id	sid	tid	token	lemma	pos
iajs-3717	1	1	361	361	NUM
iajs-3717	1	2	©	©	PROPN
iajs-3717	1	3	2025	2025	NUM
iajs-3717	1	4	the	the	DET
iajs-3717	1	5	author(s	author(s	NOUN
iajs-3717	1	6	)	)	PUNCT
iajs-3717	1	7	.	.	PUNCT
iajs-3717	2	1	published	publish	VERB
iajs-3717	2	2	by	by	ADP
iajs-3717	2	3	college	college	NOUN
iajs-3717	2	4	of	of	ADP
iajs-3717	2	5	education	education	NOUN
iajs-3717	2	6	for	for	ADP
iajs-3717	2	7	pure	pure	ADJ
iajs-3717	2	8	science	science	NOUN
iajs-3717	2	9	(	(	PUNCT
iajs-3717	2	10	ibn	ibn	PROPN
iajs-3717	2	11	al	al	PROPN
iajs-3717	2	12	-	-	PUNCT
iajs-3717	2	13	haitham	haitham	PROPN
iajs-3717	2	14	)	)	PUNCT
iajs-3717	2	15	,	,	PUNCT
iajs-3717	2	16	university	university	NOUN
iajs-3717	2	17	of	of	ADP
iajs-3717	2	18	baghdad	baghdad	PROPN
iajs-3717	2	19	.	.	PUNCT
iajs-3717	3	1	this	this	PRON
iajs-3717	3	2	is	be	AUX
iajs-3717	3	3	an	an	DET
iajs-3717	3	4	open	open	ADJ
iajs-3717	3	5	-	-	PUNCT
iajs-3717	3	6	access	access	NOUN
iajs-3717	3	7	article	article	NOUN
iajs-3717	3	8	distributed	distribute	VERB
iajs-3717	3	9	under	under	ADP
iajs-3717	3	10	the	the	DET
iajs-3717	3	11	terms	term	NOUN
iajs-3717	3	12	of	of	ADP
iajs-3717	3	13	the	the	DET
iajs-3717	3	14	creative	creative	ADJ
iajs-3717	3	15	commons	common	NOUN
iajs-3717	3	16	attribution	attribution	NOUN
iajs-3717	3	17	4.0	4.0	NUM
iajs-3717	3	18	international	international	ADJ
iajs-3717	3	19	license	license	NOUN
iajs-3717	3	20	the	the	DET
iajs-3717	3	21	time	time	NOUN
iajs-3717	3	22	delay	delay	NOUN
iajs-3717	3	23	effect	effect	NOUN
iajs-3717	3	24	and	and	CCONJ
iajs-3717	3	25	harvesting	harvesting	NOUN
iajs-3717	3	26	on	on	ADP
iajs-3717	3	27	the	the	DET
iajs-3717	3	28	predator	predator	NOUN
iajs-3717	3	29	-	-	PUNCT
iajs-3717	3	30	prey	prey	NOUN
iajs-3717	3	31	:	:	PUNCT
iajs-3717	3	32	analysis	analysis	NOUN
iajs-3717	3	33	and	and	CCONJ
iajs-3717	3	34	simulation	simulation	NOUN
iajs-3717	3	35	nidhal	nidhal	PROPN
iajs-3717	3	36	faisal	faisal	PROPN
iajs-3717	3	37	ali	ali	PROPN
iajs-3717	3	38	1,4	1,4	PROPN
iajs-3717	3	39	*	*	PROPN
iajs-3717	3	40	,	,	PUNCT
iajs-3717	3	41	hassan	hassan	PROPN
iajs-3717	3	42	f.	f.	PROPN
iajs-3717	3	43	al	al	PROPN
iajs-3717	3	44	-	-	PUNCT
iajs-3717	3	45	husseiny	husseiny	ADJ
iajs-3717	3	46	2	2	NUM
iajs-3717	3	47	,	,	PUNCT
iajs-3717	3	48	and	and	CCONJ
iajs-3717	3	49	yassine	yassine	PROPN
iajs-3717	3	50	sabbar	sabbar	NOUN
iajs-3717	3	51	3	3	PROPN
iajs-3717	3	52	1department	1department	NUM
iajs-3717	3	53	of	of	ADP
iajs-3717	3	54	mathematics	mathematic	NOUN
iajs-3717	3	55	,	,	PUNCT
iajs-3717	3	56	college	college	NOUN
iajs-3717	3	57	of	of	ADP
iajs-3717	3	58	science	science	NOUN
iajs-3717	3	59	,	,	PUNCT
iajs-3717	3	60	university	university	NOUN
iajs-3717	3	61	of	of	ADP
iajs-3717	3	62	baghdad	baghdad	PROPN
iajs-3717	3	63	,	,	PUNCT
iajs-3717	3	64	baghdad	baghdad	PROPN
iajs-3717	3	65	,	,	PUNCT
iajs-3717	3	66	iraq	iraq	PROPN
iajs-3717	3	67	.	.	PUNCT
iajs-3717	4	1	2department	2department	NUM
iajs-3717	4	2	of	of	ADP
iajs-3717	4	3	mathematics	mathematic	NOUN
iajs-3717	4	4	,	,	PUNCT
iajs-3717	4	5	college	college	NOUN
iajs-3717	4	6	of	of	ADP
iajs-3717	4	7	science	science	NOUN
iajs-3717	4	8	,	,	PUNCT
iajs-3717	4	9	university	university	NOUN
iajs-3717	4	10	of	of	ADP
iajs-3717	4	11	baghdad	baghdad	PROPN
iajs-3717	4	12	,	,	PUNCT
iajs-3717	4	13	baghdad	baghdad	PROPN
iajs-3717	4	14	,	,	PUNCT
iajs-3717	4	15	iraq	iraq	PROPN
iajs-3717	4	16	.	.	PUNCT
iajs-3717	5	1	3mais	3mais	NUM
iajs-3717	5	2	laboratory	laboratory	NOUN
iajs-3717	5	3	,	,	PUNCT
iajs-3717	5	4	mamcs	mamcs	NOUN
iajs-3717	5	5	group	group	NOUN
iajs-3717	5	6	,	,	PUNCT
iajs-3717	5	7	fst	fst	PROPN
iajs-3717	5	8	errachidia	errachidia	PROPN
iajs-3717	5	9	,	,	PUNCT
iajs-3717	5	10	moulay	moulay	PROPN
iajs-3717	5	11	ismail	ismail	PROPN
iajs-3717	5	12	university	university	PROPN
iajs-3717	5	13	of	of	ADP
iajs-3717	5	14	meknes	meknes	PROPN
iajs-3717	5	15	,	,	PUNCT
iajs-3717	5	16	morocco	morocco	PROPN
iajs-3717	5	17	.	.	PUNCT
iajs-3717	6	1	4department	4department	NUM
iajs-3717	6	2	of	of	ADP
iajs-3717	6	3	electrical	electrical	ADJ
iajs-3717	6	4	engineering	engineering	NOUN
iajs-3717	6	5	techniques	technique	NOUN
iajs-3717	6	6	,	,	PUNCT
iajs-3717	6	7	college	college	NOUN
iajs-3717	6	8	of	of	ADP
iajs-3717	6	9	electrical	electrical	ADJ
iajs-3717	6	10	engineering	engineering	NOUN
iajs-3717	6	11	technical	technical	ADJ
iajs-3717	6	12	,	,	PUNCT
iajs-3717	6	13	university	university	NOUN
iajs-3717	6	14	middle	middle	NOUN
iajs-3717	6	15	technical	technical	PROPN
iajs-3717	6	16	,	,	PUNCT
iajs-3717	6	17	baghdad	baghdad	PROPN
iajs-3717	6	18	,	,	PUNCT
iajs-3717	6	19	iraq	iraq	PROPN
iajs-3717	6	20	.	.	PUNCT
iajs-3717	7	1	*	*	PUNCT
iajs-3717	7	2	corresponding	correspond	VERB
iajs-3717	7	3	author	author	NOUN
iajs-3717	7	4	.	.	PUNCT
iajs-3717	7	5	received:14	received:14	X
iajs-3717	8	1	september	september	PROPN
iajs-3717	8	2	2023	2023	NUM
iajs-3717	8	3	accepted:12	accepted:12	X
iajs-3717	8	4	december	december	PROPN
iajs-3717	8	5	2023	2023	NUM
iajs-3717	8	6	published	publish	VERB
iajs-3717	8	7	:	:	PUNCT
iajs-3717	8	8	20	20	NUM
iajs-3717	8	9	april	april	PROPN
iajs-3717	8	10	2025	2025	NUM
iajs-3717	8	11	doi.org/10.30526/38.2.3717	doi.org/10.30526/38.2.3717	NOUN
iajs-3717	8	12	abstract	abstract	PROPN
iajs-3717	8	13	mathematical	mathematical	ADJ
iajs-3717	8	14	modeling	modeling	NOUN
iajs-3717	8	15	based	base	VERB
iajs-3717	8	16	on	on	ADP
iajs-3717	8	17	time	time	NOUN
iajs-3717	8	18	-	-	PUNCT
iajs-3717	8	19	delay	delay	NOUN
iajs-3717	8	20	differential	differential	ADJ
iajs-3717	8	21	equations	equation	NOUN
iajs-3717	8	22	is	be	AUX
iajs-3717	8	23	an	an	DET
iajs-3717	8	24	important	important	ADJ
iajs-3717	8	25	tool	tool	NOUN
iajs-3717	8	26	to	to	PART
iajs-3717	8	27	understand	understand	VERB
iajs-3717	8	28	the	the	DET
iajs-3717	8	29	effects	effect	NOUN
iajs-3717	8	30	of	of	ADP
iajs-3717	8	31	delays	delay	NOUN
iajs-3717	8	32	in	in	ADP
iajs-3717	8	33	biological	biological	ADJ
iajs-3717	8	34	systems	system	NOUN
iajs-3717	8	35	and	and	CCONJ
iajs-3717	8	36	to	to	PART
iajs-3717	8	37	analyze	analyze	VERB
iajs-3717	8	38	how	how	SCONJ
iajs-3717	8	39	they	they	PRON
iajs-3717	8	40	influence	influence	VERB
iajs-3717	8	41	the	the	DET
iajs-3717	8	42	dynamics	dynamic	NOUN
iajs-3717	8	43	of	of	ADP
iajs-3717	8	44	the	the	DET
iajs-3717	8	45	asymptotic	asymptotic	ADJ
iajs-3717	8	46	behavior	behavior	NOUN
iajs-3717	8	47	of	of	ADP
iajs-3717	8	48	these	these	DET
iajs-3717	8	49	systems	system	NOUN
iajs-3717	8	50	.	.	PUNCT
iajs-3717	9	1	the	the	DET
iajs-3717	9	2	prey	prey	NOUN
iajs-3717	9	3	-	-	PUNCT
iajs-3717	9	4	predator	predator	NOUN
iajs-3717	9	5	model	model	NOUN
iajs-3717	9	6	described	describe	VERB
iajs-3717	9	7	in	in	ADP
iajs-3717	9	8	this	this	DET
iajs-3717	9	9	paper	paper	NOUN
iajs-3717	9	10	includes	include	VERB
iajs-3717	9	11	diseases	disease	NOUN
iajs-3717	9	12	in	in	ADP
iajs-3717	9	13	the	the	DET
iajs-3717	9	14	prey	prey	PROPN
iajs-3717	9	15	species	specie	NOUN
iajs-3717	9	16	,	,	PUNCT
iajs-3717	9	17	harvests	harvest	NOUN
iajs-3717	9	18	in	in	ADP
iajs-3717	9	19	each	each	DET
iajs-3717	9	20	population	population	NOUN
iajs-3717	9	21	,	,	PUNCT
iajs-3717	9	22	and	and	CCONJ
iajs-3717	9	23	time	time	NOUN
iajs-3717	9	24	lags	lag	VERB
iajs-3717	9	25	in	in	ADP
iajs-3717	9	26	predation	predation	NOUN
iajs-3717	9	27	and	and	CCONJ
iajs-3717	9	28	gestation	gestation	NOUN
iajs-3717	9	29	of	of	ADP
iajs-3717	9	30	the	the	DET
iajs-3717	9	31	predator	predator	NOUN
iajs-3717	9	32	.	.	PUNCT
iajs-3717	10	1	the	the	DET
iajs-3717	10	2	solutions	solution	NOUN
iajs-3717	10	3	of	of	ADP
iajs-3717	10	4	the	the	DET
iajs-3717	10	5	model	model	NOUN
iajs-3717	10	6	are	be	AUX
iajs-3717	10	7	positive	positive	ADJ
iajs-3717	10	8	and	and	CCONJ
iajs-3717	10	9	bounded	bound	VERB
iajs-3717	10	10	for	for	ADP
iajs-3717	10	11	all	all	DET
iajs-3717	10	12	times	time	NOUN
iajs-3717	10	13	within	within	ADP
iajs-3717	10	14	a	a	DET
iajs-3717	10	15	realistic	realistic	ADJ
iajs-3717	10	16	region	region	NOUN
iajs-3717	10	17	.	.	PUNCT
iajs-3717	11	1	the	the	DET
iajs-3717	11	2	existence	existence	NOUN
iajs-3717	11	3	of	of	ADP
iajs-3717	11	4	all	all	DET
iajs-3717	11	5	fixed	fix	VERB
iajs-3717	11	6	points	point	NOUN
iajs-3717	11	7	has	have	AUX
iajs-3717	11	8	been	be	AUX
iajs-3717	11	9	proven	prove	VERB
iajs-3717	11	10	.	.	PUNCT
iajs-3717	12	1	when	when	SCONJ
iajs-3717	12	2	a	a	DET
iajs-3717	12	3	time	time	NOUN
iajs-3717	12	4	lag	lag	NOUN
iajs-3717	12	5	is	be	AUX
iajs-3717	12	6	present	present	ADJ
iajs-3717	12	7	,	,	PUNCT
iajs-3717	12	8	the	the	DET
iajs-3717	12	9	essential	essential	ADJ
iajs-3717	12	10	conditions	condition	NOUN
iajs-3717	12	11	for	for	ADP
iajs-3717	12	12	the	the	DET
iajs-3717	12	13	local	local	ADJ
iajs-3717	12	14	stability	stability	NOUN
iajs-3717	12	15	of	of	ADP
iajs-3717	12	16	the	the	DET
iajs-3717	12	17	positive	positive	ADJ
iajs-3717	12	18	equilibrium	equilibrium	NOUN
iajs-3717	12	19	and	and	CCONJ
iajs-3717	12	20	the	the	DET
iajs-3717	12	21	occurrence	occurrence	NOUN
iajs-3717	12	22	of	of	ADP
iajs-3717	12	23	hopf	hopf	ADJ
iajs-3717	12	24	bifurcations	bifurcation	NOUN
iajs-3717	12	25	can	can	AUX
iajs-3717	12	26	be	be	AUX
iajs-3717	12	27	determined	determine	VERB
iajs-3717	12	28	by	by	ADP
iajs-3717	12	29	analyzing	analyze	VERB
iajs-3717	12	30	the	the	DET
iajs-3717	12	31	associated	associated	ADJ
iajs-3717	12	32	characteristic	characteristic	ADJ
iajs-3717	12	33	equation	equation	NOUN
iajs-3717	12	34	.	.	PUNCT
iajs-3717	13	1	the	the	DET
iajs-3717	13	2	characteristics	characteristic	NOUN
iajs-3717	13	3	of	of	ADP
iajs-3717	13	4	the	the	DET
iajs-3717	13	5	hopf	hopf	ADJ
iajs-3717	13	6	bifurcation	bifurcation	NOUN
iajs-3717	13	7	are	be	AUX
iajs-3717	13	8	determined	determine	VERB
iajs-3717	13	9	by	by	ADP
iajs-3717	13	10	applying	apply	VERB
iajs-3717	13	11	normal	normal	ADJ
iajs-3717	13	12	form	form	NOUN
iajs-3717	13	13	theory	theory	NOUN
iajs-3717	13	14	and	and	CCONJ
iajs-3717	13	15	the	the	DET
iajs-3717	13	16	central	central	ADJ
iajs-3717	13	17	manifold	manifold	ADJ
iajs-3717	13	18	theorem	theorem	NOUN
iajs-3717	13	19	.	.	PUNCT
iajs-3717	14	1	finally	finally	ADV
iajs-3717	14	2	,	,	PUNCT
iajs-3717	14	3	we	we	PRON
iajs-3717	14	4	use	use	VERB
iajs-3717	14	5	numerical	numerical	ADJ
iajs-3717	14	6	simulations	simulation	NOUN
iajs-3717	14	7	to	to	PART
iajs-3717	14	8	validate	validate	VERB
iajs-3717	14	9	our	our	PRON
iajs-3717	14	10	analytical	analytical	ADJ
iajs-3717	14	11	results	result	NOUN
iajs-3717	14	12	.	.	PUNCT
iajs-3717	15	1	a	a	DET
iajs-3717	15	2	hopf	hopf	ADJ
iajs-3717	15	3	bifurcation	bifurcation	NOUN
iajs-3717	15	4	in	in	ADP
iajs-3717	15	5	the	the	DET
iajs-3717	15	6	system	system	NOUN
iajs-3717	15	7	occurs	occur	VERB
iajs-3717	15	8	when	when	SCONJ
iajs-3717	15	9	the	the	DET
iajs-3717	15	10	delay	delay	NOUN
iajs-3717	15	11	exceeds	exceed	VERB
iajs-3717	15	12	a	a	DET
iajs-3717	15	13	certain	certain	ADJ
iajs-3717	15	14	threshold	threshold	NOUN
iajs-3717	15	15	.	.	PUNCT
iajs-3717	16	1	keywords	keyword	NOUN
iajs-3717	16	2	:	:	PUNCT
iajs-3717	16	3	harvest	harvest	NOUN
iajs-3717	16	4	,	,	PUNCT
iajs-3717	16	5	predator	predator	NOUN
iajs-3717	16	6	–	–	PUNCT
iajs-3717	16	7	prey	prey	NOUN
iajs-3717	16	8	,	,	PUNCT
iajs-3717	16	9	time	time	NOUN
iajs-3717	16	10	delay	delay	NOUN
iajs-3717	16	11	,	,	PUNCT
iajs-3717	16	12	stability	stability	NOUN
iajs-3717	16	13	,	,	PUNCT
iajs-3717	16	14	hopf	hopf	ADJ
iajs-3717	16	15	bifurcation	bifurcation	NOUN
iajs-3717	16	16	.	.	PUNCT
iajs-3717	17	1	1	1	X
iajs-3717	17	2	.	.	X
iajs-3717	17	3	introduction	introduction	NOUN
iajs-3717	17	4	the	the	DET
iajs-3717	17	5	dynamics	dynamic	NOUN
iajs-3717	17	6	of	of	ADP
iajs-3717	17	7	interacting	interact	VERB
iajs-3717	17	8	populations	population	NOUN
iajs-3717	17	9	are	be	AUX
iajs-3717	17	10	often	often	ADV
iajs-3717	17	11	studied	study	VERB
iajs-3717	17	12	using	use	VERB
iajs-3717	17	13	mathematical	mathematical	ADJ
iajs-3717	17	14	models	model	NOUN
iajs-3717	17	15	.	.	PUNCT
iajs-3717	18	1	mathematical	mathematical	ADJ
iajs-3717	18	2	models	model	NOUN
iajs-3717	18	3	have	have	AUX
iajs-3717	18	4	become	become	VERB
iajs-3717	18	5	essential	essential	ADJ
iajs-3717	18	6	tools	tool	NOUN
iajs-3717	18	7	to	to	PART
iajs-3717	18	8	understand	understand	VERB
iajs-3717	18	9	how	how	SCONJ
iajs-3717	18	10	diseases	disease	NOUN
iajs-3717	18	11	spread	spread	VERB
iajs-3717	18	12	and	and	CCONJ
iajs-3717	18	13	are	be	AUX
iajs-3717	18	14	controlled	control	VERB
iajs-3717	18	15	.	.	PUNCT
iajs-3717	19	1	these	these	DET
iajs-3717	19	2	models	model	NOUN
iajs-3717	19	3	,	,	PUNCT
iajs-3717	19	4	referred	refer	VERB
iajs-3717	19	5	to	to	ADP
iajs-3717	19	6	as	as	ADP
iajs-3717	19	7	"	"	PUNCT
iajs-3717	19	8	epidemiological	epidemiological	ADJ
iajs-3717	19	9	models	model	NOUN
iajs-3717	19	10	,	,	PUNCT
iajs-3717	19	11	"	"	PUNCT
iajs-3717	19	12	are	be	AUX
iajs-3717	19	13	employed	employ	VERB
iajs-3717	19	14	to	to	PART
iajs-3717	19	15	study	study	VERB
iajs-3717	19	16	disease	disease	NOUN
iajs-3717	19	17	transmission	transmission	NOUN
iajs-3717	19	18	and	and	CCONJ
iajs-3717	19	19	management	management	NOUN
iajs-3717	19	20	in	in	ADP
iajs-3717	19	21	human	human	ADJ
iajs-3717	19	22	or	or	CCONJ
iajs-3717	19	23	animal	animal	NOUN
iajs-3717	19	24	populations	population	NOUN
iajs-3717	19	25	.	.	PUNCT
iajs-3717	20	1	on	on	ADP
iajs-3717	20	2	the	the	DET
iajs-3717	20	3	other	other	ADJ
iajs-3717	20	4	hand	hand	NOUN
iajs-3717	20	5	,	,	PUNCT
iajs-3717	20	6	the	the	DET
iajs-3717	20	7	term	term	NOUN
iajs-3717	20	8	"	"	PUNCT
iajs-3717	20	9	ecological	ecological	ADJ
iajs-3717	20	10	model	model	NOUN
iajs-3717	20	11	"	"	PUNCT
iajs-3717	20	12	pertains	pertain	VERB
iajs-3717	20	13	to	to	ADP
iajs-3717	20	14	mathematical	mathematical	ADJ
iajs-3717	20	15	models	model	NOUN
iajs-3717	20	16	depicting	depict	VERB
iajs-3717	20	17	the	the	DET
iajs-3717	20	18	dynamic	dynamic	ADJ
iajs-3717	20	19	interactions	interaction	NOUN
iajs-3717	20	20	among	among	ADP
iajs-3717	20	21	species	specie	NOUN
iajs-3717	20	22	in	in	ADP
iajs-3717	20	23	ecological	ecological	ADJ
iajs-3717	20	24	systems	system	NOUN
iajs-3717	20	25	.	.	PUNCT
iajs-3717	21	1	in	in	ADP
iajs-3717	21	2	1925	1925	NUM
iajs-3717	21	3	and	and	CCONJ
iajs-3717	21	4	1926	1926	NUM
iajs-3717	21	5	,	,	PUNCT
iajs-3717	21	6	(	(	PUNCT
iajs-3717	21	7	1	1	NUM
iajs-3717	21	8	,	,	PUNCT
iajs-3717	21	9	2	2	NUM
iajs-3717	21	10	)	)	PUNCT
iajs-3717	21	11	independently	independently	ADV
iajs-3717	21	12	developed	develop	VERB
iajs-3717	21	13	mathematical	mathematical	ADJ
iajs-3717	21	14	models	model	NOUN
iajs-3717	21	15	within	within	ADP
iajs-3717	21	16	ecology	ecology	NOUN
iajs-3717	21	17	,	,	PUNCT
iajs-3717	21	18	elucidating	elucidate	VERB
iajs-3717	21	19	interactions	interaction	NOUN
iajs-3717	21	20	among	among	ADP
iajs-3717	21	21	biological	biological	ADJ
iajs-3717	21	22	species	specie	NOUN
iajs-3717	21	23	.	.	PUNCT
iajs-3717	22	1	ecoepidemiological	ecoepidemiological	ADJ
iajs-3717	22	2	models	model	NOUN
iajs-3717	22	3	encompass	encompass	VERB
iajs-3717	22	4	mathematical	mathematical	ADJ
iajs-3717	22	5	representations	representation	NOUN
iajs-3717	22	6	of	of	ADP
iajs-3717	22	7	dynamic	dynamic	ADJ
iajs-3717	22	8	behaviors	behavior	NOUN
iajs-3717	22	9	within	within	ADP
iajs-3717	22	10	ecological	ecological	ADJ
iajs-3717	22	11	systems	system	NOUN
iajs-3717	22	12	,	,	PUNCT
iajs-3717	22	13	including	include	VERB
iajs-3717	22	14	disease	disease	NOUN
iajs-3717	22	15	dynamics	dynamic	NOUN
iajs-3717	22	16	.	.	PUNCT
iajs-3717	23	1	anderson	anderson	PROPN
iajs-3717	23	2	and	and	CCONJ
iajs-3717	23	3	may	may	AUX
iajs-3717	23	4	(	(	PUNCT
iajs-3717	23	5	3	3	X
iajs-3717	23	6	)	)	PUNCT
iajs-3717	23	7	studied	study	VERB
iajs-3717	23	8	the	the	DET
iajs-3717	23	9	dynamics	dynamic	NOUN
iajs-3717	23	10	of	of	ADP
iajs-3717	23	11	an	an	DET
iajs-3717	23	12	eco	eco	NOUN
iajs-3717	23	13	-	-	PUNCT
iajs-3717	23	14	epidemiology	epidemiology	NOUN
iajs-3717	23	15	model	model	NOUN
iajs-3717	23	16	that	that	PRON
iajs-3717	23	17	included	include	VERB
iajs-3717	23	18	interactions	interaction	NOUN
iajs-3717	23	19	between	between	ADP
iajs-3717	23	20	infected	infected	ADJ
iajs-3717	23	21	prey	prey	NOUN
iajs-3717	23	22	populations	population	NOUN
iajs-3717	23	23	and	and	CCONJ
iajs-3717	23	24	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
iajs-3717	23	25	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
iajs-3717	23	26	https://orcid.org/0000-0002-2136-7384	https://orcid.org/0000-0002-2136-7384	VERB
iajs-3717	23	27	mailto:nidhal.f1980@yahoo.com	mailto:nidhal.f1980@yahoo.com	PROPN
iajs-3717	23	28	https://orcid.org/0009-0007-7883-5875	https://orcid.org/0009-0007-7883-5875	PROPN
iajs-3717	23	29	mailto	mailto	NOUN
iajs-3717	23	30	:	:	PUNCT
iajs-3717	23	31	hassan.fadhil.r@sc.uobaghdad.edu%20.iq	hassan.fadhil.r@sc.uobaghdad.edu%20.iq	PROPN
iajs-3717	23	32	https://orcid.org/0000-0002-1127-4395	https://orcid.org/0000-0002-1127-4395	PROPN
iajs-3717	23	33	mailto:y.sabbar@umi.ac.ma	mailto:y.sabbar@umi.ac.ma	PROPN
iajs-3717	23	34	ihjpas	ihjpas	PROPN
iajs-3717	23	35	.	.	PUNCT
iajs-3717	24	1	2025,38(2	2025,38(2	PROPN
iajs-3717	24	2	)	)	PUNCT
iajs-3717	24	3	362	362	NUM
iajs-3717	24	4	predators	predator	NOUN
iajs-3717	24	5	in	in	ADP
iajs-3717	24	6	1986	1986	NUM
iajs-3717	24	7	.	.	PUNCT
iajs-3717	25	1	the	the	DET
iajs-3717	25	2	researchers	researcher	NOUN
iajs-3717	25	3	had	have	AUX
iajs-3717	25	4	studied	study	VERB
iajs-3717	25	5	the	the	DET
iajs-3717	25	6	dynamics	dynamic	NOUN
iajs-3717	25	7	of	of	ADP
iajs-3717	25	8	the	the	DET
iajs-3717	25	9	eco	eco	NOUN
iajs-3717	25	10	-	-	PUNCT
iajs-3717	25	11	epidemiological	epidemiological	ADJ
iajs-3717	25	12	models	model	NOUN
iajs-3717	25	13	independently	independently	ADV
iajs-3717	25	14	for	for	ADP
iajs-3717	25	15	many	many	ADJ
iajs-3717	25	16	years	year	NOUN
iajs-3717	25	17	,	,	PUNCT
iajs-3717	25	18	for	for	ADP
iajs-3717	25	19	example	example	NOUN
iajs-3717	25	20	(	(	PUNCT
iajs-3717	25	21	4	4	NUM
iajs-3717	25	22	-	-	SYM
iajs-3717	25	23	6	6	NUM
iajs-3717	25	24	)	)	PUNCT
iajs-3717	25	25	.	.	PUNCT
iajs-3717	26	1	it	it	PRON
iajs-3717	26	2	is	be	AUX
iajs-3717	26	3	well	well	ADV
iajs-3717	26	4	known	know	VERB
iajs-3717	26	5	that	that	SCONJ
iajs-3717	26	6	prey	prey	NOUN
iajs-3717	26	7	-	-	PUNCT
iajs-3717	26	8	predator	predator	NOUN
iajs-3717	26	9	models	model	NOUN
iajs-3717	26	10	,	,	PUNCT
iajs-3717	26	11	which	which	PRON
iajs-3717	26	12	may	may	AUX
iajs-3717	26	13	involve	involve	VERB
iajs-3717	26	14	a	a	DET
iajs-3717	26	15	variety	variety	NOUN
iajs-3717	26	16	of	of	ADP
iajs-3717	26	17	natural	natural	ADJ
iajs-3717	26	18	factors	factor	NOUN
iajs-3717	26	19	,	,	PUNCT
iajs-3717	26	20	can	can	AUX
iajs-3717	26	21	be	be	AUX
iajs-3717	26	22	used	use	VERB
iajs-3717	26	23	to	to	PART
iajs-3717	26	24	describe	describe	VERB
iajs-3717	26	25	the	the	DET
iajs-3717	26	26	most	most	ADV
iajs-3717	26	27	significant	significant	ADJ
iajs-3717	26	28	relationships	relationship	NOUN
iajs-3717	26	29	between	between	ADP
iajs-3717	26	30	the	the	DET
iajs-3717	26	31	individuals	individual	NOUN
iajs-3717	26	32	of	of	ADP
iajs-3717	26	33	species	specie	NOUN
iajs-3717	26	34	in	in	ADP
iajs-3717	26	35	the	the	DET
iajs-3717	26	36	environment	environment	NOUN
iajs-3717	26	37	;	;	PUNCT
iajs-3717	26	38	modeling	model	VERB
iajs-3717	26	39	predator	predator	NOUN
iajs-3717	26	40	-	-	PUNCT
iajs-3717	26	41	prey	prey	NOUN
iajs-3717	26	42	interactions	interaction	NOUN
iajs-3717	26	43	is	be	AUX
iajs-3717	26	44	becoming	become	VERB
iajs-3717	26	45	the	the	DET
iajs-3717	26	46	most	most	ADV
iajs-3717	26	47	crucial	crucial	ADJ
iajs-3717	26	48	topic	topic	NOUN
iajs-3717	26	49	for	for	ADP
iajs-3717	26	50	ecologists	ecologist	NOUN
iajs-3717	26	51	and	and	CCONJ
iajs-3717	26	52	applied	apply	VERB
iajs-3717	26	53	mathematics	mathematic	NOUN
iajs-3717	26	54	research	research	NOUN
iajs-3717	26	55	.	.	PUNCT
iajs-3717	27	1	predator	predator	NOUN
iajs-3717	27	2	-	-	PUNCT
iajs-3717	27	3	prey	prey	NOUN
iajs-3717	27	4	models	model	NOUN
iajs-3717	27	5	may	may	AUX
iajs-3717	27	6	often	often	ADV
iajs-3717	27	7	be	be	AUX
iajs-3717	27	8	divided	divide	VERB
iajs-3717	27	9	into	into	ADP
iajs-3717	27	10	three	three	NUM
iajs-3717	27	11	types	type	NOUN
iajs-3717	27	12	based	base	VERB
iajs-3717	27	13	on	on	ADP
iajs-3717	27	14	the	the	DET
iajs-3717	27	15	infectious	infectious	ADJ
iajs-3717	27	16	diseases	disease	NOUN
iajs-3717	27	17	that	that	PRON
iajs-3717	27	18	affect	affect	VERB
iajs-3717	27	19	the	the	DET
iajs-3717	27	20	population	population	NOUN
iajs-3717	27	21	.	.	PUNCT
iajs-3717	28	1	the	the	DET
iajs-3717	28	2	first	first	ADJ
iajs-3717	28	3	type	type	NOUN
iajs-3717	28	4	is	be	AUX
iajs-3717	28	5	that	that	SCONJ
iajs-3717	28	6	models	model	NOUN
iajs-3717	28	7	only	only	ADV
iajs-3717	28	8	include	include	VERB
iajs-3717	28	9	infected	infected	ADJ
iajs-3717	28	10	prey	prey	NOUN
iajs-3717	28	11	(	(	PUNCT
iajs-3717	28	12	7	7	NUM
iajs-3717	28	13	-	-	SYM
iajs-3717	28	14	9	9	NUM
iajs-3717	28	15	)	)	PUNCT
iajs-3717	28	16	.	.	PUNCT
iajs-3717	29	1	in	in	ADP
iajs-3717	29	2	2012	2012	NUM
iajs-3717	29	3	,	,	PUNCT
iajs-3717	29	4	a	a	DET
iajs-3717	29	5	prey	prey	NOUN
iajs-3717	29	6	-	-	PUNCT
iajs-3717	29	7	predator	predator	NOUN
iajs-3717	29	8	model	model	NOUN
iajs-3717	29	9	of	of	ADP
iajs-3717	29	10	the	the	DET
iajs-3717	29	11	lotka	lotka	PROPN
iajs-3717	29	12	-	-	PUNCT
iajs-3717	29	13	volterra	volterra	NOUN
iajs-3717	29	14	type	type	NOUN
iajs-3717	29	15	without	without	ADP
iajs-3717	29	16	harvesting	harvesting	NOUN
iajs-3717	29	17	was	be	AUX
iajs-3717	29	18	considered	consider	VERB
iajs-3717	29	19	by	by	ADP
iajs-3717	29	20	johri	johri	PROPN
iajs-3717	29	21	et	et	PROPN
iajs-3717	29	22	al.(10	al.(10	PROPN
iajs-3717	29	23	)	)	PUNCT
iajs-3717	29	24	.	.	PUNCT
iajs-3717	30	1	they	they	PRON
iajs-3717	30	2	assumed	assume	VERB
iajs-3717	30	3	that	that	SCONJ
iajs-3717	30	4	there	there	PRON
iajs-3717	30	5	is	be	VERB
iajs-3717	30	6	a	a	DET
iajs-3717	30	7	disease	disease	NOUN
iajs-3717	30	8	only	only	ADV
iajs-3717	30	9	in	in	ADP
iajs-3717	30	10	prey	prey	NOUN
iajs-3717	30	11	and	and	CCONJ
iajs-3717	30	12	that	that	SCONJ
iajs-3717	30	13	the	the	DET
iajs-3717	30	14	susceptible	susceptible	ADJ
iajs-3717	30	15	prey	prey	NOUN
iajs-3717	30	16	's	's	PART
iajs-3717	30	17	conversion	conversion	NOUN
iajs-3717	30	18	rate	rate	NOUN
iajs-3717	30	19	is	be	AUX
iajs-3717	30	20	the	the	DET
iajs-3717	30	21	same	same	ADJ
iajs-3717	30	22	as	as	ADP
iajs-3717	30	23	that	that	PRON
iajs-3717	30	24	of	of	ADP
iajs-3717	30	25	the	the	DET
iajs-3717	30	26	infected	infected	ADJ
iajs-3717	30	27	prey	prey	NOUN
iajs-3717	30	28	.	.	PUNCT
iajs-3717	31	1	the	the	DET
iajs-3717	31	2	ecoepidemiological	ecoepidemiological	ADJ
iajs-3717	31	3	model	model	NOUN
iajs-3717	31	4	with	with	ADP
iajs-3717	31	5	two	two	NUM
iajs-3717	31	6	prey	prey	NOUN
iajs-3717	31	7	populations	population	NOUN
iajs-3717	31	8	where	where	SCONJ
iajs-3717	31	9	one	one	NUM
iajs-3717	31	10	prey	prey	NOUN
iajs-3717	31	11	species	specie	NOUN
iajs-3717	31	12	has	have	VERB
iajs-3717	31	13	an	an	DET
iajs-3717	31	14	infectious	infectious	ADJ
iajs-3717	31	15	disease	disease	NOUN
iajs-3717	31	16	is	be	AUX
iajs-3717	31	17	suggested	suggest	VERB
iajs-3717	31	18	and	and	CCONJ
iajs-3717	31	19	studied	study	VERB
iajs-3717	31	20	(	(	PUNCT
iajs-3717	31	21	11	11	NUM
iajs-3717	31	22	)	)	PUNCT
iajs-3717	31	23	.	.	PUNCT
iajs-3717	32	1	the	the	DET
iajs-3717	32	2	second	second	ADJ
iajs-3717	32	3	type	type	NOUN
iajs-3717	32	4	only	only	ADV
iajs-3717	32	5	includes	include	VERB
iajs-3717	32	6	the	the	DET
iajs-3717	32	7	diseased	diseased	ADJ
iajs-3717	32	8	in	in	ADP
iajs-3717	32	9	the	the	DET
iajs-3717	32	10	predator	predator	NOUN
iajs-3717	32	11	(	(	PUNCT
iajs-3717	32	12	12	12	NUM
iajs-3717	32	13	-	-	SYM
iajs-3717	32	14	14	14	NUM
iajs-3717	32	15	)	)	PUNCT
iajs-3717	32	16	the	the	DET
iajs-3717	32	17	prey	prey	NOUN
iajs-3717	32	18	-	-	PUNCT
iajs-3717	32	19	predator	predator	NOUN
iajs-3717	32	20	model	model	NOUN
iajs-3717	32	21	with	with	ADP
iajs-3717	32	22	disease	disease	NOUN
iajs-3717	32	23	in	in	ADP
iajs-3717	32	24	the	the	DET
iajs-3717	32	25	predator	predator	NOUN
iajs-3717	32	26	and	and	CCONJ
iajs-3717	32	27	the	the	DET
iajs-3717	32	28	functional	functional	ADJ
iajs-3717	32	29	response	response	NOUN
iajs-3717	32	30	studied	study	VERB
iajs-3717	32	31	and	and	CCONJ
iajs-3717	32	32	proposed	propose	VERB
iajs-3717	32	33	(	(	PUNCT
iajs-3717	32	34	14	14	NUM
iajs-3717	32	35	)	)	PUNCT
iajs-3717	32	36	.	.	PUNCT
iajs-3717	33	1	the	the	DET
iajs-3717	33	2	third	third	ADJ
iajs-3717	33	3	type	type	NOUN
iajs-3717	33	4	of	of	ADP
iajs-3717	33	5	prey	prey	NOUN
iajs-3717	33	6	-	-	PUNCT
iajs-3717	33	7	predator	predator	NOUN
iajs-3717	33	8	model	model	NOUN
iajs-3717	33	9	is	be	AUX
iajs-3717	33	10	a	a	DET
iajs-3717	33	11	disease	disease	NOUN
iajs-3717	33	12	in	in	ADP
iajs-3717	33	13	both	both	DET
iajs-3717	33	14	populations	population	NOUN
iajs-3717	33	15	(	(	PUNCT
iajs-3717	33	16	15	15	NUM
iajs-3717	33	17	17	17	NUM
iajs-3717	33	18	)	)	PUNCT
iajs-3717	33	19	.	.	PUNCT
iajs-3717	34	1	kant	kant	PROPN
iajs-3717	34	2	and	and	CCONJ
iajs-3717	34	3	kumar	kumar	PROPN
iajs-3717	34	4	(	(	PUNCT
iajs-3717	34	5	16	16	NUM
iajs-3717	34	6	)	)	PUNCT
iajs-3717	34	7	investigated	investigate	VERB
iajs-3717	34	8	a	a	DET
iajs-3717	34	9	prey	prey	NOUN
iajs-3717	34	10	-	-	PUNCT
iajs-3717	34	11	predator	predator	NOUN
iajs-3717	34	12	system	system	NOUN
iajs-3717	34	13	where	where	SCONJ
iajs-3717	34	14	the	the	DET
iajs-3717	34	15	prey	prey	NOUN
iajs-3717	34	16	migrates	migrate	VERB
iajs-3717	34	17	,	,	PUNCT
iajs-3717	34	18	and	and	CCONJ
iajs-3717	34	19	both	both	DET
iajs-3717	34	20	populations	population	NOUN
iajs-3717	34	21	encounter	encounter	VERB
iajs-3717	34	22	disease	disease	NOUN
iajs-3717	34	23	infection	infection	NOUN
iajs-3717	34	24	.	.	PUNCT
iajs-3717	35	1	the	the	DET
iajs-3717	35	2	prey	prey	NOUN
iajs-3717	35	3	-	-	PUNCT
iajs-3717	35	4	predator	predator	NOUN
iajs-3717	35	5	model	model	NOUN
iajs-3717	35	6	and	and	CCONJ
iajs-3717	35	7	assumed	assume	VERB
iajs-3717	35	8	there	there	PRON
iajs-3717	35	9	is	be	VERB
iajs-3717	35	10	a	a	DET
iajs-3717	35	11	disease	disease	NOUN
iajs-3717	35	12	in	in	ADP
iajs-3717	35	13	both	both	DET
iajs-3717	35	14	populations	population	NOUN
iajs-3717	35	15	have	have	AUX
iajs-3717	35	16	been	be	AUX
iajs-3717	35	17	studied	study	VERB
iajs-3717	35	18	(	(	PUNCT
iajs-3717	35	19	17	17	NUM
iajs-3717	35	20	)	)	PUNCT
iajs-3717	35	21	.	.	PUNCT
iajs-3717	36	1	harvesting	harvesting	NOUN
iajs-3717	36	2	strongly	strongly	ADV
iajs-3717	36	3	influences	influence	VERB
iajs-3717	36	4	a	a	DET
iajs-3717	36	5	model	model	NOUN
iajs-3717	36	6	's	's	PART
iajs-3717	36	7	behavior	behavior	NOUN
iajs-3717	36	8	.	.	PUNCT
iajs-3717	37	1	it	it	PRON
iajs-3717	37	2	refers	refer	VERB
iajs-3717	37	3	to	to	ADP
iajs-3717	37	4	reducing	reduce	VERB
iajs-3717	37	5	a	a	DET
iajs-3717	37	6	population	population	NOUN
iajs-3717	37	7	through	through	ADP
iajs-3717	37	8	hunting	hunting	NOUN
iajs-3717	37	9	or	or	CCONJ
iajs-3717	37	10	individual	individual	ADJ
iajs-3717	37	11	capture	capture	NOUN
iajs-3717	37	12	.	.	PUNCT
iajs-3717	38	1	it	it	PRON
iajs-3717	38	2	may	may	AUX
iajs-3717	38	3	have	have	VERB
iajs-3717	38	4	a	a	DET
iajs-3717	38	5	detrimental	detrimental	ADJ
iajs-3717	38	6	impact	impact	NOUN
iajs-3717	38	7	on	on	ADP
iajs-3717	38	8	harvested	harvest	VERB
iajs-3717	38	9	population	population	NOUN
iajs-3717	38	10	density	density	NOUN
iajs-3717	38	11	.	.	PUNCT
iajs-3717	39	1	in	in	ADP
iajs-3717	39	2	general	general	ADJ
iajs-3717	39	3	,	,	PUNCT
iajs-3717	39	4	there	there	PRON
iajs-3717	39	5	are	be	VERB
iajs-3717	39	6	two	two	NUM
iajs-3717	39	7	kinds	kind	NOUN
iajs-3717	39	8	:	:	PUNCT
iajs-3717	39	9	linear	linear	ADJ
iajs-3717	39	10	and	and	CCONJ
iajs-3717	39	11	nonlinear	nonlinear	ADJ
iajs-3717	39	12	.	.	PUNCT
iajs-3717	40	1	however	however	ADV
iajs-3717	40	2	,	,	PUNCT
iajs-3717	40	3	from	from	ADP
iajs-3717	40	4	a	a	DET
iajs-3717	40	5	biological	biological	ADJ
iajs-3717	40	6	and	and	CCONJ
iajs-3717	40	7	economic	economic	ADJ
iajs-3717	40	8	viewpoint	viewpoint	NOUN
iajs-3717	40	9	,	,	PUNCT
iajs-3717	40	10	nonlinear	nonlinear	ADJ
iajs-3717	40	11	harvesting	harvesting	NOUN
iajs-3717	40	12	functions	function	NOUN
iajs-3717	40	13	are	be	AUX
iajs-3717	40	14	better	well	ADV
iajs-3717	40	15	suited	suited	ADJ
iajs-3717	40	16	for	for	ADP
iajs-3717	40	17	use	use	NOUN
iajs-3717	40	18	in	in	ADP
iajs-3717	40	19	reality	reality	NOUN
iajs-3717	40	20	.	.	PUNCT
iajs-3717	41	1	research	research	NOUN
iajs-3717	41	2	studies	study	NOUN
iajs-3717	41	3	have	have	AUX
iajs-3717	41	4	used	use	VERB
iajs-3717	41	5	linear	linear	ADJ
iajs-3717	41	6	harvesting	harvesting	NOUN
iajs-3717	41	7	functions	function	NOUN
iajs-3717	41	8	,	,	PUNCT
iajs-3717	41	9	constant	constant	ADJ
iajs-3717	41	10	-	-	PUNCT
iajs-3717	41	11	yield	yield	NOUN
iajs-3717	41	12	prey	prey	NOUN
iajs-3717	41	13	,	,	PUNCT
iajs-3717	41	14	or	or	CCONJ
iajs-3717	41	15	predator	predator	NOUN
iajs-3717	41	16	harvesting	harvesting	NOUN
iajs-3717	41	17	.	.	PUNCT
iajs-3717	42	1	in	in	ADP
iajs-3717	42	2	2001	2001	NUM
iajs-3717	42	3	,	,	PUNCT
iajs-3717	42	4	a	a	DET
iajs-3717	42	5	mathematical	mathematical	ADJ
iajs-3717	42	6	model	model	NOUN
iajs-3717	42	7	that	that	PRON
iajs-3717	42	8	included	include	VERB
iajs-3717	42	9	immature	immature	ADJ
iajs-3717	42	10	and	and	CCONJ
iajs-3717	42	11	mature	mature	ADJ
iajs-3717	42	12	supposes	suppose	NOUN
iajs-3717	42	13	was	be	AUX
iajs-3717	42	14	studied	study	VERB
iajs-3717	42	15	by	by	ADP
iajs-3717	42	16	song	song	NOUN
iajs-3717	42	17	and	and	CCONJ
iajs-3717	42	18	chen	chen	PROPN
iajs-3717	42	19	(	(	PUNCT
iajs-3717	42	20	18	18	NUM
iajs-3717	42	21	)	)	PUNCT
iajs-3717	42	22	.	.	PUNCT
iajs-3717	43	1	the	the	DET
iajs-3717	43	2	prey	prey	NOUN
iajs-3717	43	3	-	-	PUNCT
iajs-3717	43	4	predator	predator	NOUN
iajs-3717	43	5	system	system	NOUN
iajs-3717	43	6	considers	consider	VERB
iajs-3717	43	7	harvesting	harvesting	NOUN
iajs-3717	43	8	for	for	ADP
iajs-3717	43	9	the	the	DET
iajs-3717	43	10	prey	prey	NOUN
iajs-3717	43	11	and	and	CCONJ
iajs-3717	43	12	predator	predator	NOUN
iajs-3717	43	13	species	specie	NOUN
iajs-3717	43	14	studied	study	VERB
iajs-3717	43	15	(	(	PUNCT
iajs-3717	43	16	19).the	19).the	DET
iajs-3717	43	17	modeling	modeling	NOUN
iajs-3717	43	18	of	of	ADP
iajs-3717	43	19	prey	prey	NOUN
iajs-3717	43	20	-	-	PUNCT
iajs-3717	43	21	predator	predator	NOUN
iajs-3717	43	22	involving	involve	VERB
iajs-3717	43	23	the	the	DET
iajs-3717	43	24	harvested	harvest	VERB
iajs-3717	43	25	with	with	ADP
iajs-3717	43	26	incorporating	incorporate	VERB
iajs-3717	43	27	a	a	DET
iajs-3717	43	28	prey	prey	NOUN
iajs-3717	43	29	refuge	refuge	NOUN
iajs-3717	43	30	suggested	suggest	VERB
iajs-3717	43	31	and	and	CCONJ
iajs-3717	43	32	formulated	formulate	VERB
iajs-3717	43	33	(	(	PUNCT
iajs-3717	43	34	20	20	NUM
iajs-3717	43	35	)	)	PUNCT
iajs-3717	43	36	.	.	PUNCT
iajs-3717	44	1	however	however	ADV
iajs-3717	44	2	,	,	PUNCT
iajs-3717	44	3	it	it	PRON
iajs-3717	44	4	is	be	AUX
iajs-3717	44	5	essential	essential	ADJ
iajs-3717	44	6	to	to	PART
iajs-3717	44	7	consider	consider	VERB
iajs-3717	44	8	the	the	DET
iajs-3717	44	9	effect	effect	NOUN
iajs-3717	44	10	of	of	ADP
