id	sid	tid	token	lemma	pos
ejpam-4707	1	1	european	european	PROPN
ejpam-4707	1	2	journal	journal	PROPN
ejpam-4707	1	3	of	of	ADP
ejpam-4707	1	4	pure	pure	ADJ
ejpam-4707	1	5	and	and	CCONJ
ejpam-4707	1	6	applied	apply	VERB
ejpam-4707	1	7	mathematics	mathematic	NOUN
ejpam-4707	1	8	vol	vol	NOUN
ejpam-4707	1	9	.	.	PUNCT
ejpam-4707	2	1	16	16	NUM
ejpam-4707	2	2	,	,	PUNCT
ejpam-4707	2	3	no	no	INTJ
ejpam-4707	2	4	.	.	NOUN
ejpam-4707	2	5	2	2	NUM
ejpam-4707	2	6	,	,	PUNCT
ejpam-4707	2	7	2023	2023	NUM
ejpam-4707	2	8	,	,	PUNCT
ejpam-4707	2	9	736	736	NUM
ejpam-4707	2	10	-	-	SYM
ejpam-4707	2	11	750	750	NUM
ejpam-4707	2	12	issn	issn	PROPN
ejpam-4707	2	13	1307	1307	NUM
ejpam-4707	2	14	-	-	SYM
ejpam-4707	2	15	5543	5543	NUM
ejpam-4707	2	16	–	–	PUNCT
ejpam-4707	2	17	ejpam.com	ejpam.com	X
ejpam-4707	2	18	published	publish	VERB
ejpam-4707	2	19	by	by	ADP
ejpam-4707	2	20	new	new	PROPN
ejpam-4707	2	21	york	york	PROPN
ejpam-4707	2	22	business	business	PROPN
ejpam-4707	2	23	global	global	PROPN
ejpam-4707	2	24	a	a	DET
ejpam-4707	2	25	host	host	NOUN
ejpam-4707	2	26	-	-	PUNCT
ejpam-4707	2	27	parasitoid	parasitoid	NOUN
ejpam-4707	2	28	dynamics	dynamic	NOUN
ejpam-4707	2	29	with	with	ADP
ejpam-4707	2	30	allee	allee	NOUN
ejpam-4707	2	31	and	and	CCONJ
ejpam-4707	2	32	refuge	refuge	NOUN
ejpam-4707	2	33	effects	effect	NOUN
ejpam-4707	2	34	burcin	burcin	PROPN
ejpam-4707	2	35	kulahcioglu1	kulahcioglu1	NOUN
ejpam-4707	2	36	,	,	PUNCT
ejpam-4707	2	37	unal	unal	PROPN
ejpam-4707	2	38	ufuktepe2,∗	ufuktepe2,∗	VERB
ejpam-4707	2	39	,	,	PUNCT
ejpam-4707	2	40	antonios	antonios	PROPN
ejpam-4707	2	41	kalampakas2	kalampakas2	PROPN
ejpam-4707	2	42	1	1	NUM
ejpam-4707	2	43	faculty	faculty	NOUN
ejpam-4707	2	44	of	of	ADP
ejpam-4707	2	45	engineering	engineering	NOUN
ejpam-4707	2	46	and	and	CCONJ
ejpam-4707	2	47	architecture	architecture	NOUN
ejpam-4707	2	48	,	,	PUNCT
ejpam-4707	2	49	beykoz	beykoz	PROPN
ejpam-4707	2	50	university	university	PROPN
ejpam-4707	2	51	,	,	PUNCT
ejpam-4707	2	52	istanbul	istanbul	PROPN
ejpam-4707	2	53	,	,	PUNCT
ejpam-4707	2	54	turkey	turkey	PROPN
ejpam-4707	2	55	2	2	NUM
ejpam-4707	2	56	college	college	NOUN
ejpam-4707	2	57	of	of	ADP
ejpam-4707	2	58	engineering	engineering	NOUN
ejpam-4707	2	59	and	and	CCONJ
ejpam-4707	2	60	technology	technology	NOUN
ejpam-4707	2	61	,	,	PUNCT
ejpam-4707	2	62	american	american	PROPN
ejpam-4707	2	63	university	university	PROPN
ejpam-4707	2	64	of	of	ADP
ejpam-4707	2	65	the	the	DET
ejpam-4707	2	66	middle	middle	PROPN
ejpam-4707	2	67	east	east	PROPN
ejpam-4707	2	68	,	,	PUNCT
ejpam-4707	2	69	kuwait	kuwait	PROPN
ejpam-4707	2	70	abstract	abstract	NOUN
ejpam-4707	2	71	.	.	PUNCT
ejpam-4707	3	1	we	we	PRON
ejpam-4707	3	2	examine	examine	VERB
ejpam-4707	3	3	a	a	DET
ejpam-4707	3	4	discrete	discrete	ADJ
ejpam-4707	3	5	-	-	PUNCT
ejpam-4707	3	6	time	time	NOUN
ejpam-4707	3	7	host	host	NOUN
ejpam-4707	3	8	–	–	PUNCT
ejpam-4707	3	9	parasitoid	parasitoid	NOUN
ejpam-4707	3	10	model	model	NOUN
ejpam-4707	3	11	incorporating	incorporate	VERB
ejpam-4707	3	12	simultaneously	simultaneously	ADV
ejpam-4707	3	13	an	an	DET
ejpam-4707	3	14	allee	allee	NOUN
ejpam-4707	3	15	and	and	CCONJ
ejpam-4707	3	16	a	a	DET
ejpam-4707	3	17	refuge	refuge	NOUN
ejpam-4707	3	18	effect	effect	NOUN
ejpam-4707	3	19	on	on	ADP
ejpam-4707	3	20	the	the	DET
ejpam-4707	3	21	host	host	NOUN
ejpam-4707	3	22	.	.	PUNCT
ejpam-4707	4	1	we	we	PRON
ejpam-4707	4	2	investigate	investigate	VERB
ejpam-4707	4	3	existence	existence	NOUN
ejpam-4707	4	4	of	of	ADP
ejpam-4707	4	5	a	a	DET
ejpam-4707	4	6	positive	positive	ADJ
ejpam-4707	4	7	fixed	fix	VERB
ejpam-4707	4	8	point	point	NOUN
ejpam-4707	4	9	,	,	PUNCT
ejpam-4707	4	10	local	local	ADJ
ejpam-4707	4	11	asymptotic	asymptotic	ADJ
ejpam-4707	4	12	stability	stability	NOUN
ejpam-4707	4	13	,	,	PUNCT
ejpam-4707	4	14	global	global	ADJ
ejpam-4707	4	15	stability	stability	NOUN
ejpam-4707	4	16	of	of	ADP
ejpam-4707	4	17	the	the	DET
ejpam-4707	4	18	fixed	fix	VERB
ejpam-4707	4	19	points	point	NOUN
ejpam-4707	4	20	and	and	CCONJ
ejpam-4707	4	21	bifurcations	bifurcation	NOUN
ejpam-4707	4	22	.	.	PUNCT
ejpam-4707	5	1	numerical	numerical	ADJ
ejpam-4707	5	2	examples	example	NOUN
ejpam-4707	5	3	are	be	AUX
ejpam-4707	5	4	given	give	VERB
ejpam-4707	5	5	for	for	ADP
ejpam-4707	5	6	verification	verification	NOUN
ejpam-4707	5	7	of	of	ADP
ejpam-4707	5	8	the	the	DET
ejpam-4707	5	9	theoretical	theoretical	ADJ
ejpam-4707	5	10	results	result	NOUN
ejpam-4707	5	11	and	and	CCONJ
ejpam-4707	5	12	we	we	PRON
ejpam-4707	5	13	compare	compare	VERB
ejpam-4707	5	14	the	the	DET
ejpam-4707	5	15	model	model	NOUN
ejpam-4707	5	16	with	with	ADP
ejpam-4707	5	17	existing	exist	VERB
ejpam-4707	5	18	data	datum	NOUN
ejpam-4707	5	19	from	from	ADP
ejpam-4707	5	20	the	the	DET
ejpam-4707	5	21	literature	literature	NOUN
ejpam-4707	5	22	.	.	PUNCT
ejpam-4707	6	1	2020	2020	NUM
ejpam-4707	6	2	mathematics	mathematics	PROPN
ejpam-4707	6	3	subject	subject	NOUN
ejpam-4707	6	4	classifications	classification	NOUN
ejpam-4707	6	5	:	:	PUNCT
ejpam-4707	6	6	92d25	92d25	NUM
ejpam-4707	6	7	,	,	PUNCT
ejpam-4707	6	8	39a30	39a30	NUM
ejpam-4707	6	9	,	,	PUNCT
ejpam-4707	6	10	92d30	92d30	NUM
ejpam-4707	6	11	key	key	ADJ
ejpam-4707	6	12	words	word	NOUN
ejpam-4707	6	13	and	and	CCONJ
ejpam-4707	6	14	phrases	phrase	NOUN
ejpam-4707	6	15	:	:	PUNCT
ejpam-4707	6	16	discrete	discrete	ADJ
ejpam-4707	6	17	dynamical	dynamical	ADJ
ejpam-4707	6	18	systems	system	NOUN
ejpam-4707	6	19	,	,	PUNCT
ejpam-4707	6	20	host	host	NOUN
ejpam-4707	6	21	-	-	PUNCT
ejpam-4707	6	22	parasitoid	parasitoid	PROPN
ejpam-4707	6	23	,	,	PUNCT
ejpam-4707	6	24	nicholson	nicholson	PROPN
ejpam-4707	6	25	-	-	PUNCT
ejpam-4707	6	26	bailey	bailey	NOUN
ejpam-4707	6	27	,	,	PUNCT
ejpam-4707	6	28	bifurcation	bifurcation	NOUN
ejpam-4707	6	29	,	,	PUNCT
ejpam-4707	6	30	allee	allee	NOUN
ejpam-4707	6	31	effect	effect	NOUN
ejpam-4707	6	32	,	,	PUNCT
ejpam-4707	6	33	refuge	refuge	ADJ
ejpam-4707	6	34	effect	effect	NOUN
ejpam-4707	6	35	1	1	NUM
ejpam-4707	6	36	.	.	X
ejpam-4707	7	1	introduction	introduction	NOUN
ejpam-4707	7	2	discrete	discrete	ADJ
ejpam-4707	7	3	dynamic	dynamic	ADJ
ejpam-4707	7	4	systems	system	NOUN
ejpam-4707	7	5	(	(	PUNCT
ejpam-4707	7	6	dds	dds	PROPN
ejpam-4707	7	7	)	)	PUNCT
ejpam-4707	7	8	in	in	ADP
ejpam-4707	7	9	general	general	ADJ
ejpam-4707	7	10	have	have	AUX
ejpam-4707	7	11	been	be	AUX
ejpam-4707	7	12	studied	study	VERB
ejpam-4707	7	13	extensively	extensively	ADV
ejpam-4707	7	14	and	and	CCONJ
ejpam-4707	7	15	particularly	particularly	ADV
ejpam-4707	7	16	in	in	ADP
ejpam-4707	7	17	the	the	DET
ejpam-4707	7	18	recent	recent	ADJ
ejpam-4707	7	19	period	period	NOUN
ejpam-4707	7	20	in	in	ADP
ejpam-4707	7	21	view	view	NOUN
ejpam-4707	7	22	of	of	ADP
ejpam-4707	7	23	the	the	DET
ejpam-4707	7	24	coronavirus	coronavirus	NOUN
ejpam-4707	7	25	disease	disease	NOUN
ejpam-4707	7	26	pandemic	pandemic	ADJ
ejpam-4707	8	1	[	[	X
ejpam-4707	8	2	16],[21],[1],[17],[22	16],[21],[1],[17],[22	NUM
ejpam-4707	8	3	]	]	PUNCT
ejpam-4707	8	4	.	.	PUNCT
ejpam-4707	9	1	in	in	ADP
ejpam-4707	9	2	addition	addition	NOUN
ejpam-4707	9	3	,	,	PUNCT
ejpam-4707	9	4	it	it	PRON
ejpam-4707	9	5	has	have	AUX
ejpam-4707	9	6	been	be	AUX
ejpam-4707	9	7	shown	show	VERB
ejpam-4707	9	8	that	that	SCONJ
ejpam-4707	9	9	population	population	NOUN
ejpam-4707	9	10	dynamics	dynamic	NOUN
ejpam-4707	9	11	implementing	implement	VERB
ejpam-4707	9	12	dds	dds	PROPN
ejpam-4707	9	13	can	can	AUX
ejpam-4707	9	14	produce	produce	VERB
ejpam-4707	9	15	efficient	efficient	ADJ
ejpam-4707	9	16	computational	computational	ADJ
ejpam-4707	9	17	results	result	NOUN
ejpam-4707	9	18	for	for	ADP
ejpam-4707	9	19	host	host	NOUN
ejpam-4707	9	20	-	-	PUNCT
ejpam-4707	9	21	parasitoid	parasitoid	NOUN
ejpam-4707	9	22	interactions	interaction	NOUN
ejpam-4707	9	23	with	with	ADP
ejpam-4707	9	24	numerical	numerical	ADJ
ejpam-4707	9	25	simulations	simulation	NOUN
ejpam-4707	9	26	[	[	X
ejpam-4707	9	27	18],[9],[20	18],[9],[20	X
ejpam-4707	9	28	]	]	PUNCT
ejpam-4707	9	29	,	,	PUNCT
ejpam-4707	9	30	see	see	VERB
ejpam-4707	9	31	also	also	ADV
ejpam-4707	9	32	[	[	X
ejpam-4707	9	33	11	11	NUM
ejpam-4707	9	34	]	]	PUNCT
ejpam-4707	9	35	.	.	PUNCT
ejpam-4707	10	1	parasitoids	parasitoid	NOUN
ejpam-4707	10	2	are	be	AUX
ejpam-4707	10	3	insect	insect	NOUN
ejpam-4707	10	4	species	specie	NOUN
ejpam-4707	10	5	whose	whose	DET
ejpam-4707	10	6	larvae	larvae	NOUN
ejpam-4707	10	7	developed	develop	VERB
ejpam-4707	10	8	by	by	ADP
ejpam-4707	10	9	feeding	feed	VERB
ejpam-4707	10	10	on	on	ADP
ejpam-4707	10	11	the	the	DET
ejpam-4707	10	12	bodies	body	NOUN
ejpam-4707	10	13	of	of	ADP
ejpam-4707	10	14	other	other	ADJ
ejpam-4707	10	15	arthropods	arthropod	NOUN
ejpam-4707	10	16	,	,	PUNCT
ejpam-4707	10	17	usually	usually	ADV
ejpam-4707	10	18	killing	kill	VERB
ejpam-4707	10	19	them	they	PRON
ejpam-4707	10	20	.	.	PUNCT
ejpam-4707	11	1	larvae	larvae	PROPN
ejpam-4707	11	2	emerge	emerge	VERB
ejpam-4707	11	3	from	from	ADP
ejpam-4707	11	4	the	the	DET
ejpam-4707	11	5	host	host	NOUN
ejpam-4707	11	6	and	and	CCONJ
ejpam-4707	11	7	developed	develop	VERB
ejpam-4707	11	8	into	into	ADP
ejpam-4707	11	9	free	free	ADJ
ejpam-4707	11	10	-	-	PUNCT
ejpam-4707	11	11	living	live	VERB
ejpam-4707	11	12	adults	adult	NOUN
ejpam-4707	11	13	.	.	PUNCT
ejpam-4707	12	1	the	the	DET
ejpam-4707	12	2	adults	adult	NOUN
ejpam-4707	12	3	then	then	ADV
ejpam-4707	12	4	lay	lay	VERB
ejpam-4707	12	5	their	their	PRON
ejpam-4707	12	6	eggs	egg	NOUN
ejpam-4707	12	7	in	in	ADP
ejpam-4707	12	8	a	a	DET
ejpam-4707	12	9	subsequent	subsequent	ADJ
ejpam-4707	12	10	generation	generation	NOUN
ejpam-4707	12	11	of	of	ADP
ejpam-4707	12	12	hosts	host	NOUN
ejpam-4707	12	13	.	.	PUNCT
ejpam-4707	13	1	the	the	DET
ejpam-4707	13	2	host	host	NOUN
ejpam-4707	13	3	-	-	PUNCT
ejpam-4707	13	4	parasitoid	parasitoid	NOUN
ejpam-4707	13	5	dynamics	dynamic	NOUN
ejpam-4707	13	6	are	be	AUX
ejpam-4707	13	7	increasingly	increasingly	ADV
ejpam-4707	13	8	being	be	AUX
ejpam-4707	13	9	studied	study	VERB
ejpam-4707	13	10	for	for	ADP
ejpam-4707	13	11	habitat	habitat	NOUN
ejpam-4707	13	12	management	management	NOUN
ejpam-4707	13	13	[	[	X
ejpam-4707	13	14	13	13	NUM
ejpam-4707	13	15	]	]	PUNCT
ejpam-4707	13	16	,	,	PUNCT
ejpam-4707	13	17	controlling	control	VERB
ejpam-4707	13	18	invasive	invasive	ADJ
ejpam-4707	13	19	pests	pest	NOUN
ejpam-4707	13	20	[	[	X
ejpam-4707	13	21	5	5	NUM
ejpam-4707	13	22	]	]	PUNCT
ejpam-4707	13	23	and	and	CCONJ
ejpam-4707	13	24	[	[	X
ejpam-4707	13	25	14	14	NUM
ejpam-4707	13	26	]	]	PUNCT
ejpam-4707	13	27	,	,	PUNCT
ejpam-4707	13	28	identifying	identify	VERB
ejpam-4707	13	29	movement	movement	NOUN
ejpam-4707	13	30	among	among	ADP
ejpam-4707	13	31	habitat	habitat	NOUN
ejpam-4707	13	32	patches	patch	NOUN
ejpam-4707	14	1	[	[	X
ejpam-4707	14	2	4	4	NUM
ejpam-4707	14	3	]	]	PUNCT
ejpam-4707	14	4	and	and	CCONJ
ejpam-4707	14	5	internal	internal	ADJ
ejpam-4707	14	6	host	host	NOUN
ejpam-4707	14	7	-	-	PUNCT
ejpam-4707	14	8	parasitoid	parasitoid	NOUN
ejpam-4707	14	9	variations	variation	NOUN
ejpam-4707	14	10	[	[	X
ejpam-4707	14	11	19	19	NUM
ejpam-4707	14	12	]	]	PUNCT
ejpam-4707	14	13	.	.	PUNCT
ejpam-4707	15	1	the	the	DET
ejpam-4707	15	2	general	general	ADJ
ejpam-4707	15	3	framework	framework	NOUN
ejpam-4707	15	4	for	for	ADP
ejpam-4707	15	5	the	the	DET
ejpam-4707	15	6	study	study	NOUN
ejpam-4707	15	7	of	of	ADP
ejpam-4707	15	8	discrete	discrete	ADJ
ejpam-4707	15	9	-	-	PUNCT
ejpam-4707	15	10	type	type	NOUN
ejpam-4707	15	11	host	host	NOUN
ejpam-4707	15	12	-	-	PUNCT
ejpam-4707	15	13	parasitoid	parasitoid	NOUN
ejpam-4707	15	14	model	model	NOUN
ejpam-4707	15	15	is	be	AUX
ejpam-4707	15	16	the	the	DET
ejpam-4707	15	17	following	follow	VERB
ejpam-4707	15	18	:	:	PUNCT
ejpam-4707	15	19	ht+1	ht+1	NUM
ejpam-4707	15	20	=	=	SYM
ejpam-4707	15	21	rhtf(ht	rhtf(ht	NOUN
ejpam-4707	15	22	,	,	PUNCT
ejpam-4707	15	23	pt	pt	NOUN
ejpam-4707	15	24	)	)	PUNCT
ejpam-4707	15	25	,	,	PUNCT
ejpam-4707	15	26	pt+1	pt+1	X
ejpam-4707	16	1	=	=	SYM
ejpam-4707	16	2	βht	βht	NOUN
ejpam-4707	16	3	(	(	PUNCT
ejpam-4707	16	4	1−	1−	NUM
ejpam-4707	16	5	f(ht	f(ht	NOUN
ejpam-4707	16	6	,	,	PUNCT
ejpam-4707	16	7	pt	pt	NOUN
ejpam-4707	16	8	)	)	PUNCT
ejpam-4707	16	9	)	)	PUNCT
ejpam-4707	16	10	,	,	PUNCT
ejpam-4707	16	11	(	(	PUNCT
ejpam-4707	16	12	1	1	X
ejpam-4707	16	13	)	)	PUNCT
ejpam-4707	16	14	∗corresponding	∗corresponde	VERB
ejpam-4707	16	15	author	author	NOUN
ejpam-4707	16	16	.	.	PUNCT
ejpam-4707	17	1	doi	doi	NOUN
ejpam-4707	17	2	:	:	PUNCT
ejpam-4707	17	3	https://doi.org/10.29020/nybg.ejpam.v16i2.4707	https://doi.org/10.29020/nybg.ejpam.v16i2.4707	NUM
ejpam-4707	17	4	email	email	NOUN
ejpam-4707	17	5	addresses	address	VERB
ejpam-4707	17	6	:	:	PUNCT
ejpam-4707	17	7	burcinkulahcioglu@beykoz.edu.tr	burcinkulahcioglu@beykoz.edu.tr	PROPN
ejpam-4707	17	8	(	(	PUNCT
ejpam-4707	17	9	b.	b.	PROPN
ejpam-4707	17	10	kulahcioglu	kulahcioglu	PROPN
ejpam-4707	17	11	)	)	PUNCT
ejpam-4707	17	12	,	,	PUNCT
ejpam-4707	17	13	unal.ufuktepe@aum.edu.kw	unal.ufuktepe@aum.edu.kw	PROPN
ejpam-4707	17	14	(	(	PUNCT
ejpam-4707	17	15	u.	u.	NOUN
ejpam-4707	17	16	ufuktepe	ufuktepe	NOUN
ejpam-4707	17	17	)	)	PUNCT
ejpam-4707	17	18	,	,	PUNCT
ejpam-4707	17	19	antonios.kalampakas@aum.edu.kw	antonios.kalampakas@aum.edu.kw	PROPN
ejpam-4707	17	20	(	(	PUNCT
ejpam-4707	17	21	a.	a.	PROPN
ejpam-4707	17	22	kalampakas	kalampakas	PROPN
ejpam-4707	17	23	)	)	PUNCT
ejpam-4707	17	24	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4707	18	1	736	736	NUM
ejpam-4707	19	1	©	©	ADP
ejpam-4707	19	2	2023	2023	NUM
ejpam-4707	19	3	ejpam	ejpam	NOUN
ejpam-4707	19	4	all	all	DET
ejpam-4707	19	5	rights	right	NOUN
ejpam-4707	19	6	reserved	reserve	VERB
ejpam-4707	19	7	.	.	PUNCT
ejpam-4707	20	1	b.	b.	PROPN
ejpam-4707	20	2	kulahcioglu	kulahcioglu	PROPN
ejpam-4707	20	3	,	,	PUNCT
ejpam-4707	20	4	u.	u.	NOUN
ejpam-4707	20	5	ufuktepe	ufuktepe	NOUN
ejpam-4707	20	6	,	,	PUNCT
ejpam-4707	20	7	a.	a.	PROPN
ejpam-4707	20	8	kalampakas	kalampakas	PROPN
ejpam-4707	20	9	/	/	SYM
ejpam-4707	20	10	eur	eur	PROPN
ejpam-4707	20	11	.	.	PUNCT
ejpam-4707	21	1	j.	j.	PROPN
ejpam-4707	21	2	pure	pure	PROPN
ejpam-4707	21	3	appl	appl	PROPN
ejpam-4707	21	4	.	.	PROPN
ejpam-4707	21	5	math	math	PROPN
ejpam-4707	21	6	,	,	PUNCT
ejpam-4707	21	7	16	16	NUM
ejpam-4707	21	8	(	(	PUNCT
ejpam-4707	21	9	2	2	NUM
ejpam-4707	21	10	)	)	PUNCT
ejpam-4707	21	11	(	(	PUNCT
ejpam-4707	21	12	2023	2023	NUM
ejpam-4707	21	13	)	)	PUNCT
ejpam-4707	21	14	,	,	PUNCT
ejpam-4707	21	15	736	736	NUM
ejpam-4707	21	16	-	-	SYM
ejpam-4707	21	17	750	750	NUM
ejpam-4707	21	18	737	737	NUM
ejpam-4707	21	19	whereht	whereht	NOUN
ejpam-4707	21	20	and	and	CCONJ
ejpam-4707	21	21	pt	pt	PROPN
ejpam-4707	21	22	are	be	AUX
ejpam-4707	21	23	population	population	NOUN
ejpam-4707	21	24	sizes	size	NOUN
ejpam-4707	21	25	of	of	ADP
ejpam-4707	21	26	host	host	NOUN
ejpam-4707	21	27	and	and	CCONJ
ejpam-4707	21	28	parasitoids	parasitoid	NOUN
ejpam-4707	21	29	,	,	PUNCT
ejpam-4707	21	30	respectively	respectively	ADV
ejpam-4707	21	31	,	,	PUNCT
ejpam-4707	21	32	in	in	ADP
ejpam-4707	21	33	the	the	DET
ejpam-4707	21	34	generation	generation	NOUN
ejpam-4707	21	35	t.	t.	PROPN
ejpam-4707	21	36	in	in	ADP
ejpam-4707	21	37	the	the	DET
ejpam-4707	21	38	host	host	NOUN
ejpam-4707	21	39	population	population	NOUN
ejpam-4707	21	40	,	,	PUNCT
ejpam-4707	21	41	r	r	NOUN
ejpam-4707	21	42	is	be	AUX
ejpam-4707	21	43	the	the	DET
ejpam-4707	21	44	reproduction	reproduction	NOUN
ejpam-4707	21	45	rate	rate	NOUN
ejpam-4707	21	46	of	of	ADP
ejpam-4707	21	47	hosts	host	NOUN
ejpam-4707	21	48	,	,	PUNCT
ejpam-4707	21	49	and	and	CCONJ
ejpam-4707	21	50	the	the	DET
ejpam-4707	21	51	function	function	NOUN
ejpam-4707	21	52	f(ht	f(ht	NOUN
ejpam-4707	21	53	,	,	PUNCT
ejpam-4707	21	54	pt	pt	NOUN
ejpam-4707	21	55	)	)	PUNCT
ejpam-4707	21	56	is	be	AUX
ejpam-4707	21	57	the	the	DET
ejpam-4707	21	58	fraction	fraction	NOUN
ejpam-4707	21	59	of	of	ADP
ejpam-4707	21	60	host	host	NOUN
ejpam-4707	21	61	escaping	escape	VERB
ejpam-4707	21	62	parasitism	parasitism	NOUN
ejpam-4707	21	63	.	.	PUNCT
ejpam-4707	22	1	in	in	ADP
ejpam-4707	22	2	the	the	DET
ejpam-4707	22	3	parasitoid	parasitoid	NOUN
ejpam-4707	22	4	equation	equation	NOUN
ejpam-4707	22	5	,	,	PUNCT
ejpam-4707	22	6	β	β	X
ejpam-4707	22	7	is	be	AUX
ejpam-4707	22	8	the	the	DET
ejpam-4707	22	9	average	average	ADJ
ejpam-4707	22	10	number	number	NOUN
ejpam-4707	22	11	of	of	ADP
ejpam-4707	22	12	eggs	egg	NOUN
ejpam-4707	22	13	(	(	PUNCT
ejpam-4707	22	14	larvae	larvae	PROPN
ejpam-4707	22	15	)	)	PUNCT
ejpam-4707	22	16	released	release	VERB
ejpam-4707	22	17	by	by	ADP
ejpam-4707	22	18	parasitoid	parasitoid	NOUN
ejpam-4707	22	19	on	on	ADP
ejpam-4707	22	20	a	a	DET
ejpam-4707	22	21	single	single	ADJ
ejpam-4707	22	22	host	host	NOUN
ejpam-4707	22	23	.	.	PUNCT
ejpam-4707	23	1	an	an	DET
ejpam-4707	23	2	ecologically	ecologically	ADV
ejpam-4707	23	3	interesting	interesting	ADJ
ejpam-4707	23	4	model	model	NOUN
ejpam-4707	23	5	developed	develop	VERB
ejpam-4707	23	6	to	to	PART
ejpam-4707	23	7	describe	describe	VERB
ejpam-4707	23	8	population	population	NOUN
ejpam-4707	23	9	dynamics	dynamic	NOUN
ejpam-4707	23	10	of	of	ADP
ejpam-4707	23	11	a	a	DET
ejpam-4707	23	12	coupled	couple	VERB
ejpam-4707	23	13	host	host	NOUN
ejpam-4707	23	14	-	-	PUNCT
ejpam-4707	23	15	parasitoid	parasitoid	NOUN
ejpam-4707	23	16	system	system	NOUN
ejpam-4707	23	17	is	be	AUX
ejpam-4707	23	18	the	the	DET
ejpam-4707	23	19	nicholson	nicholson	PROPN
ejpam-4707	23	20	–	–	PUNCT
ejpam-4707	23	21	bailey	bailey	PROPN
ejpam-4707	23	22	model	model	NOUN
ejpam-4707	24	1	[	[	X
ejpam-4707	24	2	12	12	NUM
ejpam-4707	24	3	]	]	PUNCT
ejpam-4707	24	4	which	which	PRON
ejpam-4707	24	5	adds	add	VERB
ejpam-4707	24	6	further	further	ADJ
ejpam-4707	24	7	assumptions	assumption	NOUN
ejpam-4707	24	8	to	to	ADP
ejpam-4707	24	9	the	the	DET
ejpam-4707	24	10	general	general	ADJ
ejpam-4707	24	11	case	case	NOUN
ejpam-4707	24	12	.	.	PUNCT
ejpam-4707	25	1	since	since	SCONJ
ejpam-4707	25	2	most	most	ADJ
ejpam-4707	25	3	parasitoid	parasitoid	NOUN
ejpam-4707	25	4	larvae	larvae	NOUN
ejpam-4707	25	5	require	require	VERB
ejpam-4707	25	6	a	a	DET
ejpam-4707	25	7	specific	specific	ADJ
ejpam-4707	25	8	life	life	NOUN
ejpam-4707	25	9	-	-	PUNCT
ejpam-4707	25	10	stage	stage	NOUN
ejpam-4707	25	11	of	of	ADP
ejpam-4707	25	12	the	the	DET
ejpam-4707	25	13	host	host	NOUN
ejpam-4707	25	14	,	,	PUNCT
ejpam-4707	25	15	the	the	DET
ejpam-4707	25	16	parasitoid	parasitoid	NOUN
ejpam-4707	25	17	and	and	CCONJ
ejpam-4707	25	18	host	host	NOUN
ejpam-4707	25	19	generations	generation	NOUN
ejpam-4707	25	20	are	be	AUX
ejpam-4707	25	21	lined	line	VERB
ejpam-4707	25	22	to	to	ADP
ejpam-4707	25	23	one	one	NUM
ejpam-4707	25	24	another	another	PRON
ejpam-4707	25	25	[	[	X
