id	sid	tid	token	lemma	pos
ejpam-3713	1	1	european	european	PROPN
ejpam-3713	1	2	journal	journal	PROPN
ejpam-3713	1	3	of	of	ADP
ejpam-3713	1	4	pure	pure	ADJ
ejpam-3713	1	5	and	and	CCONJ
ejpam-3713	1	6	applied	apply	VERB
ejpam-3713	1	7	mathematics	mathematic	NOUN
ejpam-3713	1	8	vol	vol	NOUN
ejpam-3713	1	9	.	.	PROPN
ejpam-3713	2	1	13	13	NUM
ejpam-3713	2	2	,	,	PUNCT
ejpam-3713	2	3	no	no	INTJ
ejpam-3713	2	4	.	.	NOUN
ejpam-3713	2	5	5	5	NUM
ejpam-3713	2	6	,	,	PUNCT
ejpam-3713	2	7	2020	2020	NUM
ejpam-3713	2	8	,	,	PUNCT
ejpam-3713	2	9	1176	1176	NUM
ejpam-3713	2	10	-	-	SYM
ejpam-3713	2	11	1198	1198	NUM
ejpam-3713	2	12	issn	issn	PROPN
ejpam-3713	2	13	1307	1307	NUM
ejpam-3713	2	14	-	-	SYM
ejpam-3713	2	15	5543	5543	NUM
ejpam-3713	2	16	–	–	PUNCT
ejpam-3713	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3713	2	18	published	publish	VERB
ejpam-3713	2	19	by	by	ADP
ejpam-3713	2	20	new	new	PROPN
ejpam-3713	2	21	york	york	PROPN
ejpam-3713	2	22	business	business	PROPN
ejpam-3713	2	23	global	global	ADJ
ejpam-3713	2	24	special	special	ADJ
ejpam-3713	2	25	issue	issue	NOUN
ejpam-3713	2	26	dedicated	dedicate	VERB
ejpam-3713	2	27	to	to	ADP
ejpam-3713	2	28	professor	professor	NOUN
ejpam-3713	2	29	hari	hari	PROPN
ejpam-3713	2	30	m.	m.	PROPN
ejpam-3713	2	31	srivastava	srivastava	PROPN
ejpam-3713	2	32	on	on	ADP
ejpam-3713	2	33	the	the	DET
ejpam-3713	2	34	occasion	occasion	NOUN
ejpam-3713	2	35	of	of	ADP
ejpam-3713	2	36	his	his	PRON
ejpam-3713	2	37	80th	80th	ADJ
ejpam-3713	2	38	birthday	birthday	NOUN
ejpam-3713	2	39	analysis	analysis	NOUN
ejpam-3713	2	40	of	of	ADP
ejpam-3713	2	41	the	the	DET
ejpam-3713	2	42	picard	picard	NOUN
ejpam-3713	2	43	’s	’s	PART
ejpam-3713	2	44	iteration	iteration	NOUN
ejpam-3713	2	45	method	method	NOUN
ejpam-3713	2	46	and	and	CCONJ
ejpam-3713	2	47	stability	stability	NOUN
ejpam-3713	2	48	for	for	ADP
ejpam-3713	2	49	ecological	ecological	ADJ
ejpam-3713	2	50	initial	initial	ADJ
ejpam-3713	2	51	value	value	NOUN
ejpam-3713	2	52	problems	problem	NOUN
ejpam-3713	2	53	of	of	ADP
ejpam-3713	2	54	single	single	ADJ
ejpam-3713	2	55	species	specie	NOUN
ejpam-3713	2	56	models	model	NOUN
ejpam-3713	2	57	with	with	ADP
ejpam-3713	2	58	harvesting	harvesting	NOUN
ejpam-3713	2	59	factor	factor	NOUN
ejpam-3713	2	60	mohammad	mohammad	PROPN
ejpam-3713	2	61	hossein	hossein	PROPN
ejpam-3713	2	62	rahmani	rahmani	VERB
ejpam-3713	2	63	doust1,∗,v	doust1,∗,v	PROPN
ejpam-3713	2	64	.	.	PUNCT
ejpam-3713	3	1	lokesha2	lokesha2	NOUN
ejpam-3713	3	2	,	,	PUNCT
ejpam-3713	3	3	atena	atena	NOUN
ejpam-3713	3	4	ghasemabadi3	ghasemabadi3	NOUN
ejpam-3713	3	5	1	1	NUM
ejpam-3713	3	6	department	department	NOUN
ejpam-3713	3	7	of	of	ADP
ejpam-3713	3	8	mathematics	mathematic	NOUN
ejpam-3713	3	9	,	,	PUNCT
ejpam-3713	3	10	faculty	faculty	NOUN
ejpam-3713	3	11	of	of	ADP
ejpam-3713	3	12	sciences	science	NOUN
ejpam-3713	3	13	,	,	PUNCT
ejpam-3713	3	14	university	university	NOUN
ejpam-3713	3	15	of	of	ADP
ejpam-3713	3	16	neyshabur	neyshabur	PROPN
ejpam-3713	3	17	,	,	PUNCT
ejpam-3713	3	18	neyshabur	neyshabur	PROPN
ejpam-3713	3	19	,	,	PUNCT
ejpam-3713	3	20	khorasen	khorasen	PROPN
ejpam-3713	3	21	-	-	PUNCT
ejpam-3713	3	22	e	e	NOUN
ejpam-3713	3	23	-	-	NOUN
ejpam-3713	3	24	razavi	razavi	ADJ
ejpam-3713	3	25	,	,	PUNCT
ejpam-3713	3	26	iran	iran	PROPN
ejpam-3713	3	27	2	2	NUM
ejpam-3713	3	28	department	department	NOUN
ejpam-3713	3	29	of	of	ADP
ejpam-3713	3	30	studies	study	NOUN
ejpam-3713	3	31	in	in	ADP
ejpam-3713	3	32	mathematics	mathematic	NOUN
ejpam-3713	3	33	,	,	PUNCT
ejpam-3713	3	34	v.	v.	ADP
ejpam-3713	3	35	s.	s.	PROPN
ejpam-3713	3	36	k.	k.	PROPN
ejpam-3713	3	37	university	university	PROPN
ejpam-3713	3	38	,	,	PUNCT
ejpam-3713	3	39	vinayaka	vinayaka	PROPN
ejpam-3713	3	40	nagara	nagara	PROPN
ejpam-3713	3	41	,	,	PUNCT
ejpam-3713	3	42	ballari	ballari	NOUN
ejpam-3713	3	43	,	,	PUNCT
ejpam-3713	3	44	india	india	PROPN
ejpam-3713	3	45	3	3	NUM
ejpam-3713	3	46	esfarayen	esfarayen	PROPN
ejpam-3713	3	47	university	university	NOUN
ejpam-3713	3	48	of	of	ADP
ejpam-3713	3	49	technology	technology	NOUN
ejpam-3713	3	50	,	,	PUNCT
ejpam-3713	3	51	esfayen	esfayen	NOUN
ejpam-3713	3	52	,	,	PUNCT
ejpam-3713	3	53	north	north	PROPN
ejpam-3713	3	54	khorasan	khorasan	PROPN
ejpam-3713	3	55	,	,	PUNCT
ejpam-3713	3	56	iran	iran	PROPN
ejpam-3713	3	57	abstract	abstract	NOUN
ejpam-3713	3	58	.	.	PUNCT
ejpam-3713	4	1	in	in	ADP
ejpam-3713	4	2	the	the	DET
ejpam-3713	4	3	recent	recent	ADJ
ejpam-3713	4	4	decades	decade	NOUN
ejpam-3713	4	5	,	,	PUNCT
ejpam-3713	4	6	biology	biology	NOUN
ejpam-3713	4	7	and	and	CCONJ
ejpam-3713	4	8	ecology	ecology	NOUN
ejpam-3713	4	9	area	area	NOUN
ejpam-3713	4	10	and	and	CCONJ
ejpam-3713	4	11	also	also	ADV
ejpam-3713	4	12	computer	computer	NOUN
ejpam-3713	4	13	and	and	CCONJ
ejpam-3713	4	14	network	network	NOUN
ejpam-3713	4	15	sciences	science	NOUN
ejpam-3713	4	16	are	be	AUX
ejpam-3713	4	17	marched	march	VERB
ejpam-3713	4	18	on	on	ADP
ejpam-3713	4	19	at	at	ADP
ejpam-3713	4	20	a	a	DET
ejpam-3713	4	21	rapid	rapid	ADJ
ejpam-3713	4	22	pace	pace	NOUN
ejpam-3713	4	23	toward	toward	ADP
ejpam-3713	4	24	perfection	perfection	NOUN
ejpam-3713	4	25	by	by	ADP
ejpam-3713	4	26	help	help	NOUN
ejpam-3713	4	27	of	of	ADP
ejpam-3713	4	28	mathematical	mathematical	ADJ
ejpam-3713	4	29	concepts	concept	NOUN
ejpam-3713	4	30	such	such	ADJ
ejpam-3713	4	31	as	as	ADP
ejpam-3713	4	32	stability	stability	NOUN
ejpam-3713	4	33	,	,	PUNCT
ejpam-3713	4	34	bifurcation	bifurcation	NOUN
ejpam-3713	4	35	,	,	PUNCT
ejpam-3713	4	36	chaos	chaos	NOUN
ejpam-3713	4	37	and	and	CCONJ
ejpam-3713	4	38	etc	etc	X
ejpam-3713	4	39	.	.	X
ejpam-3713	4	40	because	because	SCONJ
ejpam-3713	4	41	of	of	ADP
ejpam-3713	4	42	no	no	DET
ejpam-3713	4	43	existing	exist	VERB
ejpam-3713	4	44	any	any	DET
ejpam-3713	4	45	interspecific	interspecific	ADJ
ejpam-3713	4	46	interaction	interaction	NOUN
ejpam-3713	4	47	in	in	ADP
ejpam-3713	4	48	the	the	DET
ejpam-3713	4	49	single	single	ADJ
ejpam-3713	4	50	species	specie	NOUN
ejpam-3713	4	51	,	,	PUNCT
ejpam-3713	4	52	one	one	PRON
ejpam-3713	4	53	is	be	AUX
ejpam-3713	4	54	able	able	ADJ
ejpam-3713	4	55	to	to	PART
ejpam-3713	4	56	see	see	VERB
ejpam-3713	4	57	that	that	SCONJ
ejpam-3713	4	58	this	this	PRON
ejpam-3713	4	59	is	be	AUX
ejpam-3713	4	60	the	the	DET
ejpam-3713	4	61	simplest	simple	ADJ
ejpam-3713	4	62	model	model	NOUN
ejpam-3713	4	63	.	.	PUNCT
ejpam-3713	5	1	meanwhile	meanwhile	ADV
ejpam-3713	5	2	by	by	ADP
ejpam-3713	5	3	adding	add	VERB
ejpam-3713	5	4	some	some	DET
ejpam-3713	5	5	assumptions	assumption	NOUN
ejpam-3713	5	6	,	,	PUNCT
ejpam-3713	5	7	we	we	PRON
ejpam-3713	5	8	see	see	VERB
ejpam-3713	5	9	that	that	SCONJ
ejpam-3713	5	10	it	it	PRON
ejpam-3713	5	11	has	have	VERB
ejpam-3713	5	12	so	so	ADV
ejpam-3713	5	13	many	many	ADJ
ejpam-3713	5	14	practical	practical	ADJ
ejpam-3713	5	15	applications	application	NOUN
ejpam-3713	5	16	in	in	ADP
ejpam-3713	5	17	the	the	DET
ejpam-3713	5	18	nature	nature	NOUN
ejpam-3713	5	19	and	and	CCONJ
ejpam-3713	5	20	any	any	DET
ejpam-3713	5	21	branch	branch	NOUN
ejpam-3713	5	22	of	of	ADP
ejpam-3713	5	23	sciences	science	NOUN
ejpam-3713	5	24	.	.	PUNCT
ejpam-3713	6	1	in	in	ADP
ejpam-3713	6	2	this	this	DET
ejpam-3713	6	3	article	article	NOUN
ejpam-3713	6	4	,	,	PUNCT
ejpam-3713	6	5	some	some	DET
ejpam-3713	6	6	dynamical	dynamical	ADJ
ejpam-3713	6	7	models	model	NOUN
ejpam-3713	6	8	of	of	ADP
ejpam-3713	6	9	single	single	ADJ
ejpam-3713	6	10	species	specie	NOUN
ejpam-3713	6	11	are	be	AUX
ejpam-3713	6	12	studied	study	VERB
ejpam-3713	6	13	.	.	PUNCT
ejpam-3713	7	1	first	first	ADV
ejpam-3713	7	2	,	,	PUNCT
ejpam-3713	7	3	picard	picard	PROPN
ejpam-3713	7	4	’s	’s	PART
ejpam-3713	7	5	iteration	iteration	NOUN
ejpam-3713	7	6	method	method	NOUN
ejpam-3713	7	7	for	for	ADP
ejpam-3713	7	8	exponential	exponential	ADJ
ejpam-3713	7	9	growth	growth	NOUN
ejpam-3713	7	10	rate	rate	NOUN
ejpam-3713	7	11	is	be	AUX
ejpam-3713	7	12	analyzed	analyze	VERB
ejpam-3713	7	13	.	.	PUNCT
ejpam-3713	8	1	in	in	ADP
ejpam-3713	8	2	continuation	continuation	NOUN
ejpam-3713	8	3	,	,	PUNCT
ejpam-3713	8	4	some	some	DET
ejpam-3713	8	5	logistic	logistic	ADJ
ejpam-3713	8	6	models	model	NOUN
ejpam-3713	8	7	for	for	ADP
ejpam-3713	8	8	both	both	DET
ejpam-3713	8	9	cases	case	NOUN
ejpam-3713	8	10	without	without	ADP
ejpam-3713	8	11	harvesting	harvesting	NOUN
ejpam-3713	8	12	and	and	CCONJ
ejpam-3713	8	13	having	have	VERB
ejpam-3713	8	14	harvested	harvest	VERB
ejpam-3713	8	15	factor	factor	NOUN
ejpam-3713	8	16	which	which	PRON
ejpam-3713	8	17	are	be	AUX
ejpam-3713	8	18	constant	constant	ADJ
ejpam-3713	8	19	or	or	CCONJ
ejpam-3713	8	20	variable	variable	NOUN
ejpam-3713	8	21	are	be	AUX
ejpam-3713	8	22	studied	study	VERB
ejpam-3713	8	23	.	.	PUNCT
ejpam-3713	9	1	indeed	indeed	ADV
ejpam-3713	9	2	,	,	PUNCT
ejpam-3713	9	3	the	the	DET
ejpam-3713	9	4	solution	solution	NOUN
ejpam-3713	9	5	and	and	CCONJ
ejpam-3713	9	6	stability	stability	NOUN
ejpam-3713	9	7	of	of	ADP
ejpam-3713	9	8	equilibria	equilibrium	NOUN
ejpam-3713	9	9	for	for	ADP
ejpam-3713	9	10	the	the	DET
ejpam-3713	9	11	said	say	VERB
ejpam-3713	9	12	models	model	NOUN
ejpam-3713	9	13	are	be	AUX
ejpam-3713	9	14	analyzed	analyze	VERB
ejpam-3713	9	15	.	.	PUNCT
ejpam-3713	10	1	finally	finally	ADV
ejpam-3713	10	2	,	,	PUNCT
ejpam-3713	10	3	in	in	ADP
ejpam-3713	10	4	the	the	DET
ejpam-3713	10	5	section	section	NOUN
ejpam-3713	10	6	of	of	ADP
ejpam-3713	10	7	simulation	simulation	NOUN
ejpam-3713	10	8	analysis	analysis	NOUN
ejpam-3713	10	9	by	by	ADP
ejpam-3713	10	10	help	help	NOUN
ejpam-3713	10	11	of	of	ADP
ejpam-3713	10	12	matlab	matlab	PROPN
ejpam-3713	10	13	software	software	NOUN
ejpam-3713	10	14	,	,	PUNCT
ejpam-3713	10	15	we	we	PRON
ejpam-3713	10	16	give	give	VERB
ejpam-3713	10	17	some	some	DET
ejpam-3713	10	18	numerical	numerical	ADJ
ejpam-3713	10	19	simulations	simulation	NOUN
ejpam-3713	10	20	to	to	PART
ejpam-3713	10	21	support	support	VERB
ejpam-3713	10	22	of	of	ADP
ejpam-3713	10	23	our	our	PRON
ejpam-3713	10	24	mathematical	mathematical	ADJ
ejpam-3713	10	25	conclusions	conclusion	NOUN
ejpam-3713	10	26	which	which	PRON
ejpam-3713	10	27	show	show	VERB
ejpam-3713	10	28	the	the	DET
ejpam-3713	10	29	stability	stability	NOUN
ejpam-3713	10	30	of	of	ADP
ejpam-3713	10	31	the	the	DET
ejpam-3713	10	32	equilibria	equilibrium	NOUN
ejpam-3713	10	33	for	for	ADP
ejpam-3713	10	34	i.v.ps	i.v.ps	PROPN
ejpam-3713	10	35	.	.	PUNCT
ejpam-3713	11	1	of	of	ADP
ejpam-3713	11	2	the	the	DET
ejpam-3713	11	3	logistic	logistic	ADJ
ejpam-3713	11	4	equation	equation	NOUN
ejpam-3713	11	5	developed	develop	VERB
ejpam-3713	11	6	.	.	PUNCT
ejpam-3713	12	1	2020	2020	NUM
ejpam-3713	12	2	mathematics	mathematic	NOUN
ejpam-3713	12	3	subject	subject	NOUN
ejpam-3713	12	4	classifications	classification	NOUN
ejpam-3713	12	5	:	:	PUNCT
ejpam-3713	12	6	34d20	34d20	NUM
ejpam-3713	12	7	,	,	PUNCT
ejpam-3713	12	8	92d40	92d40	NUM
ejpam-3713	12	9	key	key	ADJ
ejpam-3713	12	10	words	word	NOUN
ejpam-3713	12	11	and	and	CCONJ
ejpam-3713	12	12	phrases	phrase	NOUN
ejpam-3713	12	13	:	:	PUNCT
ejpam-3713	12	14	harvesting	harvesting	NOUN
ejpam-3713	12	15	factor	factor	NOUN
ejpam-3713	12	16	,	,	PUNCT
ejpam-3713	12	17	logistic	logistic	ADJ
ejpam-3713	12	18	equation	equation	NOUN
ejpam-3713	12	19	,	,	PUNCT
ejpam-3713	12	20	picard	picard	PROPN
ejpam-3713	12	21	’s	’s	PART
ejpam-3713	12	22	iteration	iteration	NOUN
ejpam-3713	12	23	method	method	NOUN
ejpam-3713	12	24	,	,	PUNCT
ejpam-3713	12	25	single	single	ADJ
ejpam-3713	12	26	species	specie	NOUN
ejpam-3713	12	27	,	,	PUNCT
ejpam-3713	12	28	stability	stability	NOUN
ejpam-3713	12	29	∗corresponding	∗corresponde	VERB
ejpam-3713	12	30	author	author	NOUN
ejpam-3713	12	31	.	.	PUNCT
ejpam-3713	13	1	doi	doi	NOUN
ejpam-3713	13	2	:	:	PUNCT
ejpam-3713	13	3	https://doi.org/10.29020/nybg.ejpam.v13i5.3713	https://doi.org/10.29020/nybg.ejpam.v13i5.3713	ADP
ejpam-3713	13	4	email	email	NOUN
ejpam-3713	13	5	addresses	address	NOUN
ejpam-3713	13	6	:	:	PUNCT
ejpam-3713	13	7	mh.rahmanidoust@neyshabur.ac.ir	mh.rahmanidoust@neyshabur.ac.ir	NOUN
ejpam-3713	13	8	(	(	PUNCT
ejpam-3713	13	9	m.h	m.h	PROPN
ejpam-3713	13	10	.	.	PROPN
ejpam-3713	13	11	rahmani	rahmani	PROPN
ejpam-3713	13	12	doust	doust	PROPN
ejpam-3713	13	13	)	)	PUNCT
ejpam-3713	13	14	,	,	PUNCT
ejpam-3713	13	15	v.lokesha@gmail.com	v.lokesha@gmail.com	X
ejpam-3713	13	16	(	(	PUNCT
ejpam-3713	13	17	v.	v.	ADP
ejpam-3713	13	18	lokesha	lokesha	PROPN
ejpam-3713	13	19	)	)	PUNCT
ejpam-3713	13	20	,	,	PUNCT
ejpam-3713	13	21	ghasemabadi.math@gmail.com	ghasemabadi.math@gmail.com	X
ejpam-3713	13	22	(	(	PUNCT
ejpam-3713	13	23	a.	a.	NOUN
ejpam-3713	13	24	ghasemabadi	ghasemabadi	NOUN
ejpam-3713	13	25	)	)	PUNCT
ejpam-3713	13	26	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-3713	13	27	1176	1176	NUM
ejpam-3713	14	1	c	c	NOUN
ejpam-3713	14	2	©	©	NOUN
ejpam-3713	14	3	2020	2020	NUM
ejpam-3713	14	4	ejpam	ejpam	VERB
ejpam-3713	14	5	all	all	DET
ejpam-3713	14	6	rights	right	NOUN
ejpam-3713	14	7	reserved	reserve	VERB
ejpam-3713	14	8	.	.	PUNCT
ejpam-3713	15	1	m.h	m.h	PROPN
ejpam-3713	15	2	.	.	PROPN
ejpam-3713	15	3	r.	r.	PROPN
ejpam-3713	15	4	doust	doust	PROPN
ejpam-3713	15	5	,	,	PUNCT
ejpam-3713	15	6	v.	v.	ADP
ejpam-3713	15	7	lokesha	lokesha	PROPN
ejpam-3713	15	8	,	,	PUNCT
ejpam-3713	15	9	a.	a.	NOUN
ejpam-3713	15	10	ghasemabadi	ghasemabadi	NOUN
ejpam-3713	15	11	/	/	SYM
ejpam-3713	15	12	eur	eur	PROPN
ejpam-3713	15	13	.	.	PUNCT
ejpam-3713	16	1	j.	j.	PROPN
ejpam-3713	16	2	pure	pure	PROPN
ejpam-3713	16	3	appl	appl	PROPN
ejpam-3713	16	4	.	.	PROPN
ejpam-3713	16	5	math	math	PROPN
ejpam-3713	16	6	,	,	PUNCT
ejpam-3713	16	7	13	13	NUM
ejpam-3713	16	8	(	(	PUNCT
ejpam-3713	16	9	5	5	NUM
ejpam-3713	16	10	)	)	PUNCT
ejpam-3713	16	11	(	(	PUNCT
ejpam-3713	16	12	2020	2020	NUM
ejpam-3713	16	13	)	)	PUNCT
ejpam-3713	16	14	,	,	PUNCT
ejpam-3713	16	15	1176	1176	NUM
ejpam-3713	16	16	-	-	SYM
ejpam-3713	16	17	1198	1198	NUM
ejpam-3713	16	18	1177	1177	NUM
ejpam-3713	16	19	1	1	NUM
ejpam-3713	16	20	.	.	PUNCT
ejpam-3713	17	1	introduction	introduction	NOUN
ejpam-3713	17	2	population	population	NOUN
ejpam-3713	17	3	ecologists	ecologist	NOUN
ejpam-3713	17	4	use	use	VERB
ejpam-3713	17	5	methods	method	NOUN
ejpam-3713	17	6	to	to	PART
ejpam-3713	17	7	model	model	VERB
ejpam-3713	17	8	the	the	DET
ejpam-3713	17	9	population	population	NOUN
ejpam-3713	17	10	dynamics	dynamic	NOUN
ejpam-3713	17	11	.	.	PUNCT
ejpam-3713	18	1	an	an	DET
ejpam-3713	18	2	accurate	accurate	ADJ
ejpam-3713	18	3	model	model	NOUN
ejpam-3713	18	4	should	should	AUX
ejpam-3713	18	5	be	be	AUX
ejpam-3713	18	6	able	able	ADJ
ejpam-3713	18	7	to	to	PART
ejpam-3713	18	8	describe	describe	VERB
ejpam-3713	18	9	the	the	DET
ejpam-3713	18	10	changes	change	NOUN
ejpam-3713	18	11	occurring	occur	VERB
ejpam-3713	18	12	in	in	ADP
ejpam-3713	18	13	a	a	DET
ejpam-3713	18	14	population	population	NOUN
ejpam-3713	18	15	and	and	CCONJ
ejpam-3713	18	16	predict	predict	VERB
ejpam-3713	18	17	future	future	ADJ
ejpam-3713	18	18	changes	change	NOUN
ejpam-3713	18	19	.	.	PUNCT
ejpam-3713	19	1	population	population	NOUN
ejpam-3713	19	2	growth	growth	NOUN
ejpam-3713	19	3	is	be	AUX
ejpam-3713	19	4	the	the	DET
ejpam-3713	19	5	most	most	ADJ
ejpam-3713	19	6	topic	topic	NOUN
ejpam-3713	19	7	in	in	ADP
ejpam-3713	19	8	ecology	ecology	NOUN
ejpam-3713	19	9	and	and	CCONJ
ejpam-3713	19	10	biology	biology	NOUN
ejpam-3713	19	11	area	area	NOUN
ejpam-3713	19	12	.	.	PUNCT
ejpam-3713	20	1	two	two	NUM
ejpam-3713	20	2	simple	simple	ADJ
ejpam-3713	20	3	models	model	NOUN
ejpam-3713	20	4	of	of	ADP
ejpam-3713	20	5	population	population	NOUN
ejpam-3713	20	6	growth	growth	NOUN
ejpam-3713	20	7	use	use	VERB
ejpam-3713	20	8	deterministic	deterministic	ADJ
ejpam-3713	20	9	equations	equation	NOUN
ejpam-3713	20	10	to	to	PART
ejpam-3713	20	11	describe	describe	VERB
ejpam-3713	20	12	the	the	DET
ejpam-3713	20	13	rate	rate	NOUN
ejpam-3713	20	14	of	of	ADP
ejpam-3713	20	15	change	change	NOUN
ejpam-3713	20	16	in	in	ADP
ejpam-3713	20	17	the	the	DET
ejpam-3713	20	18	size	size	NOUN
ejpam-3713	20	19	of	of	ADP
ejpam-3713	20	20	a	a	DET
ejpam-3713	20	21	population	population	NOUN
ejpam-3713	20	22	over	over	ADP
ejpam-3713	20	23	time	time	NOUN
ejpam-3713	20	24	.	.	PUNCT
ejpam-3713	21	1	the	the	DET
ejpam-3713	21	2	first	first	ADJ
ejpam-3713	21	3	one	one	NUM
ejpam-3713	21	4	,	,	PUNCT
ejpam-3713	21	5	exponential	exponential	ADJ
ejpam-3713	21	6	growth	growth	NOUN
ejpam-3713	21	7	,	,	PUNCT
ejpam-3713	21	8	describes	describe	VERB
ejpam-3713	21	9	theoretical	theoretical	ADJ
ejpam-3713	21	10	populations	population	NOUN
ejpam-3713	21	11	that	that	PRON
ejpam-3713	21	12	increase	increase	VERB
ejpam-3713	21	13	in	in	ADP
ejpam-3713	21	14	numbers	number	NOUN
ejpam-3713	21	15	without	without	ADP
ejpam-3713	21	16	any	any	DET
ejpam-3713	21	17	limits	limit	NOUN
ejpam-3713	21	18	to	to	ADP
ejpam-3713	21	19	their	their	PRON
ejpam-3713	21	20	growth	growth	NOUN
ejpam-3713	21	21	.	.	PUNCT
ejpam-3713	22	1	while	while	SCONJ
ejpam-3713	22	2	the	the	DET
ejpam-3713	22	3	other	other	ADJ
ejpam-3713	22	4	one	one	NOUN
ejpam-3713	22	5	,	,	PUNCT
ejpam-3713	22	6	logistic	logistic	ADJ
ejpam-3713	22	7	growth	growth	NOUN
ejpam-3713	22	8	,	,	PUNCT
ejpam-3713	22	9	introduces	introduce	VERB
ejpam-3713	22	10	limits	limit	NOUN
ejpam-3713	22	11	to	to	ADP
ejpam-3713	22	12	reproductive	reproductive	ADJ
ejpam-3713	22	13	growth	growth	NOUN
ejpam-3713	22	14	that	that	PRON
ejpam-3713	22	15	become	become	VERB
ejpam-3713	22	16	more	more	ADV
ejpam-3713	22	17	intense	intense	ADJ
ejpam-3713	22	18	as	as	SCONJ
ejpam-3713	22	19	the	the	DET
ejpam-3713	22	20	population	population	NOUN
ejpam-3713	22	21	size	size	NOUN
ejpam-3713	22	22	increases	increase	VERB
ejpam-3713	22	23	.	.	PUNCT
ejpam-3713	23	1	carrying	carry	VERB
ejpam-3713	23	2	capacity	capacity	NOUN
ejpam-3713	23	3	of	of	ADP
ejpam-3713	23	4	the	the	DET
ejpam-3713	23	5	environment	environment	NOUN
ejpam-3713	23	6	is	be	AUX
ejpam-3713	23	7	so	so	ADV
ejpam-3713	23	8	important	important	ADJ
ejpam-3713	23	9	to	to	PART
ejpam-3713	23	10	study	study	VERB
ejpam-3713	23	11	of	of	ADP
ejpam-3713	23	12	logistic	logistic	ADJ
ejpam-3713	23	13	dynamics	dynamic	NOUN
ejpam-3713	23	14	.	.	PUNCT
ejpam-3713	24	1	neither	neither	DET
ejpam-3713	24	2	model	model	NOUN
ejpam-3713	24	3	adequately	adequately	ADV
ejpam-3713	24	4	describes	describe	VERB
ejpam-3713	24	5	natural	natural	ADJ
ejpam-3713	24	6	populations	population	NOUN
ejpam-3713	24	7	,	,	PUNCT
ejpam-3713	24	8	but	but	CCONJ
ejpam-3713	24	9	they	they	PRON
ejpam-3713	24	10	provide	provide	VERB
ejpam-3713	24	11	points	point	NOUN
ejpam-3713	24	12	of	of	ADP
ejpam-3713	24	13	comparison	comparison	NOUN
ejpam-3713	24	14	.	.	PUNCT
ejpam-3713	25	1	as	as	SCONJ
ejpam-3713	25	2	time	time	NOUN
ejpam-3713	25	3	goes	go	VERB
ejpam-3713	25	4	,	,	PUNCT
ejpam-3713	25	5	any	any	DET
ejpam-3713	25	6	researcher	researcher	NOUN
ejpam-3713	25	7	may	may	AUX
ejpam-3713	25	8	see	see	VERB
ejpam-3713	25	9	the	the	DET
ejpam-3713	25	10	application	application	NOUN
ejpam-3713	25	11	of	of	ADP
ejpam-3713	25	12	mathematics	mathematic	NOUN
ejpam-3713	25	13	in	in	ADP
ejpam-3713	25	14	interdisciplinary	interdisciplinary	ADJ
ejpam-3713	25	15	sciences	science	NOUN
ejpam-3713	25	16	such	such	ADJ
ejpam-3713	25	17	as	as	ADP
ejpam-3713	25	18	biomathematics	biomathematic	NOUN
ejpam-3713	25	19	and	and	CCONJ
ejpam-3713	25	20	bioscience	bioscience	NOUN
ejpam-3713	25	21	especially	especially	ADV
ejpam-3713	25	22	in	in	ADP
ejpam-3713	25	23	the	the	DET
ejpam-3713	25	24	last	last	ADJ
ejpam-3713	25	25	century	century	NOUN
ejpam-3713	25	26	.	.	PUNCT
ejpam-3713	26	1	one	one	NUM
ejpam-3713	26	2	of	of	ADP
ejpam-3713	26	3	most	most	ADV
ejpam-3713	26	4	important	important	ADJ
ejpam-3713	26	5	mathematical	mathematical	ADJ
ejpam-3713	26	6	topics	topic	NOUN
ejpam-3713	26	7	using	use	VERB
ejpam-3713	26	8	in	in	ADP
ejpam-3713	26	9	biology	biology	NOUN
ejpam-3713	26	10	,	,	PUNCT
ejpam-3713	26	11	ecology	ecology	NOUN
ejpam-3713	26	12	etc	etc	X
ejpam-3713	26	13	.	.	X
ejpam-3713	26	14	is	be	AUX
ejpam-3713	26	15	the	the	DET
ejpam-3713	26	16	solution	solution	NOUN
ejpam-3713	26	17	finding	finding	NOUN
ejpam-3713	26	18	for	for	ADP
ejpam-3713	26	19	system	system	NOUN
ejpam-3713	26	20	of	of	ADP
ejpam-3713	26	21	differential	differential	ADJ
ejpam-3713	26	22	equations	equation	NOUN
ejpam-3713	26	23	.	.	PUNCT
ejpam-3713	27	1	most	most	ADJ
ejpam-3713	27	2	of	of	ADP
ejpam-3713	27	3	time	time	NOUN
ejpam-3713	27	4	finding	finding	NOUN
ejpam-3713	27	5	of	of	ADP
ejpam-3713	27	6	solution	solution	NOUN
ejpam-3713	27	7	for	for	ADP
ejpam-3713	27	8	a	a	DET
ejpam-3713	27	9	differential	differential	ADJ
ejpam-3713	27	10	equation	equation	NOUN
ejpam-3713	27	11	is	be	AUX
ejpam-3713	27	12	impossible	impossible	ADJ
ejpam-3713	27	13	unfortunately	unfortunately	ADV
ejpam-3713	27	14	.	.	PUNCT
ejpam-3713	28	1	on	on	ADP
ejpam-3713	28	2	other	other	ADJ
ejpam-3713	28	3	hand	hand	NOUN
ejpam-3713	28	4	having	have	VERB
ejpam-3713	28	5	an	an	DET
ejpam-3713	28	6	initial	initial	ADJ
ejpam-3713	28	7	population	population	NOUN
ejpam-3713	28	8	for	for	ADP
ejpam-3713	28	9	a	a	DET
ejpam-3713	28	10	system	system	NOUN
ejpam-3713	28	11	of	of	ADP
ejpam-3713	28	12	differential	differential	ADJ
ejpam-3713	28	13	equations	equation	NOUN
ejpam-3713	28	14	,	,	PUNCT
ejpam-3713	28	15	an	an	DET
ejpam-3713	28	16	initial	initial	ADJ
ejpam-3713	28	17	value	value	NOUN
ejpam-3713	28	18	problem	problem	NOUN
ejpam-3713	28	19	may	may	AUX
ejpam-3713	28	20	be	be	AUX
ejpam-3713	28	21	formed	form	VERB
ejpam-3713	28	22	.	.	PUNCT
ejpam-3713	29	1	we	we	PRON
ejpam-3713	29	2	should	should	AUX
ejpam-3713	29	3	find	find	VERB
ejpam-3713	29	4	out	out	ADP
ejpam-3713	29	5	the	the	DET
ejpam-3713	29	6	solution	solution	NOUN
ejpam-3713	29	7	or	or	CCONJ
ejpam-3713	29	8	analyze	analyze	VERB
ejpam-3713	29	9	its	its	PRON
ejpam-3713	29	10	behavior	behavior	NOUN
ejpam-3713	29	11	.	.	PUNCT
ejpam-3713	30	1	anybody	anybody	PRON
ejpam-3713	30	2	knows	know	VERB
ejpam-3713	30	3	the	the	DET
ejpam-3713	30	4	importance	importance	NOUN
ejpam-3713	30	5	and	and	CCONJ
ejpam-3713	30	6	effect	effect	NOUN
ejpam-3713	30	7	of	of	ADP
ejpam-3713	30	8	single	single	ADJ
ejpam-3713	30	9	species	specie	NOUN
ejpam-3713	30	10	in	in	ADP
ejpam-3713	30	11	community	community	NOUN
ejpam-3713	30	12	and	and	CCONJ
ejpam-3713	30	13	nature	nature	NOUN
ejpam-3713	30	14	,	,	PUNCT
ejpam-3713	30	15	and	and	CCONJ
ejpam-3713	30	16	so	so	ADV
ejpam-3713	30	17	we	we	PRON
ejpam-3713	30	18	present	present	VERB
ejpam-3713	30	19	a	a	DET
ejpam-3713	30	20	summary	summary	NOUN
ejpam-3713	30	21	and	and	CCONJ
ejpam-3713	30	22	brief	brief	ADJ
ejpam-3713	30	23	literature	literature	NOUN
ejpam-3713	30	24	of	of	ADP
ejpam-3713	30	25	mathematical	mathematical	ADJ
ejpam-3713	30	26	models	model	NOUN
ejpam-3713	30	27	such	such	ADJ
ejpam-3713	30	28	as	as	ADP
ejpam-3713	30	29	single	single	ADJ
ejpam-3713	30	30	species	specie	NOUN
ejpam-3713	30	31	,	,	PUNCT
ejpam-3713	30	32	exponential	exponential	NOUN
ejpam-3713	30	33	and	and	CCONJ
ejpam-3713	30	34	logistic	logistic	ADJ
ejpam-3713	30	35	modeling	modeling	NOUN
ejpam-3713	30	36	used	use	VERB
ejpam-3713	30	37	to	to	PART
ejpam-3713	30	38	describe	describe	VERB
ejpam-3713	30	39	population	population	NOUN
ejpam-3713	30	40	dynamics	dynamic	NOUN
ejpam-3713	30	41	,	,	PUNCT
ejpam-3713	30	42	which	which	PRON
ejpam-3713	30	43	may	may	AUX
ejpam-3713	30	44	help	help	VERB
ejpam-3713	30	45	us	we	PRON
ejpam-3713	30	46	future	future	ADJ
ejpam-3713	30	47	model	model	NOUN
ejpam-3713	30	48	development	development	NOUN
ejpam-3713	30	49	and	and	CCONJ
ejpam-3713	30	50	highlights	highlight	NOUN
ejpam-3713	30	51	the	the	DET
ejpam-3713	30	52	importance	importance	NOUN
ejpam-3713	30	53	of	of	ADP
ejpam-3713	30	54	population	population	NOUN
ejpam-3713	30	55	growth	growth	NOUN
ejpam-3713	30	56	rate	rate	NOUN
ejpam-3713	30	57	modeling	modeling	NOUN
ejpam-3713	30	58	in	in	ADP
ejpam-3713	30	59	biology	biology	NOUN
ejpam-3713	30	60	,	,	PUNCT
ejpam-3713	30	61	ecology	ecology	NOUN
ejpam-3713	30	62	,	,	PUNCT
ejpam-3713	30	63	and	and	CCONJ
ejpam-3713	30	64	another	another	DET
ejpam-3713	30	65	area	area	NOUN
ejpam-3713	30	66	even	even	ADV
ejpam-3713	30	67	computer	computer	NOUN
ejpam-3713	30	68	and	and	CCONJ
ejpam-3713	30	69	network	network	NOUN
ejpam-3713	30	70	sciences	sciences	PROPN
ejpam-3713	30	71	.	.	PUNCT
ejpam-3713	31	1	the	the	DET
ejpam-3713	31	2	study	study	NOUN
ejpam-3713	31	3	of	of	ADP
ejpam-3713	31	4	population	population	NOUN
ejpam-3713	31	5	change	change	NOUN
ejpam-3713	31	6	started	start	VERB
ejpam-3713	31	7	by	by	ADP
ejpam-3713	31	8	leonardo	leonardo	PROPN
ejpam-3713	31	9	of	of	ADP
ejpam-3713	31	10	pisa	pisa	PROPN
ejpam-3713	31	11	,	,	PUNCT
ejpam-3713	31	12	who	who	PRON
ejpam-3713	31	13	was	be	AUX
ejpam-3713	31	14	only	only	ADV
ejpam-3713	31	15	given	give	VERB
ejpam-3713	31	16	the	the	DET
ejpam-3713	31	17	nickname	nickname	NOUN
ejpam-3713	31	18	fibonacci	fibonacci	NOUN
ejpam-3713	31	19	.	.	PUNCT
ejpam-3713	32	1	he	he	PRON
ejpam-3713	32	2	introduced	introduce	VERB
ejpam-3713	32	3	in	in	ADP
ejpam-3713	32	4	his	his	PRON
ejpam-3713	32	5	arithmetic	arithmetic	ADJ
ejpam-3713	32	6	book	book	NOUN
ejpam-3713	32	7	of	of	ADP
ejpam-3713	32	8	1202	1202	NUM
ejpam-3713	32	9	set	set	NOUN
ejpam-3713	32	10	,	,	PUNCT
ejpam-3713	32	11	a	a	DET
ejpam-3713	32	12	modeling	modeling	NOUN
ejpam-3713	32	13	exercise	exercise	NOUN
ejpam-3713	32	14	involving	involve	VERB
ejpam-3713	32	15	a	a	DET
ejpam-3713	32	16	hypothetical	hypothetical	ADJ
ejpam-3713	32	17	growing	grow	VERB
ejpam-3713	32	18	rabbit	rabbit	NOUN
ejpam-3713	32	19	population	population	NOUN
ejpam-3713	33	1	[	[	X
ejpam-3713	33	2	9	9	NUM
ejpam-3713	33	3	]	]	PUNCT
ejpam-3713	33	4	.	.	PUNCT
ejpam-3713	34	1	environmental	environmental	ADJ
ejpam-3713	34	2	variation	variation	NOUN
ejpam-3713	34	3	in	in	ADP
ejpam-3713	34	4	ecological	ecological	ADJ
ejpam-3713	34	5	communities	community	NOUN
ejpam-3713	34	6	and	and	CCONJ
ejpam-3713	34	7	inferences	inference	NOUN
ejpam-3713	34	8	from	from	ADP
ejpam-3713	34	9	single	single	ADJ
ejpam-3713	34	10	species	specie	NOUN
ejpam-3713	34	11	data	datum	NOUN
ejpam-3713	34	12	is	be	AUX
ejpam-3713	34	13	studied	study	VERB
ejpam-3713	34	14	by	by	ADP
ejpam-3713	34	15	abbott	abbott	PROPN
ejpam-3713	34	16	et	et	PROPN
ejpam-3713	34	17	al	al	PROPN
ejpam-3713	35	1	[	[	X
ejpam-3713	35	2	2	2	NUM
ejpam-3713	35	3	]	]	PUNCT
ejpam-3713	35	4	.	.	PUNCT
ejpam-3713	36	1	they	they	PRON
ejpam-3713	36	2	present	present	VERB
ejpam-3713	36	3	a	a	DET
ejpam-3713	36	4	method	method	NOUN
ejpam-3713	36	5	for	for	ADP
ejpam-3713	36	6	estimating	estimate	VERB
ejpam-3713	36	7	dimension	dimension	NOUN
ejpam-3713	36	8	of	of	ADP
ejpam-3713	36	9	community	community	NOUN
ejpam-3713	36	10	on	on	ADP
ejpam-3713	36	11	a	a	DET
ejpam-3713	36	12	single	single	ADJ
ejpam-3713	36	13	species	specie	NOUN
ejpam-3713	36	14	.	.	PUNCT
ejpam-3713	37	1	a	a	DET
ejpam-3713	37	2	dynamics	dynamic	NOUN
ejpam-3713	37	3	of	of	ADP
ejpam-3713	37	4	single	single	ADJ
ejpam-3713	37	5	species	specie	NOUN
ejpam-3713	37	6	population	population	NOUN
ejpam-3713	37	7	growth	growth	NOUN
ejpam-3713	37	8	is	be	AUX
ejpam-3713	37	9	studied	study	VERB
ejpam-3713	37	10	by	by	ADP
ejpam-3713	37	11	mueller	mueller	PROPN
ejpam-3713	37	12	et	et	PROPN
ejpam-3713	37	13	al	al	PROPN
ejpam-3713	37	14	in	in	ADP
ejpam-3713	37	15	[	[	X
ejpam-3713	37	16	8	8	NUM
ejpam-3713	37	17	]	]	PUNCT
ejpam-3713	37	18	.	.	PUNCT
ejpam-3713	38	1	the	the	DET
ejpam-3713	38	2	stability	stability	NOUN
ejpam-3713	38	3	at	at	ADP
ejpam-3713	38	4	carrying	carry	VERB
ejpam-3713	38	5	capacity	capacity	NOUN
ejpam-3713	38	6	of	of	ADP
ejpam-3713	38	7	environment	environment	NOUN
ejpam-3713	38	8	for	for	ADP
ejpam-3713	38	9	25	25	NUM
ejpam-3713	38	10	different	different	ADJ
ejpam-3713	38	11	populations	population	NOUN
ejpam-3713	38	12	of	of	ADP
ejpam-3713	38	13	drosophila	drosophila	NOUN
ejpam-3713	38	14	melanogaster	melanogaster	NOUN
ejpam-3713	38	15	are	be	AUX
ejpam-3713	38	16	examined	examine	VERB
ejpam-3713	38	17	by	by	ADP
ejpam-3713	38	18	them	they	PRON
ejpam-3713	38	19	.	.	PUNCT
ejpam-3713	39	1	the	the	DET
ejpam-3713	39	2	spatial	spatial	ADJ
ejpam-3713	39	3	dynamics	dynamic	NOUN
ejpam-3713	39	4	single	single	ADJ
ejpam-3713	39	5	species	specie	NOUN
ejpam-3713	39	6	can	can	AUX
ejpam-3713	39	7	contribute	contribute	VERB
ejpam-3713	39	8	to	to	ADP
ejpam-3713	39	9	long	long	ADJ
ejpam-3713	39	10	term	term	NOUN
ejpam-3713	39	11	rarity	rarity	NOUN
ejpam-3713	39	12	and	and	CCONJ
ejpam-3713	39	13	commonness	commonness	NOUN
ejpam-3713	39	14	.	.	PUNCT
ejpam-3713	40	1	a	a	DET
ejpam-3713	40	2	spatial	spatial	ADJ
ejpam-3713	40	3	population	population	NOUN
ejpam-3713	40	4	dynamics	dynamic	NOUN
ejpam-3713	40	5	model	model	NOUN
ejpam-3713	40	6	and	and	CCONJ
ejpam-3713	40	7	regional	regional	ADJ
ejpam-3713	40	8	commonness	commonness	NOUN
ejpam-3713	40	9	and	and	CCONJ
ejpam-3713	40	10	regional	regional	ADJ
ejpam-3713	40	11	extinction	extinction	NOUN
ejpam-3713	40	12	are	be	AUX
ejpam-3713	40	13	investigated	investigate	VERB
ejpam-3713	40	14	in	in	ADP
ejpam-3713	40	15	[	[	X
ejpam-3713	40	16	6	6	NUM
ejpam-3713	40	17	]	]	PUNCT
ejpam-3713	40	18	.	.	PUNCT
ejpam-3713	41	1	anybody	anybody	PRON
ejpam-3713	41	2	is	be	AUX
ejpam-3713	41	3	able	able	ADJ
ejpam-3713	41	4	to	to	PART
ejpam-3713	41	5	find	find	VERB
ejpam-3713	41	6	out	out	ADP
ejpam-3713	41	7	the	the	DET
ejpam-3713	41	8	answer	answer	NOUN
ejpam-3713	41	9	of	of	ADP
ejpam-3713	41	10	question	question	NOUN
ejpam-3713	41	11	”	"	PUNCT
ejpam-3713	41	12	how	how	SCONJ
ejpam-3713	41	13	great	great	ADJ
ejpam-3713	41	14	an	an	DET
ejpam-3713	41	15	effect	effect	NOUN
ejpam-3713	41	16	does	do	AUX
ejpam-3713	41	17	self	self	NOUN
ejpam-3713	41	18	-	-	PUNCT
ejpam-3713	41	19	generated	generate	VERB
ejpam-3713	41	20	spatial	spatial	ADJ
ejpam-3713	41	21	structure	structure	NOUN
ejpam-3713	41	22	have	have	VERB
ejpam-3713	41	23	on	on	ADP
ejpam-3713	41	24	logistic	logistic	ADJ
ejpam-3713	41	25	population	population	NOUN
ejpam-3713	41	26	growth	growth	NOUN
ejpam-3713	41	27	?	?	PUNCT
ejpam-3713	41	28	”	"	PUNCT
ejpam-3713	41	29	which	which	PRON
ejpam-3713	41	30	is	be	AUX
ejpam-3713	41	31	studied	study	VERB
ejpam-3713	41	32	by	by	ADP
ejpam-3713	41	33	law	law	NOUN
ejpam-3713	41	34	et	et	NOUN
ejpam-3713	41	35	al	al	PROPN
ejpam-3713	41	36	in	in	ADP
ejpam-3713	41	37	[	[	X
ejpam-3713	41	38	7	7	NUM
ejpam-3713	41	39	]	]	PUNCT
ejpam-3713	41	40	.	.	PUNCT
ejpam-3713	42	1	they	they	PRON
ejpam-3713	42	2	showed	show	VERB
ejpam-3713	42	3	that	that	SCONJ
ejpam-3713	42	4	population	population	NOUN
ejpam-3713	42	5	growth	growth	NOUN
ejpam-3713	42	6	given	give	VERB
ejpam-3713	42	7	by	by	ADP
ejpam-3713	42	8	logistic	logistic	ADJ
ejpam-3713	42	9	model	model	NOUN
ejpam-3713	42	10	may	may	AUX
ejpam-3713	42	11	differ	differ	VERB
ejpam-3713	42	12	greatly	greatly	ADV
ejpam-3713	42	13	from	from	ADP
ejpam-3713	42	14	that	that	PRON
ejpam-3713	42	15	of	of	ADP
ejpam-3713	42	16	the	the	DET
ejpam-3713	42	17	nonspatial	nonspatial	ADJ
ejpam-3713	42	18	logistic	logistic	ADJ
ejpam-3713	42	19	equation	equation	NOUN
ejpam-3713	42	20	.	.	PUNCT
ejpam-3713	43	1	they	they	PRON
ejpam-3713	43	2	moreover	moreover	ADV
ejpam-3713	43	3	proved	prove	VERB
ejpam-3713	43	4	that	that	SCONJ
ejpam-3713	43	5	populations	population	NOUN
ejpam-3713	43	6	may	may	AUX
ejpam-3713	43	7	achieve	achieve	VERB
ejpam-3713	43	8	asymptotic	asymptotic	ADJ
ejpam-3713	43	9	densities	density	NOUN
ejpam-3713	43	10	greater	great	ADJ
ejpam-3713	43	11	than	than	ADP
ejpam-3713	43	12	or	or	CCONJ
ejpam-3713	43	13	less	less	ADJ
ejpam-3713	43	14	than	than	ADP
ejpam-3713	43	15	the	the	DET
ejpam-3713	43	16	carrying	carrying	NOUN
ejpam-3713	43	17	capacity	capacity	NOUN
ejpam-3713	43	18	of	of	ADP
ejpam-3713	43	19	logistic	logistic	ADJ
ejpam-3713	43	20	model	model	NOUN
ejpam-3713	43	21	where	where	SCONJ
ejpam-3713	43	22	it	it	PRON
ejpam-3713	43	23	is	be	AUX
ejpam-3713	43	24	not	not	PART
ejpam-3713	43	25	spatial	spatial	ADJ
ejpam-3713	43	26	,	,	PUNCT
ejpam-3713	43	27	and	and	CCONJ
ejpam-3713	43	28	can	can	AUX
ejpam-3713	43	29	even	even	ADV
ejpam-3713	43	30	tend	tend	VERB
ejpam-3713	43	31	towards	towards	ADP
ejpam-3713	43	32	extinction	extinction	NOUN
ejpam-3713	43	33	.	.	PUNCT
ejpam-3713	44	1	accounting	account	VERB
ejpam-3713	44	2	for	for	ADP
ejpam-3713	44	3	the	the	DET
ejpam-3713	44	4	local	local	ADJ
ejpam-3713	44	5	spatial	spatial	ADJ
ejpam-3713	44	6	processes	process	NOUN
ejpam-3713	44	7	indeed	indeed	ADV
ejpam-3713	44	8	brings	bring	VERB
ejpam-3713	44	9	the	the	DET
ejpam-3713	44	10	theory	theory	NOUN
ejpam-3713	44	11	of	of	ADP
ejpam-3713	44	12	single	single	ADJ
ejpam-3713	44	13	species	specie	NOUN
ejpam-3713	44	14	population	population	NOUN
ejpam-3713	44	15	growth	growth	NOUN
ejpam-3713	44	16	a	a	DET
ejpam-3713	44	17	step	step	NOUN
ejpam-3713	44	18	closer	close	ADV
ejpam-3713	44	19	to	to	ADP
ejpam-3713	44	20	the	the	DET
ejpam-3713	44	21	growth	growth	NOUN
ejpam-3713	44	22	of	of	ADP
ejpam-3713	44	23	real	real	ADJ
ejpam-3713	44	24	spatially	spatially	ADV
ejpam-3713	44	25	structured	structure	VERB
ejpam-3713	44	26	populations	population	NOUN
ejpam-3713	44	27	.	.	PUNCT
ejpam-3713	45	1	the	the	DET
ejpam-3713	45	2	population	population	NOUN
ejpam-3713	45	3	growth	growth	NOUN
ejpam-3713	45	4	of	of	ADP