iajs-3717	44	11	past	past	ADJ
iajs-3717	44	12	life	life	NOUN
iajs-3717	44	13	history	history	NOUN
iajs-3717	44	14	when	when	SCONJ
iajs-3717	44	15	analyzing	analyze	VERB
iajs-3717	44	16	the	the	DET
iajs-3717	44	17	system	system	NOUN
iajs-3717	44	18	's	's	PART
iajs-3717	44	19	stability	stability	NOUN
iajs-3717	44	20	.	.	PUNCT
iajs-3717	45	1	additionally	additionally	ADV
iajs-3717	45	2	,	,	PUNCT
iajs-3717	45	3	because	because	SCONJ
iajs-3717	45	4	time	time	NOUN
iajs-3717	45	5	delays	delay	NOUN
iajs-3717	45	6	occur	occur	VERB
iajs-3717	45	7	in	in	ADP
iajs-3717	45	8	so	so	ADV
iajs-3717	45	9	many	many	ADJ
iajs-3717	45	10	biological	biological	ADJ
iajs-3717	45	11	situations	situation	NOUN
iajs-3717	45	12	(	(	PUNCT
iajs-3717	45	13	maturation	maturation	NOUN
iajs-3717	45	14	,	,	PUNCT
iajs-3717	45	15	gestation	gestation	NOUN
iajs-3717	45	16	,	,	PUNCT
iajs-3717	45	17	capture	capture	NOUN
iajs-3717	45	18	,	,	PUNCT
iajs-3717	45	19	or	or	CCONJ
iajs-3717	45	20	other	other	ADJ
iajs-3717	45	21	factors	factor	NOUN
iajs-3717	45	22	.	.	PUNCT
iajs-3717	45	23	)	)	PUNCT
iajs-3717	46	1	in	in	ADP
iajs-3717	46	2	prey	prey	NOUN
iajs-3717	46	3	-	-	PUNCT
iajs-3717	46	4	predator	predator	NOUN
iajs-3717	46	5	systems	system	NOUN
iajs-3717	46	6	and	and	CCONJ
iajs-3717	46	7	ignoring	ignore	VERB
iajs-3717	46	8	them	they	PRON
iajs-3717	46	9	means	mean	VERB
iajs-3717	46	10	ignoring	ignore	VERB
iajs-3717	46	11	reality	reality	NOUN
iajs-3717	46	12	,	,	PUNCT
iajs-3717	46	13	delay	delay	NOUN
iajs-3717	46	14	differential	differential	ADJ
iajs-3717	46	15	equations	equation	NOUN
iajs-3717	46	16	are	be	AUX
iajs-3717	46	17	widely	widely	ADV
iajs-3717	46	18	used	use	VERB
iajs-3717	46	19	in	in	ADP
iajs-3717	46	20	the	the	DET
iajs-3717	46	21	literature	literature	NOUN
iajs-3717	46	22	on	on	ADP
iajs-3717	46	23	ecological	ecological	ADJ
iajs-3717	46	24	interactions	interaction	NOUN
iajs-3717	46	25	between	between	ADP
iajs-3717	46	26	predator	predator	NOUN
iajs-3717	46	27	and	and	CCONJ
iajs-3717	46	28	prey	prey	NOUN
iajs-3717	46	29	.	.	PUNCT
iajs-3717	47	1	on	on	ADP
iajs-3717	47	2	the	the	DET
iajs-3717	47	3	other	other	ADJ
iajs-3717	47	4	hand	hand	NOUN
iajs-3717	47	5	,	,	PUNCT
iajs-3717	47	6	several	several	ADJ
iajs-3717	47	7	studies	study	NOUN
iajs-3717	47	8	have	have	AUX
iajs-3717	47	9	been	be	AUX
iajs-3717	47	10	proposed	propose	VERB
iajs-3717	47	11	to	to	PART
iajs-3717	47	12	show	show	VERB
iajs-3717	47	13	the	the	DET
iajs-3717	47	14	effect	effect	NOUN
iajs-3717	47	15	of	of	ADP
iajs-3717	47	16	the	the	DET
iajs-3717	47	17	time	time	NOUN
iajs-3717	47	18	delay	delay	NOUN
iajs-3717	47	19	(	(	PUNCT
iajs-3717	47	20	21	21	NUM
iajs-3717	47	21	-	-	SYM
iajs-3717	47	22	27	27	NUM
iajs-3717	47	23	)	)	PUNCT
iajs-3717	47	24	.	.	PUNCT
iajs-3717	48	1	the	the	DET
iajs-3717	48	2	influence	influence	NOUN
iajs-3717	48	3	of	of	ADP
iajs-3717	48	4	a	a	DET
iajs-3717	48	5	delayed	delay	VERB
iajs-3717	48	6	incubation	incubation	NOUN
iajs-3717	48	7	period	period	NOUN
iajs-3717	48	8	on	on	ADP
iajs-3717	48	9	disease	disease	NOUN
iajs-3717	48	10	transmission	transmission	NOUN
iajs-3717	48	11	using	use	VERB
iajs-3717	48	12	a	a	DET
iajs-3717	48	13	nonlinear	nonlinear	ADJ
iajs-3717	48	14	incidence	incidence	NOUN
iajs-3717	48	15	rate	rate	NOUN
iajs-3717	48	16	in	in	ADP
iajs-3717	48	17	preypredator	preypredator	NOUN
iajs-3717	48	18	systems	system	NOUN
iajs-3717	48	19	was	be	AUX
iajs-3717	48	20	examined	examine	VERB
iajs-3717	48	21	(	(	PUNCT
iajs-3717	48	22	21	21	NUM
iajs-3717	48	23	)	)	PUNCT
iajs-3717	48	24	.	.	PUNCT
iajs-3717	49	1	al	al	PROPN
iajs-3717	49	2	-	-	PUNCT
iajs-3717	49	3	jubouri	jubouri	PROPN
iajs-3717	49	4	and	and	CCONJ
iajs-3717	49	5	naji	naji	PROPN
iajs-3717	49	6	(	(	PUNCT
iajs-3717	49	7	23	23	NUM
iajs-3717	49	8	)	)	PUNCT
iajs-3717	49	9	proposed	propose	VERB
iajs-3717	49	10	a	a	DET
iajs-3717	49	11	mathematical	mathematical	ADJ
iajs-3717	49	12	model	model	NOUN
iajs-3717	49	13	incorporating	incorporate	VERB
iajs-3717	49	14	a	a	DET
iajs-3717	49	15	time	time	NOUN
iajs-3717	49	16	delay	delay	NOUN
iajs-3717	49	17	in	in	ADP
iajs-3717	49	18	the	the	DET
iajs-3717	49	19	disease	disease	NOUN
iajs-3717	49	20	transmission	transmission	NOUN
iajs-3717	49	21	process	process	NOUN
iajs-3717	49	22	.	.	PUNCT
iajs-3717	50	1	the	the	DET
iajs-3717	50	2	effect	effect	NOUN
iajs-3717	50	3	of	of	ADP
iajs-3717	50	4	time	time	NOUN
iajs-3717	50	5	delay	delay	NOUN
iajs-3717	50	6	on	on	ADP
iajs-3717	50	7	the	the	DET
iajs-3717	50	8	dynamics	dynamic	NOUN
iajs-3717	50	9	of	of	ADP
iajs-3717	50	10	the	the	DET
iajs-3717	50	11	prey	prey	NOUN
iajs-3717	50	12	-	-	PUNCT
iajs-3717	50	13	predator	predator	NOUN
iajs-3717	50	14	model	model	NOUN
iajs-3717	50	15	with	with	ADP
iajs-3717	50	16	prey	prey	NOUN
iajs-3717	50	17	harvesting	harvesting	NOUN
iajs-3717	50	18	was	be	AUX
iajs-3717	50	19	studied	study	VERB
iajs-3717	50	20	(	(	PUNCT
iajs-3717	50	21	25	25	NUM
iajs-3717	50	22	)	)	PUNCT
iajs-3717	50	23	.	.	PUNCT
iajs-3717	51	1	in	in	ADP
iajs-3717	51	2	2011	2011	NUM
iajs-3717	51	3	,	,	PUNCT
iajs-3717	51	4	naji	naji	PROPN
iajs-3717	51	5	and	and	CCONJ
iajs-3717	51	6	ibrahim	ibrahim	PROPN
iajs-3717	51	7	(	(	PUNCT
iajs-3717	51	8	28	28	NUM
iajs-3717	51	9	)	)	PUNCT
iajs-3717	51	10	formulated	formulate	VERB
iajs-3717	51	11	the	the	DET
iajs-3717	51	12	following	following	ADJ
iajs-3717	51	13	mathematical	mathematical	ADJ
iajs-3717	51	14	model	model	NOUN
iajs-3717	51	15	.	.	PUNCT
iajs-3717	52	1	𝑑𝑆	𝑑𝑆	ADJ
iajs-3717	52	2	𝑑𝑡	𝑑𝑡	ADP
iajs-3717	52	3	=	=	PUNCT
iajs-3717	52	4	𝑟𝑆	𝑟𝑆	NOUN
iajs-3717	52	5	(	(	PUNCT
iajs-3717	52	6	1	1	NUM
iajs-3717	52	7	−	−	NOUN
iajs-3717	52	8	𝑆+𝐼	𝑆+𝐼	NOUN
iajs-3717	52	9	𝐾	𝐾	PROPN
iajs-3717	52	10	)	)	PUNCT
iajs-3717	53	1	−	−	PROPN
iajs-3717	53	2	𝐶𝑆𝐼	𝐶𝑆𝐼	PROPN
iajs-3717	53	3	−	−	NOUN
iajs-3717	54	1	𝐸1𝑆	𝐸1𝑆	ADP
iajs-3717	54	2	𝑑𝐼	𝑑𝐼	ADJ
iajs-3717	54	3	𝑑𝑡	𝑑𝑡	ADP
iajs-3717	54	4	=	=	SYM
iajs-3717	54	5	𝐶𝑆𝐼	𝐶𝑆𝐼	PROPN
iajs-3717	54	6	−	−	PROPN
iajs-3717	54	7	𝛼𝐼𝑍	𝛼𝐼𝑍	PROPN
iajs-3717	54	8	𝛾+𝐼	𝛾+𝐼	NOUN
iajs-3717	54	9	−	−	PROPN
iajs-3717	54	10	𝜆𝐼	𝜆𝐼	NOUN
iajs-3717	54	11	−	−	PROPN
iajs-3717	54	12	𝐸2𝐼	𝐸2𝐼	NUM
iajs-3717	54	13	𝑑𝑍	𝑑𝑍	PROPN
iajs-3717	54	14	𝑑𝑡	𝑑𝑡	ADP
iajs-3717	54	15	=	=	SYM
iajs-3717	54	16	−𝜃𝑍	−𝜃𝑍	PROPN
iajs-3717	54	17	+	+	CCONJ
iajs-3717	54	18	ℎ𝐼𝑍	ℎ𝐼𝑍	ADJ
iajs-3717	54	19	𝛾+𝐼	𝛾+𝐼	NOUN
iajs-3717	54	20	−	−	PROPN
iajs-3717	54	21	𝐸3𝑧	𝐸3𝑧	NOUN
iajs-3717	54	22	(	(	PUNCT
iajs-3717	54	23	1	1	NUM
iajs-3717	54	24	)	)	PUNCT
iajs-3717	54	25	where	where	SCONJ
iajs-3717	54	26	𝑆(𝑡	𝑆(𝑡	VERB
iajs-3717	54	27	)	)	PUNCT
iajs-3717	54	28	,	,	PUNCT
iajs-3717	54	29	𝐼(𝑡	𝐼(𝑡	PROPN
iajs-3717	54	30	)	)	PUNCT
iajs-3717	54	31	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
iajs-3717	54	32	𝑍(𝑡	𝑍(𝑡	NOUN
iajs-3717	54	33	)	)	PUNCT
iajs-3717	54	34	represent	represent	VERB
iajs-3717	54	35	the	the	DET
iajs-3717	54	36	number	number	NOUN
iajs-3717	54	37	of	of	ADP
iajs-3717	54	38	susceptible	susceptible	ADJ
iajs-3717	54	39	prey	prey	NOUN
iajs-3717	54	40	,	,	PUNCT
iajs-3717	54	41	infected	infected	ADJ
iajs-3717	54	42	prey	prey	NOUN
iajs-3717	54	43	and	and	CCONJ
iajs-3717	54	44	predator	predator	NOUN
iajs-3717	54	45	respectively	respectively	ADV
iajs-3717	54	46	;	;	PUNCT
iajs-3717	54	47	𝑟	𝑟	X
iajs-3717	54	48	intrinsic	intrinsic	ADJ
iajs-3717	54	49	growth	growth	NOUN
iajs-3717	54	50	rate	rate	NOUN
iajs-3717	54	51	;	;	PUNCT
iajs-3717	55	1	𝐾	𝐾	NOUN
iajs-3717	55	2	carrying	carry	VERB
iajs-3717	55	3	capacity	capacity	NOUN
iajs-3717	55	4	of	of	ADP
iajs-3717	55	5	the	the	DET
iajs-3717	55	6	prey	prey	NOUN
iajs-3717	55	7	in	in	ADP
iajs-3717	55	8	absence	absence	NOUN
iajs-3717	55	9	the	the	DET
iajs-3717	55	10	predator	predator	NOUN
iajs-3717	55	11	and	and	CCONJ
iajs-3717	55	12	harvesting	harvesting	NOUN
iajs-3717	55	13	;	;	PUNCT
iajs-3717	55	14	𝐶	𝐶	PROPN
iajs-3717	55	15	infection	infection	NOUN
iajs-3717	55	16	rate	rate	NOUN
iajs-3717	55	17	;	;	PUNCT
iajs-3717	55	18	𝛼	𝛼	X
iajs-3717	55	19	maximum	maximum	ADJ
iajs-3717	55	20	attack	attack	NOUN
iajs-3717	55	21	rate	rate	NOUN
iajs-3717	55	22	;	;	PUNCT
iajs-3717	55	23	𝜆	𝜆	DET
iajs-3717	55	24	death	death	NOUN
iajs-3717	55	25	rate	rate	NOUN
iajs-3717	55	26	of	of	ADP
iajs-3717	55	27	𝐼(𝑡	𝐼(𝑡	PROPN
iajs-3717	55	28	)	)	PUNCT
iajs-3717	55	29	;	;	PUNCT
iajs-3717	56	1	𝛾	𝛾	NUM
iajs-3717	56	2	half	half	NOUN
iajs-3717	56	3	saturation	saturation	NOUN
iajs-3717	56	4	level	level	NOUN
iajs-3717	56	5	coefficient	coefficient	NOUN
iajs-3717	56	6	;	;	PUNCT
iajs-3717	56	7	𝜃	𝜃	NUM
iajs-3717	56	8	death	death	NOUN
iajs-3717	56	9	rate	rate	NOUN
iajs-3717	56	10	of	of	ADP
iajs-3717	56	11	𝑍(𝑡	𝑍(𝑡	NOUN
iajs-3717	56	12	)	)	PUNCT
iajs-3717	56	13	;	;	PUNCT
iajs-3717	56	14	ℎ	ℎ	PROPN
iajs-3717	56	15	growth	growth	NOUN
iajs-3717	56	16	rate	rate	NOUN
iajs-3717	56	17	of	of	ADP
iajs-3717	56	18	the	the	DET
iajs-3717	56	19	𝑍(𝑡	𝑍(𝑡	NOUN
iajs-3717	56	20	)	)	PUNCT
iajs-3717	56	21	due	due	ADP
iajs-3717	56	22	to	to	ADP
iajs-3717	56	23	predation	predation	NOUN
iajs-3717	56	24	of	of	ADP
iajs-3717	56	25	the	the	DET
iajs-3717	56	26	𝐼(𝑡	𝐼(𝑡	NUM
iajs-3717	56	27	)	)	PUNCT
iajs-3717	56	28	;	;	PUNCT
iajs-3717	56	29	𝐸1	𝐸1	NOUN
iajs-3717	56	30	,	,	PUNCT
iajs-3717	56	31	𝐸2	𝐸2	ADJ
iajs-3717	56	32	𝑎𝑛𝑑	𝑎𝑛𝑑	PROPN
iajs-3717	56	33	𝐸3	𝐸3	PROPN
iajs-3717	56	34	are	be	AUX
iajs-3717	56	35	the	the	DET
iajs-3717	56	36	harvesting	harvesting	NOUN
iajs-3717	56	37	efforts	effort	NOUN
iajs-3717	56	38	for	for	ADP
iajs-3717	56	39	𝑆(𝑡	𝑆(𝑡	ADJ
iajs-3717	56	40	)	)	PUNCT
iajs-3717	56	41	,	,	PUNCT
iajs-3717	56	42	𝐼(𝑡	𝐼(𝑡	PROPN
iajs-3717	56	43	)	)	PUNCT
iajs-3717	56	44	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
iajs-3717	56	45	𝑍(𝑡	𝑍(𝑡	NOUN
iajs-3717	56	46	)	)	PUNCT
iajs-3717	56	47	respectively	respectively	ADV
iajs-3717	56	48	.	.	PUNCT
iajs-3717	57	1	the	the	DET
iajs-3717	57	2	time	time	NOUN
iajs-3717	57	3	delay	delay	NOUN
iajs-3717	57	4	impact	impact	NOUN
iajs-3717	57	5	is	be	AUX
iajs-3717	57	6	concentrated	concentrate	VERB
iajs-3717	57	7	.	.	PUNCT
iajs-3717	58	1	the	the	DET
iajs-3717	58	2	organization	organization	NOUN
iajs-3717	58	3	of	of	ADP
iajs-3717	58	4	this	this	DET
iajs-3717	58	5	paper	paper	NOUN
iajs-3717	58	6	is	be	AUX
iajs-3717	58	7	as	as	SCONJ
iajs-3717	58	8	follows	follow	VERB
iajs-3717	58	9	:	:	PUNCT
iajs-3717	58	10	first	first	ADV
iajs-3717	58	11	,	,	PUNCT
iajs-3717	58	12	the	the	DET
iajs-3717	58	13	given	give	VERB
iajs-3717	58	14	ihjpas	ihjpas	PROPN
iajs-3717	58	15	.	.	PUNCT
iajs-3717	59	1	2025,38(2	2025,38(2	NOUN
iajs-3717	59	2	)	)	PUNCT
iajs-3717	59	3	363	363	NUM
iajs-3717	59	4	system	system	NOUN
iajs-3717	59	5	(	(	PUNCT
iajs-3717	59	6	1	1	X
iajs-3717	59	7	)	)	PUNCT
iajs-3717	59	8	is	be	AUX
iajs-3717	59	9	modified	modify	VERB
iajs-3717	59	10	.	.	PUNCT
iajs-3717	60	1	second	second	ADJ
iajs-3717	60	2	,	,	PUNCT
iajs-3717	60	3	it	it	PRON
iajs-3717	60	4	illustrates	illustrate	VERB
iajs-3717	60	5	the	the	DET
iajs-3717	60	6	positivity	positivity	NOUN
iajs-3717	60	7	and	and	CCONJ
iajs-3717	60	8	bound	bind	VERB
iajs-3717	60	9	of	of	ADP
iajs-3717	60	10	solutions	solution	NOUN
iajs-3717	60	11	of	of	ADP
iajs-3717	60	12	the	the	DET
iajs-3717	60	13	system	system	NOUN
iajs-3717	60	14	(	(	PUNCT
iajs-3717	60	15	2	2	NUM
iajs-3717	60	16	)	)	PUNCT
iajs-3717	60	17	.	.	PUNCT
iajs-3717	61	1	third	third	ADV
iajs-3717	61	2	,	,	PUNCT
iajs-3717	61	3	we	we	PRON
iajs-3717	61	4	essentially	essentially	ADV
iajs-3717	61	5	investigate	investigate	VERB
iajs-3717	61	6	the	the	DET
iajs-3717	61	7	stability	stability	NOUN
iajs-3717	61	8	and	and	CCONJ
iajs-3717	61	9	existence	existence	NOUN
iajs-3717	61	10	of	of	ADP
iajs-3717	61	11	hopf	hopf	ADJ
iajs-3717	61	12	bifurcation	bifurcation	NOUN
iajs-3717	61	13	.	.	PUNCT
iajs-3717	62	1	fourth	fourth	ADJ
iajs-3717	62	2	,	,	PUNCT
iajs-3717	62	3	investigates	investigate	VERB
iajs-3717	62	4	the	the	DET
iajs-3717	62	5	properties	property	NOUN
iajs-3717	62	6	of	of	ADP
iajs-3717	62	7	the	the	DET
iajs-3717	62	8	hopf	hopf	ADJ
iajs-3717	62	9	bifurcation	bifurcation	NOUN
iajs-3717	62	10	.	.	PUNCT
iajs-3717	63	1	fifth	fifth	ADJ
iajs-3717	63	2	,	,	PUNCT
iajs-3717	63	3	the	the	DET
iajs-3717	63	4	major	major	ADJ
iajs-3717	63	5	theoretical	theoretical	ADJ
iajs-3717	63	6	results	result	NOUN
iajs-3717	63	7	and	and	CCONJ
iajs-3717	63	8	a	a	DET
iajs-3717	63	9	discussion	discussion	NOUN
iajs-3717	63	10	are	be	AUX
iajs-3717	63	11	shown	show	VERB
iajs-3717	63	12	by	by	ADP
iajs-3717	63	13	numerical	numerical	PROPN
iajs-3717	63	14	simulation	simulation	PROPN
iajs-3717	63	15	.	.	PUNCT
iajs-3717	64	1	finally	finally	ADV
iajs-3717	64	2	,	,	PUNCT
iajs-3717	64	3	the	the	DET
iajs-3717	64	4	conclusion	conclusion	NOUN
iajs-3717	64	5	.	.	PUNCT
iajs-3717	65	1	now	now	ADV
iajs-3717	65	2	,	,	PUNCT
iajs-3717	65	3	the	the	DET
iajs-3717	65	4	improved	improved	ADJ
iajs-3717	65	5	system	system	NOUN
iajs-3717	65	6	(	(	PUNCT
iajs-3717	65	7	1	1	X
iajs-3717	65	8	)	)	PUNCT
iajs-3717	65	9	can	can	AUX
iajs-3717	65	10	be	be	AUX
iajs-3717	65	11	expressed	express	VERB
iajs-3717	65	12	as	as	SCONJ
iajs-3717	65	13	follows	follow	VERB
iajs-3717	65	14	.	.	PUNCT
iajs-3717	66	1	𝑑𝑆	𝑑𝑆	ADJ
iajs-3717	66	2	𝑑𝑡	𝑑𝑡	ADP
iajs-3717	66	3	=	=	PUNCT
iajs-3717	66	4	𝑟𝑆	𝑟𝑆	NOUN
iajs-3717	66	5	(	(	PUNCT
iajs-3717	66	6	1	1	NUM
iajs-3717	66	7	−	−	NOUN
iajs-3717	66	8	𝑆+𝐼	𝑆+𝐼	NOUN
iajs-3717	66	9	𝐾	𝐾	PROPN
iajs-3717	66	10	)	)	PUNCT
iajs-3717	67	1	−	−	PROPN
iajs-3717	67	2	𝐶𝑆𝐼	𝐶𝑆𝐼	PROPN
iajs-3717	67	3	−	−	NOUN
iajs-3717	68	1	𝐸1𝑆	𝐸1𝑆	ADP
iajs-3717	68	2	𝑑𝐼	𝑑𝐼	ADJ
iajs-3717	68	3	𝑑𝑡	𝑑𝑡	ADP
iajs-3717	68	4	=	=	SYM
iajs-3717	68	5	𝐶𝑆𝐼	𝐶𝑆𝐼	PROPN
iajs-3717	68	6	−	−	PROPN
iajs-3717	68	7	𝛼𝐼(𝑡−𝜏)𝑍(𝑡−𝜏	𝛼𝐼(𝑡−𝜏)𝑍(𝑡−𝜏	PROPN
iajs-3717	68	8	)	)	PUNCT
iajs-3717	68	9	𝛾+𝐼(𝑡−𝜏	𝛾+𝐼(𝑡−𝜏	NOUN
iajs-3717	68	10	)	)	PUNCT
iajs-3717	68	11	−	−	PROPN
iajs-3717	68	12	𝜆𝐼	𝜆𝐼	NOUN
iajs-3717	68	13	−	−	NOUN
iajs-3717	68	14	𝐸2𝐼	𝐸2𝐼	NUM
iajs-3717	68	15	𝑑𝑍	𝑑𝑍	PROPN
iajs-3717	68	16	𝑑𝑡	𝑑𝑡	ADP
iajs-3717	68	17	=	=	SYM
iajs-3717	68	18	−𝜃𝑍	−𝜃𝑍	PROPN
iajs-3717	68	19	+	+	CCONJ
iajs-3717	68	20	ℎ𝐼(𝑡−𝜏)𝑍(𝑡−𝜏	ℎ𝐼(𝑡−𝜏)𝑍(𝑡−𝜏	NOUN
iajs-3717	68	21	)	)	PUNCT
iajs-3717	68	22	𝛾+𝐼(𝑡−𝜏	𝛾+𝐼(𝑡−𝜏	PROPN
iajs-3717	68	23	)	)	PUNCT
iajs-3717	68	24	−	−	PROPN
iajs-3717	68	25	𝐸3𝑧	𝐸3𝑧	NOUN
iajs-3717	68	26	(	(	PUNCT
iajs-3717	68	27	2	2	NUM
iajs-3717	68	28	)	)	PUNCT
iajs-3717	68	29	here	here	ADV
iajs-3717	68	30	,	,	PUNCT
iajs-3717	68	31	𝜏	𝜏	PROPN
iajs-3717	68	32	represents	represent	VERB
iajs-3717	68	33	time	time	NOUN
iajs-3717	68	34	delay	delay	NOUN
iajs-3717	68	35	.	.	PUNCT
iajs-3717	69	1	the	the	DET
iajs-3717	69	2	system	system	NOUN
iajs-3717	69	3	described	describe	VERB
iajs-3717	69	4	above	above	ADV
iajs-3717	69	5	has	have	VERB
iajs-3717	69	6	the	the	DET
iajs-3717	69	7	same	same	ADJ
iajs-3717	69	8	biological	biological	ADJ
iajs-3717	69	9	interpretation	interpretation	NOUN
iajs-3717	69	10	for	for	ADP
iajs-3717	69	11	its	its	PRON
iajs-3717	69	12	parameters	parameter	NOUN
iajs-3717	69	13	as	as	ADP
iajs-3717	69	14	those	those	PRON
iajs-3717	69	15	identified	identify	VERB
iajs-3717	69	16	in	in	ADP
iajs-3717	69	17	the	the	DET
iajs-3717	69	18	system	system	NOUN
iajs-3717	69	19	(	(	PUNCT
iajs-3717	69	20	1	1	NUM
iajs-3717	69	21	)	)	PUNCT
iajs-3717	69	22	.	.	PUNCT
iajs-3717	70	1	2	2	X
iajs-3717	70	2	.	.	X
iajs-3717	70	3	materials	material	NOUN
iajs-3717	70	4	and	and	CCONJ
iajs-3717	70	5	methods	method	NOUN
iajs-3717	70	6	2.1	2.1	NUM
iajs-3717	70	7	.	.	PUNCT
iajs-3717	70	8	positive	positive	ADJ
iajs-3717	70	9	and	and	CCONJ
iajs-3717	70	10	boundedness	boundedness	NOUN
iajs-3717	70	11	before	before	ADP
iajs-3717	70	12	embarking	embark	VERB
iajs-3717	70	13	on	on	ADP
iajs-3717	70	14	the	the	DET
iajs-3717	70	15	study	study	NOUN
iajs-3717	70	16	,	,	PUNCT
iajs-3717	70	17	it	it	PRON
iajs-3717	70	18	is	be	AUX
iajs-3717	70	19	essential	essential	ADJ
iajs-3717	70	20	to	to	PART
iajs-3717	70	21	verify	verify	VERB
iajs-3717	70	22	the	the	DET
iajs-3717	70	23	biological	biological	ADJ
iajs-3717	70	24	integrity	integrity	NOUN
iajs-3717	70	25	of	of	ADP
iajs-3717	70	26	the	the	DET
iajs-3717	70	27	proposed	propose	VERB
iajs-3717	70	28	model	model	NOUN
iajs-3717	70	29	.	.	PUNCT
iajs-3717	71	1	accordingly	accordingly	ADV
iajs-3717	71	2	,	,	PUNCT
iajs-3717	71	3	within	within	ADP
iajs-3717	71	4	this	this	DET
iajs-3717	71	5	section	section	NOUN
iajs-3717	71	6	,	,	PUNCT
iajs-3717	71	7	we	we	PRON
iajs-3717	71	8	introduce	introduce	VERB
iajs-3717	71	9	the	the	DET
iajs-3717	71	10	following	follow	VERB
iajs-3717	71	11	theorem	theorem	VERB
iajs-3717	71	12	,	,	PUNCT
iajs-3717	71	13	which	which	PRON
iajs-3717	71	14	investigates	investigate	VERB
iajs-3717	71	15	the	the	DET
iajs-3717	71	16	system	system	NOUN
iajs-3717	71	17	's	's	PART
iajs-3717	71	18	positivity	positivity	NOUN
iajs-3717	71	19	and	and	CCONJ
iajs-3717	71	20	boundedness	boundedness	PROPN
iajs-3717	71	21	.	.	PUNCT
iajs-3717	72	1	theorem	theorem	NOUN
iajs-3717	72	2	1	1	NUM
iajs-3717	72	3	.	.	PUNCT
iajs-3717	73	1	the	the	DET
iajs-3717	73	2	solutions	solution	NOUN
iajs-3717	73	3	of	of	ADP
iajs-3717	73	4	system	system	NOUN
iajs-3717	73	5	(	(	PUNCT
iajs-3717	73	6	2	2	X
iajs-3717	73	7	)	)	PUNCT
iajs-3717	73	8	are	be	AUX
iajs-3717	73	9	positive	positive	ADJ
iajs-3717	73	10	and	and	CCONJ
iajs-3717	73	11	bounded	bound	VERB
iajs-3717	73	12	.	.	PUNCT
iajs-3717	74	1	proof	proof	NOUN
iajs-3717	74	2	:	:	PUNCT
iajs-3717	74	3	first	first	ADV
iajs-3717	74	4	,	,	PUNCT
iajs-3717	74	5	it	it	PRON
iajs-3717	74	6	is	be	AUX
iajs-3717	74	7	proven	prove	VERB
iajs-3717	74	8	that	that	SCONJ
iajs-3717	74	9	for	for	ADP
iajs-3717	74	10	𝑡	𝑡	PROPN
iajs-3717	74	11	≥	≥	NOUN
iajs-3717	74	12	0	0	NUM
iajs-3717	75	1	all	all	DET
iajs-3717	75	2	solutions	solution	NOUN
iajs-3717	75	3	to	to	ADP
iajs-3717	75	4	system	system	NOUN
iajs-3717	75	5	(	(	PUNCT
iajs-3717	75	6	2	2	X
iajs-3717	75	7	)	)	PUNCT
iajs-3717	75	8	are	be	AUX
iajs-3717	75	9	positive	positive	ADJ
iajs-3717	75	10	.	.	PUNCT
iajs-3717	76	1	𝑑𝑆	𝑑𝑆	ADJ
iajs-3717	76	2	𝑑𝑡	𝑑𝑡	ADP
iajs-3717	76	3	≥	≥	NOUN
iajs-3717	76	4	−𝑆	−𝑆	X
iajs-3717	76	5	(	(	PUNCT
iajs-3717	76	6	𝑟(𝑆	𝑟(𝑆	X
iajs-3717	76	7	+	+	CCONJ
iajs-3717	76	8	𝐼	𝐼	PROPN
iajs-3717	76	9	)	)	PUNCT
iajs-3717	76	10	𝐾	𝐾	PROPN
iajs-3717	76	11	+	+	CCONJ
iajs-3717	76	12	𝑐𝐼	𝑐𝐼	PROPN
iajs-3717	76	13	+	+	CCONJ
iajs-3717	76	14	𝐸1	𝐸1	NOUN
iajs-3717	76	15	)	)	PUNCT
iajs-3717	76	16	consequently	consequently	ADV
iajs-3717	76	17	,	,	PUNCT
iajs-3717	76	18	it	it	PRON
iajs-3717	76	19	is	be	AUX
iajs-3717	76	20	calculated	calculate	VERB
iajs-3717	76	21	to	to	PART
iajs-3717	76	22	obtain	obtain	VERB
iajs-3717	76	23	it	it	PRON
iajs-3717	76	24	.	.	PUNCT
iajs-3717	77	1	𝑆(𝑡	𝑆(𝑡	VERB
iajs-3717	77	2	)	)	PUNCT
iajs-3717	77	3	≥	≥	NOUN
iajs-3717	78	1	𝑆(0)𝑒𝑥𝑝	𝑆(0)𝑒𝑥𝑝	NOUN
iajs-3717	78	2	−	−	PROPN
iajs-3717	78	3	{	{	PUNCT
iajs-3717	78	4	∫	∫	PROPN
iajs-3717	78	5	(	(	PUNCT
iajs-3717	78	6	𝑟(𝑆(ℴ)+𝐼(ℴ	𝑟(𝑆(ℴ)+𝐼(ℴ	PROPN
iajs-3717	78	7	)	)	PUNCT
iajs-3717	78	8	)	)	PUNCT
iajs-3717	79	1	𝐾	𝐾	PROPN
iajs-3717	79	2	+	+	CCONJ
iajs-3717	79	3	𝑐𝐼(ℴ	𝑐𝐼(ℴ	PROPN
iajs-3717	79	4	)	)	PUNCT
iajs-3717	79	5	+	+	CCONJ
iajs-3717	79	6	𝐸1	𝐸1	NOUN
iajs-3717	79	7	)	)	PUNCT
iajs-3717	79	8	𝑑(ℴ	𝑑(ℴ	NOUN
iajs-3717	79	9	)	)	PUNCT
iajs-3717	79	10	𝑡	𝑡	PROPN
iajs-3717	79	11	0	0	NUM
iajs-3717	79	12	}	}	PUNCT
iajs-3717	79	13	because	because	SCONJ
iajs-3717	79	14	𝑆(0	𝑆(0	PROPN
iajs-3717	79	15	)	)	PUNCT
iajs-3717	79	16	>	>	X
iajs-3717	79	17	0	0	X
iajs-3717	79	18	.	.	PUNCT
iajs-3717	80	1	we	we	PRON
iajs-3717	80	2	get	get	VERB
iajs-3717	80	3	𝑆(𝑡	𝑆(𝑡	VERB
iajs-3717	80	4	)	)	PUNCT
iajs-3717	80	5	>	>	X
iajs-3717	80	6	0	0	NUM
iajs-3717	81	1	for	for	ADP
iajs-3717	81	2	any	any	DET
iajs-3717	81	3	𝑆(0	𝑆(0	NUM
iajs-3717	81	4	)	)	PUNCT
iajs-3717	81	5	>	>	X
iajs-3717	81	6	0	0	X
iajs-3717	81	7	.	.	PUNCT
iajs-3717	82	1	the	the	DET
iajs-3717	82	2	proof	proof	NOUN
iajs-3717	82	3	of	of	ADP
iajs-3717	82	4	𝐼(𝑡	𝐼(𝑡	PROPN
iajs-3717	82	5	)	)	PUNCT
iajs-3717	82	6	>	>	X
iajs-3717	82	7	0	0	PUNCT
iajs-3717	82	8	and	and	CCONJ
iajs-3717	82	9	𝑍(𝑡	𝑍(𝑡	NOUN
iajs-3717	82	10	)	)	PUNCT
iajs-3717	82	11	>	>	X
iajs-3717	82	12	0	0	PUNCT
iajs-3717	82	13	for	for	SCONJ
iajs-3717	82	14	all	all	DET
iajs-3717	82	15	𝑡	𝑡	PROPN
iajs-3717	82	16	≥	≥	X
iajs-3717	82	17	0	0	NUM
iajs-3717	82	18	can	can	AUX
iajs-3717	82	19	be	be	AUX
iajs-3717	82	20	done	do	VERB
iajs-3717	82	21	in	in	ADP
iajs-3717	82	22	the	the	DET
iajs-3717	82	23	same	same	ADJ
iajs-3717	82	24	way	way	NOUN
iajs-3717	82	25	.	.	PUNCT
iajs-3717	83	1	next	next	ADV
iajs-3717	83	2	,	,	PUNCT
iajs-3717	83	3	the	the	DET
iajs-3717	83	4	following	follow	VERB
iajs-3717	83	5	is	be	AUX
iajs-3717	83	6	the	the	DET
iajs-3717	83	7	proof	proof	NOUN
iajs-3717	83	8	that	that	SCONJ
iajs-3717	83	9	the	the	DET
iajs-3717	83	10	solutions	solution	NOUN
iajs-3717	83	11	of	of	ADP
iajs-3717	83	12	system	system	NOUN
iajs-3717	83	13	(	(	PUNCT
iajs-3717	83	14	2	2	X
iajs-3717	83	15	)	)	PUNCT
iajs-3717	83	16	are	be	AUX
iajs-3717	83	17	bounded	bound	VERB
iajs-3717	83	18	for	for	ADP
iajs-3717	83	19	all	all	DET
iajs-3717	83	20	𝑡	𝑡	PROPN
iajs-3717	83	21	≥	≥	NOUN
iajs-3717	83	22	0	0	NUM
iajs-3717	83	23	.	.	PUNCT
iajs-3717	84	1	define	define	VERB
iajs-3717	84	2	𝒫(𝑡	𝒫(𝑡	NUM
iajs-3717	84	3	)	)	PUNCT
iajs-3717	84	4	=	=	PUNCT
iajs-3717	84	5	𝑆(𝑡	𝑆(𝑡	X
iajs-3717	84	6	)	)	PUNCT
iajs-3717	84	7	+	+	NUM
iajs-3717	84	8	𝐼(𝑡	𝐼(𝑡	NUM
iajs-3717	84	9	)	)	PUNCT
iajs-3717	84	10	+	+	CCONJ
iajs-3717	84	11	𝑍(𝑡	𝑍(𝑡	NOUN
iajs-3717	84	12	)	)	PUNCT
iajs-3717	84	13	as	as	ADP
iajs-3717	84	14	a	a	DET
iajs-3717	84	15	result	result	NOUN
iajs-3717	84	16	,	,	PUNCT
iajs-3717	84	17	the	the	DET
iajs-3717	84	18	following	follow	VERB
iajs-3717	84	19	is	be	AUX
iajs-3717	84	20	obtained	obtain	VERB
iajs-3717	84	21	:	:	PUNCT
iajs-3717	84	22	𝑑𝒫	𝑑𝒫	ADJ
iajs-3717	84	23	𝑑𝑡	𝑑𝑡	ADP
iajs-3717	84	24	+	+	NOUN
iajs-3717	84	25	𝓃𝒫	𝓃𝒫	NOUN
iajs-3717	84	26	≤	≤	ADJ
iajs-3717	84	27	𝑟𝑆	𝑟𝑆	NOUN
iajs-3717	84	28	,	,	PUNCT
iajs-3717	84	29	where	where	SCONJ
iajs-3717	84	30	𝓃	𝓃	NOUN
iajs-3717	84	31	=	=	SYM
iajs-3717	84	32	𝑚𝑖𝑛	𝑚𝑖𝑛	PROPN
iajs-3717	84	33	{	{	PUNCT
iajs-3717	84	34	𝐸1	𝐸1	NOUN
iajs-3717	84	35	,	,	PUNCT
iajs-3717	84	36	𝜆	𝜆	X
iajs-3717	85	1	+	+	CCONJ
iajs-3717	85	2	𝐸2	𝐸2	ADJ
iajs-3717	85	3	,	,	PUNCT
iajs-3717	85	4	𝜃	𝜃	NOUN
iajs-3717	85	5	+	+	CCONJ
iajs-3717	85	6	𝐸3	𝐸3	NOUN
iajs-3717	85	7	}	}	PUNCT
iajs-3717	85	8	.	.	PUNCT
iajs-3717	86	1	since	since	SCONJ
iajs-3717	86	2	𝑑𝑆	𝑑𝑆	ADJ
iajs-3717	86	3	𝑑𝑡	𝑑𝑡	ADP
iajs-3717	86	4	≤	≤	ADJ
iajs-3717	86	5	𝑟𝑆	𝑟𝑆	NOUN
iajs-3717	86	6	(	(	PUNCT
iajs-3717	86	7	1	1	NUM
iajs-3717	86	8	−	−	NOUN
iajs-3717	86	9	𝑆+𝐼	𝑆+𝐼	NOUN
iajs-3717	86	10	𝐾	𝐾	PROPN
iajs-3717	86	11	)	)	PUNCT
iajs-3717	86	12	−	−	PROPN
iajs-3717	86	13	𝐸1𝑆	𝐸1𝑆	ADP
iajs-3717	86	14	,	,	PUNCT
iajs-3717	86	15	we	we	PRON
iajs-3717	86	16	obtain	obtain	VERB
iajs-3717	86	17	according	accord	VERB
iajs-3717	86	18	the	the	DET
iajs-3717	86	19	comparison	comparison	NOUN
iajs-3717	86	20	theorem	theorem	NOUN
iajs-3717	86	21	(	(	PUNCT
iajs-3717	86	22	29	29	NUM
iajs-3717	86	23	)	)	PUNCT
iajs-3717	86	24	lim	lim	NOUN
iajs-3717	86	25	𝑡→∞	𝑡→∞	NUM
iajs-3717	86	26	𝑠𝑢𝑝	𝑠𝑢𝑝	PROPN
iajs-3717	86	27	𝑆(𝑡	𝑆(𝑡	VERB
iajs-3717	86	28	)	)	PUNCT
iajs-3717	86	29	≤	≤	NOUN
iajs-3717	86	30	𝐾(𝑟	𝐾(𝑟	NUM
iajs-3717	86	31	−	−	PROPN
iajs-3717	86	32	𝐸1	𝐸1	NOUN
iajs-3717	86	33	)	)	PUNCT
iajs-3717	86	34	𝑟	𝑟	NOUN
iajs-3717	86	35	thus	thus	ADV
iajs-3717	86	36	,	,	PUNCT
iajs-3717	86	37	for	for	ADP
iajs-3717	86	38	𝑡	𝑡	PROPN
iajs-3717	86	39	≥	≥	NOUN
iajs-3717	86	40	0	0	NUM
iajs-3717	86	41	,	,	PUNCT
iajs-3717	86	42	we	we	PRON
iajs-3717	86	43	have	have	AUX
iajs-3717	86	44	𝑆(𝑡	𝑆(𝑡	VERB
iajs-3717	86	45	)	)	PUNCT
iajs-3717	86	46	≤	≤	NUM
iajs-3717	86	47	𝐾(𝑟−𝐸1	𝐾(𝑟−𝐸1	NOUN
iajs-3717	86	48	)	)	PUNCT
iajs-3717	86	49	𝑟	𝑟	NOUN
iajs-3717	86	50	.	.	PUNCT
iajs-3717	87	1	which	which	PRON
iajs-3717	87	2	implies	imply	VERB
iajs-3717	87	3	that	that	SCONJ
iajs-3717	87	4	:	:	PUNCT
iajs-3717	87	5	𝑑𝒫	𝑑𝒫	ADJ
iajs-3717	87	6	𝑑𝑡	𝑑𝑡	ADP
iajs-3717	87	7	+	+	NOUN
iajs-3717	87	8	𝓃𝒫	𝓃𝒫	NOUN
iajs-3717	87	9	≤	≤	NOUN
iajs-3717	87	10	𝐾(𝑟	𝐾(𝑟	NUM
iajs-3717	87	11	−	−	PROPN
iajs-3717	87	12	𝐸1	𝐸1	NOUN
iajs-3717	87	13	)	)	PUNCT
iajs-3717	87	14	,	,	PUNCT
iajs-3717	87	15	then	then	ADV
iajs-3717	87	16	,	,	PUNCT
iajs-3717	87	17	after	after	ADP
iajs-3717	87	18	applying	apply	VERB
iajs-3717	87	19	the	the	DET
iajs-3717	87	20	gronwall	gronwall	ADJ
iajs-3717	87	21	lemma	lemma	PROPN
iajs-3717	87	22	to	to	ADP
iajs-3717	87	23	the	the	DET
iajs-3717	87	24	above	above	ADJ
iajs-3717	87	25	inequality	inequality	NOUN
iajs-3717	87	26	,	,	PUNCT
iajs-3717	87	27	we	we	PRON
iajs-3717	87	28	have	have	VERB
iajs-3717	87	29	for	for	ADP
iajs-3717	87	30	𝑡	𝑡	PROPN
iajs-3717	87	31	→	→	SYM
iajs-3717	87	32	∞	∞	NUM
iajs-3717	87	33	𝒫(𝑡	𝒫(𝑡	NUM
iajs-3717	87	34	)	)	PUNCT
iajs-3717	87	35	≤	≤	NUM
iajs-3717	87	36	𝐾(𝑟−𝐸1	𝐾(𝑟−𝐸1	NOUN
iajs-3717	87	37	)	)	PUNCT
iajs-3717	88	1	𝓃	𝓃	NOUN
iajs-3717	88	2	this	this	PRON
iajs-3717	88	3	implies	imply	VERB
iajs-3717	88	4	that	that	SCONJ
iajs-3717	88	5	the	the	DET
iajs-3717	88	6	solutions	solution	NOUN
iajs-3717	88	7	are	be	AUX
iajs-3717	88	8	bounded	bound	VERB
iajs-3717	88	9	.	.	PUNCT
iajs-3717	89	1	2.2	2.2	NUM
iajs-3717	89	2	.	.	PUNCT
iajs-3717	90	1	local	local	ADJ
iajs-3717	90	2	stability	stability	NOUN
iajs-3717	90	3	and	and	CCONJ
iajs-3717	90	4	hopf	hopf	ADJ
iajs-3717	90	5	bifurcation	bifurcation	NOUN
iajs-3717	90	6	in	in	ADP
iajs-3717	90	7	this	this	DET
iajs-3717	90	8	subsection	subsection	NOUN
iajs-3717	90	9	,	,	PUNCT
iajs-3717	90	10	we	we	PRON
iajs-3717	90	11	will	will	AUX
iajs-3717	90	12	determine	determine	VERB
iajs-3717	90	13	the	the	DET
iajs-3717	90	14	local	local	ADJ
iajs-3717	90	15	stability	stability	NOUN
iajs-3717	90	16	of	of	ADP
iajs-3717	90	17	each	each	DET
iajs-3717	90	18	equilibrium	equilibrium	NOUN
iajs-3717	90	19	point	point	NOUN
iajs-3717	90	20	within	within	ADP
iajs-3717	90	21	system	system	NOUN
iajs-3717	90	22	(	(	PUNCT
iajs-3717	90	23	2	2	NUM
iajs-3717	90	24	)	)	PUNCT
iajs-3717	90	25	.	.	PUNCT
iajs-3717	91	1	it	it	PRON
iajs-3717	91	2	is	be	AUX
iajs-3717	91	3	well	well	ADV
iajs-3717	91	4	-	-	PUNCT
iajs-3717	91	5	known	know	VERB
iajs-3717	91	6	that	that	SCONJ
iajs-3717	91	7	an	an	DET
iajs-3717	91	8	equilibrium	equilibrium	NOUN
iajs-3717	91	9	point	point	NOUN
iajs-3717	91	10	's	's	PART
iajs-3717	91	11	location	location	NOUN
iajs-3717	91	12	and	and	CCONJ
iajs-3717	91	13	number	number	NOUN
iajs-3717	91	14	unchanged	unchanged	ADJ
iajs-3717	91	15	with	with	ADP
iajs-3717	91	16	time	time	NOUN
iajs-3717	91	17	delay	delay	NOUN
iajs-3717	91	18	..	..	PUNCT
iajs-3717	91	19	as	as	ADP
iajs-3717	91	20	a	a	DET
iajs-3717	91	21	result	result	NOUN
iajs-3717	91	22	,	,	PUNCT
iajs-3717	91	23	system	system	NOUN
iajs-3717	91	24	(	(	PUNCT
iajs-3717	91	25	2	2	X
iajs-3717	91	26	)	)	PUNCT
iajs-3717	91	27	has	have	VERB
iajs-3717	91	28	four	four	NUM
iajs-3717	91	29	equilibrium	equilibrium	NOUN
iajs-3717	91	30	points	point	NOUN
iajs-3717	91	31	.	.	PUNCT
iajs-3717	92	1	for	for	ADP
iajs-3717	92	2	further	further	ADJ
iajs-3717	92	3	details	detail	NOUN
iajs-3717	92	4	,	,	PUNCT
iajs-3717	92	5	see	see	VERB
iajs-3717	92	6	(	(	PUNCT
iajs-3717	92	7	28	28	NUM
iajs-3717	92	8	)	)	PUNCT
iajs-3717	92	9	ihjpas	ihjpa	NOUN
iajs-3717	92	10	.	.	PUNCT
iajs-3717	93	1	2025,38(2	2025,38(2	PROPN
iajs-3717	93	2	)	)	PUNCT
iajs-3717	93	3	364	364	NUM
iajs-3717	93	4			NOUN
iajs-3717	93	5	the	the	DET
iajs-3717	93	6	first	first	ADJ
iajs-3717	93	7	equilibrium	equilibrium	NOUN
iajs-3717	93	8	point	point	NOUN
iajs-3717	93	9	,	,	PUNCT
iajs-3717	93	10	namely	namely	ADV
iajs-3717	93	11	the	the	DET
iajs-3717	93	12	vanishing	vanish	VERB
iajs-3717	93	13	equilibrium	equilibrium	NOUN
iajs-3717	93	14	point	point	NOUN
iajs-3717	93	15	denoted	denote	VERB
iajs-3717	93	16	𝐹0	𝐹0	NOUN
iajs-3717	93	17	=	=	SYM
iajs-3717	93	18	(	(	PUNCT
iajs-3717	93	19	0,0,0	0,0,0	NOUN
iajs-3717	93	20	)	)	PUNCT
iajs-3717	93	21	always	always	ADV
iajs-3717	93	22	exists	exist	VERB
iajs-3717	93	23	.	.	PUNCT
iajs-3717	94	1			X
iajs-3717	95	1	the	the	DET
iajs-3717	95	2	second	second	ADJ
iajs-3717	95	3	equilibrium	equilibrium	NOUN
iajs-3717	95	4	point	point	NOUN
iajs-3717	95	5	,	,	PUNCT
iajs-3717	95	6	namely	namely	ADV
iajs-3717	95	7	the	the	DET
iajs-3717	95	8	axial	axial	ADJ
iajs-3717	95	9	equilibrium	equilibrium	NOUN
iajs-3717	95	10	point	point	NOUN
iajs-3717	95	11	denoted	denote	VERB
iajs-3717	95	12	𝐹1	𝐹1	PROPN
iajs-3717	95	13	=	=	SYM
iajs-3717	95	14	(	(	PUNCT
iajs-3717	95	15	𝐾(𝑟−𝐸1	𝐾(𝑟−𝐸1	PROPN
iajs-3717	95	16	)	)	PUNCT
iajs-3717	95	17	𝑟	𝑟	NOUN
iajs-3717	95	18	,	,	PUNCT
iajs-3717	95	19	0,0	0,0	NOUN
iajs-3717	95	20	)	)	PUNCT
iajs-3717	95	21	always	always	ADV
iajs-3717	95	22	exists	exist	VERB
iajs-3717	95	23	.	.	PUNCT
iajs-3717	96	1			AUX
iajs-3717	97	1	the	the	DET
iajs-3717	97	2	third	third	ADJ
iajs-3717	97	3	equilibrium	equilibrium	NOUN
iajs-3717	97	4	point	point	NOUN
iajs-3717	97	5	,	,	PUNCT
iajs-3717	97	6	namely	namely	ADV
iajs-3717	97	7	the	the	DET
iajs-3717	97	8	planer	planer	NOUN
iajs-3717	97	9	equilibrium	equilibrium	NOUN
iajs-3717	97	10	point	point	NOUN
iajs-3717	97	11	denoted	denote	VERB
iajs-3717	97	12	𝐹2	𝐹2	PROPN
iajs-3717	97	13	=	=	SYM
iajs-3717	97	14	(	(	PUNCT
iajs-3717	97	15	𝑆̅	𝑆̅	NOUN
iajs-3717	97	16	,	,	PUNCT
iajs-3717	97	17	𝐼,̅	𝐼,̅	ADJ
iajs-3717	97	18	0	0	NUM
iajs-3717	97	19	)	)	PUNCT
iajs-3717	97	20	,	,	PUNCT
iajs-3717	97	21	where	where	SCONJ
iajs-3717	97	22	𝑆̅	𝑆̅	NOUN
iajs-3717	97	23	=	=	SYM
iajs-3717	98	1	𝐸2	𝐸2	PROPN
iajs-3717	98	2	+	+	CCONJ
iajs-3717	98	3	𝜆	𝜆	DET
iajs-3717	98	4	𝐶⁄	𝐶⁄	PROPN
iajs-3717	98	5	(	(	PUNCT
iajs-3717	98	6	3	3	NUM
iajs-3717	98	7	)	)	PUNCT
iajs-3717	98	8	𝐼	𝐼	ADP
iajs-3717	98	9	̅	̅	NOUN
iajs-3717	98	10	=	=	SYM
iajs-3717	98	11	𝐶𝐾(𝑟	𝐶𝐾(𝑟	NOUN
iajs-3717	98	12	−	−	PROPN
iajs-3717	98	13	𝐸1	𝐸1	NOUN
iajs-3717	98	14	)	)	PUNCT
iajs-3717	98	15	−	−	PROPN
iajs-3717	99	1	𝑟(𝜆	𝑟(𝜆	PROPN
iajs-3717	99	2	+	+	CCONJ
iajs-3717	99	3	𝐸2	𝐸2	ADJ
iajs-3717	99	4	)	)	PUNCT
iajs-3717	99	5	(	(	PUNCT
iajs-3717	99	6	𝑟	𝑟	X
iajs-3717	99	7	+	+	CCONJ
iajs-3717	99	8	𝐶𝐾)𝐶⁄	𝐶𝐾)𝐶⁄	PROPN
iajs-3717	99	9	(	(	PUNCT
iajs-3717	99	10	4	4	X
iajs-3717	99	11	)	)	PUNCT
iajs-3717	99	12	it	it	PRON
iajs-3717	99	13	is	be	AUX
iajs-3717	99	14	clear	clear	ADJ
iajs-3717	99	15	that	that	SCONJ
iajs-3717	99	16	𝐹2	𝐹2	PROPN
iajs-3717	99	17	is	be	AUX
iajs-3717	99	18	exists	exist	VERB
iajs-3717	99	19	if	if	SCONJ
iajs-3717	99	20	the	the	DET
iajs-3717	99	21	following	follow	VERB
iajs-3717	99	22	condition	condition	NOUN
iajs-3717	99	23	satisfied	satisfy	VERB
iajs-3717	99	24	𝑟(𝜆	𝑟(𝜆	PROPN
iajs-3717	99	25	+	+	CCONJ
iajs-3717	99	26	𝐸2	𝐸2	ADJ
iajs-3717	99	27	)	)	PUNCT
iajs-3717	99	28	<	<	X
iajs-3717	100	1	𝑐𝐾(𝑟	𝑐𝐾(𝑟	ADP
iajs-3717	100	2	−	−	PROPN
iajs-3717	100	3	𝐸1	𝐸1	NOUN
iajs-3717	100	4	)	)	PUNCT
iajs-3717	100	5	(	(	PUNCT
iajs-3717	100	6	5	5	NUM
iajs-3717	100	7	)	)	PUNCT
iajs-3717	100	8			NOUN
iajs-3717	101	1	the	the	DET
iajs-3717	101	2	fourth	fourth	ADJ
iajs-3717	101	3	equilibrium	equilibrium	NOUN
iajs-3717	101	4	point	point	NOUN
iajs-3717	101	5	,	,	PUNCT
iajs-3717	101	6	namely	namely	ADV
iajs-3717	101	7	the	the	DET
iajs-3717	101	8	positive	positive	ADJ
iajs-3717	101	9	equilibrium	equilibrium	NOUN
iajs-3717	101	10	point	point	NOUN
iajs-3717	101	11	denoted	denote	VERB
iajs-3717	101	12	𝐹3	𝐹3	PROPN
iajs-3717	101	13	=	=	SYM
iajs-3717	101	14	(	(	PUNCT
iajs-3717	101	15	𝑆∗	𝑆∗	X
iajs-3717	101	16	,	,	PUNCT
iajs-3717	101	17	𝐼∗	𝐼∗	PROPN
iajs-3717	101	18	,	,	PUNCT
iajs-3717	101	19	𝑍∗	𝑍∗	NOUN
iajs-3717	101	20	)	)	PUNCT
iajs-3717	101	21	,	,	PUNCT
iajs-3717	101	22	where	where	SCONJ
iajs-3717	101	23	𝑆∗	𝑆∗	PRON
iajs-3717	101	24	=	=	SYM