ejpam-4707	25	26	7	7	NUM
ejpam-4707	25	27	]	]	PUNCT
ejpam-4707	25	28	.	.	PUNCT
ejpam-4707	26	1	hence	hence	ADV
ejpam-4707	26	2	the	the	DET
ejpam-4707	26	3	total	total	ADJ
ejpam-4707	26	4	number	number	NOUN
ejpam-4707	26	5	of	of	ADP
ejpam-4707	26	6	encounters	encounter	NOUN
ejpam-4707	26	7	with	with	ADP
ejpam-4707	26	8	hosts	host	NOUN
ejpam-4707	26	9	by	by	ADP
ejpam-4707	26	10	parasitoids	parasitoid	NOUN
ejpam-4707	26	11	is	be	AUX
ejpam-4707	26	12	in	in	ADP
ejpam-4707	26	13	direct	direct	ADJ
ejpam-4707	26	14	proportion	proportion	NOUN
ejpam-4707	26	15	to	to	PART
ejpam-4707	26	16	host	host	NOUN
ejpam-4707	26	17	density	density	NOUN
ejpam-4707	26	18	and	and	CCONJ
ejpam-4707	26	19	the	the	DET
ejpam-4707	26	20	encounter	encounter	ADJ
ejpam-4707	26	21	number	number	NOUN
ejpam-4707	26	22	is	be	AUX
ejpam-4707	26	23	distributed	distribute	VERB
ejpam-4707	26	24	randomly	randomly	ADV
ejpam-4707	26	25	among	among	ADP
ejpam-4707	26	26	the	the	DET
ejpam-4707	26	27	available	available	ADJ
ejpam-4707	26	28	hosts	host	NOUN
ejpam-4707	26	29	.	.	PUNCT
ejpam-4707	27	1	using	use	VERB
ejpam-4707	27	2	poisson	poisson	NOUN
ejpam-4707	27	3	distribution	distribution	NOUN
ejpam-4707	27	4	model	model	NOUN
ejpam-4707	27	5	1	1	NUM
ejpam-4707	27	6	becomes	become	VERB
ejpam-4707	27	7	:	:	PUNCT
ejpam-4707	27	8	ht+1	ht+1	NUM
ejpam-4707	27	9	=	=	SYM
ejpam-4707	27	10	rhte	rhte	NOUN
ejpam-4707	27	11	−apt	−apt	ADJ
ejpam-4707	27	12	pt+1	pt+1	NOUN
ejpam-4707	28	1	=	=	SYM
ejpam-4707	28	2	βht	βht	NOUN
ejpam-4707	28	3	(	(	PUNCT
ejpam-4707	28	4	1−	1−	NUM
ejpam-4707	28	5	e−apt	e−apt	NOUN
ejpam-4707	28	6	)	)	PUNCT
ejpam-4707	28	7	,	,	PUNCT
ejpam-4707	28	8	(	(	PUNCT
ejpam-4707	28	9	2	2	X
ejpam-4707	28	10	)	)	PUNCT
ejpam-4707	28	11	where	where	SCONJ
ejpam-4707	28	12	e−apt	e−apt	NOUN
ejpam-4707	28	13	stands	stand	VERB
ejpam-4707	28	14	for	for	ADP
ejpam-4707	28	15	probability	probability	NOUN
ejpam-4707	28	16	of	of	ADP
ejpam-4707	28	17	not	not	PART
ejpam-4707	28	18	to	to	PART
ejpam-4707	28	19	be	be	AUX
ejpam-4707	28	20	infested	infest	VERB
ejpam-4707	28	21	by	by	ADP
ejpam-4707	28	22	parasitoid	parasitoid	NOUN
ejpam-4707	28	23	and	and	CCONJ
ejpam-4707	28	24	1−	1−	NUM
ejpam-4707	28	25	e−apt	e−apt	NOUN
ejpam-4707	28	26	is	be	AUX
ejpam-4707	28	27	the	the	DET
ejpam-4707	28	28	probability	probability	NOUN
ejpam-4707	28	29	of	of	ADP
ejpam-4707	28	30	being	be	AUX
ejpam-4707	28	31	infested	infest	VERB
ejpam-4707	28	32	by	by	ADP
ejpam-4707	28	33	parasitoid	parasitoid	NOUN
ejpam-4707	28	34	at	at	ADP
ejpam-4707	28	35	time	time	NOUN
ejpam-4707	28	36	t.	t.	PROPN
ejpam-4707	28	37	initial	initial	ADJ
ejpam-4707	28	38	studies	study	NOUN
ejpam-4707	28	39	on	on	ADP
ejpam-4707	28	40	host	host	NOUN
ejpam-4707	28	41	-	-	PUNCT
ejpam-4707	28	42	parasitoid	parasitoid	NOUN
ejpam-4707	28	43	interactions	interaction	NOUN
ejpam-4707	28	44	employed	employ	VERB
ejpam-4707	28	45	equations	equation	NOUN
ejpam-4707	28	46	(	(	PUNCT
ejpam-4707	28	47	2	2	NUM
ejpam-4707	28	48	)	)	PUNCT
ejpam-4707	28	49	,	,	PUNCT
ejpam-4707	28	50	known	know	VERB
ejpam-4707	28	51	as	as	ADP
ejpam-4707	28	52	nicholsanbailey	nicholsanbailey	NOUN
ejpam-4707	28	53	host	host	NOUN
ejpam-4707	28	54	-	-	PUNCT
ejpam-4707	28	55	parasitoid	parasitoid	NOUN
ejpam-4707	28	56	model	model	NOUN
ejpam-4707	28	57	.	.	PUNCT
ejpam-4707	29	1	several	several	ADJ
ejpam-4707	29	2	other	other	ADJ
ejpam-4707	29	3	host	host	NOUN
ejpam-4707	29	4	-	-	PUNCT
ejpam-4707	29	5	parasitoid	parasitoid	NOUN
ejpam-4707	29	6	models	model	NOUN
ejpam-4707	29	7	have	have	AUX
ejpam-4707	29	8	since	since	ADV
ejpam-4707	29	9	been	be	AUX
ejpam-4707	29	10	developed	develop	VERB
ejpam-4707	29	11	as	as	ADP
ejpam-4707	29	12	versions	version	NOUN
ejpam-4707	29	13	of	of	ADP
ejpam-4707	29	14	nicholsan	nicholsan	PROPN
ejpam-4707	29	15	-	-	PUNCT
ejpam-4707	29	16	bailey	bailey	NOUN
ejpam-4707	29	17	(	(	PUNCT
ejpam-4707	29	18	see	see	VERB
ejpam-4707	30	1	e.g.	e.g.	ADV
ejpam-4707	30	2	[	[	X
ejpam-4707	30	3	15]-[2	15]-[2	PROPN
ejpam-4707	30	4	]	]	X
ejpam-4707	30	5	)	)	PUNCT
ejpam-4707	30	6	.	.	PUNCT
ejpam-4707	31	1	in	in	ADP
ejpam-4707	31	2	[	[	X
ejpam-4707	31	3	11	11	NUM
ejpam-4707	31	4	]	]	PUNCT
ejpam-4707	31	5	the	the	DET
ejpam-4707	31	6	2	2	NUM
ejpam-4707	31	7	-	-	PUNCT
ejpam-4707	31	8	year	year	NOUN
ejpam-4707	31	9	oscillations	oscillation	NOUN
ejpam-4707	31	10	in	in	ADP
ejpam-4707	31	11	abundance	abundance	NOUN
ejpam-4707	31	12	of	of	ADP
ejpam-4707	31	13	xestia	xestia	PROPN
ejpam-4707	31	14	moths	moth	NOUN
ejpam-4707	31	15	were	be	AUX
ejpam-4707	31	16	investigated	investigate	VERB
ejpam-4707	31	17	by	by	ADP
ejpam-4707	31	18	testing	test	VERB
ejpam-4707	31	19	a	a	DET
ejpam-4707	31	20	hypothesized	hypothesized	ADJ
ejpam-4707	31	21	xestia	xestia	NOUN
ejpam-4707	31	22	-	-	PUNCT
ejpam-4707	31	23	ophion	ophion	NOUN
ejpam-4707	31	24	interaction	interaction	NOUN
ejpam-4707	31	25	.	.	PUNCT
ejpam-4707	32	1	using	use	VERB
ejpam-4707	32	2	statistical	statistical	ADJ
ejpam-4707	32	3	modelling	modelling	NOUN
ejpam-4707	32	4	of	of	ADP
ejpam-4707	32	5	time	time	NOUN
ejpam-4707	32	6	-	-	PUNCT
ejpam-4707	32	7	series	series	NOUN
ejpam-4707	32	8	data	datum	NOUN
ejpam-4707	32	9	the	the	DET
ejpam-4707	32	10	authors	author	NOUN
ejpam-4707	32	11	provided	provide	VERB
ejpam-4707	32	12	evidence	evidence	NOUN
ejpam-4707	32	13	demonstrating	demonstrate	VERB
ejpam-4707	32	14	the	the	DET
ejpam-4707	32	15	validity	validity	NOUN
ejpam-4707	32	16	of	of	ADP
ejpam-4707	32	17	an	an	DET
ejpam-4707	32	18	underlying	underlie	VERB
ejpam-4707	32	19	host	host	NOUN
ejpam-4707	32	20	-	-	PUNCT
ejpam-4707	32	21	parasitoid	parasitoid	NOUN
ejpam-4707	32	22	hypothesis	hypothesis	NOUN
ejpam-4707	32	23	(	(	PUNCT
ejpam-4707	32	24	see	see	VERB
ejpam-4707	32	25	also	also	ADV
ejpam-4707	32	26	[	[	X
ejpam-4707	32	27	15	15	NUM
ejpam-4707	32	28	]	]	NUM
ejpam-4707	32	29	)	)	PUNCT
ejpam-4707	32	30	.	.	PUNCT
ejpam-4707	33	1	the	the	DET
ejpam-4707	33	2	governing	govern	VERB
ejpam-4707	33	3	model	model	NOUN
ejpam-4707	33	4	is	be	AUX
ejpam-4707	33	5	nt+2	nt+2	ADP
ejpam-4707	33	6	=	=	SYM
ejpam-4707	33	7	ntg(nt)f(pt	ntg(nt)f(pt	PROPN
ejpam-4707	33	8	)	)	PUNCT
ejpam-4707	33	9	,	,	PUNCT
ejpam-4707	33	10	pt+1	pt+1	X
ejpam-4707	34	1	=	=	SYM
ejpam-4707	34	2	nt(1−	nt(1−	NUM
ejpam-4707	34	3	f(pt	f(pt	NOUN
ejpam-4707	34	4	)	)	PUNCT
ejpam-4707	34	5	)	)	PUNCT
ejpam-4707	34	6	,	,	PUNCT
ejpam-4707	34	7	(	(	PUNCT
ejpam-4707	34	8	3	3	X
ejpam-4707	34	9	)	)	PUNCT
ejpam-4707	34	10	where	where	SCONJ
ejpam-4707	34	11	nt	not	PART
ejpam-4707	34	12	and	and	CCONJ
ejpam-4707	34	13	pt	pt	PROPN
ejpam-4707	34	14	are	be	AUX
ejpam-4707	34	15	the	the	DET
ejpam-4707	34	16	population	population	NOUN
ejpam-4707	34	17	sizes	size	NOUN
ejpam-4707	34	18	of	of	ADP
ejpam-4707	34	19	the	the	DET
ejpam-4707	34	20	host	host	NOUN
ejpam-4707	34	21	(	(	PUNCT
ejpam-4707	34	22	xestia	xestia	PROPN
ejpam-4707	34	23	)	)	PUNCT
ejpam-4707	34	24	and	and	CCONJ
ejpam-4707	34	25	parasitoid	parasitoid	NOUN
ejpam-4707	34	26	(	(	PUNCT
ejpam-4707	34	27	ophion	ophion	NOUN
ejpam-4707	34	28	)	)	PUNCT
ejpam-4707	34	29	,	,	PUNCT
ejpam-4707	34	30	respectively	respectively	ADV
ejpam-4707	34	31	.	.	PUNCT
ejpam-4707	35	1	the	the	DET
ejpam-4707	35	2	function	function	PROPN
ejpam-4707	35	3	g(n	g(n	PROPN
ejpam-4707	35	4	)	)	PUNCT
ejpam-4707	35	5	denotes	denote	VERB
ejpam-4707	35	6	the	the	DET
ejpam-4707	35	7	population	population	NOUN
ejpam-4707	35	8	growth	growth	NOUN
ejpam-4707	35	9	rate	rate	NOUN
ejpam-4707	35	10	of	of	ADP
ejpam-4707	35	11	the	the	DET
ejpam-4707	35	12	host	host	NOUN
ejpam-4707	35	13	and	and	CCONJ
ejpam-4707	35	14	the	the	DET
ejpam-4707	35	15	function	function	NOUN
ejpam-4707	35	16	f(p	f(p	PROPN
ejpam-4707	35	17	)	)	PUNCT
ejpam-4707	35	18	is	be	AUX
ejpam-4707	35	19	the	the	DET
ejpam-4707	35	20	fraction	fraction	NOUN
ejpam-4707	35	21	of	of	ADP
ejpam-4707	35	22	hosts	host	NOUN
ejpam-4707	35	23	that	that	PRON
ejpam-4707	35	24	are	be	AUX
ejpam-4707	35	25	not	not	PART
ejpam-4707	35	26	parasitised	parasitise	VERB
ejpam-4707	35	27	.	.	PUNCT
ejpam-4707	36	1	this	this	DET
ejpam-4707	36	2	model	model	NOUN
ejpam-4707	36	3	assumes	assume	VERB
ejpam-4707	36	4	a	a	DET
ejpam-4707	36	5	2	2	NUM
ejpam-4707	36	6	-	-	PUNCT
ejpam-4707	36	7	year	year	NOUN
ejpam-4707	36	8	host	host	NOUN
ejpam-4707	36	9	life	life	NOUN
ejpam-4707	36	10	cycle	cycle	NOUN
ejpam-4707	36	11	as	as	SCONJ
ejpam-4707	36	12	opposed	oppose	VERB
ejpam-4707	36	13	to	to	ADP
ejpam-4707	36	14	single	single	ADJ
ejpam-4707	36	15	year	year	NOUN
ejpam-4707	36	16	life	life	NOUN
ejpam-4707	36	17	cycle	cycle	NOUN
ejpam-4707	36	18	of	of	ADP
ejpam-4707	36	19	the	the	DET
ejpam-4707	36	20	parasitoid	parasitoid	NOUN
ejpam-4707	36	21	which	which	PRON
ejpam-4707	36	22	explains	explain	VERB
ejpam-4707	36	23	the	the	DET
ejpam-4707	36	24	apparent	apparent	ADJ
ejpam-4707	36	25	2	2	NUM
ejpam-4707	36	26	-	-	PUNCT
ejpam-4707	36	27	year	year	NOUN
ejpam-4707	36	28	population	population	NOUN
ejpam-4707	36	29	oscillation	oscillation	NOUN
ejpam-4707	36	30	.	.	PUNCT
ejpam-4707	37	1	for	for	ADP
ejpam-4707	37	2	this	this	DET
ejpam-4707	37	3	reason	reason	NOUN
ejpam-4707	37	4	there	there	PRON
ejpam-4707	37	5	are	be	VERB
ejpam-4707	37	6	two	two	NUM
ejpam-4707	37	7	independent	independent	ADJ
ejpam-4707	37	8	host	host	NOUN
ejpam-4707	37	9	populations	population	NOUN
ejpam-4707	37	10	one	one	NUM
ejpam-4707	37	11	for	for	ADP
ejpam-4707	37	12	even	even	ADV
ejpam-4707	37	13	and	and	CCONJ
ejpam-4707	37	14	one	one	NUM
ejpam-4707	37	15	for	for	ADP
ejpam-4707	37	16	odd	odd	ADJ
ejpam-4707	37	17	years	year	NOUN
ejpam-4707	37	18	.	.	PUNCT
ejpam-4707	38	1	although	although	SCONJ
ejpam-4707	38	2	there	there	PRON
ejpam-4707	38	3	is	be	VERB
ejpam-4707	38	4	no	no	DET
ejpam-4707	38	5	direct	direct	ADJ
ejpam-4707	38	6	interaction	interaction	NOUN
ejpam-4707	38	7	between	between	ADP
ejpam-4707	38	8	the	the	DET
ejpam-4707	38	9	two	two	NUM
ejpam-4707	38	10	host	host	NOUN
ejpam-4707	38	11	cohorts	cohort	NOUN
ejpam-4707	38	12	,	,	PUNCT
ejpam-4707	38	13	they	they	PRON
ejpam-4707	38	14	are	be	AUX
ejpam-4707	38	15	coupled	couple	VERB
ejpam-4707	38	16	through	through	ADP
ejpam-4707	38	17	the	the	DET
ejpam-4707	38	18	the	the	DET
ejpam-4707	38	19	parasitoid	parasitoid	NOUN
ejpam-4707	38	20	population	population	NOUN
ejpam-4707	38	21	.	.	PUNCT
ejpam-4707	39	1	when	when	SCONJ
ejpam-4707	39	2	we	we	PRON
ejpam-4707	39	3	checked	check	VERB
ejpam-4707	39	4	their	their	PRON
ejpam-4707	39	5	open	open	ADJ
ejpam-4707	39	6	source	source	NOUN
ejpam-4707	39	7	data	datum	NOUN
ejpam-4707	39	8	with	with	ADP
ejpam-4707	39	9	minitab	minitab	PROPN
ejpam-4707	39	10	(	(	PUNCT
ejpam-4707	39	11	see	see	VERB
ejpam-4707	39	12	figure	figure	NOUN
ejpam-4707	39	13	12	12	NUM
ejpam-4707	39	14	.	.	PUNCT
ejpam-4707	39	15	,	,	PUNCT
ejpam-4707	39	16	figure	figure	VERB
ejpam-4707	39	17	13	13	NUM
ejpam-4707	39	18	.	.	PUNCT
ejpam-4707	39	19	,	,	PUNCT
ejpam-4707	39	20	and	and	CCONJ
ejpam-4707	39	21	figure	figure	VERB
ejpam-4707	39	22	14	14	NUM
ejpam-4707	39	23	.	.	PUNCT
ejpam-4707	39	24	)	)	PUNCT
ejpam-4707	40	1	there	there	PRON
ejpam-4707	40	2	is	be	VERB
ejpam-4707	40	3	only	only	ADV
ejpam-4707	40	4	one	one	NUM
ejpam-4707	40	5	fixed	fix	VERB
ejpam-4707	40	6	point	point	NOUN
ejpam-4707	40	7	which	which	PRON
ejpam-4707	40	8	is	be	AUX
ejpam-4707	40	9	(	(	PUNCT
ejpam-4707	40	10	0,0	0,0	NOUN
ejpam-4707	40	11	)	)	PUNCT
ejpam-4707	40	12	and	and	CCONJ
ejpam-4707	40	13	the	the	DET
ejpam-4707	40	14	the	the	DET
ejpam-4707	40	15	fraction	fraction	NOUN
ejpam-4707	40	16	of	of	ADP
ejpam-4707	40	17	the	the	DET
ejpam-4707	40	18	host	host	NOUN
ejpam-4707	40	19	escaping	escape	VERB
ejpam-4707	40	20	parasitism	parasitism	NOUN
ejpam-4707	40	21	is	be	AUX
ejpam-4707	40	22	periodic	periodic	ADJ
ejpam-4707	40	23	and	and	CCONJ
ejpam-4707	40	24	piece	piece	NOUN
ejpam-4707	40	25	-	-	PUNCT
ejpam-4707	40	26	vise	vise	NOUN
ejpam-4707	40	27	exponential	exponential	NOUN
ejpam-4707	40	28	because	because	SCONJ
ejpam-4707	40	29	of	of	ADP
ejpam-4707	40	30	the	the	DET
ejpam-4707	40	31	seasonal	seasonal	ADJ
ejpam-4707	40	32	behavior	behavior	NOUN
ejpam-4707	40	33	of	of	ADP
ejpam-4707	40	34	the	the	DET
ejpam-4707	40	35	parasitoid	parasitoid	NOUN
ejpam-4707	40	36	.	.	PUNCT
ejpam-4707	41	1	unlike	unlike	ADP
ejpam-4707	41	2	the	the	DET
ejpam-4707	41	3	predator	predator	NOUN
ejpam-4707	41	4	in	in	ADP
ejpam-4707	41	5	the	the	DET
ejpam-4707	41	6	general	general	ADJ
ejpam-4707	41	7	prey	prey	NOUN
ejpam-4707	41	8	-	-	PUNCT
ejpam-4707	41	9	predator	predator	NOUN
ejpam-4707	41	10	models	model	NOUN
ejpam-4707	41	11	,	,	PUNCT
ejpam-4707	41	12	the	the	DET
ejpam-4707	41	13	parasitoid	parasitoid	NOUN
ejpam-4707	41	14	in	in	ADP
ejpam-4707	41	15	the	the	DET
ejpam-4707	41	16	hostparasitoid	hostparasitoid	NOUN
ejpam-4707	41	17	models	model	NOUN
ejpam-4707	41	18	has	have	VERB
ejpam-4707	41	19	a	a	DET
ejpam-4707	41	20	production	production	NOUN
ejpam-4707	41	21	rate	rate	NOUN
ejpam-4707	41	22	closely	closely	ADV
ejpam-4707	41	23	defined	define	VERB
ejpam-4707	41	24	by	by	ADP
ejpam-4707	41	25	interactions	interaction	NOUN
ejpam-4707	41	26	between	between	ADP
ejpam-4707	41	27	host	host	NOUN
ejpam-4707	41	28	and	and	CCONJ
ejpam-4707	41	29	parasitoid	parasitoid	NOUN
ejpam-4707	41	30	.	.	PUNCT
ejpam-4707	42	1	hence	hence	ADV
ejpam-4707	42	2	,	,	PUNCT
ejpam-4707	42	3	generally	generally	ADV
ejpam-4707	42	4	it	it	PRON
ejpam-4707	42	5	is	be	AUX
ejpam-4707	42	6	sufficient	sufficient	ADJ
ejpam-4707	42	7	to	to	PART
ejpam-4707	42	8	use	use	VERB
ejpam-4707	42	9	a	a	DET
ejpam-4707	42	10	density	density	NOUN
ejpam-4707	42	11	dependent	dependent	ADJ
ejpam-4707	42	12	population	population	NOUN
ejpam-4707	42	13	model	model	NOUN
ejpam-4707	42	14	for	for	ADP
ejpam-4707	42	15	the	the	DET
ejpam-4707	42	16	host	host	NOUN
ejpam-4707	42	17	,	,	PUNCT
ejpam-4707	42	18	which	which	PRON
ejpam-4707	42	19	is	be	AUX
ejpam-4707	42	20	also	also	ADV
ejpam-4707	42	21	thought	think	VERB
ejpam-4707	42	22	to	to	PART
ejpam-4707	42	23	stabilize	stabilize	VERB
ejpam-4707	42	24	the	the	DET
ejpam-4707	42	25	system	system	NOUN
ejpam-4707	42	26	[	[	X
ejpam-4707	42	27	2	2	NUM
ejpam-4707	42	28	]	]	PUNCT
ejpam-4707	42	29	.	.	PUNCT
ejpam-4707	43	1	in	in	ADP
ejpam-4707	43	2	[	[	X
ejpam-4707	43	3	10	10	NUM
ejpam-4707	43	4	]	]	PUNCT
ejpam-4707	43	5	,	,	PUNCT
ejpam-4707	43	6	3	3	NUM
ejpam-4707	43	7	different	different	ADJ
ejpam-4707	43	8	model	model	NOUN
ejpam-4707	43	9	b.	b.	PROPN
ejpam-4707	43	10	kulahcioglu	kulahcioglu	PROPN
ejpam-4707	43	11	,	,	PUNCT
ejpam-4707	43	12	u.	u.	NOUN
ejpam-4707	43	13	ufuktepe	ufuktepe	NOUN
ejpam-4707	43	14	,	,	PUNCT
ejpam-4707	43	15	a.	a.	PROPN
ejpam-4707	43	16	kalampakas	kalampakas	PROPN
ejpam-4707	43	17	/	/	SYM
ejpam-4707	43	18	eur	eur	PROPN
ejpam-4707	43	19	.	.	PUNCT
ejpam-4707	44	1	j.	j.	PROPN
ejpam-4707	44	2	pure	pure	PROPN
ejpam-4707	44	3	appl	appl	PROPN
ejpam-4707	44	4	.	.	PROPN
ejpam-4707	44	5	math	math	PROPN
ejpam-4707	44	6	,	,	PUNCT
ejpam-4707	44	7	16	16	NUM
ejpam-4707	44	8	(	(	PUNCT
ejpam-4707	44	9	2	2	NUM
ejpam-4707	44	10	)	)	PUNCT
ejpam-4707	44	11	(	(	PUNCT
ejpam-4707	44	12	2023	2023	NUM
ejpam-4707	44	13	)	)	PUNCT
ejpam-4707	44	14	,	,	PUNCT
ejpam-4707	44	15	736	736	NUM
ejpam-4707	44	16	-	-	SYM
ejpam-4707	44	17	750	750	NUM
ejpam-4707	44	18	738	738	NUM
ejpam-4707	44	19	types	type	NOUN
ejpam-4707	44	20	were	be	AUX
ejpam-4707	44	21	proposed	propose	VERB
ejpam-4707	44	22	according	accord	VERB
ejpam-4707	44	23	to	to	ADP
ejpam-4707	44	24	the	the	DET
ejpam-4707	44	25	ordering	ordering	NOUN
ejpam-4707	44	26	of	of	ADP
ejpam-4707	44	27	parasitism	parasitism	NOUN
ejpam-4707	44	28	and	and	CCONJ
ejpam-4707	44	29	density	density	NOUN
ejpam-4707	44	30	dependence	dependence	NOUN
ejpam-4707	44	31	.	.	PUNCT
ejpam-4707	45	1	in	in	ADP
ejpam-4707	45	2	this	this	DET
ejpam-4707	45	3	approach	approach	NOUN
ejpam-4707	45	4	,	,	PUNCT
ejpam-4707	45	5	when	when	SCONJ
ejpam-4707	45	6	parasitism	parasitism	NOUN
ejpam-4707	45	7	acts	act	VERB
ejpam-4707	45	8	first	first	ADV
ejpam-4707	45	9	and	and	CCONJ
ejpam-4707	45	10	density	density	NOUN
ejpam-4707	45	11	dependence	dependence	NOUN
ejpam-4707	45	12	takes	take	VERB
ejpam-4707	45	13	places	place	NOUN
ejpam-4707	45	14	only	only	ADV
ejpam-4707	45	15	on	on	ADP
ejpam-4707	45	16	the	the	DET
ejpam-4707	45	17	survivors	survivor	NOUN
ejpam-4707	45	18	from	from	ADP
ejpam-4707	45	19	parasitism	parasitism	NOUN
ejpam-4707	45	20	(	(	PUNCT
ejpam-4707	45	21	i.e.	i.e.	X
ejpam-4707	45	22	htf(pt	htf(pt	NOUN
ejpam-4707	45	23	)	)	PUNCT
ejpam-4707	45	24	)	)	PUNCT
ejpam-4707	45	25	the	the	DET
ejpam-4707	45	26	model	model	NOUN
ejpam-4707	45	27	type	type	NOUN
ejpam-4707	45	28	is	be	AUX
ejpam-4707	45	29	:	:	PUNCT
ejpam-4707	45	30	ht+1	ht+1	NUM
ejpam-4707	45	31	=	=	SYM
ejpam-4707	45	32	htg(ht	htg(ht	NOUN
ejpam-4707	45	33	,	,	PUNCT
ejpam-4707	45	34	f(pt))f(pt	f(pt))f(pt	PROPN
ejpam-4707	45	35	)	)	PUNCT
ejpam-4707	45	36	,	,	PUNCT
ejpam-4707	45	37	pt+1	pt+1	X
ejpam-4707	46	1	=	=	SYM
ejpam-4707	46	2	ht	ht	PROPN
ejpam-4707	46	3	(	(	PUNCT
ejpam-4707	46	4	1−	1−	NUM
ejpam-4707	46	5	f(pt	f(pt	NOUN
ejpam-4707	46	6	)	)	PUNCT
ejpam-4707	46	7	)	)	PUNCT
ejpam-4707	46	8	.	.	PUNCT
ejpam-4707	47	1	(	(	PUNCT
ejpam-4707	47	2	4	4	X
ejpam-4707	47	3	)	)	PUNCT
ejpam-4707	47	4	choosing	choose	VERB
ejpam-4707	47	5	f(pt	f(pt	NOUN
ejpam-4707	47	6	)	)	PUNCT
ejpam-4707	47	7	=	=	SYM
ejpam-4707	47	8	exp(−bpt	exp(−bpt	PROPN
ejpam-4707	47	9	)	)	PUNCT
ejpam-4707	47	10	,	,	PUNCT
ejpam-4707	47	11	g(ht	g(ht	NOUN
ejpam-4707	47	12	,	,	PUNCT
ejpam-4707	47	13	f(pt	f(pt	NOUN
ejpam-4707	47	14	)	)	PUNCT
ejpam-4707	47	15	)	)	PUNCT
ejpam-4707	48	1	=	=	SYM
ejpam-4707	49	1	λ/(1	λ/(1	NOUN
ejpam-4707	49	2	+	+	CCONJ
ejpam-4707	49	3	khtexp(−bpt	khtexp(−bpt	NUM
ejpam-4707	49	4	)	)	PUNCT
ejpam-4707	49	5	)	)	PUNCT
ejpam-4707	50	1	and	and	CCONJ
ejpam-4707	50	2	adding	add	VERB
ejpam-4707	50	3	β	β	PRON
ejpam-4707	50	4	multiplier	multiplier	ADV
ejpam-4707	50	5	to	to	ADP
ejpam-4707	50	6	the	the	DET
ejpam-4707	50	7	second	second	ADJ
ejpam-4707	50	8	equation	equation	NOUN
ejpam-4707	50	9	,	,	PUNCT
ejpam-4707	50	10	we	we	PRON
ejpam-4707	50	11	obtain	obtain	VERB
ejpam-4707	50	12	:	:	PUNCT
ejpam-4707	50	13	ht+1	ht+1	NUM
ejpam-4707	50	14	=	=	PUNCT
ejpam-4707	50	15	λht	λht	ADJ
ejpam-4707	50	16	1	1	NUM
ejpam-4707	51	1	+	+	CCONJ
ejpam-4707	51	2	khte−bpt	khte−bpt	PROPN
ejpam-4707	51	3	e−bpt	e−bpt	NOUN
ejpam-4707	51	4	,	,	PUNCT
ejpam-4707	51	5	pt+1	pt+1	NOUN
ejpam-4707	51	6	=	=	SYM
ejpam-4707	51	7	βht(1−	βht(1−	PROPN
ejpam-4707	51	8	e−bpt	e−bpt	NOUN
ejpam-4707	51	9	)	)	PUNCT
ejpam-4707	51	10	.	.	PUNCT
ejpam-4707	52	1	(	(	PUNCT
ejpam-4707	52	2	5	5	X
ejpam-4707	52	3	)	)	PUNCT
ejpam-4707	52	4	this	this	DET
