id	sid	tid	token	lemma	pos
ejpam-7020	1	1	european	european	PROPN
ejpam-7020	1	2	journal	journal	PROPN
ejpam-7020	1	3	of	of	ADP
ejpam-7020	1	4	pure	pure	ADJ
ejpam-7020	1	5	and	and	CCONJ
ejpam-7020	1	6	applied	applied	ADJ
ejpam-7020	1	7	mathematics	mathematic	NOUN
ejpam-7020	1	8	2025	2025	NUM
ejpam-7020	1	9	,	,	PUNCT
ejpam-7020	1	10	vol	vol	NOUN
ejpam-7020	1	11	.	.	PROPN
ejpam-7020	1	12	18	18	NUM
ejpam-7020	1	13	,	,	PUNCT
ejpam-7020	1	14	issue	issue	NOUN
ejpam-7020	1	15	4	4	NUM
ejpam-7020	1	16	,	,	PUNCT
ejpam-7020	1	17	article	article	NOUN
ejpam-7020	1	18	number	number	NOUN
ejpam-7020	1	19	7020	7020	NUM
ejpam-7020	1	20	issn	issn	VERB
ejpam-7020	1	21	1307	1307	NUM
ejpam-7020	1	22	-	-	SYM
ejpam-7020	1	23	5543	5543	NUM
ejpam-7020	1	24	–	–	PUNCT
ejpam-7020	1	25	ejpam.com	ejpam.com	X
ejpam-7020	1	26	published	publish	VERB
ejpam-7020	1	27	by	by	ADP
ejpam-7020	1	28	new	new	PROPN
ejpam-7020	1	29	york	york	PROPN
ejpam-7020	1	30	business	business	PROPN
ejpam-7020	1	31	global	global	PROPN
ejpam-7020	1	32	a	a	DET
ejpam-7020	1	33	computational	computational	ADJ
ejpam-7020	1	34	guide	guide	NOUN
ejpam-7020	1	35	to	to	PART
ejpam-7020	1	36	stability	stability	VERB
ejpam-7020	1	37	analysis	analysis	NOUN
ejpam-7020	1	38	of	of	ADP
ejpam-7020	1	39	nonlinear	nonlinear	ADJ
ejpam-7020	1	40	system	system	NOUN
ejpam-7020	1	41	:	:	PUNCT
ejpam-7020	1	42	the	the	DET
ejpam-7020	1	43	lotka	lotka	PROPN
ejpam-7020	1	44	-	-	PUNCT
ejpam-7020	1	45	volterra	volterra	PROPN
ejpam-7020	1	46	and	and	CCONJ
ejpam-7020	1	47	sir	sir	NOUN
ejpam-7020	1	48	models	model	NOUN
ejpam-7020	1	49	as	as	ADP
ejpam-7020	1	50	case	case	NOUN
ejpam-7020	1	51	studies	study	NOUN
ejpam-7020	1	52	suhaila	suhaila	PROPN
ejpam-7020	1	53	saidat1	saidat1	PROPN
ejpam-7020	1	54	,	,	PUNCT
ejpam-7020	1	55	yanal	yanal	PROPN
ejpam-7020	1	56	al	al	PROPN
ejpam-7020	1	57	-	-	PUNCT
ejpam-7020	1	58	shorman	shorman	PROPN
ejpam-7020	1	59	2,∗	2,∗	NUM
ejpam-7020	1	60	,	,	PUNCT
ejpam-7020	1	61	ishak	ishak	PROPN
ejpam-7020	1	62	hashim2,3	hashim2,3	PROPN
ejpam-7020	1	63	,	,	PUNCT
ejpam-7020	1	64	obadah	obadah	PROPN
ejpam-7020	1	65	said	say	VERB
ejpam-7020	1	66	solaiman2	solaiman2	PROPN
ejpam-7020	1	67	,	,	PUNCT
ejpam-7020	1	68	ahmad	ahmad	PROPN
ejpam-7020	1	69	al	al	PROPN
ejpam-7020	1	70	-	-	PUNCT
ejpam-7020	1	71	hammouri1	hammouri1	PROPN
ejpam-7020	1	72	,	,	PUNCT
ejpam-7020	1	73	mohammad	mohammad	PROPN
ejpam-7020	1	74	almousa1	almousa1	PROPN
ejpam-7020	1	75	,	,	PUNCT
ejpam-7020	1	76	abdullah	abdullah	PROPN
ejpam-7020	1	77	alsoboh	alsoboh	NOUN
ejpam-7020	1	78	4	4	NUM
ejpam-7020	1	79	1	1	NUM
ejpam-7020	1	80	department	department	NOUN
ejpam-7020	1	81	of	of	ADP
ejpam-7020	1	82	mathematics	mathematic	NOUN
ejpam-7020	1	83	,	,	PUNCT
ejpam-7020	1	84	faculty	faculty	NOUN
ejpam-7020	1	85	of	of	ADP
ejpam-7020	1	86	science	science	NOUN
ejpam-7020	1	87	and	and	CCONJ
ejpam-7020	1	88	technology	technology	NOUN
ejpam-7020	1	89	,	,	PUNCT
ejpam-7020	1	90	irbid	irbid	VERB
ejpam-7020	1	91	national	national	ADJ
ejpam-7020	1	92	university	university	NOUN
ejpam-7020	1	93	,	,	PUNCT
ejpam-7020	1	94	irbid	irbid	PROPN
ejpam-7020	1	95	,	,	PUNCT
ejpam-7020	1	96	jordan	jordan	PROPN
ejpam-7020	1	97	2	2	NUM
ejpam-7020	1	98	department	department	NOUN
ejpam-7020	1	99	of	of	ADP
ejpam-7020	1	100	mathematical	mathematical	ADJ
ejpam-7020	1	101	sciences	science	NOUN
ejpam-7020	1	102	,	,	PUNCT
ejpam-7020	1	103	faculty	faculty	NOUN
ejpam-7020	1	104	of	of	ADP
ejpam-7020	1	105	science	science	PROPN
ejpam-7020	1	106	&	&	CCONJ
ejpam-7020	1	107	technology	technology	PROPN
ejpam-7020	1	108	,	,	PUNCT
ejpam-7020	1	109	universiti	universiti	PROPN
ejpam-7020	1	110	kebangsaan	kebangsaan	PROPN
ejpam-7020	1	111	malaysia	malaysia	PROPN
ejpam-7020	1	112	,	,	PUNCT
ejpam-7020	1	113	43600	43600	NUM
ejpam-7020	1	114	bangi	bangi	PROPN
ejpam-7020	1	115	,	,	PUNCT
ejpam-7020	1	116	selangor	selangor	PROPN
ejpam-7020	1	117	,	,	PUNCT
ejpam-7020	1	118	malaysia	malaysia	PROPN
ejpam-7020	1	119	3	3	NUM
ejpam-7020	1	120	nonlinear	nonlinear	ADJ
ejpam-7020	1	121	dynamics	dynamic	NOUN
ejpam-7020	1	122	research	research	NOUN
ejpam-7020	1	123	center	center	NOUN
ejpam-7020	1	124	(	(	PUNCT
ejpam-7020	1	125	ndrc	ndrc	PROPN
ejpam-7020	1	126	)	)	PUNCT
ejpam-7020	1	127	,	,	PUNCT
ejpam-7020	1	128	ajman	ajman	PROPN
ejpam-7020	1	129	university	university	PROPN
ejpam-7020	1	130	,	,	PUNCT
ejpam-7020	1	131	ajman	ajman	PROPN
ejpam-7020	1	132	,	,	PUNCT
ejpam-7020	1	133	p.o	p.o	PROPN
ejpam-7020	1	134	.	.	PROPN
ejpam-7020	1	135	box	box	PROPN
ejpam-7020	1	136	346	346	NUM
ejpam-7020	1	137	,	,	PUNCT
ejpam-7020	1	138	united	united	PROPN
ejpam-7020	1	139	arab	arab	PROPN
ejpam-7020	1	140	emirates	emirates	PROPN
ejpam-7020	1	141	4	4	NUM
ejpam-7020	1	142	department	department	NOUN
ejpam-7020	1	143	of	of	ADP
ejpam-7020	1	144	basic	basic	ADJ
ejpam-7020	1	145	and	and	CCONJ
ejpam-7020	1	146	applied	applied	ADJ
ejpam-7020	1	147	sciences	science	NOUN
ejpam-7020	1	148	,	,	PUNCT
ejpam-7020	1	149	college	college	NOUN
ejpam-7020	1	150	of	of	ADP
ejpam-7020	1	151	applied	apply	VERB
ejpam-7020	1	152	and	and	CCONJ
ejpam-7020	1	153	health	health	NOUN
ejpam-7020	1	154	sciences	science	NOUN
ejpam-7020	1	155	,	,	PUNCT
ejpam-7020	1	156	a’sharqiyah	a’sharqiyah	PROPN
ejpam-7020	1	157	university	university	NOUN
ejpam-7020	1	158	,	,	PUNCT
ejpam-7020	1	159	post	post	PROPN
ejpam-7020	1	160	box	box	PROPN
ejpam-7020	1	161	no	no	INTJ
ejpam-7020	1	162	.	.	PROPN
ejpam-7020	1	163	42	42	NUM
ejpam-7020	1	164	,	,	PUNCT
ejpam-7020	1	165	post	post	VERB
ejpam-7020	1	166	code	code	NOUN
ejpam-7020	1	167	no	no	INTJ
ejpam-7020	1	168	.	.	PROPN
ejpam-7020	1	169	400	400	NUM
ejpam-7020	1	170	,	,	PUNCT
ejpam-7020	1	171	ibra	ibra	NOUN
ejpam-7020	1	172	,	,	PUNCT
ejpam-7020	1	173	sultanate	sultanate	NOUN
ejpam-7020	1	174	of	of	ADP
ejpam-7020	1	175	oman	oman	PROPN
ejpam-7020	1	176	abstract	abstract	NOUN
ejpam-7020	1	177	.	.	PUNCT
ejpam-7020	2	1	this	this	DET
ejpam-7020	2	2	paper	paper	NOUN
ejpam-7020	2	3	provides	provide	VERB
ejpam-7020	2	4	a	a	DET
ejpam-7020	2	5	structured	structured	ADJ
ejpam-7020	2	6	and	and	CCONJ
ejpam-7020	2	7	reproducible	reproducible	ADJ
ejpam-7020	2	8	guide	guide	NOUN
ejpam-7020	2	9	for	for	ADP
ejpam-7020	2	10	analyzing	analyze	VERB
ejpam-7020	2	11	the	the	DET
ejpam-7020	2	12	local	local	ADJ
ejpam-7020	2	13	stability	stability	NOUN
ejpam-7020	2	14	of	of	ADP
ejpam-7020	2	15	nonlinear	nonlinear	ADJ
ejpam-7020	2	16	dynamical	dynamical	ADJ
ejpam-7020	2	17	systems	system	NOUN
ejpam-7020	2	18	by	by	ADP
ejpam-7020	2	19	systematically	systematically	ADV
ejpam-7020	2	20	combining	combine	VERB
ejpam-7020	2	21	analytical	analytical	ADJ
ejpam-7020	2	22	linearization	linearization	NOUN
ejpam-7020	2	23	with	with	ADP
ejpam-7020	2	24	computational	computational	ADJ
ejpam-7020	2	25	phase	phase	NOUN
ejpam-7020	2	26	portrait	portrait	NOUN
ejpam-7020	2	27	visualization	visualization	NOUN
ejpam-7020	2	28	.	.	PUNCT
ejpam-7020	3	1	although	although	SCONJ
ejpam-7020	3	2	these	these	DET
ejpam-7020	3	3	techniques	technique	NOUN
ejpam-7020	3	4	are	be	AUX
ejpam-7020	3	5	standard	standard	ADJ
ejpam-7020	3	6	,	,	PUNCT
ejpam-7020	3	7	introductory	introductory	ADJ
ejpam-7020	3	8	materials	material	NOUN
ejpam-7020	3	9	often	often	ADV
ejpam-7020	3	10	lack	lack	VERB
ejpam-7020	3	11	a	a	DET
ejpam-7020	3	12	unified	unified	ADJ
ejpam-7020	3	13	code	code	NOUN
ejpam-7020	3	14	-	-	PUNCT
ejpam-7020	3	15	based	base	VERB
ejpam-7020	3	16	workflow	workflow	NOUN
ejpam-7020	3	17	that	that	PRON
ejpam-7020	3	18	connects	connect	VERB
ejpam-7020	3	19	abstract	abstract	ADJ
ejpam-7020	3	20	theory	theory	NOUN
ejpam-7020	3	21	to	to	ADP
ejpam-7020	3	22	practical	practical	ADJ
ejpam-7020	3	23	,	,	PUNCT
ejpam-7020	3	24	visual	visual	ADJ
ejpam-7020	3	25	interpretation	interpretation	NOUN
ejpam-7020	3	26	.	.	PUNCT
ejpam-7020	4	1	this	this	DET
ejpam-7020	4	2	guide	guide	NOUN
ejpam-7020	4	3	bridges	bridge	NOUN
ejpam-7020	4	4	that	that	PRON
ejpam-7020	4	5	gap	gap	NOUN
ejpam-7020	4	6	using	use	VERB
ejpam-7020	4	7	two	two	NUM
ejpam-7020	4	8	canonical	canonical	ADJ
ejpam-7020	4	9	models	model	NOUN
ejpam-7020	4	10	from	from	ADP
ejpam-7020	4	11	different	different	ADJ
ejpam-7020	4	12	scientific	scientific	ADJ
ejpam-7020	4	13	domains	domain	NOUN
ejpam-7020	4	14	:	:	PUNCT
ejpam-7020	4	15	the	the	DET
ejpam-7020	4	16	lotka	lotka	PROPN
ejpam-7020	4	17	-	-	PUNCT
ejpam-7020	4	18	volterra	volterra	PROPN
ejpam-7020	4	19	predator	predator	NOUN
ejpam-7020	4	20	-	-	PUNCT
ejpam-7020	4	21	prey	prey	NOUN
ejpam-7020	4	22	model	model	NOUN
ejpam-7020	4	23	and	and	CCONJ
ejpam-7020	4	24	the	the	DET
ejpam-7020	4	25	susceptible	susceptible	ADJ
ejpam-7020	4	26	infected	infect	VERB
ejpam-7020	4	27	recovered	recover	VERB
ejpam-7020	4	28	(	(	PUNCT
ejpam-7020	4	29	sir	sir	NOUN
ejpam-7020	4	30	)	)	PUNCT
ejpam-7020	4	31	epidemic	epidemic	NOUN
ejpam-7020	4	32	model	model	NOUN
ejpam-7020	4	33	.	.	PUNCT
ejpam-7020	5	1	for	for	ADP
ejpam-7020	5	2	each	each	DET
ejpam-7020	5	3	system	system	NOUN
ejpam-7020	5	4	,	,	PUNCT
ejpam-7020	5	5	we	we	PRON
ejpam-7020	5	6	identify	identify	VERB
ejpam-7020	5	7	equilibrium	equilibrium	NOUN
ejpam-7020	5	8	points	point	NOUN
ejpam-7020	5	9	,	,	PUNCT
ejpam-7020	5	10	compute	compute	VERB
ejpam-7020	5	11	the	the	DET
ejpam-7020	5	12	jacobian	jacobian	ADJ
ejpam-7020	5	13	matrix	matrix	NOUN
ejpam-7020	5	14	,	,	PUNCT
ejpam-7020	5	15	and	and	CCONJ
ejpam-7020	5	16	use	use	VERB
ejpam-7020	5	17	eigenvalue	eigenvalue	NOUN
ejpam-7020	5	18	analysis	analysis	NOUN
ejpam-7020	5	19	to	to	PART
ejpam-7020	5	20	determine	determine	VERB
ejpam-7020	5	21	local	local	ADJ
ejpam-7020	5	22	stability	stability	NOUN
ejpam-7020	5	23	,	,	PUNCT
ejpam-7020	5	24	and	and	CCONJ
ejpam-7020	5	25	perform	perform	VERB
ejpam-7020	5	26	a	a	DET
ejpam-7020	5	27	sensitivity	sensitivity	NOUN
ejpam-7020	5	28	analysis	analysis	NOUN
ejpam-7020	5	29	to	to	PART
ejpam-7020	5	30	explore	explore	VERB
ejpam-7020	5	31	how	how	SCONJ
ejpam-7020	5	32	dynamics	dynamic	NOUN
ejpam-7020	5	33	are	be	AUX
ejpam-7020	5	34	affected	affect	VERB
ejpam-7020	5	35	by	by	ADP
ejpam-7020	5	36	key	key	ADJ
ejpam-7020	5	37	parameters	parameter	NOUN
ejpam-7020	5	38	.	.	PUNCT
ejpam-7020	6	1	by	by	ADP
ejpam-7020	6	2	comparing	compare	VERB
ejpam-7020	6	3	ecological	ecological	ADJ
ejpam-7020	6	4	and	and	CCONJ
ejpam-7020	6	5	epidemiological	epidemiological	ADJ
ejpam-7020	6	6	models	model	NOUN
ejpam-7020	6	7	,	,	PUNCT
ejpam-7020	6	8	we	we	PRON
ejpam-7020	6	9	highlight	highlight	VERB
ejpam-7020	6	10	how	how	SCONJ
ejpam-7020	6	11	shared	share	VERB
ejpam-7020	6	12	mathematical	mathematical	ADJ
ejpam-7020	6	13	principles	principle	NOUN
ejpam-7020	6	14	lead	lead	VERB
ejpam-7020	6	15	to	to	ADP
ejpam-7020	6	16	distinct	distinct	ADJ
ejpam-7020	6	17	real	real	ADJ
ejpam-7020	6	18	-	-	PUNCT
ejpam-7020	6	19	world	world	NOUN
ejpam-7020	6	20	dynamics	dynamic	NOUN
ejpam-7020	6	21	,	,	PUNCT
ejpam-7020	6	22	such	such	ADJ
ejpam-7020	6	23	as	as	ADP
ejpam-7020	6	24	persistent	persistent	ADJ
ejpam-7020	6	25	oscillations	oscillation	NOUN
ejpam-7020	6	26	versus	versus	ADP
ejpam-7020	6	27	threshold	threshold	NOUN
ejpam-7020	6	28	-	-	PUNCT
ejpam-7020	6	29	based	base	VERB
ejpam-7020	6	30	outbreaks	outbreak	NOUN
ejpam-7020	6	31	.	.	PUNCT
ejpam-7020	7	1	pythongenerated	pythongenerate	VERB
ejpam-7020	7	2	phase	phase	NOUN
ejpam-7020	7	3	portraits	portrait	NOUN
ejpam-7020	7	4	are	be	AUX
ejpam-7020	7	5	used	use	VERB
ejpam-7020	7	6	throughout	throughout	ADP
ejpam-7020	7	7	to	to	PART
ejpam-7020	7	8	visually	visually	ADV
ejpam-7020	7	9	validate	validate	VERB
ejpam-7020	7	10	the	the	DET
ejpam-7020	7	11	analytical	analytical	ADJ
ejpam-7020	7	12	results	result	NOUN
ejpam-7020	7	13	,	,	PUNCT
ejpam-7020	7	14	offering	offer	VERB
ejpam-7020	7	15	an	an	DET
ejpam-7020	7	16	intuitive	intuitive	ADJ
ejpam-7020	7	17	complement	complement	NOUN
ejpam-7020	7	18	to	to	ADP
ejpam-7020	7	19	the	the	DET
ejpam-7020	7	20	theory	theory	NOUN
ejpam-7020	7	21	.	.	PUNCT
ejpam-7020	8	1	this	this	DET
ejpam-7020	8	2	work	work	NOUN
ejpam-7020	8	3	serves	serve	VERB
ejpam-7020	8	4	as	as	ADP
ejpam-7020	8	5	a	a	DET
ejpam-7020	8	6	practical	practical	ADJ
ejpam-7020	8	7	toolkit	toolkit	NOUN
ejpam-7020	8	8	for	for	ADP
ejpam-7020	8	9	students	student	NOUN
ejpam-7020	8	10	and	and	CCONJ
ejpam-7020	8	11	researchers	researcher	NOUN
ejpam-7020	8	12	new	new	ADJ
ejpam-7020	8	13	to	to	PART
ejpam-7020	8	14	nonlinear	nonlinear	ADJ
ejpam-7020	8	15	modeling	modeling	NOUN
ejpam-7020	8	16	,	,	PUNCT
ejpam-7020	8	17	emphasizing	emphasize	VERB
ejpam-7020	8	18	a	a	DET
ejpam-7020	8	19	clear	clear	ADJ
ejpam-7020	8	20	step	step	NOUN
ejpam-7020	8	21	-	-	PUNCT
ejpam-7020	8	22	by	by	ADP
ejpam-7020	8	23	-	-	PUNCT
ejpam-7020	8	24	step	step	NOUN
ejpam-7020	8	25	process	process	NOUN
ejpam-7020	8	26	essential	essential	ADJ
ejpam-7020	8	27	for	for	ADP
ejpam-7020	8	28	both	both	CCONJ
ejpam-7020	8	29	educational	educational	ADJ
ejpam-7020	8	30	settings	setting	NOUN
ejpam-7020	8	31	and	and	CCONJ
ejpam-7020	8	32	applied	apply	VERB
ejpam-7020	8	33	research	research	NOUN
ejpam-7020	8	34	.	.	PUNCT
ejpam-7020	9	1	2020	2020	NUM
ejpam-7020	9	2	mathematics	mathematic	NOUN
ejpam-7020	9	3	subject	subject	NOUN
ejpam-7020	9	4	classifications	classification	NOUN
ejpam-7020	9	5	:	:	PUNCT
ejpam-7020	9	6	34d20	34d20	NUM
ejpam-7020	9	7	,	,	PUNCT
ejpam-7020	9	8	92d25	92d25	NUM
ejpam-7020	9	9	key	key	ADJ
ejpam-7020	9	10	words	word	NOUN
ejpam-7020	9	11	and	and	CCONJ
ejpam-7020	9	12	phrases	phrase	NOUN
ejpam-7020	9	13	:	:	PUNCT
ejpam-7020	9	14	nonlinear	nonlinear	ADJ
ejpam-7020	9	15	dynamics	dynamic	NOUN
ejpam-7020	9	16	,	,	PUNCT
ejpam-7020	9	17	stability	stability	NOUN
ejpam-7020	9	18	analysis	analysis	NOUN
ejpam-7020	9	19	,	,	PUNCT
ejpam-7020	9	20	linearization	linearization	NOUN
ejpam-7020	9	21	,	,	PUNCT
ejpam-7020	9	22	phase	phase	NOUN
ejpam-7020	9	23	portrait	portrait	NOUN
ejpam-7020	9	24	,	,	PUNCT
ejpam-7020	9	25	lotka	lotka	PROPN
ejpam-7020	9	26	-	-	PUNCT
ejpam-7020	9	27	volterra	volterra	PROPN
ejpam-7020	9	28	model	model	NOUN
ejpam-7020	9	29	,	,	PUNCT
ejpam-7020	9	30	sir	sir	NOUN
ejpam-7020	9	31	model	model	NOUN
ejpam-7020	9	32	∗corresponding	∗corresponde	VERB
ejpam-7020	9	33	author	author	NOUN
ejpam-7020	9	34	.	.	PUNCT
ejpam-7020	10	1	doi	doi	NOUN
ejpam-7020	10	2	:	:	PUNCT
ejpam-7020	10	3	https://doi.org/10.29020/nybg.ejpam.v18i4.7020	https://doi.org/10.29020/nybg.ejpam.v18i4.7020	NOUN
ejpam-7020	10	4	email	email	NOUN
ejpam-7020	10	5	addresses	address	NOUN
ejpam-7020	10	6	:	:	PUNCT
ejpam-7020	10	7	p114391@siswa.ukm.edu.my	p114391@siswa.ukm.edu.my	PROPN
ejpam-7020	10	8	(	(	PUNCT
ejpam-7020	10	9	y.	y.	PROPN
ejpam-7020	10	10	al	al	PROPN
ejpam-7020	10	11	-	-	PUNCT
ejpam-7020	10	12	shorman	shorman	PROPN
ejpam-7020	10	13	)	)	PUNCT
ejpam-7020	10	14	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-7020	10	15	1	1	NUM
ejpam-7020	10	16	copyright	copyright	NOUN
ejpam-7020	10	17	:	:	PUNCT
ejpam-7020	11	1	©	©	PROPN
ejpam-7020	11	2	2025	2025	NUM
ejpam-7020	11	3	the	the	DET
ejpam-7020	11	4	author(s	author(s	NOUN
ejpam-7020	11	5	)	)	PUNCT
ejpam-7020	11	6	.	.	PUNCT
ejpam-7020	12	1	(	(	PUNCT
ejpam-7020	12	2	cc	cc	NOUN
ejpam-7020	12	3	by	by	ADP
ejpam-7020	12	4	-	-	PUNCT
ejpam-7020	12	5	nc	nc	PROPN
ejpam-7020	12	6	4.0	4.0	NUM
ejpam-7020	12	7	)	)	PUNCT
ejpam-7020	12	8	s.	s.	PROPN
ejpam-7020	12	9	saidat	saidat	PROPN
ejpam-7020	12	10	et	et	PROPN
ejpam-7020	12	11	al	al	PROPN
ejpam-7020	12	12	.	.	PUNCT
ejpam-7020	12	13	/	/	SYM
ejpam-7020	12	14	eur	eur	PROPN
ejpam-7020	12	15	.	.	PUNCT
ejpam-7020	13	1	j.	j.	PROPN
ejpam-7020	13	2	pure	pure	PROPN
ejpam-7020	13	3	appl	appl	PROPN
ejpam-7020	13	4	.	.	PROPN
ejpam-7020	13	5	math	math	PROPN
ejpam-7020	13	6	,	,	PUNCT
ejpam-7020	13	7	18	18	NUM
ejpam-7020	13	8	(	(	PUNCT
ejpam-7020	13	9	4	4	NUM
ejpam-7020	13	10	)	)	PUNCT
ejpam-7020	13	11	(	(	PUNCT
ejpam-7020	13	12	2025	2025	NUM
ejpam-7020	13	13	)	)	PUNCT
ejpam-7020	13	14	,	,	PUNCT
ejpam-7020	13	15	7020	7020	NUM
ejpam-7020	13	16	2	2	NUM
ejpam-7020	13	17	of	of	ADP
ejpam-7020	13	18	16	16	NUM
ejpam-7020	13	19	1	1	NUM
ejpam-7020	13	20	.	.	PUNCT
ejpam-7020	14	1	introduction	introduction	NOUN
ejpam-7020	14	2	in	in	ADP
ejpam-7020	14	3	many	many	ADJ
ejpam-7020	14	4	areas	area	NOUN
ejpam-7020	14	5	of	of	ADP
ejpam-7020	14	6	science	science	NOUN
ejpam-7020	14	7	and	and	CCONJ
ejpam-7020	14	8	engineering	engineering	NOUN
ejpam-7020	14	9	,	,	PUNCT
ejpam-7020	14	10	from	from	ADP
ejpam-7020	14	11	population	population	NOUN
ejpam-7020	14	12	dynamics	dynamic	NOUN
ejpam-7020	14	13	to	to	PART
ejpam-7020	14	14	control	control	VERB
ejpam-7020	14	15	theory	theory	NOUN
ejpam-7020	14	16	,	,	PUNCT
ejpam-7020	14	17	understanding	understand	VERB
ejpam-7020	14	18	the	the	DET
ejpam-7020	14	19	stability	stability	NOUN
ejpam-7020	14	20	of	of	ADP
ejpam-7020	14	21	nonlinear	nonlinear	ADJ
ejpam-7020	14	22	systems	system	NOUN
ejpam-7020	14	23	is	be	AUX
ejpam-7020	14	24	essential	essential	ADJ
ejpam-7020	14	25	[	[	X
ejpam-7020	14	26	1	1	NUM
ejpam-7020	14	27	,	,	PUNCT
ejpam-7020	14	28	2	2	NUM
ejpam-7020	14	29	]	]	PUNCT
ejpam-7020	14	30	.	.	PUNCT
ejpam-7020	15	1	analyzing	analyze	VERB
ejpam-7020	15	2	how	how	SCONJ
ejpam-7020	15	3	a	a	DET
ejpam-7020	15	4	system	system	NOUN
ejpam-7020	15	5	behaves	behave	VERB
ejpam-7020	15	6	near	near	ADP
ejpam-7020	15	7	its	its	PRON
ejpam-7020	15	8	equilibrium	equilibrium	NOUN
ejpam-7020	15	9	points	point	NOUN
ejpam-7020	15	10	provides	provide	VERB
ejpam-7020	15	11	invaluable	invaluable	ADJ
ejpam-7020	15	12	insight	insight	NOUN
ejpam-7020	15	13	into	into	ADP
ejpam-7020	15	14	its	its	PRON
ejpam-7020	15	15	overall	overall	ADJ
ejpam-7020	15	16	structure	structure	NOUN
ejpam-7020	15	17	and	and	CCONJ
ejpam-7020	15	18	long	long	ADJ
ejpam-7020	15	19	-	-	PUNCT
ejpam-7020	15	20	term	term	NOUN
ejpam-7020	15	21	evolution	evolution	NOUN
ejpam-7020	15	22	[	[	X
ejpam-7020	15	23	3	3	NUM
ejpam-7020	15	24	,	,	PUNCT
ejpam-7020	15	25	4	4	NUM
ejpam-7020	15	26	]	]	PUNCT
ejpam-7020	15	27	.	.	PUNCT
ejpam-7020	16	1	the	the	DET
ejpam-7020	16	2	classical	classical	ADJ
ejpam-7020	16	3	tools	tool	NOUN
ejpam-7020	16	4	for	for	ADP
ejpam-7020	16	5	this	this	DET
ejpam-7020	16	6	task	task	NOUN
ejpam-7020	16	7	are	be	AUX
ejpam-7020	16	8	linearization	linearization	NOUN
ejpam-7020	16	9	and	and	CCONJ
ejpam-7020	16	10	phase	phase	NOUN
ejpam-7020	16	11	portrait	portrait	NOUN
ejpam-7020	16	12	analysis	analysis	NOUN
ejpam-7020	16	13	.	.	PUNCT
ejpam-7020	17	1	the	the	DET
ejpam-7020	17	2	theoretical	theoretical	ADJ
ejpam-7020	17	3	foundations	foundation	NOUN
ejpam-7020	17	4	for	for	ADP
ejpam-7020	17	5	this	this	DET
ejpam-7020	17	6	approach	approach	NOUN
ejpam-7020	17	7	were	be	AUX
ejpam-7020	17	8	laid	lay	VERB
ejpam-7020	17	9	out	out	ADP
ejpam-7020	17	10	in	in	ADP
ejpam-7020	17	11	inspiring	inspire	VERB
ejpam-7020	17	12	texts	text	NOUN
ejpam-7020	17	13	that	that	PRON
ejpam-7020	17	14	remain	remain	VERB
ejpam-7020	17	15	fundamental	fundamental	ADJ
ejpam-7020	17	16	to	to	ADP
ejpam-7020	17	17	the	the	DET
ejpam-7020	17	18	field	field	NOUN
ejpam-7020	17	19	today	today	NOUN
ejpam-7020	17	20	[	[	X
ejpam-7020	17	21	5	5	NUM
ejpam-7020	17	22	]	]	PUNCT
ejpam-7020	17	23	.	.	PUNCT
ejpam-7020	18	1	linearization	linearization	NOUN
ejpam-7020	18	2	provides	provide	VERB
ejpam-7020	18	3	a	a	DET
ejpam-7020	18	4	precise	precise	ADJ
ejpam-7020	18	5	criterion	criterion	NOUN
ejpam-7020	18	6	for	for	ADP
ejpam-7020	18	7	local	local	ADJ
ejpam-7020	18	8	stability	stability	NOUN
ejpam-7020	18	9	by	by	ADP
ejpam-7020	18	10	approximating	approximate	VERB
ejpam-7020	18	11	a	a	DET
ejpam-7020	18	12	nonlinear	nonlinear	ADJ
ejpam-7020	18	13	system	system	NOUN
ejpam-7020	18	14	near	near	ADP
ejpam-7020	18	15	an	an	DET
ejpam-7020	18	16	equilibrium	equilibrium	NOUN
ejpam-7020	18	17	,	,	PUNCT
ejpam-7020	18	18	while	while	SCONJ
ejpam-7020	18	19	phase	phase	NOUN
ejpam-7020	18	20	portraits	portrait	NOUN
ejpam-7020	18	21	offer	offer	VERB
ejpam-7020	18	22	an	an	DET
ejpam-7020	18	23	intuitive	intuitive	ADJ
ejpam-7020	18	24	geometric	geometric	ADJ
ejpam-7020	18	25	understanding	understanding	NOUN
ejpam-7020	18	26	of	of	ADP
ejpam-7020	18	27	the	the	DET
ejpam-7020	18	28	dynamic	dynamic	NOUN
ejpam-7020	18	29	of	of	ADP
ejpam-7020	18	30	the	the	DET
ejpam-7020	18	31	system	system	NOUN
ejpam-7020	18	32	[	[	X
ejpam-7020	18	33	6	6	NUM
ejpam-7020	18	34	,	,	PUNCT
ejpam-7020	18	35	7	7	NUM
ejpam-7020	18	36	]	]	PUNCT
ejpam-7020	18	37	.	.	PUNCT
ejpam-7020	19	1	these	these	DET
ejpam-7020	19	2	foundational	foundational	ADJ
ejpam-7020	19	3	methods	method	NOUN
ejpam-7020	19	4	continue	continue	VERB
ejpam-7020	19	5	to	to	PART
ejpam-7020	19	6	be	be	AUX
ejpam-7020	19	7	the	the	DET
ejpam-7020	19	8	bedrock	bedrock	NOUN
ejpam-7020	19	9	of	of	ADP
ejpam-7020	19	10	modern	modern	ADJ
ejpam-7020	19	11	mathematical	mathematical	ADJ
ejpam-7020	19	12	modeling	modeling	NOUN
ejpam-7020	19	13	.	.	PUNCT
ejpam-7020	20	1	the	the	DET
ejpam-7020	20	2	lotka	lotka	PROPN
ejpam-7020	20	3	-	-	PUNCT
ejpam-7020	20	4	volterra	volterra	PROPN
ejpam-7020	20	5	model	model	NOUN
ejpam-7020	20	6	,	,	PUNCT
ejpam-7020	20	7	for	for	ADP
ejpam-7020	20	8	example	example	NOUN
ejpam-7020	20	9	,	,	PUNCT
ejpam-7020	20	10	is	be	AUX
ejpam-7020	20	11	still	still	ADV
ejpam-7020	20	12	actively	actively	ADV
ejpam-7020	20	13	used	use	VERB
ejpam-7020	20	14	and	and	CCONJ
ejpam-7020	20	15	extended	extend	VERB
ejpam-7020	20	16	to	to	PART
ejpam-7020	20	17	explore	explore	VERB
ejpam-7020	20	18	complex	complex	ADJ
ejpam-7020	20	19	ecological	ecological	ADJ
ejpam-7020	20	20	interactions	interaction	NOUN
ejpam-7020	20	21	such	such	ADJ
ejpam-7020	20	22	as	as	ADP
ejpam-7020	20	23	[	[	X
ejpam-7020	20	24	8	8	NUM
ejpam-7020	20	25	]	]	PUNCT
ejpam-7020	20	26	and	and	CCONJ
ejpam-7020	20	27	[	[	X
ejpam-7020	20	28	9	9	NUM
ejpam-7020	20	29	]	]	PUNCT
ejpam-7020	20	30	.	.	PUNCT
ejpam-7020	21	1	similarly	similarly	ADV
ejpam-7020	21	2	,	,	PUNCT
ejpam-7020	21	3	the	the	DET
ejpam-7020	21	4	sir	sir	NOUN
ejpam-7020	21	5	model	model	NOUN
ejpam-7020	21	6	forms	form	VERB
ejpam-7020	21	7	the	the	DET
ejpam-7020	21	8	basis	basis	NOUN
ejpam-7020	21	9	for	for	ADP
ejpam-7020	21	10	a	a	DET
ejpam-7020	21	11	large	large	ADJ
ejpam-7020	21	12	body	body	NOUN
ejpam-7020	21	13	of	of	ADP
ejpam-7020	21	14	epidemiological	epidemiological	ADJ
ejpam-7020	21	15	research	research	NOUN
ejpam-7020	21	16	,	,	PUNCT
ejpam-7020	21	17	providing	provide	VERB
ejpam-7020	21	18	critical	critical	ADJ
ejpam-7020	21	19	insights	insight	NOUN
ejpam-7020	21	20	into	into	ADP
ejpam-7020	21	21	the	the	DET
ejpam-7020	21	22	spread	spread	NOUN
ejpam-7020	21	23	of	of	ADP
ejpam-7020	21	24	infectious	infectious	ADJ
ejpam-7020	21	25	diseases	disease	NOUN
ejpam-7020	21	26	from	from	ADP
ejpam-7020	21	27	influenza	influenza	NOUN
ejpam-7020	21	28	to	to	ADP
ejpam-7020	21	29	recent	recent	ADJ
ejpam-7020	21	30	pandemics	pandemic	NOUN
ejpam-7020	21	31	[	[	X
ejpam-7020	21	32	10	10	NUM
ejpam-7020	21	33	]	]	PUNCT
ejpam-7020	21	34	and	and	CCONJ
ejpam-7020	21	35	[	[	X
ejpam-7020	21	36	11	11	NUM
ejpam-7020	21	37	]	]	PUNCT
ejpam-7020	21	38	.	.	PUNCT
ejpam-7020	22	1	alongside	alongside	ADP
ejpam-7020	22	2	this	this	DET
ejpam-7020	22	3	research	research	NOUN
ejpam-7020	22	4	,	,	PUNCT
ejpam-7020	22	5	there	there	PRON
ejpam-7020	22	6	is	be	VERB
ejpam-7020	22	7	a	a	DET
ejpam-7020	22	8	parallel	parallel	ADJ
ejpam-7020	22	9	conversation	conversation	NOUN
ejpam-7020	22	10	on	on	ADP
ejpam-7020	22	11	the	the	DET
ejpam-7020	22	12	most	most	ADV
ejpam-7020	22	13	effective	effective	ADJ
ejpam-7020	22	14	ways	way	NOUN
ejpam-7020	22	15	to	to	PART
ejpam-7020	22	16	teach	teach	VERB
ejpam-7020	22	17	these	these	DET
ejpam-7020	22	18	concepts	concept	NOUN
ejpam-7020	22	19	.	.	PUNCT
ejpam-7020	23	1	many	many	ADJ
ejpam-7020	23	2	educators	educator	NOUN
ejpam-7020	23	3	have	have	AUX
ejpam-7020	23	4	highlighted	highlight	VERB
ejpam-7020	23	5	the	the	DET
ejpam-7020	23	6	power	power	NOUN
ejpam-7020	23	7	of	of	ADP
ejpam-7020	23	8	computational	computational	ADJ
ejpam-7020	23	9	tools	tool	NOUN
ejpam-7020	23	10	such	such	ADJ
ejpam-7020	23	11	as	as	ADP
ejpam-7020	23	12	python	python	NOUN
ejpam-7020	23	13	and	and	CCONJ
ejpam-7020	23	14	matlab	matlab	PROPN
ejpam-7020	23	15	to	to	PART
ejpam-7020	23	16	help	help	VERB
ejpam-7020	23	17	students	student	NOUN
ejpam-7020	23	18	visualize	visualize	VERB
ejpam-7020	23	19	abstract	abstract	ADJ
ejpam-7020	23	20	concepts	concept	NOUN
ejpam-7020	23	21	[	[	X
ejpam-7020	23	22	12	12	NUM
ejpam-7020	23	23	,	,	PUNCT
ejpam-7020	23	24	13	13	NUM
ejpam-7020	23	25	]	]	PUNCT
ejpam-7020	23	26	.	.	PUNCT
ejpam-7020	24	1	however	however	ADV
ejpam-7020	24	2	,	,	PUNCT
ejpam-7020	24	3	while	while	SCONJ
ejpam-7020	24	4	numerous	numerous	ADJ
ejpam-7020	24	5	resources	resource	NOUN
ejpam-7020	24	6	focus	focus	VERB
ejpam-7020	24	7	on	on	ADP
ejpam-7020	24	8	either	either	CCONJ
ejpam-7020	24	9	the	the	DET
ejpam-7020	24	10	deep	deep	NOUN
ejpam-7020	24	11	of	of	ADP
ejpam-7020	24	12	theory	theory	NOUN
ejpam-7020	24	13	[	[	X
ejpam-7020	24	14	14–16	14–16	NUM
ejpam-7020	24	15	]	]	PUNCT
ejpam-7020	24	16	or	or	CCONJ
ejpam-7020	24	17	advanced	advanced	ADJ
ejpam-7020	24	18	research	research	NOUN
ejpam-7020	24	19	applications	application	NOUN
ejpam-7020	24	20	[	[	X
ejpam-7020	24	21	17	17	NUM
ejpam-7020	24	22	]	]	PUNCT
ejpam-7020	24	23	,	,	PUNCT
ejpam-7020	24	24	there	there	PRON
ejpam-7020	24	25	remains	remain	VERB
ejpam-7020	24	26	a	a	DET
ejpam-7020	24	27	need	need	NOUN
ejpam-7020	24	28	for	for	ADP
ejpam-7020	24	29	accessible	accessible	ADJ
ejpam-7020	24	30	,	,	PUNCT
ejpam-7020	24	31	step	step	NOUN
ejpam-7020	24	32	by	by	ADP
ejpam-7020	24	33	step	step	NOUN
ejpam-7020	24	34	guides	guide	NOUN
ejpam-7020	24	35	that	that	PRON
ejpam-7020	24	36	explicitly	explicitly	ADV
ejpam-7020	24	37	connect	connect	VERB
ejpam-7020	24	38	analytical	analytical	ADJ
ejpam-7020	24	39	calculations	calculation	NOUN
ejpam-7020	24	40	of	of	ADP