iajs-3717	101	25	ℎ𝐾(𝑟−𝐸1)−(𝜃+𝐸3)[𝐾(𝑟−𝐸1)−𝛾(𝑟+𝑐𝐾	ℎ𝐾(𝑟−𝐸1)−(𝜃+𝐸3)[𝐾(𝑟−𝐸1)−𝛾(𝑟+𝑐𝐾	NOUN
iajs-3717	101	26	)	)	PUNCT
iajs-3717	101	27	]	]	PUNCT
iajs-3717	101	28	𝑟(ℎ−(𝜃+𝐸3	𝑟(ℎ−(𝜃+𝐸3	X
iajs-3717	101	29	)	)	PUNCT
iajs-3717	101	30	(	(	PUNCT
iajs-3717	101	31	6	6	NUM
iajs-3717	101	32	)	)	PUNCT
iajs-3717	101	33	𝐼∗	𝐼∗	NOUN
iajs-3717	102	1	=	=	SYM
iajs-3717	102	2	𝛾(𝐸3+𝜃	𝛾(𝐸3+𝜃	PROPN
iajs-3717	102	3	)	)	PUNCT
iajs-3717	103	1	ℎ−(𝜃+𝐸3	ℎ−(𝜃+𝐸3	NOUN
iajs-3717	103	2	)	)	PUNCT
iajs-3717	103	3	;	;	PUNCT
iajs-3717	103	4	ℎ	ℎ	PROPN
iajs-3717	103	5	−	−	PROPN
iajs-3717	103	6	(	(	PUNCT
iajs-3717	103	7	𝜃	𝜃	NOUN
iajs-3717	103	8	+	+	X
iajs-3717	103	9	𝐸3	𝐸3	NOUN
iajs-3717	103	10	)	)	PUNCT
iajs-3717	103	11	≠	≠	PROPN
iajs-3717	103	12	0	0	NUM
iajs-3717	103	13	(	(	PUNCT
iajs-3717	103	14	7	7	NUM
iajs-3717	103	15	)	)	PUNCT
iajs-3717	103	16	𝑍∗	𝑍∗	NOUN
iajs-3717	104	1	=	=	SYM
iajs-3717	104	2	(	(	PUNCT
iajs-3717	104	3	𝛾+𝐼∗)(𝐶𝑆∗−(𝜆+𝐸3	𝛾+𝐼∗)(𝐶𝑆∗−(𝜆+𝐸3	PROPN
iajs-3717	104	4	)	)	PUNCT
iajs-3717	104	5	)	)	PUNCT
iajs-3717	105	1	𝛼	𝛼	X
iajs-3717	105	2	(	(	PUNCT
iajs-3717	105	3	8)	8)	NUM
iajs-3717	105	4	it	it	PRON
iajs-3717	105	5	is	be	AUX
iajs-3717	105	6	clear	clear	ADJ
iajs-3717	105	7	that	that	SCONJ
iajs-3717	105	8	𝐹3	𝐹3	PROPN
iajs-3717	105	9	is	be	AUX
iajs-3717	105	10	exists	exist	VERB
iajs-3717	105	11	if	if	SCONJ
iajs-3717	105	12	the	the	DET
iajs-3717	105	13	following	follow	VERB
iajs-3717	105	14	conditions	condition	NOUN
iajs-3717	105	15	are	be	AUX
iajs-3717	105	16	hold	hold	VERB
iajs-3717	105	17	𝛾	𝛾	ADP
iajs-3717	105	18	<	<	X
iajs-3717	105	19	𝐾(𝑟−𝐸1)(ℎ−(𝜃+𝐸3	𝐾(𝑟−𝐸1)(ℎ−(𝜃+𝐸3	NOUN
iajs-3717	105	20	)	)	PUNCT
iajs-3717	105	21	)	)	PUNCT
iajs-3717	105	22	(	(	PUNCT
iajs-3717	105	23	𝑟+𝐶𝐾)(𝜃+𝐸3	𝑟+𝐶𝐾)(𝜃+𝐸3	NUM
iajs-3717	105	24	)	)	PUNCT
iajs-3717	105	25	(	(	PUNCT
iajs-3717	105	26	9	9	X
iajs-3717	105	27	)	)	PUNCT
iajs-3717	105	28	𝜃	𝜃	NOUN
iajs-3717	105	29	+	+	NUM
iajs-3717	105	30	𝐸3	𝐸3	NOUN
iajs-3717	105	31	<	<	X
iajs-3717	105	32	ℎ	ℎ	X
iajs-3717	105	33	(	(	PUNCT
iajs-3717	105	34	10	10	NUM
iajs-3717	105	35	)	)	PUNCT
iajs-3717	105	36	𝜆+𝐸2	𝜆+𝐸2	PROPN
iajs-3717	105	37	𝐶	𝐶	PROPN
iajs-3717	105	38	<	<	X
iajs-3717	105	39	𝑆∗	𝑆∗	X
iajs-3717	105	40	(	(	PUNCT
iajs-3717	105	41	11	11	NUM
iajs-3717	105	42	)	)	PUNCT
iajs-3717	105	43	now	now	ADV
iajs-3717	105	44	,	,	PUNCT
iajs-3717	105	45	the	the	DET
iajs-3717	105	46	linearization	linearization	NOUN
iajs-3717	105	47	method	method	NOUN
iajs-3717	105	48	is	be	AUX
iajs-3717	105	49	used	use	VERB
iajs-3717	105	50	to	to	PART
iajs-3717	105	51	determine	determine	VERB
iajs-3717	105	52	the	the	DET
iajs-3717	105	53	stability	stability	NOUN
iajs-3717	105	54	of	of	ADP
iajs-3717	105	55	the	the	DET
iajs-3717	105	56	above	above	ADJ
iajs-3717	105	57	equilibrium	equilibrium	NOUN
iajs-3717	105	58	points	point	NOUN
iajs-3717	105	59	.	.	PUNCT
iajs-3717	106	1	the	the	DET
iajs-3717	106	2	general	general	ADJ
iajs-3717	106	3	jacobian	jacobian	ADJ
iajs-3717	106	4	matrix	matrix	NOUN
iajs-3717	106	5	(	(	PUNCT
iajs-3717	106	6	𝐽𝑚	𝐽𝑚	PROPN
iajs-3717	106	7	)	)	PUNCT
iajs-3717	106	8	for	for	ADP
iajs-3717	106	9	system	system	NOUN
iajs-3717	106	10	(	(	PUNCT
iajs-3717	106	11	2	2	NUM
iajs-3717	106	12	)	)	PUNCT
iajs-3717	106	13	at	at	ADP
iajs-3717	106	14	any	any	DET
iajs-3717	106	15	equilibrium	equilibrium	NOUN
iajs-3717	106	16	point	point	NOUN
iajs-3717	106	17	𝐹	𝐹	PROPN
iajs-3717	106	18	=	=	SYM
iajs-3717	106	19	(	(	PUNCT
iajs-3717	106	20	𝑆	𝑆	PROPN
iajs-3717	106	21	,	,	PUNCT
iajs-3717	106	22	𝐼	𝐼	PROPN
iajs-3717	106	23	,	,	PUNCT
iajs-3717	106	24	𝑍	𝑍	PROPN
iajs-3717	106	25	)	)	PUNCT
iajs-3717	106	26	is	be	AUX
iajs-3717	106	27	𝐽𝐹	𝐽𝐹	PROPN
iajs-3717	106	28	=	=	SYM
iajs-3717	106	29	[	[	PUNCT
iajs-3717	106	30	𝑎𝑖𝑗	𝑎𝑖𝑗	X
iajs-3717	106	31	]	]	PUNCT
iajs-3717	106	32	,	,	PUNCT
iajs-3717	106	33	𝑖𝑗	𝑖𝑗	X
iajs-3717	106	34	=	=	SYM
iajs-3717	106	35	0,1,2,3	0,1,2,3	NUM
iajs-3717	106	36	(	(	PUNCT
iajs-3717	106	37	12	12	NUM
iajs-3717	106	38	)	)	PUNCT
iajs-3717	106	39	where	where	SCONJ
iajs-3717	106	40	𝑎11	𝑎11	VERB
iajs-3717	106	41	=	=	SYM
iajs-3717	106	42	𝑟	𝑟	NOUN
iajs-3717	106	43	−	−	PROPN
iajs-3717	106	44	(	(	PUNCT
iajs-3717	106	45	𝑟	𝑟	X
iajs-3717	106	46	𝐾	𝐾	PROPN
iajs-3717	106	47	(	(	PUNCT
iajs-3717	106	48	2𝑆	2𝑆	PROPN
iajs-3717	106	49	+	+	CCONJ
iajs-3717	106	50	𝐼	𝐼	PROPN
iajs-3717	106	51	)	)	PUNCT
iajs-3717	106	52	+	+	CCONJ
iajs-3717	106	53	𝐶𝐼	𝐶𝐼	PROPN
iajs-3717	106	54	+	+	CCONJ
iajs-3717	106	55	𝐸1	𝐸1	NOUN
iajs-3717	106	56	)	)	PUNCT
iajs-3717	106	57	;	;	PUNCT
iajs-3717	106	58	𝑎12	𝑎12	NOUN
iajs-3717	106	59	=	=	SYM
iajs-3717	106	60	−	−	PROPN
iajs-3717	106	61	(	(	PUNCT
iajs-3717	106	62	𝑟	𝑟	X
iajs-3717	106	63	𝐾	𝐾	PROPN
iajs-3717	106	64	+	+	CCONJ
iajs-3717	106	65	𝐶	𝐶	PROPN
iajs-3717	106	66	)	)	PUNCT
iajs-3717	106	67	𝑆	𝑆	PROPN
iajs-3717	106	68	;	;	PUNCT
iajs-3717	106	69	𝑎13	𝑎13	VERB
iajs-3717	106	70	=	=	SYM
iajs-3717	106	71	0	0	NUM
iajs-3717	106	72	;	;	PUNCT
iajs-3717	106	73	𝑎21	𝑎21	NOUN
iajs-3717	106	74	=	=	SYM
iajs-3717	106	75	𝐶𝐼	𝐶𝐼	PROPN
iajs-3717	106	76	;	;	PUNCT
iajs-3717	106	77	𝑎22	𝑎22	NOUN
iajs-3717	106	78	=	=	SYM
iajs-3717	106	79	𝐶𝑆	𝐶𝑆	PROPN
iajs-3717	106	80	−	−	PROPN
iajs-3717	107	1	(	(	PUNCT
iajs-3717	107	2	𝛼𝛾𝑍𝑒−𝜇𝜏	𝛼𝛾𝑍𝑒−𝜇𝜏	X
iajs-3717	107	3	(	(	PUNCT
iajs-3717	107	4	𝛾+𝐼)2	𝛾+𝐼)2	X
iajs-3717	107	5	−	−	PROPN
iajs-3717	107	6	(	(	PUNCT
iajs-3717	107	7	𝜆	𝜆	PROPN
iajs-3717	107	8	+	+	X
iajs-3717	107	9	𝐸2	𝐸2	ADJ
iajs-3717	107	10	)	)	PUNCT
iajs-3717	107	11	;	;	PUNCT
iajs-3717	107	12	𝑎23	𝑎23	NOUN
iajs-3717	107	13	=	=	SYM
iajs-3717	107	14	−𝛼𝐼𝑒−𝜇𝜏	−𝛼𝐼𝑒−𝜇𝜏	PROPN
iajs-3717	107	15	𝛾+𝐼	𝛾+𝐼	NOUN
iajs-3717	107	16	;	;	PUNCT
iajs-3717	107	17	𝑎31	𝑎31	NUM
iajs-3717	107	18	=	=	SYM
iajs-3717	107	19	0	0	NUM
iajs-3717	107	20	;	;	PUNCT
iajs-3717	107	21	𝑎32	𝑎32	NOUN
iajs-3717	107	22	=	=	SYM
iajs-3717	107	23	ℎ𝛾𝑍𝑒−𝜇𝜏	ℎ𝛾𝑍𝑒−𝜇𝜏	NOUN
iajs-3717	107	24	(	(	PUNCT
iajs-3717	107	25	𝛾+𝐼)2	𝛾+𝐼)2	NOUN
iajs-3717	107	26	;	;	PUNCT
iajs-3717	107	27	𝑎33	𝑎33	VERB
iajs-3717	107	28	=	=	SYM
iajs-3717	107	29	ℎ𝐼𝑒−𝜇𝜏	ℎ𝐼𝑒−𝜇𝜏	ADJ
iajs-3717	107	30	𝛾+𝐼	𝛾+𝐼	NOUN
iajs-3717	107	31	−	−	PROPN
iajs-3717	107	32	(	(	PUNCT
iajs-3717	107	33	𝜃	𝜃	NOUN
iajs-3717	107	34	+	+	X
iajs-3717	107	35	𝐸3	𝐸3	NOUN
iajs-3717	107	36	)	)	PUNCT
iajs-3717	107	37	.	.	PUNCT
iajs-3717	108	1	then	then	ADV
iajs-3717	108	2	,	,	PUNCT
iajs-3717	108	3	the	the	DET
iajs-3717	108	4	characteristic	characteristic	ADJ
iajs-3717	108	5	equation	equation	NOUN
iajs-3717	108	6	corresponding	correspond	VERB
iajs-3717	108	7	to	to	ADP
iajs-3717	108	8	the	the	DET
iajs-3717	108	9	matrix	matrix	NOUN
iajs-3717	108	10	above	above	ADV
iajs-3717	108	11	can	can	AUX
iajs-3717	108	12	be	be	AUX
iajs-3717	108	13	expressed	express	VERB
iajs-3717	108	14	as	as	ADP
iajs-3717	108	15	:	:	PUNCT
iajs-3717	108	16	𝑞1(𝜇	𝑞1(𝜇	PROPN
iajs-3717	108	17	)	)	PUNCT
iajs-3717	108	18	+	+	X
iajs-3717	108	19	𝑞2(𝜇)𝑒	𝑞2(𝜇)𝑒	X
iajs-3717	108	20	−𝜇𝜏	−𝜇𝜏	X
iajs-3717	108	21	=	=	SYM
iajs-3717	108	22	0	0	NUM
iajs-3717	108	23	(	(	PUNCT
iajs-3717	108	24	13	13	NUM
iajs-3717	108	25	)	)	PUNCT
iajs-3717	108	26	where	where	SCONJ
iajs-3717	108	27	𝑞1(𝜇	𝑞1(𝜇	NOUN
iajs-3717	108	28	)	)	PUNCT
iajs-3717	108	29	𝑎𝑛𝑑	𝑎𝑛𝑑	PROPN
iajs-3717	108	30	𝑞2(𝜇	𝑞2(𝜇	PROPN
iajs-3717	108	31	)	)	PUNCT
iajs-3717	108	32	are	be	AUX
iajs-3717	108	33	the	the	DET
iajs-3717	108	34	polynomial	polynomial	NOUN
iajs-3717	108	35	of	of	ADP
iajs-3717	108	36	𝜇	𝜇	ADP
iajs-3717	108	37	the	the	DET
iajs-3717	108	38	(	(	PUNCT
iajs-3717	108	39	𝐽𝑚	𝐽𝑚	PROPN
iajs-3717	108	40	)	)	PUNCT
iajs-3717	108	41	for	for	ADP
iajs-3717	108	42	system	system	NOUN
iajs-3717	108	43	(	(	PUNCT
iajs-3717	108	44	2	2	NUM
iajs-3717	108	45	)	)	PUNCT
iajs-3717	108	46	at	at	ADP
iajs-3717	108	47	𝐹0is	𝐹0is	NOUN
iajs-3717	108	48	as	as	SCONJ
iajs-3717	108	49	follows	follow	VERB
iajs-3717	108	50	:	:	PUNCT
iajs-3717	108	51	𝐽𝐹0	𝐽𝐹0	PROPN
iajs-3717	108	52	=	=	PUNCT
iajs-3717	109	1	[	[	PUNCT
iajs-3717	109	2	𝑟	𝑟	X
iajs-3717	109	3	−	−	PROPN
iajs-3717	109	4	𝐸1	𝐸1	NOUN
iajs-3717	109	5	0	0	NUM
iajs-3717	109	6	0	0	NUM
iajs-3717	109	7	0	0	NUM
iajs-3717	109	8	−(𝜆	−(𝜆	PROPN
iajs-3717	109	9	+	+	CCONJ
iajs-3717	109	10	𝐸2	𝐸2	ADJ
iajs-3717	109	11	)	)	PUNCT
iajs-3717	109	12	0	0	NUM
iajs-3717	109	13	0	0	NUM
iajs-3717	109	14	0	0	NUM
iajs-3717	109	15	−(𝜃	−(𝜃	NOUN
iajs-3717	109	16	+	+	CCONJ
iajs-3717	109	17	𝐸3	𝐸3	NOUN
iajs-3717	109	18	)	)	PUNCT
iajs-3717	109	19	]	]	PUNCT
iajs-3717	110	1	(	(	PUNCT
iajs-3717	110	2	14	14	NUM
iajs-3717	110	3	)	)	PUNCT
iajs-3717	110	4	the	the	DET
iajs-3717	110	5	eigenvalues	eigenvalue	NOUN
iajs-3717	110	6	of	of	ADP
iajs-3717	110	7	𝐽𝐹0	𝐽𝐹0	NOUN
iajs-3717	110	8	are	be	AUX
iajs-3717	110	9	𝜇01	𝜇01	NOUN
iajs-3717	110	10	=	=	SYM
iajs-3717	110	11	𝑟	𝑟	NOUN
iajs-3717	110	12	−	−	PROPN
iajs-3717	110	13	𝐸1	𝐸1	NOUN
iajs-3717	110	14	,	,	PUNCT
iajs-3717	110	15	𝜇02	𝜇02	NOUN
iajs-3717	110	16	=	=	PUNCT
iajs-3717	110	17	−(𝜆	−(𝜆	NOUN
iajs-3717	110	18	+	+	CCONJ
iajs-3717	110	19	𝐸2	𝐸2	ADJ
iajs-3717	110	20	)	)	PUNCT
iajs-3717	110	21	<	<	X
iajs-3717	110	22	0	0	PUNCT
iajs-3717	110	23	and	and	CCONJ
iajs-3717	110	24	𝜇03	𝜇03	NOUN
iajs-3717	110	25	=	=	SYM
iajs-3717	110	26	−(𝜃	−(𝜃	NOUN
iajs-3717	110	27	+	+	CCONJ
iajs-3717	110	28	𝐸3	𝐸3	NOUN
iajs-3717	110	29	)	)	PUNCT
iajs-3717	110	30	<	<	X
iajs-3717	111	1	0	0	X
iajs-3717	111	2	.	.	PUNCT
iajs-3717	112	1	the	the	DET
iajs-3717	112	2	necessary	necessary	ADJ
iajs-3717	112	3	condition	condition	NOUN
iajs-3717	112	4	of	of	ADP
iajs-3717	112	5	the	the	DET
iajs-3717	112	6	coexistence	coexistence	NOUN
iajs-3717	112	7	of	of	ADP
iajs-3717	112	8	all	all	DET
iajs-3717	112	9	species	specie	NOUN
iajs-3717	112	10	is	be	AUX
iajs-3717	112	11	𝑟	𝑟	PRON
iajs-3717	112	12	−	−	PROPN
iajs-3717	112	13	𝐸1	𝐸1	PROPN
iajs-3717	112	14	>	>	X
iajs-3717	112	15	0	0	PUNCT
iajs-3717	112	16	see	see	VERB
iajs-3717	112	17	in	in	ADP
iajs-3717	112	18	(	(	PUNCT
iajs-3717	112	19	24	24	NUM
iajs-3717	112	20	)	)	PUNCT
iajs-3717	112	21	obtained	obtain	VERB
iajs-3717	112	22	that	that	DET
iajs-3717	112	23	𝜇01	𝜇01	NOUN
iajs-3717	112	24	>	>	X
iajs-3717	112	25	0	0	NUM
iajs-3717	112	26	,	,	PUNCT
iajs-3717	112	27	thus	thus	ADV
iajs-3717	112	28	𝐹0	𝐹0	NOUN
iajs-3717	112	29	is	be	AUX
iajs-3717	112	30	unstable	unstable	ADJ
iajs-3717	112	31	saddle	saddle	NOUN
iajs-3717	112	32	point	point	NOUN
iajs-3717	112	33	for	for	ADP
iajs-3717	112	34	all	all	DET
iajs-3717	112	35	𝜏	𝜏	PRON
iajs-3717	112	36	≥	≥	NOUN
iajs-3717	112	37	0	0	NUM
iajs-3717	113	1	the	the	DET
iajs-3717	113	2	(	(	PUNCT
iajs-3717	113	3	𝐽𝑚	𝐽𝑚	PROPN
iajs-3717	113	4	)	)	PUNCT
iajs-3717	113	5	for	for	ADP
iajs-3717	113	6	system	system	NOUN
iajs-3717	113	7	(	(	PUNCT
iajs-3717	113	8	2	2	NUM
iajs-3717	113	9	)	)	PUNCT
iajs-3717	113	10	at	at	ADP
iajs-3717	113	11	𝐹1	𝐹1	PROPN
iajs-3717	113	12	is	be	AUX
iajs-3717	113	13	as	as	SCONJ
iajs-3717	113	14	follows	follow	VERB
iajs-3717	113	15	:	:	PUNCT
iajs-3717	113	16	ihjpas	ihjpas	PROPN
iajs-3717	113	17	.	.	PUNCT
iajs-3717	114	1	2025,38(2	2025,38(2	PROPN
iajs-3717	114	2	)	)	PUNCT
iajs-3717	114	3	365	365	NUM
iajs-3717	115	1	𝐽𝐹1	𝐽𝐹1	PROPN
iajs-3717	115	2	=	=	PUNCT
iajs-3717	116	1	[	[	PUNCT
iajs-3717	116	2	−(𝑟	−(𝑟	NOUN
iajs-3717	116	3	−	−	PROPN
iajs-3717	116	4	𝐸1	𝐸1	NOUN
iajs-3717	116	5	)	)	PUNCT
iajs-3717	116	6	−	−	PROPN
iajs-3717	117	1	(	(	PUNCT
iajs-3717	117	2	𝑟−𝐸1)(𝑟+𝐶𝐾	𝑟−𝐸1)(𝑟+𝐶𝐾	PROPN
iajs-3717	117	3	)	)	PUNCT
iajs-3717	117	4	𝑟	𝑟	NOUN
iajs-3717	117	5	0	0	NUM
iajs-3717	117	6	0	0	NUM
iajs-3717	117	7	𝐶𝐾(𝑟−𝐸1	𝐶𝐾(𝑟−𝐸1	NOUN
iajs-3717	117	8	)	)	PUNCT
iajs-3717	117	9	𝑟	𝑟	NOUN
iajs-3717	117	10	−	−	PROPN
iajs-3717	117	11	(	(	PUNCT
iajs-3717	117	12	𝜆	𝜆	PROPN
iajs-3717	118	1	+	+	X
iajs-3717	118	2	𝐸2	𝐸2	ADJ
iajs-3717	118	3	)	)	PUNCT
iajs-3717	118	4	0	0	NUM
iajs-3717	118	5	0	0	NUM
iajs-3717	118	6	0	0	NUM
iajs-3717	118	7	−(𝜃	−(𝜃	NOUN
iajs-3717	118	8	+	+	CCONJ
iajs-3717	118	9	𝐸3	𝐸3	NOUN
iajs-3717	118	10	)	)	PUNCT
iajs-3717	118	11	]	]	PUNCT
iajs-3717	119	1	(	(	PUNCT
iajs-3717	119	2	15	15	X
iajs-3717	119	3	)	)	PUNCT
iajs-3717	119	4	the	the	DET
iajs-3717	119	5	eigenvalues	eigenvalue	NOUN
iajs-3717	119	6	of	of	ADP
iajs-3717	119	7	𝐽𝐹1	𝐽𝐹1	PROPN
iajs-3717	119	8	are	be	AUX
iajs-3717	119	9	𝜇11	𝜇11	ADJ
iajs-3717	119	10	=	=	SYM
iajs-3717	119	11	−(𝑟	−(𝑟	NOUN
iajs-3717	119	12	−	−	PROPN
iajs-3717	119	13	𝐸1	𝐸1	NOUN
iajs-3717	119	14	)	)	PUNCT
iajs-3717	119	15	<	<	X
iajs-3717	119	16	0	0	NUM
iajs-3717	119	17	,	,	PUNCT
iajs-3717	119	18	𝜇12	𝜇12	NOUN
iajs-3717	119	19	=	=	PUNCT
iajs-3717	119	20	𝐶𝐾(𝑟−𝐸1	𝐶𝐾(𝑟−𝐸1	NOUN
iajs-3717	119	21	)	)	PUNCT
iajs-3717	119	22	𝑟	𝑟	NOUN
iajs-3717	119	23	−	−	PROPN
iajs-3717	119	24	(	(	PUNCT
iajs-3717	119	25	𝜆	𝜆	PROPN
iajs-3717	119	26	+	+	X
iajs-3717	119	27	𝐸2	𝐸2	ADJ
iajs-3717	119	28	)	)	PUNCT
iajs-3717	119	29	and	and	CCONJ
iajs-3717	119	30	𝜇13	𝜇13	PROPN
iajs-3717	119	31	=	=	SYM
iajs-3717	119	32	−(𝜃	−(𝜃	PROPN
iajs-3717	119	33	+	+	CCONJ
iajs-3717	119	34	𝐸3	𝐸3	NOUN
iajs-3717	119	35	)	)	PUNCT
iajs-3717	119	36	<	<	X
iajs-3717	120	1	0	0	X
iajs-3717	120	2	.	.	PUNCT
iajs-3717	121	1	it	it	PRON
iajs-3717	121	2	is	be	AUX
iajs-3717	121	3	clear	clear	ADJ
iajs-3717	121	4	that	that	SCONJ
iajs-3717	121	5	𝐹1	𝐹1	PROPN
iajs-3717	121	6	is	be	AUX
iajs-3717	121	7	asymptotically	asymptotically	ADV
iajs-3717	121	8	stable	stable	ADJ
iajs-3717	121	9	for	for	ADP
iajs-3717	121	10	all	all	DET
iajs-3717	121	11	𝜏	𝜏	PRON
iajs-3717	121	12	≥	≥	NOUN
iajs-3717	121	13	0	0	NUM
iajs-3717	121	14	provided	provide	VERB
iajs-3717	121	15	that	that	SCONJ
iajs-3717	121	16	the	the	DET
iajs-3717	121	17	following	follow	VERB
iajs-3717	121	18	condition	condition	NOUN
iajs-3717	121	19	is	be	AUX
iajs-3717	121	20	met	meet	VERB
iajs-3717	121	21	.	.	PUNCT
iajs-3717	122	1	𝐶𝐾(𝑟	𝐶𝐾(𝑟	NOUN
iajs-3717	122	2	−	−	PROPN
iajs-3717	122	3	𝐸1	𝐸1	NOUN
iajs-3717	122	4	)	)	PUNCT
iajs-3717	122	5	<	<	X
iajs-3717	123	1	𝑟(𝜆	𝑟(𝜆	PROPN
iajs-3717	123	2	+	+	CCONJ
iajs-3717	123	3	𝐸2	𝐸2	ADJ
iajs-3717	123	4	)	)	PUNCT
iajs-3717	123	5	(	(	PUNCT
iajs-3717	123	6	16	16	NUM
iajs-3717	123	7	)	)	PUNCT
iajs-3717	123	8	the	the	DET
iajs-3717	123	9	(	(	PUNCT
iajs-3717	123	10	𝐽𝑚	𝐽𝑚	PROPN
iajs-3717	123	11	)	)	PUNCT
iajs-3717	123	12	for	for	ADP
iajs-3717	123	13	system	system	NOUN
iajs-3717	123	14	(	(	PUNCT
iajs-3717	123	15	2	2	NUM
iajs-3717	123	16	)	)	PUNCT
iajs-3717	123	17	at	at	ADP
iajs-3717	123	18	𝐹2is	𝐹2is	PROPN
iajs-3717	123	19	as	as	SCONJ
iajs-3717	123	20	follows	follow	VERB
iajs-3717	123	21	:	:	PUNCT
iajs-3717	123	22	𝐽𝐹2	𝐽𝐹2	PROPN
iajs-3717	123	23	=	=	PRON
iajs-3717	124	1	[	[	PUNCT
iajs-3717	124	2	−	−	X
iajs-3717	124	3	𝑟	𝑟	X
iajs-3717	124	4	𝐶𝐾	𝐶𝐾	PROPN
iajs-3717	124	5	(	(	PUNCT
iajs-3717	124	6	𝜆	𝜆	NOUN
iajs-3717	124	7	+	+	X
iajs-3717	124	8	𝐸2	𝐸2	ADJ
iajs-3717	124	9	)	)	PUNCT
iajs-3717	124	10	−	−	PROPN
iajs-3717	124	11	(	(	PUNCT
iajs-3717	124	12	𝜆+𝐸2)(𝑟+𝐶𝐾	𝜆+𝐸2)(𝑟+𝐶𝐾	PROPN
iajs-3717	124	13	)	)	PUNCT
iajs-3717	124	14	𝐶𝐾	𝐶𝐾	PROPN
iajs-3717	124	15	0	0	NUM
iajs-3717	124	16	𝜂	𝜂	NOUN
iajs-3717	124	17	𝑟+𝐶𝐾	𝑟+𝐶𝐾	NUM
iajs-3717	124	18	0	0	NUM
iajs-3717	124	19	−	−	NOUN
iajs-3717	124	20	𝛼𝜂𝑒−𝜇𝜏	𝛼𝜂𝑒−𝜇𝜏	NOUN
iajs-3717	124	21	(	(	PUNCT
iajs-3717	124	22	𝛾+𝐼)̅(𝑟+𝐶𝐾	𝛾+𝐼)̅(𝑟+𝐶𝐾	NUM
iajs-3717	124	23	)	)	PUNCT
iajs-3717	124	24	0	0	NUM
iajs-3717	124	25	0	0	NUM
iajs-3717	124	26	ℎ	ℎ	PROPN
iajs-3717	124	27	𝐼	𝐼	PROPN
iajs-3717	124	28	�	�	PROPN
iajs-3717	124	29	̅	̅	NOUN
iajs-3717	124	30	�	�	NOUN
iajs-3717	124	31	−𝜇𝜏	−𝜇𝜏	NOUN
iajs-3717	124	32	𝛾+	𝛾+	PUNCT
iajs-3717	124	33	𝐼̅	𝐼̅	PROPN
iajs-3717	124	34	−	−	PROPN
iajs-3717	124	35	(	(	PUNCT
iajs-3717	124	36	𝜃	𝜃	NOUN
iajs-3717	124	37	+	+	X
iajs-3717	124	38	𝐸3	𝐸3	NOUN
iajs-3717	124	39	)	)	PUNCT
iajs-3717	124	40	;	;	PUNCT
iajs-3717	124	41	]	]	PUNCT
iajs-3717	124	42	=	=	PUNCT
iajs-3717	124	43	𝑏𝑖𝑗	𝑏𝑖𝑗	NOUN
iajs-3717	124	44	;	;	PUNCT
iajs-3717	124	45	𝑖	𝑖	X
iajs-3717	124	46	,	,	PUNCT
iajs-3717	124	47	𝑗	𝑗	NOUN
iajs-3717	124	48	=	=	NOUN
iajs-3717	124	49	1	1	NUM
iajs-3717	124	50	,	,	PUNCT
iajs-3717	124	51	.	.	PUNCT
iajs-3717	124	52	.	.	PUNCT
iajs-3717	125	1	,	,	PUNCT
iajs-3717	125	2	3	3	NUM
iajs-3717	125	3	(	(	PUNCT
iajs-3717	125	4	17	17	NUM
iajs-3717	125	5	)	)	PUNCT
iajs-3717	125	6	where	where	SCONJ
iajs-3717	125	7	𝜂	𝜂	NOUN
iajs-3717	125	8	=	=	SYM
iajs-3717	125	9	𝐶𝐾(𝑟	𝐶𝐾(𝑟	NOUN
iajs-3717	125	10	−	−	PROPN
iajs-3717	125	11	𝐸1	𝐸1	NOUN
iajs-3717	125	12	)	)	PUNCT
iajs-3717	125	13	−	−	PROPN
iajs-3717	126	1	𝑟(𝜆	𝑟(𝜆	PROPN
iajs-3717	126	2	+	+	CCONJ
iajs-3717	126	3	𝐸2	𝐸2	ADJ
iajs-3717	126	4	)	)	PUNCT
iajs-3717	126	5	clearly	clearly	ADV
iajs-3717	126	6	,	,	PUNCT
iajs-3717	126	7	the	the	DET
iajs-3717	126	8	roots	root	NOUN
iajs-3717	126	9	of	of	ADP
iajs-3717	126	10	the	the	DET
iajs-3717	126	11	following	follow	VERB
iajs-3717	126	12	equation	equation	NOUN
iajs-3717	126	13	represent	represent	VERB
iajs-3717	126	14	two	two	NUM
iajs-3717	126	15	eigenvalues	eigenvalue	NOUN
iajs-3717	126	16	of	of	ADP
iajs-3717	126	17	𝐽𝐹2	𝐽𝐹2	PROPN
iajs-3717	126	18	𝜇2	𝜇2	PROPN
iajs-3717	126	19	−	−	PROPN
iajs-3717	126	20	(	(	PUNCT
iajs-3717	126	21	𝑏11	𝑏11	PROPN
iajs-3717	126	22	+	+	CCONJ
iajs-3717	126	23	𝑏22)𝜇	𝑏22)𝜇	PROPN
iajs-3717	126	24	+	+	CCONJ
iajs-3717	126	25	𝑏11𝑏22	𝑏11𝑏22	ADJ
iajs-3717	126	26	−	−	PROPN
iajs-3717	126	27	𝑏12𝑏21	𝑏12𝑏21	PROPN
iajs-3717	126	28	=	=	SYM
iajs-3717	126	29	0	0	PROPN
iajs-3717	126	30	(	(	PUNCT
iajs-3717	126	31	18	18	NUM
iajs-3717	126	32	)	)	PUNCT
iajs-3717	126	33	the	the	DET
iajs-3717	126	34	above	above	ADJ
iajs-3717	126	35	equation	equation	NOUN
iajs-3717	126	36	have	have	VERB
iajs-3717	126	37	negative	negative	ADJ
iajs-3717	126	38	real	real	ADJ
iajs-3717	126	39	part	part	NOUN
iajs-3717	126	40	for	for	ADP
iajs-3717	126	41	all	all	DET
iajs-3717	126	42	𝜏	𝜏	PRON
iajs-3717	126	43	≥	≥	NOUN
iajs-3717	126	44	0	0	NUM
iajs-3717	126	45	under	under	ADP
iajs-3717	126	46	the	the	DET
iajs-3717	126	47	existence	existence	NOUN
iajs-3717	126	48	condition	condition	NOUN
iajs-3717	126	49	(	(	PUNCT
iajs-3717	126	50	5	5	NUM
iajs-3717	126	51	)	)	PUNCT
iajs-3717	126	52	of	of	ADP
iajs-3717	126	53	𝐹2	𝐹2	PROPN
iajs-3717	126	54	.	.	PUNCT
iajs-3717	127	1	while	while	SCONJ
iajs-3717	127	2	other	other	ADJ
iajs-3717	127	3	eigenvalue	eigenvalue	NOUN
iajs-3717	127	4	of	of	ADP
iajs-3717	127	5	𝐽𝐹2	𝐽𝐹2	PROPN
iajs-3717	127	6	is	be	AUX
iajs-3717	127	7	given	give	VERB
iajs-3717	127	8	by	by	ADP
iajs-3717	127	9	the	the	DET
iajs-3717	127	10	root	root	NOUN
iajs-3717	127	11	of	of	ADP
iajs-3717	127	12	𝜇31	𝜇31	NOUN
iajs-3717	127	13	+	+	CCONJ
iajs-3717	127	14	(	(	PUNCT
iajs-3717	127	15	𝜃	𝜃	NOUN
iajs-3717	127	16	+	+	X
iajs-3717	127	17	𝐸3	𝐸3	NOUN
iajs-3717	127	18	)	)	PUNCT
iajs-3717	127	19	−	−	PROPN
iajs-3717	128	1	ℎ	ℎ	PROPN
iajs-3717	128	2	𝐼	𝐼	PROPN
iajs-3717	128	3	�	�	PROPN
iajs-3717	128	4	̅	̅	NOUN
iajs-3717	128	5	�	�	NOUN
iajs-3717	128	6	−𝜇𝜏	−𝜇𝜏	NOUN
iajs-3717	128	7	𝛾+	𝛾+	PUNCT
iajs-3717	128	8	𝐼̅	𝐼̅	X
iajs-3717	128	9	=	=	SYM
iajs-3717	128	10	0	0	NUM
iajs-3717	128	11	(	(	PUNCT
iajs-3717	128	12	19	19	NUM
iajs-3717	128	13	)	)	PUNCT
iajs-3717	128	14	thus	thus	ADV
iajs-3717	128	15	,	,	PUNCT
iajs-3717	128	16	1if	1if	NOUN
iajs-3717	128	17	𝜏	𝜏	X
iajs-3717	128	18	=	=	SYM
iajs-3717	128	19	0	0	NUM
iajs-3717	128	20	equation	equation	NOUN
iajs-3717	128	21	(	(	PUNCT
iajs-3717	128	22	19	19	NUM
iajs-3717	128	23	)	)	PUNCT
iajs-3717	128	24	has	have	AUX
iajs-3717	128	25	eigenvalue	eigenvalue	VERB
iajs-3717	128	26	𝜇31	𝜇31	NOUN
iajs-3717	128	27	=	=	SYM
iajs-3717	128	28	ℎ	ℎ	PROPN
iajs-3717	128	29	𝐼̅	𝐼̅	PROPN
iajs-3717	128	30	𝛾+	𝛾+	X
iajs-3717	128	31	𝐼̅	𝐼̅	PROPN
iajs-3717	128	32	−	−	PROPN
iajs-3717	128	33	(	(	PUNCT
iajs-3717	128	34	𝜃	𝜃	NOUN
iajs-3717	128	35	+	+	X
iajs-3717	128	36	𝐸3	𝐸3	NOUN
iajs-3717	128	37	)	)	PUNCT
iajs-3717	128	38	which	which	PRON
iajs-3717	128	39	is	be	AUX
iajs-3717	128	40	negative	negative	ADJ
iajs-3717	128	41	under	under	ADP
iajs-3717	128	42	the	the	DET
iajs-3717	128	43	condition	condition	NOUN
iajs-3717	128	44	ℎ	ℎ	PROPN
iajs-3717	128	45	𝐼̅	𝐼̅	PROPN
iajs-3717	128	46	𝛾+	𝛾+	X
iajs-3717	128	47	𝐼̅	𝐼̅	PROPN
iajs-3717	128	48	<	<	X
iajs-3717	128	49	(	(	PUNCT
iajs-3717	128	50	𝜃	𝜃	NOUN
iajs-3717	128	51	+	+	X
iajs-3717	128	52	𝐸3	𝐸3	NOUN
iajs-3717	128	53	)	)	PUNCT
iajs-3717	128	54	(	(	PUNCT
iajs-3717	128	55	20	20	NUM
iajs-3717	128	56	)	)	PUNCT
iajs-3717	128	57	hence	hence	ADV
iajs-3717	128	58	the	the	DET
iajs-3717	128	59	𝐹2	𝐹2	NOUN
iajs-3717	128	60	is	be	AUX
iajs-3717	128	61	locally	locally	ADV
iajs-3717	128	62	asymptotically	asymptotically	ADV
iajs-3717	128	63	stable	stable	ADJ
iajs-3717	128	64	under	under	ADP
iajs-3717	128	65	the	the	DET
iajs-3717	128	66	conditions	condition	NOUN
iajs-3717	128	67	(	(	PUNCT
iajs-3717	128	68	5	5	NUM
iajs-3717	128	69	)	)	PUNCT
iajs-3717	128	70	and	and	CCONJ
iajs-3717	128	71	(	(	PUNCT
iajs-3717	128	72	20	20	NUM
iajs-3717	128	73	)	)	PUNCT
iajs-3717	128	74	when	when	SCONJ
iajs-3717	128	75	𝜏	𝜏	NOUN
iajs-3717	128	76	=	=	SYM
iajs-3717	128	77	0	0	PROPN
iajs-3717	129	1	2for	2for	PRON
iajs-3717	129	2	𝜏	𝜏	X
iajs-3717	129	3	>	>	X
iajs-3717	129	4	0	0	NUM
iajs-3717	129	5	,	,	PUNCT
iajs-3717	129	6	if	if	SCONJ
iajs-3717	129	7	equation	equation	NOUN
iajs-3717	129	8	(	(	PUNCT
iajs-3717	129	9	19	19	NUM
iajs-3717	129	10	)	)	PUNCT
iajs-3717	129	11	has	have	VERB
iajs-3717	129	12	the	the	DET
iajs-3717	129	13	roots	root	NOUN
iajs-3717	129	14	which	which	PRON
iajs-3717	129	15	a	a	DET
iajs-3717	129	16	pair	pair	NOUN
iajs-3717	129	17	of	of	ADP
iajs-3717	129	18	purely	purely	ADV
iajs-3717	129	19	imaginary	imaginary	ADJ
iajs-3717	129	20	must	must	AUX
iajs-3717	129	21	intersect	intersect	VERB
iajs-3717	129	22	the	the	DET
iajs-3717	129	23	imaginary	imaginary	ADJ
iajs-3717	129	24	axis	axis	NOUN
iajs-3717	129	25	,	,	PUNCT
iajs-3717	129	26	now	now	ADV
iajs-3717	129	27	let	let	VERB
iajs-3717	129	28	𝜇	𝜇	ADP
iajs-3717	129	29	=	=	NOUN
iajs-3717	129	30	𝑖	𝑖	SYM
iajs-3717	129	31	�	�	PROPN
iajs-3717	129	32	̅	̅	NOUN
iajs-3717	129	33	�	�	PROPN
iajs-3717	129	34	(	(	PUNCT
iajs-3717	129	35	�	�	NOUN
iajs-3717	129	36	̅	̅	NOUN
iajs-3717	129	37	�	�	PROPN
iajs-3717	129	38	>	>	X
iajs-3717	129	39	0	0	NUM
iajs-3717	129	40	)	)	PUNCT
iajs-3717	129	41	be	be	AUX
iajs-3717	129	42	the	the	DET
iajs-3717	129	43	root	root	NOUN
iajs-3717	129	44	of	of	ADP
iajs-3717	129	45	equation	equation	NOUN
iajs-3717	129	46	(	(	PUNCT
iajs-3717	129	47	19	19	NUM
iajs-3717	129	48	)	)	PUNCT
iajs-3717	129	49	by	by	ADP
iajs-3717	129	50	substituting	substitute	VERB
iajs-3717	129	51	𝜇	𝜇	ADP
iajs-3717	129	52	=	=	PROPN
iajs-3717	129	53	𝑖	𝑖	SYM
iajs-3717	129	54	�	�	PROPN
iajs-3717	129	55	̅	̅	NOUN
iajs-3717	129	56	�	�	NOUN
iajs-3717	129	57	in	in	ADP
iajs-3717	129	58	equation	equation	NOUN
iajs-3717	129	59	(	(	PUNCT
iajs-3717	129	60	19	19	NUM
iajs-3717	129	61	)	)	PUNCT
iajs-3717	129	62	,	,	PUNCT
iajs-3717	129	63	we	we	PRON
iajs-3717	129	64	obtain	obtain	VERB
iajs-3717	129	65	𝜃	𝜃	NOUN
iajs-3717	129	66	+	+	NOUN
iajs-3717	129	67	𝐸3	𝐸3	NOUN
iajs-3717	129	68	=	=	PUNCT
iajs-3717	129	69	ℎ	ℎ	PROPN
iajs-3717	129	70	𝐼	𝐼	PROPN
iajs-3717	129	71	̅	̅	NOUN
iajs-3717	129	72	𝛾+	𝛾+	PUNCT
iajs-3717	129	73	𝐼	𝐼	PROPN
iajs-3717	129	74	̅	̅	NOUN
iajs-3717	129	75	cos	cos	X
iajs-3717	129	76	�	�	PROPN
iajs-3717	129	77	̅	̅	NOUN
iajs-3717	129	78	�	�	NOUN
iajs-3717	129	79	𝜏	𝜏	ADP
iajs-3717	129	80	−	−	PROPN
iajs-3717	129	81	�	�	NOUN
iajs-3717	129	82	̅	̅	NOUN
iajs-3717	129	83	�	�	NOUN
iajs-3717	129	84	=	=	PUNCT
iajs-3717	129	85	ℎ	ℎ	PROPN
iajs-3717	129	86	𝐼	𝐼	PROPN
iajs-3717	129	87	̅	̅	NOUN
iajs-3717	129	88	𝛾+	𝛾+	PUNCT
iajs-3717	129	89	𝐼	𝐼	PROPN
iajs-3717	129	90	̅	̅	NOUN
iajs-3717	129	91	sin	sin	NOUN
iajs-3717	129	92	�	�	NOUN
iajs-3717	129	93	̅	̅	NOUN
iajs-3717	129	94	�	�	PROPN
iajs-3717	129	95	𝜏	𝜏	PROPN
iajs-3717	129	96	(	(	PUNCT
iajs-3717	129	97	21	21	NUM
iajs-3717	129	98	)	)	PUNCT
iajs-3717	129	99	squaring	square	VERB
iajs-3717	129	100	and	and	CCONJ
iajs-3717	129	101	adding	add	VERB
iajs-3717	129	102	both	both	DET
iajs-3717	129	103	sides	side	NOUN
iajs-3717	129	104	of	of	ADP
iajs-3717	129	105	equation	equation	NOUN
iajs-3717	129	106	(	(	PUNCT
iajs-3717	129	107	21	21	NUM
iajs-3717	129	108	)	)	PUNCT
iajs-3717	129	109	,	,	PUNCT
iajs-3717	129	110	we	we	PRON
iajs-3717	129	111	obtain	obtain	VERB
iajs-3717	129	112	the	the	DET
iajs-3717	129	113	following	follow	VERB
iajs-3717	129	114	result	result	NOUN
iajs-3717	129	115	:	:	PUNCT
iajs-3717	129	116	�	�	NOUN
iajs-3717	129	117	̅	̅	NOUN
iajs-3717	129	118	�	�	NOUN
iajs-3717	129	119	=	=	SYM
iajs-3717	129	120	±√	±√	NOUN
iajs-3717	129	121	(	(	PUNCT
iajs-3717	129	122	ℎ	ℎ	PROPN
iajs-3717	129	123	𝐼̅	𝐼̅	PROPN
iajs-3717	129	124	𝛾+	𝛾+	PUNCT
iajs-3717	129	125	𝐼	𝐼	PROPN
iajs-3717	129	126	)	)	PUNCT
iajs-3717	129	127	̅	̅	NOUN
iajs-3717	129	128	2	2	NUM
iajs-3717	129	129	−	−	NOUN
iajs-3717	129	130	(	(	PUNCT
iajs-3717	129	131	𝜃	𝜃	X
iajs-3717	129	132	+	+	CCONJ
iajs-3717	129	133	𝐸3)2	𝐸3)2	PROPN
iajs-3717	129	134	(	(	PUNCT
iajs-3717	129	135	22	22	NUM
iajs-3717	129	136	)	)	PUNCT
iajs-3717	129	137	note	note	VERB
iajs-3717	129	138	that	that	SCONJ
iajs-3717	129	139	,	,	PUNCT
iajs-3717	129	140	from	from	ADP
iajs-3717	129	141	the	the	DET
iajs-3717	129	142	condition	condition	NOUN
iajs-3717	129	143	(	(	PUNCT
iajs-3717	129	144	20	20	NUM
iajs-3717	129	145	)	)	PUNCT
iajs-3717	129	146	,	,	PUNCT
iajs-3717	129	147	we	we	PRON
iajs-3717	129	148	have	have	VERB
iajs-3717	129	149	�	�	NOUN
iajs-3717	129	150	̅	̅	NOUN
iajs-3717	129	151	�	�	NOUN
iajs-3717	129	152	(𝜏	(𝜏	VERB
iajs-3717	129	153	)	)	PUNCT
iajs-3717	129	154	when	when	SCONJ
iajs-3717	129	155	𝜏	𝜏	X
iajs-3717	129	156	>	>	X
iajs-3717	129	157	0	0	NUM
iajs-3717	130	1	it	it	PRON
iajs-3717	130	2	can	can	AUX
iajs-3717	130	3	not	not	PART
iajs-3717	130	4	be	be	AUX
iajs-3717	130	5	real	real	ADJ
iajs-3717	130	6	,	,	PUNCT
iajs-3717	130	7	which	which	PRON
iajs-3717	130	8	is	be	AUX
iajs-3717	130	9	in	in	ADP
iajs-3717	130	10	opposition	opposition	NOUN
iajs-3717	130	11	to	to	ADP
iajs-3717	130	12	the	the	DET
iajs-3717	130	13	assumption	assumption	NOUN
iajs-3717	130	14	.	.	PUNCT
iajs-3717	131	1	as	as	ADP
iajs-3717	131	2	a	a	DET
iajs-3717	131	3	result	result	NOUN
iajs-3717	131	4	,	,	PUNCT
iajs-3717	131	5	the	the	DET
iajs-3717	131	6	root	root	NOUN
iajs-3717	131	7	of	of	ADP
iajs-3717	131	8	the	the	DET
iajs-3717	131	9	characteristic	characteristic	ADJ
iajs-3717	131	10	equation	equation	NOUN
iajs-3717	131	11	(	(	PUNCT
iajs-3717	131	12	19	19	NUM
iajs-3717	131	13	)	)	PUNCT
iajs-3717	131	14	can	can	AUX
iajs-3717	131	15	not	not	PART
iajs-3717	131	16	be	be	AUX
iajs-3717	131	17	purely	purely	ADV
iajs-3717	131	18	imaginary	imaginary	ADJ
iajs-3717	131	19	,	,	PUNCT
iajs-3717	131	20	and	and	CCONJ
iajs-3717	131	21	is	be	AUX
iajs-3717	131	22	asymptotically	asymptotically	ADV
iajs-3717	131	23	stable	stable	ADJ
iajs-3717	131	24	for	for	ADP
iajs-3717	131	25	all	all	PRON
iajs-3717	131	26	.	.	PUNCT
iajs-3717	132	1	for	for	ADP
iajs-3717	132	2	all	all	DET
iajs-3717	132	3	𝜏	𝜏	PRON
iajs-3717	132	4	≥	≥	NOUN
iajs-3717	132	5	0	0	NUM
iajs-3717	132	6	,	,	PUNCT
iajs-3717	132	7	the	the	DET
iajs-3717	132	8	equilibrium	equilibrium	NOUN
iajs-3717	132	9	point	point	NOUN
iajs-3717	132	10	𝐹2	𝐹2	NOUN
iajs-3717	132	11	demonstrates	demonstrate	VERB
iajs-3717	132	12	asymptotic	asymptotic	ADJ
iajs-3717	132	13	stability	stability	NOUN
iajs-3717	132	14	.	.	PUNCT
iajs-3717	133	1	the	the	DET
iajs-3717	133	2	(	(	PUNCT
iajs-3717	133	3	𝐽𝑚	𝐽𝑚	PROPN
iajs-3717	133	4	)	)	PUNCT
iajs-3717	133	5	for	for	ADP
iajs-3717	133	6	system	system	NOUN
iajs-3717	133	7	(	(	PUNCT
iajs-3717	133	8	2	2	NUM
iajs-3717	133	9	)	)	PUNCT
iajs-3717	133	10	at	at	ADP
iajs-3717	133	11	𝐹3	𝐹3	PROPN
iajs-3717	133	12	is	be	AUX
iajs-3717	133	13	as	as	SCONJ
iajs-3717	133	14	follows	follow	VERB
iajs-3717	133	15	:	:	PUNCT
iajs-3717	133	16	ihjpas	ihjpas	PROPN
iajs-3717	133	17	.	.	PUNCT
iajs-3717	134	1	2025,38(2	2025,38(2	PROPN
iajs-3717	134	2	)	)	PUNCT
iajs-3717	134	3	366	366	NUM
iajs-3717	134	4	𝐽𝐹3	𝐽𝐹3	NOUN
iajs-3717	134	5	=	=	PUNCT
iajs-3717	134	6	[	[	PUNCT
iajs-3717	134	7	𝑟−	𝑟−	NUM
iajs-3717	134	8	𝑅1	𝑅1	PROPN
iajs-3717	134	9	−𝑅2𝑆∗	−𝑅2𝑆∗	NUM
iajs-3717	134	10	0	0	NUM
iajs-3717	134	11	𝐶𝐼∗	𝐶𝐼∗	PROPN
iajs-3717	134	12	𝑅5	𝑅5	PROPN
iajs-3717	135	1	−	−	ADP
iajs-3717	135	2	𝛼𝑅3𝑒	𝛼𝑅3𝑒	PROPN
iajs-3717	135	3	−𝜇𝜏	−𝜇𝜏	ADP
iajs-3717	135	4	−	−	PROPN
iajs-3717	135	5	𝛼𝑅4𝑒−𝜇𝜏	𝛼𝑅4𝑒−𝜇𝜏	NOUN
iajs-3717	135	6	0	0	NUM
iajs-3717	135	7	ℎ𝑅3𝑒	ℎ𝑅3𝑒	NOUN
iajs-3717	135	8	−𝜇𝜏	−𝜇𝜏	ADP
iajs-3717	135	9	ℎ𝑅4𝑒	ℎ𝑅4𝑒	VERB
iajs-3717	135	10	−𝜇𝜏	−𝜇𝜏	ADP
iajs-3717	135	11	−	−	PROPN
iajs-3717	135	12	𝑅6	𝑅6	NOUN
iajs-3717	135	13	]	]	PUNCT
iajs-3717	135	14	=	=	SYM
iajs-3717	135	15	𝑐𝑖𝑗	𝑐𝑖𝑗	PROPN
iajs-3717	135	16	;	;	PUNCT
iajs-3717	135	17	𝑖	𝑖	X
iajs-3717	135	18	,	,	PUNCT
iajs-3717	135	19	𝑗	𝑗	NOUN
iajs-3717	135	20	=	=	NOUN
iajs-3717	135	21	1	1	NUM
iajs-3717	135	22	,	,	PUNCT
iajs-3717	135	23	.	.	PUNCT
iajs-3717	136	1	.3	.3	NUM
iajs-3717	136	2	(	(	PUNCT
iajs-3717	136	3	23	23	NUM
iajs-3717	136	4	)	)	PUNCT
iajs-3717	137	1	where	where	SCONJ
iajs-3717	137	2	𝑅1	𝑅1	NOUN
iajs-3717	137	3	=	=	PUNCT
iajs-3717	137	4	𝑟	𝑟	X
iajs-3717	137	5	𝐾	𝐾	PROPN
iajs-3717	137	6	(	(	PUNCT
iajs-3717	137	7	2𝑆∗	2𝑆∗	NUM
iajs-3717	137	8	+	+	SYM
iajs-3717	137	9	𝐼∗	𝐼∗	NOUN
iajs-3717	137	10	)	)	PUNCT
iajs-3717	137	11	+	+	CCONJ
iajs-3717	137	12	𝐶𝐼∗	𝐶𝐼∗	PROPN
iajs-3717	137	13	+	+	CCONJ
iajs-3717	137	14	𝐸1	𝐸1	NOUN
iajs-3717	137	15	>	>	X
iajs-3717	137	16	0	0	NUM
iajs-3717	137	17	;	;	PUNCT
iajs-3717	138	1	𝑅2	𝑅2	ADP
iajs-3717	138	2	=	=	PUNCT
iajs-3717	138	3	𝑟	𝑟	X
iajs-3717	138	4	𝐾	𝐾	PROPN
iajs-3717	138	5	+	+	CCONJ
iajs-3717	138	6	𝐶	𝐶	PROPN
iajs-3717	138	7	>	>	X
iajs-3717	138	8	0	0	NUM
iajs-3717	138	9	;	;	PUNCT
iajs-3717	138	10	𝑅3	𝑅3	PROPN
iajs-3717	138	11	=	=	SYM
iajs-3717	138	12	𝛾𝑍∗	𝛾𝑍∗	PROPN
iajs-3717	138	13	(	(	PUNCT
iajs-3717	138	14	𝛾+𝐼∗)2	𝛾+𝐼∗)2	ADJ
iajs-3717	138	15	>	>	X
iajs-3717	138	16	0	0	NUM
iajs-3717	138	17	;	;	PUNCT
iajs-3717	138	18	𝑅4	𝑅4	X
iajs-3717	138	19	=	=	SYM
iajs-3717	138	20	𝐼∗	𝐼∗	PROPN
iajs-3717	138	21	𝛾+𝐼∗	𝛾+𝐼∗	NOUN
iajs-3717	138	22	;	;	PUNCT
iajs-3717	138	23	𝑅5	𝑅5	X
iajs-3717	138	24	=	=	SYM
iajs-3717	138	25	𝐶𝑆∗	𝐶𝑆∗	PROPN
iajs-3717	138	26	−	−	PROPN
iajs-3717	138	27	(	(	PUNCT
iajs-3717	138	28	𝜆	𝜆	NOUN
iajs-3717	138	29	+	+	X
iajs-3717	138	30	𝐸3	𝐸3	NOUN
iajs-3717	138	31	)	)	PUNCT
iajs-3717	138	32	>	>	X
iajs-3717	138	33	0	0	NUM
iajs-3717	138	34	;	;	PUNCT
iajs-3717	138	35	𝑅6	𝑅6	NOUN
iajs-3717	138	36	=	=	PUNCT
iajs-3717	138	37	(	(	PUNCT
iajs-3717	138	38	𝜃	𝜃	NOUN
iajs-3717	138	39	+	+	X
iajs-3717	138	40	𝐸3	𝐸3	NOUN
iajs-3717	138	41	)	)	PUNCT
iajs-3717	138	42	>	>	X
iajs-3717	138	43	0	0	X
iajs-3717	138	44	.	.	PUNCT
iajs-3717	139	1	the	the	DET
iajs-3717	139	2	characteristic	characteristic	ADJ
iajs-3717	139	3	equation	equation	NOUN
iajs-3717	139	4	of	of	ADP
iajs-3717	139	5	𝐽𝐹3	𝐽𝐹3	PROPN
iajs-3717	139	6	is	be	AUX
iajs-3717	139	7	𝜇3	𝜇3	PROPN
iajs-3717	140	1	+	+	PROPN
iajs-3717	140	2	𝒜1𝜇	𝒜1𝜇	PROPN
iajs-3717	140	3	2	2	NUM
iajs-3717	140	4	+	+	NOUN
iajs-3717	140	5	𝒜2𝜇+𝒜3	𝒜2𝜇+𝒜3	NOUN
iajs-3717	140	6	+	+	CCONJ
iajs-3717	140	7	(	(	PUNCT
iajs-3717	140	8	𝒜4𝜇	𝒜4𝜇	NOUN
iajs-3717	140	9	2	2	NUM
iajs-3717	140	10	+	+	NOUN
iajs-3717	140	11	𝒜5𝜇+𝒜6)𝑒	𝒜5𝜇+𝒜6)𝑒	NOUN
iajs-3717	140	12	−𝜇𝜏	−𝜇𝜏	X
iajs-3717	140	13	=	=	SYM
iajs-3717	140	14	0	0	PROPN
iajs-3717	140	15	(	(	PUNCT
iajs-3717	140	16	24	24	NUM
iajs-3717	140	17	)	)	PUNCT
iajs-3717	140	18	where	where	SCONJ
iajs-3717	140	19	𝒜1	𝒜1	NOUN
iajs-3717	140	20	=	=	SYM
iajs-3717	140	21	𝑅1	𝑅1	PROPN
iajs-3717	140	22	+	+	NUM
iajs-3717	140	23	𝑅6	𝑅6	NOUN
iajs-3717	141	1	−	−	PROPN
iajs-3717	141	2	(	(	PUNCT
iajs-3717	141	3	𝑟	𝑟	X
iajs-3717	141	4	+	+	NUM
iajs-3717	141	5	𝑅5	𝑅5	PROPN
iajs-3717	141	6	)	)	PUNCT
iajs-3717	141	7	𝒜2	𝒜2	PROPN
iajs-3717	142	1	=	=	PUNCT
iajs-3717	142	2	(	(	PUNCT
iajs-3717	142	3	𝑟−	𝑟−	NOUN
iajs-3717	142	4	𝑅1)(𝑅5	𝑅1)(𝑅5	NOUN
iajs-3717	142	5	−	−	PROPN
iajs-3717	142	6	𝑅6	𝑅6	NOUN
iajs-3717	142	7	)	)	PUNCT
iajs-3717	143	1	+	+	CCONJ