ejpam-4707	52	5	model	model	NOUN
ejpam-4707	52	6	(	(	PUNCT
ejpam-4707	52	7	5	5	NUM
ejpam-4707	52	8	)	)	PUNCT
ejpam-4707	52	9	was	be	AUX
ejpam-4707	52	10	formulated	formulate	VERB
ejpam-4707	52	11	and	and	CCONJ
ejpam-4707	52	12	analyzed	analyze	VERB
ejpam-4707	52	13	in	in	ADP
ejpam-4707	52	14	[	[	X
ejpam-4707	52	15	6	6	NUM
ejpam-4707	52	16	]	]	PUNCT
ejpam-4707	52	17	.	.	PUNCT
ejpam-4707	53	1	in	in	ADP
ejpam-4707	53	2	this	this	DET
ejpam-4707	53	3	setup	setup	NOUN
ejpam-4707	53	4	,	,	PUNCT
ejpam-4707	53	5	the	the	DET
ejpam-4707	53	6	host	host	NOUN
ejpam-4707	53	7	population	population	NOUN
ejpam-4707	53	8	in	in	ADP
ejpam-4707	53	9	the	the	DET
ejpam-4707	53	10	absence	absence	NOUN
ejpam-4707	53	11	of	of	ADP
ejpam-4707	53	12	the	the	DET
ejpam-4707	53	13	parasitoid	parasitoid	NOUN
ejpam-4707	53	14	is	be	AUX
ejpam-4707	53	15	modeled	model	VERB
ejpam-4707	53	16	by	by	ADP
ejpam-4707	53	17	beverton	beverton	PROPN
ejpam-4707	53	18	-	-	PUNCT
ejpam-4707	53	19	holt	holt	PROPN
ejpam-4707	53	20	equation	equation	NOUN
ejpam-4707	53	21	λh/(1	λh/(1	PUNCT
ejpam-4707	54	1	+	+	CCONJ
ejpam-4707	54	2	kh	kh	NOUN
ejpam-4707	54	3	)	)	PUNCT
ejpam-4707	54	4	.	.	PUNCT
ejpam-4707	55	1	the	the	DET
ejpam-4707	55	2	parameter	parameter	NOUN
ejpam-4707	55	3	β	β	PROPN
ejpam-4707	55	4	represents	represent	VERB
ejpam-4707	55	5	the	the	DET
ejpam-4707	55	6	average	average	ADJ
ejpam-4707	55	7	number	number	NOUN
ejpam-4707	55	8	of	of	ADP
ejpam-4707	55	9	egg	egg	NOUN
ejpam-4707	55	10	(	(	PUNCT
ejpam-4707	55	11	larvae	larvae	PROPN
ejpam-4707	55	12	)	)	PUNCT
ejpam-4707	55	13	released	release	VERB
ejpam-4707	55	14	by	by	ADP
ejpam-4707	55	15	parasitoid	parasitoid	NOUN
ejpam-4707	55	16	on	on	ADP
ejpam-4707	55	17	a	a	DET
ejpam-4707	55	18	single	single	ADJ
ejpam-4707	55	19	host	host	NOUN
ejpam-4707	55	20	and	and	CCONJ
ejpam-4707	55	21	all	all	DET
ejpam-4707	55	22	parameters	parameter	NOUN
ejpam-4707	55	23	are	be	AUX
ejpam-4707	55	24	positive	positive	ADJ
ejpam-4707	55	25	.	.	PUNCT
ejpam-4707	56	1	allee	allee	PROPN
ejpam-4707	56	2	and	and	CCONJ
ejpam-4707	56	3	the	the	DET
ejpam-4707	56	4	refuge	refuge	NOUN
ejpam-4707	56	5	effects	effect	NOUN
ejpam-4707	56	6	were	be	AUX
ejpam-4707	56	7	separately	separately	ADV
ejpam-4707	56	8	added	add	VERB
ejpam-4707	56	9	to	to	ADP
ejpam-4707	56	10	this	this	DET
ejpam-4707	56	11	model	model	NOUN
ejpam-4707	56	12	in	in	ADP
ejpam-4707	56	13	[	[	X
ejpam-4707	56	14	8	8	NUM
ejpam-4707	56	15	]	]	PUNCT
ejpam-4707	56	16	.	.	PUNCT
ejpam-4707	57	1	in	in	ADP
ejpam-4707	57	2	this	this	DET
ejpam-4707	57	3	paper	paper	NOUN
ejpam-4707	57	4	,	,	PUNCT
ejpam-4707	57	5	we	we	PRON
ejpam-4707	57	6	incorporate	incorporate	VERB
ejpam-4707	57	7	both	both	DET
ejpam-4707	57	8	effects	effect	NOUN
ejpam-4707	57	9	simultaneously	simultaneously	ADV
ejpam-4707	57	10	and	and	CCONJ
ejpam-4707	57	11	study	study	VERB
ejpam-4707	57	12	the	the	DET
ejpam-4707	57	13	dynamics	dynamic	NOUN
ejpam-4707	57	14	of	of	ADP
ejpam-4707	57	15	the	the	DET
ejpam-4707	57	16	resulting	result	VERB
ejpam-4707	57	17	model	model	NOUN
ejpam-4707	57	18	.	.	PUNCT
ejpam-4707	58	1	our	our	PRON
ejpam-4707	58	2	discrete	discrete	ADJ
ejpam-4707	58	3	-	-	PUNCT
ejpam-4707	58	4	time	time	NOUN
ejpam-4707	58	5	host	host	NOUN
ejpam-4707	58	6	–	–	PUNCT
ejpam-4707	58	7	parasitoid	parasitoid	NOUN
ejpam-4707	58	8	model	model	NOUN
ejpam-4707	58	9	is	be	AUX
ejpam-4707	58	10	presented	present	VERB
ejpam-4707	58	11	in	in	ADP
ejpam-4707	58	12	section	section	NOUN
ejpam-4707	58	13	2	2	NUM
ejpam-4707	58	14	.	.	PUNCT
ejpam-4707	59	1	in	in	ADP
ejpam-4707	59	2	section	section	NOUN
ejpam-4707	59	3	3	3	NUM
ejpam-4707	59	4	we	we	PRON
ejpam-4707	59	5	determine	determine	VERB
ejpam-4707	59	6	the	the	DET
ejpam-4707	59	7	conditions	condition	NOUN
ejpam-4707	59	8	under	under	ADP
ejpam-4707	59	9	which	which	PRON
ejpam-4707	59	10	a	a	DET
ejpam-4707	59	11	positive	positive	ADJ
ejpam-4707	59	12	fixed	fix	VERB
ejpam-4707	59	13	point	point	NOUN
ejpam-4707	59	14	exists	exist	VERB
ejpam-4707	59	15	and	and	CCONJ
ejpam-4707	59	16	is	be	AUX
ejpam-4707	59	17	unique	unique	ADJ
ejpam-4707	59	18	.	.	PUNCT
ejpam-4707	60	1	in	in	ADP
ejpam-4707	60	2	section	section	NOUN
ejpam-4707	60	3	4	4	NUM
ejpam-4707	60	4	we	we	PRON
ejpam-4707	60	5	study	study	VERB
ejpam-4707	60	6	local	local	ADJ
ejpam-4707	60	7	asymptotic	asymptotic	ADJ
ejpam-4707	60	8	stability	stability	NOUN
ejpam-4707	60	9	,	,	PUNCT
ejpam-4707	60	10	global	global	ADJ
ejpam-4707	60	11	fixed	fix	VERB
ejpam-4707	60	12	point	point	NOUN
ejpam-4707	60	13	stability	stability	NOUN
ejpam-4707	60	14	and	and	CCONJ
ejpam-4707	60	15	types	type	NOUN
ejpam-4707	60	16	of	of	ADP
ejpam-4707	60	17	bifurcations	bifurcation	NOUN
ejpam-4707	60	18	.	.	PUNCT
ejpam-4707	61	1	numerical	numerical	ADJ
ejpam-4707	61	2	examples	example	NOUN
ejpam-4707	61	3	for	for	ADP
ejpam-4707	61	4	verification	verification	NOUN
ejpam-4707	61	5	of	of	ADP
ejpam-4707	61	6	the	the	DET
ejpam-4707	61	7	theoretical	theoretical	ADJ
ejpam-4707	61	8	results	result	NOUN
ejpam-4707	61	9	are	be	AUX
ejpam-4707	61	10	given	give	VERB
ejpam-4707	61	11	in	in	ADP
ejpam-4707	61	12	section	section	NOUN
ejpam-4707	61	13	5	5	NUM
ejpam-4707	61	14	where	where	SCONJ
ejpam-4707	61	15	the	the	DET
ejpam-4707	61	16	data	datum	NOUN
ejpam-4707	61	17	of	of	ADP
ejpam-4707	61	18	[	[	X
ejpam-4707	61	19	11	11	NUM
ejpam-4707	61	20	]	]	PUNCT
ejpam-4707	61	21	are	be	AUX
ejpam-4707	61	22	checked	check	VERB
ejpam-4707	61	23	with	with	ADP
ejpam-4707	61	24	minitab	minitab	PROPN
ejpam-4707	61	25	in	in	ADP
ejpam-4707	61	26	comparison	comparison	NOUN
ejpam-4707	61	27	to	to	ADP
ejpam-4707	61	28	our	our	PRON
ejpam-4707	61	29	model	model	NOUN
ejpam-4707	61	30	.	.	PUNCT
ejpam-4707	62	1	2	2	X
ejpam-4707	62	2	.	.	X
ejpam-4707	62	3	host	host	NOUN
ejpam-4707	62	4	–	–	PUNCT
ejpam-4707	62	5	parasitoid	parasitoid	NOUN
ejpam-4707	62	6	model	model	NOUN
ejpam-4707	62	7	with	with	ADP
ejpam-4707	62	8	allee	allee	NOUN
ejpam-4707	62	9	and	and	CCONJ
ejpam-4707	62	10	refuge	refuge	NOUN
ejpam-4707	62	11	effects	effect	NOUN
ejpam-4707	62	12	in	in	ADP
ejpam-4707	62	13	this	this	DET
ejpam-4707	62	14	section	section	NOUN
ejpam-4707	62	15	we	we	PRON
ejpam-4707	62	16	will	will	AUX
ejpam-4707	62	17	introduce	introduce	VERB
ejpam-4707	62	18	a	a	DET
ejpam-4707	62	19	discrete	discrete	ADJ
ejpam-4707	62	20	-	-	PUNCT
ejpam-4707	62	21	time	time	NOUN
ejpam-4707	62	22	host	host	NOUN
ejpam-4707	62	23	–	–	PUNCT
ejpam-4707	62	24	parasitoid	parasitoid	NOUN
ejpam-4707	62	25	model	model	NOUN
ejpam-4707	62	26	incorporating	incorporate	VERB
ejpam-4707	62	27	simultaneously	simultaneously	ADV
ejpam-4707	62	28	an	an	DET
ejpam-4707	62	29	allee	allee	NOUN
ejpam-4707	62	30	and	and	CCONJ
ejpam-4707	62	31	a	a	DET
ejpam-4707	62	32	refuge	refuge	NOUN
ejpam-4707	62	33	effect	effect	NOUN
ejpam-4707	62	34	on	on	ADP
ejpam-4707	62	35	the	the	DET
ejpam-4707	62	36	host	host	NOUN
ejpam-4707	62	37	.	.	PUNCT
ejpam-4707	63	1	we	we	PRON
ejpam-4707	63	2	start	start	VERB
ejpam-4707	63	3	from	from	ADP
ejpam-4707	63	4	the	the	DET
ejpam-4707	63	5	system	system	NOUN
ejpam-4707	63	6	of	of	ADP
ejpam-4707	63	7	equations	equation	NOUN
ejpam-4707	63	8	(	(	PUNCT
ejpam-4707	63	9	5	5	NUM
ejpam-4707	63	10	)	)	PUNCT
ejpam-4707	63	11	.	.	PUNCT
ejpam-4707	64	1	it	it	PRON
ejpam-4707	64	2	has	have	VERB
ejpam-4707	64	3	four	four	NUM
ejpam-4707	64	4	parameters	parameter	NOUN
ejpam-4707	64	5	,	,	PUNCT
ejpam-4707	64	6	namely	namely	ADV
ejpam-4707	64	7	,	,	PUNCT
ejpam-4707	64	8	λ	λ	PROPN
ejpam-4707	64	9	,	,	PUNCT
ejpam-4707	64	10	b	b	PROPN
ejpam-4707	64	11	,	,	PUNCT
ejpam-4707	64	12	k	k	PROPN
ejpam-4707	64	13	and	and	CCONJ
ejpam-4707	64	14	β	β	X
ejpam-4707	64	15	.	.	PUNCT
ejpam-4707	65	1	we	we	PRON
ejpam-4707	65	2	can	can	AUX
ejpam-4707	65	3	simplify	simplify	VERB
ejpam-4707	65	4	it	it	PRON
ejpam-4707	65	5	by	by	ADP
ejpam-4707	65	6	substituting	substitute	VERB
ejpam-4707	65	7	nt	not	PART
ejpam-4707	65	8	=	=	SYM
ejpam-4707	65	9	βht	βht	PROPN
ejpam-4707	65	10	and	and	CCONJ
ejpam-4707	65	11	yt	yt	PROPN
ejpam-4707	65	12	=	=	SYM
ejpam-4707	65	13	bpt	bpt	PROPN
ejpam-4707	65	14	.	.	PROPN
ejpam-4707	65	15	nt+1	nt+1	PROPN
ejpam-4707	66	1	=	=	SYM
ejpam-4707	66	2	λnt	λnt	NOUN
ejpam-4707	66	3	1	1	NUM
ejpam-4707	66	4	+	+	CCONJ
ejpam-4707	66	5	k	k	PROPN
ejpam-4707	66	6	βnte−yt	βnte−yt	X
ejpam-4707	66	7	e−yt	e−yt	PROPN
ejpam-4707	66	8	,	,	PUNCT
ejpam-4707	66	9	yt+1	yt+1	PROPN
ejpam-4707	66	10	=	=	SYM
ejpam-4707	66	11	bnt	bnt	PROPN
ejpam-4707	66	12	(	(	PUNCT
ejpam-4707	66	13	1−	1−	NUM
ejpam-4707	66	14	e−yt	e−yt	PROPN
ejpam-4707	66	15	)	)	PUNCT
ejpam-4707	66	16	.	.	PUNCT
ejpam-4707	67	1	(	(	PUNCT
ejpam-4707	67	2	6	6	X
ejpam-4707	67	3	)	)	PUNCT
ejpam-4707	67	4	let	let	VERB
ejpam-4707	67	5	xt	xt	PUNCT
ejpam-4707	68	1	=	=	PROPN
ejpam-4707	68	2	bnt	bnt	PROPN
ejpam-4707	68	3	and	and	CCONJ
ejpam-4707	68	4	c	c	NOUN
ejpam-4707	68	5	=	=	SYM
ejpam-4707	68	6	k/(βb	k/(βb	ADJ
ejpam-4707	68	7	)	)	PUNCT
ejpam-4707	68	8	,	,	PUNCT
ejpam-4707	68	9	then	then	ADV
ejpam-4707	68	10	the	the	DET
ejpam-4707	68	11	model	model	NOUN
ejpam-4707	68	12	(	(	PUNCT
ejpam-4707	68	13	6	6	NUM
ejpam-4707	68	14	)	)	PUNCT
ejpam-4707	68	15	can	can	AUX
ejpam-4707	68	16	be	be	AUX
ejpam-4707	68	17	written	write	VERB
ejpam-4707	68	18	as	as	SCONJ
ejpam-4707	68	19	follows	follow	VERB
ejpam-4707	68	20	:	:	PUNCT
ejpam-4707	68	21	xt+1	xt+1	PUNCT
ejpam-4707	69	1	=	=	SYM
ejpam-4707	69	2	λxte	λxte	NOUN
ejpam-4707	69	3	−yt	−yt	X
ejpam-4707	69	4	1	1	NUM
ejpam-4707	69	5	+	+	CCONJ
ejpam-4707	69	6	cxte−yt	cxte−yt	NOUN
ejpam-4707	69	7	,	,	PUNCT
ejpam-4707	69	8	yt+1	yt+1	PROPN
ejpam-4707	69	9	=	=	SYM
ejpam-4707	69	10	xt	xt	PROPN
ejpam-4707	69	11	(	(	PUNCT
ejpam-4707	69	12	1−	1−	NUM
ejpam-4707	69	13	e−yt	e−yt	PROPN
ejpam-4707	69	14	)	)	PUNCT
ejpam-4707	69	15	,	,	PUNCT
ejpam-4707	69	16	(	(	PUNCT
ejpam-4707	69	17	7	7	X
ejpam-4707	69	18	)	)	PUNCT
ejpam-4707	69	19	b.	b.	NOUN
ejpam-4707	69	20	kulahcioglu	kulahcioglu	PROPN
ejpam-4707	69	21	,	,	PUNCT
ejpam-4707	69	22	u.	u.	NOUN
ejpam-4707	69	23	ufuktepe	ufuktepe	NOUN
ejpam-4707	69	24	,	,	PUNCT
ejpam-4707	69	25	a.	a.	PROPN
ejpam-4707	69	26	kalampakas	kalampakas	PROPN
ejpam-4707	69	27	/	/	SYM
ejpam-4707	69	28	eur	eur	PROPN
ejpam-4707	69	29	.	.	PUNCT
ejpam-4707	70	1	j.	j.	PROPN
ejpam-4707	70	2	pure	pure	PROPN
ejpam-4707	70	3	appl	appl	PROPN
ejpam-4707	70	4	.	.	PROPN
ejpam-4707	70	5	math	math	PROPN
ejpam-4707	70	6	,	,	PUNCT
ejpam-4707	70	7	16	16	NUM
ejpam-4707	70	8	(	(	PUNCT
ejpam-4707	70	9	2	2	NUM
ejpam-4707	70	10	)	)	PUNCT
ejpam-4707	70	11	(	(	PUNCT
ejpam-4707	70	12	2023	2023	NUM
ejpam-4707	70	13	)	)	PUNCT
ejpam-4707	70	14	,	,	PUNCT
ejpam-4707	70	15	736	736	NUM
ejpam-4707	70	16	-	-	SYM
ejpam-4707	70	17	750	750	NUM
ejpam-4707	70	18	739	739	NUM
ejpam-4707	70	19	where	where	SCONJ
ejpam-4707	70	20	xt	xt	PUNCT
ejpam-4707	70	21	and	and	CCONJ
ejpam-4707	70	22	yt	yt	PROPN
ejpam-4707	70	23	denotes	denote	NOUN
ejpam-4707	70	24	the	the	DET
ejpam-4707	70	25	population	population	NOUN
ejpam-4707	70	26	sizes	size	NOUN
ejpam-4707	70	27	of	of	ADP
ejpam-4707	70	28	host	host	NOUN
ejpam-4707	70	29	and	and	CCONJ
ejpam-4707	70	30	parasitoid	parasitoid	NOUN
ejpam-4707	70	31	,	,	PUNCT
ejpam-4707	70	32	respectively	respectively	ADV
ejpam-4707	70	33	at	at	ADP
ejpam-4707	70	34	time	time	NOUN
ejpam-4707	70	35	t.	t.	PROPN
ejpam-4707	70	36	we	we	PRON
ejpam-4707	70	37	add	add	VERB
ejpam-4707	70	38	a	a	DET
ejpam-4707	70	39	constant	constant	ADJ
ejpam-4707	70	40	proportion	proportion	NOUN
ejpam-4707	70	41	refuge	refuge	NOUN
ejpam-4707	70	42	effect	effect	NOUN
ejpam-4707	70	43	and	and	CCONJ
ejpam-4707	70	44	the	the	DET
ejpam-4707	70	45	mate	mate	NOUN
ejpam-4707	70	46	limitation	limitation	NOUN
ejpam-4707	70	47	allee	allee	ADJ
ejpam-4707	70	48	effect	effect	NOUN
ejpam-4707	70	49	to	to	ADP
ejpam-4707	70	50	the	the	DET
ejpam-4707	70	51	model	model	NOUN
ejpam-4707	70	52	(	(	PUNCT
ejpam-4707	70	53	7	7	NUM
ejpam-4707	70	54	)	)	PUNCT
ejpam-4707	70	55	.	.	PUNCT
ejpam-4707	71	1	we	we	PRON
ejpam-4707	71	2	obtain	obtain	VERB
ejpam-4707	71	3	:	:	PUNCT
ejpam-4707	71	4	xt+1	xt+1	X
ejpam-4707	72	1	=	=	PRON
ejpam-4707	73	1	(	(	PUNCT
ejpam-4707	73	2	1−ψ)λxt	1−ψ)λxt	NUM
ejpam-4707	73	3	1	1	NUM
ejpam-4707	73	4	+	+	NUM
ejpam-4707	73	5	cxt	cxt	PROPN
ejpam-4707	73	6	xt	xt	PROPN
ejpam-4707	73	7	s+	s+	ADV
ejpam-4707	73	8	xt	xt	PROPN
ejpam-4707	74	1	+	+	CCONJ
ejpam-4707	74	2	ψλxte	ψλxte	NOUN
ejpam-4707	74	3	−yt	−yt	X
ejpam-4707	74	4	1	1	NUM
ejpam-4707	74	5	+	+	CCONJ
ejpam-4707	74	6	cxte−yt	cxte−yt	X
ejpam-4707	74	7	xt	xt	X
ejpam-4707	74	8	s+	s+	X
ejpam-4707	74	9	xt	xt	PROPN
ejpam-4707	74	10	,	,	PUNCT
ejpam-4707	74	11	yt+1	yt+1	PROPN
ejpam-4707	74	12	=	=	PUNCT
ejpam-4707	74	13	ψxt	ψxt	NOUN
ejpam-4707	74	14	(	(	PUNCT
ejpam-4707	74	15	1−	1−	NUM
ejpam-4707	74	16	e−yt	e−yt	PROPN
ejpam-4707	74	17	)	)	PUNCT
ejpam-4707	74	18	,	,	PUNCT
ejpam-4707	74	19	(	(	PUNCT
ejpam-4707	74	20	8)	8)	NUM
ejpam-4707	74	21	where	where	SCONJ
ejpam-4707	74	22	0	0	NUM
ejpam-4707	74	23	<	<	X
ejpam-4707	74	24	ψ	ψ	X
ejpam-4707	74	25	≤	≤	NUM
ejpam-4707	74	26	1	1	NUM
ejpam-4707	74	27	is	be	AUX
ejpam-4707	74	28	the	the	DET
ejpam-4707	74	29	proportion	proportion	NOUN
ejpam-4707	74	30	of	of	ADP
ejpam-4707	74	31	host	host	NOUN
ejpam-4707	74	32	available	available	ADJ
ejpam-4707	74	33	to	to	ADP
ejpam-4707	74	34	parasitoid	parasitoid	NOUN
ejpam-4707	74	35	,	,	PUNCT
ejpam-4707	74	36	(	(	PUNCT
ejpam-4707	74	37	1−ψ	1−ψ	NUM
ejpam-4707	74	38	)	)	PUNCT
ejpam-4707	74	39	is	be	AUX
ejpam-4707	74	40	proportion	proportion	NOUN
ejpam-4707	74	41	of	of	ADP
ejpam-4707	74	42	protective	protective	ADJ
ejpam-4707	74	43	refuge	refuge	NOUN
ejpam-4707	74	44	,	,	PUNCT
ejpam-4707	74	45	and	and	CCONJ
ejpam-4707	74	46	s	s	VERB
ejpam-4707	74	47	>	>	X
ejpam-4707	74	48	0	0	NUM
ejpam-4707	74	49	is	be	AUX
ejpam-4707	74	50	the	the	DET
ejpam-4707	74	51	allee	allee	PROPN
ejpam-4707	74	52	effect	effect	NOUN
ejpam-4707	74	53	constant	constant	ADJ
ejpam-4707	74	54	.	.	PUNCT
ejpam-4707	75	1	in	in	ADP
ejpam-4707	75	2	the	the	DET
ejpam-4707	75	3	following	follow	VERB
ejpam-4707	75	4	sections	section	NOUN
ejpam-4707	75	5	we	we	PRON
ejpam-4707	75	6	will	will	AUX
ejpam-4707	75	7	study	study	VERB
ejpam-4707	75	8	the	the	DET
ejpam-4707	75	9	dynamics	dynamic	NOUN
ejpam-4707	75	10	of	of	ADP
ejpam-4707	75	11	(	(	PUNCT
ejpam-4707	75	12	8)	8)	NUM
ejpam-4707	75	13	.	.	NOUN
ejpam-4707	75	14	3	3	NUM
ejpam-4707	75	15	.	.	PUNCT
ejpam-4707	75	16	fixed	fix	VERB
ejpam-4707	75	17	points	point	NOUN
ejpam-4707	75	18	in	in	ADP
ejpam-4707	75	19	this	this	DET
ejpam-4707	75	20	section	section	NOUN
ejpam-4707	75	21	we	we	PRON
ejpam-4707	75	22	find	find	VERB
ejpam-4707	75	23	the	the	DET
ejpam-4707	75	24	fixed	fix	VERB
ejpam-4707	75	25	points	point	NOUN
ejpam-4707	75	26	of	of	ADP
ejpam-4707	75	27	the	the	DET
ejpam-4707	75	28	system	system	NOUN
ejpam-4707	75	29	,	,	PUNCT
ejpam-4707	75	30	and	and	CCONJ
ejpam-4707	75	31	identify	identify	VERB
ejpam-4707	75	32	conditions	condition	NOUN
ejpam-4707	75	33	for	for	ADP
ejpam-4707	75	34	the	the	DET
ejpam-4707	75	35	existence	existence	NOUN
ejpam-4707	75	36	and	and	CCONJ
ejpam-4707	75	37	uniqueness	uniqueness	NOUN
ejpam-4707	75	38	of	of	ADP
ejpam-4707	75	39	a	a	DET
ejpam-4707	75	40	positive	positive	ADJ
ejpam-4707	75	41	fixed	fix	VERB
ejpam-4707	75	42	point	point	NOUN
ejpam-4707	75	43	.	.	PUNCT
ejpam-4707	76	1	x	x	X
ejpam-4707	76	2	=	=	PUNCT
ejpam-4707	77	1	(	(	PUNCT
ejpam-4707	77	2	1−ψ)λx	1−ψ)λx	NUM
ejpam-4707	77	3	1	1	NUM
ejpam-4707	77	4	+	+	NUM
ejpam-4707	77	5	cx	cx	NOUN
ejpam-4707	77	6	x	x	SYM
ejpam-4707	77	7	s+	s+	ADV
ejpam-4707	77	8	x	x	X
ejpam-4707	77	9	+	+	CCONJ
ejpam-4707	77	10	ψλxe−y	ψλxe−y	PRON
ejpam-4707	77	11	1	1	NUM
ejpam-4707	77	12	+	+	NUM
ejpam-4707	77	13	cxe−y	cxe−y	PROPN
ejpam-4707	77	14	x	x	SYM
ejpam-4707	77	15	s+	s+	X
ejpam-4707	77	16	x	x	INTJ
ejpam-4707	77	17	,	,	PUNCT
ejpam-4707	77	18	y	y	PROPN
ejpam-4707	77	19	=	=	PUNCT
ejpam-4707	77	20	ψx	ψx	PROPN
ejpam-4707	77	21	(	(	PUNCT
ejpam-4707	77	22	1−	1−	NUM
ejpam-4707	77	23	e−y	e−y	PROPN
ejpam-4707	77	24	)	)	PUNCT
ejpam-4707	77	25	.	.	PUNCT
ejpam-4707	78	1	(	(	PUNCT
ejpam-4707	78	2	9	9	NUM
ejpam-4707	78	3	)	)	PUNCT
ejpam-4707	78	4	(	(	PUNCT
ejpam-4707	78	5	i	i	NOUN
ejpam-4707	78	6	)	)	PUNCT
ejpam-4707	78	7	f0	f0	PROPN
ejpam-4707	78	8	=	=	SYM
ejpam-4707	78	9	(	(	PUNCT
ejpam-4707	78	10	0	0	NUM
ejpam-4707	78	11	,	,	PUNCT
ejpam-4707	78	12	0	0	NUM
ejpam-4707	78	13	)	)	PUNCT
ejpam-4707	78	14	is	be	AUX
ejpam-4707	78	15	extinction	extinction	NOUN
ejpam-4707	78	16	fixed	fix	VERB
ejpam-4707	78	17	point	point	NOUN
ejpam-4707	78	18	for	for	ADP
ejpam-4707	78	19	all	all	DET
ejpam-4707	78	20	values	value	NOUN
ejpam-4707	78	21	of	of	ADP
ejpam-4707	78	22	parameters	parameter	NOUN
ejpam-4707	78	23	.	.	PUNCT
ejpam-4707	79	1	(	(	PUNCT
ejpam-4707	79	2	ii	ii	NOUN
ejpam-4707	79	3	)	)	PUNCT
ejpam-4707	79	4	f1	f1	NOUN
ejpam-4707	79	5	=	=	SYM
ejpam-4707	79	6	(	(	PUNCT
ejpam-4707	79	7	a+	a+	CCONJ
ejpam-4707	79	8	√	√	PROPN
ejpam-4707	79	9	a2−4cs	a2−4cs	NOUN
ejpam-4707	79	10	2c	2c	NOUN
ejpam-4707	79	11	,	,	PUNCT
ejpam-4707	79	12	0	0	NUM
ejpam-4707	79	13	)	)	PUNCT
ejpam-4707	79	14	and	and	CCONJ
ejpam-4707	79	15	f2	f2	ADV
ejpam-4707	79	16	=	=	SYM
ejpam-4707	79	17	(	(	PUNCT
ejpam-4707	79	18	a−	a−	NOUN
ejpam-4707	79	19	√	√	PRON
ejpam-4707	79	20	a2−4cs	a2−4cs	NOUN
ejpam-4707	79	21	2c	2c	NOUN
ejpam-4707	79	22	,	,	PUNCT
ejpam-4707	79	23	0	0	NUM
ejpam-4707	79	24	)	)	PUNCT
ejpam-4707	79	25	are	be	AUX
ejpam-4707	79	26	axial	axial	ADJ
ejpam-4707	79	27	fixed	fix	VERB
ejpam-4707	79	28	points	point	NOUN
ejpam-4707	79	29	wherea	wherea	VERB
ejpam-4707	80	1	=	=	X
ejpam-4707	80	2	λ−cs−1	λ−cs−1	NOUN
ejpam-4707	80	3	for	for	ADP
ejpam-4707	80	4	(	(	PUNCT
ejpam-4707	80	5	1	1	NUM
ejpam-4707	80	6	+	+	CCONJ
ejpam-4707	80	7	√	√	ADP
ejpam-4707	80	8	cs	cs	ADJ
ejpam-4707	80	9	)	)	PUNCT
ejpam-4707	80	10	2	2	NUM
ejpam-4707	80	11	≤	≤	NOUN
ejpam-4707	80	12	λ	λ	NOUN
ejpam-4707	80	13	(	(	PUNCT
ejpam-4707	80	14	extinction	extinction	NOUN
ejpam-4707	80	15	of	of	ADP
ejpam-4707	80	16	the	the	DET
ejpam-4707	80	17	parasite	parasite	NOUN
ejpam-4707	80	18	)	)	PUNCT
ejpam-4707	80	19	.	.	PUNCT
ejpam-4707	81	1	(	(	PUNCT
ejpam-4707	81	2	iii	iii	X
ejpam-4707	81	3	)	)	PUNCT
ejpam-4707	81	4	let	let	VERB
ejpam-4707	81	5	f3	f3	PROPN
ejpam-4707	81	6	=	=	SYM
ejpam-4707	81	7	(	(	PUNCT
ejpam-4707	81	8	x∗	x∗	PROPN
ejpam-4707	81	9	,	,	PUNCT
ejpam-4707	81	10	y∗	y∗	PROPN
ejpam-4707	81	11	)	)	PUNCT
ejpam-4707	81	12	(	(	PUNCT
ejpam-4707	81	13	the	the	DET
ejpam-4707	81	14	host	host	NOUN
ejpam-4707	81	15	and	and	CCONJ
ejpam-4707	81	16	the	the	DET
ejpam-4707	81	17	parasite	parasite	NOUN
ejpam-4707	81	18	survive	survive	NOUN
ejpam-4707	81	19	)	)	PUNCT