ejpam-3713	45	5	infection	infection	NOUN
ejpam-3713	45	6	of	of	ADP
ejpam-3713	45	7	virus	virus	NOUN
ejpam-3713	45	8	and	and	CCONJ
ejpam-3713	45	9	worm	worm	NOUN
ejpam-3713	45	10	in	in	ADP
ejpam-3713	45	11	computer	computer	NOUN
ejpam-3713	45	12	networks	network	NOUN
ejpam-3713	45	13	is	be	AUX
ejpam-3713	45	14	analyzed	analyze	VERB
ejpam-3713	45	15	by	by	ADP
ejpam-3713	45	16	help	help	NOUN
ejpam-3713	45	17	of	of	ADP
ejpam-3713	45	18	logistic	logistic	ADJ
ejpam-3713	45	19	modeling	modeling	NOUN
ejpam-3713	45	20	[	[	X
ejpam-3713	45	21	1	1	NUM
ejpam-3713	45	22	]	]	PUNCT
ejpam-3713	45	23	.	.	PUNCT
ejpam-3713	46	1	pollutant	pollutant	ADJ
ejpam-3713	46	2	and	and	CCONJ
ejpam-3713	46	3	virus	virus	NOUN
ejpam-3713	46	4	m.h	m.h	PROPN
ejpam-3713	46	5	.	.	PROPN
ejpam-3713	46	6	r.	r.	PROPN
ejpam-3713	46	7	doust	doust	PROPN
ejpam-3713	46	8	,	,	PUNCT
ejpam-3713	46	9	v.	v.	ADP
ejpam-3713	46	10	lokesha	lokesha	PROPN
ejpam-3713	46	11	,	,	PUNCT
ejpam-3713	46	12	a.	a.	NOUN
ejpam-3713	46	13	ghasemabadi	ghasemabadi	NOUN
ejpam-3713	46	14	/	/	SYM
ejpam-3713	46	15	eur	eur	PROPN
ejpam-3713	46	16	.	.	PUNCT
ejpam-3713	47	1	j.	j.	PROPN
ejpam-3713	47	2	pure	pure	PROPN
ejpam-3713	47	3	appl	appl	PROPN
ejpam-3713	47	4	.	.	PROPN
ejpam-3713	47	5	math	math	PROPN
ejpam-3713	47	6	,	,	PUNCT
ejpam-3713	47	7	13	13	NUM
ejpam-3713	47	8	(	(	PUNCT
ejpam-3713	47	9	5	5	NUM
ejpam-3713	47	10	)	)	PUNCT
ejpam-3713	47	11	(	(	PUNCT
ejpam-3713	47	12	2020	2020	NUM
ejpam-3713	47	13	)	)	PUNCT
ejpam-3713	47	14	,	,	PUNCT
ejpam-3713	47	15	1176	1176	NUM
ejpam-3713	47	16	-	-	SYM
ejpam-3713	47	17	1198	1198	NUM
ejpam-3713	47	18	1178	1178	NUM
ejpam-3713	47	19	induced	induce	VERB
ejpam-3713	47	20	disease	disease	NOUN
ejpam-3713	47	21	effect	effect	NOUN
ejpam-3713	47	22	of	of	ADP
ejpam-3713	47	23	on	on	ADP
ejpam-3713	47	24	single	single	ADJ
ejpam-3713	47	25	species	specie	NOUN
ejpam-3713	47	26	animal	animal	NOUN
ejpam-3713	47	27	population	population	NOUN
ejpam-3713	47	28	and	and	CCONJ
ejpam-3713	47	29	its	its	PRON
ejpam-3713	47	30	essential	essential	ADJ
ejpam-3713	47	31	mathematical	mathematical	ADJ
ejpam-3713	47	32	features	feature	NOUN
ejpam-3713	47	33	by	by	ADP
ejpam-3713	47	34	help	help	NOUN
ejpam-3713	47	35	of	of	ADP
ejpam-3713	47	36	the	the	DET
ejpam-3713	47	37	logistic	logistic	ADJ
ejpam-3713	47	38	modeling	modeling	NOUN
ejpam-3713	47	39	.	.	PUNCT
ejpam-3713	48	1	moreover	moreover	ADV
ejpam-3713	48	2	,	,	PUNCT
ejpam-3713	48	3	it	it	PRON
ejpam-3713	48	4	is	be	AUX
ejpam-3713	48	5	shown	show	VERB
ejpam-3713	48	6	that	that	SCONJ
ejpam-3713	48	7	the	the	DET
ejpam-3713	48	8	susceptible	susceptible	ADJ
ejpam-3713	48	9	population	population	NOUN
ejpam-3713	48	10	does	do	AUX
ejpam-3713	48	11	not	not	PART
ejpam-3713	48	12	vanish	vanish	VERB
ejpam-3713	48	13	when	when	SCONJ
ejpam-3713	48	14	it	it	PRON
ejpam-3713	48	15	is	be	AUX
ejpam-3713	48	16	only	only	ADV
ejpam-3713	48	17	under	under	ADP
ejpam-3713	48	18	the	the	DET
ejpam-3713	48	19	effect	effect	NOUN
ejpam-3713	48	20	of	of	ADP
ejpam-3713	48	21	infection	infection	NOUN
ejpam-3713	48	22	meanwhile	meanwhile	ADV
ejpam-3713	48	23	in	in	ADP
ejpam-3713	48	24	the	the	DET
ejpam-3713	48	25	polluted	polluted	ADJ
ejpam-3713	48	26	environment	environment	NOUN
ejpam-3713	48	27	,	,	PUNCT
ejpam-3713	48	28	it	it	PRON
ejpam-3713	48	29	can	can	AUX
ejpam-3713	48	30	extinct	extinct	VERB
ejpam-3713	48	31	[	[	X
ejpam-3713	48	32	5	5	NUM
ejpam-3713	48	33	]	]	PUNCT
ejpam-3713	48	34	.	.	PUNCT
ejpam-3713	49	1	an	an	DET
ejpam-3713	49	2	application	application	NOUN
ejpam-3713	49	3	of	of	ADP
ejpam-3713	49	4	exponential	exponential	ADJ
ejpam-3713	49	5	and	and	CCONJ
ejpam-3713	49	6	logistic	logistic	ADJ
ejpam-3713	49	7	growths	growth	NOUN
ejpam-3713	49	8	for	for	ADP
ejpam-3713	49	9	single	single	ADJ
ejpam-3713	49	10	-	-	PUNCT
ejpam-3713	49	11	cell	cell	NOUN
ejpam-3713	49	12	models	model	NOUN
ejpam-3713	49	13	that	that	PRON
ejpam-3713	49	14	are	be	AUX
ejpam-3713	49	15	incapable	incapable	ADJ
ejpam-3713	49	16	or	or	CCONJ
ejpam-3713	49	17	misleading	misleading	ADJ
ejpam-3713	49	18	for	for	ADP
ejpam-3713	49	19	inferring	infer	VERB
ejpam-3713	49	20	population	population	NOUN
ejpam-3713	49	21	dynamics	dynamic	NOUN
ejpam-3713	49	22	as	as	SCONJ
ejpam-3713	49	23	there	there	PRON
ejpam-3713	49	24	is	be	VERB
ejpam-3713	49	25	no	no	DET
ejpam-3713	49	26	any	any	DET
ejpam-3713	49	27	interactions	interaction	NOUN
ejpam-3713	49	28	between	between	ADP
ejpam-3713	49	29	cells	cell	NOUN
ejpam-3713	49	30	via	via	ADP
ejpam-3713	49	31	metabolites	metabolite	NOUN
ejpam-3713	49	32	or	or	CCONJ
ejpam-3713	49	33	physical	physical	ADJ
ejpam-3713	49	34	contact	contact	NOUN
ejpam-3713	49	35	,	,	PUNCT
ejpam-3713	49	36	nor	nor	CCONJ
ejpam-3713	49	37	competition	competition	NOUN
ejpam-3713	49	38	for	for	ADP
ejpam-3713	49	39	limited	limited	ADJ
ejpam-3713	49	40	resources	resource	NOUN
ejpam-3713	49	41	such	such	ADJ
ejpam-3713	49	42	as	as	ADP
ejpam-3713	49	43	nutrients	nutrient	NOUN
ejpam-3713	49	44	or	or	CCONJ
ejpam-3713	49	45	space	space	NOUN
ejpam-3713	49	46	is	be	AUX
ejpam-3713	49	47	studied	study	VERB
ejpam-3713	49	48	in	in	ADP
ejpam-3713	49	49	[	[	X
ejpam-3713	49	50	4	4	NUM
ejpam-3713	49	51	]	]	PUNCT
ejpam-3713	49	52	.	.	PUNCT
ejpam-3713	50	1	some	some	PRON
ejpam-3713	50	2	more	more	ADJ
ejpam-3713	50	3	text	text	NOUN
ejpam-3713	50	4	on	on	ADP
ejpam-3713	50	5	applications	application	NOUN
ejpam-3713	50	6	of	of	ADP
ejpam-3713	50	7	single	single	ADJ
ejpam-3713	50	8	species	specie	NOUN
ejpam-3713	50	9	with	with	ADP
ejpam-3713	50	10	exponential	exponential	ADJ
ejpam-3713	50	11	or	or	CCONJ
ejpam-3713	50	12	logistic	logistic	ADJ
ejpam-3713	50	13	growth	growth	NOUN
ejpam-3713	50	14	rate	rate	NOUN
ejpam-3713	50	15	having	have	VERB
ejpam-3713	50	16	harvesting	harvesting	NOUN
ejpam-3713	50	17	factor	factor	NOUN
ejpam-3713	50	18	can	can	AUX
ejpam-3713	50	19	be	be	AUX
ejpam-3713	50	20	seen	see	VERB
ejpam-3713	50	21	in	in	ADP
ejpam-3713	50	22	[	[	X
ejpam-3713	50	23	3	3	NUM
ejpam-3713	50	24	]	]	PUNCT
ejpam-3713	50	25	,	,	PUNCT
ejpam-3713	50	26	[	[	X
ejpam-3713	50	27	9	9	NUM
ejpam-3713	50	28	]	]	PUNCT
ejpam-3713	50	29	,	,	PUNCT
ejpam-3713	50	30	[	[	X
ejpam-3713	50	31	10	10	NUM
ejpam-3713	50	32	]	]	PUNCT
ejpam-3713	50	33	,	,	PUNCT
ejpam-3713	50	34	[	[	X
ejpam-3713	50	35	11	11	NUM
ejpam-3713	50	36	]	]	PUNCT
ejpam-3713	50	37	and	and	CCONJ
ejpam-3713	50	38	[	[	X
ejpam-3713	50	39	13	13	NUM
ejpam-3713	50	40	]	]	PUNCT
ejpam-3713	50	41	.	.	PUNCT
ejpam-3713	51	1	exponential	exponential	ADJ
ejpam-3713	51	2	growth	growth	NOUN
ejpam-3713	51	3	is	be	AUX
ejpam-3713	51	4	associated	associate	VERB
ejpam-3713	51	5	with	with	ADP
ejpam-3713	51	6	the	the	DET
ejpam-3713	51	7	name	name	NOUN
ejpam-3713	51	8	of	of	ADP
ejpam-3713	51	9	thomas	thomas	PROPN
ejpam-3713	51	10	robert	robert	PROPN
ejpam-3713	51	11	malthus	malthus	PROPN
ejpam-3713	51	12	(	(	PUNCT
ejpam-3713	51	13	17661834	17661834	NUM
ejpam-3713	51	14	)	)	PUNCT
ejpam-3713	51	15	who	who	PRON
ejpam-3713	51	16	first	first	ADV
ejpam-3713	51	17	realized	realize	VERB
ejpam-3713	51	18	that	that	SCONJ
ejpam-3713	51	19	any	any	DET
ejpam-3713	51	20	species	specie	NOUN
ejpam-3713	51	21	can	can	AUX
ejpam-3713	51	22	potentially	potentially	ADV
ejpam-3713	51	23	increase	increase	VERB
ejpam-3713	51	24	in	in	ADP
ejpam-3713	51	25	numbers	number	NOUN
ejpam-3713	51	26	according	accord	VERB
ejpam-3713	51	27	to	to	ADP
ejpam-3713	51	28	a	a	DET
ejpam-3713	51	29	geometric	geometric	ADJ
ejpam-3713	51	30	series	series	NOUN
ejpam-3713	51	31	[	[	X
ejpam-3713	51	32	12	12	NUM
ejpam-3713	51	33	]	]	PUNCT
ejpam-3713	51	34	.	.	PUNCT
ejpam-3713	52	1	he	he	PRON
ejpam-3713	52	2	published	publish	VERB
ejpam-3713	52	3	his	his	PRON
ejpam-3713	52	4	book	book	NOUN
ejpam-3713	52	5	in	in	ADP
ejpam-3713	52	6	1798	1798	NUM
ejpam-3713	52	7	stating	state	VERB
ejpam-3713	52	8	that	that	SCONJ
ejpam-3713	52	9	populations	population	NOUN
ejpam-3713	52	10	with	with	ADP
ejpam-3713	52	11	abundant	abundant	ADJ
ejpam-3713	52	12	natural	natural	ADJ
ejpam-3713	52	13	resources	resource	NOUN
ejpam-3713	52	14	grow	grow	VERB
ejpam-3713	52	15	very	very	ADV
ejpam-3713	52	16	rapidly	rapidly	ADV
ejpam-3713	52	17	;	;	PUNCT
ejpam-3713	52	18	however	however	ADV
ejpam-3713	52	19	,	,	PUNCT
ejpam-3713	52	20	they	they	PRON
ejpam-3713	52	21	limit	limit	VERB
ejpam-3713	52	22	further	further	ADJ
ejpam-3713	52	23	growth	growth	NOUN
ejpam-3713	52	24	by	by	ADP
ejpam-3713	52	25	depleting	deplete	VERB
ejpam-3713	52	26	their	their	PRON
ejpam-3713	52	27	resources	resource	NOUN
ejpam-3713	52	28	.	.	PUNCT
ejpam-3713	53	1	the	the	DET
ejpam-3713	53	2	early	early	ADJ
ejpam-3713	53	3	pattern	pattern	NOUN
ejpam-3713	53	4	of	of	ADP
ejpam-3713	53	5	accelerating	accelerate	VERB
ejpam-3713	53	6	population	population	NOUN
ejpam-3713	53	7	size	size	NOUN
ejpam-3713	53	8	is	be	AUX
ejpam-3713	53	9	called	call	VERB
ejpam-3713	53	10	exponential	exponential	ADJ
ejpam-3713	53	11	growth	growth	NOUN
ejpam-3713	53	12	.	.	PUNCT
ejpam-3713	54	1	charles	charles	PROPN
ejpam-3713	54	2	darwin	darwin	PROPN
ejpam-3713	54	3	,	,	PUNCT
ejpam-3713	54	4	in	in	ADP
ejpam-3713	54	5	developing	develop	VERB
ejpam-3713	54	6	his	his	PRON
ejpam-3713	54	7	theory	theory	NOUN
ejpam-3713	54	8	of	of	ADP
ejpam-3713	54	9	natural	natural	ADJ
ejpam-3713	54	10	selection	selection	NOUN
ejpam-3713	54	11	,	,	PUNCT
ejpam-3713	54	12	was	be	AUX
ejpam-3713	54	13	influenced	influence	VERB
ejpam-3713	54	14	by	by	ADP
ejpam-3713	54	15	malthus	malthus	PROPN
ejpam-3713	54	16	.	.	PUNCT
ejpam-3713	55	1	generally	generally	ADV
ejpam-3713	55	2	,	,	PUNCT
ejpam-3713	55	3	in	in	ADP
ejpam-3713	55	4	open	open	ADJ
ejpam-3713	55	5	population	population	NOUN
ejpam-3713	55	6	or	or	CCONJ
ejpam-3713	55	7	open	open	ADJ
ejpam-3713	55	8	system	system	NOUN
ejpam-3713	55	9	,	,	PUNCT
ejpam-3713	55	10	there	there	PRON
ejpam-3713	55	11	is	be	VERB
ejpam-3713	55	12	the	the	DET
ejpam-3713	55	13	following	follow	VERB
ejpam-3713	55	14	equality	equality	NOUN
ejpam-3713	55	15	population	population	NOUN
ejpam-3713	55	16	change	change	NOUN
ejpam-3713	55	17	=	=	NOUN
ejpam-3713	55	18	births	birth	NOUN
ejpam-3713	55	19	-	-	PUNCT
ejpam-3713	55	20	deaths+immigrations	deaths+immigration	NOUN
ejpam-3713	55	21	-	-	PUNCT
ejpam-3713	55	22	emigrations	emigration	NOUN
ejpam-3713	55	23	by	by	ADP
ejpam-3713	55	24	assuming	assume	VERB
ejpam-3713	55	25	there	there	PRON
ejpam-3713	55	26	is	be	VERB
ejpam-3713	55	27	no	no	DET
ejpam-3713	55	28	any	any	DET
ejpam-3713	55	29	immigrations	immigration	NOUN
ejpam-3713	55	30	or	or	CCONJ
ejpam-3713	55	31	emigrations	emigration	NOUN
ejpam-3713	55	32	in	in	ADP
ejpam-3713	55	33	our	our	PRON
ejpam-3713	55	34	population	population	NOUN
ejpam-3713	55	35	,	,	PUNCT
ejpam-3713	55	36	we	we	PRON
ejpam-3713	55	37	consider	consider	VERB
ejpam-3713	55	38	a	a	DET
ejpam-3713	55	39	closed	closed	ADJ
ejpam-3713	55	40	population	population	NOUN
ejpam-3713	55	41	or	or	CCONJ
ejpam-3713	55	42	closed	closed	ADJ
ejpam-3713	55	43	system	system	NOUN
ejpam-3713	55	44	.	.	PUNCT
ejpam-3713	56	1	that	that	PRON
ejpam-3713	56	2	is	be	AUX
ejpam-3713	56	3	the	the	DET
ejpam-3713	56	4	population	population	NOUN
ejpam-3713	56	5	has	have	AUX
ejpam-3713	56	6	changed	change	VERB
ejpam-3713	56	7	only	only	ADV
ejpam-3713	56	8	by	by	ADP
ejpam-3713	56	9	the	the	DET
ejpam-3713	56	10	occurrence	occurrence	NOUN
ejpam-3713	56	11	of	of	ADP
ejpam-3713	56	12	birth	birth	NOUN
ejpam-3713	56	13	and	and	CCONJ
ejpam-3713	56	14	death	death	NOUN
ejpam-3713	56	15	.	.	PUNCT
ejpam-3713	57	1	moreover	moreover	ADV
ejpam-3713	57	2	,	,	PUNCT
ejpam-3713	57	3	by	by	ADP
ejpam-3713	57	4	considering	consider	VERB
ejpam-3713	57	5	x(t	x(t	PROPN
ejpam-3713	57	6	)	)	PUNCT
ejpam-3713	57	7	denotes	denote	VERB
ejpam-3713	57	8	the	the	DET
ejpam-3713	57	9	size	size	NOUN
ejpam-3713	57	10	of	of	ADP
ejpam-3713	57	11	population	population	NOUN
ejpam-3713	57	12	at	at	ADP
ejpam-3713	57	13	time	time	NOUN
ejpam-3713	57	14	t	t	PROPN
ejpam-3713	57	15	;	;	PUNCT
ejpam-3713	57	16	b	b	X
ejpam-3713	57	17	and	and	CCONJ
ejpam-3713	57	18	d	d	NOUN
ejpam-3713	57	19	denote	denote	VERB
ejpam-3713	57	20	the	the	DET
ejpam-3713	57	21	birth	birth	NOUN
ejpam-3713	57	22	rate	rate	NOUN
ejpam-3713	57	23	and	and	CCONJ
ejpam-3713	57	24	death	death	NOUN
ejpam-3713	57	25	rate	rate	NOUN
ejpam-3713	57	26	respectively	respectively	ADV
ejpam-3713	57	27	,	,	PUNCT
ejpam-3713	57	28	in	in	ADP
ejpam-3713	57	29	the	the	DET
ejpam-3713	57	30	time	time	NOUN
ejpam-3713	57	31	interval	interval	NOUN
ejpam-3713	57	32	[	[	X
ejpam-3713	57	33	t	t	PROPN
ejpam-3713	57	34	,	,	PUNCT
ejpam-3713	57	35	t	t	PROPN
ejpam-3713	57	36	+	+	CCONJ
ejpam-3713	57	37	∆t	∆t	PROPN
ejpam-3713	57	38	]	]	PUNCT
ejpam-3713	57	39	,	,	PUNCT
ejpam-3713	57	40	then	then	ADV
ejpam-3713	57	41	we	we	PRON
ejpam-3713	57	42	get	get	VERB
ejpam-3713	57	43	x(t	x(t	PROPN
ejpam-3713	57	44	+	+	CCONJ
ejpam-3713	57	45	∆t)−	∆t)−	PROPN
ejpam-3713	57	46	x(t	x(t	PROPN
ejpam-3713	57	47	)	)	PUNCT
ejpam-3713	57	48	=	=	SYM
ejpam-3713	58	1	bx(t)∆t−	bx(t)∆t−	NOUN
ejpam-3713	58	2	dx(t)∆t	dx(t)∆t	NOUN
ejpam-3713	58	3	.	.	PUNCT
ejpam-3713	59	1	⇒	⇒	PROPN
ejpam-3713	59	2	dx	dx	PROPN
ejpam-3713	60	1	dt	dt	X
ejpam-3713	61	1	=	=	SYM
ejpam-3713	61	2	lim	lim	PROPN
ejpam-3713	61	3	∆t→0	∆t→0	VERB
ejpam-3713	61	4	x(t	x(t	PROPN
ejpam-3713	61	5	+	+	NUM
ejpam-3713	61	6	∆t)−	∆t)−	PROPN
ejpam-3713	61	7	x(t	x(t	NOUN
ejpam-3713	61	8	)	)	PUNCT
ejpam-3713	61	9	∆t	∆t	PROPN
ejpam-3713	62	1	=	=	SYM
ejpam-3713	62	2	lim	lim	PROPN
ejpam-3713	62	3	∆t→0	∆t→0	PROPN
ejpam-3713	62	4	bx(t)∆t	bx(t)∆t	PROPN
ejpam-3713	62	5	∆t	∆t	PROPN
ejpam-3713	62	6	−	−	PROPN
ejpam-3713	62	7	lim	lim	NOUN
ejpam-3713	62	8	∆t→0	∆t→0	VERB
ejpam-3713	62	9	dx(t)∆t	dx(t)∆t	NOUN
ejpam-3713	62	10	∆t	∆t	PROPN
ejpam-3713	62	11	=	=	SYM
ejpam-3713	62	12	bx(t)−	bx(t)−	PROPN
ejpam-3713	62	13	dx(t	dx(t	NOUN
ejpam-3713	62	14	)	)	PUNCT
ejpam-3713	62	15	,	,	PUNCT
ejpam-3713	62	16	and	and	CCONJ
ejpam-3713	62	17	so	so	ADV
ejpam-3713	62	18	,	,	PUNCT
ejpam-3713	62	19	by	by	ADP
ejpam-3713	62	20	taking	take	VERB
ejpam-3713	62	21	r	r	NOUN
ejpam-3713	62	22	=	=	PUNCT
ejpam-3713	62	23	b−	b−	PROPN
ejpam-3713	62	24	d	d	PROPN
ejpam-3713	62	25	,	,	PUNCT
ejpam-3713	62	26	we	we	PRON
ejpam-3713	62	27	have	have	VERB
ejpam-3713	62	28	dx	dx	PROPN
ejpam-3713	62	29	dt	dt	NOUN
ejpam-3713	62	30	=	=	SYM
ejpam-3713	62	31	rx(t	rx(t	PROPN
ejpam-3713	62	32	)	)	PUNCT
ejpam-3713	62	33	.	.	PUNCT
ejpam-3713	63	1	(	(	PUNCT
ejpam-3713	63	2	1	1	X
ejpam-3713	63	3	)	)	PUNCT
ejpam-3713	63	4	the	the	DET
ejpam-3713	63	5	value	value	NOUN
ejpam-3713	63	6	of	of	ADP
ejpam-3713	63	7	parameter	parameter	NOUN
ejpam-3713	63	8	r	r	NOUN
ejpam-3713	63	9	as	as	ADP
ejpam-3713	63	10	intrinsic	intrinsic	ADJ
ejpam-3713	63	11	growth	growth	NOUN
ejpam-3713	63	12	rate	rate	NOUN
ejpam-3713	63	13	of	of	ADP
ejpam-3713	63	14	population	population	NOUN
ejpam-3713	63	15	can	can	AUX
ejpam-3713	63	16	be	be	AUX
ejpam-3713	63	17	positive	positive	ADJ
ejpam-3713	63	18	,	,	PUNCT
ejpam-3713	63	19	meaning	mean	VERB
ejpam-3713	63	20	the	the	DET
ejpam-3713	63	21	population	population	NOUN
ejpam-3713	63	22	is	be	AUX
ejpam-3713	63	23	increasing	increase	VERB
ejpam-3713	63	24	in	in	ADP
ejpam-3713	63	25	size	size	NOUN
ejpam-3713	63	26	(	(	PUNCT
ejpam-3713	63	27	the	the	DET
ejpam-3713	63	28	rate	rate	NOUN
ejpam-3713	63	29	of	of	ADP
ejpam-3713	63	30	change	change	NOUN
ejpam-3713	63	31	is	be	AUX
ejpam-3713	63	32	positive	positive	ADJ
ejpam-3713	63	33	)	)	PUNCT
ejpam-3713	63	34	;	;	PUNCT
ejpam-3713	63	35	or	or	CCONJ
ejpam-3713	63	36	negative	negative	ADJ
ejpam-3713	63	37	,	,	PUNCT
ejpam-3713	63	38	meaning	mean	VERB
ejpam-3713	63	39	the	the	DET
ejpam-3713	63	40	population	population	NOUN
ejpam-3713	63	41	is	be	AUX
ejpam-3713	63	42	decreasing	decrease	VERB
ejpam-3713	63	43	in	in	ADP
ejpam-3713	63	44	size	size	NOUN
ejpam-3713	63	45	;	;	PUNCT
ejpam-3713	63	46	or	or	CCONJ
ejpam-3713	63	47	zero	zero	NUM
ejpam-3713	63	48	,	,	PUNCT
ejpam-3713	63	49	in	in	ADP
ejpam-3713	63	50	which	which	DET
ejpam-3713	63	51	case	case	NOUN
ejpam-3713	63	52	the	the	DET
ejpam-3713	63	53	population	population	NOUN
ejpam-3713	63	54	size	size	NOUN
ejpam-3713	63	55	is	be	AUX
ejpam-3713	63	56	unchanging	unchanging	ADJ
ejpam-3713	63	57	i.e.	i.e.	X
ejpam-3713	63	58	the	the	DET
ejpam-3713	63	59	population	population	NOUN
ejpam-3713	63	60	is	be	AUX
ejpam-3713	63	61	constant	constant	ADJ
ejpam-3713	63	62	.	.	PUNCT
ejpam-3713	64	1	we	we	PRON
ejpam-3713	64	2	now	now	ADV
ejpam-3713	64	3	present	present	VERB
ejpam-3713	64	4	an	an	DET
ejpam-3713	64	5	example	example	NOUN
ejpam-3713	64	6	of	of	ADP
ejpam-3713	64	7	exponential	exponential	ADJ
ejpam-3713	64	8	growth	growth	NOUN
ejpam-3713	64	9	for	for	ADP
ejpam-3713	64	10	bacteria	bacteria	NOUN
ejpam-3713	64	11	population	population	NOUN
ejpam-3713	64	12	in	in	ADP
ejpam-3713	64	13	the	the	DET
ejpam-3713	64	14	following	following	NOUN
ejpam-3713	64	15	:	:	PUNCT
ejpam-3713	64	16	m.h	m.h	PROPN
ejpam-3713	64	17	.	.	PROPN
ejpam-3713	64	18	r.	r.	PROPN
ejpam-3713	64	19	doust	doust	PROPN
ejpam-3713	64	20	,	,	PUNCT
ejpam-3713	64	21	v.	v.	ADP
ejpam-3713	64	22	lokesha	lokesha	PROPN
ejpam-3713	64	23	,	,	PUNCT
ejpam-3713	64	24	a.	a.	NOUN
ejpam-3713	64	25	ghasemabadi	ghasemabadi	NOUN
ejpam-3713	64	26	/	/	SYM
ejpam-3713	64	27	eur	eur	PROPN
ejpam-3713	64	28	.	.	PUNCT
ejpam-3713	65	1	j.	j.	PROPN
ejpam-3713	65	2	pure	pure	PROPN
ejpam-3713	65	3	appl	appl	PROPN
ejpam-3713	65	4	.	.	PROPN
ejpam-3713	65	5	math	math	PROPN
ejpam-3713	65	6	,	,	PUNCT
ejpam-3713	65	7	13	13	NUM
ejpam-3713	65	8	(	(	PUNCT
ejpam-3713	65	9	5	5	NUM
ejpam-3713	65	10	)	)	PUNCT
ejpam-3713	65	11	(	(	PUNCT
ejpam-3713	65	12	2020	2020	NUM
ejpam-3713	65	13	)	)	PUNCT
ejpam-3713	65	14	,	,	PUNCT
ejpam-3713	65	15	1176	1176	NUM
ejpam-3713	65	16	-	-	SYM
ejpam-3713	65	17	1198	1198	NUM
ejpam-3713	65	18	1179	1179	NUM
ejpam-3713	65	19	example	example	NOUN
ejpam-3713	65	20	1	1	NUM
ejpam-3713	65	21	.	.	PUNCT
ejpam-3713	66	1	the	the	DET
ejpam-3713	66	2	famous	famous	ADJ
ejpam-3713	66	3	example	example	NOUN
ejpam-3713	66	4	of	of	ADP
ejpam-3713	66	5	exponential	exponential	ADJ
ejpam-3713	66	6	growth	growth	NOUN
ejpam-3713	66	7	in	in	ADP
ejpam-3713	66	8	organisms	organism	NOUN
ejpam-3713	66	9	indeed	indeed	ADV
ejpam-3713	66	10	is	be	AUX
ejpam-3713	66	11	seen	see	VERB
ejpam-3713	66	12	in	in	ADP
ejpam-3713	66	13	bacteria	bacteria	NOUN
ejpam-3713	66	14	.	.	PUNCT
ejpam-3713	67	1	bacteria	bacteria	NOUN
ejpam-3713	67	2	are	be	AUX
ejpam-3713	67	3	prokaryotes	prokaryote	NOUN
ejpam-3713	67	4	that	that	PRON
ejpam-3713	67	5	reproduce	reproduce	VERB
ejpam-3713	67	6	largely	largely	ADV
ejpam-3713	67	7	by	by	ADP
ejpam-3713	67	8	binary	binary	ADJ
ejpam-3713	67	9	fission	fission	NOUN
ejpam-3713	67	10	.	.	PUNCT
ejpam-3713	68	1	this	this	DET
ejpam-3713	68	2	division	division	NOUN
ejpam-3713	68	3	takes	take	VERB
ejpam-3713	68	4	about	about	ADV
ejpam-3713	68	5	an	an	PRON
ejpam-3713	68	6	hour	hour	NOUN
ejpam-3713	68	7	for	for	ADP
ejpam-3713	68	8	many	many	ADJ
ejpam-3713	68	9	bacterial	bacterial	ADJ
ejpam-3713	68	10	species	specie	NOUN
ejpam-3713	68	11	.	.	PUNCT
ejpam-3713	69	1	if	if	SCONJ
ejpam-3713	69	2	1000	1000	NUM
ejpam-3713	69	3	bacteria	bacteria	NOUN
ejpam-3713	69	4	are	be	AUX
ejpam-3713	69	5	placed	place	VERB
ejpam-3713	69	6	in	in	ADP
ejpam-3713	69	7	a	a	DET
ejpam-3713	69	8	large	large	ADJ
ejpam-3713	69	9	flask	flask	NOUN
ejpam-3713	69	10	with	with	ADP
ejpam-3713	69	11	an	an	DET
ejpam-3713	69	12	abundant	abundant	ADJ
ejpam-3713	69	13	supply	supply	NOUN
ejpam-3713	69	14	of	of	ADP
ejpam-3713	69	15	nutrients	nutrient	NOUN
ejpam-3713	69	16	,	,	PUNCT
ejpam-3713	69	17	the	the	DET
ejpam-3713	69	18	number	number	NOUN
ejpam-3713	69	19	of	of	ADP
ejpam-3713	69	20	bacteria	bacteria	NOUN
ejpam-3713	69	21	will	will	AUX
ejpam-3713	69	22	have	have	AUX
ejpam-3713	69	23	doubled	double	VERB
ejpam-3713	69	24	from	from	ADP
ejpam-3713	69	25	1000	1000	NUM
ejpam-3713	69	26	to	to	ADP
ejpam-3713	69	27	2000	2000	NUM
ejpam-3713	69	28	after	after	ADP
ejpam-3713	69	29	just	just	ADV
ejpam-3713	69	30	an	an	DET
ejpam-3713	69	31	hour	hour	NOUN
ejpam-3713	69	32	.	.	PUNCT
ejpam-3713	70	1	in	in	ADP
ejpam-3713	70	2	another	another	DET
ejpam-3713	70	3	hour	hour	NOUN
ejpam-3713	70	4	,	,	PUNCT
ejpam-3713	70	5	each	each	PRON
ejpam-3713	70	6	of	of	ADP
ejpam-3713	70	7	the	the	DET
ejpam-3713	70	8	2000	2000	NUM
ejpam-3713	70	9	bacteria	bacteria	NOUN
ejpam-3713	70	10	will	will	AUX
ejpam-3713	70	11	divide	divide	VERB
ejpam-3713	70	12	,	,	PUNCT
ejpam-3713	70	13	producing	produce	VERB
ejpam-3713	70	14	4000	4000	NUM
ejpam-3713	70	15	bacteria	bacteria	NOUN
ejpam-3713	70	16	.	.	PUNCT
ejpam-3713	71	1	after	after	ADP
ejpam-3713	71	2	the	the	DET
ejpam-3713	71	3	third	third	ADJ
ejpam-3713	71	4	hour	hour	NOUN
ejpam-3713	71	5	,	,	PUNCT
ejpam-3713	71	6	there	there	PRON
ejpam-3713	71	7	should	should	AUX
ejpam-3713	71	8	be	be	AUX
ejpam-3713	71	9	8000	8000	NUM
ejpam-3713	71	10	bacteria	bacteria	NOUN
ejpam-3713	71	11	in	in	ADP
ejpam-3713	71	12	the	the	DET
ejpam-3713	71	13	flask	flask	NOUN
ejpam-3713	71	14	.	.	PUNCT
ejpam-3713	72	1	the	the	DET
ejpam-3713	72	2	important	important	ADJ
ejpam-3713	72	3	concept	concept	NOUN
ejpam-3713	72	4	of	of	ADP
ejpam-3713	72	5	exponential	exponential	ADJ
ejpam-3713	72	6	growth	growth	NOUN
ejpam-3713	72	7	is	be	AUX
ejpam-3713	72	8	that	that	SCONJ
ejpam-3713	72	9	the	the	DET
ejpam-3713	72	10	growth	growth	NOUN
ejpam-3713	72	11	rate	rate	NOUN
ejpam-3713	72	12	-	-	PUNCT
ejpam-3713	72	13	the	the	DET
ejpam-3713	72	14	number	number	NOUN
ejpam-3713	72	15	of	of	ADP
ejpam-3713	72	16	organisms	organism	NOUN
ejpam-3713	72	17	added	add	VERB
ejpam-3713	72	18	in	in	ADP
ejpam-3713	72	19	each	each	DET
ejpam-3713	72	20	reproductive	reproductive	ADJ
ejpam-3713	72	21	generation	generation	NOUN
ejpam-3713	72	22	-	-	PUNCT
ejpam-3713	72	23	is	be	AUX
ejpam-3713	72	24	itself	itself	PRON
ejpam-3713	72	25	increasing	increase	VERB
ejpam-3713	72	26	;	;	PUNCT
ejpam-3713	72	27	that	that	ADV
ejpam-3713	72	28	is	is	ADV
ejpam-3713	72	29	,	,	PUNCT
ejpam-3713	72	30	the	the	DET
ejpam-3713	72	31	population	population	NOUN
ejpam-3713	72	32	size	size	NOUN
ejpam-3713	72	33	is	be	AUX
ejpam-3713	72	34	increasing	increase	VERB
ejpam-3713	72	35	at	at	ADP
ejpam-3713	72	36	a	a	DET
ejpam-3713	72	37	greater	great	ADJ
ejpam-3713	72	38	and	and	CCONJ
ejpam-3713	72	39	greater	great	ADJ
ejpam-3713	72	40	rate	rate	NOUN
ejpam-3713	72	41	.	.	PUNCT
ejpam-3713	73	1	after	after	ADP
ejpam-3713	73	2	24	24	NUM
ejpam-3713	73	3	of	of	ADP
ejpam-3713	73	4	these	these	DET
ejpam-3713	73	5	cycles	cycle	NOUN
ejpam-3713	73	6	,	,	PUNCT
ejpam-3713	73	7	the	the	DET
ejpam-3713	73	8	population	population	NOUN
ejpam-3713	73	9	would	would	AUX
ejpam-3713	73	10	have	have	AUX
ejpam-3713	73	11	increased	increase	VERB
ejpam-3713	73	12	from	from	ADP
ejpam-3713	73	13	1000	1000	NUM
ejpam-3713	73	14	to	to	ADP
ejpam-3713	73	15	more	more	ADJ
ejpam-3713	73	16	than	than	ADP
ejpam-3713	73	17	16	16	NUM
ejpam-3713	73	18	billion	billion	NUM
ejpam-3713	73	19	bacteria	bacteria	NOUN
ejpam-3713	73	20	.	.	PUNCT
ejpam-3713	74	1	when	when	SCONJ
ejpam-3713	74	2	the	the	DET
ejpam-3713	74	3	population	population	NOUN
ejpam-3713	74	4	size	size	NOUN
ejpam-3713	74	5	x(t	x(t	PROPN
ejpam-3713	74	6	)	)	PUNCT
ejpam-3713	74	7	is	be	AUX
ejpam-3713	74	8	plotted	plot	VERB
ejpam-3713	74	9	over	over	ADP
ejpam-3713	74	10	time	time	NOUN
ejpam-3713	74	11	,	,	PUNCT
ejpam-3713	74	12	a	a	DET
ejpam-3713	74	13	j	j	NOUN
ejpam-3713	74	14	-	-	PUNCT
ejpam-3713	74	15	shaped	shape	VERB
ejpam-3713	74	16	growth	growth	NOUN
ejpam-3713	74	17	curve	curve	NOUN
ejpam-3713	74	18	is	be	AUX
ejpam-3713	74	19	produced	produce	VERB
ejpam-3713	74	20	.	.	PUNCT
ejpam-3713	75	1	the	the	DET
ejpam-3713	75	2	bacteria	bacteria	NOUN
ejpam-3713	75	3	-	-	PUNCT
ejpam-3713	75	4	in	in	ADP
ejpam-3713	75	5	-	-	PUNCT
ejpam-3713	75	6	a	a	DET
ejpam-3713	75	7	-	-	PUNCT
ejpam-3713	75	8	flask	flask	NOUN
ejpam-3713	75	9	example	example	NOUN
ejpam-3713	75	10	indeed	indeed	ADV
ejpam-3713	75	11	is	be	AUX
ejpam-3713	75	12	not	not	PART
ejpam-3713	75	13	truly	truly	ADV
ejpam-3713	75	14	representative	representative	ADJ
ejpam-3713	75	15	of	of	ADP
ejpam-3713	75	16	the	the	DET
ejpam-3713	75	17	real	real	ADJ
ejpam-3713	75	18	world	world	NOUN
ejpam-3713	75	19	where	where	SCONJ
ejpam-3713	75	20	resources	resource	NOUN
ejpam-3713	75	21	are	be	AUX
ejpam-3713	75	22	usually	usually	ADV
ejpam-3713	75	23	limited	limited	ADJ
ejpam-3713	75	24	.	.	PUNCT
ejpam-3713	76	1	however	however	ADV
ejpam-3713	76	2	,	,	PUNCT
ejpam-3713	76	3	when	when	SCONJ
ejpam-3713	76	4	a	a	DET
ejpam-3713	76	5	species	species	NOUN
ejpam-3713	76	6	is	be	AUX
ejpam-3713	76	7	introduced	introduce	VERB
ejpam-3713	76	8	into	into	ADP
ejpam-3713	76	9	a	a	DET
ejpam-3713	76	10	new	new	ADJ
ejpam-3713	76	11	habitat	habitat	NOUN
ejpam-3713	76	12	that	that	SCONJ
ejpam-3713	76	13	it	it	PRON
ejpam-3713	76	14	finds	find	VERB
ejpam-3713	76	15	suitable	suitable	ADJ
ejpam-3713	76	16	,	,	PUNCT
ejpam-3713	76	17	it	it	PRON
ejpam-3713	76	18	may	may	AUX
ejpam-3713	76	19	show	show	VERB
ejpam-3713	76	20	exponential	exponential	ADJ
ejpam-3713	76	21	growth	growth	NOUN
ejpam-3713	76	22	for	for	ADP
ejpam-3713	76	23	a	a	DET
ejpam-3713	76	24	while	while	NOUN
ejpam-3713	76	25	.	.	PUNCT
ejpam-3713	77	1	in	in	ADP
ejpam-3713	77	2	the	the	DET
ejpam-3713	77	3	case	case	NOUN
ejpam-3713	77	4	of	of	ADP
ejpam-3713	77	5	the	the	DET
ejpam-3713	77	6	bacteria	bacteria	NOUN
ejpam-3713	77	7	in	in	ADP
ejpam-3713	77	8	the	the	DET
ejpam-3713	77	9	flask	flask	NOUN
ejpam-3713	77	10	,	,	PUNCT
ejpam-3713	77	11	some	some	DET
ejpam-3713	77	12	bacteria	bacteria	NOUN
ejpam-3713	77	13	will	will	AUX
ejpam-3713	77	14	die	die	VERB
ejpam-3713	77	15	during	during	ADP
ejpam-3713	77	16	the	the	DET
ejpam-3713	77	17	experiment	experiment	NOUN
ejpam-3713	77	18	and	and	CCONJ
ejpam-3713	77	19	thus	thus	ADV
ejpam-3713	77	20	not	not	PART
ejpam-3713	77	21	reproduce	reproduce	VERB
ejpam-3713	77	22	;	;	PUNCT
ejpam-3713	77	23	therefore	therefore	ADV
ejpam-3713	77	24	,	,	PUNCT
ejpam-3713	77	25	the	the	DET
ejpam-3713	77	26	growth	growth	NOUN
ejpam-3713	77	27	rate	rate	NOUN
ejpam-3713	77	28	is	be	AUX
ejpam-3713	77	29	lowered	lower	VERB
ejpam-3713	77	30	from	from	ADP
ejpam-3713	77	31	a	a	DET
ejpam-3713	77	32	maximal	maximal	ADJ
ejpam-3713	77	33	rate	rate	NOUN
ejpam-3713	77	34	in	in	ADP
ejpam-3713	77	35	which	which	PRON
ejpam-3713	77	36	there	there	PRON
ejpam-3713	77	37	is	be	VERB
ejpam-3713	77	38	no	no	DET
ejpam-3713	77	39	mortality	mortality	NOUN
ejpam-3713	77	40	.	.	PUNCT
ejpam-3713	78	1	the	the	DET
ejpam-3713	78	2	growth	growth	NOUN
ejpam-3713	78	3	rate	rate	NOUN
ejpam-3713	78	4	of	of	ADP
ejpam-3713	78	5	a	a	DET
ejpam-3713	78	6	population	population	NOUN
ejpam-3713	78	7	is	be	AUX
ejpam-3713	78	8	largely	largely	ADV
ejpam-3713	78	9	determined	determine	VERB
ejpam-3713	78	10	by	by	ADP
ejpam-3713	78	11	subtracting	subtract	VERB
ejpam-3713	78	12	the	the	DET
ejpam-3713	78	13	death	death	NOUN
ejpam-3713	78	14	rate	rate	NOUN
ejpam-3713	78	15	(	(	PUNCT
ejpam-3713	78	16	d	d	NOUN
ejpam-3713	78	17	)	)	PUNCT
ejpam-3713	78	18	from	from	ADP
ejpam-3713	78	19	the	the	DET
ejpam-3713	78	20	birth	birth	NOUN
ejpam-3713	78	21	rate	rate	NOUN
ejpam-3713	78	22	(	(	PUNCT
ejpam-3713	78	23	b	b	NOUN
ejpam-3713	78	24	)	)	PUNCT
ejpam-3713	78	25	.	.	PUNCT
ejpam-3713	79	1	the	the	DET
ejpam-3713	79	2	growth	growth	NOUN
ejpam-3713	79	3	rate	rate	NOUN
ejpam-3713	79	4	can	can	AUX
ejpam-3713	79	5	be	be	AUX
ejpam-3713	79	6	expressed	express	VERB
ejpam-3713	79	7	in	in	ADP
ejpam-3713	79	8	a	a	DET
ejpam-3713	79	9	simple	simple	ADJ
ejpam-3713	79	10	equation	equation	NOUN
ejpam-3713	79	11	that	that	PRON
ejpam-3713	79	12	combines	combine	VERB
ejpam-3713	79	13	the	the	DET
ejpam-3713	79	14	birth	birth	NOUN
ejpam-3713	79	15	and	and	CCONJ
ejpam-3713	79	16	death	death	NOUN
ejpam-3713	79	17	rates	rate	NOUN
ejpam-3713	79	18	into	into	ADP
ejpam-3713	79	19	a	a	DET
ejpam-3713	79	20	single	single	ADJ
ejpam-3713	79	21	factor	factor	NOUN
ejpam-3713	79	22	r	r	NOUN
ejpam-3713	79	23	which	which	PRON
ejpam-3713	79	24	is	be	AUX
ejpam-3713	79	25	shown	show	VERB
ejpam-3713	79	26	in	in	ADP
ejpam-3713	79	27	the	the	DET
ejpam-3713	79	28	previous	previous	ADJ
ejpam-3713	79	29	formula	formula	NOUN
ejpam-3713	79	30	.	.	PUNCT
ejpam-3713	80	1	it	it	PRON
ejpam-3713	80	2	is	be	AUX
ejpam-3713	80	3	clear	clear	ADJ
ejpam-3713	80	4	that	that	SCONJ
ejpam-3713	80	5	malthus	malthus	PROPN
ejpam-3713	80	6	’s	’s	PART
ejpam-3713	80	7	model	model	NOUN
ejpam-3713	80	8	is	be	AUX
ejpam-3713	80	9	applicable	applicable	ADJ
ejpam-3713	80	10	only	only	ADV
ejpam-3713	80	11	if	if	SCONJ
ejpam-3713	80	12	the	the	DET
ejpam-3713	80	13	number	number	NOUN
ejpam-3713	80	14	of	of	ADP
ejpam-3713	80	15	species	specie	NOUN
ejpam-3713	80	16	is	be	AUX
ejpam-3713	80	17	small	small	ADJ
ejpam-3713	80	18	.	.	PUNCT
ejpam-3713	81	1	otherwise	otherwise	ADV
ejpam-3713	81	2	,	,	PUNCT
ejpam-3713	81	3	the	the	DET
ejpam-3713	81	4	limited	limited	ADJ
ejpam-3713	81	5	resources	resource	NOUN
ejpam-3713	81	6	such	such	ADJ
ejpam-3713	81	7	as	as	ADP
ejpam-3713	81	8	food	food	NOUN
ejpam-3713	81	9	and	and	CCONJ
ejpam-3713	81	10	place	place	NOUN
ejpam-3713	81	11	limit	limit	VERB
ejpam-3713	81	12	the	the	DET
ejpam-3713	81	13	growth	growth	NOUN
ejpam-3713	81	14	of	of	ADP
ejpam-3713	81	15	population	population	NOUN
ejpam-3713	81	16	.	.	PUNCT
ejpam-3713	82	1	the	the	DET
ejpam-3713	82	2	above	above	ADJ
ejpam-3713	82	3	i.v.p	i.v.p	NOUN
ejpam-3713	82	4	.	.	PUNCT
ejpam-3713	82	5	is	be	AUX
ejpam-3713	82	6	valid	valid	ADJ
ejpam-3713	82	7	for	for	ADP
ejpam-3713	82	8	a	a	DET
ejpam-3713	82	9	short	short	ADJ
ejpam-3713	82	10	period	period	NOUN
ejpam-3713	82	11	and	and	CCONJ
ejpam-3713	82	12	ca	can	AUX
ejpam-3713	82	13	n’t	not	PART
ejpam-3713	82	14	go	go	VERB
ejpam-3713	82	15	on	on	ADP
ejpam-3713	82	16	forever	forever	ADV
ejpam-3713	82	17	.	.	PUNCT
ejpam-3713	83	1	however	however	ADV
ejpam-3713	83	2	,	,	PUNCT
ejpam-3713	83	3	the	the	DET
ejpam-3713	83	4	exponential	exponential	ADJ
ejpam-3713	83	5	growth	growth	NOUN
ejpam-3713	83	6	applications	application	NOUN
ejpam-3713	83	7	in	in	ADP
ejpam-3713	83	8	the	the	DET
ejpam-3713	83	9	nature	nature	NOUN
ejpam-3713	83	10	is	be	AUX
ejpam-3713	83	11	so	so	ADV
ejpam-3713	83	12	much	much	ADJ
ejpam-3713	83	13	.	.	PUNCT
ejpam-3713	84	1	indeed	indeed	ADV
ejpam-3713	84	2	,	,	PUNCT
ejpam-3713	84	3	there	there	PRON
ejpam-3713	84	4	is	be	VERB
ejpam-3713	84	5	no	no	DET
ejpam-3713	84	6	an	an	DET
ejpam-3713	84	7	area	area	NOUN
ejpam-3713	84	8	of	of	ADP
ejpam-3713	84	9	science	science	NOUN
ejpam-3713	84	10	that	that	PRON
ejpam-3713	84	11	no	no	DET
ejpam-3713	84	12	need	need	NOUN
ejpam-3713	84	13	to	to	PART
ejpam-3713	84	14	help	help	VERB
ejpam-3713	84	15	of	of	ADP
ejpam-3713	84	16	exponential	exponential	ADJ
ejpam-3713	84	17	growth	growth	NOUN
ejpam-3713	84	18	.	.	PUNCT
ejpam-3713	85	1	some	some	PRON
ejpam-3713	85	2	of	of	ADP
ejpam-3713	85	3	them	they	PRON
ejpam-3713	85	4	are	be	AUX
ejpam-3713	85	5	microbiology	microbiology	NOUN
ejpam-3713	85	6	(	(	PUNCT
ejpam-3713	85	7	growth	growth	NOUN
ejpam-3713	85	8	of	of	ADP
ejpam-3713	85	9	bacteria	bacteria	NOUN
ejpam-3713	85	10	)	)	PUNCT
ejpam-3713	85	11	,	,	PUNCT
ejpam-3713	85	12	conservation	conservation	NOUN
ejpam-3713	85	13	biology	biology	NOUN
ejpam-3713	85	14	(	(	PUNCT
ejpam-3713	85	15	restoration	restoration	NOUN
ejpam-3713	85	16	of	of	ADP
ejpam-3713	85	17	disturbed	disturbed	ADJ
ejpam-3713	85	18	populations	population	NOUN
ejpam-3713	85	19	)	)	PUNCT
ejpam-3713	85	20	,	,	PUNCT
ejpam-3713	85	21	insect	insect	NOUN
ejpam-3713	85	22	rearing	rearing	NOUN
ejpam-3713	85	23	(	(	PUNCT
ejpam-3713	85	24	prediction	prediction	NOUN
ejpam-3713	85	25	of	of	ADP
ejpam-3713	85	26	yield	yield	NOUN
ejpam-3713	85	27	)	)	PUNCT
ejpam-3713	85	28	,	,	PUNCT
ejpam-3713	85	29	plant	plant	NOUN
ejpam-3713	85	30	or	or	CCONJ
ejpam-3713	85	31	insect	insect	NOUN
ejpam-3713	85	32	quarantine	quarantine	NOUN
ejpam-3713	85	33	(	(	PUNCT
ejpam-3713	85	34	population	population	NOUN
ejpam-3713	85	35	growth	growth	NOUN
ejpam-3713	85	36	of	of	ADP
ejpam-3713	85	37	introduced	introduce	VERB
ejpam-3713	85	38	species	specie	NOUN
ejpam-3713	85	39	)	)	PUNCT
ejpam-3713	85	40	,	,	PUNCT
ejpam-3713	85	41	fishery	fishery	NOUN
ejpam-3713	85	42	(	(	PUNCT
ejpam-3713	85	43	prediction	prediction	NOUN
ejpam-3713	85	44	of	of	ADP
ejpam-3713	85	45	fish	fish	NOUN
ejpam-3713	85	46	dynamics	dynamic	NOUN
ejpam-3713	85	47	)	)	PUNCT
ejpam-3713	85	48	,	,	PUNCT
ejpam-3713	85	49	biochemical(radioactivity	biochemical(radioactivity	NOUN
ejpam-3713	85	50	)	)	PUNCT
ejpam-3713	85	51	.	.	PUNCT
ejpam-3713	86	1	2	2	X
ejpam-3713	86	2	.	.	X
ejpam-3713	86	3	modeling	modeling	NOUN
ejpam-3713	86	4	and	and	CCONJ
ejpam-3713	86	5	discussion	discussion	NOUN
ejpam-3713	86	6	we	we	PRON
ejpam-3713	86	7	now	now	ADV
ejpam-3713	86	8	in	in	ADP
ejpam-3713	86	9	a	a	DET
ejpam-3713	86	10	position	position	NOUN
ejpam-3713	86	11	to	to	PART
ejpam-3713	86	12	construct	construct	VERB
ejpam-3713	86	13	and	and	CCONJ
ejpam-3713	86	14	study	study	VERB
ejpam-3713	86	15	some	some	DET
ejpam-3713	86	16	ecological	ecological	ADJ
ejpam-3713	86	17	i.v.ps	i.v.ps	NOUN
ejpam-3713	86	18	.	.	PUNCT
ejpam-3713	87	1	of	of	ADP
ejpam-3713	87	2	single	single	ADJ
ejpam-3713	87	3	species	specie	NOUN