iajs-3717	143	2	𝑅2𝐶	𝑅2𝐶	X
iajs-3717	143	3	𝑆	𝑆	PROPN
iajs-3717	143	4	∗𝐼∗	∗𝐼∗	PRON
iajs-3717	143	5	−	−	PROPN
iajs-3717	143	6	𝑅5𝑅6	𝑅5𝑅6	PROPN
iajs-3717	143	7	𝒜3	𝒜3	NOUN
iajs-3717	143	8	=	=	X
iajs-3717	143	9	(	(	PUNCT
iajs-3717	143	10	𝑟−	𝑟−	NOUN
iajs-3717	143	11	𝑅1)𝑅5𝑅6	𝑅1)𝑅5𝑅6	NOUN
iajs-3717	143	12	+	+	CCONJ
iajs-3717	143	13	𝑅2𝑅6𝐶	𝑅2𝑅6𝐶	VERB
iajs-3717	143	14	𝑆	𝑆	PROPN
iajs-3717	143	15	∗𝐼∗	∗𝐼∗	PRON
iajs-3717	143	16	𝒜4	𝒜4	NOUN
iajs-3717	143	17	=	=	SYM
iajs-3717	143	18	𝛼𝑅3	𝛼𝑅3	PROPN
iajs-3717	143	19	−	−	NOUN
iajs-3717	143	20	ℎ𝑅2	ℎ𝑅2	NOUN
iajs-3717	143	21	𝒜5	𝒜5	NOUN
iajs-3717	143	22	=	=	PUNCT
iajs-3717	143	23	ℎ𝑅5𝑅6	ℎ𝑅5𝑅6	NOUN
iajs-3717	144	1	+	+	NUM
iajs-3717	145	1	𝛼	𝛼	X
iajs-3717	145	2	𝑅3𝑅6	𝑅3𝑅6	ADJ
iajs-3717	145	3	+	+	CCONJ
iajs-3717	145	4	(	(	PUNCT
iajs-3717	145	5	𝑟−	𝑟−	PROPN
iajs-3717	145	6	𝑅1	𝑅1	PROPN
iajs-3717	145	7	)	)	PUNCT
iajs-3717	145	8	(	(	PUNCT
iajs-3717	145	9	ℎ𝑅4−	ℎ𝑅4−	PROPN
iajs-3717	145	10	𝛼𝑅3	𝛼𝑅3	PROPN
iajs-3717	145	11	)	)	PUNCT
iajs-3717	145	12	𝒜6	𝒜6	NOUN
iajs-3717	146	1	=	=	SYM
iajs-3717	147	1	−	−	PROPN
iajs-3717	147	2	ℎ𝑅4(𝑅2𝐶	ℎ𝑅4(𝑅2𝐶	NOUN
iajs-3717	147	3	𝑆	𝑆	PROPN
iajs-3717	147	4	∗𝐼∗	∗𝐼∗	X
iajs-3717	147	5	+	+	CCONJ
iajs-3717	147	6	𝑅5(𝑟−	𝑅5(𝑟−	PROPN
iajs-3717	147	7	𝑅1))−	𝑅1))−	NOUN
iajs-3717	147	8	𝛼𝑅3𝑅6𝑒	𝛼𝑅3𝑅6𝑒	NUM
iajs-3717	147	9	−𝜇𝜏(𝑟−	−𝜇𝜏(𝑟−	NUM
iajs-3717	147	10	𝑅1	𝑅1	NOUN
iajs-3717	147	11	)	)	PUNCT
iajs-3717	147	12	thus	thus	ADV
iajs-3717	147	13	,	,	PUNCT
iajs-3717	147	14	1	1	X
iajs-3717	147	15	.	.	PUNCT
iajs-3717	148	1	if	if	SCONJ
iajs-3717	148	2	𝜏	𝜏	NOUN
iajs-3717	148	3	=	=	SYM
iajs-3717	148	4	0	0	NUM
iajs-3717	148	5	,	,	PUNCT
iajs-3717	148	6	then	then	ADV
iajs-3717	148	7	equation	equation	NOUN
iajs-3717	148	8	(	(	PUNCT
iajs-3717	148	9	24	24	NUM
iajs-3717	148	10	)	)	PUNCT
iajs-3717	148	11	becomes	become	VERB
iajs-3717	148	12	:	:	PUNCT
iajs-3717	148	13	𝜇3	𝜇3	NOUN
iajs-3717	148	14	+	+	CCONJ
iajs-3717	148	15	𝜇2(𝒜1	𝜇2(𝒜1	NOUN
iajs-3717	148	16	+	+	NOUN
iajs-3717	148	17	𝒜4	𝒜4	ADJ
iajs-3717	148	18	)	)	PUNCT
iajs-3717	149	1	+	+	CCONJ
iajs-3717	150	1	𝜇(𝒜2	𝜇(𝒜2	PROPN
iajs-3717	150	2	+	+	ADJ
iajs-3717	150	3	𝒜5	𝒜5	NOUN
iajs-3717	150	4	)	)	PUNCT
iajs-3717	151	1	+	+	CCONJ
iajs-3717	151	2	(	(	PUNCT
iajs-3717	151	3	𝒜3	𝒜3	NOUN
iajs-3717	151	4	+	+	NOUN
iajs-3717	151	5	𝒜6	𝒜6	NOUN
iajs-3717	151	6	)	)	PUNCT
iajs-3717	152	1	=	=	SYM
iajs-3717	152	2	0	0	PUNCT
iajs-3717	152	3	(	(	PUNCT
iajs-3717	152	4	25	25	NUM
iajs-3717	152	5	)	)	PUNCT
iajs-3717	152	6	according	accord	VERB
iajs-3717	152	7	to	to	ADP
iajs-3717	152	8	the	the	DET
iajs-3717	152	9	hurwitz	hurwitz	PROPN
iajs-3717	152	10	criterion	criterion	NOUN
iajs-3717	152	11	,	,	PUNCT
iajs-3717	152	12	equation	equation	NOUN
iajs-3717	152	13	(	(	PUNCT
iajs-3717	152	14	25	25	NUM
iajs-3717	152	15	)	)	PUNCT
iajs-3717	152	16	have	have	VERB
iajs-3717	152	17	three	three	NUM
iajs-3717	152	18	negative	negative	ADJ
iajs-3717	152	19	roots	root	NOUN
iajs-3717	152	20	if	if	SCONJ
iajs-3717	152	21	the	the	DET
iajs-3717	152	22	following	follow	VERB
iajs-3717	152	23	conditions	condition	NOUN
iajs-3717	152	24	are	be	AUX
iajs-3717	152	25	satisfied	satisfied	ADJ
iajs-3717	152	26	.	.	PUNCT
iajs-3717	153	1	𝑟	𝑟	X
iajs-3717	153	2	<	<	X
iajs-3717	153	3	𝑅1	𝑅1	PROPN
iajs-3717	153	4	(	(	PUNCT
iajs-3717	153	5	26	26	NUM
iajs-3717	153	6	)	)	PUNCT
iajs-3717	153	7	𝑅5	𝑅5	NOUN
iajs-3717	153	8	<	<	X
iajs-3717	153	9	𝛼	𝛼	PROPN
iajs-3717	153	10	𝑅3	𝑅3	PROPN
iajs-3717	153	11	(	(	PUNCT
iajs-3717	153	12	27	27	NUM
iajs-3717	153	13	)	)	PUNCT
iajs-3717	153	14	ℎ𝑅4	ℎ𝑅4	PROPN
iajs-3717	153	15	<	<	X
iajs-3717	153	16	𝑅6	𝑅6	NOUN
iajs-3717	153	17	(	(	PUNCT
iajs-3717	153	18	28	28	NUM
iajs-3717	153	19	)	)	PUNCT
iajs-3717	153	20	𝑅8	𝑅8	PROPN
iajs-3717	153	21	<	<	X
iajs-3717	153	22	𝑅7	𝑅7	PROPN
iajs-3717	153	23	(	(	PUNCT
iajs-3717	153	24	29	29	NUM
iajs-3717	153	25	)	)	PUNCT
iajs-3717	153	26	here	here	ADV
iajs-3717	153	27	𝑅7	𝑅7	NOUN
iajs-3717	154	1	=	=	PUNCT
iajs-3717	154	2	(	(	PUNCT
iajs-3717	154	3	𝑐11	𝑐11	NOUN
iajs-3717	154	4	+	+	CCONJ
iajs-3717	154	5	𝑐22	𝑐22	VERB
iajs-3717	154	6	+	+	CCONJ
iajs-3717	154	7	𝑐33)[−	𝑐33)[−	NOUN
iajs-3717	154	8	𝑐11	𝑐11	NOUN
iajs-3717	154	9	(	(	PUNCT
iajs-3717	154	10	𝑐22	𝑐22	VERB
iajs-3717	154	11	+	+	CCONJ
iajs-3717	154	12	𝑐33)−	𝑐33)−	X
iajs-3717	154	13	𝑐22	𝑐22	NOUN
iajs-3717	154	14	𝑐33	𝑐33	NOUN
iajs-3717	154	15	+	+	CCONJ
iajs-3717	154	16	𝑐23	𝑐23	NOUN
iajs-3717	154	17	𝑐32	𝑐32	NOUN
iajs-3717	154	18	+	+	CCONJ
iajs-3717	154	19	𝑐12	𝑐12	NUM
iajs-3717	154	20	𝑐21	𝑐21	NOUN
iajs-3717	154	21	]	]	PUNCT
iajs-3717	154	22	𝑅8	𝑅8	PROPN
iajs-3717	155	1	=	=	PUNCT
iajs-3717	155	2	−	−	PROPN
iajs-3717	155	3	[	[	PUNCT
iajs-3717	155	4	𝑐11	𝑐11	NOUN
iajs-3717	155	5	(	(	PUNCT
iajs-3717	155	6	𝑐22	𝑐22	X
iajs-3717	155	7	𝑐33−	𝑐33−	PROPN
iajs-3717	155	8	𝑐23	𝑐23	NOUN
iajs-3717	155	9	𝑐32	𝑐32	NOUN
iajs-3717	155	10	)	)	PUNCT
iajs-3717	155	11	−	−	NOUN
iajs-3717	155	12	𝑐33	𝑐33	VERB
iajs-3717	155	13	𝑐12	𝑐12	NOUN
iajs-3717	155	14	𝑐21	𝑐21	NOUN
iajs-3717	155	15	]	]	PUNCT
iajs-3717	155	16	and	and	CCONJ
iajs-3717	155	17	𝑐𝑖𝑗	𝑐𝑖𝑗	NOUN
iajs-3717	155	18	;	;	PUNCT
iajs-3717	155	19	𝑖	𝑖	X
iajs-3717	155	20	,	,	PUNCT
iajs-3717	155	21	𝑗	𝑗	NOUN
iajs-3717	155	22	=	=	NOUN
iajs-3717	155	23	1	1	NUM
iajs-3717	155	24	,	,	PUNCT
iajs-3717	155	25	.	.	PUNCT
iajs-3717	156	1	.3	.3	NUM
iajs-3717	156	2	define	define	VERB
iajs-3717	156	3	in	in	ADP
iajs-3717	156	4	equation	equation	NOUN
iajs-3717	156	5	(	(	PUNCT
iajs-3717	156	6	23	23	NUM
iajs-3717	156	7	)	)	PUNCT
iajs-3717	156	8	hence	hence	ADV
iajs-3717	156	9	the	the	DET
iajs-3717	156	10	𝐹3	𝐹3	PROPN
iajs-3717	156	11	is	be	AUX
iajs-3717	156	12	locally	locally	ADV
iajs-3717	156	13	asymptotically	asymptotically	ADV
iajs-3717	156	14	stable	stable	ADJ
iajs-3717	156	15	under	under	ADP
iajs-3717	156	16	the	the	DET
iajs-3717	156	17	conditions	condition	NOUN
iajs-3717	156	18	(	(	PUNCT
iajs-3717	156	19	26	26	NUM
iajs-3717	156	20	-	-	SYM
iajs-3717	156	21	29	29	NUM
iajs-3717	156	22	)	)	PUNCT
iajs-3717	157	1	2when	2when	PRON
iajs-3717	157	2	𝜏	𝜏	X
iajs-3717	157	3	>	>	X
iajs-3717	157	4	0	0	NUM
iajs-3717	157	5	,	,	PUNCT
iajs-3717	157	6	assume	assume	VERB
iajs-3717	157	7	that	that	SCONJ
iajs-3717	157	8	the	the	DET
iajs-3717	157	9	root	root	NOUN
iajs-3717	157	10	of	of	ADP
iajs-3717	157	11	equation	equation	NOUN
iajs-3717	157	12	(	(	PUNCT
iajs-3717	157	13	24	24	NUM
iajs-3717	157	14	)	)	PUNCT
iajs-3717	157	15	is	be	AUX
iajs-3717	157	16	purely	purely	ADV
iajs-3717	157	17	imaginary	imaginary	ADJ
iajs-3717	157	18	,	,	PUNCT
iajs-3717	157	19	namely	namely	ADV
iajs-3717	157	20	𝜇	𝜇	ADP
iajs-3717	157	21	=	=	NOUN
iajs-3717	157	22	±𝑖𝜔	±𝑖𝜔	NOUN
iajs-3717	157	23	(	(	PUNCT
iajs-3717	157	24	𝜔	𝜔	X
iajs-3717	157	25	>	>	X
iajs-3717	157	26	0	0	NUM
iajs-3717	157	27	)	)	PUNCT
iajs-3717	157	28	if	if	SCONJ
iajs-3717	157	29	in	in	ADP
iajs-3717	157	30	addition	addition	NOUN
iajs-3717	157	31	to	to	ADP
iajs-3717	157	32	condition	condition	NOUN
iajs-3717	157	33	(	(	PUNCT
iajs-3717	157	34	26	26	NUM
iajs-3717	157	35	,	,	PUNCT
iajs-3717	157	36	27	27	NUM
iajs-3717	157	37	)	)	PUNCT
iajs-3717	157	38	and	and	CCONJ
iajs-3717	157	39	the	the	DET
iajs-3717	157	40	following	follow	VERB
iajs-3717	157	41	condition	condition	NOUN
iajs-3717	157	42	hold	hold	VERB
iajs-3717	157	43	𝒜6	𝒜6	NOUN
iajs-3717	157	44	>	>	X
iajs-3717	157	45	𝒜3	𝒜3	PROPN
iajs-3717	157	46	(	(	PUNCT
iajs-3717	157	47	30	30	NUM
iajs-3717	157	48	)	)	PUNCT
iajs-3717	157	49	let	let	VERB
iajs-3717	157	50	𝜇	𝜇	SCONJ
iajs-3717	157	51	=	=	X
iajs-3717	157	52	𝑖𝜔	𝑖𝜔	PROPN
iajs-3717	157	53	is	be	AUX
iajs-3717	157	54	the	the	DET
iajs-3717	157	55	root	root	NOUN
iajs-3717	157	56	of	of	ADP
iajs-3717	157	57	equation	equation	NOUN
iajs-3717	157	58	(	(	PUNCT
iajs-3717	157	59	24	24	NUM
iajs-3717	157	60	)	)	PUNCT
iajs-3717	157	61	and	and	CCONJ
iajs-3717	157	62	by	by	ADP
iajs-3717	157	63	separating	separate	VERB
iajs-3717	157	64	equation	equation	NOUN
iajs-3717	157	65	(	(	PUNCT
iajs-3717	157	66	24	24	NUM
iajs-3717	157	67	)	)	PUNCT
iajs-3717	157	68	to	to	ADP
iajs-3717	157	69	the	the	DET
iajs-3717	157	70	real	real	ADJ
iajs-3717	157	71	and	and	CCONJ
iajs-3717	157	72	imaginary	imaginary	ADJ
iajs-3717	157	73	part	part	NOUN
iajs-3717	157	74	,	,	PUNCT
iajs-3717	157	75	yields	yield	NOUN
iajs-3717	157	76	(	(	PUNCT
iajs-3717	157	77	𝒜4𝜔	𝒜4𝜔	PROPN
iajs-3717	157	78	2	2	NUM
iajs-3717	157	79	−𝒜6	−𝒜6	NOUN
iajs-3717	157	80	)	)	PUNCT
iajs-3717	157	81	𝑠𝑖𝑛𝜔𝜏	𝑠𝑖𝑛𝜔𝜏	VERB
iajs-3717	158	1	+	+	ADV
iajs-3717	158	2	𝒜5	𝒜5	ADJ
iajs-3717	158	3	𝜔	𝜔	ADP
iajs-3717	158	4	𝑐𝑜𝑠	𝑐𝑜𝑠	NOUN
iajs-3717	158	5	𝜔𝜏	𝜔𝜏	NOUN
iajs-3717	158	6	=	=	NOUN
iajs-3717	158	7	𝜔	𝜔	SYM
iajs-3717	158	8	3	3	NUM
iajs-3717	158	9	−𝒜2	−𝒜2	NOUN
iajs-3717	158	10	𝜔	𝜔	PART
iajs-3717	158	11	𝒜5	𝒜5	NOUN
iajs-3717	159	1	𝜔	𝜔	AUX
iajs-3717	159	2	𝑠𝑖𝑛𝜔𝜏	𝑠𝑖𝑛𝜔𝜏	ADJ
iajs-3717	159	3	+	+	NOUN
iajs-3717	159	4	(	(	PUNCT
iajs-3717	159	5	𝒜6	𝒜6	NOUN
iajs-3717	159	6	−𝒜4𝜔	−𝒜4𝜔	NOUN
iajs-3717	159	7	2	2	X
iajs-3717	159	8	)	)	PUNCT
iajs-3717	159	9	𝑐𝑜𝑠	𝑐𝑜𝑠	NOUN
iajs-3717	159	10	𝜔𝜏	𝜔𝜏	NOUN
iajs-3717	159	11	=	=	PUNCT
iajs-3717	159	12	𝒜1	𝒜1	NOUN
iajs-3717	159	13	𝜔	𝜔	SYM
iajs-3717	159	14	2	2	NUM
iajs-3717	159	15	−𝒜3	−𝒜3	NOUN
iajs-3717	159	16	(	(	PUNCT
iajs-3717	159	17	31	31	NUM
iajs-3717	159	18	)	)	PUNCT
iajs-3717	159	19	the	the	DET
iajs-3717	159	20	result	result	NOUN
iajs-3717	159	21	of	of	ADP
iajs-3717	159	22	squaring	square	VERB
iajs-3717	159	23	and	and	CCONJ
iajs-3717	159	24	summing	sum	VERB
iajs-3717	159	25	the	the	DET
iajs-3717	159	26	above	above	ADJ
iajs-3717	159	27	equations	equation	NOUN
iajs-3717	159	28	yields	yield	VERB
iajs-3717	159	29	:	:	PUNCT
iajs-3717	159	30	𝜔6	𝜔6	PROPN
iajs-3717	159	31	+	+	CCONJ
iajs-3717	159	32	𝒞1𝜔	𝒞1𝜔	PROPN
iajs-3717	159	33	4	4	NUM
iajs-3717	159	34	+	+	NUM
iajs-3717	159	35	𝒞2𝜔	𝒞2𝜔	PROPN
iajs-3717	159	36	2	2	NUM
iajs-3717	159	37	+	+	NUM
iajs-3717	159	38	𝒞3	𝒞3	NOUN
iajs-3717	159	39	=	=	SYM
iajs-3717	159	40	0	0	PUNCT
iajs-3717	159	41	(	(	PUNCT
iajs-3717	159	42	32	32	NUM
iajs-3717	159	43	)	)	PUNCT
iajs-3717	159	44	where	where	SCONJ
iajs-3717	159	45	𝒞1	𝒞1	PROPN
iajs-3717	159	46	=	=	SYM
iajs-3717	159	47	𝒜1	𝒜1	PROPN
iajs-3717	159	48	2	2	NUM
iajs-3717	159	49	−	−	NOUN
iajs-3717	159	50	𝒜4	𝒜4	NOUN
iajs-3717	159	51	2	2	NUM
iajs-3717	159	52	−	−	NOUN
iajs-3717	159	53	2𝒜2	2𝒜2	NUM
iajs-3717	159	54	;	;	PUNCT
iajs-3717	159	55	𝒞2	𝒞2	PROPN
iajs-3717	159	56	=	=	PUNCT
iajs-3717	159	57	𝒜2	𝒜2	NOUN
iajs-3717	159	58	2	2	NUM
iajs-3717	159	59	−	−	NOUN
iajs-3717	159	60	𝒜5	𝒜5	NOUN
iajs-3717	159	61	2	2	NUM
iajs-3717	159	62	−	−	PROPN
iajs-3717	159	63	2𝒜1𝒜3	2𝒜1𝒜3	NOUN
iajs-3717	159	64	+	+	CCONJ
iajs-3717	159	65	2	2	NUM
iajs-3717	159	66	𝒜4	𝒜4	NOUN
iajs-3717	159	67	𝒜6	𝒜6	NOUN
iajs-3717	159	68	;	;	PUNCT
iajs-3717	159	69	ihjpas	ihjpas	PROPN
iajs-3717	159	70	.	.	PUNCT
iajs-3717	160	1	2025,38(2	2025,38(2	PROPN
iajs-3717	160	2	)	)	PUNCT
iajs-3717	160	3	367	367	NUM
iajs-3717	160	4	𝒞3	𝒞3	NOUN
iajs-3717	160	5	=	=	PUNCT
iajs-3717	160	6	𝒜3	𝒜3	PROPN
iajs-3717	160	7	2	2	NUM
iajs-3717	160	8	−	−	NOUN
iajs-3717	160	9	𝒜6	𝒜6	NOUN
iajs-3717	160	10	2	2	NUM
iajs-3717	160	11	put	put	VERB
iajs-3717	160	12	ℋ	ℋ	NOUN
iajs-3717	160	13	=	=	SYM
iajs-3717	160	14	𝜔2	𝜔2	PROPN
iajs-3717	160	15	,	,	PUNCT
iajs-3717	160	16	then	then	ADV
iajs-3717	160	17	equation	equation	NOUN
iajs-3717	160	18	(	(	PUNCT
iajs-3717	160	19	32	32	NUM
iajs-3717	160	20	)	)	PUNCT
iajs-3717	160	21	becomes	become	VERB
iajs-3717	160	22	ℋ3	ℋ3	NOUN
iajs-3717	161	1	+	+	CCONJ
iajs-3717	161	2	𝒞1ℋ	𝒞1ℋ	PROPN
iajs-3717	161	3	2	2	NUM
iajs-3717	162	1	+	+	CCONJ
iajs-3717	162	2	𝒞2ℋ	𝒞2ℋ	PROPN
iajs-3717	162	3	+	+	CCONJ
iajs-3717	162	4	𝒞3	𝒞3	NOUN
iajs-3717	162	5	=	=	SYM
iajs-3717	162	6	0	0	NUM
iajs-3717	162	7	(	(	PUNCT
iajs-3717	162	8	33	33	NUM
iajs-3717	162	9	)	)	PUNCT
iajs-3717	162	10	under	under	ADP
iajs-3717	162	11	the	the	DET
iajs-3717	162	12	conditions	condition	NOUN
iajs-3717	162	13	(	(	PUNCT
iajs-3717	162	14	27,28	27,28	NUM
iajs-3717	162	15	)	)	PUNCT
iajs-3717	162	16	and	and	CCONJ
iajs-3717	162	17	condition	condition	NOUN
iajs-3717	162	18	(	(	PUNCT
iajs-3717	162	19	30	30	NUM
iajs-3717	162	20	)	)	PUNCT
iajs-3717	162	21	we	we	PRON
iajs-3717	162	22	have	have	VERB
iajs-3717	162	23	𝒞3	𝒞3	NOUN
iajs-3717	162	24	<	<	X
iajs-3717	162	25	0	0	PUNCT
iajs-3717	162	26	.	.	PUNCT
iajs-3717	163	1	the	the	DET
iajs-3717	163	2	equation	equation	NOUN
iajs-3717	163	3	(	(	PUNCT
iajs-3717	163	4	33	33	NUM
iajs-3717	163	5	)	)	PUNCT
iajs-3717	163	6	have	have	VERB
iajs-3717	163	7	a	a	DET
iajs-3717	163	8	positive	positive	ADJ
iajs-3717	163	9	root	root	NOUN
iajs-3717	163	10	which	which	PRON
iajs-3717	163	11	is	be	AUX
iajs-3717	163	12	unique	unique	ADJ
iajs-3717	163	13	say	say	VERB
iajs-3717	163	14	𝜔0	𝜔0	NOUN
iajs-3717	163	15	by	by	ADP
iajs-3717	163	16	using	use	VERB
iajs-3717	163	17	descartes	descarte	NOUN
iajs-3717	163	18	'	'	PART
iajs-3717	163	19	rule	rule	NOUN
iajs-3717	163	20	of	of	ADP
iajs-3717	163	21	sign	sign	NOUN
iajs-3717	163	22	.	.	PUNCT
iajs-3717	164	1	hence	hence	ADV
iajs-3717	164	2	𝜔0	𝜔0	NOUN
iajs-3717	164	3	is	be	AUX
iajs-3717	164	4	also	also	ADV
iajs-3717	164	5	the	the	DET
iajs-3717	164	6	positive	positive	ADJ
iajs-3717	164	7	root	root	NOUN
iajs-3717	164	8	of	of	ADP
iajs-3717	164	9	equation	equation	NOUN
iajs-3717	164	10	(	(	PUNCT
iajs-3717	164	11	32	32	NUM
iajs-3717	164	12	)	)	PUNCT
iajs-3717	164	13	.	.	PUNCT
iajs-3717	165	1	hence	hence	ADV
iajs-3717	165	2	,	,	PUNCT
iajs-3717	165	3	there	there	PRON
iajs-3717	165	4	exists	exist	VERB
iajs-3717	165	5	at	at	ADP
iajs-3717	165	6	least	least	ADJ
iajs-3717	165	7	a	a	DET
iajs-3717	165	8	pair	pair	NOUN
iajs-3717	165	9	of	of	ADP
iajs-3717	165	10	imaginary	imaginary	ADJ
iajs-3717	165	11	roots	root	NOUN
iajs-3717	165	12	,	,	PUNCT
iajs-3717	165	13	denoted	denote	VERB
iajs-3717	165	14	as	as	ADP
iajs-3717	165	15	±𝑖𝜔0	±𝑖𝜔0	CCONJ
iajs-3717	165	16	,	,	PUNCT
iajs-3717	165	17	that	that	PRON
iajs-3717	165	18	satisfies	satisfy	VERB
iajs-3717	165	19	equation	equation	NOUN
iajs-3717	165	20	(	(	PUNCT
iajs-3717	165	21	24	24	NUM
iajs-3717	165	22	)	)	PUNCT
iajs-3717	165	23	.	.	PUNCT
iajs-3717	166	1	from	from	ADP
iajs-3717	166	2	equation	equation	NOUN
iajs-3717	166	3	(	(	PUNCT
iajs-3717	166	4	31	31	NUM
iajs-3717	166	5	)	)	PUNCT
iajs-3717	166	6	after	after	ADP
iajs-3717	166	7	substituting	substitute	VERB
iajs-3717	166	8	𝜔0	𝜔0	NOUN
iajs-3717	166	9	,	,	PUNCT
iajs-3717	166	10	we	we	PRON
iajs-3717	166	11	obtain	obtain	VERB
iajs-3717	166	12	:	:	PUNCT
iajs-3717	166	13	cos	cos	X
iajs-3717	166	14	𝜔0𝜏	𝜔0𝜏	PUNCT
iajs-3717	166	15	=	=	PROPN
iajs-3717	166	16	𝒷1	𝒷1	PROPN
iajs-3717	166	17	𝒷2	𝒷2	ADV
iajs-3717	166	18	here	here	ADV
iajs-3717	166	19	𝒷1	𝒷1	PROPN
iajs-3717	166	20	=	=	SYM
iajs-3717	166	21	(	(	PUNCT
iajs-3717	166	22	𝒜5	𝒜5	NOUN
iajs-3717	166	23	−	−	PROPN
iajs-3717	166	24	𝒜1	𝒜1	NOUN
iajs-3717	166	25	𝒜4	𝒜4	ADJ
iajs-3717	166	26	)	)	PUNCT
iajs-3717	166	27	𝜔0	𝜔0	NOUN
iajs-3717	166	28	4	4	NUM
iajs-3717	166	29	+	+	CCONJ
iajs-3717	166	30	(	(	PUNCT
iajs-3717	166	31	𝒜1	𝒜1	NOUN
iajs-3717	166	32	𝒜	𝒜	NOUN
iajs-3717	166	33	6	6	NUM
iajs-3717	166	34	+	+	NOUN
iajs-3717	166	35	𝒜3	𝒜3	NOUN
iajs-3717	166	36	𝒜	𝒜	NOUN
iajs-3717	166	37	4	4	NUM
iajs-3717	166	38	−	−	NOUN
iajs-3717	166	39	𝒜2	𝒜2	PROPN
iajs-3717	166	40	𝒜5	𝒜5	NOUN
iajs-3717	166	41	)	)	PUNCT
iajs-3717	166	42	𝜔0	𝜔0	NOUN
iajs-3717	166	43	2	2	NUM
iajs-3717	166	44	−	−	NOUN
iajs-3717	166	45	𝒜3	𝒜3	PROPN
iajs-3717	166	46	𝒜6	𝒜6	NOUN
iajs-3717	166	47	𝒷2	𝒷2	ADV
iajs-3717	166	48	=	=	SYM
iajs-3717	166	49	𝒜	𝒜	PROPN
iajs-3717	166	50	4	4	NUM
iajs-3717	166	51	2𝜔0	2𝜔0	NUM
iajs-3717	166	52	4	4	NUM
iajs-3717	166	53	+	+	CCONJ
iajs-3717	166	54	(	(	PUNCT
iajs-3717	166	55	𝒜	𝒜	NOUN
iajs-3717	166	56	5	5	NUM
iajs-3717	166	57	2	2	NUM
iajs-3717	166	58	−	−	NOUN
iajs-3717	166	59	2𝒜4	2𝒜4	NUM
iajs-3717	166	60	𝒜6	𝒜6	NOUN
iajs-3717	166	61	)	)	PUNCT
iajs-3717	166	62	𝜔0	𝜔0	NOUN
iajs-3717	166	63	2	2	NUM
iajs-3717	166	64	+	+	NOUN
iajs-3717	166	65	𝒜	𝒜	NOUN
iajs-3717	166	66	6	6	NUM
iajs-3717	166	67	2	2	NUM
iajs-3717	166	68	then	then	ADV
iajs-3717	166	69	,	,	PUNCT
iajs-3717	166	70	𝜏𝑚	𝜏𝑚	PROPN
iajs-3717	166	71	corresponding	correspond	VERB
iajs-3717	166	72	to	to	PART
iajs-3717	166	73	𝜔0	𝜔0	VERB
iajs-3717	166	74	as	as	ADV
iajs-3717	166	75	below	below	ADP
iajs-3717	166	76	𝜏𝑚	𝜏𝑚	NOUN
iajs-3717	166	77	=	=	SYM
iajs-3717	166	78	1	1	NUM
iajs-3717	166	79	𝜔0	𝜔0	NOUN
iajs-3717	166	80	(	(	PUNCT
iajs-3717	166	81	cos−1	cos−1	NOUN
iajs-3717	166	82	(	(	PUNCT
iajs-3717	166	83	ℓ1	ℓ1	ADJ
iajs-3717	166	84	ℓ2	ℓ2	NOUN
iajs-3717	166	85	)	)	PUNCT
iajs-3717	167	1	+	+	CCONJ
iajs-3717	167	2	2𝜋𝑚	2𝜋𝑚	ADJ
iajs-3717	167	3	)	)	PUNCT
iajs-3717	167	4	;	;	PUNCT
iajs-3717	167	5	𝑚	𝑚	X
iajs-3717	167	6	=	=	SYM
iajs-3717	167	7	0,1,2	0,1,2	NUM
iajs-3717	167	8	,	,	PUNCT
iajs-3717	167	9	…	…	PUNCT
iajs-3717	167	10	(	(	PUNCT
iajs-3717	167	11	34	34	NUM
iajs-3717	167	12	)	)	PUNCT
iajs-3717	167	13	define	define	VERB
iajs-3717	167	14	𝜏0	𝜏0	PROPN
iajs-3717	167	15	=	=	SYM
iajs-3717	167	16	𝑚𝑖𝑛	𝑚𝑖𝑛	PROPN
iajs-3717	167	17	𝑚≥0	𝑚≥0	PROPN
iajs-3717	167	18	𝜏𝑚	𝜏𝑚	NOUN
iajs-3717	167	19	then	then	ADV
iajs-3717	167	20	,	,	PUNCT
iajs-3717	167	21	we	we	PRON
iajs-3717	167	22	obtain	obtain	VERB
iajs-3717	167	23	the	the	DET
iajs-3717	167	24	following	follow	VERB
iajs-3717	167	25	theorem	theorem	NOUN
iajs-3717	167	26	theorem	theorem	NOUN
iajs-3717	167	27	2	2	NUM
iajs-3717	167	28	.	.	PUNCT
iajs-3717	167	29	the	the	DET
iajs-3717	167	30	system	system	NOUN
iajs-3717	167	31	(	(	PUNCT
iajs-3717	167	32	2	2	X
iajs-3717	167	33	)	)	PUNCT
iajs-3717	167	34	asymptotic	asymptotic	ADJ
iajs-3717	167	35	stability	stability	NOUN
iajs-3717	167	36	at	at	ADP
iajs-3717	167	37	𝐹3within	𝐹3within	PRON
iajs-3717	167	38	the	the	DET
iajs-3717	167	39	τ	τ	PROPN
iajs-3717	167	40	∈	∈	PROPN
iajs-3717	167	41	[	[	X
iajs-3717	167	42	0	0	NUM
iajs-3717	167	43	,	,	PUNCT
iajs-3717	167	44	τ0	τ0	NOUN
iajs-3717	167	45	)	)	PUNCT
iajs-3717	167	46	and	and	CCONJ
iajs-3717	167	47	a	a	DET
iajs-3717	167	48	hopf	hopf	ADJ
iajs-3717	167	49	bifurcation	bifurcation	NOUN
iajs-3717	167	50	occurs	occur	VERB
iajs-3717	167	51	at	at	ADP
iajs-3717	167	52	𝜏	𝜏	NOUN
iajs-3717	167	53	=	=	VERB
iajs-3717	167	54	τ0	τ0	NOUN
iajs-3717	167	55	when	when	SCONJ
iajs-3717	167	56	specific	specific	ADJ
iajs-3717	167	57	conditions	condition	NOUN
iajs-3717	167	58	are	be	AUX
iajs-3717	167	59	met	meet	VERB
iajs-3717	167	60	.	.	PUNCT
iajs-3717	168	1	3(𝜔0	3(𝜔0	PROPN
iajs-3717	168	2	2)2	2)2	NUM
iajs-3717	169	1	+	+	CCONJ
iajs-3717	169	2	2𝒞1𝜔0	2𝒞1𝜔0	NUM
iajs-3717	169	3	2	2	NUM
iajs-3717	169	4	+	+	NUM
iajs-3717	169	5	𝒞2	𝒞2	PROPN
iajs-3717	169	6	≠	≠	PROPN
iajs-3717	169	7	0	0	NUM
iajs-3717	169	8	(	(	PUNCT
iajs-3717	169	9	35	35	NUM
iajs-3717	169	10	)	)	PUNCT
iajs-3717	169	11	proof	proof	NOUN
iajs-3717	169	12	.	.	PUNCT
iajs-3717	170	1	for	for	ADP
iajs-3717	170	2	𝜏	𝜏	PROPN
iajs-3717	170	3	∈	∈	PROPN
iajs-3717	170	4	[	[	X
iajs-3717	170	5	0	0	NUM
iajs-3717	170	6	,	,	PUNCT
iajs-3717	170	7	τ0	τ0	NOUN
iajs-3717	170	8	)	)	PUNCT
iajs-3717	170	9	𝐹3	𝐹3	PROPN
iajs-3717	170	10	is	be	AUX
iajs-3717	170	11	asymptotically	asymptotically	ADV
iajs-3717	170	12	stable	stable	ADJ
iajs-3717	170	13	as	as	SCONJ
iajs-3717	170	14	shown	show	VERB
iajs-3717	170	15	in	in	ADP
iajs-3717	170	16	conditions	condition	NOUN
iajs-3717	170	17	(	(	PUNCT
iajs-3717	170	18	26	26	NUM
iajs-3717	170	19	)	)	PUNCT
iajs-3717	170	20	(	(	PUNCT
iajs-3717	170	21	29	29	NUM
iajs-3717	170	22	)	)	PUNCT
iajs-3717	170	23	.	.	PUNCT
iajs-3717	171	1	however	however	ADV
iajs-3717	171	2	,	,	PUNCT
iajs-3717	171	3	when	when	SCONJ
iajs-3717	171	4	𝜏	𝜏	X
iajs-3717	171	5	=	=	SYM
iajs-3717	171	6	τ0	τ0	NOUN
iajs-3717	171	7	,	,	PUNCT
iajs-3717	171	8	we	we	PRON
iajs-3717	171	9	can	can	AUX
iajs-3717	171	10	demonstrate	demonstrate	VERB
iajs-3717	171	11	the	the	DET
iajs-3717	171	12	presence	presence	NOUN
iajs-3717	171	13	of	of	ADP
iajs-3717	171	14	a	a	DET
iajs-3717	171	15	hopf	hopf	ADJ
iajs-3717	171	16	bifurcation	bifurcation	NOUN
iajs-3717	171	17	by	by	ADP
iajs-3717	171	18	establishing	establish	VERB
iajs-3717	171	19	that	that	SCONJ
iajs-3717	171	20	𝐹3	𝐹3	PROPN
iajs-3717	171	21	is	be	AUX
iajs-3717	171	22	conditionally	conditionally	ADV
iajs-3717	171	23	stable	stable	ADJ
iajs-3717	171	24	,	,	PUNCT
iajs-3717	171	25	specifically	specifically	ADV
iajs-3717	171	26	,	,	PUNCT
iajs-3717	171	27	by	by	ADP
iajs-3717	171	28	confirming	confirm	VERB
iajs-3717	171	29	that	that	SCONJ
iajs-3717	171	30	equation	equation	NOUN
iajs-3717	171	31	(	(	PUNCT
iajs-3717	171	32	24	24	NUM
iajs-3717	171	33	)	)	PUNCT
iajs-3717	171	34	exhibits	exhibit	VERB
iajs-3717	171	35	purely	purely	ADV
iajs-3717	171	36	imaginary	imaginary	ADJ
iajs-3717	171	37	roots	root	NOUN
iajs-3717	171	38	±𝑖	±𝑖	NOUN
iajs-3717	171	39	𝜔0	𝜔0	NOUN
iajs-3717	171	40	at	at	ADP
iajs-3717	171	41	𝜏	𝜏	NOUN
iajs-3717	171	42	=	=	SYM
iajs-3717	171	43	τ0	τ0	NOUN
iajs-3717	171	44	,	,	PUNCT
iajs-3717	171	45	this	this	DET
iajs-3717	171	46	condition	condition	NOUN
iajs-3717	171	47	can	can	AUX
iajs-3717	171	48	be	be	AUX
iajs-3717	171	49	expressed	express	VERB
iajs-3717	171	50	[	[	PUNCT
iajs-3717	171	51	𝑑(𝑅𝑒𝜆(𝜏	𝑑(𝑅𝑒𝜆(𝜏	NOUN
iajs-3717	171	52	)	)	PUNCT
iajs-3717	171	53	)	)	PUNCT
iajs-3717	172	1	𝑑𝜏	𝑑𝜏	NOUN
iajs-3717	172	2	]	]	PUNCT
iajs-3717	172	3	𝜏=𝜏0	𝜏=𝜏0	PROPN
iajs-3717	172	4	≠	≠	PROPN
iajs-3717	172	5	0	0	NUM
iajs-3717	172	6	if	if	SCONJ
iajs-3717	172	7	we	we	PRON
iajs-3717	172	8	assume	assume	VERB
iajs-3717	172	9	that	that	SCONJ
iajs-3717	172	10	equation	equation	NOUN
iajs-3717	172	11	(	(	PUNCT
iajs-3717	172	12	24	24	NUM
iajs-3717	172	13	)	)	PUNCT
iajs-3717	172	14	has	have	VERB
iajs-3717	172	15	the	the	DET
iajs-3717	172	16	eigenvalue	eigenvalue	NOUN
iajs-3717	172	17	that	that	PRON
iajs-3717	172	18	is	be	AUX
iajs-3717	172	19	𝜇(𝜏	𝜇(𝜏	PROPN
iajs-3717	172	20	)	)	PUNCT
iajs-3717	172	21	=	=	SYM
iajs-3717	172	22	ð(𝜏	ð(𝜏	NOUN
iajs-3717	172	23	)	)	PUNCT
iajs-3717	173	1	+	+	CCONJ
iajs-3717	173	2	𝑖𝜔(𝜏	𝑖𝜔(𝜏	NOUN
iajs-3717	173	3	)	)	PUNCT
iajs-3717	174	1	such	such	ADJ
iajs-3717	174	2	that	that	DET
iajs-3717	174	3	ð(τ0	ð(τ0	NOUN
iajs-3717	174	4	)	)	PUNCT
iajs-3717	175	1	=	=	SYM
iajs-3717	175	2	0	0	NUM
iajs-3717	175	3	and	and	CCONJ
iajs-3717	175	4	𝜔(τ0	𝜔(τ0	NOUN
iajs-3717	175	5	)	)	PUNCT
iajs-3717	175	6	=	=	SYM
iajs-3717	175	7	𝜔0	𝜔0	NOUN
iajs-3717	175	8	>	>	X
iajs-3717	175	9	0	0	X
iajs-3717	175	10	.	.	PUNCT
iajs-3717	176	1	τ0	τ0	NOUN
iajs-3717	176	2	define	define	VERB
iajs-3717	176	3	in	in	ADP
iajs-3717	176	4	equation	equation	NOUN
iajs-3717	176	5	(	(	PUNCT
iajs-3717	176	6	34	34	NUM
iajs-3717	176	7	)	)	PUNCT
iajs-3717	176	8	.	.	PUNCT
iajs-3717	177	1	when	when	SCONJ
iajs-3717	177	2	we	we	PRON
iajs-3717	177	3	differentiate	differentiate	VERB
iajs-3717	177	4	equation	equation	NOUN
iajs-3717	177	5	(	(	PUNCT
iajs-3717	177	6	24	24	NUM
iajs-3717	177	7	)	)	PUNCT
iajs-3717	177	8	with	with	ADP
iajs-3717	177	9	respect	respect	NOUN
iajs-3717	177	10	to	to	ADP
iajs-3717	177	11	𝜏	𝜏	NUM
iajs-3717	177	12	,	,	PUNCT
iajs-3717	177	13	and	and	CCONJ
iajs-3717	177	14	apply	apply	VERB
iajs-3717	177	15	the	the	DET
iajs-3717	177	16	chain	chain	NOUN
iajs-3717	177	17	rule	rule	NOUN
iajs-3717	177	18	.	.	PUNCT
iajs-3717	178	1	this	this	DET
iajs-3717	178	2	results	result	VERB
iajs-3717	178	3	in	in	ADP
iajs-3717	178	4	the	the	DET
iajs-3717	178	5	following	follow	VERB
iajs-3717	178	6	expression	expression	NOUN
iajs-3717	178	7	:	:	PUNCT
iajs-3717	179	1	[	[	X
iajs-3717	179	2	3𝜇2	3𝜇2	NUM
iajs-3717	179	3	+	+	SYM
iajs-3717	179	4	2	2	NUM
iajs-3717	179	5	𝒜1𝜇	𝒜1𝜇	NOUN
iajs-3717	179	6	+	+	CCONJ
iajs-3717	179	7	𝒜2	𝒜2	NOUN
iajs-3717	179	8	+	+	CCONJ
iajs-3717	179	9	(	(	PUNCT
iajs-3717	179	10	2	2	NUM
iajs-3717	179	11	𝒜4𝜇	𝒜4𝜇	NOUN
iajs-3717	179	12	+	+	CCONJ
iajs-3717	179	13	𝒜5)𝑒	𝒜5)𝑒	NOUN
iajs-3717	179	14	−𝜇𝜏	−𝜇𝜏	ADP
iajs-3717	179	15	−	−	PRON
iajs-3717	179	16	𝜏	𝜏	PROPN
iajs-3717	179	17	(	(	PUNCT
iajs-3717	179	18	𝒜4𝜇	𝒜4𝜇	PROPN
iajs-3717	179	19	2	2	NUM
iajs-3717	179	20	+	+	CCONJ
iajs-3717	179	21	𝒜5𝜇	𝒜5𝜇	PROPN
iajs-3717	180	1	+	+	CCONJ
iajs-3717	180	2	𝒜6)𝑒	𝒜6)𝑒	X
iajs-3717	180	3	−𝜇𝜏	−𝜇𝜏	X
iajs-3717	180	4	]	]	X
iajs-3717	180	5	𝑑𝜇	𝑑𝜇	ADP
iajs-3717	180	6	𝑑𝜏	𝑑𝜏	NOUN
iajs-3717	180	7	=	=	SYM
iajs-3717	180	8	𝜇	𝜇	X
iajs-3717	180	9	(	(	PUNCT
iajs-3717	180	10	𝒜4𝜇	𝒜4𝜇	PROPN
iajs-3717	180	11	2	2	NUM
iajs-3717	180	12	+	+	CCONJ
iajs-3717	180	13	𝒜5𝜇	𝒜5𝜇	PROPN
iajs-3717	181	1	+	+	PUNCT
iajs-3717	181	2	𝒜6)𝑒	𝒜6)𝑒	X
iajs-3717	181	3	−𝜇𝜏	−𝜇𝜏	X
iajs-3717	181	4	(	(	PUNCT
iajs-3717	181	5	36	36	NUM
iajs-3717	181	6	)	)	PUNCT
iajs-3717	181	7	from	from	ADP
iajs-3717	181	8	equation	equation	NOUN
iajs-3717	181	9	(	(	PUNCT
iajs-3717	181	10	24	24	NUM
iajs-3717	181	11	)	)	PUNCT
iajs-3717	181	12	,	,	PUNCT
iajs-3717	181	13	we	we	PRON
iajs-3717	181	14	have	have	VERB
iajs-3717	181	15	[	[	PUNCT
iajs-3717	181	16	𝑑𝜇	𝑑𝜇	ADP
iajs-3717	181	17	𝑑𝜏	𝑑𝜏	NOUN
iajs-3717	181	18	]	]	PUNCT
iajs-3717	181	19	−1	−1	NOUN
iajs-3717	181	20	=	=	SYM
iajs-3717	181	21	(	(	PUNCT
iajs-3717	181	22	3𝜇2	3𝜇2	PROPN
iajs-3717	181	23	+	+	NOUN
iajs-3717	181	24	2	2	NUM
iajs-3717	181	25	𝒜1𝜇+	𝒜1𝜇+	VERB
iajs-3717	181	26	𝒜2)𝑒	𝒜2)𝑒	PUNCT
iajs-3717	181	27	𝜇𝜏	𝜇𝜏	NOUN
iajs-3717	181	28	𝜇	𝜇	NOUN
iajs-3717	181	29	(	(	PUNCT
iajs-3717	181	30	𝒜4𝜇2	𝒜4𝜇2	ADV
iajs-3717	181	31	+	+	CCONJ
iajs-3717	181	32	𝒜5𝜇+	𝒜5𝜇+	ADJ
iajs-3717	181	33	𝒜6	𝒜6	NOUN
iajs-3717	181	34	)	)	PUNCT
iajs-3717	182	1	+	+	CCONJ
iajs-3717	182	2	2	2	X
iajs-3717	182	3	𝒜4𝜇	𝒜4𝜇	NOUN
iajs-3717	182	4	+	+	CCONJ
iajs-3717	182	5	𝒜5	𝒜5	NOUN
iajs-3717	182	6	𝜇	𝜇	ADP
iajs-3717	182	7	(	(	PUNCT
iajs-3717	182	8	𝒜4𝜇2	𝒜4𝜇2	ADV
iajs-3717	182	9	+	+	CCONJ
iajs-3717	182	10	𝒜5𝜇+	𝒜5𝜇+	ADJ
iajs-3717	182	11	𝒜6	𝒜6	NOUN
iajs-3717	182	12	)	)	PUNCT
iajs-3717	183	1	−	−	ADP
iajs-3717	183	2	𝜏	𝜏	X
iajs-3717	183	3	𝜇	𝜇	X
iajs-3717	183	4	(	(	PUNCT
iajs-3717	183	5	37	37	NUM
iajs-3717	183	6	)	)	PUNCT
iajs-3717	183	7	since	since	SCONJ
iajs-3717	183	8	for	for	ADP
iajs-3717	183	9	𝜏	𝜏	PROPN
iajs-3717	183	10	=	=	SYM
iajs-3717	183	11	𝜏0	𝜏0	PROPN
iajs-3717	183	12	,	,	PUNCT
iajs-3717	183	13	and	and	CCONJ
iajs-3717	183	14	𝜇	𝜇	X
iajs-3717	183	15	=	=	X
iajs-3717	183	16	𝑖𝜔0	𝑖𝜔0	PROPN
iajs-3717	183	17	we	we	PRON
iajs-3717	183	18	get	get	VERB
iajs-3717	183	19	[	[	PUNCT
iajs-3717	183	20	𝑑𝜇	𝑑𝜇	ADP
iajs-3717	183	21	𝑑𝜏	𝑑𝜏	NOUN
iajs-3717	183	22	]	]	PUNCT
iajs-3717	183	23	−1	−1	NOUN
iajs-3717	183	24	=	=	SYM
iajs-3717	183	25	(	(	PUNCT
iajs-3717	183	26	(	(	PUNCT
iajs-3717	183	27	𝒜2	𝒜2	PROPN
iajs-3717	183	28	−	−	PROPN
iajs-3717	183	29	3𝜔0	3𝜔0	NUM
iajs-3717	183	30	2	2	NUM
iajs-3717	183	31	)	)	PUNCT
iajs-3717	184	1	+	+	NUM
iajs-3717	184	2	2𝑖	2𝑖	NOUN
iajs-3717	184	3	𝒜1𝜔0	𝒜1𝜔0	ADJ
iajs-3717	184	4	)	)	PUNCT
iajs-3717	184	5	(	(	PUNCT
iajs-3717	184	6	cos𝜔0𝜏	cos𝜔0𝜏	PUNCT
iajs-3717	184	7	+	+	CCONJ
iajs-3717	184	8	𝑖	𝑖	SYM
iajs-3717	184	9	sin𝜔0𝜏	sin𝜔0𝜏	NOUN
iajs-3717	184	10	)	)	PUNCT
iajs-3717	184	11	−	−	PROPN
iajs-3717	184	12	𝒜5𝜔0	𝒜5𝜔0	NOUN
iajs-3717	184	13	2	2	NUM
iajs-3717	184	14	+	+	CCONJ
iajs-3717	184	15	𝑖𝜔0	𝑖𝜔0	PROPN
iajs-3717	184	16	(	(	PUNCT
iajs-3717	184	17	𝒜6	𝒜6	NOUN
iajs-3717	184	18	−	−	NOUN
iajs-3717	184	19	𝒜4𝜔0	𝒜4𝜔0	ADJ
iajs-3717	184	20	2	2	NUM
iajs-3717	184	21	)	)	PUNCT
iajs-3717	184	22	+	+	CCONJ
iajs-3717	184	23	𝒜5	𝒜5	ADJ
iajs-3717	184	24	+	+	CCONJ
iajs-3717	184	25	2𝑖	2𝑖	NOUN
iajs-3717	184	26	𝒜4𝜔0	𝒜4𝜔0	ADV
iajs-3717	184	27	−	−	ADP
iajs-3717	184	28	𝒜5𝜔0	𝒜5𝜔0	NOUN
iajs-3717	184	29	2	2	NUM
iajs-3717	184	30	+	+	CCONJ
iajs-3717	184	31	𝑖𝜔0	𝑖𝜔0	PROPN
iajs-3717	184	32	(	(	PUNCT
iajs-3717	184	33	𝒜6	𝒜6	NOUN
iajs-3717	184	34	−	−	NOUN
iajs-3717	184	35	𝒜4𝜔0	𝒜4𝜔0	ADJ
iajs-3717	184	36	2	2	NUM
iajs-3717	184	37	)	)	PUNCT
iajs-3717	184	38	−	−	PROPN
iajs-3717	185	1	𝜏0	𝜏0	PROPN
iajs-3717	185	2	𝑖𝜔0	𝑖𝜔0	PROPN
iajs-3717	186	1	now	now	ADV
iajs-3717	186	2	since	since	SCONJ
iajs-3717	186	3	𝑠𝑖𝑔𝑛	𝑠𝑖𝑔𝑛	NOUN
iajs-3717	186	4	[	[	PUNCT
iajs-3717	186	5	𝑑(𝑅𝑒𝜇	𝑑(𝑅𝑒𝜇	NUM
iajs-3717	186	6	)	)	PUNCT
iajs-3717	186	7	𝑑𝜏	𝑑𝜏	NOUN
iajs-3717	186	8	]	]	PUNCT
iajs-3717	186	9	𝜏=𝜏0	𝜏=𝜏0	PUNCT
iajs-3717	186	10	=	=	SYM
iajs-3717	186	11	𝑠𝑖𝑔𝑛	𝑠𝑖𝑔𝑛	NOUN
iajs-3717	187	1	[	[	X
iajs-3717	187	2	𝑅𝑒	𝑅𝑒	PROPN
iajs-3717	187	3	(	(	PUNCT
iajs-3717	187	4	𝑑𝜇	𝑑𝜇	ADP
iajs-3717	187	5	𝑑𝜏	𝑑𝜏	NOUN
iajs-3717	187	6	)	)	PUNCT
iajs-3717	187	7	−1	−1	NOUN
iajs-3717	187	8	]	]	X
iajs-3717	188	1	𝜇=𝑖𝜔0	𝜇=𝑖𝜔0	PROPN
iajs-3717	188	2	.	.	PUNCT
iajs-3717	189	1	(	(	PUNCT
iajs-3717	189	2	38	38	NUM
iajs-3717	189	3	)	)	PUNCT
iajs-3717	189	4	it	it	PRON
iajs-3717	189	5	is	be	AUX
iajs-3717	189	6	clear	clear	ADJ
iajs-3717	189	7	that	that	SCONJ
iajs-3717	189	8	:	:	PUNCT
iajs-3717	189	9	ihjpas	ihjpas	PROPN
iajs-3717	189	10	.	.	PUNCT
iajs-3717	190	1	2025,38(2	2025,38(2	PROPN
iajs-3717	190	2	)	)	PUNCT
iajs-3717	190	3	368	368	NUM
iajs-3717	191	1	[	[	PUNCT
iajs-3717	191	2	𝑑𝜇	𝑑𝜇	ADP
iajs-3717	191	3	𝑑𝜏	𝑑𝜏	NOUN
iajs-3717	191	4	]	]	PUNCT
iajs-3717	191	5	−1	−1	NOUN
iajs-3717	191	6	=	=	SYM
iajs-3717	191	7	(	(	PUNCT
iajs-3717	191	8	(	(	PUNCT
iajs-3717	191	9	𝒜2	𝒜2	PROPN
iajs-3717	191	10	−	−	PROPN
iajs-3717	191	11	3𝜔0	3𝜔0	NUM
iajs-3717	191	12	2	2	NUM
iajs-3717	191	13	)	)	PUNCT
iajs-3717	192	1	+	+	NUM
iajs-3717	192	2	2𝑖	2𝑖	NOUN
iajs-3717	192	3	𝒜1𝜔0	𝒜1𝜔0	ADJ
iajs-3717	192	4	)	)	PUNCT
iajs-3717	192	5	(	(	PUNCT
iajs-3717	192	6	cos𝜔0𝜏	cos𝜔0𝜏	PUNCT
iajs-3717	192	7	+	+	CCONJ
iajs-3717	192	8	𝑖	𝑖	SYM
iajs-3717	192	9	sin𝜔0𝜏	sin𝜔0𝜏	NOUN
iajs-3717	192	10	)	)	PUNCT
iajs-3717	192	11	−	−	PROPN
iajs-3717	192	12	𝒜5𝜔0	𝒜5𝜔0	NOUN
iajs-3717	192	13	2	2	NUM
iajs-3717	192	14	+	+	CCONJ
iajs-3717	192	15	𝑖𝜔0	𝑖𝜔0	PROPN
iajs-3717	192	16	(	(	PUNCT
iajs-3717	192	17	𝒜6	𝒜6	NOUN
iajs-3717	192	18	−	−	NOUN
iajs-3717	192	19	𝒜4𝜔0	𝒜4𝜔0	ADJ
iajs-3717	192	20	2	2	NUM
iajs-3717	192	21	)	)	PUNCT
iajs-3717	192	22	+	+	CCONJ
iajs-3717	192	23	𝒜5	𝒜5	ADJ
iajs-3717	192	24	+	+	CCONJ
iajs-3717	192	25	2𝑖	2𝑖	NOUN
iajs-3717	192	26	𝒜4𝜔0	𝒜4𝜔0	ADV
iajs-3717	192	27	−	−	ADP
iajs-3717	192	28	𝒜5𝜔0	𝒜5𝜔0	NOUN
iajs-3717	192	29	2	2	NUM
iajs-3717	192	30	+	+	CCONJ
iajs-3717	192	31	𝑖𝜔0	𝑖𝜔0	PROPN
iajs-3717	192	32	(	(	PUNCT
iajs-3717	192	33	𝒜6	𝒜6	NOUN
iajs-3717	192	34	−	−	NOUN
iajs-3717	192	35	𝒜4𝜔0	𝒜4𝜔0	ADJ
iajs-3717	192	36	2	2	NUM
iajs-3717	192	37	)	)	PUNCT
iajs-3717	192	38	−	−	PROPN
iajs-3717	193	1	𝜏0	𝜏0	PROPN
iajs-3717	193	2	𝑖𝜔0	𝑖𝜔0	PROPN
iajs-3717	193	3	hence	hence	ADV
iajs-3717	193	4	,	,	PUNCT
iajs-3717	193	5	we	we	PRON
iajs-3717	193	6	have	have	AUX
iajs-3717	193	7	𝑅𝑒	𝑅𝑒	VERB
iajs-3717	193	8	[	[	PUNCT
iajs-3717	193	9	𝑑𝜇	𝑑𝜇	ADP
iajs-3717	193	10	𝑑𝜏	𝑑𝜏	X
iajs-3717	193	11	]	]	PUNCT
iajs-3717	193	12	𝜏=𝜏0	𝜏=𝜏0	X
iajs-3717	193	13	−1	−1	NOUN
iajs-3717	193	14	=	=	PUNCT
iajs-3717	194	1	𝑅𝑒	𝑅𝑒	VERB
iajs-3717	194	2	(	(	PUNCT
iajs-3717	194	3	(	(	PUNCT
iajs-3717	194	4	𝒜2−3𝜔0	𝒜2−3𝜔0	PROPN
iajs-3717	194	5	2)+2𝑖	2)+2𝑖	PROPN
iajs-3717	194	6	𝒜1𝜔0	𝒜1𝜔0	ADJ
iajs-3717	194	7	)	)	PUNCT
iajs-3717	194	8	(	(	PUNCT
iajs-3717	194	9	cos𝜔0𝜏+𝑖	cos𝜔0𝜏+𝑖	NOUN
iajs-3717	194	10	sin𝜔0𝜏	sin𝜔0𝜏	ADJ
iajs-3717	194	11	)	)	PUNCT
iajs-3717	195	1	−	−	PROPN
iajs-3717	195	2	𝒜5𝜔0	𝒜5𝜔0	NOUN
iajs-3717	195	3	2+𝑖𝜔0	2+𝑖𝜔0	NUM
iajs-3717	195	4	(	(	PUNCT
iajs-3717	195	5	𝒜6−	𝒜6−	NOUN
iajs-3717	195	6	𝒜4𝜔0	𝒜4𝜔0	ADJ
iajs-3717	195	7	2	2	NUM
iajs-3717	195	8	)	)	PUNCT
iajs-3717	195	9	+	+	CCONJ
iajs-3717	196	1	𝑅𝑒	𝑅𝑒	VERB
iajs-3717	196	2	𝒜5	𝒜5	ADJ
iajs-3717	196	3	+	+	NOUN
iajs-3717	196	4	2𝑖	2𝑖	NOUN
iajs-3717	196	5	𝒜4𝜔0	𝒜4𝜔0	ADV
iajs-3717	196	6	−	−	ADP
iajs-3717	196	7	𝒜5𝜔0	𝒜5𝜔0	NOUN
iajs-3717	196	8	2+𝑖𝜔0	2+𝑖𝜔0	NUM
iajs-3717	196	9	(	(	PUNCT
iajs-3717	196	10	𝒜6−	𝒜6−	NOUN
iajs-3717	196	11	𝒜4𝜔0	𝒜4𝜔0	ADJ
iajs-3717	196	12	2	2	X
iajs-3717	196	13	)	)	PUNCT
iajs-3717	196	14	𝑅𝑒	𝑅𝑒	VERB
iajs-3717	196	15	[	[	PUNCT
iajs-3717	196	16	𝑑𝜇	𝑑𝜇	ADP
iajs-3717	196	17	𝑑𝜏	𝑑𝜏	X
iajs-3717	196	18	]	]	PUNCT
iajs-3717	196	19	𝜏=𝜏0	𝜏=𝜏0	PROPN
iajs-3717	196	20	−1	−1	NOUN
iajs-3717	196	21	=	=	SYM
iajs-3717	196	22	𝜔0	𝜔0	PROPN