ejpam-4707	81	20	be	be	VERB
ejpam-4707	81	21	the	the	DET
ejpam-4707	81	22	positive	positive	ADJ
ejpam-4707	81	23	fixed	fix	VERB
ejpam-4707	81	24	point	point	NOUN
ejpam-4707	81	25	,	,	PUNCT
ejpam-4707	81	26	where	where	SCONJ
ejpam-4707	81	27	x∗	x∗	PROPN
ejpam-4707	81	28	=	=	SYM
ejpam-4707	81	29	y∗	y∗	ADV
ejpam-4707	81	30	ψ(1−e−y∗	ψ(1−e−y∗	ADJ
ejpam-4707	81	31	)	)	PUNCT
ejpam-4707	81	32	by	by	ADP
ejpam-4707	81	33	the	the	DET
ejpam-4707	81	34	second	second	ADJ
ejpam-4707	81	35	equation	equation	NOUN
ejpam-4707	81	36	of	of	ADP
ejpam-4707	81	37	(	(	PUNCT
ejpam-4707	81	38	9	9	NUM
ejpam-4707	81	39	)	)	PUNCT
ejpam-4707	81	40	.	.	PUNCT
ejpam-4707	82	1	first	first	ADV
ejpam-4707	82	2	,	,	PUNCT
ejpam-4707	82	3	we	we	PRON
ejpam-4707	82	4	show	show	VERB
ejpam-4707	82	5	the	the	DET
ejpam-4707	82	6	existence	existence	NOUN
ejpam-4707	82	7	of	of	ADP
ejpam-4707	82	8	f3	f3	PROPN
ejpam-4707	82	9	.	.	PUNCT
ejpam-4707	83	1	if	if	SCONJ
ejpam-4707	83	2	we	we	PRON
ejpam-4707	83	3	substitute	substitute	VERB
ejpam-4707	83	4	x	x	PUNCT
ejpam-4707	83	5	=	=	SYM
ejpam-4707	83	6	y/(ψ(1−	y/(ψ(1−	PROPN
ejpam-4707	83	7	e−y	e−y	PROPN
ejpam-4707	83	8	)	)	PUNCT
ejpam-4707	83	9	)	)	PUNCT
ejpam-4707	83	10	in	in	ADP
ejpam-4707	83	11	the	the	DET
ejpam-4707	83	12	first	first	ADJ
ejpam-4707	83	13	equation	equation	NOUN
ejpam-4707	83	14	of	of	ADP
ejpam-4707	83	15	(	(	PUNCT
ejpam-4707	83	16	9	9	NUM
ejpam-4707	83	17	)	)	PUNCT
ejpam-4707	83	18	,	,	PUNCT
ejpam-4707	83	19	we	we	PRON
ejpam-4707	83	20	obtain	obtain	VERB
ejpam-4707	83	21	1	1	NUM
ejpam-4707	83	22	λ	λ	PROPN
ejpam-4707	83	23	=	=	SYM
ejpam-4707	83	24	f(y	f(y	NOUN
ejpam-4707	83	25	)	)	PUNCT
ejpam-4707	83	26	+	+	SYM
ejpam-4707	83	27	g(y	g(y	NOUN
ejpam-4707	83	28	)	)	PUNCT
ejpam-4707	83	29	,	,	PUNCT
ejpam-4707	83	30	(	(	PUNCT
ejpam-4707	83	31	10	10	NUM
ejpam-4707	83	32	)	)	PUNCT
ejpam-4707	83	33	where	where	SCONJ
ejpam-4707	83	34	f(y	f(y	NOUN
ejpam-4707	83	35	)	)	PUNCT
ejpam-4707	83	36	=	=	PUNCT
ejpam-4707	84	1	(	(	PUNCT
ejpam-4707	84	2	1−ψ)ψey	1−ψ)ψey	NUM
ejpam-4707	84	3	(	(	PUNCT
ejpam-4707	84	4	ey	ey	INTJ
ejpam-4707	84	5	−	−	NOUN
ejpam-4707	84	6	1	1	NUM
ejpam-4707	84	7	)	)	PUNCT
ejpam-4707	84	8	y	y	PROPN
ejpam-4707	84	9	(	(	PUNCT
ejpam-4707	84	10	ψ	ψ	X
ejpam-4707	84	11	(	(	PUNCT
ejpam-4707	84	12	ey	ey	INTJ
ejpam-4707	84	13	−	−	PROPN
ejpam-4707	84	14	1	1	NUM
ejpam-4707	84	15	)	)	PUNCT
ejpam-4707	84	16	s+	s+	X
ejpam-4707	84	17	eyy	eyy	PROPN
ejpam-4707	84	18	)	)	PUNCT
ejpam-4707	84	19	(	(	PUNCT
ejpam-4707	84	20	ey(ψ	ey(ψ	NUM
ejpam-4707	85	1	+	+	CCONJ
ejpam-4707	85	2	cy)−ψ	cy)−ψ	NOUN
ejpam-4707	85	3	)	)	PUNCT
ejpam-4707	85	4	,	,	PUNCT
ejpam-4707	85	5	(	(	PUNCT
ejpam-4707	85	6	11	11	NUM
ejpam-4707	85	7	)	)	PUNCT
ejpam-4707	85	8	and	and	CCONJ
ejpam-4707	85	9	g(y	g(y	NOUN
ejpam-4707	85	10	)	)	PUNCT
ejpam-4707	85	11	=	=	NUM
ejpam-4707	85	12	ψ2	ψ2	NOUN
ejpam-4707	85	13	(	(	PUNCT
ejpam-4707	85	14	ey	ey	INTJ
ejpam-4707	85	15	−	−	PROPN
ejpam-4707	85	16	1	1	NUM
ejpam-4707	85	17	)	)	PUNCT
ejpam-4707	85	18	y	y	PROPN
ejpam-4707	85	19	(	(	PUNCT
ejpam-4707	85	20	ψ	ψ	X
ejpam-4707	85	21	(	(	PUNCT
ejpam-4707	85	22	ey	ey	INTJ
ejpam-4707	85	23	−	−	NOUN
ejpam-4707	85	24	1	1	NUM
ejpam-4707	85	25	)	)	PUNCT
ejpam-4707	85	26	+	+	CCONJ
ejpam-4707	85	27	cy	cy	NOUN
ejpam-4707	85	28	)	)	PUNCT
ejpam-4707	85	29	(	(	PUNCT
ejpam-4707	85	30	ψ	ψ	X
ejpam-4707	85	31	(	(	PUNCT
ejpam-4707	85	32	ey	ey	INTJ
ejpam-4707	85	33	−	−	PROPN
ejpam-4707	85	34	1	1	NUM
ejpam-4707	85	35	)	)	PUNCT
ejpam-4707	85	36	s+	s+	X
ejpam-4707	85	37	eyy	eyy	PROPN
ejpam-4707	85	38	)	)	PUNCT
ejpam-4707	85	39	.	.	PUNCT
ejpam-4707	86	1	(	(	PUNCT
ejpam-4707	86	2	12	12	NUM
ejpam-4707	86	3	)	)	PUNCT
ejpam-4707	86	4	since	since	SCONJ
ejpam-4707	86	5	g′(y	g′(y	NUM
ejpam-4707	86	6	)	)	PUNCT
ejpam-4707	86	7	=	=	SYM
ejpam-4707	87	1	−	−	PROPN
ejpam-4707	87	2	ψ2eyy	ψ2eyy	NUM
ejpam-4707	88	1	(	(	PUNCT
ejpam-4707	88	2	ey	ey	INTJ
ejpam-4707	88	3	−	−	PROPN
ejpam-4707	88	4	y	y	NOUN
ejpam-4707	88	5	−	−	PROPN
ejpam-4707	88	6	1	1	NUM
ejpam-4707	88	7	)	)	PUNCT
ejpam-4707	88	8	(	(	PUNCT
ejpam-4707	88	9	ψ	ψ	X
ejpam-4707	88	10	(	(	PUNCT
ejpam-4707	88	11	ey	ey	INTJ
ejpam-4707	88	12	−	−	NOUN
ejpam-4707	88	13	1	1	NUM
ejpam-4707	88	14	)	)	PUNCT
ejpam-4707	88	15	+	+	CCONJ
ejpam-4707	88	16	cy	cy	NOUN
ejpam-4707	88	17	)	)	PUNCT
ejpam-4707	88	18	(	(	PUNCT
ejpam-4707	88	19	ψ	ψ	X
ejpam-4707	88	20	(	(	PUNCT
ejpam-4707	88	21	ey	ey	INTJ
ejpam-4707	88	22	−	−	PROPN
ejpam-4707	88	23	1	1	NUM
ejpam-4707	88	24	)	)	PUNCT
ejpam-4707	88	25	s+	s+	PUNCT
ejpam-4707	89	1	eyy)2	eyy)2	PROPN
ejpam-4707	89	2	−	−	PROPN
ejpam-4707	89	3	b.	b.	PROPN
ejpam-4707	89	4	kulahcioglu	kulahcioglu	PROPN
ejpam-4707	89	5	,	,	PUNCT
ejpam-4707	89	6	u.	u.	NOUN
ejpam-4707	89	7	ufuktepe	ufuktepe	NOUN
ejpam-4707	89	8	,	,	PUNCT
ejpam-4707	89	9	a.	a.	PROPN
ejpam-4707	89	10	kalampakas	kalampakas	PROPN
ejpam-4707	89	11	/	/	SYM
ejpam-4707	89	12	eur	eur	PROPN
ejpam-4707	89	13	.	.	PUNCT
ejpam-4707	90	1	j.	j.	PROPN
ejpam-4707	90	2	pure	pure	PROPN
ejpam-4707	90	3	appl	appl	PROPN
ejpam-4707	90	4	.	.	PROPN
ejpam-4707	90	5	math	math	PROPN
ejpam-4707	90	6	,	,	PUNCT
ejpam-4707	90	7	16	16	NUM
ejpam-4707	90	8	(	(	PUNCT
ejpam-4707	90	9	2	2	NUM
ejpam-4707	90	10	)	)	PUNCT
ejpam-4707	90	11	(	(	PUNCT
ejpam-4707	90	12	2023	2023	NUM
ejpam-4707	90	13	)	)	PUNCT
ejpam-4707	90	14	,	,	PUNCT
ejpam-4707	90	15	736	736	NUM
ejpam-4707	90	16	-	-	SYM
ejpam-4707	90	17	750	750	NUM
ejpam-4707	90	18	740	740	NUM
ejpam-4707	90	19	ψ3	ψ3	NOUN
ejpam-4707	90	20	(	(	PUNCT
ejpam-4707	90	21	ey	ey	INTJ
ejpam-4707	90	22	−	−	PROPN
ejpam-4707	90	23	1	1	NUM
ejpam-4707	90	24	)	)	PUNCT
ejpam-4707	90	25	(	(	PUNCT
ejpam-4707	90	26	1	1	NUM
ejpam-4707	90	27	+	+	NUM
ejpam-4707	90	28	ey(y	ey(y	NOUN
ejpam-4707	90	29	−	−	PROPN
ejpam-4707	90	30	1	1	NUM
ejpam-4707	90	31	)	)	PUNCT
ejpam-4707	90	32	)	)	PUNCT
ejpam-4707	91	1	(	(	PUNCT
ejpam-4707	91	2	ψ	ψ	X
ejpam-4707	91	3	(	(	PUNCT
ejpam-4707	91	4	ey	ey	INTJ
ejpam-4707	91	5	−	−	NOUN
ejpam-4707	91	6	1	1	NUM
ejpam-4707	91	7	)	)	PUNCT
ejpam-4707	91	8	+	+	CCONJ
ejpam-4707	91	9	cy)2	cy)2	NOUN
ejpam-4707	91	10	(	(	PUNCT
ejpam-4707	91	11	ψ	ψ	X
ejpam-4707	91	12	(	(	PUNCT
ejpam-4707	91	13	ey	ey	INTJ
ejpam-4707	91	14	−	−	PROPN
ejpam-4707	91	15	1	1	NUM
ejpam-4707	91	16	)	)	PUNCT
ejpam-4707	91	17	s+	s+	X
ejpam-4707	91	18	eyy	eyy	PROPN
ejpam-4707	91	19	)	)	PUNCT
ejpam-4707	91	20	<	<	X
ejpam-4707	91	21	0	0	NUM
ejpam-4707	91	22	,	,	PUNCT
ejpam-4707	91	23	(	(	PUNCT
ejpam-4707	91	24	13	13	NUM
ejpam-4707	91	25	)	)	PUNCT
ejpam-4707	91	26	the	the	DET
ejpam-4707	91	27	function	function	NOUN
ejpam-4707	91	28	g(y	g(y	PROPN
ejpam-4707	91	29	)	)	PUNCT
ejpam-4707	91	30	is	be	AUX
ejpam-4707	91	31	a	a	DET
ejpam-4707	91	32	decreasing	decrease	VERB
ejpam-4707	91	33	function	function	NOUN
ejpam-4707	91	34	of	of	ADP
ejpam-4707	91	35	y.	y.	PROPN
ejpam-4707	91	36	and	and	CCONJ
ejpam-4707	91	37	we	we	PRON
ejpam-4707	91	38	have	have	VERB
ejpam-4707	91	39	lim	lim	PROPN
ejpam-4707	91	40	y→0	y→0	PROPN
ejpam-4707	91	41	g(y	g(y	PROPN
ejpam-4707	91	42	)	)	PUNCT
ejpam-4707	92	1	=	=	NUM
ejpam-4707	92	2	ψ2	ψ2	NOUN
ejpam-4707	92	3	(	(	PUNCT
ejpam-4707	92	4	c+ψ)(1	c+ψ)(1	X
ejpam-4707	92	5	+	+	CCONJ
ejpam-4707	92	6	ψs	ψs	X
ejpam-4707	92	7	)	)	PUNCT
ejpam-4707	92	8	(	(	PUNCT
ejpam-4707	92	9	14	14	NUM
ejpam-4707	92	10	)	)	PUNCT
ejpam-4707	92	11	now	now	ADV
ejpam-4707	92	12	,	,	PUNCT
ejpam-4707	92	13	we	we	PRON
ejpam-4707	92	14	continue	continue	VERB
ejpam-4707	92	15	with	with	ADP
ejpam-4707	92	16	the	the	DET
ejpam-4707	92	17	graphical	graphical	ADJ
ejpam-4707	92	18	properties	property	NOUN
ejpam-4707	92	19	of	of	ADP
ejpam-4707	92	20	f(y	f(y	NOUN
ejpam-4707	92	21	)	)	PUNCT
ejpam-4707	92	22	.	.	PUNCT
ejpam-4707	93	1	f	f	PROPN
ejpam-4707	93	2	′(y	′(y	PROPN
ejpam-4707	93	3	)	)	PUNCT
ejpam-4707	94	1	=	=	SYM
ejpam-4707	94	2	(	(	PUNCT
ejpam-4707	94	3	1−ψ)ψey	1−ψ)ψey	NUM
ejpam-4707	94	4	(	(	PUNCT
ejpam-4707	94	5	ey	ey	INTJ
ejpam-4707	94	6	−	−	PROPN
ejpam-4707	94	7	y	y	NOUN
ejpam-4707	94	8	−	−	PROPN
ejpam-4707	94	9	1	1	NUM
ejpam-4707	94	10	)	)	PUNCT
ejpam-4707	94	11	(	(	PUNCT
ejpam-4707	94	12	ψ2	ψ2	NOUN
ejpam-4707	94	13	(	(	PUNCT
ejpam-4707	94	14	ey	ey	INTJ
ejpam-4707	94	15	−	−	PROPN
ejpam-4707	94	16	1)2	1)2	NUM
ejpam-4707	94	17	s−	s−	PROPN
ejpam-4707	94	18	ce2yy2	ce2yy2	NOUN
ejpam-4707	94	19	)	)	PUNCT
ejpam-4707	94	20	(	(	PUNCT
ejpam-4707	94	21	ψ	ψ	X
ejpam-4707	94	22	(	(	PUNCT
ejpam-4707	94	23	ey	ey	INTJ
ejpam-4707	94	24	−	−	PROPN
ejpam-4707	94	25	1	1	NUM
ejpam-4707	94	26	)	)	PUNCT
ejpam-4707	94	27	s+	s+	PUNCT
ejpam-4707	95	1	eyy)2	eyy)2	PROPN
ejpam-4707	95	2	(	(	PUNCT
ejpam-4707	95	3	ψ−	ψ−	VERB
ejpam-4707	95	4	ey(ψ	ey(ψ	PRON
ejpam-4707	95	5	+	+	NUM
ejpam-4707	95	6	cy))2	cy))2	NOUN
ejpam-4707	95	7	.	.	PUNCT
ejpam-4707	96	1	(	(	PUNCT
ejpam-4707	96	2	15	15	NUM
ejpam-4707	96	3	)	)	PUNCT
ejpam-4707	96	4	if	if	SCONJ
ejpam-4707	96	5	s	s	VERB
ejpam-4707	96	6	<	<	X
ejpam-4707	96	7	c	c	NOUN
ejpam-4707	96	8	ψ2	ψ2	NOUN
ejpam-4707	96	9	,	,	PUNCT
ejpam-4707	96	10	then	then	ADV
ejpam-4707	96	11	f	f	PROPN
ejpam-4707	96	12	′(y	′(y	PROPN
ejpam-4707	96	13	)	)	PUNCT
ejpam-4707	96	14	<	<	X
ejpam-4707	96	15	0	0	NUM
ejpam-4707	96	16	,	,	PUNCT
ejpam-4707	96	17	which	which	PRON
ejpam-4707	96	18	means	mean	VERB
ejpam-4707	96	19	f(y	f(y	NOUN
ejpam-4707	96	20	)	)	PUNCT
ejpam-4707	96	21	is	be	AUX
ejpam-4707	96	22	decreasing	decrease	VERB
ejpam-4707	96	23	function	function	NOUN
ejpam-4707	96	24	.	.	PUNCT
ejpam-4707	97	1	and	and	CCONJ
ejpam-4707	97	2	also	also	ADV
ejpam-4707	97	3	lim	lim	PROPN
ejpam-4707	97	4	y→0	y→0	PROPN
ejpam-4707	97	5	f(y	f(y	PROPN
ejpam-4707	97	6	)	)	PUNCT
ejpam-4707	98	1	=	=	PUNCT
ejpam-4707	98	2	(	(	PUNCT
ejpam-4707	98	3	1−ψ)ψ	1−ψ)ψ	NUM
ejpam-4707	98	4	(	(	PUNCT
ejpam-4707	98	5	c+ψ)(1	c+ψ)(1	NOUN
ejpam-4707	98	6	+	+	CCONJ
ejpam-4707	98	7	ψs	ψs	NOUN
ejpam-4707	98	8	)	)	PUNCT
ejpam-4707	98	9	.	.	PUNCT
ejpam-4707	99	1	(	(	PUNCT
ejpam-4707	99	2	16	16	X
ejpam-4707	99	3	)	)	PUNCT
ejpam-4707	99	4	let	let	VERB
ejpam-4707	99	5	h(y	h(y	NOUN
ejpam-4707	99	6	)	)	PUNCT
ejpam-4707	99	7	=	=	SYM
ejpam-4707	99	8	f(y	f(y	NOUN
ejpam-4707	99	9	)	)	PUNCT
ejpam-4707	99	10	+	+	SYM
ejpam-4707	100	1	g(y	g(y	NOUN
ejpam-4707	100	2	)	)	PUNCT
ejpam-4707	100	3	,	,	PUNCT
ejpam-4707	100	4	h(y	h(y	ADV
ejpam-4707	100	5	)	)	PUNCT
ejpam-4707	100	6	is	be	AUX
ejpam-4707	100	7	a	a	DET
ejpam-4707	100	8	decreasing	decrease	VERB
ejpam-4707	100	9	function	function	NOUN
ejpam-4707	100	10	of	of	ADP
ejpam-4707	100	11	y	y	PROPN
ejpam-4707	100	12	if	if	SCONJ
ejpam-4707	100	13	s	s	VERB
ejpam-4707	100	14	<	<	X
ejpam-4707	100	15	c	c	NOUN
ejpam-4707	100	16	ψ2	ψ2	NOUN
ejpam-4707	100	17	.	.	PUNCT
ejpam-4707	101	1	and	and	CCONJ
ejpam-4707	101	2	lim	lim	PROPN
ejpam-4707	101	3	y→0	y→0	PROPN
ejpam-4707	101	4	h(y	h(y	ADV
ejpam-4707	101	5	)	)	PUNCT
ejpam-4707	102	1	=	=	SYM
ejpam-4707	102	2	(	(	PUNCT
ejpam-4707	102	3	1−ψ)ψ	1−ψ)ψ	NUM
ejpam-4707	102	4	(	(	PUNCT
ejpam-4707	102	5	c+ψ)(1	c+ψ)(1	NOUN
ejpam-4707	102	6	+	+	CCONJ
ejpam-4707	102	7	ψs	ψs	ADJ
ejpam-4707	102	8	)	)	PUNCT
ejpam-4707	102	9	+	+	NUM
ejpam-4707	102	10	ψ2	ψ2	NOUN
ejpam-4707	102	11	(	(	PUNCT
ejpam-4707	102	12	c+ψ)(1	c+ψ)(1	X
ejpam-4707	102	13	+	+	CCONJ
ejpam-4707	102	14	ψs	ψs	NOUN
ejpam-4707	102	15	)	)	PUNCT
ejpam-4707	102	16	=	=	SYM
ejpam-4707	102	17	ψ	ψ	X
ejpam-4707	102	18	(	(	PUNCT
ejpam-4707	102	19	c+ψ)(1	c+ψ)(1	X
ejpam-4707	102	20	+	+	CCONJ
ejpam-4707	102	21	ψs	ψs	X
ejpam-4707	102	22	)	)	PUNCT
ejpam-4707	102	23	(	(	PUNCT
ejpam-4707	102	24	17	17	NUM
ejpam-4707	102	25	)	)	PUNCT
ejpam-4707	102	26	the	the	DET
ejpam-4707	102	27	positive	positive	ADJ
ejpam-4707	102	28	fixed	fix	VERB
ejpam-4707	102	29	point	point	NOUN
ejpam-4707	102	30	exists	exist	VERB
ejpam-4707	102	31	if	if	SCONJ
ejpam-4707	102	32	λ	λ	NOUN
ejpam-4707	102	33	=	=	NOUN
ejpam-4707	102	34	1	1	NUM
ejpam-4707	102	35	h(y	h(y	NOUN
ejpam-4707	102	36	)	)	PUNCT
ejpam-4707	103	1	where	where	SCONJ
ejpam-4707	103	2	h(y	h(y	ADV
ejpam-4707	103	3	)	)	PUNCT
ejpam-4707	103	4	̸=	̸=	PROPN
ejpam-4707	103	5	0	0	NUM
ejpam-4707	103	6	.	.	NOUN
ejpam-4707	103	7	1	1	NUM
ejpam-4707	103	8	h(y	h(y	ADV
ejpam-4707	103	9	)	)	PUNCT
ejpam-4707	103	10	is	be	AUX
ejpam-4707	103	11	an	an	DET
ejpam-4707	103	12	increasing	increase	VERB
ejpam-4707	103	13	function	function	NOUN
ejpam-4707	103	14	of	of	ADP
ejpam-4707	103	15	y	y	PROPN
ejpam-4707	103	16	and	and	CCONJ
ejpam-4707	103	17	lim	lim	PROPN
ejpam-4707	103	18	y→0	y→0	PROPN
ejpam-4707	103	19	1	1	NUM
ejpam-4707	103	20	h(y	h(y	ADV
ejpam-4707	103	21	)	)	PUNCT
ejpam-4707	104	1	=	=	SYM
ejpam-4707	104	2	(	(	PUNCT
ejpam-4707	104	3	c+ψ)(1	c+ψ)(1	X
ejpam-4707	104	4	+	+	CCONJ
ejpam-4707	104	5	ψs	ψs	NOUN
ejpam-4707	104	6	)	)	PUNCT
ejpam-4707	104	7	ψ	ψ	NOUN
ejpam-4707	104	8	.	.	PUNCT
ejpam-4707	105	1	(	(	PUNCT
ejpam-4707	105	2	18	18	NUM
ejpam-4707	105	3	)	)	PUNCT
ejpam-4707	105	4	as	as	ADP
ejpam-4707	105	5	a	a	DET
ejpam-4707	105	6	result	result	NOUN
ejpam-4707	105	7	(	(	PUNCT
ejpam-4707	105	8	see	see	VERB
ejpam-4707	105	9	figure	figure	NOUN
ejpam-4707	105	10	1	1	NUM
ejpam-4707	105	11	)	)	PUNCT
ejpam-4707	105	12	a	a	DET
ejpam-4707	105	13	positive	positive	ADJ
ejpam-4707	105	14	fixed	fix	VERB
ejpam-4707	105	15	point	point	NOUN
ejpam-4707	105	16	exists	exist	VERB
ejpam-4707	105	17	and	and	CCONJ
ejpam-4707	105	18	it	it	PRON
ejpam-4707	105	19	is	be	AUX
ejpam-4707	105	20	unique	unique	ADJ
ejpam-4707	105	21	if	if	SCONJ
ejpam-4707	105	22	s	s	VERB
ejpam-4707	105	23	<	<	X
ejpam-4707	105	24	c	c	NOUN
ejpam-4707	105	25	ψ2	ψ2	NOUN
ejpam-4707	105	26	and	and	CCONJ
ejpam-4707	105	27	λ	λ	X
ejpam-4707	105	28	>	>	X
ejpam-4707	105	29	(	(	PUNCT
ejpam-4707	105	30	c+ψ)(1+ψs	c+ψ)(1+ψs	NOUN
ejpam-4707	105	31	)	)	PUNCT
ejpam-4707	105	32	ψ	ψ	NOUN
ejpam-4707	105	33	.	.	PUNCT
ejpam-4707	106	1	otherwise	otherwise	ADV
ejpam-4707	106	2	,	,	PUNCT
ejpam-4707	106	3	neither	neither	CCONJ
ejpam-4707	106	4	the	the	DET
ejpam-4707	106	5	existence	existence	NOUN
ejpam-4707	106	6	nor	nor	CCONJ
ejpam-4707	106	7	the	the	DET
ejpam-4707	106	8	uniqueness	uniqueness	NOUN
ejpam-4707	106	9	is	be	AUX
ejpam-4707	106	10	guaranteed	guarantee	VERB
ejpam-4707	106	11	(	(	PUNCT
ejpam-4707	106	12	figure	figure	NOUN
ejpam-4707	106	13	2	2	NUM
ejpam-4707	106	14	and	and	CCONJ
ejpam-4707	106	15	figure	figure	VERB
ejpam-4707	106	16	3	3	NUM
ejpam-4707	106	17	)	)	PUNCT
ejpam-4707	106	18	.	.	PUNCT
ejpam-4707	107	1	4	4	X
ejpam-4707	107	2	.	.	X
ejpam-4707	107	3	local	local	ADJ
ejpam-4707	107	4	asymptotic	asymptotic	ADJ
ejpam-4707	107	5	stability	stability	NOUN
ejpam-4707	107	6	and	and	CCONJ
ejpam-4707	107	7	global	global	ADJ
ejpam-4707	107	8	behaviors	behavior	NOUN
ejpam-4707	107	9	in	in	ADP
ejpam-4707	107	10	this	this	DET
ejpam-4707	107	11	section	section	NOUN
ejpam-4707	107	12	we	we	PRON
ejpam-4707	107	13	investigate	investigate	VERB
ejpam-4707	107	14	local	local	ADJ
ejpam-4707	107	15	asymptotic	asymptotic	ADJ
ejpam-4707	107	16	stability	stability	NOUN
ejpam-4707	107	17	,	,	PUNCT
ejpam-4707	107	18	global	global	ADJ
ejpam-4707	107	19	stability	stability	NOUN
ejpam-4707	107	20	and	and	CCONJ
ejpam-4707	107	21	bifurcations	bifurcation	NOUN
ejpam-4707	107	22	.	.	PUNCT
ejpam-4707	108	1	the	the	DET
ejpam-4707	108	2	corresponding	corresponding	ADJ
ejpam-4707	108	3	jacobian	jacobian	ADJ
ejpam-4707	108	4	matrix	matrix	NOUN
ejpam-4707	108	5	of	of	ADP
ejpam-4707	108	6	(	(	PUNCT
ejpam-4707	108	7	8)	8)	NUM
ejpam-4707	108	8	is	be	AUX
ejpam-4707	108	9	as	as	SCONJ
ejpam-4707	108	10	follows	follow	VERB
ejpam-4707	108	11	:	:	PUNCT
ejpam-4707	108	12	ja=	ja=	PROPN
ejpam-4707	108	13			PROPN
ejpam-4707	108	14	λx((ey+cx)2(x+s(2+cx))−ψ(−1+ey)(ey(2s+x+csx)+cx(s−cx2	λx((ey+cx)2(x+s(2+cx))−ψ(−1+ey)(ey(2s+x+csx)+cx(s−cx2	NOUN
ejpam-4707	108	15	)	)	PUNCT
ejpam-4707	108	16	)	)	PUNCT
ejpam-4707	108	17	)	)	PUNCT
ejpam-4707	109	1	(	(	PUNCT
ejpam-4707	109	2	s+x)2(1+cx)2(ey+cx)2	s+x)2(1+cx)2(ey+cx)2	VERB
ejpam-4707	109	3	−	−	PROPN
ejpam-4707	109	4	λψeyx2	λψeyx2	X
ejpam-4707	110	1	(	(	PUNCT
ejpam-4707	110	2	s+x)(ey+cx)2	s+x)(ey+cx)2	NOUN
ejpam-4707	110	3	ψ(1−	ψ(1−	NOUN
ejpam-4707	110	4	e−y	e−y	PROPN
ejpam-4707	110	5	)	)	PUNCT
ejpam-4707	110	6	ψe−yx	ψe−yx	NOUN
ejpam-4707	110	7	.	.	PROPN
ejpam-4707	111	1	(	(	PUNCT
ejpam-4707	111	2	i	i	NOUN
ejpam-4707	111	3	)	)	PUNCT
ejpam-4707	111	4	ja(f0	ja(f0	NOUN
ejpam-4707	111	5	)	)	PUNCT
ejpam-4707	111	6	is	be	AUX
ejpam-4707	111	7	0	0	NUM
ejpam-4707	111	8	matrix	matrix	NOUN
ejpam-4707	111	9	,	,	PUNCT
ejpam-4707	111	10	so	so	CCONJ
ejpam-4707	111	11	f0	f0	PROPN
ejpam-4707	111	12	is	be	AUX
ejpam-4707	111	13	stable	stable	ADJ
ejpam-4707	111	14	for	for	ADP
ejpam-4707	111	15	all	all	DET
ejpam-4707	111	16	parameter	parameter	NOUN
ejpam-4707	111	17	values	value	NOUN
ejpam-4707	111	18	by	by	ADP
ejpam-4707	111	19	trace	trace	NOUN
ejpam-4707	111	20	-	-	PUNCT
ejpam-4707	111	21	determinant	determinant	ADJ
ejpam-4707	111	22	theorem	theorem	NOUN
ejpam-4707	111	23	(	(	PUNCT
ejpam-4707	111	24	see	see	VERB
ejpam-4707	111	25	figure	figure	NOUN
ejpam-4707	111	26	4	4	NUM
ejpam-4707	111	27	.	.	NUM
ejpam-4707	111	28	,	,	PUNCT
ejpam-4707	111	29	and	and	CCONJ
ejpam-4707	111	30	figure	figure	VERB
ejpam-4707	111	31	9	9	NUM
ejpam-4707	111	32	.	.	PUNCT
ejpam-4707	111	33	)	)	PUNCT
ejpam-4707	111	34	.	.	PUNCT
ejpam-4707	112	1	b.	b.	PROPN
ejpam-4707	112	2	kulahcioglu	kulahcioglu	PROPN
ejpam-4707	112	3	,	,	PUNCT
ejpam-4707	112	4	u.	u.	NOUN
ejpam-4707	112	5	ufuktepe	ufuktepe	NOUN
ejpam-4707	112	6	,	,	PUNCT
ejpam-4707	112	7	a.	a.	PROPN
ejpam-4707	112	8	kalampakas	kalampakas	PROPN
ejpam-4707	112	9	/	/	SYM
ejpam-4707	112	10	eur	eur	PROPN
ejpam-4707	112	11	.	.	PUNCT
ejpam-4707	113	1	j.	j.	PROPN
ejpam-4707	113	2	pure	pure	PROPN
ejpam-4707	113	3	appl	appl	PROPN
ejpam-4707	113	4	.	.	PROPN
ejpam-4707	113	5	math	math	PROPN
ejpam-4707	113	6	,	,	PUNCT
ejpam-4707	113	7	16	16	NUM
ejpam-4707	113	8	(	(	PUNCT
ejpam-4707	113	9	2	2	NUM
ejpam-4707	113	10	)	)	PUNCT
ejpam-4707	113	11	(	(	PUNCT
ejpam-4707	113	12	2023	2023	NUM
ejpam-4707	113	13	)	)	PUNCT
ejpam-4707	113	14	,	,	PUNCT
ejpam-4707	113	15	736	736	NUM
ejpam-4707	113	16	-	-	SYM
ejpam-4707	113	17	750	750	NUM
ejpam-4707	113	18	741	741	NUM
ejpam-4707	113	19	0	0	NUM
ejpam-4707	113	20	2	2	NUM
ejpam-4707	113	21	4	4	NUM
ejpam-4707	113	22	6	6	NUM
ejpam-4707	113	23	8	8	NUM
ejpam-4707	113	24	10	10	NUM
ejpam-4707	113	25	0.02	0.02	NUM
ejpam-4707	113	26	0.04	0.04	NUM
ejpam-4707	113	27	0.06	0.06	NUM
ejpam-4707	113	28	0.08	0.08	NUM
ejpam-4707	113	29	0.10	0.10	NUM
ejpam-4707	113	30	0.12	0.12	NUM
ejpam-4707	113	31	y	y	PROPN
ejpam-4707	113	32	1	1	NUM
ejpam-4707	113	33	λ	λ	PROPN
ejpam-4707	113	34	hhyl	hhyl	NOUN
ejpam-4707	113	35	figure	figure	NOUN
ejpam-4707	113	36	1	1	NUM
ejpam-4707	113	37	:	:	PUNCT
ejpam-4707	113	38	the	the	DET
ejpam-4707	113	39	positive	positive	ADJ