ejpam-7020	24	41	stability	stability	NOUN
ejpam-7020	24	42	with	with	ADP
ejpam-7020	24	43	their	their	PRON
ejpam-7020	24	44	computational	computational	ADJ
ejpam-7020	24	45	visualization	visualization	NOUN
ejpam-7020	24	46	.	.	PUNCT
ejpam-7020	25	1	this	this	PRON
ejpam-7020	25	2	is	be	AUX
ejpam-7020	25	3	particularly	particularly	ADV
ejpam-7020	25	4	true	true	ADJ
ejpam-7020	25	5	for	for	ADP
ejpam-7020	25	6	cross	cross	ADJ
ejpam-7020	25	7	-	-	ADJ
ejpam-7020	25	8	disciplinary	disciplinary	ADJ
ejpam-7020	25	9	leaners	leaner	NOUN
ejpam-7020	25	10	who	who	PRON
ejpam-7020	25	11	need	need	VERB
ejpam-7020	25	12	to	to	PART
ejpam-7020	25	13	apply	apply	VERB
ejpam-7020	25	14	these	these	DET
ejpam-7020	25	15	methods	method	NOUN
ejpam-7020	25	16	without	without	ADP
ejpam-7020	25	17	necessarily	necessarily	ADV
ejpam-7020	25	18	having	have	VERB
ejpam-7020	25	19	a	a	DET
ejpam-7020	25	20	deep	deep	ADJ
ejpam-7020	25	21	mathematical	mathematical	ADJ
ejpam-7020	25	22	background	background	NOUN
ejpam-7020	25	23	.	.	PUNCT
ejpam-7020	26	1	linearization	linearization	NOUN
ejpam-7020	26	2	techniques	technique	NOUN
ejpam-7020	26	3	can	can	AUX
ejpam-7020	26	4	be	be	AUX
ejpam-7020	26	5	used	use	VERB
ejpam-7020	26	6	to	to	PART
ejpam-7020	26	7	approximate	approximate	VERB
ejpam-7020	26	8	a	a	DET
ejpam-7020	26	9	linear	linear	ADJ
ejpam-7020	26	10	system	system	NOUN
ejpam-7020	26	11	that	that	PRON
ejpam-7020	26	12	closely	closely	ADV
ejpam-7020	26	13	resembles	resemble	VERB
ejpam-7020	26	14	a	a	DET
ejpam-7020	26	15	nonlinear	nonlinear	ADJ
ejpam-7020	26	16	system	system	NOUN
ejpam-7020	26	17	at	at	ADP
ejpam-7020	26	18	its	its	PRON
ejpam-7020	26	19	equilibrium	equilibrium	NOUN
ejpam-7020	26	20	points	point	NOUN
ejpam-7020	27	1	[	[	X
ejpam-7020	27	2	18	18	NUM
ejpam-7020	27	3	]	]	PUNCT
ejpam-7020	27	4	.	.	PUNCT
ejpam-7020	28	1	standard	standard	ADJ
ejpam-7020	28	2	linear	linear	PROPN
ejpam-7020	28	3	algebraic	algebraic	ADJ
ejpam-7020	28	4	methods	method	NOUN
ejpam-7020	28	5	can	can	AUX
ejpam-7020	28	6	be	be	AUX
ejpam-7020	28	7	employed	employ	VERB
ejpam-7020	28	8	to	to	PART
ejpam-7020	28	9	analyze	analyze	VERB
ejpam-7020	28	10	the	the	DET
ejpam-7020	28	11	jacobian	jacobian	ADJ
ejpam-7020	28	12	matrix	matrix	NOUN
ejpam-7020	28	13	in	in	ADP
ejpam-7020	28	14	these	these	DET
ejpam-7020	28	15	places	place	NOUN
ejpam-7020	28	16	to	to	PART
ejpam-7020	28	17	determine	determine	VERB
ejpam-7020	28	18	the	the	DET
ejpam-7020	28	19	nature	nature	NOUN
ejpam-7020	28	20	and	and	CCONJ
ejpam-7020	28	21	stability	stability	NOUN
ejpam-7020	28	22	of	of	ADP
ejpam-7020	28	23	the	the	DET
ejpam-7020	28	24	equilibria	equilibrium	NOUN
ejpam-7020	29	1	[	[	X
ejpam-7020	29	2	19	19	NUM
ejpam-7020	29	3	,	,	PUNCT
ejpam-7020	29	4	20	20	NUM
ejpam-7020	29	5	]	]	PUNCT
ejpam-7020	29	6	.	.	PUNCT
ejpam-7020	30	1	the	the	DET
ejpam-7020	30	2	eigenvalues	eigenvalue	NOUN
ejpam-7020	30	3	of	of	ADP
ejpam-7020	30	4	the	the	DET
ejpam-7020	30	5	jacobian	jacobian	PROPN
ejpam-7020	30	6	indicate	indicate	VERB
ejpam-7020	30	7	whether	whether	SCONJ
ejpam-7020	30	8	an	an	DET
ejpam-7020	30	9	equilibrium	equilibrium	NOUN
ejpam-7020	30	10	point	point	NOUN
ejpam-7020	30	11	is	be	AUX
ejpam-7020	30	12	a	a	DET
ejpam-7020	30	13	saddle	saddle	NOUN
ejpam-7020	30	14	,	,	PUNCT
ejpam-7020	30	15	node	node	NOUN
ejpam-7020	30	16	,	,	PUNCT
ejpam-7020	30	17	or	or	CCONJ
ejpam-7020	30	18	spiral	spiral	ADJ
ejpam-7020	30	19	,	,	PUNCT
ejpam-7020	30	20	as	as	ADV
ejpam-7020	30	21	well	well	ADV
ejpam-7020	30	22	as	as	ADP
ejpam-7020	30	23	its	its	PRON
ejpam-7020	30	24	stability	stability	NOUN
ejpam-7020	30	25	or	or	CCONJ
ejpam-7020	30	26	instability	instability	NOUN
ejpam-7020	30	27	[	[	X
ejpam-7020	30	28	20	20	NUM
ejpam-7020	30	29	]	]	PUNCT
ejpam-7020	30	30	.	.	PUNCT
ejpam-7020	31	1	recent	recent	ADJ
ejpam-7020	31	2	applications	application	NOUN
ejpam-7020	31	3	of	of	ADP
ejpam-7020	31	4	these	these	DET
ejpam-7020	31	5	methods	method	NOUN
ejpam-7020	31	6	can	can	AUX
ejpam-7020	31	7	be	be	AUX
ejpam-7020	31	8	found	find	VERB
ejpam-7020	31	9	in	in	ADP
ejpam-7020	31	10	[	[	X
ejpam-7020	31	11	21–37	21–37	NUM
ejpam-7020	31	12	]	]	PUNCT
ejpam-7020	31	13	.	.	PUNCT
ejpam-7020	32	1	to	to	PART
ejpam-7020	32	2	enhance	enhance	VERB
ejpam-7020	32	3	the	the	DET
ejpam-7020	32	4	analysis	analysis	NOUN
ejpam-7020	32	5	,	,	PUNCT
ejpam-7020	32	6	we	we	PRON
ejpam-7020	32	7	incorporate	incorporate	VERB
ejpam-7020	32	8	a	a	DET
ejpam-7020	32	9	parameter	parameter	NOUN
ejpam-7020	32	10	sensitivity	sensitivity	NOUN
ejpam-7020	32	11	study	study	NOUN
ejpam-7020	32	12	,	,	PUNCT
ejpam-7020	32	13	in	in	ADP
ejpam-7020	32	14	particular	particular	ADJ
ejpam-7020	32	15	,	,	PUNCT
ejpam-7020	32	16	the	the	DET
ejpam-7020	32	17	predation	predation	NOUN
ejpam-7020	32	18	rate	rate	NOUN
ejpam-7020	32	19	parameter	parameter	PROPN
ejpam-7020	32	20	b	b	PROPN
ejpam-7020	32	21	,	,	PUNCT
ejpam-7020	32	22	to	to	PART
ejpam-7020	32	23	investigate	investigate	VERB
ejpam-7020	32	24	how	how	SCONJ
ejpam-7020	32	25	changes	change	NOUN
ejpam-7020	32	26	in	in	ADP
ejpam-7020	32	27	interaction	interaction	NOUN
ejpam-7020	32	28	strength	strength	NOUN
ejpam-7020	32	29	affect	affect	VERB
ejpam-7020	32	30	equilibrium	equilibrium	NOUN
ejpam-7020	32	31	configurations	configuration	NOUN
ejpam-7020	32	32	and	and	CCONJ
ejpam-7020	32	33	stability	stability	NOUN
ejpam-7020	32	34	of	of	ADP
ejpam-7020	32	35	the	the	DET
ejpam-7020	32	36	system	system	NOUN
ejpam-7020	32	37	.	.	PUNCT
ejpam-7020	33	1	beyond	beyond	ADP
ejpam-7020	33	2	predator	predator	NOUN
ejpam-7020	33	3	-	-	PUNCT
ejpam-7020	33	4	prey	prey	NOUN
ejpam-7020	33	5	dynamics	dynamic	NOUN
ejpam-7020	33	6	,	,	PUNCT
ejpam-7020	33	7	nonlinear	nonlinear	ADJ
ejpam-7020	33	8	modeling	modeling	NOUN
ejpam-7020	33	9	is	be	AUX
ejpam-7020	33	10	also	also	ADV
ejpam-7020	33	11	fundamental	fundamental	ADJ
ejpam-7020	33	12	in	in	ADP
ejpam-7020	33	13	epidemiology	epidemiology	NOUN
ejpam-7020	33	14	.	.	PUNCT
ejpam-7020	34	1	the	the	DET
ejpam-7020	34	2	susceptible	susceptible	ADJ
ejpam-7020	34	3	infected	infect	VERB
ejpam-7020	34	4	recovered	recovered	ADJ
ejpam-7020	34	5	model	model	NOUN
ejpam-7020	34	6	is	be	AUX
ejpam-7020	34	7	a	a	DET
ejpam-7020	34	8	cornerstone	cornerstone	NOUN
ejpam-7020	34	9	of	of	ADP
ejpam-7020	34	10	mathematical	mathematical	ADJ
ejpam-7020	34	11	epidemiology	epidemiology	NOUN
ejpam-7020	34	12	,	,	PUNCT
ejpam-7020	34	13	describing	describe	VERB
ejpam-7020	34	14	the	the	DET
ejpam-7020	34	15	spread	spread	NOUN
ejpam-7020	34	16	of	of	ADP
ejpam-7020	34	17	infectious	infectious	ADJ
ejpam-7020	34	18	diseases	disease	NOUN
ejpam-7020	34	19	through	through	ADP
ejpam-7020	34	20	compartments	compartment	NOUN
ejpam-7020	34	21	that	that	PRON
ejpam-7020	34	22	represent	represent	VERB
ejpam-7020	34	23	different	different	ADJ
ejpam-7020	34	24	health	health	NOUN
ejpam-7020	34	25	states	state	NOUN
ejpam-7020	34	26	of	of	ADP
ejpam-7020	34	27	the	the	DET
ejpam-7020	34	28	population	population	NOUN
ejpam-7020	35	1	[	[	X
ejpam-7020	35	2	11	11	NUM
ejpam-7020	35	3	]	]	PUNCT
ejpam-7020	35	4	.	.	PUNCT
ejpam-7020	36	1	the	the	DET
ejpam-7020	36	2	sir	sir	PROPN
ejpam-7020	36	3	model	model	NOUN
ejpam-7020	36	4	,	,	PUNCT
ejpam-7020	36	5	like	like	ADP
ejpam-7020	36	6	the	the	DET
ejpam-7020	36	7	lotka	lotka	PROPN
ejpam-7020	36	8	-	-	PUNCT
ejpam-7020	36	9	volterra	volterra	PROPN
ejpam-7020	36	10	system	system	NOUN
ejpam-7020	36	11	,	,	PUNCT
ejpam-7020	36	12	is	be	AUX
ejpam-7020	36	13	nonlinear	nonlinear	ADJ
ejpam-7020	36	14	and	and	CCONJ
ejpam-7020	36	15	admits	admit	VERB
ejpam-7020	36	16	equilibrium	equilibrium	NOUN
ejpam-7020	36	17	points	point	NOUN
ejpam-7020	36	18	whose	whose	DET
ejpam-7020	36	19	stability	stability	NOUN
ejpam-7020	36	20	can	can	AUX
ejpam-7020	36	21	be	be	AUX
ejpam-7020	36	22	analyzed	analyze	VERB
ejpam-7020	36	23	using	use	VERB
ejpam-7020	36	24	jacobian	jacobian	ADJ
ejpam-7020	36	25	linearization	linearization	NOUN
ejpam-7020	36	26	[	[	X
ejpam-7020	36	27	38	38	NUM
ejpam-7020	36	28	]	]	PUNCT
ejpam-7020	36	29	.	.	PUNCT
ejpam-7020	37	1	in	in	ADP
ejpam-7020	37	2	this	this	DET
ejpam-7020	37	3	work	work	NOUN
ejpam-7020	37	4	,	,	PUNCT
ejpam-7020	37	5	we	we	PRON
ejpam-7020	37	6	include	include	VERB
ejpam-7020	37	7	a	a	DET
ejpam-7020	37	8	comparative	comparative	ADJ
ejpam-7020	37	9	analysis	analysis	NOUN
ejpam-7020	37	10	between	between	ADP
ejpam-7020	37	11	the	the	DET
ejpam-7020	37	12	lotka	lotka	PROPN
ejpam-7020	37	13	-	-	PUNCT
ejpam-7020	37	14	volterra	volterra	PROPN
ejpam-7020	37	15	and	and	CCONJ
ejpam-7020	37	16	sir	sir	NOUN
ejpam-7020	37	17	models	model	NOUN
ejpam-7020	37	18	,	,	PUNCT
ejpam-7020	37	19	highlighting	highlight	VERB
ejpam-7020	37	20	how	how	SCONJ
ejpam-7020	37	21	similar	similar	ADJ
ejpam-7020	37	22	mathematical	mathematical	ADJ
ejpam-7020	37	23	tools	tool	NOUN
ejpam-7020	37	24	,	,	PUNCT
ejpam-7020	37	25	such	such	ADJ
ejpam-7020	37	26	as	as	ADP
ejpam-7020	37	27	local	local	ADJ
ejpam-7020	37	28	linearization	linearization	NOUN
ejpam-7020	37	29	,	,	PUNCT
ejpam-7020	37	30	eigenvalue	eigenvalue	ADJ
ejpam-7020	37	31	classification	classification	NOUN
ejpam-7020	37	32	,	,	PUNCT
ejpam-7020	37	33	and	and	CCONJ
ejpam-7020	37	34	phase	phase	NOUN
ejpam-7020	37	35	portraits	portrait	NOUN
ejpam-7020	37	36	,	,	PUNCT
ejpam-7020	37	37	can	can	AUX
ejpam-7020	37	38	be	be	AUX
ejpam-7020	37	39	applied	apply	VERB
ejpam-7020	37	40	to	to	ADP
ejpam-7020	37	41	problems	problem	NOUN
ejpam-7020	37	42	from	from	ADP
ejpam-7020	37	43	different	different	ADJ
ejpam-7020	37	44	domains	domain	NOUN
ejpam-7020	37	45	.	.	PUNCT
ejpam-7020	38	1	this	this	DET
ejpam-7020	38	2	cross	cross	ADJ
ejpam-7020	38	3	-	-	ADJ
ejpam-7020	38	4	domain	domain	ADJ
ejpam-7020	38	5	perspective	perspective	NOUN
ejpam-7020	38	6	enriches	enrich	VERB
ejpam-7020	38	7	the	the	DET
ejpam-7020	38	8	learning	learning	NOUN
ejpam-7020	38	9	process	process	NOUN
ejpam-7020	38	10	for	for	ADP
ejpam-7020	38	11	students	student	NOUN
ejpam-7020	38	12	and	and	CCONJ
ejpam-7020	38	13	emphasizes	emphasize	VERB
ejpam-7020	38	14	s.	s.	PROPN
ejpam-7020	38	15	saidat	saidat	PROPN
ejpam-7020	38	16	et	et	PROPN
ejpam-7020	38	17	al	al	PROPN
ejpam-7020	38	18	.	.	PUNCT
ejpam-7020	38	19	/	/	SYM
ejpam-7020	38	20	eur	eur	PROPN
ejpam-7020	38	21	.	.	PUNCT
ejpam-7020	39	1	j.	j.	PROPN
ejpam-7020	39	2	pure	pure	PROPN
ejpam-7020	39	3	appl	appl	PROPN
ejpam-7020	39	4	.	.	PROPN
ejpam-7020	39	5	math	math	PROPN
ejpam-7020	39	6	,	,	PUNCT
ejpam-7020	39	7	18	18	NUM
ejpam-7020	39	8	(	(	PUNCT
ejpam-7020	39	9	4	4	NUM
ejpam-7020	39	10	)	)	PUNCT
ejpam-7020	39	11	(	(	PUNCT
ejpam-7020	39	12	2025	2025	NUM
ejpam-7020	39	13	)	)	PUNCT
ejpam-7020	39	14	,	,	PUNCT
ejpam-7020	39	15	7020	7020	NUM
ejpam-7020	39	16	3	3	NUM
ejpam-7020	39	17	of	of	ADP
ejpam-7020	39	18	16	16	NUM
ejpam-7020	39	19	the	the	DET
ejpam-7020	39	20	broad	broad	ADJ
ejpam-7020	39	21	applicability	applicability	NOUN
ejpam-7020	39	22	of	of	ADP
ejpam-7020	39	23	nonlinear	nonlinear	ADJ
ejpam-7020	39	24	stability	stability	NOUN
ejpam-7020	39	25	analysis	analysis	NOUN
ejpam-7020	39	26	in	in	ADP
ejpam-7020	39	27	applied	applied	ADJ
ejpam-7020	39	28	mathematics	mathematic	NOUN
ejpam-7020	39	29	.	.	PUNCT
ejpam-7020	40	1	this	this	DET
ejpam-7020	40	2	paper	paper	NOUN
ejpam-7020	40	3	aims	aim	VERB
ejpam-7020	40	4	to	to	PART
ejpam-7020	40	5	bridge	bridge	VERB
ejpam-7020	40	6	the	the	DET
ejpam-7020	40	7	pedagogical	pedagogical	ADJ
ejpam-7020	40	8	gap	gap	NOUN
ejpam-7020	40	9	by	by	ADP
ejpam-7020	40	10	proposed	propose	VERB
ejpam-7020	40	11	a	a	DET
ejpam-7020	40	12	clear	clear	ADJ
ejpam-7020	40	13	,	,	PUNCT
ejpam-7020	40	14	step	step	NOUN
ejpam-7020	40	15	by	by	ADP
ejpam-7020	40	16	step	step	NOUN
ejpam-7020	40	17	computational	computational	ADJ
ejpam-7020	40	18	workflow	workflow	NOUN
ejpam-7020	40	19	that	that	PRON
ejpam-7020	40	20	unifies	unify	VERB
ejpam-7020	40	21	these	these	DET
ejpam-7020	40	22	techniques	technique	NOUN
ejpam-7020	40	23	.	.	PUNCT
ejpam-7020	41	1	we	we	PRON
ejpam-7020	41	2	demonstrate	demonstrate	VERB
ejpam-7020	41	3	this	this	DET
ejpam-7020	41	4	integrated	integrate	VERB
ejpam-7020	41	5	approach	approach	NOUN
ejpam-7020	41	6	using	use	VERB
ejpam-7020	41	7	two	two	NUM
ejpam-7020	41	8	celebrated	celebrated	ADJ
ejpam-7020	41	9	models	model	NOUN
ejpam-7020	41	10	:	:	PUNCT
ejpam-7020	41	11	the	the	DET
ejpam-7020	41	12	lotka	lotka	PROPN
ejpam-7020	41	13	-	-	PUNCT
ejpam-7020	41	14	volterra	volterra	PROPN
ejpam-7020	41	15	predator	predator	NOUN
ejpam-7020	41	16	-	-	PUNCT
ejpam-7020	41	17	prey	prey	NOUN
ejpam-7020	41	18	model	model	NOUN
ejpam-7020	41	19	and	and	CCONJ
ejpam-7020	41	20	the	the	DET
ejpam-7020	41	21	sir	sir	PROPN
ejpam-7020	41	22	model	model	NOUN
ejpam-7020	41	23	,	,	PUNCT
ejpam-7020	41	24	which	which	PRON
ejpam-7020	41	25	are	be	AUX
ejpam-7020	41	26	nonlinear	nonlinear	ADJ
ejpam-7020	41	27	systems	system	NOUN
ejpam-7020	41	28	widely	widely	ADV
ejpam-7020	41	29	used	use	VERB
ejpam-7020	41	30	in	in	ADP
ejpam-7020	41	31	ecology	ecology	NOUN
ejpam-7020	41	32	and	and	CCONJ
ejpam-7020	41	33	theoretical	theoretical	ADJ
ejpam-7020	41	34	biology	biology	NOUN
ejpam-7020	41	35	.	.	PUNCT
ejpam-7020	42	1	the	the	DET
ejpam-7020	42	2	goal	goal	NOUN
ejpam-7020	42	3	is	be	AUX
ejpam-7020	42	4	not	not	PART
ejpam-7020	42	5	to	to	PART
ejpam-7020	42	6	introduce	introduce	VERB
ejpam-7020	42	7	new	new	ADJ
ejpam-7020	42	8	mathematical	mathematical	ADJ
ejpam-7020	42	9	theory	theory	NOUN
ejpam-7020	42	10	but	but	CCONJ
ejpam-7020	42	11	rather	rather	ADV
ejpam-7020	42	12	to	to	PART
ejpam-7020	42	13	provide	provide	VERB
ejpam-7020	42	14	an	an	DET
ejpam-7020	42	15	accessible	accessible	ADJ
ejpam-7020	42	16	and	and	CCONJ
ejpam-7020	42	17	introducible	introducible	ADJ
ejpam-7020	42	18	guide	guide	NOUN
ejpam-7020	42	19	that	that	PRON
ejpam-7020	42	20	empowers	empower	VERB
ejpam-7020	42	21	learners	learner	NOUN
ejpam-7020	42	22	and	and	CCONJ
ejpam-7020	42	23	practitioners	practitioner	NOUN
ejpam-7020	42	24	to	to	PART
ejpam-7020	42	25	confidently	confidently	ADV
ejpam-7020	42	26	apply	apply	VERB
ejpam-7020	42	27	stability	stability	NOUN
ejpam-7020	42	28	analysis	analysis	NOUN
ejpam-7020	42	29	to	to	ADP
ejpam-7020	42	30	nonlinear	nonlinear	ADJ
ejpam-7020	42	31	models	model	NOUN
ejpam-7020	42	32	.	.	PUNCT
ejpam-7020	43	1	by	by	ADP
ejpam-7020	43	2	placing	place	VERB
ejpam-7020	43	3	these	these	DET
ejpam-7020	43	4	two	two	NUM
ejpam-7020	43	5	distinct	distinct	ADJ
ejpam-7020	43	6	models	model	NOUN
ejpam-7020	43	7	’	'	PUNCT
ejpam-7020	43	8	side	side	NOUN
ejpam-7020	43	9	by	by	ADP
ejpam-7020	43	10	side	side	NOUN
ejpam-7020	43	11	,	,	PUNCT
ejpam-7020	43	12	we	we	PRON
ejpam-7020	43	13	emphasize	emphasize	VERB
ejpam-7020	43	14	the	the	DET
ejpam-7020	43	15	universal	universal	ADJ
ejpam-7020	43	16	power	power	NOUN
ejpam-7020	43	17	of	of	ADP
ejpam-7020	43	18	these	these	DET
ejpam-7020	43	19	mathematical	mathematical	ADJ
ejpam-7020	43	20	tools	tool	NOUN
ejpam-7020	43	21	and	and	CCONJ
ejpam-7020	43	22	explore	explore	VERB
ejpam-7020	43	23	the	the	DET
ejpam-7020	43	24	rich	rich	ADJ
ejpam-7020	43	25	domainspecific	domainspecific	ADJ
ejpam-7020	43	26	insights	insight	NOUN
ejpam-7020	43	27	they	they	PRON
ejpam-7020	43	28	can	can	AUX
ejpam-7020	43	29	reveal	reveal	VERB
ejpam-7020	43	30	.	.	PUNCT
ejpam-7020	44	1	the	the	DET
ejpam-7020	44	2	remainder	remainder	NOUN
ejpam-7020	44	3	of	of	ADP
ejpam-7020	44	4	this	this	DET
ejpam-7020	44	5	paper	paper	NOUN
ejpam-7020	44	6	is	be	AUX
ejpam-7020	44	7	structured	structure	VERB
ejpam-7020	44	8	as	as	SCONJ
ejpam-7020	44	9	follows	follow	VERB
ejpam-7020	44	10	.	.	PUNCT
ejpam-7020	45	1	section	section	NOUN
ejpam-7020	45	2	2	2	NUM
ejpam-7020	45	3	details	detail	NOUN
ejpam-7020	45	4	the	the	DET
ejpam-7020	45	5	mathematical	mathematical	ADJ
ejpam-7020	45	6	methodology	methodology	NOUN
ejpam-7020	45	7	.	.	PUNCT
ejpam-7020	46	1	section	section	NOUN
ejpam-7020	46	2	3	3	NUM
ejpam-7020	46	3	applies	apply	VERB
ejpam-7020	46	4	this	this	DET
ejpam-7020	46	5	methodology	methodology	NOUN
ejpam-7020	46	6	to	to	ADP
ejpam-7020	46	7	the	the	DET
ejpam-7020	46	8	lotka	lotka	PROPN
ejpam-7020	46	9	-	-	PUNCT
ejpam-7020	46	10	volterra	volterra	PROPN
ejpam-7020	46	11	model	model	NOUN
ejpam-7020	46	12	,	,	PUNCT
ejpam-7020	46	13	including	include	VERB
ejpam-7020	46	14	a	a	DET
ejpam-7020	46	15	parameter	parameter	NOUN
ejpam-7020	46	16	sensitivity	sensitivity	NOUN
ejpam-7020	46	17	analysis	analysis	NOUN
ejpam-7020	46	18	.	.	PUNCT
ejpam-7020	47	1	in	in	ADP
ejpam-7020	47	2	section	section	NOUN
ejpam-7020	47	3	4	4	NUM
ejpam-7020	47	4	,	,	PUNCT
ejpam-7020	47	5	we	we	PRON
ejpam-7020	47	6	present	present	VERB
ejpam-7020	47	7	a	a	DET
ejpam-7020	47	8	complete	complete	ADJ
ejpam-7020	47	9	analysis	analysis	NOUN
ejpam-7020	47	10	of	of	ADP
ejpam-7020	47	11	the	the	DET
ejpam-7020	47	12	sir	sir	PROPN
ejpam-7020	47	13	model	model	NOUN
ejpam-7020	47	14	,	,	PUNCT
ejpam-7020	47	15	setting	set	VERB
ejpam-7020	47	16	the	the	DET
ejpam-7020	47	17	stage	stage	NOUN
ejpam-7020	47	18	for	for	ADP
ejpam-7020	47	19	a	a	DET
ejpam-7020	47	20	direct	direct	ADJ
ejpam-7020	47	21	comparison	comparison	NOUN
ejpam-7020	47	22	.	.	PUNCT
ejpam-7020	48	1	section	section	NOUN
ejpam-7020	48	2	5	5	NUM
ejpam-7020	48	3	discussed	discuss	VERB
ejpam-7020	48	4	the	the	DET
ejpam-7020	48	5	visual	visual	ADJ
ejpam-7020	48	6	results	result	NOUN
ejpam-7020	48	7	of	of	ADP
ejpam-7020	48	8	the	the	DET
ejpam-7020	48	9	phase	phase	NOUN
ejpam-7020	48	10	portraits	portrait	NOUN
ejpam-7020	48	11	for	for	ADP
ejpam-7020	48	12	both	both	DET
ejpam-7020	48	13	systems	system	NOUN
ejpam-7020	48	14	.	.	PUNCT
ejpam-7020	49	1	finally	finally	ADV
ejpam-7020	49	2	,	,	PUNCT
ejpam-7020	49	3	section	section	NOUN
ejpam-7020	49	4	6	6	NUM
ejpam-7020	49	5	concludes	conclude	VERB
ejpam-7020	49	6	with	with	ADP
ejpam-7020	49	7	a	a	DET
ejpam-7020	49	8	summary	summary	NOUN
ejpam-7020	49	9	of	of	ADP
ejpam-7020	49	10	the	the	DET
ejpam-7020	49	11	findings	finding	NOUN
ejpam-7020	49	12	and	and	CCONJ
ejpam-7020	49	13	their	their	PRON
ejpam-7020	49	14	implications	implication	NOUN
ejpam-7020	49	15	.	.	PUNCT
ejpam-7020	50	1	2	2	X
ejpam-7020	50	2	.	.	X
ejpam-7020	50	3	methods	method	NOUN
ejpam-7020	50	4	with	with	ADP
ejpam-7020	50	5	our	our	PRON
ejpam-7020	50	6	main	main	ADJ
ejpam-7020	50	7	goal	goal	NOUN
ejpam-7020	50	8	set	set	NOUN
ejpam-7020	50	9	,	,	PUNCT
ejpam-7020	50	10	this	this	DET
ejpam-7020	50	11	section	section	NOUN
ejpam-7020	50	12	is	be	AUX
ejpam-7020	50	13	all	all	ADV
ejpam-7020	50	14	about	about	ADP
ejpam-7020	50	15	building	build	VERB
ejpam-7020	50	16	our	our	PRON
ejpam-7020	50	17	toolkit	toolkit	NOUN
ejpam-7020	50	18	.	.	PUNCT
ejpam-7020	51	1	to	to	PART
ejpam-7020	51	2	make	make	VERB
ejpam-7020	51	3	sure	sure	ADJ
ejpam-7020	51	4	our	our	PRON
ejpam-7020	51	5	approach	approach	NOUN
ejpam-7020	51	6	is	be	AUX
ejpam-7020	51	7	perfectly	perfectly	ADV
ejpam-7020	51	8	clear	clear	ADJ
ejpam-7020	51	9	,	,	PUNCT
ejpam-7020	51	10	we	we	PRON
ejpam-7020	51	11	have	have	AUX
ejpam-7020	51	12	broken	break	VERB
ejpam-7020	51	13	it	it	PRON
ejpam-7020	51	14	down	down	ADP
ejpam-7020	51	15	into	into	ADP
ejpam-7020	51	16	two	two	NUM
ejpam-7020	51	17	parts	part	NOUN
ejpam-7020	51	18	.	.	PUNCT
ejpam-7020	52	1	first	first	ADV
ejpam-7020	52	2	,	,	PUNCT
ejpam-7020	52	3	in	in	ADP
ejpam-7020	52	4	section	section	NOUN
ejpam-7020	52	5	2.1	2.1	NUM
ejpam-7020	52	6	,	,	PUNCT
ejpam-7020	52	7	we	we	PRON
ejpam-7020	52	8	will	will	AUX
ejpam-7020	52	9	walk	walk	VERB
ejpam-7020	52	10	gently	gently	ADV
ejpam-7020	52	11	through	through	ADP
ejpam-7020	52	12	the	the	DET
ejpam-7020	52	13	essential	essential	ADJ
ejpam-7020	52	14	mathematical	mathematical	ADJ
ejpam-7020	52	15	theory	theory	NOUN
ejpam-7020	52	16	behind	behind	ADP
ejpam-7020	52	17	stability	stability	NOUN
ejpam-7020	52	18	analysis	analysis	NOUN
ejpam-7020	52	19	.	.	PUNCT
ejpam-7020	53	1	then	then	ADV
ejpam-7020	53	2	,	,	PUNCT
ejpam-7020	53	3	in	in	ADP
ejpam-7020	53	4	section	section	NOUN
ejpam-7020	53	5	2.2	2.2	NUM
ejpam-7020	53	6	,	,	PUNCT
ejpam-7020	53	7	we	we	PRON
ejpam-7020	53	8	will	will	AUX
ejpam-7020	53	9	lay	lay	VERB
ejpam-7020	53	10	out	out	ADP
ejpam-7020	53	11	the	the	DET
ejpam-7020	53	12	concrete	concrete	ADJ
ejpam-7020	53	13	step	step	NOUN
ejpam-7020	53	14	by	by	ADP
ejpam-7020	53	15	step	step	NOUN
ejpam-7020	53	16	workflow	workflow	NOUN
ejpam-7020	53	17	we	we	PRON
ejpam-7020	53	18	will	will	AUX
ejpam-7020	53	19	follow	follow	VERB
ejpam-7020	53	20	for	for	ADP
ejpam-7020	53	21	our	our	PRON
ejpam-7020	53	22	case	case	NOUN
ejpam-7020	53	23	studies	study	NOUN
ejpam-7020	53	24	,	,	PUNCT
ejpam-7020	53	25	showing	show	VERB
ejpam-7020	53	26	exactly	exactly	ADV
ejpam-7020	53	27	how	how	SCONJ
ejpam-7020	53	28	we	we	PRON
ejpam-7020	53	29	will	will	AUX
ejpam-7020	53	30	put	put	VERB
ejpam-7020	53	31	that	that	DET
ejpam-7020	53	32	theory	theory	NOUN
ejpam-7020	53	33	into	into	ADP
ejpam-7020	53	34	practice	practice	NOUN
ejpam-7020	53	35	.	.	PUNCT
ejpam-7020	54	1	2.1	2.1	NUM
ejpam-7020	54	2	.	.	PUNCT
ejpam-7020	54	3	mathematical	mathematical	ADJ
ejpam-7020	54	4	foundations	foundation	NOUN
ejpam-7020	54	5	of	of	ADP
ejpam-7020	54	6	stability	stability	NOUN
ejpam-7020	54	7	analysis	analysis	NOUN
ejpam-7020	54	8	we	we	PRON
ejpam-7020	54	9	consider	consider	VERB
ejpam-7020	54	10	a	a	DET
ejpam-7020	54	11	general	general	ADJ
ejpam-7020	54	12	n	n	CCONJ
ejpam-7020	54	13	-	-	PUNCT
ejpam-7020	54	14	dimensional	dimensional	ADJ
ejpam-7020	54	15	autonomous	autonomous	ADJ
ejpam-7020	54	16	system	system	NOUN
ejpam-7020	54	17	of	of	ADP
ejpam-7020	54	18	first	first	ADJ
ejpam-7020	54	19	-	-	PUNCT
ejpam-7020	54	20	order	order	NOUN
ejpam-7020	54	21	ordinary	ordinary	ADJ
ejpam-7020	54	22	differential	differential	ADJ
ejpam-7020	54	23	equations	equation	NOUN
ejpam-7020	54	24	(	(	PUNCT
ejpam-7020	54	25	odes	ode	NOUN
ejpam-7020	54	26	):	):	PUNCT
ejpam-7020	54	27	dx	dx	PROPN
ejpam-7020	54	28	dt	dt	NOUN
ejpam-7020	54	29	=	=	SYM
ejpam-7020	54	30	f(x	f(x	PROPN
ejpam-7020	54	31	)	)	PUNCT
ejpam-7020	54	32	.	.	PUNCT
ejpam-7020	55	1	(	(	PUNCT
ejpam-7020	55	2	1	1	X
ejpam-7020	55	3	)	)	PUNCT
ejpam-7020	55	4	here	here	ADV
ejpam-7020	55	5	,	,	PUNCT
ejpam-7020	55	6	x(t	x(t	PROPN
ejpam-7020	55	7	)	)	PUNCT
ejpam-7020	55	8	∈	∈	PROPN
ejpam-7020	55	9	rn	rn	PROPN
ejpam-7020	55	10	and	and	CCONJ
ejpam-7020	55	11	f	f	PROPN
ejpam-7020	55	12	:	:	PUNCT
ejpam-7020	55	13	rn	rn	PROPN
ejpam-7020	55	14	→	→	PROPN
ejpam-7020	55	15	rn	rn	PROPN
ejpam-7020	55	16	is	be	AUX
ejpam-7020	55	17	a	a	DET
ejpam-7020	55	18	continuously	continuously	ADV
ejpam-7020	55	19	differentiable	differentiable	ADJ
ejpam-7020	55	20	function	function	NOUN
ejpam-7020	55	21	.	.	PUNCT
ejpam-7020	56	1	an	an	DET
ejpam-7020	56	2	equilibrium	equilibrium	NOUN
ejpam-7020	56	3	point	point	NOUN
ejpam-7020	56	4	,	,	PUNCT
ejpam-7020	56	5	denoted	denote	VERB
ejpam-7020	56	6	by	by	ADP
ejpam-7020	56	7	x∗	x∗	PROPN
ejpam-7020	56	8	,	,	PUNCT
ejpam-7020	56	9	is	be	AUX
ejpam-7020	56	10	a	a	DET
ejpam-7020	56	11	point	point	NOUN
ejpam-7020	56	12	where	where	SCONJ
ejpam-7020	56	13	the	the	DET
ejpam-7020	56	14	dynamics	dynamic	NOUN
ejpam-7020	56	15	of	of	ADP
ejpam-7020	56	16	the	the	DET
ejpam-7020	56	17	system	system	NOUN
ejpam-7020	56	18	stops	stop	VERB
ejpam-7020	56	19	,	,	PUNCT
ejpam-7020	56	20	i.e.	i.e.	X
ejpam-7020	56	21	,	,	PUNCT
ejpam-7020	56	22	it	it	PRON
ejpam-7020	56	23	satisfies	satisfy	VERB
ejpam-7020	56	24	f(x∗	f(x∗	PART
ejpam-7020	56	25	)	)	PUNCT
ejpam-7020	56	26	=	=	SYM
ejpam-7020	57	1	0	0	X
ejpam-7020	57	2	.	.	PUNCT
ejpam-7020	57	3	to	to	PART
ejpam-7020	57	4	study	study	VERB
ejpam-7020	57	5	the	the	DET
ejpam-7020	57	6	local	local	ADJ
ejpam-7020	57	7	stability	stability	NOUN
ejpam-7020	57	8	near	near	ADP
ejpam-7020	57	9	an	an	DET
ejpam-7020	57	10	equilibrium	equilibrium	NOUN
ejpam-7020	57	11	,	,	PUNCT
ejpam-7020	57	12	we	we	PRON
ejpam-7020	57	13	linearize	linearize	VERB
ejpam-7020	57	14	the	the	DET
ejpam-7020	57	15	system	system	NOUN
ejpam-7020	57	16	by	by	ADP
ejpam-7020	57	17	approximating	approximate	VERB
ejpam-7020	57	18	f(x	f(x	PROPN
ejpam-7020	57	19	)	)	PUNCT
ejpam-7020	57	20	with	with	ADP
ejpam-7020	57	21	its	its	PRON
ejpam-7020	57	22	first	first	ADJ
ejpam-7020	57	23	-	-	PUNCT
ejpam-7020	57	24	order	order	NOUN
ejpam-7020	57	25	taylor	taylor	NOUN
ejpam-7020	57	26	expansion	expansion	NOUN
ejpam-7020	57	27	around	around	ADP
ejpam-7020	57	28	x∗.	x∗.	PUNCT
ejpam-7020	58	1	the	the	DET
ejpam-7020	58	2	result	result	NOUN
ejpam-7020	58	3	is	be	AUX
ejpam-7020	58	4	a	a	DET
ejpam-7020	58	5	linear	linear	ADJ
ejpam-7020	58	6	system	system	NOUN
ejpam-7020	58	7	governed	govern	VERB
ejpam-7020	58	8	by	by	ADP
ejpam-7020	58	9	the	the	DET
ejpam-7020	58	10	jacobian	jacobian	ADJ
ejpam-7020	58	11	matrix	matrix	NOUN
ejpam-7020	58	12	j	j	PROPN
ejpam-7020	58	13	,	,	PUNCT
ejpam-7020	58	14	which	which	PRON
ejpam-7020	58	15	consists	consist	VERB
ejpam-7020	58	16	of	of	ADP
ejpam-7020	58	17	all	all	DET
ejpam-7020	58	18	first	first	ADJ
ejpam-7020	58	19	-	-	PUNCT
ejpam-7020	58	20	order	order	NOUN
ejpam-7020	58	21	partial	partial	ADJ
ejpam-7020	58	22	derivatives	derivative	NOUN
ejpam-7020	58	23	of	of	ADP
ejpam-7020	58	24	f	f	NOUN
ejpam-7020	58	25	:	:	PUNCT
ejpam-7020	58	26	j(x	j(x	PROPN
ejpam-7020	58	27	)	)	PUNCT
ejpam-7020	58	28	=	=	SYM
ejpam-7020	59	1			ADJ
ejpam-7020	59	2	∂f1	∂f1	NOUN
ejpam-7020	59	3	∂x1	∂x1	PROPN
ejpam-7020	59	4	∂f1	∂f1	PROPN
ejpam-7020	59	5	∂x2	∂x2	NOUN
ejpam-7020	59	6	·	·	PUNCT
ejpam-7020	59	7	·	·	PUNCT
ejpam-7020	59	8	·	·	PUNCT
ejpam-7020	60	1	∂f1	∂f1	NOUN
ejpam-7020	60	2	∂xn	∂xn	VERB
ejpam-7020	60	3	∂f2	∂f2	NOUN
ejpam-7020	60	4	∂x1	∂x1	NOUN
ejpam-7020	60	5	∂f2	∂f2	VERB
ejpam-7020	60	6	∂x2	∂x2	NOUN
ejpam-7020	60	7	·	·	PUNCT
ejpam-7020	60	8	·	·	PUNCT
ejpam-7020	60	9	·	·	PUNCT
ejpam-7020	60	10	∂f2	∂f2	NOUN
ejpam-7020	60	11	∂xn	∂xn	NOUN
ejpam-7020	60	12	...	...	PUNCT
ejpam-7020	60	13	...	...	PUNCT