iajs-3717	196	23	2[3𝜔0	2[3𝜔0	NUM
iajs-3717	196	24	4	4	NUM
iajs-3717	196	25	+	+	CCONJ
iajs-3717	196	26	(	(	PUNCT
iajs-3717	196	27	2𝒜1	2𝒜1	NUM
iajs-3717	196	28	2	2	NUM
iajs-3717	196	29	−	−	NUM
iajs-3717	196	30	4𝒜2	4𝒜2	NUM
iajs-3717	196	31	−	−	NOUN
iajs-3717	196	32	2𝒜4	2𝒜4	NUM
iajs-3717	196	33	2)𝜔0	2)𝜔0	NUM
iajs-3717	196	34	2	2	NUM
iajs-3717	196	35	+	+	CCONJ
iajs-3717	196	36	(	(	PUNCT
iajs-3717	196	37	𝒜2	𝒜2	PROPN
iajs-3717	196	38	2	2	NUM
iajs-3717	196	39	−	−	PROPN
iajs-3717	196	40	2𝒜1𝒜3	2𝒜1𝒜3	NOUN
iajs-3717	196	41	−𝒜5	−𝒜5	ADP
iajs-3717	196	42	2	2	NUM
iajs-3717	196	43	+	+	NUM
iajs-3717	196	44	2𝒜4𝒜6	2𝒜4𝒜6	NOUN
iajs-3717	196	45	)	)	PUNCT
iajs-3717	196	46	]	]	PUNCT
iajs-3717	196	47	(	(	PUNCT
iajs-3717	196	48	𝒜5𝜔0	𝒜5𝜔0	NOUN
iajs-3717	196	49	2)2	2)2	NUM
iajs-3717	196	50	+	+	CCONJ
iajs-3717	196	51	(	(	PUNCT
iajs-3717	196	52	𝒜6	𝒜6	NOUN
iajs-3717	196	53	−𝒜4𝜔0	−𝒜4𝜔0	ADJ
iajs-3717	196	54	2)2	2)2	NUM
iajs-3717	196	55	=	=	SYM
iajs-3717	196	56	𝑓′(𝜔0	𝑓′(𝜔0	NOUN
iajs-3717	196	57	2	2	NUM
iajs-3717	196	58	)	)	PUNCT
iajs-3717	196	59	(	(	PUNCT
iajs-3717	196	60	𝒜5𝜔0	𝒜5𝜔0	NOUN
iajs-3717	196	61	2)2	2)2	NUM
iajs-3717	196	62	+	+	CCONJ
iajs-3717	196	63	(	(	PUNCT
iajs-3717	196	64	𝒜6	𝒜6	NOUN
iajs-3717	196	65	−𝒜4𝜔0	−𝒜4𝜔0	NOUN
iajs-3717	196	66	2)2	2)2	NUM
iajs-3717	196	67	here	here	ADV
iajs-3717	196	68	𝑓′(𝜔0	𝑓′(𝜔0	PROPN
iajs-3717	196	69	2	2	NUM
iajs-3717	196	70	)	)	PUNCT
iajs-3717	196	71	=	=	SYM
iajs-3717	196	72	3(𝜔0	3(𝜔0	PROPN
iajs-3717	196	73	2)2	2)2	NUM
iajs-3717	197	1	+	+	CCONJ
iajs-3717	197	2	2𝒞1𝜔0	2𝒞1𝜔0	NUM
iajs-3717	197	3	2	2	NUM
iajs-3717	197	4	+	+	NUM
iajs-3717	197	5	𝒞2	𝒞2	PROPN
iajs-3717	197	6	≠	≠	NOUN
iajs-3717	197	7	0	0	NUM
iajs-3717	197	8	due	due	ADP
iajs-3717	197	9	to	to	ADP
iajs-3717	197	10	condition	condition	NOUN
iajs-3717	197	11	(	(	PUNCT
iajs-3717	197	12	35	35	NUM
iajs-3717	197	13	)	)	PUNCT
iajs-3717	197	14	.	.	PUNCT
iajs-3717	198	1	so	so	ADV
iajs-3717	198	2	,	,	PUNCT
iajs-3717	198	3	we	we	PRON
iajs-3717	198	4	have	have	VERB
iajs-3717	198	5	𝑆𝑖𝑔𝑛	𝑆𝑖𝑔𝑛	PROPN
iajs-3717	198	6	{	{	PUNCT
iajs-3717	198	7	𝑑	𝑑	PROPN
iajs-3717	198	8	𝑑𝜏	𝑑𝜏	PROPN
iajs-3717	198	9	(	(	PUNCT
iajs-3717	198	10	𝑅𝑒𝜇)|𝜏=𝜏0	𝑅𝑒𝜇)|𝜏=𝜏0	NOUN
iajs-3717	198	11	}	}	PUNCT
iajs-3717	198	12	=	=	SYM
iajs-3717	198	13	𝑆𝑖𝑔𝑛	𝑆𝑖𝑔𝑛	PROPN
iajs-3717	198	14	{	{	PUNCT
iajs-3717	198	15	𝑅𝑒	𝑅𝑒	PROPN
iajs-3717	198	16	(	(	PUNCT
iajs-3717	198	17	𝑑𝜇	𝑑𝜇	ADP
iajs-3717	198	18	𝑑𝜏	𝑑𝜏	PROPN
iajs-3717	198	19	)	)	PUNCT
iajs-3717	198	20	𝜏=𝜏0	𝜏=𝜏0	PROPN
iajs-3717	198	21	−1	−1	NOUN
iajs-3717	198	22	}	}	PUNCT
iajs-3717	198	23	=	=	PUNCT
iajs-3717	198	24	𝑆𝑖𝑔𝑛{𝑓′(𝜔0	𝑆𝑖𝑔𝑛{𝑓′(𝜔0	NUM
iajs-3717	198	25	2	2	NUM
iajs-3717	198	26	)	)	PUNCT
iajs-3717	198	27	}	}	PUNCT
iajs-3717	198	28	assuming	assume	VERB
iajs-3717	198	29	that	that	SCONJ
iajs-3717	198	30	𝑑	𝑑	PROPN
iajs-3717	198	31	𝑑𝜏	𝑑𝜏	PROPN
iajs-3717	198	32	(	(	PUNCT
iajs-3717	198	33	𝑅𝑒𝜇)|𝜏=𝜏0	𝑅𝑒𝜇)|𝜏=𝜏0	SYM
iajs-3717	198	34	<	<	X
iajs-3717	198	35	0	0	NUM
iajs-3717	198	36	,	,	PUNCT
iajs-3717	198	37	it	it	PRON
iajs-3717	198	38	is	be	AUX
iajs-3717	198	39	implies	imply	VERB
iajs-3717	198	40	that	that	SCONJ
iajs-3717	198	41	the	the	DET
iajs-3717	198	42	roots	root	NOUN
iajs-3717	198	43	of	of	ADP
iajs-3717	198	44	the	the	DET
iajs-3717	198	45	characteristic	characteristic	NOUN
iajs-3717	198	46	has	have	VERB
iajs-3717	198	47	roots	root	NOUN
iajs-3717	198	48	with	with	ADP
iajs-3717	198	49	positive	positive	ADJ
iajs-3717	198	50	real	real	ADJ
iajs-3717	198	51	parts	part	NOUN
iajs-3717	198	52	at	at	ADP
iajs-3717	198	53	𝜏	𝜏	NOUN
iajs-3717	198	54	=	=	SYM
iajs-3717	198	55	𝜏0	𝜏0	PROPN
iajs-3717	198	56	.	.	PUNCT
iajs-3717	199	1	this	this	PRON
iajs-3717	199	2	contradicts	contradict	VERB
iajs-3717	199	3	the	the	DET
iajs-3717	199	4	local	local	ADJ
iajs-3717	199	5	stability	stability	NOUN
iajs-3717	199	6	of	of	ADP
iajs-3717	199	7	the	the	DET
iajs-3717	199	8	positive	positive	ADJ
iajs-3717	199	9	equilibrium	equilibrium	NOUN
iajs-3717	199	10	point	point	NOUN
iajs-3717	199	11	.therefore	.therefore	ADV
iajs-3717	199	12	,	,	PUNCT
iajs-3717	199	13	we	we	PRON
iajs-3717	199	14	can	can	AUX
iajs-3717	199	15	deduce	deduce	VERB
iajs-3717	199	16	that	that	SCONJ
iajs-3717	199	17	[	[	PUNCT
iajs-3717	199	18	𝑑(𝑅𝑒𝜇	𝑑(𝑅𝑒𝜇	NUM
iajs-3717	199	19	)	)	PUNCT
iajs-3717	199	20	𝑑𝜏	𝑑𝜏	NOUN
iajs-3717	199	21	]	]	PUNCT
iajs-3717	199	22	𝜏=τ0	𝜏=τ0	X
iajs-3717	199	23	>	>	X
iajs-3717	199	24	0	0	PUNCT
iajs-3717	200	1	under	under	ADP
iajs-3717	200	2	condition	condition	NOUN
iajs-3717	200	3	(	(	PUNCT
iajs-3717	200	4	35).consequently	35).consequently	NUM
iajs-3717	200	5	,	,	PUNCT
iajs-3717	200	6	the	the	DET
iajs-3717	200	7	transversality	transversality	NOUN
iajs-3717	200	8	condition	condition	NOUN
iajs-3717	200	9	is	be	AUX
iajs-3717	200	10	satisfied	satisfied	ADJ
iajs-3717	200	11	,	,	PUNCT
iajs-3717	200	12	leading	lead	VERB
iajs-3717	200	13	to	to	ADP
iajs-3717	200	14	a	a	DET
iajs-3717	200	15	hopf	hopf	ADJ
iajs-3717	200	16	bifurcation	bifurcation	NOUN
iajs-3717	200	17	happens	happen	VERB
iajs-3717	200	18	at	at	ADP
iajs-3717	200	19	𝜏	𝜏	NOUN
iajs-3717	200	20	=	=	SYM
iajs-3717	200	21	𝜏0	𝜏0	PROPN
iajs-3717	200	22	,	,	PUNCT
iajs-3717	200	23	and	and	CCONJ
iajs-3717	200	24	𝜇	𝜇	X
iajs-3717	200	25	=	=	PROPN
iajs-3717	200	26	𝑖𝜔0	𝑖𝜔0	PROPN
iajs-3717	200	27	.	.	PROPN
iajs-3717	201	1	2.3	2.3	NUM
iajs-3717	201	2	.	.	PUNCT
iajs-3717	202	1	the	the	DET
iajs-3717	202	2	direction	direction	NOUN
iajs-3717	202	3	and	and	CCONJ
iajs-3717	202	4	stability	stability	NOUN
iajs-3717	202	5	of	of	ADP
iajs-3717	202	6	the	the	DET
iajs-3717	202	7	hopf	hopf	ADJ
iajs-3717	202	8	bifurcation	bifurcation	NOUN
iajs-3717	202	9	.	.	PUNCT
iajs-3717	203	1	in	in	ADP
iajs-3717	203	2	this	this	DET
iajs-3717	203	3	section	section	NOUN
iajs-3717	203	4	,	,	PUNCT
iajs-3717	203	5	we	we	PRON
iajs-3717	203	6	investigate	investigate	VERB
iajs-3717	203	7	the	the	DET
iajs-3717	203	8	orientation	orientation	NOUN
iajs-3717	203	9	of	of	ADP
iajs-3717	203	10	the	the	DET
iajs-3717	203	11	hopf	hopf	ADJ
iajs-3717	203	12	bifurcation	bifurcation	NOUN
iajs-3717	203	13	near	near	ADP
iajs-3717	203	14	𝐹3	𝐹3	PROPN
iajs-3717	203	15	at	at	ADP
iajs-3717	203	16	𝜏	𝜏	PROPN
iajs-3717	203	17	=	=	SYM
iajs-3717	203	18	𝜏0and	𝜏0and	PRON
iajs-3717	203	19	establish	establish	VERB
iajs-3717	203	20	the	the	DET
iajs-3717	203	21	prerequisites	prerequisite	NOUN
iajs-3717	203	22	for	for	ADP
iajs-3717	203	23	the	the	DET
iajs-3717	203	24	stability	stability	NOUN
iajs-3717	203	25	of	of	ADP
iajs-3717	203	26	the	the	DET
iajs-3717	203	27	resulting	result	VERB
iajs-3717	203	28	periodic	periodic	ADJ
iajs-3717	203	29	solution	solution	NOUN
iajs-3717	203	30	in	in	ADP
iajs-3717	203	31	the	the	DET
iajs-3717	203	32	system	system	NOUN
iajs-3717	203	33	(	(	PUNCT
iajs-3717	203	34	2	2	NUM
iajs-3717	203	35	)	)	PUNCT
iajs-3717	203	36	.	.	PUNCT
iajs-3717	204	1	we	we	PRON
iajs-3717	204	2	accomplish	accomplish	VERB
iajs-3717	204	3	this	this	PRON
iajs-3717	204	4	by	by	ADP
iajs-3717	204	5	applying	apply	VERB
iajs-3717	204	6	hassard	hassard	NOUN
iajs-3717	204	7	's	's	PART
iajs-3717	204	8	center	center	NOUN
iajs-3717	204	9	manifold	manifold	ADJ
iajs-3717	204	10	theorem	theorem	NOUN
iajs-3717	204	11	and	and	CCONJ
iajs-3717	204	12	normal	normal	ADJ
iajs-3717	204	13	form	form	NOUN
iajs-3717	204	14	theory	theory	NOUN
iajs-3717	204	15	)	)	PUNCT
iajs-3717	204	16	30	30	NUM
iajs-3717	204	17	(	(	PUNCT
iajs-3717	204	18	.	.	PUNCT
iajs-3717	205	1	theorem	theorem	NOUN
iajs-3717	205	2	3	3	NUM
iajs-3717	205	3	.	.	PUNCT
iajs-3717	205	4	)	)	PUNCT
iajs-3717	206	1	i	i	PRON
iajs-3717	206	2	)	)	PUNCT
iajs-3717	206	3	if	if	SCONJ
iajs-3717	206	4	ℳ2	ℳ2	PROPN
iajs-3717	206	5	>	>	X
iajs-3717	206	6	0	0	NUM
iajs-3717	206	7	,	,	PUNCT
iajs-3717	206	8	then	then	ADV
iajs-3717	206	9	the	the	DET
iajs-3717	206	10	hopf	hopf	ADJ
iajs-3717	206	11	bifurcation	bifurcation	NOUN
iajs-3717	206	12	is	be	AUX
iajs-3717	206	13	supercritical	supercritical	ADJ
iajs-3717	206	14	and	and	CCONJ
iajs-3717	206	15	the	the	DET
iajs-3717	206	16	bifurcating	bifurcate	VERB
iajs-3717	206	17	periodic	periodic	ADJ
iajs-3717	206	18	solutions	solution	NOUN
iajs-3717	206	19	exist	exist	VERB
iajs-3717	206	20	for	for	ADP
iajs-3717	206	21	𝜏	𝜏	X
iajs-3717	206	22	>	>	X
iajs-3717	206	23	𝜏0	𝜏0	PROPN
iajs-3717	206	24	,	,	PUNCT
iajs-3717	206	25	and	and	CCONJ
iajs-3717	206	26	if	if	SCONJ
iajs-3717	206	27	ℳ2	ℳ2	PROPN
iajs-3717	206	28	<	<	X
iajs-3717	206	29	0	0	PROPN
iajs-3717	206	30	,	,	PUNCT
iajs-3717	206	31	then	then	ADV
iajs-3717	206	32	the	the	DET
iajs-3717	206	33	hopf	hopf	ADJ
iajs-3717	206	34	bifurcation	bifurcation	NOUN
iajs-3717	206	35	is	be	AUX
iajs-3717	206	36	subcritical	subcritical	ADJ
iajs-3717	206	37	and	and	CCONJ
iajs-3717	206	38	the	the	DET
iajs-3717	206	39	bifurcating	bifurcate	VERB
iajs-3717	206	40	periodic	periodic	ADJ
iajs-3717	206	41	solutions	solution	NOUN
iajs-3717	206	42	exist	exist	VERB
iajs-3717	206	43	for	for	ADP
iajs-3717	206	44	𝜏	𝜏	X
iajs-3717	206	45	<	<	X
iajs-3717	206	46	𝜏0	𝜏0	PROPN
iajs-3717	206	47	.	.	PUNCT
iajs-3717	207	1	(	(	PUNCT
iajs-3717	207	2	ii	ii	NOUN
iajs-3717	207	3	)	)	PUNCT
iajs-3717	207	4	if	if	SCONJ
iajs-3717	207	5	𝒰2	𝒰2	PROPN
iajs-3717	207	6	<	<	X
iajs-3717	207	7	0	0	PROPN
iajs-3717	207	8	,	,	PUNCT
iajs-3717	207	9	then	then	ADV
iajs-3717	207	10	the	the	DET
iajs-3717	207	11	bifurcating	bifurcate	VERB
iajs-3717	207	12	periodic	periodic	ADJ
iajs-3717	207	13	solution	solution	NOUN
iajs-3717	207	14	are	be	AUX
iajs-3717	207	15	stable	stable	ADJ
iajs-3717	207	16	,	,	PUNCT
iajs-3717	207	17	and	and	CCONJ
iajs-3717	207	18	if	if	SCONJ
iajs-3717	207	19	𝒰2	𝒰2	PROPN
iajs-3717	207	20	>	>	X
iajs-3717	207	21	0	0	PROPN
iajs-3717	207	22	,	,	PUNCT
iajs-3717	207	23	then	then	ADV
iajs-3717	207	24	the	the	DET
iajs-3717	207	25	bifurcating	bifurcate	VERB
iajs-3717	207	26	periodic	periodic	ADJ
iajs-3717	207	27	solution	solution	NOUN
iajs-3717	207	28	are	be	AUX
iajs-3717	207	29	unstable	unstable	ADJ
iajs-3717	207	30	(	(	PUNCT
iajs-3717	207	31	iii	iii	NOUN
iajs-3717	207	32	)	)	PUNCT
iajs-3717	207	33	if	if	SCONJ
iajs-3717	207	34	𝒯2	𝒯2	PROPN
iajs-3717	207	35	>	>	X
iajs-3717	207	36	0	0	PROPN
iajs-3717	207	37	,	,	PUNCT
iajs-3717	207	38	the	the	DET
iajs-3717	207	39	period	period	NOUN
iajs-3717	207	40	of	of	ADP
iajs-3717	207	41	the	the	DET
iajs-3717	207	42	bifurcating	bifurcate	VERB
iajs-3717	207	43	cyclic	cyclic	ADJ
iajs-3717	207	44	solutions	solution	NOUN
iajs-3717	207	45	increases	increase	NOUN
iajs-3717	207	46	,	,	PUNCT
iajs-3717	207	47	and	and	CCONJ
iajs-3717	207	48	if	if	SCONJ
iajs-3717	207	49	𝒯2	𝒯2	PRON
iajs-3717	207	50	<	<	X
iajs-3717	207	51	0	0	PROPN
iajs-3717	207	52	,	,	PUNCT
iajs-3717	207	53	the	the	DET
iajs-3717	207	54	period	period	NOUN
iajs-3717	207	55	decreases	decrease	VERB
iajs-3717	207	56	.	.	PUNCT
iajs-3717	208	1	where	where	SCONJ
iajs-3717	208	2	ℳ2	ℳ2	PROPN
iajs-3717	208	3	,	,	PUNCT
iajs-3717	208	4	𝒰2and	𝒰2and	PROPN
iajs-3717	208	5	𝒯2	𝒯2	PROPN
iajs-3717	208	6	are	be	AUX
iajs-3717	208	7	given	give	VERB
iajs-3717	208	8	𝐶1(0	𝐶1(0	PRON
iajs-3717	208	9	)	)	PUNCT
iajs-3717	208	10	=	=	SYM
iajs-3717	208	11	𝑖	𝑖	SYM
iajs-3717	208	12	2𝜔0𝜏0	2𝜔0𝜏0	NUM
iajs-3717	208	13	(	(	PUNCT
iajs-3717	208	14	𝒢11	𝒢11	PROPN
iajs-3717	208	15	𝒢20	𝒢20	PRON
iajs-3717	208	16	−	−	PUNCT
iajs-3717	208	17	2|𝒢11|	2|𝒢11|	NOUN
iajs-3717	208	18	2	2	NUM
iajs-3717	208	19	−	−	PROPN
iajs-3717	208	20	|𝒢02|	|𝒢02|	PROPN
iajs-3717	208	21	2	2	NUM
iajs-3717	208	22	3	3	NUM
iajs-3717	208	23	)	)	PUNCT
iajs-3717	209	1	+	+	CCONJ
iajs-3717	209	2	𝒢21	𝒢21	NOUN
iajs-3717	209	3	2	2	NUM
iajs-3717	209	4	,	,	PUNCT
iajs-3717	209	5	ℳ2	ℳ2	PROPN
iajs-3717	209	6	=	=	SYM
iajs-3717	209	7	−	−	PROPN
iajs-3717	209	8	𝑅𝑒{𝐶1(0	𝑅𝑒{𝐶1(0	PROPN
iajs-3717	209	9	)	)	PUNCT
iajs-3717	209	10	}	}	PUNCT
iajs-3717	210	1	𝑅𝑒	𝑅𝑒	VERB
iajs-3717	210	2	{	{	PUNCT
iajs-3717	210	3	𝑑𝜇	𝑑𝜇	ADP
iajs-3717	210	4	𝑑𝜏	𝑑𝜏	PROPN
iajs-3717	210	5	(	(	PUNCT
iajs-3717	210	6	𝜏0	𝜏0	PROPN
iajs-3717	210	7	)	)	PUNCT
iajs-3717	210	8	}	}	PUNCT
iajs-3717	210	9	,	,	PUNCT
iajs-3717	210	10	𝒰2	𝒰2	NOUN
iajs-3717	210	11	=	=	PROPN
iajs-3717	210	12	2𝑅𝑒{𝐶1(0	2𝑅𝑒{𝐶1(0	NUM
iajs-3717	210	13	)	)	PUNCT
iajs-3717	210	14	}	}	PUNCT
iajs-3717	210	15	,	,	PUNCT
iajs-3717	210	16	𝒯2	𝒯2	PROPN
iajs-3717	210	17	=	=	PUNCT
iajs-3717	211	1	−𝐼𝑚{𝐶1(0)}+ℳ2	−𝐼𝑚{𝐶1(0)}+ℳ2	X
iajs-3717	211	2	𝐼𝑚	𝐼𝑚	NOUN
iajs-3717	211	3	{	{	PUNCT
iajs-3717	211	4	𝑑𝜇	𝑑𝜇	ADP
iajs-3717	211	5	𝑑𝜏	𝑑𝜏	PROPN
iajs-3717	211	6	(	(	PUNCT
iajs-3717	211	7	𝜏0	𝜏0	PROPN
iajs-3717	211	8	)	)	PUNCT
iajs-3717	211	9	}	}	PUNCT
iajs-3717	211	10	𝜔0𝜏0	𝜔0𝜏0	PUNCT
iajs-3717	211	11	.	.	PUNCT
iajs-3717	211	12	}	}	PUNCT
iajs-3717	211	13	(	(	PUNCT
iajs-3717	211	14	39	39	NUM
iajs-3717	211	15	)	)	PUNCT
iajs-3717	211	16	and	and	CCONJ
iajs-3717	211	17	𝒢11	𝒢11	PROPN
iajs-3717	211	18	,	,	PUNCT
iajs-3717	211	19	𝒢20	𝒢20	PROPN
iajs-3717	211	20	,	,	PUNCT
iajs-3717	211	21	𝒢02	𝒢02	PROPN
iajs-3717	211	22	and	and	CCONJ
iajs-3717	211	23	𝒢21	𝒢21	PROPN
iajs-3717	211	24	are	be	AUX
iajs-3717	211	25	given	give	VERB
iajs-3717	211	26	in	in	ADP
iajs-3717	211	27	the	the	DET
iajs-3717	211	28	proof	proof	ADJ
iajs-3717	211	29	proof	proof	NOUN
iajs-3717	211	30	.	.	PUNCT
iajs-3717	212	1	let	let	VERB
iajs-3717	212	2	𝔘1(𝑡	𝔘1(𝑡	PRON
iajs-3717	212	3	)	)	PUNCT
iajs-3717	212	4	=	=	PUNCT
iajs-3717	212	5	𝑆(𝑡	𝑆(𝑡	VERB
iajs-3717	212	6	)	)	PUNCT
iajs-3717	212	7	−	−	PROPN
iajs-3717	212	8	𝑆	𝑆	PROPN
iajs-3717	212	9	∗	∗	NOUN
iajs-3717	212	10	,	,	PUNCT
iajs-3717	212	11	𝔘2(𝑡	𝔘2(𝑡	NOUN
iajs-3717	212	12	)	)	PUNCT
iajs-3717	212	13	=	=	SYM
iajs-3717	213	1	𝐼(𝑡	𝐼(𝑡	PROPN
iajs-3717	213	2	)	)	PUNCT
iajs-3717	213	3	−	−	PROPN
iajs-3717	213	4	𝐼∗	𝐼∗	PROPN
iajs-3717	213	5	,	,	PUNCT
iajs-3717	213	6	𝔘3(𝑡	𝔘3(𝑡	PROPN
iajs-3717	213	7	)	)	PUNCT
iajs-3717	214	1	=	=	SYM
iajs-3717	215	1	𝑍(𝑡	𝑍(𝑡	NOUN
iajs-3717	215	2	)	)	PUNCT
iajs-3717	215	3	−	−	PRON
iajs-3717	215	4	𝑍	𝑍	NOUN
iajs-3717	215	5	∗	∗	NOUN
iajs-3717	215	6	,	,	PUNCT
iajs-3717	215	7	and	and	CCONJ
iajs-3717	215	8	𝜏	𝜏	X
iajs-3717	215	9	=	=	SYM
iajs-3717	215	10	𝜏0	𝜏0	PROPN
iajs-3717	215	11	+	+	CCONJ
iajs-3717	215	12	𝒮	𝒮	PROPN
iajs-3717	215	13	,	,	PUNCT
iajs-3717	215	14	here	here	ADV
iajs-3717	215	15	𝜏0	𝜏0	PROPN
iajs-3717	215	16	is	be	AUX
iajs-3717	215	17	define	define	VERB
iajs-3717	215	18	by	by	ADP
iajs-3717	215	19	equation	equation	NOUN
iajs-3717	215	20	(	(	PUNCT
iajs-3717	215	21	34	34	NUM
iajs-3717	215	22	)	)	PUNCT
iajs-3717	215	23	and	and	CCONJ
iajs-3717	215	24	𝒮	𝒮	PROPN
iajs-3717	215	25	∈	∈	PROPN
iajs-3717	215	26	𝑅	𝑅	PROPN
iajs-3717	215	27	.	.	PUNCT
iajs-3717	216	1	it	it	PRON
iajs-3717	216	2	is	be	AUX
iajs-3717	216	3	possible	possible	ADJ
iajs-3717	216	4	to	to	PART
iajs-3717	216	5	convert	convert	VERB
iajs-3717	216	6	system	system	NOUN
iajs-3717	216	7	(	(	PUNCT
iajs-3717	216	8	2	2	NUM
iajs-3717	216	9	)	)	PUNCT
iajs-3717	216	10	into	into	ADP
iajs-3717	216	11	a	a	DET
iajs-3717	216	12	functional	functional	ADJ
iajs-3717	216	13	differential	differential	NOUN
iajs-3717	216	14	equation	equation	NOUN
iajs-3717	216	15	in	in	ADP
iajs-3717	216	16	𝐶	𝐶	PROPN
iajs-3717	216	17	=	=	PUNCT
iajs-3717	216	18	𝐶([−1,0],𝑅3	𝐶([−1,0],𝑅3	PROPN
iajs-3717	216	19	)	)	PUNCT
iajs-3717	216	20	then	then	ADV
iajs-3717	216	21	𝔘′(𝑡	𝔘′(𝑡	X
iajs-3717	216	22	)	)	PUNCT
iajs-3717	216	23	=	=	SYM
iajs-3717	216	24	𝐿𝒮(𝔘𝑡	𝐿𝒮(𝔘𝑡	PROPN
iajs-3717	216	25	)	)	PUNCT
iajs-3717	217	1	+	+	CCONJ
iajs-3717	217	2	ℱ(𝒮	ℱ(𝒮	ADV
iajs-3717	217	3	,	,	PUNCT
iajs-3717	217	4	𝔘𝑡	𝔘𝑡	PROPN
iajs-3717	217	5	)	)	PUNCT
iajs-3717	217	6	,	,	PUNCT
iajs-3717	217	7	(	(	PUNCT
iajs-3717	217	8	40	40	NUM
iajs-3717	217	9	)	)	PUNCT
iajs-3717	217	10	ihjpas	ihjpa	NOUN
iajs-3717	217	11	.	.	PUNCT
iajs-3717	218	1	2025,38(2	2025,38(2	PROPN
iajs-3717	218	2	)	)	PUNCT
iajs-3717	218	3	369	369	NUM
iajs-3717	218	4	where	where	SCONJ
iajs-3717	218	5	𝔘(𝑡	𝔘(𝑡	ADP
iajs-3717	218	6	)	)	PUNCT
iajs-3717	218	7	=	=	SYM
iajs-3717	218	8	(	(	PUNCT
iajs-3717	218	9	𝔘1(𝑡	𝔘1(𝑡	PROPN
iajs-3717	218	10	)	)	PUNCT
iajs-3717	218	11	,	,	PUNCT
iajs-3717	218	12	𝔘2(𝑡	𝔘2(𝑡	PROPN
iajs-3717	218	13	)	)	PUNCT
iajs-3717	218	14	,	,	PUNCT
iajs-3717	218	15	𝔘3(𝑡	𝔘3(𝑡	PROPN
iajs-3717	218	16	)	)	PUNCT
iajs-3717	218	17	)	)	PUNCT
iajs-3717	218	18	𝑇	𝑇	PROPN
iajs-3717	218	19	∈	∈	PROPN
iajs-3717	218	20	𝐶	𝐶	PROPN
iajs-3717	218	21	=	=	PUNCT
iajs-3717	218	22	𝐶([−1,0	𝐶([−1,0	NOUN
iajs-3717	218	23	]	]	X
iajs-3717	218	24	,	,	PUNCT
iajs-3717	218	25	𝑅3	𝑅3	PROPN
iajs-3717	218	26	)	)	PUNCT
iajs-3717	218	27	and	and	CCONJ
iajs-3717	218	28	𝐿𝒮	𝐿𝒮	PROPN
iajs-3717	218	29	:	:	PUNCT
iajs-3717	218	30	𝐶	𝐶	PROPN
iajs-3717	218	31	→	→	SYM
iajs-3717	218	32	𝑅3	𝑅3	PROPN
iajs-3717	218	33	,	,	PUNCT
iajs-3717	218	34	ℱ:𝑅	ℱ:𝑅	PROPN
iajs-3717	218	35	×	×	PROPN
iajs-3717	218	36	𝐶	𝐶	PROPN
iajs-3717	218	37	→	→	SYM
iajs-3717	218	38	𝑅3	𝑅3	PROPN
iajs-3717	218	39	are	be	AUX
iajs-3717	218	40	given	give	VERB
iajs-3717	218	41	by	by	ADP
iajs-3717	218	42	:	:	PUNCT
iajs-3717	218	43	𝐿𝒮(γ	𝐿𝒮(γ	ADJ
iajs-3717	218	44	)	)	PUNCT
iajs-3717	219	1	=	=	SYM
iajs-3717	219	2	(	(	PUNCT
iajs-3717	219	3	𝒮	𝒮	PROPN
iajs-3717	219	4	+	+	SYM
iajs-3717	219	5	𝜏0)[𝔇1γ(0	𝜏0)[𝔇1γ(0	PROPN
iajs-3717	219	6	)	)	PUNCT
iajs-3717	219	7	+	+	NUM
iajs-3717	219	8	𝔇2γ(−1	𝔇2γ(−1	NOUN
iajs-3717	219	9	)	)	PUNCT
iajs-3717	219	10	]	]	PUNCT
iajs-3717	219	11	(	(	PUNCT
iajs-3717	219	12	41	41	NUM
iajs-3717	219	13	)	)	PUNCT
iajs-3717	219	14	the	the	DET
iajs-3717	219	15	nonlinear	nonlinear	NOUN
iajs-3717	219	16	is	be	AUX
iajs-3717	219	17	ℱ(𝒮	ℱ(𝒮	ADJ
iajs-3717	219	18	,	,	PUNCT
iajs-3717	219	19	γ	γ	NOUN
iajs-3717	219	20	)	)	PUNCT
iajs-3717	219	21	=	=	SYM
iajs-3717	219	22	(	(	PUNCT
iajs-3717	219	23	𝒮	𝒮	PROPN
iajs-3717	219	24	+	+	NUM
iajs-3717	219	25	𝜏0	𝜏0	PROPN
iajs-3717	219	26	)	)	PUNCT
iajs-3717	219	27	(	(	PUNCT
iajs-3717	219	28	ℋ1	ℋ1	NOUN
iajs-3717	219	29	ℋ2	ℋ2	PROPN
iajs-3717	219	30	ℋ3	ℋ3	NOUN
iajs-3717	219	31	)	)	PUNCT
iajs-3717	220	1	where	where	SCONJ
iajs-3717	220	2	𝔇1	𝔇1	NOUN
iajs-3717	220	3	=	=	PRON
iajs-3717	221	1	[	[	PUNCT
iajs-3717	221	2	ℱ10	ℱ10	PROPN
iajs-3717	221	3	(	(	PUNCT
iajs-3717	221	4	1	1	NUM
iajs-3717	221	5	)	)	PUNCT
iajs-3717	221	6	ℱ01	ℱ01	PROPN
iajs-3717	222	1	(	(	PUNCT
iajs-3717	222	2	1	1	NUM
iajs-3717	222	3	)	)	PUNCT
iajs-3717	222	4	0	0	NUM
iajs-3717	222	5	ℱ1000	ℱ1000	X
iajs-3717	222	6	(	(	PUNCT
iajs-3717	222	7	2	2	NUM
iajs-3717	222	8	)	)	PUNCT
iajs-3717	222	9	ℱ0100	ℱ0100	X
iajs-3717	222	10	(	(	PUNCT
iajs-3717	222	11	2	2	NUM
iajs-3717	222	12	)	)	PUNCT
iajs-3717	222	13	0	0	NUM
iajs-3717	222	14	0	0	NUM
iajs-3717	222	15	0	0	NUM
iajs-3717	222	16	ℱ100	ℱ100	X
iajs-3717	222	17	(	(	PUNCT
iajs-3717	222	18	3	3	NUM
iajs-3717	222	19	)	)	PUNCT
iajs-3717	222	20	]	]	PUNCT
iajs-3717	223	1	=	=	PUNCT
iajs-3717	223	2	[	[	PUNCT
iajs-3717	223	3	𝑟	𝑟	X
iajs-3717	223	4	−	−	PROPN
iajs-3717	223	5	𝑅1	𝑅1	PROPN
iajs-3717	223	6	−𝑅2𝑆∗	−𝑅2𝑆∗	PUNCT
iajs-3717	223	7	0	0	NUM
iajs-3717	224	1	𝐶𝐼∗	𝐶𝐼∗	PROPN
iajs-3717	224	2	𝑅5	𝑅5	NOUN
iajs-3717	224	3	0	0	NUM
iajs-3717	224	4	0	0	NUM
iajs-3717	224	5	0	0	NUM
iajs-3717	224	6	−𝑅6	−𝑅6	PROPN
iajs-3717	224	7	]	]	PUNCT
iajs-3717	224	8	,	,	PUNCT
iajs-3717	224	9	𝔇2	𝔇2	NOUN
iajs-3717	224	10	=	=	PUNCT
iajs-3717	224	11	[	[	PUNCT
iajs-3717	224	12	0	0	NUM
iajs-3717	224	13	0	0	NUM
iajs-3717	224	14	0	0	NUM
iajs-3717	224	15	ℱ0010	ℱ0010	NOUN
iajs-3717	224	16	(	(	PUNCT
iajs-3717	224	17	2	2	NUM
iajs-3717	224	18	)	)	PUNCT
iajs-3717	224	19	0	0	NUM
iajs-3717	224	20	ℱ0001	ℱ0001	PROPN
iajs-3717	224	21	(	(	PUNCT
iajs-3717	224	22	2	2	NUM
iajs-3717	224	23	)	)	PUNCT
iajs-3717	224	24	ℱ010	ℱ010	NOUN
iajs-3717	224	25	(	(	PUNCT
iajs-3717	224	26	3	3	NUM
iajs-3717	224	27	)	)	PUNCT
iajs-3717	224	28	0	0	NUM
iajs-3717	225	1	ℱ001	ℱ001	NUM
iajs-3717	225	2	(	(	PUNCT
iajs-3717	225	3	3	3	NUM
iajs-3717	225	4	)	)	PUNCT
iajs-3717	225	5	]	]	PUNCT
iajs-3717	226	1	=	=	PUNCT
iajs-3717	226	2	[	[	PUNCT
iajs-3717	226	3	0	0	NUM
iajs-3717	226	4	0	0	NUM
iajs-3717	226	5	0	0	NUM
iajs-3717	226	6	−𝛼𝑅3	−𝛼𝑅3	NOUN
iajs-3717	226	7	0	0	NUM
iajs-3717	227	1	−	−	NOUN
iajs-3717	227	2	𝛼𝑅4	𝛼𝑅4	PROPN
iajs-3717	228	1	ℎ𝑅3	ℎ𝑅3	PROPN
iajs-3717	228	2	0	0	NUM
iajs-3717	228	3	ℎ𝑅4	ℎ𝑅4	PROPN
iajs-3717	228	4	]	]	PUNCT
iajs-3717	228	5	,	,	PUNCT
iajs-3717	228	6	with	with	ADP
iajs-3717	228	7	𝑅1	𝑅1	PROPN
iajs-3717	228	8	,	,	PUNCT
iajs-3717	228	9	𝑅2	𝑅2	ADP
iajs-3717	228	10	,	,	PUNCT
iajs-3717	228	11	𝑅3	𝑅3	PROPN
iajs-3717	228	12	and	and	CCONJ
iajs-3717	228	13	𝑅4	𝑅4	PRON
iajs-3717	228	14	are	be	AUX
iajs-3717	228	15	define	define	NOUN
iajs-3717	228	16	in	in	ADP
iajs-3717	228	17	the	the	DET
iajs-3717	228	18	𝐽𝐹3	𝐽𝐹3	PROPN
iajs-3717	228	19	,	,	PUNCT
iajs-3717	228	20	while	while	SCONJ
iajs-3717	228	21	ℋ1	ℋ1	PROPN
iajs-3717	228	22	=	=	PUNCT
iajs-3717	228	23	∑	∑	PROPN
iajs-3717	228	24	1	1	NUM
iajs-3717	228	25	𝑖!𝑗!𝑖+𝑗≥2	𝑖!𝑗!𝑖+𝑗≥2	NOUN
iajs-3717	229	1	ℱ𝑖𝑗	ℱ𝑖𝑗	PROPN
iajs-3717	229	2	(	(	PUNCT
iajs-3717	229	3	1)γ1	1)γ1	NUM
iajs-3717	229	4	𝑖(0)γ2	𝑖(0)γ2	NOUN
iajs-3717	229	5	𝑗(0	𝑗(0	NOUN
iajs-3717	229	6	)	)	PUNCT
iajs-3717	229	7	,	,	PUNCT
iajs-3717	229	8	ℋ2	ℋ2	PROPN
iajs-3717	229	9	=	=	SYM
iajs-3717	229	10	∑	∑	PROPN
iajs-3717	229	11	1	1	NUM
iajs-3717	229	12	𝑖	𝑖	NOUN
iajs-3717	229	13	!	!	PUNCT
iajs-3717	230	1	𝑗!𝑚	𝑗!𝑚	PROPN
iajs-3717	230	2	!	!	PUNCT
iajs-3717	231	1	𝑛	𝑛	PROPN
iajs-3717	231	2	!	!	PUNCT
iajs-3717	232	1	𝑖+𝑗+𝑚+𝑛≥2	𝑖+𝑗+𝑚+𝑛≥2	NUM
iajs-3717	232	2	ℱ𝑖𝑗𝑚𝑛	ℱ𝑖𝑗𝑚𝑛	PROPN
iajs-3717	232	3	(	(	PUNCT
iajs-3717	232	4	2	2	NUM
iajs-3717	232	5	)	)	PUNCT
iajs-3717	232	6	γ1	γ1	NOUN
iajs-3717	232	7	𝑖(0)γ2	𝑖(0)γ2	NOUN
iajs-3717	232	8	𝑗(0)γ̃1	𝑗(0)γ̃1	PROPN
iajs-3717	232	9	𝑚(−1)γ̃2	𝑚(−1)γ̃2	PUNCT
iajs-3717	232	10	𝑛(−1	𝑛(−1	PROPN
iajs-3717	232	11	)	)	PUNCT
iajs-3717	232	12	,	,	PUNCT
iajs-3717	232	13	ℋ3	ℋ3	X
iajs-3717	232	14	=	=	PUNCT
iajs-3717	232	15	∑	∑	PROPN
iajs-3717	232	16	1	1	NUM
iajs-3717	232	17	𝑘!𝑚	𝑘!𝑚	PROPN
iajs-3717	232	18	!	!	PUNCT
iajs-3717	233	1	𝑛	𝑛	ADP
iajs-3717	233	2	!	!	NOUN
iajs-3717	233	3	𝑘+𝑚+𝑛≥2	𝑘+𝑚+𝑛≥2	ADJ
iajs-3717	234	1	ℱ𝑘𝑚𝑛	ℱ𝑘𝑚𝑛	PROPN
iajs-3717	234	2	(	(	PUNCT
iajs-3717	234	3	3	3	X
iajs-3717	234	4	)	)	PUNCT
iajs-3717	234	5	γ3	γ3	NOUN
iajs-3717	234	6	𝑘(0)γ̃1	𝑘(0)γ̃1	PROPN
iajs-3717	234	7	𝑚(−1)γ̃2	𝑚(−1)γ̃2	PUNCT
iajs-3717	234	8	𝑛(−1	𝑛(−1	PROPN
iajs-3717	234	9	)	)	PUNCT
iajs-3717	234	10	,	,	PUNCT
iajs-3717	234	11	where	where	SCONJ
iajs-3717	234	12	,	,	PUNCT
iajs-3717	234	13	γ(𝜐0	γ(𝜐0	X
iajs-3717	234	14	)	)	PUNCT
iajs-3717	234	15	=	=	PRON
iajs-3717	234	16	(	(	PUNCT
iajs-3717	234	17	γ1(𝜐0	γ1(𝜐0	NOUN
iajs-3717	234	18	)	)	PUNCT
iajs-3717	234	19	,	,	PUNCT
iajs-3717	234	20	γ2(𝜐0	γ2(𝜐0	ADP
iajs-3717	234	21	)	)	PUNCT
iajs-3717	234	22	,	,	PUNCT
iajs-3717	234	23	γ3(𝜐0	γ3(𝜐0	NUM
iajs-3717	234	24	)	)	PUNCT
iajs-3717	234	25	)	)	PUNCT
iajs-3717	235	1	∈	∈	PROPN
iajs-3717	235	2	𝐶,−1	𝐶,−1	VERB
iajs-3717	235	3	≤	≤	NUM
iajs-3717	235	4	𝜐0	𝜐0	NOUN
iajs-3717	235	5	≤	≤	NOUN
iajs-3717	235	6	0	0	NUM
iajs-3717	235	7	,	,	PUNCT
iajs-3717	235	8	and	and	CCONJ
iajs-3717	235	9	ℱ𝑖𝑗	ℱ𝑖𝑗	PROPN
iajs-3717	235	10	(	(	PUNCT
iajs-3717	235	11	1)𝛤1	1)𝛤1	NUM
iajs-3717	235	12	𝑖(0)𝛤2	𝑖(0)𝛤2	ADJ
iajs-3717	235	13	𝑗(0	𝑗(0	NOUN
iajs-3717	235	14	)	)	PUNCT
iajs-3717	235	15	,	,	PUNCT
iajs-3717	235	16	=	=	PUNCT
iajs-3717	235	17	𝜕𝑖+𝑗ℱ(1	𝜕𝑖+𝑗ℱ(1	NOUN
iajs-3717	235	18	)	)	PUNCT
iajs-3717	235	19	𝜕𝛤1	𝜕𝛤1	PROPN
iajs-3717	235	20	𝑖𝛤2	𝑖𝛤2	PUNCT
iajs-3717	235	21	𝑗	𝑗	INTJ
iajs-3717	235	22	|	|	ADV
iajs-3717	235	23	(	(	PUNCT
iajs-3717	235	24	𝛤1,𝛤2)=(0,0	𝛤1,𝛤2)=(0,0	NOUN
iajs-3717	235	25	)	)	PUNCT
iajs-3717	235	26	,	,	PUNCT
iajs-3717	235	27	ℱijmn	ℱijmn	PROPN
iajs-3717	235	28	(	(	PUNCT
iajs-3717	235	29	2	2	NUM
iajs-3717	235	30	)	)	PUNCT
iajs-3717	235	31	γ1	γ1	NOUN
iajs-3717	235	32	i(0)γ2	i(0)γ2	NOUN
iajs-3717	235	33	j(0)γ̃1	j(0)γ̃1	PROPN
iajs-3717	235	34	m(−1)γ̃2	m(−1)γ̃2	NOUN
iajs-3717	235	35	n(−1	n(−1	PROPN
iajs-3717	235	36	)	)	PUNCT
iajs-3717	235	37	=	=	SYM
iajs-3717	235	38	∂i+j+m+nℱ(2	∂i+j+m+nℱ(2	PROPN
iajs-3717	235	39	)	)	PUNCT
iajs-3717	235	40	∂γ1	∂γ1	PROPN
iajs-3717	236	1	i	i	PRON
iajs-3717	236	2	γ2	γ2	VERB
iajs-3717	236	3	j	j	PROPN
iajs-3717	236	4	γ̃1	γ̃1	PROPN
iajs-3717	236	5	mγ̃2	mγ̃2	NOUN
iajs-3717	236	6	n	n	CCONJ
iajs-3717	237	1	|	|	ADV
iajs-3717	237	2	(	(	PUNCT
iajs-3717	237	3	γ1,γ2,γ̃1,γ̃2)=(0,0,−1,−1	γ1,γ2,γ̃1,γ̃2)=(0,0,−1,−1	NOUN
iajs-3717	237	4	)	)	PUNCT
iajs-3717	237	5	,	,	PUNCT
iajs-3717	237	6	ℱ𝑘𝑚𝑛	ℱ𝑘𝑚𝑛	PROPN
iajs-3717	237	7	(	(	PUNCT
iajs-3717	237	8	3	3	NUM
iajs-3717	237	9	)	)	PUNCT
iajs-3717	237	10	γ3	γ3	NOUN
iajs-3717	237	11	𝑘(0)γ̃1	𝑘(0)γ̃1	PROPN
iajs-3717	237	12	𝑚(−1)γ̃2	𝑚(−1)γ̃2	PUNCT
iajs-3717	237	13	𝑛(−1	𝑛(−1	PROPN
iajs-3717	237	14	)	)	PUNCT
iajs-3717	237	15	=	=	SYM
iajs-3717	237	16	𝜕𝑘+𝑚+𝑛ℱ(3	𝜕𝑘+𝑚+𝑛ℱ(3	NOUN
iajs-3717	237	17	)	)	PUNCT
iajs-3717	237	18	𝜕γ3	𝜕γ3	VERB
iajs-3717	237	19	𝑘γ̃1	𝑘γ̃1	NOUN
iajs-3717	237	20	𝑚γ̃2	𝑚γ̃2	NOUN
iajs-3717	238	1	𝑛	𝑛	VERB
iajs-3717	238	2	|	|	ADV
iajs-3717	238	3	(	(	PUNCT
iajs-3717	238	4	γ3,γ̃1,γ̃2)=(0,−1,−1	γ3,γ̃1,γ̃2)=(0,−1,−1	PROPN
iajs-3717	238	5	)	)	PUNCT
iajs-3717	238	6	.	.	PUNCT
iajs-3717	239	1	based	base	VERB
iajs-3717	239	2	on	on	ADP
iajs-3717	239	3	the	the	DET
iajs-3717	239	4	riesz	riesz	PROPN
iajs-3717	239	5	representation	representation	NOUN
iajs-3717	239	6	theorem	theorem	NOUN
iajs-3717	239	7	,	,	PUNCT
iajs-3717	239	8	a	a	DET
iajs-3717	239	9	3×3	3×3	NUM
iajs-3717	239	10	matrix	matrix	NOUN
iajs-3717	239	11	function	function	NOUN
iajs-3717	239	12	ℳ0	ℳ0	NOUN
iajs-3717	239	13	(	(	PUNCT
iajs-3717	239	14	𝜐0	𝜐0	NOUN
iajs-3717	239	15	,	,	PUNCT
iajs-3717	239	16	𝒮	𝒮	PROPN
iajs-3717	239	17	)	)	PUNCT
iajs-3717	239	18	exists	exist	VERB
iajs-3717	239	19	for	for	ADP
iajs-3717	239	20	−1	−1	NOUN
iajs-3717	239	21	≤	≤	NUM
iajs-3717	239	22	𝜐0	𝜐0	NOUN
iajs-3717	239	23	≤	≤	NOUN
iajs-3717	239	24	0	0	NUM
iajs-3717	239	25	such	such	ADJ
iajs-3717	239	26	that	that	PRON
iajs-3717	239	27	.	.	PUNCT
iajs-3717	240	1	𝐿𝒮(γ	𝐿𝒮(γ	PROPN
iajs-3717	240	2	)	)	PUNCT
iajs-3717	241	1	=	=	SYM
iajs-3717	241	2	∫	∫	PROPN
iajs-3717	241	3	𝑑	𝑑	PROPN
iajs-3717	241	4	0	0	NUM
iajs-3717	241	5	−1	−1	NOUN
iajs-3717	241	6	ℳ0(𝜐0,𝒮)γ(𝜐0	ℳ0(𝜐0,𝒮)γ(𝜐0	PROPN
iajs-3717	241	7	)	)	PUNCT
iajs-3717	241	8	𝑓𝑜𝑟	𝑓𝑜𝑟	ADV
iajs-3717	241	9	γ𝜖𝐶.	γ𝜖𝐶.	PROPN
iajs-3717	241	10	(	(	PUNCT
iajs-3717	241	11	42	42	NUM
iajs-3717	241	12	)	)	PUNCT
iajs-3717	241	13	in	in	ADP
iajs-3717	241	14	actuality	actuality	NOUN
iajs-3717	241	15	,	,	PUNCT
iajs-3717	241	16	it	it	PRON
iajs-3717	241	17	can	can	AUX
iajs-3717	241	18	be	be	AUX
iajs-3717	241	19	chosen	choose	VERB
iajs-3717	241	20	.	.	PUNCT
iajs-3717	242	1	ℳ0(𝜐0,𝒮	ℳ0(𝜐0,𝒮	PROPN
iajs-3717	242	2	)	)	PUNCT
iajs-3717	242	3	=	=	PUNCT
iajs-3717	242	4	(	(	PUNCT
iajs-3717	242	5	𝜏0	𝜏0	PROPN
iajs-3717	242	6	+	+	CCONJ
iajs-3717	242	7	𝒮	𝒮	PROPN
iajs-3717	242	8	)	)	PUNCT
iajs-3717	242	9	(	(	PUNCT
iajs-3717	242	10	𝔇1𝜎(𝜐0)−𝔇2𝜎(𝜐0	𝔇1𝜎(𝜐0)−𝔇2𝜎(𝜐0	ADP
iajs-3717	242	11	+	+	NUM
iajs-3717	242	12	1	1	NUM
iajs-3717	242	13	)	)	PUNCT
iajs-3717	242	14	)	)	PUNCT
iajs-3717	243	1	,	,	PUNCT
iajs-3717	243	2	(	(	PUNCT
iajs-3717	243	3	43	43	NUM
iajs-3717	243	4	)	)	PUNCT
iajs-3717	243	5	here	here	ADV
iajs-3717	243	6	,	,	PUNCT
iajs-3717	243	7	𝜎	𝜎	PROPN
iajs-3717	243	8	is	be	AUX
iajs-3717	243	9	called	call	VERB
iajs-3717	243	10	the	the	DET
iajs-3717	243	11	dirac	dirac	NOUN
iajs-3717	243	12	delta	delta	NOUN
iajs-3717	243	13	function	function	NOUN
iajs-3717	243	14	and	and	CCONJ
iajs-3717	243	15	𝜎(𝜐0	𝜎(𝜐0	NUM
iajs-3717	243	16	)	)	PUNCT
iajs-3717	243	17	=	=	PRON
iajs-3717	243	18	{	{	PUNCT
iajs-3717	243	19	1	1	NUM
iajs-3717	243	20	𝜐0	𝜐0	NOUN
iajs-3717	243	21	=	=	NOUN
iajs-3717	243	22	0	0	SYM
iajs-3717	243	23	0	0	NUM
iajs-3717	243	24	𝜐0	𝜐0	NOUN
iajs-3717	243	25	≠	≠	PROPN
iajs-3717	243	26	0	0	NUM
iajs-3717	243	27	.	.	PUNCT
iajs-3717	244	1	for	for	ADP
iajs-3717	244	2	γ	γ	PROPN
iajs-3717	244	3	∈	∈	PROPN
iajs-3717	244	4	𝐶([−1,0	𝐶([−1,0	NOUN
iajs-3717	244	5	]	]	X
iajs-3717	244	6	,	,	PUNCT
iajs-3717	244	7	𝑅3	𝑅3	PROPN
iajs-3717	244	8	)	)	PUNCT
iajs-3717	244	9	,	,	PUNCT
iajs-3717	244	10	define	define	VERB
iajs-3717	244	11	𝒜(𝒮)γ(𝜐0	𝒜(𝒮)γ(𝜐0	NOUN
iajs-3717	244	12	)	)	PUNCT
iajs-3717	244	13	=	=	PRON
iajs-3717	244	14	{	{	PUNCT
iajs-3717	244	15	𝑑γ(𝜐0	𝑑γ(𝜐0	ADJ
iajs-3717	244	16	)	)	PUNCT
iajs-3717	244	17	𝑑𝜐0	𝑑𝜐0	NOUN
iajs-3717	244	18	,	,	PUNCT
iajs-3717	244	19	−1	−1	NOUN
iajs-3717	244	20	≤	≤	NOUN
iajs-3717	244	21	𝜐0	𝜐0	NOUN
iajs-3717	244	22	<	<	X
iajs-3717	244	23	0	0	NUM
iajs-3717	244	24	,	,	PUNCT
iajs-3717	244	25	∫	∫	PROPN
iajs-3717	244	26	𝑑	𝑑	PROPN
iajs-3717	244	27	0	0	NUM
iajs-3717	244	28	−1	−1	NOUN
iajs-3717	244	29	𝜂	𝜂	NOUN
iajs-3717	244	30	0	0	PUNCT
iajs-3717	244	31	(	(	PUNCT
iajs-3717	244	32	ℌ0,𝜎0)𝜑0(ℌ0	ℌ0,𝜎0)𝜑0(ℌ0	PROPN
iajs-3717	244	33	)	)	PUNCT
iajs-3717	244	34	,	,	PUNCT
iajs-3717	244	35	𝜐0	𝜐0	NOUN
iajs-3717	244	36	=	=	SYM
iajs-3717	244	37	0	0	NUM
iajs-3717	244	38	,	,	PUNCT
iajs-3717	244	39	(	(	PUNCT
iajs-3717	244	40	44	44	NUM
iajs-3717	244	41	)	)	PUNCT
iajs-3717	244	42	and	and	CCONJ
iajs-3717	244	43	ihjpas	ihjpa	NOUN
iajs-3717	244	44	.	.	PUNCT
iajs-3717	245	1	2025,38(2	2025,38(2	PROPN
iajs-3717	245	2	)	)	PUNCT
iajs-3717	245	3	370	370	NUM
iajs-3717	245	4	ℛ(𝒮)γ(𝜐0	ℛ(𝒮)γ(𝜐0	NOUN
iajs-3717	245	5	)	)	PUNCT
iajs-3717	245	6	=	=	PRON
iajs-3717	245	7	{	{	PUNCT
iajs-3717	245	8	0	0	NUM
iajs-3717	245	9	,	,	PUNCT
iajs-3717	245	10	−1	−1	NOUN
iajs-3717	245	11	≤	≤	NOUN
iajs-3717	245	12	𝜐0	𝜐0	NOUN
iajs-3717	245	13	<	<	X
iajs-3717	245	14	0	0	NUM
iajs-3717	245	15	,	,	PUNCT
iajs-3717	245	16	ℱ(𝒮	ℱ(𝒮	CCONJ
iajs-3717	245	17	,	,	PUNCT
iajs-3717	245	18	γ	γ	NOUN
iajs-3717	245	19	)	)	PUNCT
iajs-3717	245	20	,	,	PUNCT
iajs-3717	245	21	𝜐0	𝜐0	NOUN
iajs-3717	245	22	=	=	NOUN
iajs-3717	245	23	0	0	NUM
iajs-3717	245	24	.	.	PUNCT
iajs-3717	246	1	(	(	PUNCT
iajs-3717	246	2	45	45	NUM
iajs-3717	246	3	)	)	PUNCT
iajs-3717	246	4	hence	hence	ADV
iajs-3717	246	5	,	,	PUNCT
iajs-3717	246	6	the	the	DET
iajs-3717	246	7	system	system	NOUN
iajs-3717	246	8	(	(	PUNCT
iajs-3717	246	9	39	39	NUM
iajs-3717	246	10	)	)	PUNCT
iajs-3717	246	11	is	be	AUX
iajs-3717	246	12	equivalent	equivalent	ADJ
iajs-3717	246	13	𝔘′(𝑡	𝔘′(𝑡	PROPN
iajs-3717	246	14	)	)	PUNCT
iajs-3717	246	15	=	=	SYM
iajs-3717	247	1	𝒜(𝒮)𝔘𝑡	𝒜(𝒮)𝔘𝑡	PROPN
iajs-3717	247	2	+	+	CCONJ
iajs-3717	247	3	ℛ(𝒮)𝔘𝑡	ℛ(𝒮)𝔘𝑡	PROPN
iajs-3717	247	4	.	.	PUNCT
iajs-3717	248	1	(	(	PUNCT
iajs-3717	248	2	46	46	NUM
iajs-3717	248	3	)	)	PUNCT
iajs-3717	249	1	where	where	SCONJ
iajs-3717	249	2	,	,	PUNCT
iajs-3717	249	3	𝔘𝑡	𝔘𝑡	PROPN
iajs-3717	249	4	=	=	SYM
iajs-3717	249	5	𝔘(t	𝔘(t	PROPN
iajs-3717	250	1	+	+	CCONJ
iajs-3717	250	2	𝜐0),−1	𝜐0),−1	PROPN
iajs-3717	250	3	≤	≤	NOUN
iajs-3717	250	4	𝜐0	𝜐0	NOUN
iajs-3717	250	5	≤	≤	NOUN
iajs-3717	250	6	0	0	NUM
iajs-3717	250	7	.	.	PUNCT
iajs-3717	251	1	for	for	ADP
iajs-3717	251	2	𝛹0	𝛹0	PROPN
iajs-3717	251	3	∈	∈	PROPN
iajs-3717	251	4	𝐶1([−1,0	𝐶1([−1,0	NOUN
iajs-3717	251	5	]	]	X
iajs-3717	251	6	,	,	PUNCT
iajs-3717	251	7	𝑅3	𝑅3	PROPN
iajs-3717	251	8	)	)	PUNCT
iajs-3717	251	9	,	,	PUNCT
iajs-3717	251	10	the	the	DET
iajs-3717	251	11	adjoint	adjoint	NOUN
iajs-3717	251	12	operator	operator	NOUN
iajs-3717	251	13	𝒜∗of	𝒜∗of	PROPN
iajs-3717	251	14	𝒜(0	𝒜(0	PUNCT
iajs-3717	251	15	)	)	PUNCT
iajs-3717	251	16	is	be	AUX
iajs-3717	251	17	𝒜∗	𝒜∗	PROPN
iajs-3717	251	18	𝛹0(ℌ0	𝛹0(ℌ0	NOUN
iajs-3717	251	19	)	)	PUNCT
iajs-3717	251	20	=	=	PRON
iajs-3717	251	21	{	{	PUNCT
iajs-3717	251	22	−	−	PROPN
iajs-3717	251	23	𝑑𝛹0(ℌ0	𝑑𝛹0(ℌ0	NOUN
iajs-3717	251	24	)	)	PUNCT
iajs-3717	251	25	𝑑ℌ0	𝑑ℌ0	NOUN
iajs-3717	251	26	,	,	PUNCT
iajs-3717	251	27	0	0	PUNCT
iajs-3717	251	28	<	<	X
iajs-3717	251	29	ℌ0	ℌ0	PROPN
iajs-3717	251	30	≤	≤	ADV
iajs-3717	251	31	1	1	NUM
iajs-3717	251	32	,	,	PUNCT
iajs-3717	251	33	∫	∫	PROPN
iajs-3717	251	34	𝑑	𝑑	PROPN
iajs-3717	251	35	0	0	NUM
iajs-3717	251	36	−1	−1	NOUN
iajs-3717	251	37	γ𝑇(ℰ0	γ𝑇(ℰ0	NOUN
iajs-3717	251	38	,	,	PUNCT
iajs-3717	251	39	0)𝛹0(−ℰ0	0)𝛹0(−ℰ0	NOUN
iajs-3717	251	40	)	)	PUNCT