ejpam-4707	113	40	fixed	fix	VERB
ejpam-4707	113	41	point	point	NOUN
ejpam-4707	113	42	of	of	ADP
ejpam-4707	113	43	the	the	DET
ejpam-4707	113	44	model	model	NOUN
ejpam-4707	113	45	(	(	PUNCT
ejpam-4707	113	46	8)	8)	NUM
ejpam-4707	113	47	exists	exist	VERB
ejpam-4707	113	48	if	if	SCONJ
ejpam-4707	113	49	the	the	DET
ejpam-4707	113	50	two	two	NUM
ejpam-4707	113	51	functions	function	NOUN
ejpam-4707	113	52	intersect	intersect	ADJ
ejpam-4707	113	53	.	.	PUNCT
ejpam-4707	114	1	if	if	SCONJ
ejpam-4707	114	2	s	s	VERB
ejpam-4707	114	3	<	<	X
ejpam-4707	114	4	c	c	NOUN
ejpam-4707	114	5	ψ2	ψ2	NOUN
ejpam-4707	114	6	and	and	CCONJ
ejpam-4707	114	7	λ	λ	X
ejpam-4707	114	8	>	>	X
ejpam-4707	114	9	(	(	PUNCT
ejpam-4707	114	10	c+ψ)(1+ψs	c+ψ)(1+ψs	NOUN
ejpam-4707	114	11	)	)	PUNCT
ejpam-4707	114	12	ψ	ψ	NOUN
ejpam-4707	114	13	,	,	PUNCT
ejpam-4707	114	14	they	they	PRON
ejpam-4707	114	15	intersect	intersect	VERB
ejpam-4707	114	16	once	once	ADV
ejpam-4707	114	17	(	(	PUNCT
ejpam-4707	114	18	unique	unique	ADJ
ejpam-4707	114	19	positive	positive	ADJ
ejpam-4707	114	20	fixed	fix	VERB
ejpam-4707	114	21	point	point	NOUN
ejpam-4707	114	22	)	)	PUNCT
ejpam-4707	114	23	.	.	PUNCT
ejpam-4707	115	1	the	the	DET
ejpam-4707	115	2	figure	figure	NOUN
ejpam-4707	115	3	depicts	depict	VERB
ejpam-4707	115	4	this	this	DET
ejpam-4707	115	5	case	case	NOUN
ejpam-4707	115	6	for	for	ADP
ejpam-4707	115	7	λ	λ	NOUN
ejpam-4707	115	8	=	=	SYM
ejpam-4707	115	9	10	10	NUM
ejpam-4707	115	10	,	,	PUNCT
ejpam-4707	115	11	c	c	NOUN
ejpam-4707	115	12	=	=	SYM
ejpam-4707	115	13	1	1	NUM
ejpam-4707	115	14	,	,	PUNCT
ejpam-4707	115	15	s	s	PART
ejpam-4707	115	16	=	=	SYM
ejpam-4707	115	17	3	3	NUM
ejpam-4707	115	18	,	,	PUNCT
ejpam-4707	115	19	and	and	CCONJ
ejpam-4707	115	20	ψ	ψ	X
ejpam-4707	115	21	=	=	NOUN
ejpam-4707	115	22	0.5	0.5	NUM
ejpam-4707	115	23	.	.	NOUN
ejpam-4707	115	24	0	0	NUM
ejpam-4707	116	1	10	10	NUM
ejpam-4707	116	2	20	20	NUM
ejpam-4707	116	3	30	30	NUM
ejpam-4707	116	4	40	40	NUM
ejpam-4707	116	5	0.26	0.26	NUM
ejpam-4707	116	6	0.27	0.27	NUM
ejpam-4707	116	7	0.28	0.28	NUM
ejpam-4707	116	8	0.29	0.29	NUM
ejpam-4707	116	9	0.30	0.30	NUM
ejpam-4707	116	10	0.31	0.31	NUM
ejpam-4707	116	11	0.32	0.32	NUM
ejpam-4707	116	12	0.33	0.33	NUM
ejpam-4707	116	13	y	y	NUM
ejpam-4707	116	14	1	1	NUM
ejpam-4707	116	15	λ	λ	PROPN
ejpam-4707	116	16	hhyl	hhyl	NOUN
ejpam-4707	116	17	figure	figure	NOUN
ejpam-4707	116	18	2	2	NUM
ejpam-4707	116	19	:	:	PUNCT
ejpam-4707	116	20	the	the	DET
ejpam-4707	116	21	case	case	NOUN
ejpam-4707	116	22	s	s	VERB
ejpam-4707	116	23	>	>	X
ejpam-4707	116	24	c	c	NOUN
ejpam-4707	116	25	ψ2	ψ2	NOUN
ejpam-4707	116	26	for	for	ADP
ejpam-4707	116	27	λ	λ	NOUN
ejpam-4707	116	28	=	=	NOUN
ejpam-4707	116	29	3.8	3.8	NUM
ejpam-4707	116	30	,	,	PUNCT
ejpam-4707	116	31	c	c	NOUN
ejpam-4707	116	32	=	=	NOUN
ejpam-4707	116	33	0.01	0.01	NUM
ejpam-4707	116	34	,	,	PUNCT
ejpam-4707	116	35	s	s	NOUN
ejpam-4707	116	36	=	=	SYM
ejpam-4707	116	37	5	5	NUM
ejpam-4707	116	38	,	,	PUNCT
ejpam-4707	116	39	and	and	CCONJ
ejpam-4707	116	40	ψ	ψ	X
ejpam-4707	116	41	=	=	SYM
ejpam-4707	116	42	0.5.multiple	0.5.multiple	NUM
ejpam-4707	116	43	intersections	intersection	NOUN
ejpam-4707	116	44	,	,	PUNCT
ejpam-4707	116	45	multiple	multiple	ADJ
ejpam-4707	116	46	positive	positive	ADJ
ejpam-4707	116	47	fixed	fix	VERB
ejpam-4707	116	48	points	point	NOUN
ejpam-4707	116	49	.	.	PUNCT
ejpam-4707	117	1	0	0	NUM
ejpam-4707	117	2	2	2	NUM
ejpam-4707	117	3	4	4	NUM
ejpam-4707	117	4	6	6	NUM
ejpam-4707	117	5	8	8	NUM
ejpam-4707	117	6	10	10	NUM
ejpam-4707	117	7	0.0	0.0	NUM
ejpam-4707	117	8	0.1	0.1	NUM
ejpam-4707	117	9	0.2	0.2	NUM
ejpam-4707	117	10	0.3	0.3	NUM
ejpam-4707	117	11	0.4	0.4	NUM
ejpam-4707	117	12	0.5	0.5	NUM
ejpam-4707	117	13	y	y	PROPN
ejpam-4707	117	14	1	1	NUM
ejpam-4707	117	15	λ	λ	PROPN
ejpam-4707	117	16	hhyl	hhyl	NOUN
ejpam-4707	117	17	figure	figure	VERB
ejpam-4707	117	18	3	3	NUM
ejpam-4707	117	19	:	:	PUNCT
ejpam-4707	117	20	the	the	DET
ejpam-4707	117	21	case	case	NOUN
ejpam-4707	117	22	λ	λ	X
ejpam-4707	117	23	<	<	X
ejpam-4707	117	24	(	(	PUNCT
ejpam-4707	117	25	c+ψ)(1+ψs	c+ψ)(1+ψs	NOUN
ejpam-4707	117	26	)	)	PUNCT
ejpam-4707	117	27	ψ	ψ	NOUN
ejpam-4707	117	28	for	for	ADP
ejpam-4707	117	29	λ	λ	PROPN
ejpam-4707	117	30	=	=	SYM
ejpam-4707	117	31	2	2	NUM
ejpam-4707	117	32	,	,	PUNCT
ejpam-4707	117	33	c	c	NOUN
ejpam-4707	117	34	=	=	SYM
ejpam-4707	117	35	1	1	NUM
ejpam-4707	117	36	,	,	PUNCT
ejpam-4707	117	37	s	s	PART
ejpam-4707	117	38	=	=	SYM
ejpam-4707	117	39	3	3	NUM
ejpam-4707	117	40	,	,	PUNCT
ejpam-4707	117	41	and	and	CCONJ
ejpam-4707	117	42	ψ	ψ	X
ejpam-4707	117	43	=	=	NOUN
ejpam-4707	117	44	0.5	0.5	NUM
ejpam-4707	117	45	.	.	PUNCT
ejpam-4707	118	1	the	the	DET
ejpam-4707	118	2	positive	positive	ADJ
ejpam-4707	118	3	fixed	fix	VERB
ejpam-4707	118	4	point	point	NOUN
ejpam-4707	118	5	of	of	ADP
ejpam-4707	118	6	the	the	DET
ejpam-4707	118	7	model	model	NOUN
ejpam-4707	118	8	(	(	PUNCT
ejpam-4707	118	9	8)	8)	NUM
ejpam-4707	118	10	exists	exist	VERB
ejpam-4707	118	11	if	if	SCONJ
ejpam-4707	118	12	the	the	DET
ejpam-4707	118	13	two	two	NUM
ejpam-4707	118	14	functions	function	NOUN
ejpam-4707	118	15	intersect.no	intersect.no	PUNCT
ejpam-4707	118	16	intersection	intersection	NOUN
ejpam-4707	118	17	,	,	PUNCT
ejpam-4707	118	18	no	no	DET
ejpam-4707	118	19	positive	positive	ADJ
ejpam-4707	118	20	fixed	fix	VERB
ejpam-4707	118	21	point	point	NOUN
ejpam-4707	118	22	.	.	PUNCT
ejpam-4707	119	1	(	(	PUNCT
ejpam-4707	119	2	ii	ii	NOUN
ejpam-4707	119	3	)	)	PUNCT
ejpam-4707	119	4	the	the	DET
ejpam-4707	119	5	jacobian	jacobian	ADJ
ejpam-4707	119	6	matrix	matrix	NOUN
ejpam-4707	119	7	evaluated	evaluate	VERB
ejpam-4707	119	8	at	at	ADP
ejpam-4707	119	9	f1	f1	PROPN
ejpam-4707	119	10	is	be	AUX
ejpam-4707	119	11	b.	b.	PROPN
ejpam-4707	119	12	kulahcioglu	kulahcioglu	PROPN
ejpam-4707	119	13	,	,	PUNCT
ejpam-4707	119	14	u.	u.	NOUN
ejpam-4707	119	15	ufuktepe	ufuktepe	NOUN
ejpam-4707	119	16	,	,	PUNCT
ejpam-4707	119	17	a.	a.	PROPN
ejpam-4707	119	18	kalampakas	kalampakas	PROPN
ejpam-4707	119	19	/	/	SYM
ejpam-4707	119	20	eur	eur	PROPN
ejpam-4707	119	21	.	.	PUNCT
ejpam-4707	120	1	j.	j.	PROPN
ejpam-4707	120	2	pure	pure	PROPN
ejpam-4707	120	3	appl	appl	PROPN
ejpam-4707	120	4	.	.	PROPN
ejpam-4707	120	5	math	math	PROPN
ejpam-4707	120	6	,	,	PUNCT
ejpam-4707	120	7	16	16	NUM
ejpam-4707	120	8	(	(	PUNCT
ejpam-4707	120	9	2	2	NUM
ejpam-4707	120	10	)	)	PUNCT
ejpam-4707	120	11	(	(	PUNCT
ejpam-4707	120	12	2023	2023	NUM
ejpam-4707	120	13	)	)	PUNCT
ejpam-4707	120	14	,	,	PUNCT
ejpam-4707	120	15	736	736	NUM
ejpam-4707	120	16	-	-	SYM
ejpam-4707	120	17	750	750	NUM
ejpam-4707	120	18	742	742	NUM
ejpam-4707	120	19	figure	figure	NOUN
ejpam-4707	120	20	4	4	NUM
ejpam-4707	120	21	:	:	PUNCT
ejpam-4707	120	22	the	the	DET
ejpam-4707	120	23	determinations	determination	NOUN
ejpam-4707	120	24	of	of	ADP
ejpam-4707	120	25	eigenvalues	eigenvalue	NOUN
ejpam-4707	120	26	in	in	ADP
ejpam-4707	120	27	all	all	DET
ejpam-4707	120	28	the	the	DET
ejpam-4707	120	29	regions	region	NOUN
ejpam-4707	120	30	in	in	ADP
ejpam-4707	120	31	the	the	DET
ejpam-4707	120	32	det	det	NOUN
ejpam-4707	120	33	-	-	PUNCT
ejpam-4707	120	34	trace	trace	NOUN
ejpam-4707	120	35	plane	plane	NOUN
ejpam-4707	120	36	[	[	X
ejpam-4707	120	37	3	3	NUM
ejpam-4707	120	38	]	]	PUNCT
ejpam-4707	120	39	.	.	PUNCT
ejpam-4707	121	1	ja(f1	ja(f1	X
ejpam-4707	121	2	)	)	PUNCT
ejpam-4707	122	1	=	=	PRON
ejpam-4707	122	2			X
ejpam-4707	122	3	1−	1−	NUM
ejpam-4707	122	4	√	√	PROPN
ejpam-4707	122	5	a2−4cs	a2−4cs	NOUN
ejpam-4707	122	6	λ	λ	X
ejpam-4707	122	7	ψ(1−λ−cs−	ψ(1−λ−cs−	NOUN
ejpam-4707	122	8	√	√	PROPN
ejpam-4707	122	9	a2−4cs	a2−4cs	NOUN
ejpam-4707	122	10	)	)	PUNCT
ejpam-4707	123	1	2λc	2λc	NOUN
ejpam-4707	123	2	0	0	NUM
ejpam-4707	123	3	ψ(a+	ψ(a+	NOUN
ejpam-4707	123	4	√	√	NOUN
ejpam-4707	123	5	a2−4cs	a2−4cs	NOUN
ejpam-4707	123	6	)	)	PUNCT
ejpam-4707	123	7	2c	2c	NOUN
ejpam-4707	123	8	.	.	VERB
ejpam-4707	124	1	we	we	PRON
ejpam-4707	124	2	have	have	VERB
ejpam-4707	124	3	λ1	λ1	VERB
ejpam-4707	124	4	=	=	SYM
ejpam-4707	124	5	1−	1−	NUM
ejpam-4707	124	6	√	√	PROPN
ejpam-4707	124	7	a2−4cs	a2−4cs	NOUN
ejpam-4707	124	8	λ	λ	PROPN
ejpam-4707	124	9	and	and	CCONJ
ejpam-4707	124	10	λ2	λ2	NOUN
ejpam-4707	124	11	=	=	SYM
ejpam-4707	124	12	ψ(a+	ψ(a+	NOUN
ejpam-4707	124	13	√	√	NOUN
ejpam-4707	124	14	a2−4cs	a2−4cs	NOUN
ejpam-4707	124	15	)	)	PUNCT
ejpam-4707	124	16	2c	2c	NOUN
ejpam-4707	124	17	.	.	PUNCT
ejpam-4707	125	1	hence	hence	ADV
ejpam-4707	125	2	,	,	PUNCT
ejpam-4707	125	3	|λ1,2|	|λ1,2|	NOUN
ejpam-4707	125	4	<	<	X
ejpam-4707	125	5	1	1	NUM
ejpam-4707	125	6	if	if	SCONJ
ejpam-4707	125	7	s	s	VERB
ejpam-4707	125	8	<	<	X
ejpam-4707	125	9	c	c	NOUN
ejpam-4707	125	10	ψ2	ψ2	NOUN
ejpam-4707	125	11	and	and	CCONJ
ejpam-4707	125	12	(	(	PUNCT
ejpam-4707	125	13	1	1	NUM
ejpam-4707	125	14	+	+	CCONJ
ejpam-4707	125	15	√	√	ADP
ejpam-4707	125	16	cs	cs	ADJ
ejpam-4707	125	17	)	)	PUNCT
ejpam-4707	125	18	2	2	NUM
ejpam-4707	125	19	<	<	X
ejpam-4707	125	20	λ	λ	X
ejpam-4707	125	21	<	<	X
ejpam-4707	125	22	(	(	PUNCT
ejpam-4707	125	23	c+ψ)(1+ψs	c+ψ)(1+ψs	NOUN
ejpam-4707	125	24	)	)	PUNCT
ejpam-4707	125	25	ψ	ψ	NOUN
ejpam-4707	125	26	.	.	PUNCT
ejpam-4707	126	1	under	under	ADP
ejpam-4707	126	2	these	these	DET
ejpam-4707	126	3	conditions	condition	NOUN
ejpam-4707	126	4	f1	f1	NOUN
ejpam-4707	126	5	is	be	AUX
ejpam-4707	126	6	stable	stable	ADJ
ejpam-4707	126	7	(	(	PUNCT
ejpam-4707	126	8	see	see	VERB
ejpam-4707	126	9	figure	figure	NOUN
ejpam-4707	126	10	4	4	NUM
ejpam-4707	126	11	.	.	NUM
ejpam-4707	126	12	,	,	PUNCT
ejpam-4707	126	13	and	and	CCONJ
ejpam-4707	126	14	figure	figure	VERB
ejpam-4707	126	15	11	11	NUM
ejpam-4707	126	16	.	.	PUNCT
ejpam-4707	126	17	)	)	PUNCT
ejpam-4707	126	18	.	.	PUNCT
ejpam-4707	127	1	(	(	PUNCT
ejpam-4707	127	2	iii	iii	X
ejpam-4707	127	3	)	)	PUNCT
ejpam-4707	127	4	the	the	DET
ejpam-4707	127	5	jacobian	jacobian	ADJ
ejpam-4707	127	6	matrix	matrix	NOUN
ejpam-4707	127	7	at	at	ADP
ejpam-4707	127	8	f2	f2	PROPN
ejpam-4707	127	9	is	be	AUX
ejpam-4707	127	10	ja(f2	ja(f2	NOUN
ejpam-4707	127	11	)	)	PUNCT
ejpam-4707	128	1	=	=	PRON
ejpam-4707	128	2			VERB
ejpam-4707	128	3	1	1	NUM
ejpam-4707	128	4	+	+	CCONJ
ejpam-4707	128	5	√	√	VERB
ejpam-4707	128	6	a2−4cs	a2−4cs	NOUN
ejpam-4707	128	7	λ	λ	PROPN
ejpam-4707	128	8	ψ(1−λ−cs+	ψ(1−λ−cs+	ADJ
ejpam-4707	128	9	√	√	NUM
ejpam-4707	128	10	a2−4cs	a2−4cs	NOUN
ejpam-4707	128	11	)	)	PUNCT
ejpam-4707	129	1	2λc	2λc	NOUN
ejpam-4707	129	2	0	0	NUM
ejpam-4707	129	3	ψ(a−	ψ(a−	PROPN
ejpam-4707	129	4	√	√	NUM
ejpam-4707	129	5	a2−4cs	a2−4cs	NOUN
ejpam-4707	129	6	)	)	PUNCT
ejpam-4707	129	7	2c	2c	NOUN
ejpam-4707	129	8	.	.	VERB
ejpam-4707	130	1	we	we	PRON
ejpam-4707	130	2	have	have	VERB
ejpam-4707	130	3	λ1	λ1	VERB
ejpam-4707	130	4	=	=	SYM
ejpam-4707	130	5	1	1	NUM
ejpam-4707	130	6	+	+	CCONJ
ejpam-4707	130	7	√	√	PROPN
ejpam-4707	130	8	a2−4cs	a2−4cs	NOUN
ejpam-4707	130	9	λ	λ	PROPN
ejpam-4707	130	10	and	and	CCONJ
ejpam-4707	130	11	λ2	λ2	PROPN
ejpam-4707	130	12	=	=	SYM
ejpam-4707	130	13	ψ(a−	ψ(a−	ADJ
ejpam-4707	130	14	√	√	NUM
ejpam-4707	130	15	a2−4cs	a2−4cs	NOUN
ejpam-4707	130	16	=	=	SYM
ejpam-4707	130	17	det	det	PROPN
ejpam-4707	130	18	(	(	PUNCT
ejpam-4707	130	19	)	)	PUNCT
ejpam-4707	130	20	2c	2c	NOUN
ejpam-4707	130	21	.	.	PUNCT
ejpam-4707	131	1	case	case	NOUN
ejpam-4707	131	2	1	1	NUM
ejpam-4707	131	3	:	:	PUNCT
ejpam-4707	132	1	if	if	SCONJ
ejpam-4707	132	2	a2	a2	PROPN
ejpam-4707	132	3	=	=	SYM
ejpam-4707	132	4	4cs	4cs	ADJ
ejpam-4707	132	5	⇒	⇒	NOUN
ejpam-4707	132	6	λ1	λ1	PROPN
ejpam-4707	132	7	=	=	SYM
ejpam-4707	132	8	1	1	NUM
ejpam-4707	132	9	and	and	CCONJ
ejpam-4707	132	10	λ2	λ2	NOUN
ejpam-4707	132	11	=	=	PUNCT
ejpam-4707	132	12	ψa	ψa	NOUN
ejpam-4707	132	13	2c	2c	NOUN
ejpam-4707	132	14	=	=	SYM
ejpam-4707	132	15	det(ja	det(ja	PROPN
ejpam-4707	132	16	)	)	PUNCT
ejpam-4707	133	1	so	so	CCONJ
ejpam-4707	133	2	we	we	PRON
ejpam-4707	133	3	have	have	VERB
ejpam-4707	133	4	non	non	ADJ
ejpam-4707	133	5	-	-	ADJ
ejpam-4707	133	6	hyperbolic	hyperbolic	ADJ
ejpam-4707	133	7	case	case	NOUN
ejpam-4707	133	8	and	and	CCONJ
ejpam-4707	133	9	it	it	PRON
ejpam-4707	133	10	is	be	AUX
ejpam-4707	133	11	saddle	saddle	NOUN
ejpam-4707	133	12	-	-	PUNCT
ejpam-4707	133	13	node	node	NOUN
ejpam-4707	133	14	(	(	PUNCT
ejpam-4707	133	15	fold	fold	ADJ
ejpam-4707	133	16	)	)	PUNCT
ejpam-4707	133	17	bifurcation	bifurcation	NOUN
ejpam-4707	133	18	if	if	SCONJ
ejpam-4707	133	19	0	0	NUM
ejpam-4707	133	20	<	<	X
ejpam-4707	133	21	λ2	λ2	NOUN
ejpam-4707	133	22	<	<	X
ejpam-4707	133	23	1	1	NUM
ejpam-4707	133	24	then	then	ADV
ejpam-4707	133	25	by	by	ADP
ejpam-4707	133	26	the	the	DET
ejpam-4707	133	27	center	center	NOUN
ejpam-4707	133	28	manifold	manifold	ADJ
ejpam-4707	133	29	theory[3	theory[3	NOUN
ejpam-4707	133	30	]	]	X
ejpam-4707	133	31	f2	f2	PROPN
ejpam-4707	133	32	is	be	AUX
ejpam-4707	133	33	oscillatory	oscillatory	ADJ
ejpam-4707	133	34	:	:	PUNCT
ejpam-4707	133	35	it	it	PRON
ejpam-4707	133	36	is	be	AUX
ejpam-4707	133	37	oscillatory	oscillatory	ADJ
ejpam-4707	133	38	source	source	NOUN
ejpam-4707	133	39	if	if	SCONJ
ejpam-4707	133	40	ψa	ψa	ADP
ejpam-4707	133	41	>	>	X
ejpam-4707	133	42	2c	2c	NOUN
ejpam-4707	133	43	.	.	PUNCT
ejpam-4707	134	1	it	it	PRON
ejpam-4707	134	2	is	be	AUX
ejpam-4707	134	3	oscillatory	oscillatory	ADJ
ejpam-4707	134	4	saddle	saddle	NOUN
ejpam-4707	134	5	if	if	SCONJ
ejpam-4707	134	6	ψa	ψa	ADP
ejpam-4707	134	7	<	<	X
ejpam-4707	134	8	2c	2c	NUM
ejpam-4707	134	9	.	.	PUNCT
ejpam-4707	135	1	case	case	NOUN
ejpam-4707	135	2	2	2	NUM
ejpam-4707	135	3	:	:	PUNCT
ejpam-4707	135	4	if	if	SCONJ
ejpam-4707	135	5	a2	a2	PROPN
ejpam-4707	135	6	−	−	PROPN
ejpam-4707	135	7	4cs	4cs	NOUN
ejpam-4707	135	8	>	>	X
ejpam-4707	135	9	0	0	PUNCT
ejpam-4707	136	1	then	then	ADV
ejpam-4707	136	2	λ1	λ1	X
ejpam-4707	136	3	>	>	X
ejpam-4707	136	4	1	1	NUM
ejpam-4707	136	5	and	and	CCONJ
ejpam-4707	136	6	f2	f2	PROPN
ejpam-4707	136	7	is	be	AUX
ejpam-4707	136	8	a	a	DET
ejpam-4707	136	9	spiral	spiral	ADJ
ejpam-4707	136	10	source	source	NOUN
ejpam-4707	136	11	.	.	PUNCT
ejpam-4707	137	1	(	(	PUNCT
ejpam-4707	137	2	see	see	VERB
ejpam-4707	137	3	figure	figure	NOUN
ejpam-4707	137	4	5	5	NUM
ejpam-4707	137	5	.	.	PUNCT
ejpam-4707	137	6	,	,	PUNCT
ejpam-4707	137	7	figure	figure	VERB
ejpam-4707	137	8	6	6	NUM
ejpam-4707	137	9	,	,	PUNCT
ejpam-4707	137	10	and	and	CCONJ
ejpam-4707	137	11	figure	figure	VERB
ejpam-4707	137	12	10	10	NUM
ejpam-4707	137	13	.	.	PUNCT
ejpam-4707	137	14	)	)	PUNCT
ejpam-4707	138	1	numerical	numerical	ADJ
ejpam-4707	138	2	simulations	simulation	NOUN
ejpam-4707	138	3	to	to	PART
ejpam-4707	138	4	investigate	investigate	VERB
ejpam-4707	138	5	the	the	DET
ejpam-4707	138	6	behavior	behavior	NOUN
ejpam-4707	138	7	of	of	ADP
ejpam-4707	138	8	the	the	DET
ejpam-4707	138	9	fixed	fix	VERB
ejpam-4707	138	10	point	point	NOUN
ejpam-4707	138	11	f3	f3	PROPN
ejpam-4707	138	12	will	will	AUX
ejpam-4707	138	13	be	be	AUX
ejpam-4707	138	14	implemented	implement	VERB
ejpam-4707	138	15	in	in	ADP
ejpam-4707	138	16	section	section	NOUN
ejpam-4707	138	17	5	5	NUM
ejpam-4707	138	18	.	.	PUNCT
ejpam-4707	139	1	for	for	ADP
ejpam-4707	139	2	the	the	DET
ejpam-4707	139	3	model	model	NOUN
ejpam-4707	139	4	(	(	PUNCT
ejpam-4707	139	5	8)	8)	NUM
ejpam-4707	139	6	,	,	PUNCT
ejpam-4707	139	7	f0	f0	PROPN
ejpam-4707	139	8	=	=	SYM
ejpam-4707	139	9	(	(	PUNCT
ejpam-4707	139	10	0	0	NUM
ejpam-4707	139	11	,	,	PUNCT
ejpam-4707	139	12	0	0	NUM
ejpam-4707	139	13	)	)	PUNCT
ejpam-4707	139	14	is	be	AUX
ejpam-4707	139	15	globally	globally	ADV
ejpam-4707	139	16	asymptotically	asymptotically	ADV
ejpam-4707	139	17	stable	stable	ADJ
ejpam-4707	139	18	if	if	SCONJ
ejpam-4707	139	19	λ	λ	X
ejpam-4707	139	20	<	<	X
ejpam-4707	139	21	1	1	NUM
ejpam-4707	139	22	.	.	PUNCT
ejpam-4707	140	1	we	we	PRON
ejpam-4707	140	2	have	have	VERB
ejpam-4707	140	3	xt+1	xt+1	NUM
ejpam-4707	141	1	=	=	SYM
ejpam-4707	142	1	(	(	PUNCT
ejpam-4707	142	2	1−ψ)λxt	1−ψ)λxt	NUM
ejpam-4707	142	3	1	1	NUM
ejpam-4707	142	4	+	+	NUM
ejpam-4707	142	5	cxt	cxt	PROPN
ejpam-4707	142	6	xt	xt	PROPN
ejpam-4707	142	7	s+	s+	ADV
ejpam-4707	142	8	xt	xt	X
ejpam-4707	143	1	+	+	CCONJ
ejpam-4707	143	2	ψλxt	ψλxt	PROPN
ejpam-4707	143	3	eyt	eyt	PROPN
ejpam-4707	143	4	+	+	PROPN
ejpam-4707	143	5	cxt	cxt	PROPN
ejpam-4707	143	6	xt	xt	PROPN
ejpam-4707	143	7	s+	s+	X
ejpam-4707	143	8	xt	xt	PROPN
ejpam-4707	143	9	b.	b.	PROPN
ejpam-4707	143	10	kulahcioglu	kulahcioglu	PROPN
ejpam-4707	143	11	,	,	PUNCT
ejpam-4707	143	12	u.	u.	NOUN
ejpam-4707	143	13	ufuktepe	ufuktepe	NOUN
ejpam-4707	143	14	,	,	PUNCT
ejpam-4707	143	15	a.	a.	PROPN
ejpam-4707	143	16	kalampakas	kalampakas	PROPN
ejpam-4707	143	17	/	/	SYM
ejpam-4707	143	18	eur	eur	PROPN
ejpam-4707	143	19	.	.	PUNCT
ejpam-4707	144	1	j.	j.	PROPN
ejpam-4707	144	2	pure	pure	PROPN
ejpam-4707	144	3	appl	appl	PROPN
ejpam-4707	144	4	.	.	PROPN
ejpam-4707	144	5	math	math	PROPN
ejpam-4707	144	6	,	,	PUNCT
ejpam-4707	144	7	16	16	NUM
ejpam-4707	144	8	(	(	PUNCT
ejpam-4707	144	9	2	2	NUM
ejpam-4707	144	10	)	)	PUNCT
ejpam-4707	144	11	(	(	PUNCT
ejpam-4707	144	12	2023	2023	NUM
ejpam-4707	144	13	)	)	PUNCT
ejpam-4707	144	14	,	,	PUNCT
ejpam-4707	144	15	736	736	NUM
ejpam-4707	144	16	-	-	SYM
ejpam-4707	144	17	750	750	NUM
ejpam-4707	144	18	743	743	NUM
ejpam-4707	144	19	figure	figure	NOUN
ejpam-4707	144	20	5	5	NUM
ejpam-4707	144	21	:	:	PUNCT
ejpam-4707	144	22	classification	classification	NOUN
ejpam-4707	144	23	of	of	ADP
ejpam-4707	144	24	the	the	DET
ejpam-4707	144	25	fixed	fix	VERB
ejpam-4707	144	26	points	point	NOUN
ejpam-4707	144	27	and	and	CCONJ
ejpam-4707	144	28	bifurcations	bifurcation	NOUN
ejpam-4707	144	29	in	in	ADP
ejpam-4707	144	30	all	all	DET
ejpam-4707	144	31	the	the	DET
ejpam-4707	144	32	regions	region	NOUN
ejpam-4707	144	33	in	in	ADP
ejpam-4707	144	34	the	the	DET
ejpam-4707	144	35	det	det	NOUN
ejpam-4707	144	36	-	-	PUNCT
ejpam-4707	144	37	trace	trace	NOUN
ejpam-4707	144	38	plane	plane	NOUN
ejpam-4707	144	39	.	.	PUNCT
ejpam-4707	145	1	by	by	ADP
ejpam-4707	145	2	comparison	comparison	NOUN
ejpam-4707	145	3	we	we	PRON
ejpam-4707	145	4	obtain	obtain	VERB
ejpam-4707	145	5	xt+1	xt+1	X
ejpam-4707	145	6	≤	≤	NUM
ejpam-4707	145	7	λxt	λxt	VERB
ejpam-4707	145	8	1	1	NUM
ejpam-4707	145	9	+	+	CCONJ
ejpam-4707	145	10	cxt	cxt	PROPN
ejpam-4707	145	11	xt	xt	PROPN
ejpam-4707	145	12	s+	s+	ADV
ejpam-4707	145	13	xt	xt	X
ejpam-4707	146	1	<	<	X
ejpam-4707	147	1	λxt	λxt	VERB
ejpam-4707	147	2	1	1	NUM
ejpam-4707	147	3	+	+	CCONJ
ejpam-4707	147	4	cxt	cxt	X
ejpam-4707	147	5	<	<	X
ejpam-4707	147	6	λxt	λxt	VERB
ejpam-4707	147	7	<	<	X
ejpam-4707	147	8	xt	xt	X
ejpam-4707	148	1	if	if	SCONJ
ejpam-4707	148	2	λ	λ	X
ejpam-4707	148	3	<	<	X
ejpam-4707	148	4	1	1	NUM
ejpam-4707	148	5	.	.	PUNCT
ejpam-4707	149	1	then	then	ADV
ejpam-4707	149	2	lim	lim	PROPN