ejpam-7020	60	14	.	.	PUNCT
ejpam-7020	60	15	.	.	PUNCT
ejpam-7020	60	16	.	.	PUNCT
ejpam-7020	61	1	...	...	PUNCT
ejpam-7020	62	1	∂fn	∂fn	VERB
ejpam-7020	62	2	∂x1	∂x1	NOUN
ejpam-7020	62	3	∂fn	∂fn	VERB
ejpam-7020	62	4	∂x2	∂x2	NOUN
ejpam-7020	62	5	·	·	PUNCT
ejpam-7020	62	6	·	·	PUNCT
ejpam-7020	62	7	·	·	PUNCT
ejpam-7020	63	1	∂fn	∂fn	VERB
ejpam-7020	63	2	∂xn	∂xn	NOUN
ejpam-7020	63	3			VERB
ejpam-7020	63	4	.	.	PUNCT
ejpam-7020	64	1	(	(	PUNCT
ejpam-7020	64	2	2	2	X
ejpam-7020	64	3	)	)	PUNCT
ejpam-7020	64	4	s.	s.	PROPN
ejpam-7020	64	5	saidat	saidat	PROPN
ejpam-7020	64	6	et	et	PROPN
ejpam-7020	64	7	al	al	PROPN
ejpam-7020	64	8	.	.	PUNCT
ejpam-7020	64	9	/	/	SYM
ejpam-7020	64	10	eur	eur	PROPN
ejpam-7020	64	11	.	.	PUNCT
ejpam-7020	65	1	j.	j.	PROPN
ejpam-7020	65	2	pure	pure	PROPN
ejpam-7020	65	3	appl	appl	PROPN
ejpam-7020	65	4	.	.	PROPN
ejpam-7020	65	5	math	math	PROPN
ejpam-7020	65	6	,	,	PUNCT
ejpam-7020	65	7	18	18	NUM
ejpam-7020	65	8	(	(	PUNCT
ejpam-7020	65	9	4	4	NUM
ejpam-7020	65	10	)	)	PUNCT
ejpam-7020	65	11	(	(	PUNCT
ejpam-7020	65	12	2025	2025	NUM
ejpam-7020	65	13	)	)	PUNCT
ejpam-7020	65	14	,	,	PUNCT
ejpam-7020	65	15	7020	7020	NUM
ejpam-7020	65	16	4	4	NUM
ejpam-7020	65	17	of	of	ADP
ejpam-7020	65	18	16	16	NUM
ejpam-7020	65	19	the	the	DET
ejpam-7020	65	20	linearized	linearize	VERB
ejpam-7020	65	21	system	system	NOUN
ejpam-7020	65	22	that	that	PRON
ejpam-7020	65	23	describes	describe	VERB
ejpam-7020	65	24	the	the	DET
ejpam-7020	65	25	evolution	evolution	NOUN
ejpam-7020	65	26	of	of	ADP
ejpam-7020	65	27	a	a	DET
ejpam-7020	65	28	small	small	ADJ
ejpam-7020	65	29	perturbation	perturbation	NOUN
ejpam-7020	65	30	u	u	NOUN
ejpam-7020	65	31	=	=	PROPN
ejpam-7020	65	32	x−	x−	PROPN
ejpam-7020	65	33	x∗	x∗	PROPN
ejpam-7020	65	34	is	be	AUX
ejpam-7020	65	35	given	give	VERB
ejpam-7020	65	36	by	by	ADP
ejpam-7020	65	37	du	du	PROPN
ejpam-7020	65	38	dt	dt	PROPN
ejpam-7020	65	39	=	=	PUNCT
ejpam-7020	66	1	j(x∗)u	j(x∗)u	PROPN
ejpam-7020	66	2	(	(	PUNCT
ejpam-7020	66	3	3	3	X
ejpam-7020	66	4	)	)	PUNCT
ejpam-7020	66	5	the	the	DET
ejpam-7020	66	6	stability	stability	NOUN
ejpam-7020	66	7	of	of	ADP
ejpam-7020	66	8	the	the	DET
ejpam-7020	66	9	equilibrium	equilibrium	NOUN
ejpam-7020	66	10	point	point	NOUN
ejpam-7020	66	11	x∗	x∗	PROPN
ejpam-7020	66	12	is	be	AUX
ejpam-7020	66	13	determined	determine	VERB
ejpam-7020	66	14	by	by	ADP
ejpam-7020	66	15	the	the	DET
ejpam-7020	66	16	eigenvalues	eigenvalues	PROPN
ejpam-7020	66	17	λ	λ	PROPN
ejpam-7020	66	18	of	of	ADP
ejpam-7020	66	19	the	the	DET
ejpam-7020	66	20	jacobian	jacobian	ADJ
ejpam-7020	66	21	matrix	matrix	NOUN
ejpam-7020	66	22	evaluated	evaluate	VERB
ejpam-7020	66	23	at	at	ADP
ejpam-7020	66	24	the	the	DET
ejpam-7020	66	25	point	point	NOUN
ejpam-7020	66	26	j(x∗	j(x∗	NOUN
ejpam-7020	66	27	):	):	PUNCT
ejpam-7020	66	28	j(x∗)v	j(x∗)v	PROPN
ejpam-7020	67	1	=	=	SYM
ejpam-7020	67	2	λv	λv	PROPN
ejpam-7020	67	3	,	,	PUNCT
ejpam-7020	67	4	where	where	SCONJ
ejpam-7020	67	5	v	v	NOUN
ejpam-7020	67	6	is	be	AUX
ejpam-7020	67	7	the	the	DET
ejpam-7020	67	8	corresponding	corresponding	ADJ
ejpam-7020	67	9	eigenvector	eigenvector	NOUN
ejpam-7020	67	10	.	.	PROPN
ejpam-7020	67	11	•	•	NUM
ejpam-7020	67	12	if	if	SCONJ
ejpam-7020	67	13	all	all	DET
ejpam-7020	67	14	eigenvalues	eigenvalue	NOUN
ejpam-7020	67	15	have	have	VERB
ejpam-7020	67	16	negative	negative	ADJ
ejpam-7020	67	17	real	real	ADJ
ejpam-7020	67	18	parts	part	NOUN
ejpam-7020	67	19	,	,	PUNCT
ejpam-7020	67	20	then	then	ADV
ejpam-7020	67	21	x∗	x∗	PROPN
ejpam-7020	67	22	is	be	AUX
ejpam-7020	67	23	locally	locally	ADV
ejpam-7020	67	24	asymptotically	asymptotically	ADV
ejpam-7020	67	25	stable	stable	ADJ
ejpam-7020	67	26	.	.	PUNCT
ejpam-7020	68	1	•	•	INTJ
ejpam-7020	68	2	if	if	SCONJ
ejpam-7020	68	3	at	at	ADV
ejpam-7020	68	4	least	least	ADV
ejpam-7020	68	5	one	one	NUM
ejpam-7020	68	6	eigenvalue	eigenvalue	NOUN
ejpam-7020	68	7	has	have	VERB
ejpam-7020	68	8	a	a	DET
ejpam-7020	68	9	positive	positive	ADJ
ejpam-7020	68	10	real	real	ADJ
ejpam-7020	68	11	part	part	NOUN
ejpam-7020	68	12	,	,	PUNCT
ejpam-7020	68	13	then	then	ADV
ejpam-7020	68	14	x∗	x∗	PROPN
ejpam-7020	68	15	is	be	AUX
ejpam-7020	68	16	unstable	unstable	ADJ
ejpam-7020	68	17	.	.	PUNCT
ejpam-7020	69	1	•	•	INTJ
ejpam-7020	69	2	if	if	SCONJ
ejpam-7020	69	3	all	all	DET
ejpam-7020	69	4	eigenvalues	eigenvalue	VERB
ejpam-7020	69	5	have	have	VERB
ejpam-7020	69	6	non	non	ADJ
ejpam-7020	69	7	-	-	ADJ
ejpam-7020	69	8	positive	positive	ADJ
ejpam-7020	69	9	real	real	ADJ
ejpam-7020	69	10	parts	part	NOUN
ejpam-7020	69	11	with	with	ADP
ejpam-7020	69	12	at	at	ADV
ejpam-7020	69	13	least	least	ADV
ejpam-7020	69	14	one	one	NUM
ejpam-7020	69	15	having	have	VERB
ejpam-7020	69	16	a	a	DET
ejpam-7020	69	17	zero	zero	NUM
ejpam-7020	69	18	real	real	ADJ
ejpam-7020	69	19	part	part	NOUN
ejpam-7020	69	20	,	,	PUNCT
ejpam-7020	69	21	the	the	DET
ejpam-7020	69	22	linear	linear	ADJ
ejpam-7020	69	23	analysis	analysis	NOUN
ejpam-7020	69	24	is	be	AUX
ejpam-7020	69	25	inconclusive	inconclusive	ADJ
ejpam-7020	69	26	,	,	PUNCT
ejpam-7020	69	27	and	and	CCONJ
ejpam-7020	69	28	higher	high	ADJ
ejpam-7020	69	29	-	-	PUNCT
ejpam-7020	69	30	order	order	NOUN
ejpam-7020	69	31	terms	term	NOUN
ejpam-7020	69	32	are	be	AUX
ejpam-7020	69	33	needed	need	VERB
ejpam-7020	69	34	.	.	PUNCT
ejpam-7020	70	1	for	for	ADP
ejpam-7020	70	2	two	two	NUM
ejpam-7020	70	3	-	-	PUNCT
ejpam-7020	70	4	dimensional	dimensional	ADJ
ejpam-7020	70	5	systems	system	NOUN
ejpam-7020	70	6	,	,	PUNCT
ejpam-7020	70	7	the	the	DET
ejpam-7020	70	8	trace	trace	NOUN
ejpam-7020	70	9	tr(j	tr(j	NOUN
ejpam-7020	70	10	)	)	PUNCT
ejpam-7020	70	11	and	and	CCONJ
ejpam-7020	70	12	the	the	DET
ejpam-7020	70	13	determinant	determinant	ADJ
ejpam-7020	70	14	det(j	det(j	PROPN
ejpam-7020	70	15	)	)	PUNCT
ejpam-7020	70	16	of	of	ADP
ejpam-7020	70	17	the	the	DET
ejpam-7020	70	18	jacobian	jacobian	ADJ
ejpam-7020	70	19	matrix	matrix	NOUN
ejpam-7020	70	20	can	can	AUX
ejpam-7020	70	21	be	be	AUX
ejpam-7020	70	22	used	use	VERB
ejpam-7020	70	23	to	to	PART
ejpam-7020	70	24	classify	classify	VERB
ejpam-7020	70	25	the	the	DET
ejpam-7020	70	26	type	type	NOUN
ejpam-7020	70	27	of	of	ADP
ejpam-7020	70	28	equilibrium	equilibrium	NOUN
ejpam-7020	70	29	(	(	PUNCT
ejpam-7020	70	30	e.g.	e.g.	ADV
ejpam-7020	70	31	node	node	NOUN
ejpam-7020	70	32	,	,	PUNCT
ejpam-7020	70	33	saddle	saddle	NOUN
ejpam-7020	70	34	,	,	PUNCT
ejpam-7020	70	35	spiral	spiral	ADJ
ejpam-7020	70	36	,	,	PUNCT
ejpam-7020	70	37	or	or	CCONJ
ejpam-7020	70	38	center	center	NOUN
ejpam-7020	70	39	)	)	PUNCT
ejpam-7020	70	40	.	.	PUNCT
ejpam-7020	71	1	2.2	2.2	NUM
ejpam-7020	71	2	.	.	PUNCT
ejpam-7020	71	3	applied	apply	VERB
ejpam-7020	71	4	workflow	workflow	NOUN
ejpam-7020	71	5	in	in	ADP
ejpam-7020	71	6	this	this	DET
ejpam-7020	71	7	study	study	NOUN
ejpam-7020	72	1	,	,	PUNCT
ejpam-7020	72	2	we	we	PRON
ejpam-7020	72	3	apply	apply	VERB
ejpam-7020	72	4	this	this	DET
ejpam-7020	72	5	mathematical	mathematical	ADJ
ejpam-7020	72	6	framework	framework	NOUN
ejpam-7020	72	7	to	to	ADP
ejpam-7020	72	8	our	our	PRON
ejpam-7020	72	9	case	case	NOUN
ejpam-7020	72	10	studies	study	NOUN
ejpam-7020	72	11	using	use	VERB
ejpam-7020	72	12	the	the	DET
ejpam-7020	72	13	following	follow	VERB
ejpam-7020	72	14	structured	structured	ADJ
ejpam-7020	72	15	workflow	workflow	NOUN
ejpam-7020	72	16	:	:	PUNCT
ejpam-7020	72	17	(	(	PUNCT
ejpam-7020	72	18	i	i	NOUN
ejpam-7020	72	19	)	)	PUNCT
ejpam-7020	72	20	identify	identify	VERB
ejpam-7020	72	21	equilibrium	equilibrium	NOUN
ejpam-7020	72	22	points	point	NOUN
ejpam-7020	72	23	:	:	PUNCT
ejpam-7020	72	24	analytically	analytically	ADV
ejpam-7020	72	25	solve	solve	VERB
ejpam-7020	72	26	f(x	f(x	PROPN
ejpam-7020	72	27	)	)	PUNCT
ejpam-7020	72	28	=	=	SYM
ejpam-7020	72	29	0	0	PUNCT
ejpam-7020	72	30	to	to	PART
ejpam-7020	72	31	find	find	VERB
ejpam-7020	72	32	all	all	DET
ejpam-7020	72	33	equilibria	equilibrium	NOUN
ejpam-7020	72	34	.	.	PUNCT
ejpam-7020	73	1	(	(	PUNCT
ejpam-7020	73	2	ii	ii	NOUN
ejpam-7020	73	3	)	)	PUNCT
ejpam-7020	73	4	perform	perform	VERB
ejpam-7020	73	5	linearization	linearization	NOUN
ejpam-7020	73	6	:	:	PUNCT
ejpam-7020	73	7	compute	compute	VERB
ejpam-7020	73	8	the	the	DET
ejpam-7020	73	9	jacobian	jacobian	ADJ
ejpam-7020	73	10	matrix	matrix	NOUN
ejpam-7020	73	11	j(x	j(x	NOUN
ejpam-7020	73	12	)	)	PUNCT
ejpam-7020	73	13	and	and	CCONJ
ejpam-7020	73	14	evaluate	evaluate	VERB
ejpam-7020	73	15	it	it	PRON
ejpam-7020	73	16	at	at	ADP
ejpam-7020	73	17	each	each	DET
ejpam-7020	73	18	equilibrium	equilibrium	NOUN
ejpam-7020	73	19	point	point	NOUN
ejpam-7020	73	20	x∗.	x∗.	PUNCT
ejpam-7020	74	1	(	(	PUNCT
ejpam-7020	74	2	iii	iii	NOUN
ejpam-7020	74	3	)	)	PUNCT
ejpam-7020	74	4	classify	classify	VERB
ejpam-7020	74	5	stability	stability	NOUN
ejpam-7020	74	6	:	:	PUNCT
ejpam-7020	74	7	calculate	calculate	VERB
ejpam-7020	74	8	the	the	DET
ejpam-7020	74	9	eigenvalues	eigenvalue	NOUN
ejpam-7020	74	10	of	of	ADP
ejpam-7020	74	11	each	each	DET
ejpam-7020	74	12	j(x∗	j(x∗	NOUN
ejpam-7020	74	13	)	)	PUNCT
ejpam-7020	74	14	to	to	PART
ejpam-7020	74	15	determine	determine	VERB
ejpam-7020	74	16	the	the	DET
ejpam-7020	74	17	local	local	ADJ
ejpam-7020	74	18	stability	stability	NOUN
ejpam-7020	74	19	and	and	CCONJ
ejpam-7020	74	20	type	type	NOUN
ejpam-7020	74	21	of	of	ADP
ejpam-7020	74	22	each	each	DET
ejpam-7020	74	23	equilibrium	equilibrium	NOUN
ejpam-7020	74	24	.	.	PUNCT
ejpam-7020	75	1	(	(	PUNCT
ejpam-7020	75	2	iv	iv	X
ejpam-7020	75	3	)	)	PUNCT
ejpam-7020	75	4	visualize	visualize	VERB
ejpam-7020	75	5	dynamics	dynamic	NOUN
ejpam-7020	75	6	:	:	PUNCT
ejpam-7020	75	7	generate	generate	VERB
ejpam-7020	75	8	phase	phase	NOUN
ejpam-7020	75	9	portraits	portrait	NOUN
ejpam-7020	75	10	using	use	VERB
ejpam-7020	75	11	python	python	NOUN
ejpam-7020	75	12	to	to	PART
ejpam-7020	75	13	visually	visually	ADV
ejpam-7020	75	14	confirm	confirm	VERB
ejpam-7020	75	15	the	the	DET
ejpam-7020	75	16	analytical	analytical	ADJ
ejpam-7020	75	17	predictions	prediction	NOUN
ejpam-7020	75	18	.	.	PUNCT
ejpam-7020	76	1	(	(	PUNCT
ejpam-7020	76	2	v	v	NOUN
ejpam-7020	76	3	)	)	PUNCT
ejpam-7020	76	4	conduct	conduct	NOUN
ejpam-7020	76	5	sensitivity	sensitivity	NOUN
ejpam-7020	76	6	analysis	analysis	NOUN
ejpam-7020	76	7	:	:	PUNCT
ejpam-7020	76	8	for	for	ADP
ejpam-7020	76	9	the	the	DET
ejpam-7020	76	10	lotka	lotka	PROPN
ejpam-7020	76	11	–	–	PUNCT
ejpam-7020	76	12	volterra	volterra	NOUN
ejpam-7020	76	13	model	model	NOUN
ejpam-7020	76	14	,	,	PUNCT
ejpam-7020	76	15	investigate	investigate	VERB
ejpam-7020	76	16	how	how	SCONJ
ejpam-7020	76	17	varying	vary	VERB
ejpam-7020	76	18	a	a	DET
ejpam-7020	76	19	key	key	ADJ
ejpam-7020	76	20	parameter	parameter	NOUN
ejpam-7020	76	21	affects	affect	VERB
ejpam-7020	76	22	the	the	DET
ejpam-7020	76	23	system	system	NOUN
ejpam-7020	76	24	’s	’s	PART
ejpam-7020	76	25	dynamics	dynamic	NOUN
ejpam-7020	76	26	.	.	PUNCT
ejpam-7020	77	1	we	we	PRON
ejpam-7020	77	2	identify	identify	VERB
ejpam-7020	77	3	the	the	DET
ejpam-7020	77	4	equilibrium	equilibrium	NOUN
ejpam-7020	77	5	points	point	NOUN
ejpam-7020	77	6	,	,	PUNCT
ejpam-7020	77	7	compute	compute	VERB
ejpam-7020	77	8	the	the	DET
ejpam-7020	77	9	jacobian	jacobian	ADJ
ejpam-7020	77	10	matrix	matrix	NOUN
ejpam-7020	77	11	at	at	ADP
ejpam-7020	77	12	each	each	DET
ejpam-7020	77	13	point	point	NOUN
ejpam-7020	77	14	,	,	PUNCT
ejpam-7020	77	15	and	and	CCONJ
ejpam-7020	77	16	perform	perform	VERB
ejpam-7020	77	17	an	an	DET
ejpam-7020	77	18	eigenvalue	eigenvalue	ADJ
ejpam-7020	77	19	analysis	analysis	NOUN
ejpam-7020	77	20	to	to	PART
ejpam-7020	77	21	classify	classify	VERB
ejpam-7020	77	22	their	their	PRON
ejpam-7020	77	23	stability	stability	NOUN
ejpam-7020	77	24	.	.	PUNCT
ejpam-7020	78	1	phase	phase	NOUN
ejpam-7020	78	2	portraits	portrait	NOUN
ejpam-7020	78	3	are	be	AUX
ejpam-7020	78	4	generated	generate	VERB
ejpam-7020	78	5	to	to	PART
ejpam-7020	78	6	visualize	visualize	VERB
ejpam-7020	78	7	the	the	DET
ejpam-7020	78	8	local	local	ADJ
ejpam-7020	78	9	behavior	behavior	NOUN
ejpam-7020	78	10	near	near	ADP
ejpam-7020	78	11	each	each	DET
ejpam-7020	78	12	equilibrium	equilibrium	NOUN
ejpam-7020	78	13	,	,	PUNCT
ejpam-7020	78	14	confirming	confirm	VERB
ejpam-7020	78	15	the	the	DET
ejpam-7020	78	16	analytical	analytical	ADJ
ejpam-7020	78	17	predictions	prediction	NOUN
ejpam-7020	78	18	.	.	PUNCT
ejpam-7020	79	1	s.	s.	PROPN
ejpam-7020	79	2	saidat	saidat	PROPN
ejpam-7020	79	3	et	et	PROPN
ejpam-7020	79	4	al	al	PROPN
ejpam-7020	79	5	.	.	PUNCT
ejpam-7020	79	6	/	/	SYM
ejpam-7020	79	7	eur	eur	PROPN
ejpam-7020	79	8	.	.	PUNCT
ejpam-7020	80	1	j.	j.	PROPN
ejpam-7020	80	2	pure	pure	PROPN
ejpam-7020	80	3	appl	appl	PROPN
ejpam-7020	80	4	.	.	PROPN
ejpam-7020	80	5	math	math	PROPN
ejpam-7020	80	6	,	,	PUNCT
ejpam-7020	80	7	18	18	NUM
ejpam-7020	80	8	(	(	PUNCT
ejpam-7020	80	9	4	4	NUM
ejpam-7020	80	10	)	)	PUNCT
ejpam-7020	80	11	(	(	PUNCT
ejpam-7020	80	12	2025	2025	NUM
ejpam-7020	80	13	)	)	PUNCT
ejpam-7020	80	14	,	,	PUNCT
ejpam-7020	80	15	7020	7020	NUM
ejpam-7020	80	16	5	5	NUM
ejpam-7020	80	17	of	of	ADP
ejpam-7020	80	18	16	16	NUM
ejpam-7020	80	19	3	3	NUM
ejpam-7020	80	20	.	.	PUNCT
ejpam-7020	80	21	case	case	NOUN
ejpam-7020	80	22	study	study	NOUN
ejpam-7020	80	23	:	:	PUNCT
ejpam-7020	80	24	lotka	lotka	PROPN
ejpam-7020	80	25	-	-	PUNCT
ejpam-7020	80	26	volterra	volterra	PROPN
ejpam-7020	80	27	predator	predator	NOUN
ejpam-7020	80	28	-	-	PUNCT
ejpam-7020	80	29	prey	prey	NOUN
ejpam-7020	80	30	model	model	NOUN
ejpam-7020	80	31	our	our	PRON
ejpam-7020	80	32	first	first	ADJ
ejpam-7020	80	33	case	case	NOUN
ejpam-7020	80	34	study	study	NOUN
ejpam-7020	80	35	is	be	AUX
ejpam-7020	80	36	the	the	DET
ejpam-7020	80	37	classical	classical	ADJ
ejpam-7020	80	38	lotka	lotka	PROPN
ejpam-7020	80	39	–	–	PUNCT
ejpam-7020	80	40	volterra	volterra	NOUN
ejpam-7020	80	41	model	model	NOUN
ejpam-7020	80	42	,	,	PUNCT
ejpam-7020	80	43	which	which	PRON
ejpam-7020	80	44	describes	describe	VERB
ejpam-7020	80	45	the	the	DET
ejpam-7020	80	46	dynamic	dynamic	ADJ
ejpam-7020	80	47	relationship	relationship	NOUN
ejpam-7020	80	48	between	between	ADP
ejpam-7020	80	49	a	a	DET
ejpam-7020	80	50	predator	predator	NOUN
ejpam-7020	80	51	and	and	CCONJ
ejpam-7020	80	52	its	its	PRON
ejpam-7020	80	53	prey	prey	NOUN
ejpam-7020	80	54	.	.	PUNCT
ejpam-7020	81	1	for	for	SCONJ
ejpam-7020	81	2	this	this	DET
ejpam-7020	81	3	model	model	NOUN
ejpam-7020	81	4	to	to	PART
ejpam-7020	81	5	be	be	AUX
ejpam-7020	81	6	biologically	biologically	ADV
ejpam-7020	81	7	meaningful	meaningful	ADJ
ejpam-7020	81	8	,	,	PUNCT
ejpam-7020	81	9	we	we	PRON
ejpam-7020	81	10	assume	assume	VERB
ejpam-7020	81	11	that	that	SCONJ
ejpam-7020	81	12	all	all	DET
ejpam-7020	81	13	parameters	parameter	NOUN
ejpam-7020	81	14	(	(	PUNCT
ejpam-7020	81	15	a	a	PRON
ejpam-7020	81	16	,	,	PUNCT
ejpam-7020	81	17	b	b	NOUN
ejpam-7020	81	18	,	,	PUNCT
ejpam-7020	81	19	c	c	NOUN
ejpam-7020	81	20	,	,	PUNCT
ejpam-7020	81	21	d	d	NOUN
ejpam-7020	81	22	)	)	PUNCT
ejpam-7020	81	23	,	,	PUNCT
ejpam-7020	81	24	representing	represent	VERB
ejpam-7020	81	25	birth	birth	NOUN
ejpam-7020	81	26	,	,	PUNCT
ejpam-7020	81	27	death	death	NOUN
ejpam-7020	81	28	,	,	PUNCT
ejpam-7020	81	29	and	and	CCONJ
ejpam-7020	81	30	interaction	interaction	NOUN
ejpam-7020	81	31	rates	rate	NOUN
ejpam-7020	81	32	,	,	PUNCT
ejpam-7020	81	33	are	be	AUX
ejpam-7020	81	34	positive	positive	ADJ
ejpam-7020	81	35	real	real	ADJ
ejpam-7020	81	36	constants:	constants:	NOUN
ejpam-7020	81	37	dx	dx	PROPN
ejpam-7020	81	38	dt	dt	X
ejpam-7020	81	39	=	=	SYM
ejpam-7020	81	40	ax−	ax−	NUM
ejpam-7020	81	41	bxy	bxy	NOUN
ejpam-7020	81	42	,	,	PUNCT
ejpam-7020	81	43	dy	dy	NOUN
ejpam-7020	81	44	dt	dt	NOUN
ejpam-7020	81	45	=	=	SYM
ejpam-7020	82	1	−cy	−cy	PROPN
ejpam-7020	83	1	+	+	CCONJ
ejpam-7020	83	2	dxy	dxy	PROPN
ejpam-7020	83	3	,	,	PUNCT
ejpam-7020	83	4	(	(	PUNCT
ejpam-7020	83	5	4	4	NUM
ejpam-7020	83	6	)	)	PUNCT
ejpam-7020	84	1	where	where	SCONJ
ejpam-7020	84	2	x(t	x(t	PROPN
ejpam-7020	84	3	)	)	PUNCT
ejpam-7020	84	4	and	and	CCONJ
ejpam-7020	84	5	y(t	y(t	NUM
ejpam-7020	84	6	)	)	PUNCT
ejpam-7020	84	7	represent	represent	VERB
ejpam-7020	84	8	the	the	DET
ejpam-7020	84	9	prey	prey	NOUN
ejpam-7020	84	10	and	and	CCONJ
ejpam-7020	84	11	predator	predator	NOUN
ejpam-7020	84	12	populations	population	NOUN
ejpam-7020	84	13	,	,	PUNCT
ejpam-7020	84	14	respectively	respectively	ADV
ejpam-7020	84	15	,	,	PUNCT
ejpam-7020	84	16	and	and	CCONJ
ejpam-7020	84	17	a	a	DET
ejpam-7020	84	18	,	,	PUNCT
ejpam-7020	84	19	b	b	NOUN
ejpam-7020	84	20	,	,	PUNCT
ejpam-7020	84	21	c	c	NOUN
ejpam-7020	84	22	,	,	PUNCT
ejpam-7020	84	23	d	d	X
ejpam-7020	84	24	>	>	X
ejpam-7020	84	25	0	0	NUM
ejpam-7020	84	26	are	be	AUX
ejpam-7020	84	27	constant	constant	ADJ
ejpam-7020	84	28	parameters	parameter	NOUN
ejpam-7020	84	29	.	.	PUNCT
ejpam-7020	85	1	3.1	3.1	NUM
ejpam-7020	85	2	.	.	PUNCT
ejpam-7020	85	3	equilibrium	equilibrium	NOUN
ejpam-7020	85	4	points	point	VERB
ejpam-7020	85	5	the	the	DET
ejpam-7020	85	6	first	first	ADJ
ejpam-7020	85	7	step	step	NOUN
ejpam-7020	85	8	is	be	AUX
ejpam-7020	85	9	to	to	PART
ejpam-7020	85	10	find	find	VERB
ejpam-7020	85	11	the	the	DET
ejpam-7020	85	12	equilibrium	equilibrium	NOUN
ejpam-7020	85	13	points	point	NOUN
ejpam-7020	85	14	of	of	ADP
ejpam-7020	85	15	the	the	DET
ejpam-7020	85	16	system	system	NOUN
ejpam-7020	85	17	by	by	ADP
ejpam-7020	85	18	setting	set	VERB
ejpam-7020	85	19	both	both	DET
ejpam-7020	85	20	derivatives	derivative	NOUN
ejpam-7020	85	21	to	to	ADP
ejpam-7020	85	22	zero	zero	NUM
ejpam-7020	85	23	.	.	PUNCT
ejpam-7020	86	1			PRON
ejpam-7020	86	2	ax−	ax−	VERB
ejpam-7020	86	3	bxy	bxy	NOUN
ejpam-7020	86	4	=	=	SYM
ejpam-7020	86	5	0	0	NUM
ejpam-7020	86	6	,	,	PUNCT
ejpam-7020	86	7	−cy	−cy	PROPN
ejpam-7020	87	1	+	+	CCONJ
ejpam-7020	87	2	dxy	dxy	PROPN
ejpam-7020	87	3	=	=	SYM
ejpam-7020	87	4	0	0	X
ejpam-7020	87	5	.	.	PUNCT
ejpam-7020	87	6	factoring	factor	VERB
ejpam-7020	87	7	both	both	DET
ejpam-7020	87	8	equations	equation	NOUN
ejpam-7020	87	9	,	,	PUNCT
ejpam-7020	87	10	we	we	PRON
ejpam-7020	87	11	obtain	obtain	VERB
ejpam-7020	87	12	the	the	DET
ejpam-7020	87	13	following	following	NOUN
ejpam-7020	87	14	:	:	PUNCT
ejpam-7020	87	15	x(a−	x(a−	PROPN
ejpam-7020	87	16	by	by	ADP
ejpam-7020	87	17	)	)	PUNCT
ejpam-7020	87	18	=	=	SYM
ejpam-7020	87	19	0	0	NUM
ejpam-7020	87	20	,	,	PUNCT
ejpam-7020	87	21	y(−c	y(−c	VERB
ejpam-7020	88	1	+	+	CCONJ
ejpam-7020	88	2	dx	dx	X
ejpam-7020	88	3	)	)	PUNCT
ejpam-7020	89	1	=	=	SYM
ejpam-7020	89	2	0	0	X
ejpam-7020	89	3	.	.	PUNCT
ejpam-7020	90	1	this	this	PRON
ejpam-7020	90	2	yields	yield	VERB
ejpam-7020	90	3	two	two	NUM
ejpam-7020	90	4	biologically	biologically	ADV
ejpam-7020	90	5	relevant	relevant	ADJ
ejpam-7020	90	6	equilibrium	equilibrium	NOUN
ejpam-7020	90	7	points	point	NOUN
ejpam-7020	90	8	:	:	PUNCT
ejpam-7020	90	9	•	•	NUM
ejpam-7020	90	10	trivial	trivial	ADJ
ejpam-7020	90	11	equilibrium	equilibrium	NOUN
ejpam-7020	90	12	:	:	PUNCT
ejpam-7020	90	13	e1	e1	NOUN
ejpam-7020	90	14	=	=	SYM
ejpam-7020	90	15	(	(	PUNCT
ejpam-7020	90	16	0	0	NUM
ejpam-7020	90	17	,	,	PUNCT
ejpam-7020	90	18	0	0	NUM
ejpam-7020	90	19	)	)	PUNCT
ejpam-7020	90	20	.	.	PUNCT
ejpam-7020	91	1	this	this	PRON
ejpam-7020	91	2	represents	represent	VERB
ejpam-7020	91	3	the	the	DET
ejpam-7020	91	4	complete	complete	ADJ
ejpam-7020	91	5	absence	absence	NOUN
ejpam-7020	91	6	of	of	ADP
ejpam-7020	91	7	both	both	DET
ejpam-7020	91	8	prey	prey	NOUN
ejpam-7020	91	9	and	and	CCONJ
ejpam-7020	91	10	predators	predator	NOUN
ejpam-7020	91	11	.	.	PUNCT
ejpam-7020	92	1	•	•	NUM
ejpam-7020	92	2	co	co	NOUN
ejpam-7020	92	3	-	-	NOUN
ejpam-7020	92	4	existence	existence	NOUN
ejpam-7020	92	5	equilibrium	equilibrium	NOUN
ejpam-7020	92	6	:	:	PUNCT
ejpam-7020	92	7	e2	e2	PROPN
ejpam-7020	92	8	=	=	PUNCT
ejpam-7020	92	9	(	(	PUNCT
ejpam-7020	92	10	c	c	NOUN
ejpam-7020	92	11	d	d	PROPN
ejpam-7020	92	12	,	,	PUNCT
ejpam-7020	92	13	a	a	DET
ejpam-7020	92	14	b	b	NOUN
ejpam-7020	92	15	)	)	PUNCT
ejpam-7020	92	16	.	.	PUNCT
ejpam-7020	93	1	this	this	PRON
ejpam-7020	93	2	represents	represent	VERB
ejpam-7020	93	3	a	a	DET
ejpam-7020	93	4	state	state	NOUN
ejpam-7020	93	5	where	where	SCONJ
ejpam-7020	93	6	both	both	DET
ejpam-7020	93	7	populations	population	NOUN
ejpam-7020	93	8	co	co	NOUN
ejpam-7020	93	9	-	-	VERB
ejpam-7020	93	10	exist	exist	VERB
ejpam-7020	93	11	with	with	ADP
ejpam-7020	93	12	stable	stable	ADJ
ejpam-7020	93	13	average	average	ADJ
ejpam-7020	93	14	populations	population	NOUN
ejpam-7020	93	15	.	.	PUNCT
ejpam-7020	94	1	3.2	3.2	NUM
ejpam-7020	94	2	.	.	PUNCT
ejpam-7020	95	1	stability	stability	NOUN
ejpam-7020	95	2	analysis	analysis	NOUN
ejpam-7020	95	3	with	with	SCONJ
ejpam-7020	95	4	the	the	DET
ejpam-7020	95	5	equilibria	equilibrium	NOUN
ejpam-7020	95	6	identified	identify	VERB
ejpam-7020	95	7	,	,	PUNCT
ejpam-7020	95	8	our	our	PRON
ejpam-7020	95	9	next	next	ADJ
ejpam-7020	95	10	step	step	NOUN
ejpam-7020	95	11	is	be	AUX
ejpam-7020	95	12	to	to	PART
ejpam-7020	95	13	use	use	VERB
ejpam-7020	95	14	linearization	linearization	NOUN
ejpam-7020	95	15	to	to	PART
ejpam-7020	95	16	understand	understand	VERB
ejpam-7020	95	17	the	the	DET
ejpam-7020	95	18	stability	stability	NOUN
ejpam-7020	95	19	of	of	ADP
ejpam-7020	95	20	each	each	DET
ejpam-7020	95	21	point	point	NOUN
ejpam-7020	95	22	.	.	PUNCT
ejpam-7020	96	1	we	we	PRON
ejpam-7020	96	2	first	first	ADV
ejpam-7020	96	3	compute	compute	VERB
ejpam-7020	96	4	the	the	DET
ejpam-7020	96	5	general	general	ADJ
ejpam-7020	96	6	jacobian	jacobian	ADJ
ejpam-7020	96	7	matrix	matrix	NOUN
ejpam-7020	96	8	for	for	ADP
ejpam-7020	96	9	the	the	DET
ejpam-7020	96	10	system	system	NOUN
ejpam-7020	96	11	:	:	PUNCT
ejpam-7020	96	12	j(x	j(x	PROPN
ejpam-7020	96	13	,	,	PUNCT
ejpam-7020	96	14	y	y	PROPN
ejpam-7020	96	15	)	)	PUNCT
ejpam-7020	97	1	=	=	NOUN
ejpam-7020	97	2	[	[	PUNCT
ejpam-7020	97	3	a−	a−	NOUN
ejpam-7020	97	4	by	by	ADP
ejpam-7020	97	5	−bx	−bx	PROPN
ejpam-7020	97	6	dy	dy	NOUN
ejpam-7020	97	7	−c	−c	NOUN
ejpam-7020	97	8	+	+	CCONJ
ejpam-7020	97	9	dx	dx	X
ejpam-7020	97	10	]	]	PUNCT
ejpam-7020	97	11	.	.	PUNCT
ejpam-7020	98	1	we	we	PRON
ejpam-7020	98	2	now	now	ADV
ejpam-7020	98	3	evaluate	evaluate	VERB
ejpam-7020	98	4	this	this	DET
ejpam-7020	98	5	jacobian	jacobian	NOUN
ejpam-7020	98	6	at	at	ADP
ejpam-7020	98	7	each	each	DET
ejpam-7020	98	8	equilibrium	equilibrium	NOUN
ejpam-7020	98	9	point	point	NOUN
ejpam-7020	98	10	:	:	PUNCT
ejpam-7020	98	11	s.	s.	PROPN
ejpam-7020	98	12	saidat	saidat	VERB
ejpam-7020	98	13	et	et	PROPN
ejpam-7020	98	14	al	al	PROPN
ejpam-7020	98	15	.	.	PUNCT
ejpam-7020	98	16	/	/	SYM
ejpam-7020	98	17	eur	eur	PROPN
ejpam-7020	98	18	.	.	PUNCT
ejpam-7020	99	1	j.	j.	PROPN
ejpam-7020	99	2	pure	pure	PROPN
ejpam-7020	99	3	appl	appl	PROPN
ejpam-7020	99	4	.	.	PROPN
ejpam-7020	99	5	math	math	PROPN
ejpam-7020	99	6	,	,	PUNCT
ejpam-7020	99	7	18	18	NUM
ejpam-7020	99	8	(	(	PUNCT
ejpam-7020	99	9	4	4	NUM
ejpam-7020	99	10	)	)	PUNCT
ejpam-7020	99	11	(	(	PUNCT
ejpam-7020	99	12	2025	2025	NUM
ejpam-7020	99	13	)	)	PUNCT
ejpam-7020	99	14	,	,	PUNCT
ejpam-7020	99	15	7020	7020	NUM
ejpam-7020	99	16	6	6	NUM
ejpam-7020	99	17	of	of	ADP
ejpam-7020	99	18	16	16	NUM
ejpam-7020	99	19	(	(	PUNCT
ejpam-7020	99	20	i	i	NOUN
ejpam-7020	99	21	)	)	PUNCT
ejpam-7020	99	22	analysis	analysis	NOUN
ejpam-7020	99	23	in	in	ADP
ejpam-7020	99	24	the	the	DET
ejpam-7020	99	25	trivial	trivial	ADJ
ejpam-7020	99	26	equilibrium	equilibrium	NOUN
ejpam-7020	99	27	e1	e1	NOUN
ejpam-7020	99	28	=	=	SYM
ejpam-7020	99	29	(	(	PUNCT
ejpam-7020	99	30	0	0	NUM
ejpam-7020	99	31	,	,	PUNCT
ejpam-7020	99	32	0	0	NUM
ejpam-7020	99	33	)	)	PUNCT
ejpam-7020	99	34	.	.	PUNCT
ejpam-7020	100	1	evaluating	evaluate	VERB
ejpam-7020	100	2	the	the	DET
ejpam-7020	100	3	jacobian	jacobian	NOUN
ejpam-7020	100	4	at	at	ADP
ejpam-7020	100	5	(	(	PUNCT
ejpam-7020	100	6	0	0	NUM
ejpam-7020	100	7	,	,	PUNCT
ejpam-7020	100	8	0	0	NUM
ejpam-7020	100	9	)	)	PUNCT
ejpam-7020	100	10	gives	give	VERB
ejpam-7020	100	11	:	:	PUNCT
ejpam-7020	100	12	j(0	j(0	PROPN
ejpam-7020	100	13	,	,	PUNCT
ejpam-7020	100	14	0	0	NUM
ejpam-7020	100	15	)	)	PUNCT
ejpam-7020	100	16	=	=	NOUN
ejpam-7020	101	1	[	[	PUNCT
ejpam-7020	101	2	a	a	DET
ejpam-7020	101	3	0	0	NUM
ejpam-7020	101	4	0	0	NUM
ejpam-7020	101	5	−c	−c	NOUN
ejpam-7020	101	6	]	]	PUNCT
ejpam-7020	101	7	.	.	PUNCT
ejpam-7020	102	1	the	the	DET
ejpam-7020	102	2	eigenvalues	eigenvalue	NOUN
ejpam-7020	102	3	are	be	AUX
ejpam-7020	102	4	the	the	DET
ejpam-7020	102	5	diagonal	diagonal	ADJ
ejpam-7020	102	6	entries	entry	NOUN
ejpam-7020	102	7	:	:	PUNCT
ejpam-7020	102	8	λ1	λ1	PROPN
ejpam-7020	102	9	=	=	PUNCT
ejpam-7020	102	10	a	a	PRON
ejpam-7020	102	11	and	and	CCONJ
ejpam-7020	102	12	λ2	λ2	NOUN
ejpam-7020	102	13	=	=	NOUN
ejpam-7020	102	14	−c	−c	NOUN
ejpam-7020	102	15	.	.	PUNCT
ejpam-7020	103	1	since	since	SCONJ
ejpam-7020	103	2	a	a	DET
ejpam-7020	103	3	>	>	X
ejpam-7020	103	4	0	0	PUNCT
ejpam-7020	103	5	and	and	CCONJ
ejpam-7020	103	6	−c	−c	VERB
ejpam-7020	103	7	<	<	X
ejpam-7020	103	8	0	0	PROPN
ejpam-7020	103	9	,	,	PUNCT
ejpam-7020	103	10	the	the	DET
ejpam-7020	103	11	eigenvalues	eigenvalue	NOUN
ejpam-7020	103	12	are	be	AUX
ejpam-7020	103	13	real	real	ADJ
ejpam-7020	103	14	and	and	CCONJ
ejpam-7020	103	15	have	have	VERB
ejpam-7020	103	16	opposite	opposite	ADJ
ejpam-7020	103	17	signs	sign	NOUN
ejpam-7020	103	18	.	.	PUNCT
ejpam-7020	104	1	thus	thus	ADV
ejpam-7020	104	2	,	,	PUNCT
ejpam-7020	104	3	the	the	DET
ejpam-7020	104	4	origin	origin	NOUN
ejpam-7020	104	5	is	be	AUX
ejpam-7020	104	6	an	an	DET
ejpam-7020	104	7	unstable	unstable	ADJ
ejpam-7020	104	8	saddle	saddle	NOUN
ejpam-7020	104	9	point	point	NOUN
ejpam-7020	104	10	.	.	PUNCT
ejpam-7020	105	1	trajectories	trajectory	NOUN
ejpam-7020	105	2	near	near	ADP
ejpam-7020	105	3	the	the	DET
ejpam-7020	105	4	origin	origin	NOUN
ejpam-7020	105	5	will	will	AUX
ejpam-7020	105	6	be	be	AUX
ejpam-7020	105	7	pushed	push	VERB
ejpam-7020	105	8	away	away	ADV
ejpam-7020	105	9	,	,	PUNCT
ejpam-7020	105	10	indicating	indicate	VERB
