264	264	NUM
ejpam-4716	407	13	,	,	PUNCT
ejpam-4716	407	14	2014	2014	NUM
ejpam-4716	407	15	.	.	PUNCT
ejpam-4716	408	1	[	[	X
ejpam-4716	408	2	9	9	NUM
ejpam-4716	408	3	]	]	PUNCT
ejpam-4716	408	4	p.	p.	NOUN
ejpam-4716	408	5	fisher	fisher	PROPN
ejpam-4716	408	6	.	.	PUNCT
ejpam-4716	409	1	sur	sur	PROPN
ejpam-4716	409	2	legilibre	legilibre	PROPN
ejpam-4716	409	3	de	de	X
ejpam-4716	409	4	faunas	faunas	PROPN
ejpam-4716	409	5	:	:	PUNCT
ejpam-4716	409	6	interactions	interaction	NOUN
ejpam-4716	409	7	des	des	PROPN
ejpam-4716	409	8	moules	moule	NOUN
ejpam-4716	409	9	,	,	PUNCT
ejpam-4716	409	10	des	des	X
ejpam-4716	409	11	poupreset	poupreset	PROPN
ejpam-4716	409	12	des	des	PROPN
ejpam-4716	409	13	cripedaed	cripedaed	PROPN
ejpam-4716	409	14	.	.	PUNCT
ejpam-4716	410	1	c.r	c.r	PROPN
ejpam-4716	410	2	.	.	PROPN
ejpam-4716	410	3	soc	soc	PROPN
ejpam-4716	410	4	.	.	PUNCT
ejpam-4716	411	1	biologeogr	biologeogr	PROPN
ejpam-4716	411	2	,	,	PUNCT
ejpam-4716	411	3	92:47–48	92:47–48	NUM
ejpam-4716	411	4	,	,	PUNCT
ejpam-4716	411	5	1934	1934	NUM
ejpam-4716	411	6	.	.	PUNCT
ejpam-4716	412	1	[	[	X
ejpam-4716	412	2	10	10	NUM
ejpam-4716	412	3	]	]	SYM
ejpam-4716	412	4	v	v	ADP
ejpam-4716	412	5	hadžiabdić	hadžiabdić	PROPN
ejpam-4716	412	6	,	,	PUNCT
ejpam-4716	412	7	mmehuljić	mmehuljić	NOUN
ejpam-4716	412	8	,	,	PUNCT
ejpam-4716	412	9	and	and	CCONJ
ejpam-4716	412	10	j	j	PROPN
ejpam-4716	412	11	bektešević.	bektešević.	PROPN
ejpam-4716	412	12	lotka	lotka	PROPN
ejpam-4716	412	13	-	-	PUNCT
ejpam-4716	412	14	volterra	volterra	PROPN
ejpam-4716	412	15	model	model	NOUN
ejpam-4716	412	16	with	with	ADP
ejpam-4716	412	17	two	two	NUM
ejpam-4716	412	18	predators	predator	NOUN
ejpam-4716	412	19	and	and	CCONJ
ejpam-4716	412	20	their	their	PRON
ejpam-4716	412	21	prey	prey	NOUN
ejpam-4716	412	22	.	.	PUNCT
ejpam-4716	413	1	tem	tem	PROPN
ejpam-4716	413	2	journal	journal	PROPN
ejpam-4716	413	3	,	,	PUNCT
ejpam-4716	413	4	6:132–136	6:132–136	NUM
ejpam-4716	413	5	,	,	PUNCT
ejpam-4716	413	6	2017	2017	NUM
ejpam-4716	413	7	.	.	PUNCT
ejpam-4716	414	1	[	[	X
ejpam-4716	414	2	11	11	NUM
ejpam-4716	414	3	]	]	X
ejpam-4716	414	4	c	c	PROPN
ejpam-4716	414	5	s	s	PART
ejpam-4716	414	6	holling	holle	VERB
ejpam-4716	414	7	.	.	PUNCT
ejpam-4716	415	1	principles	principle	NOUN
ejpam-4716	415	2	of	of	ADP
ejpam-4716	415	3	insect	insect	NOUN
ejpam-4716	415	4	predation	predation	NOUN
ejpam-4716	415	5	.	.	PUNCT
ejpam-4716	416	1	annual	annual	ADJ
ejpam-4716	416	2	review	review	NOUN
ejpam-4716	416	3	of	of	ADP
ejpam-4716	416	4	entomology	entomology	NOUN
ejpam-4716	416	5	,	,	PUNCT