iajs-3717	251	41	,	,	PUNCT
iajs-3717	251	42	ℌ0	ℌ0	PROPN
iajs-3717	251	43	=	=	SYM
iajs-3717	251	44	0	0	PROPN
iajs-3717	251	45	.	.	PUNCT
iajs-3717	252	1	(	(	PUNCT
iajs-3717	252	2	47	47	NUM
iajs-3717	252	3	)	)	PUNCT
iajs-3717	252	4	for	for	ADP
iajs-3717	252	5	γ	γ	PROPN
iajs-3717	252	6	∈	∈	PROPN
iajs-3717	252	7	𝐶([−1,0	𝐶([−1,0	NOUN
iajs-3717	252	8	]	]	X
iajs-3717	252	9	,	,	PUNCT
iajs-3717	252	10	𝑅3	𝑅3	PROPN
iajs-3717	252	11	)	)	PUNCT
iajs-3717	252	12	,	,	PUNCT
iajs-3717	252	13	and	and	CCONJ
iajs-3717	252	14	𝛹0	𝛹0	PROPN
iajs-3717	252	15	∈	∈	PROPN
iajs-3717	252	16	(	(	PUNCT
iajs-3717	252	17	𝐶1[−1,0	𝐶1[−1,0	PROPN
iajs-3717	252	18	]	]	PUNCT
iajs-3717	252	19	,	,	PUNCT
iajs-3717	252	20	(	(	PUNCT
iajs-3717	252	21	𝑅3)∗	𝑅3)∗	NOUN
iajs-3717	252	22	)	)	PUNCT
iajs-3717	252	23	.	.	PUNCT
iajs-3717	253	1	we	we	PRON
iajs-3717	253	2	define	define	VERB
iajs-3717	253	3	the	the	DET
iajs-3717	253	4	bilinear	bilinear	NOUN
iajs-3717	253	5	inner	inner	ADJ
iajs-3717	253	6	product	product	NOUN
iajs-3717	253	7	〈	〈	PROPN
iajs-3717	253	8	𝛹0(ℌ0	𝛹0(ℌ0	PROPN
iajs-3717	253	9	)	)	PUNCT
iajs-3717	253	10	,	,	PUNCT
iajs-3717	253	11	γ(𝜐0	γ(𝜐0	X
iajs-3717	253	12	)	)	PUNCT
iajs-3717	253	13	〉	〉	NOUN
iajs-3717	253	14	=	=	SYM
iajs-3717	253	15	𝛹0(0)γ(0	𝛹0(0)γ(0	PROPN
iajs-3717	253	16	)	)	PUNCT
iajs-3717	253	17	−	−	NOUN
iajs-3717	253	18	∫	∫	PROPN
iajs-3717	253	19	∫	∫	PROPN
iajs-3717	253	20	𝛹0	𝛹0	PROPN
iajs-3717	253	21	𝑇	𝑇	PROPN
iajs-3717	253	22	(	(	PUNCT
iajs-3717	253	23	𝜍0	𝜍0	NOUN
iajs-3717	253	24	−	−	NOUN
iajs-3717	253	25	𝜐0	𝜐0	NOUN
iajs-3717	253	26	)	)	PUNCT
iajs-3717	253	27	𝑑ℳ0(𝜐0)γ(𝜍0)𝑑𝜍0	𝑑ℳ0(𝜐0)γ(𝜍0)𝑑𝜍0	NOUN
iajs-3717	253	28	,	,	PUNCT
iajs-3717	253	29	𝜐0	𝜐0	NOUN
iajs-3717	253	30	𝜍0=0	𝜍0=0	NOUN
iajs-3717	253	31	0	0	NUM
iajs-3717	254	1	𝜐0=−1	𝜐0=−1	NOUN
iajs-3717	254	2	(	(	PUNCT
iajs-3717	254	3	48	48	NUM
iajs-3717	254	4	)	)	PUNCT
iajs-3717	254	5	given	give	VERB
iajs-3717	254	6	ℳ0(𝜐0	ℳ0(𝜐0	PROPN
iajs-3717	254	7	)	)	PUNCT
iajs-3717	254	8	=	=	PUNCT
iajs-3717	254	9	ℳ0(𝜐0	ℳ0(𝜐0	PROPN
iajs-3717	254	10	,	,	PUNCT
iajs-3717	254	11	0	0	NUM
iajs-3717	254	12	.	.	NUM
iajs-3717	254	13	,	,	PUNCT
iajs-3717	254	14	it	it	PRON
iajs-3717	254	15	follows	follow	VERB
iajs-3717	254	16	that	that	SCONJ
iajs-3717	254	17	𝒜	𝒜	NOUN
iajs-3717	254	18	=	=	SYM
iajs-3717	254	19	𝒜	𝒜	NOUN
iajs-3717	254	20	(	(	PUNCT
iajs-3717	254	21	0	0	NUM
iajs-3717	254	22	)	)	PUNCT
iajs-3717	254	23	and	and	CCONJ
iajs-3717	254	24	𝒜∗	𝒜∗	NUM
iajs-3717	254	25	are	be	AUX
iajs-3717	254	26	adjoint	adjoint	NOUN
iajs-3717	254	27	operators	operator	NOUN
iajs-3717	254	28	.	.	PUNCT
iajs-3717	255	1	referring	refer	VERB
iajs-3717	255	2	to	to	ADP
iajs-3717	255	3	the	the	DET
iajs-3717	255	4	previous	previous	ADJ
iajs-3717	255	5	theorem	theorem	NOUN
iajs-3717	255	6	2	2	NUM
iajs-3717	255	7	,	,	PUNCT
iajs-3717	255	8	we	we	PRON
iajs-3717	255	9	can	can	AUX
iajs-3717	255	10	deduce	deduce	VERB
iajs-3717	255	11	that	that	SCONJ
iajs-3717	255	12	±𝑖	±𝑖	NOUN
iajs-3717	255	13	𝜔0	𝜔0	NOUN
iajs-3717	255	14	are	be	AUX
iajs-3717	255	15	eigenvalues	eigenvalue	NOUN
iajs-3717	255	16	of	of	ADP
iajs-3717	255	17	𝒜	𝒜	NOUN
iajs-3717	255	18	(	(	PUNCT
iajs-3717	255	19	0	0	NUM
iajs-3717	255	20	)	)	PUNCT
iajs-3717	255	21	and	and	CCONJ
iajs-3717	255	22	𝒜∗	𝒜∗	NUM
iajs-3717	255	23	,	,	PUNCT
iajs-3717	255	24	respectively	respectively	ADV
iajs-3717	255	25	.	.	PUNCT
iajs-3717	256	1	by	by	ADP
iajs-3717	256	2	performing	perform	VERB
iajs-3717	256	3	a	a	DET
iajs-3717	256	4	straightforward	straightforward	ADJ
iajs-3717	256	5	calculation	calculation	NOUN
iajs-3717	256	6	,	,	PUNCT
iajs-3717	256	7	it	it	PRON
iajs-3717	256	8	becomes	become	VERB
iajs-3717	256	9	evident	evident	ADJ
iajs-3717	256	10	that	that	SCONJ
iajs-3717	256	11	.	.	PUNCT
iajs-3717	257	1	𝑝(𝜐0	𝑝(𝜐0	X
iajs-3717	257	2	)	)	PUNCT
iajs-3717	257	3	=	=	PUNCT
iajs-3717	258	1	(	(	PUNCT
iajs-3717	258	2	1	1	NUM
iajs-3717	258	3	,	,	PUNCT
iajs-3717	258	4	𝑝1	𝑝1	NOUN
iajs-3717	258	5	,	,	PUNCT
iajs-3717	258	6	𝑝2	𝑝2	NOUN
iajs-3717	258	7	)	)	PUNCT
iajs-3717	258	8	𝑇	𝑇	PROPN
iajs-3717	258	9	𝑒𝑖𝑤0𝜏0𝜐0	𝑒𝑖𝑤0𝜏0𝜐0	PROPN
iajs-3717	258	10	𝑝∗(ℌ0	𝑝∗(ℌ0	PROPN
iajs-3717	258	11	)	)	PUNCT
iajs-3717	258	12	=	=	SYM
iajs-3717	258	13	𝐷0(1	𝐷0(1	NOUN
iajs-3717	258	14	,	,	PUNCT
iajs-3717	258	15	𝑝1	𝑝1	NOUN
iajs-3717	258	16	∗	∗	NOUN
iajs-3717	258	17	,	,	PUNCT
iajs-3717	258	18	𝑝2	𝑝2	NOUN
iajs-3717	258	19	∗)𝑇	∗)𝑇	NOUN
iajs-3717	258	20	𝑒−𝑖𝑤0𝜏0ℌ0	𝑒−𝑖𝑤0𝜏0ℌ0	NOUN
iajs-3717	258	21	here	here	ADV
iajs-3717	258	22	𝑝1	𝑝1	NOUN
iajs-3717	258	23	=	=	SYM
iajs-3717	258	24	𝑖𝑤0−ℱ10	𝑖𝑤0−ℱ10	PROPN
iajs-3717	258	25	(	(	PUNCT
iajs-3717	258	26	1	1	X
iajs-3717	258	27	)	)	PUNCT
iajs-3717	258	28	ℱ01	ℱ01	PROPN
iajs-3717	258	29	(	(	PUNCT
iajs-3717	258	30	1	1	NUM
iajs-3717	258	31	)	)	PUNCT
iajs-3717	258	32	,	,	PUNCT
iajs-3717	258	33	𝑝2	𝑝2	NOUN
iajs-3717	258	34	=	=	SYM
iajs-3717	258	35	−	−	PROPN
iajs-3717	258	36	ℱ1000	ℱ1000	NOUN
iajs-3717	258	37	(	(	PUNCT
iajs-3717	258	38	2	2	NUM
iajs-3717	258	39	)	)	PUNCT
iajs-3717	259	1	+	+	NOUN
iajs-3717	259	2	ℱ0010	ℱ0010	NOUN
iajs-3717	259	3	(	(	PUNCT
iajs-3717	259	4	2	2	NUM
iajs-3717	259	5	)	)	PUNCT
iajs-3717	259	6	𝑒−𝑖𝑤0𝜏0+(ℱ0100	𝑒−𝑖𝑤0𝜏0+(ℱ0100	PROPN
iajs-3717	259	7	(	(	PUNCT
iajs-3717	259	8	2	2	NUM
iajs-3717	259	9	)	)	PUNCT
iajs-3717	259	10	−𝑖𝑤0)𝑝1	−𝑖𝑤0)𝑝1	PROPN
iajs-3717	259	11	𝑓0001	𝑓0001	ADJ
iajs-3717	259	12	(	(	PUNCT
iajs-3717	259	13	2	2	NUM
iajs-3717	259	14	)	)	PUNCT
iajs-3717	259	15	𝑒𝑖𝑤0𝜏0	𝑒𝑖𝑤0𝜏0	NOUN
iajs-3717	259	16	,	,	PUNCT
iajs-3717	259	17	𝑝1	𝑝1	NOUN
iajs-3717	259	18	∗	∗	NOUN
iajs-3717	259	19	=	=	PUNCT
iajs-3717	260	1	−	−	PROPN
iajs-3717	260	2	ℱ10	ℱ10	PROPN
iajs-3717	260	3	(	(	PUNCT
iajs-3717	260	4	1	1	NUM
iajs-3717	260	5	)	)	PUNCT
iajs-3717	260	6	ℱ0100	ℱ0100	X
iajs-3717	260	7	(	(	PUNCT
iajs-3717	260	8	2	2	NUM
iajs-3717	260	9	)	)	PUNCT
iajs-3717	260	10	+	+	PUNCT
iajs-3717	260	11	+	+	ADJ
iajs-3717	260	12	𝑖𝑤0	𝑖𝑤0	ADJ
iajs-3717	260	13	,	,	PUNCT
iajs-3717	260	14	𝑝1	𝑝1	NOUN
iajs-3717	260	15	∗	∗	NOUN
iajs-3717	260	16	=	=	PUNCT
iajs-3717	260	17	−	−	PROPN
iajs-3717	260	18	ℱ10	ℱ10	PROPN
iajs-3717	260	19	(	(	PUNCT
iajs-3717	260	20	2	2	NUM
iajs-3717	260	21	)	)	PUNCT
iajs-3717	260	22	+	+	NOUN
iajs-3717	260	23	𝑖𝑤0+(ℱ1000	𝑖𝑤0+(ℱ1000	NUM
iajs-3717	260	24	(	(	PUNCT
iajs-3717	260	25	2	2	NUM
iajs-3717	260	26	)	)	PUNCT
iajs-3717	260	27	+	+	NOUN
iajs-3717	260	28	ℱ0010	ℱ0010	NOUN
iajs-3717	260	29	(	(	PUNCT
iajs-3717	260	30	2	2	X
iajs-3717	260	31	)	)	PUNCT
iajs-3717	260	32	𝑒−𝑖𝜏0𝑤0)𝑝1	𝑒−𝑖𝜏0𝑤0)𝑝1	PROPN
iajs-3717	260	33	∗	∗	VERB
iajs-3717	260	34	ℱ010	ℱ010	PROPN
iajs-3717	260	35	(	(	PUNCT
iajs-3717	260	36	2	2	NUM
iajs-3717	260	37	)	)	PUNCT
iajs-3717	260	38	𝑒−𝑖𝑤0𝜏0	𝑒−𝑖𝑤0𝜏0	PRON
iajs-3717	260	39	.	.	PUNCT
iajs-3717	261	1	from	from	ADP
iajs-3717	261	2	equation	equation	NOUN
iajs-3717	261	3	(	(	PUNCT
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iajs-3717	261	10	⟨𝑝∗(ℌ0	⟨𝑝∗(ℌ0	PROPN
iajs-3717	261	11	)	)	PUNCT
iajs-3717	261	12	,	,	PUNCT
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iajs-3717	262	5	1	1	NUM
iajs-3717	262	6	+	+	NUM
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iajs-3717	262	8	̅	̅	NOUN
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iajs-3717	262	10	1	1	NUM
iajs-3717	262	11	∗𝑝1	∗𝑝1	PROPN
iajs-3717	262	12	+	+	NUM
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iajs-3717	262	14	̅	̅	NOUN
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iajs-3717	262	25	(	(	PUNCT
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iajs-3717	262	36	)	)	PUNCT
iajs-3717	263	1	+	+	NOUN
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iajs-3717	263	3	̅	̅	NOUN
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iajs-3717	263	8	(	(	PUNCT
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iajs-3717	263	13	+	+	NOUN
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iajs-3717	263	16	3	3	NUM
iajs-3717	263	17	)	)	PUNCT
iajs-3717	263	18	𝑝2	𝑝2	NOUN
iajs-3717	263	19	)	)	PUNCT
iajs-3717	263	20	]	]	PUNCT
iajs-3717	263	21	.	.	PUNCT
iajs-3717	264	1	(	(	PUNCT
iajs-3717	264	2	49	49	X
iajs-3717	264	3	)	)	PUNCT
iajs-3717	264	4	let	let	VERB
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iajs-3717	265	3	+	+	NUM
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iajs-3717	265	6	�	�	PROPN
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iajs-3717	265	16	2	2	NUM
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iajs-3717	265	19	𝑒	𝑒	PROPN
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iajs-3717	266	1	[	[	X
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iajs-3717	266	12	2	2	NUM
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iajs-3717	266	14	�	�	NOUN
iajs-3717	266	15	̅	̅	NOUN
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iajs-3717	266	17	2)+	2)+	NUM
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iajs-3717	266	20	(	(	PUNCT
iajs-3717	266	21	ℱ010	ℱ010	PROPN
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iajs-3717	267	6	�	�	NOUN
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iajs-3717	267	9	2	2	NUM
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iajs-3717	267	12	]	]	X
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iajs-3717	267	21	conjugate	conjugate	ADJ
iajs-3717	267	22	complex	complex	ADJ
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iajs-3717	267	25	𝐷0	𝐷0	PROPN
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iajs-3717	267	30	,	,	PUNCT
iajs-3717	267	31	𝑝⟩	𝑝⟩	PUNCT
iajs-3717	267	32	=	=	NOUN
iajs-3717	267	33	1	1	NUM
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iajs-3717	267	36	,	,	PUNCT
iajs-3717	267	37	�	�	NOUN
iajs-3717	267	38	̅	̅	NOUN
iajs-3717	267	39	�	�	NOUN
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iajs-3717	268	13	,	,	PUNCT
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iajs-3717	268	18	hopf	hopf	ADJ
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iajs-3717	268	21	properties	property	NOUN
iajs-3717	268	22	:	:	PUNCT
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iajs-3717	269	6	+	+	CCONJ
iajs-3717	269	7	ℏ5	ℏ5	PROPN
iajs-3717	269	8	�	�	NOUN
iajs-3717	269	9	̅	̅	NOUN
iajs-3717	269	10	�	�	NOUN
iajs-3717	269	11	1	1	NUM
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iajs-3717	269	13	+	+	CCONJ
iajs-3717	269	14	ℏ9	ℏ9	PROPN
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iajs-3717	270	6	+	+	SYM
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iajs-3717	270	11	1	1	NUM
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iajs-3717	271	6	+	+	CCONJ
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iajs-3717	271	8	�	�	NOUN
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iajs-3717	273	5	1	1	X
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iajs-3717	273	9	+	+	CCONJ
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iajs-3717	273	13	1	1	NUM
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iajs-3717	274	1	+	+	NUM
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iajs-3717	275	5	1	1	X
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iajs-3717	275	9	�	�	NOUN
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iajs-3717	275	11	+	+	NOUN
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iajs-3717	275	29	(	(	PUNCT
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iajs-3717	275	32	+	+	CCONJ
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iajs-3717	275	41	1	1	NUM
iajs-3717	275	42	)	)	PUNCT
iajs-3717	275	43	(	(	PUNCT
iajs-3717	275	44	0	0	NUM
iajs-3717	275	45	)	)	PUNCT
iajs-3717	275	46	+	+	CCONJ
iajs-3717	275	47	1	1	NUM
iajs-3717	275	48	2	2	NUM
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iajs-3717	275	50	(	(	PUNCT
iajs-3717	275	51	2	2	NUM
iajs-3717	275	52	)	)	PUNCT
iajs-3717	275	53	(	(	PUNCT
iajs-3717	275	54	0	0	NUM
iajs-3717	275	55	)	)	PUNCT
iajs-3717	275	56	+	+	CCONJ
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iajs-3717	275	59	2	2	NUM
iajs-3717	275	60	)	)	PUNCT
iajs-3717	275	61	(	(	PUNCT
iajs-3717	275	62	0	0	NUM
iajs-3717	275	63	)	)	PUNCT
iajs-3717	275	64	)	)	PUNCT
iajs-3717	276	1	+	+	VERB
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iajs-3717	276	4	1	1	NUM
iajs-3717	276	5	)	)	PUNCT
iajs-3717	276	6	(	(	PUNCT
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iajs-3717	276	9	1	1	NUM
iajs-3717	276	10	)	)	PUNCT
iajs-3717	276	11	(	(	PUNCT
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iajs-3717	276	14	+	+	CCONJ
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iajs-3717	276	17	(	(	PUNCT
iajs-3717	276	18	1	1	NUM
iajs-3717	276	19	)	)	PUNCT
iajs-3717	276	20	(	(	PUNCT
iajs-3717	276	21	0	0	NUM
iajs-3717	276	22	)	)	PUNCT
iajs-3717	276	23	)	)	PUNCT
iajs-3717	276	24	,	,	PUNCT
iajs-3717	276	25	ℏ5	ℏ5	PROPN
iajs-3717	276	26	=	=	SYM
iajs-3717	276	27	ℱ1100	ℱ1100	X
iajs-3717	276	28	(	(	PUNCT
iajs-3717	276	29	2	2	NUM
iajs-3717	276	30	)	)	PUNCT
iajs-3717	276	31	𝑃1	𝑃1	NOUN
iajs-3717	276	32	+	+	PROPN
iajs-3717	276	33	ℱ0020	ℱ0020	PROPN
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iajs-3717	276	35	2	2	NUM
iajs-3717	276	36	)	)	PUNCT
iajs-3717	276	37	𝑃1	𝑃1	NOUN
iajs-3717	276	38	(	(	PUNCT
iajs-3717	276	39	2	2	NUM
iajs-3717	276	40	)	)	PUNCT
iajs-3717	276	41	𝑒−2𝑖𝑤0𝜏0	𝑒−2𝑖𝑤0𝜏0	PUNCT
iajs-3717	277	1	+	+	ADP
iajs-3717	277	2	ℱ0011	ℱ0011	PROPN
iajs-3717	277	3	(	(	PUNCT
iajs-3717	277	4	2	2	X
iajs-3717	277	5	)	)	PUNCT
iajs-3717	277	6	𝑃1𝑃2	𝑃1𝑃2	NOUN
iajs-3717	277	7	𝑒	𝑒	PROPN
iajs-3717	277	8	−2𝑖𝑤0𝜏0	−2𝑖𝑤0𝜏0	PROPN
iajs-3717	277	9	,	,	PUNCT
iajs-3717	277	10	ihjpas	ihjpas	PROPN
iajs-3717	277	11	.	.	PUNCT
iajs-3717	278	1	2025,38(2	2025,38(2	PROPN
iajs-3717	278	2	)	)	PUNCT
iajs-3717	278	3	371	371	NUM
iajs-3717	278	4	ℏ6	ℏ6	NOUN
iajs-3717	278	5	=	=	SYM
iajs-3717	278	6	ℱ1100	ℱ1100	X
iajs-3717	278	7	(	(	PUNCT
iajs-3717	278	8	2	2	NUM
iajs-3717	278	9	)	)	PUNCT
iajs-3717	278	10	(	(	PUNCT
iajs-3717	278	11	𝑃1	𝑃1	NOUN
iajs-3717	278	12	+	+	CCONJ
iajs-3717	278	13	�	�	NOUN
iajs-3717	278	14	̅	̅	NOUN
iajs-3717	278	15	�	�	NOUN
iajs-3717	278	16	1	1	NUM
iajs-3717	278	17	)	)	PUNCT
iajs-3717	279	1	+	+	NUM
iajs-3717	279	2	2ℱ0020	2ℱ0020	NOUN
iajs-3717	279	3	(	(	PUNCT
iajs-3717	279	4	2	2	NUM
iajs-3717	279	5	)	)	PUNCT
iajs-3717	279	6	𝑃1	𝑃1	NOUN
iajs-3717	279	7	�	�	NOUN
iajs-3717	279	8	̅	̅	NOUN
iajs-3717	279	9	�	�	NOUN
iajs-3717	279	10	1	1	NUM
iajs-3717	279	11	+	+	SYM
iajs-3717	279	12	2	2	NUM
iajs-3717	279	13	𝑃1𝑃2ℱ0011	𝑃1𝑃2ℱ0011	PROPN
iajs-3717	279	14	(	(	PUNCT
iajs-3717	279	15	2	2	NUM
iajs-3717	279	16	)	)	PUNCT
iajs-3717	279	17	,	,	PUNCT
iajs-3717	279	18	ℏ7	ℏ7	PROPN
iajs-3717	279	19	=	=	SYM
iajs-3717	279	20	ℱ1100	ℱ1100	X
iajs-3717	279	21	(	(	PUNCT
iajs-3717	279	22	2	2	NUM
iajs-3717	279	23	)	)	PUNCT
iajs-3717	279	24	�	�	NOUN
iajs-3717	279	25	̅	̅	NOUN
iajs-3717	279	26	�	�	NOUN
iajs-3717	279	27	1	1	NUM
iajs-3717	279	28	+	+	NUM
iajs-3717	279	29	𝑓0020	𝑓0020	PROPN
iajs-3717	279	30	(	(	PUNCT
iajs-3717	279	31	2	2	NUM
iajs-3717	279	32	)	)	PUNCT
iajs-3717	279	33	�	�	NOUN
iajs-3717	279	34	̅	̅	NOUN
iajs-3717	279	35	�	�	NOUN
iajs-3717	279	36	1	1	NUM
iajs-3717	279	37	2𝑒2𝑖𝑤0𝜏0	2𝑒2𝑖𝑤0𝜏0	NUM
iajs-3717	279	38	+	+	ADJ
iajs-3717	279	39	�	�	NOUN
iajs-3717	279	40	̅	̅	NOUN
iajs-3717	279	41	�	�	NOUN
iajs-3717	279	42	1	1	NUM
iajs-3717	279	43	�	�	NOUN
iajs-3717	279	44	̅	̅	NOUN
iajs-3717	279	45	�	�	NOUN
iajs-3717	279	46	2𝑒	2𝑒	NUM
iajs-3717	279	47	2𝑖𝑤0𝜏0	2𝑖𝑤0𝜏0	NUM
iajs-3717	279	48	,	,	PUNCT
iajs-3717	279	49	ℏ8	ℏ8	PROPN
iajs-3717	279	50	=	=	SYM
iajs-3717	279	51	ℱ1100	ℱ1100	X
iajs-3717	279	52	(	(	PUNCT
iajs-3717	279	53	2	2	NUM
iajs-3717	279	54	)	)	PUNCT
iajs-3717	279	55	(	(	PUNCT
iajs-3717	279	56	1	1	NUM
iajs-3717	279	57	2	2	NUM
iajs-3717	279	58	�	�	NOUN
iajs-3717	279	59	̅	̅	NOUN
iajs-3717	279	60	�	�	NOUN
iajs-3717	279	61	1	1	NUM
iajs-3717	279	62	𝑤20	𝑤20	NOUN
iajs-3717	279	63	(	(	PUNCT
iajs-3717	279	64	1	1	NUM
iajs-3717	279	65	)	)	PUNCT
iajs-3717	279	66	(	(	PUNCT
iajs-3717	279	67	0	0	NUM
iajs-3717	279	68	)	)	PUNCT
iajs-3717	279	69	+	+	CCONJ
iajs-3717	279	70	𝑃1𝑤11	𝑃1𝑤11	PROPN
iajs-3717	279	71	(	(	PUNCT
iajs-3717	279	72	1	1	NUM
iajs-3717	279	73	)	)	PUNCT
iajs-3717	279	74	(	(	PUNCT
iajs-3717	279	75	0	0	NUM
iajs-3717	279	76	)	)	PUNCT
iajs-3717	279	77	+	+	CCONJ
iajs-3717	279	78	1	1	NUM
iajs-3717	279	79	2	2	NUM
iajs-3717	279	80	𝑤20	𝑤20	NOUN
iajs-3717	279	81	(	(	PUNCT
iajs-3717	279	82	2	2	NUM
iajs-3717	279	83	)	)	PUNCT
iajs-3717	279	84	(	(	PUNCT
iajs-3717	279	85	0	0	NUM
iajs-3717	279	86	)	)	PUNCT
iajs-3717	279	87	+	+	CCONJ
iajs-3717	279	88	𝑤11	𝑤11	ADJ
iajs-3717	279	89	(	(	PUNCT
iajs-3717	279	90	2	2	NUM
iajs-3717	279	91	)	)	PUNCT
iajs-3717	279	92	(	(	PUNCT
iajs-3717	279	93	0	0	NUM
iajs-3717	279	94	)	)	PUNCT
iajs-3717	279	95	)	)	PUNCT
iajs-3717	280	1	+	+	PROPN
iajs-3717	280	2	ℱ0020	ℱ0020	PROPN
iajs-3717	280	3	(	(	PUNCT
iajs-3717	280	4	2	2	NUM
iajs-3717	280	5	)	)	PUNCT
iajs-3717	280	6	(	(	PUNCT
iajs-3717	280	7	�	�	NOUN
iajs-3717	280	8	̅	̅	NOUN
iajs-3717	280	9	�	�	NOUN
iajs-3717	280	10	1	1	NUM
iajs-3717	280	11	𝑤20	𝑤20	NOUN
iajs-3717	280	12	(	(	PUNCT
iajs-3717	280	13	2	2	NUM
iajs-3717	280	14	)	)	PUNCT
iajs-3717	280	15	(	(	PUNCT
iajs-3717	280	16	−1)𝑒𝑖𝑤0𝜏0	−1)𝑒𝑖𝑤0𝜏0	NOUN
iajs-3717	280	17	+	+	CCONJ
iajs-3717	280	18	2𝑃1	2𝑃1	NUM
iajs-3717	280	19	𝑤11	𝑤11	NOUN
iajs-3717	280	20	(	(	PUNCT
iajs-3717	280	21	2	2	NUM
iajs-3717	280	22	)	)	PUNCT
iajs-3717	280	23	(	(	PUNCT
iajs-3717	280	24	−1)𝑒−𝑖𝑤0𝜏0	−1)𝑒−𝑖𝑤0𝜏0	PRON
iajs-3717	280	25	)	)	PUNCT
iajs-3717	280	26	+	+	VERB
iajs-3717	280	27	ℱ0011	ℱ0011	NOUN
iajs-3717	280	28	(	(	PUNCT
iajs-3717	280	29	2	2	NUM
iajs-3717	280	30	)	)	PUNCT
iajs-3717	280	31	(	(	PUNCT
iajs-3717	280	32	1	1	NUM
iajs-3717	280	33	2	2	NUM
iajs-3717	280	34	(	(	PUNCT
iajs-3717	280	35	𝑃̅̅	𝑃̅̅	NOUN
iajs-3717	280	36	1̅	1̅	PROPN
iajs-3717	280	37	+	+	NUM
iajs-3717	280	38	�	�	NOUN
iajs-3717	280	39	̅	̅	NOUN
iajs-3717	280	40	�	�	NOUN
iajs-3717	280	41	2)𝑤20	2)𝑤20	NUM
iajs-3717	280	42	(	(	PUNCT
iajs-3717	280	43	2	2	NUM
iajs-3717	280	44	)	)	PUNCT
iajs-3717	280	45	(	(	PUNCT
iajs-3717	280	46	−1	−1	NOUN
iajs-3717	280	47	)	)	PUNCT
iajs-3717	280	48	𝑒𝑖𝑤0𝜏0	𝑒𝑖𝑤0𝜏0	NOUN
iajs-3717	280	49	+	+	CCONJ
iajs-3717	280	50	(	(	PUNCT
iajs-3717	280	51	𝑃1	𝑃1	NOUN
iajs-3717	280	52	+	+	CCONJ
iajs-3717	280	53	𝑃2	𝑃2	X
iajs-3717	280	54	)	)	PUNCT
iajs-3717	280	55	𝑤11	𝑤11	NOUN
iajs-3717	280	56	(	(	PUNCT
iajs-3717	280	57	3	3	NUM
iajs-3717	280	58	)	)	PUNCT
iajs-3717	280	59	(	(	PUNCT
iajs-3717	280	60	−1	−1	NOUN
iajs-3717	280	61	)	)	PUNCT
iajs-3717	280	62	𝑒−𝑖𝑤0𝜏0	𝑒−𝑖𝑤0𝜏0	PRON
iajs-3717	280	63	)	)	PUNCT
iajs-3717	280	64	ℏ9	ℏ9	PROPN
iajs-3717	280	65	=	=	SYM
iajs-3717	280	66	ℱ020	ℱ020	PROPN
iajs-3717	280	67	(	(	PUNCT
iajs-3717	280	68	3	3	NUM
iajs-3717	280	69	)	)	PUNCT
iajs-3717	280	70	𝑃1	𝑃1	NOUN
iajs-3717	280	71	2	2	NUM
iajs-3717	280	72	𝑒−2𝑖𝑤0𝜏0	𝑒−2𝑖𝑤0𝜏0	PUNCT
iajs-3717	280	73	+	+	PROPN
iajs-3717	280	74	ℱ011	ℱ011	NUM
iajs-3717	280	75	(	(	PUNCT
iajs-3717	280	76	3	3	X
iajs-3717	280	77	)	)	PUNCT
iajs-3717	280	78	𝑃1𝑃2	𝑃1𝑃2	NOUN
iajs-3717	280	79	𝑒	𝑒	PROPN
iajs-3717	280	80	−2𝑖𝑤0𝜏0	−2𝑖𝑤0𝜏0	PROPN
iajs-3717	280	81	,	,	PUNCT
iajs-3717	280	82	ℏ10	ℏ10	NOUN
iajs-3717	280	83	=	=	SYM
iajs-3717	280	84	2ℱ020	2ℱ020	NUM
iajs-3717	280	85	(	(	PUNCT
iajs-3717	280	86	3	3	NUM
iajs-3717	280	87	)	)	PUNCT
iajs-3717	280	88	𝑃1	𝑃1	NOUN
iajs-3717	280	89	�	�	NOUN
iajs-3717	280	90	̅	̅	NOUN
iajs-3717	280	91	�	�	NOUN
iajs-3717	280	92	1	1	NUM
iajs-3717	280	93	+	+	SYM
iajs-3717	280	94	2ℱ011	2ℱ011	NUM
iajs-3717	280	95	(	(	PUNCT
iajs-3717	280	96	3	3	X
iajs-3717	280	97	)	)	PUNCT
iajs-3717	280	98	𝑃1𝑃2	𝑃1𝑃2	NOUN
iajs-3717	280	99	,	,	PUNCT
iajs-3717	280	100	ℏ11	ℏ11	NOUN
iajs-3717	280	101	=	=	SYM
iajs-3717	280	102	ℱ020	ℱ020	PROPN
iajs-3717	280	103	(	(	PUNCT
iajs-3717	280	104	3	3	NUM
iajs-3717	280	105	)	)	PUNCT
iajs-3717	280	106	�	�	NOUN
iajs-3717	280	107	̅	̅	NOUN
iajs-3717	280	108	�	�	NOUN
iajs-3717	280	109	1	1	NUM
iajs-3717	280	110	2	2	NUM
iajs-3717	280	111	𝑒2𝑖𝑤0𝜏0	𝑒2𝑖𝑤0𝜏0	VERB
iajs-3717	280	112	+	+	PROPN
iajs-3717	280	113	ℱ011	ℱ011	NUM
iajs-3717	280	114	(	(	PUNCT
iajs-3717	280	115	3	3	NUM
iajs-3717	280	116	)	)	PUNCT
iajs-3717	280	117	�	�	NOUN
iajs-3717	280	118	̅	̅	NOUN
iajs-3717	280	119	�	�	NOUN
iajs-3717	280	120	1	1	NUM
iajs-3717	280	121	�	�	NOUN
iajs-3717	280	122	̅	̅	NOUN
iajs-3717	280	123	�	�	NOUN
iajs-3717	280	124	2	2	NUM
iajs-3717	280	125	𝑒	𝑒	ADP
iajs-3717	280	126	2𝑖𝑤0𝜏0	2𝑖𝑤0𝜏0	NUM
iajs-3717	280	127	,	,	PUNCT
iajs-3717	280	128	ℏ12	ℏ12	ADP
iajs-3717	280	129	=	=	SYM
iajs-3717	280	130	ℱ020	ℱ020	PROPN
iajs-3717	280	131	(	(	PUNCT
iajs-3717	280	132	3	3	NUM
iajs-3717	280	133	)	)	PUNCT
iajs-3717	280	134	(	(	PUNCT
iajs-3717	280	135	�	�	NOUN
iajs-3717	280	136	̅	̅	NOUN
iajs-3717	280	137	�	�	NOUN
iajs-3717	280	138	1	1	NUM
iajs-3717	280	139	𝑤20	𝑤20	NOUN
iajs-3717	280	140	(	(	PUNCT
iajs-3717	280	141	1	1	NUM
iajs-3717	280	142	)	)	PUNCT
iajs-3717	280	143	(	(	PUNCT
iajs-3717	280	144	−1	−1	NOUN
iajs-3717	280	145	)	)	PUNCT
iajs-3717	280	146	𝑒𝑖𝑤0𝜏0	𝑒𝑖𝑤0𝜏0	NOUN
iajs-3717	281	1	+	+	CCONJ
iajs-3717	281	2	2𝑃1𝑤11	2𝑃1𝑤11	NUM
iajs-3717	281	3	(	(	PUNCT
iajs-3717	281	4	1	1	NUM
iajs-3717	281	5	)	)	PUNCT
iajs-3717	281	6	(	(	PUNCT
iajs-3717	281	7	−1)𝑒−𝑖𝑤0𝜏0	−1)𝑒−𝑖𝑤0𝜏0	X
iajs-3717	281	8	)	)	PUNCT
iajs-3717	282	1	+	+	NOUN
iajs-3717	282	2	ℱ011	ℱ011	NUM
iajs-3717	282	3	(	(	PUNCT
iajs-3717	282	4	3	3	NUM
iajs-3717	282	5	)	)	PUNCT
iajs-3717	282	6	(	(	PUNCT
iajs-3717	282	7	1	1	NUM
iajs-3717	282	8	2	2	NUM
iajs-3717	282	9	(	(	PUNCT
iajs-3717	282	10	�	�	NOUN
iajs-3717	282	11	̅	̅	NOUN
iajs-3717	282	12	�	�	NOUN
iajs-3717	282	13	1	1	NUM
iajs-3717	282	14	+	+	NUM
iajs-3717	282	15	�	�	NOUN
iajs-3717	282	16	̅	̅	NOUN
iajs-3717	282	17	�	�	NOUN
iajs-3717	282	18	2)𝑤20	2)𝑤20	NUM
iajs-3717	282	19	(	(	PUNCT
iajs-3717	282	20	2	2	NUM
iajs-3717	282	21	)	)	PUNCT
iajs-3717	282	22	(	(	PUNCT
iajs-3717	282	23	−1	−1	NOUN
iajs-3717	282	24	)	)	PUNCT
iajs-3717	282	25	𝑒𝑖𝑤0𝜏0	𝑒𝑖𝑤0𝜏0	NOUN
iajs-3717	282	26	+	+	CCONJ
iajs-3717	282	27	(	(	PUNCT
iajs-3717	282	28	𝑃1	𝑃1	NOUN
iajs-3717	282	29	+	+	CCONJ
iajs-3717	282	30	𝑃2	𝑃2	X
iajs-3717	282	31	)	)	PUNCT
iajs-3717	282	32	𝑤11	𝑤11	NOUN
iajs-3717	282	33	(	(	PUNCT
iajs-3717	282	34	3	3	NUM
iajs-3717	282	35	)	)	PUNCT
iajs-3717	282	36	(	(	PUNCT
iajs-3717	282	37	−1	−1	NOUN
iajs-3717	282	38	)	)	PUNCT
iajs-3717	282	39	𝑒−𝑖𝑤0𝜏0	𝑒−𝑖𝑤0𝜏0	PROPN
iajs-3717	282	40	)	)	PUNCT
iajs-3717	282	41	with	with	ADP
iajs-3717	282	42	𝑤20(𝜐0	𝑤20(𝜐0	NOUN
iajs-3717	282	43	)	)	PUNCT
iajs-3717	282	44	=	=	PUNCT
iajs-3717	283	1	𝑖𝒢	𝑖𝒢	PUNCT
iajs-3717	283	2	20	20	NUM
iajs-3717	283	3	𝑤0𝜏0	𝑤0𝜏0	NOUN
iajs-3717	283	4	𝑃(0)𝑒𝑖𝑤0𝜏0𝜐0	𝑃(0)𝑒𝑖𝑤0𝜏0𝜐0	ADJ
iajs-3717	283	5	+	+	CCONJ
iajs-3717	283	6	𝑖	𝑖	SYM
iajs-3717	283	7	�	�	NOUN
iajs-3717	283	8	̅	̅	NOUN
iajs-3717	283	9	�	�	PROPN
iajs-3717	283	10	02	02	NUM
iajs-3717	283	11	3𝑤0𝜏0	3𝑤0𝜏0	NUM
iajs-3717	283	12	�	�	NOUN
iajs-3717	283	13	̅	̅	NOUN
iajs-3717	283	14	�	�	NOUN
iajs-3717	283	15	(0)𝑒−𝑖𝑤0𝜏0𝜐0	(0)𝑒−𝑖𝑤0𝜏0𝜐0	NOUN
iajs-3717	283	16	+	+	CCONJ
iajs-3717	283	17	ℒ1𝑒	ℒ1𝑒	PROPN
iajs-3717	283	18	2𝑖𝑤0𝜏𝜐0	2𝑖𝑤0𝜏𝜐0	NUM
iajs-3717	283	19	.	.	PUNCT
iajs-3717	284	1	(	(	PUNCT
iajs-3717	284	2	51	51	NUM
iajs-3717	284	3	)	)	PUNCT
iajs-3717	284	4	𝑤11(𝜐0	𝑤11(𝜐0	PROPN
iajs-3717	284	5	)	)	PUNCT
iajs-3717	285	1	=	=	SYM
iajs-3717	285	2	−	−	PROPN
iajs-3717	285	3	𝑖𝒢11	𝑖𝒢11	NUM
iajs-3717	285	4	𝑤0𝜏0	𝑤0𝜏0	X
iajs-3717	285	5	𝑃(0	𝑃(0	NOUN
iajs-3717	285	6	)	)	PUNCT
iajs-3717	285	7	𝑒𝑖𝑤0𝜏0𝜐0	𝑒𝑖𝑤0𝜏0𝜐0	PROPN
iajs-3717	285	8	+	+	CCONJ
iajs-3717	285	9	𝑖	𝑖	SYM
iajs-3717	285	10	�	�	NOUN
iajs-3717	285	11	̅	̅	NOUN
iajs-3717	285	12	�	�	NOUN
iajs-3717	285	13	11	11	NUM
iajs-3717	285	14	𝑤0𝜏0	𝑤0𝜏0	SYM
iajs-3717	285	15	�	�	NOUN
iajs-3717	285	16	̅	̅	NOUN
iajs-3717	285	17	�	�	NOUN
iajs-3717	285	18	(0	(0	PUNCT
iajs-3717	285	19	)	)	PUNCT
iajs-3717	285	20	𝑒−𝑖𝑤0𝜏0𝜐0	𝑒−𝑖𝑤0𝜏0𝜐0	PROPN
iajs-3717	285	21	+	+	CCONJ
iajs-3717	285	22	ℒ2	ℒ2	NOUN
iajs-3717	285	23	.	.	PUNCT
iajs-3717	286	1	(	(	PUNCT
iajs-3717	286	2	52	52	NUM
iajs-3717	286	3	)	)	PUNCT
iajs-3717	286	4	her	her	PRON
iajs-3717	286	5	ℒ1	ℒ1	NOUN
iajs-3717	286	6	=	=	PUNCT
iajs-3717	286	7	(	(	PUNCT
iajs-3717	286	8	ℒ1	ℒ1	PROPN
iajs-3717	286	9	(	(	PUNCT
iajs-3717	286	10	1	1	NUM
iajs-3717	286	11	)	)	PUNCT
iajs-3717	286	12	,	,	PUNCT
iajs-3717	286	13	ℒ1	ℒ1	PROPN
iajs-3717	286	14	(	(	PUNCT
iajs-3717	286	15	2	2	NUM
iajs-3717	286	16	)	)	PUNCT
iajs-3717	286	17	,	,	PUNCT
iajs-3717	286	18	ℒ1	ℒ1	PROPN
iajs-3717	286	19	(	(	PUNCT
iajs-3717	286	20	3	3	NUM
iajs-3717	286	21	)	)	PUNCT
iajs-3717	286	22	)	)	PUNCT
iajs-3717	286	23	𝑇	𝑇	PROPN
iajs-3717	286	24	and	and	CCONJ
iajs-3717	286	25	ℒ2	ℒ2	NOUN
iajs-3717	286	26	=	=	SYM
iajs-3717	286	27	(	(	PUNCT
iajs-3717	286	28	ℒ2	ℒ2	PROPN
iajs-3717	286	29	(	(	PUNCT
iajs-3717	286	30	1	1	NUM
iajs-3717	286	31	)	)	PUNCT
iajs-3717	286	32	,	,	PUNCT
iajs-3717	286	33	ℒ2	ℒ2	PROPN
iajs-3717	286	34	(	(	PUNCT
iajs-3717	286	35	2	2	NUM
iajs-3717	286	36	)	)	PUNCT
iajs-3717	286	37	,	,	PUNCT
iajs-3717	286	38	ℒ2	ℒ2	PROPN
iajs-3717	286	39	(	(	PUNCT
iajs-3717	286	40	3	3	NUM
iajs-3717	286	41	)	)	PUNCT
iajs-3717	286	42	)	)	PUNCT
iajs-3717	287	1	𝑇	𝑇	PROPN
iajs-3717	287	2	can	can	AUX
iajs-3717	287	3	be	be	AUX
iajs-3717	287	4	calculated	calculate	VERB
iajs-3717	287	5	by	by	ADP
iajs-3717	287	6	the	the	DET
iajs-3717	287	7	following	follow	VERB
iajs-3717	287	8	equations	equation	NOUN
iajs-3717	287	9	:	:	PUNCT
iajs-3717	287	10	𝒿1	𝒿1	NOUN
iajs-3717	287	11	∗ℒ1	∗ℒ1	PUNCT
iajs-3717	287	12	=	=	PUNCT
iajs-3717	287	13	2𝜏0𝒿1	2𝜏0𝒿1	PROPN
iajs-3717	287	14	.	.	PUNCT
iajs-3717	288	1	(	(	PUNCT
iajs-3717	288	2	53	53	NUM
iajs-3717	288	3	)	)	PUNCT
iajs-3717	288	4	𝒿2	𝒿2	NOUN
iajs-3717	288	5	∗	∗	NOUN
iajs-3717	288	6	ℒ2	ℒ2	PROPN
iajs-3717	289	1	=	=	SYM
iajs-3717	289	2	−𝜏0𝒿2	−𝜏0𝒿2	PROPN
iajs-3717	289	3	.	.	PUNCT
iajs-3717	290	1	(	(	PUNCT
iajs-3717	290	2	54	54	NUM
iajs-3717	290	3	)	)	PUNCT
iajs-3717	290	4	where	where	SCONJ
iajs-3717	290	5	,	,	PUNCT
iajs-3717	290	6	𝒿1	𝒿1	NOUN
iajs-3717	290	7	∗	∗	NOUN
iajs-3717	290	8	=	=	PUNCT
iajs-3717	290	9	(	(	PUNCT
iajs-3717	290	10	2𝑖𝑤0𝜏0𝐼	2𝑖𝑤0𝜏0𝐼	NUM
iajs-3717	290	11	−	−	NOUN
iajs-3717	290	12	∫	∫	PROPN
iajs-3717	290	13	0	0	NUM
iajs-3717	290	14	−1	−1	NOUN
iajs-3717	290	15	𝑑ℳ0(𝜐0	𝑑ℳ0(𝜐0	NOUN
iajs-3717	290	16	)	)	PUNCT
iajs-3717	290	17	𝑒	𝑒	PROPN
iajs-3717	290	18	2𝑖𝑤0𝜏0𝜐0	2𝑖𝑤0𝜏0𝜐0	NUM
iajs-3717	290	19	)	)	PUNCT
iajs-3717	290	20	,	,	PUNCT
iajs-3717	290	21	𝒿2	𝒿2	NOUN
iajs-3717	290	22	∗	∗	NOUN
iajs-3717	290	23	=	=	SYM
iajs-3717	290	24	(	(	PUNCT
iajs-3717	290	25	∫	∫	PROPN
iajs-3717	290	26	0	0	NUM
iajs-3717	290	27	−1	−1	NOUN
iajs-3717	290	28	𝑑ℳ0(𝜐0	𝑑ℳ0(𝜐0	NOUN
iajs-3717	290	29	)	)	PUNCT
iajs-3717	290	30	)	)	PUNCT
iajs-3717	290	31	,	,	PUNCT
iajs-3717	290	32	𝒿1	𝒿1	X
iajs-3717	290	33	=	=	PUNCT
iajs-3717	290	34	(	(	PUNCT
iajs-3717	290	35	ℏ1	ℏ1	PROPN
iajs-3717	290	36	ℏ5	ℏ5	NOUN
iajs-3717	290	37	ℏ9	ℏ9	PROPN
iajs-3717	290	38	)	)	PUNCT
iajs-3717	290	39	𝑇	𝑇	PROPN
iajs-3717	290	40	,	,	PUNCT
iajs-3717	290	41	𝒿2	𝒿2	NOUN
iajs-3717	290	42	=	=	SYM
iajs-3717	290	43	(	(	PUNCT
iajs-3717	290	44	ℏ2	ℏ2	NOUN
iajs-3717	290	45	ℏ6	ℏ6	PROPN
iajs-3717	290	46	ℏ10	ℏ10	ADJ
iajs-3717	290	47	)	)	PUNCT
iajs-3717	290	48	𝑇.	𝑇.	PROPN
iajs-3717	290	49	accordingly	accordingly	ADV
iajs-3717	290	50	,	,	PUNCT
iajs-3717	290	51	it	it	PRON
iajs-3717	290	52	is	be	AUX
iajs-3717	290	53	determined	determine	VERB
iajs-3717	290	54	that	that	SCONJ
iajs-3717	290	55	:	:	PUNCT
iajs-3717	290	56	ℒ1	ℒ1	NOUN
iajs-3717	290	57	=	=	SYM
iajs-3717	290	58	2	2	NUM
iajs-3717	290	59	𝒿1	𝒿1	NOUN
iajs-3717	290	60	(	(	PUNCT
iajs-3717	290	61	2𝑖𝑤0	2𝑖𝑤0	NUM
iajs-3717	290	62	−	−	PROPN
iajs-3717	290	63	ℱ10	ℱ10	PROPN
iajs-3717	290	64	(	(	PUNCT
iajs-3717	290	65	1	1	NUM
iajs-3717	290	66	)	)	PUNCT
iajs-3717	290	67	−ℱ01	−ℱ01	PROPN
iajs-3717	290	68	(	(	PUNCT
iajs-3717	290	69	1	1	NUM
iajs-3717	290	70	)	)	PUNCT
iajs-3717	290	71	0	0	NUM
iajs-3717	291	1	−ℱ10000	−ℱ10000	NUM
iajs-3717	291	2	(	(	PUNCT
iajs-3717	291	3	2	2	NUM
iajs-3717	291	4	)	)	PUNCT
iajs-3717	291	5	−	−	PROPN
iajs-3717	291	6	ℱ0010	ℱ0010	NOUN
iajs-3717	291	7	(	(	PUNCT
iajs-3717	291	8	2	2	NUM
iajs-3717	291	9	)	)	PUNCT
iajs-3717	291	10	𝑒2𝑖𝑤0𝜏0𝜐0	𝑒2𝑖𝑤0𝜏0𝜐0	NOUN
iajs-3717	291	11	2𝑖𝑤0	2𝑖𝑤0	NUM
iajs-3717	291	12	−	−	PROPN
iajs-3717	292	1	ℱ0100	ℱ0100	X
iajs-3717	292	2	(	(	PUNCT
iajs-3717	292	3	2	2	X
iajs-3717	292	4	)	)	PUNCT
iajs-3717	292	5	ℱ0001	ℱ0001	NOUN
iajs-3717	292	6	(	(	PUNCT
iajs-3717	292	7	2	2	NUM
iajs-3717	292	8	)	)	PUNCT
iajs-3717	292	9	𝑒2𝑖𝑤0𝜏0𝜐0	𝑒2𝑖𝑤0𝜏0𝜐0	PROPN
iajs-3717	292	10	−ℱ010	−ℱ010	NOUN
iajs-3717	292	11	(	(	PUNCT
iajs-3717	292	12	3	3	X
iajs-3717	292	13	)	)	PUNCT
iajs-3717	292	14	𝑒2𝑖𝑤0𝜏0𝜐0	𝑒2𝑖𝑤0𝜏0𝜐0	NOUN
iajs-3717	292	15	0	0	NUM
iajs-3717	292	16	2𝑖𝑤0	2𝑖𝑤0	NUM
iajs-3717	292	17	−	−	PROPN
iajs-3717	292	18	ℱ100	ℱ100	PROPN
iajs-3717	292	19	(	(	PUNCT
iajs-3717	292	20	3	3	NUM
iajs-3717	292	21	)	)	PUNCT
iajs-3717	292	22	−	−	PROPN
iajs-3717	292	23	ℱ001	ℱ001	PROPN
iajs-3717	292	24	(	(	PUNCT
iajs-3717	292	25	3	3	NUM
iajs-3717	292	26	)	)	PUNCT
iajs-3717	292	27	𝑒2𝑖𝑤0𝜏0𝜐0	𝑒2𝑖𝑤0𝜏0𝜐0	PROPN
iajs-3717	292	28	)	)	PUNCT
iajs-3717	292	29	−1	−1	NOUN
iajs-3717	292	30	.	.	PUNCT
iajs-3717	293	1	ℒ1	ℒ1	PROPN
iajs-3717	293	2	=	=	PUNCT
iajs-3717	294	1	−	−	PROPN
iajs-3717	294	2	𝒿2	𝒿2	NOUN
iajs-3717	294	3	(	(	PUNCT
iajs-3717	294	4	−ℱ10	−ℱ10	PROPN
iajs-3717	294	5	(	(	PUNCT
iajs-3717	294	6	1	1	NUM
iajs-3717	294	7	)	)	PUNCT
iajs-3717	294	8	−ℱ01	−ℱ01	PROPN
iajs-3717	294	9	(	(	PUNCT
iajs-3717	294	10	1	1	NUM
iajs-3717	294	11	)	)	PUNCT
iajs-3717	294	12	0	0	NUM
iajs-3717	295	1	−ℱ1000	−ℱ1000	NUM
iajs-3717	295	2	(	(	PUNCT
iajs-3717	295	3	2	2	NUM
iajs-3717	295	4	)	)	PUNCT
iajs-3717	295	5	−ℱ0010	−ℱ0010	NOUN
iajs-3717	295	6	(	(	PUNCT
iajs-3717	295	7	2	2	NUM
iajs-3717	295	8	)	)	PUNCT
iajs-3717	295	9	−ℱ0100	−ℱ0100	NOUN
iajs-3717	295	10	(	(	PUNCT
iajs-3717	295	11	2	2	NUM
iajs-3717	295	12	)	)	PUNCT
iajs-3717	295	13	−ℱ0001	−ℱ0001	NOUN
iajs-3717	295	14	(	(	PUNCT
iajs-3717	295	15	2	2	NUM
iajs-3717	295	16	)	)	PUNCT
iajs-3717	295	17	−ℱ010	−ℱ010	NOUN
iajs-3717	295	18	(	(	PUNCT
iajs-3717	295	19	3	3	NUM
iajs-3717	295	20	)	)	PUNCT
iajs-3717	295	21	0	0	NUM
iajs-3717	296	1	−ℱ100	−ℱ100	NOUN
iajs-3717	296	2	(	(	PUNCT
iajs-3717	296	3	3	3	NUM
iajs-3717	296	4	)	)	PUNCT
iajs-3717	296	5	−ℱ001	−ℱ001	NOUN
iajs-3717	296	6	(	(	PUNCT
iajs-3717	296	7	3	3	NUM
iajs-3717	296	8	)	)	PUNCT
iajs-3717	296	9	)	)	PUNCT
iajs-3717	296	10	−1	−1	NOUN
iajs-3717	296	11	.	.	PUNCT
iajs-3717	297	1	ihjpas	ihjpas	PROPN
iajs-3717	297	2	.	.	PUNCT
iajs-3717	298	1	2025,38(2	2025,38(2	PROPN
iajs-3717	298	2	)	)	PUNCT
iajs-3717	299	1	372	372	NUM
iajs-3717	299	2	thus	thus	ADV
iajs-3717	299	3	,	,	PUNCT
iajs-3717	299	4	equations	equation	NOUN
iajs-3717	299	5	(	(	PUNCT
iajs-3717	299	6	51	51	NUM
iajs-3717	299	7	)	)	PUNCT
iajs-3717	299	8	–	–	PUNCT
iajs-3717	299	9	(	(	PUNCT
iajs-3717	299	10	54	54	NUM
iajs-3717	299	11	)	)	PUNCT
iajs-3717	299	12	can	can	AUX
iajs-3717	299	13	be	be	AUX
iajs-3717	299	14	used	use	VERB
iajs-3717	299	15	to	to	PART
iajs-3717	299	16	calculate	calculate	VERB
iajs-3717	299	17	𝑤20(𝜐0	𝑤20(𝜐0	NOUN
iajs-3717	299	18	)	)	PUNCT
iajs-3717	299	19	and	and	CCONJ
iajs-3717	299	20	𝑤11(𝜐0	𝑤11(𝜐0	NUM
iajs-3717	299	21	)	)	PUNCT
iajs-3717	299	22	.	.	PUNCT
iajs-3717	300	1	following	follow	VERB
iajs-3717	300	2	that	that	PRON
iajs-3717	300	3	,	,	PUNCT
iajs-3717	300	4	the	the	DET
iajs-3717	300	5	proof	proof	NOUN
iajs-3717	300	6	can	can	AUX
iajs-3717	300	7	be	be	AUX
iajs-3717	300	8	completed	complete	VERB
iajs-3717	300	9	by	by	ADP
iajs-3717	300	10	determining	determine	VERB
iajs-3717	300	11	the	the	DET
iajs-3717	300	12	expressions	expression	NOUN
iajs-3717	300	13	given	give	VERB
iajs-3717	300	14	in	in	ADP
iajs-3717	300	15	equation	equation	NOUN
iajs-3717	300	16	(	(	PUNCT
iajs-3717	300	17	39	39	NUM
iajs-3717	300	18	)	)	PUNCT
iajs-3717	300	19	based	base	VERB
iajs-3717	300	20	on	on	ADP
iajs-3717	300	21	those	those	PRON