ejpam-7020	105	11	that	that	SCONJ
ejpam-7020	105	12	if	if	SCONJ
ejpam-7020	105	13	even	even	ADV
ejpam-7020	105	14	a	a	DET
ejpam-7020	105	15	few	few	ADJ
ejpam-7020	105	16	prey	prey	NOUN
ejpam-7020	105	17	and	and	CCONJ
ejpam-7020	105	18	predators	predator	NOUN
ejpam-7020	105	19	are	be	AUX
ejpam-7020	105	20	present	present	ADJ
ejpam-7020	105	21	,	,	PUNCT
ejpam-7020	105	22	the	the	DET
ejpam-7020	105	23	populations	population	NOUN
ejpam-7020	105	24	will	will	AUX
ejpam-7020	105	25	not	not	PART
ejpam-7020	105	26	die	die	VERB
ejpam-7020	105	27	out	out	ADP
ejpam-7020	105	28	.	.	PUNCT
ejpam-7020	106	1	(	(	PUNCT
ejpam-7020	106	2	ii	ii	NOUN
ejpam-7020	106	3	)	)	PUNCT
ejpam-7020	106	4	analysis	analysis	NOUN
ejpam-7020	106	5	in	in	ADP
ejpam-7020	106	6	the	the	DET
ejpam-7020	106	7	co	co	NOUN
ejpam-7020	106	8	-	-	NOUN
ejpam-7020	106	9	existence	existence	NOUN
ejpam-7020	106	10	equilibrium	equilibrium	NOUN
ejpam-7020	106	11	e2	e2	PROPN
ejpam-7020	106	12	=	=	PUNCT
ejpam-7020	106	13	(	(	PUNCT
ejpam-7020	106	14	c	c	NOUN
ejpam-7020	106	15	d	d	PROPN
ejpam-7020	106	16	,	,	PUNCT
ejpam-7020	106	17	a	a	DET
ejpam-7020	106	18	b	b	NOUN
ejpam-7020	106	19	)	)	PUNCT
ejpam-7020	106	20	.	.	PUNCT
ejpam-7020	107	1	evaluating	evaluate	VERB
ejpam-7020	107	2	the	the	DET
ejpam-7020	107	3	jacobian	jacobian	NOUN
ejpam-7020	107	4	at	at	ADP
ejpam-7020	107	5	this	this	DET
ejpam-7020	107	6	point	point	NOUN
ejpam-7020	107	7	gives	give	VERB
ejpam-7020	107	8	:	:	PUNCT
ejpam-7020	107	9	j	j	PROPN
ejpam-7020	107	10	(	(	PUNCT
ejpam-7020	107	11	c	c	NOUN
ejpam-7020	107	12	d	d	PROPN
ejpam-7020	107	13	,	,	PUNCT
ejpam-7020	107	14	a	a	DET
ejpam-7020	107	15	b	b	NOUN
ejpam-7020	107	16	)	)	PUNCT
ejpam-7020	107	17	=	=	PUNCT
ejpam-7020	108	1	[	[	PUNCT
ejpam-7020	108	2	0	0	NUM
ejpam-7020	108	3	−	−	NUM
ejpam-7020	108	4	bc	bc	PROPN
ejpam-7020	108	5	d	d	X
ejpam-7020	108	6	ad	ad	PROPN
ejpam-7020	108	7	b	b	PROPN
ejpam-7020	108	8	0	0	NUM
ejpam-7020	108	9	]	]	PUNCT
ejpam-7020	108	10	.	.	PUNCT
ejpam-7020	109	1	to	to	PART
ejpam-7020	109	2	find	find	VERB
ejpam-7020	109	3	the	the	DET
ejpam-7020	109	4	eigenvalues	eigenvalue	NOUN
ejpam-7020	109	5	,	,	PUNCT
ejpam-7020	109	6	we	we	PRON
ejpam-7020	109	7	solve	solve	VERB
ejpam-7020	109	8	the	the	DET
ejpam-7020	109	9	characteristic	characteristic	ADJ
ejpam-7020	109	10	equation	equation	NOUN
ejpam-7020	109	11	det(j	det(j	PROPN
ejpam-7020	109	12	−	−	PROPN
ejpam-7020	109	13	λi	λi	NOUN
ejpam-7020	109	14	)	)	PUNCT
ejpam-7020	109	15	=	=	SYM
ejpam-7020	109	16	0	0	NUM
ejpam-7020	109	17	⇒	⇒	NOUN
ejpam-7020	109	18	λ2	λ2	NOUN
ejpam-7020	109	19	+	+	CCONJ
ejpam-7020	109	20	ac	ac	PROPN
ejpam-7020	109	21	=	=	SYM
ejpam-7020	109	22	0	0	PROPN
ejpam-7020	109	23	.	.	PUNCT
ejpam-7020	110	1	this	this	PRON
ejpam-7020	110	2	yields	yield	VERB
ejpam-7020	110	3	the	the	DET
ejpam-7020	110	4	purely	purely	ADV
ejpam-7020	110	5	imaginary	imaginary	ADJ
ejpam-7020	110	6	eigenvalues	eigenvalue	NOUN
ejpam-7020	110	7	λ	λ	NOUN
ejpam-7020	110	8	=	=	PUNCT
ejpam-7020	110	9	±i	±i	PROPN
ejpam-7020	110	10	√	√	PROPN
ejpam-7020	110	11	ac	ac	PROPN
ejpam-7020	110	12	.	.	PUNCT
ejpam-7020	111	1	purely	purely	ADV
ejpam-7020	111	2	imaginary	imaginary	ADJ
ejpam-7020	111	3	eigenvalues	eigenvalue	NOUN
ejpam-7020	111	4	correspond	correspond	VERB
ejpam-7020	111	5	to	to	ADP
ejpam-7020	111	6	a	a	DET
ejpam-7020	111	7	center	center	NOUN
ejpam-7020	111	8	.	.	PUNCT
ejpam-7020	112	1	thus	thus	ADV
ejpam-7020	112	2	,	,	PUNCT
ejpam-7020	112	3	the	the	DET
ejpam-7020	112	4	analytical	analytical	ADJ
ejpam-7020	112	5	result	result	NOUN
ejpam-7020	112	6	predicts	predict	VERB
ejpam-7020	112	7	that	that	SCONJ
ejpam-7020	112	8	,	,	PUNCT
ejpam-7020	112	9	in	in	ADP
ejpam-7020	112	10	the	the	DET
ejpam-7020	112	11	vicinity	vicinity	NOUN
ejpam-7020	112	12	of	of	ADP
ejpam-7020	112	13	the	the	DET
ejpam-7020	112	14	co	co	NOUN
ejpam-7020	112	15	-	-	NOUN
ejpam-7020	112	16	existence	existence	NOUN
ejpam-7020	112	17	point	point	NOUN
ejpam-7020	112	18	,	,	PUNCT
ejpam-7020	112	19	the	the	DET
ejpam-7020	112	20	predator	predator	NOUN
ejpam-7020	112	21	and	and	CCONJ
ejpam-7020	112	22	prey	prey	NOUN
ejpam-7020	112	23	populations	population	NOUN
ejpam-7020	112	24	will	will	AUX
ejpam-7020	112	25	oscillate	oscillate	VERB
ejpam-7020	112	26	in	in	ADP
ejpam-7020	112	27	endless	endless	ADJ
ejpam-7020	112	28	,	,	PUNCT
ejpam-7020	112	29	stable	stable	ADJ
ejpam-7020	112	30	cycles	cycle	NOUN
ejpam-7020	112	31	.	.	PUNCT
ejpam-7020	113	1	3.3	3.3	NUM
ejpam-7020	113	2	.	.	PUNCT
ejpam-7020	114	1	parameter	parameter	NOUN
ejpam-7020	114	2	sensitivity	sensitivity	NOUN
ejpam-7020	114	3	analysis	analysis	NOUN
ejpam-7020	114	4	a	a	DET
ejpam-7020	114	5	powerful	powerful	ADJ
ejpam-7020	114	6	feature	feature	NOUN
ejpam-7020	114	7	of	of	ADP
ejpam-7020	114	8	a	a	DET
ejpam-7020	114	9	good	good	ADJ
ejpam-7020	114	10	model	model	NOUN
ejpam-7020	114	11	is	be	AUX
ejpam-7020	114	12	understanding	understand	VERB
ejpam-7020	114	13	how	how	SCONJ
ejpam-7020	114	14	its	its	PRON
ejpam-7020	114	15	predictions	prediction	NOUN
ejpam-7020	114	16	change	change	VERB
ejpam-7020	114	17	when	when	SCONJ
ejpam-7020	114	18	its	its	PRON
ejpam-7020	114	19	parameters	parameter	NOUN
ejpam-7020	114	20	are	be	AUX
ejpam-7020	114	21	tweaked	tweak	VERB
ejpam-7020	114	22	.	.	PUNCT
ejpam-7020	115	1	this	this	PRON
ejpam-7020	115	2	is	be	AUX
ejpam-7020	115	3	known	know	VERB
ejpam-7020	115	4	as	as	ADP
ejpam-7020	115	5	a	a	DET
ejpam-7020	115	6	sensitivity	sensitivity	NOUN
ejpam-7020	115	7	analysis	analysis	NOUN
ejpam-7020	115	8	.	.	PUNCT
ejpam-7020	116	1	in	in	ADP
ejpam-7020	116	2	our	our	PRON
ejpam-7020	116	3	lotka	lotka	PROPN
ejpam-7020	116	4	–	–	PUNCT
ejpam-7020	116	5	volterra	volterra	NOUN
ejpam-7020	116	6	model	model	NOUN
ejpam-7020	116	7	,	,	PUNCT
ejpam-7020	116	8	a	a	DET
ejpam-7020	116	9	particularly	particularly	ADV
ejpam-7020	116	10	interesting	interesting	ADJ
ejpam-7020	116	11	parameter	parameter	NOUN
ejpam-7020	116	12	is	be	AUX
ejpam-7020	116	13	b	b	NOUN
ejpam-7020	116	14	,	,	PUNCT
ejpam-7020	116	15	which	which	PRON
ejpam-7020	116	16	represents	represent	VERB
ejpam-7020	116	17	the	the	DET
ejpam-7020	116	18	rate	rate	NOUN
ejpam-7020	116	19	at	at	ADP
ejpam-7020	116	20	which	which	PRON
ejpam-7020	116	21	prey	prey	NOUN
ejpam-7020	116	22	is	be	AUX
ejpam-7020	116	23	consumed	consume	VERB
ejpam-7020	116	24	by	by	ADP
ejpam-7020	116	25	predators	predator	NOUN
ejpam-7020	116	26	,	,	PUNCT
ejpam-7020	116	27	or	or	CCONJ
ejpam-7020	116	28	the	the	DET
ejpam-7020	116	29	impact	impact	NOUN
ejpam-7020	116	30	of	of	ADP
ejpam-7020	116	31	each	each	DET
ejpam-7020	116	32	predation	predation	NOUN
ejpam-7020	116	33	event	event	NOUN
ejpam-7020	116	34	.	.	PUNCT
ejpam-7020	117	1	what	what	PRON
ejpam-7020	117	2	happens	happen	VERB
ejpam-7020	117	3	to	to	ADP
ejpam-7020	117	4	the	the	DET
ejpam-7020	117	5	system	system	NOUN
ejpam-7020	117	6	if	if	SCONJ
ejpam-7020	117	7	this	this	DET
ejpam-7020	117	8	rate	rate	NOUN
ejpam-7020	117	9	changes	change	NOUN
ejpam-7020	117	10	?	?	PUNCT
ejpam-7020	118	1	let	let	VERB
ejpam-7020	118	2	us	we	PRON
ejpam-7020	118	3	consider	consider	VERB
ejpam-7020	118	4	the	the	DET
ejpam-7020	118	5	co	co	NOUN
ejpam-7020	118	6	-	-	NOUN
ejpam-7020	118	7	existence	existence	NOUN
ejpam-7020	118	8	equilibrium	equilibrium	NOUN
ejpam-7020	118	9	e2	e2	PROPN
ejpam-7020	118	10	=	=	PUNCT
ejpam-7020	118	11	(	(	PUNCT
ejpam-7020	118	12	c	c	NOUN
ejpam-7020	118	13	d	d	PROPN
ejpam-7020	118	14	,	,	PUNCT
ejpam-7020	118	15	a	a	DET
ejpam-7020	118	16	b	b	NOUN
ejpam-7020	118	17	)	)	PUNCT
ejpam-7020	118	18	.	.	PUNCT
ejpam-7020	119	1	we	we	PRON
ejpam-7020	119	2	can	can	AUX
ejpam-7020	119	3	immediately	immediately	ADV
ejpam-7020	119	4	see	see	VERB
ejpam-7020	119	5	that	that	SCONJ
ejpam-7020	119	6	the	the	DET
ejpam-7020	119	7	equilibrium	equilibrium	NOUN
ejpam-7020	119	8	predator	predator	NOUN
ejpam-7020	119	9	population	population	NOUN
ejpam-7020	119	10	,	,	PUNCT
ejpam-7020	119	11	y∗	y∗	PROPN
ejpam-7020	119	12	=	=	PUNCT
ejpam-7020	119	13	a	a	DET
ejpam-7020	119	14	b	b	NOUN
ejpam-7020	119	15	,	,	PUNCT
ejpam-7020	119	16	depends	depend	VERB
ejpam-7020	119	17	directly	directly	ADV
ejpam-7020	119	18	on	on	ADP
ejpam-7020	119	19	b.	b.	PROPN
ejpam-7020	119	20	if	if	SCONJ
ejpam-7020	119	21	the	the	DET
ejpam-7020	119	22	predation	predation	NOUN
ejpam-7020	119	23	rate	rate	NOUN
ejpam-7020	119	24	(	(	PUNCT
ejpam-7020	119	25	b	b	NOUN
ejpam-7020	119	26	)	)	PUNCT
ejpam-7020	119	27	increases	increase	NOUN
ejpam-7020	119	28	,	,	PUNCT
ejpam-7020	119	29	the	the	DET
ejpam-7020	119	30	steady	steady	ADJ
ejpam-7020	119	31	-	-	PUNCT
ejpam-7020	119	32	state	state	NOUN
ejpam-7020	119	33	predator	predator	NOUN
ejpam-7020	119	34	population	population	NOUN
ejpam-7020	119	35	(	(	PUNCT
ejpam-7020	119	36	y∗	y∗	ADV
ejpam-7020	119	37	)	)	PUNCT
ejpam-7020	119	38	required	require	VERB
ejpam-7020	119	39	to	to	PART
ejpam-7020	119	40	maintain	maintain	VERB
ejpam-7020	119	41	equilibrium	equilibrium	NOUN
ejpam-7020	119	42	decreases	decrease	NOUN
ejpam-7020	119	43	.	.	PUNCT
ejpam-7020	120	1	this	this	PRON
ejpam-7020	120	2	reflects	reflect	VERB
ejpam-7020	120	3	a	a	DET
ejpam-7020	120	4	more	more	ADJ
ejpam-7020	120	5	“	"	PUNCT
ejpam-7020	120	6	efficient	efficient	ADJ
ejpam-7020	120	7	”	"	PUNCT
ejpam-7020	120	8	system	system	NOUN
ejpam-7020	120	9	where	where	SCONJ
ejpam-7020	120	10	fewer	few	ADJ
ejpam-7020	120	11	predators	predator	NOUN
ejpam-7020	120	12	are	be	AUX
ejpam-7020	120	13	needed	need	VERB
ejpam-7020	120	14	to	to	PART
ejpam-7020	120	15	control	control	VERB
ejpam-7020	120	16	the	the	DET
ejpam-7020	120	17	prey	prey	NOUN
ejpam-7020	120	18	.	.	PUNCT
ejpam-7020	121	1	but	but	CCONJ
ejpam-7020	121	2	does	do	AUX
ejpam-7020	121	3	this	this	PRON
ejpam-7020	121	4	change	change	VERB
ejpam-7020	121	5	the	the	DET
ejpam-7020	121	6	stability	stability	NOUN
ejpam-7020	121	7	of	of	ADP
ejpam-7020	121	8	the	the	DET
ejpam-7020	121	9	system	system	NOUN
ejpam-7020	121	10	?	?	PUNCT
ejpam-7020	122	1	we	we	PRON
ejpam-7020	122	2	find	find	VERB
ejpam-7020	122	3	that	that	SCONJ
ejpam-7020	122	4	the	the	DET
ejpam-7020	122	5	eigenvalues	eigenvalue	NOUN
ejpam-7020	122	6	in	in	ADP
ejpam-7020	122	7	this	this	DET
ejpam-7020	122	8	equilibrium	equilibrium	NOUN
ejpam-7020	122	9	are	be	AUX
ejpam-7020	122	10	λ	λ	X
ejpam-7020	122	11	=	=	SYM
ejpam-7020	122	12	±i	±i	PROPN
ejpam-7020	122	13	√	√	PROPN
ejpam-7020	122	14	ac	ac	PROPN
ejpam-7020	122	15	.	.	PUNCT
ejpam-7020	123	1	s.	s.	PROPN
ejpam-7020	123	2	saidat	saidat	PROPN
ejpam-7020	123	3	et	et	PROPN
ejpam-7020	123	4	al	al	PROPN
ejpam-7020	123	5	.	.	PUNCT
ejpam-7020	123	6	/	/	SYM
ejpam-7020	123	7	eur	eur	PROPN
ejpam-7020	123	8	.	.	PUNCT
ejpam-7020	124	1	j.	j.	PROPN
ejpam-7020	124	2	pure	pure	PROPN
ejpam-7020	124	3	appl	appl	PROPN
ejpam-7020	124	4	.	.	PROPN
ejpam-7020	124	5	math	math	PROPN
ejpam-7020	124	6	,	,	PUNCT
ejpam-7020	124	7	18	18	NUM
ejpam-7020	124	8	(	(	PUNCT
ejpam-7020	124	9	4	4	NUM
ejpam-7020	124	10	)	)	PUNCT
ejpam-7020	124	11	(	(	PUNCT
ejpam-7020	124	12	2025	2025	NUM
ejpam-7020	124	13	)	)	PUNCT
ejpam-7020	124	14	,	,	PUNCT
ejpam-7020	124	15	7020	7020	NUM
ejpam-7020	124	16	7	7	NUM
ejpam-7020	124	17	of	of	ADP
ejpam-7020	124	18	16	16	NUM
ejpam-7020	124	19	notice	notice	NOUN
ejpam-7020	124	20	that	that	SCONJ
ejpam-7020	124	21	the	the	DET
ejpam-7020	124	22	parameter	parameter	PROPN
ejpam-7020	124	23	b	b	PROPN
ejpam-7020	124	24	does	do	AUX
ejpam-7020	124	25	not	not	PART
ejpam-7020	124	26	appear	appear	VERB
ejpam-7020	124	27	in	in	ADP
ejpam-7020	124	28	this	this	DET
ejpam-7020	124	29	expression	expression	NOUN
ejpam-7020	124	30	at	at	ADV
ejpam-7020	124	31	all	all	ADV
ejpam-7020	124	32	.	.	PUNCT
ejpam-7020	125	1	this	this	PRON
ejpam-7020	125	2	leads	lead	VERB
ejpam-7020	125	3	to	to	ADP
ejpam-7020	125	4	a	a	DET
ejpam-7020	125	5	crucial	crucial	ADJ
ejpam-7020	125	6	insight	insight	NOUN
ejpam-7020	125	7	:	:	PUNCT
ejpam-7020	125	8	while	while	SCONJ
ejpam-7020	125	9	the	the	DET
ejpam-7020	125	10	predation	predation	NOUN
ejpam-7020	125	11	rate	rate	NOUN
ejpam-7020	125	12	b	b	PROPN
ejpam-7020	125	13	changes	change	VERB
ejpam-7020	125	14	the	the	DET
ejpam-7020	125	15	equilibrium	equilibrium	NOUN
ejpam-7020	125	16	level	level	NOUN
ejpam-7020	125	17	of	of	ADP
ejpam-7020	125	18	the	the	DET
ejpam-7020	125	19	predator	predator	NOUN
ejpam-7020	125	20	population	population	NOUN
ejpam-7020	125	21	,	,	PUNCT
ejpam-7020	125	22	it	it	PRON
ejpam-7020	125	23	does	do	AUX
ejpam-7020	125	24	not	not	PART
ejpam-7020	125	25	change	change	VERB
ejpam-7020	125	26	the	the	DET
ejpam-7020	125	27	fundamental	fundamental	ADJ
ejpam-7020	125	28	nature	nature	NOUN
ejpam-7020	125	29	of	of	ADP
ejpam-7020	125	30	the	the	DET
ejpam-7020	125	31	coexistence	coexistence	NOUN
ejpam-7020	125	32	equilibrium	equilibrium	NOUN
ejpam-7020	125	33	.	.	PUNCT
ejpam-7020	126	1	the	the	DET
ejpam-7020	126	2	equilibrium	equilibrium	NOUN
ejpam-7020	126	3	remains	remain	VERB
ejpam-7020	126	4	a	a	DET
ejpam-7020	126	5	center	center	NOUN
ejpam-7020	126	6	,	,	PUNCT
ejpam-7020	126	7	and	and	CCONJ
ejpam-7020	126	8	therefore	therefore	ADV
ejpam-7020	126	9	no	no	DET
ejpam-7020	126	10	bifurcation	bifurcation	NOUN
ejpam-7020	126	11	occurs	occur	VERB
ejpam-7020	126	12	with	with	ADP
ejpam-7020	126	13	respect	respect	NOUN
ejpam-7020	126	14	to	to	ADP
ejpam-7020	126	15	this	this	DET
ejpam-7020	126	16	parameter	parameter	NOUN
ejpam-7020	126	17	.	.	PUNCT
ejpam-7020	127	1	the	the	DET
ejpam-7020	127	2	tendency	tendency	NOUN
ejpam-7020	127	3	of	of	ADP
ejpam-7020	127	4	the	the	DET
ejpam-7020	127	5	system	system	NOUN
ejpam-7020	127	6	to	to	PART
ejpam-7020	127	7	oscillate	oscillate	VERB
ejpam-7020	127	8	is	be	AUX
ejpam-7020	127	9	a	a	DET
ejpam-7020	127	10	robust	robust	ADJ
ejpam-7020	127	11	feature	feature	NOUN
ejpam-7020	127	12	.	.	PUNCT
ejpam-7020	128	1	this	this	PRON
ejpam-7020	128	2	will	will	AUX
ejpam-7020	128	3	be	be	AUX
ejpam-7020	128	4	clearly	clearly	ADV
ejpam-7020	128	5	illustrated	illustrate	VERB
ejpam-7020	128	6	in	in	ADP
ejpam-7020	128	7	the	the	DET
ejpam-7020	128	8	phase	phase	NOUN
ejpam-7020	128	9	portraits	portrait	NOUN
ejpam-7020	128	10	presented	present	VERB
ejpam-7020	128	11	in	in	ADP
ejpam-7020	128	12	section	section	NOUN
ejpam-7020	128	13	5	5	NUM
ejpam-7020	128	14	.	.	PUNCT
ejpam-7020	128	15	to	to	PART
ejpam-7020	128	16	demonstrate	demonstrate	VERB
ejpam-7020	128	17	this	this	DET
ejpam-7020	128	18	effect	effect	NOUN
ejpam-7020	128	19	,	,	PUNCT
ejpam-7020	128	20	we	we	PRON
ejpam-7020	128	21	simulate	simulate	VERB
ejpam-7020	128	22	the	the	DET
ejpam-7020	128	23	system	system	NOUN
ejpam-7020	128	24	for	for	ADP
ejpam-7020	128	25	three	three	NUM
ejpam-7020	128	26	representative	representative	ADJ
ejpam-7020	128	27	values	value	NOUN
ejpam-7020	128	28	of	of	ADP
ejpam-7020	128	29	the	the	DET
ejpam-7020	128	30	predation	predation	NOUN
ejpam-7020	128	31	rate	rate	NOUN
ejpam-7020	128	32	,	,	PUNCT
ejpam-7020	128	33	b	b	PROPN
ejpam-7020	128	34	∈	∈	PROPN
ejpam-7020	128	35	{	{	PUNCT
ejpam-7020	128	36	0.2	0.2	NUM
ejpam-7020	128	37	,	,	PUNCT
ejpam-7020	128	38	0.5	0.5	NUM
ejpam-7020	128	39	,	,	PUNCT
ejpam-7020	128	40	0.8	0.8	NUM
ejpam-7020	128	41	}	}	PUNCT
ejpam-7020	128	42	,	,	PUNCT
ejpam-7020	128	43	while	while	SCONJ
ejpam-7020	128	44	keeping	keep	VERB
ejpam-7020	128	45	the	the	DET
ejpam-7020	128	46	other	other	ADJ
ejpam-7020	128	47	parameters	parameter	NOUN
ejpam-7020	128	48	fixed	fix	VERB
ejpam-7020	128	49	.	.	PUNCT
ejpam-7020	129	1	these	these	DET
ejpam-7020	129	2	simulations	simulation	NOUN
ejpam-7020	129	3	will	will	AUX
ejpam-7020	129	4	show	show	VERB
ejpam-7020	129	5	how	how	SCONJ
ejpam-7020	129	6	changing	changing	ADJ
ejpam-7020	129	7	b	b	NOUN
ejpam-7020	129	8	alters	alter	VERB
ejpam-7020	129	9	the	the	DET
ejpam-7020	129	10	shape	shape	NOUN
ejpam-7020	129	11	of	of	ADP
ejpam-7020	129	12	the	the	DET
ejpam-7020	129	13	orbital	orbital	ADJ
ejpam-7020	129	14	cycles	cycle	NOUN
ejpam-7020	129	15	but	but	CCONJ
ejpam-7020	129	16	does	do	AUX
ejpam-7020	129	17	not	not	PART
ejpam-7020	129	18	break	break	VERB
ejpam-7020	129	19	their	their	PRON
ejpam-7020	129	20	closed	closed	ADJ
ejpam-7020	129	21	-	-	PUNCT
ejpam-7020	129	22	loop	loop	NOUN
ejpam-7020	129	23	structure	structure	NOUN
ejpam-7020	129	24	.	.	PUNCT
ejpam-7020	130	1	4	4	X
ejpam-7020	130	2	.	.	X
ejpam-7020	130	3	comparative	comparative	ADJ
ejpam-7020	130	4	case	case	NOUN
ejpam-7020	130	5	study	study	NOUN
ejpam-7020	130	6	:	:	PUNCT
ejpam-7020	130	7	susceptible	susceptible	ADJ
ejpam-7020	130	8	-	-	PUNCT
ejpam-7020	130	9	infected	infect	VERB
ejpam-7020	130	10	-	-	PUNCT
ejpam-7020	130	11	recovered	recover	VERB
ejpam-7020	130	12	epidemic	epidemic	NOUN
ejpam-7020	130	13	model	model	NOUN
ejpam-7020	130	14	in	in	ADP
ejpam-7020	130	15	this	this	DET
ejpam-7020	130	16	section	section	NOUN
ejpam-7020	130	17	,	,	PUNCT
ejpam-7020	130	18	we	we	PRON
ejpam-7020	130	19	extend	extend	VERB
ejpam-7020	130	20	our	our	PRON
ejpam-7020	130	21	mathematical	mathematical	ADJ
ejpam-7020	130	22	framework	framework	NOUN
ejpam-7020	130	23	to	to	PART
ejpam-7020	130	24	analyze	analyze	VERB
ejpam-7020	130	25	the	the	DET
ejpam-7020	130	26	classical	classical	ADJ
ejpam-7020	130	27	susceptible	susceptible	ADJ
ejpam-7020	130	28	-	-	PUNCT
ejpam-7020	130	29	infected	infect	VERB
ejpam-7020	130	30	-	-	PUNCT
ejpam-7020	130	31	recovered	recover	VERB
ejpam-7020	130	32	(	(	PUNCT
ejpam-7020	130	33	sir	sir	NOUN
ejpam-7020	130	34	)	)	PUNCT
ejpam-7020	130	35	epidemic	epidemic	NOUN
ejpam-7020	130	36	model	model	NOUN
ejpam-7020	130	37	.	.	PUNCT
ejpam-7020	131	1	this	this	DET
ejpam-7020	131	2	model	model	NOUN
ejpam-7020	131	3	captures	capture	VERB
ejpam-7020	131	4	the	the	DET
ejpam-7020	131	5	spread	spread	NOUN
ejpam-7020	131	6	of	of	ADP
ejpam-7020	131	7	infectious	infectious	ADJ
ejpam-7020	131	8	diseases	disease	NOUN
ejpam-7020	131	9	within	within	ADP
ejpam-7020	131	10	a	a	DET
ejpam-7020	131	11	closed	closed	ADJ
ejpam-7020	131	12	population	population	NOUN
ejpam-7020	131	13	by	by	ADP
ejpam-7020	131	14	dividing	divide	VERB
ejpam-7020	131	15	the	the	DET
ejpam-7020	131	16	population	population	NOUN
ejpam-7020	131	17	into	into	ADP
ejpam-7020	131	18	three	three	NUM
ejpam-7020	131	19	compartments	compartment	NOUN
ejpam-7020	131	20	:	:	PUNCT
ejpam-7020	131	21	s(t	s(t	NUM
ejpam-7020	131	22	):	):	PUNCT
ejpam-7020	131	23	number	number	NOUN
ejpam-7020	131	24	of	of	ADP
ejpam-7020	131	25	susceptible	susceptible	ADJ
ejpam-7020	131	26	individuals	individual	NOUN
ejpam-7020	131	27	,	,	PUNCT
ejpam-7020	131	28	i(t	i(t	PROPN
ejpam-7020	131	29	):	):	PUNCT
ejpam-7020	131	30	number	number	NOUN
ejpam-7020	131	31	of	of	ADP
ejpam-7020	131	32	infected	infected	ADJ
ejpam-7020	131	33	individuals	individual	NOUN
ejpam-7020	131	34	,	,	PUNCT
ejpam-7020	131	35	and	and	CCONJ
ejpam-7020	131	36	r(t	r(t	NOUN
ejpam-7020	131	37	):	):	PUNCT
ejpam-7020	131	38	number	number	NOUN
ejpam-7020	131	39	of	of	ADP
ejpam-7020	131	40	recovered	recovered	ADJ
ejpam-7020	131	41	(	(	PUNCT
ejpam-7020	131	42	or	or	CCONJ
ejpam-7020	131	43	removed	remove	VERB
ejpam-7020	131	44	)	)	PUNCT
ejpam-7020	131	45	individuals	individual	NOUN
ejpam-7020	131	46	.	.	PUNCT
ejpam-7020	132	1	the	the	DET
ejpam-7020	132	2	dynamics	dynamic	NOUN
ejpam-7020	132	3	of	of	ADP
ejpam-7020	132	4	the	the	DET
ejpam-7020	132	5	model	model	NOUN
ejpam-7020	132	6	are	be	AUX
ejpam-7020	132	7	governed	govern	VERB
ejpam-7020	132	8	by	by	ADP
ejpam-7020	132	9	the	the	DET
ejpam-7020	132	10	following	follow	VERB
ejpam-7020	132	11	system	system	NOUN
ejpam-7020	132	12	of	of	ADP
ejpam-7020	132	13	differential	differential	ADJ
ejpam-7020	132	14	equations	equation	NOUN
ejpam-7020	132	15	:	:	PUNCT
ejpam-7020	132	16			NUM
ejpam-7020	132	17	ds	ds	ADJ
ejpam-7020	132	18	dt	dt	NOUN
ejpam-7020	132	19	=	=	SYM
ejpam-7020	132	20	−βsi	−βsi	NOUN
ejpam-7020	132	21	,	,	PUNCT
ejpam-7020	132	22	di	di	NOUN
ejpam-7020	132	23	dt	dt	NOUN
ejpam-7020	132	24	=	=	NOUN
ejpam-7020	132	25	βsi	βsi	NOUN
ejpam-7020	132	26	−	−	PROPN
ejpam-7020	132	27	γi	γi	NOUN
ejpam-7020	132	28	,	,	PUNCT
ejpam-7020	132	29	dr	dr	PROPN
ejpam-7020	132	30	dt	dt	PROPN
ejpam-7020	132	31	=	=	SYM
ejpam-7020	132	32	γi	γi	PROPN
ejpam-7020	132	33	,	,	PUNCT
ejpam-7020	132	34	where	where	SCONJ
ejpam-7020	132	35	β	β	X
ejpam-7020	132	36	>	>	X
ejpam-7020	132	37	0	0	NUM
ejpam-7020	132	38	is	be	AUX
ejpam-7020	132	39	the	the	DET
ejpam-7020	132	40	transmission	transmission	NOUN
ejpam-7020	132	41	rate	rate	NOUN
ejpam-7020	132	42	and	and	CCONJ
ejpam-7020	132	43	γ	γ	X
ejpam-7020	132	44	>	>	X
ejpam-7020	132	45	0	0	NUM
ejpam-7020	132	46	is	be	AUX
ejpam-7020	132	47	the	the	DET
ejpam-7020	132	48	recovery	recovery	NOUN
ejpam-7020	132	49	rate	rate	NOUN
ejpam-7020	132	50	.	.	PUNCT
ejpam-7020	133	1	we	we	PRON
ejpam-7020	133	2	will	will	AUX
ejpam-7020	133	3	identify	identify	VERB
ejpam-7020	133	4	the	the	DET
ejpam-7020	133	5	equilibrium	equilibrium	NOUN
ejpam-7020	133	6	points	point	NOUN
ejpam-7020	133	7	,	,	PUNCT
ejpam-7020	133	8	perform	perform	VERB
ejpam-7020	133	9	a	a	DET
ejpam-7020	133	10	linear	linear	ADJ
ejpam-7020	133	11	stability	stability	NOUN
ejpam-7020	133	12	analysis	analysis	NOUN
ejpam-7020	133	13	using	use	VERB
ejpam-7020	133	14	the	the	DET
ejpam-7020	133	15	jacobian	jacobian	ADJ
ejpam-7020	133	16	matrix	matrix	NOUN
ejpam-7020	133	17	,	,	PUNCT
ejpam-7020	133	18	and	and	CCONJ
ejpam-7020	133	19	illustrate	illustrate	VERB
ejpam-7020	133	20	the	the	DET
ejpam-7020	133	21	system	system	NOUN
ejpam-7020	133	22	behavior	behavior	NOUN
ejpam-7020	133	23	using	use	VERB
ejpam-7020	133	24	phase	phase	NOUN
ejpam-7020	133	25	portraits	portrait	NOUN
ejpam-7020	133	26	.	.	PUNCT
ejpam-7020	134	1	beyond	beyond	ADP
ejpam-7020	134	2	its	its	PRON
ejpam-7020	134	3	biological	biological	ADJ
ejpam-7020	134	4	relevance	relevance	NOUN
ejpam-7020	134	5	,	,	PUNCT
ejpam-7020	134	6	the	the	DET
ejpam-7020	134	7	sir	sir	NOUN
ejpam-7020	134	8	model	model	NOUN
ejpam-7020	134	9	serves	serve	VERB
ejpam-7020	134	10	as	as	ADP
ejpam-7020	134	11	an	an	DET
ejpam-7020	134	12	effective	effective	ADJ
ejpam-7020	134	13	pedagogical	pedagogical	ADJ
ejpam-7020	134	14	bridge	bridge	NOUN
ejpam-7020	134	15	between	between	ADP
ejpam-7020	134	16	biological	biological	ADJ
ejpam-7020	134	17	systems	system	NOUN
ejpam-7020	134	18	and	and	CCONJ
ejpam-7020	134	19	general	general	ADJ
ejpam-7020	134	20	dynamical	dynamical	ADJ
ejpam-7020	134	21	systems	system	NOUN
ejpam-7020	134	22	theory	theory	NOUN
ejpam-7020	134	23	.	.	PUNCT
ejpam-7020	135	1	by	by	ADP
ejpam-7020	135	2	comparing	compare	VERB
ejpam-7020	135	3	this	this	DET
ejpam-7020	135	4	model	model	NOUN
ejpam-7020	135	5	with	with	ADP
ejpam-7020	135	6	other	other	ADJ
ejpam-7020	135	7	biological	biological	ADJ
ejpam-7020	135	8	and	and	CCONJ
ejpam-7020	135	9	epidemiological	epidemiological	ADJ
ejpam-7020	135	10	frameworks	framework	NOUN
ejpam-7020	135	11	,	,	PUNCT
ejpam-7020	135	12	learners	learner	NOUN
ejpam-7020	135	13	can	can	AUX
ejpam-7020	135	14	better	well	ADV
ejpam-7020	135	15	understand	understand	VERB
ejpam-7020	135	16	how	how	SCONJ
ejpam-7020	135	17	concepts	concept	NOUN
ejpam-7020	135	18	such	such	ADJ
ejpam-7020	135	19	as	as	ADP
ejpam-7020	135	20	equilibrium	equilibrium	NOUN
ejpam-7020	135	21	,	,	PUNCT
ejpam-7020	135	22	stability	stability	NOUN
ejpam-7020	135	23	,	,	PUNCT
ejpam-7020	135	24	and	and	CCONJ
ejpam-7020	135	25	bifurcation	bifurcation	NOUN
ejpam-7020	135	26	transcend	transcend	VERB
ejpam-7020	135	27	disciplinary	disciplinary	ADJ
ejpam-7020	135	28	s.	s.	PROPN
ejpam-7020	135	29	saidat	saidat	PROPN
ejpam-7020	135	30	et	et	PROPN
ejpam-7020	135	31	al	al	PROPN
ejpam-7020	135	32	.	.	PUNCT
ejpam-7020	135	33	/	/	SYM
ejpam-7020	135	34	eur	eur	PROPN
ejpam-7020	135	35	.	.	PUNCT
ejpam-7020	136	1	j.	j.	PROPN
ejpam-7020	136	2	pure	pure	PROPN
ejpam-7020	136	3	appl	appl	PROPN
ejpam-7020	136	4	.	.	PROPN
ejpam-7020	136	5	math	math	PROPN
ejpam-7020	136	6	,	,	PUNCT
ejpam-7020	136	7	18	18	NUM
ejpam-7020	136	8	(	(	PUNCT
ejpam-7020	136	9	4	4	NUM
ejpam-7020	136	10	)	)	PUNCT
ejpam-7020	136	11	(	(	PUNCT
ejpam-7020	136	12	2025	2025	NUM
ejpam-7020	136	13	)	)	PUNCT
ejpam-7020	136	14	,	,	PUNCT
ejpam-7020	136	15	7020	7020	NUM
ejpam-7020	136	16	8	8	NUM
ejpam-7020	136	17	of	of	ADP
ejpam-7020	136	18	16	16	NUM
ejpam-7020	136	19	boundaries	boundary	NOUN
ejpam-7020	136	20	.	.	PUNCT
ejpam-7020	137	1	this	this	DET
ejpam-7020	137	2	comparison	comparison	NOUN
ejpam-7020	137	3	reinforces	reinforce	VERB
ejpam-7020	137	4	the	the	DET
ejpam-7020	137	5	universality	universality	NOUN
ejpam-7020	137	6	of	of	ADP
ejpam-7020	137	7	mathematical	mathematical	ADJ
ejpam-7020	137	8	tools	tool	NOUN
ejpam-7020	137	9	used	use	VERB
ejpam-7020	137	10	to	to	PART
ejpam-7020	137	11	describe	describe	VERB
ejpam-7020	137	12	population	population	NOUN
ejpam-7020	137	13	dynamics	dynamic	NOUN
ejpam-7020	137	14	,	,	PUNCT
ejpam-7020	137	15	reaction	reaction	NOUN
ejpam-7020	137	16	kinetics	kinetic	NOUN
ejpam-7020	137	17	,	,	PUNCT
ejpam-7020	137	18	and	and	CCONJ
ejpam-7020	137	19	even	even	ADV
ejpam-7020	137	20	ecological	ecological	ADJ
ejpam-7020	137	21	or	or	CCONJ
ejpam-7020	137	22	biochemical	biochemical	ADJ
ejpam-7020	137	23	interactions	interaction	NOUN
ejpam-7020	137	24	.	.	PUNCT
ejpam-7020	138	1	in	in	ADP
ejpam-7020	138	2	particular	particular	ADJ
ejpam-7020	138	3	,	,	PUNCT
ejpam-7020	138	4	analyzing	analyze	VERB
ejpam-7020	138	5	the	the	DET
ejpam-7020	138	6	stability	stability	NOUN
ejpam-7020	138	7	of	of	ADP
ejpam-7020	138	8	disease	disease	NOUN
ejpam-7020	138	9	-	-	PUNCT
ejpam-7020	138	10	free	free	ADJ
ejpam-7020	138	11	and	and	CCONJ
ejpam-7020	138	12	endemic	endemic	ADJ
ejpam-7020	138	13	equilibria	equilibrium	NOUN
ejpam-7020	138	14	provides	provide	VERB
ejpam-7020	138	15	a	a	DET
ejpam-7020	138	16	concrete	concrete	ADJ
ejpam-7020	138	17	,	,	PUNCT
ejpam-7020	138	18	intuitive	intuitive	ADJ
ejpam-7020	138	19	context	context	NOUN