ejpam-4716	416	6	6:163–182	6:163–182	NOUN
ejpam-4716	416	7	,	,	PUNCT
ejpam-4716	416	8	1961	1961	NUM
ejpam-4716	416	9	.	.	PUNCT
ejpam-4716	417	1	[	[	X
ejpam-4716	417	2	12	12	NUM
ejpam-4716	417	3	]	]	SYM
ejpam-4716	417	4	s	s	PART
ejpam-4716	417	5	l	l	NOUN
ejpam-4716	417	6	jianhua	jianhua	NOUN
ejpam-4716	417	7	and	and	CCONJ
ejpam-4716	417	8	w	w	PROPN
ejpam-4716	417	9	h	h	PROPN
ejpam-4716	417	10	ni	ni	PROPN
ejpam-4716	417	11	.	.	PROPN
ejpam-4716	417	12	steady	steady	ADJ
ejpam-4716	417	13	-	-	PUNCT
ejpam-4716	417	14	state	state	NOUN
ejpam-4716	417	15	bifurcation	bifurcation	NOUN
ejpam-4716	417	16	and	and	CCONJ
ejpam-4716	417	17	hopf	hopf	ADJ
ejpam-4716	417	18	bifurcation	bifurcation	NOUN
ejpam-4716	417	19	for	for	ADP
ejpam-4716	417	20	a	a	DET
ejpam-4716	417	21	diffusive	diffusive	ADJ
ejpam-4716	417	22	leslie	leslie	PROPN
ejpam-4716	417	23	–	–	PUNCT
ejpam-4716	417	24	gower	gower	PROPN
ejpam-4716	417	25	predator	predator	PROPN
ejpam-4716	417	26	–	–	PUNCT
ejpam-4716	417	27	prey	prey	PROPN
ejpam-4716	417	28	model	model	NOUN
ejpam-4716	417	29	.	.	PUNCT
ejpam-4716	418	1	computers	computer	NOUN
ejpam-4716	418	2	and	and	CCONJ
ejpam-4716	418	3	mathematics	mathematic	NOUN
ejpam-4716	418	4	with	with	ADP
ejpam-4716	418	5	applications	application	NOUN
ejpam-4716	418	6	,	,	PUNCT
ejpam-4716	418	7	70:3043–3056	70:3043–3056	NUM
ejpam-4716	418	8	,	,	PUNCT
ejpam-4716	418	9	2015	2015	NUM
ejpam-4716	418	10	.	.	PUNCT
ejpam-4716	419	1	[	[	X
ejpam-4716	419	2	13	13	NUM
ejpam-4716	419	3	]	]	SYM
ejpam-4716	419	4	j	j	PROPN
ejpam-4716	419	5	h	h	PROPN
ejpam-4716	419	6	lawton	lawton	PROPN
ejpam-4716	419	7	,	,	PUNCT
ejpam-4716	419	8	j	j	PROPN
ejpam-4716	419	9	r	r	PROPN
ejpam-4716	419	10	beddington	beddington	NOUN
ejpam-4716	419	11	,	,	PUNCT
ejpam-4716	419	12	and	and	CCONJ
ejpam-4716	419	13	r	r	NOUN
ejpam-4716	419	14	bonser	bonser	NOUN
ejpam-4716	419	15	.	.	PUNCT
ejpam-4716	420	1	switching	switch	VERB
ejpam-4716	420	2	in	in	ADP
ejpam-4716	420	3	invertebrate	invertebrate	NOUN
ejpam-4716	420	4	predators	predator	NOUN
ejpam-4716	420	5	.	.	PUNCT
ejpam-4716	421	1	springer	springer	PROPN
ejpam-4716	421	2	us	us	PROPN
ejpam-4716	421	3	,	,	PUNCT
ejpam-4716	421	4	boston	boston	PROPN
ejpam-4716	421	5	,	,	PUNCT
ejpam-4716	421	6	ma	ma	PROPN
ejpam-4716	421	7	,	,	PUNCT
ejpam-4716	421	8	1974	1974	NUM
ejpam-4716	421	9	.	.	PUNCT
ejpam-4716	422	1	[	[	X
ejpam-4716	422	2	14	14	NUM
ejpam-4716	422	3	]	]	X
ejpam-4716	422	4	j	j	PROPN
ejpam-4716	422	5	l	l	NOUN
ejpam-4716	422	6	moiola	moiola	PROPN
ejpam-4716	422	7	and	and	CCONJ
ejpam-4716	422	8	g	g	PROPN