ejpam-3713	87	4	models	model	NOUN
ejpam-3713	87	5	based	base	VERB
ejpam-3713	87	6	on	on	ADP
ejpam-3713	87	7	p.	p.	NOUN
ejpam-3713	87	8	verhulst(1838	verhulst(1838	NOUN
ejpam-3713	87	9	-	-	PUNCT
ejpam-3713	87	10	1845	1845	NUM
ejpam-3713	87	11	)	)	PUNCT
ejpam-3713	87	12	idea	idea	NOUN
ejpam-3713	87	13	which	which	PRON
ejpam-3713	87	14	is	be	AUX
ejpam-3713	87	15	published	publish	VERB
ejpam-3713	87	16	for	for	ADP
ejpam-3713	87	17	human	human	ADJ
ejpam-3713	87	18	population	population	NOUN
ejpam-3713	87	19	growth	growth	NOUN
ejpam-3713	87	20	rate	rate	NOUN
ejpam-3713	88	1	[	[	X
ejpam-3713	88	2	12	12	NUM
ejpam-3713	88	3	]	]	PUNCT
ejpam-3713	88	4	.	.	PUNCT
ejpam-3713	89	1	the	the	DET
ejpam-3713	89	2	larger	large	ADJ
ejpam-3713	89	3	population	population	NOUN
ejpam-3713	89	4	means	mean	VERB
ejpam-3713	89	5	fewer	few	ADJ
ejpam-3713	89	6	resources	resource	NOUN
ejpam-3713	89	7	such	such	ADJ
ejpam-3713	89	8	as	as	ADP
ejpam-3713	89	9	food	food	NOUN
ejpam-3713	89	10	,	,	PUNCT
ejpam-3713	89	11	place	place	NOUN
ejpam-3713	89	12	etc	etc	X
ejpam-3713	89	13	.	.	X
ejpam-3713	89	14	which	which	PRON
ejpam-3713	89	15	are	be	AUX
ejpam-3713	89	16	limited	limited	ADJ
ejpam-3713	89	17	.	.	PUNCT
ejpam-3713	90	1	and	and	CCONJ
ejpam-3713	90	2	so	so	ADV
ejpam-3713	90	3	,	,	PUNCT
ejpam-3713	90	4	this	this	PRON
ejpam-3713	90	5	implies	imply	VERB
ejpam-3713	90	6	a	a	DET
ejpam-3713	90	7	smaller	small	ADJ
ejpam-3713	90	8	rate	rate	NOUN
ejpam-3713	90	9	of	of	ADP
ejpam-3713	90	10	growth	growth	NOUN
ejpam-3713	90	11	rate	rate	NOUN
ejpam-3713	90	12	.	.	PUNCT
ejpam-3713	91	1	in	in	ADP
ejpam-3713	91	2	the	the	DET
ejpam-3713	91	3	simplest	simple	ADJ
ejpam-3713	91	4	case	case	NOUN
ejpam-3713	91	5	,	,	PUNCT
ejpam-3713	91	6	he	he	PRON
ejpam-3713	91	7	considered	consider	VERB
ejpam-3713	91	8	that	that	SCONJ
ejpam-3713	91	9	the	the	DET
ejpam-3713	91	10	rate	rate	NOUN
ejpam-3713	91	11	decreases	decrease	VERB
ejpam-3713	91	12	linearly	linearly	ADV
ejpam-3713	91	13	as	as	ADP
ejpam-3713	91	14	a	a	DET
ejpam-3713	91	15	function	function	NOUN
ejpam-3713	91	16	of	of	ADP
ejpam-3713	91	17	x.	x.	NOUN
ejpam-3713	91	18	2.1	2.1	NUM
ejpam-3713	91	19	.	.	PUNCT
ejpam-3713	92	1	the	the	DET
ejpam-3713	92	2	exponential	exponential	ADJ
ejpam-3713	92	3	model	model	NOUN
ejpam-3713	92	4	;	;	PUNCT
ejpam-3713	92	5	having	have	VERB
ejpam-3713	92	6	constant	constant	ADJ
ejpam-3713	92	7	harvesting	harvesting	NOUN
ejpam-3713	92	8	factor	factor	NOUN
ejpam-3713	92	9	having	having	AUX
ejpam-3713	92	10	considered	consider	VERB
ejpam-3713	92	11	x(0	x(0	PRON
ejpam-3713	92	12	)	)	PUNCT
ejpam-3713	93	1	=	=	PUNCT
ejpam-3713	93	2	x0	x0	PROPN
ejpam-3713	93	3	initial	initial	ADJ
ejpam-3713	93	4	population	population	NOUN
ejpam-3713	93	5	for	for	ADP
ejpam-3713	93	6	equation	equation	NOUN
ejpam-3713	93	7	(	(	PUNCT
ejpam-3713	93	8	1	1	NUM
ejpam-3713	93	9	)	)	PUNCT
ejpam-3713	93	10	,	,	PUNCT
ejpam-3713	93	11	we	we	PRON
ejpam-3713	93	12	obtain	obtain	VERB
ejpam-3713	93	13	the	the	DET
ejpam-3713	93	14	following	follow	VERB
ejpam-3713	93	15	the	the	DET
ejpam-3713	93	16	initial	initial	ADJ
ejpam-3713	93	17	value	value	NOUN
ejpam-3713	93	18	problem	problem	NOUN
ejpam-3713	93	19	named	name	VERB
ejpam-3713	93	20	i.v.p	i.v.p	NOUN
ejpam-3713	93	21	.	.	PUNCT
ejpam-3713	94	1	:	:	PUNCT
ejpam-3713	94	2	{	{	PUNCT
ejpam-3713	94	3	dx	dx	X
ejpam-3713	94	4	dt	dt	X
ejpam-3713	94	5	=	=	SYM
ejpam-3713	94	6	rx	rx	VERB
ejpam-3713	94	7	x(0	x(0	PROPN
ejpam-3713	94	8	)	)	PUNCT
ejpam-3713	95	1	=	=	PUNCT
ejpam-3713	95	2	x0	x0	PROPN
ejpam-3713	95	3	(	(	PUNCT
ejpam-3713	95	4	2	2	X
ejpam-3713	95	5	)	)	PUNCT
ejpam-3713	95	6	m.h	m.h	PROPN
ejpam-3713	95	7	.	.	PROPN
ejpam-3713	95	8	r.	r.	PROPN
ejpam-3713	95	9	doust	doust	PROPN
ejpam-3713	95	10	,	,	PUNCT
ejpam-3713	95	11	v.	v.	ADP
ejpam-3713	95	12	lokesha	lokesha	PROPN
ejpam-3713	95	13	,	,	PUNCT
ejpam-3713	95	14	a.	a.	NOUN
ejpam-3713	95	15	ghasemabadi	ghasemabadi	NOUN
ejpam-3713	95	16	/	/	SYM
ejpam-3713	95	17	eur	eur	PROPN
ejpam-3713	95	18	.	.	PUNCT
ejpam-3713	96	1	j.	j.	PROPN
ejpam-3713	96	2	pure	pure	PROPN
ejpam-3713	96	3	appl	appl	PROPN
ejpam-3713	96	4	.	.	PROPN
ejpam-3713	96	5	math	math	PROPN
ejpam-3713	96	6	,	,	PUNCT
ejpam-3713	96	7	13	13	NUM
ejpam-3713	96	8	(	(	PUNCT
ejpam-3713	96	9	5	5	NUM
ejpam-3713	96	10	)	)	PUNCT
ejpam-3713	96	11	(	(	PUNCT
ejpam-3713	96	12	2020	2020	NUM
ejpam-3713	96	13	)	)	PUNCT
ejpam-3713	96	14	,	,	PUNCT
ejpam-3713	96	15	1176	1176	NUM
ejpam-3713	96	16	-	-	SYM
ejpam-3713	96	17	1198	1198	NUM
ejpam-3713	96	18	1180	1180	NUM
ejpam-3713	96	19	where	where	SCONJ
ejpam-3713	96	20	its	its	PRON
ejpam-3713	96	21	solution	solution	NOUN
ejpam-3713	96	22	as	as	SCONJ
ejpam-3713	96	23	follows	follow	VERB
ejpam-3713	96	24	:	:	PUNCT
ejpam-3713	96	25	x(t	x(t	PROPN
ejpam-3713	96	26	)	)	PUNCT
ejpam-3713	96	27	=	=	PUNCT
ejpam-3713	96	28	x0exp(rt	x0exp(rt	NUM
ejpam-3713	96	29	)	)	PUNCT
ejpam-3713	96	30	.	.	PUNCT
ejpam-3713	97	1	(	(	PUNCT
ejpam-3713	97	2	3	3	X
ejpam-3713	97	3	)	)	PUNCT
ejpam-3713	97	4	adding	add	VERB
ejpam-3713	97	5	constant	constant	ADJ
ejpam-3713	97	6	harvesting	harvesting	NOUN
ejpam-3713	97	7	factor	factor	NOUN
ejpam-3713	97	8	h	h	NOUN
ejpam-3713	97	9	in	in	ADP
ejpam-3713	97	10	i.v.p	i.v.p	NOUN
ejpam-3713	97	11	exponential	exponential	ADJ
ejpam-3713	97	12	growth	growth	NOUN
ejpam-3713	97	13	rate	rate	NOUN
ejpam-3713	97	14	(	(	PUNCT
ejpam-3713	97	15	2	2	NUM
ejpam-3713	97	16	)	)	PUNCT
ejpam-3713	97	17	,	,	PUNCT
ejpam-3713	97	18	we	we	PRON
ejpam-3713	97	19	obtain	obtain	VERB
ejpam-3713	97	20	the	the	DET
ejpam-3713	97	21	following	follow	VERB
ejpam-3713	97	22	i.v.p	i.v.p	NOUN
ejpam-3713	97	23	.	.	PUNCT
ejpam-3713	97	24	:	:	PUNCT
ejpam-3713	97	25	{	{	PUNCT
ejpam-3713	97	26	dx	dx	PROPN
ejpam-3713	97	27	dt	dt	X
ejpam-3713	97	28	=	=	PUNCT
ejpam-3713	97	29	rx−	rx−	NUM
ejpam-3713	97	30	h	h	NOUN
ejpam-3713	97	31	x(0	x(0	PROPN
ejpam-3713	97	32	)	)	PUNCT
ejpam-3713	98	1	=	=	PUNCT
ejpam-3713	98	2	x0	x0	PROPN
ejpam-3713	98	3	(	(	PUNCT
ejpam-3713	98	4	4	4	NUM
ejpam-3713	98	5	)	)	PUNCT
ejpam-3713	98	6	where	where	SCONJ
ejpam-3713	98	7	the	the	DET
ejpam-3713	98	8	above	above	ADJ
ejpam-3713	98	9	i.v.p	i.v.p	NOUN
ejpam-3713	98	10	.	.	PUNCT
ejpam-3713	98	11	solution	solution	NOUN
ejpam-3713	98	12	is	be	AUX
ejpam-3713	98	13	given	give	VERB
ejpam-3713	98	14	by	by	ADP
ejpam-3713	98	15	x(t	x(t	PROPN
ejpam-3713	98	16	)	)	PUNCT
ejpam-3713	98	17	=	=	PUNCT
ejpam-3713	99	1	(	(	PUNCT
ejpam-3713	99	2	x0	x0	PROPN
ejpam-3713	99	3	−	−	PROPN
ejpam-3713	99	4	h	h	NOUN
ejpam-3713	99	5	r	r	NOUN
ejpam-3713	99	6	)	)	PUNCT
ejpam-3713	99	7	exp(rt	exp(rt	ADV
ejpam-3713	99	8	)	)	PUNCT
ejpam-3713	100	1	+	+	CCONJ
ejpam-3713	100	2	h	h	NOUN
ejpam-3713	100	3	r	r	NOUN
ejpam-3713	100	4	.	.	PUNCT
ejpam-3713	101	1	(	(	PUNCT
ejpam-3713	101	2	5	5	X
ejpam-3713	101	3	)	)	PUNCT
ejpam-3713	101	4	we	we	PRON
ejpam-3713	101	5	are	be	AUX
ejpam-3713	101	6	now	now	ADV
ejpam-3713	101	7	going	go	VERB
ejpam-3713	101	8	to	to	PART
ejpam-3713	101	9	analyze	analyze	VERB
ejpam-3713	101	10	the	the	DET
ejpam-3713	101	11	solution	solution	NOUN
ejpam-3713	101	12	of	of	ADP
ejpam-3713	101	13	i.v.ps	i.v.ps	NOUN
ejpam-3713	101	14	.	.	PUNCT
ejpam-3713	102	1	(	(	PUNCT
ejpam-3713	102	2	2	2	NUM
ejpam-3713	102	3	)	)	PUNCT
ejpam-3713	102	4	and	and	CCONJ
ejpam-3713	102	5	(	(	PUNCT
ejpam-3713	102	6	4	4	NUM
ejpam-3713	102	7	)	)	PUNCT
ejpam-3713	102	8	by	by	ADP
ejpam-3713	102	9	picard	picard	PROPN
ejpam-3713	102	10	’s	’s	PART
ejpam-3713	102	11	iteration	iteration	NOUN
ejpam-3713	102	12	method	method	NOUN
ejpam-3713	102	13	.	.	PUNCT
ejpam-3713	102	14	theorem	theorem	NOUN
ejpam-3713	102	15	1	1	NUM
ejpam-3713	102	16	.	.	PUNCT
ejpam-3713	103	1	the	the	DET
ejpam-3713	103	2	following	follow	VERB
ejpam-3713	103	3	statements	statement	NOUN
ejpam-3713	103	4	for	for	ADP
ejpam-3713	103	5	i.v.ps	i.v.ps	NOUN
ejpam-3713	103	6	.	.	PUNCT
ejpam-3713	103	7	of	of	ADP
ejpam-3713	103	8	exponential	exponential	ADJ
ejpam-3713	103	9	growth	growth	NOUN
ejpam-3713	103	10	models	model	NOUN
ejpam-3713	103	11	are	be	AUX
ejpam-3713	103	12	true	true	ADJ
ejpam-3713	103	13	:	:	PUNCT
ejpam-3713	103	14	(	(	PUNCT
ejpam-3713	103	15	i	i	NOUN
ejpam-3713	103	16	)	)	PUNCT
ejpam-3713	103	17	the	the	DET
ejpam-3713	103	18	series	series	NOUN
ejpam-3713	103	19	solution	solution	NOUN
ejpam-3713	103	20	of	of	ADP
ejpam-3713	103	21	i.v.p	i.v.p	NOUN
ejpam-3713	103	22	.	.	PUNCT
ejpam-3713	104	1	(	(	PUNCT
ejpam-3713	104	2	2	2	X
ejpam-3713	104	3	)	)	PUNCT
ejpam-3713	104	4	is	be	AUX
ejpam-3713	104	5	x(t	x(t	PROPN
ejpam-3713	104	6	)	)	PUNCT
ejpam-3713	105	1	=	=	PUNCT
ejpam-3713	106	1	x0	x0	PROPN
ejpam-3713	106	2	k=∞∑	k=∞∑	PROPN
ejpam-3713	106	3	k=0	k=0	PROPN
ejpam-3713	106	4	(	(	PUNCT
ejpam-3713	106	5	rt)k	rt)k	PROPN
ejpam-3713	106	6	k	k	X
ejpam-3713	106	7	!	!	PUNCT
ejpam-3713	107	1	(	(	PUNCT
ejpam-3713	107	2	6	6	NUM
ejpam-3713	107	3	)	)	PUNCT
ejpam-3713	107	4	(	(	PUNCT
ejpam-3713	107	5	ii	ii	NOUN
ejpam-3713	107	6	)	)	PUNCT
ejpam-3713	107	7	the	the	DET
ejpam-3713	107	8	series	series	NOUN
ejpam-3713	107	9	solution	solution	NOUN
ejpam-3713	107	10	of	of	ADP
ejpam-3713	107	11	i.v.p	i.v.p	NOUN
ejpam-3713	107	12	.	.	PUNCT
ejpam-3713	108	1	(	(	PUNCT
ejpam-3713	108	2	4	4	X
ejpam-3713	108	3	)	)	PUNCT
ejpam-3713	108	4	is	be	AUX
ejpam-3713	108	5	x(t	x(t	PROPN
ejpam-3713	108	6	)	)	PUNCT
ejpam-3713	109	1	=	=	SYM
ejpam-3713	110	1	h	h	NOUN
ejpam-3713	111	1	r	r	NOUN
ejpam-3713	111	2	+	+	CCONJ
ejpam-3713	111	3	(	(	PUNCT
ejpam-3713	111	4	x0	x0	PROPN
ejpam-3713	111	5	−	−	PROPN
ejpam-3713	111	6	h	h	NOUN
ejpam-3713	111	7	r	r	NOUN
ejpam-3713	111	8	)	)	PUNCT
ejpam-3713	111	9	k=∞∑	k=∞∑	NOUN
ejpam-3713	111	10	k=0	k=0	PROPN
ejpam-3713	111	11	(	(	PUNCT
ejpam-3713	111	12	rt)k	rt)k	PROPN
ejpam-3713	111	13	k	k	X
ejpam-3713	111	14	!	!	PUNCT
ejpam-3713	112	1	(	(	PUNCT
ejpam-3713	112	2	7	7	X
ejpam-3713	112	3	)	)	PUNCT
ejpam-3713	112	4	proof	proof	NOUN
ejpam-3713	112	5	.	.	PUNCT
ejpam-3713	113	1	(	(	PUNCT
ejpam-3713	113	2	i	i	NOUN
ejpam-3713	113	3	)	)	PUNCT
ejpam-3713	113	4	first	first	ADV
ejpam-3713	113	5	,	,	PUNCT
ejpam-3713	113	6	we	we	PRON
ejpam-3713	113	7	should	should	AUX
ejpam-3713	113	8	consider	consider	VERB
ejpam-3713	113	9	the	the	DET
ejpam-3713	113	10	following	follow	VERB
ejpam-3713	113	11	iteration	iteration	NOUN
ejpam-3713	113	12	scheme	scheme	NOUN
ejpam-3713	113	13	:	:	PUNCT
ejpam-3713	113	14	xn(t	xn(t	NUM
ejpam-3713	113	15	)	)	PUNCT
ejpam-3713	114	1	=	=	PUNCT
ejpam-3713	114	2	x0	x0	PROPN
ejpam-3713	115	1	+	+	CCONJ
ejpam-3713	115	2	∫	∫	PROPN
ejpam-3713	115	3	s	s	PART
ejpam-3713	115	4	=	=	PROPN
ejpam-3713	115	5	t	t	X
ejpam-3713	115	6	s=0	s=0	PUNCT
ejpam-3713	115	7	rxn−1(s)ds	rxn−1(s)ds	PROPN
ejpam-3713	115	8	.	.	PUNCT
ejpam-3713	116	1	(	(	PUNCT
ejpam-3713	116	2	8)	8)	NUM
ejpam-3713	116	3	at	at	ADP
ejpam-3713	116	4	the	the	DET
ejpam-3713	116	5	first	first	ADJ
ejpam-3713	116	6	step	step	NOUN
ejpam-3713	116	7	,	,	PUNCT
ejpam-3713	116	8	we	we	PRON
ejpam-3713	116	9	calculate	calculate	VERB
ejpam-3713	116	10	x1(t	x1(t	PROPN
ejpam-3713	116	11	)	)	PUNCT
ejpam-3713	116	12	x1(t	x1(t	PUNCT
ejpam-3713	116	13	)	)	PUNCT
ejpam-3713	117	1	=	=	SYM
ejpam-3713	117	2	x0	x0	PROPN
ejpam-3713	118	1	+	+	CCONJ
ejpam-3713	119	1	∫	∫	PROPN
ejpam-3713	119	2	s	s	PART
ejpam-3713	119	3	=	=	PROPN
ejpam-3713	119	4	t	t	X
ejpam-3713	119	5	s=0	s=0	X
ejpam-3713	119	6	rx0ds	rx0ds	PROPN
ejpam-3713	119	7	=	=	PUNCT
ejpam-3713	119	8	x0	x0	PROPN
ejpam-3713	119	9	+	+	CCONJ
ejpam-3713	119	10	rx0	rx0	PROPN
ejpam-3713	119	11	t	t	NOUN
ejpam-3713	119	12	=	=	SYM
ejpam-3713	119	13	xo(1	xo(1	PROPN
ejpam-3713	119	14	+	+	CCONJ
ejpam-3713	119	15	rt	rt	PROPN
ejpam-3713	119	16	)	)	PUNCT
ejpam-3713	119	17	,	,	PUNCT
ejpam-3713	119	18	and	and	CCONJ
ejpam-3713	119	19	so	so	ADV
ejpam-3713	119	20	,	,	PUNCT
ejpam-3713	119	21	x1(t	x1(t	PROPN
ejpam-3713	119	22	)	)	PUNCT
ejpam-3713	119	23	=	=	PUNCT
ejpam-3713	119	24	xo(1	xo(1	PROPN
ejpam-3713	119	25	+	+	CCONJ
ejpam-3713	119	26	rt	rt	PROPN
ejpam-3713	119	27	)	)	PUNCT
ejpam-3713	119	28	.	.	PUNCT
ejpam-3713	120	1	(	(	PUNCT
ejpam-3713	120	2	9	9	X
ejpam-3713	120	3	)	)	PUNCT
ejpam-3713	120	4	at	at	ADP
ejpam-3713	120	5	the	the	DET
ejpam-3713	120	6	second	second	ADJ
ejpam-3713	120	7	step	step	NOUN
ejpam-3713	120	8	,	,	PUNCT
ejpam-3713	120	9	we	we	PRON
ejpam-3713	120	10	calculate	calculate	VERB
ejpam-3713	120	11	the	the	DET
ejpam-3713	120	12	x2(t	x2(t	PROPN
ejpam-3713	120	13	)	)	PUNCT
ejpam-3713	120	14	x2(t	x2(t	PROPN
ejpam-3713	120	15	)	)	PUNCT
ejpam-3713	121	1	=	=	PUNCT
ejpam-3713	121	2	x0	x0	PROPN
ejpam-3713	122	1	+	+	CCONJ
ejpam-3713	122	2	∫	∫	PROPN
ejpam-3713	122	3	s	s	PART
ejpam-3713	122	4	=	=	PROPN
ejpam-3713	122	5	t	t	X
ejpam-3713	122	6	s=0	s=0	NOUN
ejpam-3713	122	7	rx1(s)ds	rx1(s)ds	PROPN
ejpam-3713	123	1	=	=	PUNCT
ejpam-3713	123	2	x0	x0	PROPN
ejpam-3713	124	1	+	+	CCONJ
ejpam-3713	124	2	∫	∫	PROPN
ejpam-3713	124	3	s	s	PART
ejpam-3713	124	4	=	=	PROPN
ejpam-3713	124	5	t	t	ADJ
ejpam-3713	124	6	s=0	s=0	X
ejpam-3713	124	7	rx0(1	rx0(1	VERB
ejpam-3713	124	8	+	+	CCONJ
ejpam-3713	124	9	rs)ds	rs)ds	X
ejpam-3713	124	10	m.h	m.h	PROPN
ejpam-3713	124	11	.	.	PROPN
ejpam-3713	124	12	r.	r.	PROPN
ejpam-3713	124	13	doust	doust	PROPN
ejpam-3713	124	14	,	,	PUNCT
ejpam-3713	124	15	v.	v.	ADP
ejpam-3713	124	16	lokesha	lokesha	PROPN
ejpam-3713	124	17	,	,	PUNCT
ejpam-3713	124	18	a.	a.	NOUN
ejpam-3713	124	19	ghasemabadi	ghasemabadi	NOUN
ejpam-3713	124	20	/	/	SYM
ejpam-3713	124	21	eur	eur	PROPN
ejpam-3713	124	22	.	.	PUNCT
ejpam-3713	125	1	j.	j.	PROPN
ejpam-3713	125	2	pure	pure	PROPN
ejpam-3713	125	3	appl	appl	PROPN
ejpam-3713	125	4	.	.	PROPN
ejpam-3713	125	5	math	math	PROPN
ejpam-3713	125	6	,	,	PUNCT
ejpam-3713	125	7	13	13	NUM
ejpam-3713	125	8	(	(	PUNCT
ejpam-3713	125	9	5	5	NUM
ejpam-3713	125	10	)	)	PUNCT
ejpam-3713	125	11	(	(	PUNCT
ejpam-3713	125	12	2020	2020	NUM
ejpam-3713	125	13	)	)	PUNCT
ejpam-3713	125	14	,	,	PUNCT
ejpam-3713	125	15	1176	1176	NUM
ejpam-3713	125	16	-	-	SYM
ejpam-3713	125	17	1198	1198	NUM
ejpam-3713	125	18	1181	1181	NUM
ejpam-3713	125	19	=	=	SYM
ejpam-3713	126	1	x0	x0	PROPN
ejpam-3713	126	2	+	+	CCONJ
ejpam-3713	126	3	x0[rs	x0[rs	PROPN
ejpam-3713	126	4	+	+	CCONJ
ejpam-3713	126	5	(	(	PUNCT
ejpam-3713	126	6	rs)2	rs)2	NOUN
ejpam-3713	126	7	2	2	NUM
ejpam-3713	126	8	]	]	SYM
ejpam-3713	126	9	s	s	NOUN
ejpam-3713	126	10	=	=	X
ejpam-3713	126	11	t	t	NOUN
ejpam-3713	126	12	s=0	s=0	NOUN
ejpam-3713	127	1	=	=	PUNCT
ejpam-3713	128	1	x0	x0	PROPN
ejpam-3713	129	1	+	+	CCONJ
ejpam-3713	129	2	x0t(r	x0t(r	PROPN
ejpam-3713	129	3	+	+	CCONJ
ejpam-3713	129	4	(	(	PUNCT
ejpam-3713	129	5	rt)2	rt)2	NOUN
ejpam-3713	129	6	2	2	NUM
ejpam-3713	129	7	)	)	PUNCT
ejpam-3713	129	8	.	.	PUNCT
ejpam-3713	130	1	thus	thus	ADV
ejpam-3713	130	2	,	,	PUNCT
ejpam-3713	130	3	x2(t	x2(t	PROPN
ejpam-3713	130	4	)	)	PUNCT
ejpam-3713	130	5	=	=	SYM
ejpam-3713	130	6	x0(1	x0(1	PROPN
ejpam-3713	130	7	+	+	CCONJ
ejpam-3713	130	8	rt	rt	PROPN
ejpam-3713	130	9	+	+	CCONJ
ejpam-3713	130	10	(	(	PUNCT
ejpam-3713	130	11	rt)2	rt)2	PROPN
ejpam-3713	130	12	2	2	NUM
ejpam-3713	130	13	)	)	PUNCT
ejpam-3713	130	14	.	.	PUNCT
ejpam-3713	131	1	(	(	PUNCT
ejpam-3713	131	2	10	10	NUM
ejpam-3713	131	3	)	)	PUNCT
ejpam-3713	131	4	at	at	ADP
ejpam-3713	131	5	the	the	DET
ejpam-3713	131	6	third	third	ADJ
ejpam-3713	131	7	step	step	NOUN
ejpam-3713	131	8	,	,	PUNCT
ejpam-3713	131	9	we	we	PRON
ejpam-3713	131	10	calculate	calculate	VERB
ejpam-3713	131	11	the	the	DET
ejpam-3713	131	12	x3(t	x3(t	PROPN
ejpam-3713	131	13	)	)	PUNCT
ejpam-3713	131	14	x3(t	x3(t	PROPN
ejpam-3713	131	15	)	)	PUNCT
ejpam-3713	132	1	=	=	SYM
ejpam-3713	132	2	x0	x0	PROPN
ejpam-3713	133	1	+	+	CCONJ
ejpam-3713	134	1	∫	∫	PROPN
ejpam-3713	134	2	s	s	PART
ejpam-3713	134	3	=	=	PROPN
ejpam-3713	134	4	t	t	X
ejpam-3713	134	5	s=0	s=0	NOUN
ejpam-3713	134	6	rx2(s)ds	rx2(s)ds	PROPN
ejpam-3713	134	7	=	=	PUNCT
ejpam-3713	135	1	x0	x0	PROPN
ejpam-3713	136	1	+	+	CCONJ
ejpam-3713	136	2	∫	∫	PROPN
ejpam-3713	136	3	s	s	PART
ejpam-3713	136	4	=	=	PROPN
ejpam-3713	136	5	t	t	ADJ
ejpam-3713	136	6	s=0	s=0	X
ejpam-3713	136	7	rx0(1	rx0(1	VERB
ejpam-3713	136	8	+	+	CCONJ
ejpam-3713	136	9	rs	rs	ADJ
ejpam-3713	137	1	+	+	CCONJ
ejpam-3713	137	2	(	(	PUNCT
ejpam-3713	137	3	rs)2	rs)2	NOUN
ejpam-3713	137	4	2	2	NUM
ejpam-3713	137	5	)	)	PUNCT
ejpam-3713	137	6	ds	ds	NOUN
ejpam-3713	137	7	=	=	SYM
ejpam-3713	137	8	x0	x0	PROPN
ejpam-3713	137	9	+	+	CCONJ
ejpam-3713	137	10	x0[rs	x0[rs	PROPN
ejpam-3713	137	11	+	+	CCONJ
ejpam-3713	137	12	(	(	PUNCT
ejpam-3713	137	13	rs)2	rs)2	NOUN
ejpam-3713	137	14	2	2	NUM
ejpam-3713	137	15	+	+	CCONJ
ejpam-3713	137	16	(	(	PUNCT
ejpam-3713	137	17	rs)3	rs)3	ADJ
ejpam-3713	137	18	2×	2×	NUM
ejpam-3713	137	19	3	3	NUM
ejpam-3713	137	20	]	]	SYM
ejpam-3713	137	21	s	s	NOUN
ejpam-3713	137	22	=	=	X
ejpam-3713	137	23	t	t	NOUN
ejpam-3713	137	24	s=0	s=0	PROPN
ejpam-3713	137	25	=	=	SYM
ejpam-3713	137	26	x0(1	x0(1	PROPN
ejpam-3713	137	27	+	+	CCONJ
ejpam-3713	137	28	rt	rt	PROPN
ejpam-3713	138	1	+	+	CCONJ
ejpam-3713	138	2	(	(	PUNCT
ejpam-3713	138	3	rt)2	rt)2	PROPN
ejpam-3713	138	4	2	2	NUM
ejpam-3713	138	5	+	+	CCONJ
ejpam-3713	138	6	(	(	PUNCT
ejpam-3713	138	7	rt)3	rt)3	NOUN
ejpam-3713	138	8	2×	2×	NUM
ejpam-3713	138	9	3	3	NUM
ejpam-3713	138	10	)	)	PUNCT
ejpam-3713	138	11	.	.	PUNCT
ejpam-3713	139	1	hence	hence	ADV
ejpam-3713	139	2	,	,	PUNCT
ejpam-3713	139	3	x3(t	x3(t	PROPN
ejpam-3713	139	4	)	)	PUNCT
ejpam-3713	139	5	=	=	SYM
ejpam-3713	139	6	x0(1	x0(1	PROPN
ejpam-3713	139	7	+	+	CCONJ
ejpam-3713	139	8	rt	rt	PROPN
ejpam-3713	140	1	+	+	CCONJ
ejpam-3713	140	2	(	(	PUNCT
ejpam-3713	140	3	rt)2	rt)2	PROPN
ejpam-3713	140	4	2	2	NUM
ejpam-3713	140	5	+	+	CCONJ
ejpam-3713	140	6	(	(	PUNCT
ejpam-3713	140	7	rt)3	rt)3	NOUN
ejpam-3713	140	8	2×	2×	NUM
ejpam-3713	140	9	3	3	NUM
ejpam-3713	140	10	)	)	PUNCT
ejpam-3713	140	11	.	.	PUNCT
ejpam-3713	141	1	(	(	PUNCT
ejpam-3713	141	2	11	11	NUM
ejpam-3713	141	3	)	)	PUNCT
ejpam-3713	141	4	at	at	ADP
ejpam-3713	141	5	the	the	DET
ejpam-3713	141	6	forth	forth	ADJ
ejpam-3713	141	7	step	step	NOUN
ejpam-3713	141	8	,	,	PUNCT
ejpam-3713	141	9	we	we	PRON
ejpam-3713	141	10	calculate	calculate	VERB
ejpam-3713	141	11	the	the	DET
ejpam-3713	141	12	x4(t	x4(t	PROPN
ejpam-3713	141	13	)	)	PUNCT
ejpam-3713	141	14	x4(t	x4(t	PROPN
ejpam-3713	141	15	)	)	PUNCT
ejpam-3713	141	16	=	=	SYM
ejpam-3713	142	1	x0	x0	PROPN
ejpam-3713	143	1	+	+	CCONJ
ejpam-3713	144	1	∫	∫	PROPN
ejpam-3713	144	2	s	s	PART
ejpam-3713	144	3	=	=	PROPN
ejpam-3713	144	4	t	t	X
ejpam-3713	144	5	s=0	s=0	X
ejpam-3713	144	6	rx3(s)ds	rx3(s)ds	PUNCT
ejpam-3713	145	1	=	=	PUNCT
ejpam-3713	146	1	x0	x0	PROPN
ejpam-3713	147	1	+	+	CCONJ
ejpam-3713	147	2	∫	∫	PROPN
ejpam-3713	147	3	s	s	PART
ejpam-3713	147	4	=	=	PROPN
ejpam-3713	147	5	t	t	ADJ
ejpam-3713	147	6	s=0	s=0	X
ejpam-3713	147	7	rx0(1	rx0(1	VERB
ejpam-3713	147	8	+	+	CCONJ
ejpam-3713	147	9	rs	rs	ADJ
ejpam-3713	148	1	+	+	CCONJ
ejpam-3713	148	2	(	(	PUNCT
ejpam-3713	148	3	rs)2	rs)2	NOUN
ejpam-3713	148	4	2	2	NUM
ejpam-3713	148	5	+	+	CCONJ
ejpam-3713	148	6	(	(	PUNCT
ejpam-3713	148	7	rs)3	rs)3	ADJ
ejpam-3713	148	8	2×	2×	NUM
ejpam-3713	148	9	3	3	NUM
ejpam-3713	148	10	)	)	PUNCT
ejpam-3713	148	11	ds	ds	NOUN
ejpam-3713	148	12	=	=	SYM
ejpam-3713	148	13	x0	x0	PROPN
ejpam-3713	148	14	+	+	CCONJ
ejpam-3713	148	15	x0[rs	x0[rs	PROPN
ejpam-3713	148	16	+	+	CCONJ
ejpam-3713	148	17	(	(	PUNCT
ejpam-3713	148	18	rs)2	rs)2	NOUN
ejpam-3713	148	19	2	2	NUM
ejpam-3713	148	20	+	+	CCONJ
ejpam-3713	148	21	(	(	PUNCT
ejpam-3713	148	22	rs)3	rs)3	ADJ
ejpam-3713	148	23	2×	2×	NUM
ejpam-3713	148	24	3	3	NUM
ejpam-3713	148	25	]	]	SYM
ejpam-3713	148	26	s	s	NOUN
ejpam-3713	148	27	=	=	X
ejpam-3713	148	28	t	t	NOUN
ejpam-3713	148	29	s=0	s=0	PROPN
ejpam-3713	148	30	=	=	SYM
ejpam-3713	148	31	x0(1	x0(1	PROPN
ejpam-3713	149	1	+	+	CCONJ
ejpam-3713	149	2	rt	rt	PROPN
ejpam-3713	150	1	+	+	CCONJ
ejpam-3713	150	2	(	(	PUNCT
ejpam-3713	150	3	rt)2	rt)2	PROPN
ejpam-3713	150	4	2	2	NUM
ejpam-3713	150	5	+	+	CCONJ
ejpam-3713	150	6	(	(	PUNCT
ejpam-3713	150	7	rt)3	rt)3	NOUN
ejpam-3713	150	8	2×	2×	NUM
ejpam-3713	150	9	3	3	NUM
ejpam-3713	150	10	+	+	CCONJ
ejpam-3713	150	11	(	(	PUNCT
ejpam-3713	150	12	rs)4	rs)4	PROPN
ejpam-3713	150	13	2×	2×	NUM
ejpam-3713	150	14	3×	3×	NUM
ejpam-3713	150	15	4	4	NUM
ejpam-3713	150	16	)	)	PUNCT
ejpam-3713	150	17	.	.	PUNCT
ejpam-3713	151	1	then	then	ADV
ejpam-3713	151	2	,	,	PUNCT
ejpam-3713	151	3	x4(t	x4(t	PROPN
ejpam-3713	151	4	)	)	PUNCT
ejpam-3713	151	5	=	=	SYM
ejpam-3713	151	6	x0(1	x0(1	PROPN
ejpam-3713	151	7	+	+	CCONJ
ejpam-3713	151	8	rt	rt	PROPN
ejpam-3713	151	9	+	+	CCONJ
ejpam-3713	151	10	(	(	PUNCT
ejpam-3713	151	11	rt)2	rt)2	PROPN
ejpam-3713	151	12	2	2	NUM
ejpam-3713	151	13	+	+	CCONJ
ejpam-3713	151	14	(	(	PUNCT
ejpam-3713	151	15	rt)3	rt)3	NOUN
ejpam-3713	151	16	2×	2×	NUM
ejpam-3713	151	17	3	3	NUM
ejpam-3713	151	18	+	+	CCONJ
ejpam-3713	151	19	(	(	PUNCT
ejpam-3713	151	20	rt)4	rt)4	PROPN
ejpam-3713	151	21	2×	2×	NUM
ejpam-3713	151	22	3×	3×	NUM
ejpam-3713	151	23	4	4	NUM
ejpam-3713	151	24	)	)	PUNCT
ejpam-3713	151	25	.	.	PUNCT
ejpam-3713	152	1	(	(	PUNCT
ejpam-3713	152	2	12	12	NUM
ejpam-3713	152	3	)	)	PUNCT
ejpam-3713	152	4	paying	pay	VERB
ejpam-3713	152	5	attention	attention	NOUN
ejpam-3713	152	6	to	to	ADP
ejpam-3713	152	7	relations	relation	NOUN
ejpam-3713	152	8	(	(	PUNCT
ejpam-3713	152	9	9),(10),(11	9),(10),(11	NUM
ejpam-3713	152	10	)	)	PUNCT
ejpam-3713	152	11	and	and	CCONJ
ejpam-3713	152	12	(	(	PUNCT
ejpam-3713	152	13	12	12	NUM
ejpam-3713	152	14	)	)	PUNCT
ejpam-3713	152	15	,	,	PUNCT
ejpam-3713	152	16	one	one	PRON
ejpam-3713	152	17	may	may	AUX
ejpam-3713	152	18	guess	guess	VERB
ejpam-3713	152	19	the	the	DET
ejpam-3713	152	20	following	follow	VERB
ejpam-3713	152	21	series	series	NOUN
ejpam-3713	152	22	:	:	PUNCT
ejpam-3713	152	23	xn(t	xn(t	NUM
ejpam-3713	152	24	)	)	PUNCT
ejpam-3713	153	1	=	=	PUNCT
ejpam-3713	154	1	x0	x0	PROPN
ejpam-3713	155	1	k	k	PROPN
ejpam-3713	156	1	=	=	PROPN
ejpam-3713	156	2	n∑	n∑	NOUN
ejpam-3713	156	3	k=0	k=0	PROPN
ejpam-3713	156	4	(	(	PUNCT
ejpam-3713	156	5	rt)k	rt)k	PROPN
ejpam-3713	156	6	k	k	X
ejpam-3713	156	7	!	!	PUNCT
ejpam-3713	156	8	.	.	PUNCT
ejpam-3713	157	1	(	(	PUNCT
ejpam-3713	157	2	13	13	X
ejpam-3713	157	3	)	)	PUNCT
ejpam-3713	157	4	m.h	m.h	PROPN
ejpam-3713	157	5	.	.	PROPN
ejpam-3713	157	6	r.	r.	PROPN
ejpam-3713	157	7	doust	doust	PROPN
ejpam-3713	157	8	,	,	PUNCT
ejpam-3713	157	9	v.	v.	ADP
ejpam-3713	157	10	lokesha	lokesha	PROPN
ejpam-3713	157	11	,	,	PUNCT
ejpam-3713	157	12	a.	a.	NOUN
ejpam-3713	157	13	ghasemabadi	ghasemabadi	NOUN
ejpam-3713	157	14	/	/	SYM
ejpam-3713	157	15	eur	eur	PROPN
ejpam-3713	157	16	.	.	PUNCT
ejpam-3713	158	1	j.	j.	PROPN
ejpam-3713	158	2	pure	pure	PROPN
ejpam-3713	158	3	appl	appl	PROPN
ejpam-3713	158	4	.	.	PROPN
ejpam-3713	158	5	math	math	PROPN
ejpam-3713	158	6	,	,	PUNCT
ejpam-3713	158	7	13	13	NUM
ejpam-3713	158	8	(	(	PUNCT
ejpam-3713	158	9	5	5	NUM
ejpam-3713	158	10	)	)	PUNCT
ejpam-3713	158	11	(	(	PUNCT
ejpam-3713	158	12	2020	2020	NUM
ejpam-3713	158	13	)	)	PUNCT
ejpam-3713	158	14	,	,	PUNCT
ejpam-3713	158	15	1176	1176	NUM
ejpam-3713	158	16	-	-	SYM
ejpam-3713	158	17	1198	1198	NUM
ejpam-3713	158	18	1182	1182	NUM
ejpam-3713	158	19	approaching	approach	VERB
ejpam-3713	158	20	n	n	NUM
ejpam-3713	158	21	to	to	ADP
ejpam-3713	158	22	infinity	infinity	NOUN
ejpam-3713	158	23	,	,	PUNCT
ejpam-3713	158	24	we	we	PRON
ejpam-3713	158	25	see	see	VERB
ejpam-3713	158	26	that	that	SCONJ
ejpam-3713	158	27	the	the	DET
ejpam-3713	158	28	series	series	NOUN
ejpam-3713	158	29	solution	solution	NOUN
ejpam-3713	158	30	of	of	ADP
ejpam-3713	158	31	i.v.p	i.v.p	NOUN
ejpam-3713	158	32	.	.	PUNCT
ejpam-3713	159	1	(	(	PUNCT
ejpam-3713	159	2	2	2	X
ejpam-3713	159	3	)	)	PUNCT
ejpam-3713	159	4	may	may	AUX
ejpam-3713	159	5	be	be	AUX
ejpam-3713	159	6	obtained	obtain	VERB
ejpam-3713	159	7	as	as	ADP
ejpam-3713	159	8	follows	follow	VERB
ejpam-3713	159	9	:	:	PUNCT
ejpam-3713	159	10	x(t	x(t	PROPN
ejpam-3713	159	11	)	)	PUNCT
ejpam-3713	159	12	=	=	SYM
ejpam-3713	159	13	limn→∞xn(t	limn→∞xn(t	NOUN
ejpam-3713	159	14	)	)	PUNCT
ejpam-3713	160	1	=	=	PUNCT
ejpam-3713	161	1	x0	x0	PROPN
ejpam-3713	161	2	k=∞∑	k=∞∑	PROPN
ejpam-3713	161	3	k=0	k=0	PROPN
ejpam-3713	161	4	(	(	PUNCT
ejpam-3713	161	5	rt)k	rt)k	PROPN
ejpam-3713	161	6	k	k	X
ejpam-3713	161	7	!	!	PUNCT
ejpam-3713	162	1	(	(	PUNCT
ejpam-3713	162	2	14	14	NUM
ejpam-3713	162	3	)	)	PUNCT
ejpam-3713	162	4	therefore	therefore	ADV
ejpam-3713	162	5	,	,	PUNCT
ejpam-3713	162	6	the	the	DET
ejpam-3713	162	7	truth	truth	NOUN
ejpam-3713	162	8	of	of	ADP
ejpam-3713	162	9	relation	relation	NOUN
ejpam-3713	162	10	(	(	PUNCT
ejpam-3713	162	11	6	6	NUM
ejpam-3713	162	12	)	)	PUNCT
ejpam-3713	162	13	is	be	AUX
ejpam-3713	162	14	proved	prove	VERB
ejpam-3713	162	15	.	.	PUNCT
ejpam-3713	163	1	(	(	PUNCT
ejpam-3713	163	2	ii	ii	NOUN
ejpam-3713	163	3	)	)	PUNCT
ejpam-3713	163	4	now	now	ADV
ejpam-3713	163	5	,	,	PUNCT
ejpam-3713	163	6	consider	consider	VERB
ejpam-3713	163	7	the	the	DET
ejpam-3713	163	8	following	follow	VERB
ejpam-3713	163	9	iteration	iteration	NOUN
ejpam-3713	163	10	scheme	scheme	NOUN
ejpam-3713	163	11	:	:	PUNCT
ejpam-3713	163	12	xn(t	xn(t	NUM
ejpam-3713	163	13	)	)	PUNCT
ejpam-3713	164	1	=	=	PUNCT
ejpam-3713	164	2	x0	x0	PROPN
ejpam-3713	165	1	+	+	CCONJ
ejpam-3713	166	1	∫	∫	PROPN
ejpam-3713	166	2	s	s	PART
ejpam-3713	166	3	=	=	PROPN
ejpam-3713	166	4	t	t	X
ejpam-3713	166	5	s=0	s=0	X
ejpam-3713	166	6	(	(	PUNCT
ejpam-3713	166	7	rx(n−	rx(n−	PROPN
ejpam-3713	166	8	1)(s)−	1)(s)−	NUM
ejpam-3713	167	1	h)ds	h)ds	PROPN
ejpam-3713	167	2	(	(	PUNCT
ejpam-3713	167	3	15	15	NUM
ejpam-3713	167	4	)	)	PUNCT
ejpam-3713	167	5	at	at	ADP
ejpam-3713	167	6	the	the	DET
ejpam-3713	167	7	first	first	ADJ
ejpam-3713	167	8	,	,	PUNCT
ejpam-3713	167	9	step	step	NOUN
ejpam-3713	167	10	we	we	PRON
ejpam-3713	167	11	calculate	calculate	VERB
ejpam-3713	167	12	x1(t	x1(t	PROPN
ejpam-3713	167	13	)	)	PUNCT
ejpam-3713	167	14	x1(t	x1(t	PUNCT
ejpam-3713	167	15	)	)	PUNCT
ejpam-3713	168	1	=	=	SYM
ejpam-3713	168	2	x0	x0	PROPN
ejpam-3713	169	1	+	+	CCONJ
ejpam-3713	170	1	∫	∫	PROPN
ejpam-3713	170	2	s	s	PART
ejpam-3713	170	3	=	=	PROPN
ejpam-3713	170	4	t	t	X
ejpam-3713	170	5	s=0	s=0	PUNCT
ejpam-3713	170	6	(	(	PUNCT
ejpam-3713	170	7	rx0	rx0	X
ejpam-3713	170	8	−	−	PROPN
ejpam-3713	171	1	h)ds	h)ds	PROPN
ejpam-3713	171	2	=	=	PUNCT
ejpam-3713	171	3	x0	x0	PROPN
ejpam-3713	171	4	+	+	CCONJ
ejpam-3713	171	5	(	(	PUNCT
ejpam-3713	171	6	x0	x0	PROPN
ejpam-3713	171	7	−	−	PROPN
ejpam-3713	172	1	h	h	NOUN
ejpam-3713	172	2	r	r	NOUN
ejpam-3713	172	3	)	)	PUNCT
ejpam-3713	172	4	rt	rt	PROPN
ejpam-3713	172	5	.	.	PUNCT
ejpam-3713	173	1	for	for	ADP
ejpam-3713	173	2	simplifying	simplify	VERB
ejpam-3713	173	3	take	take	VERB
ejpam-3713	173	4	a	a	PRON
ejpam-3713	173	5	=	=	NOUN
ejpam-3713	173	6	x0	x0	NUM
ejpam-3713	174	1	−	−	NOUN
ejpam-3713	175	1	h	h	NOUN
ejpam-3713	175	2	r	r	NOUN
ejpam-3713	175	3	,	,	PUNCT
ejpam-3713	175	4	(	(	PUNCT
ejpam-3713	175	5	16	16	NUM
ejpam-3713	175	6	)	)	PUNCT
ejpam-3713	175	7	which	which	PRON
ejpam-3713	175	8	it	it	PRON
ejpam-3713	175	9	implies	imply	VERB
ejpam-3713	175	10	that	that	SCONJ
ejpam-3713	175	11	x1(t	x1(t	PUNCT
ejpam-3713	175	12	)	)	PUNCT
ejpam-3713	175	13	=	=	SYM
ejpam-3713	176	1	x0	x0	PROPN
ejpam-3713	176	2	+	+	NUM
ejpam-3713	176	3	art	art	NOUN
ejpam-3713	176	4	.	.	PUNCT
ejpam-3713	177	1	(	(	PUNCT
ejpam-3713	177	2	17	17	NUM
ejpam-3713	177	3	)	)	PUNCT
ejpam-3713	177	4	at	at	ADP
ejpam-3713	177	5	the	the	DET
ejpam-3713	177	6	second	second	ADJ
ejpam-3713	177	7	step	step	NOUN
ejpam-3713	177	8	,	,	PUNCT
ejpam-3713	177	9	we	we	PRON
ejpam-3713	177	10	calculate	calculate	VERB
ejpam-3713	177	11	the	the	DET
ejpam-3713	177	12	x2(t	x2(t	PROPN
ejpam-3713	177	13	)	)	PUNCT
ejpam-3713	177	14	x2(t	x2(t	PROPN
ejpam-3713	177	15	)	)	PUNCT
ejpam-3713	178	1	=	=	PUNCT
ejpam-3713	178	2	x0	x0	PROPN
ejpam-3713	179	1	+	+	CCONJ
ejpam-3713	180	1	∫	∫	PROPN
ejpam-3713	180	2	s	s	PART
ejpam-3713	180	3	=	=	PROPN
ejpam-3713	180	4	t	t	X
ejpam-3713	180	5	s=0	s=0	PUNCT
ejpam-3713	180	6	(	(	PUNCT
ejpam-3713	180	7	rx1(s)−	rx1(s)−	PROPN
ejpam-3713	180	8	h)ds	h)ds	PROPN
ejpam-3713	180	9	=	=	PUNCT
ejpam-3713	180	10	x0	x0	PROPN
ejpam-3713	181	1	+	+	CCONJ
ejpam-3713	182	1	∫	∫	PROPN
ejpam-3713	182	2	s	s	PART
ejpam-3713	182	3	=	=	PROPN
ejpam-3713	182	4	t	t	X
ejpam-3713	182	5	s=0	s=0	PUNCT
ejpam-3713	182	6	(	(	PUNCT
ejpam-3713	182	7	r(x0	r(x0	NOUN
ejpam-3713	182	8	+	+	X
ejpam-3713	182	9	ars)−	ars)−	ADP
ejpam-3713	182	10	h)ds	h)ds	PROPN
ejpam-3713	182	11	=	=	PUNCT
ejpam-3713	182	12	x0	x0	PROPN
ejpam-3713	183	1	+	+	PUNCT
ejpam-3713	184	1	[	[	X
ejpam-3713	184	2	rx0s	rx0	NOUN
ejpam-3713	184	3	+	+	X
ejpam-3713	184	4	a	a	DET
ejpam-3713	184	5	(	(	PUNCT
ejpam-3713	184	6	rs)2	rs)2	NOUN
ejpam-3713	184	7	2	2	NUM
ejpam-3713	184	8	−	−	NOUN
ejpam-3713	184	9	hs]s	hs]s	PROPN
ejpam-3713	184	10	=	=	PUNCT
ejpam-3713	184	11	t	t	NOUN
ejpam-3713	184	12	s=0	s=0	NOUN
ejpam-3713	184	13	=	=	PUNCT
ejpam-3713	185	1	x0	x0	PROPN
ejpam-3713	185	2	+	+	CCONJ
ejpam-3713	185	3	rx0	rx0	PROPN
ejpam-3713	185	4	t	t	PROPN
ejpam-3713	185	5	+	+	CCONJ
ejpam-3713	185	6	a	a	DET
ejpam-3713	185	7	(	(	PUNCT
ejpam-3713	185	8	rt)2	rt)2	PROPN
ejpam-3713	185	9	2	2	NUM
ejpam-3713	185	10	−	−	PROPN
ejpam-3713	185	11	ht	ht	INTJ
ejpam-3713	185	12	.	.	PUNCT
ejpam-3713	186	1	then	then	ADV
ejpam-3713	186	2	,	,	PUNCT
ejpam-3713	186	3	x2(t	x2(t	PROPN
ejpam-3713	186	4	)	)	PUNCT
ejpam-3713	186	5	=	=	PUNCT
ejpam-3713	187	1	x0	x0	PROPN
ejpam-3713	187	2	+	+	CCONJ
ejpam-3713	187	3	a(rt	a(rt	PROPN
ejpam-3713	187	4	+	+	SYM
ejpam-3713	187	5	(	(	PUNCT
ejpam-3713	187	6	rt)2	rt)2	PROPN
ejpam-3713	187	7	2	2	NUM
ejpam-3713	187	8	)	)	PUNCT
ejpam-3713	187	9	.	.	PUNCT
ejpam-3713	188	1	(	(	PUNCT
ejpam-3713	188	2	18	18	NUM
ejpam-3713	188	3	)	)	PUNCT
ejpam-3713	188	4	at	at	ADP
ejpam-3713	188	5	the	the	DET
ejpam-3713	188	6	third	third	ADJ
ejpam-3713	188	7	step	step	NOUN
ejpam-3713	188	8	,	,	PUNCT
ejpam-3713	188	9	we	we	PRON
ejpam-3713	188	10	calculate	calculate	VERB
ejpam-3713	188	11	the	the	DET
ejpam-3713	188	12	x3(t	x3(t	PROPN
ejpam-3713	188	13	)	)	PUNCT
ejpam-3713	188	14	x3(t	x3(t	PROPN
ejpam-3713	188	15	)	)	PUNCT
ejpam-3713	188	16	=	=	SYM
ejpam-3713	189	1	x0	x0	PROPN
ejpam-3713	190	1	+	+	CCONJ
ejpam-3713	190	2	∫	∫	PROPN
ejpam-3713	190	3	s	s	PART
ejpam-3713	190	4	=	=	PROPN
ejpam-3713	190	5	t	t	X
ejpam-3713	190	6	s=0	s=0	PUNCT
ejpam-3713	190	7	(	(	PUNCT
ejpam-3713	190	8	rx2(s)−	rx2(s)−	VERB
ejpam-3713	190	9	h)ds	h)ds	PROPN
ejpam-3713	190	10	=	=	SYM
ejpam-3713	191	1	x0	x0	PROPN
ejpam-3713	191	2	+	+	CCONJ
ejpam-3713	191	3	∫	∫	PROPN
ejpam-3713	191	4	s	s	PART
ejpam-3713	191	5	=	=	PROPN
ejpam-3713	191	6	t	t	X
ejpam-3713	191	7	s=0	s=0	PUNCT
ejpam-3713	191	8	(	(	PUNCT
ejpam-3713	191	9	r(x0	r(x0	NOUN
ejpam-3713	191	10	+	+	CCONJ
ejpam-3713	191	11	ars	ar	NOUN
ejpam-3713	191	12	+	+	CCONJ
ejpam-3713	191	13	a	a	DET
ejpam-3713	191	14	(	(	PUNCT
ejpam-3713	191	15	rs)2	rs)2	NOUN
ejpam-3713	191	16	2	2	NUM
ejpam-3713	191	17	)	)	PUNCT
ejpam-3713	191	18	−	−	PROPN
ejpam-3713	192	1	h)ds	h)ds	PROPN
ejpam-3713	192	2	m.h	m.h	PROPN
ejpam-3713	192	3	.	.	PROPN
ejpam-3713	192	4	r.	r.	PROPN
ejpam-3713	192	5	doust	doust	PROPN
ejpam-3713	192	6	,	,	PUNCT
ejpam-3713	192	7	v.	v.	ADP
ejpam-3713	192	8	lokesha	lokesha	PROPN
ejpam-3713	192	9	,	,	PUNCT
ejpam-3713	192	10	a.	a.	NOUN
ejpam-3713	192	11	ghasemabadi	ghasemabadi	NOUN
ejpam-3713	192	12	/	/	SYM
ejpam-3713	192	13	eur	eur	PROPN
ejpam-3713	192	14	.	.	PUNCT
ejpam-3713	193	1	j.	j.	PROPN
ejpam-3713	193	2	pure	pure	PROPN
ejpam-3713	193	3	appl	appl	PROPN
ejpam-3713	193	4	.	.	PROPN
ejpam-3713	193	5	math	math	PROPN
ejpam-3713	193	6	,	,	PUNCT
ejpam-3713	193	7	13	13	NUM
ejpam-3713	193	8	(	(	PUNCT
ejpam-3713	193	9	5	5	NUM
ejpam-3713	193	10	)	)	PUNCT
ejpam-3713	193	11	(	(	PUNCT
ejpam-3713	193	12	2020	2020	NUM
ejpam-3713	193	13	)	)	PUNCT
ejpam-3713	193	14	,	,	PUNCT
ejpam-3713	193	15	1176	1176	NUM
ejpam-3713	193	16	-	-	SYM
ejpam-3713	193	17	1198	1198	NUM
ejpam-3713	193	18	1183	1183	NUM
ejpam-3713	193	19	=	=	NOUN
ejpam-3713	194	1	x0	x0	PROPN
ejpam-3713	195	1	+	+	PUNCT
ejpam-3713	196	1	[	[	X
ejpam-3713	196	2	rx0	rx0	X
ejpam-3713	196	3	+	+	X
ejpam-3713	196	4	ar2s	ar2s	PROPN
ejpam-3713	196	5	+	+	CCONJ
ejpam-3713	196	6	a	a	DET
ejpam-3713	196	7	r3	r3	PROPN
ejpam-3713	196	8	2	2	NUM
ejpam-3713	196	9	s2	s2	NOUN
ejpam-3713	196	10	−	−	NOUN
ejpam-3713	196	11	hs]s	hs]s	PROPN
ejpam-3713	196	12	=	=	PUNCT
ejpam-3713	196	13	t	t	NOUN
ejpam-3713	196	14	s=0	s=0	NOUN
ejpam-3713	196	15	=	=	PUNCT
ejpam-3713	197	1	x0	x0	PROPN
ejpam-3713	198	1	+	+	CCONJ
ejpam-3713	198	2	rx0t−	rx0t−	VERB
ejpam-3713	198	3	ht	ht	PROPN
ejpam-3713	199	1	+	+	CCONJ
ejpam-3713	199	2	a	a	DET
ejpam-3713	199	3	(	(	PUNCT
ejpam-3713	199	4	rt)2	rt)2	NOUN
ejpam-3713	199	5	2	2	NUM
ejpam-3713	199	6	+	+	CCONJ
ejpam-3713	199	7	a	a	DET
ejpam-3713	199	8	(	(	PUNCT
ejpam-3713	199	9	rt)3	rt)3	NOUN
ejpam-3713	199	10	2	2	NUM
ejpam-3713	199	11	.	.	PUNCT
ejpam-3713	200	1	thus	thus	ADV
ejpam-3713	200	2	,	,	PUNCT
ejpam-3713	200	3	x3(t	x3(t	PROPN
ejpam-3713	200	4	)	)	PUNCT
ejpam-3713	200	5	=	=	SYM
ejpam-3713	200	6	x0	x0	PROPN
ejpam-3713	200	7	+	+	CCONJ
ejpam-3713	200	8	a(rt	a(rt	PROPN
ejpam-3713	200	9	+	+	SYM
ejpam-3713	200	10	(	(	PUNCT
ejpam-3713	200	11	rt)2	rt)2	PROPN
ejpam-3713	200	12	2	2	NUM
ejpam-3713	200	13	+	+	CCONJ
ejpam-3713	200	14	(	(	PUNCT
ejpam-3713	200	15	rt)3	rt)3	NOUN
ejpam-3713	200	16	2×	2×	NUM
ejpam-3713	200	17	3	3	NUM
ejpam-3713	200	18	)	)	PUNCT
ejpam-3713	200	19	.	.	PUNCT