ejpam-7020	138	20	through	through	ADP
ejpam-7020	138	21	which	which	PRON
ejpam-7020	138	22	students	student	NOUN
ejpam-7020	138	23	can	can	AUX
ejpam-7020	138	24	grasp	grasp	VERB
ejpam-7020	138	25	abstract	abstract	ADJ
ejpam-7020	138	26	notions	notion	NOUN
ejpam-7020	138	27	of	of	ADP
ejpam-7020	138	28	local	local	ADJ
ejpam-7020	138	29	and	and	CCONJ
ejpam-7020	138	30	global	global	ADJ
ejpam-7020	138	31	stability	stability	NOUN
ejpam-7020	138	32	,	,	PUNCT
ejpam-7020	138	33	eigenvalue	eigenvalue	NOUN
ejpam-7020	138	34	behavior	behavior	NOUN
ejpam-7020	138	35	,	,	PUNCT
ejpam-7020	138	36	and	and	CCONJ
ejpam-7020	138	37	nonlinear	nonlinear	ADJ
ejpam-7020	138	38	feedback	feedback	NOUN
ejpam-7020	138	39	mechanisms	mechanism	NOUN
ejpam-7020	138	40	.	.	PUNCT
ejpam-7020	139	1	thus	thus	ADV
ejpam-7020	139	2	,	,	PUNCT
ejpam-7020	139	3	the	the	DET
ejpam-7020	139	4	sir	sir	NOUN
ejpam-7020	139	5	model	model	NOUN
ejpam-7020	139	6	not	not	PART
ejpam-7020	139	7	only	only	ADV
ejpam-7020	139	8	exemplifies	exemplify	VERB
ejpam-7020	139	9	epidemiological	epidemiological	ADJ
ejpam-7020	139	10	reasoning	reasoning	NOUN
ejpam-7020	139	11	but	but	CCONJ
ejpam-7020	139	12	also	also	ADV
ejpam-7020	139	13	deepens	deepen	VERB
ejpam-7020	139	14	the	the	DET
ejpam-7020	139	15	conceptual	conceptual	ADJ
ejpam-7020	139	16	understanding	understanding	NOUN
ejpam-7020	139	17	of	of	ADP
ejpam-7020	139	18	dynamical	dynamical	ADJ
ejpam-7020	139	19	stability	stability	NOUN
ejpam-7020	139	20	in	in	ADP
ejpam-7020	139	21	life	life	NOUN
ejpam-7020	139	22	sciences	science	NOUN
ejpam-7020	139	23	and	and	CCONJ
ejpam-7020	139	24	applied	apply	VERB
ejpam-7020	139	25	mathematics	mathematic	NOUN
ejpam-7020	139	26	.	.	PUNCT
ejpam-7020	140	1	4.1	4.1	NUM
ejpam-7020	140	2	.	.	PUNCT
ejpam-7020	140	3	equilibrium	equilibrium	NOUN
ejpam-7020	140	4	points	point	NOUN
ejpam-7020	140	5	setting	set	VERB
ejpam-7020	140	6	ds	ds	ADJ
ejpam-7020	140	7	dt	dt	NOUN
ejpam-7020	140	8	=	=	SYM
ejpam-7020	140	9	0	0	NUM
ejpam-7020	140	10	and	and	CCONJ
ejpam-7020	140	11	di	di	ADJ
ejpam-7020	140	12	dt	dt	NOUN
ejpam-7020	140	13	=	=	SYM
ejpam-7020	140	14	0	0	NUM
ejpam-7020	140	15	,	,	PUNCT
ejpam-7020	140	16	we	we	PRON
ejpam-7020	140	17	find	find	VERB
ejpam-7020	140	18	two	two	NUM
ejpam-7020	140	19	biologically	biologically	ADV
ejpam-7020	140	20	relevant	relevant	ADJ
ejpam-7020	140	21	equilibria	equilibrium	NOUN
ejpam-7020	140	22	:	:	PUNCT
ejpam-7020	140	23	•	•	PUNCT
ejpam-7020	140	24	disease	disease	NOUN
ejpam-7020	140	25	-	-	PUNCT
ejpam-7020	140	26	free	free	ADJ
ejpam-7020	140	27	equilibrium	equilibrium	NOUN
ejpam-7020	140	28	(	(	PUNCT
ejpam-7020	140	29	dfe	dfe	PROPN
ejpam-7020	140	30	):	):	PUNCT
ejpam-7020	140	31	edfe	edfe	NOUN
ejpam-7020	140	32	=	=	SYM
ejpam-7020	140	33	(	(	PUNCT
ejpam-7020	140	34	s	s	PROPN
ejpam-7020	140	35	,	,	PUNCT
ejpam-7020	140	36	i	i	NOUN
ejpam-7020	140	37	)	)	PUNCT
ejpam-7020	140	38	=	=	PUNCT
ejpam-7020	140	39	(	(	PUNCT
ejpam-7020	140	40	n	n	CCONJ
ejpam-7020	140	41	,	,	PUNCT
ejpam-7020	140	42	0	0	NUM
ejpam-7020	140	43	)	)	PUNCT
ejpam-7020	140	44	,	,	PUNCT
ejpam-7020	140	45	which	which	PRON
ejpam-7020	140	46	corresponds	correspond	VERB
ejpam-7020	140	47	to	to	ADP
ejpam-7020	140	48	a	a	DET
ejpam-7020	140	49	state	state	NOUN
ejpam-7020	140	50	without	without	ADP
ejpam-7020	140	51	disease	disease	NOUN
ejpam-7020	140	52	in	in	ADP
ejpam-7020	140	53	the	the	DET
ejpam-7020	140	54	population	population	NOUN
ejpam-7020	140	55	.	.	PUNCT
ejpam-7020	141	1	•	•	NUM
ejpam-7020	141	2	endemic	endemic	ADJ
ejpam-7020	141	3	equilibrium	equilibrium	NOUN
ejpam-7020	141	4	(	(	PUNCT
ejpam-7020	141	5	ee	ee	PROPN
ejpam-7020	141	6	):	):	PUNCT
ejpam-7020	141	7	eee	eee	X
ejpam-7020	141	8	=	=	SYM
ejpam-7020	141	9	(	(	PUNCT
ejpam-7020	141	10	s∗	s∗	PROPN
ejpam-7020	141	11	,	,	PUNCT
ejpam-7020	141	12	i∗	i∗	NOUN
ejpam-7020	141	13	)	)	PUNCT
ejpam-7020	141	14	=	=	PUNCT
ejpam-7020	141	15	(	(	PUNCT
ejpam-7020	141	16	γ	γ	X
ejpam-7020	141	17	β	β	X
ejpam-7020	141	18	,	,	PUNCT
ejpam-7020	141	19	n	n	CCONJ
ejpam-7020	141	20	−	−	PROPN
ejpam-7020	141	21	γ	γ	X
ejpam-7020	141	22	β	β	PROPN
ejpam-7020	141	23	)	)	PUNCT
ejpam-7020	141	24	.	.	PUNCT
ejpam-7020	142	1	this	this	DET
ejpam-7020	142	2	equilibrium	equilibrium	NOUN
ejpam-7020	142	3	is	be	AUX
ejpam-7020	142	4	only	only	ADV
ejpam-7020	142	5	physically	physically	ADV
ejpam-7020	142	6	meaningful	meaningful	ADJ
ejpam-7020	142	7	if	if	SCONJ
ejpam-7020	142	8	s∗	s∗	PROPN
ejpam-7020	142	9	<	<	X
ejpam-7020	142	10	n	n	X
ejpam-7020	142	11	,	,	PUNCT
ejpam-7020	142	12	which	which	PRON
ejpam-7020	142	13	requires	require	VERB
ejpam-7020	142	14	γ	γ	X
ejpam-7020	142	15	β	β	X
ejpam-7020	142	16	<	<	X
ejpam-7020	142	17	n	n	ADV
ejpam-7020	142	18	or	or	CCONJ
ejpam-7020	142	19	equivalently	equivalently	ADV
ejpam-7020	142	20	βn	βn	VERB
ejpam-7020	142	21	γ	γ	X
ejpam-7020	142	22	>	>	X
ejpam-7020	142	23	1	1	NUM
ejpam-7020	142	24	.	.	PUNCT
ejpam-7020	143	1	this	this	PRON
ejpam-7020	143	2	introduces	introduce	VERB
ejpam-7020	143	3	the	the	DET
ejpam-7020	143	4	basic	basic	ADJ
ejpam-7020	143	5	reproduction	reproduction	NOUN
ejpam-7020	143	6	number	number	NOUN
ejpam-7020	143	7	r0	r0	NOUN
ejpam-7020	143	8	=	=	PUNCT
ejpam-7020	143	9	βn	βn	PROPN
ejpam-7020	143	10	γ	γ	X
ejpam-7020	143	11	,	,	PUNCT
ejpam-7020	143	12	which	which	PRON
ejpam-7020	143	13	is	be	AUX
ejpam-7020	143	14	the	the	DET
ejpam-7020	143	15	key	key	ADJ
ejpam-7020	143	16	threshold	threshold	NOUN
ejpam-7020	143	17	parameter	parameter	NOUN
ejpam-7020	143	18	.	.	PUNCT
ejpam-7020	144	1	the	the	DET
ejpam-7020	144	2	endemic	endemic	ADJ
ejpam-7020	144	3	equilibrium	equilibrium	NOUN
ejpam-7020	144	4	exists	exist	VERB
ejpam-7020	144	5	only	only	ADV
ejpam-7020	144	6	if	if	SCONJ
ejpam-7020	144	7	r0	r0	NOUN
ejpam-7020	144	8	>	>	X
ejpam-7020	144	9	1	1	NUM
ejpam-7020	144	10	.	.	X
ejpam-7020	144	11	4.2	4.2	NUM
ejpam-7020	144	12	.	.	PUNCT
ejpam-7020	145	1	stability	stability	NOUN
ejpam-7020	145	2	analysis	analysis	NOUN
ejpam-7020	145	3	the	the	DET
ejpam-7020	145	4	jacobian	jacobian	ADJ
ejpam-7020	145	5	matrix	matrix	NOUN
ejpam-7020	145	6	for	for	ADP
ejpam-7020	145	7	the	the	DET
ejpam-7020	145	8	sir	sir	NOUN
ejpam-7020	145	9	system	system	NOUN
ejpam-7020	145	10	is	be	AUX
ejpam-7020	145	11	:	:	PUNCT
ejpam-7020	145	12	j(s	j(s	PROPN
ejpam-7020	145	13	,	,	PUNCT
ejpam-7020	145	14	i	i	NOUN
ejpam-7020	145	15	)	)	PUNCT
ejpam-7020	146	1	=	=	PUNCT
ejpam-7020	146	2	[	[	PUNCT
ejpam-7020	146	3	−βi	−βi	NOUN
ejpam-7020	146	4	−βs	−βs	INTJ
ejpam-7020	146	5	βi	βi	INTJ
ejpam-7020	146	6	βs	βs	NOUN
ejpam-7020	146	7	−	−	PROPN
ejpam-7020	146	8	γ	γ	X
ejpam-7020	146	9	]	]	PUNCT
ejpam-7020	146	10	.	.	PUNCT
ejpam-7020	147	1	stability	stability	NOUN
ejpam-7020	147	2	of	of	ADP
ejpam-7020	147	3	the	the	DET
ejpam-7020	147	4	disease	disease	NOUN
ejpam-7020	147	5	-	-	PUNCT
ejpam-7020	147	6	free	free	ADJ
ejpam-7020	147	7	equilibrium	equilibrium	NOUN
ejpam-7020	147	8	(	(	PUNCT
ejpam-7020	147	9	dfe	dfe	PROPN
ejpam-7020	147	10	):	):	PUNCT
ejpam-7020	147	11	evaluating	evaluate	VERB
ejpam-7020	147	12	the	the	DET
ejpam-7020	147	13	jacobian	jacobian	NOUN
ejpam-7020	147	14	at	at	ADP
ejpam-7020	147	15	edfe	edfe	NOUN
ejpam-7020	147	16	=	=	SYM
ejpam-7020	147	17	(	(	PUNCT
ejpam-7020	147	18	n	n	CCONJ
ejpam-7020	147	19	,	,	PUNCT
ejpam-7020	147	20	0	0	NUM
ejpam-7020	147	21	)	)	PUNCT
ejpam-7020	147	22	gives	give	VERB
ejpam-7020	147	23	:	:	PUNCT
ejpam-7020	147	24	j(n	j(n	PROPN
ejpam-7020	147	25	,	,	PUNCT
ejpam-7020	147	26	0	0	NUM
ejpam-7020	147	27	)	)	PUNCT
ejpam-7020	148	1	=	=	SYM
ejpam-7020	148	2	0	0	PROPN
ejpam-7020	148	3	−βn	−βn	PROPN
ejpam-7020	148	4	0	0	NUM
ejpam-7020	148	5	βn	βn	PROPN
ejpam-7020	148	6	−	−	PROPN
ejpam-7020	148	7	γ	γ	NOUN
ejpam-7020	148	8			NOUN
ejpam-7020	148	9	.	.	PUNCT
ejpam-7020	149	1	s.	s.	PROPN
ejpam-7020	149	2	saidat	saidat	PROPN
ejpam-7020	149	3	et	et	PROPN
ejpam-7020	149	4	al	al	PROPN
ejpam-7020	149	5	.	.	PUNCT
ejpam-7020	149	6	/	/	SYM
ejpam-7020	149	7	eur	eur	PROPN
ejpam-7020	149	8	.	.	PUNCT
ejpam-7020	150	1	j.	j.	PROPN
ejpam-7020	150	2	pure	pure	PROPN
ejpam-7020	150	3	appl	appl	PROPN
ejpam-7020	150	4	.	.	PROPN
ejpam-7020	150	5	math	math	PROPN
ejpam-7020	150	6	,	,	PUNCT
ejpam-7020	150	7	18	18	NUM
ejpam-7020	150	8	(	(	PUNCT
ejpam-7020	150	9	4	4	NUM
ejpam-7020	150	10	)	)	PUNCT
ejpam-7020	150	11	(	(	PUNCT
ejpam-7020	150	12	2025	2025	NUM
ejpam-7020	150	13	)	)	PUNCT
ejpam-7020	150	14	,	,	PUNCT
ejpam-7020	150	15	7020	7020	NUM
ejpam-7020	150	16	9	9	NUM
ejpam-7020	150	17	of	of	ADP
ejpam-7020	150	18	16	16	NUM
ejpam-7020	150	19	the	the	DET
ejpam-7020	150	20	eigenvalues	eigenvalue	NOUN
ejpam-7020	150	21	are	be	AUX
ejpam-7020	150	22	the	the	DET
ejpam-7020	150	23	diagonal	diagonal	ADJ
ejpam-7020	150	24	entries	entry	NOUN
ejpam-7020	150	25	:	:	PUNCT
ejpam-7020	150	26	λ1	λ1	PROPN
ejpam-7020	150	27	=	=	SYM
ejpam-7020	150	28	0	0	NUM
ejpam-7020	150	29	,	,	PUNCT
ejpam-7020	150	30	λ2	λ2	NOUN
ejpam-7020	150	31	=	=	SYM
ejpam-7020	150	32	βn	βn	NOUN
ejpam-7020	150	33	−	−	PROPN
ejpam-7020	150	34	γ	γ	X
ejpam-7020	150	35	=	=	PUNCT
ejpam-7020	150	36	γ(r0	γ(r0	NOUN
ejpam-7020	150	37	−	−	PROPN
ejpam-7020	150	38	1	1	NUM
ejpam-7020	150	39	)	)	PUNCT
ejpam-7020	150	40	.	.	PUNCT
ejpam-7020	151	1	the	the	DET
ejpam-7020	151	2	stability	stability	NOUN
ejpam-7020	151	3	is	be	AUX
ejpam-7020	151	4	determined	determine	VERB
ejpam-7020	151	5	by	by	ADP
ejpam-7020	151	6	λ2	λ2	NOUN
ejpam-7020	151	7	:	:	PUNCT
ejpam-7020	151	8	•	•	ADP
ejpam-7020	151	9	if	if	SCONJ
ejpam-7020	151	10	r0	r0	NOUN
ejpam-7020	151	11	<	<	X
ejpam-7020	151	12	1	1	NUM
ejpam-7020	151	13	,	,	PUNCT
ejpam-7020	151	14	then	then	ADV
ejpam-7020	151	15	λ2	λ2	NOUN
ejpam-7020	151	16	<	<	X
ejpam-7020	151	17	0	0	PUNCT
ejpam-7020	152	1	and	and	CCONJ
ejpam-7020	152	2	the	the	DET
ejpam-7020	152	3	dfe	dfe	PROPN
ejpam-7020	152	4	is	be	AUX
ejpam-7020	152	5	stable	stable	ADJ
ejpam-7020	152	6	;	;	PUNCT
ejpam-7020	152	7	the	the	DET
ejpam-7020	152	8	disease	disease	NOUN
ejpam-7020	152	9	dies	die	VERB
ejpam-7020	152	10	.	.	PUNCT
ejpam-7020	153	1	•	•	INTJ
ejpam-7020	153	2	if	if	SCONJ
ejpam-7020	153	3	r0	r0	NOUN
ejpam-7020	153	4	>	>	X
ejpam-7020	153	5	1	1	NUM
ejpam-7020	153	6	,	,	PUNCT
ejpam-7020	153	7	then	then	ADV
ejpam-7020	153	8	λ2	λ2	NOUN
ejpam-7020	153	9	>	>	X
ejpam-7020	153	10	0	0	PUNCT
ejpam-7020	154	1	and	and	CCONJ
ejpam-7020	154	2	the	the	DET
ejpam-7020	154	3	dfe	dfe	PROPN
ejpam-7020	154	4	is	be	AUX
ejpam-7020	154	5	unstable	unstable	ADJ
ejpam-7020	154	6	;	;	PUNCT
ejpam-7020	154	7	an	an	DET
ejpam-7020	154	8	outbreak	outbreak	NOUN
ejpam-7020	154	9	can	can	AUX
ejpam-7020	154	10	occur	occur	VERB
ejpam-7020	154	11	.	.	PUNCT
ejpam-7020	155	1	stability	stability	NOUN
ejpam-7020	155	2	of	of	ADP
ejpam-7020	155	3	the	the	DET
ejpam-7020	155	4	endistic	endistic	ADJ
ejpam-7020	155	5	equilibrium	equilibrium	NOUN
ejpam-7020	155	6	(	(	PUNCT
ejpam-7020	155	7	ee	ee	PROPN
ejpam-7020	155	8	,	,	PUNCT
ejpam-7020	155	9	r0	r0	NOUN
ejpam-7020	155	10	>	>	X
ejpam-7020	155	11	1	1	NUM
ejpam-7020	155	12	):	):	PUNCT
ejpam-7020	155	13	evaluating	evaluate	VERB
ejpam-7020	155	14	the	the	DET
ejpam-7020	155	15	jacobian	jacobian	NOUN
ejpam-7020	155	16	at	at	ADP
ejpam-7020	155	17	eee	eee	NOUN
ejpam-7020	155	18	=	=	SYM
ejpam-7020	155	19	(	(	PUNCT
ejpam-7020	155	20	γ	γ	X
ejpam-7020	155	21	β	β	X
ejpam-7020	155	22	,	,	PUNCT
ejpam-7020	155	23	n	n	CCONJ
ejpam-7020	155	24	−	−	PROPN
ejpam-7020	155	25	γ	γ	X
ejpam-7020	155	26	β	β	NOUN
ejpam-7020	155	27	)	)	PUNCT
ejpam-7020	155	28	gives	give	VERB
ejpam-7020	155	29	:	:	PUNCT
ejpam-7020	155	30	j(eee	j(eee	NOUN
ejpam-7020	155	31	)	)	PUNCT
ejpam-7020	156	1	=	=	SYM
ejpam-7020	156	2			NOUN
ejpam-7020	156	3	−β	−β	NOUN
ejpam-7020	156	4	(	(	PUNCT
ejpam-7020	156	5	n	n	ADV
ejpam-7020	156	6	−	−	PROPN
ejpam-7020	156	7	γ	γ	X
ejpam-7020	156	8	β	β	NOUN
ejpam-7020	156	9	)	)	PUNCT
ejpam-7020	156	10	−γ	−γ	ADP
ejpam-7020	156	11	β	β	X
ejpam-7020	156	12	(	(	PUNCT
ejpam-7020	156	13	n	n	CCONJ
ejpam-7020	156	14	−	−	PROPN
ejpam-7020	156	15	γ	γ	X
ejpam-7020	156	16	β	β	X
ejpam-7020	156	17	)	)	PUNCT
ejpam-7020	156	18	0	0	NUM
ejpam-7020	157	1			NOUN
ejpam-7020	157	2	.	.	PUNCT
ejpam-7020	158	1	the	the	DET
ejpam-7020	158	2	trace	trace	NOUN
ejpam-7020	158	3	and	and	CCONJ
ejpam-7020	158	4	determinant	determinant	ADJ
ejpam-7020	158	5	are	be	AUX
ejpam-7020	158	6	:	:	PUNCT
ejpam-7020	158	7	tr(j	tr(j	X
ejpam-7020	158	8	)	)	PUNCT
ejpam-7020	159	1	=	=	SYM
ejpam-7020	159	2	−β	−β	NOUN
ejpam-7020	159	3	(	(	PUNCT
ejpam-7020	159	4	n	n	CCONJ
ejpam-7020	159	5	−	−	PROPN
ejpam-7020	159	6	γ	γ	X
ejpam-7020	159	7	β	β	X
ejpam-7020	159	8	)	)	PUNCT
ejpam-7020	159	9	=	=	PUNCT
ejpam-7020	160	1	−βi∗	−βi∗	X
ejpam-7020	160	2	<	<	X
ejpam-7020	160	3	0	0	NUM
ejpam-7020	160	4	,	,	PUNCT
ejpam-7020	160	5	det(j	det(j	PROPN
ejpam-7020	160	6	)	)	PUNCT
ejpam-7020	160	7	=	=	PUNCT
ejpam-7020	160	8	γβi∗	γβi∗	NOUN
ejpam-7020	160	9	>	>	X
ejpam-7020	160	10	0	0	X
ejpam-7020	160	11	.	.	PUNCT
ejpam-7020	160	12	since	since	SCONJ
ejpam-7020	160	13	tr(j	tr(j	NOUN
ejpam-7020	160	14	)	)	PUNCT
ejpam-7020	160	15	<	<	X
ejpam-7020	160	16	0	0	PUNCT
ejpam-7020	160	17	and	and	CCONJ
ejpam-7020	160	18	det(j	det(j	PROPN
ejpam-7020	160	19	)	)	PUNCT
ejpam-7020	160	20	>	>	X
ejpam-7020	160	21	0	0	NUM
ejpam-7020	160	22	,	,	PUNCT
ejpam-7020	160	23	both	both	PRON
ejpam-7020	160	24	eigenvalues	eigenvalue	VERB
ejpam-7020	160	25	have	have	VERB
ejpam-7020	160	26	negative	negative	ADJ
ejpam-7020	160	27	real	real	ADJ
ejpam-7020	160	28	parts	part	NOUN
ejpam-7020	160	29	.	.	PUNCT
ejpam-7020	161	1	therefore	therefore	ADV
ejpam-7020	161	2	,	,	PUNCT
ejpam-7020	161	3	the	the	DET
ejpam-7020	161	4	endemic	endemic	ADJ
ejpam-7020	161	5	equilibrium	equilibrium	NOUN
ejpam-7020	161	6	is	be	AUX
ejpam-7020	161	7	locally	locally	ADV
ejpam-7020	161	8	asymptotically	asymptotically	ADV
ejpam-7020	161	9	stable	stable	ADJ
ejpam-7020	161	10	whenever	whenever	SCONJ
ejpam-7020	161	11	it	it	PRON
ejpam-7020	161	12	exists	exist	VERB
ejpam-7020	161	13	.	.	PUNCT
ejpam-7020	162	1	this	this	PRON
ejpam-7020	162	2	means	mean	VERB
ejpam-7020	162	3	that	that	SCONJ
ejpam-7020	162	4	if	if	SCONJ
ejpam-7020	162	5	a	a	DET
ejpam-7020	162	6	disease	disease	NOUN
ejpam-7020	162	7	becomes	becomes	AUX
ejpam-7020	162	8	established	establish	VERB
ejpam-7020	162	9	(	(	PUNCT
ejpam-7020	162	10	r0	r0	NOUN
ejpam-7020	162	11	>	>	X
ejpam-7020	162	12	1	1	NUM
ejpam-7020	162	13	)	)	PUNCT
ejpam-7020	162	14	,	,	PUNCT
ejpam-7020	162	15	the	the	DET
ejpam-7020	162	16	system	system	NOUN
ejpam-7020	162	17	will	will	AUX
ejpam-7020	162	18	converge	converge	VERB
ejpam-7020	162	19	to	to	ADP
ejpam-7020	162	20	a	a	DET
ejpam-7020	162	21	steady	steady	ADJ
ejpam-7020	162	22	state	state	NOUN
ejpam-7020	162	23	where	where	SCONJ
ejpam-7020	162	24	the	the	DET
ejpam-7020	162	25	disease	disease	NOUN
ejpam-7020	162	26	persists	persist	VERB
ejpam-7020	162	27	in	in	ADP
ejpam-7020	162	28	the	the	DET
ejpam-7020	162	29	population	population	NOUN
ejpam-7020	162	30	.	.	PUNCT
ejpam-7020	163	1	5	5	X
ejpam-7020	163	2	.	.	X
ejpam-7020	163	3	results	result	NOUN
ejpam-7020	163	4	and	and	CCONJ
ejpam-7020	163	5	discussion	discussion	NOUN
ejpam-7020	163	6	:	:	PUNCT
ejpam-7020	163	7	a	a	DET
ejpam-7020	163	8	visual	visual	ADJ
ejpam-7020	163	9	comparison	comparison	NOUN
ejpam-7020	163	10	in	in	ADP
ejpam-7020	163	11	this	this	DET
ejpam-7020	163	12	section	section	NOUN
ejpam-7020	163	13	,	,	PUNCT
ejpam-7020	163	14	we	we	PRON
ejpam-7020	163	15	will	will	AUX
ejpam-7020	163	16	demonstrate	demonstrate	VERB
ejpam-7020	163	17	how	how	SCONJ
ejpam-7020	163	18	the	the	DET
ejpam-7020	163	19	analytical	analytical	ADJ
ejpam-7020	163	20	predication	predication	NOUN
ejpam-7020	163	21	of	of	ADP
ejpam-7020	163	22	our	our	PRON
ejpam-7020	163	23	systems	system	NOUN
ejpam-7020	163	24	should	should	AUX
ejpam-7020	163	25	behave	behave	VERB
ejpam-7020	163	26	,	,	PUNCT
ejpam-7020	163	27	and	and	CCONJ
ejpam-7020	163	28	show	show	VERB
ejpam-7020	163	29	how	how	SCONJ
ejpam-7020	163	30	this	this	DET
ejpam-7020	163	31	behavior	behavior	NOUN
ejpam-7020	163	32	looks	look	VERB
ejpam-7020	163	33	like	like	ADP
ejpam-7020	163	34	,	,	PUNCT
ejpam-7020	163	35	thus	thus	ADV
ejpam-7020	163	36	,	,	PUNCT
ejpam-7020	163	37	we	we	PRON
ejpam-7020	163	38	will	will	AUX
ejpam-7020	163	39	bring	bring	VERB
ejpam-7020	163	40	the	the	DET
ejpam-7020	163	41	theory	theory	NOUN
ejpam-7020	163	42	to	to	ADP
ejpam-7020	163	43	life	life	NOUN
ejpam-7020	163	44	by	by	ADP
ejpam-7020	163	45	generating	generate	VERB
ejpam-7020	163	46	phase	phase	NOUN
ejpam-7020	163	47	portraits	portrait	NOUN
ejpam-7020	163	48	for	for	ADP
ejpam-7020	163	49	both	both	PRON
ejpam-7020	163	50	of	of	ADP
ejpam-7020	163	51	our	our	PRON
ejpam-7020	163	52	models	model	NOUN
ejpam-7020	163	53	.	.	PUNCT
ejpam-7020	164	1	we	we	PRON
ejpam-7020	164	2	will	will	AUX
ejpam-7020	164	3	first	first	ADV
ejpam-7020	164	4	visualize	visualize	VERB
ejpam-7020	164	5	each	each	DET
ejpam-7020	164	6	system	system	NOUN
ejpam-7020	164	7	on	on	ADP
ejpam-7020	164	8	its	its	PRON
ejpam-7020	164	9	own	own	ADJ
ejpam-7020	164	10	to	to	PART
ejpam-7020	164	11	confirm	confirm	VERB
ejpam-7020	164	12	our	our	PRON
ejpam-7020	164	13	findings	finding	NOUN
ejpam-7020	164	14	,	,	PUNCT
ejpam-7020	164	15	and	and	CCONJ
ejpam-7020	164	16	then	then	ADV
ejpam-7020	164	17	place	place	VERB
ejpam-7020	164	18	them	they	PRON
ejpam-7020	164	19	side	side	NOUN
ejpam-7020	164	20	by	by	ADP
ejpam-7020	164	21	side	side	NOUN
ejpam-7020	164	22	to	to	PART
ejpam-7020	164	23	draw	draw	VERB
ejpam-7020	164	24	out	out	ADP
ejpam-7020	164	25	the	the	DET
ejpam-7020	164	26	crucial	crucial	ADJ
ejpam-7020	164	27	insights	insight	NOUN
ejpam-7020	164	28	that	that	SCONJ
ejpam-7020	164	29	only	only	ADV
ejpam-7020	164	30	a	a	DET
ejpam-7020	164	31	direct	direct	ADJ
ejpam-7020	164	32	comparison	comparison	NOUN
ejpam-7020	164	33	can	can	AUX
ejpam-7020	164	34	reveal	reveal	VERB
ejpam-7020	164	35	.	.	PUNCT
ejpam-7020	165	1	5.1	5.1	NUM
ejpam-7020	165	2	.	.	PUNCT
ejpam-7020	166	1	lotka	lotka	PROPN
ejpam-7020	166	2	-	-	PUNCT
ejpam-7020	166	3	volterra	volterra	PROPN
ejpam-7020	166	4	dynamics	dynamic	NOUN
ejpam-7020	166	5	:	:	PUNCT
ejpam-7020	167	1	persistent	persistent	ADJ
ejpam-7020	167	2	oscillations	oscillation	NOUN
ejpam-7020	167	3	the	the	DET
ejpam-7020	167	4	phase	phase	NOUN
ejpam-7020	167	5	portrait	portrait	NOUN
ejpam-7020	167	6	for	for	ADP
ejpam-7020	167	7	the	the	DET
ejpam-7020	167	8	lotka	lotka	PROPN
ejpam-7020	167	9	–	–	PUNCT
ejpam-7020	167	10	volterra	volterra	PROPN
ejpam-7020	167	11	model	model	NOUN
ejpam-7020	167	12	visually	visually	ADV
ejpam-7020	167	13	confirms	confirm	VERB
ejpam-7020	167	14	the	the	DET
ejpam-7020	167	15	analytical	analytical	ADJ
ejpam-7020	167	16	findings	finding	NOUN
ejpam-7020	167	17	.	.	PUNCT
ejpam-7020	168	1	the	the	DET
ejpam-7020	168	2	equilibrium	equilibrium	NOUN
ejpam-7020	168	3	at	at	ADP
ejpam-7020	168	4	the	the	DET
ejpam-7020	168	5	origin	origin	NOUN
ejpam-7020	168	6	(	(	PUNCT
ejpam-7020	168	7	0	0	NUM
ejpam-7020	168	8	,	,	PUNCT
ejpam-7020	168	9	0	0	NUM
ejpam-7020	168	10	)	)	PUNCT
ejpam-7020	168	11	is	be	AUX
ejpam-7020	168	12	a	a	DET
ejpam-7020	168	13	saddle	saddle	NOUN
ejpam-7020	168	14	point	point	NOUN
ejpam-7020	168	15	,	,	PUNCT
ejpam-7020	168	16	while	while	SCONJ
ejpam-7020	168	17	the	the	DET
ejpam-7020	168	18	interior	interior	ADJ
ejpam-7020	168	19	equilibrium	equilibrium	NOUN
ejpam-7020	168	20	(	(	PUNCT
ejpam-7020	168	21	c	c	NOUN
ejpam-7020	168	22	d	d	PROPN
ejpam-7020	168	23	,	,	PUNCT
ejpam-7020	168	24	a	a	DET
ejpam-7020	168	25	b	b	NOUN
ejpam-7020	168	26	)	)	PUNCT
ejpam-7020	168	27	is	be	AUX
ejpam-7020	168	28	a	a	DET
ejpam-7020	168	29	center	center	NOUN
ejpam-7020	168	30	,	,	PUNCT
ejpam-7020	168	31	characterized	characterize	VERB
ejpam-7020	168	32	by	by	ADP
ejpam-7020	168	33	a	a	DET
ejpam-7020	168	34	family	family	NOUN
ejpam-7020	168	35	of	of	ADP
ejpam-7020	168	36	closed	close	VERB
ejpam-7020	168	37	periodic	periodic	ADJ
ejpam-7020	168	38	orbits	orbit	NOUN
ejpam-7020	168	39	.	.	PUNCT
ejpam-7020	169	1	this	this	DET
ejpam-7020	169	2	neutrally	neutrally	ADV
ejpam-7020	169	3	stable	stable	ADJ
ejpam-7020	169	4	structure	structure	NOUN
ejpam-7020	169	5	reflects	reflect	VERB
ejpam-7020	169	6	the	the	DET
ejpam-7020	169	7	endless	endless	ADJ
ejpam-7020	169	8	cycle	cycle	NOUN
ejpam-7020	169	9	of	of	ADP
ejpam-7020	169	10	predator	predator	NOUN
ejpam-7020	169	11	-	-	PUNCT
ejpam-7020	169	12	prey	prey	NOUN
ejpam-7020	169	13	populations	population	NOUN
ejpam-7020	169	14	in	in	ADP
ejpam-7020	169	15	this	this	DET
ejpam-7020	169	16	idealized	idealized	ADJ
ejpam-7020	169	17	model	model	NOUN
ejpam-7020	169	18	,	,	PUNCT
ejpam-7020	169	19	as	as	SCONJ
ejpam-7020	169	20	depicted	depict	VERB
ejpam-7020	169	21	in	in	ADP
ejpam-7020	169	22	figure	figure	NOUN
ejpam-7020	169	23	1	1	NUM
ejpam-7020	169	24	.	.	PUNCT
ejpam-7020	170	1	s.	s.	PROPN
ejpam-7020	170	2	saidat	saidat	PROPN
ejpam-7020	170	3	et	et	PROPN
ejpam-7020	170	4	al	al	PROPN
ejpam-7020	170	5	.	.	PUNCT
ejpam-7020	170	6	/	/	SYM
ejpam-7020	170	7	eur	eur	PROPN
ejpam-7020	170	8	.	.	PUNCT
ejpam-7020	171	1	j.	j.	PROPN
ejpam-7020	171	2	pure	pure	PROPN
ejpam-7020	171	3	appl	appl	PROPN
ejpam-7020	171	4	.	.	PROPN
ejpam-7020	171	5	math	math	PROPN
ejpam-7020	171	6	,	,	PUNCT
ejpam-7020	171	7	18	18	NUM
ejpam-7020	171	8	(	(	PUNCT
ejpam-7020	171	9	4	4	NUM
ejpam-7020	171	10	)	)	PUNCT
ejpam-7020	171	11	(	(	PUNCT
ejpam-7020	171	12	2025	2025	NUM
ejpam-7020	171	13	)	)	PUNCT
ejpam-7020	171	14	,	,	PUNCT
ejpam-7020	171	15	7020	7020	NUM
ejpam-7020	171	16	10	10	NUM
ejpam-7020	171	17	of	of	ADP
ejpam-7020	171	18	16	16	NUM
ejpam-7020	171	19	figure	figure	NOUN
ejpam-7020	171	20	1	1	NUM
ejpam-7020	171	21	:	:	PUNCT
ejpam-7020	171	22	phase	phase	NOUN
ejpam-7020	171	23	portraits	portrait	NOUN
ejpam-7020	171	24	of	of	ADP
ejpam-7020	171	25	the	the	DET
ejpam-7020	171	26	lotka	lotka	PROPN
ejpam-7020	171	27	-	-	PUNCT
ejpam-7020	171	28	volterra	volterra	PROPN
ejpam-7020	171	29	predator	predator	NOUN
ejpam-7020	171	30	-	-	PUNCT
ejpam-7020	171	31	prey	prey	NOUN
ejpam-7020	171	32	system	system	NOUN
ejpam-7020	171	33	to	to	PART
ejpam-7020	171	34	further	far	ADV
ejpam-7020	171	35	investigate	investigate	VERB
ejpam-7020	171	36	the	the	DET
ejpam-7020	171	37	behavior	behavior	NOUN
ejpam-7020	171	38	of	of	ADP
ejpam-7020	171	39	the	the	DET
ejpam-7020	171	40	system	system	NOUN
ejpam-7020	171	41	,	,	PUNCT
ejpam-7020	171	42	we	we	PRON
ejpam-7020	171	43	examined	examine	VERB
ejpam-7020	171	44	the	the	DET
ejpam-7020	171	45	sensitivity	sensitivity	NOUN
ejpam-7020	171	46	of	of	ADP
ejpam-7020	171	47	the	the	DET
ejpam-7020	171	48	lotka	lotka	PROPN
ejpam-7020	171	49	–	–	PUNCT
ejpam-7020	171	50	volterra	volterra	NOUN
ejpam-7020	171	51	model	model	NOUN
ejpam-7020	171	52	to	to	ADP
ejpam-7020	171	53	variations	variation	NOUN
ejpam-7020	171	54	in	in	ADP
ejpam-7020	171	55	the	the	DET
ejpam-7020	171	56	interaction	interaction	NOUN
ejpam-7020	171	57	rate	rate	NOUN
ejpam-7020	171	58	parameter	parameter	PROPN
ejpam-7020	171	59	b.	b.	PROPN
ejpam-7020	172	1	this	this	DET
ejpam-7020	172	2	parameter	parameter	NOUN
ejpam-7020	172	3	directly	directly	ADV
ejpam-7020	172	4	influences	influence	VERB
ejpam-7020	172	5	the	the	DET
ejpam-7020	172	6	predator	predator	NOUN
ejpam-7020	172	7	’s	’s	PART
ejpam-7020	172	8	efficiency	efficiency	NOUN
ejpam-7020	172	9	in	in	ADP
ejpam-7020	172	10	capturing	capture	VERB
ejpam-7020	172	11	prey	prey	NOUN
ejpam-7020	172	12	.	.	PUNCT
ejpam-7020	173	1	we	we	PRON
ejpam-7020	173	2	considered	consider	VERB
ejpam-7020	173	3	three	three	NUM
ejpam-7020	173	4	representative	representative	ADJ
ejpam-7020	173	5	values	value	NOUN
ejpam-7020	173	6	:	:	PUNCT
ejpam-7020	173	7	b	b	X
ejpam-7020	173	8	=	=	SYM
ejpam-7020	173	9	0.2	0.2	NUM
ejpam-7020	173	10	,	,	PUNCT
ejpam-7020	173	11	0.5	0.5	NUM
ejpam-7020	173	12	,	,	PUNCT
ejpam-7020	173	13	and	and	CCONJ
ejpam-7020	173	14	0.8	0.8	NUM
ejpam-7020	173	15	,	,	PUNCT
ejpam-7020	173	16	while	while	SCONJ
ejpam-7020	173	17	keeping	keep	VERB
ejpam-7020	173	18	a	a	PRON
ejpam-7020	173	19	=	=	SYM
ejpam-7020	173	20	1	1	NUM
ejpam-7020	173	21	,	,	PUNCT
ejpam-7020	173	22	c	c	NOUN
ejpam-7020	173	23	=	=	SYM
ejpam-7020	173	24	1.5	1.5	NUM
ejpam-7020	173	25	,	,	PUNCT
ejpam-7020	173	26	and	and	CCONJ
ejpam-7020	173	27	d	d	X
ejpam-7020	173	28	=	=	SYM
ejpam-7020	173	29	0.075	0.075	NUM
ejpam-7020	173	30	fixed	fix	VERB
ejpam-7020	173	31	.	.	PUNCT
ejpam-7020	174	1	the	the	DET
ejpam-7020	174	2	resulting	result	VERB
ejpam-7020	174	3	trajectories	trajectory	NOUN
ejpam-7020	174	4	reveal	reveal	VERB
ejpam-7020	174	5	that	that	SCONJ
ejpam-7020	174	6	while	while	SCONJ
ejpam-7020	174	7	a	a	DET
ejpam-7020	174	8	higher	high	ADJ
ejpam-7020	174	9	interaction	interaction	NOUN
ejpam-7020	174	10	rate	rate	NOUN
ejpam-7020	174	11	(	(	PUNCT
ejpam-7020	174	12	b	b	NOUN
ejpam-7020	174	13	)	)	PUNCT
ejpam-7020	174	14	alters	alter	VERB
ejpam-7020	174	15	the	the	DET
ejpam-7020	174	16	position	position	NOUN
ejpam-7020	174	17	and	and	CCONJ
ejpam-7020	174	18	shape	shape	NOUN
ejpam-7020	174	19	of	of	ADP
ejpam-7020	174	20	the	the	DET
ejpam-7020	174	21	orbits	orbit	NOUN
ejpam-7020	174	22	,	,	PUNCT
ejpam-7020	174	23	it	it	PRON
ejpam-7020	174	24	does	do	AUX
ejpam-7020	174	25	not	not	PART
ejpam-7020	174	26	break	break	VERB
ejpam-7020	174	27	the	the	DET
ejpam-7020	174	28	underlying	underlie	VERB
ejpam-7020	174	29	oscillatory	oscillatory	ADJ
ejpam-7020	174	30	dynamics	dynamic	NOUN
ejpam-7020	174	31	.	.	PUNCT
ejpam-7020	175	1	this	this	DET
ejpam-7020	175	2	sensitivity	sensitivity	NOUN
ejpam-7020	175	3	analysis	analysis	NOUN
ejpam-7020	175	4	is	be	AUX
ejpam-7020	175	5	illustrated	illustrate	VERB
ejpam-7020	175	6	in	in	ADP
ejpam-7020	175	7	figure	figure	NOUN
ejpam-7020	175	8	2	2	NUM
ejpam-7020	175	9	.	.	PUNCT
ejpam-7020	175	10	figure	figure	NOUN
ejpam-7020	175	11	2	2	NUM
ejpam-7020	175	12	:	:	PUNCT
ejpam-7020	175	13	sensitivity	sensitivity	NOUN