ejpam-4707	149	3	t→∞	t→∞	X
ejpam-4707	149	4	xt	xt	PROPN
ejpam-4707	150	1	=	=	SYM
ejpam-4707	150	2	0	0	PROPN
ejpam-4707	150	3	,	,	PUNCT
ejpam-4707	150	4	which	which	PRON
ejpam-4707	150	5	also	also	ADV
ejpam-4707	150	6	implies	imply	VERB
ejpam-4707	150	7	lim	lim	PROPN
ejpam-4707	150	8	t→∞	t→∞	ADP
ejpam-4707	150	9	yt	yt	NOUN
ejpam-4707	151	1	=	=	NOUN
ejpam-4707	151	2	0	0	X
ejpam-4707	151	3	.	.	PUNCT
ejpam-4707	152	1	hence	hence	ADV
ejpam-4707	152	2	,	,	PUNCT
ejpam-4707	152	3	the	the	DET
ejpam-4707	152	4	fixed	fix	VERB
ejpam-4707	152	5	point	point	NOUN
ejpam-4707	152	6	f0	f0	PROPN
ejpam-4707	152	7	is	be	AUX
ejpam-4707	152	8	globally	globally	ADV
ejpam-4707	152	9	attracting	attract	VERB
ejpam-4707	152	10	if	if	SCONJ
ejpam-4707	152	11	λ	λ	PROPN
ejpam-4707	152	12	<	<	X
ejpam-4707	152	13	1	1	NUM
ejpam-4707	152	14	,	,	PUNCT
ejpam-4707	152	15	and	and	CCONJ
ejpam-4707	152	16	it	it	PRON
ejpam-4707	152	17	is	be	AUX
ejpam-4707	152	18	locally	locally	ADV
ejpam-4707	152	19	asymptotically	asymptotically	ADV
ejpam-4707	152	20	stable	stable	ADJ
ejpam-4707	152	21	for	for	ADP
ejpam-4707	152	22	all	all	DET
ejpam-4707	152	23	values	value	NOUN
ejpam-4707	152	24	of	of	ADP
ejpam-4707	152	25	parameters	parameter	NOUN
ejpam-4707	152	26	.	.	PUNCT
ejpam-4707	153	1	thus	thus	ADV
ejpam-4707	153	2	,	,	PUNCT
ejpam-4707	153	3	it	it	PRON
ejpam-4707	153	4	is	be	AUX
ejpam-4707	153	5	globally	globally	ADV
ejpam-4707	153	6	asymptotically	asymptotically	ADV
ejpam-4707	153	7	stable	stable	ADJ
ejpam-4707	153	8	if	if	SCONJ
ejpam-4707	153	9	λ	λ	X
ejpam-4707	153	10	<	<	X
ejpam-4707	153	11	1	1	NUM
ejpam-4707	153	12	.	.	PUNCT
ejpam-4707	154	1	the	the	DET
ejpam-4707	154	2	global	global	ADJ
ejpam-4707	154	3	behavior	behavior	NOUN
ejpam-4707	154	4	of	of	ADP
ejpam-4707	154	5	the	the	DET
ejpam-4707	154	6	other	other	ADJ
ejpam-4707	154	7	fixed	fix	VERB
ejpam-4707	154	8	points	point	NOUN
ejpam-4707	154	9	is	be	AUX
ejpam-4707	154	10	omitted	omit	VERB
ejpam-4707	154	11	,	,	PUNCT
ejpam-4707	154	12	since	since	SCONJ
ejpam-4707	154	13	local	local	ADJ
ejpam-4707	154	14	stability	stability	NOUN
ejpam-4707	154	15	of	of	ADP
ejpam-4707	154	16	(	(	PUNCT
ejpam-4707	154	17	0	0	NUM
ejpam-4707	154	18	,	,	PUNCT
ejpam-4707	154	19	0	0	NUM
ejpam-4707	154	20	)	)	PUNCT
ejpam-4707	154	21	does	do	AUX
ejpam-4707	154	22	not	not	PART
ejpam-4707	154	23	allow	allow	VERB
ejpam-4707	154	24	any	any	DET
ejpam-4707	154	25	other	other	ADJ
ejpam-4707	154	26	fixed	fix	VERB
ejpam-4707	154	27	points	point	NOUN
ejpam-4707	154	28	to	to	PART
ejpam-4707	154	29	behave	behave	VERB
ejpam-4707	154	30	stable	stable	ADJ
ejpam-4707	154	31	,	,	PUNCT
ejpam-4707	154	32	globally	globally	ADV
ejpam-4707	154	33	.	.	PUNCT
ejpam-4707	155	1	since	since	SCONJ
ejpam-4707	155	2	f0	f0	PROPN
ejpam-4707	155	3	is	be	AUX
ejpam-4707	155	4	locally	locally	ADV
ejpam-4707	155	5	asymptotically	asymptotically	ADV
ejpam-4707	155	6	stable	stable	ADJ
ejpam-4707	155	7	for	for	ADP
ejpam-4707	155	8	all	all	DET
ejpam-4707	155	9	values	value	NOUN
ejpam-4707	155	10	of	of	ADP
ejpam-4707	155	11	parameters	parameter	NOUN
ejpam-4707	155	12	,	,	PUNCT
ejpam-4707	155	13	at	at	ADP
ejpam-4707	155	14	least	least	ADJ
ejpam-4707	155	15	with	with	ADP
ejpam-4707	155	16	a	a	DET
ejpam-4707	155	17	very	very	ADV
ejpam-4707	155	18	small	small	ADJ
ejpam-4707	155	19	initial	initial	ADJ
ejpam-4707	155	20	value	value	NOUN
ejpam-4707	155	21	,	,	PUNCT
ejpam-4707	155	22	the	the	DET
ejpam-4707	155	23	system	system	NOUN
ejpam-4707	155	24	goes	go	VERB
ejpam-4707	155	25	to	to	ADP
ejpam-4707	155	26	extinction	extinction	NOUN
ejpam-4707	155	27	even	even	ADV
ejpam-4707	155	28	with	with	ADP
ejpam-4707	155	29	a	a	DET
ejpam-4707	155	30	large	large	ADJ
ejpam-4707	155	31	growth	growth	NOUN
ejpam-4707	155	32	parameter	parameter	NOUN
ejpam-4707	155	33	λ	λ	PROPN
ejpam-4707	155	34	.	.	PUNCT
ejpam-4707	156	1	as	as	ADP
ejpam-4707	156	2	a	a	DET
ejpam-4707	156	3	result	result	NOUN
ejpam-4707	156	4	,	,	PUNCT
ejpam-4707	156	5	the	the	DET
ejpam-4707	156	6	other	other	ADJ
ejpam-4707	156	7	points	point	NOUN
ejpam-4707	156	8	can	can	AUX
ejpam-4707	156	9	not	not	PART
ejpam-4707	156	10	be	be	AUX
ejpam-4707	156	11	globally	globally	ADV
ejpam-4707	156	12	attractive	attractive	ADJ
ejpam-4707	156	13	.	.	PUNCT
ejpam-4707	157	1	5	5	X
ejpam-4707	157	2	.	.	X
ejpam-4707	157	3	numerical	numerical	ADJ
ejpam-4707	157	4	simulations	simulation	NOUN
ejpam-4707	157	5	in	in	ADP
ejpam-4707	157	6	this	this	DET
ejpam-4707	157	7	section	section	NOUN
ejpam-4707	157	8	we	we	PRON
ejpam-4707	157	9	verify	verify	VERB
ejpam-4707	157	10	the	the	DET
ejpam-4707	157	11	theoretical	theoretical	ADJ
ejpam-4707	157	12	results	result	NOUN
ejpam-4707	157	13	of	of	ADP
ejpam-4707	157	14	our	our	PRON
ejpam-4707	157	15	model	model	NOUN
ejpam-4707	157	16	by	by	ADP
ejpam-4707	157	17	numerical	numerical	ADJ
ejpam-4707	157	18	simulations	simulation	NOUN
ejpam-4707	157	19	and	and	CCONJ
ejpam-4707	157	20	compare	compare	VERB
ejpam-4707	157	21	it	it	PRON
ejpam-4707	157	22	by	by	ADP
ejpam-4707	157	23	using	use	VERB
ejpam-4707	157	24	the	the	DET
ejpam-4707	157	25	data	datum	NOUN
ejpam-4707	157	26	of	of	ADP
ejpam-4707	157	27	[	[	X
ejpam-4707	157	28	11	11	NUM
ejpam-4707	157	29	]	]	PUNCT
ejpam-4707	157	30	by	by	ADP
ejpam-4707	157	31	using	use	VERB
ejpam-4707	157	32	minitab	minitab	PROPN
ejpam-4707	157	33	.	.	PUNCT
ejpam-4707	158	1	in	in	ADP
ejpam-4707	158	2	order	order	NOUN
ejpam-4707	158	3	to	to	PART
ejpam-4707	158	4	investigate	investigate	VERB
ejpam-4707	158	5	the	the	DET
ejpam-4707	158	6	impact	impact	NOUN
ejpam-4707	158	7	of	of	ADP
ejpam-4707	158	8	λ	λ	PROPN
ejpam-4707	158	9	to	to	ADP
ejpam-4707	158	10	the	the	DET
ejpam-4707	158	11	model	model	NOUN
ejpam-4707	158	12	,	,	PUNCT
ejpam-4707	158	13	we	we	PRON
ejpam-4707	158	14	fix	fix	VERB
ejpam-4707	158	15	c	c	NOUN
ejpam-4707	158	16	=	=	SYM
ejpam-4707	158	17	1	1	NUM
ejpam-4707	158	18	,	,	PUNCT
ejpam-4707	158	19	ψ	ψ	X
ejpam-4707	158	20	=	=	NOUN
ejpam-4707	158	21	0.5	0.5	NUM
ejpam-4707	158	22	,	,	PUNCT
ejpam-4707	158	23	and	and	CCONJ
ejpam-4707	158	24	s	s	AUX
ejpam-4707	158	25	=	=	SYM
ejpam-4707	158	26	0.5	0.5	NUM
ejpam-4707	158	27	and	and	CCONJ
ejpam-4707	158	28	consider	consider	VERB
ejpam-4707	158	29	cases	case	NOUN
ejpam-4707	158	30	,	,	PUNCT
ejpam-4707	158	31	which	which	PRON
ejpam-4707	158	32	satisfy	satisfy	VERB
ejpam-4707	158	33	the	the	DET
ejpam-4707	158	34	conditions	condition	NOUN
ejpam-4707	158	35	s	s	PART
ejpam-4707	158	36	<	<	X
ejpam-4707	158	37	c	c	NOUN
ejpam-4707	158	38	ψ2	ψ2	NOUN
ejpam-4707	158	39	and	and	CCONJ
ejpam-4707	158	40	λ	λ	X
ejpam-4707	158	41	>	>	X
ejpam-4707	158	42	(	(	PUNCT
ejpam-4707	158	43	c+ψ)(1+ψs	c+ψ)(1+ψs	NOUN
ejpam-4707	158	44	)	)	PUNCT
ejpam-4707	158	45	ψ	ψ	NOUN
ejpam-4707	158	46	.	.	PUNCT
ejpam-4707	159	1	assume	assume	VERB
ejpam-4707	159	2	that	that	SCONJ
ejpam-4707	159	3	λ	λ	NOUN
ejpam-4707	159	4	=	=	NOUN
ejpam-4707	159	5	4	4	X
ejpam-4707	159	6	.	.	PUNCT
ejpam-4707	160	1	then	then	ADV
ejpam-4707	160	2	the	the	DET
ejpam-4707	160	3	positive	positive	ADJ
ejpam-4707	160	4	fixed	fix	VERB
ejpam-4707	160	5	point	point	NOUN
ejpam-4707	160	6	is	be	AUX
ejpam-4707	160	7	f3	f3	ADJ
ejpam-4707	160	8	=	=	SYM
ejpam-4707	160	9	(	(	PUNCT
ejpam-4707	160	10	2.16476	2.16476	NUM
ejpam-4707	160	11	,	,	PUNCT
ejpam-4707	160	12	0.160471	0.160471	NUM
ejpam-4707	160	13	)	)	PUNCT
ejpam-4707	160	14	with	with	ADP
ejpam-4707	160	15	corresponding	correspond	VERB
ejpam-4707	160	16	eigenvalues	eigenvalue	NOUN
ejpam-4707	160	17	(	(	PUNCT
ejpam-4707	160	18	0.834265	0.834265	NUM
ejpam-4707	160	19	,	,	PUNCT
ejpam-4707	160	20	0.608611	0.608611	NUM
ejpam-4707	160	21	)	)	PUNCT
ejpam-4707	160	22	.	.	PUNCT
ejpam-4707	161	1	as	as	ADP
ejpam-4707	161	2	a	a	DET
ejpam-4707	161	3	result	result	NOUN
ejpam-4707	161	4	,	,	PUNCT
ejpam-4707	161	5	f3	f3	PROPN
ejpam-4707	161	6	is	be	AUX
ejpam-4707	161	7	a	a	DET
ejpam-4707	161	8	sink	sink	NOUN
ejpam-4707	161	9	.	.	PUNCT
ejpam-4707	162	1	in	in	ADP
ejpam-4707	162	2	figure	figure	NOUN
ejpam-4707	162	3	6	6	NUM
ejpam-4707	162	4	,	,	PUNCT
ejpam-4707	162	5	we	we	PRON
ejpam-4707	162	6	b.	b.	PROPN
ejpam-4707	162	7	kulahcioglu	kulahcioglu	PROPN
ejpam-4707	162	8	,	,	PUNCT
ejpam-4707	162	9	u.	u.	NOUN
ejpam-4707	162	10	ufuktepe	ufuktepe	NOUN
ejpam-4707	162	11	,	,	PUNCT
ejpam-4707	162	12	a.	a.	PROPN
ejpam-4707	162	13	kalampakas	kalampakas	PROPN
ejpam-4707	162	14	/	/	SYM
ejpam-4707	162	15	eur	eur	PROPN
ejpam-4707	162	16	.	.	PUNCT
ejpam-4707	163	1	j.	j.	PROPN
ejpam-4707	163	2	pure	pure	PROPN
ejpam-4707	163	3	appl	appl	PROPN
ejpam-4707	163	4	.	.	PROPN
ejpam-4707	163	5	math	math	PROPN
ejpam-4707	163	6	,	,	PUNCT
ejpam-4707	163	7	16	16	NUM
ejpam-4707	163	8	(	(	PUNCT
ejpam-4707	163	9	2	2	NUM
ejpam-4707	163	10	)	)	PUNCT
ejpam-4707	163	11	(	(	PUNCT
ejpam-4707	163	12	2023	2023	NUM
ejpam-4707	163	13	)	)	PUNCT
ejpam-4707	163	14	,	,	PUNCT
ejpam-4707	163	15	736	736	NUM
ejpam-4707	163	16	-	-	SYM
ejpam-4707	163	17	750	750	NUM
ejpam-4707	163	18	744	744	NUM
ejpam-4707	163	19	0.5	0.5	NUM
ejpam-4707	163	20	1.0	1.0	NUM
ejpam-4707	163	21	1.5	1.5	NUM
ejpam-4707	163	22	2.0	2.0	NUM
ejpam-4707	163	23	x	x	SYM
ejpam-4707	163	24	0.05	0.05	NUM
ejpam-4707	163	25	0.10	0.10	NUM
ejpam-4707	163	26	0.15	0.15	NUM
ejpam-4707	163	27	0.20	0.20	NUM
ejpam-4707	163	28	y	y	PROPN
ejpam-4707	163	29	8x	8x	PROPN
ejpam-4707	163	30	,	,	PUNCT
ejpam-4707	163	31	y	y	PROPN
ejpam-4707	163	32	<	<	X
ejpam-4707	163	33	figure	figure	NOUN
ejpam-4707	163	34	6	6	NUM
ejpam-4707	163	35	:	:	PUNCT
ejpam-4707	163	36	phase	phase	NOUN
ejpam-4707	163	37	portrait	portrait	NOUN
ejpam-4707	163	38	for	for	ADP
ejpam-4707	163	39	the	the	DET
ejpam-4707	163	40	model	model	NOUN
ejpam-4707	163	41	(	(	PUNCT
ejpam-4707	163	42	8)	8)	NUM
ejpam-4707	163	43	for	for	ADP
ejpam-4707	163	44	ψ	ψ	NOUN
ejpam-4707	163	45	=	=	SYM
ejpam-4707	163	46	0.5	0.5	NUM
ejpam-4707	163	47	,	,	PUNCT
ejpam-4707	163	48	c	c	NOUN
ejpam-4707	163	49	=	=	SYM
ejpam-4707	163	50	1	1	NUM
ejpam-4707	163	51	,	,	PUNCT
ejpam-4707	163	52	s	s	PART
ejpam-4707	163	53	=	=	SYM
ejpam-4707	163	54	0.5	0.5	NUM
ejpam-4707	163	55	and	and	CCONJ
ejpam-4707	163	56	λ	λ	X
ejpam-4707	163	57	=	=	NOUN
ejpam-4707	163	58	4	4	NUM
ejpam-4707	163	59	.	.	NOUN
ejpam-4707	163	60	50	50	NUM
ejpam-4707	163	61	100	100	NUM
ejpam-4707	163	62	150	150	NUM
ejpam-4707	163	63	200	200	NUM
ejpam-4707	163	64	2.05	2.05	NUM
ejpam-4707	163	65	2.10	2.10	NUM
ejpam-4707	163	66	2.15	2.15	NUM
ejpam-4707	163	67	2.20	2.20	NUM
ejpam-4707	163	68	2.25	2.25	NUM
ejpam-4707	163	69	figure	figure	NOUN
ejpam-4707	163	70	7	7	NUM
ejpam-4707	163	71	:	:	PUNCT
ejpam-4707	163	72	a	a	X
ejpam-4707	163	73	)	)	PUNCT
ejpam-4707	163	74	time	time	NOUN
ejpam-4707	163	75	series	series	NOUN
ejpam-4707	163	76	of	of	ADP
ejpam-4707	163	77	x	x	PUNCT
ejpam-4707	163	78	for	for	ADP
ejpam-4707	163	79	the	the	DET
ejpam-4707	163	80	model	model	NOUN
ejpam-4707	163	81	(	(	PUNCT
ejpam-4707	163	82	8)	8)	NUM
ejpam-4707	163	83	for	for	ADP
ejpam-4707	163	84	ψ	ψ	NOUN
ejpam-4707	163	85	=	=	SYM
ejpam-4707	163	86	0.5	0.5	NUM
ejpam-4707	163	87	,	,	PUNCT
ejpam-4707	163	88	c	c	NOUN
ejpam-4707	163	89	=	=	SYM
ejpam-4707	163	90	1	1	NUM
ejpam-4707	163	91	,	,	PUNCT
ejpam-4707	163	92	s	s	PART
ejpam-4707	163	93	=	=	SYM
ejpam-4707	163	94	0.5	0.5	NUM
ejpam-4707	163	95	and	and	CCONJ
ejpam-4707	163	96	λ	λ	X
ejpam-4707	163	97	=	=	NOUN
ejpam-4707	163	98	4	4	NUM
ejpam-4707	163	99	.	.	NOUN
ejpam-4707	163	100	b	b	NUM
ejpam-4707	163	101	)	)	PUNCT
ejpam-4707	163	102	time	time	NOUN
ejpam-4707	163	103	series	series	NOUN
ejpam-4707	163	104	of	of	ADP
ejpam-4707	163	105	(	(	PUNCT
ejpam-4707	163	106	x	x	PROPN
ejpam-4707	163	107	,	,	PUNCT
ejpam-4707	163	108	y	y	PROPN
ejpam-4707	163	109	)	)	PUNCT
ejpam-4707	163	110	for	for	ADP
ejpam-4707	163	111	the	the	DET
ejpam-4707	163	112	model	model	NOUN
ejpam-4707	163	113	(	(	PUNCT
ejpam-4707	163	114	8)	8)	NUM
ejpam-4707	163	115	for	for	ADP
ejpam-4707	163	116	λ	λ	NOUN
ejpam-4707	163	117	=	=	SYM
ejpam-4707	163	118	2	2	NUM
ejpam-4707	163	119	,	,	PUNCT
ejpam-4707	163	120	s	s	PART
ejpam-4707	163	121	=	=	SYM
ejpam-4707	163	122	3	3	NUM
ejpam-4707	163	123	,	,	PUNCT
ejpam-4707	163	124	c	c	NOUN
ejpam-4707	163	125	=	=	SYM
ejpam-4707	163	126	1	1	NUM
ejpam-4707	163	127	,	,	PUNCT
ejpam-4707	163	128	ψ	ψ	X
ejpam-4707	163	129	=	=	NOUN
ejpam-4707	163	130	0.5	0.5	NUM
ejpam-4707	163	131	.	.	PUNCT
ejpam-4707	163	132	give	give	VERB
ejpam-4707	163	133	the	the	DET
ejpam-4707	163	134	phase	phase	NOUN
ejpam-4707	163	135	portrait	portrait	NOUN
ejpam-4707	163	136	and	and	CCONJ
ejpam-4707	163	137	we	we	PRON
ejpam-4707	163	138	give	give	VERB
ejpam-4707	163	139	the	the	DET
ejpam-4707	163	140	times	time	NOUN
ejpam-4707	163	141	series	series	PROPN
ejpam-4707	163	142	diagrams	diagram	NOUN
ejpam-4707	163	143	in	in	ADP
ejpam-4707	163	144	figure	figure	NOUN
ejpam-4707	163	145	7	7	NUM
ejpam-4707	163	146	.	.	PUNCT
ejpam-4707	164	1	if	if	SCONJ
ejpam-4707	164	2	we	we	PRON
ejpam-4707	164	3	assign	assign	VERB
ejpam-4707	164	4	a	a	DET
ejpam-4707	164	5	large	large	ADJ
ejpam-4707	164	6	growth	growth	NOUN
ejpam-4707	164	7	rate	rate	NOUN
ejpam-4707	164	8	λ	λ	NOUN
ejpam-4707	164	9	=	=	NOUN
ejpam-4707	164	10	10	10	NUM
ejpam-4707	164	11	,	,	PUNCT
ejpam-4707	164	12	then	then	ADV
ejpam-4707	164	13	the	the	DET
ejpam-4707	164	14	fixed	fixed	ADJ
ejpam-4707	164	15	point	point	NOUN
ejpam-4707	164	16	f3	f3	PROPN
ejpam-4707	164	17	=	=	SYM
ejpam-4707	164	18	(	(	PUNCT
ejpam-4707	164	19	5.31214	5.31214	NUM
ejpam-4707	164	20	,	,	PUNCT
ejpam-4707	164	21	2.41985	2.41985	NUM
ejpam-4707	164	22	)	)	PUNCT
ejpam-4707	164	23	and	and	CCONJ
ejpam-4707	164	24	eigenvalues	eigenvalue	NOUN
ejpam-4707	164	25	are	be	AUX
ejpam-4707	164	26	0.312199±0.669214i	0.312199±0.669214i	NOUN
ejpam-4707	164	27	.	.	PUNCT
ejpam-4707	165	1	f3	f3	PROPN
ejpam-4707	165	2	is	be	AUX
ejpam-4707	165	3	a	a	DET
ejpam-4707	165	4	spiral	spiral	ADJ
ejpam-4707	165	5	sink	sink	NOUN
ejpam-4707	165	6	.	.	PUNCT
ejpam-4707	166	1	we	we	PRON
ejpam-4707	166	2	observe	observe	VERB
ejpam-4707	166	3	that	that	SCONJ
ejpam-4707	166	4	the	the	DET
ejpam-4707	166	5	positive	positive	ADJ
ejpam-4707	166	6	fixed	fix	VERB
ejpam-4707	166	7	point	point	NOUN
ejpam-4707	166	8	remains	remain	VERB
ejpam-4707	166	9	stable	stable	ADJ
ejpam-4707	166	10	for	for	ADP
ejpam-4707	166	11	a	a	DET
ejpam-4707	166	12	large	large	ADJ
ejpam-4707	166	13	interval	interval	NOUN
ejpam-4707	166	14	of	of	ADP
ejpam-4707	166	15	growth	growth	NOUN
ejpam-4707	166	16	parameter	parameter	NOUN
ejpam-4707	166	17	λ	λ	PROPN
ejpam-4707	166	18	.	.	PUNCT
ejpam-4707	167	1	in	in	ADP
ejpam-4707	167	2	figure	figure	NOUN
ejpam-4707	167	3	8	8	NUM
ejpam-4707	167	4	,	,	PUNCT
ejpam-4707	167	5	we	we	PRON
ejpam-4707	167	6	give	give	VERB
ejpam-4707	167	7	the	the	DET
ejpam-4707	167	8	bifurcation	bifurcation	NOUN
ejpam-4707	167	9	diagram	diagram	NOUN
ejpam-4707	167	10	.	.	PUNCT
ejpam-4707	168	1	finally	finally	ADV
ejpam-4707	168	2	,	,	PUNCT
ejpam-4707	168	3	we	we	PRON
ejpam-4707	168	4	give	give	VERB
ejpam-4707	168	5	the	the	DET
ejpam-4707	168	6	basin	basin	NOUN
ejpam-4707	168	7	of	of	ADP
ejpam-4707	168	8	attraction	attraction	NOUN
ejpam-4707	168	9	for	for	ADP
ejpam-4707	168	10	the	the	DET
ejpam-4707	168	11	model	model	NOUN
ejpam-4707	168	12	(	(	PUNCT
ejpam-4707	168	13	8)	8)	NUM
ejpam-4707	168	14	in	in	ADP
ejpam-4707	168	15	figures	figure	NOUN
ejpam-4707	168	16	9	9	NUM
ejpam-4707	168	17	-	-	SYM
ejpam-4707	168	18	11	11	NUM
ejpam-4707	168	19	.	.	PUNCT
ejpam-4707	169	1	in	in	ADP
ejpam-4707	169	2	the	the	DET
ejpam-4707	169	3	analytical	analytical	ADJ
ejpam-4707	169	4	results	result	NOUN
ejpam-4707	169	5	,	,	PUNCT
ejpam-4707	169	6	we	we	PRON
ejpam-4707	169	7	show	show	VERB
ejpam-4707	169	8	that	that	SCONJ
ejpam-4707	169	9	the	the	DET
ejpam-4707	169	10	fixed	fix	VERB
ejpam-4707	169	11	point	point	NOUN
ejpam-4707	169	12	f0	f0	PROPN
ejpam-4707	169	13	=	=	SYM
ejpam-4707	169	14	(	(	PUNCT
ejpam-4707	169	15	0	0	NUM
ejpam-4707	169	16	,	,	PUNCT
ejpam-4707	169	17	0	0	NUM
ejpam-4707	169	18	)	)	PUNCT
ejpam-4707	169	19	is	be	AUX
ejpam-4707	169	20	stable	stable	ADJ
ejpam-4707	169	21	for	for	ADP
ejpam-4707	169	22	all	all	DET
ejpam-4707	169	23	values	value	NOUN
ejpam-4707	169	24	of	of	ADP
ejpam-4707	169	25	parameters	parameter	NOUN
ejpam-4707	169	26	.	.	PUNCT
ejpam-4707	170	1	in	in	ADP
ejpam-4707	170	2	the	the	DET
ejpam-4707	170	3	numerical	numerical	ADJ
ejpam-4707	170	4	simulations	simulation	NOUN
ejpam-4707	170	5	,	,	PUNCT
ejpam-4707	170	6	we	we	PRON
ejpam-4707	170	7	show	show	VERB
ejpam-4707	170	8	that	that	SCONJ
ejpam-4707	170	9	the	the	DET
ejpam-4707	170	10	positive	positive	ADJ
ejpam-4707	170	11	fixed	fix	VERB
ejpam-4707	170	12	point	point	NOUN
ejpam-4707	170	13	f3	f3	PROPN
ejpam-4707	170	14	is	be	AUX
ejpam-4707	170	15	stable	stable	ADJ
ejpam-4707	170	16	for	for	ADP
ejpam-4707	170	17	ψ	ψ	X
ejpam-4707	170	18	=	=	SYM
ejpam-4707	170	19	0.5	0.5	NUM
ejpam-4707	170	20	,	,	PUNCT
ejpam-4707	170	21	c	c	NOUN
ejpam-4707	170	22	=	=	SYM
ejpam-4707	170	23	1	1	NUM
ejpam-4707	170	24	,	,	PUNCT
ejpam-4707	170	25	s	s	PART
ejpam-4707	170	26	=	=	SYM
ejpam-4707	170	27	0.5	0.5	NUM
ejpam-4707	170	28	and	and	CCONJ
ejpam-4707	170	29	λ	λ	X
ejpam-4707	170	30	=	=	NOUN
ejpam-4707	170	31	4	4	X
ejpam-4707	170	32	.	.	X
ejpam-4707	171	1	we	we	PRON
ejpam-4707	171	2	present	present	VERB
ejpam-4707	171	3	the	the	DET
ejpam-4707	171	4	basin	basin	NOUN
ejpam-4707	171	5	of	of	ADP
ejpam-4707	171	6	attraction	attraction	NOUN
ejpam-4707	171	7	to	to	PART
ejpam-4707	171	8	show	show	VERB
ejpam-4707	171	9	the	the	DET
ejpam-4707	171	10	set	set	NOUN
ejpam-4707	171	11	of	of	ADP
ejpam-4707	171	12	points	point	NOUN
ejpam-4707	171	13	which	which	PRON
ejpam-4707	171	14	are	be	AUX
ejpam-4707	171	15	eventually	eventually	ADV
ejpam-4707	171	16	iterated	iterate	VERB
ejpam-4707	171	17	to	to	ADP
ejpam-4707	171	18	either	either	CCONJ
ejpam-4707	171	19	f0	f0	PROPN
ejpam-4707	171	20	or	or	CCONJ
ejpam-4707	171	21	f3	f3	PROPN
ejpam-4707	171	22	under	under	ADP
ejpam-4707	171	23	this	this	DET
ejpam-4707	171	24	set	set	NOUN
ejpam-4707	171	25	of	of	ADP
ejpam-4707	171	26	parameters	parameter	NOUN
ejpam-4707	171	27	.	.	PUNCT
ejpam-4707	172	1	on	on	ADP
ejpam-4707	172	2	the	the	DET
ejpam-4707	172	3	other	other	ADJ
ejpam-4707	172	4	hand	hand	NOUN
ejpam-4707	172	5	,	,	PUNCT
ejpam-4707	172	6	if	if	SCONJ
ejpam-4707	172	7	we	we	PRON
ejpam-4707	172	8	let	let	VERB
ejpam-4707	172	9	s	s	VERB
ejpam-4707	172	10	=	=	NOUN
ejpam-4707	172	11	0	0	NUM
ejpam-4707	172	12	,	,	PUNCT
ejpam-4707	172	13	that	that	PRON
ejpam-4707	172	14	means	mean	VERB
ejpam-4707	172	15	there	there	PRON
ejpam-4707	172	16	is	be	VERB
ejpam-4707	172	17	no	no	DET
ejpam-4707	172	18	allee	allee	ADJ