ejpam-3713	201	1	(	(	PUNCT
ejpam-3713	201	2	19	19	NUM
ejpam-3713	201	3	)	)	PUNCT
ejpam-3713	201	4	at	at	ADP
ejpam-3713	201	5	the	the	DET
ejpam-3713	201	6	forth	forth	ADJ
ejpam-3713	201	7	step	step	NOUN
ejpam-3713	201	8	,	,	PUNCT
ejpam-3713	201	9	we	we	PRON
ejpam-3713	201	10	calculate	calculate	VERB
ejpam-3713	201	11	the	the	DET
ejpam-3713	201	12	x4(t	x4(t	PROPN
ejpam-3713	201	13	)	)	PUNCT
ejpam-3713	201	14	x4(t	x4(t	PROPN
ejpam-3713	201	15	)	)	PUNCT
ejpam-3713	201	16	=	=	SYM
ejpam-3713	202	1	x0	x0	PROPN
ejpam-3713	203	1	+	+	CCONJ
ejpam-3713	204	1	∫	∫	PROPN
ejpam-3713	204	2	s	s	PART
ejpam-3713	204	3	=	=	PROPN
ejpam-3713	204	4	t	t	X
ejpam-3713	204	5	s=0	s=0	PUNCT
ejpam-3713	204	6	(	(	PUNCT
ejpam-3713	204	7	rx3(s)−	rx3(s)−	ADV
ejpam-3713	204	8	h)ds	h)ds	PROPN
ejpam-3713	204	9	=	=	SYM
ejpam-3713	204	10	x0	x0	PROPN
ejpam-3713	205	1	+	+	CCONJ
ejpam-3713	206	1	∫	∫	PROPN
ejpam-3713	206	2	s	s	PART
ejpam-3713	206	3	=	=	PROPN
ejpam-3713	206	4	t	t	X
ejpam-3713	206	5	s=0	s=0	PUNCT
ejpam-3713	206	6	(	(	PUNCT
ejpam-3713	206	7	r(x0	r(x0	NOUN
ejpam-3713	206	8	+	+	CCONJ
ejpam-3713	206	9	ars	ar	NOUN
ejpam-3713	206	10	+	+	CCONJ
ejpam-3713	206	11	a	a	DET
ejpam-3713	206	12	(	(	PUNCT
ejpam-3713	206	13	rs)2	rs)2	NOUN
ejpam-3713	206	14	2	2	NUM
ejpam-3713	206	15	+	+	CCONJ
ejpam-3713	206	16	a	a	DET
ejpam-3713	206	17	(	(	PUNCT
ejpam-3713	206	18	rs)3	rs)3	ADJ
ejpam-3713	206	19	2×	2×	NUM
ejpam-3713	206	20	3	3	NUM
ejpam-3713	206	21	)	)	PUNCT
ejpam-3713	206	22	−	−	PROPN
ejpam-3713	207	1	h)ds	h)ds	PROPN
ejpam-3713	207	2	=	=	PUNCT
ejpam-3713	207	3	x0	x0	PROPN
ejpam-3713	208	1	+	+	PUNCT
ejpam-3713	209	1	[	[	X
ejpam-3713	209	2	rx0	rx0	X
ejpam-3713	209	3	+	+	X
ejpam-3713	209	4	ar2s	ar2s	PROPN
ejpam-3713	209	5	+	+	CCONJ
ejpam-3713	209	6	a	a	DET
ejpam-3713	209	7	r3	r3	PROPN
ejpam-3713	209	8	2	2	NUM
ejpam-3713	209	9	s2	s2	NOUN
ejpam-3713	209	10	+	+	CCONJ
ejpam-3713	209	11	a	a	DET
ejpam-3713	209	12	r4	r4	ADJ
ejpam-3713	209	13	2×	2×	NUM
ejpam-3713	209	14	3	3	NUM
ejpam-3713	209	15	s3	s3	PROPN
ejpam-3713	209	16	−	−	PROPN
ejpam-3713	209	17	hs]s	hs]s	PROPN
ejpam-3713	209	18	=	=	PUNCT
ejpam-3713	209	19	t	t	NOUN
ejpam-3713	209	20	s=0	s=0	NOUN
ejpam-3713	210	1	=	=	PUNCT
ejpam-3713	210	2	x0	x0	PROPN
ejpam-3713	211	1	+	+	CCONJ
ejpam-3713	211	2	rx0t−	rx0t−	VERB
ejpam-3713	211	3	ht	ht	PROPN
ejpam-3713	212	1	+	+	CCONJ
ejpam-3713	212	2	a	a	DET
ejpam-3713	212	3	(	(	PUNCT
ejpam-3713	212	4	rt)2	rt)2	NOUN
ejpam-3713	212	5	2	2	NUM
ejpam-3713	212	6	+	+	CCONJ
ejpam-3713	212	7	a	a	DET
ejpam-3713	212	8	(	(	PUNCT
ejpam-3713	212	9	rt)3	rt)3	NOUN
ejpam-3713	212	10	2	2	NUM
ejpam-3713	212	11	+	+	CCONJ
ejpam-3713	212	12	a	a	DET
ejpam-3713	212	13	(	(	PUNCT
ejpam-3713	212	14	rt)4	rt)4	PROPN
ejpam-3713	212	15	2×	2×	NUM
ejpam-3713	212	16	3×	3×	NUM
ejpam-3713	212	17	4	4	NUM
ejpam-3713	212	18	.	.	PUNCT
ejpam-3713	213	1	therefore	therefore	ADV
ejpam-3713	213	2	,	,	PUNCT
ejpam-3713	213	3	x4(t	x4(t	PROPN
ejpam-3713	213	4	)	)	PUNCT
ejpam-3713	213	5	=	=	X
ejpam-3713	213	6	x0	x0	PROPN
ejpam-3713	213	7	+	+	CCONJ
ejpam-3713	213	8	a(rt	a(rt	PROPN
ejpam-3713	213	9	+	+	SYM
ejpam-3713	213	10	(	(	PUNCT
ejpam-3713	213	11	rt)2	rt)2	PROPN
ejpam-3713	213	12	2	2	NUM
ejpam-3713	213	13	+	+	CCONJ
ejpam-3713	213	14	(	(	PUNCT
ejpam-3713	213	15	rt)2	rt)2	PROPN
ejpam-3713	213	16	2×	2×	NUM
ejpam-3713	213	17	3	3	NUM
ejpam-3713	213	18	+	+	CCONJ
ejpam-3713	213	19	(	(	PUNCT
ejpam-3713	213	20	rt)4	rt)4	PROPN
ejpam-3713	213	21	2×	2×	NUM
ejpam-3713	213	22	3×	3×	NUM
ejpam-3713	213	23	4	4	NUM
ejpam-3713	213	24	)	)	PUNCT
ejpam-3713	213	25	.	.	PUNCT
ejpam-3713	214	1	(	(	PUNCT
ejpam-3713	214	2	20	20	X
ejpam-3713	214	3	)	)	PUNCT
ejpam-3713	214	4	paying	pay	VERB
ejpam-3713	214	5	attention	attention	NOUN
ejpam-3713	214	6	to	to	ADP
ejpam-3713	214	7	relations	relation	NOUN
ejpam-3713	214	8	(	(	PUNCT
ejpam-3713	214	9	17	17	NUM
ejpam-3713	214	10	)	)	PUNCT
ejpam-3713	214	11	,	,	PUNCT
ejpam-3713	214	12	(	(	PUNCT
ejpam-3713	214	13	18	18	NUM
ejpam-3713	214	14	)	)	PUNCT
ejpam-3713	214	15	,	,	PUNCT
ejpam-3713	214	16	(	(	PUNCT
ejpam-3713	214	17	19	19	NUM
ejpam-3713	214	18	)	)	PUNCT
ejpam-3713	214	19	and	and	CCONJ
ejpam-3713	214	20	(	(	PUNCT
ejpam-3713	214	21	20	20	NUM
ejpam-3713	214	22	)	)	PUNCT
ejpam-3713	214	23	,	,	PUNCT
ejpam-3713	214	24	we	we	PRON
ejpam-3713	214	25	guess	guess	VERB
ejpam-3713	214	26	the	the	DET
ejpam-3713	214	27	following	follow	VERB
ejpam-3713	214	28	series	series	NOUN
ejpam-3713	214	29	:	:	PUNCT
ejpam-3713	214	30	xn(t	xn(t	NUM
ejpam-3713	214	31	)	)	PUNCT
ejpam-3713	215	1	=	=	PUNCT
ejpam-3713	215	2	x0	x0	PROPN
ejpam-3713	216	1	+	+	CCONJ
ejpam-3713	216	2	a	a	DET
ejpam-3713	216	3	k	k	NOUN
ejpam-3713	216	4	=	=	NOUN
ejpam-3713	216	5	n∑	n∑	NOUN
ejpam-3713	216	6	k=1	k=1	X
ejpam-3713	216	7	(	(	PUNCT
ejpam-3713	216	8	rt)k	rt)k	PROPN
ejpam-3713	216	9	k	k	X
ejpam-3713	216	10	!	!	PUNCT
ejpam-3713	216	11	.	.	PUNCT
ejpam-3713	217	1	(	(	PUNCT
ejpam-3713	217	2	21	21	NUM
ejpam-3713	217	3	)	)	PUNCT
ejpam-3713	217	4	and	and	CCONJ
ejpam-3713	217	5	so	so	ADV
ejpam-3713	217	6	,	,	PUNCT
ejpam-3713	217	7	xn(t	xn(t	PUNCT
ejpam-3713	217	8	)	)	PUNCT
ejpam-3713	218	1	=	=	SYM
ejpam-3713	218	2	x0	x0	PROPN
ejpam-3713	218	3	−a	−a	NOUN
ejpam-3713	218	4	(	(	PUNCT
ejpam-3713	218	5	rt)0	rt)0	NOUN
ejpam-3713	218	6	0	0	NUM
ejpam-3713	218	7	!	!	PUNCT
ejpam-3713	219	1	+	+	CCONJ
ejpam-3713	219	2	a	a	DET
ejpam-3713	219	3	k	k	NOUN
ejpam-3713	219	4	=	=	PROPN
ejpam-3713	219	5	n∑	n∑	NOUN
ejpam-3713	219	6	k=0	k=0	PROPN
ejpam-3713	219	7	(	(	PUNCT
ejpam-3713	219	8	rt)k	rt)k	PROPN
ejpam-3713	219	9	k	k	X
ejpam-3713	219	10	!	!	PUNCT
ejpam-3713	220	1	=	=	PUNCT
ejpam-3713	221	1	x0	x0	PROPN
ejpam-3713	221	2	−	−	PROPN
ejpam-3713	222	1	(	(	PUNCT
ejpam-3713	222	2	x0	x0	PROPN
ejpam-3713	222	3	−	−	PROPN
ejpam-3713	222	4	h	h	NOUN
ejpam-3713	222	5	r	r	NOUN
ejpam-3713	222	6	)	)	PUNCT
ejpam-3713	223	1	+	+	CCONJ
ejpam-3713	223	2	a	a	DET
ejpam-3713	223	3	k	k	NOUN
ejpam-3713	223	4	=	=	PROPN
ejpam-3713	223	5	n∑	n∑	NOUN
ejpam-3713	223	6	k=0	k=0	PROPN
ejpam-3713	223	7	(	(	PUNCT
ejpam-3713	223	8	rt)k	rt)k	PROPN
ejpam-3713	223	9	k	k	X
ejpam-3713	223	10	!	!	PUNCT
ejpam-3713	223	11	.	.	PUNCT
ejpam-3713	224	1	therefore	therefore	ADV
ejpam-3713	224	2	,	,	PUNCT
ejpam-3713	224	3	xn(t	xn(t	PUNCT
ejpam-3713	224	4	)	)	PUNCT
ejpam-3713	225	1	=	=	SYM
ejpam-3713	225	2	h	h	NOUN
ejpam-3713	226	1	r	r	NOUN
ejpam-3713	227	1	+	+	CCONJ
ejpam-3713	227	2	a	a	DET
ejpam-3713	227	3	k	k	PROPN
ejpam-3713	227	4	=	=	PROPN
ejpam-3713	227	5	n∑	n∑	NOUN
ejpam-3713	227	6	k=0	k=0	PROPN
ejpam-3713	227	7	(	(	PUNCT
ejpam-3713	227	8	rt)k	rt)k	PROPN
ejpam-3713	227	9	k	k	X
ejpam-3713	227	10	!	!	PUNCT
ejpam-3713	227	11	.	.	PUNCT
ejpam-3713	228	1	(	(	PUNCT
ejpam-3713	228	2	22	22	X
ejpam-3713	228	3	)	)	PUNCT
ejpam-3713	228	4	approaching	approach	VERB
ejpam-3713	228	5	n	n	ADV
ejpam-3713	228	6	to	to	ADP
ejpam-3713	228	7	infinity	infinity	NOUN
ejpam-3713	228	8	,	,	PUNCT
ejpam-3713	228	9	we	we	PRON
ejpam-3713	228	10	see	see	VERB
ejpam-3713	228	11	that	that	SCONJ
ejpam-3713	228	12	the	the	DET
ejpam-3713	228	13	series	series	NOUN
ejpam-3713	228	14	solution	solution	NOUN
ejpam-3713	228	15	of	of	ADP
ejpam-3713	228	16	i.v.p	i.v.p	NOUN
ejpam-3713	228	17	.	.	PUNCT
ejpam-3713	229	1	(	(	PUNCT
ejpam-3713	229	2	4	4	X
ejpam-3713	229	3	)	)	PUNCT
ejpam-3713	229	4	may	may	AUX
ejpam-3713	229	5	be	be	AUX
ejpam-3713	229	6	obtained	obtain	VERB
ejpam-3713	229	7	as	as	ADP
ejpam-3713	229	8	follows	follow	VERB
ejpam-3713	229	9	:	:	PUNCT
ejpam-3713	229	10	x(t	x(t	PROPN
ejpam-3713	229	11	)	)	PUNCT
ejpam-3713	229	12	=	=	SYM
ejpam-3713	229	13	limn→∞xn(t	limn→∞xn(t	NOUN
ejpam-3713	229	14	)	)	PUNCT
ejpam-3713	230	1	=	=	SYM
ejpam-3713	230	2	h	h	NOUN
ejpam-3713	230	3	r	r	NOUN
ejpam-3713	230	4	+	+	CCONJ
ejpam-3713	230	5	a	a	DET
ejpam-3713	230	6	k=∞∑	k=∞∑	NOUN
ejpam-3713	230	7	k=0	k=0	PROPN
ejpam-3713	230	8	(	(	PUNCT
ejpam-3713	230	9	rt)k	rt)k	PROPN
ejpam-3713	230	10	k	k	X
ejpam-3713	230	11	!	!	PUNCT
ejpam-3713	230	12	m.h	m.h	PROPN
ejpam-3713	230	13	.	.	PROPN
ejpam-3713	230	14	r.	r.	PROPN
ejpam-3713	230	15	doust	doust	PROPN
ejpam-3713	230	16	,	,	PUNCT
ejpam-3713	230	17	v.	v.	ADP
ejpam-3713	230	18	lokesha	lokesha	PROPN
ejpam-3713	230	19	,	,	PUNCT
ejpam-3713	230	20	a.	a.	NOUN
ejpam-3713	230	21	ghasemabadi	ghasemabadi	NOUN
ejpam-3713	230	22	/	/	SYM
ejpam-3713	230	23	eur	eur	PROPN
ejpam-3713	230	24	.	.	PUNCT
ejpam-3713	231	1	j.	j.	PROPN
ejpam-3713	231	2	pure	pure	PROPN
ejpam-3713	231	3	appl	appl	PROPN
ejpam-3713	231	4	.	.	PROPN
ejpam-3713	231	5	math	math	PROPN
ejpam-3713	231	6	,	,	PUNCT
ejpam-3713	231	7	13	13	NUM
ejpam-3713	231	8	(	(	PUNCT
ejpam-3713	231	9	5	5	NUM
ejpam-3713	231	10	)	)	PUNCT
ejpam-3713	231	11	(	(	PUNCT
ejpam-3713	231	12	2020	2020	NUM
ejpam-3713	231	13	)	)	PUNCT
ejpam-3713	231	14	,	,	PUNCT
ejpam-3713	231	15	1176	1176	NUM
ejpam-3713	231	16	-	-	SYM
ejpam-3713	231	17	1198	1198	NUM
ejpam-3713	231	18	1184	1184	NUM
ejpam-3713	231	19	which	which	PRON
ejpam-3713	231	20	implies	imply	VERB
ejpam-3713	231	21	that	that	SCONJ
ejpam-3713	231	22	x(t	x(t	PROPN
ejpam-3713	231	23	)	)	PUNCT
ejpam-3713	232	1	=	=	SYM
ejpam-3713	233	1	h	h	NOUN
ejpam-3713	234	1	r	r	NOUN
ejpam-3713	234	2	+	+	CCONJ
ejpam-3713	234	3	a	a	DET
ejpam-3713	234	4	k=∞∑	k=∞∑	NOUN
ejpam-3713	234	5	k=0	k=0	PROPN
ejpam-3713	234	6	(	(	PUNCT
ejpam-3713	234	7	rt)k	rt)k	PROPN
ejpam-3713	234	8	k	k	X
ejpam-3713	234	9	!	!	PUNCT
ejpam-3713	235	1	(	(	PUNCT
ejpam-3713	235	2	23	23	NUM
ejpam-3713	235	3	)	)	PUNCT
ejpam-3713	235	4	regarding	regard	VERB
ejpam-3713	235	5	the	the	DET
ejpam-3713	235	6	relation	relation	NOUN
ejpam-3713	235	7	(	(	PUNCT
ejpam-3713	235	8	16	16	NUM
ejpam-3713	235	9	)	)	PUNCT
ejpam-3713	235	10	,	,	PUNCT
ejpam-3713	235	11	we	we	PRON
ejpam-3713	235	12	may	may	AUX
ejpam-3713	235	13	work	work	VERB
ejpam-3713	235	14	out	out	ADP
ejpam-3713	235	15	the	the	DET
ejpam-3713	235	16	relation	relation	NOUN
ejpam-3713	235	17	(	(	PUNCT
ejpam-3713	235	18	7	7	NUM
ejpam-3713	235	19	)	)	PUNCT
ejpam-3713	235	20	which	which	PRON
ejpam-3713	235	21	completes	complete	VERB
ejpam-3713	235	22	the	the	DET
ejpam-3713	235	23	proof	proof	NOUN
ejpam-3713	235	24	of	of	ADP
ejpam-3713	235	25	(	(	PUNCT
ejpam-3713	235	26	ii	ii	NOUN
ejpam-3713	235	27	)	)	PUNCT
ejpam-3713	235	28	.	.	PUNCT
ejpam-3713	236	1	therefore	therefore	ADV
ejpam-3713	236	2	,	,	PUNCT
ejpam-3713	236	3	the	the	DET
ejpam-3713	236	4	proof	proof	NOUN
ejpam-3713	236	5	of	of	ADP
ejpam-3713	236	6	theorem	theorem	NOUN
ejpam-3713	236	7	is	be	AUX
ejpam-3713	236	8	done	do	VERB
ejpam-3713	236	9	.	.	PUNCT
ejpam-3713	237	1	2.2	2.2	NUM
ejpam-3713	237	2	.	.	PUNCT
ejpam-3713	238	1	the	the	DET
ejpam-3713	238	2	logistic	logistic	ADJ
ejpam-3713	238	3	model	model	NOUN
ejpam-3713	238	4	without	without	ADP
ejpam-3713	238	5	harvesting	harvesting	NOUN
ejpam-3713	238	6	factor	factor	NOUN
ejpam-3713	238	7	extended	extend	VERB
ejpam-3713	238	8	exponential	exponential	ADJ
ejpam-3713	238	9	growth	growth	NOUN
ejpam-3713	238	10	is	be	AUX
ejpam-3713	238	11	possible	possible	ADJ
ejpam-3713	238	12	only	only	ADV
ejpam-3713	238	13	when	when	SCONJ
ejpam-3713	238	14	infinite	infinite	ADJ
ejpam-3713	238	15	natural	natural	ADJ
ejpam-3713	238	16	resources	resource	NOUN
ejpam-3713	238	17	are	be	AUX
ejpam-3713	238	18	available	available	ADJ
ejpam-3713	238	19	;	;	PUNCT
ejpam-3713	238	20	this	this	PRON
ejpam-3713	238	21	is	be	AUX
ejpam-3713	238	22	not	not	PART
ejpam-3713	238	23	the	the	DET
ejpam-3713	238	24	case	case	NOUN
ejpam-3713	238	25	in	in	ADP
ejpam-3713	238	26	the	the	DET
ejpam-3713	238	27	real	real	ADJ
ejpam-3713	238	28	world	world	NOUN
ejpam-3713	238	29	.	.	PUNCT
ejpam-3713	239	1	charles	charles	PROPN
ejpam-3713	239	2	darwin	darwin	PROPN
ejpam-3713	239	3	recognized	recognize	VERB
ejpam-3713	239	4	this	this	DET
ejpam-3713	239	5	fact	fact	NOUN
ejpam-3713	239	6	in	in	ADP
ejpam-3713	239	7	his	his	PRON
ejpam-3713	239	8	description	description	NOUN
ejpam-3713	239	9	of	of	ADP
ejpam-3713	239	10	the	the	DET
ejpam-3713	239	11	”	"	PUNCT
ejpam-3713	239	12	struggle	struggle	NOUN
ejpam-3713	239	13	for	for	ADP
ejpam-3713	239	14	existence	existence	NOUN
ejpam-3713	239	15	,	,	PUNCT
ejpam-3713	239	16	”	"	PUNCT
ejpam-3713	239	17	which	which	PRON
ejpam-3713	239	18	states	state	VERB
ejpam-3713	239	19	that	that	SCONJ
ejpam-3713	239	20	individuals	individual	NOUN
ejpam-3713	239	21	will	will	AUX
ejpam-3713	239	22	compete	compete	VERB
ejpam-3713	239	23	(	(	PUNCT
ejpam-3713	239	24	with	with	ADP
ejpam-3713	239	25	members	member	NOUN
ejpam-3713	239	26	of	of	ADP
ejpam-3713	239	27	their	their	PRON
ejpam-3713	239	28	own	own	ADJ
ejpam-3713	239	29	or	or	CCONJ
ejpam-3713	239	30	other	other	ADJ
ejpam-3713	239	31	species	specie	NOUN
ejpam-3713	239	32	)	)	PUNCT
ejpam-3713	239	33	for	for	ADP
ejpam-3713	239	34	limited	limited	ADJ
ejpam-3713	239	35	resources	resource	NOUN
ejpam-3713	239	36	.	.	PUNCT
ejpam-3713	240	1	the	the	DET
ejpam-3713	240	2	successful	successful	ADJ
ejpam-3713	240	3	ones	one	NOUN
ejpam-3713	240	4	are	be	AUX
ejpam-3713	240	5	more	more	ADV
ejpam-3713	240	6	likely	likely	ADJ
ejpam-3713	240	7	to	to	PART
ejpam-3713	240	8	survive	survive	VERB
ejpam-3713	240	9	and	and	CCONJ
ejpam-3713	240	10	pass	pass	VERB
ejpam-3713	240	11	on	on	ADP
ejpam-3713	240	12	the	the	DET
ejpam-3713	240	13	traits	trait	NOUN
ejpam-3713	240	14	that	that	PRON
ejpam-3713	240	15	made	make	VERB
ejpam-3713	240	16	them	they	PRON
ejpam-3713	240	17	successful	successful	ADJ
ejpam-3713	240	18	to	to	ADP
ejpam-3713	240	19	the	the	DET
ejpam-3713	240	20	next	next	ADJ
ejpam-3713	240	21	generation	generation	NOUN
ejpam-3713	240	22	at	at	ADP
ejpam-3713	240	23	a	a	DET
ejpam-3713	240	24	greater	great	ADJ
ejpam-3713	240	25	rate	rate	NOUN
ejpam-3713	240	26	(	(	PUNCT
ejpam-3713	240	27	natural	natural	ADJ
ejpam-3713	240	28	selection	selection	NOUN
ejpam-3713	240	29	)	)	PUNCT
ejpam-3713	240	30	.	.	PUNCT
ejpam-3713	241	1	to	to	PART
ejpam-3713	241	2	model	model	VERB
ejpam-3713	241	3	the	the	DET
ejpam-3713	241	4	reality	reality	NOUN
ejpam-3713	241	5	of	of	ADP
ejpam-3713	241	6	limited	limited	ADJ
ejpam-3713	241	7	resources	resource	NOUN
ejpam-3713	241	8	,	,	PUNCT
ejpam-3713	241	9	population	population	NOUN
ejpam-3713	241	10	ecologists	ecologist	NOUN
ejpam-3713	241	11	developed	develop	VERB
ejpam-3713	241	12	the	the	DET
ejpam-3713	241	13	logistic	logistic	ADJ
ejpam-3713	241	14	growth	growth	NOUN
ejpam-3713	241	15	model	model	NOUN
ejpam-3713	241	16	.	.	PUNCT
ejpam-3713	242	1	in	in	ADP
ejpam-3713	242	2	the	the	DET
ejpam-3713	242	3	real	real	ADJ
ejpam-3713	242	4	world	world	NOUN
ejpam-3713	242	5	,	,	PUNCT
ejpam-3713	242	6	with	with	ADP
ejpam-3713	242	7	its	its	PRON
ejpam-3713	242	8	limited	limited	ADJ
ejpam-3713	242	9	resources	resource	NOUN
ejpam-3713	242	10	,	,	PUNCT
ejpam-3713	242	11	exponential	exponential	ADJ
ejpam-3713	242	12	growth	growth	NOUN
ejpam-3713	242	13	can	can	AUX
ejpam-3713	242	14	not	not	PART
ejpam-3713	242	15	continue	continue	VERB
ejpam-3713	242	16	indefinitely	indefinitely	ADV
ejpam-3713	242	17	.	.	PUNCT
ejpam-3713	243	1	exponential	exponential	ADJ
ejpam-3713	243	2	growth	growth	NOUN
ejpam-3713	243	3	may	may	AUX
ejpam-3713	243	4	occur	occur	VERB
ejpam-3713	243	5	in	in	ADP
ejpam-3713	243	6	environments	environment	NOUN
ejpam-3713	243	7	where	where	SCONJ
ejpam-3713	243	8	there	there	PRON
ejpam-3713	243	9	are	be	VERB
ejpam-3713	243	10	few	few	ADJ
ejpam-3713	243	11	individuals	individual	NOUN
ejpam-3713	243	12	and	and	CCONJ
ejpam-3713	243	13	plentiful	plentiful	ADJ
ejpam-3713	243	14	resources	resource	NOUN
ejpam-3713	243	15	,	,	PUNCT
ejpam-3713	243	16	but	but	CCONJ
ejpam-3713	243	17	when	when	SCONJ
ejpam-3713	243	18	the	the	DET
ejpam-3713	243	19	number	number	NOUN
ejpam-3713	243	20	of	of	ADP
ejpam-3713	243	21	individuals	individual	NOUN
ejpam-3713	243	22	gets	get	VERB
ejpam-3713	243	23	large	large	ADJ
ejpam-3713	243	24	enough	enough	ADV
ejpam-3713	243	25	,	,	PUNCT
ejpam-3713	243	26	resources	resource	NOUN
ejpam-3713	243	27	will	will	AUX
ejpam-3713	243	28	be	be	AUX
ejpam-3713	243	29	depleted	deplete	VERB
ejpam-3713	243	30	and	and	CCONJ
ejpam-3713	243	31	the	the	DET
ejpam-3713	243	32	growth	growth	NOUN
ejpam-3713	243	33	rate	rate	NOUN
ejpam-3713	243	34	will	will	AUX
ejpam-3713	243	35	slow	slow	VERB
ejpam-3713	243	36	down	down	ADP
ejpam-3713	243	37	.	.	PUNCT
ejpam-3713	244	1	eventually	eventually	ADV
ejpam-3713	244	2	,	,	PUNCT
ejpam-3713	244	3	the	the	DET
ejpam-3713	244	4	growth	growth	NOUN
ejpam-3713	244	5	rate	rate	NOUN
ejpam-3713	244	6	will	will	AUX
ejpam-3713	244	7	plateau	plateau	VERB
ejpam-3713	244	8	or	or	CCONJ
ejpam-3713	244	9	level	level	VERB
ejpam-3713	244	10	off	off	ADP
ejpam-3713	244	11	.	.	PUNCT
ejpam-3713	245	1	this	this	DET
ejpam-3713	245	2	population	population	NOUN
ejpam-3713	245	3	size	size	NOUN
ejpam-3713	245	4	,	,	PUNCT
ejpam-3713	245	5	which	which	PRON
ejpam-3713	245	6	is	be	AUX
ejpam-3713	245	7	determined	determine	VERB
ejpam-3713	245	8	by	by	ADP
ejpam-3713	245	9	the	the	DET
ejpam-3713	245	10	maximum	maximum	ADJ
ejpam-3713	245	11	population	population	NOUN
ejpam-3713	245	12	size	size	NOUN
ejpam-3713	245	13	that	that	PRON
ejpam-3713	245	14	a	a	DET
ejpam-3713	245	15	particular	particular	ADJ
ejpam-3713	245	16	environment	environment	NOUN
ejpam-3713	245	17	can	can	AUX
ejpam-3713	245	18	sustain	sustain	VERB
ejpam-3713	245	19	,	,	PUNCT
ejpam-3713	245	20	is	be	AUX
ejpam-3713	245	21	called	call	VERB
ejpam-3713	245	22	the	the	DET
ejpam-3713	245	23	carrying	carrying	NOUN
ejpam-3713	245	24	capacity	capacity	NOUN
ejpam-3713	245	25	.	.	PUNCT
ejpam-3713	246	1	in	in	ADP
ejpam-3713	246	2	real	real	ADJ
ejpam-3713	246	3	populations	population	NOUN
ejpam-3713	246	4	,	,	PUNCT
ejpam-3713	246	5	a	a	DET
ejpam-3713	246	6	growing	grow	VERB
ejpam-3713	246	7	population	population	NOUN
ejpam-3713	246	8	often	often	ADV
ejpam-3713	246	9	overshoots	overshoot	VERB
ejpam-3713	246	10	its	its	PRON
ejpam-3713	246	11	carrying	carrying	NOUN
ejpam-3713	246	12	capacity	capacity	NOUN
ejpam-3713	246	13	,	,	PUNCT
ejpam-3713	246	14	and	and	CCONJ
ejpam-3713	246	15	the	the	DET
ejpam-3713	246	16	death	death	NOUN
ejpam-3713	246	17	rate	rate	NOUN
ejpam-3713	246	18	increases	increase	NOUN
ejpam-3713	246	19	beyond	beyond	ADP
ejpam-3713	246	20	the	the	DET
ejpam-3713	246	21	birth	birth	NOUN
ejpam-3713	246	22	rate	rate	NOUN
ejpam-3713	246	23	causing	cause	VERB
ejpam-3713	246	24	the	the	DET
ejpam-3713	246	25	population	population	NOUN
ejpam-3713	246	26	size	size	NOUN
ejpam-3713	246	27	to	to	PART
ejpam-3713	246	28	decline	decline	VERB
ejpam-3713	246	29	back	back	ADV
ejpam-3713	246	30	to	to	ADP
ejpam-3713	246	31	the	the	DET
ejpam-3713	246	32	carrying	carrying	NOUN
ejpam-3713	246	33	capacity	capacity	NOUN
ejpam-3713	246	34	or	or	CCONJ
ejpam-3713	246	35	below	below	ADP
ejpam-3713	246	36	it	it	PRON
ejpam-3713	246	37	.	.	PUNCT
ejpam-3713	247	1	most	most	ADJ
ejpam-3713	247	2	populations	population	NOUN
ejpam-3713	247	3	usually	usually	ADV
ejpam-3713	247	4	fluctuate	fluctuate	VERB
ejpam-3713	247	5	around	around	ADP
ejpam-3713	247	6	the	the	DET
ejpam-3713	247	7	carrying	carry	VERB
ejpam-3713	247	8	capacity	capacity	NOUN
ejpam-3713	247	9	in	in	ADP
ejpam-3713	247	10	an	an	DET
ejpam-3713	247	11	undulating	undulate	VERB
ejpam-3713	247	12	fashion	fashion	NOUN
ejpam-3713	247	13	rather	rather	ADV
ejpam-3713	247	14	than	than	ADP
ejpam-3713	247	15	existing	exist	VERB
ejpam-3713	247	16	right	right	ADV
ejpam-3713	247	17	at	at	ADP
ejpam-3713	247	18	it	it	PRON
ejpam-3713	247	19	.	.	PUNCT
ejpam-3713	248	1	we	we	PRON
ejpam-3713	248	2	are	be	AUX
ejpam-3713	248	3	now	now	ADV
ejpam-3713	248	4	in	in	ADP
ejpam-3713	248	5	a	a	DET
ejpam-3713	248	6	position	position	NOUN
ejpam-3713	248	7	model	model	NOUN
ejpam-3713	248	8	the	the	DET
ejpam-3713	248	9	logistic	logistic	ADJ
ejpam-3713	248	10	growth	growth	NOUN
ejpam-3713	248	11	.	.	PUNCT
ejpam-3713	249	1	by	by	ADP
ejpam-3713	249	2	this	this	DET
ejpam-3713	249	3	mean	mean	NOUN
ejpam-3713	249	4	consider	consider	VERB
ejpam-3713	249	5	positive	positive	ADJ
ejpam-3713	249	6	parameters	parameter	NOUN
ejpam-3713	249	7	m	m	VERB
ejpam-3713	249	8	and	and	CCONJ
ejpam-3713	249	9	r	r	NOUN
ejpam-3713	249	10	as	as	ADP
ejpam-3713	249	11	the	the	DET
ejpam-3713	249	12	carrying	carrying	NOUN
ejpam-3713	249	13	capacity	capacity	NOUN
ejpam-3713	249	14	of	of	ADP
ejpam-3713	249	15	the	the	DET
ejpam-3713	249	16	environment	environment	NOUN
ejpam-3713	249	17	and	and	CCONJ
ejpam-3713	249	18	the	the	DET
ejpam-3713	249	19	rate	rate	NOUN
ejpam-3713	249	20	of	of	ADP
ejpam-3713	249	21	growth	growth	NOUN
ejpam-3713	249	22	for	for	ADP
ejpam-3713	249	23	small	small	ADJ
ejpam-3713	249	24	population	population	NOUN
ejpam-3713	249	25	numbers	number	NOUN
ejpam-3713	249	26	,	,	PUNCT
ejpam-3713	249	27	respectively	respectively	ADV
ejpam-3713	249	28	.	.	PUNCT
ejpam-3713	250	1	it	it	PRON
ejpam-3713	250	2	is	be	AUX
ejpam-3713	250	3	obvious	obvious	ADJ
ejpam-3713	250	4	that	that	SCONJ
ejpam-3713	250	5	the	the	DET
ejpam-3713	250	6	factor	factor	NOUN
ejpam-3713	250	7	rx	rx	VERB
ejpam-3713	250	8	represents	represent	VERB
ejpam-3713	250	9	unhampered	unhampered	ADJ
ejpam-3713	250	10	growth	growth	NOUN
ejpam-3713	250	11	and	and	CCONJ
ejpam-3713	250	12	reduced	reduce	VERB
ejpam-3713	250	13	by	by	ADP
ejpam-3713	250	14	the	the	DET
ejpam-3713	250	15	term	term	NOUN
ejpam-3713	250	16	r	r	NOUN
ejpam-3713	250	17	m	m	NOUN
ejpam-3713	250	18	x2	x2	NOUN
ejpam-3713	250	19	that	that	PRON
ejpam-3713	250	20	corresponds	correspond	VERB
ejpam-3713	250	21	to	to	ADP
ejpam-3713	250	22	competition	competition	NOUN
ejpam-3713	250	23	for	for	ADP
ejpam-3713	250	24	limited	limited	ADJ
ejpam-3713	250	25	resources	resource	NOUN
ejpam-3713	250	26	within	within	ADP
ejpam-3713	250	27	the	the	DET
ejpam-3713	250	28	population	population	NOUN
ejpam-3713	250	29	.	.	PUNCT
ejpam-3713	251	1	thus	thus	ADV
ejpam-3713	251	2	the	the	DET
ejpam-3713	251	3	form	form	NOUN
ejpam-3713	251	4	the	the	DET
ejpam-3713	251	5	following	follow	VERB
ejpam-3713	251	6	equation	equation	NOUN
ejpam-3713	251	7	may	may	AUX
ejpam-3713	251	8	be	be	AUX
ejpam-3713	251	9	obtained	obtain	VERB
ejpam-3713	251	10	:	:	PUNCT
ejpam-3713	251	11	dx	dx	PROPN
ejpam-3713	251	12	dt	dt	NOUN
ejpam-3713	252	1	=	=	PUNCT
ejpam-3713	252	2	rx(1−	rx(1−	PROPN
ejpam-3713	252	3	x	x	X
ejpam-3713	252	4	m	m	PROPN
ejpam-3713	252	5	)	)	PUNCT
ejpam-3713	252	6	.	.	PUNCT
ejpam-3713	253	1	(	(	PUNCT
ejpam-3713	253	2	24	24	NUM
ejpam-3713	253	3	)	)	PUNCT
ejpam-3713	253	4	this	this	DET
ejpam-3713	253	5	equation	equation	NOUN
ejpam-3713	253	6	is	be	AUX
ejpam-3713	253	7	known	know	VERB
ejpam-3713	253	8	as	as	ADP
ejpam-3713	253	9	the	the	DET
ejpam-3713	253	10	logistic	logistic	ADJ
ejpam-3713	253	11	equation	equation	NOUN
ejpam-3713	253	12	.	.	PUNCT
ejpam-3713	254	1	in	in	ADP
ejpam-3713	254	2	precisely	precisely	ADV
ejpam-3713	254	3	speaking	speak	VERB
ejpam-3713	254	4	,	,	PUNCT
ejpam-3713	254	5	the	the	DET
ejpam-3713	254	6	above	above	ADJ
ejpam-3713	254	7	formula	formula	NOUN
ejpam-3713	254	8	used	use	VERB
ejpam-3713	254	9	to	to	PART
ejpam-3713	254	10	calculate	calculate	VERB
ejpam-3713	254	11	logistic	logistic	ADJ
ejpam-3713	254	12	growth	growth	NOUN
ejpam-3713	254	13	adds	add	VERB
ejpam-3713	254	14	the	the	DET
ejpam-3713	254	15	carrying	carrying	NOUN
ejpam-3713	254	16	capacity	capacity	NOUN
ejpam-3713	254	17	as	as	ADP
ejpam-3713	254	18	a	a	DET
ejpam-3713	254	19	moderating	moderate	VERB
ejpam-3713	254	20	force	force	NOUN
ejpam-3713	254	21	in	in	ADP
ejpam-3713	254	22	the	the	DET
ejpam-3713	254	23	growth	growth	NOUN
ejpam-3713	254	24	rate	rate	NOUN
ejpam-3713	254	25	.	.	PUNCT
ejpam-3713	255	1	the	the	DET
ejpam-3713	255	2	expression	expression	NOUN
ejpam-3713	255	3	m	m	VERB
ejpam-3713	255	4	−	−	NOUN
ejpam-3713	255	5	x	x	VERB
ejpam-3713	255	6	is	be	AUX
ejpam-3713	255	7	equal	equal	ADJ
ejpam-3713	255	8	to	to	ADP
ejpam-3713	255	9	the	the	DET
ejpam-3713	255	10	number	number	NOUN
ejpam-3713	255	11	of	of	ADP
ejpam-3713	255	12	individuals	individual	NOUN
ejpam-3713	255	13	that	that	PRON
ejpam-3713	255	14	may	may	AUX
ejpam-3713	255	15	be	be	AUX
ejpam-3713	255	16	added	add	VERB
ejpam-3713	255	17	to	to	ADP
ejpam-3713	255	18	a	a	DET
ejpam-3713	255	19	population	population	NOUN
ejpam-3713	255	20	at	at	ADP
ejpam-3713	255	21	a	a	DET
ejpam-3713	255	22	given	give	VERB
ejpam-3713	255	23	time	time	NOUN
ejpam-3713	255	24	,	,	PUNCT
ejpam-3713	255	25	and	and	CCONJ
ejpam-3713	255	26	we	we	PRON
ejpam-3713	255	27	saw	see	VERB
ejpam-3713	255	28	that	that	SCONJ
ejpam-3713	255	29	m	m	VERB
ejpam-3713	255	30	−	−	NOUN
ejpam-3713	255	31	x	x	VERB
ejpam-3713	255	32	is	be	AUX
ejpam-3713	255	33	divided	divide	VERB
ejpam-3713	255	34	by	by	ADP
ejpam-3713	255	35	m	m	PROPN
ejpam-3713	255	36	is	be	AUX
ejpam-3713	255	37	the	the	DET
ejpam-3713	255	38	fraction	fraction	NOUN
ejpam-3713	255	39	of	of	ADP
ejpam-3713	255	40	the	the	DET
ejpam-3713	255	41	carrying	carry	VERB
ejpam-3713	255	42	capacity	capacity	NOUN
ejpam-3713	255	43	available	available	ADJ
ejpam-3713	255	44	for	for	ADP
ejpam-3713	255	45	further	further	ADJ
ejpam-3713	255	46	growth	growth	NOUN
ejpam-3713	255	47	.	.	PUNCT
ejpam-3713	256	1	thus	thus	ADV
ejpam-3713	256	2	,	,	PUNCT
ejpam-3713	256	3	the	the	DET
ejpam-3713	256	4	exponential	exponential	ADJ
ejpam-3713	256	5	growth	growth	NOUN
ejpam-3713	256	6	model	model	NOUN
ejpam-3713	256	7	is	be	AUX
ejpam-3713	256	8	restricted	restrict	VERB
ejpam-3713	256	9	by	by	ADP
ejpam-3713	256	10	this	this	DET
ejpam-3713	256	11	factor	factor	NOUN
ejpam-3713	256	12	to	to	PART
ejpam-3713	256	13	generate	generate	VERB
ejpam-3713	256	14	the	the	DET
ejpam-3713	256	15	logistic	logistic	ADJ
ejpam-3713	256	16	growth	growth	NOUN
ejpam-3713	256	17	equation	equation	NOUN
ejpam-3713	256	18	.	.	PUNCT
ejpam-3713	257	1	therefore	therefore	ADV
ejpam-3713	257	2	,	,	PUNCT
ejpam-3713	257	3	we	we	PRON
ejpam-3713	257	4	can	can	AUX
ejpam-3713	257	5	take	take	VERB
ejpam-3713	257	6	a	a	DET
ejpam-3713	257	7	result	result	NOUN
ejpam-3713	257	8	as	as	SCONJ
ejpam-3713	257	9	”	"	PUNCT
ejpam-3713	257	10	carrying	carry	VERB
ejpam-3713	257	11	capacity	capacity	NOUN
ejpam-3713	257	12	is	be	AUX
ejpam-3713	257	13	the	the	DET
ejpam-3713	257	14	most	most	ADJ
ejpam-3713	257	15	and	and	CCONJ
ejpam-3713	257	16	important	important	ADJ
ejpam-3713	257	17	subject	subject	NOUN
ejpam-3713	257	18	in	in	ADP
ejpam-3713	257	19	any	any	DET
ejpam-3713	257	20	logistic	logistic	ADJ
ejpam-3713	257	21	modeling	modeling	NOUN
ejpam-3713	257	22	”	"	PUNCT
ejpam-3713	257	23	.	.	PUNCT
ejpam-3713	258	1	when	when	SCONJ
ejpam-3713	258	2	the	the	DET
ejpam-3713	258	3	population	population	NOUN
ejpam-3713	258	4	size	size	NOUN
ejpam-3713	258	5	is	be	AUX
ejpam-3713	258	6	equal	equal	ADJ
ejpam-3713	258	7	to	to	ADP
ejpam-3713	258	8	the	the	DET
ejpam-3713	258	9	carrying	carrying	NOUN
ejpam-3713	258	10	capacity	capacity	NOUN
ejpam-3713	258	11	,	,	PUNCT
ejpam-3713	258	12	the	the	DET
ejpam-3713	258	13	quantity	quantity	NOUN
ejpam-3713	258	14	in	in	ADP
ejpam-3713	258	15	m.h	m.h	PROPN
ejpam-3713	258	16	.	.	PROPN
ejpam-3713	258	17	r.	r.	PROPN
ejpam-3713	258	18	doust	doust	PROPN
ejpam-3713	258	19	,	,	PUNCT
ejpam-3713	258	20	v.	v.	ADP
ejpam-3713	258	21	lokesha	lokesha	PROPN
ejpam-3713	258	22	,	,	PUNCT
ejpam-3713	258	23	a.	a.	NOUN
ejpam-3713	258	24	ghasemabadi	ghasemabadi	NOUN
ejpam-3713	258	25	/	/	SYM
ejpam-3713	258	26	eur	eur	PROPN
ejpam-3713	258	27	.	.	PUNCT
ejpam-3713	259	1	j.	j.	PROPN
ejpam-3713	259	2	pure	pure	PROPN
ejpam-3713	259	3	appl	appl	PROPN
ejpam-3713	259	4	.	.	PROPN
ejpam-3713	259	5	math	math	PROPN
ejpam-3713	259	6	,	,	PUNCT
ejpam-3713	259	7	13	13	NUM
ejpam-3713	259	8	(	(	PUNCT
ejpam-3713	259	9	5	5	NUM
ejpam-3713	259	10	)	)	PUNCT
ejpam-3713	259	11	(	(	PUNCT
ejpam-3713	259	12	2020	2020	NUM
ejpam-3713	259	13	)	)	PUNCT
ejpam-3713	259	14	,	,	PUNCT
ejpam-3713	259	15	1176	1176	NUM
ejpam-3713	259	16	-	-	SYM
ejpam-3713	259	17	1198	1198	NUM
ejpam-3713	259	18	1185	1185	NUM
ejpam-3713	259	19	parentheses	parenthesis	NOUN
ejpam-3713	259	20	is	be	AUX
ejpam-3713	259	21	equal	equal	ADJ
ejpam-3713	259	22	to	to	ADP
ejpam-3713	259	23	zero	zero	NUM
ejpam-3713	259	24	and	and	CCONJ
ejpam-3713	259	25	growth	growth	NOUN
ejpam-3713	259	26	is	be	AUX
ejpam-3713	259	27	equal	equal	ADJ
ejpam-3713	259	28	to	to	ADP
ejpam-3713	259	29	zero	zero	NUM
ejpam-3713	259	30	.	.	PUNCT
ejpam-3713	260	1	a	a	DET
ejpam-3713	260	2	graph	graph	NOUN
ejpam-3713	260	3	of	of	ADP
ejpam-3713	260	4	this	this	DET
ejpam-3713	260	5	equation	equation	NOUN
ejpam-3713	260	6	yields	yield	VERB
ejpam-3713	260	7	the	the	DET
ejpam-3713	260	8	s	s	NOUN
ejpam-3713	260	9	-	-	PUNCT
ejpam-3713	260	10	shaped	shape	VERB
ejpam-3713	260	11	curve	curve	NOUN
ejpam-3713	260	12	.	.	PUNCT
ejpam-3713	261	1	it	it	PRON
ejpam-3713	261	2	is	be	AUX
ejpam-3713	261	3	a	a	DET
ejpam-3713	261	4	more	more	ADV
ejpam-3713	261	5	realistic	realistic	ADJ
ejpam-3713	261	6	model	model	NOUN
ejpam-3713	261	7	of	of	ADP
ejpam-3713	261	8	population	population	NOUN
ejpam-3713	261	9	growth	growth	NOUN
ejpam-3713	261	10	than	than	ADP
ejpam-3713	261	11	exponential	exponential	ADJ
ejpam-3713	261	12	growth	growth	NOUN
ejpam-3713	261	13	.	.	PUNCT
ejpam-3713	262	1	there	there	PRON
ejpam-3713	262	2	are	be	VERB
ejpam-3713	262	3	three	three	NUM
ejpam-3713	262	4	different	different	ADJ
ejpam-3713	262	5	sections	section	NOUN
ejpam-3713	262	6	to	to	ADP
ejpam-3713	262	7	an	an	DET
ejpam-3713	262	8	s	s	ADV
ejpam-3713	262	9	-	-	PUNCT
ejpam-3713	262	10	shaped	shape	VERB
ejpam-3713	262	11	curve	curve	NOUN
ejpam-3713	262	12	.	.	PUNCT
ejpam-3713	263	1	initially	initially	ADV
ejpam-3713	263	2	,	,	PUNCT
ejpam-3713	263	3	growth	growth	NOUN
ejpam-3713	263	4	is	be	AUX
ejpam-3713	263	5	exponential	exponential	ADJ
ejpam-3713	263	6	because	because	SCONJ
ejpam-3713	263	7	there	there	PRON
ejpam-3713	263	8	are	be	VERB
ejpam-3713	263	9	few	few	ADJ
ejpam-3713	263	10	individuals	individual	NOUN
ejpam-3713	263	11	and	and	CCONJ
ejpam-3713	263	12	ample	ample	ADJ
ejpam-3713	263	13	resources	resource	NOUN
ejpam-3713	263	14	available	available	ADJ
ejpam-3713	263	15	.	.	PUNCT
ejpam-3713	264	1	then	then	ADV
ejpam-3713	264	2	,	,	PUNCT
ejpam-3713	264	3	as	as	SCONJ
ejpam-3713	264	4	resources	resource	NOUN
ejpam-3713	264	5	begin	begin	VERB
ejpam-3713	264	6	to	to	PART
ejpam-3713	264	7	become	become	VERB
ejpam-3713	264	8	limited	limited	ADJ
ejpam-3713	264	9	,	,	PUNCT
ejpam-3713	264	10	the	the	DET
ejpam-3713	264	11	growth	growth	NOUN
ejpam-3713	264	12	rate	rate	NOUN
ejpam-3713	264	13	decreases	decrease	NOUN
ejpam-3713	264	14	.	.	PUNCT
ejpam-3713	265	1	finally	finally	ADV
ejpam-3713	265	2	,	,	PUNCT
ejpam-3713	265	3	the	the	DET
ejpam-3713	265	4	growth	growth	NOUN
ejpam-3713	265	5	rate	rate	NOUN
ejpam-3713	265	6	levels	level	NOUN
ejpam-3713	265	7	off	off	ADP
ejpam-3713	265	8	at	at	ADP
ejpam-3713	265	9	the	the	DET
ejpam-3713	265	10	carrying	carry	VERB
ejpam-3713	265	11	capacity	capacity	NOUN
ejpam-3713	265	12	of	of	ADP
ejpam-3713	265	13	the	the	DET
ejpam-3713	265	14	environment	environment	NOUN
ejpam-3713	265	15	,	,	PUNCT
ejpam-3713	265	16	with	with	ADP
ejpam-3713	265	17	little	little	ADJ
ejpam-3713	265	18	change	change	NOUN
ejpam-3713	265	19	in	in	ADP
ejpam-3713	265	20	population	population	NOUN
ejpam-3713	265	21	number	number	NOUN
ejpam-3713	265	22	over	over	ADP
ejpam-3713	265	23	time	time	NOUN
ejpam-3713	265	24	.	.	PUNCT
ejpam-3713	266	1	making	make	VERB
ejpam-3713	266	2	assumption	assumption	NOUN
ejpam-3713	266	3	x(t0	x(t0	NOUN
ejpam-3713	266	4	)	)	PUNCT
ejpam-3713	267	1	=	=	PUNCT
ejpam-3713	267	2	x0	x0	PROPN
ejpam-3713	267	3	as	as	ADP
ejpam-3713	267	4	the	the	DET
ejpam-3713	267	5	initial	initial	ADJ
ejpam-3713	267	6	population	population	NOUN
ejpam-3713	267	7	for	for	ADP
ejpam-3713	267	8	time	time	NOUN
ejpam-3713	267	9	t0	t0	PROPN
ejpam-3713	267	10	in	in	ADP
ejpam-3713	267	11	logistic	logistic	ADJ
ejpam-3713	267	12	equation	equation	NOUN
ejpam-3713	267	13	(	(	PUNCT
ejpam-3713	267	14	24	24	NUM
ejpam-3713	267	15	)	)	PUNCT
ejpam-3713	267	16	,	,	PUNCT
ejpam-3713	267	17	we	we	PRON
ejpam-3713	267	18	may	may	AUX
ejpam-3713	267	19	obtain	obtain	VERB
ejpam-3713	267	20	an	an	DET
ejpam-3713	267	21	ecological	ecological	ADJ
ejpam-3713	267	22	i.v.p	i.v.p	NOUN
ejpam-3713	267	23	.	.	PUNCT
ejpam-3713	268	1	for	for	ADP
ejpam-3713	268	2	simplifying	simplifying	NOUN
ejpam-3713	268	3	,	,	PUNCT
ejpam-3713	268	4	we	we	PRON
ejpam-3713	268	5	denoted	denote	VERB
ejpam-3713	268	6	t0	t0	PROPN
ejpam-3713	268	7	by	by	ADP
ejpam-3713	268	8	0	0	PROPN
ejpam-3713	268	9	.	.	PUNCT
ejpam-3713	268	10	{	{	PUNCT
ejpam-3713	269	1	dx	dx	PROPN
ejpam-3713	269	2	dt	dt	NOUN
ejpam-3713	269	3	=	=	PUNCT
ejpam-3713	270	1	rx(1−	rx(1−	PROPN
ejpam-3713	270	2	x	x	X
ejpam-3713	270	3	m	m	NOUN
ejpam-3713	270	4	)	)	PUNCT
ejpam-3713	270	5	x(0	x(0	PROPN
ejpam-3713	270	6	)	)	PUNCT
ejpam-3713	271	1	=	=	PUNCT
ejpam-3713	271	2	x0	x0	PROPN
ejpam-3713	271	3	.	.	PUNCT
ejpam-3713	272	1	(	(	PUNCT
ejpam-3713	272	2	25	25	NUM
ejpam-3713	272	3	)	)	PUNCT
ejpam-3713	272	4	by	by	ADP
ejpam-3713	272	5	using	use	VERB
ejpam-3713	272	6	integration	integration	NOUN
ejpam-3713	272	7	part	part	NOUN
ejpam-3713	272	8	by	by	ADP
ejpam-3713	272	9	part	part	NOUN
ejpam-3713	272	10	,	,	PUNCT
ejpam-3713	272	11	the	the	DET
ejpam-3713	272	12	solution	solution	NOUN
ejpam-3713	272	13	of	of	ADP
ejpam-3713	272	14	above	above	ADJ