ejpam-7020	175	14	analysis	analysis	NOUN
ejpam-7020	175	15	5.2	5.2	NUM
ejpam-7020	175	16	.	.	PUNCT
ejpam-7020	176	1	susceptible	susceptible	ADJ
ejpam-7020	176	2	-	-	PUNCT
ejpam-7020	176	3	infected	infect	VERB
ejpam-7020	176	4	-	-	PUNCT
ejpam-7020	176	5	recovered	recover	VERB
ejpam-7020	176	6	dynamics	dynamic	NOUN
ejpam-7020	176	7	:	:	PUNCT
ejpam-7020	176	8	threshold	threshold	NOUN
ejpam-7020	176	9	behavior	behavior	NOUN
ejpam-7020	176	10	the	the	DET
ejpam-7020	176	11	sir	sir	PROPN
ejpam-7020	176	12	epidemic	epidemic	NOUN
ejpam-7020	176	13	model	model	NOUN
ejpam-7020	176	14	displays	display	VERB
ejpam-7020	176	15	a	a	DET
ejpam-7020	176	16	fundamentally	fundamentally	ADV
ejpam-7020	176	17	different	different	ADJ
ejpam-7020	176	18	behavior	behavior	NOUN
ejpam-7020	176	19	,	,	PUNCT
ejpam-7020	176	20	governed	govern	VERB
ejpam-7020	176	21	by	by	ADP
ejpam-7020	176	22	the	the	DET
ejpam-7020	176	23	threshold	threshold	NOUN
ejpam-7020	176	24	r0	r0	NOUN
ejpam-7020	176	25	.	.	PUNCT
ejpam-7020	177	1	when	when	SCONJ
ejpam-7020	177	2	r0	r0	VERB
ejpam-7020	177	3	<	<	X
ejpam-7020	177	4	1	1	NUM
ejpam-7020	177	5	,	,	PUNCT
ejpam-7020	177	6	all	all	DET
ejpam-7020	177	7	trajectories	trajectory	NOUN
ejpam-7020	177	8	converge	converge	VERB
ejpam-7020	177	9	to	to	ADP
ejpam-7020	177	10	the	the	DET
ejpam-7020	177	11	stable	stable	ADJ
ejpam-7020	177	12	disease	disease	NOUN
ejpam-7020	177	13	-	-	PUNCT
ejpam-7020	177	14	free	free	ADJ
ejpam-7020	177	15	equilibrium	equilibrium	NOUN
ejpam-7020	177	16	(	(	PUNCT
ejpam-7020	177	17	n	n	CCONJ
ejpam-7020	177	18	,	,	PUNCT
ejpam-7020	177	19	0	0	NUM
ejpam-7020	177	20	)	)	PUNCT
ejpam-7020	177	21	,	,	PUNCT
ejpam-7020	177	22	indicating	indicate	VERB
ejpam-7020	177	23	that	that	SCONJ
ejpam-7020	177	24	the	the	DET
ejpam-7020	177	25	disease	disease	NOUN
ejpam-7020	177	26	does	do	AUX
ejpam-7020	177	27	not	not	PART
ejpam-7020	177	28	spread	spread	VERB
ejpam-7020	177	29	or	or	CCONJ
ejpam-7020	177	30	die	die	VERB
ejpam-7020	177	31	out	out	ADP
ejpam-7020	177	32	,	,	PUNCT
ejpam-7020	177	33	as	as	SCONJ
ejpam-7020	177	34	shown	show	VERB
ejpam-7020	177	35	in	in	ADP
ejpam-7020	177	36	figure	figure	NOUN
ejpam-7020	177	37	3	3	NUM
ejpam-7020	177	38	.	.	PUNCT
ejpam-7020	178	1	s.	s.	PROPN
ejpam-7020	178	2	saidat	saidat	PROPN
ejpam-7020	178	3	et	et	PROPN
ejpam-7020	178	4	al	al	PROPN
ejpam-7020	178	5	.	.	PUNCT
ejpam-7020	178	6	/	/	SYM
ejpam-7020	178	7	eur	eur	PROPN
ejpam-7020	178	8	.	.	PUNCT
ejpam-7020	179	1	j.	j.	PROPN
ejpam-7020	179	2	pure	pure	PROPN
ejpam-7020	179	3	appl	appl	PROPN
ejpam-7020	179	4	.	.	PROPN
ejpam-7020	179	5	math	math	PROPN
ejpam-7020	179	6	,	,	PUNCT
ejpam-7020	179	7	18	18	NUM
ejpam-7020	179	8	(	(	PUNCT
ejpam-7020	179	9	4	4	NUM
ejpam-7020	179	10	)	)	PUNCT
ejpam-7020	179	11	(	(	PUNCT
ejpam-7020	179	12	2025	2025	NUM
ejpam-7020	179	13	)	)	PUNCT
ejpam-7020	179	14	,	,	PUNCT
ejpam-7020	179	15	7020	7020	NUM
ejpam-7020	179	16	11	11	NUM
ejpam-7020	179	17	of	of	ADP
ejpam-7020	179	18	16	16	NUM
ejpam-7020	179	19	figure	figure	NOUN
ejpam-7020	179	20	3	3	NUM
ejpam-7020	179	21	:	:	PUNCT
ejpam-7020	179	22	phase	phase	NOUN
ejpam-7020	179	23	portrait	portrait	NOUN
ejpam-7020	179	24	of	of	ADP
ejpam-7020	179	25	the	the	DET
ejpam-7020	179	26	sir	sir	NOUN
ejpam-7020	179	27	model	model	NOUN
ejpam-7020	179	28	for	for	ADP
ejpam-7020	179	29	r0	r0	NOUN
ejpam-7020	179	30	<	<	X
ejpam-7020	179	31	1	1	NUM
ejpam-7020	179	32	,	,	PUNCT
ejpam-7020	179	33	showing	show	VERB
ejpam-7020	179	34	convergence	convergence	NOUN
ejpam-7020	179	35	of	of	ADP
ejpam-7020	179	36	all	all	DET
ejpam-7020	179	37	trajectories	trajectory	NOUN
ejpam-7020	179	38	to	to	ADP
ejpam-7020	179	39	the	the	DET
ejpam-7020	179	40	diseasefree	diseasefree	PROPN
ejpam-7020	179	41	equilibrium	equilibrium	NOUN
ejpam-7020	179	42	(	(	PUNCT
ejpam-7020	179	43	n	n	CCONJ
ejpam-7020	179	44	,	,	PUNCT
ejpam-7020	179	45	0	0	NUM
ejpam-7020	179	46	)	)	PUNCT
ejpam-7020	179	47	.	.	PUNCT
ejpam-7020	180	1	in	in	ADP
ejpam-7020	180	2	stark	stark	ADJ
ejpam-7020	180	3	contrast	contrast	NOUN
ejpam-7020	180	4	,	,	PUNCT
ejpam-7020	180	5	when	when	SCONJ
ejpam-7020	180	6	r0	r0	NOUN
ejpam-7020	180	7	>	>	X
ejpam-7020	180	8	1	1	NUM
ejpam-7020	180	9	,	,	PUNCT
ejpam-7020	180	10	the	the	DET
ejpam-7020	180	11	dfe	dfe	PROPN
ejpam-7020	180	12	becomes	become	VERB
ejpam-7020	180	13	unstable	unstable	ADJ
ejpam-7020	180	14	.	.	PUNCT
ejpam-7020	181	1	as	as	SCONJ
ejpam-7020	181	2	shown	show	VERB
ejpam-7020	181	3	in	in	ADP
ejpam-7020	181	4	the	the	DET
ejpam-7020	181	5	phase	phase	NOUN
ejpam-7020	181	6	portrait	portrait	NOUN
ejpam-7020	181	7	,	,	PUNCT
ejpam-7020	181	8	trajectories	trajectory	NOUN
ejpam-7020	181	9	starting	start	VERB
ejpam-7020	181	10	near	near	ADP
ejpam-7020	181	11	the	the	DET
ejpam-7020	181	12	dfe	dfe	PROPN
ejpam-7020	181	13	are	be	AUX
ejpam-7020	181	14	initially	initially	ADV
ejpam-7020	181	15	repelled	repel	VERB
ejpam-7020	181	16	,	,	PUNCT
ejpam-7020	181	17	leading	lead	VERB
ejpam-7020	181	18	to	to	ADP
ejpam-7020	181	19	an	an	DET
ejpam-7020	181	20	outbreak	outbreak	NOUN
ejpam-7020	181	21	where	where	SCONJ
ejpam-7020	181	22	the	the	DET
ejpam-7020	181	23	number	number	NOUN
ejpam-7020	181	24	of	of	ADP
ejpam-7020	181	25	infected	infect	VERB
ejpam-7020	181	26	individuals	individual	NOUN
ejpam-7020	181	27	increases	increase	VERB
ejpam-7020	181	28	.	.	PUNCT
ejpam-7020	182	1	these	these	DET
ejpam-7020	182	2	trajectories	trajectory	NOUN
ejpam-7020	182	3	do	do	AUX
ejpam-7020	182	4	not	not	PART
ejpam-7020	182	5	grow	grow	VERB
ejpam-7020	182	6	indefinitely	indefinitely	ADV
ejpam-7020	182	7	,	,	PUNCT
ejpam-7020	182	8	instead	instead	ADV
ejpam-7020	182	9	,	,	PUNCT
ejpam-7020	182	10	they	they	PRON
ejpam-7020	182	11	spiral	spiral	VERB
ejpam-7020	182	12	towards	towards	ADP
ejpam-7020	182	13	the	the	DET
ejpam-7020	182	14	stable	stable	ADJ
ejpam-7020	182	15	endemic	endemic	ADJ
ejpam-7020	182	16	equilibrium	equilibrium	NOUN
ejpam-7020	182	17	,	,	PUNCT
ejpam-7020	182	18	which	which	PRON
ejpam-7020	182	19	was	be	AUX
ejpam-7020	182	20	shown	show	VERB
ejpam-7020	182	21	to	to	PART
ejpam-7020	182	22	be	be	AUX
ejpam-7020	182	23	a	a	DET
ejpam-7020	182	24	stable	stable	ADJ
ejpam-7020	182	25	node	node	NOUN
ejpam-7020	182	26	or	or	CCONJ
ejpam-7020	182	27	spiral	spiral	ADJ
ejpam-7020	182	28	.	.	PUNCT
ejpam-7020	183	1	this	this	PRON
ejpam-7020	183	2	shows	show	VERB
ejpam-7020	183	3	that	that	SCONJ
ejpam-7020	183	4	the	the	DET
ejpam-7020	183	5	disease	disease	NOUN
ejpam-7020	183	6	will	will	AUX
ejpam-7020	183	7	persist	persist	VERB
ejpam-7020	183	8	in	in	ADP
ejpam-7020	183	9	the	the	DET
ejpam-7020	183	10	population	population	NOUN
ejpam-7020	183	11	at	at	ADP
ejpam-7020	183	12	a	a	DET
ejpam-7020	183	13	constant	constant	ADJ
ejpam-7020	183	14	level	level	NOUN
ejpam-7020	183	15	.	.	PUNCT
ejpam-7020	184	1	as	as	SCONJ
ejpam-7020	184	2	shown	show	VERB
ejpam-7020	184	3	in	in	ADP
ejpam-7020	184	4	figure	figure	NOUN
ejpam-7020	184	5	4	4	NUM
ejpam-7020	184	6	.	.	PUNCT
ejpam-7020	185	1	s.	s.	PROPN
ejpam-7020	185	2	saidat	saidat	PROPN
ejpam-7020	185	3	et	et	PROPN
ejpam-7020	185	4	al	al	PROPN
ejpam-7020	185	5	.	.	PUNCT
ejpam-7020	185	6	/	/	SYM
ejpam-7020	185	7	eur	eur	PROPN
ejpam-7020	185	8	.	.	PUNCT
ejpam-7020	186	1	j.	j.	PROPN
ejpam-7020	186	2	pure	pure	PROPN
ejpam-7020	186	3	appl	appl	PROPN
ejpam-7020	186	4	.	.	PROPN
ejpam-7020	186	5	math	math	PROPN
ejpam-7020	186	6	,	,	PUNCT
ejpam-7020	186	7	18	18	NUM
ejpam-7020	186	8	(	(	PUNCT
ejpam-7020	186	9	4	4	NUM
ejpam-7020	186	10	)	)	PUNCT
ejpam-7020	186	11	(	(	PUNCT
ejpam-7020	186	12	2025	2025	NUM
ejpam-7020	186	13	)	)	PUNCT
ejpam-7020	186	14	,	,	PUNCT
ejpam-7020	186	15	7020	7020	NUM
ejpam-7020	186	16	12	12	NUM
ejpam-7020	186	17	of	of	ADP
ejpam-7020	186	18	16	16	NUM
ejpam-7020	186	19	figure	figure	NOUN
ejpam-7020	186	20	4	4	NUM
ejpam-7020	186	21	:	:	PUNCT
ejpam-7020	186	22	sir	sir	NOUN
ejpam-7020	186	23	system	system	NOUN
ejpam-7020	186	24	with	with	ADP
ejpam-7020	186	25	r0	r0	PROPN
ejpam-7020	186	26	>	>	X
ejpam-7020	186	27	1	1	NUM
ejpam-7020	186	28	.	.	X
ejpam-7020	186	29	5.3	5.3	NUM
ejpam-7020	186	30	.	.	PUNCT
ejpam-7020	187	1	comparative	comparative	ADJ
ejpam-7020	187	2	analysis	analysis	NOUN
ejpam-7020	187	3	of	of	ADP
ejpam-7020	187	4	stability	stability	NOUN
ejpam-7020	187	5	the	the	DET
ejpam-7020	187	6	side	side	NOUN
ejpam-7020	187	7	-	-	PUNCT
ejpam-7020	187	8	by	by	ADP
ejpam-7020	187	9	-	-	PUNCT
ejpam-7020	187	10	side	side	NOUN
ejpam-7020	187	11	analysis	analysis	NOUN
ejpam-7020	187	12	reveals	reveal	VERB
ejpam-7020	187	13	a	a	DET
ejpam-7020	187	14	crucial	crucial	ADJ
ejpam-7020	187	15	distinction	distinction	NOUN
ejpam-7020	187	16	rooted	root	VERB
ejpam-7020	187	17	in	in	ADP
ejpam-7020	187	18	the	the	DET
ejpam-7020	187	19	stability	stability	NOUN
ejpam-7020	187	20	of	of	ADP
ejpam-7020	187	21	the	the	DET
ejpam-7020	187	22	non	non	ADJ
ejpam-7020	187	23	-	-	ADJ
ejpam-7020	187	24	trivial	trivial	ADJ
ejpam-7020	187	25	equilibria	equilibrium	NOUN
ejpam-7020	187	26	.	.	PUNCT
ejpam-7020	188	1	in	in	ADP
ejpam-7020	188	2	the	the	DET
ejpam-7020	188	3	lotka	lotka	PROPN
ejpam-7020	188	4	–	–	PUNCT
ejpam-7020	188	5	volterra	volterra	NOUN
ejpam-7020	188	6	model	model	NOUN
ejpam-7020	188	7	,	,	PUNCT
ejpam-7020	188	8	the	the	DET
ejpam-7020	188	9	interior	interior	ADJ
ejpam-7020	188	10	equilibrium	equilibrium	NOUN
ejpam-7020	188	11	is	be	AUX
ejpam-7020	188	12	a	a	DET
ejpam-7020	188	13	neutrally	neutrally	ADV
ejpam-7020	188	14	stable	stable	ADJ
ejpam-7020	188	15	center	center	NOUN
ejpam-7020	188	16	,	,	PUNCT
ejpam-7020	188	17	leading	lead	VERB
ejpam-7020	188	18	to	to	ADP
ejpam-7020	188	19	persistent	persistent	ADJ
ejpam-7020	188	20	oscillations	oscillation	NOUN
ejpam-7020	188	21	whose	whose	DET
ejpam-7020	188	22	amplitudes	amplitude	NOUN
ejpam-7020	188	23	depend	depend	VERB
ejpam-7020	188	24	strongly	strongly	ADV
ejpam-7020	188	25	on	on	ADP
ejpam-7020	188	26	initial	initial	ADJ
ejpam-7020	188	27	conditions	condition	NOUN
ejpam-7020	188	28	.	.	PUNCT
ejpam-7020	189	1	this	this	DET
ejpam-7020	189	2	cyclical	cyclical	ADJ
ejpam-7020	189	3	dynamic	dynamic	NOUN
ejpam-7020	189	4	reflects	reflect	VERB
ejpam-7020	189	5	the	the	DET
ejpam-7020	189	6	endless	endless	ADJ
ejpam-7020	189	7	predator	predator	NOUN
ejpam-7020	189	8	–	–	PUNCT
ejpam-7020	189	9	prey	prey	NOUN
ejpam-7020	189	10	cycles	cycle	NOUN
ejpam-7020	189	11	of	of	ADP
ejpam-7020	189	12	the	the	DET
ejpam-7020	189	13	idealized	idealized	ADJ
ejpam-7020	189	14	system	system	NOUN
ejpam-7020	189	15	.	.	PUNCT
ejpam-7020	190	1	in	in	ADP
ejpam-7020	190	2	contrast	contrast	NOUN
ejpam-7020	190	3	,	,	PUNCT
ejpam-7020	190	4	the	the	DET
ejpam-7020	190	5	sir	sir	NOUN
ejpam-7020	190	6	epidemic	epidemic	NOUN
ejpam-7020	190	7	model	model	NOUN
ejpam-7020	190	8	demonstrates	demonstrate	VERB
ejpam-7020	190	9	a	a	DET
ejpam-7020	190	10	qualitatively	qualitatively	ADV
ejpam-7020	190	11	different	different	ADJ
ejpam-7020	190	12	form	form	NOUN
ejpam-7020	190	13	of	of	ADP
ejpam-7020	190	14	stability	stability	NOUN
ejpam-7020	190	15	behavior	behavior	NOUN
ejpam-7020	190	16	.	.	PUNCT
ejpam-7020	191	1	the	the	DET
ejpam-7020	191	2	disease	disease	NOUN
ejpam-7020	191	3	-	-	PUNCT
ejpam-7020	191	4	free	free	ADJ
ejpam-7020	191	5	equilibrium	equilibrium	NOUN
ejpam-7020	191	6	(	(	PUNCT
ejpam-7020	191	7	dfe	dfe	PROPN
ejpam-7020	191	8	)	)	PUNCT
ejpam-7020	191	9	corresponds	correspond	VERB
ejpam-7020	191	10	to	to	ADP
ejpam-7020	191	11	the	the	DET
ejpam-7020	191	12	state	state	NOUN
ejpam-7020	191	13	(	(	PUNCT
ejpam-7020	191	14	s	s	PROPN
ejpam-7020	191	15	,	,	PUNCT
ejpam-7020	191	16	i	i	PRON
ejpam-7020	191	17	,	,	PUNCT
ejpam-7020	191	18	r	r	NOUN
ejpam-7020	191	19	)	)	PUNCT
ejpam-7020	191	20	=	=	SYM
ejpam-7020	191	21	(	(	PUNCT
ejpam-7020	191	22	1	1	NUM
ejpam-7020	191	23	,	,	PUNCT
ejpam-7020	191	24	0	0	NUM
ejpam-7020	191	25	,	,	PUNCT
ejpam-7020	191	26	0	0	NUM
ejpam-7020	191	27	)	)	PUNCT
ejpam-7020	191	28	,	,	PUNCT
ejpam-7020	191	29	whose	whose	DET
ejpam-7020	191	30	jacobian	jacobian	ADJ
ejpam-7020	191	31	matrix	matrix	NOUN
ejpam-7020	191	32	yields	yield	VERB
ejpam-7020	191	33	one	one	NUM
ejpam-7020	191	34	zero	zero	NUM
ejpam-7020	191	35	eigenvalue	eigenvalue	NOUN
ejpam-7020	191	36	λ1	λ1	PROPN
ejpam-7020	191	37	=	=	SYM
ejpam-7020	191	38	0	0	PROPN
ejpam-7020	191	39	.	.	PUNCT
ejpam-7020	192	1	the	the	DET
ejpam-7020	192	2	presence	presence	NOUN
ejpam-7020	192	3	of	of	ADP
ejpam-7020	192	4	a	a	DET
ejpam-7020	192	5	zero	zero	NUM
ejpam-7020	192	6	eigenvalue	eigenvalue	NOUN
ejpam-7020	192	7	implies	imply	VERB
ejpam-7020	192	8	that	that	SCONJ
ejpam-7020	192	9	the	the	DET
ejpam-7020	192	10	linear	linear	ADJ
ejpam-7020	192	11	stability	stability	NOUN
ejpam-7020	192	12	analysis	analysis	NOUN
ejpam-7020	192	13	is	be	AUX
ejpam-7020	192	14	inconclusive	inconclusive	ADJ
ejpam-7020	192	15	in	in	ADP
ejpam-7020	192	16	this	this	DET
ejpam-7020	192	17	direction	direction	NOUN
ejpam-7020	192	18	.	.	PUNCT
ejpam-7020	193	1	formally	formally	ADV
ejpam-7020	193	2	,	,	PUNCT
ejpam-7020	193	3	confirming	confirm	VERB
ejpam-7020	193	4	the	the	DET
ejpam-7020	193	5	local	local	ADJ
ejpam-7020	193	6	stability	stability	NOUN
ejpam-7020	193	7	of	of	ADP
ejpam-7020	193	8	the	the	DET
ejpam-7020	193	9	dfe	dfe	PROPN
ejpam-7020	193	10	when	when	SCONJ
ejpam-7020	193	11	r0	r0	NOUN
ejpam-7020	193	12	<	<	X
ejpam-7020	193	13	1	1	NUM
ejpam-7020	193	14	requires	require	VERB
ejpam-7020	193	15	a	a	DET
ejpam-7020	193	16	nonlinear	nonlinear	ADJ
ejpam-7020	193	17	analysis	analysis	NOUN
ejpam-7020	193	18	,	,	PUNCT
ejpam-7020	193	19	such	such	ADJ
ejpam-7020	193	20	as	as	ADP
ejpam-7020	193	21	through	through	ADP
ejpam-7020	193	22	the	the	DET
ejpam-7020	193	23	center	center	NOUN
ejpam-7020	193	24	manifold	manifold	ADJ
ejpam-7020	193	25	theorem	theorem	NOUN
ejpam-7020	193	26	or	or	CCONJ
ejpam-7020	193	27	a	a	DET
ejpam-7020	193	28	sufficiently	sufficiently	ADV
ejpam-7020	193	29	constructed	construct	VERB
ejpam-7020	193	30	lyapunov	lyapunov	NOUN
ejpam-7020	193	31	function	function	NOUN
ejpam-7020	193	32	.	.	PUNCT
ejpam-7020	194	1	this	this	DET
ejpam-7020	194	2	observation	observation	NOUN
ejpam-7020	194	3	underscores	underscore	VERB
ejpam-7020	194	4	that	that	SCONJ
ejpam-7020	194	5	,	,	PUNCT
ejpam-7020	194	6	while	while	SCONJ
ejpam-7020	194	7	linearization	linearization	NOUN
ejpam-7020	194	8	provides	provide	VERB
ejpam-7020	194	9	valuable	valuable	ADJ
ejpam-7020	194	10	insight	insight	NOUN
ejpam-7020	194	11	,	,	PUNCT
ejpam-7020	194	12	it	it	PRON
ejpam-7020	194	13	may	may	AUX
ejpam-7020	194	14	not	not	PART
ejpam-7020	194	15	fully	fully	ADV
ejpam-7020	194	16	capture	capture	VERB
ejpam-7020	194	17	the	the	DET
ejpam-7020	194	18	dynamical	dynamical	ADJ
ejpam-7020	194	19	behavior	behavior	NOUN
ejpam-7020	194	20	of	of	ADP
ejpam-7020	194	21	the	the	DET
ejpam-7020	194	22	system	system	NOUN
ejpam-7020	194	23	near	near	ADP
ejpam-7020	194	24	critical	critical	ADJ
ejpam-7020	194	25	thresholds	threshold	NOUN
ejpam-7020	194	26	.	.	PUNCT
ejpam-7020	195	1	moreover	moreover	ADV
ejpam-7020	195	2	,	,	PUNCT
ejpam-7020	195	3	when	when	SCONJ
ejpam-7020	195	4	r0	r0	NOUN
ejpam-7020	195	5	crosses	cross	VERB
ejpam-7020	195	6	the	the	DET
ejpam-7020	195	7	critical	critical	ADJ
ejpam-7020	195	8	value	value	NOUN
ejpam-7020	195	9	r0	r0	NOUN
ejpam-7020	195	10	=	=	SYM
ejpam-7020	195	11	1	1	NUM
ejpam-7020	195	12	,	,	PUNCT
ejpam-7020	195	13	the	the	DET
ejpam-7020	195	14	sir	sir	NOUN
ejpam-7020	195	15	model	model	NOUN
ejpam-7020	195	16	undergoes	undergo	VERB
ejpam-7020	195	17	a	a	DET
ejpam-7020	195	18	transcritical	transcritical	ADJ
ejpam-7020	195	19	bifurcation	bifurcation	NOUN
ejpam-7020	195	20	.	.	PUNCT
ejpam-7020	196	1	at	at	ADP
ejpam-7020	196	2	this	this	DET
ejpam-7020	196	3	point	point	NOUN
ejpam-7020	196	4	,	,	PUNCT
ejpam-7020	196	5	the	the	DET
ejpam-7020	196	6	dfe	dfe	PROPN
ejpam-7020	196	7	loses	lose	VERB
ejpam-7020	196	8	stability	stability	NOUN
ejpam-7020	196	9	and	and	CCONJ
ejpam-7020	196	10	an	an	DET
ejpam-7020	196	11	endemic	endemic	ADJ
ejpam-7020	196	12	equilibrium	equilibrium	NOUN
ejpam-7020	196	13	emerges	emerge	VERB
ejpam-7020	196	14	,	,	PUNCT
ejpam-7020	196	15	exchanging	exchange	VERB
ejpam-7020	196	16	stability	stability	NOUN
ejpam-7020	196	17	properties	property	NOUN
ejpam-7020	196	18	with	with	ADP
ejpam-7020	196	19	the	the	DET
ejpam-7020	196	20	dfe	dfe	PROPN
ejpam-7020	196	21	.	.	PUNCT
ejpam-7020	197	1	this	this	DET
ejpam-7020	197	2	bifurcation	bifurcation	NOUN
ejpam-7020	197	3	marks	mark	VERB
ejpam-7020	197	4	the	the	DET
ejpam-7020	197	5	fundamental	fundamental	ADJ
ejpam-7020	197	6	epidemiological	epidemiological	ADJ
ejpam-7020	197	7	transition	transition	NOUN
ejpam-7020	197	8	between	between	ADP
ejpam-7020	197	9	disease	disease	NOUN
ejpam-7020	197	10	elimination	elimination	NOUN
ejpam-7020	197	11	(	(	PUNCT
ejpam-7020	197	12	r0	r0	NOUN
ejpam-7020	197	13	<	<	X
ejpam-7020	197	14	1	1	NUM
ejpam-7020	197	15	)	)	PUNCT
ejpam-7020	197	16	and	and	CCONJ
ejpam-7020	197	17	sustained	sustain	VERB
ejpam-7020	197	18	infection	infection	NOUN
ejpam-7020	197	19	(	(	PUNCT
ejpam-7020	197	20	r0	r0	NOUN
ejpam-7020	197	21	>	>	X
ejpam-7020	197	22	1	1	NUM
ejpam-7020	197	23	)	)	PUNCT
ejpam-7020	197	24	.	.	PUNCT
ejpam-7020	198	1	thus	thus	ADV
ejpam-7020	198	2	,	,	PUNCT
ejpam-7020	198	3	while	while	SCONJ
ejpam-7020	198	4	both	both	DET
ejpam-7020	198	5	models	model	NOUN
ejpam-7020	198	6	share	share	VERB
ejpam-7020	198	7	a	a	DET
ejpam-7020	198	8	common	common	ADJ
ejpam-7020	198	9	analytical	analytical	ADJ
ejpam-7020	198	10	framework	framework	NOUN
ejpam-7020	198	11	,	,	PUNCT
ejpam-7020	198	12	their	their	PRON
ejpam-7020	198	13	stability	stability	NOUN
ejpam-7020	198	14	properties	property	NOUN
ejpam-7020	198	15	highlight	highlight	VERB
ejpam-7020	198	16	profoundly	profoundly	ADV
ejpam-7020	198	17	different	different	ADJ
ejpam-7020	198	18	biological	biological	ADJ
ejpam-7020	198	19	realities	reality	NOUN
ejpam-7020	198	20	—	—	PUNCT
ejpam-7020	198	21	endless	endless	ADJ
ejpam-7020	198	22	oscils	oscil	NOUN
ejpam-7020	198	23	.	.	PUNCT
ejpam-7020	199	1	saidat	saidat	NOUN
ejpam-7020	199	2	et	et	PROPN
ejpam-7020	199	3	al	al	PROPN
ejpam-7020	199	4	.	.	PUNCT
ejpam-7020	199	5	/	/	SYM
ejpam-7020	199	6	eur	eur	PROPN
ejpam-7020	199	7	.	.	PUNCT
ejpam-7020	200	1	j.	j.	PROPN
ejpam-7020	200	2	pure	pure	PROPN
ejpam-7020	200	3	appl	appl	PROPN
ejpam-7020	200	4	.	.	PROPN
ejpam-7020	200	5	math	math	PROPN
ejpam-7020	200	6	,	,	PUNCT
ejpam-7020	200	7	18	18	NUM
ejpam-7020	200	8	(	(	PUNCT
ejpam-7020	200	9	4	4	NUM
ejpam-7020	200	10	)	)	PUNCT
ejpam-7020	200	11	(	(	PUNCT
ejpam-7020	200	12	2025	2025	NUM
ejpam-7020	200	13	)	)	PUNCT
ejpam-7020	200	14	,	,	PUNCT
ejpam-7020	200	15	7020	7020	NUM
ejpam-7020	200	16	13	13	NUM
ejpam-7020	200	17	of	of	ADP
ejpam-7020	200	18	16	16	NUM
ejpam-7020	200	19	lations	lation	NOUN
ejpam-7020	200	20	in	in	ADP
ejpam-7020	200	21	predator	predator	NOUN
ejpam-7020	200	22	–	–	PUNCT
ejpam-7020	200	23	prey	prey	NOUN
ejpam-7020	200	24	dynamics	dynamic	NOUN
ejpam-7020	200	25	versus	versus	ADP
ejpam-7020	200	26	a	a	DET
ejpam-7020	200	27	bifurcation	bifurcation	NOUN
ejpam-7020	200	28	-	-	PUNCT
ejpam-7020	200	29	driven	drive	VERB
ejpam-7020	200	30	transition	transition	NOUN
ejpam-7020	200	31	and	and	CCONJ
ejpam-7020	200	32	asymptotic	asymptotic	ADJ
ejpam-7020	200	33	convergence	convergence	NOUN
ejpam-7020	200	34	in	in	ADP
ejpam-7020	200	35	epidemic	epidemic	NOUN
ejpam-7020	200	36	dynamics	dynamic	NOUN
ejpam-7020	200	37	.	.	PUNCT
ejpam-7020	201	1	6	6	X
ejpam-7020	201	2	.	.	X
ejpam-7020	201	3	conclusion	conclusion	NOUN
ejpam-7020	201	4	this	this	DET
ejpam-7020	201	5	paper	paper	NOUN
ejpam-7020	201	6	has	have	AUX
ejpam-7020	201	7	presented	present	VERB
ejpam-7020	201	8	a	a	DET
ejpam-7020	201	9	structured	structured	ADJ
ejpam-7020	201	10	,	,	PUNCT
ejpam-7020	201	11	computational	computational	ADJ
ejpam-7020	201	12	guide	guide	NOUN
ejpam-7020	201	13	to	to	ADP
ejpam-7020	201	14	local	local	ADJ
ejpam-7020	201	15	stability	stability	NOUN
ejpam-7020	201	16	analysis	analysis	NOUN
ejpam-7020	201	17	,	,	PUNCT
ejpam-7020	201	18	a	a	DET
ejpam-7020	201	19	cornerstone	cornerstone	NOUN
ejpam-7020	201	20	of	of	ADP
ejpam-7020	201	21	nonlinear	nonlinear	ADJ
ejpam-7020	201	22	dynamics	dynamic	NOUN
ejpam-7020	201	23	.	.	PUNCT
ejpam-7020	202	1	by	by	ADP
ejpam-7020	202	2	combining	combine	VERB
ejpam-7020	202	3	jacobian	jacobian	ADJ
ejpam-7020	202	4	-	-	PUNCT
ejpam-7020	202	5	based	base	VERB
ejpam-7020	202	6	linearization	linearization	NOUN
ejpam-7020	202	7	with	with	ADP
ejpam-7020	202	8	phase	phase	NOUN
ejpam-7020	202	9	portrait	portrait	NOUN
ejpam-7020	202	10	visualization	visualization	NOUN
ejpam-7020	202	11	,	,	PUNCT
ejpam-7020	202	12	we	we	PRON
ejpam-7020	202	13	developed	develop	VERB
ejpam-7020	202	14	a	a	DET
ejpam-7020	202	15	cohesive	cohesive	ADJ
ejpam-7020	202	16	workflow	workflow	NOUN
ejpam-7020	202	17	and	and	CCONJ
ejpam-7020	202	18	applied	apply	VERB
ejpam-7020	202	19	it	it	PRON
ejpam-7020	202	20	to	to	ADP
ejpam-7020	202	21	two	two	NUM
ejpam-7020	202	22	classical	classical	ADJ
ejpam-7020	202	23	models	model	NOUN
ejpam-7020	202	24	:	:	PUNCT
ejpam-7020	202	25	the	the	DET
ejpam-7020	202	26	lotka	lotka	PROPN
ejpam-7020	202	27	–	–	PUNCT
ejpam-7020	202	28	volterra	volterra	NOUN
ejpam-7020	202	29	predator	predator	NOUN
ejpam-7020	202	30	–	–	PUNCT
ejpam-7020	202	31	prey	prey	NOUN
ejpam-7020	202	32	system	system	NOUN
ejpam-7020	202	33	and	and	CCONJ
ejpam-7020	202	34	the	the	DET
ejpam-7020	202	35	sir	sir	NOUN
ejpam-7020	202	36	epidemic	epidemic	NOUN
ejpam-7020	202	37	model	model	NOUN
ejpam-7020	202	38	.	.	PUNCT
ejpam-7020	203	1	our	our	PRON
ejpam-7020	203	2	analysis	analysis	NOUN
ejpam-7020	203	3	of	of	ADP
ejpam-7020	203	4	the	the	DET
ejpam-7020	203	5	lotka	lotka	PROPN
ejpam-7020	203	6	–	–	PUNCT
ejpam-7020	203	7	volterra	volterra	NOUN
ejpam-7020	203	8	system	system	NOUN
ejpam-7020	203	9	demonstrated	demonstrate	VERB
ejpam-7020	203	10	the	the	DET
ejpam-7020	203	11	emergence	emergence	NOUN
ejpam-7020	203	12	of	of	ADP
ejpam-7020	203	13	persistent	persistent	ADJ
ejpam-7020	203	14	predator	predator	NOUN
ejpam-7020	203	15	–	–	PUNCT
ejpam-7020	203	16	prey	prey	NOUN
ejpam-7020	203	17	oscillations	oscillation	NOUN
ejpam-7020	203	18	,	,	PUNCT
ejpam-7020	203	19	corresponding	correspond	VERB
ejpam-7020	203	20	to	to	ADP
ejpam-7020	203	21	a	a	DET
ejpam-7020	203	22	neutrally	neutrally	ADV
ejpam-7020	203	23	stable	stable	ADJ
ejpam-7020	203	24	center	center	NOUN
ejpam-7020	203	25	.	.	PUNCT
ejpam-7020	204	1	in	in	ADP
ejpam-7020	204	2	contrast	contrast	NOUN
ejpam-7020	204	3	,	,	PUNCT
ejpam-7020	204	4	complete	complete	VERB
ejpam-7020	204	5	analysis	analysis	NOUN
ejpam-7020	204	6	of	of	ADP
ejpam-7020	204	7	the	the	DET
ejpam-7020	204	8	sir	sir	NOUN
ejpam-7020	204	9	model	model	NOUN
ejpam-7020	204	10	revealed	reveal	VERB
ejpam-7020	204	11	a	a	DET
ejpam-7020	204	12	critical	critical	ADJ
ejpam-7020	204	13	threshold	threshold	NOUN
ejpam-7020	204	14	phenomenon	phenomenon	NOUN
ejpam-7020	204	15	governed	govern	VERB
ejpam-7020	204	16	by	by	ADP
ejpam-7020	204	17	the	the	DET
ejpam-7020	204	18	basic	basic	ADJ
ejpam-7020	204	19	reproduction	reproduction	NOUN
ejpam-7020	204	20	number	number	NOUN
ejpam-7020	204	21	r0	r0	NOUN
ejpam-7020	204	22	.	.	PUNCT
ejpam-7020	205	1	when	when	SCONJ
ejpam-7020	205	2	r0	r0	VERB
ejpam-7020	205	3	<	<	X
ejpam-7020	205	4	1	1	NUM
ejpam-7020	205	5	,	,	PUNCT
ejpam-7020	205	6	the	the	DET
ejpam-7020	205	7	system	system	NOUN
ejpam-7020	205	8	converges	converge	VERB
ejpam-7020	205	9	to	to	ADP
ejpam-7020	205	10	disease	disease	NOUN
ejpam-7020	205	11	-	-	PUNCT
ejpam-7020	205	12	free	free	ADJ
ejpam-7020	205	13	equilibrium	equilibrium	NOUN
ejpam-7020	205	14	,	,	PUNCT
ejpam-7020	205	15	whereas	whereas	SCONJ
ejpam-7020	205	16	for	for	ADP
ejpam-7020	205	17	r0	r0	NOUN
ejpam-7020	205	18	>	>	X
ejpam-7020	205	19	1	1	NUM
ejpam-7020	205	20	,	,	PUNCT
ejpam-7020	205	21	trajectories	trajectory	NOUN
ejpam-7020	205	22	approach	approach	VERB
ejpam-7020	205	23	a	a	DET
ejpam-7020	205	24	stable	stable	ADJ
ejpam-7020	205	25	endemic	endemic	ADJ
ejpam-7020	205	26	equilibrium	equilibrium	NOUN
ejpam-7020	205	27	.	.	PUNCT
ejpam-7020	206	1	the	the	DET
ejpam-7020	206	2	direct	direct	ADJ
ejpam-7020	206	3	comparison	comparison	NOUN
ejpam-7020	206	4	between	between	ADP
ejpam-7020	206	5	the	the	DET
ejpam-7020	206	6	two	two	NUM
ejpam-7020	206	7	models	model	NOUN
ejpam-7020	206	8	proved	prove	VERB
ejpam-7020	206	9	particularly	particularly	ADV
ejpam-7020	206	10	insightful	insightful	ADJ
ejpam-7020	206	11	,	,	PUNCT
ejpam-7020	206	12	showing	show	VERB
ejpam-7020	206	13	how	how	SCONJ
ejpam-7020	206	14	subtle	subtle	ADJ
ejpam-7020	206	15	differences	difference	NOUN
ejpam-7020	206	16	in	in	ADP
ejpam-7020	206	17	nonlinear	nonlinear	ADJ
ejpam-7020	206	18	structure	structure	NOUN
ejpam-7020	206	19	can	can	AUX
ejpam-7020	206	20	lead	lead	VERB
ejpam-7020	206	21	to	to	ADP
ejpam-7020	206	22	profoundly	profoundly	ADV
ejpam-7020	206	23	different	different	ADJ
ejpam-7020	206	24	long	long	ADJ
ejpam-7020	206	25	-	-	PUNCT
ejpam-7020	206	26	term	term	NOUN
ejpam-7020	206	27	behaviors	behavior	NOUN
ejpam-7020	206	28	:	:	PUNCT
ejpam-7020	206	29	persistent	persistent	ADJ
ejpam-7020	206	30	oscillations	oscillation	NOUN
ejpam-7020	206	31	versus	versus	ADP
ejpam-7020	206	32	convergence	convergence	NOUN
ejpam-7020	206	33	to	to	ADP
ejpam-7020	206	34	a	a	DET
ejpam-7020	206	35	steady	steady	ADJ
ejpam-7020	206	36	state	state	NOUN
ejpam-7020	206	37	.	.	PUNCT
ejpam-7020	207	1	the	the	DET
ejpam-7020	207	2	primary	primary	ADJ
ejpam-7020	207	3	contribution	contribution	NOUN
ejpam-7020	207	4	of	of	ADP
ejpam-7020	207	5	this	this	DET
ejpam-7020	207	6	work	work	NOUN
ejpam-7020	207	7	is	be	AUX
ejpam-7020	207	8	pedagogical	pedagogical	ADJ
ejpam-7020	207	9	.	.	PUNCT
ejpam-7020	208	1	it	it	PRON
ejpam-7020	208	2	offers	offer	VERB