iajs-3717	300	22	in	in	ADP
iajs-3717	300	23	equation	equation	NOUN
iajs-3717	300	24	(	(	PUNCT
iajs-3717	300	25	50	50	NUM
iajs-3717	300	26	)	)	PUNCT
iajs-3717	300	27	.	.	PUNCT
iajs-3717	301	1	3	3	X
iajs-3717	301	2	.	.	X
iajs-3717	301	3	numerical	numerical	PROPN
iajs-3717	301	4	simulation	simulation	PROPN
iajs-3717	301	5	in	in	ADP
iajs-3717	301	6	this	this	DET
iajs-3717	301	7	section	section	NOUN
iajs-3717	301	8	,	,	PUNCT
iajs-3717	301	9	we	we	PRON
iajs-3717	301	10	present	present	VERB
iajs-3717	301	11	essential	essential	ADJ
iajs-3717	301	12	findings	finding	NOUN
iajs-3717	301	13	through	through	ADP
iajs-3717	301	14	numerical	numerical	ADJ
iajs-3717	301	15	representation	representation	NOUN
iajs-3717	301	16	,	,	PUNCT
iajs-3717	301	17	utilizing	utilize	VERB
iajs-3717	301	18	a	a	DET
iajs-3717	301	19	set	set	NOUN
iajs-3717	301	20	of	of	ADP
iajs-3717	301	21	biologically	biologically	ADV
iajs-3717	301	22	reasonable	reasonable	ADJ
iajs-3717	301	23	hypothetical	hypothetical	ADJ
iajs-3717	301	24	values	value	NOUN
iajs-3717	301	25	as	as	SCONJ
iajs-3717	301	26	provided	provide	VERB
iajs-3717	301	27	below	below	ADV
iajs-3717	301	28	.	.	PUNCT
iajs-3717	302	1	the	the	DET
iajs-3717	302	2	goal	goal	NOUN
iajs-3717	302	3	is	be	AUX
iajs-3717	302	4	to	to	PART
iajs-3717	302	5	validate	validate	VERB
iajs-3717	302	6	the	the	DET
iajs-3717	302	7	theoretically	theoretically	ADV
iajs-3717	302	8	generated	generate	VERB
iajs-3717	302	9	outcomes	outcome	NOUN
iajs-3717	302	10	and	and	CCONJ
iajs-3717	302	11	gain	gain	VERB
iajs-3717	302	12	insights	insight	NOUN
iajs-3717	302	13	into	into	ADP
iajs-3717	302	14	the	the	DET
iajs-3717	302	15	parameters	parameter	NOUN
iajs-3717	302	16	'	'	PART
iajs-3717	302	17	impact	impact	NOUN
iajs-3717	302	18	on	on	ADP
iajs-3717	302	19	the	the	DET
iajs-3717	302	20	system	system	NOUN
iajs-3717	302	21	dynamics	dynamic	NOUN
iajs-3717	302	22	(	(	PUNCT
iajs-3717	302	23	2	2	NUM
iajs-3717	302	24	)	)	PUNCT
iajs-3717	302	25	.	.	PUNCT
iajs-3717	303	1	𝑟	𝑟	NOUN
iajs-3717	303	2	=	=	SYM
iajs-3717	303	3	0.009	0.009	NUM
iajs-3717	303	4	,	,	PUNCT
iajs-3717	303	5	𝑘	𝑘	X
iajs-3717	303	6	=	=	SYM
iajs-3717	303	7	40	40	NUM
iajs-3717	303	8	,	,	PUNCT
iajs-3717	303	9	𝑐	𝑐	NOUN
iajs-3717	303	10	=	=	SYM
iajs-3717	303	11	0.0002	0.0002	NUM
iajs-3717	303	12	,	,	PUNCT
iajs-3717	303	13	𝐸1	𝐸1	NOUN
iajs-3717	303	14	=	=	SYM
iajs-3717	303	15	0.001	0.001	NUM
iajs-3717	303	16	,	,	PUNCT
iajs-3717	303	17	𝛼	𝛼	NOUN
iajs-3717	303	18	=	=	NOUN
iajs-3717	303	19	0.001	0.001	NUM
iajs-3717	303	20	,	,	PUNCT
iajs-3717	303	21	𝛾	𝛾	NOUN
iajs-3717	303	22	=	=	SYM
iajs-3717	303	23	1.2	1.2	NUM
iajs-3717	303	24	,	,	PUNCT
iajs-3717	303	25	𝜆	𝜆	NOUN
iajs-3717	303	26	=	=	SYM
iajs-3717	303	27	0.02	0.02	NUM
iajs-3717	303	28	𝐸2	𝐸2	NOUN
iajs-3717	303	29	=	=	PROPN
iajs-3717	303	30	0.005	0.005	NUM
iajs-3717	303	31	;	;	PUNCT
iajs-3717	303	32	𝜃	𝜃	X
iajs-3717	303	33	=	=	SYM
iajs-3717	303	34	0.001	0.001	NUM
iajs-3717	303	35	,	,	PUNCT
iajs-3717	303	36	ℎ	ℎ	X
iajs-3717	303	37	=	=	NOUN
iajs-3717	303	38	0.03	0.03	NUM
iajs-3717	303	39	,	,	PUNCT
iajs-3717	303	40	𝐸3	𝐸3	NOUN
iajs-3717	303	41	=	=	NOUN
iajs-3717	303	42	0.02	0.02	NUM
iajs-3717	303	43	,	,	PUNCT
iajs-3717	303	44	𝜏	𝜏	NOUN
iajs-3717	303	45	=	=	SYM
iajs-3717	303	46	15.0	15.0	NUM
iajs-3717	303	47	,	,	PUNCT
iajs-3717	303	48	𝑛	𝑛	PROPN
iajs-3717	303	49	=	=	SYM
iajs-3717	303	50	5000	5000	NUM
iajs-3717	303	51	(	(	PUNCT
iajs-3717	303	52	55	55	NUM
iajs-3717	303	53	)	)	PUNCT
iajs-3717	303	54	it	it	PRON
iajs-3717	303	55	is	be	AUX
iajs-3717	303	56	noted	note	VERB
iajs-3717	303	57	that	that	SCONJ
iajs-3717	303	58	for	for	ADP
iajs-3717	303	59	all	all	DET
iajs-3717	303	60	𝜏	𝜏	DET
iajs-3717	303	61	≥	≥	NOUN
iajs-3717	303	62	0	0	NUM
iajs-3717	303	63	and	and	CCONJ
iajs-3717	303	64	the	the	DET
iajs-3717	303	65	data	datum	NOUN
iajs-3717	303	66	provided	provide	VERB
iajs-3717	303	67	the	the	DET
iajs-3717	303	68	solution	solution	NOUN
iajs-3717	303	69	of	of	ADP
iajs-3717	303	70	system	system	NOUN
iajs-3717	303	71	(	(	PUNCT
iajs-3717	303	72	2	2	X
iajs-3717	303	73	)	)	PUNCT
iajs-3717	303	74	has	have	VERB
iajs-3717	303	75	globally	globally	ADV
iajs-3717	303	76	asymptotically	asymptotically	ADV
iajs-3717	303	77	stable	stable	ADJ
iajs-3717	303	78	𝐹1	𝐹1	NOUN
iajs-3717	303	79	as	as	SCONJ
iajs-3717	303	80	shown	show	VERB
iajs-3717	303	81	in	in	ADP
iajs-3717	303	82	figure	figure	NOUN
iajs-3717	303	83	1	1	NUM
iajs-3717	303	84	.	.	PUNCT
iajs-3717	303	85	figure	figure	NOUN
iajs-3717	303	86	1	1	NUM
iajs-3717	303	87	.	.	PUNCT
iajs-3717	304	1	the	the	DET
iajs-3717	304	2	system	system	NOUN
iajs-3717	304	3	's	's	PART
iajs-3717	304	4	(	(	PUNCT
iajs-3717	304	5	2	2	NUM
iajs-3717	304	6	)	)	PUNCT
iajs-3717	304	7	trajectory	trajectory	NOUN
iajs-3717	304	8	based	base	VERB
iajs-3717	304	9	on	on	ADP
iajs-3717	304	10	the	the	DET
iajs-3717	304	11	data	datum	NOUN
iajs-3717	304	12	provided	provide	VERB
iajs-3717	304	13	in	in	ADP
iajs-3717	304	14	equation	equation	NOUN
iajs-3717	304	15	(	(	PUNCT
iajs-3717	304	16	55	55	NUM
iajs-3717	304	17	)	)	PUNCT
iajs-3717	304	18	.	.	PUNCT
iajs-3717	305	1	(	(	PUNCT
iajs-3717	305	2	a	a	X
iajs-3717	305	3	)	)	PUNCT
iajs-3717	305	4	the	the	DET
iajs-3717	305	5	system	system	NOUN
iajs-3717	305	6	's	's	PART
iajs-3717	305	7	(	(	PUNCT
iajs-3717	305	8	2	2	NUM
iajs-3717	305	9	)	)	PUNCT
iajs-3717	305	10	time	time	NOUN
iajs-3717	305	11	series	series	NOUN
iajs-3717	305	12	gradually	gradually	ADV
iajs-3717	305	13	converge	converge	VERB
iajs-3717	305	14	to	to	ADP
iajs-3717	305	15	𝐹1	𝐹1	PROPN
iajs-3717	305	16	.	.	PUNCT
iajs-3717	306	1	(	(	PUNCT
iajs-3717	306	2	b	b	X
iajs-3717	306	3	)	)	PUNCT
iajs-3717	306	4	3d	3d	NOUN
iajs-3717	306	5	phase	phase	NOUN
iajs-3717	306	6	diagram	diagram	NOUN
iajs-3717	306	7	representing	represent	VERB
iajs-3717	306	8	the	the	DET
iajs-3717	306	9	globally	globally	ADV
iajs-3717	306	10	asymptotic	asymptotic	ADJ
iajs-3717	306	11	stability	stability	NOUN
iajs-3717	306	12	of	of	ADP
iajs-3717	306	13	point	point	NOUN
iajs-3717	306	14	𝐹1	𝐹1	NOUN
iajs-3717	306	15	.	.	PUNCT
iajs-3717	307	1	it	it	PRON
iajs-3717	307	2	is	be	AUX
iajs-3717	307	3	observed	observe	VERB
iajs-3717	307	4	that	that	SCONJ
iajs-3717	307	5	the	the	DET
iajs-3717	307	6	same	same	ADJ
iajs-3717	307	7	data	datum	NOUN
iajs-3717	307	8	from	from	ADP
iajs-3717	307	9	equation	equation	NOUN
iajs-3717	307	10	(	(	PUNCT
iajs-3717	307	11	55	55	NUM
iajs-3717	307	12	)	)	PUNCT
iajs-3717	307	13	,	,	PUNCT
iajs-3717	307	14	with	with	ADP
iajs-3717	307	15	𝑐	𝑐	PROPN
iajs-3717	307	16	=	=	SYM
iajs-3717	307	17	0.02	0.02	NUM
iajs-3717	307	18	and	and	CCONJ
iajs-3717	307	19	ℎ	ℎ	PROPN
iajs-3717	307	20	=	=	SYM
iajs-3717	307	21	0.001	0.001	NUM
iajs-3717	307	22	system	system	NOUN
iajs-3717	307	23	(	(	PUNCT
iajs-3717	307	24	2	2	X
iajs-3717	307	25	)	)	PUNCT
iajs-3717	307	26	exhibits	exhibit	VERB
iajs-3717	307	27	global	global	ADJ
iajs-3717	307	28	asymptotic	asymptotic	ADJ
iajs-3717	307	29	stability	stability	NOUN
iajs-3717	307	30	for𝐹2	for𝐹2	VERB
iajs-3717	307	31	as	as	SCONJ
iajs-3717	307	32	depicted	depict	VERB
iajs-3717	307	33	in	in	ADP
iajs-3717	307	34	figure	figure	NOUN
iajs-3717	307	35	2	2	NUM
iajs-3717	307	36	.	.	PUNCT
iajs-3717	307	37	figure	figure	NOUN
iajs-3717	307	38	2	2	NUM
iajs-3717	307	39	.	.	PUNCT
iajs-3717	308	1	the	the	DET
iajs-3717	308	2	system	system	NOUN
iajs-3717	308	3	's	's	PART
iajs-3717	308	4	(	(	PUNCT
iajs-3717	308	5	2	2	NUM
iajs-3717	308	6	)	)	PUNCT
iajs-3717	308	7	trajectory	trajectory	NOUN
iajs-3717	308	8	based	base	VERB
iajs-3717	308	9	on	on	ADP
iajs-3717	308	10	the	the	DET
iajs-3717	308	11	data	datum	NOUN
iajs-3717	308	12	provided	provide	VERB
iajs-3717	308	13	in	in	ADP
iajs-3717	308	14	equation	equation	NOUN
iajs-3717	308	15	(	(	PUNCT
iajs-3717	308	16	55	55	NUM
iajs-3717	308	17	)	)	PUNCT
iajs-3717	308	18	with	with	ADP
iajs-3717	308	19	𝑐	𝑐	PROPN
iajs-3717	308	20	=	=	SYM
iajs-3717	308	21	0.02	0.02	NUM
iajs-3717	308	22	and	and	CCONJ
iajs-3717	308	23	ℎ	ℎ	X
iajs-3717	308	24	=	=	NOUN
iajs-3717	308	25	0.001	0.001	NUM
iajs-3717	308	26	.(a	.(a	PUNCT
iajs-3717	308	27	)	)	PUNCT
iajs-3717	309	1	the	the	DET
iajs-3717	309	2	system	system	NOUN
iajs-3717	309	3	's	's	PART
iajs-3717	309	4	(	(	PUNCT
iajs-3717	309	5	2	2	NUM
iajs-3717	309	6	)	)	PUNCT
iajs-3717	309	7	time	time	NOUN
iajs-3717	309	8	series	series	NOUN
iajs-3717	309	9	gradually	gradually	ADV
iajs-3717	309	10	converge	converge	VERB
iajs-3717	309	11	to	to	ADP
iajs-3717	309	12	𝐹2	𝐹2	PROPN
iajs-3717	309	13	.	.	PUNCT
iajs-3717	310	1	(	(	PUNCT
iajs-3717	310	2	b	b	X
iajs-3717	310	3	)	)	PUNCT
iajs-3717	310	4	3d	3d	NOUN
iajs-3717	310	5	phase	phase	NOUN
iajs-3717	310	6	diagram	diagram	NOUN
iajs-3717	310	7	representing	represent	VERB
iajs-3717	310	8	the	the	DET
iajs-3717	310	9	globally	globally	ADV
iajs-3717	310	10	asymptotic	asymptotic	ADJ
iajs-3717	310	11	stability	stability	NOUN
iajs-3717	310	12	of	of	ADP
iajs-3717	310	13	point	point	NOUN
iajs-3717	310	14	𝐹2	𝐹2	PROPN
iajs-3717	310	15	.	.	PUNCT
iajs-3717	311	1	here	here	ADV
iajs-3717	311	2	,	,	PUNCT
iajs-3717	311	3	we	we	PRON
iajs-3717	311	4	discuss	discuss	VERB
iajs-3717	311	5	the	the	DET
iajs-3717	311	6	impact	impact	NOUN
iajs-3717	311	7	of	of	ADP
iajs-3717	311	8	time	time	NOUN
iajs-3717	311	9	delays	delay	NOUN
iajs-3717	311	10	on	on	ADP
iajs-3717	311	11	the	the	DET
iajs-3717	311	12	behavior	behavior	NOUN
iajs-3717	311	13	of	of	ADP
iajs-3717	311	14	the	the	DET
iajs-3717	311	15	system	system	NOUN
iajs-3717	311	16	(	(	PUNCT
iajs-3717	311	17	2	2	NUM
iajs-3717	311	18	)	)	PUNCT
iajs-3717	311	19	near	near	ADP
iajs-3717	311	20	the	the	DET
iajs-3717	311	21	𝐹3	𝐹3	PROPN
iajs-3717	311	22	point	point	NOUN
iajs-3717	311	23	it	it	PRON
iajs-3717	311	24	is	be	AUX
iajs-3717	311	25	noticed	notice	VERB
iajs-3717	311	26	that	that	SCONJ
iajs-3717	311	27	the	the	DET
iajs-3717	311	28	conditions	condition	NOUN
iajs-3717	311	29	of	of	ADP
iajs-3717	311	30	theorem	theorem	ADJ
iajs-3717	311	31	2	2	NUM
iajs-3717	311	32	are	be	AUX
iajs-3717	311	33	met	meet	VERB
iajs-3717	311	34	for	for	ADP
iajs-3717	311	35	the	the	DET
iajs-3717	311	36	parameters	parameter	NOUN
iajs-3717	311	37	in	in	ADP
iajs-3717	311	38	the	the	DET
iajs-3717	311	39	data	datum	NOUN
iajs-3717	311	40	of	of	ADP
iajs-3717	311	41	equation	equation	NOUN
iajs-3717	311	42	(	(	PUNCT
iajs-3717	311	43	55	55	NUM
iajs-3717	311	44	)	)	PUNCT
iajs-3717	311	45	with	with	ADP
iajs-3717	311	46	=	=	PROPN
iajs-3717	311	47	0.02	0.02	NUM
iajs-3717	311	48	.	.	PUNCT
iajs-3717	312	1	it	it	PRON
iajs-3717	312	2	is	be	AUX
iajs-3717	312	3	observed	observe	VERB
iajs-3717	312	4	that	that	SCONJ
iajs-3717	312	5	when	when	SCONJ
iajs-3717	312	6	𝜏	𝜏	X
iajs-3717	312	7	=	=	SYM
iajs-3717	312	8	15	15	NUM
iajs-3717	312	9	the	the	DET
iajs-3717	312	10	𝐹3	𝐹3	PROPN
iajs-3717	312	11	point	point	NOUN
iajs-3717	312	12	is	be	AUX
iajs-3717	312	13	asymptotic	asymptotic	ADJ
iajs-3717	312	14	stable	stable	ADJ
iajs-3717	312	15	as	as	SCONJ
iajs-3717	312	16	shown	show	VERB
iajs-3717	312	17	in	in	ADP
iajs-3717	312	18	fig	fig	NOUN
iajs-3717	312	19	.	.	PUNCT
iajs-3717	313	1	(	(	PUNCT
iajs-3717	313	2	3	3	X
iajs-3717	313	3	)	)	PUNCT
iajs-3717	313	4	while	while	SCONJ
iajs-3717	313	5	for	for	ADP
iajs-3717	313	6	𝜏	𝜏	NOUN
iajs-3717	313	7	=	=	SYM
iajs-3717	313	8	τ0	τ0	NOUN
iajs-3717	313	9	=	=	PUNCT
iajs-3717	313	10	45	45	NUM
iajs-3717	313	11	a	a	DET
iajs-3717	313	12	hopf	hopf	ADJ
iajs-3717	313	13	bifurcation	bifurcation	NOUN
iajs-3717	313	14	occurs	occur	VERB
iajs-3717	313	15	at	at	ADP
iajs-3717	313	16	𝐹3	𝐹3	PROPN
iajs-3717	313	17	as	as	SCONJ
iajs-3717	313	18	shown	show	VERB
iajs-3717	313	19	in	in	ADP
iajs-3717	313	20	figure	figure	NOUN
iajs-3717	313	21	4	4	NUM
iajs-3717	313	22	.	.	PUNCT
iajs-3717	314	1	on	on	ADP
iajs-3717	314	2	other	other	ADJ
iajs-3717	314	3	hand	hand	NOUN
iajs-3717	314	4	for	for	ADP
iajs-3717	314	5	τ	τ	PROPN
iajs-3717	314	6	=	=	SYM
iajs-3717	314	7	60	60	PROPN
iajs-3717	314	8	>	>	SYM
iajs-3717	314	9	τ0	τ0	NOUN
iajs-3717	314	10	=	=	PUNCT
iajs-3717	314	11	45	45	NUM
iajs-3717	314	12	increasing	increase	VERB
iajs-3717	314	13	period	period	NOUN
iajs-3717	314	14	as	as	ADP
iajs-3717	314	15	𝜏	𝜏	DET
iajs-3717	314	16	increases	increase	NOUN
iajs-3717	314	17	as	as	SCONJ
iajs-3717	314	18	shown	show	VERB
iajs-3717	314	19	in	in	ADP
iajs-3717	314	20	figure	figure	NOUN
iajs-3717	314	21	5	5	NUM
iajs-3717	314	22	.	.	PUNCT
iajs-3717	314	23	ihjpas	ihjpas	PROPN
iajs-3717	314	24	.	.	PUNCT
iajs-3717	315	1	2025,38(2	2025,38(2	PROPN
iajs-3717	315	2	)	)	PUNCT
iajs-3717	316	1	373	373	NUM
iajs-3717	316	2	figure	figure	VERB
iajs-3717	316	3	3.the	3.the	PRON
iajs-3717	316	4	system	system	NOUN
iajs-3717	316	5	's	's	PART
iajs-3717	316	6	(	(	PUNCT
iajs-3717	316	7	2	2	NUM
iajs-3717	316	8	)	)	PUNCT
iajs-3717	316	9	trajectory	trajectory	NOUN
iajs-3717	316	10	based	base	VERB
iajs-3717	316	11	on	on	ADP
iajs-3717	316	12	the	the	DET
iajs-3717	316	13	data	datum	NOUN
iajs-3717	316	14	provided	provide	VERB
iajs-3717	316	15	in	in	ADP
iajs-3717	316	16	equation	equation	NOUN
iajs-3717	316	17	(	(	PUNCT
iajs-3717	316	18	55	55	NUM
iajs-3717	316	19	)	)	PUNCT
iajs-3717	316	20	with	with	ADP
iajs-3717	316	21	𝑐	𝑐	PROPN
iajs-3717	316	22	=	=	SYM
iajs-3717	316	23	0.02	0.02	NUM
iajs-3717	316	24	and	and	CCONJ
iajs-3717	316	25	𝜏	𝜏	NOUN
iajs-3717	316	26	=	=	SYM
iajs-3717	316	27	15	15	NUM
iajs-3717	316	28	(	(	PUNCT
iajs-3717	316	29	a)the	a)the	DET
iajs-3717	316	30	system	system	NOUN
iajs-3717	316	31	's	's	PART
iajs-3717	316	32	(	(	PUNCT
iajs-3717	316	33	2	2	NUM
iajs-3717	316	34	)	)	PUNCT
iajs-3717	316	35	time	time	NOUN
iajs-3717	316	36	series	series	NOUN
iajs-3717	316	37	gradually	gradually	ADV
iajs-3717	316	38	converge	converge	VERB
iajs-3717	316	39	to	to	ADP
iajs-3717	316	40	𝐹3	𝐹3	PROPN
iajs-3717	316	41	.	.	PUNCT
iajs-3717	317	1	(	(	PUNCT
iajs-3717	317	2	b	b	X
iajs-3717	317	3	)	)	PUNCT
iajs-3717	317	4	3d	3d	NOUN
iajs-3717	317	5	phase	phase	NOUN
iajs-3717	317	6	diagram	diagram	NOUN
iajs-3717	317	7	representing	represent	VERB
iajs-3717	317	8	the	the	DET
iajs-3717	317	9	globally	globally	ADV
iajs-3717	317	10	asymptotic	asymptotic	ADJ
iajs-3717	317	11	stability	stability	NOUN
iajs-3717	317	12	of	of	ADP
iajs-3717	317	13	point	point	NOUN
iajs-3717	317	14	.	.	PUNCT
iajs-3717	318	1	figure	figure	VERB
iajs-3717	318	2	4.the	4.the	DET
iajs-3717	318	3	system	system	NOUN
iajs-3717	318	4	's	's	PART
iajs-3717	318	5	(	(	PUNCT
iajs-3717	318	6	2	2	NUM
iajs-3717	318	7	)	)	PUNCT
iajs-3717	318	8	trajectory	trajectory	NOUN
iajs-3717	318	9	based	base	VERB
iajs-3717	318	10	on	on	ADP
iajs-3717	318	11	the	the	DET
iajs-3717	318	12	data	datum	NOUN
iajs-3717	318	13	provided	provide	VERB
iajs-3717	318	14	in	in	ADP
iajs-3717	318	15	equation(55	equation(55	NOUN
iajs-3717	318	16	)	)	PUNCT
iajs-3717	318	17	with	with	ADP
iajs-3717	318	18	𝑐	𝑐	PROPN
iajs-3717	318	19	=	=	SYM
iajs-3717	318	20	0.02	0.02	NUM
iajs-3717	318	21	𝑎𝑛𝑑	𝑎𝑛𝑑	NOUN
iajs-3717	318	22	𝜏	𝜏	PROPN
iajs-3717	318	23	=	=	NOUN
iajs-3717	318	24	τ0	τ0	NOUN
iajs-3717	318	25	=	=	PUNCT
iajs-3717	318	26	45	45	NUM
iajs-3717	318	27	.(a	.(a	SYM
iajs-3717	318	28	)	)	PUNCT
iajs-3717	318	29	a	a	DET
iajs-3717	318	30	periodic	periodic	ADJ
iajs-3717	318	31	solution	solution	NOUN
iajs-3717	318	32	's	's	PART
iajs-3717	318	33	existence	existence	NOUN
iajs-3717	318	34	near	near	ADP
iajs-3717	318	35	𝐹3	𝐹3	PROPN
iajs-3717	318	36	near	near	ADP
iajs-3717	318	37	𝐹3	𝐹3	PROPN
iajs-3717	318	38	(	(	PUNCT
iajs-3717	318	39	b	b	NOUN
iajs-3717	318	40	)	)	PUNCT
iajs-3717	318	41	3d	3d	NOUN
iajs-3717	318	42	periodic	periodic	ADJ
iajs-3717	318	43	solution	solution	NOUN
iajs-3717	318	44	.	.	PUNCT
iajs-3717	319	1	figure	figure	NOUN
iajs-3717	319	2	5	5	NUM
iajs-3717	319	3	.	.	PUNCT
iajs-3717	320	1	the	the	DET
iajs-3717	320	2	system	system	NOUN
iajs-3717	320	3	's	's	PART
iajs-3717	320	4	(	(	PUNCT
iajs-3717	320	5	2	2	NUM
iajs-3717	320	6	)	)	PUNCT
iajs-3717	320	7	trajectory	trajectory	NOUN
iajs-3717	320	8	based	base	VERB
iajs-3717	320	9	on	on	ADP
iajs-3717	320	10	the	the	DET
iajs-3717	320	11	data	datum	NOUN
iajs-3717	320	12	provided	provide	VERB
iajs-3717	320	13	in	in	ADP
iajs-3717	320	14	equation(55	equation(55	NOUN
iajs-3717	320	15	)	)	PUNCT
iajs-3717	320	16	with	with	ADP
iajs-3717	320	17	𝑐	𝑐	PROPN
iajs-3717	320	18	=	=	SYM
iajs-3717	320	19	0.02	0.02	NUM
iajs-3717	320	20	and	and	CCONJ
iajs-3717	320	21	τ	τ	X
iajs-3717	320	22	=	=	PUNCT
iajs-3717	320	23	60	60	NUM
iajs-3717	320	24	>	>	SYM
iajs-3717	320	25	τ0	τ0	NOUN
iajs-3717	320	26	=	=	PUNCT
iajs-3717	320	27	45	45	NUM
iajs-3717	320	28	.(a	.(a	SYM
iajs-3717	320	29	)	)	PUNCT
iajs-3717	320	30	a	a	DET
iajs-3717	320	31	periodic	periodic	ADJ
iajs-3717	320	32	solution	solution	NOUN
iajs-3717	320	33	's	's	PART
iajs-3717	320	34	existence	existence	NOUN
iajs-3717	320	35	near	near	ADP
iajs-3717	320	36	𝐹3	𝐹3	PROPN
iajs-3717	320	37	(	(	PUNCT
iajs-3717	320	38	b	b	NOUN
iajs-3717	320	39	)	)	PUNCT
iajs-3717	320	40	3d	3d	NOUN
iajs-3717	320	41	periodic	periodic	ADJ
iajs-3717	320	42	solution	solution	NOUN
iajs-3717	320	43	.	.	PUNCT
iajs-3717	321	1	4	4	X
iajs-3717	321	2	.	.	X
iajs-3717	321	3	conclusions	conclusion	NOUN
iajs-3717	321	4	in	in	ADP
iajs-3717	321	5	this	this	DET
iajs-3717	321	6	study	study	NOUN
iajs-3717	321	7	,	,	PUNCT
iajs-3717	321	8	a	a	DET
iajs-3717	321	9	delayed	delay	VERB
iajs-3717	321	10	predator	predator	NOUN
iajs-3717	321	11	-	-	PUNCT
iajs-3717	321	12	prey	prey	NOUN
iajs-3717	321	13	model	model	NOUN
iajs-3717	321	14	with	with	ADP
iajs-3717	321	15	harvests	harvest	NOUN
iajs-3717	321	16	is	be	AUX
iajs-3717	321	17	proposed	propose	VERB
iajs-3717	321	18	.	.	PUNCT
iajs-3717	322	1	our	our	PRON
iajs-3717	322	2	aim	aim	NOUN
iajs-3717	322	3	is	be	AUX
iajs-3717	322	4	to	to	PART
iajs-3717	322	5	understand	understand	VERB
iajs-3717	322	6	how	how	SCONJ
iajs-3717	322	7	the	the	DET
iajs-3717	322	8	stability	stability	NOUN
iajs-3717	322	9	of	of	ADP
iajs-3717	322	10	the	the	DET
iajs-3717	322	11	model	model	NOUN
iajs-3717	322	12	is	be	AUX
iajs-3717	322	13	affected	affect	VERB
iajs-3717	322	14	by	by	ADP
iajs-3717	322	15	the	the	DET
iajs-3717	322	16	latent	latent	ADJ
iajs-3717	322	17	time	time	NOUN
iajs-3717	322	18	of	of	ADP
iajs-3717	322	19	predation	predation	NOUN
iajs-3717	322	20	and	and	CCONJ
iajs-3717	322	21	the	the	DET
iajs-3717	322	22	gestation	gestation	NOUN
iajs-3717	322	23	period	period	NOUN
iajs-3717	322	24	of	of	ADP
iajs-3717	322	25	the	the	DET
iajs-3717	322	26	predators	predator	NOUN
iajs-3717	322	27	.	.	PUNCT
iajs-3717	323	1	all	all	DET
iajs-3717	323	2	properties	property	NOUN
iajs-3717	323	3	of	of	ADP
iajs-3717	323	4	the	the	DET
iajs-3717	323	5	solution	solution	NOUN
iajs-3717	323	6	,	,	PUNCT
iajs-3717	323	7	such	such	ADJ
iajs-3717	323	8	as	as	ADP
iajs-3717	323	9	positivity	positivity	NOUN
iajs-3717	323	10	and	and	CCONJ
iajs-3717	323	11	boundedness	boundedness	NOUN
iajs-3717	323	12	,	,	PUNCT
iajs-3717	323	13	were	be	AUX
iajs-3717	323	14	investigated	investigate	VERB
iajs-3717	323	15	.	.	PUNCT
iajs-3717	324	1	it	it	PRON
iajs-3717	324	2	was	be	AUX
iajs-3717	324	3	found	find	VERB
iajs-3717	324	4	that	that	SCONJ
iajs-3717	324	5	the	the	DET
iajs-3717	324	6	system	system	NOUN
iajs-3717	324	7	(	(	PUNCT
iajs-3717	324	8	2	2	X
iajs-3717	324	9	)	)	PUNCT
iajs-3717	324	10	can	can	AUX
iajs-3717	324	11	have	have	VERB
iajs-3717	324	12	four	four	NUM
iajs-3717	324	13	equilibrium	equilibrium	NOUN
iajs-3717	324	14	points	point	NOUN
iajs-3717	324	15	.	.	PUNCT
iajs-3717	325	1	the	the	DET
iajs-3717	325	2	stability	stability	NOUN
iajs-3717	325	3	analysis	analysis	NOUN
iajs-3717	325	4	has	have	AUX
iajs-3717	325	5	shown	show	VERB
iajs-3717	325	6	that	that	SCONJ
iajs-3717	325	7	the	the	DET
iajs-3717	325	8	discrete	discrete	ADJ
iajs-3717	325	9	time	time	NOUN
iajs-3717	325	10	delay	delay	NOUN
iajs-3717	325	11	has	have	VERB
iajs-3717	325	12	no	no	DET
iajs-3717	325	13	effect	effect	NOUN
iajs-3717	325	14	on	on	ADP
iajs-3717	325	15	the	the	DET
iajs-3717	325	16	stability	stability	NOUN
iajs-3717	325	17	ihjpas	ihjpa	VERB
iajs-3717	325	18	.	.	PUNCT
iajs-3717	326	1	2025,38(2	2025,38(2	PROPN
iajs-3717	326	2	)	)	PUNCT
iajs-3717	326	3	374	374	NUM
iajs-3717	326	4	of	of	ADP
iajs-3717	326	5	the	the	DET
iajs-3717	326	6	axial	axial	ADJ
iajs-3717	326	7	equilibrium	equilibrium	NOUN
iajs-3717	326	8	point	point	NOUN
iajs-3717	326	9	and	and	CCONJ
iajs-3717	326	10	the	the	DET
iajs-3717	326	11	planer	planer	NOUN
iajs-3717	326	12	equilibrium	equilibrium	NOUN
iajs-3717	326	13	point	point	NOUN
iajs-3717	326	14	,	,	PUNCT
iajs-3717	326	15	so	so	CCONJ
iajs-3717	326	16	it	it	PRON
iajs-3717	326	17	is	be	AUX
iajs-3717	326	18	still	still	ADV
iajs-3717	326	19	locally	locally	ADV
iajs-3717	326	20	asymptotically	asymptotically	ADV
iajs-3717	326	21	stable	stable	ADJ
iajs-3717	326	22	for	for	ADP
iajs-3717	326	23	all	all	DET
iajs-3717	326	24	𝜏≥0	𝜏≥0	PROPN
iajs-3717	326	25	.	.	PUNCT
iajs-3717	327	1	it	it	PRON
iajs-3717	327	2	has	have	AUX
iajs-3717	327	3	been	be	AUX
iajs-3717	327	4	demonstrated	demonstrate	VERB
iajs-3717	327	5	that	that	SCONJ
iajs-3717	327	6	the	the	DET
iajs-3717	327	7	coexistence	coexistence	NOUN
iajs-3717	327	8	equilibrium	equilibrium	NOUN
iajs-3717	327	9	point	point	NOUN
iajs-3717	327	10	is	be	AUX
iajs-3717	327	11	characterized	characterize	VERB
iajs-3717	327	12	by	by	ADP
iajs-3717	327	13	asymptotic	asymptotic	ADJ
iajs-3717	327	14	stability	stability	NOUN
iajs-3717	327	15	when	when	SCONJ
iajs-3717	327	16	the	the	DET
iajs-3717	327	17	delay	delay	NOUN
iajs-3717	327	18	does	do	AUX
iajs-3717	327	19	not	not	PART
iajs-3717	327	20	approach	approach	VERB
iajs-3717	327	21	a	a	DET
iajs-3717	327	22	critical	critical	ADJ
iajs-3717	327	23	value	value	NOUN
iajs-3717	327	24	of	of	ADP
iajs-3717	327	25	,	,	PUNCT
iajs-3717	327	26	τ-0	τ-0	PROPN
iajs-3717	327	27	..	..	PUNCT
iajs-3717	327	28	however	however	ADV
iajs-3717	327	29	,	,	PUNCT
iajs-3717	327	30	a	a	DET
iajs-3717	327	31	hopf	hopf	ADJ
iajs-3717	327	32	bifurcation	bifurcation	NOUN
iajs-3717	327	33	occurs	occur	VERB
iajs-3717	327	34	when	when	SCONJ
iajs-3717	327	35	=	=	NOUN
iajs-3717	327	36	,	,	PUNCT
iajs-3717	327	37	τ-0	τ-0	NUM
iajs-3717	327	38	.	.	PUNCT
iajs-3717	328	1	,	,	PUNCT
iajs-3717	328	2	making	make	VERB
iajs-3717	328	3	it	it	PRON
iajs-3717	328	4	an	an	DET
iajs-3717	328	5	unstable	unstable	ADJ
iajs-3717	328	6	point	point	NOUN
iajs-3717	328	7	,	,	PUNCT
iajs-3717	328	8	and	and	CCONJ
iajs-3717	328	9	the	the	DET
iajs-3717	328	10	solution	solution	NOUN
iajs-3717	328	11	approaches	approach	VERB
iajs-3717	328	12	asymptotically	asymptotically	ADV
iajs-3717	328	13	to	to	ADP
iajs-3717	328	14	periodic	periodic	ADJ
iajs-3717	328	15	dynamics	dynamic	NOUN
iajs-3717	328	16	for	for	ADP
iajs-3717	328	17	τ>,τ-0	τ>,τ-0	PROPN
iajs-3717	328	18	..	..	PUNCT
iajs-3717	328	19	additionally	additionally	ADV
iajs-3717	328	20	,	,	PUNCT
iajs-3717	328	21	the	the	DET
iajs-3717	328	22	center	center	NOUN
iajs-3717	328	23	manifold	manifold	ADJ
iajs-3717	328	24	theorem	theorem	NOUN
iajs-3717	328	25	was	be	AUX
iajs-3717	328	26	applied	apply	VERB
iajs-3717	328	27	to	to	PART
iajs-3717	328	28	investigate	investigate	VERB
iajs-3717	328	29	the	the	DET
iajs-3717	328	30	stability	stability	NOUN
iajs-3717	328	31	and	and	CCONJ
iajs-3717	328	32	direction	direction	NOUN
iajs-3717	328	33	of	of	ADP
iajs-3717	328	34	bifurcating	bifurcate	VERB
iajs-3717	328	35	periodic	periodic	ADJ
iajs-3717	328	36	dynamics	dynamic	NOUN
iajs-3717	328	37	.	.	PUNCT
iajs-3717	329	1	finally	finally	ADV
iajs-3717	329	2	,	,	PUNCT
iajs-3717	329	3	the	the	DET
iajs-3717	329	4	matlab	matlab	PROPN
iajs-3717	329	5	program	program	NOUN
iajs-3717	329	6	is	be	AUX
iajs-3717	329	7	employed	employ	VERB
iajs-3717	329	8	for	for	ADP
iajs-3717	329	9	a	a	DET
iajs-3717	329	10	numerical	numerical	ADJ
iajs-3717	329	11	investigation	investigation	NOUN
iajs-3717	329	12	of	of	ADP
iajs-3717	329	13	the	the	DET
iajs-3717	329	14	system	system	NOUN
iajs-3717	329	15	's	's	PART
iajs-3717	329	16	global	global	ADJ
iajs-3717	329	17	dynamics	dynamic	NOUN
iajs-3717	329	18	.	.	PUNCT
iajs-3717	330	1	for	for	ADP
iajs-3717	330	2	the	the	DET
iajs-3717	330	3	given	give	VERB
iajs-3717	330	4	data	datum	NOUN
iajs-3717	330	5	in	in	ADP
iajs-3717	330	6	equation	equation	NOUN
iajs-3717	330	7	(	(	PUNCT
iajs-3717	330	8	55	55	NUM
iajs-3717	330	9	)	)	PUNCT
iajs-3717	330	10	,	,	PUNCT
iajs-3717	330	11	,	,	PUNCT
iajs-3717	330	12	-1	-1	INTJ
iajs-3717	330	13	.	.	PUNCT
iajs-3717	330	14	is	be	AUX
iajs-3717	330	15	globally	globally	ADV
iajs-3717	330	16	asymptotically	asymptotically	ADV
iajs-3717	330	17	stable	stable	ADJ
iajs-3717	330	18	.	.	PUNCT
iajs-3717	331	1	when	when	SCONJ
iajs-3717	331	2	the	the	DET
iajs-3717	331	3	same	same	ADJ
iajs-3717	331	4	data	datum	NOUN
iajs-3717	331	5	from	from	ADP
iajs-3717	331	6	equation	equation	NOUN
iajs-3717	331	7	(	(	PUNCT
iajs-3717	331	8	55	55	NUM
iajs-3717	331	9	)	)	PUNCT
iajs-3717	331	10	is	be	AUX
iajs-3717	331	11	used	use	VERB
iajs-3717	331	12	with	with	ADP
iajs-3717	331	13	=	=	PROPN
iajs-3717	331	14	0.02	0.02	NUM
iajs-3717	331	15	and	and	CCONJ
iajs-3717	331	16	ℎ=0.001	ℎ=0.001	NUM
iajs-3717	331	17	,	,	PUNCT
iajs-3717	331	18	it	it	PRON
iajs-3717	331	19	is	be	AUX
iajs-3717	331	20	observed	observe	VERB
iajs-3717	331	21	that	that	SCONJ
iajs-3717	331	22	,	,	PUNCT
iajs-3717	331	23	𝐹-2	𝐹-2	PROPN
iajs-3717	331	24	.	.	PUNCT
iajs-3717	332	1	is	be	AUX
iajs-3717	332	2	globally	globally	ADV
iajs-3717	332	3	asymptotically	asymptotically	ADV
iajs-3717	332	4	stable	stable	ADJ
iajs-3717	332	5	.	.	PUNCT
iajs-3717	333	1	for	for	ADP
iajs-3717	333	2	the	the	DET
iajs-3717	333	3	data	datum	NOUN
iajs-3717	333	4	in	in	ADP
iajs-3717	333	5	equation	equation	NOUN
iajs-3717	333	6	(	(	PUNCT
iajs-3717	333	7	55	55	NUM
iajs-3717	333	8	)	)	PUNCT
iajs-3717	333	9	with	with	ADP
iajs-3717	333	10	=	=	NOUN
iajs-3717	333	11	0.02	0.02	NUM
iajs-3717	333	12	,	,	PUNCT
iajs-3717	333	13	it	it	PRON
iajs-3717	333	14	is	be	AUX
iajs-3717	333	15	noted	note	VERB
iajs-3717	333	16	that	that	SCONJ
iajs-3717	333	17	,	,	PUNCT
iajs-3717	333	18	𝐹-3	𝐹-3	PROPN
iajs-3717	333	19	.	.	PUNCT
iajs-3717	333	20	is	be	AUX
iajs-3717	333	21	asymptotically	asymptotically	ADV
iajs-3717	333	22	stable	stable	ADJ
iajs-3717	333	23	when	when	SCONJ
iajs-3717	333	24	𝜏=15	𝜏=15	X
iajs-3717	333	25	.	.	PUNCT
iajs-3717	334	1	however	however	ADV
iajs-3717	334	2	,	,	PUNCT
iajs-3717	334	3	when	when	SCONJ
iajs-3717	334	4	,	,	PUNCT
iajs-3717	334	5	=	=	NOUN
iajs-3717	334	6	τ-0.=45	τ-0.=45	NOUN
iajs-3717	334	7	,	,	PUNCT
iajs-3717	334	8	a	a	DET
iajs-3717	334	9	hopf	hopf	ADJ
iajs-3717	334	10	bifurcation	bifurcation	NOUN
iajs-3717	334	11	occurs	occur	VERB
iajs-3717	334	12	.	.	PUNCT
iajs-3717	335	1	acknowledgements	acknowledgement	NOUN
iajs-3717	335	2	we	we	PRON
iajs-3717	335	3	would	would	AUX
iajs-3717	335	4	like	like	VERB
iajs-3717	335	5	to	to	PART
iajs-3717	335	6	express	express	VERB
iajs-3717	335	7	our	our	PRON
iajs-3717	335	8	gratitude	gratitude	NOUN
iajs-3717	335	9	other	other	ADJ
iajs-3717	335	10	referees	referee	NOUN
iajs-3717	335	11	for	for	ADP
iajs-3717	335	12	their	their	PRON
iajs-3717	335	13	valuable	valuable	ADJ
iajs-3717	335	14	comments	comment	NOUN
iajs-3717	335	15	and	and	CCONJ
iajs-3717	335	16	suggestions	suggestion	NOUN
iajs-3717	335	17	that	that	PRON
iajs-3717	335	18	led	lead	VERB
iajs-3717	335	19	to	to	ADP
iajs-3717	335	20	a	a	DET
iajs-3717	335	21	truly	truly	ADV
iajs-3717	335	22	significant	significant	ADJ
iajs-3717	335	23	improvement	improvement	NOUN
iajs-3717	335	24	of	of	ADP
iajs-3717	335	25	the	the	DET
iajs-3717	335	26	paper	paper	NOUN
iajs-3717	335	27	.	.	PUNCT
iajs-3717	336	1	conflict	conflict	NOUN
iajs-3717	336	2	of	of	ADP
iajs-3717	336	3	interest	interest	NOUN
iajs-3717	336	4	the	the	DET
iajs-3717	336	5	authors	author	NOUN
iajs-3717	336	6	declare	declare	VERB
iajs-3717	336	7	that	that	SCONJ
iajs-3717	336	8	there	there	PRON
iajs-3717	336	9	are	be	VERB
iajs-3717	336	10	no	no	DET
iajs-3717	336	11	competing	compete	VERB
iajs-3717	336	12	interests	interest	NOUN
iajs-3717	336	13	regarding	regard	VERB
iajs-3717	336	14	the	the	DET
iajs-3717	336	15	publication	publication	NOUN
iajs-3717	336	16	of	of	ADP
iajs-3717	336	17	this	this	DET
iajs-3717	336	18	paper	paper	NOUN
iajs-3717	336	19	.	.	PUNCT
iajs-3717	337	1	funding	fund	VERB
iajs-3717	337	2	this	this	DET
iajs-3717	337	3	work	work	NOUN
iajs-3717	337	4	is	be	AUX
iajs-3717	337	5	not	not	PART
iajs-3717	337	6	supported	support	VERB
iajs-3717	337	7	by	by	ADP
iajs-3717	337	8	any	any	DET
iajs-3717	337	9	the	the	DET
iajs-3717	337	10	foundation	foundation	NOUN
iajs-3717	337	11	.	.	PUNCT
iajs-3717	338	1	references	reference	NOUN
iajs-3717	338	2	1	1	NUM
iajs-3717	338	3	.	.	X
iajs-3717	338	4	lotka	lotka	PROPN
iajs-3717	338	5	aj	aj	PROPN
iajs-3717	338	6	.	.	PUNCT
iajs-3717	339	1	elements	element	NOUN
iajs-3717	339	2	of	of	ADP
iajs-3717	339	3	physical	physical	ADJ
iajs-3717	339	4	biology	biology	NOUN
iajs-3717	339	5	.	.	PUNCT
iajs-3717	340	1	baltimore	baltimore	PROPN
iajs-3717	340	2	:	:	PUNCT
iajs-3717	340	3	williams	williams	PROPN
iajs-3717	340	4	&	&	CCONJ
iajs-3717	340	5	wilkins	wilkins	PROPN
iajs-3717	340	6	;	;	PUNCT
iajs-3717	340	7	1925	1925	NUM
iajs-3717	340	8	.	.	PUNCT
iajs-3717	341	1	2	2	X
iajs-3717	341	2	.	.	X
iajs-3717	341	3	volterra	volterra	PROPN
iajs-3717	341	4	v.	v.	ADP
iajs-3717	341	5	variazioni	variazioni	PROPN
iajs-3717	341	6	e	e	X
iajs-3717	341	7	fluttuazioni	fluttuazioni	X
iajs-3717	341	8	del	del	X
iajs-3717	341	9	numero	numero	PROPN
iajs-3717	341	10	d'individui	d'individui	PROPN
iajs-3717	341	11	in	in	ADP
iajs-3717	341	12	specie	specie	PROPN
iajs-3717	341	13	animali	animali	PROPN
iajs-3717	341	14	conviventi	conviventi	PROPN
iajs-3717	341	15	.	.	PUNCT
iajs-3717	342	1	rome	rome	PROPN
iajs-3717	342	2	:	:	PUNCT
iajs-3717	343	1	società	società	PROPN
iajs-3717	343	2	anonima	anonima	PROPN
iajs-3717	343	3	tipografica	tipografica	PROPN
iajs-3717	343	4	"	"	PUNCT
iajs-3717	343	5	leonardo	leonardo	PROPN
iajs-3717	343	6	da	da	PROPN
iajs-3717	343	7	vinci	vinci	PROPN
iajs-3717	343	8	"	"	PUNCT
iajs-3717	343	9	;	;	PUNCT
iajs-3717	343	10	1927	1927	NUM
iajs-3717	343	11	.	.	PUNCT
iajs-3717	344	1	3	3	X
iajs-3717	344	2	.	.	X
iajs-3717	344	3	anderson	anderson	PROPN
iajs-3717	344	4	rm	rm	PROPN
iajs-3717	344	5	,	,	PUNCT
iajs-3717	344	6	may	may	PROPN
iajs-3717	344	7	rm	rm	PROPN
iajs-3717	344	8	.	.	PUNCT
iajs-3717	345	1	the	the	DET
iajs-3717	345	2	invasion	invasion	NOUN
iajs-3717	345	3	,	,	PUNCT
iajs-3717	345	4	persistence	persistence	NOUN
iajs-3717	345	5	,	,	PUNCT
iajs-3717	345	6	and	and	CCONJ
iajs-3717	345	7	spread	spread	VERB
iajs-3717	345	8	of	of	ADP
iajs-3717	345	9	infectious	infectious	ADJ
iajs-3717	345	10	diseases	disease	NOUN
iajs-3717	345	11	within	within	ADP
iajs-3717	345	12	animal	animal	NOUN
iajs-3717	345	13	and	and	CCONJ
iajs-3717	345	14	plant	plant	NOUN
iajs-3717	345	15	communities	community	NOUN
iajs-3717	345	16	.	.	PUNCT
iajs-3717	346	1	philos	philos	PROPN
iajs-3717	347	1	trans	trans	PROPN
iajs-3717	347	2	r	r	PROPN
iajs-3717	347	3	soc	soc	PROPN
iajs-3717	347	4	lond	lond	PROPN
iajs-3717	347	5	b	b	PROPN
iajs-3717	347	6	biol	biol	PROPN
iajs-3717	347	7	sci	sci	PROPN
iajs-3717	347	8	.	.	PROPN
iajs-3717	347	9	1986;314(1167):533570	1986;314(1167):533570	NUM
iajs-3717	347	10	.	.	PUNCT
iajs-3717	348	1	https://doi.org/10.1098/rstb.1986.0072	https://doi.org/10.1098/rstb.1986.0072	NOUN