ejpam-3713	272	15	i.v.p	i.v.p	NOUN
ejpam-3713	272	16	.	.	PUNCT
ejpam-3713	273	1	may	may	AUX
ejpam-3713	273	2	be	be	AUX
ejpam-3713	273	3	found	find	VERB
ejpam-3713	273	4	as	as	SCONJ
ejpam-3713	273	5	follows	follow	VERB
ejpam-3713	273	6	:	:	PUNCT
ejpam-3713	273	7	x(t	x(t	PROPN
ejpam-3713	273	8	)	)	PUNCT
ejpam-3713	274	1	=	=	PUNCT
ejpam-3713	275	1	mx0	mx0	PROPN
ejpam-3713	275	2	x0	x0	PROPN
ejpam-3713	275	3	+	+	CCONJ
ejpam-3713	275	4	(	(	PUNCT
ejpam-3713	275	5	m	m	VERB
ejpam-3713	275	6	−	−	PROPN
ejpam-3713	275	7	x0)exp(−rt	x0)exp(−rt	NUM
ejpam-3713	275	8	)	)	PUNCT
ejpam-3713	275	9	(	(	PUNCT
ejpam-3713	275	10	26	26	NUM
ejpam-3713	275	11	)	)	PUNCT
ejpam-3713	275	12	it	it	PRON
ejpam-3713	275	13	is	be	AUX
ejpam-3713	275	14	clear	clear	ADJ
ejpam-3713	275	15	that	that	SCONJ
ejpam-3713	275	16	the	the	DET
ejpam-3713	275	17	following	follow	VERB
ejpam-3713	275	18	properties	property	NOUN
ejpam-3713	275	19	for	for	ADP
ejpam-3713	275	20	the	the	DET
ejpam-3713	275	21	last	last	ADJ
ejpam-3713	275	22	i.v.p	i.v.p	NOUN
ejpam-3713	275	23	.	.	PUNCT
ejpam-3713	276	1	may	may	AUX
ejpam-3713	276	2	be	be	AUX
ejpam-3713	276	3	obtained	obtain	VERB
ejpam-3713	276	4	:	:	PUNCT
ejpam-3713	276	5	(	(	PUNCT
ejpam-3713	276	6	a	a	X
ejpam-3713	276	7	)	)	PUNCT
ejpam-3713	276	8	it	it	PRON
ejpam-3713	276	9	has	have	VERB
ejpam-3713	276	10	two	two	NUM
ejpam-3713	276	11	equilibria	equilibrium	NOUN
ejpam-3713	276	12	x	x	PUNCT
ejpam-3713	277	1	=	=	SYM
ejpam-3713	277	2	0,m	0,m	NOUN
ejpam-3713	277	3	.	.	PUNCT
ejpam-3713	278	1	that	that	PRON
ejpam-3713	278	2	is	be	AUX
ejpam-3713	278	3	the	the	DET
ejpam-3713	278	4	density	density	NOUN
ejpam-3713	278	5	does	do	AUX
ejpam-3713	278	6	not	not	PART
ejpam-3713	278	7	change	change	VERB
ejpam-3713	278	8	in	in	ADP
ejpam-3713	278	9	these	these	DET
ejpam-3713	278	10	cases	case	NOUN
ejpam-3713	278	11	.	.	PUNCT
ejpam-3713	279	1	for	for	ADP
ejpam-3713	279	2	0	0	NUM
ejpam-3713	279	3	<	<	X
ejpam-3713	279	4	x	x	X
ejpam-3713	279	5	<	<	X
ejpam-3713	279	6	m	m	X
ejpam-3713	279	7	,	,	PUNCT
ejpam-3713	279	8	it	it	PRON
ejpam-3713	279	9	increases	increase	VERB
ejpam-3713	279	10	,	,	PUNCT
ejpam-3713	279	11	and	and	CCONJ
ejpam-3713	279	12	for	for	ADP
ejpam-3713	279	13	x	x	SYM
ejpam-3713	279	14	>	>	X
ejpam-3713	279	15	m	m	VERB
ejpam-3713	279	16	it	it	PRON
ejpam-3713	279	17	decreases	decrease	VERB
ejpam-3713	279	18	;	;	PUNCT
ejpam-3713	279	19	(	(	PUNCT
ejpam-3713	279	20	b	b	X
ejpam-3713	279	21	)	)	PUNCT
ejpam-3713	279	22	if	if	SCONJ
ejpam-3713	279	23	x0	x0	PROPN
ejpam-3713	279	24	<	<	X
ejpam-3713	279	25	m	m	PROPN
ejpam-3713	279	26	,	,	PUNCT
ejpam-3713	279	27	then	then	ADV
ejpam-3713	279	28	the	the	DET
ejpam-3713	279	29	population	population	NOUN
ejpam-3713	279	30	grows	grow	VERB
ejpam-3713	279	31	and	and	CCONJ
ejpam-3713	279	32	approaches	approach	NOUN
ejpam-3713	279	33	to	to	ADP
ejpam-3713	279	34	m	m	PRON
ejpam-3713	279	35	asymptotically	asymptotically	ADV
ejpam-3713	279	36	as	as	ADP
ejpam-3713	279	37	t→∞	t→∞	NUM
ejpam-3713	279	38	;	;	PUNCT
ejpam-3713	279	39	(	(	PUNCT
ejpam-3713	279	40	c	c	X
ejpam-3713	279	41	)	)	PUNCT
ejpam-3713	279	42	if	if	SCONJ
ejpam-3713	279	43	x0	x0	PROPN
ejpam-3713	279	44	>	>	X
ejpam-3713	279	45	m	m	PROPN
ejpam-3713	279	46	,	,	PUNCT
ejpam-3713	279	47	then	then	ADV
ejpam-3713	279	48	the	the	DET
ejpam-3713	279	49	population	population	NOUN
ejpam-3713	279	50	decreases	decrease	VERB
ejpam-3713	279	51	,	,	PUNCT
ejpam-3713	279	52	again	again	ADV
ejpam-3713	279	53	approaching	approach	VERB
ejpam-3713	279	54	m	m	PRON
ejpam-3713	279	55	asymptotically	asymptotically	ADV
ejpam-3713	279	56	as	as	ADP
ejpam-3713	279	57	t→∞	t→∞	NUM
ejpam-3713	279	58	;	;	PUNCT
ejpam-3713	279	59	(	(	PUNCT
ejpam-3713	279	60	d	d	X
ejpam-3713	279	61	)	)	PUNCT
ejpam-3713	279	62	if	if	SCONJ
ejpam-3713	279	63	x0	x0	PROPN
ejpam-3713	279	64	=	=	PROPN
ejpam-3713	279	65	m	m	PROPN
ejpam-3713	279	66	,	,	PUNCT
ejpam-3713	279	67	then	then	ADV
ejpam-3713	279	68	the	the	DET
ejpam-3713	279	69	population	population	NOUN
ejpam-3713	279	70	remains	remain	VERB
ejpam-3713	279	71	in	in	ADP
ejpam-3713	279	72	time	time	NOUN
ejpam-3713	279	73	at	at	ADP
ejpam-3713	279	74	x	x	X
ejpam-3713	279	75	=	=	VERB
ejpam-3713	279	76	m	m	NOUN
ejpam-3713	279	77	.	.	PUNCT
ejpam-3713	280	1	(	(	PUNCT
ejpam-3713	280	2	e	e	NOUN
ejpam-3713	280	3	)	)	PUNCT
ejpam-3713	280	4	equilibrium	equilibrium	NOUN
ejpam-3713	280	5	pointx	pointx	NOUN
ejpam-3713	280	6	=	=	X
ejpam-3713	280	7	m	m	NOUN
ejpam-3713	280	8	is	be	AUX
ejpam-3713	280	9	globally	globally	ADV
ejpam-3713	280	10	stable	stable	ADJ
ejpam-3713	280	11	;	;	PUNCT
ejpam-3713	280	12	i.e.	i.e.	X
ejpam-3713	280	13	lim	lim	PROPN
ejpam-3713	280	14	t→∞	t→∞	ADP
ejpam-3713	280	15	x(t	x(t	PROPN
ejpam-3713	280	16	)	)	PUNCT
ejpam-3713	280	17	=	=	PUNCT
ejpam-3713	280	18	m	m	NOUN
ejpam-3713	280	19	;	;	PUNCT
ejpam-3713	280	20	(	(	PUNCT
ejpam-3713	280	21	f	f	X
ejpam-3713	280	22	)	)	PUNCT
ejpam-3713	280	23	the	the	DET
ejpam-3713	280	24	behavior	behavior	NOUN
ejpam-3713	280	25	of	of	ADP
ejpam-3713	280	26	solution	solution	NOUN
ejpam-3713	280	27	in	in	ADP
ejpam-3713	280	28	the	the	DET
ejpam-3713	280	29	region	region	NOUN
ejpam-3713	280	30	between	between	ADP
ejpam-3713	280	31	0	0	NUM
ejpam-3713	280	32	and	and	CCONJ
ejpam-3713	280	33	m	m	PROPN
ejpam-3713	280	34	is	be	AUX
ejpam-3713	280	35	known	know	VERB
ejpam-3713	280	36	as	as	ADP
ejpam-3713	280	37	logistic	logistic	ADJ
ejpam-3713	280	38	growth	growth	NOUN
ejpam-3713	280	39	.	.	PUNCT
ejpam-3713	281	1	the	the	DET
ejpam-3713	281	2	above	above	ADJ
ejpam-3713	281	3	discussion	discussion	NOUN
ejpam-3713	281	4	is	be	AUX
ejpam-3713	281	5	verified	verify	VERB
ejpam-3713	281	6	by	by	ADP
ejpam-3713	281	7	numerical	numerical	ADJ
ejpam-3713	281	8	simulation	simulation	NOUN
ejpam-3713	281	9	for	for	ADP
ejpam-3713	281	10	some	some	DET
ejpam-3713	281	11	different	different	ADJ
ejpam-3713	281	12	values	value	NOUN
ejpam-3713	281	13	of	of	ADP
ejpam-3713	281	14	r	r	NOUN
ejpam-3713	281	15	and	and	CCONJ
ejpam-3713	281	16	m	m	VERB
ejpam-3713	281	17	in	in	ADP
ejpam-3713	281	18	section	section	NOUN
ejpam-3713	281	19	3	3	NUM
ejpam-3713	281	20	and	and	CCONJ
ejpam-3713	281	21	shown	show	VERB
ejpam-3713	281	22	in	in	ADP
ejpam-3713	281	23	figure	figure	NOUN
ejpam-3713	281	24	(	(	PUNCT
ejpam-3713	281	25	1	1	NUM
ejpam-3713	281	26	)	)	PUNCT
ejpam-3713	281	27	.	.	PUNCT
ejpam-3713	282	1	2.3	2.3	NUM
ejpam-3713	282	2	.	.	PUNCT
ejpam-3713	283	1	the	the	DET
ejpam-3713	283	2	logistic	logistic	ADJ
ejpam-3713	283	3	modeling	modeling	NOUN
ejpam-3713	283	4	with	with	ADP
ejpam-3713	283	5	constant	constant	ADJ
ejpam-3713	283	6	harvesting	harvesting	NOUN
ejpam-3713	283	7	factor	factor	NOUN
ejpam-3713	283	8	having	having	AUX
ejpam-3713	283	9	assumed	assume	VERB
ejpam-3713	283	10	the	the	DET
ejpam-3713	283	11	positive	positive	ADJ
ejpam-3713	283	12	constant	constant	ADJ
ejpam-3713	283	13	number	number	NOUN
ejpam-3713	283	14	h	h	NOUN
ejpam-3713	283	15	of	of	ADP
ejpam-3713	283	16	population	population	NOUN
ejpam-3713	283	17	removed	remove	VERB
ejpam-3713	283	18	per	per	ADP
ejpam-3713	283	19	each	each	DET
ejpam-3713	283	20	duration	duration	NOUN
ejpam-3713	283	21	,	,	PUNCT
ejpam-3713	283	22	we	we	PRON
ejpam-3713	283	23	can	can	AUX
ejpam-3713	283	24	extend	extend	VERB
ejpam-3713	283	25	i.v.p	i.v.p	NOUN
ejpam-3713	283	26	.	.	PUNCT
ejpam-3713	284	1	(	(	PUNCT
ejpam-3713	284	2	25	25	NUM
ejpam-3713	284	3	)	)	PUNCT
ejpam-3713	284	4	as	as	SCONJ
ejpam-3713	284	5	follows	follow	VERB
ejpam-3713	284	6	:	:	PUNCT
ejpam-3713	284	7	{	{	PUNCT
ejpam-3713	284	8	dx	dx	PROPN
ejpam-3713	284	9	dt	dt	X
ejpam-3713	284	10	=	=	PUNCT
ejpam-3713	285	1	rx(1−	rx(1−	PROPN
ejpam-3713	285	2	x	x	PROPN
ejpam-3713	285	3	m	m	NOUN
ejpam-3713	285	4	)	)	PUNCT
ejpam-3713	285	5	−	−	PROPN
ejpam-3713	285	6	h	h	NOUN
ejpam-3713	285	7	x(0	x(0	PROPN
ejpam-3713	285	8	)	)	PUNCT
ejpam-3713	285	9	=	=	PUNCT
ejpam-3713	286	1	x0	x0	PROPN
ejpam-3713	286	2	.	.	PUNCT
ejpam-3713	287	1	(	(	PUNCT
ejpam-3713	287	2	27	27	NUM
ejpam-3713	287	3	)	)	PUNCT
ejpam-3713	287	4	the	the	DET
ejpam-3713	287	5	above	above	ADJ
ejpam-3713	287	6	i.v.p	i.v.p	NOUN
ejpam-3713	287	7	.	.	PUNCT
ejpam-3713	288	1	exhibits	exhibit	VERB
ejpam-3713	288	2	the	the	DET
ejpam-3713	288	3	limited	limited	ADJ
ejpam-3713	288	4	population	population	NOUN
ejpam-3713	288	5	.	.	PUNCT
ejpam-3713	289	1	m.h	m.h	PROPN
ejpam-3713	289	2	.	.	PROPN
ejpam-3713	289	3	r.	r.	PROPN
ejpam-3713	289	4	doust	doust	PROPN
ejpam-3713	289	5	,	,	PUNCT
ejpam-3713	289	6	v.	v.	ADP
ejpam-3713	289	7	lokesha	lokesha	PROPN
ejpam-3713	289	8	,	,	PUNCT
ejpam-3713	289	9	a.	a.	NOUN
ejpam-3713	289	10	ghasemabadi	ghasemabadi	NOUN
ejpam-3713	289	11	/	/	SYM
ejpam-3713	289	12	eur	eur	PROPN
ejpam-3713	289	13	.	.	PUNCT
ejpam-3713	290	1	j.	j.	PROPN
ejpam-3713	290	2	pure	pure	PROPN
ejpam-3713	290	3	appl	appl	PROPN
ejpam-3713	290	4	.	.	PROPN
ejpam-3713	290	5	math	math	PROPN
ejpam-3713	290	6	,	,	PUNCT
ejpam-3713	290	7	13	13	NUM
ejpam-3713	290	8	(	(	PUNCT
ejpam-3713	290	9	5	5	NUM
ejpam-3713	290	10	)	)	PUNCT
ejpam-3713	290	11	(	(	PUNCT
ejpam-3713	290	12	2020	2020	NUM
ejpam-3713	290	13	)	)	PUNCT
ejpam-3713	290	14	,	,	PUNCT
ejpam-3713	290	15	1176	1176	NUM
ejpam-3713	290	16	-	-	SYM
ejpam-3713	290	17	1198	1198	NUM
ejpam-3713	290	18	1186	1186	NUM
ejpam-3713	290	19	theorem	theorem	NOUN
ejpam-3713	290	20	2	2	NUM
ejpam-3713	290	21	.	.	NOUN
ejpam-3713	290	22	ecological	ecological	ADJ
ejpam-3713	290	23	i.v.p	i.v.p	NOUN
ejpam-3713	290	24	.	.	PUNCT
ejpam-3713	291	1	(	(	PUNCT
ejpam-3713	291	2	27	27	NUM
ejpam-3713	291	3	)	)	PUNCT
ejpam-3713	291	4	has	have	VERB
ejpam-3713	291	5	two	two	NUM
ejpam-3713	291	6	equilibria	equilibrium	NOUN
ejpam-3713	291	7	x1	x1	PROPN
ejpam-3713	291	8	and	and	CCONJ
ejpam-3713	291	9	x2	x2	PROPN
ejpam-3713	291	10	as	as	SCONJ
ejpam-3713	291	11	follows	follow	VERB
ejpam-3713	291	12	:	:	PUNCT
ejpam-3713	292	1	x1	x1	PROPN
ejpam-3713	292	2	=	=	PUNCT
ejpam-3713	292	3	m	m	VERB
ejpam-3713	292	4	2	2	NUM
ejpam-3713	292	5	(	(	PUNCT
ejpam-3713	292	6	1−	1−	NUM
ejpam-3713	292	7	√	√	NUM
ejpam-3713	292	8	1−	1−	NUM
ejpam-3713	292	9	4h	4h	NUM
ejpam-3713	292	10	rm	rm	PROPN
ejpam-3713	292	11	)	)	PUNCT
ejpam-3713	292	12	,	,	PUNCT
ejpam-3713	293	1	x2	x2	PROPN
ejpam-3713	293	2	=	=	PUNCT
ejpam-3713	294	1	m	m	VERB
ejpam-3713	294	2	2	2	NUM
ejpam-3713	294	3	(	(	PUNCT
ejpam-3713	294	4	1	1	NUM
ejpam-3713	294	5	+	+	CCONJ
ejpam-3713	294	6	√	√	PROPN
ejpam-3713	294	7	1−	1−	NUM
ejpam-3713	294	8	4h	4h	NUM
ejpam-3713	294	9	rm	rm	PROPN
ejpam-3713	294	10	)	)	PUNCT
ejpam-3713	294	11	.	.	PUNCT
ejpam-3713	295	1	(	(	PUNCT
ejpam-3713	295	2	28	28	NUM
ejpam-3713	295	3	)	)	PUNCT
ejpam-3713	295	4	moreover	moreover	ADV
ejpam-3713	295	5	,	,	PUNCT
ejpam-3713	295	6	the	the	DET
ejpam-3713	295	7	above	above	ADJ
ejpam-3713	295	8	equilibrium	equilibrium	NOUN
ejpam-3713	295	9	points	point	NOUN
ejpam-3713	295	10	are	be	AUX
ejpam-3713	295	11	unstable	unstable	ADJ
ejpam-3713	295	12	and	and	CCONJ
ejpam-3713	295	13	asymptotic	asymptotic	ADJ
ejpam-3713	295	14	stable	stable	ADJ
ejpam-3713	295	15	,	,	PUNCT
ejpam-3713	295	16	respectively	respectively	ADV
ejpam-3713	295	17	.	.	PUNCT
ejpam-3713	296	1	proof	proof	NOUN
ejpam-3713	296	2	.	.	PUNCT
ejpam-3713	297	1	it	it	PRON
ejpam-3713	297	2	is	be	AUX
ejpam-3713	297	3	clear	clear	ADJ
ejpam-3713	297	4	that	that	SCONJ
ejpam-3713	297	5	by	by	ADP
ejpam-3713	297	6	setting	set	VERB
ejpam-3713	297	7	dx	dx	PROPN
ejpam-3713	297	8	dt	dt	X
ejpam-3713	297	9	,	,	PUNCT
ejpam-3713	297	10	we	we	PRON
ejpam-3713	297	11	get	get	VERB
ejpam-3713	297	12	r	r	NOUN
ejpam-3713	297	13	m	m	NOUN
ejpam-3713	297	14	x2	x2	NOUN
ejpam-3713	298	1	−	−	NOUN
ejpam-3713	298	2	rx	rx	VERB
ejpam-3713	298	3	+	+	CCONJ
ejpam-3713	298	4	h	h	NOUN
ejpam-3713	298	5	=	=	NOUN
ejpam-3713	298	6	0	0	PROPN
ejpam-3713	298	7	.	.	PUNCT
ejpam-3713	299	1	the	the	DET
ejpam-3713	299	2	roots	root	NOUN
ejpam-3713	299	3	of	of	ADP
ejpam-3713	299	4	last	last	ADJ
ejpam-3713	299	5	equation	equation	NOUN
ejpam-3713	299	6	are	be	AUX
ejpam-3713	299	7	equilibria	equilibrium	NOUN
ejpam-3713	299	8	of	of	ADP
ejpam-3713	299	9	i.v.p	i.v.p	NOUN
ejpam-3713	299	10	.	.	PUNCT
ejpam-3713	300	1	which	which	PRON
ejpam-3713	300	2	are	be	AUX
ejpam-3713	300	3	in	in	ADP
ejpam-3713	300	4	(	(	PUNCT
ejpam-3713	300	5	28	28	NUM
ejpam-3713	300	6	)	)	PUNCT
ejpam-3713	300	7	.	.	PUNCT
ejpam-3713	301	1	paying	pay	VERB
ejpam-3713	301	2	attention	attention	NOUN
ejpam-3713	301	3	to	to	ADP
ejpam-3713	301	4	the	the	DET
ejpam-3713	301	5	above	above	ADJ
ejpam-3713	301	6	equilibria	equilibria	X
ejpam-3713	301	7	,	,	PUNCT
ejpam-3713	301	8	we	we	PRON
ejpam-3713	301	9	are	be	AUX
ejpam-3713	301	10	able	able	ADJ
ejpam-3713	301	11	to	to	PART
ejpam-3713	301	12	see	see	VERB
ejpam-3713	301	13	the	the	DET
ejpam-3713	301	14	following	follow	VERB
ejpam-3713	301	15	properties	property	NOUN
ejpam-3713	301	16	immediately	immediately	ADV
ejpam-3713	301	17	:	:	PUNCT
ejpam-3713	301	18	(	(	PUNCT
ejpam-3713	301	19	a	a	X
ejpam-3713	301	20	)	)	PUNCT
ejpam-3713	301	21	regarding	regard	VERB
ejpam-3713	301	22	x(t	x(t	PROPN
ejpam-3713	301	23	)	)	PUNCT
ejpam-3713	301	24	denotes	denote	VERB
ejpam-3713	301	25	the	the	DET
ejpam-3713	301	26	density	density	NOUN
ejpam-3713	301	27	or	or	CCONJ
ejpam-3713	301	28	number	number	NOUN
ejpam-3713	301	29	of	of	ADP
ejpam-3713	301	30	population	population	NOUN
ejpam-3713	301	31	,	,	PUNCT
ejpam-3713	301	32	we	we	PRON
ejpam-3713	301	33	have	have	VERB
ejpam-3713	301	34	h	h	NOUN
ejpam-3713	301	35	<	<	X
ejpam-3713	301	36	rm	rm	PROPN
ejpam-3713	301	37	4	4	NUM
ejpam-3713	301	38	;	;	PUNCT
ejpam-3713	301	39	(	(	PUNCT
ejpam-3713	301	40	b	b	X
ejpam-3713	301	41	)	)	PUNCT
ejpam-3713	301	42	x1	x1	PROPN
ejpam-3713	301	43	is	be	AUX
ejpam-3713	301	44	positive	positive	ADJ
ejpam-3713	301	45	provided	provide	VERB
ejpam-3713	301	46	√	√	PROPN
ejpam-3713	301	47	1−	1−	NUM
ejpam-3713	301	48	4h	4h	NUM
ejpam-3713	301	49	rm	rm	NOUN
ejpam-3713	301	50	<	<	X
ejpam-3713	301	51	1	1	NUM
ejpam-3713	301	52	;	;	PUNCT
ejpam-3713	301	53	(	(	PUNCT
ejpam-3713	301	54	c	c	X
ejpam-3713	301	55	)	)	PUNCT
ejpam-3713	301	56	since	since	SCONJ
ejpam-3713	301	57	h	h	PROPN
ejpam-3713	301	58	>	>	X
ejpam-3713	301	59	0	0	NUM
ejpam-3713	301	60	,	,	PUNCT
ejpam-3713	301	61	0	0	PUNCT
ejpam-3713	301	62	<	<	X
ejpam-3713	302	1	x1	x1	X
ejpam-3713	302	2	<	<	X
ejpam-3713	302	3	x2	x2	X
ejpam-3713	302	4	<	<	X
ejpam-3713	302	5	m	m	VERB
ejpam-3713	302	6	.	.	PUNCT
ejpam-3713	303	1	regarding	regard	VERB
ejpam-3713	303	2	relations	relation	NOUN
ejpam-3713	303	3	(	(	PUNCT
ejpam-3713	303	4	28	28	NUM
ejpam-3713	303	5	)	)	PUNCT
ejpam-3713	303	6	,	,	PUNCT
ejpam-3713	303	7	we	we	PRON
ejpam-3713	303	8	get	get	VERB
ejpam-3713	303	9	:	:	PUNCT
ejpam-3713	303	10	rx(1−	rx(1−	PROPN
ejpam-3713	303	11	x	x	PROPN
ejpam-3713	303	12	m	m	NOUN
ejpam-3713	303	13	)	)	PUNCT
ejpam-3713	303	14	−	−	PROPN
ejpam-3713	304	1	h	h	NOUN
ejpam-3713	304	2	=	=	SYM
ejpam-3713	304	3	a(x−	a(x−	PROPN
ejpam-3713	304	4	x1)(x−	x1)(x−	PROPN
ejpam-3713	304	5	x2	x2	PROPN
ejpam-3713	304	6	)	)	PUNCT
ejpam-3713	304	7	.	.	PUNCT
ejpam-3713	305	1	(	(	PUNCT
ejpam-3713	305	2	29	29	NUM
ejpam-3713	305	3	)	)	PUNCT
ejpam-3713	305	4	and	and	CCONJ
ejpam-3713	305	5	so	so	ADV
ejpam-3713	305	6	.	.	PUNCT
ejpam-3713	306	1	i.v.p	i.v.p	NOUN
ejpam-3713	306	2	.	.	PUNCT
ejpam-3713	307	1	(	(	PUNCT
ejpam-3713	307	2	27	27	NUM
ejpam-3713	307	3	)	)	PUNCT
ejpam-3713	307	4	leads	lead	VERB
ejpam-3713	307	5	to	to	ADP
ejpam-3713	307	6	the	the	DET
ejpam-3713	307	7	following	follow	VERB
ejpam-3713	307	8	i.v.p	i.v.p	NOUN
ejpam-3713	307	9	.	.	PUNCT
ejpam-3713	308	1	:	:	PUNCT
ejpam-3713	308	2	{	{	PUNCT
ejpam-3713	308	3	dx	dx	PROPN
ejpam-3713	308	4	dt	dt	X
ejpam-3713	308	5	=	=	SYM
ejpam-3713	308	6	a(x−	a(x−	PROPN
ejpam-3713	308	7	x1)(x−	x1)(x−	PROPN
ejpam-3713	308	8	x2	x2	PROPN
ejpam-3713	308	9	)	)	PUNCT
ejpam-3713	308	10	x(0	x(0	PROPN
ejpam-3713	308	11	)	)	PUNCT
ejpam-3713	309	1	=	=	PUNCT
ejpam-3713	309	2	x0	x0	PROPN
ejpam-3713	309	3	.	.	PUNCT
ejpam-3713	310	1	(	(	PUNCT
ejpam-3713	310	2	30	30	NUM
ejpam-3713	310	3	)	)	PUNCT
ejpam-3713	310	4	where	where	SCONJ
ejpam-3713	310	5	its	its	PRON
ejpam-3713	310	6	solution	solution	NOUN
ejpam-3713	310	7	is	be	AUX
ejpam-3713	310	8	given	give	VERB
ejpam-3713	310	9	by	by	ADP
ejpam-3713	310	10	:	:	PUNCT
ejpam-3713	310	11	x(t	x(t	PROPN
ejpam-3713	310	12	)	)	PUNCT
ejpam-3713	311	1	=	=	PUNCT
ejpam-3713	311	2	x2(x0	x2(x0	NOUN
ejpam-3713	311	3	−	−	PROPN
ejpam-3713	312	1	x1)−	x1)−	PROPN
ejpam-3713	312	2	x1(x0	x1(x0	ADV
ejpam-3713	313	1	−	−	PROPN
ejpam-3713	314	1	x2)exp(−	x2)exp(−	PROPN
ejpam-3713	314	2	r	r	NOUN
ejpam-3713	314	3	m	m	VERB
ejpam-3713	315	1	(	(	PUNCT
ejpam-3713	315	2	x2	x2	INTJ
ejpam-3713	315	3	−	−	PROPN
ejpam-3713	315	4	x1)t	x1)t	PROPN
ejpam-3713	315	5	)	)	PUNCT
ejpam-3713	316	1	(	(	PUNCT
ejpam-3713	316	2	x0	x0	PROPN
ejpam-3713	316	3	−	−	PROPN
ejpam-3713	317	1	x1)−	x1)−	PROPN
ejpam-3713	317	2	(	(	PUNCT
ejpam-3713	317	3	x0	x0	PROPN
ejpam-3713	317	4	−	−	PROPN
ejpam-3713	318	1	x2)exp(−	x2)exp(−	PROPN
ejpam-3713	318	2	r	r	NOUN
ejpam-3713	318	3	m	m	PROPN
ejpam-3713	318	4	(	(	PUNCT
ejpam-3713	318	5	x2	x2	INTJ
ejpam-3713	318	6	−	−	PROPN
ejpam-3713	318	7	x1)t	x1)t	PROPN
ejpam-3713	318	8	)	)	PUNCT
ejpam-3713	318	9	(	(	PUNCT
ejpam-3713	318	10	31	31	NUM
ejpam-3713	318	11	)	)	PUNCT
ejpam-3713	318	12	since	since	SCONJ
ejpam-3713	318	13	the	the	DET
ejpam-3713	318	14	following	follow	VERB
ejpam-3713	318	15	inequality	inequality	NOUN
ejpam-3713	318	16	is	be	AUX
ejpam-3713	318	17	true	true	ADJ
ejpam-3713	318	18	−	−	PROPN
ejpam-3713	318	19	r	r	NOUN
ejpam-3713	318	20	m	m	NOUN
ejpam-3713	319	1	(	(	PUNCT
ejpam-3713	319	2	x2	x2	INTJ
ejpam-3713	319	3	−	−	PROPN
ejpam-3713	319	4	x1)t	x1)t	NOUN
ejpam-3713	319	5	<	<	X
ejpam-3713	319	6	0	0	X
ejpam-3713	319	7	,	,	PUNCT
ejpam-3713	319	8	for	for	ADP
ejpam-3713	319	9	all	all	DET
ejpam-3713	319	10	t	t	PROPN
ejpam-3713	319	11	>	>	X
ejpam-3713	319	12	0	0	NUM
ejpam-3713	319	13	;	;	PUNCT
ejpam-3713	319	14	limn→∞exp(−	limn→∞exp(−	PROPN
ejpam-3713	319	15	r	r	PROPN
ejpam-3713	319	16	m	m	PROPN
ejpam-3713	319	17	(	(	PUNCT
ejpam-3713	319	18	x2	x2	INTJ
ejpam-3713	319	19	−	−	PROPN
ejpam-3713	319	20	x1)t	x1)t	NOUN
ejpam-3713	319	21	)	)	PUNCT
ejpam-3713	319	22	=	=	SYM
ejpam-3713	320	1	0	0	X
ejpam-3713	320	2	.	.	PUNCT
ejpam-3713	321	1	if	if	SCONJ
ejpam-3713	321	2	x0	x0	PROPN
ejpam-3713	321	3	>	>	X
ejpam-3713	321	4	x1	x1	PROPN
ejpam-3713	321	5	,	,	PUNCT
ejpam-3713	321	6	we	we	PRON
ejpam-3713	321	7	get	get	VERB
ejpam-3713	321	8	x(t	x(t	PROPN
ejpam-3713	321	9	)	)	PUNCT
ejpam-3713	322	1	=	=	SYM
ejpam-3713	322	2	x2	x2	PROPN
ejpam-3713	322	3	.	.	PUNCT
ejpam-3713	323	1	thus	thus	ADV
ejpam-3713	323	2	,	,	PUNCT
ejpam-3713	323	3	x(t	x(t	PROPN
ejpam-3713	323	4	)	)	PUNCT
ejpam-3713	324	1	=	=	SYM
ejpam-3713	324	2	x2	x2	PROPN
ejpam-3713	324	3	is	be	AUX
ejpam-3713	324	4	an	an	DET
ejpam-3713	324	5	equilibrium	equilibrium	NOUN
ejpam-3713	324	6	limiting	limit	VERB
ejpam-3713	324	7	solution	solution	NOUN
ejpam-3713	324	8	.	.	PUNCT
ejpam-3713	325	1	therefore	therefore	ADV
ejpam-3713	325	2	,	,	PUNCT
ejpam-3713	325	3	the	the	DET
ejpam-3713	325	4	point	point	NOUN
ejpam-3713	325	5	of	of	ADP
ejpam-3713	325	6	x	x	PUNCT
ejpam-3713	325	7	=	=	SYM
ejpam-3713	325	8	x2	x2	PROPN
ejpam-3713	325	9	is	be	AUX
ejpam-3713	325	10	stable	stable	ADJ
ejpam-3713	325	11	point	point	NOUN
ejpam-3713	325	12	.	.	PUNCT
ejpam-3713	326	1	we	we	PRON
ejpam-3713	326	2	now	now	ADV
ejpam-3713	326	3	analyze	analyze	VERB
ejpam-3713	326	4	the	the	DET
ejpam-3713	326	5	solution	solution	NOUN
ejpam-3713	326	6	behavior	behavior	NOUN
ejpam-3713	326	7	of	of	ADP
ejpam-3713	326	8	equation	equation	NOUN
ejpam-3713	326	9	(	(	PUNCT
ejpam-3713	326	10	31	31	NUM
ejpam-3713	326	11	)	)	PUNCT
ejpam-3713	326	12	in	in	ADP
ejpam-3713	326	13	case	case	NOUN
ejpam-3713	326	14	of	of	ADP
ejpam-3713	326	15	x0	x0	PROPN
ejpam-3713	326	16	<	<	X
ejpam-3713	326	17	x1	x1	PROPN
ejpam-3713	326	18	.	.	PUNCT
ejpam-3713	327	1	by	by	ADP
ejpam-3713	327	2	assuming	assume	VERB
ejpam-3713	327	3	x0	x0	PROPN
ejpam-3713	327	4	−	−	PROPN
ejpam-3713	327	5	x1	x1	PROPN
ejpam-3713	328	1	=	=	PRON
ejpam-3713	328	2	(	(	PUNCT
ejpam-3713	328	3	x0	x0	PROPN
ejpam-3713	328	4	−	−	PROPN
ejpam-3713	329	1	x2)exp(−	x2)exp(−	PROPN
ejpam-3713	329	2	r	r	NOUN
ejpam-3713	329	3	m	m	PROPN
ejpam-3713	329	4	(	(	PUNCT
ejpam-3713	329	5	x2	x2	INTJ
ejpam-3713	329	6	−	−	PROPN
ejpam-3713	329	7	x1)t	x1)t	PROPN
ejpam-3713	329	8	)	)	PUNCT
ejpam-3713	329	9	,	,	PUNCT
ejpam-3713	329	10	we	we	PRON
ejpam-3713	329	11	get	get	VERB
ejpam-3713	329	12	m.h	m.h	PROPN
ejpam-3713	329	13	.	.	PROPN
ejpam-3713	329	14	r.	r.	PROPN
ejpam-3713	329	15	doust	doust	PROPN
ejpam-3713	329	16	,	,	PUNCT
ejpam-3713	329	17	v.	v.	ADP
ejpam-3713	329	18	lokesha	lokesha	PROPN
ejpam-3713	329	19	,	,	PUNCT
ejpam-3713	329	20	a.	a.	NOUN
ejpam-3713	329	21	ghasemabadi	ghasemabadi	NOUN
ejpam-3713	329	22	/	/	SYM
ejpam-3713	329	23	eur	eur	PROPN
ejpam-3713	329	24	.	.	PUNCT
ejpam-3713	330	1	j.	j.	PROPN
ejpam-3713	330	2	pure	pure	PROPN
ejpam-3713	330	3	appl	appl	PROPN
ejpam-3713	330	4	.	.	PROPN
ejpam-3713	330	5	math	math	PROPN
ejpam-3713	330	6	,	,	PUNCT
ejpam-3713	330	7	13	13	NUM
ejpam-3713	330	8	(	(	PUNCT
ejpam-3713	330	9	5	5	NUM
ejpam-3713	330	10	)	)	PUNCT
ejpam-3713	330	11	(	(	PUNCT
ejpam-3713	330	12	2020	2020	NUM
ejpam-3713	330	13	)	)	PUNCT
ejpam-3713	330	14	,	,	PUNCT
ejpam-3713	330	15	1176	1176	NUM
ejpam-3713	330	16	-	-	SYM
ejpam-3713	330	17	1198	1198	NUM
ejpam-3713	330	18	1187	1187	NUM
ejpam-3713	330	19	t	t	NOUN
ejpam-3713	330	20	=	=	SYM
ejpam-3713	330	21	1	1	NUM
ejpam-3713	330	22	−	−	NOUN
ejpam-3713	330	23	r	r	NOUN
ejpam-3713	330	24	m	m	NOUN
ejpam-3713	331	1	(	(	PUNCT
ejpam-3713	331	2	x2	x2	NOUN
ejpam-3713	331	3	−	−	PROPN
ejpam-3713	331	4	x1	x1	PROPN
ejpam-3713	331	5	)	)	PUNCT
ejpam-3713	332	1	ln	ln	ADV
ejpam-3713	332	2	x0	x0	PROPN
ejpam-3713	332	3	−	−	PROPN
ejpam-3713	333	1	x1	x1	NUM
ejpam-3713	333	2	x0	x0	PROPN
ejpam-3713	334	1	−	−	PROPN
ejpam-3713	334	2	x2	x2	INTJ
ejpam-3713	334	3	.	.	PUNCT
ejpam-3713	335	1	now	now	ADV
ejpam-3713	335	2	,	,	PUNCT
ejpam-3713	335	3	let	let	VERB
ejpam-3713	335	4	t1	t1	NOUN
ejpam-3713	335	5	be	be	AUX
ejpam-3713	335	6	as	as	ADP
ejpam-3713	335	7	following	follow	VERB
ejpam-3713	335	8	constant	constant	ADJ
ejpam-3713	335	9	value	value	NOUN
ejpam-3713	335	10	:	:	PUNCT
ejpam-3713	335	11	t1	t1	NOUN
ejpam-3713	335	12	=	=	SYM
ejpam-3713	335	13	1	1	NUM
ejpam-3713	335	14	−	−	NOUN
ejpam-3713	336	1	r	r	NOUN
ejpam-3713	336	2	m	m	NOUN
ejpam-3713	337	1	(	(	PUNCT
ejpam-3713	337	2	x2	x2	NOUN
ejpam-3713	337	3	−	−	PROPN
ejpam-3713	337	4	x1	x1	PROPN
ejpam-3713	337	5	)	)	PUNCT
ejpam-3713	338	1	ln	ln	ADV
ejpam-3713	338	2	x0	x0	PROPN
ejpam-3713	338	3	−	−	PROPN
ejpam-3713	339	1	x1	x1	NUM
ejpam-3713	339	2	x0	x0	PROPN
ejpam-3713	340	1	−	−	PROPN
ejpam-3713	340	2	x2	x2	INTJ
ejpam-3713	340	3	.	.	PUNCT
ejpam-3713	341	1	(	(	PUNCT
ejpam-3713	341	2	32	32	NUM
ejpam-3713	341	3	)	)	PUNCT
ejpam-3713	341	4	by	by	ADP
ejpam-3713	341	5	setting	set	VERB
ejpam-3713	341	6	the	the	DET
ejpam-3713	341	7	value	value	NOUN
ejpam-3713	341	8	of	of	ADP
ejpam-3713	341	9	t1	t1	NOUN
ejpam-3713	341	10	in	in	ADP
ejpam-3713	341	11	solution	solution	NOUN
ejpam-3713	341	12	(	(	PUNCT
ejpam-3713	341	13	31	31	NUM
ejpam-3713	341	14	)	)	PUNCT
ejpam-3713	341	15	we	we	PRON
ejpam-3713	341	16	have	have	AUX
ejpam-3713	341	17	:	:	PUNCT
ejpam-3713	341	18	x(t1	x(t1	X
ejpam-3713	341	19	)	)	PUNCT
ejpam-3713	342	1	=	=	SYM
ejpam-3713	342	2	x2(x0	x2(x0	NOUN
ejpam-3713	342	3	−	−	PROPN
ejpam-3713	343	1	x1)−	x1)−	PROPN
ejpam-3713	344	1	x1(x0	x1(x0	ADV
ejpam-3713	344	2	−	−	PROPN
ejpam-3713	345	1	x2)exp[−	x2)exp[−	CCONJ
ejpam-3713	346	1	r	r	NOUN
ejpam-3713	346	2	m	m	VERB
ejpam-3713	346	3	(	(	PUNCT
ejpam-3713	346	4	x2	x2	NOUN
ejpam-3713	346	5	−	−	PROPN
ejpam-3713	346	6	x1	x1	PROPN
ejpam-3713	346	7	)	)	PUNCT
ejpam-3713	346	8	1	1	NUM
ejpam-3713	346	9	−	−	NOUN
ejpam-3713	346	10	r	r	NOUN
ejpam-3713	346	11	m	m	VERB
ejpam-3713	346	12	(	(	PUNCT
ejpam-3713	346	13	x2−x1	x2−x1	PROPN
ejpam-3713	346	14	)	)	PUNCT
ejpam-3713	346	15	ln	ln	ADJ
ejpam-3713	346	16	x0−x1	x0−x1	PROPN
ejpam-3713	346	17	x0−x2	x0−x2	X
ejpam-3713	346	18	]	]	PUNCT
ejpam-3713	346	19	(	(	PUNCT
ejpam-3713	346	20	x0	x0	PROPN
ejpam-3713	346	21	−	−	PROPN
ejpam-3713	347	1	x1)−	x1)−	PROPN
ejpam-3713	347	2	(	(	PUNCT
ejpam-3713	347	3	x0	x0	PROPN
ejpam-3713	347	4	−	−	PROPN
ejpam-3713	348	1	x2)exp[−	x2)exp[−	NOUN
ejpam-3713	349	1	r	r	NOUN
ejpam-3713	349	2	m	m	VERB
ejpam-3713	349	3	(	(	PUNCT
ejpam-3713	349	4	x2	x2	NOUN
ejpam-3713	349	5	−	−	PROPN
ejpam-3713	349	6	x1	x1	PROPN
ejpam-3713	349	7	)	)	PUNCT
ejpam-3713	349	8	1	1	NUM
ejpam-3713	349	9	−	−	NOUN
ejpam-3713	350	1	r	r	NOUN
ejpam-3713	350	2	m	m	VERB
ejpam-3713	350	3	(	(	PUNCT
ejpam-3713	350	4	x2−x1	x2−x1	PROPN
ejpam-3713	350	5	)	)	PUNCT
ejpam-3713	350	6	ln	ln	ADJ
ejpam-3713	350	7	x0−x1	x0−x1	PROPN
ejpam-3713	350	8	x0−x2	x0−x2	X
ejpam-3713	350	9	]	]	PUNCT
ejpam-3713	350	10	.	.	PUNCT
ejpam-3713	351	1	since	since	SCONJ
ejpam-3713	351	2	the	the	DET
ejpam-3713	351	3	numerator	numerator	NOUN
ejpam-3713	351	4	of	of	ADP
ejpam-3713	351	5	the	the	DET
ejpam-3713	351	6	above	above	ADJ
ejpam-3713	351	7	fraction	fraction	NOUN
ejpam-3713	351	8	is	be	AUX
ejpam-3713	351	9	negative	negative	ADJ
ejpam-3713	351	10	and	and	CCONJ
ejpam-3713	351	11	it	it	PRON
ejpam-3713	351	12	’s	’	VERB
ejpam-3713	351	13	denominator	denominator	NOUN
ejpam-3713	351	14	is	be	AUX
ejpam-3713	351	15	zero	zero	NUM
ejpam-3713	351	16	,	,	PUNCT
ejpam-3713	351	17	we	we	PRON
ejpam-3713	351	18	get	get	VERB
ejpam-3713	351	19	x(t1	x(t1	NOUN
ejpam-3713	351	20	)	)	PUNCT
ejpam-3713	352	1	=	=	SYM
ejpam-3713	352	2	−∞.	−∞.	PROPN
ejpam-3713	352	3	therefore	therefore	ADV
ejpam-3713	352	4	,	,	PUNCT
ejpam-3713	352	5	the	the	DET
ejpam-3713	352	6	value	value	NOUN
ejpam-3713	352	7	of	of	ADP
ejpam-3713	352	8	the	the	DET
ejpam-3713	352	9	population	population	NOUN
ejpam-3713	352	10	function	function	VERB
ejpam-3713	352	11	x(t	x(t	PROPN
ejpam-3713	352	12	)	)	PUNCT
ejpam-3713	352	13	at	at	ADP
ejpam-3713	352	14	t	t	PROPN
ejpam-3713	353	1	=	=	SYM
ejpam-3713	354	1	x1	x1	PROPN
ejpam-3713	354	2	is	be	AUX
ejpam-3713	354	3	a	a	DET
ejpam-3713	354	4	threshold	threshold	NOUN
ejpam-3713	354	5	and	and	CCONJ
ejpam-3713	354	6	consequently	consequently	ADV
ejpam-3713	354	7	,	,	PUNCT
ejpam-3713	354	8	point	point	NOUN
ejpam-3713	354	9	x	x	PUNCT
ejpam-3713	355	1	=	=	SYM
ejpam-3713	355	2	x1	x1	PROPN
ejpam-3713	355	3	is	be	AUX
ejpam-3713	355	4	a	a	DET
ejpam-3713	355	5	unstable	unstable	ADJ
ejpam-3713	355	6	equilibrium	equilibrium	NOUN
ejpam-3713	355	7	point	point	NOUN
ejpam-3713	355	8	.	.	PUNCT
ejpam-3713	356	1	this	this	PRON
ejpam-3713	356	2	means	mean	VERB
ejpam-3713	356	3	that	that	SCONJ
ejpam-3713	356	4	the	the	DET
ejpam-3713	356	5	proof	proof	NOUN
ejpam-3713	356	6	is	be	AUX
ejpam-3713	356	7	completed	complete	VERB
ejpam-3713	356	8	.	.	PUNCT
ejpam-3713	357	1	2.4	2.4	NUM
ejpam-3713	357	2	.	.	PUNCT
ejpam-3713	358	1	the	the	DET
ejpam-3713	358	2	logistic	logistic	ADJ
ejpam-3713	358	3	modeling	modeling	NOUN
ejpam-3713	358	4	with	with	ADP
ejpam-3713	358	5	variable	variable	ADJ
ejpam-3713	358	6	harvesting	harvesting	NOUN
ejpam-3713	358	7	factor	factor	NOUN
ejpam-3713	358	8	now	now	ADV
ejpam-3713	358	9	we	we	PRON
ejpam-3713	358	10	are	be	AUX
ejpam-3713	358	11	going	go	VERB
ejpam-3713	358	12	to	to	PART
ejpam-3713	358	13	extend	extend	VERB
ejpam-3713	358	14	the	the	DET
ejpam-3713	358	15	logistic	logistic	ADJ
ejpam-3713	358	16	population	population	NOUN
ejpam-3713	358	17	harvesting	harvesting	NOUN
ejpam-3713	358	18	into	into	ADP
ejpam-3713	358	19	case	case	NOUN
ejpam-3713	358	20	of	of	ADP
ejpam-3713	358	21	harvesting	harvesting	NOUN
ejpam-3713	358	22	parameter	parameter	NOUN
ejpam-3713	358	23	h	h	NOUN
ejpam-3713	358	24	in	in	ADP
ejpam-3713	358	25	i.v.p	i.v.p	NOUN
ejpam-3713	358	26	.	.	PUNCT
ejpam-3713	359	1	(	(	PUNCT
ejpam-3713	359	2	27	27	NUM
ejpam-3713	359	3	)	)	PUNCT
ejpam-3713	359	4	is	be	AUX
ejpam-3713	359	5	not	not	PART
ejpam-3713	359	6	constant	constant	ADJ
ejpam-3713	359	7	.	.	PUNCT
ejpam-3713	360	1	consider	consider	VERB
ejpam-3713	360	2	the	the	DET
ejpam-3713	360	3	situation	situation	NOUN
ejpam-3713	360	4	that	that	SCONJ
ejpam-3713	360	5	the	the	DET
ejpam-3713	360	6	population	population	NOUN
ejpam-3713	360	7	has	have	VERB
ejpam-3713	360	8	logistic	logistic	ADJ
ejpam-3713	360	9	growth	growth	NOUN
ejpam-3713	360	10	rate	rate	NOUN
ejpam-3713	360	11	and	and	CCONJ
ejpam-3713	360	12	harvesting	harvesting	NOUN
ejpam-3713	360	13	coefficient	coefficient	NOUN
ejpam-3713	360	14	is	be	AUX
ejpam-3713	360	15	not	not	PART
ejpam-3713	360	16	constant	constant	ADJ
ejpam-3713	360	17	.	.	PUNCT
ejpam-3713	361	1	therefore	therefore	ADV
ejpam-3713	361	2	,	,	PUNCT
ejpam-3713	361	3	the	the	DET
ejpam-3713	361	4	general	general	ADJ
ejpam-3713	361	5	case	case	NOUN
ejpam-3713	361	6	of	of	ADP
ejpam-3713	361	7	this	this	DET
ejpam-3713	361	8	model	model	NOUN
ejpam-3713	361	9	is	be	AUX
ejpam-3713	361	10	as	as	SCONJ
ejpam-3713	361	11	follows	follow	VERB
ejpam-3713	361	12	:	:	PUNCT
ejpam-3713	361	13	dx	dx	PROPN
ejpam-3713	361	14	dt	dt	X
ejpam-3713	361	15	=	=	PUNCT
ejpam-3713	362	1	rx(1−	rx(1−	PROPN
ejpam-3713	362	2	x	x	PROPN
ejpam-3713	362	3	m	m	NOUN
ejpam-3713	362	4	)	)	PUNCT
ejpam-3713	362	5	−	−	PROPN
ejpam-3713	362	6	f(x	f(x	PROPN
ejpam-3713	362	7	)	)	PUNCT
ejpam-3713	362	8	(	(	PUNCT
ejpam-3713	362	9	33	33	NUM
ejpam-3713	362	10	)	)	PUNCT
ejpam-3713	362	11	where	where	SCONJ
ejpam-3713	362	12	f(x	f(x	PROPN
ejpam-3713	362	13	)	)	PUNCT
ejpam-3713	362	14	is	be	AUX
ejpam-3713	362	15	an	an	DET
ejpam-3713	362	16	arbitrary	arbitrary	ADJ
ejpam-3713	362	17	function	function	NOUN
ejpam-3713	362	18	.	.	PUNCT
ejpam-3713	363	1	there	there	PRON
ejpam-3713	363	2	is	be	VERB
ejpam-3713	363	3	no	no	DET
ejpam-3713	363	4	general	general	ADJ
ejpam-3713	363	5	way	way	NOUN
ejpam-3713	363	6	to	to	PART
ejpam-3713	363	7	solve	solve	VERB
ejpam-3713	363	8	the	the	DET
ejpam-3713	363	9	above	above	ADJ
ejpam-3713	363	10	equation	equation	NOUN
ejpam-3713	363	11	;	;	PUNCT
ejpam-3713	363	12	and	and	CCONJ
ejpam-3713	363	13	so	so	ADV
ejpam-3713	363	14	we	we	PRON
ejpam-3713	363	15	should	should	AUX
ejpam-3713	363	16	restrict	restrict	VERB
ejpam-3713	363	17	our	our	PRON
ejpam-3713	363	18	attention	attention	NOUN
ejpam-3713	363	19	to	to	ADP
ejpam-3713	363	20	a	a	DET
ejpam-3713	363	21	few	few	ADJ
ejpam-3713	363	22	special	special	ADJ
ejpam-3713	363	23	cases	case	NOUN
ejpam-3713	363	24	.	.	PUNCT
ejpam-3713	364	1	in	in	ADP
ejpam-3713	364	2	continuation	continuation	NOUN
ejpam-3713	364	3	,	,	PUNCT
ejpam-3713	364	4	we	we	PRON
ejpam-3713	364	5	study	study	VERB
ejpam-3713	364	6	two	two	NUM
ejpam-3713	364	7	cases	case	NOUN
ejpam-3713	364	8	for	for	ADP
ejpam-3713	364	9	variable	variable	ADJ
ejpam-3713	364	10	harvesting	harvesting	NOUN
ejpam-3713	364	11	factor	factor	NOUN
ejpam-3713	364	12	which	which	PRON
ejpam-3713	364	13	are	be	AUX
ejpam-3713	364	14	cubic	cubic	ADJ
ejpam-3713	364	15	and	and	CCONJ
ejpam-3713	364	16	fractional	fractional	ADJ
ejpam-3713	364	17	.	.	PUNCT
ejpam-3713	365	1	2.4.1	2.4.1	NUM
ejpam-3713	365	2	.	.	PUNCT
ejpam-3713	365	3	case	case	NOUN
ejpam-3713	365	4	of	of	ADP
ejpam-3713	365	5	fractional	fractional	ADJ
ejpam-3713	365	6	harvesting	harvesting	NOUN
ejpam-3713	365	7	factor	factor	NOUN
ejpam-3713	365	8	let	let	VERB
ejpam-3713	365	9	us	we	PRON
ejpam-3713	365	10	make	make	VERB
ejpam-3713	365	11	assumption	assumption	NOUN
ejpam-3713	365	12	that	that	SCONJ
ejpam-3713	365	13	the	the	DET
ejpam-3713	365	14	harvesting	harvesting	NOUN
ejpam-3713	365	15	factor	factor	NOUN
ejpam-3713	365	16	be	be	AUX
ejpam-3713	365	17	following	follow	VERB
ejpam-3713	365	18	function	function	NOUN
ejpam-3713	365	19	:	:	PUNCT
ejpam-3713	365	20	f(x	f(x	PROPN
ejpam-3713	365	21	)	)	PUNCT
ejpam-3713	366	1	=	=	SYM
ejpam-3713	366	2	h	h	NOUN
ejpam-3713	366	3	x	x	SYM
ejpam-3713	366	4	1	1	NUM
ejpam-3713	366	5	+	+	CCONJ
ejpam-3713	366	6	x	x	X
ejpam-3713	366	7	.	.	PUNCT
ejpam-3713	367	1	(	(	PUNCT
ejpam-3713	367	2	34	34	NUM
ejpam-3713	367	3	)	)	PUNCT
ejpam-3713	367	4	and	and	CCONJ
ejpam-3713	367	5	so	so	ADV
ejpam-3713	367	6	,	,	PUNCT
ejpam-3713	367	7	one	one	NUM
ejpam-3713	367	8	of	of	ADP
ejpam-3713	367	9	the	the	DET
ejpam-3713	367	10	extension	extension	NOUN
ejpam-3713	367	11	of	of	ADP
ejpam-3713	367	12	the	the	DET
ejpam-3713	367	13	logistic	logistic	ADJ
ejpam-3713	367	14	population	population	NOUN
ejpam-3713	367	15	harvesting	harvesting	NOUN
ejpam-3713	367	16	factor	factor	NOUN
ejpam-3713	367	17	will	will	AUX
ejpam-3713	367	18	be	be	AUX
ejpam-3713	367	19	appeared	appear	VERB
ejpam-3713	367	20	as	as	SCONJ
ejpam-3713	367	21	follows	follow	VERB
ejpam-3713	367	22	:	:	PUNCT
ejpam-3713	368	1	dx	dx	PROPN
ejpam-3713	368	2	dt	dt	X
ejpam-3713	368	3	=	=	PUNCT
ejpam-3713	369	1	rx(1−	rx(1−	PROPN
ejpam-3713	369	2	x	x	PROPN
ejpam-3713	369	3	m	m	NOUN
ejpam-3713	369	4	)	)	PUNCT
ejpam-3713	369	5	−	−	PROPN
ejpam-3713	370	1	h	h	NOUN
ejpam-3713	370	2	x	x	NOUN
ejpam-3713	370	3	1	1	NUM
ejpam-3713	370	4	+	+	NUM
ejpam-3713	370	5	x	x	SYM
ejpam-3713	370	6	(	(	PUNCT
ejpam-3713	370	7	35	35	NUM
ejpam-3713	370	8	)	)	PUNCT
ejpam-3713	370	9	m.h	m.h	PROPN
ejpam-3713	370	10	.	.	PROPN
ejpam-3713	370	11	r.	r.	PROPN
ejpam-3713	370	12	doust	doust	PROPN
ejpam-3713	370	13	,	,	PUNCT
ejpam-3713	370	14	v.	v.	ADP