ejpam-7020	208	3	a	a	DET
ejpam-7020	208	4	clear	clear	ADJ
ejpam-7020	208	5	and	and	CCONJ
ejpam-7020	208	6	reproducible	reproducible	ADJ
ejpam-7020	208	7	template	template	NOUN
ejpam-7020	208	8	for	for	ADP
ejpam-7020	208	9	students	student	NOUN
ejpam-7020	208	10	,	,	PUNCT
ejpam-7020	208	11	educators	educator	NOUN
ejpam-7020	208	12	,	,	PUNCT
ejpam-7020	208	13	and	and	CCONJ
ejpam-7020	208	14	practitioners	practitioner	NOUN
ejpam-7020	208	15	who	who	PRON
ejpam-7020	208	16	are	be	AUX
ejpam-7020	208	17	new	new	ADJ
ejpam-7020	208	18	to	to	PART
ejpam-7020	208	19	nonlinear	nonlinear	VERB
ejpam-7020	208	20	modeling	modeling	NOUN
ejpam-7020	208	21	.	.	PUNCT
ejpam-7020	209	1	by	by	ADP
ejpam-7020	209	2	bridging	bridge	VERB
ejpam-7020	209	3	abstract	abstract	ADJ
ejpam-7020	209	4	theory	theory	NOUN
ejpam-7020	209	5	with	with	ADP
ejpam-7020	209	6	computational	computational	ADJ
ejpam-7020	209	7	practice	practice	NOUN
ejpam-7020	209	8	,	,	PUNCT
ejpam-7020	209	9	this	this	DET
ejpam-7020	209	10	guide	guide	NOUN
ejpam-7020	209	11	fosters	foster	VERB
ejpam-7020	209	12	a	a	DET
ejpam-7020	209	13	deeper	deep	ADJ
ejpam-7020	209	14	and	and	CCONJ
ejpam-7020	209	15	more	more	ADV
ejpam-7020	209	16	intuitive	intuitive	ADJ
ejpam-7020	209	17	understanding	understanding	NOUN
ejpam-7020	209	18	of	of	ADP
ejpam-7020	209	19	how	how	SCONJ
ejpam-7020	209	20	mathematical	mathematical	ADJ
ejpam-7020	209	21	tools	tool	NOUN
ejpam-7020	209	22	can	can	AUX
ejpam-7020	209	23	be	be	AUX
ejpam-7020	209	24	used	use	VERB
ejpam-7020	209	25	to	to	PART
ejpam-7020	209	26	explore	explore	VERB
ejpam-7020	209	27	complex	complex	ADJ
ejpam-7020	209	28	systems	system	NOUN
ejpam-7020	209	29	in	in	ADP
ejpam-7020	209	30	ecology	ecology	NOUN
ejpam-7020	209	31	,	,	PUNCT
ejpam-7020	209	32	epidemiology	epidemiology	NOUN
ejpam-7020	209	33	,	,	PUNCT
ejpam-7020	209	34	and	and	CCONJ
ejpam-7020	209	35	beyond	beyond	ADP
ejpam-7020	209	36	.	.	PUNCT
ejpam-7020	210	1	future	future	ADJ
ejpam-7020	210	2	work	work	NOUN
ejpam-7020	210	3	could	could	AUX
ejpam-7020	210	4	extend	extend	VERB
ejpam-7020	210	5	this	this	DET
ejpam-7020	210	6	guide	guide	NOUN
ejpam-7020	210	7	to	to	PART
ejpam-7020	210	8	include	include	VERB
ejpam-7020	210	9	bifurcation	bifurcation	NOUN
ejpam-7020	210	10	analysis	analysis	NOUN
ejpam-7020	210	11	,	,	PUNCT
ejpam-7020	210	12	systems	system	NOUN
ejpam-7020	210	13	exhibiting	exhibit	VERB
ejpam-7020	210	14	limit	limit	NOUN
ejpam-7020	210	15	cycles	cycle	NOUN
ejpam-7020	210	16	,	,	PUNCT
ejpam-7020	210	17	stochastic	stochastic	ADJ
ejpam-7020	210	18	effects	effect	NOUN
ejpam-7020	210	19	,	,	PUNCT
ejpam-7020	210	20	or	or	CCONJ
ejpam-7020	210	21	the	the	DET
ejpam-7020	210	22	dynamics	dynamic	NOUN
ejpam-7020	210	23	of	of	ADP
ejpam-7020	210	24	higher	high	ADJ
ejpam-7020	210	25	–	–	PUNCT
ejpam-7020	210	26	dimensional	dimensional	ADJ
ejpam-7020	210	27	models	model	NOUN
ejpam-7020	210	28	.	.	PUNCT
ejpam-7020	211	1	such	such	ADJ
ejpam-7020	211	2	extensions	extension	NOUN
ejpam-7020	211	3	would	would	AUX
ejpam-7020	211	4	further	far	ADV
ejpam-7020	211	5	enrich	enrich	VERB
ejpam-7020	211	6	the	the	DET
ejpam-7020	211	7	study	study	NOUN
ejpam-7020	211	8	of	of	ADP
ejpam-7020	211	9	nonlinear	nonlinear	ADJ
ejpam-7020	211	10	systems	system	NOUN
ejpam-7020	211	11	and	and	CCONJ
ejpam-7020	211	12	broaden	broaden	VERB
ejpam-7020	211	13	the	the	DET
ejpam-7020	211	14	applicability	applicability	NOUN
ejpam-7020	211	15	of	of	ADP
ejpam-7020	211	16	this	this	DET
ejpam-7020	211	17	framework	framework	NOUN
ejpam-7020	211	18	to	to	ADP
ejpam-7020	211	19	more	more	ADV
ejpam-7020	211	20	realistic	realistic	ADJ
ejpam-7020	211	21	scenarios	scenario	NOUN
ejpam-7020	211	22	.	.	PUNCT
ejpam-7020	212	1	references	reference	NOUN
ejpam-7020	212	2	[	[	X
ejpam-7020	212	3	1	1	X
ejpam-7020	212	4	]	]	PUNCT
ejpam-7020	212	5	michael	michael	PROPN
ejpam-7020	212	6	ghil	ghil	PROPN
ejpam-7020	212	7	and	and	CCONJ
ejpam-7020	212	8	denise	denise	PROPN
ejpam-7020	212	9	sciamarella	sciamarella	PROPN
ejpam-7020	212	10	.	.	PUNCT
ejpam-7020	213	1	dynamical	dynamical	ADJ
ejpam-7020	213	2	systems	system	NOUN
ejpam-7020	213	3	,	,	PUNCT
ejpam-7020	213	4	algebraic	algebraic	ADJ
ejpam-7020	213	5	topology	topology	NOUN
ejpam-7020	213	6	and	and	CCONJ
ejpam-7020	213	7	the	the	DET
ejpam-7020	213	8	climate	climate	NOUN
ejpam-7020	213	9	sciences	sciences	PROPN
ejpam-7020	213	10	.	.	PUNCT
ejpam-7020	214	1	nonlinear	nonlinear	ADJ
ejpam-7020	214	2	processes	process	NOUN
ejpam-7020	214	3	in	in	ADP
ejpam-7020	214	4	geophysics	geophysic	NOUN
ejpam-7020	214	5	,	,	PUNCT
ejpam-7020	214	6	30(4):399–434	30(4):399–434	NUM
ejpam-7020	214	7	,	,	PUNCT
ejpam-7020	214	8	2023	2023	NUM
ejpam-7020	214	9	.	.	PUNCT
ejpam-7020	215	1	[	[	X
ejpam-7020	215	2	2	2	NUM
ejpam-7020	215	3	]	]	X
ejpam-7020	215	4	steven	steven	PROPN
ejpam-7020	215	5	h.	h.	PROPN
ejpam-7020	215	6	strogatz	strogatz	PROPN
ejpam-7020	215	7	.	.	PUNCT
ejpam-7020	216	1	nonlinear	nonlinear	ADJ
ejpam-7020	216	2	dynamics	dynamic	NOUN
ejpam-7020	216	3	and	and	CCONJ
ejpam-7020	216	4	chaos	chaos	NOUN
ejpam-7020	216	5	:	:	PUNCT
ejpam-7020	216	6	with	with	ADP
ejpam-7020	216	7	applications	application	NOUN
ejpam-7020	216	8	to	to	ADP
ejpam-7020	216	9	physics	physics	NOUN
ejpam-7020	216	10	,	,	PUNCT
ejpam-7020	216	11	biology	biology	NOUN
ejpam-7020	216	12	,	,	PUNCT
ejpam-7020	216	13	chemistry	chemistry	NOUN
ejpam-7020	216	14	,	,	PUNCT
ejpam-7020	216	15	and	and	CCONJ
ejpam-7020	216	16	engineering	engineering	NOUN
ejpam-7020	216	17	.	.	PUNCT
ejpam-7020	217	1	chapman	chapman	NOUN
ejpam-7020	217	2	and	and	CCONJ
ejpam-7020	217	3	hall	hall	PROPN
ejpam-7020	217	4	/	/	SYM
ejpam-7020	217	5	crc	crc	PROPN
ejpam-7020	217	6	,	,	PUNCT
ejpam-7020	217	7	2024	2024	NUM
ejpam-7020	217	8	.	.	PUNCT
ejpam-7020	218	1	[	[	X
ejpam-7020	218	2	3	3	X
ejpam-7020	218	3	]	]	X
ejpam-7020	218	4	miguel	miguel	PROPN
ejpam-7020	218	5	a.	a.	PROPN
ejpam-7020	218	6	gonzález	gonzález	PROPN
ejpam-7020	218	7	-	-	PUNCT
ejpam-7020	218	8	casado	casado	NOUN
ejpam-7020	218	9	,	,	PUNCT
ejpam-7020	218	10	antônio	antônio	PROPN
ejpam-7020	218	11	s.	s.	PROPN
ejpam-7020	218	12	teixeira	teixeira	PROPN
ejpam-7020	218	13	,	,	PUNCT
ejpam-7020	218	14	and	and	CCONJ
ejpam-7020	218	15	angel	angel	NOUN
ejpam-7020	218	16	sánchez	sánchez	PROPN
ejpam-7020	218	17	.	.	PUNCT
ejpam-7020	218	18	evidence	evidence	NOUN
ejpam-7020	218	19	of	of	ADP
ejpam-7020	218	20	equilibrium	equilibrium	NOUN
ejpam-7020	218	21	dynamics	dynamic	NOUN
ejpam-7020	218	22	in	in	ADP
ejpam-7020	218	23	human	human	ADJ
ejpam-7020	218	24	social	social	ADJ
ejpam-7020	218	25	networks	network	NOUN
ejpam-7020	218	26	evolving	evolve	VERB
ejpam-7020	218	27	in	in	ADP
ejpam-7020	218	28	time	time	NOUN
ejpam-7020	218	29	.	.	PUNCT
ejpam-7020	219	1	communications	communication	NOUN
ejpam-7020	219	2	physics	physics	PROPN
ejpam-7020	219	3	,	,	PUNCT
ejpam-7020	219	4	8(1):227	8(1):227	NUM
ejpam-7020	219	5	,	,	PUNCT
ejpam-7020	219	6	2025	2025	NUM
ejpam-7020	219	7	.	.	PUNCT
ejpam-7020	220	1	[	[	X
ejpam-7020	220	2	4	4	X
ejpam-7020	220	3	]	]	PUNCT
ejpam-7020	220	4	j.	j.	PROPN
ejpam-7020	220	5	huang	huang	PROPN
ejpam-7020	220	6	et	et	PROPN
ejpam-7020	220	7	al	al	PROPN
ejpam-7020	220	8	.	.	PUNCT
ejpam-7020	221	1	an	an	DET
ejpam-7020	221	2	overview	overview	NOUN
ejpam-7020	221	3	of	of	ADP
ejpam-7020	221	4	agent	agent	NOUN
ejpam-7020	221	5	-	-	PUNCT
ejpam-7020	221	6	based	base	VERB
ejpam-7020	221	7	models	model	NOUN
ejpam-7020	221	8	for	for	ADP
ejpam-7020	221	9	transport	transport	NOUN
ejpam-7020	221	10	simulation	simulation	NOUN
ejpam-7020	221	11	and	and	CCONJ
ejpam-7020	221	12	analysis	analysis	NOUN
ejpam-7020	221	13	.	.	PUNCT
ejpam-7020	222	1	journal	journal	NOUN
ejpam-7020	222	2	of	of	ADP
ejpam-7020	222	3	advanced	advanced	ADJ
ejpam-7020	222	4	transportation	transportation	NOUN
ejpam-7020	222	5	,	,	PUNCT
ejpam-7020	222	6	2022(1):1252534	2022(1):1252534	NUM
ejpam-7020	222	7	,	,	PUNCT
ejpam-7020	222	8	2022	2022	NUM
ejpam-7020	222	9	.	.	PUNCT
ejpam-7020	223	1	[	[	X
ejpam-7020	223	2	5	5	X
ejpam-7020	223	3	]	]	PUNCT
ejpam-7020	223	4	s.	s.	PROPN
ejpam-7020	223	5	nardean	nardean	PROPN
ejpam-7020	223	6	,	,	PUNCT
ejpam-7020	223	7	m.	m.	NOUN
ejpam-7020	223	8	ferronato	ferronato	NOUN
ejpam-7020	223	9	,	,	PUNCT
ejpam-7020	223	10	and	and	CCONJ
ejpam-7020	223	11	a.	a.	NOUN
ejpam-7020	223	12	abushaikha	abushaikha	PROPN
ejpam-7020	223	13	.	.	PUNCT
ejpam-7020	224	1	linear	linear	PROPN
ejpam-7020	224	2	solvers	solver	NOUN
ejpam-7020	224	3	for	for	ADP
ejpam-7020	224	4	reservoir	reservoir	PROPN
ejpam-7020	224	5	simulation	simulation	NOUN
ejpam-7020	224	6	problems	problem	NOUN
ejpam-7020	224	7	:	:	PUNCT
ejpam-7020	224	8	an	an	DET
ejpam-7020	224	9	overview	overview	NOUN
ejpam-7020	224	10	and	and	CCONJ
ejpam-7020	224	11	recent	recent	ADJ
ejpam-7020	224	12	developments	development	NOUN
ejpam-7020	224	13	.	.	PUNCT
ejpam-7020	225	1	archives	archive	NOUN
ejpam-7020	225	2	of	of	ADP
ejpam-7020	225	3	computational	computational	ADJ
ejpam-7020	225	4	methods	method	NOUN
ejpam-7020	225	5	in	in	ADP
ejpam-7020	225	6	engineering	engineering	NOUN
ejpam-7020	225	7	,	,	PUNCT
ejpam-7020	225	8	29(6):4341–4378	29(6):4341–4378	PROPN
ejpam-7020	225	9	,	,	PUNCT
ejpam-7020	225	10	2022	2022	NUM
ejpam-7020	225	11	.	.	PUNCT
ejpam-7020	226	1	[	[	X
ejpam-7020	226	2	6	6	NUM
ejpam-7020	226	3	]	]	PUNCT
ejpam-7020	226	4	c.	c.	PROPN
ejpam-7020	226	5	maczka	maczka	PROPN
ejpam-7020	226	6	,	,	PUNCT
ejpam-7020	226	7	s.	s.	PROPN
ejpam-7020	226	8	skurativskyi	skurativskyi	PROPN
ejpam-7020	226	9	,	,	PUNCT
ejpam-7020	226	10	and	and	CCONJ
ejpam-7020	226	11	v.	v.	ADP
ejpam-7020	226	12	vladimirov	vladimirov	PROPN
ejpam-7020	226	13	.	.	PUNCT
ejpam-7020	226	14	study	study	NOUN
ejpam-7020	226	15	of	of	ADP
ejpam-7020	226	16	linear	linear	PROPN
ejpam-7020	226	17	and	and	CCONJ
ejpam-7020	226	18	nonlinear	nonlinear	ADJ
ejpam-7020	226	19	models	model	NOUN
ejpam-7020	226	20	with	with	ADP
ejpam-7020	226	21	mathematica	mathematica	PROPN
ejpam-7020	226	22	.	.	PUNCT
ejpam-7020	227	1	world	world	PROPN
ejpam-7020	227	2	scientific	scientific	ADJ
ejpam-7020	227	3	,	,	PUNCT
ejpam-7020	227	4	2022	2022	NUM
ejpam-7020	227	5	.	.	PUNCT
ejpam-7020	228	1	s.	s.	PROPN
ejpam-7020	228	2	saidat	saidat	PROPN
ejpam-7020	228	3	et	et	PROPN
ejpam-7020	228	4	al	al	PROPN
ejpam-7020	228	5	.	.	PUNCT
ejpam-7020	228	6	/	/	SYM
ejpam-7020	228	7	eur	eur	PROPN
ejpam-7020	228	8	.	.	PUNCT
ejpam-7020	229	1	j.	j.	PROPN
ejpam-7020	229	2	pure	pure	PROPN
ejpam-7020	229	3	appl	appl	PROPN
ejpam-7020	229	4	.	.	PROPN
ejpam-7020	229	5	math	math	PROPN
ejpam-7020	229	6	,	,	PUNCT
ejpam-7020	229	7	18	18	NUM
ejpam-7020	229	8	(	(	PUNCT
ejpam-7020	229	9	4	4	NUM
ejpam-7020	229	10	)	)	PUNCT
ejpam-7020	229	11	(	(	PUNCT
ejpam-7020	229	12	2025	2025	NUM
ejpam-7020	229	13	)	)	PUNCT
ejpam-7020	229	14	,	,	PUNCT
ejpam-7020	229	15	7020	7020	NUM
ejpam-7020	229	16	14	14	NUM
ejpam-7020	229	17	of	of	ADP
ejpam-7020	229	18	16	16	NUM
ejpam-7020	230	1	[	[	X
ejpam-7020	230	2	7	7	X
ejpam-7020	230	3	]	]	X
ejpam-7020	231	1	h.	h.	PROPN
ejpam-7020	231	2	oersted	oerste	VERB
ejpam-7020	231	3	and	and	CCONJ
ejpam-7020	231	4	y.	y.	PROPN
ejpam-7020	231	5	ma	ma	PROPN
ejpam-7020	231	6	.	.	PROPN
ejpam-7020	232	1	geometric	geometric	ADJ
ejpam-7020	232	2	and	and	CCONJ
ejpam-7020	232	3	feedback	feedback	NOUN
ejpam-7020	232	4	linearization	linearization	NOUN
ejpam-7020	232	5	on	on	ADP
ejpam-7020	232	6	uav	uav	PROPN
ejpam-7020	232	7	,	,	PUNCT
ejpam-7020	232	8	2023	2023	NUM
ejpam-7020	232	9	.	.	PUNCT
ejpam-7020	233	1	arxiv	arxiv	PROPN
ejpam-7020	233	2	preprint	preprint	VERB
ejpam-7020	233	3	arxiv:2311.06784	arxiv:2311.06784	NOUN
ejpam-7020	233	4	.	.	PUNCT
ejpam-7020	234	1	[	[	X
ejpam-7020	234	2	8	8	X
ejpam-7020	234	3	]	]	PUNCT
ejpam-7020	234	4	j.	j.	PROPN
ejpam-7020	234	5	d.	d.	PROPN
ejpam-7020	234	6	davis	davis	PROPN
ejpam-7020	234	7	et	et	PROPN
ejpam-7020	234	8	al	al	PROPN
ejpam-7020	234	9	.	.	PUNCT
ejpam-7020	234	10	methods	method	NOUN
ejpam-7020	234	11	of	of	ADP
ejpam-7020	234	12	quantifying	quantify	VERB
ejpam-7020	234	13	interactions	interaction	NOUN
ejpam-7020	234	14	among	among	ADP
ejpam-7020	234	15	populations	population	NOUN
ejpam-7020	234	16	using	use	VERB
ejpam-7020	234	17	lotka	lotka	PROPN
ejpam-7020	234	18	–	–	PUNCT
ejpam-7020	234	19	volterra	volterra	NOUN
ejpam-7020	234	20	models	model	NOUN
ejpam-7020	234	21	.	.	PUNCT
ejpam-7020	235	1	frontiers	frontier	NOUN
ejpam-7020	235	2	in	in	ADP
ejpam-7020	235	3	systems	system	NOUN
ejpam-7020	235	4	biology	biology	NOUN
ejpam-7020	235	5	,	,	PUNCT
ejpam-7020	235	6	2:1021897	2:1021897	NUM
ejpam-7020	235	7	,	,	PUNCT
ejpam-7020	235	8	2022	2022	NUM
ejpam-7020	235	9	.	.	PUNCT
ejpam-7020	236	1	[	[	X
ejpam-7020	236	2	9	9	NUM
ejpam-7020	236	3	]	]	PUNCT
ejpam-7020	236	4	m.	m.	NOUN
ejpam-7020	236	5	mahmoudi	mahmoudi	NOUN
ejpam-7020	236	6	and	and	CCONJ
ejpam-7020	236	7	z.	z.	PROPN
ejpam-7020	236	8	eskandari	eskandari	PROPN
ejpam-7020	236	9	.	.	PUNCT
ejpam-7020	237	1	fractional	fractional	ADJ
ejpam-7020	237	2	calculus	calculus	NOUN
ejpam-7020	237	3	in	in	ADP
ejpam-7020	237	4	ecological	ecological	ADJ
ejpam-7020	237	5	systems	system	NOUN
ejpam-7020	237	6	:	:	PUNCT
ejpam-7020	237	7	bifurcation	bifurcation	NOUN
ejpam-7020	237	8	analysis	analysis	NOUN
ejpam-7020	237	9	and	and	CCONJ
ejpam-7020	237	10	continuation	continuation	NOUN
ejpam-7020	237	11	techniques	technique	NOUN
ejpam-7020	237	12	for	for	ADP
ejpam-7020	237	13	discrete	discrete	ADJ
ejpam-7020	237	14	lotka	lotka	PROPN
ejpam-7020	237	15	–	–	PUNCT
ejpam-7020	237	16	volterra	volterra	NOUN
ejpam-7020	237	17	models	model	NOUN
ejpam-7020	237	18	.	.	PUNCT
ejpam-7020	238	1	mathematical	mathematical	ADJ
ejpam-7020	238	2	methods	method	NOUN
ejpam-7020	238	3	in	in	ADP
ejpam-7020	238	4	the	the	DET
ejpam-7020	238	5	applied	apply	VERB
ejpam-7020	238	6	sciences	science	NOUN
ejpam-7020	238	7	,	,	PUNCT
ejpam-7020	238	8	2024	2024	NUM
ejpam-7020	238	9	.	.	PUNCT
ejpam-7020	239	1	[	[	X
ejpam-7020	239	2	10	10	NUM
ejpam-7020	239	3	]	]	PUNCT
ejpam-7020	239	4	j.	j.	PROPN
ejpam-7020	239	5	huang	huang	PROPN
ejpam-7020	239	6	and	and	CCONJ
ejpam-7020	239	7	j.	j.	PROPN
ejpam-7020	239	8	s.	s.	PROPN
ejpam-7020	239	9	morris	morris	PROPN
ejpam-7020	239	10	.	.	PROPN
ejpam-7020	239	11	infectious	infectious	ADJ
ejpam-7020	239	12	disease	disease	NOUN
ejpam-7020	239	13	modeling	modeling	NOUN
ejpam-7020	239	14	.	.	PUNCT
ejpam-7020	240	1	annual	annual	ADJ
ejpam-7020	240	2	review	review	NOUN
ejpam-7020	240	3	of	of	ADP
ejpam-7020	240	4	statistics	statistic	NOUN
ejpam-7020	240	5	and	and	CCONJ
ejpam-7020	240	6	its	its	PRON
ejpam-7020	240	7	application	application	NOUN
ejpam-7020	240	8	,	,	PUNCT
ejpam-7020	240	9	12	12	NUM
ejpam-7020	240	10	,	,	PUNCT
ejpam-7020	240	11	2024	2024	NUM
ejpam-7020	240	12	.	.	PUNCT
ejpam-7020	241	1	[	[	X
ejpam-7020	241	2	11	11	NUM
ejpam-7020	241	3	]	]	X
ejpam-7020	241	4	s.	s.	PROPN
ejpam-7020	241	5	peddinti	peddinti	PROPN
ejpam-7020	241	6	and	and	CCONJ
ejpam-7020	241	7	y.	y.	PROPN
ejpam-7020	241	8	sabbani	sabbani	PROPN
ejpam-7020	241	9	.	.	PUNCT
ejpam-7020	242	1	mathematical	mathematical	ADJ
ejpam-7020	242	2	modeling	modeling	NOUN
ejpam-7020	242	3	of	of	ADP
ejpam-7020	242	4	infectious	infectious	ADJ
ejpam-7020	242	5	disease	disease	NOUN
ejpam-7020	242	6	spread	spread	VERB
ejpam-7020	242	7	using	use	VERB
ejpam-7020	242	8	differential	differential	ADJ
ejpam-7020	242	9	equations	equation	NOUN
ejpam-7020	242	10	and	and	CCONJ
ejpam-7020	242	11	epidemiological	epidemiological	ADJ
ejpam-7020	242	12	insights	insight	NOUN
ejpam-7020	242	13	.	.	PUNCT
ejpam-7020	243	1	journal	journal	PROPN
ejpam-7020	243	2	of	of	ADP
ejpam-7020	243	3	nonlinear	nonlinear	ADJ
ejpam-7020	243	4	analysis	analysis	NOUN
ejpam-7020	243	5	and	and	CCONJ
ejpam-7020	243	6	optimization	optimization	NOUN
ejpam-7020	243	7	,	,	PUNCT
ejpam-7020	243	8	15:114–122	15:114–122	PROPN
ejpam-7020	243	9	,	,	PUNCT
ejpam-7020	243	10	2024	2024	NUM
ejpam-7020	243	11	.	.	PUNCT
ejpam-7020	244	1	[	[	X
ejpam-7020	244	2	12	12	NUM
ejpam-7020	244	3	]	]	X
ejpam-7020	244	4	d.	d.	PROPN
ejpam-7020	244	5	ahmed	ahmed	PROPN
ejpam-7020	244	6	,	,	PUNCT
ejpam-7020	244	7	f.	f.	PROPN
ejpam-7020	244	8	roshayanti	roshayanti	PROPN
ejpam-7020	244	9	,	,	PUNCT
ejpam-7020	244	10	and	and	CCONJ
ejpam-7020	244	11	m.	m.	NOUN
ejpam-7020	244	12	novita	novita	PROPN
ejpam-7020	244	13	.	.	PUNCT
ejpam-7020	245	1	applying	apply	VERB
ejpam-7020	245	2	matlab	matlab	PROPN
ejpam-7020	245	3	to	to	PART
ejpam-7020	245	4	visualize	visualize	VERB
ejpam-7020	245	5	college	college	NOUN
ejpam-7020	245	6	physics	physics	NOUN
ejpam-7020	245	7	concepts	concept	NOUN
ejpam-7020	245	8	and	and	CCONJ
ejpam-7020	245	9	enhance	enhance	VERB
ejpam-7020	245	10	student	student	NOUN
ejpam-7020	245	11	understanding	understanding	NOUN
ejpam-7020	245	12	.	.	PUNCT
ejpam-7020	246	1	international	international	ADJ
ejpam-7020	246	2	journal	journal	NOUN
ejpam-7020	246	3	of	of	ADP
ejpam-7020	246	4	innovative	innovative	ADJ
ejpam-7020	246	5	science	science	NOUN
ejpam-7020	246	6	,	,	PUNCT
ejpam-7020	246	7	engineering	engineering	NOUN
ejpam-7020	246	8	and	and	CCONJ
ejpam-7020	246	9	technology	technology	NOUN
ejpam-7020	246	10	,	,	PUNCT
ejpam-7020	246	11	11(12):52–60	11(12):52–60	NUM
ejpam-7020	246	12	,	,	PUNCT
ejpam-7020	246	13	2024	2024	NUM
ejpam-7020	246	14	.	.	PUNCT
ejpam-7020	247	1	[	[	X
ejpam-7020	247	2	13	13	NUM
ejpam-7020	247	3	]	]	X
ejpam-7020	247	4	s.	s.	PROPN
ejpam-7020	247	5	niazai	niazai	PROPN
ejpam-7020	247	6	,	,	PUNCT
ejpam-7020	247	7	a.	a.	NOUN
ejpam-7020	247	8	a.	a.	NOUN
ejpam-7020	247	9	rahimzai	rahimzai	PROPN
ejpam-7020	247	10	,	,	PUNCT
ejpam-7020	247	11	and	and	CCONJ
ejpam-7020	247	12	h.	h.	PROPN
ejpam-7020	247	13	atifnigar	atifnigar	PROPN
ejpam-7020	247	14	.	.	PUNCT
ejpam-7020	248	1	applications	application	NOUN
ejpam-7020	248	2	of	of	ADP
ejpam-7020	248	3	matlab	matlab	PROPN
ejpam-7020	248	4	in	in	ADP
ejpam-7020	248	5	natural	natural	ADJ
ejpam-7020	248	6	sciences	science	NOUN
ejpam-7020	248	7	:	:	PUNCT
ejpam-7020	248	8	a	a	DET
ejpam-7020	248	9	comprehensive	comprehensive	ADJ
ejpam-7020	248	10	review	review	NOUN
ejpam-7020	248	11	.	.	PUNCT
ejpam-7020	249	1	european	european	PROPN
ejpam-7020	249	2	journal	journal	PROPN
ejpam-7020	249	3	of	of	ADP
ejpam-7020	249	4	theoretical	theoretical	ADJ
ejpam-7020	249	5	and	and	CCONJ
ejpam-7020	249	6	applied	apply	VERB
ejpam-7020	249	7	sciences	science	NOUN
ejpam-7020	249	8	,	,	PUNCT
ejpam-7020	249	9	1(5):1006–1015	1(5):1006–1015	PROPN
ejpam-7020	249	10	,	,	PUNCT
ejpam-7020	249	11	2023	2023	NUM
ejpam-7020	249	12	.	.	PUNCT
ejpam-7020	250	1	[	[	X
ejpam-7020	250	2	14	14	NUM
ejpam-7020	250	3	]	]	PUNCT
ejpam-7020	250	4	a.	a.	NOUN
ejpam-7020	250	5	abbas	abbas	PROPN
ejpam-7020	250	6	.	.	PUNCT
ejpam-7020	251	1	mathematical	mathematical	ADJ
ejpam-7020	251	2	modeling	modeling	NOUN
ejpam-7020	251	3	and	and	CCONJ
ejpam-7020	251	4	qualitative	qualitative	ADJ
ejpam-7020	251	5	analysis	analysis	NOUN
ejpam-7020	251	6	of	of	ADP
ejpam-7020	251	7	dynamical	dynamical	ADJ
ejpam-7020	251	8	systems	system	NOUN
ejpam-7020	251	9	.	.	PUNCT
ejpam-7020	252	1	2025	2025	NUM
ejpam-7020	252	2	.	.	PUNCT
ejpam-7020	253	1	[	[	X
ejpam-7020	253	2	15	15	NUM
ejpam-7020	253	3	]	]	X
ejpam-7020	253	4	d.	d.	PROPN
ejpam-7020	253	5	krawczyk	krawczyk	PROPN
ejpam-7020	253	6	,	,	PUNCT
ejpam-7020	253	7	s.	s.	PROPN
ejpam-7020	253	8	kolomiiets	kolomiiets	PROPN
ejpam-7020	253	9	,	,	PUNCT
ejpam-7020	253	10	and	and	CCONJ
ejpam-7020	253	11	y.	y.	PROPN
ejpam-7020	253	12	chvankin	chvankin	PROPN
ejpam-7020	253	13	.	.	PUNCT
ejpam-7020	254	1	nonlinear	nonlinear	ADJ
ejpam-7020	254	2	models	model	NOUN
ejpam-7020	254	3	of	of	ADP
ejpam-7020	254	4	economic	economic	ADJ
ejpam-7020	254	5	dynamics	dynamic	NOUN
ejpam-7020	254	6	as	as	ADP
ejpam-7020	254	7	a	a	DET
ejpam-7020	254	8	tool	tool	NOUN
ejpam-7020	254	9	for	for	ADP
ejpam-7020	254	10	public	public	ADJ
ejpam-7020	254	11	health	health	NOUN
ejpam-7020	254	12	research	research	NOUN
ejpam-7020	254	13	.	.	PUNCT
ejpam-7020	255	1	health	health	NOUN
ejpam-7020	255	2	economics	economic	NOUN
ejpam-7020	255	3	and	and	CCONJ
ejpam-7020	255	4	management	management	NOUN
ejpam-7020	255	5	review	review	NOUN
ejpam-7020	255	6	,	,	PUNCT
ejpam-7020	255	7	6(1):179–196	6(1):179–196	NUM
ejpam-7020	255	8	,	,	PUNCT
ejpam-7020	255	9	2025	2025	NUM
ejpam-7020	255	10	.	.	PUNCT
ejpam-7020	256	1	[	[	X
ejpam-7020	256	2	16	16	NUM
ejpam-7020	256	3	]	]	PUNCT
ejpam-7020	256	4	b.	b.	PROPN
ejpam-7020	256	5	müller	müller	PROPN
ejpam-7020	256	6	.	.	PUNCT
ejpam-7020	257	1	stability	stability	NOUN
ejpam-7020	257	2	of	of	ADP
ejpam-7020	257	3	linear	linear	PROPN
ejpam-7020	257	4	dynamical	dynamical	ADJ
ejpam-7020	257	5	systems	system	NOUN
ejpam-7020	257	6	and	and	CCONJ
ejpam-7020	257	7	application	application	NOUN
ejpam-7020	257	8	to	to	ADP
ejpam-7020	257	9	lotka	lotka	PROPN
ejpam-7020	257	10	–	–	PUNCT
ejpam-7020	257	11	volterra	volterra	NOUN
ejpam-7020	257	12	equations	equation	NOUN
ejpam-7020	257	13	and	and	CCONJ
ejpam-7020	257	14	epidemiology	epidemiology	NOUN
ejpam-7020	257	15	,	,	PUNCT
ejpam-7020	257	16	2021	2021	NUM
ejpam-7020	257	17	.	.	PUNCT
ejpam-7020	258	1	[	[	X
ejpam-7020	258	2	17	17	NUM
ejpam-7020	258	3	]	]	X
ejpam-7020	258	4	r.	r.	PROPN
ejpam-7020	258	5	ganikhodzhaev	ganikhodzhaev	PROPN
ejpam-7020	258	6	et	et	PROPN
ejpam-7020	258	7	al	al	PROPN
ejpam-7020	258	8	.	.	PUNCT
ejpam-7020	259	1	some	some	DET
ejpam-7020	259	2	degenerate	degenerate	ADJ
ejpam-7020	259	3	cases	case	NOUN
ejpam-7020	259	4	of	of	ADP
ejpam-7020	259	5	discrete	discrete	ADJ
ejpam-7020	259	6	lotka	lotka	PROPN
ejpam-7020	259	7	–	–	PUNCT
ejpam-7020	259	8	volterra	volterra	NOUN
ejpam-7020	259	9	dynamical	dynamical	ADJ
ejpam-7020	259	10	systems	system	NOUN
ejpam-7020	259	11	and	and	CCONJ
ejpam-7020	259	12	their	their	PRON
ejpam-7020	259	13	applications	application	NOUN
ejpam-7020	259	14	in	in	ADP
ejpam-7020	259	15	epidemiology	epidemiology	NOUN
ejpam-7020	259	16	.	.	PUNCT
ejpam-7020	260	1	journal	journal	PROPN
ejpam-7020	260	2	of	of	ADP
ejpam-7020	260	3	mathematical	mathematical	ADJ
ejpam-7020	260	4	sciences	science	NOUN
ejpam-7020	260	5	,	,	PUNCT
ejpam-7020	260	6	pages	page	NOUN
ejpam-7020	260	7	1–15	1–15	PROPN
ejpam-7020	260	8	,	,	PUNCT
ejpam-7020	260	9	2024	2024	NUM
ejpam-7020	260	10	.	.	PUNCT
ejpam-7020	261	1	[	[	X
ejpam-7020	261	2	18	18	NUM
ejpam-7020	261	3	]	]	PUNCT
ejpam-7020	261	4	h.-g	h.-g	PROPN
ejpam-7020	261	5	.	.	PUNCT
ejpam-7020	262	1	lee	lee	PROPN
ejpam-7020	262	2	.	.	PROPN
ejpam-7020	262	3	linearization	linearization	PROPN
ejpam-7020	262	4	of	of	ADP
ejpam-7020	262	5	nonlinear	nonlinear	ADJ
ejpam-7020	262	6	control	control	PROPN
ejpam-7020	262	7	systems	system	NOUN
ejpam-7020	262	8	.	.	PUNCT
ejpam-7020	263	1	springer	springer	NOUN
ejpam-7020	263	2	,	,	PUNCT
ejpam-7020	263	3	2022	2022	NUM
ejpam-7020	263	4	.	.	PUNCT
ejpam-7020	264	1	[	[	X
ejpam-7020	264	2	19	19	NUM
ejpam-7020	264	3	]	]	PUNCT
ejpam-7020	264	4	j.	j.	PROPN
ejpam-7020	264	5	dagar	dagar	PROPN
ejpam-7020	264	6	.	.	PUNCT
ejpam-7020	265	1	applications	application	NOUN
ejpam-7020	265	2	of	of	ADP
ejpam-7020	265	3	linear	linear	PROPN
ejpam-7020	265	4	algebraic	algebraic	ADJ
ejpam-7020	265	5	equations	equation	NOUN
ejpam-7020	265	6	in	in	ADP
ejpam-7020	265	7	engineering	engineering	NOUN
ejpam-7020	265	8	systems	system	NOUN
ejpam-7020	265	9	:	:	PUNCT
ejpam-7020	265	10	a	a	DET
ejpam-7020	265	11	comprehensive	comprehensive	ADJ
ejpam-7020	265	12	study	study	NOUN
ejpam-7020	265	13	,	,	PUNCT
ejpam-7020	265	14	2024	2024	NUM
ejpam-7020	265	15	.	.	PUNCT
ejpam-7020	266	1	[	[	X
ejpam-7020	266	2	20	20	NUM
ejpam-7020	266	3	]	]	PUNCT
ejpam-7020	266	4	s.	s.	PROPN
ejpam-7020	266	5	saeedinia	saeedinia	PROPN
ejpam-7020	266	6	.	.	PUNCT
ejpam-7020	267	1	extending	extend	VERB
ejpam-7020	267	2	jacobian	jacobian	ADJ
ejpam-7020	267	3	matrix	matrix	NOUN
ejpam-7020	267	4	in	in	ADP
ejpam-7020	267	5	proving	prove	VERB
ejpam-7020	267	6	stability	stability	NOUN
ejpam-7020	267	7	for	for	ADP
ejpam-7020	267	8	nonlinear	nonlinear	ADJ
ejpam-7020	267	9	systems	system	NOUN
ejpam-7020	267	10	with	with	ADP
ejpam-7020	267	11	one	one	NUM
ejpam-7020	267	12	equilibrium	equilibrium	NOUN
ejpam-7020	267	13	point	point	NOUN
ejpam-7020	267	14	such	such	ADJ
ejpam-7020	267	15	as	as	ADP
ejpam-7020	267	16	compressor	compressor	NOUN
ejpam-7020	267	17	,	,	PUNCT
ejpam-7020	267	18	2024	2024	NUM
ejpam-7020	267	19	.	.	PUNCT
ejpam-7020	268	1	arxiv	arxiv	PROPN
ejpam-7020	268	2	preprint	preprint	VERB
ejpam-7020	268	3	arxiv:2410.22191	arxiv:2410.22191	PROPN
ejpam-7020	268	4	.	.	PUNCT
ejpam-7020	269	1	[	[	X
ejpam-7020	269	2	21	21	NUM
ejpam-7020	269	3	]	]	X
ejpam-7020	269	4	shadi	shadi	PROPN
ejpam-7020	269	5	al	al	PROPN
ejpam-7020	269	6	-	-	PUNCT
ejpam-7020	269	7	ahmad	ahmad	PROPN
ejpam-7020	269	8	,	,	PUNCT
ejpam-7020	269	9	mustafa	mustafa	PROPN
ejpam-7020	269	10	mamat	mamat	PROPN
ejpam-7020	269	11	,	,	PUNCT
ejpam-7020	269	12	nidal	nidal	PROPN
ejpam-7020	269	13	anakira	anakira	PROPN
ejpam-7020	269	14	,	,	PUNCT
ejpam-7020	269	15	and	and	CCONJ
ejpam-7020	269	16	rami	rami	PROPN
ejpam-7020	269	17	alahmad	alahmad	PROPN
ejpam-7020	269	18	.	.	PUNCT
ejpam-7020	270	1	modified	modify	VERB
ejpam-7020	270	2	differential	differential	ADJ
ejpam-7020	270	3	transformation	transformation	NOUN
ejpam-7020	270	4	method	method	NOUN
ejpam-7020	270	5	for	for	ADP
ejpam-7020	270	6	solving	solve	VERB
ejpam-7020	270	7	classes	class	NOUN
ejpam-7020	270	8	of	of	ADP
ejpam-7020	270	9	non	non	ADJ
ejpam-7020	270	10	-	-	ADJ
ejpam-7020	270	11	linear	linear	ADJ
ejpam-7020	270	12	differential	differential	ADJ
ejpam-7020	270	13	equations	equation	NOUN
ejpam-7020	270	14	.	.	PUNCT
ejpam-7020	271	1	twms	twms	PROPN
ejpam-7020	271	2	journal	journal	PROPN
ejpam-7020	271	3	of	of	ADP
ejpam-7020	271	4	applied	apply	VERB
ejpam-7020	271	5	and	and	CCONJ
ejpam-7020	271	6	engineering	engineering	NOUN
ejpam-7020	271	7	mathematics	mathematic	NOUN