iajs-3717	348	2	4	4	NUM
iajs-3717	348	3	.	.	PUNCT
iajs-3717	349	1	al	al	PROPN
iajs-3717	349	2	-	-	PUNCT
iajs-3717	349	3	momen	momen	PROPN
iajs-3717	349	4	sm	sm	PROPN
iajs-3717	349	5	,	,	PUNCT
iajs-3717	349	6	naji	naji	PROPN
iajs-3717	349	7	rk	rk	PROPN
iajs-3717	349	8	.	.	PUNCT
iajs-3717	350	1	the	the	DET
iajs-3717	350	2	dynamics	dynamic	NOUN
iajs-3717	350	3	of	of	ADP
iajs-3717	350	4	modified	modify	VERB
iajs-3717	350	5	leslie	leslie	PROPN
iajs-3717	350	6	-	-	PUNCT
iajs-3717	350	7	gower	gower	PROPN
iajs-3717	350	8	predator	predator	NOUN
iajs-3717	350	9	-	-	PUNCT
iajs-3717	350	10	prey	prey	NOUN
iajs-3717	350	11	model	model	NOUN
iajs-3717	350	12	under	under	ADP
iajs-3717	350	13	the	the	DET
iajs-3717	350	14	influence	influence	NOUN
iajs-3717	350	15	of	of	ADP
iajs-3717	350	16	nonlinear	nonlinear	ADJ
iajs-3717	350	17	harvesting	harvesting	NOUN
iajs-3717	350	18	and	and	CCONJ
iajs-3717	350	19	fear	fear	NOUN
iajs-3717	350	20	effect	effect	NOUN
iajs-3717	350	21	.	.	PUNCT
iajs-3717	351	1	iraqi	iraqi	ADJ
iajs-3717	351	2	j	j	PROPN
iajs-3717	351	3	sci	sci	PROPN
iajs-3717	351	4	.	.	PUNCT
iajs-3717	352	1	2022;63(1):259	2022;63(1):259	NUM
iajs-3717	352	2	–	–	PUNCT
iajs-3717	352	3	282	282	NUM
iajs-3717	352	4	.	.	PUNCT
iajs-3717	352	5	https://doi.org/10.24996/ijs.2022.63.1.27	https://doi.org/10.24996/ijs.2022.63.1.27	PROPN
iajs-3717	353	1	5	5	X
iajs-3717	353	2	.	.	PUNCT
iajs-3717	353	3	dehingia	dehingia	PROPN
iajs-3717	353	4	k	k	PROPN
iajs-3717	353	5	,	,	PUNCT
iajs-3717	353	6	mohsen	mohsen	PROPN
iajs-3717	353	7	aa	aa	PROPN
iajs-3717	353	8	,	,	PUNCT
iajs-3717	353	9	alharbi	alharbi	PROPN
iajs-3717	353	10	sa	sa	PROPN
iajs-3717	353	11	,	,	PUNCT
iajs-3717	353	12	alsemiry	alsemiry	PROPN
iajs-3717	353	13	rd	rd	PROPN
iajs-3717	353	14	,	,	PUNCT
iajs-3717	353	15	rezapour	rezapour	PROPN
iajs-3717	353	16	s.	s.	PROPN
iajs-3717	353	17	dynamical	dynamical	ADJ
iajs-3717	353	18	behavior	behavior	NOUN
iajs-3717	353	19	of	of	ADP
iajs-3717	353	20	a	a	DET
iajs-3717	353	21	fractional	fractional	ADJ
iajs-3717	353	22	order	order	NOUN
iajs-3717	353	23	model	model	NOUN
iajs-3717	353	24	for	for	ADP
iajs-3717	353	25	within	within	ADP
iajs-3717	353	26	-	-	PUNCT
iajs-3717	353	27	host	host	NOUN
iajs-3717	353	28	sars	sar	NOUN
iajs-3717	353	29	-	-	PUNCT
iajs-3717	353	30	cov-2	cov-2	NOUN
iajs-3717	353	31	.	.	PUNCT
iajs-3717	354	1	mathematics	mathematic	NOUN
iajs-3717	354	2	.	.	PUNCT
iajs-3717	355	1	2022;10(13):2344	2022;10(13):2344	X
iajs-3717	355	2	.	.	PUNCT
iajs-3717	355	3	https://doi.org/10.3390/math10132344	https://doi.org/10.3390/math10132344	PROPN
iajs-3717	355	4	6	6	NUM
iajs-3717	355	5	.	.	PUNCT
iajs-3717	356	1	hussien	hussien	PROPN
iajs-3717	356	2	rm	rm	PROPN
iajs-3717	356	3	,	,	PUNCT
iajs-3717	356	4	naji	naji	PROPN
iajs-3717	356	5	rk	rk	PROPN
iajs-3717	356	6	.	.	PUNCT
iajs-3717	357	1	the	the	DET
iajs-3717	357	2	dynamics	dynamic	NOUN
iajs-3717	357	3	of	of	ADP
iajs-3717	357	4	a	a	DET
iajs-3717	357	5	delayed	delay	VERB
iajs-3717	357	6	ecological	ecological	ADJ
iajs-3717	357	7	model	model	NOUN
iajs-3717	357	8	with	with	ADP
iajs-3717	357	9	predator	predator	NOUN
iajs-3717	357	10	refuge	refuge	NOUN
iajs-3717	357	11	and	and	CCONJ
iajs-3717	357	12	cannibalism	cannibalism	NOUN
iajs-3717	357	13	.	.	PUNCT
iajs-3717	358	1	commun	commun	PROPN
iajs-3717	358	2	math	math	PROPN
iajs-3717	358	3	biol	biol	PROPN
iajs-3717	358	4	neurosci	neurosci	PROPN
iajs-3717	358	5	.	.	PUNCT
iajs-3717	359	1	2023;2023:7988	2023;2023:7988	NUM
iajs-3717	359	2	.	.	PUNCT
iajs-3717	360	1	https://doi.org/10.28919/cmbn/7988	https://doi.org/10.28919/cmbn/7988	PROPN
iajs-3717	360	2	7	7	NUM
iajs-3717	360	3	.	.	PUNCT
iajs-3717	360	4	ali	ali	PROPN
iajs-3717	360	5	nf	nf	PROPN
iajs-3717	360	6	.	.	PUNCT
iajs-3717	361	1	modeling	modeling	NOUN
iajs-3717	361	2	and	and	CCONJ
iajs-3717	361	3	stability	stability	NOUN
iajs-3717	361	4	of	of	ADP
iajs-3717	361	5	prey	prey	NOUN
iajs-3717	361	6	-	-	PUNCT
iajs-3717	361	7	predator	predator	NOUN
iajs-3717	361	8	system	system	NOUN
iajs-3717	361	9	involving	involve	VERB
iajs-3717	361	10	infectious	infectious	ADJ
iajs-3717	361	11	disease	disease	NOUN
iajs-3717	361	12	in	in	ADP
iajs-3717	361	13	each	each	DET
iajs-3717	361	14	population	population	NOUN
iajs-3717	361	15	with	with	ADP
iajs-3717	361	16	harvesting	harvesting	NOUN
iajs-3717	361	17	of	of	ADP
iajs-3717	361	18	the	the	DET
iajs-3717	361	19	prey	prey	NOUN
iajs-3717	361	20	.	.	PUNCT
iajs-3717	362	1	al	al	PROPN
iajs-3717	362	2	-	-	PUNCT
iajs-3717	362	3	nahrain	nahrain	PROPN
iajs-3717	362	4	j	j	PROPN
iajs-3717	362	5	sci	sci	PROPN
iajs-3717	362	6	.	.	PUNCT
iajs-3717	362	7	2015;18(4):144152	2015;18(4):144152	NUM
iajs-3717	362	8	.	.	PUNCT
iajs-3717	363	1	https://doi.org/10.22401/jnus.18.4.20	https://doi.org/10.22401/jnus.18.4.20	PROPN
iajs-3717	363	2	8	8	NUM
iajs-3717	363	3	.	.	PUNCT
iajs-3717	364	1	hassan	hassan	PROPN
iajs-3717	364	2	k	k	PROPN
iajs-3717	364	3	,	,	PUNCT
iajs-3717	364	4	mustafa	mustafa	PROPN
iajs-3717	364	5	a	a	PROPN
iajs-3717	364	6	,	,	PUNCT
iajs-3717	364	7	hama	hama	PROPN
iajs-3717	364	8	m.	m.	NOUN
iajs-3717	364	9	an	an	DET
iajs-3717	364	10	eco	eco	NOUN
iajs-3717	364	11	-	-	PUNCT
iajs-3717	364	12	epidemiological	epidemiological	ADJ
iajs-3717	364	13	model	model	NOUN
iajs-3717	364	14	incorporating	incorporate	VERB
iajs-3717	364	15	harvesting	harvesting	NOUN
iajs-3717	364	16	factors	factor	NOUN
iajs-3717	364	17	.	.	PUNCT
iajs-3717	365	1	symmetry	symmetry	NOUN
iajs-3717	365	2	.	.	PUNCT
iajs-3717	366	1	2021;13(11):2179	2021;13(11):2179	X
iajs-3717	366	2	.	.	PUNCT
iajs-3717	367	1	https://doi.org/10.3390/sym13112179	https://doi.org/10.3390/sym13112179	NOUN
iajs-3717	367	2	9	9	NUM
iajs-3717	367	3	.	.	X
iajs-3717	367	4	ali	ali	PROPN
iajs-3717	367	5	nf	nf	PROPN
iajs-3717	367	6	,	,	PUNCT
iajs-3717	367	7	aaid	aaid	PROPN
iajs-3717	367	8	aa	aa	PROPN
iajs-3717	367	9	.	.	PUNCT
iajs-3717	368	1	on	on	ADP
iajs-3717	368	2	the	the	DET
iajs-3717	368	3	dynamics	dynamic	NOUN
iajs-3717	368	4	of	of	ADP
iajs-3717	368	5	prey	prey	NOUN
iajs-3717	368	6	-	-	PUNCT
iajs-3717	368	7	predator	predator	NOUN
iajs-3717	368	8	model	model	NOUN
iajs-3717	368	9	involving	involve	VERB
iajs-3717	368	10	treatment	treatment	NOUN
iajs-3717	368	11	and	and	CCONJ
iajs-3717	368	12	infections	infection	NOUN
iajs-3717	368	13	disease	disease	NOUN
iajs-3717	368	14	in	in	ADP
iajs-3717	368	15	prey	prey	PROPN
iajs-3717	368	16	population	population	PROPN
iajs-3717	368	17	.	.	PUNCT
iajs-3717	369	1	iraqi	iraqi	PROPN
iajs-3717	369	2	j	j	PROPN
iajs-3717	369	3	sci	sci	PROPN
iajs-3717	369	4	.	.	PUNCT
iajs-3717	370	1	2015;56(3c):26542673	2015;56(3c):26542673	PROPN
iajs-3717	370	2	.	.	PUNCT
iajs-3717	370	3	https://doi.org/10.24996/ijs.2015.56.3c.27	https://doi.org/10.24996/ijs.2015.56.3c.27	PUNCT
iajs-3717	371	1	10	10	NUM
iajs-3717	371	2	.	.	PUNCT
iajs-3717	372	1	johri	johri	PROPN
iajs-3717	372	2	a	a	PRON
iajs-3717	372	3	,	,	PUNCT
iajs-3717	372	4	trivedi	trivedi	PROPN
iajs-3717	372	5	n	n	CCONJ
iajs-3717	372	6	,	,	PUNCT
iajs-3717	372	7	sisodiya	sisodiya	ADV
iajs-3717	372	8	a	a	PRON
iajs-3717	372	9	,	,	PUNCT
iajs-3717	372	10	sing	sing	NOUN
iajs-3717	372	11	b	b	NUM
iajs-3717	372	12	,	,	PUNCT
iajs-3717	372	13	jain	jain	PROPN
iajs-3717	372	14	s.	s.	PROPN
iajs-3717	372	15	study	study	PROPN
iajs-3717	372	16	of	of	ADP
iajs-3717	372	17	a	a	DET
iajs-3717	372	18	prey	prey	NOUN
iajs-3717	372	19	-	-	PUNCT
iajs-3717	372	20	predator	predator	NOUN
iajs-3717	372	21	model	model	NOUN
iajs-3717	372	22	with	with	ADP
iajs-3717	372	23	diseased	diseased	ADJ
iajs-3717	372	24	prey	prey	NOUN
iajs-3717	372	25	.	.	PUNCT
iajs-3717	373	1	int	int	PROPN
iajs-3717	373	2	j	j	PROPN
iajs-3717	373	3	contemp	contemp	PROPN
iajs-3717	373	4	math	math	PROPN
iajs-3717	373	5	sci	sci	PROPN
iajs-3717	373	6	.	.	PUNCT
iajs-3717	373	7	2012;7(10):489	2012;7(10):489	PROPN
iajs-3717	373	8	-	-	PUNCT
iajs-3717	373	9	498	498	NUM
iajs-3717	373	10	.	.	PUNCT
iajs-3717	374	1	https://doi.org/10.1098/rstb.1986.0072	https://doi.org/10.1098/rstb.1986.0072	PROPN
iajs-3717	374	2	https://doi.org/10.24996/ijs.2022.63.1.27	https://doi.org/10.24996/ijs.2022.63.1.27	PROPN
iajs-3717	374	3	https://doi.org/10.3390/math10132344	https://doi.org/10.3390/math10132344	NOUN
iajs-3717	374	4	https://doi.org/10.28919/cmbn/7988	https://doi.org/10.28919/cmbn/7988	PROPN
iajs-3717	374	5	https://doi.org/10.22401/jnus.18.4.20	https://doi.org/10.22401/jnus.18.4.20	PROPN
iajs-3717	374	6	https://doi.org/10.3390/sym13112179	https://doi.org/10.3390/sym13112179	NOUN
iajs-3717	374	7	https://doi.org/10.24996/ijs.2015.56.3c.27	https://doi.org/10.24996/ijs.2015.56.3c.27	PRON
iajs-3717	374	8	ihjpas	ihjpas	PROPN
iajs-3717	374	9	.	.	PUNCT
iajs-3717	375	1	2025,38(2	2025,38(2	PROPN
iajs-3717	375	2	)	)	PUNCT
iajs-3717	375	3	375	375	NUM
iajs-3717	375	4	11	11	NUM
iajs-3717	375	5	.	.	PUNCT
iajs-3717	376	1	sharma	sharma	PROPN
iajs-3717	376	2	s	s	PROPN
iajs-3717	376	3	,	,	PUNCT
iajs-3717	376	4	samanta	samanta	PROPN
iajs-3717	376	5	gp	gp	NOUN
iajs-3717	376	6	.	.	PUNCT
iajs-3717	377	1	analysis	analysis	NOUN
iajs-3717	377	2	of	of	ADP
iajs-3717	377	3	a	a	DET
iajs-3717	377	4	two	two	NUM
iajs-3717	377	5	prey	prey	NOUN
iajs-3717	377	6	one	one	NUM
iajs-3717	377	7	predator	predator	NOUN
iajs-3717	377	8	system	system	NOUN
iajs-3717	377	9	with	with	ADP
iajs-3717	377	10	disease	disease	NOUN
iajs-3717	377	11	in	in	ADP
iajs-3717	377	12	the	the	DET
iajs-3717	377	13	first	first	ADJ
iajs-3717	377	14	prey	prey	PROPN
iajs-3717	377	15	population	population	NOUN
iajs-3717	377	16	.	.	PUNCT
iajs-3717	378	1	int	int	PROPN
iajs-3717	378	2	j	j	PROPN
iajs-3717	378	3	dyn	dyn	PROPN
iajs-3717	378	4	control	control	NOUN
iajs-3717	378	5	.	.	PUNCT
iajs-3717	379	1	2015;3(3):210–224	2015;3(3):210–224	NUM
iajs-3717	379	2	.	.	PUNCT
iajs-3717	379	3	https://doi.org/10.1007/s40435-014-0107-4	https://doi.org/10.1007/s40435-014-0107-4	PROPN
iajs-3717	379	4	12	12	NUM
iajs-3717	379	5	.	.	PUNCT
iajs-3717	380	1	ahmed	ahmed	PROPN
iajs-3717	380	2	ls	ls	PROPN
iajs-3717	380	3	,	,	PUNCT
iajs-3717	380	4	al	al	PROPN
iajs-3717	380	5	-	-	PUNCT
iajs-3717	380	6	husseiny	husseiny	PROPN
iajs-3717	380	7	hf	hf	PROPN
iajs-3717	380	8	.	.	PUNCT
iajs-3717	381	1	dynamical	dynamical	ADJ
iajs-3717	381	2	behavior	behavior	NOUN
iajs-3717	381	3	of	of	ADP
iajs-3717	381	4	an	an	DET
iajs-3717	381	5	eco	eco	NOUN
iajs-3717	381	6	-	-	PUNCT
iajs-3717	381	7	epidemiological	epidemiological	ADJ
iajs-3717	381	8	model	model	NOUN
iajs-3717	381	9	involving	involve	VERB
iajs-3717	381	10	disease	disease	NOUN
iajs-3717	381	11	in	in	ADP
iajs-3717	381	12	predator	predator	NOUN
iajs-3717	381	13	and	and	CCONJ
iajs-3717	381	14	stage	stage	NOUN
iajs-3717	381	15	structure	structure	NOUN
iajs-3717	381	16	in	in	ADP
iajs-3717	381	17	prey	prey	PROPN
iajs-3717	381	18	.	.	PUNCT
iajs-3717	382	1	iraqi	iraqi	PROPN
iajs-3717	382	2	j	j	PROPN
iajs-3717	382	3	sci	sci	PROPN
iajs-3717	382	4	.	.	PUNCT
iajs-3717	383	1	2019;60(8):1766	2019;60(8):1766	NUM
iajs-3717	383	2	–	–	PUNCT
iajs-3717	383	3	1782	1782	NUM
iajs-3717	383	4	.	.	PUNCT
iajs-3717	384	1	https://doi.org/10.24996/ijs.2019.60.8.14	https://doi.org/10.24996/ijs.2019.60.8.14	PROPN
iajs-3717	384	2	13	13	NUM
iajs-3717	384	3	.	.	PUNCT
iajs-3717	385	1	hugo	hugo	PROPN
iajs-3717	385	2	a	a	PRON
iajs-3717	385	3	,	,	PUNCT
iajs-3717	385	4	simanjilo	simanjilo	PROPN
iajs-3717	385	5	e.	e.	PROPN
iajs-3717	385	6	analysis	analysis	NOUN
iajs-3717	385	7	of	of	ADP
iajs-3717	385	8	an	an	DET
iajs-3717	385	9	eco	eco	NOUN
iajs-3717	385	10	-	-	PUNCT
iajs-3717	385	11	epidemiological	epidemiological	ADJ
iajs-3717	385	12	model	model	NOUN
iajs-3717	385	13	under	under	ADP
iajs-3717	385	14	optimal	optimal	ADJ
iajs-3717	385	15	control	control	NOUN
iajs-3717	385	16	measures	measure	NOUN
iajs-3717	385	17	for	for	ADP
iajs-3717	385	18	infected	infected	ADJ
iajs-3717	385	19	prey	prey	NOUN
iajs-3717	385	20	.	.	PUNCT
iajs-3717	386	1	appl	appl	PROPN
iajs-3717	386	2	appl	appl	PROPN
iajs-3717	386	3	math	math	PROPN
iajs-3717	386	4	.	.	PUNCT
iajs-3717	387	1	2019;14(1):117138	2019;14(1):117138	NUM
iajs-3717	387	2	.	.	PUNCT
iajs-3717	388	1	https://digitalcommons.pvamu.edu/aam/vol14/iss1/8	https://digitalcommons.pvamu.edu/aam/vol14/iss1/8	PROPN
iajs-3717	388	2	14	14	NUM
iajs-3717	388	3	.	.	PUNCT
iajs-3717	389	1	yp	yp	PROPN
iajs-3717	389	2	,	,	PUNCT
iajs-3717	389	3	ma	ma	PROPN
iajs-3717	389	4	mj	mj	PROPN
iajs-3717	389	5	,	,	PUNCT
iajs-3717	389	6	zuo	zuo	PROPN
iajs-3717	389	7	p	p	PROPN
iajs-3717	389	8	,	,	PUNCT
iajs-3717	389	9	liang	liang	PROPN
iajs-3717	389	10	x.	x.	NOUN
iajs-3717	389	11	analysis	analysis	NOUN
iajs-3717	389	12	of	of	ADP
iajs-3717	389	13	an	an	DET
iajs-3717	389	14	eco	eco	NOUN
iajs-3717	389	15	-	-	PUNCT
iajs-3717	389	16	epidemiological	epidemiological	ADJ
iajs-3717	389	17	model	model	NOUN
iajs-3717	389	18	with	with	ADP
iajs-3717	389	19	disease	disease	NOUN
iajs-3717	389	20	in	in	ADP
iajs-3717	389	21	the	the	DET
iajs-3717	389	22	predator	predator	NOUN
iajs-3717	389	23	.	.	PUNCT
iajs-3717	390	1	appl	appl	PROPN
iajs-3717	390	2	mech	mech	PROPN
iajs-3717	390	3	mater	mater	NOUN
iajs-3717	390	4	.	.	PUNCT
iajs-3717	391	1	2014;536:861	2014;536:861	NUM
iajs-3717	391	2	-	-	SYM
iajs-3717	391	3	864	864	NUM
iajs-3717	391	4	.	.	PUNCT
iajs-3717	392	1	https://doi.org/10.4028/www.scientific.net/amm.536537.861	https://doi.org/10.4028/www.scientific.net/amm.536537.861	PRON
iajs-3717	392	2	15	15	NUM
iajs-3717	392	3	.	.	PUNCT
iajs-3717	393	1	abdul	abdul	PROPN
iajs-3717	393	2	satar	satar	PROPN
iajs-3717	393	3	h	h	PROPN
iajs-3717	393	4	,	,	PUNCT
iajs-3717	393	5	naji	naji	PROPN
iajs-3717	393	6	rk	rk	PROPN
iajs-3717	393	7	.	.	PROPN
iajs-3717	393	8	stability	stability	NOUN
iajs-3717	393	9	and	and	CCONJ
iajs-3717	393	10	bifurcation	bifurcation	NOUN
iajs-3717	393	11	of	of	ADP
iajs-3717	393	12	a	a	DET
iajs-3717	393	13	prey	prey	NOUN
iajs-3717	393	14	-	-	PUNCT
iajs-3717	393	15	predator	predator	NOUN
iajs-3717	393	16	-	-	PUNCT
iajs-3717	393	17	scavenger	scavenger	NOUN
iajs-3717	393	18	model	model	NOUN
iajs-3717	393	19	in	in	ADP
iajs-3717	393	20	the	the	DET
iajs-3717	393	21	existence	existence	NOUN
iajs-3717	393	22	of	of	ADP
iajs-3717	393	23	toxicant	toxicant	NOUN
iajs-3717	393	24	and	and	CCONJ
iajs-3717	393	25	harvesting	harvesting	NOUN
iajs-3717	393	26	.	.	PUNCT
iajs-3717	394	1	int	int	PROPN
iajs-3717	395	1	j	j	PROPN
iajs-3717	395	2	math	math	PROPN
iajs-3717	395	3	math	math	PROPN
iajs-3717	395	4	sci	sci	PROPN
iajs-3717	395	5	.	.	PUNCT
iajs-3717	396	1	2019;2019:1540015	2019;2019:1540015	NUM
iajs-3717	396	2	.	.	PUNCT
iajs-3717	397	1	https://doi.org/10.1155/2019/1540015	https://doi.org/10.1155/2019/1540015	PROPN
iajs-3717	397	2	16	16	NUM
iajs-3717	397	3	.	.	PUNCT
iajs-3717	398	1	kant	kant	PROPN
iajs-3717	398	2	s	s	PROPN
iajs-3717	398	3	,	,	PUNCT
iajs-3717	398	4	kumar	kumar	PROPN
iajs-3717	398	5	v.	v.	PROPN
iajs-3717	398	6	stability	stability	PROPN
iajs-3717	398	7	analysis	analysis	NOUN
iajs-3717	398	8	of	of	ADP
iajs-3717	398	9	predator	predator	NOUN
iajs-3717	398	10	–	–	PUNCT
iajs-3717	398	11	prey	prey	NOUN
iajs-3717	398	12	system	system	NOUN
iajs-3717	398	13	with	with	ADP
iajs-3717	398	14	migrating	migrating	NOUN
iajs-3717	398	15	prey	prey	NOUN
iajs-3717	398	16	and	and	CCONJ
iajs-3717	398	17	disease	disease	NOUN
iajs-3717	398	18	infection	infection	NOUN
iajs-3717	398	19	in	in	ADP
iajs-3717	398	20	both	both	DET
iajs-3717	398	21	species	specie	NOUN
iajs-3717	398	22	.	.	PUNCT
iajs-3717	399	1	appl	appl	PROPN
iajs-3717	399	2	math	math	PROPN
iajs-3717	399	3	model	model	PROPN
iajs-3717	399	4	.	.	PUNCT
iajs-3717	400	1	2017;42:509539	2017;42:509539	NUM
iajs-3717	400	2	.	.	PUNCT
iajs-3717	401	1	https://doi.org/10.1016/j.apm.2017.07.017	https://doi.org/10.1016/j.apm.2017.07.017	PROPN
iajs-3717	401	2	17	17	NUM
iajs-3717	401	3	.	.	PUNCT
iajs-3717	402	1	naji	naji	PROPN
iajs-3717	402	2	rk	rk	PROPN
iajs-3717	402	3	,	,	PUNCT
iajs-3717	402	4	ali	ali	PROPN
iajs-3717	402	5	nf	nf	PROPN
iajs-3717	402	6	.	.	PUNCT
iajs-3717	403	1	modeling	modeling	NOUN
iajs-3717	403	2	and	and	CCONJ
iajs-3717	403	3	stability	stability	NOUN
iajs-3717	403	4	of	of	ADP
iajs-3717	403	5	lotka	lotka	PROPN
iajs-3717	403	6	-	-	PUNCT
iajs-3717	403	7	volterra	volterra	PROPN
iajs-3717	403	8	prey	prey	NOUN
iajs-3717	403	9	-	-	PUNCT
iajs-3717	403	10	predator	predator	NOUN
iajs-3717	403	11	system	system	NOUN
iajs-3717	403	12	involving	involve	VERB
iajs-3717	403	13	infectious	infectious	ADJ
iajs-3717	403	14	disease	disease	NOUN
iajs-3717	403	15	in	in	ADP
iajs-3717	403	16	each	each	DET
iajs-3717	403	17	population	population	NOUN
iajs-3717	403	18	.	.	PUNCT
iajs-3717	404	1	iraqi	iraqi	PROPN
iajs-3717	404	2	j	j	PROPN
iajs-3717	404	3	sci	sci	PROPN
iajs-3717	404	4	.	.	PUNCT
iajs-3717	405	1	2014;55(2):491	2014;55(2):491	NUM
iajs-3717	405	2	-	-	SYM
iajs-3717	405	3	505	505	NUM
iajs-3717	405	4	.	.	PUNCT
iajs-3717	405	5	18	18	NUM
iajs-3717	405	6	.	.	PUNCT
iajs-3717	405	7	song	song	PROPN
iajs-3717	405	8	x	x	PROPN
iajs-3717	405	9	,	,	PUNCT
iajs-3717	405	10	chen	chen	PROPN
iajs-3717	405	11	l.	l.	PROPN
iajs-3717	405	12	optimal	optimal	ADJ
iajs-3717	405	13	harvesting	harvesting	NOUN
iajs-3717	405	14	and	and	CCONJ
iajs-3717	405	15	stability	stability	NOUN
iajs-3717	405	16	for	for	ADP
iajs-3717	405	17	a	a	DET
iajs-3717	405	18	two	two	NUM
iajs-3717	405	19	-	-	PUNCT
iajs-3717	405	20	species	specie	NOUN
iajs-3717	405	21	competitive	competitive	ADJ
iajs-3717	405	22	system	system	NOUN
iajs-3717	405	23	with	with	ADP
iajs-3717	405	24	stage	stage	NOUN
iajs-3717	405	25	structure	structure	NOUN
iajs-3717	405	26	.	.	PUNCT
iajs-3717	406	1	math	math	PROPN
iajs-3717	406	2	biosci	biosci	PROPN
iajs-3717	406	3	.	.	PUNCT
iajs-3717	407	1	2001;170(2):173	2001;170(2):173	PROPN
iajs-3717	407	2	-	-	SYM
iajs-3717	407	3	186	186	NUM
iajs-3717	407	4	.	.	PUNCT
iajs-3717	408	1	https://doi.org/10.1016/s0025-5564(01)00060-0	https://doi.org/10.1016/s0025-5564(01)00060-0	PROPN
iajs-3717	408	2	19	19	NUM
iajs-3717	408	3	.	.	PUNCT
iajs-3717	409	1	das	das	PROPN
iajs-3717	409	2	a	a	DET
iajs-3717	409	3	,	,	PUNCT
iajs-3717	409	4	pal	pal	ADJ
iajs-3717	409	5	m.	m.	NOUN
iajs-3717	409	6	theoretical	theoretical	ADJ
iajs-3717	409	7	analysis	analysis	NOUN
iajs-3717	409	8	of	of	ADP
iajs-3717	409	9	an	an	DET
iajs-3717	409	10	imprecise	imprecise	ADV
iajs-3717	409	11	prey	prey	NOUN
iajs-3717	409	12	-	-	PUNCT
iajs-3717	409	13	predator	predator	NOUN
iajs-3717	409	14	model	model	NOUN
iajs-3717	409	15	with	with	ADP
iajs-3717	409	16	harvesting	harvesting	NOUN
iajs-3717	409	17	and	and	CCONJ
iajs-3717	409	18	optimal	optimal	ADJ
iajs-3717	409	19	control	control	NOUN
iajs-3717	409	20	.	.	PUNCT
iajs-3717	410	1	j	j	PROPN
iajs-3717	410	2	optim	optim	VERB
iajs-3717	410	3	.	.	PUNCT
iajs-3717	411	1	2019;2019:1	2019;2019:1	NUM
iajs-3717	411	2	-	-	SYM
iajs-3717	411	3	12	12	NUM
iajs-3717	411	4	.	.	PUNCT
iajs-3717	412	1	20	20	NUM
iajs-3717	412	2	.	.	PUNCT
iajs-3717	413	1	kar	kar	PROPN
iajs-3717	413	2	tk	tk	PROPN
iajs-3717	413	3	.	.	PROPN
iajs-3717	413	4	modelling	modelling	NOUN
iajs-3717	413	5	and	and	CCONJ
iajs-3717	413	6	analysis	analysis	NOUN
iajs-3717	413	7	of	of	ADP
iajs-3717	413	8	a	a	DET
iajs-3717	413	9	harvested	harvest	VERB
iajs-3717	413	10	prey	prey	NOUN
iajs-3717	413	11	–	–	PUNCT
iajs-3717	413	12	predator	predator	NOUN
iajs-3717	413	13	system	system	NOUN
iajs-3717	413	14	incorporating	incorporate	VERB
iajs-3717	413	15	a	a	DET
iajs-3717	413	16	prey	prey	NOUN
iajs-3717	413	17	refuge	refuge	NOUN
iajs-3717	413	18	.	.	PUNCT
iajs-3717	414	1	j	j	PROPN
iajs-3717	414	2	comput	comput	PROPN
iajs-3717	414	3	appl	appl	PROPN
iajs-3717	414	4	math	math	PROPN
iajs-3717	414	5	.	.	PUNCT
iajs-3717	415	1	2006;185(1):19	2006;185(1):19	NUM
iajs-3717	415	2	-	-	SYM
iajs-3717	415	3	33	33	NUM
iajs-3717	415	4	.	.	PUNCT
iajs-3717	416	1	21	21	NUM
iajs-3717	416	2	.	.	PUNCT
iajs-3717	417	1	hale	hale	PROPN
iajs-3717	417	2	jh	jh	PROPN
iajs-3717	417	3	.	.	PUNCT
iajs-3717	418	1	ordinary	ordinary	ADJ
iajs-3717	418	2	differential	differential	ADJ
iajs-3717	418	3	equations	equation	NOUN
iajs-3717	418	4	.	.	PUNCT
iajs-3717	419	1	new	new	PROPN
iajs-3717	419	2	york	york	PROPN
iajs-3717	419	3	:	:	PUNCT
iajs-3717	419	4	wiley	wiley	PROPN
iajs-3717	419	5	-	-	PUNCT
iajs-3717	419	6	interscience	interscience	NOUN
iajs-3717	419	7	;	;	PUNCT
iajs-3717	419	8	1969	1969	NUM
iajs-3717	419	9	.	.	PUNCT
iajs-3717	420	1	22	22	NUM
iajs-3717	420	2	.	.	PUNCT
iajs-3717	421	1	hassard	hassard	PROPN
iajs-3717	421	2	bd	bd	PROPN
iajs-3717	421	3	,	,	PUNCT
iajs-3717	421	4	kazarinoff	kazarinoff	PROPN
iajs-3717	421	5	nd	nd	PROPN
iajs-3717	421	6	,	,	PUNCT
iajs-3717	421	7	wan	wan	PROPN
iajs-3717	421	8	y	y	PROPN
iajs-3717	421	9	-	-	PUNCT
iajs-3717	421	10	h.	h.	PROPN
iajs-3717	421	11	theory	theory	NOUN
iajs-3717	421	12	and	and	CCONJ
iajs-3717	421	13	applications	application	NOUN
iajs-3717	421	14	of	of	ADP
iajs-3717	421	15	hopf	hopf	ADJ
iajs-3717	421	16	bifurcation	bifurcation	NOUN
iajs-3717	421	17	.	.	PUNCT
iajs-3717	422	1	cambridge	cambridge	PROPN
iajs-3717	422	2	:	:	PUNCT
iajs-3717	422	3	cambridge	cambridge	PROPN
iajs-3717	422	4	university	university	PROPN
iajs-3717	422	5	press	press	NOUN
iajs-3717	422	6	;	;	PUNCT
iajs-3717	422	7	1981	1981	NUM
iajs-3717	422	8	.	.	PUNCT
iajs-3717	423	1	23	23	NUM
iajs-3717	423	2	.	.	PUNCT
iajs-3717	424	1	al	al	PROPN
iajs-3717	424	2	-	-	PUNCT
iajs-3717	424	3	jubouri	jubouri	PROPN
iajs-3717	424	4	kq	kq	PROPN
iajs-3717	424	5	,	,	PUNCT
iajs-3717	424	6	naji	naji	PROPN
iajs-3717	424	7	rk	rk	PROPN
iajs-3717	424	8	.	.	PROPN
iajs-3717	424	9	delay	delay	NOUN
iajs-3717	424	10	in	in	ADP
iajs-3717	424	11	eco	eco	PROPN
iajs-3717	424	12	-	-	PUNCT
iajs-3717	424	13	epidemiological	epidemiological	ADJ
iajs-3717	424	14	prey	prey	NOUN
iajs-3717	424	15	-	-	PUNCT
iajs-3717	424	16	predator	predator	NOUN
iajs-3717	424	17	model	model	NOUN
iajs-3717	424	18	with	with	ADP
iajs-3717	424	19	predation	predation	NOUN
iajs-3717	424	20	fear	fear	NOUN
iajs-3717	424	21	and	and	CCONJ
iajs-3717	424	22	hunting	hunt	VERB
iajs-3717	424	23	cooperation	cooperation	NOUN
iajs-3717	424	24	.	.	PUNCT
iajs-3717	425	1	commun	commun	PROPN
iajs-3717	425	2	math	math	PROPN
iajs-3717	425	3	biol	biol	PROPN
iajs-3717	425	4	neurosci	neurosci	PROPN
iajs-3717	425	5	.	.	PUNCT
iajs-3717	426	1	2023;2023:89	2023;2023:89	NUM
iajs-3717	426	2	.	.	PUNCT
iajs-3717	427	1	https://doi.org/10.28919/cmbn/8081	https://doi.org/10.28919/cmbn/8081	PROPN
iajs-3717	427	2	24	24	NUM
iajs-3717	427	3	.	.	PUNCT
iajs-3717	427	4	pal	pal	PROPN
iajs-3717	427	5	ak	ak	PROPN
iajs-3717	427	6	,	,	PUNCT
iajs-3717	427	7	bhattacharyya	bhattacharyya	ADJ
iajs-3717	427	8	a	a	DET
iajs-3717	427	9	,	,	PUNCT
iajs-3717	427	10	pal	pal	ADJ
iajs-3717	427	11	s.	s.	PROPN
iajs-3717	427	12	study	study	PROPN
iajs-3717	427	13	of	of	ADP
iajs-3717	427	14	delay	delay	NOUN
iajs-3717	427	15	induced	induce	VERB
iajs-3717	427	16	eco	eco	PROPN
iajs-3717	427	17	-	-	PUNCT
iajs-3717	427	18	epidemiological	epidemiological	ADJ
iajs-3717	427	19	model	model	NOUN
iajs-3717	427	20	incorporating	incorporate	VERB
iajs-3717	427	21	a	a	DET
iajs-3717	427	22	prey	prey	NOUN
iajs-3717	427	23	refuge	refuge	NOUN
iajs-3717	427	24	.	.	PUNCT
iajs-3717	428	1	filomat	filomat	NOUN
iajs-3717	428	2	.	.	PUNCT
iajs-3717	429	1	2022;36(2):557	2022;36(2):557	PROPN
iajs-3717	429	2	-	-	PUNCT
iajs-3717	429	3	578	578	NUM
iajs-3717	429	4	.	.	PUNCT
iajs-3717	430	1	https://doi.org/10.2298/fil2202557p	https://doi.org/10.2298/fil2202557p	PROPN
iajs-3717	430	2	25	25	NUM
iajs-3717	430	3	.	.	PUNCT
iajs-3717	431	1	tankam	tankam	PROPN
iajs-3717	431	2	i	i	NOUN
iajs-3717	431	3	,	,	PUNCT
iajs-3717	431	4	tchinda	tchinda	PROPN
iajs-3717	431	5	mouofo	mouofo	PROPN
iajs-3717	431	6	p	p	PROPN
iajs-3717	431	7	,	,	PUNCT
iajs-3717	431	8	mendy	mendy	PROPN
iajs-3717	431	9	a	a	PROPN
iajs-3717	431	10	,	,	PUNCT
iajs-3717	431	11	lam	lam	PROPN
iajs-3717	431	12	m	m	PROPN
iajs-3717	431	13	,	,	PUNCT
iajs-3717	431	14	tewa	tewa	PROPN
iajs-3717	431	15	jj	jj	PROPN
iajs-3717	431	16	,	,	PUNCT
iajs-3717	431	17	bowong	bowong	PROPN
iajs-3717	431	18	s.	s.	PROPN
iajs-3717	431	19	local	local	ADJ
iajs-3717	431	20	bifurcations	bifurcation	NOUN
iajs-3717	431	21	and	and	CCONJ
iajs-3717	431	22	optimal	optimal	ADJ
iajs-3717	431	23	theory	theory	NOUN
iajs-3717	431	24	in	in	ADP
iajs-3717	431	25	a	a	DET
iajs-3717	431	26	delayed	delay	VERB
iajs-3717	431	27	predator	predator	NOUN
iajs-3717	431	28	–	–	PUNCT
iajs-3717	431	29	prey	prey	NOUN
iajs-3717	431	30	model	model	NOUN
iajs-3717	431	31	with	with	ADP
iajs-3717	431	32	threshold	threshold	NOUN
iajs-3717	431	33	prey	prey	PROPN
iajs-3717	431	34	harvesting	harvesting	NOUN
iajs-3717	431	35	.	.	PUNCT
iajs-3717	432	1	int	int	NOUN
iajs-3717	432	2	j	j	PROPN
iajs-3717	432	3	bifurcat	bifurcat	NOUN
iajs-3717	432	4	chaos	chaos	NOUN
iajs-3717	432	5	.	.	PUNCT
iajs-3717	433	1	2015;25(7):1540015	2015;25(7):1540015	PROPN
iajs-3717	433	2	.	.	PUNCT
iajs-3717	434	1	https://doi.org/10.1142/s021812741540015x	https://doi.org/10.1142/s021812741540015x	NOUN
iajs-3717	434	2	26	26	NUM
iajs-3717	434	3	.	.	PUNCT
iajs-3717	435	1	samanta	samanta	PROPN
iajs-3717	435	2	s	s	PROPN
iajs-3717	435	3	,	,	PUNCT
iajs-3717	435	4	tiwari	tiwari	ADJ
iajs-3717	435	5	pk	pk	PROPN
iajs-3717	435	6	,	,	PUNCT
iajs-3717	435	7	alzahrani	alzahrani	PROPN
iajs-3717	435	8	ak	ak	PROPN
iajs-3717	435	9	,	,	PUNCT
iajs-3717	435	10	alshomrani	alshomrani	PROPN
iajs-3717	435	11	as	as	ADP
iajs-3717	435	12	.	.	PUNCT
iajs-3717	435	13	chaos	chaos	NOUN
iajs-3717	435	14	in	in	ADP
iajs-3717	435	15	a	a	DET
iajs-3717	435	16	nonautonomous	nonautonomous	ADJ
iajs-3717	435	17	ecoepidemiological	ecoepidemiological	ADJ
iajs-3717	435	18	model	model	NOUN
iajs-3717	435	19	with	with	ADP
iajs-3717	435	20	delay	delay	NOUN
iajs-3717	435	21	.	.	PUNCT
iajs-3717	436	1	appl	appl	PROPN
iajs-3717	436	2	math	math	PROPN
iajs-3717	436	3	model	model	NOUN
iajs-3717	436	4	.	.	PUNCT
iajs-3717	437	1	2020;79:865880	2020;79:865880	NUM
iajs-3717	437	2	.	.	PUNCT
iajs-3717	437	3	https://doi.org/10.1016/j.apm.2019.10.040	https://doi.org/10.1016/j.apm.2019.10.040	NOUN
iajs-3717	437	4	27	27	NUM
iajs-3717	437	5	.	.	PUNCT
iajs-3717	438	1	zhang	zhang	PROPN
iajs-3717	438	2	x	x	PROPN
iajs-3717	438	3	,	,	PUNCT
iajs-3717	438	4	liu	liu	PROPN
iajs-3717	438	5	z.	z.	PROPN
iajs-3717	438	6	hopf	hopf	PROPN
iajs-3717	438	7	bifurcation	bifurcation	NOUN
iajs-3717	438	8	analysis	analysis	NOUN
iajs-3717	438	9	in	in	ADP
iajs-3717	438	10	a	a	DET
iajs-3717	438	11	predator	predator	NOUN
iajs-3717	438	12	-	-	PUNCT
iajs-3717	438	13	prey	prey	NOUN
iajs-3717	438	14	model	model	NOUN
iajs-3717	438	15	with	with	ADP
iajs-3717	438	16	predator	predator	NOUN
iajs-3717	438	17	-	-	PUNCT
iajs-3717	438	18	age	age	NOUN
iajs-3717	438	19	structure	structure	NOUN
iajs-3717	438	20	and	and	CCONJ
iajs-3717	438	21	predator	predator	NOUN
iajs-3717	438	22	-	-	PUNCT
iajs-3717	438	23	prey	prey	NOUN
iajs-3717	438	24	reaction	reaction	NOUN
iajs-3717	438	25	time	time	NOUN
iajs-3717	438	26	delay	delay	NOUN
iajs-3717	438	27	.	.	PUNCT
iajs-3717	439	1	appl	appl	PROPN
iajs-3717	439	2	math	math	PROPN
iajs-3717	439	3	model	model	NOUN
iajs-3717	439	4	.	.	PUNCT
iajs-3717	440	1	2021;91:530548	2021;91:530548	X
iajs-3717	440	2	.	.	PUNCT
iajs-3717	441	1	https://doi.org/10.1016/j.apm.2020.10.040	https://doi.org/10.1016/j.apm.2020.10.040	PROPN
iajs-3717	441	2	28	28	NUM
iajs-3717	441	3	.	.	PUNCT
iajs-3717	442	1	kamel	kamel	PROPN
iajs-3717	442	2	naji	naji	PROPN
iajs-3717	442	3	r	r	PROPN
iajs-3717	442	4	,	,	PUNCT
iajs-3717	442	5	abdullah	abdullah	PROPN
iajs-3717	442	6	ibrahim	ibrahim	PROPN
iajs-3717	442	7	h.	h.	PROPN
iajs-3717	442	8	chaos	chaos	PROPN
iajs-3717	442	9	in	in	ADP
iajs-3717	442	10	a	a	DET
iajs-3717	442	11	harvested	harvest	VERB
iajs-3717	442	12	prey	prey	NOUN
iajs-3717	442	13	-	-	PUNCT
iajs-3717	442	14	predator	predator	NOUN
iajs-3717	442	15	model	model	NOUN
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iajs-3717	442	17	infectious	infectious	ADJ
iajs-3717	442	18	disease	disease	NOUN
iajs-3717	442	19	in	in	ADP
iajs-3717	442	20	the	the	DET
iajs-3717	442	21	prey	prey	NOUN
iajs-3717	442	22	.	.	PUNCT
iajs-3717	443	1	j	j	PROPN
iajs-3717	443	2	al	al	PROPN
iajs-3717	443	3	-	-	PUNCT
iajs-3717	443	4	qadisiyah	qadisiyah	NOUN
iajs-3717	443	5	comput	comput	VERB
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iajs-3717	443	8	.	.	PUNCT
iajs-3717	444	1	2011;3(2):1	2011;3(2):1	PROPN
iajs-3717	444	2	-	-	PUNCT
iajs-3717	444	3	21	21	NUM
iajs-3717	444	4	.	.	PUNCT
iajs-3717	444	5	29	29	NUM
iajs-3717	444	6	.	.	PUNCT
iajs-3717	445	1	hale	hale	PROPN
iajs-3717	445	2	jh	jh	PROPN
iajs-3717	445	3	.	.	PUNCT
iajs-3717	446	1	ordinary	ordinary	ADJ
iajs-3717	446	2	differential	differential	ADJ
iajs-3717	446	3	equations	equation	NOUN
iajs-3717	446	4	.	.	PUNCT
iajs-3717	447	1	new	new	PROPN
iajs-3717	447	2	york	york	PROPN
iajs-3717	447	3	:	:	PUNCT
iajs-3717	447	4	wiley	wiley	PROPN
iajs-3717	447	5	-	-	PUNCT
iajs-3717	447	6	interscience	interscience	NOUN
iajs-3717	447	7	;	;	PUNCT
iajs-3717	447	8	1969	1969	NUM
iajs-3717	447	9	.	.	PUNCT
iajs-3717	448	1	30	30	NUM
iajs-3717	448	2	.	.	PUNCT
iajs-3717	449	1	hassard	hassard	PROPN
iajs-3717	449	2	bd	bd	PROPN
iajs-3717	449	3	,	,	PUNCT
iajs-3717	449	4	kazarinoff	kazarinoff	PROPN
iajs-3717	449	5	nd	nd	PROPN
iajs-3717	449	6	,	,	PUNCT
iajs-3717	449	7	wan	wan	PROPN
iajs-3717	449	8	y	y	PROPN
iajs-3717	449	9	-	-	PUNCT
iajs-3717	449	10	h.	h.	PROPN
iajs-3717	449	11	theory	theory	NOUN
iajs-3717	449	12	and	and	CCONJ
iajs-3717	449	13	applications	application	NOUN
iajs-3717	449	14	of	of	ADP
iajs-3717	449	15	hopf	hopf	ADJ
iajs-3717	449	16	bifurcation	bifurcation	NOUN
iajs-3717	449	17	.	.	PUNCT
iajs-3717	450	1	cambridge	cambridge	PROPN
iajs-3717	450	2	:	:	PUNCT
iajs-3717	450	3	cambridge	cambridge	PROPN
iajs-3717	450	4	university	university	PROPN
iajs-3717	450	5	press	press	NOUN
iajs-3717	450	6	;	;	PUNCT
iajs-3717	450	7	1981	1981	NUM
iajs-3717	450	8	.	.	PUNCT
iajs-3717	451	1	https://doi.org/10.1007/s40435-014-0107-4	https://doi.org/10.1007/s40435-014-0107-4	PROPN
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iajs-3717	452	2	https://digitalcommons.pvamu.edu/aam/vol14/iss1/8	https://digitalcommons.pvamu.edu/aam/vol14/iss1/8	PROPN
iajs-3717	452	3	https://doi.org/10.4028/www.scientific.net/amm.536-537.861	https://doi.org/10.4028/www.scientific.net/amm.536-537.861	PROPN
iajs-3717	452	4	https://doi.org/10.4028/www.scientific.net/amm.536-537.861	https://doi.org/10.4028/www.scientific.net/amm.536-537.861	PROPN
iajs-3717	452	5	https://doi.org/10.1155/2019/1540015	https://doi.org/10.1155/2019/1540015	PROPN
iajs-3717	452	6	https://doi.org/10.1016/j.apm.2017.07.017	https://doi.org/10.1016/j.apm.2017.07.017	PROPN
iajs-3717	452	7	https://doi.org/10.1016/s0025-5564(01)00060-0	https://doi.org/10.1016/s0025-5564(01)00060-0	PROPN
iajs-3717	452	8	https://doi.org/10.28919/cmbn/8081	https://doi.org/10.28919/cmbn/8081	PROPN
iajs-3717	452	9	https://doi.org/10.2298/fil2202557p	https://doi.org/10.2298/fil2202557p	PROPN
iajs-3717	452	10	https://doi.org/10.1142/s021812741540015x	https://doi.org/10.1142/s021812741540015x	NOUN
iajs-3717	452	11	https://doi.org/10.1016/j.apm.2019.10.040	https://doi.org/10.1016/j.apm.2019.10.040	NOUN
iajs-3717	452	12	https://doi.org/10.1016/j.apm.2020.10.040	https://doi.org/10.1016/j.apm.2020.10.040	NOUN