ejpam-3713	370	15	lokesha	lokesha	PROPN
ejpam-3713	370	16	,	,	PUNCT
ejpam-3713	370	17	a.	a.	NOUN
ejpam-3713	370	18	ghasemabadi	ghasemabadi	NOUN
ejpam-3713	370	19	/	/	SYM
ejpam-3713	370	20	eur	eur	PROPN
ejpam-3713	370	21	.	.	PUNCT
ejpam-3713	371	1	j.	j.	PROPN
ejpam-3713	371	2	pure	pure	PROPN
ejpam-3713	371	3	appl	appl	PROPN
ejpam-3713	371	4	.	.	PROPN
ejpam-3713	371	5	math	math	PROPN
ejpam-3713	371	6	,	,	PUNCT
ejpam-3713	371	7	13	13	NUM
ejpam-3713	371	8	(	(	PUNCT
ejpam-3713	371	9	5	5	NUM
ejpam-3713	371	10	)	)	PUNCT
ejpam-3713	371	11	(	(	PUNCT
ejpam-3713	371	12	2020	2020	NUM
ejpam-3713	371	13	)	)	PUNCT
ejpam-3713	371	14	,	,	PUNCT
ejpam-3713	371	15	1176	1176	NUM
ejpam-3713	371	16	-	-	SYM
ejpam-3713	371	17	1198	1198	NUM
ejpam-3713	371	18	1188	1188	NUM
ejpam-3713	371	19	the	the	DET
ejpam-3713	371	20	last	last	ADJ
ejpam-3713	371	21	equation	equation	NOUN
ejpam-3713	371	22	exhibits	exhibit	VERB
ejpam-3713	371	23	that	that	SCONJ
ejpam-3713	371	24	the	the	DET
ejpam-3713	371	25	harvesting	harvesting	NOUN
ejpam-3713	371	26	coefficient	coefficient	NOUN
ejpam-3713	371	27	for	for	ADP
ejpam-3713	371	28	each	each	DET
ejpam-3713	371	29	term	term	NOUN
ejpam-3713	371	30	depends	depend	VERB
ejpam-3713	371	31	on	on	ADP
ejpam-3713	371	32	it	it	PRON
ejpam-3713	371	33	’s	’	VERB
ejpam-3713	371	34	population	population	NOUN
ejpam-3713	371	35	density	density	NOUN
ejpam-3713	371	36	.	.	PUNCT
ejpam-3713	372	1	by	by	ADP
ejpam-3713	372	2	adding	add	VERB
ejpam-3713	372	3	initial	initial	ADJ
ejpam-3713	372	4	population	population	NOUN
ejpam-3713	372	5	x(0	x(0	PROPN
ejpam-3713	372	6	)	)	PUNCT
ejpam-3713	372	7	=	=	PUNCT
ejpam-3713	372	8	x0	x0	PROPN
ejpam-3713	372	9	in	in	ADP
ejpam-3713	372	10	the	the	DET
ejpam-3713	372	11	equation	equation	NOUN
ejpam-3713	372	12	(	(	PUNCT
ejpam-3713	372	13	35	35	NUM
ejpam-3713	372	14	)	)	PUNCT
ejpam-3713	372	15	,	,	PUNCT
ejpam-3713	372	16	we	we	PRON
ejpam-3713	372	17	get	get	VERB
ejpam-3713	372	18	the	the	DET
ejpam-3713	372	19	following	follow	VERB
ejpam-3713	372	20	i.v.p	i.v.p	NOUN
ejpam-3713	372	21	.	.	PUNCT
ejpam-3713	372	22	:	:	PUNCT
ejpam-3713	372	23	{	{	PUNCT
ejpam-3713	372	24	dx	dx	X
ejpam-3713	372	25	dt	dt	X
ejpam-3713	372	26	=	=	PUNCT
ejpam-3713	373	1	rx(1−	rx(1−	PROPN
ejpam-3713	373	2	x	x	PROPN
ejpam-3713	373	3	m	m	NOUN
ejpam-3713	373	4	)	)	PUNCT
ejpam-3713	374	1	−	−	PROPN
ejpam-3713	374	2	h	h	NOUN
ejpam-3713	374	3	x	x	SYM
ejpam-3713	374	4	x+1	x+1	PROPN
ejpam-3713	374	5	x(0	x(0	PROPN
ejpam-3713	374	6	)	)	PUNCT
ejpam-3713	375	1	=	=	PUNCT
ejpam-3713	375	2	x0	x0	PROPN
ejpam-3713	375	3	.	.	PUNCT
ejpam-3713	376	1	(	(	PUNCT
ejpam-3713	376	2	36	36	NUM
ejpam-3713	376	3	)	)	PUNCT
ejpam-3713	376	4	since	since	SCONJ
ejpam-3713	376	5	x	x	X
ejpam-3713	376	6	1+x	1+x	NUM
ejpam-3713	376	7	<	<	X
ejpam-3713	376	8	1	1	NUM
ejpam-3713	376	9	,	,	PUNCT
ejpam-3713	376	10	the	the	DET
ejpam-3713	376	11	term	term	NOUN
ejpam-3713	376	12	of	of	ADP
ejpam-3713	376	13	harvesting	harvesting	NOUN
ejpam-3713	376	14	factor	factor	NOUN
ejpam-3713	376	15	has	have	VERB
ejpam-3713	376	16	inverse	inverse	NOUN
ejpam-3713	376	17	relation	relation	NOUN
ejpam-3713	376	18	respect	respect	NOUN
ejpam-3713	376	19	to	to	ADP
ejpam-3713	376	20	density	density	NOUN
ejpam-3713	376	21	of	of	ADP
ejpam-3713	376	22	population	population	NOUN
ejpam-3713	376	23	.	.	PUNCT
ejpam-3713	377	1	in	in	ADP
ejpam-3713	377	2	the	the	DET
ejpam-3713	377	3	other	other	ADJ
ejpam-3713	377	4	word	word	NOUN
ejpam-3713	377	5	,	,	PUNCT
ejpam-3713	377	6	the	the	DET
ejpam-3713	377	7	term	term	NOUN
ejpam-3713	377	8	of	of	ADP
ejpam-3713	377	9	harvesting	harvesting	NOUN
ejpam-3713	377	10	decreases	decrease	NOUN
ejpam-3713	377	11	as	as	ADP
ejpam-3713	377	12	population	population	NOUN
ejpam-3713	377	13	increases	increase	NOUN
ejpam-3713	377	14	.	.	PUNCT
ejpam-3713	378	1	theorem	theorem	VERB
ejpam-3713	378	2	3	3	NUM
ejpam-3713	378	3	.	.	PUNCT
ejpam-3713	379	1	the	the	DET
ejpam-3713	379	2	following	follow	VERB
ejpam-3713	379	3	statements	statement	NOUN
ejpam-3713	379	4	for	for	ADP
ejpam-3713	379	5	logistic	logistic	ADJ
ejpam-3713	379	6	modeling	modeling	NOUN
ejpam-3713	379	7	i.v.p	i.v.p	NOUN
ejpam-3713	379	8	.	.	PUNCT
ejpam-3713	380	1	(	(	PUNCT
ejpam-3713	380	2	36	36	NUM
ejpam-3713	380	3	)	)	PUNCT
ejpam-3713	380	4	are	be	AUX
ejpam-3713	380	5	true	true	ADJ
ejpam-3713	380	6	:	:	PUNCT
ejpam-3713	380	7	(	(	PUNCT
ejpam-3713	380	8	i	i	NOUN
ejpam-3713	380	9	)	)	PUNCT
ejpam-3713	380	10	it	it	PRON
ejpam-3713	380	11	has	have	VERB
ejpam-3713	380	12	three	three	NUM
ejpam-3713	380	13	equilibria	equilibrium	NOUN
ejpam-3713	380	14	x1	x1	NUM
ejpam-3713	380	15	,	,	PUNCT
ejpam-3713	380	16	x2	x2	PROPN
ejpam-3713	380	17	and	and	CCONJ
ejpam-3713	380	18	x3	x3	ADJ
ejpam-3713	380	19	as	as	SCONJ
ejpam-3713	380	20	follows	follow	VERB
ejpam-3713	380	21	:	:	PUNCT
ejpam-3713	380	22	x1	x1	PROPN
ejpam-3713	380	23	=	=	SYM
ejpam-3713	380	24	0	0	PROPN
ejpam-3713	380	25	,	,	PUNCT
ejpam-3713	380	26	x2,3	x2,3	PROPN
ejpam-3713	381	1	=	=	PUNCT
ejpam-3713	382	1	m	m	VERB
ejpam-3713	382	2	−	−	NUM
ejpam-3713	382	3	1	1	NUM
ejpam-3713	382	4	2	2	NUM
ejpam-3713	382	5	±	±	NUM
ejpam-3713	382	6	m	m	NOUN
ejpam-3713	382	7	2	2	NUM
ejpam-3713	382	8	√	√	PROPN
ejpam-3713	382	9	(	(	PUNCT
ejpam-3713	382	10	1	1	NUM
ejpam-3713	382	11	m	m	NOUN
ejpam-3713	382	12	−	−	PROPN
ejpam-3713	382	13	1)2	1)2	NUM
ejpam-3713	382	14	+	+	CCONJ
ejpam-3713	382	15	4	4	NUM
ejpam-3713	382	16	m	m	NOUN
ejpam-3713	382	17	(	(	PUNCT
ejpam-3713	382	18	1−	1−	NUM
ejpam-3713	382	19	h	h	NOUN
ejpam-3713	382	20	r	r	NOUN
ejpam-3713	382	21	)	)	PUNCT
ejpam-3713	382	22	;	;	PUNCT
ejpam-3713	382	23	(	(	PUNCT
ejpam-3713	382	24	37	37	NUM
ejpam-3713	382	25	)	)	PUNCT
ejpam-3713	382	26	(	(	PUNCT
ejpam-3713	382	27	ii	ii	NOUN
ejpam-3713	382	28	)	)	PUNCT
ejpam-3713	382	29	the	the	DET
ejpam-3713	382	30	equilibria	equilibrium	NOUN
ejpam-3713	382	31	x2	x2	NOUN
ejpam-3713	382	32	and	and	CCONJ
ejpam-3713	382	33	x3	x3	PROPN
ejpam-3713	382	34	are	be	AUX
ejpam-3713	382	35	real	real	ADJ
ejpam-3713	382	36	number	number	NOUN
ejpam-3713	382	37	provided	provide	VERB
ejpam-3713	382	38	h	h	NOUN
ejpam-3713	382	39	r	r	NOUN
ejpam-3713	382	40	≤	≤	NUM
ejpam-3713	382	41	1	1	NUM
ejpam-3713	382	42	+	+	NUM
ejpam-3713	382	43	m	m	VERB
ejpam-3713	382	44	4	4	NUM
ejpam-3713	382	45	(	(	PUNCT
ejpam-3713	382	46	1−	1−	NUM
ejpam-3713	382	47	1	1	NUM
ejpam-3713	382	48	m	m	NOUN
ejpam-3713	382	49	)	)	PUNCT
ejpam-3713	382	50	2	2	NUM
ejpam-3713	382	51	;	;	PUNCT
ejpam-3713	382	52	(	(	PUNCT
ejpam-3713	382	53	iii	iii	X
ejpam-3713	382	54	)	)	PUNCT
ejpam-3713	382	55	it	it	PRON
ejpam-3713	382	56	is	be	AUX
ejpam-3713	382	57	impossible	impossible	ADJ
ejpam-3713	382	58	that	that	SCONJ
ejpam-3713	382	59	both	both	DET
ejpam-3713	382	60	equilibria	equilibrium	NOUN
ejpam-3713	382	61	x2	x2	NOUN
ejpam-3713	382	62	and	and	CCONJ
ejpam-3713	382	63	x3	x3	PROPN
ejpam-3713	382	64	are	be	AUX
ejpam-3713	382	65	positive	positive	ADJ
ejpam-3713	382	66	;	;	PUNCT
ejpam-3713	382	67	(	(	PUNCT
ejpam-3713	382	68	iv	iv	X
ejpam-3713	382	69	)	)	PUNCT
ejpam-3713	382	70	the	the	DET
ejpam-3713	382	71	solution	solution	NOUN
ejpam-3713	382	72	of	of	ADP
ejpam-3713	382	73	this	this	DET
ejpam-3713	382	74	i.v.p	i.v.p	NOUN
ejpam-3713	382	75	.	.	PUNCT
ejpam-3713	383	1	is	be	AUX
ejpam-3713	383	2	as	as	SCONJ
ejpam-3713	383	3	follows	follow	VERB
ejpam-3713	383	4	:	:	PUNCT
ejpam-3713	383	5	xb1(x−	xb1(x−	PROPN
ejpam-3713	383	6	x2)b2(x−	x2)b2(x−	PROPN
ejpam-3713	383	7	x3)b3	x3)b3	PUNCT
ejpam-3713	384	1	=	=	SYM
ejpam-3713	384	2	x0	x0	PROPN
ejpam-3713	384	3	b1(x0	b1(x0	NOUN
ejpam-3713	384	4	−	−	PROPN
ejpam-3713	384	5	x2)b2(x0	x2)b2(x0	PROPN
ejpam-3713	385	1	−	−	PROPN
ejpam-3713	385	2	x3)b3exp	x3)b3exp	PROPN
ejpam-3713	385	3	(	(	PUNCT
ejpam-3713	385	4	−rt	−rt	NOUN
ejpam-3713	385	5	m	m	VERB
ejpam-3713	385	6	)	)	PUNCT
ejpam-3713	385	7	(	(	PUNCT
ejpam-3713	385	8	38	38	NUM
ejpam-3713	385	9	)	)	PUNCT
ejpam-3713	385	10	(	(	PUNCT
ejpam-3713	385	11	v	v	NOUN
ejpam-3713	385	12	)	)	PUNCT
ejpam-3713	385	13	in	in	ADP
ejpam-3713	385	14	case	case	NOUN
ejpam-3713	385	15	of	of	ADP
ejpam-3713	385	16	m	m	PROPN
ejpam-3713	385	17	=	=	NOUN
ejpam-3713	385	18	r	r	NOUN
ejpam-3713	385	19	=	=	SYM
ejpam-3713	385	20	h	h	NOUN
ejpam-3713	385	21	=	=	SYM
ejpam-3713	385	22	1	1	NUM
ejpam-3713	385	23	,	,	PUNCT
ejpam-3713	385	24	i.v.p	i.v.p	NOUN
ejpam-3713	385	25	.	.	PUNCT
ejpam-3713	385	26	has	have	VERB
ejpam-3713	385	27	equilibria	equilibrium	NOUN
ejpam-3713	385	28	x	x	PUNCT
ejpam-3713	386	1	=	=	SYM
ejpam-3713	386	2	0	0	NUM
ejpam-3713	386	3	which	which	PRON
ejpam-3713	386	4	is	be	AUX
ejpam-3713	386	5	stable	stable	ADJ
ejpam-3713	386	6	point	point	NOUN
ejpam-3713	386	7	.	.	PUNCT
ejpam-3713	387	1	proof	proof	NOUN
ejpam-3713	387	2	.	.	PUNCT
ejpam-3713	388	1	(	(	PUNCT
ejpam-3713	388	2	i	i	NOUN
ejpam-3713	388	3	)	)	PUNCT
ejpam-3713	388	4	we	we	PRON
ejpam-3713	388	5	first	first	ADV
ejpam-3713	388	6	set	set	VERB
ejpam-3713	388	7	dx	dx	PROPN
ejpam-3713	388	8	dt	dt	PROPN
ejpam-3713	388	9	=	=	PUNCT
ejpam-3713	388	10	0	0	X
ejpam-3713	388	11	.	.	PUNCT
ejpam-3713	389	1	by	by	ADP
ejpam-3713	389	2	a	a	DET
ejpam-3713	389	3	simple	simple	ADJ
ejpam-3713	389	4	calculation	calculation	NOUN
ejpam-3713	389	5	,	,	PUNCT
ejpam-3713	389	6	we	we	PRON
ejpam-3713	389	7	find	find	VERB
ejpam-3713	389	8	equilibria	equilibrium	NOUN
ejpam-3713	389	9	which	which	PRON
ejpam-3713	389	10	are	be	AUX
ejpam-3713	389	11	given	give	VERB
ejpam-3713	389	12	(	(	PUNCT
ejpam-3713	389	13	37	37	NUM
ejpam-3713	389	14	)	)	PUNCT
ejpam-3713	389	15	easily	easily	ADV
ejpam-3713	389	16	.	.	PUNCT
ejpam-3713	390	1	(	(	PUNCT
ejpam-3713	390	2	ii	ii	NOUN
ejpam-3713	390	3	)	)	PUNCT
ejpam-3713	390	4	paying	pay	VERB
ejpam-3713	390	5	attention	attention	NOUN
ejpam-3713	390	6	to	to	ADP
ejpam-3713	390	7	(	(	PUNCT
ejpam-3713	390	8	37	37	NUM
ejpam-3713	390	9	)	)	PUNCT
ejpam-3713	390	10	,	,	PUNCT
ejpam-3713	390	11	we	we	PRON
ejpam-3713	390	12	see	see	VERB
ejpam-3713	390	13	that	that	PRON
ejpam-3713	390	14	for	for	ADP
ejpam-3713	390	15	equilibria	equilibrium	NOUN
ejpam-3713	390	16	x2	x2	PROPN
ejpam-3713	390	17	and	and	CCONJ
ejpam-3713	390	18	x3	x3	PROPN
ejpam-3713	390	19	are	be	AUX
ejpam-3713	390	20	real	real	ADJ
ejpam-3713	390	21	number	number	NOUN
ejpam-3713	390	22	provided	provide	VERB
ejpam-3713	390	23	h	h	NOUN
ejpam-3713	390	24	r	r	NOUN
ejpam-3713	390	25	≤	≤	NUM
ejpam-3713	390	26	1	1	NUM
ejpam-3713	390	27	+	+	NUM
ejpam-3713	390	28	m	m	VERB
ejpam-3713	390	29	4	4	NUM
ejpam-3713	390	30	(	(	PUNCT
ejpam-3713	390	31	1−	1−	NUM
ejpam-3713	390	32	1	1	NUM
ejpam-3713	390	33	m	m	NOUN
ejpam-3713	390	34	)	)	PUNCT
ejpam-3713	390	35	2	2	NUM
ejpam-3713	390	36	;	;	PUNCT
ejpam-3713	390	37	(	(	PUNCT
ejpam-3713	390	38	iii	iii	NOUN
ejpam-3713	390	39	)	)	PUNCT
ejpam-3713	390	40	now	now	ADV
ejpam-3713	390	41	,	,	PUNCT
ejpam-3713	390	42	let	let	VERB
ejpam-3713	390	43	us	we	PRON
ejpam-3713	390	44	take	take	VERB
ejpam-3713	390	45	they	they	PRON
ejpam-3713	390	46	are	be	AUX
ejpam-3713	390	47	positive	positive	ADJ
ejpam-3713	390	48	.	.	PUNCT
ejpam-3713	391	1	it	it	PRON
ejpam-3713	391	2	implies	imply	VERB
ejpam-3713	391	3	that	that	SCONJ
ejpam-3713	391	4	1−	1−	NUM
ejpam-3713	391	5	1	1	NUM
ejpam-3713	391	6	m	m	NOUN
ejpam-3713	391	7	<	<	X
ejpam-3713	391	8	√	√	X
ejpam-3713	391	9	(	(	PUNCT
ejpam-3713	391	10	1−	1−	NUM
ejpam-3713	391	11	1	1	NUM
ejpam-3713	391	12	m	m	NOUN
ejpam-3713	391	13	)	)	PUNCT
ejpam-3713	391	14	2	2	NUM
ejpam-3713	391	15	−	−	PROPN
ejpam-3713	391	16	4	4	NUM
ejpam-3713	391	17	m	m	NOUN
ejpam-3713	391	18	(	(	PUNCT
ejpam-3713	391	19	h	h	NOUN
ejpam-3713	391	20	r	r	NOUN
ejpam-3713	391	21	−	−	NOUN
ejpam-3713	391	22	1	1	NUM
ejpam-3713	391	23	)	)	PUNCT
ejpam-3713	391	24	<	<	X
ejpam-3713	391	25	1	1	NUM
ejpam-3713	391	26	m	m	NOUN
ejpam-3713	391	27	−	−	NOUN
ejpam-3713	392	1	1	1	NUM
ejpam-3713	392	2	.	.	PUNCT
ejpam-3713	393	1	if	if	SCONJ
ejpam-3713	393	2	we	we	PRON
ejpam-3713	393	3	take	take	VERB
ejpam-3713	393	4	m	m	PRON
ejpam-3713	393	5	<	<	X
ejpam-3713	393	6	1	1	NUM
ejpam-3713	393	7	,	,	PUNCT
ejpam-3713	393	8	the	the	DET
ejpam-3713	393	9	following	follow	VERB
ejpam-3713	393	10	contradiction	contradiction	NOUN
ejpam-3713	393	11	is	be	AUX
ejpam-3713	393	12	followed:√	followed:√	NOUN
ejpam-3713	393	13	(	(	PUNCT
ejpam-3713	393	14	1−	1−	NUM
ejpam-3713	393	15	1	1	NUM
ejpam-3713	393	16	m	m	NOUN
ejpam-3713	393	17	)	)	PUNCT
ejpam-3713	393	18	2	2	NUM
ejpam-3713	393	19	−	−	PROPN
ejpam-3713	393	20	4	4	NUM
ejpam-3713	393	21	m	m	NOUN
ejpam-3713	393	22	(	(	PUNCT
ejpam-3713	394	1	h	h	NOUN
ejpam-3713	394	2	r	r	NOUN
ejpam-3713	394	3	−	−	NOUN
ejpam-3713	394	4	1	1	NUM
ejpam-3713	394	5	)	)	PUNCT
ejpam-3713	394	6	<	<	X
ejpam-3713	394	7	0	0	NUM
ejpam-3713	394	8	m.h	m.h	PROPN
ejpam-3713	394	9	.	.	PROPN
ejpam-3713	394	10	r.	r.	PROPN
ejpam-3713	394	11	doust	doust	PROPN
ejpam-3713	394	12	,	,	PUNCT
ejpam-3713	394	13	v.	v.	ADP
ejpam-3713	394	14	lokesha	lokesha	PROPN
ejpam-3713	394	15	,	,	PUNCT
ejpam-3713	394	16	a.	a.	NOUN
ejpam-3713	394	17	ghasemabadi	ghasemabadi	NOUN
ejpam-3713	394	18	/	/	SYM
ejpam-3713	394	19	eur	eur	PROPN
ejpam-3713	394	20	.	.	PUNCT
ejpam-3713	395	1	j.	j.	PROPN
ejpam-3713	395	2	pure	pure	PROPN
ejpam-3713	395	3	appl	appl	PROPN
ejpam-3713	395	4	.	.	PROPN
ejpam-3713	395	5	math	math	PROPN
ejpam-3713	395	6	,	,	PUNCT
ejpam-3713	395	7	13	13	NUM
ejpam-3713	395	8	(	(	PUNCT
ejpam-3713	395	9	5	5	NUM
ejpam-3713	395	10	)	)	PUNCT
ejpam-3713	395	11	(	(	PUNCT
ejpam-3713	395	12	2020	2020	NUM
ejpam-3713	395	13	)	)	PUNCT
ejpam-3713	395	14	,	,	PUNCT
ejpam-3713	395	15	1176	1176	NUM
ejpam-3713	395	16	-	-	SYM
ejpam-3713	395	17	1198	1198	NUM
ejpam-3713	395	18	1189	1189	NUM
ejpam-3713	395	19	which	which	PRON
ejpam-3713	395	20	implies	imply	VERB
ejpam-3713	395	21	that	that	SCONJ
ejpam-3713	395	22	the	the	DET
ejpam-3713	395	23	truth	truth	NOUN
ejpam-3713	395	24	of	of	ADP
ejpam-3713	395	25	(	(	PUNCT
ejpam-3713	395	26	iii	iii	NOUN
ejpam-3713	395	27	)	)	PUNCT
ejpam-3713	395	28	.	.	PUNCT
ejpam-3713	396	1	(	(	PUNCT
ejpam-3713	396	2	iv	iv	X
ejpam-3713	396	3	)	)	PUNCT
ejpam-3713	396	4	if	if	SCONJ
ejpam-3713	396	5	we	we	PRON
ejpam-3713	396	6	take	take	VERB
ejpam-3713	396	7	m	m	VERB
ejpam-3713	396	8	=	=	NOUN
ejpam-3713	396	9	1	1	NUM
ejpam-3713	396	10	,	,	PUNCT
ejpam-3713	396	11	we	we	PRON
ejpam-3713	396	12	see	see	VERB
ejpam-3713	396	13	that	that	PRON
ejpam-3713	396	14	x2,3	x2,3	PROPN
ejpam-3713	396	15	=	=	PUNCT
ejpam-3713	396	16	±	±	PROPN
ejpam-3713	396	17	√	√	NOUN
ejpam-3713	396	18	1−	1−	NUM
ejpam-3713	397	1	h	h	NOUN
ejpam-3713	397	2	r	r	NOUN
ejpam-3713	397	3	for	for	ADP
ejpam-3713	397	4	simplifying	simplify	VERB
ejpam-3713	397	5	we	we	PRON
ejpam-3713	397	6	consider	consider	VERB
ejpam-3713	397	7	dx	dx	PRON
ejpam-3713	397	8	dt	dt	PROPN
ejpam-3713	398	1	=	=	PUNCT
ejpam-3713	398	2	−r	−r	PROPN
ejpam-3713	398	3	m	m	NOUN
ejpam-3713	398	4	x	x	PUNCT
ejpam-3713	398	5	x	x	PUNCT
ejpam-3713	398	6	+	+	NUM
ejpam-3713	398	7	1	1	NUM
ejpam-3713	398	8	(	(	PUNCT
ejpam-3713	398	9	x−	x−	PROPN
ejpam-3713	398	10	x2)(x−	x2)(x−	PROPN
ejpam-3713	398	11	x3	x3	ADJ
ejpam-3713	398	12	)	)	PUNCT
ejpam-3713	398	13	(	(	PUNCT
ejpam-3713	398	14	39	39	NUM
ejpam-3713	398	15	)	)	PUNCT
ejpam-3713	398	16	then	then	ADV
ejpam-3713	398	17	,	,	PUNCT
ejpam-3713	398	18	we	we	PRON
ejpam-3713	398	19	get	get	VERB
ejpam-3713	398	20	1	1	NUM
ejpam-3713	398	21	+	+	CCONJ
ejpam-3713	398	22	x	x	SYM
ejpam-3713	398	23	x(x−	x(x−	PROPN
ejpam-3713	398	24	x2)(x−	x2)(x−	ADP
ejpam-3713	398	25	x3	x3	ADJ
ejpam-3713	398	26	)	)	PUNCT
ejpam-3713	398	27	dx	dx	PROPN
ejpam-3713	399	1	=	=	SYM
ejpam-3713	399	2	−r	−r	PROPN
ejpam-3713	399	3	m	m	VERB
ejpam-3713	399	4	dt	dt	PROPN
ejpam-3713	399	5	.	.	PUNCT
ejpam-3713	399	6	by	by	ADP
ejpam-3713	399	7	decomposing	decompose	VERB
ejpam-3713	399	8	method	method	NOUN
ejpam-3713	399	9	,	,	PUNCT
ejpam-3713	399	10	we	we	PRON
ejpam-3713	399	11	may	may	AUX
ejpam-3713	399	12	find	find	VERB
ejpam-3713	399	13	the	the	DET
ejpam-3713	399	14	parameters	parameter	NOUN
ejpam-3713	399	15	b1	b1	NOUN
ejpam-3713	399	16	,	,	PUNCT
ejpam-3713	399	17	b2	b2	NOUN
ejpam-3713	399	18	and	and	CCONJ
ejpam-3713	399	19	b3	b3	NOUN
ejpam-3713	399	20	which	which	PRON
ejpam-3713	399	21	satisfy	satisfy	VERB
ejpam-3713	399	22	in	in	ADP
ejpam-3713	399	23	the	the	DET
ejpam-3713	399	24	following	follow	VERB
ejpam-3713	399	25	equation	equation	NOUN
ejpam-3713	399	26	:	:	PUNCT
ejpam-3713	399	27	1	1	NUM
ejpam-3713	399	28	+	+	CCONJ
ejpam-3713	399	29	x	x	SYM
ejpam-3713	399	30	x(x−	x(x−	PROPN
ejpam-3713	399	31	x2)(x−	x2)(x−	ADP
ejpam-3713	399	32	x3	x3	ADJ
ejpam-3713	399	33	)	)	PUNCT
ejpam-3713	400	1	=	=	SYM
ejpam-3713	400	2	b1	b1	NOUN
ejpam-3713	400	3	x	x	PUNCT
ejpam-3713	400	4	+	+	NUM
ejpam-3713	400	5	b2	b2	NOUN
ejpam-3713	400	6	x−	x−	PROPN
ejpam-3713	400	7	x2	x2	PROPN
ejpam-3713	401	1	+	+	CCONJ
ejpam-3713	401	2	b3	b3	PROPN
ejpam-3713	401	3	x−	x−	PROPN
ejpam-3713	401	4	x3	x3	PROPN
ejpam-3713	401	5	.	.	PUNCT
ejpam-3713	402	1	by	by	ADP
ejpam-3713	402	2	multiply	multiply	NOUN
ejpam-3713	402	3	the	the	DET
ejpam-3713	402	4	above	above	ADJ
ejpam-3713	402	5	equation	equation	NOUN
ejpam-3713	402	6	into	into	ADP
ejpam-3713	402	7	the	the	DET
ejpam-3713	402	8	phrases	phrase	NOUN
ejpam-3713	402	9	x	x	X
ejpam-3713	402	10	,	,	PUNCT
ejpam-3713	402	11	x	x	PROPN
ejpam-3713	402	12	−	−	NOUN
ejpam-3713	402	13	x2	x2	INTJ
ejpam-3713	402	14	and	and	CCONJ
ejpam-3713	402	15	x	x	ADJ
ejpam-3713	402	16	−	−	NOUN
ejpam-3713	402	17	x3	x3	ADJ
ejpam-3713	402	18	;	;	PUNCT
ejpam-3713	402	19	and	and	CCONJ
ejpam-3713	402	20	setting	set	VERB
ejpam-3713	402	21	x	x	X
ejpam-3713	402	22	=	=	SYM
ejpam-3713	402	23	0	0	NUM
ejpam-3713	402	24	,	,	PUNCT
ejpam-3713	402	25	x	x	X
ejpam-3713	402	26	=	=	SYM
ejpam-3713	402	27	x2	x2	PROPN
ejpam-3713	402	28	and	and	CCONJ
ejpam-3713	402	29	x	x	X
ejpam-3713	402	30	=	=	SYM
ejpam-3713	402	31	x3	x3	ADJ
ejpam-3713	402	32	respectively	respectively	ADV
ejpam-3713	402	33	in	in	ADP
ejpam-3713	402	34	three	three	NUM
ejpam-3713	402	35	steps	step	NOUN
ejpam-3713	402	36	,	,	PUNCT
ejpam-3713	402	37	we	we	PRON
ejpam-3713	402	38	have	have	VERB
ejpam-3713	402	39	b1	b1	NOUN
ejpam-3713	402	40	=	=	SYM
ejpam-3713	402	41	1	1	NUM
ejpam-3713	402	42	x2x3	x2x3	NOUN
ejpam-3713	402	43	,	,	PUNCT
ejpam-3713	402	44	b2	b2	NOUN
ejpam-3713	402	45	=	=	NOUN
ejpam-3713	402	46	1	1	NUM
ejpam-3713	403	1	+	+	NUM
ejpam-3713	403	2	x2	x2	PROPN
ejpam-3713	403	3	x2(x2	x2(x2	NOUN
ejpam-3713	403	4	−	−	NOUN
ejpam-3713	403	5	x3	x3	ADJ
ejpam-3713	403	6	)	)	PUNCT
ejpam-3713	403	7	,	,	PUNCT
ejpam-3713	403	8	b3	b3	NOUN
ejpam-3713	403	9	=	=	SYM
ejpam-3713	403	10	1	1	NUM
ejpam-3713	404	1	+	+	NUM
ejpam-3713	404	2	x2	x2	PROPN
ejpam-3713	405	1	x3(x3	x3(x3	NUM
ejpam-3713	405	2	−	−	PROPN
ejpam-3713	405	3	x2	x2	PROPN
ejpam-3713	405	4	)	)	PUNCT
ejpam-3713	405	5	.	.	PUNCT
ejpam-3713	406	1	thus	thus	ADV
ejpam-3713	406	2	,	,	PUNCT
ejpam-3713	406	3	∫	∫	PROPN
ejpam-3713	406	4	1	1	NUM
ejpam-3713	407	1	+	+	CCONJ
ejpam-3713	407	2	x	x	PROPN
ejpam-3713	407	3	x(x−	x(x−	PROPN
ejpam-3713	407	4	x2)(x−	x2)(x−	ADP
ejpam-3713	407	5	x3	x3	ADJ
ejpam-3713	407	6	)	)	PUNCT
ejpam-3713	407	7	dx	dx	PROPN
ejpam-3713	407	8	=	=	PROPN
ejpam-3713	407	9	ln[xb1(x−	ln[xb1(x−	PROPN
ejpam-3713	407	10	x2)b2(x−	x2)b2(x−	PROPN
ejpam-3713	407	11	x3)b3	x3)b3	PROPN
ejpam-3713	407	12	]	]	PUNCT
ejpam-3713	408	1	which	which	PRON
ejpam-3713	408	2	it	it	PRON
ejpam-3713	408	3	implies	imply	VERB
ejpam-3713	408	4	that	that	SCONJ
ejpam-3713	408	5	xb1(x−	xb1(x−	PROPN
ejpam-3713	408	6	x2)b2(x−	x2)b2(x−	PROPN
ejpam-3713	408	7	x3)b3	x3)b3	PUNCT
ejpam-3713	409	1	=	=	SYM
ejpam-3713	409	2	cexp	cexp	PROPN
ejpam-3713	409	3	(	(	PUNCT
ejpam-3713	409	4	−rt	−rt	NOUN
ejpam-3713	409	5	m	m	PROPN
ejpam-3713	409	6	)	)	PUNCT
ejpam-3713	409	7	,	,	PUNCT
ejpam-3713	409	8	(	(	PUNCT
ejpam-3713	409	9	40	40	NUM
ejpam-3713	409	10	)	)	PUNCT
ejpam-3713	409	11	where	where	SCONJ
ejpam-3713	409	12	c	c	NOUN
ejpam-3713	409	13	is	be	AUX
ejpam-3713	409	14	constant	constant	ADJ
ejpam-3713	409	15	.	.	PUNCT
ejpam-3713	410	1	by	by	ADP
ejpam-3713	410	2	setting	set	VERB
ejpam-3713	410	3	x(0	x(0	PROPN
ejpam-3713	410	4	)	)	PUNCT
ejpam-3713	410	5	=	=	PUNCT
ejpam-3713	410	6	x0	x0	PROPN
ejpam-3713	410	7	in	in	ADP
ejpam-3713	410	8	(	(	PUNCT
ejpam-3713	410	9	40	40	NUM
ejpam-3713	410	10	)	)	PUNCT
ejpam-3713	410	11	,	,	PUNCT
ejpam-3713	410	12	we	we	PRON
ejpam-3713	410	13	see	see	VERB
ejpam-3713	410	14	that	that	SCONJ
ejpam-3713	410	15	the	the	DET
ejpam-3713	410	16	solution	solution	NOUN
ejpam-3713	410	17	given	give	VERB
ejpam-3713	410	18	by	by	ADP
ejpam-3713	410	19	formula	formula	NOUN
ejpam-3713	410	20	(	(	PUNCT
ejpam-3713	410	21	38	38	NUM
ejpam-3713	410	22	)	)	PUNCT
ejpam-3713	410	23	is	be	AUX
ejpam-3713	410	24	right	right	ADJ
ejpam-3713	410	25	.	.	PUNCT
ejpam-3713	411	1	(	(	PUNCT
ejpam-3713	411	2	v	v	NOUN
ejpam-3713	411	3	)	)	PUNCT
ejpam-3713	411	4	taking	take	VERB
ejpam-3713	411	5	m	m	NOUN
ejpam-3713	411	6	=	=	SYM
ejpam-3713	411	7	r	r	NOUN
ejpam-3713	411	8	=	=	SYM
ejpam-3713	411	9	h	h	NOUN
ejpam-3713	412	1	=	=	SYM
ejpam-3713	412	2	1	1	NUM
ejpam-3713	412	3	,	,	PUNCT
ejpam-3713	412	4	we	we	PRON
ejpam-3713	412	5	see	see	VERB
ejpam-3713	412	6	equation	equation	NOUN
ejpam-3713	412	7	(	(	PUNCT
ejpam-3713	412	8	35	35	NUM
ejpam-3713	412	9	)	)	PUNCT
ejpam-3713	412	10	leads	lead	VERB
ejpam-3713	412	11	to	to	ADP
ejpam-3713	412	12	the	the	DET
ejpam-3713	412	13	following	follow	VERB
ejpam-3713	412	14	equation	equation	NOUN
ejpam-3713	412	15	:	:	PUNCT
ejpam-3713	413	1	dx	dx	PROPN
ejpam-3713	413	2	dt	dt	PROPN
ejpam-3713	414	1	=	=	PUNCT
ejpam-3713	414	2	x(1−	x(1−	PROPN
ejpam-3713	415	1	x)−	x)−	PROPN
ejpam-3713	415	2	x	x	X
ejpam-3713	415	3	1	1	NUM
ejpam-3713	415	4	+	+	CCONJ
ejpam-3713	415	5	x	x	SYM
ejpam-3713	415	6	⇒	⇒	NOUN
ejpam-3713	415	7	x3	x3	NOUN
ejpam-3713	415	8	=	=	SYM
ejpam-3713	415	9	0	0	PUNCT
ejpam-3713	416	1	thus	thus	ADV
ejpam-3713	416	2	x	x	X
ejpam-3713	416	3	=	=	SYM
ejpam-3713	416	4	0	0	NUM
ejpam-3713	416	5	is	be	AUX
ejpam-3713	416	6	equilibria	equilibrium	NOUN
ejpam-3713	416	7	of	of	ADP
ejpam-3713	416	8	(	(	PUNCT
ejpam-3713	416	9	35	35	NUM
ejpam-3713	416	10	)	)	PUNCT
ejpam-3713	416	11	.	.	PUNCT
ejpam-3713	417	1	as	as	ADP
ejpam-3713	417	2	regarding	regard	VERB
ejpam-3713	417	3	x−	x−	PROPN
ejpam-3713	417	4	x2	x2	PROPN
ejpam-3713	418	1	−	−	PROPN
ejpam-3713	418	2	x	x	SYM
ejpam-3713	419	1	x+1	x+1	PROPN
ejpam-3713	419	2	=	=	SYM
ejpam-3713	419	3	−	−	PROPN
ejpam-3713	419	4	x3	x3	INTJ
ejpam-3713	419	5	x+1	x+1	PROPN
ejpam-3713	419	6	<	<	X
ejpam-3713	419	7	0	0	NUM
ejpam-3713	419	8	;	;	PUNCT
ejpam-3713	419	9	we	we	PRON
ejpam-3713	419	10	have	have	VERB
ejpam-3713	419	11	x−	x−	PROPN
ejpam-3713	419	12	x2	x2	PROPN
ejpam-3713	420	1	−	−	PROPN
ejpam-3713	421	1	x	x	PUNCT
ejpam-3713	422	1	x	x	PUNCT
ejpam-3713	423	1	+	+	NUM
ejpam-3713	423	2	1	1	NUM
ejpam-3713	423	3	<	<	SYM
ejpam-3713	423	4	0	0	NUM
ejpam-3713	423	5	m.h	m.h	PROPN
ejpam-3713	423	6	.	.	PROPN
ejpam-3713	423	7	r.	r.	PROPN
ejpam-3713	423	8	doust	doust	PROPN
ejpam-3713	423	9	,	,	PUNCT
ejpam-3713	423	10	v.	v.	ADP
ejpam-3713	423	11	lokesha	lokesha	PROPN
ejpam-3713	423	12	,	,	PUNCT
ejpam-3713	423	13	a.	a.	NOUN
ejpam-3713	423	14	ghasemabadi	ghasemabadi	NOUN
ejpam-3713	423	15	/	/	SYM
ejpam-3713	423	16	eur	eur	PROPN
ejpam-3713	423	17	.	.	PUNCT
ejpam-3713	424	1	j.	j.	PROPN
ejpam-3713	424	2	pure	pure	PROPN
ejpam-3713	424	3	appl	appl	PROPN
ejpam-3713	424	4	.	.	PROPN
ejpam-3713	424	5	math	math	PROPN
ejpam-3713	424	6	,	,	PUNCT
ejpam-3713	424	7	13	13	NUM
ejpam-3713	424	8	(	(	PUNCT
ejpam-3713	424	9	5	5	NUM
ejpam-3713	424	10	)	)	PUNCT
ejpam-3713	424	11	(	(	PUNCT
ejpam-3713	424	12	2020	2020	NUM
ejpam-3713	424	13	)	)	PUNCT
ejpam-3713	424	14	,	,	PUNCT
ejpam-3713	424	15	1176	1176	NUM
ejpam-3713	424	16	-	-	SYM
ejpam-3713	424	17	1198	1198	NUM
ejpam-3713	424	18	1190	1190	NUM
ejpam-3713	424	19	and	and	CCONJ
ejpam-3713	424	20	so	so	ADV
ejpam-3713	424	21	,	,	PUNCT
ejpam-3713	424	22	x(t	x(t	PROPN
ejpam-3713	424	23	)	)	PUNCT
ejpam-3713	424	24	is	be	AUX
ejpam-3713	424	25	decreasing	decrease	VERB
ejpam-3713	424	26	.	.	PUNCT
ejpam-3713	425	1	therefore	therefore	ADV
ejpam-3713	425	2	,	,	PUNCT
ejpam-3713	425	3	lim	lim	PROPN
ejpam-3713	425	4	t→∞	t→∞	ADP
ejpam-3713	425	5	x(t	x(t	PROPN
ejpam-3713	425	6	)	)	PUNCT
ejpam-3713	425	7	=	=	SYM
ejpam-3713	425	8	0	0	X
ejpam-3713	425	9	.	.	PUNCT
ejpam-3713	426	1	the	the	DET
ejpam-3713	426	2	above	above	ADJ
ejpam-3713	426	3	population	population	NOUN
ejpam-3713	426	4	function	function	NOUN
ejpam-3713	426	5	is	be	AUX
ejpam-3713	426	6	an	an	DET
ejpam-3713	426	7	implicit	implicit	ADJ
ejpam-3713	426	8	function	function	NOUN
ejpam-3713	426	9	and	and	CCONJ
ejpam-3713	426	10	so	so	ADV
ejpam-3713	426	11	,	,	PUNCT
ejpam-3713	426	12	we	we	PRON
ejpam-3713	426	13	ca	can	AUX
ejpam-3713	426	14	n’t	not	PART
ejpam-3713	426	15	sketch	sketch	VERB
ejpam-3713	426	16	the	the	DET
ejpam-3713	426	17	graph	graph	NOUN
ejpam-3713	426	18	of	of	ADP
ejpam-3713	426	19	solution	solution	NOUN
ejpam-3713	426	20	x(t	x(t	NOUN
ejpam-3713	426	21	)	)	PUNCT
ejpam-3713	426	22	respect	respect	NOUN
ejpam-3713	426	23	to	to	ADP
ejpam-3713	426	24	t	t	PROPN
ejpam-3713	426	25	clearly	clearly	ADV
ejpam-3713	426	26	.	.	PUNCT
ejpam-3713	427	1	applying	apply	VERB
ejpam-3713	427	2	variation	variation	NOUN
ejpam-3713	427	3	table	table	NOUN
ejpam-3713	427	4	for	for	ADP
ejpam-3713	427	5	function	function	NOUN
ejpam-3713	427	6	g(x	g(x	NOUN
ejpam-3713	427	7	)	)	PUNCT
ejpam-3713	428	1	=	=	PUNCT
ejpam-3713	429	1	rx(1−	rx(1−	PROPN
ejpam-3713	429	2	x	x	SYM
ejpam-3713	429	3	m	m	NOUN
ejpam-3713	429	4	)	)	PUNCT
ejpam-3713	429	5	−h	−h	ADJ
ejpam-3713	429	6	x	x	SYM
ejpam-3713	429	7	x+1	x+1	PROPN
ejpam-3713	429	8	,	,	PUNCT
ejpam-3713	429	9	one	one	PRON
ejpam-3713	429	10	is	be	AUX
ejpam-3713	429	11	able	able	ADJ
ejpam-3713	429	12	to	to	PART
ejpam-3713	429	13	determine	determine	VERB
ejpam-3713	429	14	the	the	DET
ejpam-3713	429	15	monotonicity	monotonicity	NOUN
ejpam-3713	429	16	(	(	PUNCT
ejpam-3713	429	17	increasing	increase	VERB
ejpam-3713	429	18	or	or	CCONJ
ejpam-3713	429	19	decreasing	decrease	VERB
ejpam-3713	429	20	)	)	PUNCT
ejpam-3713	429	21	of	of	ADP
ejpam-3713	429	22	the	the	DET
ejpam-3713	429	23	above	above	ADJ
ejpam-3713	429	24	implicit	implicit	ADJ
ejpam-3713	429	25	function	function	NOUN
ejpam-3713	429	26	.	.	PUNCT
ejpam-3713	430	1	in	in	ADP
ejpam-3713	430	2	the	the	DET
ejpam-3713	430	3	next	next	ADJ
ejpam-3713	430	4	section	section	NOUN
ejpam-3713	430	5	,	,	PUNCT
ejpam-3713	430	6	we	we	PRON
ejpam-3713	430	7	describe	describe	VERB
ejpam-3713	430	8	the	the	DET
ejpam-3713	430	9	solution	solution	NOUN
ejpam-3713	430	10	behavior	behavior	NOUN
ejpam-3713	430	11	by	by	ADP
ejpam-3713	430	12	help	help	NOUN
ejpam-3713	430	13	of	of	ADP
ejpam-3713	430	14	method	method	NOUN
ejpam-3713	430	15	of	of	ADP
ejpam-3713	430	16	numerical	numerical	ADJ
ejpam-3713	430	17	simulation	simulation	NOUN
ejpam-3713	430	18	.	.	PUNCT
ejpam-3713	431	1	2.4.2	2.4.2	NUM
ejpam-3713	431	2	.	.	PUNCT
ejpam-3713	431	3	case	case	NOUN
ejpam-3713	431	4	of	of	ADP
ejpam-3713	431	5	cubic	cubic	ADJ
ejpam-3713	431	6	harvesting	harvesting	NOUN
ejpam-3713	431	7	factor	factor	NOUN
ejpam-3713	431	8	in	in	ADP
ejpam-3713	431	9	the	the	DET
ejpam-3713	431	10	second	second	ADJ
ejpam-3713	431	11	case	case	NOUN
ejpam-3713	431	12	,	,	PUNCT
ejpam-3713	431	13	we	we	PRON
ejpam-3713	431	14	make	make	VERB
ejpam-3713	431	15	assumption	assumption	NOUN
ejpam-3713	431	16	that	that	SCONJ
ejpam-3713	431	17	the	the	DET
ejpam-3713	431	18	harvesting	harvesting	NOUN
ejpam-3713	431	19	function	function	NOUN
ejpam-3713	431	20	be	be	VERB
ejpam-3713	431	21	as	as	SCONJ
ejpam-3713	431	22	follows	follow	VERB
ejpam-3713	431	23	:	:	PUNCT
ejpam-3713	431	24	f(x	f(x	PROPN
ejpam-3713	431	25	)	)	PUNCT
ejpam-3713	431	26	=	=	SYM
ejpam-3713	432	1	x3	x3	ADJ
ejpam-3713	432	2	,	,	PUNCT
ejpam-3713	432	3	(	(	PUNCT
ejpam-3713	432	4	41	41	NUM
ejpam-3713	432	5	)	)	PUNCT
ejpam-3713	432	6	and	and	CCONJ
ejpam-3713	432	7	so	so	ADV
ejpam-3713	432	8	we	we	PRON
ejpam-3713	432	9	get	get	VERB
ejpam-3713	432	10	:	:	PUNCT
ejpam-3713	433	1	dx	dx	PROPN
ejpam-3713	433	2	dt	dt	NOUN
ejpam-3713	433	3	=	=	PUNCT
ejpam-3713	434	1	rx(1−	rx(1−	PROPN
ejpam-3713	434	2	x	x	PROPN
ejpam-3713	434	3	m	m	NOUN
ejpam-3713	434	4	)	)	PUNCT
ejpam-3713	434	5	−	−	PROPN
ejpam-3713	434	6	hx3	hx3	PRON
ejpam-3713	434	7	(	(	PUNCT
ejpam-3713	434	8	42	42	NUM
ejpam-3713	434	9	)	)	PUNCT
ejpam-3713	434	10	like	like	ADP
ejpam-3713	434	11	the	the	DET
ejpam-3713	434	12	previous	previous	ADJ
ejpam-3713	434	13	case	case	NOUN
ejpam-3713	434	14	,	,	PUNCT
ejpam-3713	434	15	by	by	ADP
ejpam-3713	434	16	adding	add	VERB
ejpam-3713	434	17	initial	initial	ADJ
ejpam-3713	434	18	population	population	NOUN
ejpam-3713	434	19	x(0	x(0	PROPN
ejpam-3713	434	20	)	)	PUNCT
ejpam-3713	435	1	=	=	PUNCT
ejpam-3713	435	2	x0	x0	PROPN
ejpam-3713	435	3	in	in	ADP
ejpam-3713	435	4	the	the	DET
ejpam-3713	435	5	equation	equation	NOUN
ejpam-3713	435	6	(	(	PUNCT
ejpam-3713	435	7	42	42	NUM
ejpam-3713	435	8	)	)	PUNCT
ejpam-3713	435	9	,	,	PUNCT
ejpam-3713	435	10	we	we	PRON
ejpam-3713	435	11	get	get	VERB
ejpam-3713	435	12	the	the	DET
ejpam-3713	435	13	following	follow	VERB
ejpam-3713	435	14	i.v.p	i.v.p	NOUN
ejpam-3713	435	15	.	.	PUNCT
ejpam-3713	435	16	:	:	PUNCT
ejpam-3713	435	17	{	{	PUNCT
ejpam-3713	435	18	dx	dx	X
ejpam-3713	435	19	dt	dt	X
ejpam-3713	435	20	=	=	PUNCT
ejpam-3713	436	1	rx(1−	rx(1−	PROPN
ejpam-3713	436	2	x	x	PROPN
ejpam-3713	436	3	m	m	NOUN
ejpam-3713	436	4	)	)	PUNCT
ejpam-3713	436	5	−	−	PROPN
ejpam-3713	437	1	hx3	hx3	PRON
ejpam-3713	437	2	x(0	x(0	PROPN
ejpam-3713	437	3	)	)	PUNCT
ejpam-3713	437	4	=	=	PUNCT
ejpam-3713	437	5	x0	x0	PROPN
ejpam-3713	437	6	.	.	PUNCT
ejpam-3713	438	1	(	(	PUNCT
ejpam-3713	438	2	43	43	NUM
ejpam-3713	438	3	)	)	PUNCT
ejpam-3713	438	4	theorem	theorem	VERB
ejpam-3713	438	5	4	4	NUM
ejpam-3713	438	6	.	.	PUNCT
ejpam-3713	439	1	the	the	DET
ejpam-3713	439	2	following	follow	VERB
ejpam-3713	439	3	statements	statement	NOUN
ejpam-3713	439	4	for	for	ADP
ejpam-3713	439	5	logistic	logistic	ADJ
ejpam-3713	439	6	modeling	modeling	NOUN
ejpam-3713	439	7	i.v.p	i.v.p	NOUN
ejpam-3713	439	8	.	.	PUNCT
ejpam-3713	440	1	(	(	PUNCT
ejpam-3713	440	2	43	43	NUM
ejpam-3713	440	3	)	)	PUNCT
ejpam-3713	440	4	are	be	AUX
ejpam-3713	440	5	true	true	ADJ
ejpam-3713	440	6	:	:	PUNCT
ejpam-3713	440	7	(	(	PUNCT
ejpam-3713	440	8	i	i	NOUN
ejpam-3713	440	9	)	)	PUNCT
ejpam-3713	440	10	it	it	PRON
ejpam-3713	440	11	has	have	VERB
ejpam-3713	440	12	three	three	NUM
ejpam-3713	440	13	equilibria	equilibrium	NOUN
ejpam-3713	440	14	x1	x1	NUM
ejpam-3713	440	15	,	,	PUNCT
ejpam-3713	440	16	x2	x2	PROPN
ejpam-3713	440	17	and	and	CCONJ
ejpam-3713	440	18	x3	x3	ADJ
ejpam-3713	440	19	as	as	SCONJ
ejpam-3713	440	20	follows	follow	VERB
ejpam-3713	440	21	:	:	PUNCT
ejpam-3713	440	22	x1	x1	PROPN
ejpam-3713	440	23	=	=	SYM
ejpam-3713	440	24	0	0	PROPN
ejpam-3713	440	25	,	,	PUNCT
ejpam-3713	440	26	x2,3	x2,3	PROPN
ejpam-3713	440	27	=	=	PUNCT
ejpam-3713	440	28	r	r	NOUN
ejpam-3713	440	29	±∆	±∆	PROPN
ejpam-3713	440	30	2hm	2hm	NOUN
ejpam-3713	440	31	where	where	SCONJ
ejpam-3713	440	32	∆	∆	VERB
ejpam-3713	440	33	=	=	SYM
ejpam-3713	440	34	√	√	NUM
ejpam-3713	440	35	r2	r2	PROPN
ejpam-3713	440	36	+	+	CCONJ
ejpam-3713	440	37	4hrm2	4hrm2	PROPN
ejpam-3713	440	38	;	;	PUNCT
ejpam-3713	440	39	(	(	PUNCT
ejpam-3713	440	40	44	44	NUM
ejpam-3713	440	41	)	)	PUNCT
ejpam-3713	440	42	(	(	PUNCT
ejpam-3713	440	43	ii	ii	NOUN
ejpam-3713	440	44	)	)	PUNCT
ejpam-3713	440	45	the	the	DET
ejpam-3713	440	46	solution	solution	NOUN
ejpam-3713	440	47	of	of	ADP
ejpam-3713	440	48	this	this	DET
ejpam-3713	440	49	i.v.p	i.v.p	NOUN
ejpam-3713	440	50	.	.	PUNCT
ejpam-3713	441	1	is	be	AUX
ejpam-3713	441	2	the	the	DET
ejpam-3713	441	3	following	follow	VERB
ejpam-3713	441	4	implicit	implicit	ADJ
ejpam-3713	441	5	function	function	NOUN
ejpam-3713	441	6	:	:	PUNCT
ejpam-3713	441	7	x	x	SYM
ejpam-3713	441	8	h	h	NOUN
ejpam-3713	442	1	r	r	NOUN
ejpam-3713	442	2	(	(	PUNCT
ejpam-3713	442	3	x−	x−	PROPN
ejpam-3713	442	4	x2	x2	PROPN
ejpam-3713	442	5	)	)	PUNCT
ejpam-3713	442	6	r−∆	r−∆	NOUN
ejpam-3713	442	7	−2∆	−2∆	NOUN
ejpam-3713	442	8	(	(	PUNCT
ejpam-3713	442	9	x−	x−	PROPN
ejpam-3713	442	10	x3	x3	PROPN
ejpam-3713	442	11	)	)	PUNCT
ejpam-3713	442	12	r+∆	r+∆	VERB
ejpam-3713	442	13	−2∆	−2∆	NOUN
ejpam-3713	443	1	=	=	PUNCT
ejpam-3713	444	1	x	x	PUNCT
ejpam-3713	444	2	h	h	NOUN
ejpam-3713	444	3	r	r	NOUN
ejpam-3713	444	4	0	0	NUM
ejpam-3713	445	1	(	(	PUNCT
ejpam-3713	445	2	x0	x0	PROPN
ejpam-3713	445	3	−	−	PROPN
ejpam-3713	445	4	x2	x2	PROPN
ejpam-3713	445	5	)	)	PUNCT
ejpam-3713	445	6	r−∆	r−∆	NOUN
ejpam-3713	446	1	−2∆	−2∆	NOUN
ejpam-3713	446	2	(	(	PUNCT
ejpam-3713	446	3	x0	x0	PROPN
ejpam-3713	446	4	−	−	PROPN
ejpam-3713	446	5	x3	x3	ADJ
ejpam-3713	446	6	)	)	PUNCT
ejpam-3713	446	7	r+∆	r+∆	VERB
ejpam-3713	446	8	−2∆	−2∆	NOUN
ejpam-3713	446	9	;	;	PUNCT
ejpam-3713	446	10	(	(	PUNCT
ejpam-3713	446	11	45	45	NUM
ejpam-3713	446	12	)	)	PUNCT
ejpam-3713	446	13	(	(	PUNCT
ejpam-3713	446	14	iii	iii	NOUN
ejpam-3713	446	15	)	)	PUNCT
ejpam-3713	446	16	in	in	ADP
ejpam-3713	446	17	case	case	NOUN
ejpam-3713	446	18	of	of	ADP
ejpam-3713	446	19	m	m	PROPN
ejpam-3713	446	20	=	=	NOUN
ejpam-3713	446	21	r	r	NOUN
ejpam-3713	446	22	=	=	SYM
ejpam-3713	446	23	h	h	NOUN
ejpam-3713	446	24	=	=	SYM
ejpam-3713	446	25	1	1	NUM
ejpam-3713	446	26	,	,	PUNCT
ejpam-3713	446	27	the	the	DET