ejpam-4707	172	19	effect	effect	NOUN
ejpam-4707	172	20	.	.	PUNCT
ejpam-4707	173	1	by	by	ADP
ejpam-4707	173	2	keeping	keep	VERB
ejpam-4707	173	3	the	the	DET
ejpam-4707	173	4	other	other	ADJ
ejpam-4707	173	5	parameters	parameter	NOUN
ejpam-4707	173	6	the	the	DET
ejpam-4707	173	7	same	same	ADJ
ejpam-4707	173	8	,	,	PUNCT
ejpam-4707	173	9	only	only	ADV
ejpam-4707	173	10	the	the	DET
ejpam-4707	173	11	positive	positive	ADJ
ejpam-4707	173	12	fixed	fix	VERB
ejpam-4707	173	13	point	point	NOUN
ejpam-4707	173	14	is	be	AUX
ejpam-4707	173	15	stable	stable	ADJ
ejpam-4707	173	16	.	.	PUNCT
ejpam-4707	174	1	for	for	ADP
ejpam-4707	174	2	the	the	DET
ejpam-4707	174	3	basin	basin	NOUN
ejpam-4707	174	4	of	of	ADP
ejpam-4707	174	5	attraction	attraction	NOUN
ejpam-4707	174	6	code	code	NOUN
ejpam-4707	174	7	,	,	PUNCT
ejpam-4707	174	8	we	we	PRON
ejpam-4707	174	9	refer	refer	VERB
ejpam-4707	174	10	to	to	ADP
ejpam-4707	174	11	[	[	X
ejpam-4707	174	12	18	18	NUM
ejpam-4707	174	13	]	]	PUNCT
ejpam-4707	174	14	.	.	PUNCT
ejpam-4707	175	1	b.	b.	PROPN
ejpam-4707	175	2	kulahcioglu	kulahcioglu	PROPN
ejpam-4707	175	3	,	,	PUNCT
ejpam-4707	175	4	u.	u.	NOUN
ejpam-4707	175	5	ufuktepe	ufuktepe	NOUN
ejpam-4707	175	6	,	,	PUNCT
ejpam-4707	175	7	a.	a.	PROPN
ejpam-4707	175	8	kalampakas	kalampakas	PROPN
ejpam-4707	175	9	/	/	SYM
ejpam-4707	175	10	eur	eur	PROPN
ejpam-4707	175	11	.	.	PUNCT
ejpam-4707	176	1	j.	j.	PROPN
ejpam-4707	176	2	pure	pure	PROPN
ejpam-4707	176	3	appl	appl	PROPN
ejpam-4707	176	4	.	.	PROPN
ejpam-4707	176	5	math	math	PROPN
ejpam-4707	176	6	,	,	PUNCT
ejpam-4707	176	7	16	16	NUM
ejpam-4707	176	8	(	(	PUNCT
ejpam-4707	176	9	2	2	NUM
ejpam-4707	176	10	)	)	PUNCT
ejpam-4707	176	11	(	(	PUNCT
ejpam-4707	176	12	2023	2023	NUM
ejpam-4707	176	13	)	)	PUNCT
ejpam-4707	176	14	,	,	PUNCT
ejpam-4707	176	15	736	736	NUM
ejpam-4707	176	16	-	-	SYM
ejpam-4707	176	17	750	750	NUM
ejpam-4707	176	18	745	745	NUM
ejpam-4707	176	19	figure	figure	NOUN
ejpam-4707	176	20	8	8	NUM
ejpam-4707	176	21	:	:	PUNCT
ejpam-4707	176	22	the	the	DET
ejpam-4707	176	23	bifurcation	bifurcation	NOUN
ejpam-4707	176	24	diagram	diagram	NOUN
ejpam-4707	176	25	of	of	ADP
ejpam-4707	176	26	the	the	DET
ejpam-4707	176	27	model	model	NOUN
ejpam-4707	176	28	(	(	PUNCT
ejpam-4707	176	29	8)	8)	NUM
ejpam-4707	176	30	for	for	ADP
ejpam-4707	176	31	s	s	NOUN
ejpam-4707	176	32	=	=	SYM
ejpam-4707	176	33	0.5	0.5	NUM
ejpam-4707	176	34	.	.	PUNCT
ejpam-4707	176	35	figure	figure	NOUN
ejpam-4707	176	36	9	9	NUM
ejpam-4707	176	37	:	:	PUNCT
ejpam-4707	176	38	initial	initial	ADJ
ejpam-4707	176	39	point	point	NOUN
ejpam-4707	176	40	(	(	PUNCT
ejpam-4707	176	41	2,1	2,1	NUM
ejpam-4707	176	42	)	)	PUNCT
ejpam-4707	176	43	λ	λ	NOUN
ejpam-4707	176	44	=	=	SYM
ejpam-4707	176	45	2	2	NUM
ejpam-4707	176	46	,	,	PUNCT
ejpam-4707	176	47	s	s	PART
ejpam-4707	176	48	=	=	SYM
ejpam-4707	176	49	3	3	NUM
ejpam-4707	176	50	,	,	PUNCT
ejpam-4707	176	51	c	c	NOUN
ejpam-4707	176	52	=	=	SYM
ejpam-4707	176	53	1	1	NUM
ejpam-4707	176	54	,	,	PUNCT
ejpam-4707	176	55	ψ	ψ	X
ejpam-4707	176	56	=	=	NOUN
ejpam-4707	176	57	0.5	0.5	NUM
ejpam-4707	176	58	.	.	NOUN
ejpam-4707	176	59	6	6	NUM
ejpam-4707	176	60	.	.	X
ejpam-4707	177	1	conclusion	conclusion	NOUN
ejpam-4707	177	2	in	in	ADP
ejpam-4707	177	3	this	this	DET
ejpam-4707	177	4	paper	paper	NOUN
ejpam-4707	177	5	,	,	PUNCT
ejpam-4707	177	6	the	the	DET
ejpam-4707	177	7	complex	complex	ADJ
ejpam-4707	177	8	dynamics	dynamic	NOUN
ejpam-4707	177	9	of	of	ADP
ejpam-4707	177	10	a	a	DET
ejpam-4707	177	11	nonlinear	nonlinear	ADJ
ejpam-4707	177	12	discrete	discrete	ADJ
ejpam-4707	177	13	-	-	PUNCT
ejpam-4707	177	14	time	time	NOUN
ejpam-4707	177	15	host	host	NOUN
ejpam-4707	177	16	-	-	PUNCT
ejpam-4707	177	17	parasitoid	parasitoid	NOUN
ejpam-4707	177	18	system	system	NOUN
ejpam-4707	177	19	with	with	ADP
ejpam-4707	177	20	allee	allee	NOUN
ejpam-4707	177	21	and	and	CCONJ
ejpam-4707	177	22	refuge	refuge	NOUN
ejpam-4707	177	23	effects	effect	NOUN
ejpam-4707	177	24	are	be	AUX
ejpam-4707	177	25	analyzed	analyze	VERB
ejpam-4707	177	26	.	.	PUNCT
ejpam-4707	178	1	we	we	PRON
ejpam-4707	178	2	examined	examine	VERB
ejpam-4707	178	3	fixed	fix	VERB
ejpam-4707	178	4	point	point	NOUN
ejpam-4707	178	5	stability	stability	NOUN
ejpam-4707	178	6	and	and	CCONJ
ejpam-4707	178	7	bifurcations	bifurcation	NOUN
ejpam-4707	178	8	and	and	CCONJ
ejpam-4707	178	9	investigated	investigate	VERB
ejpam-4707	178	10	global	global	ADJ
ejpam-4707	178	11	and	and	CCONJ
ejpam-4707	178	12	local	local	ADJ
ejpam-4707	178	13	fixed	fix	VERB
ejpam-4707	178	14	point	point	NOUN
ejpam-4707	178	15	stability	stability	NOUN
ejpam-4707	178	16	.	.	PUNCT
ejpam-4707	179	1	by	by	ADP
ejpam-4707	179	2	the	the	DET
ejpam-4707	179	3	study	study	NOUN
ejpam-4707	179	4	of	of	ADP
ejpam-4707	179	5	numerical	numerical	ADJ
ejpam-4707	179	6	simulations	simulation	NOUN
ejpam-4707	179	7	with	with	ADP
ejpam-4707	179	8	the	the	DET
ejpam-4707	179	9	data	datum	NOUN
ejpam-4707	179	10	of	of	ADP
ejpam-4707	179	11	[	[	X
ejpam-4707	179	12	11	11	NUM
ejpam-4707	179	13	]	]	PUNCT
ejpam-4707	179	14	using	use	VERB
ejpam-4707	179	15	minitab	minitab	PROPN
ejpam-4707	179	16	and	and	CCONJ
ejpam-4707	179	17	our	our	PRON
ejpam-4707	179	18	mathematica	mathematica	PROPN
ejpam-4707	179	19	codes	code	NOUN
ejpam-4707	179	20	we	we	PRON
ejpam-4707	179	21	find	find	VERB
ejpam-4707	179	22	that	that	SCONJ
ejpam-4707	179	23	the	the	DET
ejpam-4707	179	24	behavior	behavior	NOUN
ejpam-4707	179	25	of	of	ADP
ejpam-4707	179	26	the	the	DET
ejpam-4707	179	27	system	system	NOUN
ejpam-4707	179	28	is	be	AUX
ejpam-4707	179	29	simultaneously	simultaneously	ADV
ejpam-4707	179	30	periodic	periodic	ADJ
ejpam-4707	179	31	and	and	CCONJ
ejpam-4707	179	32	chaotic	chaotic	ADJ
ejpam-4707	179	33	.	.	PUNCT
ejpam-4707	180	1	a	a	DET
ejpam-4707	180	2	future	future	ADJ
ejpam-4707	180	3	research	research	NOUN
ejpam-4707	180	4	direction	direction	NOUN
ejpam-4707	180	5	is	be	AUX
ejpam-4707	180	6	to	to	PART
ejpam-4707	180	7	create	create	VERB
ejpam-4707	180	8	a	a	DET
ejpam-4707	180	9	specific	specific	ADJ
ejpam-4707	180	10	model	model	NOUN
ejpam-4707	180	11	for	for	ADP
ejpam-4707	180	12	this	this	DET
ejpam-4707	180	13	type	type	NOUN
ejpam-4707	180	14	of	of	ADP
ejpam-4707	180	15	data	datum	NOUN
ejpam-4707	180	16	with	with	ADP
ejpam-4707	180	17	hybrid	hybrid	ADJ
ejpam-4707	180	18	models	model	NOUN
ejpam-4707	180	19	.	.	PUNCT
ejpam-4707	181	1	b.	b.	PROPN
ejpam-4707	181	2	kulahcioglu	kulahcioglu	PROPN
ejpam-4707	181	3	,	,	PUNCT
ejpam-4707	181	4	u.	u.	NOUN
ejpam-4707	181	5	ufuktepe	ufuktepe	NOUN
ejpam-4707	181	6	,	,	PUNCT
ejpam-4707	181	7	a.	a.	PROPN
ejpam-4707	181	8	kalampakas	kalampakas	PROPN
ejpam-4707	181	9	/	/	SYM
ejpam-4707	181	10	eur	eur	PROPN
ejpam-4707	181	11	.	.	PUNCT
ejpam-4707	182	1	j.	j.	PROPN
ejpam-4707	182	2	pure	pure	PROPN
ejpam-4707	182	3	appl	appl	PROPN
ejpam-4707	182	4	.	.	PROPN
ejpam-4707	182	5	math	math	PROPN
ejpam-4707	182	6	,	,	PUNCT
ejpam-4707	182	7	16	16	NUM
ejpam-4707	182	8	(	(	PUNCT
ejpam-4707	182	9	2	2	NUM
ejpam-4707	182	10	)	)	PUNCT
ejpam-4707	182	11	(	(	PUNCT
ejpam-4707	182	12	2023	2023	NUM
ejpam-4707	182	13	)	)	PUNCT
ejpam-4707	182	14	,	,	PUNCT
ejpam-4707	182	15	736	736	NUM
ejpam-4707	182	16	-	-	SYM
ejpam-4707	182	17	750	750	NUM
ejpam-4707	182	18	746	746	NUM
ejpam-4707	182	19	figure	figure	NOUN
ejpam-4707	182	20	10	10	NUM
ejpam-4707	182	21	:	:	PUNCT
ejpam-4707	182	22	initial	initial	ADJ
ejpam-4707	182	23	point	point	NOUN
ejpam-4707	182	24	(	(	PUNCT
ejpam-4707	182	25	2,1	2,1	NUM
ejpam-4707	182	26	)	)	PUNCT
ejpam-4707	182	27	λ	λ	NOUN
ejpam-4707	182	28	=	=	SYM
ejpam-4707	182	29	7	7	NUM
ejpam-4707	182	30	,	,	PUNCT
ejpam-4707	182	31	s	s	PART
ejpam-4707	182	32	=	=	SYM
ejpam-4707	182	33	2	2	NUM
ejpam-4707	182	34	,	,	PUNCT
ejpam-4707	182	35	c	c	NOUN
ejpam-4707	182	36	=	=	SYM
ejpam-4707	182	37	1	1	NUM
ejpam-4707	182	38	,	,	PUNCT
ejpam-4707	182	39	ψ	ψ	X
ejpam-4707	182	40	=	=	SYM
ejpam-4707	182	41	0.4	0.4	NUM
ejpam-4707	182	42	.	.	PUNCT
ejpam-4707	183	1	figure	figure	NOUN
ejpam-4707	183	2	11	11	NUM
ejpam-4707	183	3	:	:	PUNCT
ejpam-4707	183	4	initial	initial	ADJ
ejpam-4707	183	5	point	point	NOUN
ejpam-4707	183	6	(	(	PUNCT
ejpam-4707	183	7	2,0	2,0	NUM
ejpam-4707	183	8	)	)	PUNCT
ejpam-4707	183	9	λ	λ	NOUN
ejpam-4707	183	10	=	=	SYM
ejpam-4707	183	11	7	7	NUM
ejpam-4707	183	12	,	,	PUNCT
ejpam-4707	183	13	s	s	PART
ejpam-4707	183	14	=	=	SYM
ejpam-4707	183	15	2	2	NUM
ejpam-4707	183	16	,	,	PUNCT
ejpam-4707	183	17	c	c	NOUN
ejpam-4707	183	18	=	=	SYM
ejpam-4707	183	19	1	1	NUM
ejpam-4707	183	20	,	,	PUNCT
ejpam-4707	183	21	ψ	ψ	X
ejpam-4707	183	22	=	=	SYM
ejpam-4707	183	23	0.4	0.4	NUM
ejpam-4707	183	24	b.	b.	PROPN
ejpam-4707	183	25	kulahcioglu	kulahcioglu	PROPN
ejpam-4707	183	26	,	,	PUNCT
ejpam-4707	183	27	u.	u.	NOUN
ejpam-4707	183	28	ufuktepe	ufuktepe	NOUN
ejpam-4707	183	29	,	,	PUNCT
ejpam-4707	183	30	a.	a.	PROPN
ejpam-4707	183	31	kalampakas	kalampakas	PROPN
ejpam-4707	183	32	/	/	SYM
ejpam-4707	183	33	eur	eur	PROPN
ejpam-4707	183	34	.	.	PUNCT
ejpam-4707	184	1	j.	j.	PROPN
ejpam-4707	184	2	pure	pure	PROPN
ejpam-4707	184	3	appl	appl	PROPN
ejpam-4707	184	4	.	.	PROPN
ejpam-4707	184	5	math	math	PROPN
ejpam-4707	184	6	,	,	PUNCT
ejpam-4707	184	7	16	16	NUM
ejpam-4707	184	8	(	(	PUNCT
ejpam-4707	184	9	2	2	NUM
ejpam-4707	184	10	)	)	PUNCT
ejpam-4707	184	11	(	(	PUNCT
ejpam-4707	184	12	2023	2023	NUM
ejpam-4707	184	13	)	)	PUNCT
ejpam-4707	184	14	,	,	PUNCT
ejpam-4707	184	15	736	736	NUM
ejpam-4707	184	16	-	-	SYM
ejpam-4707	184	17	750	750	NUM
ejpam-4707	184	18	747	747	NUM
ejpam-4707	184	19	figure	figure	NOUN
ejpam-4707	184	20	12	12	NUM
ejpam-4707	184	21	:	:	PUNCT
ejpam-4707	184	22	numerical	numerical	ADJ
ejpam-4707	184	23	simulation	simulation	NOUN
ejpam-4707	184	24	of	of	ADP
ejpam-4707	184	25	the	the	DET
ejpam-4707	184	26	stability	stability	NOUN
ejpam-4707	184	27	of	of	ADP
ejpam-4707	184	28	the	the	DET
ejpam-4707	184	29	(	(	PUNCT
ejpam-4707	184	30	0,0	0,0	NOUN
ejpam-4707	184	31	)	)	PUNCT
ejpam-4707	184	32	fixed	fix	VERB
ejpam-4707	184	33	point	point	NOUN
ejpam-4707	184	34	.	.	PUNCT
ejpam-4707	185	1	figure	figure	VERB
ejpam-4707	185	2	13	13	NUM
ejpam-4707	185	3	:	:	PUNCT
ejpam-4707	185	4	interactions	interaction	NOUN
ejpam-4707	185	5	of	of	ADP
ejpam-4707	185	6	ophion	ophion	NOUN
ejpam-4707	185	7	and	and	CCONJ
ejpam-4707	185	8	xest	xest	VERB
ejpam-4707	185	9	with	with	ADP
ejpam-4707	185	10	respect	respect	NOUN
ejpam-4707	185	11	to	to	ADP
ejpam-4707	185	12	years	year	NOUN
ejpam-4707	185	13	.	.	PUNCT
ejpam-4707	186	1	references	reference	NOUN
ejpam-4707	186	2	748	748	NUM
ejpam-4707	186	3	figure	figure	NOUN
ejpam-4707	186	4	14	14	NUM
ejpam-4707	186	5	:	:	PUNCT
ejpam-4707	186	6	time	time	NOUN
ejpam-4707	186	7	series	series	NOUN
ejpam-4707	186	8	of	of	ADP
ejpam-4707	186	9	xest	xest	PROPN
ejpam-4707	186	10	.	.	PUNCT
ejpam-4707	187	1	references	reference	NOUN
ejpam-4707	187	2	[	[	X
ejpam-4707	187	3	1	1	NUM
ejpam-4707	187	4	]	]	PUNCT
ejpam-4707	187	5	joel	joel	PROPN
ejpam-4707	187	6	alba	alba	PROPN
ejpam-4707	187	7	-	-	PUNCT
ejpam-4707	187	8	pérez	pérez	PROPN
ejpam-4707	187	9	and	and	CCONJ
ejpam-4707	187	10	jorge	jorge	NOUN
ejpam-4707	187	11	e	e	PROPN
ejpam-4707	187	12	maćıas	maćıas	PROPN
ejpam-4707	187	13	-	-	PUNCT
ejpam-4707	187	14	dı́az	dı́az	NOUN
ejpam-4707	187	15	.	.	PUNCT
ejpam-4707	188	1	analysis	analysis	NOUN
ejpam-4707	188	2	of	of	ADP
ejpam-4707	188	3	structure	structure	NOUN
ejpam-4707	188	4	-	-	PUNCT
ejpam-4707	188	5	preserving	preserve	VERB
ejpam-4707	188	6	discrete	discrete	ADJ
ejpam-4707	188	7	models	model	NOUN
ejpam-4707	188	8	for	for	ADP
ejpam-4707	188	9	predator	predator	NOUN
ejpam-4707	188	10	-	-	PUNCT
ejpam-4707	188	11	prey	prey	NOUN
ejpam-4707	188	12	systems	system	NOUN
ejpam-4707	188	13	with	with	ADP
ejpam-4707	188	14	anomalous	anomalous	ADJ
ejpam-4707	188	15	diffusion	diffusion	NOUN
ejpam-4707	188	16	.	.	PUNCT
ejpam-4707	189	1	mathematics	mathematic	NOUN
ejpam-4707	189	2	,	,	PUNCT
ejpam-4707	189	3	7(12):1172	7(12):1172	NOUN
ejpam-4707	189	4	,	,	PUNCT
ejpam-4707	189	5	2019	2019	NUM
ejpam-4707	189	6	.	.	PUNCT
ejpam-4707	190	1	[	[	X
ejpam-4707	190	2	2	2	X
ejpam-4707	190	3	]	]	X
ejpam-4707	190	4	john	john	PROPN
ejpam-4707	190	5	r	r	PROPN
ejpam-4707	190	6	beddington	beddington	PROPN
ejpam-4707	190	7	.	.	PUNCT
ejpam-4707	191	1	mutual	mutual	ADJ
ejpam-4707	191	2	interference	interference	NOUN
ejpam-4707	191	3	between	between	ADP
ejpam-4707	191	4	parasites	parasite	NOUN
ejpam-4707	191	5	or	or	CCONJ
ejpam-4707	191	6	predators	predator	NOUN
ejpam-4707	191	7	and	and	CCONJ
ejpam-4707	191	8	its	its	PRON
ejpam-4707	191	9	effect	effect	NOUN
ejpam-4707	191	10	on	on	ADP
ejpam-4707	191	11	searching	search	VERB
ejpam-4707	191	12	efficiency	efficiency	NOUN
ejpam-4707	191	13	.	.	PUNCT
ejpam-4707	192	1	the	the	DET
ejpam-4707	192	2	journal	journal	NOUN
ejpam-4707	192	3	of	of	ADP
ejpam-4707	192	4	animal	animal	NOUN
ejpam-4707	192	5	ecology	ecology	NOUN
ejpam-4707	192	6	,	,	PUNCT
ejpam-4707	192	7	pages	page	NOUN
ejpam-4707	192	8	331–340	331–340	NUM
ejpam-4707	192	9	,	,	PUNCT
ejpam-4707	192	10	1975	1975	NUM
ejpam-4707	192	11	.	.	PUNCT
ejpam-4707	193	1	[	[	X
ejpam-4707	193	2	3	3	NUM
ejpam-4707	193	3	]	]	X
ejpam-4707	193	4	saber	saber	NOUN
ejpam-4707	193	5	n	n	PRON
ejpam-4707	193	6	elaydi	elaydi	VERB
ejpam-4707	193	7	.	.	PUNCT
ejpam-4707	194	1	discrete	discrete	ADJ
ejpam-4707	194	2	chaos	chaos	NOUN
ejpam-4707	194	3	:	:	PUNCT
ejpam-4707	194	4	with	with	ADP
ejpam-4707	194	5	applications	application	NOUN
ejpam-4707	194	6	in	in	ADP
ejpam-4707	194	7	science	science	NOUN
ejpam-4707	194	8	and	and	CCONJ
ejpam-4707	194	9	engineering	engineering	NOUN
ejpam-4707	194	10	.	.	PUNCT
ejpam-4707	195	1	chapman	chapman	NOUN
ejpam-4707	195	2	and	and	CCONJ
ejpam-4707	195	3	hall	hall	PROPN
ejpam-4707	195	4	/	/	SYM
ejpam-4707	195	5	crc	crc	PROPN
ejpam-4707	195	6	,	,	PUNCT
ejpam-4707	195	7	2007	2007	NUM
ejpam-4707	195	8	.	.	PUNCT
ejpam-4707	196	1	[	[	X
ejpam-4707	196	2	4	4	X
ejpam-4707	196	3	]	]	PUNCT
ejpam-4707	196	4	edward	edward	PROPN
ejpam-4707	196	5	w	w	PROPN
ejpam-4707	196	6	evans	evans	PROPN
ejpam-4707	196	7	.	.	PUNCT
ejpam-4707	196	8	dispersal	dispersal	NOUN
ejpam-4707	196	9	in	in	ADP
ejpam-4707	196	10	host	host	NOUN
ejpam-4707	196	11	–	–	PUNCT
ejpam-4707	196	12	parasitoid	parasitoid	NOUN
ejpam-4707	196	13	interactions	interaction	NOUN
ejpam-4707	196	14	:	:	PUNCT
ejpam-4707	196	15	crop	crop	NOUN
ejpam-4707	196	16	colonization	colonization	NOUN
ejpam-4707	196	17	by	by	ADP
ejpam-4707	196	18	pests	pest	NOUN
ejpam-4707	196	19	and	and	CCONJ
ejpam-4707	196	20	specialist	specialist	ADJ
ejpam-4707	196	21	enemies	enemy	NOUN
ejpam-4707	196	22	.	.	PUNCT
ejpam-4707	197	1	insects	insect	NOUN
ejpam-4707	197	2	,	,	PUNCT
ejpam-4707	197	3	9(4):134	9(4):134	NUM
ejpam-4707	197	4	,	,	PUNCT
ejpam-4707	197	5	2018	2018	NUM
ejpam-4707	197	6	.	.	PUNCT
ejpam-4707	198	1	[	[	X
ejpam-4707	198	2	5	5	X
ejpam-4707	198	3	]	]	X
ejpam-4707	198	4	james	james	PROPN
ejpam-4707	198	5	r	r	PROPN
ejpam-4707	198	6	hepler	hepler	PROPN
ejpam-4707	198	7	,	,	PUNCT
ejpam-4707	198	8	kacie	kacie	PROPN
ejpam-4707	198	9	athey	athey	PROPN
ejpam-4707	198	10	,	,	PUNCT
ejpam-4707	198	11	david	david	PROPN
ejpam-4707	198	12	enicks	enicks	PROPN
ejpam-4707	198	13	,	,	PUNCT
ejpam-4707	198	14	paul	paul	PROPN
ejpam-4707	198	15	k	k	PROPN
ejpam-4707	198	16	abram	abram	PROPN
ejpam-4707	198	17	,	,	PUNCT
ejpam-4707	198	18	tara	tara	PROPN
ejpam-4707	198	19	d	d	PROPN
ejpam-4707	198	20	gariepy	gariepy	PROPN
ejpam-4707	198	21	,	,	PUNCT
ejpam-4707	198	22	elijah	elijah	PROPN
ejpam-4707	198	23	j	j	PROPN
ejpam-4707	198	24	talamas	talamas	PROPN
ejpam-4707	198	25	,	,	PUNCT
ejpam-4707	198	26	and	and	CCONJ
ejpam-4707	198	27	elizabeth	elizabeth	PROPN
ejpam-4707	198	28	beers	beers	PROPN
ejpam-4707	198	29	.	.	PUNCT
ejpam-4707	199	1	hidden	hide	VERB
ejpam-4707	199	2	host	host	NOUN
ejpam-4707	199	3	mortality	mortality	NOUN
ejpam-4707	199	4	from	from	ADP
ejpam-4707	199	5	an	an	DET
ejpam-4707	199	6	introduced	introduce	VERB
ejpam-4707	199	7	parasitoid	parasitoid	NOUN
ejpam-4707	199	8	:	:	PUNCT
ejpam-4707	199	9	conventional	conventional	ADJ
ejpam-4707	199	10	and	and	CCONJ
ejpam-4707	199	11	molecular	molecular	ADJ
ejpam-4707	199	12	evaluation	evaluation	NOUN
ejpam-4707	199	13	of	of	ADP
ejpam-4707	199	14	non	non	ADJ
ejpam-4707	199	15	-	-	ADJ
ejpam-4707	199	16	target	target	ADJ
ejpam-4707	199	17	risk	risk	NOUN
ejpam-4707	199	18	.	.	PUNCT
ejpam-4707	200	1	insects	insect	NOUN
ejpam-4707	200	2	,	,	PUNCT
ejpam-4707	200	3	11(11):822	11(11):822	NUM
ejpam-4707	200	4	,	,	PUNCT
ejpam-4707	200	5	2020	2020	NUM
ejpam-4707	200	6	.	.	PUNCT
ejpam-4707	201	1	[	[	X
ejpam-4707	201	2	6	6	NUM
ejpam-4707	201	3	]	]	X
ejpam-4707	201	4	sophia	sophia	PROPN
ejpam-4707	201	5	r	r	PROPN
ejpam-4707	201	6	-	-	PUNCT
ejpam-4707	201	7	j	j	PROPN
ejpam-4707	201	8	jang	jang	PROPN
ejpam-4707	201	9	and	and	CCONJ
ejpam-4707	201	10	jui	jui	PROPN
ejpam-4707	201	11	-	-	PUNCT
ejpam-4707	201	12	ling	ling	PROPN
ejpam-4707	201	13	yu	yu	PROPN
ejpam-4707	201	14	.	.	PUNCT
ejpam-4707	202	1	a	a	DET
ejpam-4707	202	2	discrete	discrete	ADJ
ejpam-4707	202	3	-	-	PUNCT
ejpam-4707	202	4	time	time	NOUN
ejpam-4707	202	5	host	host	NOUN
ejpam-4707	202	6	-	-	PUNCT
ejpam-4707	202	7	parasitoid	parasitoid	NOUN
ejpam-4707	202	8	model	model	NOUN
ejpam-4707	202	9	.	.	PUNCT
ejpam-4707	203	1	in	in	ADP
ejpam-4707	203	2	proceedings	proceeding	NOUN
ejpam-4707	203	3	of	of	ADP
ejpam-4707	203	4	the	the	DET
ejpam-4707	203	5	conference	conference	NOUN
ejpam-4707	203	6	on	on	ADP
ejpam-4707	203	7	differential	differential	ADJ
ejpam-4707	203	8	and	and	CCONJ
ejpam-4707	203	9	difference	difference	NOUN
ejpam-4707	203	10	equations	equation	NOUN
ejpam-4707	203	11	and	and	CCONJ
ejpam-4707	203	12	applications	application	NOUN
ejpam-4707	203	13	.	.	PUNCT
ejpam-4707	204	1	hindawi	hindawi	ADJ
ejpam-4707	204	2	publishing	publishing	PROPN
ejpam-4707	204	3	corporation	corporation	NOUN
ejpam-4707	204	4	,	,	PUNCT
ejpam-4707	204	5	pages	page	NOUN
ejpam-4707	204	6	451–455	451–455	NUM
ejpam-4707	204	7	,	,	PUNCT
ejpam-4707	204	8	2006	2006	NUM
ejpam-4707	204	9	.	.	PUNCT
ejpam-4707	205	1	[	[	X
ejpam-4707	205	2	7	7	X
ejpam-4707	205	3	]	]	PUNCT
ejpam-4707	205	4	abdul	abdul	PROPN
ejpam-4707	205	5	qadeer	qadeer	PROPN
ejpam-4707	205	6	khan	khan	PROPN
ejpam-4707	205	7	and	and	CCONJ
ejpam-4707	205	8	muhammad	muhammad	PROPN
ejpam-4707	205	9	naeem	naeem	PROPN
ejpam-4707	205	10	qureshi	qureshi	PROPN
ejpam-4707	205	11	.	.	PUNCT
ejpam-4707	206	1	dynamics	dynamic	NOUN
ejpam-4707	206	2	of	of	ADP
ejpam-4707	206	3	a	a	DET
ejpam-4707	206	4	modified	modify	VERB
ejpam-4707	206	5	nicholson	nicholson	PROPN
ejpam-4707	206	6	-	-	PUNCT
ejpam-4707	206	7	bailey	bailey	PROPN