ejpam-7020	271	8	,	,	PUNCT
ejpam-7020	271	9	2022	2022	NUM
ejpam-7020	271	10	.	.	PUNCT
ejpam-7020	272	1	[	[	X
ejpam-7020	272	2	22	22	NUM
ejpam-7020	272	3	]	]	X
ejpam-7020	272	4	y.	y.	PROPN
ejpam-7020	272	5	al	al	PROPN
ejpam-7020	272	6	-	-	PUNCT
ejpam-7020	272	7	qudah	qudah	PROPN
ejpam-7020	272	8	,	,	PUNCT
ejpam-7020	272	9	f.	f.	PROPN
ejpam-7020	272	10	al	al	PROPN
ejpam-7020	272	11	-	-	PUNCT
ejpam-7020	272	12	sharqi	sharqi	PROPN
ejpam-7020	272	13	,	,	PUNCT
ejpam-7020	272	14	m.	m.	NOUN
ejpam-7020	272	15	mishlish	mishlish	NOUN
ejpam-7020	272	16	,	,	PUNCT
ejpam-7020	272	17	and	and	CCONJ
ejpam-7020	272	18	m.	m.	NOUN
ejpam-7020	272	19	m.	m.	PROPN
ejpam-7020	272	20	rasheed	rasheed	PROPN
ejpam-7020	272	21	.	.	PUNCT
ejpam-7020	272	22	hybrid	hybrid	ADJ
ejpam-7020	272	23	integrated	integrate	VERB
ejpam-7020	272	24	decision	decision	NOUN
ejpam-7020	272	25	-	-	PUNCT
ejpam-7020	272	26	making	make	VERB
ejpam-7020	272	27	algorithm	algorithm	NOUN
ejpam-7020	272	28	based	base	VERB
ejpam-7020	272	29	on	on	ADP
ejpam-7020	272	30	ao	ao	PROPN
ejpam-7020	272	31	of	of	ADP
ejpam-7020	272	32	possibility	possibility	NOUN
ejpam-7020	272	33	interval	interval	NOUN
ejpam-7020	272	34	-	-	PUNCT
ejpam-7020	272	35	valued	value	VERB
ejpam-7020	272	36	neutrosophic	neutrosophic	ADJ
ejpam-7020	272	37	soft	soft	ADJ
ejpam-7020	272	38	settings	setting	NOUN
ejpam-7020	272	39	.	.	PUNCT
ejpam-7020	273	1	international	international	ADJ
ejpam-7020	273	2	journal	journal	PROPN
ejpam-7020	273	3	of	of	ADP
ejpam-7020	273	4	neutrosophic	neutrosophic	ADJ
ejpam-7020	273	5	science	science	NOUN
ejpam-7020	273	6	,	,	PUNCT
ejpam-7020	273	7	22(3):84–98	22(3):84–98	NUM
ejpam-7020	273	8	,	,	PUNCT
ejpam-7020	273	9	2023	2023	NUM
ejpam-7020	273	10	.	.	PUNCT
ejpam-7020	274	1	[	[	X
ejpam-7020	274	2	23	23	NUM
ejpam-7020	274	3	]	]	X
ejpam-7020	274	4	y.	y.	PROPN
ejpam-7020	274	5	al	al	PROPN
ejpam-7020	274	6	-	-	PUNCT
ejpam-7020	274	7	qudah	qudah	PROPN
ejpam-7020	274	8	,	,	PUNCT
ejpam-7020	274	9	k.	k.	PROPN
ejpam-7020	274	10	alhazaymeh	alhazaymeh	PROPN
ejpam-7020	274	11	,	,	PUNCT
ejpam-7020	274	12	n.	n.	PROPN
ejpam-7020	274	13	hassan	hassan	PROPN
ejpam-7020	274	14	,	,	PUNCT
ejpam-7020	274	15	m.	m.	NOUN
ejpam-7020	274	16	almousa	almousa	NOUN
ejpam-7020	274	17	,	,	PUNCT
ejpam-7020	274	18	and	and	CCONJ
ejpam-7020	274	19	m.	m.	NOUN
ejpam-7020	274	20	alaroud	alaroud	PROPN
ejpam-7020	274	21	.	.	PUNCT
ejpam-7020	275	1	transitive	transitive	ADJ
ejpam-7020	275	2	closure	closure	NOUN
ejpam-7020	275	3	of	of	ADP
ejpam-7020	275	4	vague	vague	ADJ
ejpam-7020	275	5	soft	soft	ADJ
ejpam-7020	275	6	set	set	NOUN
ejpam-7020	275	7	relations	relation	NOUN
ejpam-7020	275	8	and	and	CCONJ
ejpam-7020	275	9	its	its	PRON
ejpam-7020	275	10	operators	operator	NOUN
ejpam-7020	275	11	.	.	PUNCT
ejpam-7020	276	1	international	international	ADJ
ejpam-7020	276	2	journal	journal	NOUN
ejpam-7020	276	3	of	of	ADP
ejpam-7020	276	4	fuzzy	fuzzy	ADJ
ejpam-7020	276	5	logic	logic	NOUN
ejpam-7020	276	6	and	and	CCONJ
ejpam-7020	276	7	intelligent	intelligent	ADJ
ejpam-7020	276	8	systems	system	NOUN
ejpam-7020	276	9	,	,	PUNCT
ejpam-7020	276	10	22(1):59–68	22(1):59–68	NUM
ejpam-7020	276	11	,	,	PUNCT
ejpam-7020	276	12	2022	2022	NUM
ejpam-7020	276	13	.	.	PUNCT
ejpam-7020	277	1	s.	s.	PROPN
ejpam-7020	277	2	saidat	saidat	PROPN
ejpam-7020	277	3	et	et	PROPN
ejpam-7020	277	4	al	al	PROPN
ejpam-7020	277	5	.	.	PUNCT
ejpam-7020	277	6	/	/	SYM
ejpam-7020	277	7	eur	eur	PROPN
ejpam-7020	277	8	.	.	PUNCT
ejpam-7020	278	1	j.	j.	PROPN
ejpam-7020	278	2	pure	pure	PROPN
ejpam-7020	278	3	appl	appl	PROPN
ejpam-7020	278	4	.	.	PROPN
ejpam-7020	278	5	math	math	PROPN
ejpam-7020	278	6	,	,	PUNCT
ejpam-7020	278	7	18	18	NUM
ejpam-7020	278	8	(	(	PUNCT
ejpam-7020	278	9	4	4	NUM
ejpam-7020	278	10	)	)	PUNCT
ejpam-7020	278	11	(	(	PUNCT
ejpam-7020	278	12	2025	2025	NUM
ejpam-7020	278	13	)	)	PUNCT
ejpam-7020	278	14	,	,	PUNCT
ejpam-7020	278	15	7020	7020	NUM
ejpam-7020	278	16	15	15	NUM
ejpam-7020	278	17	of	of	ADP
ejpam-7020	278	18	16	16	NUM
ejpam-7020	278	19	[	[	X
ejpam-7020	278	20	24	24	NUM
ejpam-7020	278	21	]	]	X
ejpam-7020	278	22	y.	y.	PROPN
ejpam-7020	278	23	al	al	PROPN
ejpam-7020	278	24	-	-	PUNCT
ejpam-7020	278	25	shorman	shorman	PROPN
ejpam-7020	278	26	,	,	PUNCT
ejpam-7020	278	27	a.	a.	NOUN
ejpam-7020	278	28	alsoboh	alsoboh	PROPN
ejpam-7020	278	29	,	,	PUNCT
ejpam-7020	278	30	obadah	obadah	PROPN
ejpam-7020	278	31	s.	s.	PROPN
ejpam-7020	278	32	solaiman	solaiman	PROPN
ejpam-7020	278	33	,	,	PUNCT
ejpam-7020	278	34	and	and	CCONJ
ejpam-7020	278	35	i.	i.	PROPN
ejpam-7020	278	36	hashim	hashim	PROPN
ejpam-7020	278	37	.	.	PUNCT
ejpam-7020	279	1	derivative	derivative	ADJ
ejpam-7020	279	2	-	-	PUNCT
ejpam-7020	279	3	free	free	ADJ
ejpam-7020	279	4	method	method	NOUN
ejpam-7020	279	5	for	for	ADP
ejpam-7020	279	6	nonlinear	nonlinear	ADJ
ejpam-7020	279	7	systems	system	NOUN
ejpam-7020	279	8	with	with	ADP
ejpam-7020	279	9	some	some	DET
ejpam-7020	279	10	real	real	ADJ
ejpam-7020	279	11	-	-	PUNCT
ejpam-7020	279	12	life	life	NOUN
ejpam-7020	279	13	applications	application	NOUN
ejpam-7020	279	14	.	.	PUNCT
ejpam-7020	280	1	european	european	ADJ
ejpam-7020	280	2	journal	journal	PROPN
ejpam-7020	280	3	of	of	ADP
ejpam-7020	280	4	pure	pure	ADJ
ejpam-7020	280	5	and	and	CCONJ
ejpam-7020	280	6	applied	applied	ADJ
ejpam-7020	280	7	mathematics	mathematic	NOUN
ejpam-7020	280	8	,	,	PUNCT
ejpam-7020	280	9	18(3):6262	18(3):6262	NUM
ejpam-7020	280	10	,	,	PUNCT
ejpam-7020	280	11	2025	2025	NUM
ejpam-7020	280	12	.	.	PUNCT
ejpam-7020	281	1	[	[	X
ejpam-7020	281	2	25	25	NUM
ejpam-7020	281	3	]	]	PUNCT
ejpam-7020	281	4	a.	a.	NOUN
ejpam-7020	281	5	alsoboh	alsoboh	PROPN
ejpam-7020	281	6	,	,	PUNCT
ejpam-7020	281	7	a.	a.	PROPN
ejpam-7020	281	8	amourah	amourah	PROPN
ejpam-7020	281	9	,	,	PUNCT
ejpam-7020	281	10	m.	m.	NOUN
ejpam-7020	281	11	darus	darus	NOUN
ejpam-7020	281	12	,	,	PUNCT
ejpam-7020	281	13	and	and	CCONJ
ejpam-7020	281	14	c.	c.	PROPN
ejpam-7020	281	15	a.	a.	NOUN
ejpam-7020	281	16	rudder	rudder	NOUN
ejpam-7020	281	17	.	.	PUNCT
ejpam-7020	282	1	studying	study	VERB
ejpam-7020	282	2	the	the	DET
ejpam-7020	282	3	harmonic	harmonic	ADJ
ejpam-7020	282	4	functions	function	NOUN
ejpam-7020	282	5	associated	associate	VERB
ejpam-7020	282	6	with	with	ADP
ejpam-7020	282	7	quantum	quantum	NOUN
ejpam-7020	282	8	calculus	calculus	NOUN
ejpam-7020	282	9	.	.	PUNCT
ejpam-7020	283	1	mathematics	mathematic	NOUN
ejpam-7020	283	2	,	,	PUNCT
ejpam-7020	283	3	11(10):2220	11(10):2220	NUM
ejpam-7020	283	4	,	,	PUNCT
ejpam-7020	283	5	2023	2023	NUM
ejpam-7020	283	6	.	.	PUNCT
ejpam-7020	284	1	[	[	X
ejpam-7020	284	2	26	26	NUM
ejpam-7020	284	3	]	]	X
ejpam-7020	284	4	abdullah	abdullah	PROPN
ejpam-7020	284	5	alsoboh	alsoboh	PROPN
ejpam-7020	284	6	,	,	PUNCT
ejpam-7020	284	7	ala	ala	PROPN
ejpam-7020	284	8	amourah	amourah	PROPN
ejpam-7020	284	9	,	,	PUNCT
ejpam-7020	284	10	omar	omar	PROPN
ejpam-7020	284	11	alnajar	alnajar	PROPN
ejpam-7020	284	12	,	,	PUNCT
ejpam-7020	284	13	mamoon	mamoon	NOUN
ejpam-7020	284	14	ahmed	ahmed	PROPN
ejpam-7020	284	15	,	,	PUNCT
ejpam-7020	284	16	and	and	CCONJ
ejpam-7020	284	17	tamer	tame	ADJ
ejpam-7020	284	18	m	m	VERB
ejpam-7020	284	19	seoudy	seoudy	ADJ
ejpam-7020	284	20	.	.	PUNCT
ejpam-7020	285	1	exploring	explore	VERB
ejpam-7020	285	2	q	q	ADJ
ejpam-7020	285	3	-	-	PUNCT
ejpam-7020	285	4	fibonacci	fibonacci	NOUN
ejpam-7020	285	5	numbers	number	NOUN
ejpam-7020	285	6	in	in	ADP
ejpam-7020	285	7	geometric	geometric	ADJ
ejpam-7020	285	8	function	function	NOUN
ejpam-7020	285	9	theory	theory	NOUN
ejpam-7020	285	10	:	:	PUNCT
ejpam-7020	285	11	univalence	univalence	NOUN
ejpam-7020	285	12	and	and	CCONJ
ejpam-7020	285	13	shell	shell	NOUN
ejpam-7020	285	14	-	-	PUNCT
ejpam-7020	285	15	like	like	ADJ
ejpam-7020	285	16	starlike	starlike	NOUN
ejpam-7020	285	17	curves	curve	NOUN
ejpam-7020	285	18	.	.	PUNCT
ejpam-7020	286	1	mathematics	mathematic	NOUN
ejpam-7020	286	2	,	,	PUNCT
ejpam-7020	286	3	13(8):1294	13(8):1294	NUM
ejpam-7020	286	4	,	,	PUNCT
ejpam-7020	286	5	2025	2025	NUM
ejpam-7020	286	6	.	.	PUNCT
ejpam-7020	287	1	[	[	X
ejpam-7020	287	2	27	27	NUM
ejpam-7020	287	3	]	]	X
ejpam-7020	287	4	abdullah	abdullah	PROPN
ejpam-7020	287	5	alsoboh	alsoboh	PROPN
ejpam-7020	287	6	,	,	PUNCT
ejpam-7020	287	7	murat	murat	PROPN
ejpam-7020	287	8	çağlar	çağlar	PROPN
ejpam-7020	287	9	,	,	PUNCT
ejpam-7020	287	10	and	and	CCONJ
ejpam-7020	287	11	mucahit	mucahit	ADJ
ejpam-7020	287	12	buyankara	buyankara	NOUN
ejpam-7020	287	13	.	.	PUNCT
ejpam-7020	288	1	fekete	fekete	NOUN
ejpam-7020	288	2	-	-	PUNCT
ejpam-7020	288	3	szegö	szegö	PROPN
ejpam-7020	288	4	inequality	inequality	NOUN
ejpam-7020	288	5	for	for	ADP
ejpam-7020	288	6	a	a	DET
ejpam-7020	288	7	subclass	subclass	NOUN
ejpam-7020	288	8	of	of	ADP
ejpam-7020	288	9	bi	bi	ADJ
ejpam-7020	288	10	-	-	ADJ
ejpam-7020	288	11	univalent	univalent	ADJ
ejpam-7020	288	12	functions	function	NOUN
ejpam-7020	288	13	linked	link	VERB
ejpam-7020	288	14	to	to	ADP
ejpam-7020	288	15	q	q	ADJ
ejpam-7020	288	16	-	-	ADJ
ejpam-7020	288	17	ultraspherical	ultraspherical	ADJ
ejpam-7020	288	18	polynomials	polynomial	NOUN
ejpam-7020	288	19	.	.	PUNCT
ejpam-7020	289	1	contemporary	contemporary	ADJ
ejpam-7020	289	2	mathematics	mathematic	NOUN
ejpam-7020	289	3	,	,	PUNCT
ejpam-7020	289	4	pages	page	NOUN
ejpam-7020	289	5	2531–2545	2531–2545	NUM
ejpam-7020	289	6	,	,	PUNCT
ejpam-7020	289	7	2024	2024	NUM
ejpam-7020	289	8	.	.	PUNCT
ejpam-7020	290	1	[	[	X
ejpam-7020	290	2	28	28	NUM
ejpam-7020	290	3	]	]	X
ejpam-7020	290	4	abdullah	abdullah	PROPN
ejpam-7020	290	5	alsoboh	alsoboh	PROPN
ejpam-7020	290	6	and	and	CCONJ
ejpam-7020	290	7	georgia	georgia	PROPN
ejpam-7020	290	8	irina	irina	PROPN
ejpam-7020	290	9	oros	oros	PROPN
ejpam-7020	290	10	.	.	PUNCT
ejpam-7020	291	1	a	a	DET
ejpam-7020	291	2	class	class	NOUN
ejpam-7020	291	3	of	of	ADP
ejpam-7020	291	4	bi	bi	ADJ
ejpam-7020	291	5	-	-	ADJ
ejpam-7020	291	6	univalent	univalent	ADJ
ejpam-7020	291	7	functions	function	NOUN
ejpam-7020	291	8	in	in	ADP
ejpam-7020	291	9	a	a	DET
ejpam-7020	291	10	leaf	leaf	NOUN
ejpam-7020	291	11	-	-	PUNCT
ejpam-7020	291	12	like	like	ADJ
ejpam-7020	291	13	domain	domain	NOUN
ejpam-7020	291	14	defined	define	VERB
ejpam-7020	291	15	through	through	ADP
ejpam-7020	291	16	subordination	subordination	NOUN
ejpam-7020	291	17	via	via	ADP
ejpam-7020	291	18	q	q	NOUN
ejpam-7020	291	19	-	-	NOUN
ejpam-7020	291	20	calculus	calculus	NOUN
ejpam-7020	291	21	.	.	PUNCT
ejpam-7020	292	1	mathematics	mathematic	NOUN
ejpam-7020	292	2	,	,	PUNCT
ejpam-7020	292	3	12(10):1594	12(10):1594	NUM
ejpam-7020	292	4	,	,	PUNCT
ejpam-7020	292	5	2024	2024	NUM
ejpam-7020	292	6	.	.	PUNCT
ejpam-7020	293	1	[	[	X
ejpam-7020	293	2	29	29	NUM
ejpam-7020	293	3	]	]	PUNCT
ejpam-7020	293	4	a.	a.	NOUN
ejpam-7020	293	5	amourah	amourah	PROPN
ejpam-7020	293	6	,	,	PUNCT
ejpam-7020	293	7	a.	a.	PROPN
ejpam-7020	293	8	alsoboh	alsoboh	PROPN
ejpam-7020	293	9	,	,	PUNCT
ejpam-7020	293	10	d.	d.	PROPN
ejpam-7020	293	11	breaz	breaz	PROPN
ejpam-7020	293	12	,	,	PUNCT
ejpam-7020	293	13	and	and	CCONJ
ejpam-7020	293	14	s.	s.	PROPN
ejpam-7020	293	15	m.	m.	PROPN
ejpam-7020	293	16	el	el	PROPN
ejpam-7020	293	17	-	-	PROPN
ejpam-7020	293	18	deeb	deeb	PROPN
ejpam-7020	293	19	.	.	PUNCT
ejpam-7020	294	1	a	a	DET
ejpam-7020	294	2	bi	bi	ADJ
ejpam-7020	294	3	-	-	ADJ
ejpam-7020	294	4	starlike	starlike	ADJ
ejpam-7020	294	5	class	class	NOUN
ejpam-7020	294	6	in	in	ADP
ejpam-7020	294	7	a	a	DET
ejpam-7020	294	8	leaf	leaf	NOUN
ejpam-7020	294	9	-	-	PUNCT
ejpam-7020	294	10	like	like	ADJ
ejpam-7020	294	11	domain	domain	NOUN
ejpam-7020	294	12	defined	define	VERB
ejpam-7020	294	13	through	through	ADP
ejpam-7020	294	14	subordination	subordination	NOUN
ejpam-7020	294	15	via	via	ADP
ejpam-7020	294	16	q	q	NOUN
ejpam-7020	294	17	-	-	NOUN
ejpam-7020	294	18	calculus	calculus	NOUN
ejpam-7020	294	19	.	.	PUNCT
ejpam-7020	295	1	mathematics	mathematic	NOUN
ejpam-7020	295	2	,	,	PUNCT
ejpam-7020	295	3	12(11):1735	12(11):1735	NUM
ejpam-7020	295	4	,	,	PUNCT
ejpam-7020	295	5	2024	2024	NUM
ejpam-7020	295	6	.	.	PUNCT
ejpam-7020	296	1	[	[	X
ejpam-7020	296	2	30	30	NUM
ejpam-7020	296	3	]	]	PUNCT
ejpam-7020	296	4	n	n	PRON
ejpam-7020	296	5	ratib	ratib	PROPN
ejpam-7020	296	6	anakira	anakira	PROPN
ejpam-7020	296	7	,	,	PUNCT
ejpam-7020	296	8	ak	ak	PROPN
ejpam-7020	296	9	alomari	alomari	PROPN
ejpam-7020	296	10	,	,	PUNCT
ejpam-7020	296	11	and	and	CCONJ
ejpam-7020	296	12	ishak	ishak	VERB
ejpam-7020	296	13	hashim	hashim	PROPN
ejpam-7020	296	14	.	.	PUNCT
ejpam-7020	297	1	application	application	NOUN
ejpam-7020	297	2	of	of	ADP
ejpam-7020	297	3	optimal	optimal	ADJ
ejpam-7020	297	4	homotopy	homotopy	NOUN
ejpam-7020	297	5	asymptotic	asymptotic	ADJ
ejpam-7020	297	6	method	method	NOUN
ejpam-7020	297	7	for	for	ADP
ejpam-7020	297	8	solving	solve	VERB
ejpam-7020	297	9	linear	linear	ADJ
ejpam-7020	297	10	delay	delay	NOUN
ejpam-7020	297	11	differential	differential	ADJ
ejpam-7020	297	12	equations	equation	NOUN
ejpam-7020	297	13	.	.	PUNCT
ejpam-7020	298	1	in	in	ADP
ejpam-7020	298	2	aip	aip	PROPN
ejpam-7020	298	3	conference	conference	NOUN
ejpam-7020	298	4	proceedings	proceeding	NOUN
ejpam-7020	298	5	,	,	PUNCT
ejpam-7020	298	6	volume	volume	NOUN
ejpam-7020	298	7	1571	1571	NUM
ejpam-7020	298	8	,	,	PUNCT
ejpam-7020	298	9	pages	page	NOUN
ejpam-7020	298	10	1013–1019	1013–1019	NUM
ejpam-7020	298	11	.	.	PUNCT
ejpam-7020	299	1	american	american	PROPN
ejpam-7020	299	2	institute	institute	PROPN
ejpam-7020	299	3	of	of	ADP
ejpam-7020	299	4	physics	physics	PROPN
ejpam-7020	299	5	,	,	PUNCT
ejpam-7020	299	6	2013	2013	NUM
ejpam-7020	299	7	.	.	PUNCT
ejpam-7020	300	1	[	[	X
ejpam-7020	300	2	31	31	NUM
ejpam-7020	300	3	]	]	PUNCT
ejpam-7020	300	4	a.	a.	NOUN
ejpam-7020	300	5	a.	a.	NOUN
ejpam-7020	300	6	lupaş	lupaş	PROPN
ejpam-7020	300	7	,	,	PUNCT
ejpam-7020	300	8	a.	a.	PROPN
ejpam-7020	300	9	s.	s.	PROPN
ejpam-7020	300	10	tayyah	tayyah	PROPN
ejpam-7020	300	11	,	,	PUNCT
ejpam-7020	300	12	and	and	CCONJ
ejpam-7020	300	13	j.	j.	PROPN
ejpam-7020	300	14	sokó	sokó	PROPN
ejpam-7020	300	15	l.	l.	PROPN
ejpam-7020	300	16	sharp	sharp	PROPN
ejpam-7020	300	17	bounds	bound	NOUN
ejpam-7020	300	18	on	on	ADP
ejpam-7020	300	19	hankel	hankel	NOUN
ejpam-7020	300	20	determinants	determinant	NOUN
ejpam-7020	300	21	for	for	ADP
ejpam-7020	300	22	starlike	starlike	NOUN
ejpam-7020	300	23	functions	function	NOUN
ejpam-7020	300	24	defined	define	VERB
ejpam-7020	300	25	by	by	ADP
ejpam-7020	300	26	symmetry	symmetry	NOUN
ejpam-7020	300	27	with	with	ADP
ejpam-7020	300	28	respect	respect	NOUN
ejpam-7020	300	29	to	to	ADP
ejpam-7020	300	30	symmetric	symmetric	ADJ
ejpam-7020	300	31	domains	domain	NOUN
ejpam-7020	300	32	.	.	PUNCT
ejpam-7020	301	1	symmetry	symmetry	PROPN
ejpam-7020	301	2	,	,	PUNCT
ejpam-7020	301	3	17(8):1244	17(8):1244	NUM
ejpam-7020	301	4	,	,	PUNCT
ejpam-7020	301	5	2025	2025	NUM
ejpam-7020	301	6	.	.	PUNCT
ejpam-7020	302	1	[	[	X
ejpam-7020	302	2	32	32	NUM
ejpam-7020	302	3	]	]	PUNCT
ejpam-7020	302	4	h.	h.	PROPN
ejpam-7020	302	5	qoqazeh	qoqazeh	PROPN
ejpam-7020	302	6	,	,	PUNCT
ejpam-7020	302	7	y.	y.	PROPN
ejpam-7020	302	8	al	al	PROPN
ejpam-7020	302	9	-	-	PUNCT
ejpam-7020	302	10	qudah	qudah	PROPN
ejpam-7020	302	11	,	,	PUNCT
ejpam-7020	302	12	m.	m.	NOUN
ejpam-7020	302	13	almousa	almousa	NOUN
ejpam-7020	302	14	,	,	PUNCT
ejpam-7020	302	15	and	and	CCONJ
ejpam-7020	302	16	a.	a.	NOUN
ejpam-7020	302	17	jaradat	jaradat	PROPN
ejpam-7020	302	18	.	.	PUNCT
ejpam-7020	303	1	on	on	ADP
ejpam-7020	303	2	d	d	ADJ
ejpam-7020	303	3	-	-	ADJ
ejpam-7020	303	4	compact	compact	ADJ
ejpam-7020	303	5	topological	topological	ADJ
ejpam-7020	303	6	spaces	space	NOUN
ejpam-7020	303	7	.	.	PUNCT
ejpam-7020	304	1	journal	journal	NOUN
ejpam-7020	304	2	of	of	ADP
ejpam-7020	304	3	applied	apply	VERB
ejpam-7020	304	4	mathematics	mathematic	NOUN
ejpam-7020	304	5	and	and	CCONJ
ejpam-7020	304	6	informatics	informatic	NOUN
ejpam-7020	304	7	,	,	PUNCT
ejpam-7020	304	8	39(5–6):883–894	39(5–6):883–894	PROPN
ejpam-7020	304	9	,	,	PUNCT
ejpam-7020	304	10	2021	2021	NUM
ejpam-7020	304	11	.	.	PUNCT
ejpam-7020	305	1	[	[	X
ejpam-7020	305	2	33	33	NUM
ejpam-7020	305	3	]	]	PUNCT
ejpam-7020	305	4	a.	a.	PROPN
ejpam-7020	305	5	s.	s.	PROPN
ejpam-7020	305	6	tayyah	tayyah	PROPN
ejpam-7020	305	7	,	,	PUNCT
ejpam-7020	305	8	w.	w.	PROPN
ejpam-7020	305	9	g.	g.	PROPN
ejpam-7020	305	10	atshan	atshan	PROPN
ejpam-7020	305	11	,	,	PUNCT
ejpam-7020	305	12	and	and	CCONJ
ejpam-7020	305	13	g.	g.	PROPN
ejpam-7020	305	14	i.	i.	PROPN
ejpam-7020	305	15	oros	oros	PROPN
ejpam-7020	305	16	.	.	PUNCT
ejpam-7020	306	1	third	third	ADJ
ejpam-7020	306	2	-	-	PUNCT
ejpam-7020	306	3	order	order	NOUN
ejpam-7020	306	4	differential	differential	ADJ
ejpam-7020	306	5	subordination	subordination	NOUN
ejpam-7020	306	6	results	result	NOUN
ejpam-7020	306	7	for	for	ADP
ejpam-7020	306	8	meromorphic	meromorphic	ADJ
ejpam-7020	306	9	functions	function	NOUN
ejpam-7020	306	10	associated	associate	VERB
ejpam-7020	306	11	with	with	ADP
ejpam-7020	306	12	the	the	DET
ejpam-7020	306	13	inverse	inverse	NOUN
ejpam-7020	306	14	of	of	ADP
ejpam-7020	306	15	the	the	DET
ejpam-7020	306	16	legendre	legendre	PROPN
ejpam-7020	306	17	chi	chi	PROPN
ejpam-7020	306	18	function	function	PROPN
ejpam-7020	306	19	via	via	ADP
ejpam-7020	306	20	the	the	DET
ejpam-7020	306	21	mittag	mittag	ADJ
ejpam-7020	306	22	-	-	PUNCT
ejpam-7020	306	23	leffler	leffler	NOUN
ejpam-7020	306	24	identity	identity	NOUN
ejpam-7020	306	25	.	.	PUNCT
ejpam-7020	307	1	mathematics	mathematic	NOUN
ejpam-7020	307	2	,	,	PUNCT
ejpam-7020	307	3	13(13):2089	13(13):2089	NUM
ejpam-7020	307	4	,	,	PUNCT
ejpam-7020	307	5	2025	2025	NUM
ejpam-7020	307	6	.	.	PUNCT
ejpam-7020	308	1	[	[	X
ejpam-7020	308	2	34	34	NUM
ejpam-7020	308	3	]	]	PUNCT
ejpam-7020	308	4	a.	a.	PROPN
ejpam-7020	308	5	al	al	PROPN
ejpam-7020	308	6	-	-	PUNCT
ejpam-7020	308	7	hammouri	hammouri	PROPN
ejpam-7020	308	8	and	and	CCONJ
ejpam-7020	308	9	a.	a.	NOUN
ejpam-7020	308	10	ashyralyev	ashyralyev	PROPN
ejpam-7020	308	11	.	.	PUNCT
ejpam-7020	309	1	a	a	DET
ejpam-7020	309	2	note	note	NOUN
ejpam-7020	309	3	on	on	ADP
ejpam-7020	309	4	the	the	DET
ejpam-7020	309	5	second	second	ADJ
ejpam-7020	309	6	order	order	NOUN
ejpam-7020	309	7	of	of	ADP
ejpam-7020	309	8	accuracy	accuracy	NOUN
ejpam-7020	309	9	difference	difference	NOUN
ejpam-7020	309	10	scheme	scheme	NOUN
ejpam-7020	309	11	for	for	ADP
ejpam-7020	309	12	the	the	DET
ejpam-7020	309	13	elliptic	elliptic	ADJ
ejpam-7020	309	14	-	-	PUNCT
ejpam-7020	309	15	telegraph	telegraph	NOUN
ejpam-7020	309	16	identification	identification	NOUN
ejpam-7020	309	17	problem	problem	NOUN
ejpam-7020	309	18	with	with	ADP
ejpam-7020	309	19	dirichlet	dirichlet	PROPN
ejpam-7020	309	20	boundary	boundary	PROPN
ejpam-7020	309	21	condition	condition	NOUN
ejpam-7020	309	22	.	.	PUNCT
ejpam-7020	310	1	international	international	ADJ
ejpam-7020	310	2	journal	journal	NOUN
ejpam-7020	310	3	of	of	ADP
ejpam-7020	310	4	applied	apply	VERB
ejpam-7020	310	5	mathematics	mathematic	NOUN
ejpam-7020	310	6	,	,	PUNCT
ejpam-7020	310	7	38(1):1–13	38(1):1–13	NUM
ejpam-7020	310	8	,	,	PUNCT
ejpam-7020	310	9	2025	2025	NUM
ejpam-7020	310	10	.	.	PUNCT
ejpam-7020	311	1	[	[	X
ejpam-7020	311	2	35	35	NUM
ejpam-7020	311	3	]	]	PUNCT
ejpam-7020	311	4	a.	a.	NOUN
ejpam-7020	311	5	ashyralyev	ashyralyev	NOUN
ejpam-7020	311	6	and	and	CCONJ
ejpam-7020	311	7	a.	a.	PROPN
ejpam-7020	311	8	al	al	PROPN
ejpam-7020	311	9	-	-	PUNCT
ejpam-7020	311	10	hammouri	hammouri	NOUN
ejpam-7020	311	11	.	.	PUNCT
ejpam-7020	312	1	a	a	DET
ejpam-7020	312	2	note	note	NOUN
ejpam-7020	312	3	on	on	ADP
ejpam-7020	312	4	the	the	DET
ejpam-7020	312	5	elliptic	elliptic	ADJ
ejpam-7020	312	6	-	-	PUNCT
ejpam-7020	312	7	telegraph	telegraph	NOUN
ejpam-7020	312	8	identification	identification	NOUN
ejpam-7020	312	9	problem	problem	NOUN
ejpam-7020	312	10	with	with	ADP
ejpam-7020	312	11	non	non	ADJ
ejpam-7020	312	12	-	-	ADJ
ejpam-7020	312	13	local	local	ADJ
ejpam-7020	312	14	condition	condition	NOUN
ejpam-7020	312	15	.	.	PUNCT
ejpam-7020	313	1	aip	aip	PROPN
ejpam-7020	313	2	conference	conference	NOUN
ejpam-7020	313	3	proceedings	proceeding	NOUN
ejpam-7020	313	4	,	,	PUNCT
ejpam-7020	313	5	2334(1):060006	2334(1):060006	NUM
ejpam-7020	313	6	,	,	PUNCT
ejpam-7020	313	7	2021	2021	NUM
ejpam-7020	313	8	.	.	PUNCT
ejpam-7020	314	1	[	[	X
ejpam-7020	314	2	36	36	NUM
ejpam-7020	314	3	]	]	PUNCT
ejpam-7020	314	4	a.	a.	NOUN
ejpam-7020	314	5	almousa	almousa	NOUN
ejpam-7020	314	6	,	,	PUNCT
ejpam-7020	314	7	s.	s.	PROPN
ejpam-7020	314	8	saidat	saidat	PROPN
ejpam-7020	314	9	,	,	PUNCT
ejpam-7020	314	10	a.	a.	PROPN
ejpam-7020	314	11	al	al	PROPN
ejpam-7020	314	12	-	-	PUNCT
ejpam-7020	314	13	hammouri	hammouri	PROPN
ejpam-7020	314	14	,	,	PUNCT
ejpam-7020	314	15	s.	s.	PROPN
ejpam-7020	314	16	alsaadi	alsaadi	PROPN
ejpam-7020	314	17	,	,	PUNCT
ejpam-7020	314	18	and	and	CCONJ
ejpam-7020	314	19	g.	g.	PROPN
ejpam-7020	314	20	banihani	banihani	PROPN
ejpam-7020	314	21	.	.	PUNCT
ejpam-7020	315	1	solutions	solution	NOUN
ejpam-7020	315	2	of	of	ADP
ejpam-7020	315	3	nonlinear	nonlinear	ADJ
ejpam-7020	315	4	integro	integro	ADJ
ejpam-7020	315	5	-	-	PUNCT
ejpam-7020	315	6	differential	differential	NOUN
ejpam-7020	315	7	equations	equation	NOUN
ejpam-7020	315	8	using	use	VERB
ejpam-7020	315	9	a	a	DET
ejpam-7020	315	10	hybrid	hybrid	ADJ
ejpam-7020	315	11	adomian	adomian	NOUN
ejpam-7020	315	12	decomposition	decomposition	NOUN
ejpam-7020	315	13	method	method	NOUN
ejpam-7020	315	14	with	with	ADP
ejpam-7020	315	15	modified	modify	VERB
ejpam-7020	315	16	bernstein	bernstein	PROPN
ejpam-7020	315	17	polynomials	polynomial	NOUN
ejpam-7020	315	18	.	.	PUNCT
ejpam-7020	316	1	international	international	ADJ
ejpam-7020	316	2	journal	journal	NOUN
ejpam-7020	316	3	of	of	ADP
ejpam-7020	316	4	fuzzy	fuzzy	ADJ
ejpam-7020	316	5	logic	logic	NOUN
ejpam-7020	316	6	and	and	CCONJ
ejpam-7020	316	7	intelligent	intelligent	ADJ
ejpam-7020	316	8	systems	system	NOUN
ejpam-7020	316	9	,	,	PUNCT
ejpam-7020	316	10	24(3):271–279	24(3):271–279	PROPN
ejpam-7020	316	11	,	,	PUNCT
ejpam-7020	316	12	2024	2024	NUM
ejpam-7020	316	13	.	.	PUNCT
ejpam-7020	317	1	[	[	X
ejpam-7020	317	2	37	37	NUM
ejpam-7020	317	3	]	]	PUNCT
ejpam-7020	317	4	m.	m.	NOUN
ejpam-7020	317	5	almousa	almousa	NOUN
ejpam-7020	317	6	,	,	PUNCT
ejpam-7020	317	7	a.	a.	PROPN
ejpam-7020	317	8	al	al	PROPN
ejpam-7020	317	9	-	-	PUNCT
ejpam-7020	317	10	hammouri	hammouri	PROPN
ejpam-7020	317	11	,	,	PUNCT
ejpam-7020	317	12	s.	s.	PROPN
ejpam-7020	317	13	saidat	saidat	PROPN
ejpam-7020	317	14	,	,	PUNCT
ejpam-7020	317	15	s.	s.	PROPN
ejpam-7020	317	16	alsaadi	alsaadi	PROPN
ejpam-7020	317	17	,	,	PUNCT
ejpam-7020	317	18	and	and	CCONJ
ejpam-7020	317	19	g.	g.	PROPN
ejpam-7020	317	20	banihani	banihani	PROPN
ejpam-7020	317	21	.	.	PUNCT
ejpam-7020	318	1	a	a	DET
ejpam-7020	318	2	hybrid	hybrid	ADJ
ejpam-7020	318	3	laplace	laplace	NOUN
ejpam-7020	318	4	transform	transform	NOUN
ejpam-7020	318	5	-	-	PUNCT
ejpam-7020	318	6	optimal	optimal	ADJ
ejpam-7020	318	7	homotopy	homotopy	NOUN
ejpam-7020	318	8	asymptotic	asymptotic	ADJ
ejpam-7020	318	9	method	method	NOUN
ejpam-7020	318	10	(	(	PUNCT
ejpam-7020	318	11	lt	lt	NOUN
ejpam-7020	318	12	-	-	PUNCT
ejpam-7020	318	13	oham	oham	NOUN
ejpam-7020	318	14	)	)	PUNCT
ejpam-7020	318	15	for	for	ADP
ejpam-7020	318	16	solving	solve	VERB
ejpam-7020	318	17	integro	integro	ADJ
ejpam-7020	318	18	-	-	PUNCT
ejpam-7020	318	19	differential	differential	NOUN
ejpam-7020	318	20	equations	equation	NOUN
ejpam-7020	318	21	of	of	ADP
ejpam-7020	318	22	the	the	DET
ejpam-7020	318	23	second	second	ADJ
ejpam-7020	318	24	kind	kind	NOUN
ejpam-7020	318	25	.	.	PUNCT
ejpam-7020	319	1	international	international	ADJ
ejpam-7020	319	2	journal	journal	NOUN
ejpam-7020	319	3	of	of	ADP
ejpam-7020	319	4	analysis	analysis	NOUN
ejpam-7020	319	5	and	and	CCONJ
ejpam-7020	319	6	applications	application	NOUN
ejpam-7020	319	7	,	,	PUNCT
ejpam-7020	319	8	22:17	22:17	NUM
ejpam-7020	319	9	,	,	PUNCT
ejpam-7020	319	10	2024	2024	NUM
ejpam-7020	319	11	.	.	PUNCT
ejpam-7020	320	1	[	[	X
ejpam-7020	320	2	38	38	NUM
ejpam-7020	320	3	]	]	PUNCT
ejpam-7020	320	4	m.	m.	NOUN
ejpam-7020	320	5	ye	ye	INTJ
ejpam-7020	320	6	et	et	PROPN
ejpam-7020	320	7	al	al	PROPN
ejpam-7020	320	8	.	.	PUNCT
ejpam-7020	320	9	applications	application	NOUN
ejpam-7020	320	10	of	of	ADP
ejpam-7020	320	11	the	the	DET
ejpam-7020	320	12	poincaré–hopf	poincaré–hopf	NOUN
ejpam-7020	320	13	theorem	theorem	ADJ
ejpam-7020	320	14	:	:	PUNCT
ejpam-7020	320	15	epidemic	epidemic	NOUN
ejpam-7020	320	16	models	model	NOUN
ejpam-7020	320	17	and	and	CCONJ
ejpam-7020	320	18	s.	s.	PROPN
ejpam-7020	320	19	saidat	saidat	PROPN
ejpam-7020	320	20	et	et	PROPN
ejpam-7020	320	21	al	al	PROPN
ejpam-7020	320	22	.	.	PUNCT
ejpam-7020	320	23	/	/	SYM
ejpam-7020	320	24	eur	eur	PROPN
ejpam-7020	320	25	.	.	PUNCT
ejpam-7020	321	1	j.	j.	PROPN
ejpam-7020	321	2	pure	pure	PROPN
ejpam-7020	321	3	appl	appl	PROPN
ejpam-7020	321	4	.	.	PROPN
ejpam-7020	321	5	math	math	PROPN
ejpam-7020	321	6	,	,	PUNCT
ejpam-7020	321	7	18	18	NUM
ejpam-7020	321	8	(	(	PUNCT
ejpam-7020	321	9	4	4	NUM
ejpam-7020	321	10	)	)	PUNCT
ejpam-7020	321	11	(	(	PUNCT
ejpam-7020	321	12	2025	2025	NUM
ejpam-7020	321	13	)	)	PUNCT
ejpam-7020	321	14	,	,	PUNCT
ejpam-7020	321	15	7020	7020	NUM
ejpam-7020	321	16	16	16	NUM
ejpam-7020	321	17	of	of	ADP
ejpam-7020	321	18	16	16	NUM
ejpam-7020	321	19	lotka	lotka	PROPN
ejpam-7020	321	20	–	–	PUNCT
ejpam-7020	321	21	volterra	volterra	NOUN
ejpam-7020	321	22	systems	system	NOUN
ejpam-7020	321	23	.	.	PUNCT
ejpam-7020	322	1	ieee	ieee	NOUN
ejpam-7020	322	2	transactions	transaction	NOUN
ejpam-7020	322	3	on	on	ADP
ejpam-7020	322	4	automatic	automatic	ADJ
ejpam-7020	322	5	control	control	NOUN
ejpam-7020	322	6	,	,	PUNCT
ejpam-7020	322	7	67(4):1609	67(4):1609	NUM
ejpam-7020	322	8	–	–	PUNCT
ejpam-7020	322	9	1624	1624	NUM
ejpam-7020	322	10	,	,	PUNCT
ejpam-7020	322	11	2021	2021	NUM
ejpam-7020	322	12	.	.	PUNCT