ejpam-3713	446	28	solution	solution	NOUN
ejpam-3713	446	29	of	of	ADP
ejpam-3713	446	30	this	this	DET
ejpam-3713	446	31	i.v.p	i.v.p	NOUN
ejpam-3713	446	32	.	.	PUNCT
ejpam-3713	447	1	is	be	AUX
ejpam-3713	447	2	decreasing	decrease	VERB
ejpam-3713	447	3	function	function	NOUN
ejpam-3713	447	4	.	.	PUNCT
ejpam-3713	448	1	moreover	moreover	ADV
ejpam-3713	448	2	,	,	PUNCT
ejpam-3713	448	3	the	the	DET
ejpam-3713	448	4	equilibria	equilibrium	NOUN
ejpam-3713	448	5	x1	x1	PUNCT
ejpam-3713	449	1	=	=	SYM
ejpam-3713	449	2	0	0	PUNCT
ejpam-3713	449	3	is	be	AUX
ejpam-3713	449	4	asymptotically	asymptotically	ADV
ejpam-3713	449	5	stable	stable	ADJ
ejpam-3713	449	6	.	.	PUNCT
ejpam-3713	450	1	proof	proof	NOUN
ejpam-3713	450	2	.	.	PUNCT
ejpam-3713	451	1	(	(	PUNCT
ejpam-3713	451	2	i	i	NOUN
ejpam-3713	451	3	)	)	PUNCT
ejpam-3713	451	4	by	by	ADP
ejpam-3713	451	5	setting	set	VERB
ejpam-3713	451	6	dx	dx	PROPN
ejpam-3713	451	7	dt	dt	NOUN
ejpam-3713	451	8	=	=	SYM
ejpam-3713	451	9	0	0	PROPN
ejpam-3713	451	10	,	,	PUNCT
ejpam-3713	451	11	then	then	ADV
ejpam-3713	451	12	we	we	PRON
ejpam-3713	451	13	see	see	VERB
ejpam-3713	451	14	that	that	SCONJ
ejpam-3713	451	15	the	the	DET
ejpam-3713	451	16	first	first	ADJ
ejpam-3713	451	17	equilibrium	equilibrium	NOUN
ejpam-3713	451	18	point	point	NOUN
ejpam-3713	451	19	is	be	AUX
ejpam-3713	451	20	x1	x1	PROPN
ejpam-3713	451	21	=	=	SYM
ejpam-3713	451	22	0	0	NUM
ejpam-3713	451	23	.	.	PUNCT
ejpam-3713	452	1	another	another	DET
ejpam-3713	452	2	equilibria	equilibrium	NOUN
ejpam-3713	452	3	are	be	AUX
ejpam-3713	452	4	the	the	DET
ejpam-3713	452	5	roots	root	NOUN
ejpam-3713	452	6	of	of	ADP
ejpam-3713	452	7	following	follow	VERB
ejpam-3713	452	8	quadratic	quadratic	ADJ
ejpam-3713	452	9	polynomial	polynomial	NOUN
ejpam-3713	452	10	:	:	PUNCT
ejpam-3713	452	11	−hx2	−hx2	NOUN
ejpam-3713	452	12	−	−	PUNCT
ejpam-3713	453	1	r	r	NOUN
ejpam-3713	453	2	m	m	VERB
ejpam-3713	453	3	x	x	PUNCT
ejpam-3713	454	1	+	+	CCONJ
ejpam-3713	454	2	r	r	NOUN
ejpam-3713	454	3	,	,	PUNCT
ejpam-3713	454	4	m.h	m.h	PROPN
ejpam-3713	454	5	.	.	PROPN
ejpam-3713	454	6	r.	r.	PROPN
ejpam-3713	454	7	doust	doust	PROPN
ejpam-3713	454	8	,	,	PUNCT
ejpam-3713	454	9	v.	v.	ADP
ejpam-3713	454	10	lokesha	lokesha	PROPN
ejpam-3713	454	11	,	,	PUNCT
ejpam-3713	454	12	a.	a.	NOUN
ejpam-3713	454	13	ghasemabadi	ghasemabadi	NOUN
ejpam-3713	454	14	/	/	SYM
ejpam-3713	454	15	eur	eur	PROPN
ejpam-3713	454	16	.	.	PUNCT
ejpam-3713	455	1	j.	j.	PROPN
ejpam-3713	455	2	pure	pure	PROPN
ejpam-3713	455	3	appl	appl	PROPN
ejpam-3713	455	4	.	.	PROPN
ejpam-3713	455	5	math	math	PROPN
ejpam-3713	455	6	,	,	PUNCT
ejpam-3713	455	7	13	13	NUM
ejpam-3713	455	8	(	(	PUNCT
ejpam-3713	455	9	5	5	NUM
ejpam-3713	455	10	)	)	PUNCT
ejpam-3713	455	11	(	(	PUNCT
ejpam-3713	455	12	2020	2020	NUM
ejpam-3713	455	13	)	)	PUNCT
ejpam-3713	455	14	,	,	PUNCT
ejpam-3713	455	15	1176	1176	NUM
ejpam-3713	455	16	-	-	SYM
ejpam-3713	455	17	1198	1198	NUM
ejpam-3713	455	18	1191	1191	NUM
ejpam-3713	455	19	⇒	⇒	VERB
ejpam-3713	455	20	x2,3	x2,3	PROPN
ejpam-3713	456	1	=	=	PUNCT
ejpam-3713	456	2	r	r	NOUN
ejpam-3713	456	3	±	±	NUM
ejpam-3713	456	4	√	√	PROPN
ejpam-3713	456	5	r2	r2	PROPN
ejpam-3713	456	6	+	+	CCONJ
ejpam-3713	456	7	4hrm	4hrm	PROPN
ejpam-3713	456	8	2hm	2hm	NOUN
ejpam-3713	456	9	,	,	PUNCT
ejpam-3713	456	10	which	which	PRON
ejpam-3713	456	11	implies	imply	VERB
ejpam-3713	456	12	the	the	DET
ejpam-3713	456	13	truth	truth	NOUN
ejpam-3713	456	14	of	of	ADP
ejpam-3713	456	15	(	(	PUNCT
ejpam-3713	456	16	44	44	NUM
ejpam-3713	456	17	)	)	PUNCT
ejpam-3713	456	18	.	.	PUNCT
ejpam-3713	457	1	(	(	PUNCT
ejpam-3713	457	2	ii	ii	NOUN
ejpam-3713	457	3	)	)	PUNCT
ejpam-3713	457	4	then	then	ADV
ejpam-3713	457	5	,	,	PUNCT
ejpam-3713	457	6	we	we	PRON
ejpam-3713	457	7	get	get	VERB
ejpam-3713	457	8	dx	dx	PROPN
ejpam-3713	457	9	dt	dt	PROPN
ejpam-3713	457	10	=	=	SYM
ejpam-3713	457	11	x(x−	x(x−	PROPN
ejpam-3713	457	12	r	r	NOUN
ejpam-3713	457	13	−∆	−∆	NOUN
ejpam-3713	457	14	2hm	2hm	NOUN
ejpam-3713	457	15	)	)	PUNCT
ejpam-3713	457	16	(	(	PUNCT
ejpam-3713	457	17	x−	x−	PROPN
ejpam-3713	457	18	r	r	PROPN
ejpam-3713	457	19	+	+	CCONJ
ejpam-3713	457	20	∆	∆	PROPN
ejpam-3713	457	21	2hm	2hm	NOUN
ejpam-3713	457	22	)	)	PUNCT
ejpam-3713	457	23	(	(	PUNCT
ejpam-3713	457	24	46	46	NUM
ejpam-3713	457	25	)	)	PUNCT
ejpam-3713	457	26	.	.	PUNCT
ejpam-3713	458	1	after	after	ADP
ejpam-3713	458	2	calculation	calculation	NOUN
ejpam-3713	458	3	,	,	PUNCT
ejpam-3713	458	4	we	we	PRON
ejpam-3713	458	5	get:∫	get:∫	VERB
ejpam-3713	458	6	dt	dt	PUNCT
ejpam-3713	459	1	=	=	SYM
ejpam-3713	459	2	∫	∫	PROPN
ejpam-3713	459	3	(	(	PUNCT
ejpam-3713	459	4	h	h	NOUN
ejpam-3713	459	5	r	r	NOUN
ejpam-3713	459	6	x	x	PUNCT
ejpam-3713	459	7	+	+	NUM
ejpam-3713	459	8	r−∆	r−∆	NOUN
ejpam-3713	459	9	−2∆	−2∆	PROPN
ejpam-3713	459	10	x−	x−	PROPN
ejpam-3713	459	11	x2	x2	PROPN
ejpam-3713	460	1	+	+	CCONJ
ejpam-3713	460	2	r+∆	r+∆	NOUN
ejpam-3713	460	3	−2∆	−2∆	PROPN
ejpam-3713	460	4	x−	x−	PROPN
ejpam-3713	460	5	x3	x3	PROPN
ejpam-3713	460	6	)	)	PUNCT
ejpam-3713	460	7	dx	dx	PROPN
ejpam-3713	460	8	,	,	PUNCT
ejpam-3713	460	9	we	we	PRON
ejpam-3713	460	10	therefore	therefore	ADV
ejpam-3713	460	11	obtain	obtain	VERB
ejpam-3713	460	12	the	the	DET
ejpam-3713	460	13	solution	solution	NOUN
ejpam-3713	460	14	of	of	ADP
ejpam-3713	460	15	(	(	PUNCT
ejpam-3713	460	16	42	42	NUM
ejpam-3713	460	17	)	)	PUNCT
ejpam-3713	460	18	as	as	SCONJ
ejpam-3713	460	19	follows	follow	VERB
ejpam-3713	460	20	:	:	PUNCT
ejpam-3713	460	21	x	x	SYM
ejpam-3713	460	22	h	h	NOUN
ejpam-3713	460	23	r	r	NOUN
ejpam-3713	460	24	(	(	PUNCT
ejpam-3713	460	25	x−	x−	PROPN
ejpam-3713	460	26	x2	x2	PROPN
ejpam-3713	460	27	)	)	PUNCT
ejpam-3713	460	28	r−∆	r−∆	NOUN
ejpam-3713	460	29	−2∆	−2∆	NOUN
ejpam-3713	460	30	(	(	PUNCT
ejpam-3713	460	31	x−	x−	PROPN
ejpam-3713	460	32	x3	x3	PROPN
ejpam-3713	460	33	)	)	PUNCT
ejpam-3713	460	34	r+∆	r+∆	VERB
ejpam-3713	460	35	−2∆	−2∆	NOUN
ejpam-3713	460	36	=	=	SYM
ejpam-3713	460	37	kexp(t	kexp(t	PROPN
ejpam-3713	460	38	)	)	PUNCT
ejpam-3713	460	39	.	.	PUNCT
ejpam-3713	461	1	(	(	PUNCT
ejpam-3713	461	2	47	47	NUM
ejpam-3713	461	3	)	)	PUNCT
ejpam-3713	461	4	therefore	therefore	ADV
ejpam-3713	461	5	,	,	PUNCT
ejpam-3713	461	6	considering	consider	VERB
ejpam-3713	461	7	initial	initial	ADJ
ejpam-3713	461	8	population	population	NOUN
ejpam-3713	461	9	x(0	x(0	PROPN
ejpam-3713	461	10	)	)	PUNCT
ejpam-3713	461	11	=	=	PUNCT
ejpam-3713	462	1	x0	x0	PROPN
ejpam-3713	462	2	,	,	PUNCT
ejpam-3713	462	3	we	we	PRON
ejpam-3713	462	4	see	see	VERB
ejpam-3713	462	5	that	that	SCONJ
ejpam-3713	462	6	the	the	DET
ejpam-3713	462	7	solution	solution	NOUN
ejpam-3713	462	8	of	of	ADP
ejpam-3713	462	9	i.v.p	i.v.p	NOUN
ejpam-3713	462	10	.	.	PUNCT
ejpam-3713	463	1	(	(	PUNCT
ejpam-3713	463	2	43	43	NUM
ejpam-3713	463	3	)	)	PUNCT
ejpam-3713	463	4	may	may	AUX
ejpam-3713	463	5	be	be	AUX
ejpam-3713	463	6	found	find	VERB
ejpam-3713	463	7	as	as	SCONJ
ejpam-3713	463	8	follows	follow	VERB
ejpam-3713	463	9	:	:	PUNCT
ejpam-3713	463	10	x	x	SYM
ejpam-3713	463	11	h	h	NOUN
ejpam-3713	463	12	r	r	NOUN
ejpam-3713	463	13	(	(	PUNCT
ejpam-3713	463	14	x−	x−	PROPN
ejpam-3713	463	15	x2	x2	PROPN
ejpam-3713	463	16	)	)	PUNCT
ejpam-3713	463	17	r−∆	r−∆	NOUN
ejpam-3713	463	18	−2∆	−2∆	NOUN
ejpam-3713	463	19	(	(	PUNCT
ejpam-3713	463	20	x−	x−	PROPN
ejpam-3713	463	21	x3	x3	PROPN
ejpam-3713	463	22	)	)	PUNCT
ejpam-3713	463	23	r+∆	r+∆	VERB
ejpam-3713	464	1	−2∆	−2∆	NOUN
ejpam-3713	464	2	=	=	PUNCT
ejpam-3713	465	1	x	x	PUNCT
ejpam-3713	465	2	h	h	NOUN
ejpam-3713	465	3	r	r	NOUN
ejpam-3713	465	4	0	0	NUM
ejpam-3713	466	1	(	(	PUNCT
ejpam-3713	466	2	x0	x0	PROPN
ejpam-3713	466	3	−	−	PROPN
ejpam-3713	466	4	x2	x2	PROPN
ejpam-3713	466	5	)	)	PUNCT
ejpam-3713	466	6	r−∆	r−∆	NOUN
ejpam-3713	467	1	−2∆	−2∆	NOUN
ejpam-3713	467	2	(	(	PUNCT
ejpam-3713	467	3	x0	x0	PROPN
ejpam-3713	467	4	−	−	PROPN
ejpam-3713	467	5	x3	x3	ADJ
ejpam-3713	467	6	)	)	PUNCT
ejpam-3713	468	1	r+∆	r+∆	VERB
ejpam-3713	468	2	−2∆	−2∆	PROPN
ejpam-3713	468	3	exp(t	exp(t	PROPN
ejpam-3713	468	4	)	)	PUNCT
ejpam-3713	468	5	(	(	PUNCT
ejpam-3713	468	6	48	48	NUM
ejpam-3713	468	7	)	)	PUNCT
ejpam-3713	468	8	which	which	PRON
ejpam-3713	468	9	is	be	AUX
ejpam-3713	468	10	implicit	implicit	ADJ
ejpam-3713	468	11	function	function	NOUN
ejpam-3713	468	12	.	.	PUNCT
ejpam-3713	469	1	(	(	PUNCT
ejpam-3713	469	2	iii	iii	NOUN
ejpam-3713	469	3	)	)	PUNCT
ejpam-3713	469	4	making	make	VERB
ejpam-3713	469	5	assumption	assumption	NOUN
ejpam-3713	469	6	m	m	NOUN
ejpam-3713	469	7	=	=	SYM
ejpam-3713	469	8	r	r	NOUN
ejpam-3713	469	9	=	=	SYM
ejpam-3713	469	10	h	h	NOUN
ejpam-3713	469	11	=	=	SYM
ejpam-3713	469	12	1	1	NUM
ejpam-3713	469	13	,	,	PUNCT
ejpam-3713	469	14	implies	imply	VERB
ejpam-3713	469	15	that	that	SCONJ
ejpam-3713	469	16	the	the	DET
ejpam-3713	469	17	equation	equation	NOUN
ejpam-3713	469	18	(	(	PUNCT
ejpam-3713	469	19	42	42	NUM
ejpam-3713	469	20	)	)	PUNCT
ejpam-3713	469	21	leads	lead	VERB
ejpam-3713	469	22	to	to	ADP
ejpam-3713	469	23	the	the	DET
ejpam-3713	469	24	following	follow	VERB
ejpam-3713	469	25	equation	equation	NOUN
ejpam-3713	469	26	:	:	PUNCT
ejpam-3713	469	27	dx	dx	PROPN
ejpam-3713	470	1	dt	dt	PROPN
ejpam-3713	471	1	=	=	PUNCT
ejpam-3713	471	2	x(1−	x(1−	PROPN
ejpam-3713	471	3	x)−	x)−	PROPN
ejpam-3713	471	4	x3	x3	PROPN
ejpam-3713	471	5	as	as	ADP
ejpam-3713	471	6	regarding	regard	VERB
ejpam-3713	471	7	x(t	x(t	PROPN
ejpam-3713	471	8	)	)	PUNCT
ejpam-3713	471	9	describes	describe	VERB
ejpam-3713	471	10	the	the	DET
ejpam-3713	471	11	number	number	NOUN
ejpam-3713	471	12	of	of	ADP
ejpam-3713	471	13	population	population	NOUN
ejpam-3713	471	14	which	which	PRON
ejpam-3713	471	15	is	be	AUX
ejpam-3713	471	16	positive	positive	ADJ
ejpam-3713	471	17	integer	integer	NOUN
ejpam-3713	471	18	.	.	PUNCT
ejpam-3713	472	1	and	and	CCONJ
ejpam-3713	472	2	so	so	ADV
ejpam-3713	472	3	it	it	PRON
ejpam-3713	472	4	takes	take	VERB
ejpam-3713	472	5	the	the	DET
ejpam-3713	472	6	number	number	NOUN
ejpam-3713	472	7	one	one	NUM
ejpam-3713	472	8	at	at	ADV
ejpam-3713	472	9	least	least	ADJ
ejpam-3713	472	10	.	.	PUNCT
ejpam-3713	473	1	we	we	PRON
ejpam-3713	473	2	see	see	VERB
ejpam-3713	473	3	that	that	SCONJ
ejpam-3713	473	4	x	x	X
ejpam-3713	473	5	<	<	X
ejpam-3713	473	6	x2	x2	X
ejpam-3713	473	7	<	<	X
ejpam-3713	473	8	x3	x3	ADJ
ejpam-3713	473	9	⇒	⇒	PROPN
ejpam-3713	473	10	dx	dx	PROPN
ejpam-3713	473	11	dt	dt	PROPN
ejpam-3713	474	1	=	=	PUNCT
ejpam-3713	474	2	x−	x−	PROPN
ejpam-3713	474	3	x2	x2	PROPN
ejpam-3713	475	1	−	−	PROPN
ejpam-3713	475	2	x3	x3	ADV
ejpam-3713	475	3	<	<	X
ejpam-3713	475	4	0	0	PUNCT
ejpam-3713	475	5	therefore	therefore	ADV
ejpam-3713	475	6	,	,	PUNCT
ejpam-3713	475	7	x(t	x(t	PROPN
ejpam-3713	475	8	)	)	PUNCT
ejpam-3713	475	9	is	be	AUX
ejpam-3713	475	10	decreasing	decrease	VERB
ejpam-3713	475	11	function	function	NOUN
ejpam-3713	475	12	.	.	PUNCT
ejpam-3713	476	1	lim	lim	PROPN
ejpam-3713	476	2	t→∞	t→∞	PART
ejpam-3713	476	3	x(t	x(t	PROPN
ejpam-3713	476	4	)	)	PUNCT
ejpam-3713	476	5	=	=	SYM
ejpam-3713	476	6	0	0	X
ejpam-3713	476	7	.	.	PUNCT
ejpam-3713	477	1	therefore	therefore	ADV
ejpam-3713	477	2	,	,	PUNCT
ejpam-3713	477	3	the	the	DET
ejpam-3713	477	4	equilibria	equilibrium	NOUN
ejpam-3713	477	5	x1	x1	PUNCT
ejpam-3713	478	1	=	=	SYM
ejpam-3713	478	2	0	0	PUNCT
ejpam-3713	478	3	is	be	AUX
ejpam-3713	478	4	asymptotically	asymptotically	ADV
ejpam-3713	478	5	stable	stable	ADJ
ejpam-3713	478	6	.	.	PUNCT
ejpam-3713	479	1	because	because	SCONJ
ejpam-3713	479	2	of	of	ADP
ejpam-3713	479	3	being	be	AUX
ejpam-3713	479	4	implicit	implicit	ADJ
ejpam-3713	479	5	the	the	DET
ejpam-3713	479	6	solution	solution	NOUN
ejpam-3713	479	7	x(t	x(t	PROPN
ejpam-3713	479	8	)	)	PUNCT
ejpam-3713	479	9	,	,	PUNCT
ejpam-3713	479	10	it	it	PRON
ejpam-3713	479	11	is	be	AUX
ejpam-3713	479	12	impossible	impossible	ADJ
ejpam-3713	479	13	to	to	PART
ejpam-3713	479	14	sketch	sketch	VERB
ejpam-3713	479	15	the	the	DET
ejpam-3713	479	16	graph	graph	NOUN
ejpam-3713	479	17	of	of	ADP
ejpam-3713	479	18	this	this	DET
ejpam-3713	479	19	solution	solution	NOUN
ejpam-3713	479	20	.	.	PUNCT
ejpam-3713	480	1	applying	apply	VERB
ejpam-3713	480	2	variation	variation	NOUN
ejpam-3713	480	3	table	table	NOUN
ejpam-3713	480	4	,	,	PUNCT
ejpam-3713	480	5	one	one	PRON
ejpam-3713	480	6	is	be	AUX
ejpam-3713	480	7	able	able	ADJ
ejpam-3713	480	8	to	to	PART
ejpam-3713	480	9	determine	determine	VERB
ejpam-3713	480	10	the	the	DET
ejpam-3713	480	11	monotonicity	monotonicity	NOUN
ejpam-3713	480	12	(	(	PUNCT
ejpam-3713	480	13	increasing	increase	VERB
ejpam-3713	480	14	or	or	CCONJ
ejpam-3713	480	15	decreasing	decrease	VERB
ejpam-3713	480	16	)	)	PUNCT
ejpam-3713	480	17	of	of	ADP
ejpam-3713	480	18	the	the	DET
ejpam-3713	480	19	above	above	ADJ
ejpam-3713	480	20	implicit	implicit	ADJ
ejpam-3713	480	21	function	function	NOUN
ejpam-3713	480	22	.	.	PUNCT
ejpam-3713	481	1	in	in	ADP
ejpam-3713	481	2	the	the	DET
ejpam-3713	481	3	next	next	ADJ
ejpam-3713	481	4	section	section	NOUN
ejpam-3713	481	5	,	,	PUNCT
ejpam-3713	481	6	we	we	PRON
ejpam-3713	481	7	describe	describe	VERB
ejpam-3713	481	8	the	the	DET
ejpam-3713	481	9	solution	solution	NOUN
ejpam-3713	481	10	behavior	behavior	NOUN
ejpam-3713	481	11	by	by	ADP
ejpam-3713	481	12	help	help	NOUN
ejpam-3713	481	13	of	of	ADP
ejpam-3713	481	14	simulation	simulation	NOUN
ejpam-3713	481	15	method	method	NOUN
ejpam-3713	481	16	.	.	PUNCT
ejpam-3713	482	1	in	in	ADP
ejpam-3713	482	2	the	the	DET
ejpam-3713	482	3	next	next	ADJ
ejpam-3713	482	4	section	section	NOUN
ejpam-3713	482	5	,	,	PUNCT
ejpam-3713	482	6	we	we	PRON
ejpam-3713	482	7	describe	describe	VERB
ejpam-3713	482	8	the	the	DET
ejpam-3713	482	9	solution	solution	NOUN
ejpam-3713	482	10	behavior	behavior	NOUN
ejpam-3713	482	11	by	by	ADP
ejpam-3713	482	12	help	help	NOUN
ejpam-3713	482	13	of	of	ADP
ejpam-3713	482	14	method	method	NOUN
ejpam-3713	482	15	of	of	ADP
ejpam-3713	482	16	numerical	numerical	ADJ
ejpam-3713	482	17	simulation	simulation	PROPN
ejpam-3713	482	18	.	.	PUNCT
ejpam-3713	483	1	m.h	m.h	PROPN
ejpam-3713	483	2	.	.	PROPN
ejpam-3713	483	3	r.	r.	PROPN
ejpam-3713	483	4	doust	doust	PROPN
ejpam-3713	483	5	,	,	PUNCT
ejpam-3713	483	6	v.	v.	ADP
ejpam-3713	483	7	lokesha	lokesha	PROPN
ejpam-3713	483	8	,	,	PUNCT
ejpam-3713	483	9	a.	a.	NOUN
ejpam-3713	483	10	ghasemabadi	ghasemabadi	NOUN
ejpam-3713	483	11	/	/	SYM
ejpam-3713	483	12	eur	eur	PROPN
ejpam-3713	483	13	.	.	PUNCT
ejpam-3713	484	1	j.	j.	PROPN
ejpam-3713	484	2	pure	pure	PROPN
ejpam-3713	484	3	appl	appl	PROPN
ejpam-3713	484	4	.	.	PROPN
ejpam-3713	484	5	math	math	PROPN
ejpam-3713	484	6	,	,	PUNCT
ejpam-3713	484	7	13	13	NUM
ejpam-3713	484	8	(	(	PUNCT
ejpam-3713	484	9	5	5	NUM
ejpam-3713	484	10	)	)	PUNCT
ejpam-3713	484	11	(	(	PUNCT
ejpam-3713	484	12	2020	2020	NUM
ejpam-3713	484	13	)	)	PUNCT
ejpam-3713	484	14	,	,	PUNCT
ejpam-3713	484	15	1176	1176	NUM
ejpam-3713	484	16	-	-	SYM
ejpam-3713	484	17	1198	1198	NUM
ejpam-3713	484	18	1192	1192	NUM
ejpam-3713	484	19	3	3	NUM
ejpam-3713	484	20	.	.	PUNCT
ejpam-3713	484	21	numerical	numerical	PROPN
ejpam-3713	484	22	simulation	simulation	PROPN
ejpam-3713	484	23	in	in	ADP
ejpam-3713	484	24	this	this	DET
ejpam-3713	484	25	section	section	NOUN
ejpam-3713	484	26	,	,	PUNCT
ejpam-3713	484	27	we	we	PRON
ejpam-3713	484	28	discuss	discuss	VERB
ejpam-3713	484	29	the	the	DET
ejpam-3713	484	30	analytical	analytical	ADJ
ejpam-3713	484	31	results	result	NOUN
ejpam-3713	484	32	by	by	ADP
ejpam-3713	484	33	making	make	VERB
ejpam-3713	484	34	some	some	DET
ejpam-3713	484	35	simulations	simulation	NOUN
ejpam-3713	484	36	on	on	ADP
ejpam-3713	484	37	studied	study	VERB
ejpam-3713	484	38	i.v.p	i.v.p	NOUN
ejpam-3713	484	39	.	.	PUNCT
ejpam-3713	485	1	describing	describe	VERB
ejpam-3713	485	2	logistic	logistic	ADJ
ejpam-3713	485	3	modeling	modeling	NOUN
ejpam-3713	485	4	having	have	VERB
ejpam-3713	485	5	and	and	CCONJ
ejpam-3713	485	6	without	without	ADP
ejpam-3713	485	7	harvesting	harvesting	NOUN
ejpam-3713	485	8	factor	factor	NOUN
ejpam-3713	485	9	analyzed	analyze	VERB
ejpam-3713	485	10	in	in	ADP
ejpam-3713	485	11	section	section	NOUN
ejpam-3713	485	12	2	2	NUM
ejpam-3713	485	13	.	.	PUNCT
ejpam-3713	486	1	first	first	ADV
ejpam-3713	486	2	,	,	PUNCT
ejpam-3713	486	3	the	the	DET
ejpam-3713	486	4	behavior	behavior	NOUN
ejpam-3713	486	5	of	of	ADP
ejpam-3713	486	6	solution	solution	NOUN
ejpam-3713	486	7	(	(	PUNCT
ejpam-3713	486	8	26	26	NUM
ejpam-3713	486	9	)	)	PUNCT
ejpam-3713	486	10	for	for	ADP
ejpam-3713	486	11	i.v.p	i.v.p	NOUN
ejpam-3713	486	12	.	.	PUNCT
ejpam-3713	487	1	(	(	PUNCT
ejpam-3713	487	2	25	25	NUM
ejpam-3713	487	3	)	)	PUNCT
ejpam-3713	487	4	is	be	AUX
ejpam-3713	487	5	simulated	simulate	VERB
ejpam-3713	487	6	.	.	PUNCT
ejpam-3713	488	1	an	an	DET
ejpam-3713	488	2	numerical	numerical	ADJ
ejpam-3713	488	3	simulation	simulation	NOUN
ejpam-3713	488	4	for	for	ADP
ejpam-3713	488	5	various	various	ADJ
ejpam-3713	488	6	values	value	NOUN
ejpam-3713	488	7	to	to	ADP
ejpam-3713	488	8	the	the	DET
ejpam-3713	488	9	carrying	carrying	NOUN
ejpam-3713	488	10	capacity	capacity	NOUN
ejpam-3713	488	11	m	m	NOUN
ejpam-3713	488	12	and	and	CCONJ
ejpam-3713	488	13	growth	growth	NOUN
ejpam-3713	488	14	rate	rate	NOUN
ejpam-3713	488	15	r	r	NOUN
ejpam-3713	488	16	is	be	AUX
ejpam-3713	488	17	formulated	formulate	VERB
ejpam-3713	488	18	as	as	SCONJ
ejpam-3713	488	19	follows	follow	VERB
ejpam-3713	488	20	:	:	PUNCT
ejpam-3713	488	21	.	.	PUNCT
ejpam-3713	489	1	(	(	PUNCT
ejpam-3713	489	2	i	i	NOUN
ejpam-3713	489	3	)	)	PUNCT
ejpam-3713	489	4	x0	x0	PROPN
ejpam-3713	490	1	=	=	PUNCT
ejpam-3713	491	1	m	m	VERB
ejpam-3713	491	2	+	+	NUM
ejpam-3713	492	1	i	i	PRON
ejpam-3713	492	2	,	,	PUNCT
ejpam-3713	492	3	where	where	SCONJ
ejpam-3713	492	4	i	i	PRON
ejpam-3713	492	5	=	=	NOUN
ejpam-3713	492	6	20	20	NUM
ejpam-3713	492	7	,	,	PUNCT
ejpam-3713	492	8	40	40	NUM
ejpam-3713	492	9	,	,	PUNCT
ejpam-3713	492	10	60	60	NUM
ejpam-3713	492	11	and	and	CCONJ
ejpam-3713	492	12	80	80	NUM
ejpam-3713	492	13	;	;	PUNCT
ejpam-3713	492	14	(	(	PUNCT
ejpam-3713	492	15	ii	ii	NOUN
ejpam-3713	492	16	)	)	PUNCT
ejpam-3713	492	17	x0	x0	PROPN
ejpam-3713	493	1	=	=	PUNCT
ejpam-3713	493	2	m	m	VERB
ejpam-3713	493	3	2	2	NUM
ejpam-3713	493	4	+	+	CCONJ
ejpam-3713	493	5	j	j	PROPN
ejpam-3713	493	6	,	,	PUNCT
ejpam-3713	493	7	where	where	SCONJ
ejpam-3713	493	8	i	i	PRON
ejpam-3713	493	9	=	=	NOUN
ejpam-3713	493	10	10	10	NUM
ejpam-3713	493	11	,	,	PUNCT
ejpam-3713	493	12	20	20	NUM
ejpam-3713	493	13	,	,	PUNCT
ejpam-3713	493	14	30	30	NUM
ejpam-3713	493	15	and	and	CCONJ
ejpam-3713	493	16	40	40	NUM
ejpam-3713	493	17	;	;	PUNCT
ejpam-3713	493	18	(	(	PUNCT
ejpam-3713	493	19	iii	iii	X
ejpam-3713	493	20	)	)	PUNCT
ejpam-3713	493	21	x0	x0	PROPN
ejpam-3713	494	1	=	=	PUNCT
ejpam-3713	495	1	m	m	VERB
ejpam-3713	495	2	k	k	NOUN
ejpam-3713	495	3	,	,	PUNCT
ejpam-3713	495	4	where	where	SCONJ
ejpam-3713	495	5	i	i	PRON
ejpam-3713	495	6	=	=	SYM
ejpam-3713	495	7	3	3	NUM
ejpam-3713	495	8	,	,	PUNCT
ejpam-3713	495	9	4	4	NUM
ejpam-3713	495	10	,	,	PUNCT
ejpam-3713	495	11	5	5	NUM
ejpam-3713	495	12	and	and	CCONJ
ejpam-3713	495	13	6	6	NUM
ejpam-3713	495	14	.	.	PUNCT
ejpam-3713	495	15	indeed	indeed	ADV
ejpam-3713	495	16	,	,	PUNCT
ejpam-3713	495	17	in	in	ADP
ejpam-3713	495	18	each	each	DET
ejpam-3713	495	19	column	column	NOUN
ejpam-3713	495	20	of	of	ADP
ejpam-3713	495	21	table	table	NOUN
ejpam-3713	495	22	(	(	PUNCT
ejpam-3713	495	23	1	1	NUM
ejpam-3713	495	24	)	)	PUNCT
ejpam-3713	495	25	by	by	ADP
ejpam-3713	495	26	considering	consider	VERB
ejpam-3713	495	27	carrying	carry	VERB
ejpam-3713	495	28	capacity	capacity	NOUN
ejpam-3713	495	29	(	(	PUNCT
ejpam-3713	495	30	m	m	NOUN
ejpam-3713	495	31	)	)	PUNCT
ejpam-3713	495	32	,	,	PUNCT
ejpam-3713	495	33	we	we	PRON
ejpam-3713	495	34	worked	work	VERB
ejpam-3713	495	35	out	out	ADP
ejpam-3713	495	36	formula	formula	NOUN
ejpam-3713	495	37	for	for	ADP
ejpam-3713	495	38	finding	find	VERB
ejpam-3713	495	39	suitable	suitable	ADJ
ejpam-3713	495	40	initial	initial	ADJ
ejpam-3713	495	41	populations	population	NOUN
ejpam-3713	495	42	.	.	PUNCT
ejpam-3713	496	1	and	and	CCONJ
ejpam-3713	496	2	so	so	ADV
ejpam-3713	496	3	,	,	PUNCT
ejpam-3713	496	4	for	for	ADP
ejpam-3713	496	5	rows	row	NOUN
ejpam-3713	496	6	a	a	DET
ejpam-3713	496	7	,	,	PUNCT
ejpam-3713	496	8	b	b	NOUN
ejpam-3713	496	9	,	,	PUNCT
ejpam-3713	496	10	c	c	NOUN
ejpam-3713	496	11	,	,	PUNCT
ejpam-3713	496	12	d	d	NOUN
ejpam-3713	496	13	,	,	PUNCT
ejpam-3713	496	14	e	e	NOUN
ejpam-3713	496	15	,	,	PUNCT
ejpam-3713	496	16	f	f	X
ejpam-3713	496	17	;	;	PUNCT
ejpam-3713	496	18	we	we	PRON
ejpam-3713	496	19	have	have	VERB
ejpam-3713	496	20	:	:	PUNCT
ejpam-3713	496	21	in	in	ADP
ejpam-3713	496	22	case	case	NOUN
ejpam-3713	496	23	(	(	PUNCT
ejpam-3713	496	24	i	i	NOUN
ejpam-3713	496	25	):	):	PUNCT
ejpam-3713	496	26	calculated	calculate	VERB
ejpam-3713	496	27	initial	initial	ADJ
ejpam-3713	496	28	populations	population	NOUN
ejpam-3713	496	29	is	be	AUX
ejpam-3713	496	30	greater	great	ADJ
ejpam-3713	496	31	than	than	ADP
ejpam-3713	496	32	the	the	DET
ejpam-3713	496	33	carrying	carrying	NOUN
ejpam-3713	496	34	capacity	capacity	NOUN
ejpam-3713	496	35	.	.	PUNCT
ejpam-3713	497	1	in	in	ADP
ejpam-3713	497	2	this	this	DET
ejpam-3713	497	3	case	case	NOUN
ejpam-3713	497	4	,	,	PUNCT
ejpam-3713	497	5	obtained	obtain	VERB
ejpam-3713	497	6	graphs	graph	NOUN
ejpam-3713	497	7	shows	show	VERB
ejpam-3713	497	8	the	the	DET
ejpam-3713	497	9	being	being	NOUN
ejpam-3713	497	10	of	of	ADP
ejpam-3713	497	11	solutions	solution	NOUN
ejpam-3713	497	12	decreasing	decrease	VERB
ejpam-3713	497	13	.	.	PUNCT
ejpam-3713	498	1	in	in	ADP
ejpam-3713	498	2	case	case	NOUN
ejpam-3713	498	3	(	(	PUNCT
ejpam-3713	498	4	ii	ii	NOUN
ejpam-3713	498	5	):	):	PUNCT
ejpam-3713	498	6	calculated	calculate	VERB
ejpam-3713	498	7	initial	initial	ADJ
ejpam-3713	498	8	populations	population	NOUN
ejpam-3713	498	9	are	be	AUX
ejpam-3713	498	10	located	locate	VERB
ejpam-3713	498	11	between	between	ADP
ejpam-3713	498	12	m	m	PROPN
ejpam-3713	498	13	2	2	NUM
ejpam-3713	498	14	and	and	CCONJ
ejpam-3713	498	15	m	m	NOUN
ejpam-3713	498	16	.	.	PUNCT
ejpam-3713	499	1	that	that	PRON
ejpam-3713	499	2	is	be	AUX
ejpam-3713	499	3	they	they	PRON
ejpam-3713	499	4	are	be	AUX
ejpam-3713	499	5	greater	great	ADJ
ejpam-3713	499	6	than	than	ADP
ejpam-3713	499	7	m	m	PROPN
ejpam-3713	499	8	2	2	NUM
ejpam-3713	499	9	and	and	CCONJ
ejpam-3713	499	10	less	less	ADJ
ejpam-3713	499	11	than	than	ADP
ejpam-3713	499	12	the	the	DET
ejpam-3713	499	13	carrying	carrying	NOUN
ejpam-3713	499	14	capacity	capacity	NOUN
ejpam-3713	499	15	m	m	PRON
ejpam-3713	499	16	.	.	PUNCT
ejpam-3713	500	1	in	in	ADP
ejpam-3713	500	2	case	case	NOUN
ejpam-3713	500	3	(	(	PUNCT
ejpam-3713	500	4	iii	iii	NOUN
ejpam-3713	500	5	):	):	PUNCT
ejpam-3713	500	6	calculated	calculate	VERB
ejpam-3713	500	7	initial	initial	ADJ
ejpam-3713	500	8	populations	population	NOUN
ejpam-3713	500	9	is	be	AUX
ejpam-3713	500	10	less	less	ADJ
ejpam-3713	500	11	than	than	ADP
ejpam-3713	500	12	m	m	PROPN
ejpam-3713	500	13	2	2	NUM
ejpam-3713	500	14	.	.	PUNCT
ejpam-3713	501	1	in	in	ADP
ejpam-3713	501	2	this	this	DET
ejpam-3713	501	3	case	case	NOUN
ejpam-3713	501	4	,	,	PUNCT
ejpam-3713	501	5	obtained	obtain	VERB
ejpam-3713	501	6	graphs	graph	NOUN
ejpam-3713	501	7	shows	show	VERB
ejpam-3713	501	8	that	that	SCONJ
ejpam-3713	501	9	all	all	DET
ejpam-3713	501	10	solutions	solution	NOUN
ejpam-3713	501	11	have	have	VERB
ejpam-3713	501	12	turning	turn	VERB
ejpam-3713	501	13	behavior	behavior	NOUN
ejpam-3713	501	14	at	at	ADP
ejpam-3713	501	15	the	the	DET
ejpam-3713	501	16	point	point	NOUN
ejpam-3713	501	17	x	x	PUNCT
ejpam-3713	502	1	=	=	NOUN
ejpam-3713	502	2	m	m	VERB
ejpam-3713	502	3	2	2	NUM
ejpam-3713	502	4	.	.	PUNCT
ejpam-3713	503	1	in	in	ADP
ejpam-3713	503	2	all	all	PRON
ejpam-3713	503	3	of	of	ADP
ejpam-3713	503	4	above	above	ADP
ejpam-3713	503	5	cases	case	NOUN
ejpam-3713	503	6	,	,	PUNCT
ejpam-3713	503	7	the	the	DET
ejpam-3713	503	8	solutions	solution	NOUN
ejpam-3713	503	9	tend	tend	VERB
ejpam-3713	503	10	to	to	PART
ejpam-3713	503	11	m	m	VERB
ejpam-3713	503	12	asymptotically	asymptotically	ADV
ejpam-3713	503	13	.	.	PUNCT
ejpam-3713	504	1	this	this	DET
ejpam-3713	504	2	numerical	numerical	ADJ
ejpam-3713	504	3	argument	argument	NOUN
ejpam-3713	504	4	is	be	AUX
ejpam-3713	504	5	shown	show	VERB
ejpam-3713	504	6	in	in	ADP
ejpam-3713	504	7	the	the	DET
ejpam-3713	504	8	table	table	NOUN
ejpam-3713	504	9	(	(	PUNCT
ejpam-3713	504	10	1	1	NUM
ejpam-3713	504	11	)	)	PUNCT
ejpam-3713	504	12	.	.	PUNCT
ejpam-3713	505	1	the	the	DET
ejpam-3713	505	2	graphs	graph	NOUN
ejpam-3713	505	3	related	relate	VERB
ejpam-3713	505	4	to	to	ADP
ejpam-3713	505	5	solution	solution	NOUN
ejpam-3713	505	6	(	(	PUNCT
ejpam-3713	505	7	26	26	NUM
ejpam-3713	505	8	)	)	PUNCT
ejpam-3713	505	9	are	be	AUX
ejpam-3713	505	10	drawn	draw	VERB
ejpam-3713	505	11	in	in	ADP
ejpam-3713	505	12	figure	figure	NOUN
ejpam-3713	505	13	1	1	NUM
ejpam-3713	505	14	(	(	PUNCT
ejpam-3713	505	15	a	a	DET
ejpam-3713	505	16	,	,	PUNCT
ejpam-3713	505	17	b	b	NOUN
ejpam-3713	505	18	,	,	PUNCT
ejpam-3713	505	19	c	c	PROPN
ejpam-3713	505	20	and	and	CCONJ
ejpam-3713	505	21	d	d	NOUN
ejpam-3713	505	22	)	)	PUNCT
ejpam-3713	505	23	which	which	PRON
ejpam-3713	505	24	verify	verify	VERB
ejpam-3713	505	25	the	the	DET
ejpam-3713	505	26	presented	present	VERB
ejpam-3713	505	27	mathematical	mathematical	ADJ
ejpam-3713	505	28	discussion	discussion	NOUN
ejpam-3713	505	29	.	.	PUNCT
ejpam-3713	506	1	indeed	indeed	ADV
ejpam-3713	506	2	,	,	PUNCT
ejpam-3713	506	3	green	green	ADJ
ejpam-3713	506	4	graphs	graph	NOUN
ejpam-3713	506	5	,	,	PUNCT
ejpam-3713	506	6	which	which	PRON
ejpam-3713	506	7	are	be	AUX
ejpam-3713	506	8	started	start	VERB
ejpam-3713	506	9	with	with	ADP
ejpam-3713	506	10	value	value	NOUN
ejpam-3713	506	11	greater	great	ADJ
ejpam-3713	506	12	than	than	ADP
ejpam-3713	506	13	m	m	PROPN
ejpam-3713	506	14	,	,	PUNCT
ejpam-3713	506	15	are	be	AUX
ejpam-3713	506	16	decreasing	decrease	VERB
ejpam-3713	506	17	and	and	CCONJ
ejpam-3713	506	18	tend	tend	VERB
ejpam-3713	506	19	to	to	PART
ejpam-3713	506	20	m	m	VERB
ejpam-3713	506	21	asymptotically	asymptotically	ADV
ejpam-3713	506	22	.	.	PUNCT
ejpam-3713	507	1	blue	blue	ADJ
ejpam-3713	507	2	graphs	graph	NOUN
ejpam-3713	507	3	,	,	PUNCT
ejpam-3713	507	4	which	which	PRON
ejpam-3713	507	5	are	be	AUX
ejpam-3713	507	6	located	locate	VERB
ejpam-3713	507	7	betweenm	betweenm	NOUN
ejpam-3713	507	8	2	2	NUM
ejpam-3713	507	9	and	and	CCONJ
ejpam-3713	507	10	m	m	PRON
ejpam-3713	507	11	,	,	PUNCT
ejpam-3713	507	12	are	be	AUX
ejpam-3713	507	13	increasing	increase	VERB
ejpam-3713	507	14	and	and	CCONJ
ejpam-3713	507	15	tend	tend	VERB
ejpam-3713	507	16	to	to	PART
ejpam-3713	507	17	m	m	VERB
ejpam-3713	507	18	asymptotically	asymptotically	ADV
ejpam-3713	507	19	.	.	PUNCT
ejpam-3713	508	1	red	red	ADJ
ejpam-3713	508	2	graphs	graph	NOUN
ejpam-3713	508	3	,	,	PUNCT
ejpam-3713	508	4	which	which	PRON
ejpam-3713	508	5	are	be	AUX
ejpam-3713	508	6	started	start	VERB
ejpam-3713	508	7	with	with	ADP
ejpam-3713	508	8	value	value	NOUN
ejpam-3713	508	9	less	less	ADJ
ejpam-3713	508	10	than	than	ADP
ejpam-3713	508	11	the	the	DET
ejpam-3713	508	12	m	m	NOUN
ejpam-3713	508	13	2	2	NUM
ejpam-3713	508	14	,	,	PUNCT
ejpam-3713	508	15	are	be	AUX
ejpam-3713	508	16	increasing	increase	VERB
ejpam-3713	508	17	and	and	CCONJ
ejpam-3713	508	18	tend	tend	VERB
ejpam-3713	508	19	to	to	PART
ejpam-3713	508	20	m	m	VERB
ejpam-3713	508	21	asymptotically	asymptotically	ADV
ejpam-3713	508	22	.	.	PUNCT
ejpam-3713	509	1	it	it	PRON
ejpam-3713	509	2	is	be	AUX
ejpam-3713	509	3	clear	clear	ADJ
ejpam-3713	509	4	that	that	SCONJ
ejpam-3713	509	5	it	it	PRON
ejpam-3713	509	6	decrease	decrease	VERB
ejpam-3713	509	7	slowly	slowly	ADV
ejpam-3713	509	8	whenever	whenever	SCONJ
ejpam-3713	509	9	growth	growth	NOUN
ejpam-3713	509	10	rate	rate	NOUN
ejpam-3713	509	11	r	r	NOUN
ejpam-3713	509	12	is	be	AUX
ejpam-3713	509	13	less	less	ADJ
ejpam-3713	509	14	than	than	ADP
ejpam-3713	509	15	1	1	NUM
ejpam-3713	509	16	,	,	PUNCT
ejpam-3713	509	17	meanwhile	meanwhile	ADV
ejpam-3713	509	18	it	it	PRON
ejpam-3713	509	19	decreases	decrease	VERB
ejpam-3713	509	20	rapidly	rapidly	ADV
ejpam-3713	509	21	whenever	whenever	SCONJ
ejpam-3713	509	22	growth	growth	NOUN
ejpam-3713	509	23	rate	rate	NOUN
ejpam-3713	509	24	r	r	NOUN
ejpam-3713	509	25	is	be	AUX
ejpam-3713	509	26	greater	great	ADJ
ejpam-3713	509	27	than	than	ADP
ejpam-3713	509	28	1	1	NUM
ejpam-3713	509	29	.	.	PUNCT
ejpam-3713	509	30	to	to	PART
ejpam-3713	509	31	verify	verify	VERB
ejpam-3713	509	32	the	the	DET
ejpam-3713	509	33	the	the	DET
ejpam-3713	509	34	results	result	NOUN
ejpam-3713	509	35	of	of	ADP
ejpam-3713	509	36	theorem	theorem	ADJ
ejpam-3713	509	37	2.2	2.2	NUM
ejpam-3713	509	38	,	,	PUNCT
ejpam-3713	509	39	we	we	PRON
ejpam-3713	509	40	make	make	VERB
ejpam-3713	509	41	simulation	simulation	NOUN
ejpam-3713	509	42	for	for	ADP
ejpam-3713	509	43	solution	solution	NOUN
ejpam-3713	509	44	(	(	PUNCT
ejpam-3713	509	45	31	31	NUM
ejpam-3713	509	46	)	)	PUNCT
ejpam-3713	509	47	of	of	ADP
ejpam-3713	509	48	i.v.p.(27	i.v.p.(27	NOUN
ejpam-3713	509	49	)	)	PUNCT
ejpam-3713	509	50	describing	describe	VERB
ejpam-3713	509	51	logistic	logistic	ADJ
ejpam-3713	509	52	modeling	modeling	NOUN
ejpam-3713	509	53	with	with	ADP
ejpam-3713	509	54	constant	constant	ADJ
ejpam-3713	509	55	harvesting	harvesting	NOUN
ejpam-3713	509	56	factor	factor	NOUN
ejpam-3713	509	57	.	.	PUNCT
ejpam-3713	510	1	by	by	ADP
ejpam-3713	510	2	giving	give	VERB
ejpam-3713	510	3	some	some	DET
ejpam-3713	510	4	different	different	ADJ
ejpam-3713	510	5	values	value	NOUN
ejpam-3713	510	6	to	to	ADP
ejpam-3713	510	7	carrying	carry	VERB
ejpam-3713	510	8	capacity	capacity	NOUN
ejpam-3713	510	9	m	m	NOUN
ejpam-3713	510	10	,	,	PUNCT
ejpam-3713	510	11	growth	growth	NOUN
ejpam-3713	510	12	rate	rate	NOUN
ejpam-3713	510	13	r	r	NOUN
ejpam-3713	510	14	and	and	CCONJ
ejpam-3713	510	15	harvesting	harvesting	NOUN
ejpam-3713	510	16	factor	factor	NOUN
ejpam-3713	510	17	h	h	NOUN
ejpam-3713	510	18	,	,	PUNCT
ejpam-3713	510	19	we	we	PRON
ejpam-3713	510	20	obtain	obtain	VERB
ejpam-3713	510	21	the	the	DET
ejpam-3713	510	22	related	related	ADJ
ejpam-3713	510	23	equilibria	equilibrium	NOUN
ejpam-3713	510	24	x1	x1	PROPN
ejpam-3713	510	25	and	and	CCONJ
ejpam-3713	510	26	x2	x2	PROPN
ejpam-3713	510	27	.	.	PUNCT
ejpam-3713	511	1	this	this	DET
ejpam-3713	511	2	argument	argument	NOUN
ejpam-3713	511	3	has	have	AUX
ejpam-3713	511	4	been	be	AUX
ejpam-3713	511	5	brought	bring	VERB
ejpam-3713	511	6	in	in	ADP
ejpam-3713	511	7	table	table	NOUN
ejpam-3713	511	8	2	2	NUM
ejpam-3713	511	9	.	.	PUNCT
ejpam-3713	511	10	paying	pay	VERB
ejpam-3713	511	11	attention	attention	NOUN
ejpam-3713	511	12	to	to	ADP
ejpam-3713	511	13	drawn	draw	VERB
ejpam-3713	511	14	graphs	graph	NOUN
ejpam-3713	511	15	in	in	ADP
ejpam-3713	511	16	figure	figure	NOUN
ejpam-3713	511	17	2	2	NUM
ejpam-3713	511	18	,	,	PUNCT
ejpam-3713	511	19	we	we	PRON
ejpam-3713	511	20	see	see	VERB
ejpam-3713	511	21	that	that	SCONJ
ejpam-3713	511	22	the	the	DET
ejpam-3713	511	23	equilibrium	equilibrium	NOUN
ejpam-3713	511	24	point	point	NOUN
ejpam-3713	511	25	x1	x1	PROPN
ejpam-3713	511	26	is	be	AUX
ejpam-3713	511	27	unstable	unstable	ADJ
ejpam-3713	511	28	and	and	CCONJ
ejpam-3713	511	29	the	the	DET
ejpam-3713	511	30	equilibrium	equilibrium	NOUN
ejpam-3713	511	31	point	point	NOUN
ejpam-3713	511	32	x2	x2	PROPN
ejpam-3713	511	33	is	be	AUX
ejpam-3713	511	34	asymptotically	asymptotically	ADV
ejpam-3713	511	35	stable	stable	ADJ
ejpam-3713	511	36	which	which	PRON
ejpam-3713	511	37	are	be	AUX
ejpam-3713	511	38	proved	prove	VERB
ejpam-3713	511	39	in	in	ADP
ejpam-3713	511	40	theorem	theorem	NOUN
ejpam-3713	511	41	2.2	2.2	NUM
ejpam-3713	511	42	.	.	PUNCT
ejpam-3713	512	1	the	the	DET
ejpam-3713	512	2	details	detail	NOUN
ejpam-3713	512	3	may	may	AUX
ejpam-3713	512	4	be	be	AUX
ejpam-3713	512	5	seen	see	VERB
ejpam-3713	512	6	in	in	ADP
ejpam-3713	512	7	figure	figure	NOUN
ejpam-3713	512	8	2	2	NUM
ejpam-3713	512	9	.	.	PUNCT
ejpam-3713	513	1	the	the	DET
ejpam-3713	513	2	solution	solution	NOUN
ejpam-3713	513	3	graphs	graph	NOUN
ejpam-3713	513	4	are	be	AUX
ejpam-3713	513	5	shown	show	VERB
ejpam-3713	513	6	in	in	ADP
ejpam-3713	513	7	this	this	DET
ejpam-3713	513	8	figure	figure	NOUN
ejpam-3713	513	9	(	(	PUNCT
ejpam-3713	513	10	a	a	DET
ejpam-3713	513	11	,	,	PUNCT
ejpam-3713	513	12	b	b	NOUN
ejpam-3713	513	13	,	,	PUNCT
ejpam-3713	513	14	c	c	NOUN
ejpam-3713	513	15	,	,	PUNCT
ejpam-3713	513	16	d	d	NOUN
ejpam-3713	513	17	)	)	PUNCT
ejpam-3713	513	18	clearly	clearly	ADV
ejpam-3713	513	19	.	.	PUNCT
ejpam-3713	514	1	we	we	PRON
ejpam-3713	514	2	now	now	ADV
ejpam-3713	514	3	make	make	VERB
ejpam-3713	514	4	simulation	simulation	NOUN
ejpam-3713	514	5	for	for	ADP
ejpam-3713	514	6	solution	solution	NOUN
ejpam-3713	514	7	(	(	PUNCT
ejpam-3713	514	8	38	38	NUM
ejpam-3713	514	9	)	)	PUNCT
ejpam-3713	514	10	of	of	ADP
ejpam-3713	514	11	i.v.p	i.v.p	NOUN
ejpam-3713	514	12	.	.	PUNCT
ejpam-3713	515	1	(	(	PUNCT
ejpam-3713	515	2	36	36	NUM
ejpam-3713	515	3	)	)	PUNCT
ejpam-3713	515	4	.	.	PUNCT
ejpam-3713	516	1	this	this	DET
ejpam-3713	516	2	i.v.p	i.v.p	NOUN
ejpam-3713	516	3	.	.	PUNCT
ejpam-3713	516	4	describes	describe	VERB
ejpam-3713	516	5	the	the	DET
ejpam-3713	516	6	logistic	logistic	ADJ
ejpam-3713	516	7	modeling	model	VERB