ejpam-4707	206	8	host	host	NOUN
ejpam-4707	206	9	-	-	PUNCT
ejpam-4707	206	10	parasitoid	parasitoid	NOUN
ejpam-4707	206	11	model	model	NOUN
ejpam-4707	206	12	.	.	PUNCT
ejpam-4707	207	1	advances	advance	NOUN
ejpam-4707	207	2	in	in	ADP
ejpam-4707	207	3	difference	difference	NOUN
ejpam-4707	207	4	equations	equation	NOUN
ejpam-4707	207	5	,	,	PUNCT
ejpam-4707	207	6	2015(1):1	2015(1):1	X
ejpam-4707	207	7	–	–	PUNCT
ejpam-4707	207	8	15	15	NUM
ejpam-4707	207	9	,	,	PUNCT
ejpam-4707	207	10	2015	2015	NUM
ejpam-4707	207	11	.	.	PUNCT
ejpam-4707	208	1	[	[	X
ejpam-4707	208	2	8	8	NUM
ejpam-4707	208	3	]	]	PUNCT
ejpam-4707	208	4	burcin	burcin	PROPN
ejpam-4707	208	5	kulahcioglu	kulahcioglu	NOUN
ejpam-4707	208	6	and	and	CCONJ
ejpam-4707	208	7	unal	unal	ADJ
ejpam-4707	208	8	ufuktepe	ufuktepe	NOUN
ejpam-4707	208	9	.	.	PUNCT
ejpam-4707	209	1	a	a	DET
ejpam-4707	209	2	density	density	NOUN
ejpam-4707	209	3	dependent	dependent	ADJ
ejpam-4707	209	4	host	host	NOUN
ejpam-4707	209	5	-	-	PUNCT
ejpam-4707	209	6	parasitoid	parasitoid	NOUN
ejpam-4707	209	7	model	model	NOUN
ejpam-4707	209	8	with	with	ADP
ejpam-4707	209	9	allee	allee	NOUN
ejpam-4707	209	10	and	and	CCONJ
ejpam-4707	209	11	refuge	refuge	NOUN
ejpam-4707	209	12	effects	effect	NOUN
ejpam-4707	209	13	.	.	PUNCT
ejpam-4707	210	1	in	in	ADP
ejpam-4707	210	2	computational	computational	ADJ
ejpam-4707	210	3	science	science	NOUN
ejpam-4707	210	4	and	and	CCONJ
ejpam-4707	210	5	its	its	PRON
ejpam-4707	210	6	applications	application	NOUN
ejpam-4707	210	7	–	–	PUNCT
ejpam-4707	210	8	iccsa	iccsa	ADJ
ejpam-4707	210	9	references	reference	NOUN
ejpam-4707	210	10	749	749	NUM
ejpam-4707	210	11	2016	2016	NUM
ejpam-4707	210	12	:	:	PUNCT
ejpam-4707	210	13	16th	16th	ADJ
ejpam-4707	210	14	international	international	ADJ
ejpam-4707	210	15	conference	conference	NOUN
ejpam-4707	210	16	,	,	PUNCT
ejpam-4707	210	17	beijing	beijing	PROPN
ejpam-4707	210	18	,	,	PUNCT
ejpam-4707	210	19	china	china	PROPN
ejpam-4707	210	20	,	,	PUNCT
ejpam-4707	210	21	july	july	PROPN
ejpam-4707	210	22	4	4	NUM
ejpam-4707	210	23	-	-	SYM
ejpam-4707	210	24	7	7	NUM
ejpam-4707	210	25	,	,	PUNCT
ejpam-4707	210	26	2016	2016	NUM
ejpam-4707	210	27	,	,	PUNCT
ejpam-4707	210	28	proceedings	proceeding	NOUN
ejpam-4707	210	29	,	,	PUNCT
ejpam-4707	210	30	part	part	NOUN
ejpam-4707	210	31	iii	iii	NUM
ejpam-4707	210	32	16	16	NUM
ejpam-4707	210	33	,	,	PUNCT
ejpam-4707	210	34	pages	page	NOUN
ejpam-4707	210	35	228–239	228–239	NUM
ejpam-4707	210	36	.	.	PUNCT
ejpam-4707	210	37	springer	springer	NOUN
ejpam-4707	210	38	,	,	PUNCT
ejpam-4707	210	39	2016	2016	NUM
ejpam-4707	210	40	.	.	PUNCT
ejpam-4707	211	1	[	[	X
ejpam-4707	211	2	9	9	NUM
ejpam-4707	211	3	]	]	SYM
ejpam-4707	211	4	xiaorong	xiaorong	PROPN
ejpam-4707	211	5	ma	ma	PROPN
ejpam-4707	211	6	,	,	PUNCT
ejpam-4707	211	7	qamar	qamar	PROPN
ejpam-4707	211	8	din	din	PROPN
ejpam-4707	211	9	,	,	PUNCT
ejpam-4707	211	10	muhammad	muhammad	PROPN
ejpam-4707	211	11	rafaqat	rafaqat	PROPN
ejpam-4707	211	12	,	,	PUNCT
ejpam-4707	211	13	nasir	nasir	PROPN
ejpam-4707	211	14	javaid	javaid	PROPN
ejpam-4707	211	15	,	,	PUNCT
ejpam-4707	211	16	and	and	CCONJ
ejpam-4707	211	17	yongliang	yongliang	PROPN
ejpam-4707	211	18	feng	feng	PROPN
ejpam-4707	211	19	.	.	PUNCT
ejpam-4707	212	1	a	a	DET
ejpam-4707	212	2	density	density	NOUN
ejpam-4707	212	3	-	-	PUNCT
ejpam-4707	212	4	dependent	dependent	ADJ
ejpam-4707	212	5	host	host	NOUN
ejpam-4707	212	6	-	-	PUNCT
ejpam-4707	212	7	parasitoid	parasitoid	NOUN
ejpam-4707	212	8	model	model	NOUN
ejpam-4707	212	9	with	with	ADP
ejpam-4707	212	10	stability	stability	NOUN
ejpam-4707	212	11	,	,	PUNCT
ejpam-4707	212	12	bifurcation	bifurcation	NOUN
ejpam-4707	212	13	and	and	CCONJ
ejpam-4707	212	14	chaos	chaos	NOUN
ejpam-4707	212	15	control	control	NOUN
ejpam-4707	212	16	.	.	PUNCT
ejpam-4707	213	1	mathematics	mathematic	NOUN
ejpam-4707	213	2	,	,	PUNCT
ejpam-4707	213	3	8(4):536	8(4):536	NUM
ejpam-4707	213	4	,	,	PUNCT
ejpam-4707	213	5	2020	2020	NUM
ejpam-4707	213	6	.	.	PUNCT
ejpam-4707	214	1	[	[	X
ejpam-4707	214	2	10	10	NUM
ejpam-4707	214	3	]	]	X
ejpam-4707	214	4	rm	rm	NOUN
ejpam-4707	214	5	may	may	AUX
ejpam-4707	214	6	,	,	PUNCT
ejpam-4707	214	7	mp	mp	PROPN
ejpam-4707	214	8	hassell	hassell	PROPN
ejpam-4707	214	9	,	,	PUNCT
ejpam-4707	214	10	rm	rm	PROPN
ejpam-4707	214	11	anderson	anderson	PROPN
ejpam-4707	214	12	,	,	PUNCT
ejpam-4707	214	13	and	and	CCONJ
ejpam-4707	214	14	dw	dw	PROPN
ejpam-4707	214	15	tonkyn	tonkyn	PROPN
ejpam-4707	214	16	.	.	PUNCT
ejpam-4707	215	1	density	density	NOUN
ejpam-4707	215	2	dependence	dependence	NOUN
ejpam-4707	215	3	in	in	ADP
ejpam-4707	215	4	hostparasitoid	hostparasitoid	NOUN
ejpam-4707	215	5	models	model	NOUN
ejpam-4707	215	6	.	.	PUNCT
ejpam-4707	216	1	the	the	DET
ejpam-4707	216	2	journal	journal	NOUN
ejpam-4707	216	3	of	of	ADP
ejpam-4707	216	4	animal	animal	NOUN
ejpam-4707	216	5	ecology	ecology	NOUN
ejpam-4707	216	6	,	,	PUNCT
ejpam-4707	216	7	pages	page	NOUN
ejpam-4707	216	8	855–865	855–865	NUM
ejpam-4707	216	9	,	,	PUNCT
ejpam-4707	216	10	1981	1981	NUM
ejpam-4707	216	11	.	.	PUNCT
ejpam-4707	217	1	[	[	X
ejpam-4707	217	2	11	11	NUM
ejpam-4707	217	3	]	]	SYM
ejpam-4707	217	4	marko	marko	PROPN
ejpam-4707	217	5	mutanen	mutanen	PROPN
ejpam-4707	217	6	,	,	PUNCT
ejpam-4707	217	7	otso	otso	PROPN
ejpam-4707	217	8	ovaskainen	ovaskainen	PROPN
ejpam-4707	217	9	,	,	PUNCT
ejpam-4707	217	10	gergely	gergely	ADV
ejpam-4707	217	11	várkonyi	várkonyi	PROPN
ejpam-4707	217	12	,	,	PUNCT
ejpam-4707	217	13	juhani	juhani	ADJ
ejpam-4707	217	14	itämies	itämie	NOUN
ejpam-4707	217	15	,	,	PUNCT
ejpam-4707	217	16	sean	sean	PROPN
ejpam-4707	217	17	wj	wj	PROPN
ejpam-4707	217	18	prosser	prosser	PROPN
ejpam-4707	217	19	,	,	PUNCT
ejpam-4707	217	20	paul	paul	PROPN
ejpam-4707	217	21	dn	dn	PROPN
ejpam-4707	217	22	hebert	hebert	PROPN
ejpam-4707	217	23	,	,	PUNCT
ejpam-4707	217	24	and	and	CCONJ
ejpam-4707	217	25	ilkka	ilkka	VERB
ejpam-4707	217	26	hanski	hanski	ADJ
ejpam-4707	217	27	.	.	PUNCT
ejpam-4707	218	1	dynamics	dynamic	NOUN
ejpam-4707	218	2	of	of	ADP
ejpam-4707	218	3	a	a	DET
ejpam-4707	218	4	host	host	NOUN
ejpam-4707	218	5	–	–	PUNCT
ejpam-4707	218	6	parasitoid	parasitoid	NOUN
ejpam-4707	218	7	interaction	interaction	NOUN
ejpam-4707	218	8	clarified	clarify	VERB
ejpam-4707	218	9	by	by	ADP
ejpam-4707	218	10	modelling	modelling	NOUN
ejpam-4707	218	11	and	and	CCONJ
ejpam-4707	218	12	dna	dna	NOUN
ejpam-4707	218	13	sequencing	sequencing	NOUN
ejpam-4707	218	14	.	.	PUNCT
ejpam-4707	219	1	ecology	ecology	NOUN
ejpam-4707	219	2	letters	letter	NOUN
ejpam-4707	219	3	,	,	PUNCT
ejpam-4707	219	4	23(5):851–859	23(5):851–859	NUM
ejpam-4707	219	5	,	,	PUNCT
ejpam-4707	219	6	2020	2020	NUM
ejpam-4707	219	7	.	.	PUNCT
ejpam-4707	220	1	[	[	X
ejpam-4707	220	2	12	12	NUM
ejpam-4707	220	3	]	]	X
ejpam-4707	220	4	alexander	alexander	PROPN
ejpam-4707	220	5	j	j	PROPN
ejpam-4707	220	6	nicholson	nicholson	PROPN
ejpam-4707	220	7	and	and	CCONJ
ejpam-4707	220	8	victor	victor	PROPN
ejpam-4707	220	9	a	a	DET
ejpam-4707	220	10	bailey	bailey	NOUN
ejpam-4707	220	11	.	.	PUNCT
ejpam-4707	221	1	the	the	DET
ejpam-4707	221	2	balance	balance	NOUN
ejpam-4707	221	3	of	of	ADP
ejpam-4707	221	4	animal	animal	NOUN
ejpam-4707	221	5	populations.—part	populations.—part	PROPN
ejpam-4707	221	6	i.	i.	NOUN
ejpam-4707	221	7	in	in	ADP
ejpam-4707	221	8	proceedings	proceeding	NOUN
ejpam-4707	221	9	of	of	ADP
ejpam-4707	221	10	the	the	DET
ejpam-4707	221	11	zoological	zoological	ADJ
ejpam-4707	221	12	society	society	NOUN
ejpam-4707	221	13	of	of	ADP
ejpam-4707	221	14	london	london	PROPN
ejpam-4707	221	15	,	,	PUNCT
ejpam-4707	221	16	volume	volume	NOUN
ejpam-4707	221	17	105	105	NUM
ejpam-4707	221	18	,	,	PUNCT
ejpam-4707	221	19	pages	page	NOUN
ejpam-4707	221	20	551–598	551–598	NUM
ejpam-4707	221	21	.	.	PUNCT
ejpam-4707	222	1	wiley	wiley	PROPN
ejpam-4707	222	2	online	online	PROPN
ejpam-4707	222	3	library	library	PROPN
ejpam-4707	222	4	,	,	PUNCT
ejpam-4707	222	5	1935	1935	NUM
ejpam-4707	222	6	.	.	PUNCT
ejpam-4707	223	1	[	[	X
ejpam-4707	223	2	13	13	NUM
ejpam-4707	223	3	]	]	PUNCT
ejpam-4707	223	4	ainara	ainara	ADJ
ejpam-4707	223	5	peñalver	peñalver	NOUN
ejpam-4707	223	6	-	-	PUNCT
ejpam-4707	223	7	cruz	cruz	PROPN
ejpam-4707	223	8	,	,	PUNCT
ejpam-4707	223	9	bruno	bruno	PROPN
ejpam-4707	223	10	jaloux	jaloux	PROPN
ejpam-4707	223	11	,	,	PUNCT
ejpam-4707	223	12	and	and	CCONJ
ejpam-4707	223	13	blas	blas	PROPN
ejpam-4707	223	14	lavandero	lavandero	PROPN
ejpam-4707	223	15	.	.	PUNCT
ejpam-4707	224	1	the	the	DET
ejpam-4707	224	2	host	host	NOUN
ejpam-4707	224	3	-	-	PUNCT
ejpam-4707	224	4	plant	plant	NOUN
ejpam-4707	224	5	origin	origin	NOUN
ejpam-4707	224	6	affects	affect	VERB
ejpam-4707	224	7	the	the	DET
ejpam-4707	224	8	morphological	morphological	ADJ
ejpam-4707	224	9	traits	trait	NOUN
ejpam-4707	224	10	and	and	CCONJ
ejpam-4707	224	11	the	the	DET
ejpam-4707	224	12	reproductive	reproductive	ADJ
ejpam-4707	224	13	behavior	behavior	NOUN
ejpam-4707	224	14	of	of	ADP
ejpam-4707	224	15	the	the	DET
ejpam-4707	224	16	aphid	aphid	NOUN
ejpam-4707	224	17	parasitoid	parasitoid	PROPN
ejpam-4707	224	18	aphelinus	aphelinus	PRON
ejpam-4707	224	19	mali	mali	PROPN
ejpam-4707	224	20	.	.	PUNCT
ejpam-4707	225	1	agronomy	agronomy	NOUN
ejpam-4707	225	2	,	,	PUNCT
ejpam-4707	225	3	12(1):101	12(1):101	NUM
ejpam-4707	225	4	,	,	PUNCT
ejpam-4707	225	5	2022	2022	NUM
ejpam-4707	225	6	.	.	PUNCT
ejpam-4707	226	1	[	[	X
ejpam-4707	226	2	14	14	NUM
ejpam-4707	226	3	]	]	X
ejpam-4707	226	4	serge	serge	PROPN
ejpam-4707	226	5	quilici	quilici	NOUN
ejpam-4707	226	6	and	and	CCONJ
ejpam-4707	226	7	pascal	pascal	PROPN
ejpam-4707	226	8	rousse	rousse	PROPN
ejpam-4707	226	9	.	.	PUNCT
ejpam-4707	227	1	location	location	NOUN
ejpam-4707	227	2	of	of	ADP
ejpam-4707	227	3	host	host	NOUN
ejpam-4707	227	4	and	and	CCONJ
ejpam-4707	227	5	host	host	NOUN
ejpam-4707	227	6	habitat	habitat	NOUN
ejpam-4707	227	7	by	by	ADP
ejpam-4707	227	8	fruit	fruit	NOUN
ejpam-4707	227	9	fly	fly	NOUN
ejpam-4707	227	10	parasitoids	parasitoid	NOUN
ejpam-4707	227	11	.	.	PUNCT
ejpam-4707	228	1	insects	insect	NOUN
ejpam-4707	228	2	,	,	PUNCT
ejpam-4707	228	3	3(4):1220–1235	3(4):1220–1235	NUM
ejpam-4707	228	4	,	,	PUNCT
ejpam-4707	228	5	2012	2012	NUM
ejpam-4707	228	6	.	.	PUNCT
ejpam-4707	229	1	[	[	X
ejpam-4707	229	2	15	15	NUM
ejpam-4707	229	3	]	]	X
ejpam-4707	229	4	m	m	VERB
ejpam-4707	229	5	rost	rost	PROPN
ejpam-4707	229	6	,	,	PUNCT
ejpam-4707	229	7	g	g	PROPN
ejpam-4707	229	8	várkonyi	várkonyi	PROPN
ejpam-4707	229	9	,	,	PUNCT
ejpam-4707	229	10	and	and	CCONJ
ejpam-4707	229	11	i	i	PRON
ejpam-4707	229	12	hanski	hanski	VERB
ejpam-4707	229	13	.	.	PUNCT
ejpam-4707	230	1	patterns	pattern	NOUN
ejpam-4707	230	2	of	of	ADP
ejpam-4707	230	3	2	2	NUM
ejpam-4707	230	4	-	-	PUNCT
ejpam-4707	230	5	year	year	NOUN
ejpam-4707	230	6	population	population	NOUN
ejpam-4707	230	7	cycles	cycle	NOUN
ejpam-4707	230	8	in	in	ADP
ejpam-4707	230	9	spatially	spatially	ADV
ejpam-4707	230	10	extended	extend	VERB
ejpam-4707	230	11	host	host	NOUN
ejpam-4707	230	12	–	–	PUNCT
ejpam-4707	230	13	parasitoid	parasitoid	NOUN
ejpam-4707	230	14	systems	system	NOUN
ejpam-4707	230	15	.	.	PUNCT
ejpam-4707	231	1	theoretical	theoretical	ADJ
ejpam-4707	231	2	population	population	NOUN
ejpam-4707	231	3	biology	biology	NOUN
ejpam-4707	231	4	,	,	PUNCT
ejpam-4707	231	5	59(3):223–233	59(3):223–233	NUM
ejpam-4707	231	6	,	,	PUNCT
ejpam-4707	231	7	2001	2001	NUM
ejpam-4707	231	8	.	.	PUNCT
ejpam-4707	232	1	[	[	X
ejpam-4707	232	2	16	16	NUM
ejpam-4707	232	3	]	]	PUNCT
ejpam-4707	232	4	bellie	bellie	PROPN
ejpam-4707	232	5	sivakumar	sivakumar	PROPN
ejpam-4707	232	6	and	and	CCONJ
ejpam-4707	232	7	bhadran	bhadran	PROPN
ejpam-4707	232	8	deepthi	deepthi	PROPN
ejpam-4707	232	9	.	.	PUNCT
ejpam-4707	233	1	complexity	complexity	NOUN
ejpam-4707	233	2	of	of	ADP
ejpam-4707	233	3	covid-19	covid-19	PROPN
ejpam-4707	233	4	dynamics	dynamic	NOUN
ejpam-4707	233	5	.	.	PUNCT
ejpam-4707	234	1	entropy	entropy	PROPN
ejpam-4707	234	2	,	,	PUNCT
ejpam-4707	234	3	24(1):50	24(1):50	NUM
ejpam-4707	234	4	,	,	PUNCT
ejpam-4707	234	5	2022	2022	NUM
ejpam-4707	234	6	.	.	PUNCT
ejpam-4707	235	1	[	[	X
ejpam-4707	235	2	17	17	NUM
ejpam-4707	235	3	]	]	X
ejpam-4707	235	4	agus	agus	PROPN
ejpam-4707	235	5	suryanto	suryanto	NOUN
ejpam-4707	235	6	,	,	PUNCT
ejpam-4707	235	7	isnani	isnani	VERB
ejpam-4707	235	8	darti	darti	PROPN
ejpam-4707	235	9	,	,	PUNCT
ejpam-4707	235	10	hasan	hasan	PROPN
ejpam-4707	235	11	s.	s.	PROPN
ejpam-4707	235	12	panigoro	panigoro	ADV
ejpam-4707	235	13	,	,	PUNCT
ejpam-4707	235	14	and	and	CCONJ
ejpam-4707	235	15	adem	adem	PROPN
ejpam-4707	235	16	kilicman	kilicman	PROPN
ejpam-4707	235	17	.	.	PUNCT
ejpam-4707	236	1	a	a	DET
ejpam-4707	236	2	fractionalorder	fractionalorder	ADJ
ejpam-4707	236	3	predator	predator	NOUN
ejpam-4707	236	4	–	–	PUNCT
ejpam-4707	236	5	prey	prey	NOUN
ejpam-4707	236	6	model	model	NOUN
ejpam-4707	236	7	with	with	ADP
ejpam-4707	236	8	ratio	ratio	NOUN
ejpam-4707	236	9	-	-	PUNCT
ejpam-4707	236	10	dependent	dependent	ADJ
ejpam-4707	236	11	functional	functional	ADJ
ejpam-4707	236	12	response	response	NOUN
ejpam-4707	236	13	and	and	CCONJ
ejpam-4707	236	14	linear	linear	ADJ
ejpam-4707	236	15	harvesting	harvesting	NOUN
ejpam-4707	236	16	.	.	PUNCT
ejpam-4707	237	1	mathematics	mathematic	NOUN
ejpam-4707	237	2	,	,	PUNCT
ejpam-4707	237	3	7(11):1100	7(11):1100	NUM
ejpam-4707	237	4	,	,	PUNCT
ejpam-4707	237	5	2019	2019	NUM
ejpam-4707	237	6	.	.	PUNCT
ejpam-4707	238	1	[	[	X
ejpam-4707	238	2	18	18	NUM
ejpam-4707	238	3	]	]	X
ejpam-4707	238	4	unal	unal	ADJ
ejpam-4707	238	5	ufuktepe	ufuktepe	NOUN
ejpam-4707	238	6	and	and	CCONJ
ejpam-4707	238	7	sinan	sinan	PROPN
ejpam-4707	238	8	kapcak	kapcak	PROPN
ejpam-4707	238	9	.	.	PUNCT
ejpam-4707	239	1	applications	application	NOUN
ejpam-4707	239	2	of	of	ADP
ejpam-4707	239	3	discrete	discrete	ADJ
ejpam-4707	239	4	dynamical	dynamical	ADJ
ejpam-4707	239	5	systems	system	NOUN
ejpam-4707	239	6	with	with	ADP
ejpam-4707	239	7	mathematica	mathematica	PROPN
ejpam-4707	239	8	.	.	PUNCT
ejpam-4707	240	1	rims	rims	PROPN
ejpam-4707	240	2	kyoto	kyoto	PROPN
ejpam-4707	240	3	proceedings	proceeding	NOUN
ejpam-4707	240	4	,	,	PUNCT
ejpam-4707	240	5	1909:207–216	1909:207–216	NUM
ejpam-4707	240	6	,	,	PUNCT
ejpam-4707	240	7	2014	2014	NUM
ejpam-4707	240	8	.	.	PUNCT
ejpam-4707	241	1	[	[	X
ejpam-4707	241	2	19	19	NUM
ejpam-4707	241	3	]	]	X
ejpam-4707	241	4	saskya	saskya	PROPN
ejpam-4707	241	5	van	van	PROPN
ejpam-4707	241	6	nouhuys	nouhuys	PROPN
ejpam-4707	241	7	,	,	PUNCT
ejpam-4707	241	8	suvi	suvi	PROPN
ejpam-4707	241	9	niemikapee	niemikapee	NOUN
ejpam-4707	241	10	,	,	PUNCT
ejpam-4707	241	11	and	and	CCONJ
ejpam-4707	241	12	ilkka	ilkka	VERB
ejpam-4707	241	13	hanski	hanski	ADJ
ejpam-4707	241	14	.	.	PUNCT
ejpam-4707	242	1	variation	variation	NOUN
ejpam-4707	242	2	in	in	ADP
ejpam-4707	242	3	a	a	DET
ejpam-4707	242	4	host	host	NOUN
ejpam-4707	242	5	–	–	PUNCT
ejpam-4707	242	6	parasitoid	parasitoid	NOUN
ejpam-4707	242	7	interaction	interaction	NOUN
ejpam-4707	242	8	across	across	ADP
ejpam-4707	242	9	independent	independent	ADJ
ejpam-4707	242	10	populations	population	NOUN
ejpam-4707	242	11	.	.	PUNCT
ejpam-4707	243	1	insects	insect	NOUN
ejpam-4707	243	2	,	,	PUNCT
ejpam-4707	243	3	3(4):1236–1256	3(4):1236–1256	PROPN
ejpam-4707	243	4	,	,	PUNCT
ejpam-4707	243	5	2012	2012	NUM
ejpam-4707	243	6	.	.	PUNCT
ejpam-4707	244	1	[	[	X
ejpam-4707	244	2	20	20	NUM
ejpam-4707	244	3	]	]	PUNCT
ejpam-4707	244	4	gergely	gergely	ADV
ejpam-4707	244	5	várkonyi	várkonyi	PROPN
ejpam-4707	244	6	,	,	PUNCT
ejpam-4707	244	7	ilkka	ilkka	NOUN
ejpam-4707	244	8	hanski	hanski	PROPN
ejpam-4707	244	9	,	,	PUNCT
ejpam-4707	244	10	martin	martin	PROPN
ejpam-4707	244	11	rost	rost	PROPN
ejpam-4707	244	12	,	,	PUNCT
ejpam-4707	244	13	and	and	CCONJ
ejpam-4707	244	14	juhani	juhani	ADJ
ejpam-4707	244	15	itämies	itämie	NOUN
ejpam-4707	244	16	.	.	PUNCT
ejpam-4707	245	1	host	host	NOUN
ejpam-4707	245	2	-	-	PUNCT
ejpam-4707	245	3	parasitoid	parasitoid	NOUN
ejpam-4707	245	4	dynamics	dynamic	NOUN
ejpam-4707	245	5	in	in	ADP
ejpam-4707	245	6	periodic	periodic	ADJ
ejpam-4707	245	7	boreal	boreal	ADJ
ejpam-4707	245	8	moths	moth	NOUN
ejpam-4707	245	9	.	.	PUNCT
ejpam-4707	246	1	oikos	oikos	ADJ
ejpam-4707	246	2	,	,	PUNCT
ejpam-4707	246	3	98(3):421–430	98(3):421–430	PROPN
ejpam-4707	246	4	,	,	PUNCT
ejpam-4707	246	5	2002	2002	NUM
ejpam-4707	246	6	.	.	PUNCT
ejpam-4707	247	1	[	[	X
ejpam-4707	247	2	21	21	NUM
ejpam-4707	247	3	]	]	X
ejpam-4707	247	4	sandra	sandra	PROPN
ejpam-4707	247	5	vaz	vaz	PROPN
ejpam-4707	247	6	and	and	CCONJ
ejpam-4707	247	7	delfim	delfim	PROPN
ejpam-4707	247	8	fm	fm	PROPN
ejpam-4707	247	9	torres	torre	NOUN
ejpam-4707	247	10	.	.	PUNCT
ejpam-4707	248	1	a	a	DET
ejpam-4707	248	2	discrete	discrete	ADJ
ejpam-4707	248	3	-	-	PUNCT
ejpam-4707	248	4	time	time	NOUN
ejpam-4707	248	5	compartmental	compartmental	ADJ
ejpam-4707	248	6	epidemiological	epidemiological	ADJ
ejpam-4707	248	7	model	model	NOUN
ejpam-4707	248	8	for	for	ADP
ejpam-4707	248	9	covid-19	covid-19	PROPN
ejpam-4707	248	10	with	with	ADP
ejpam-4707	248	11	a	a	DET
ejpam-4707	248	12	case	case	NOUN
ejpam-4707	248	13	study	study	NOUN
ejpam-4707	248	14	for	for	ADP
ejpam-4707	248	15	portugal	portugal	PROPN
ejpam-4707	248	16	.	.	PUNCT
ejpam-4707	249	1	axioms	axiom	NOUN
ejpam-4707	249	2	,	,	PUNCT
ejpam-4707	249	3	10(4):314	10(4):314	NOUN
ejpam-4707	249	4	,	,	PUNCT
ejpam-4707	249	5	2021	2021	NUM
ejpam-4707	249	6	.	.	PUNCT
ejpam-4707	250	1	references	reference	NOUN
ejpam-4707	250	2	750	750	NUM
ejpam-4707	250	3	[	[	X
ejpam-4707	250	4	22	22	NUM
ejpam-4707	250	5	]	]	PUNCT
ejpam-4707	250	6	jianming	jianme	VERB
ejpam-4707	250	7	zhang	zhang	PROPN
ejpam-4707	250	8	,	,	PUNCT
ejpam-4707	250	9	lijun	lijun	PROPN
ejpam-4707	250	10	zhang	zhang	PROPN
ejpam-4707	250	11	,	,	PUNCT
ejpam-4707	250	12	and	and	CCONJ
ejpam-4707	250	13	yuzhen	yuzhen	PROPN
ejpam-4707	250	14	bai	bai	PROPN
ejpam-4707	250	15	.	.	PUNCT
ejpam-4707	251	1	stability	stability	NOUN
ejpam-4707	251	2	and	and	CCONJ
ejpam-4707	251	3	bifurcation	bifurcation	NOUN
ejpam-4707	251	4	analysis	analysis	NOUN
ejpam-4707	251	5	on	on	ADP
ejpam-4707	251	6	a	a	DET
ejpam-4707	251	7	predator	predator	NOUN
ejpam-4707	251	8	–	–	PUNCT
ejpam-4707	251	9	prey	prey	NOUN
ejpam-4707	251	10	system	system	NOUN
ejpam-4707	251	11	with	with	ADP
ejpam-4707	251	12	the	the	DET
ejpam-4707	251	13	weak	weak	ADJ
ejpam-4707	251	14	allee	allee	NOUN
ejpam-4707	251	15	effect	effect	NOUN
ejpam-4707	251	16	.	.	PUNCT
ejpam-4707	252	1	mathematics	mathematic	NOUN
ejpam-4707	252	2	,	,	PUNCT
ejpam-4707	252	3	7(5):432	7(5):432	NUM
ejpam-4707	252	4	,	,	PUNCT
ejpam-4707	252	5	2019	2019	NUM
ejpam-4707	252	6	.	.	PUNCT