ejpam-4716	422	9	chen	chen	PROPN
ejpam-4716	422	10	.	.	PUNCT
ejpam-4716	423	1	hopf	hopf	ADJ
ejpam-4716	423	2	bifurcation	bifurcation	NOUN
ejpam-4716	423	3	analysis	analysis	NOUN
ejpam-4716	423	4	:	:	PUNCT
ejpam-4716	423	5	a	a	DET
ejpam-4716	423	6	frequency	frequency	NOUN
ejpam-4716	423	7	domain	domain	NOUN
ejpam-4716	423	8	approach	approach	NOUN
ejpam-4716	423	9	.	.	PUNCT
ejpam-4716	424	1	world	world	NOUN
ejpam-4716	424	2	scientific	scientific	ADJ
ejpam-4716	424	3	,	,	PUNCT
ejpam-4716	424	4	1996	1996	NUM
ejpam-4716	424	5	.	.	PUNCT
ejpam-4716	425	1	[	[	X
ejpam-4716	425	2	15	15	NUM
ejpam-4716	425	3	]	]	X
ejpam-4716	425	4	s	s	VERB
ejpam-4716	425	5	rahman	rahman	PROPN
ejpam-4716	425	6	,	,	PUNCT
ejpam-4716	425	7	s	s	VERB
ejpam-4716	425	8	islam	islam	PROPN
ejpam-4716	425	9	,	,	PUNCT
ejpam-4716	425	10	and	and	CCONJ
ejpam-4716	425	11	s	s	VERB
ejpam-4716	425	12	sarwardi	sarwardi	PROPN
ejpam-4716	425	13	.	.	PUNCT
ejpam-4716	426	1	effects	effect	NOUN
ejpam-4716	426	2	of	of	ADP
ejpam-4716	426	3	prey	prey	NOUN
ejpam-4716	426	4	refuge	refuge	NOUN
ejpam-4716	426	5	with	with	ADP
ejpam-4716	426	6	holling	holle	VERB
ejpam-4716	426	7	type	type	NOUN
ejpam-4716	426	8	iv	iv	NUM
ejpam-4716	426	9	functional	functional	ADJ
ejpam-4716	426	10	response	response	NOUN
ejpam-4716	426	11	dependent	dependent	ADJ
ejpam-4716	426	12	prey	prey	NOUN
ejpam-4716	426	13	predator	predator	NOUN
ejpam-4716	426	14	model	model	NOUN
ejpam-4716	426	15	.	.	PUNCT
ejpam-4716	427	1	international	international	ADJ
ejpam-4716	427	2	journal	journal	NOUN
ejpam-4716	427	3	of	of	ADP
ejpam-4716	427	4	modelling	modelling	NOUN
ejpam-4716	427	5	and	and	CCONJ
ejpam-4716	427	6	simulation	simulation	NOUN
ejpam-4716	427	7	,	,	PUNCT
ejpam-4716	427	8	0:1–19	0:1–19	NUM
ejpam-4716	427	9	,	,	PUNCT
ejpam-4716	427	10	2023	2023	NUM
ejpam-4716	427	11	.	.	PUNCT
ejpam-4716	428	1	[	[	X
ejpam-4716	428	2	16	16	NUM
ejpam-4716	428	3	]	]	X
ejpam-4716	428	4	m	m	VERB
ejpam-4716	428	5	tansky	tansky	ADJ
ejpam-4716	428	6	.	.	PUNCT
ejpam-4716	429	1	switching	switch	VERB
ejpam-4716	429	2	effects	effect	NOUN
ejpam-4716	429	3	in	in	ADP
ejpam-4716	429	4	prey	prey	NOUN
ejpam-4716	429	5	–	–	PUNCT
ejpam-4716	429	6	predator	predator	NOUN
ejpam-4716	429	7	system	system	NOUN
ejpam-4716	429	8	.	.	PUNCT
ejpam-4716	430	1	j.	j.	PROPN
ejpam-4716	430	2	theor	theor	PROPN
ejpam-4716	430	3	.	.	PUNCT
ejpam-4716	431	1	biol	biol	PROPN
ejpam-4716	431	2	,	,	PUNCT
ejpam-4716	431	3	70:263–271	70:263–271	NOUN
ejpam-4716	431	4	,	,	PUNCT
ejpam-4716	431	5	1978	1978	NUM
ejpam-4716	431	6	.	.	PUNCT