ejpam-3713	516	8	variable	variable	ADJ
ejpam-3713	516	9	harvesting	harvesting	NOUN
ejpam-3713	516	10	factor	factor	NOUN
ejpam-3713	516	11	.	.	PUNCT
ejpam-3713	517	1	indeed	indeed	ADV
ejpam-3713	517	2	,	,	PUNCT
ejpam-3713	517	3	in	in	ADP
ejpam-3713	517	4	this	this	DET
ejpam-3713	517	5	case	case	NOUN
ejpam-3713	517	6	harvesting	harvesting	NOUN
ejpam-3713	517	7	factor	factor	NOUN
ejpam-3713	517	8	is	be	AUX
ejpam-3713	517	9	a	a	DET
ejpam-3713	517	10	fractional	fractional	ADJ
ejpam-3713	517	11	function	function	NOUN
ejpam-3713	517	12	f(x	f(x	PROPN
ejpam-3713	517	13	)	)	PUNCT
ejpam-3713	518	1	=	=	PUNCT
ejpam-3713	519	1	x	x	PUNCT
ejpam-3713	519	2	x+1	x+1	PROPN
ejpam-3713	519	3	.	.	PUNCT
ejpam-3713	520	1	the	the	DET
ejpam-3713	520	2	details	detail	NOUN
ejpam-3713	520	3	of	of	ADP
ejpam-3713	520	4	parameters	parameter	NOUN
ejpam-3713	520	5	:	:	PUNCT
ejpam-3713	520	6	carrying	carry	VERB
ejpam-3713	520	7	capacity(m	capacity(m	NOUN
ejpam-3713	520	8	)	)	PUNCT
ejpam-3713	520	9	,	,	PUNCT
ejpam-3713	520	10	growth	growth	NOUN
ejpam-3713	520	11	m.h	m.h	PROPN
ejpam-3713	520	12	.	.	PROPN
ejpam-3713	520	13	r.	r.	PROPN
ejpam-3713	520	14	doust	doust	PROPN
ejpam-3713	520	15	,	,	PUNCT
ejpam-3713	520	16	v.	v.	ADP
ejpam-3713	520	17	lokesha	lokesha	PROPN
ejpam-3713	520	18	,	,	PUNCT
ejpam-3713	520	19	a.	a.	NOUN
ejpam-3713	520	20	ghasemabadi	ghasemabadi	NOUN
ejpam-3713	520	21	/	/	SYM
ejpam-3713	520	22	eur	eur	PROPN
ejpam-3713	520	23	.	.	PUNCT
ejpam-3713	521	1	j.	j.	PROPN
ejpam-3713	521	2	pure	pure	PROPN
ejpam-3713	521	3	appl	appl	PROPN
ejpam-3713	521	4	.	.	PROPN
ejpam-3713	521	5	math	math	PROPN
ejpam-3713	521	6	,	,	PUNCT
ejpam-3713	521	7	13	13	NUM
ejpam-3713	521	8	(	(	PUNCT
ejpam-3713	521	9	5	5	NUM
ejpam-3713	521	10	)	)	PUNCT
ejpam-3713	521	11	(	(	PUNCT
ejpam-3713	521	12	2020	2020	NUM
ejpam-3713	521	13	)	)	PUNCT
ejpam-3713	521	14	,	,	PUNCT
ejpam-3713	521	15	1176	1176	NUM
ejpam-3713	521	16	-	-	SYM
ejpam-3713	521	17	1198	1198	NUM
ejpam-3713	521	18	1193	1193	NUM
ejpam-3713	521	19	rate(r	rate(r	NOUN
ejpam-3713	521	20	)	)	PUNCT
ejpam-3713	521	21	,	,	PUNCT
ejpam-3713	521	22	harvesting	harvesting	NOUN
ejpam-3713	521	23	factor(h	factor(h	NOUN
ejpam-3713	521	24	)	)	PUNCT
ejpam-3713	521	25	and	and	CCONJ
ejpam-3713	521	26	initial	initial	ADJ
ejpam-3713	521	27	populations(x0	populations(x0	NOUN
ejpam-3713	521	28	)	)	PUNCT
ejpam-3713	521	29	are	be	AUX
ejpam-3713	521	30	presented	present	VERB
ejpam-3713	521	31	in	in	ADP
ejpam-3713	521	32	table	table	NOUN
ejpam-3713	521	33	(	(	PUNCT
ejpam-3713	521	34	2	2	NUM
ejpam-3713	521	35	)	)	PUNCT
ejpam-3713	521	36	.	.	PUNCT
ejpam-3713	522	1	we	we	PRON
ejpam-3713	522	2	see	see	VERB
ejpam-3713	522	3	that	that	PRON
ejpam-3713	522	4	for	for	ADP
ejpam-3713	522	5	case	case	NOUN
ejpam-3713	522	6	of	of	ADP
ejpam-3713	522	7	m	m	PROPN
ejpam-3713	522	8	=	=	NOUN
ejpam-3713	522	9	r	r	NOUN
ejpam-3713	522	10	=	=	NOUN
ejpam-3713	522	11	h	h	NOUN
ejpam-3713	522	12	=	=	NOUN
ejpam-3713	522	13	1	1	NUM
ejpam-3713	522	14	all	all	PRON
ejpam-3713	522	15	of	of	ADP
ejpam-3713	522	16	equilibria	equilibrium	NOUN
ejpam-3713	522	17	for	for	ADP
ejpam-3713	522	18	(	(	PUNCT
ejpam-3713	522	19	36	36	NUM
ejpam-3713	522	20	)	)	PUNCT
ejpam-3713	522	21	are	be	AUX
ejpam-3713	522	22	x	x	X
ejpam-3713	522	23	=	=	SYM
ejpam-3713	522	24	0	0	NUM
ejpam-3713	522	25	.	.	PUNCT
ejpam-3713	523	1	the	the	DET
ejpam-3713	523	2	related	relate	VERB
ejpam-3713	523	3	graphs	graph	NOUN
ejpam-3713	523	4	verifying	verify	VERB
ejpam-3713	523	5	the	the	DET
ejpam-3713	523	6	results	result	NOUN
ejpam-3713	523	7	of	of	ADP
ejpam-3713	523	8	theorem	theorem	ADJ
ejpam-3713	523	9	2.3	2.3	NUM
ejpam-3713	523	10	are	be	AUX
ejpam-3713	523	11	shown	show	VERB
ejpam-3713	523	12	in	in	ADP
ejpam-3713	523	13	figure	figure	NOUN
ejpam-3713	523	14	(	(	PUNCT
ejpam-3713	523	15	3	3	NUM
ejpam-3713	523	16	)	)	PUNCT
ejpam-3713	523	17	.	.	PUNCT
ejpam-3713	524	1	these	these	DET
ejpam-3713	524	2	graphs	graph	NOUN
ejpam-3713	524	3	are	be	AUX
ejpam-3713	524	4	simulated	simulate	VERB
ejpam-3713	524	5	in	in	ADP
ejpam-3713	524	6	two	two	NUM
ejpam-3713	524	7	scale	scale	NOUN
ejpam-3713	524	8	0	0	NUM
ejpam-3713	524	9	≤	≤	NOUN
ejpam-3713	524	10	t	t	PROPN
ejpam-3713	524	11	<	<	X
ejpam-3713	524	12	30	30	NUM
ejpam-3713	524	13	and	and	CCONJ
ejpam-3713	524	14	0	0	NUM
ejpam-3713	524	15	≤	≤	NOUN
ejpam-3713	524	16	t	t	X
ejpam-3713	524	17	<	<	X
ejpam-3713	524	18	1000	1000	NUM
ejpam-3713	524	19	.	.	PUNCT
ejpam-3713	525	1	for	for	ADP
ejpam-3713	525	2	the	the	DET
ejpam-3713	525	3	final	final	ADJ
ejpam-3713	525	4	case	case	NOUN
ejpam-3713	525	5	,	,	PUNCT
ejpam-3713	525	6	we	we	PRON
ejpam-3713	525	7	make	make	VERB
ejpam-3713	525	8	simulation	simulation	NOUN
ejpam-3713	525	9	for	for	ADP
ejpam-3713	525	10	solution	solution	NOUN
ejpam-3713	525	11	of	of	ADP
ejpam-3713	525	12	(	(	PUNCT
ejpam-3713	525	13	45	45	NUM
ejpam-3713	525	14	)	)	PUNCT
ejpam-3713	525	15	of	of	ADP
ejpam-3713	525	16	i.v.p	i.v.p	NOUN
ejpam-3713	525	17	.	.	PUNCT
ejpam-3713	526	1	(	(	PUNCT
ejpam-3713	526	2	43	43	NUM
ejpam-3713	526	3	)	)	PUNCT
ejpam-3713	526	4	.	.	PUNCT
ejpam-3713	527	1	this	this	DET
ejpam-3713	527	2	i.v.p	i.v.p	NOUN
ejpam-3713	527	3	.	.	PUNCT
ejpam-3713	527	4	describes	describe	VERB
ejpam-3713	527	5	logistic	logistic	ADJ
ejpam-3713	527	6	modeling	modeling	NOUN
ejpam-3713	527	7	having	have	VERB
ejpam-3713	527	8	variable	variable	ADJ
ejpam-3713	527	9	harvesting	harvesting	NOUN
ejpam-3713	527	10	factor	factor	NOUN
ejpam-3713	527	11	.	.	PUNCT
ejpam-3713	528	1	it	it	PRON
ejpam-3713	528	2	is	be	AUX
ejpam-3713	528	3	assumed	assume	VERB
ejpam-3713	528	4	that	that	SCONJ
ejpam-3713	528	5	in	in	ADP
ejpam-3713	528	6	this	this	DET
ejpam-3713	528	7	model	model	NOUN
ejpam-3713	528	8	harvesting	harvesting	NOUN
ejpam-3713	528	9	factor	factor	NOUN
ejpam-3713	528	10	is	be	AUX
ejpam-3713	528	11	cubic	cubic	ADJ
ejpam-3713	528	12	function	function	NOUN
ejpam-3713	528	13	f(x	f(x	PROPN
ejpam-3713	528	14	)	)	PUNCT
ejpam-3713	528	15	=	=	PUNCT
ejpam-3713	529	1	x3	x3	ADJ
ejpam-3713	529	2	.	.	PUNCT
ejpam-3713	530	1	considering	consider	VERB
ejpam-3713	530	2	assumption	assumption	NOUN
ejpam-3713	530	3	as	as	ADP
ejpam-3713	530	4	m	m	NOUN
ejpam-3713	530	5	=	=	SYM
ejpam-3713	530	6	r	r	NOUN
ejpam-3713	530	7	=	=	NOUN
ejpam-3713	530	8	h	h	NOUN
ejpam-3713	530	9	=	=	SYM
ejpam-3713	530	10	1	1	NUM
ejpam-3713	530	11	implies	imply	VERB
ejpam-3713	530	12	that	that	SCONJ
ejpam-3713	530	13	equilibria	equilibrium	NOUN
ejpam-3713	530	14	are	be	AUX
ejpam-3713	530	15	given	give	VERB
ejpam-3713	530	16	by	by	ADP
ejpam-3713	530	17	x1	x1	PROPN
ejpam-3713	530	18	=	=	SYM
ejpam-3713	530	19	0	0	PROPN
ejpam-3713	530	20	,	,	PUNCT
ejpam-3713	530	21	x2	x2	NOUN
ejpam-3713	530	22	=	=	PUNCT
ejpam-3713	531	1	−1.618and	−1.618and	NUM
ejpam-3713	531	2	x3	x3	NOUN
ejpam-3713	531	3	=	=	SYM
ejpam-3713	531	4	6.18×	6.18×	NUM
ejpam-3713	531	5	10	10	NUM
ejpam-3713	531	6	.	.	PUNCT
ejpam-3713	532	1	if	if	SCONJ
ejpam-3713	532	2	we	we	PRON
ejpam-3713	532	3	consider	consider	VERB
ejpam-3713	532	4	m	m	NOUN
ejpam-3713	532	5	=	=	PUNCT
ejpam-3713	532	6	×106	×106	PROPN
ejpam-3713	532	7	,	,	PUNCT
ejpam-3713	532	8	r	r	NOUN
ejpam-3713	532	9	=	=	SYM
ejpam-3713	532	10	1	1	NUM
ejpam-3713	532	11	,	,	PUNCT
ejpam-3713	532	12	h	h	NOUN
ejpam-3713	533	1	=	=	PUNCT
ejpam-3713	533	2	×10−6	×10−6	NOUN
ejpam-3713	533	3	,	,	PUNCT
ejpam-3713	533	4	we	we	PRON
ejpam-3713	533	5	have	have	VERB
ejpam-3713	533	6	equilibria	equilibrium	NOUN
ejpam-3713	533	7	as	as	SCONJ
ejpam-3713	533	8	follows	follow	VERB
ejpam-3713	533	9	:	:	PUNCT
ejpam-3713	533	10	x1	x1	PROPN
ejpam-3713	533	11	=	=	SYM
ejpam-3713	533	12	0	0	PROPN
ejpam-3713	533	13	,	,	PUNCT
ejpam-3713	534	1	x2	x2	NOUN
ejpam-3713	534	2	=	=	PUNCT
ejpam-3713	534	3	−1.0005×	−1.0005×	NUM
ejpam-3713	534	4	103	103	NUM
ejpam-3713	534	5	and	and	CCONJ
ejpam-3713	534	6	x3	x3	ADJ
ejpam-3713	534	7	=	=	SYM
ejpam-3713	534	8	9.995×	9.995×	NUM
ejpam-3713	534	9	103	103	NUM
ejpam-3713	534	10	.	.	PUNCT
ejpam-3713	535	1	in	in	ADP
ejpam-3713	535	2	both	both	PRON
ejpam-3713	535	3	of	of	ADP
ejpam-3713	535	4	the	the	DET
ejpam-3713	535	5	above	above	ADJ
ejpam-3713	535	6	cases	case	NOUN
ejpam-3713	535	7	,	,	PUNCT
ejpam-3713	535	8	the	the	DET
ejpam-3713	535	9	equilibria	equilibrium	NOUN
ejpam-3713	535	10	are	be	AUX
ejpam-3713	535	11	negative	negative	ADJ
ejpam-3713	535	12	,	,	PUNCT
ejpam-3713	535	13	zero	zero	NUM
ejpam-3713	535	14	and	and	CCONJ
ejpam-3713	535	15	positive	positive	ADJ
ejpam-3713	535	16	which	which	PRON
ejpam-3713	535	17	are	be	AUX
ejpam-3713	535	18	proved	prove	VERB
ejpam-3713	535	19	in	in	ADP
ejpam-3713	535	20	theorem	theorem	ADJ
ejpam-3713	535	21	2.4	2.4	NUM
ejpam-3713	535	22	.	.	PUNCT
ejpam-3713	536	1	the	the	DET
ejpam-3713	536	2	another	another	DET
ejpam-3713	536	3	result	result	NOUN
ejpam-3713	536	4	of	of	ADP
ejpam-3713	536	5	solution	solution	NOUN
ejpam-3713	536	6	behavior	behavior	NOUN
ejpam-3713	536	7	which	which	PRON
ejpam-3713	536	8	are	be	AUX
ejpam-3713	536	9	studied	study	VERB
ejpam-3713	536	10	in	in	ADP
ejpam-3713	536	11	said	say	VERB
ejpam-3713	536	12	theorem	theorem	VERB
ejpam-3713	536	13	are	be	AUX
ejpam-3713	536	14	shown	show	VERB
ejpam-3713	536	15	in	in	ADP
ejpam-3713	536	16	figure	figure	NOUN
ejpam-3713	536	17	(	(	PUNCT
ejpam-3713	536	18	4	4	NUM
ejpam-3713	536	19	)	)	PUNCT
ejpam-3713	536	20	.	.	PUNCT
ejpam-3713	537	1	table	table	NOUN
ejpam-3713	537	2	1	1	NUM
ejpam-3713	537	3	:	:	PUNCT
ejpam-3713	537	4	parameters	parameter	NOUN
ejpam-3713	537	5	,	,	PUNCT
ejpam-3713	537	6	equilibria	equilibrium	NOUN
ejpam-3713	537	7	and	and	CCONJ
ejpam-3713	537	8	initial	initial	ADJ
ejpam-3713	537	9	populations	population	NOUN
ejpam-3713	537	10	for	for	ADP
ejpam-3713	537	11	i.v.p.(25	i.v.p.(25	NOUN
ejpam-3713	537	12	)	)	PUNCT
ejpam-3713	538	1	a	a	DET
ejpam-3713	538	2	b	b	NOUN
ejpam-3713	538	3	c	c	NOUN
ejpam-3713	538	4	d	d	NOUN
ejpam-3713	538	5	m	m	VERB
ejpam-3713	538	6	102	102	NUM
ejpam-3713	538	7	102	102	NUM
ejpam-3713	538	8	103	103	NUM
ejpam-3713	538	9	103	103	NUM
ejpam-3713	538	10	r	r	NOUN
ejpam-3713	538	11	5	5	NUM
ejpam-3713	538	12	×	×	NOUN
ejpam-3713	538	13	10	10	NUM
ejpam-3713	538	14	2	2	NUM
ejpam-3713	538	15	0.5	0.5	NUM
ejpam-3713	538	16	2	2	NUM
ejpam-3713	538	17	x1	x1	NOUN
ejpam-3713	538	18	0	0	NUM
ejpam-3713	538	19	0	0	NUM
ejpam-3713	538	20	0	0	NUM
ejpam-3713	538	21	0	0	NUM
ejpam-3713	539	1	x2	x2	NOUN
ejpam-3713	539	2	102	102	NUM
ejpam-3713	539	3	102	102	NUM
ejpam-3713	539	4	103	103	NUM
ejpam-3713	539	5	103	103	NUM
ejpam-3713	539	6	x01	x01	PROPN
ejpam-3713	539	7	1.667	1.667	NUM
ejpam-3713	539	8	×	×	NOUN
ejpam-3713	539	9	10	10	NUM
ejpam-3713	539	10	1.666	1.666	NUM
ejpam-3713	539	11	×	×	NOUN
ejpam-3713	539	12	102	102	NUM
ejpam-3713	539	13	50	50	NUM
ejpam-3713	539	14	1.666	1.666	NUM
ejpam-3713	539	15	×	×	NOUN
ejpam-3713	539	16	102	102	NUM
ejpam-3713	539	17	x02	x02	NOUN
ejpam-3713	539	18	20	20	NUM
ejpam-3713	539	19	20	20	NUM
ejpam-3713	539	20	200	200	NUM
ejpam-3713	539	21	2	2	NUM
ejpam-3713	539	22	×	×	NOUN
ejpam-3713	539	23	102	102	NUM
ejpam-3713	539	24	x03	x03	NOUN
ejpam-3713	539	25	25	25	NUM
ejpam-3713	539	26	25	25	NUM
ejpam-3713	539	27	250	250	NUM
ejpam-3713	539	28	2.5	2.5	NUM
ejpam-3713	539	29	×	×	NOUN
ejpam-3713	539	30	102	102	NUM
ejpam-3713	539	31	x04	x04	NOUN
ejpam-3713	539	32	3.333	3.333	NUM
ejpam-3713	539	33	×	×	NOUN
ejpam-3713	539	34	10	10	NUM
ejpam-3713	539	35	3.333	3.333	NUM
ejpam-3713	539	36	×	×	NOUN
ejpam-3713	539	37	102	102	NUM
ejpam-3713	539	38	3.333	3.333	NUM
ejpam-3713	539	39	×	×	NOUN
ejpam-3713	539	40	103	103	NUM
ejpam-3713	539	41	3.333	3.333	NUM
ejpam-3713	539	42	×	×	NOUN
ejpam-3713	539	43	103	103	NUM
ejpam-3713	539	44	x05	x05	PROPN
ejpam-3713	539	45	6	6	NUM
ejpam-3713	539	46	×	×	NOUN
ejpam-3713	539	47	10	10	NUM
ejpam-3713	539	48	6	6	NUM
ejpam-3713	539	49	×	×	NOUN
ejpam-3713	539	50	10	10	NUM
ejpam-3713	539	51	5.1	5.1	NUM
ejpam-3713	539	52	×	×	NOUN
ejpam-3713	539	53	102	102	NUM
ejpam-3713	539	54	5.1	5.1	NUM
ejpam-3713	539	55	×	×	NOUN
ejpam-3713	539	56	102	102	NUM
ejpam-3713	539	57	x06	x06	NOUN
ejpam-3713	539	58	7	7	NUM
ejpam-3713	539	59	×	×	NOUN
ejpam-3713	539	60	10	10	NUM
ejpam-3713	539	61	7	7	NUM
ejpam-3713	539	62	×	×	NOUN
ejpam-3713	539	63	10	10	NUM
ejpam-3713	539	64	5.2	5.2	NUM
ejpam-3713	539	65	×	×	NOUN
ejpam-3713	539	66	102	102	NUM
ejpam-3713	539	67	5.2	5.2	NUM
ejpam-3713	539	68	×	×	NOUN
ejpam-3713	539	69	102	102	NUM
ejpam-3713	539	70	x07	x07	NUM
ejpam-3713	539	71	8	8	NUM
ejpam-3713	539	72	×	×	NOUN
ejpam-3713	539	73	10	10	NUM
ejpam-3713	539	74	8	8	NUM
ejpam-3713	539	75	×	×	NOUN
ejpam-3713	539	76	10	10	NUM
ejpam-3713	539	77	5.3	5.3	NUM
ejpam-3713	539	78	×	×	NOUN
ejpam-3713	539	79	102	102	NUM
ejpam-3713	539	80	5.3	5.3	NUM
ejpam-3713	539	81	×	×	NOUN
ejpam-3713	539	82	102	102	NUM
ejpam-3713	539	83	x08	x08	NOUN
ejpam-3713	539	84	9	9	NUM
ejpam-3713	539	85	×	×	NOUN
ejpam-3713	539	86	10	10	NUM
ejpam-3713	539	87	9	9	NUM
ejpam-3713	539	88	×	×	NOUN
ejpam-3713	539	89	10	10	NUM
ejpam-3713	539	90	5.4	5.4	NUM
ejpam-3713	539	91	×	×	NOUN
ejpam-3713	539	92	102	102	NUM
ejpam-3713	539	93	5.4	5.4	NUM
ejpam-3713	539	94	×	×	NOUN
ejpam-3713	539	95	102	102	NUM
ejpam-3713	539	96	x09	x09	PROPN
ejpam-3713	539	97	1.2	1.2	NUM
ejpam-3713	539	98	×	×	NOUN
ejpam-3713	539	99	10	10	NUM
ejpam-3713	539	100	1.2	1.2	NUM
ejpam-3713	539	101	×	×	NOUN
ejpam-3713	539	102	102	102	NUM
ejpam-3713	539	103	1.2	1.2	NUM
ejpam-3713	539	104	×	×	NOUN
ejpam-3713	539	105	103	103	NUM
ejpam-3713	539	106	1.2	1.2	NUM
ejpam-3713	539	107	×	×	NOUN
ejpam-3713	539	108	103	103	NUM
ejpam-3713	539	109	x010	x010	PROPN
ejpam-3713	539	110	1.4	1.4	NUM
ejpam-3713	539	111	×	×	NOUN
ejpam-3713	539	112	10	10	NUM
ejpam-3713	539	113	1.4	1.4	NUM
ejpam-3713	539	114	×	×	PROPN
ejpam-3713	539	115	10	10	NUM
ejpam-3713	539	116	1.4	1.4	NUM
ejpam-3713	539	117	×	×	NOUN
ejpam-3713	539	118	103	103	NUM
ejpam-3713	539	119	1.4	1.4	NUM
ejpam-3713	539	120	×	×	NOUN
ejpam-3713	539	121	103	103	NUM
ejpam-3713	539	122	x011	x011	PROPN
ejpam-3713	539	123	1.6	1.6	NUM
ejpam-3713	539	124	×	×	NOUN
ejpam-3713	539	125	10	10	NUM
ejpam-3713	539	126	1.6	1.6	NUM
ejpam-3713	539	127	×	×	NOUN
ejpam-3713	539	128	10	10	NUM
ejpam-3713	539	129	1.6	1.6	NUM
ejpam-3713	539	130	×	×	NOUN
ejpam-3713	539	131	103	103	NUM
ejpam-3713	539	132	1.6	1.6	NUM
ejpam-3713	539	133	×	×	NOUN
ejpam-3713	539	134	103	103	NUM
ejpam-3713	539	135	x012	x012	PROPN
ejpam-3713	539	136	1.8	1.8	NUM
ejpam-3713	539	137	×	×	NOUN
ejpam-3713	539	138	10	10	NUM
ejpam-3713	539	139	1.8	1.8	NUM
ejpam-3713	539	140	×	×	NOUN
ejpam-3713	539	141	10	10	NUM
ejpam-3713	539	142	1.8	1.8	NUM
ejpam-3713	539	143	×	×	NOUN
ejpam-3713	539	144	103	103	NUM
ejpam-3713	539	145	1.8	1.8	NUM
ejpam-3713	539	146	×	×	NOUN
ejpam-3713	539	147	103	103	NUM
ejpam-3713	539	148	table	table	NOUN
ejpam-3713	539	149	2	2	NUM
ejpam-3713	539	150	:	:	PUNCT
ejpam-3713	539	151	parameters	parameter	NOUN
ejpam-3713	539	152	,	,	PUNCT
ejpam-3713	539	153	equilibria	equilibrium	NOUN
ejpam-3713	539	154	and	and	CCONJ
ejpam-3713	539	155	initial	initial	ADJ
ejpam-3713	539	156	populations	population	NOUN
ejpam-3713	539	157	for	for	ADP
ejpam-3713	539	158	i.v.p.(27	i.v.p.(27	NOUN
ejpam-3713	539	159	)	)	PUNCT
ejpam-3713	539	160	a	a	DET
ejpam-3713	539	161	b	b	NOUN
ejpam-3713	539	162	c	c	NOUN
ejpam-3713	539	163	d	d	NOUN
ejpam-3713	539	164	m	m	VERB
ejpam-3713	539	165	104	104	NUM
ejpam-3713	539	166	104	104	NUM
ejpam-3713	539	167	104	104	NUM
ejpam-3713	539	168	104	104	NUM
ejpam-3713	539	169	r	r	NOUN
ejpam-3713	539	170	.5	.5	NUM
ejpam-3713	539	171	.5	.5	NUM
ejpam-3713	539	172	10	10	NUM
ejpam-3713	539	173	10	10	NUM
ejpam-3713	539	174	h	h	NOUN
ejpam-3713	539	175	102	102	NUM
ejpam-3713	539	176	102	102	NUM
ejpam-3713	539	177	103	103	NUM
ejpam-3713	539	178	103	103	NUM
ejpam-3713	539	179	x1	x1	NOUN
ejpam-3713	539	180	0	0	NUM
ejpam-3713	539	181	0	0	NUM
ejpam-3713	539	182	0	0	NUM
ejpam-3713	539	183	0	0	NUM
ejpam-3713	540	1	x2	x2	NUM
ejpam-3713	540	2	2.041	2.041	NUM
ejpam-3713	540	3	×	×	NOUN
ejpam-3713	540	4	102	102	NUM
ejpam-3713	540	5	2.041	2.041	NUM
ejpam-3713	540	6	×	×	NOUN
ejpam-3713	540	7	102	102	NUM
ejpam-3713	540	8	1.001	1.001	NUM
ejpam-3713	540	9	×	×	NOUN
ejpam-3713	540	10	10	10	NUM
ejpam-3713	540	11	1.001	1.001	NUM
ejpam-3713	540	12	×	×	NOUN
ejpam-3713	540	13	10	10	NUM
ejpam-3713	540	14	x3	x3	NOUN
ejpam-3713	540	15	9.795	9.795	NUM
ejpam-3713	540	16	×	×	NOUN
ejpam-3713	540	17	103	103	NUM
ejpam-3713	540	18	9.795	9.795	NUM
ejpam-3713	540	19	×	×	NOUN
ejpam-3713	540	20	103	103	NUM
ejpam-3713	540	21	9.899	9.899	NUM
ejpam-3713	540	22	×	×	NOUN
ejpam-3713	540	23	103	103	NUM
ejpam-3713	540	24	9.899	9.899	NUM
ejpam-3713	540	25	×	×	NOUN
ejpam-3713	540	26	103	103	NUM
ejpam-3713	540	27	x01	x01	NOUN
ejpam-3713	540	28	2.2	2.2	NUM
ejpam-3713	540	29	×	×	NOUN
ejpam-3713	540	30	102	102	NUM
ejpam-3713	540	31	1.8	1.8	NUM
ejpam-3713	540	32	×	×	NOUN
ejpam-3713	540	33	102	102	NUM
ejpam-3713	540	34	50	50	NUM
ejpam-3713	540	35	10	10	NUM
ejpam-3713	540	36	x02	x02	PROPN
ejpam-3713	540	37	5	5	NUM
ejpam-3713	540	38	×	×	NOUN
ejpam-3713	540	39	102	102	NUM
ejpam-3713	540	40	5	5	NUM
ejpam-3713	540	41	×	×	NOUN
ejpam-3713	540	42	102	102	NUM
ejpam-3713	540	43	5	5	NUM
ejpam-3713	540	44	×	×	NOUN
ejpam-3713	540	45	102	102	NUM
ejpam-3713	540	46	5	5	NUM
ejpam-3713	540	47	×	×	NOUN
ejpam-3713	540	48	102	102	NUM
ejpam-3713	540	49	x03	x03	NOUN
ejpam-3713	540	50	2	2	NUM
ejpam-3713	540	51	×	×	NOUN
ejpam-3713	540	52	103	103	NUM
ejpam-3713	540	53	2	2	NUM
ejpam-3713	540	54	×	×	NOUN
ejpam-3713	540	55	103	103	NUM
ejpam-3713	540	56	2	2	NUM
ejpam-3713	540	57	×	×	NOUN
ejpam-3713	540	58	103	103	NUM
ejpam-3713	540	59	2	2	NUM
ejpam-3713	540	60	×	×	PROPN
ejpam-3713	540	61	103	103	NUM
ejpam-3713	540	62	x04	x04	NOUN
ejpam-3713	540	63	9	9	NUM
ejpam-3713	540	64	×	×	NOUN
ejpam-3713	540	65	103	103	NUM
ejpam-3713	540	66	9	9	NUM
ejpam-3713	540	67	×	×	NOUN
ejpam-3713	540	68	103	103	NUM
ejpam-3713	540	69	9	9	NUM
ejpam-3713	540	70	×	×	NOUN
ejpam-3713	540	71	103	103	NUM
ejpam-3713	540	72	9	9	NUM
ejpam-3713	540	73	×	×	NOUN
ejpam-3713	540	74	103	103	NUM
ejpam-3713	540	75	x05	x05	PROPN
ejpam-3713	540	76	1.2	1.2	NUM
ejpam-3713	540	77	×	×	NOUN
ejpam-3713	540	78	103	103	NUM
ejpam-3713	540	79	1.2	1.2	NUM
ejpam-3713	540	80	×	×	NOUN
ejpam-3713	540	81	103	103	NUM
ejpam-3713	540	82	1.3	1.3	NUM
ejpam-3713	540	83	×	×	NOUN
ejpam-3713	540	84	103	103	NUM
ejpam-3713	540	85	1.3	1.3	NUM
ejpam-3713	540	86	×	×	NOUN
ejpam-3713	540	87	103	103	NUM
ejpam-3713	540	88	x06	x06	NOUN
ejpam-3713	540	89	1.5	1.5	NUM
ejpam-3713	540	90	×	×	NOUN
ejpam-3713	540	91	103	103	NUM
ejpam-3713	540	92	1.5	1.5	NUM
ejpam-3713	540	93	×	×	NOUN
ejpam-3713	540	94	103	103	NUM
ejpam-3713	540	95	1.5	1.5	NUM
ejpam-3713	540	96	×	×	NOUN
ejpam-3713	540	97	103	103	NUM
ejpam-3713	540	98	1.5	1.5	NUM
ejpam-3713	540	99	×	×	NOUN
ejpam-3713	540	100	103	103	NUM
ejpam-3713	540	101	m.h	m.h	PROPN
ejpam-3713	540	102	.	.	PROPN
ejpam-3713	540	103	r.	r.	PROPN
ejpam-3713	540	104	doust	doust	PROPN
ejpam-3713	540	105	,	,	PUNCT
ejpam-3713	540	106	v.	v.	ADP
ejpam-3713	540	107	lokesha	lokesha	PROPN
ejpam-3713	540	108	,	,	PUNCT
ejpam-3713	540	109	a.	a.	NOUN
ejpam-3713	540	110	ghasemabadi	ghasemabadi	NOUN
ejpam-3713	540	111	/	/	SYM
ejpam-3713	540	112	eur	eur	PROPN
ejpam-3713	540	113	.	.	PUNCT
ejpam-3713	541	1	j.	j.	PROPN
ejpam-3713	541	2	pure	pure	PROPN
ejpam-3713	541	3	appl	appl	PROPN
ejpam-3713	541	4	.	.	PROPN
ejpam-3713	541	5	math	math	PROPN
ejpam-3713	541	6	,	,	PUNCT
ejpam-3713	541	7	13	13	NUM
ejpam-3713	541	8	(	(	PUNCT
ejpam-3713	541	9	5	5	NUM
ejpam-3713	541	10	)	)	PUNCT
ejpam-3713	541	11	(	(	PUNCT
ejpam-3713	541	12	2020	2020	NUM
ejpam-3713	541	13	)	)	PUNCT
ejpam-3713	541	14	,	,	PUNCT
ejpam-3713	541	15	1176	1176	NUM
ejpam-3713	541	16	-	-	SYM
ejpam-3713	541	17	1198	1198	NUM
ejpam-3713	541	18	1194	1194	NUM
ejpam-3713	541	19	table	table	NOUN
ejpam-3713	541	20	3	3	NUM
ejpam-3713	541	21	:	:	PUNCT
ejpam-3713	541	22	parameters	parameter	NOUN
ejpam-3713	541	23	,	,	PUNCT
ejpam-3713	541	24	equilibria	equilibrium	NOUN
ejpam-3713	541	25	and	and	CCONJ
ejpam-3713	541	26	initial	initial	ADJ
ejpam-3713	541	27	populations	population	NOUN
ejpam-3713	541	28	for	for	ADP
ejpam-3713	541	29	i.v.p.(36	i.v.p.(36	NOUN
ejpam-3713	541	30	)	)	PUNCT
ejpam-3713	541	31	a	a	DET
ejpam-3713	541	32	b	b	NOUN
ejpam-3713	541	33	m	m	VERB
ejpam-3713	541	34	1	1	NUM
ejpam-3713	541	35	106	106	NUM
ejpam-3713	541	36	r	r	NOUN
ejpam-3713	541	37	1	1	NUM
ejpam-3713	541	38	1	1	NUM
ejpam-3713	541	39	h	h	NOUN
ejpam-3713	541	40	1	1	NUM
ejpam-3713	541	41	10−6	10−6	NUM
ejpam-3713	542	1	x1	x1	NUM
ejpam-3713	542	2	0	0	NUM
ejpam-3713	542	3	0	0	NUM
ejpam-3713	543	1	x2	x2	NOUN
ejpam-3713	543	2	0	0	PUNCT
ejpam-3713	543	3	−9.9999	−9.9999	PROPN
ejpam-3713	543	4	×	×	PROPN
ejpam-3713	543	5	10−1	10−1	NUM
ejpam-3713	543	6	x3	x3	ADJ
ejpam-3713	543	7	0	0	NUM
ejpam-3713	543	8	9.9999	9.9999	NUM
ejpam-3713	543	9	×	×	NOUN
ejpam-3713	543	10	105	105	NUM
ejpam-3713	543	11	x01	x01	NUM
ejpam-3713	543	12	105	105	NUM
ejpam-3713	543	13	106	106	NUM
ejpam-3713	543	14	x02	x02	PROPN
ejpam-3713	543	15	9	9	NUM
ejpam-3713	543	16	×	×	NOUN
ejpam-3713	543	17	104	104	NUM
ejpam-3713	543	18	9	9	NUM
ejpam-3713	543	19	×	×	NOUN
ejpam-3713	543	20	105	105	NUM
ejpam-3713	543	21	x03	x03	NOUN
ejpam-3713	543	22	8	8	NUM
ejpam-3713	543	23	×	×	NOUN
ejpam-3713	543	24	104	104	NUM
ejpam-3713	543	25	8	8	NUM
ejpam-3713	543	26	×	×	NOUN
ejpam-3713	543	27	105	105	NUM
ejpam-3713	543	28	x04	x04	NOUN
ejpam-3713	543	29	7	7	NUM
ejpam-3713	543	30	×	×	NOUN
ejpam-3713	543	31	104	104	NUM
ejpam-3713	543	32	7	7	NUM
ejpam-3713	543	33	×	×	NOUN
ejpam-3713	543	34	105	105	NUM
ejpam-3713	543	35	x05	x05	PROPN
ejpam-3713	543	36	6	6	NUM
ejpam-3713	543	37	×	×	NOUN
ejpam-3713	543	38	104	104	NUM
ejpam-3713	543	39	6	6	NUM
ejpam-3713	543	40	×	×	NOUN
ejpam-3713	543	41	105	105	NUM
ejpam-3713	543	42	x06	x06	NOUN
ejpam-3713	543	43	5	5	NUM
ejpam-3713	543	44	×	×	NOUN
ejpam-3713	543	45	104	104	NUM
ejpam-3713	543	46	5	5	NUM
ejpam-3713	543	47	×	×	NOUN
ejpam-3713	543	48	105	105	NUM
ejpam-3713	543	49	x07	x07	NUM
ejpam-3713	543	50	4	4	NUM
ejpam-3713	543	51	×	×	NOUN
ejpam-3713	543	52	104	104	NUM
ejpam-3713	543	53	4	4	NUM
ejpam-3713	543	54	×	×	NOUN
ejpam-3713	543	55	105	105	NUM
ejpam-3713	543	56	x08	x08	NOUN
ejpam-3713	543	57	3	3	NUM
ejpam-3713	543	58	×	×	NOUN
ejpam-3713	543	59	104	104	NUM
ejpam-3713	543	60	3	3	NUM
ejpam-3713	543	61	×	×	NOUN
ejpam-3713	543	62	105	105	NUM
ejpam-3713	543	63	x09	x09	NOUN
ejpam-3713	543	64	2	2	NUM
ejpam-3713	543	65	×	×	NOUN
ejpam-3713	543	66	104	104	NUM
ejpam-3713	543	67	2	2	NUM
ejpam-3713	543	68	×	×	NOUN
ejpam-3713	543	69	105	105	NUM
ejpam-3713	543	70	x10	x10	NOUN
ejpam-3713	543	71	104	104	NUM
ejpam-3713	543	72	105	105	NUM
ejpam-3713	543	73	x011	x011	NUM
ejpam-3713	543	74	6	6	NUM
ejpam-3713	543	75	×	×	NOUN
ejpam-3713	543	76	103	103	NUM
ejpam-3713	543	77	6	6	NUM
ejpam-3713	543	78	×	×	NOUN
ejpam-3713	543	79	104	104	NUM
ejpam-3713	543	80	x012	x012	NUM
ejpam-3713	543	81	4	4	NUM
ejpam-3713	543	82	×	×	NOUN
ejpam-3713	543	83	103	103	NUM
ejpam-3713	543	84	4	4	NUM
ejpam-3713	543	85	×	×	NOUN
ejpam-3713	543	86	104	104	NUM
ejpam-3713	543	87	x013	x013	PROPN
ejpam-3713	543	88	2	2	NUM
ejpam-3713	543	89	×	×	NOUN
ejpam-3713	543	90	103	103	NUM
ejpam-3713	543	91	2	2	NUM
ejpam-3713	543	92	×	×	NOUN
ejpam-3713	543	93	104	104	NUM
ejpam-3713	543	94	x014	x014	PROPN
ejpam-3713	543	95	103	103	NUM
ejpam-3713	543	96	104	104	NUM
ejpam-3713	543	97	table	table	NOUN
ejpam-3713	543	98	4	4	NUM
ejpam-3713	543	99	:	:	PUNCT
ejpam-3713	543	100	parameters	parameter	NOUN
ejpam-3713	543	101	,	,	PUNCT
ejpam-3713	543	102	equilibria	equilibrium	NOUN
ejpam-3713	543	103	and	and	CCONJ
ejpam-3713	543	104	initial	initial	ADJ
ejpam-3713	543	105	populations	population	NOUN
ejpam-3713	543	106	for	for	ADP
ejpam-3713	543	107	i.v.p.(43	i.v.p.(43	NOUN
ejpam-3713	543	108	)	)	PUNCT
ejpam-3713	544	1	a	a	DET
ejpam-3713	544	2	b	b	NOUN
ejpam-3713	544	3	m	m	VERB
ejpam-3713	544	4	1	1	NUM
ejpam-3713	544	5	106	106	NUM
ejpam-3713	544	6	r	r	NOUN
ejpam-3713	544	7	1	1	NUM
ejpam-3713	544	8	1	1	NUM
ejpam-3713	544	9	h	h	NOUN
ejpam-3713	544	10	1	1	NUM
ejpam-3713	544	11	10−6	10−6	NUM
ejpam-3713	544	12	x1	x1	NUM
ejpam-3713	544	13	0	0	NUM
ejpam-3713	544	14	0	0	NUM
ejpam-3713	545	1	x2	x2	PRON
ejpam-3713	546	1	−1.618	−1.618	INTJ
ejpam-3713	547	1	−1.0005	−1.0005	X
ejpam-3713	547	2	×	×	PROPN
ejpam-3713	547	3	103	103	NUM
ejpam-3713	547	4	x3	x3	NOUN
ejpam-3713	547	5	6.18	6.18	NUM
ejpam-3713	547	6	×	×	NOUN
ejpam-3713	547	7	10−1	10−1	NUM
ejpam-3713	547	8	9.9950	9.9950	NUM
ejpam-3713	547	9	×	×	NOUN
ejpam-3713	547	10	103	103	NUM
ejpam-3713	547	11	x01	x01	NOUN
ejpam-3713	547	12	105	105	NUM
ejpam-3713	547	13	106	106	NUM
ejpam-3713	547	14	x02	x02	PROPN
ejpam-3713	547	15	9	9	NUM
ejpam-3713	547	16	×	×	NOUN
ejpam-3713	547	17	104	104	NUM
ejpam-3713	547	18	9	9	NUM
ejpam-3713	547	19	×	×	NOUN
ejpam-3713	547	20	105	105	NUM
ejpam-3713	547	21	x03	x03	NOUN
ejpam-3713	547	22	8	8	NUM
ejpam-3713	547	23	×	×	NOUN
ejpam-3713	547	24	104	104	NUM
ejpam-3713	547	25	8	8	NUM
ejpam-3713	547	26	×	×	NOUN
ejpam-3713	547	27	105	105	NUM
ejpam-3713	547	28	x04	x04	NOUN
ejpam-3713	547	29	7	7	NUM
ejpam-3713	547	30	×	×	NOUN
ejpam-3713	547	31	104	104	NUM
ejpam-3713	547	32	7	7	NUM
ejpam-3713	547	33	×	×	NOUN
ejpam-3713	547	34	105	105	NUM
ejpam-3713	547	35	x05	x05	PROPN
ejpam-3713	547	36	6	6	NUM
ejpam-3713	547	37	×	×	NOUN
ejpam-3713	547	38	104	104	NUM
ejpam-3713	547	39	6	6	NUM
ejpam-3713	547	40	×	×	NOUN
ejpam-3713	547	41	105	105	NUM
ejpam-3713	547	42	x06	x06	NOUN
ejpam-3713	547	43	5	5	NUM
ejpam-3713	547	44	×	×	NOUN
ejpam-3713	547	45	104	104	NUM
ejpam-3713	547	46	5	5	NUM
ejpam-3713	547	47	×	×	NOUN
ejpam-3713	547	48	105	105	NUM
ejpam-3713	547	49	x07	x07	NUM
ejpam-3713	548	1	4	4	NUM
ejpam-3713	548	2	×	×	NOUN
ejpam-3713	548	3	104	104	NUM
ejpam-3713	548	4	4	4	NUM
ejpam-3713	548	5	×	×	NOUN
ejpam-3713	548	6	105	105	NUM
ejpam-3713	548	7	x08	x08	NOUN
ejpam-3713	548	8	3	3	NUM
ejpam-3713	548	9	×	×	NOUN
ejpam-3713	548	10	104	104	NUM
ejpam-3713	548	11	3	3	NUM
ejpam-3713	548	12	×	×	NOUN
ejpam-3713	548	13	105	105	NUM
ejpam-3713	548	14	x09	x09	NOUN
ejpam-3713	548	15	2	2	NUM
ejpam-3713	548	16	×	×	NOUN
ejpam-3713	548	17	104	104	NUM
ejpam-3713	548	18	2	2	NUM
ejpam-3713	548	19	×	×	NOUN
ejpam-3713	548	20	105	105	NUM
ejpam-3713	548	21	x10	x10	NOUN
ejpam-3713	548	22	104	104	NUM
ejpam-3713	548	23	105	105	NUM
ejpam-3713	548	24	x011	x011	NUM
ejpam-3713	548	25	6	6	NUM
ejpam-3713	548	26	×	×	NOUN
ejpam-3713	548	27	103	103	NUM
ejpam-3713	548	28	6	6	NUM
ejpam-3713	548	29	×	×	NOUN
ejpam-3713	548	30	104	104	NUM
ejpam-3713	548	31	x012	x012	NUM
ejpam-3713	548	32	4	4	NUM
ejpam-3713	548	33	×	×	NOUN
ejpam-3713	548	34	103	103	NUM
ejpam-3713	548	35	4	4	NUM
ejpam-3713	548	36	×	×	NOUN
ejpam-3713	548	37	104	104	NUM
ejpam-3713	548	38	x013	x013	PROPN
ejpam-3713	548	39	2	2	NUM
ejpam-3713	548	40	×	×	NOUN
ejpam-3713	548	41	103	103	NUM
ejpam-3713	548	42	2	2	NUM
ejpam-3713	548	43	×	×	NOUN
ejpam-3713	548	44	104	104	NUM
ejpam-3713	548	45	x014	x014	PROPN
ejpam-3713	548	46	104	104	NUM
ejpam-3713	548	47	104	104	NUM
ejpam-3713	548	48	m.h	m.h	PROPN
ejpam-3713	548	49	.	.	PROPN
ejpam-3713	548	50	r.	r.	PROPN
ejpam-3713	548	51	doust	doust	PROPN
ejpam-3713	548	52	,	,	PUNCT
ejpam-3713	548	53	v.	v.	ADP
ejpam-3713	548	54	lokesha	lokesha	PROPN
ejpam-3713	548	55	,	,	PUNCT
ejpam-3713	548	56	a.	a.	NOUN
ejpam-3713	548	57	ghasemabadi	ghasemabadi	NOUN
ejpam-3713	548	58	/	/	SYM
ejpam-3713	548	59	eur	eur	PROPN
ejpam-3713	548	60	.	.	PUNCT
ejpam-3713	549	1	j.	j.	PROPN
ejpam-3713	549	2	pure	pure	PROPN
ejpam-3713	549	3	appl	appl	PROPN
ejpam-3713	549	4	.	.	PROPN
ejpam-3713	549	5	math	math	PROPN
ejpam-3713	549	6	,	,	PUNCT
ejpam-3713	549	7	13	13	NUM
ejpam-3713	549	8	(	(	PUNCT
ejpam-3713	549	9	5	5	NUM
ejpam-3713	549	10	)	)	PUNCT
ejpam-3713	549	11	(	(	PUNCT
ejpam-3713	549	12	2020	2020	NUM
ejpam-3713	549	13	)	)	PUNCT
ejpam-3713	549	14	,	,	PUNCT
ejpam-3713	549	15	1176	1176	NUM
ejpam-3713	549	16	-	-	SYM
ejpam-3713	549	17	1198	1198	NUM
ejpam-3713	549	18	1195	1195	NUM
ejpam-3713	549	19	figure	figure	NOUN
ejpam-3713	549	20	1	1	NUM
ejpam-3713	549	21	:	:	PUNCT
ejpam-3713	549	22	i.v.p	i.v.p	NOUN
ejpam-3713	549	23	.	.	PUNCT
ejpam-3713	550	1	(	(	PUNCT
ejpam-3713	550	2	2.24	2.24	NUM
ejpam-3713	550	3	)	)	PUNCT
ejpam-3713	550	4	figure	figure	NOUN
ejpam-3713	550	5	2	2	NUM
ejpam-3713	550	6	:	:	PUNCT
ejpam-3713	550	7	i.v.p	i.v.p	NOUN
ejpam-3713	550	8	.	.	PUNCT
ejpam-3713	551	1	(	(	PUNCT
ejpam-3713	551	2	2.26	2.26	NUM
ejpam-3713	551	3	)	)	PUNCT
ejpam-3713	551	4	m.h	m.h	PROPN
ejpam-3713	551	5	.	.	PROPN
ejpam-3713	551	6	r.	r.	PROPN
ejpam-3713	551	7	doust	doust	PROPN
ejpam-3713	551	8	,	,	PUNCT
ejpam-3713	551	9	v.	v.	ADP
ejpam-3713	551	10	lokesha	lokesha	PROPN
ejpam-3713	551	11	,	,	PUNCT
ejpam-3713	551	12	a.	a.	NOUN
ejpam-3713	551	13	ghasemabadi	ghasemabadi	NOUN
ejpam-3713	551	14	/	/	SYM
ejpam-3713	551	15	eur	eur	PROPN
ejpam-3713	551	16	.	.	PUNCT
ejpam-3713	552	1	j.	j.	PROPN
ejpam-3713	552	2	pure	pure	PROPN
ejpam-3713	552	3	appl	appl	PROPN
ejpam-3713	552	4	.	.	PROPN
ejpam-3713	552	5	math	math	PROPN
ejpam-3713	552	6	,	,	PUNCT
ejpam-3713	552	7	13	13	NUM
ejpam-3713	552	8	(	(	PUNCT
ejpam-3713	552	9	5	5	NUM
ejpam-3713	552	10	)	)	PUNCT
ejpam-3713	552	11	(	(	PUNCT
ejpam-3713	552	12	2020	2020	NUM
ejpam-3713	552	13	)	)	PUNCT
ejpam-3713	552	14	,	,	PUNCT
ejpam-3713	552	15	1176	1176	NUM
ejpam-3713	552	16	-	-	SYM
ejpam-3713	552	17	1198	1198	NUM
ejpam-3713	552	18	1196	1196	NUM
ejpam-3713	552	19	figure	figure	NOUN
ejpam-3713	552	20	3	3	NUM
ejpam-3713	552	21	:	:	PUNCT
ejpam-3713	552	22	i.v.p	i.v.p	NOUN
ejpam-3713	552	23	.	.	PUNCT
ejpam-3713	553	1	(	(	PUNCT
ejpam-3713	553	2	2.35	2.35	NUM
ejpam-3713	553	3	)	)	PUNCT
ejpam-3713	553	4	figure	figure	NOUN
ejpam-3713	553	5	4	4	NUM
ejpam-3713	553	6	:	:	PUNCT
ejpam-3713	553	7	i.v.p	i.v.p	NOUN
ejpam-3713	553	8	.	.	PUNCT
ejpam-3713	554	1	(	(	PUNCT
ejpam-3713	554	2	2.42	2.42	NUM
ejpam-3713	554	3	)	)	PUNCT
ejpam-3713	554	4	references	reference	NOUN
ejpam-3713	554	5	1197	1197	NUM
ejpam-3713	554	6	4	4	NUM
ejpam-3713	554	7	.	.	PUNCT
ejpam-3713	555	1	conclusion	conclusion	VERB
ejpam-3713	555	2	the	the	DET
ejpam-3713	555	3	importance	importance	NOUN
ejpam-3713	555	4	and	and	CCONJ
ejpam-3713	555	5	effects	effect	NOUN
ejpam-3713	555	6	of	of	ADP
ejpam-3713	555	7	single	single	ADJ
ejpam-3713	555	8	species	specie	NOUN
ejpam-3713	555	9	in	in	ADP
ejpam-3713	555	10	the	the	DET
ejpam-3713	555	11	nature	nature	NOUN
ejpam-3713	555	12	and	and	CCONJ
ejpam-3713	555	13	community	community	NOUN
ejpam-3713	555	14	is	be	AUX
ejpam-3713	555	15	clear	clear	ADJ
ejpam-3713	555	16	for	for	ADP
ejpam-3713	555	17	anybody	anybody	PRON
ejpam-3713	555	18	.	.	PUNCT
ejpam-3713	556	1	the	the	DET
ejpam-3713	556	2	discussed	discuss	VERB
ejpam-3713	556	3	models	model	NOUN
ejpam-3713	556	4	in	in	ADP
ejpam-3713	556	5	this	this	DET
ejpam-3713	556	6	work	work	NOUN
ejpam-3713	556	7	have	have	VERB
ejpam-3713	556	8	so	so	ADV
ejpam-3713	556	9	many	many	ADJ
ejpam-3713	556	10	practical	practical	ADJ
ejpam-3713	556	11	application	application	NOUN
ejpam-3713	556	12	.	.	PUNCT
ejpam-3713	557	1	in	in	ADP
ejpam-3713	557	2	deed	deed	NOUN
ejpam-3713	557	3	,	,	PUNCT
ejpam-3713	557	4	by	by	ADP
ejpam-3713	557	5	help	help	NOUN
ejpam-3713	557	6	of	of	ADP
ejpam-3713	557	7	these	these	DET
ejpam-3713	557	8	models	model	NOUN
ejpam-3713	557	9	,	,	PUNCT
ejpam-3713	557	10	one	one	PRON
ejpam-3713	557	11	may	may	AUX
ejpam-3713	557	12	predict	predict	VERB
ejpam-3713	557	13	,	,	PUNCT
ejpam-3713	557	14	check	check	VERB
ejpam-3713	557	15	and	and	CCONJ
ejpam-3713	557	16	defence	defence	NOUN
ejpam-3713	557	17	to	to	PART
ejpam-3713	557	18	spread	spread	VERB
ejpam-3713	557	19	of	of	ADP
ejpam-3713	557	20	viruses	virus	NOUN
ejpam-3713	557	21	,	,	PUNCT
ejpam-3713	557	22	microbe	microbe	NOUN
ejpam-3713	557	23	and	and	CCONJ
ejpam-3713	557	24	bacteria	bacteria	NOUN
ejpam-3713	557	25	in	in	ADP
ejpam-3713	557	26	a	a	DET
ejpam-3713	557	27	community	community	NOUN
ejpam-3713	557	28	.	.	PUNCT
ejpam-3713	558	1	there	there	PRON
ejpam-3713	558	2	are	be	VERB
ejpam-3713	558	3	so	so	ADV
ejpam-3713	558	4	many	many	ADJ
ejpam-3713	558	5	dangerous	dangerous	ADJ
ejpam-3713	558	6	viruses	virus	NOUN
ejpam-3713	558	7	for	for	ADP
ejpam-3713	558	8	humanity	humanity	NOUN
ejpam-3713	558	9	.	.	PUNCT
ejpam-3713	559	1	anybody	anybody	PRON
ejpam-3713	559	2	gets	get	AUX
ejpam-3713	559	3	involved	involve	VERB
ejpam-3713	559	4	with	with	ADP
ejpam-3713	559	5	microbe	microbe	NOUN
ejpam-3713	559	6	viruses	virus	NOUN
ejpam-3713	559	7	and	and	CCONJ
ejpam-3713	559	8	such	such	ADJ
ejpam-3713	559	9	as	as	ADP
ejpam-3713	559	10	black	black	ADJ
ejpam-3713	559	11	death	death	NOUN
ejpam-3713	559	12	,	,	PUNCT
ejpam-3713	559	13	spanish	spanish	ADJ
ejpam-3713	559	14	flu	flu	NOUN
ejpam-3713	559	15	,	,	PUNCT
ejpam-3713	559	16	hiv	hiv	PROPN
ejpam-3713	559	17	/	/	SYM
ejpam-3713	559	18	aids	aids	PROPN
ejpam-3713	559	19	,	,	PUNCT
ejpam-3713	559	20	swine	swine	ADJ
ejpam-3713	559	21	flu	flu	NOUN
ejpam-3713	559	22	,	,	PUNCT
ejpam-3713	559	23	ebola	ebola	PROPN
ejpam-3713	559	24	virus	virus	PROPN
ejpam-3713	559	25	,	,	PUNCT
ejpam-3713	559	26	zika	zika	X
ejpam-3713	559	27	virus	virus	NOUN
ejpam-3713	559	28	,	,	PUNCT
ejpam-3713	559	29	corona	corona	NOUN
ejpam-3713	559	30	viruses	virus	NOUN
ejpam-3713	559	31	such	such	ADJ
ejpam-3713	559	32	as	as	ADP
ejpam-3713	559	33	:	:	PUNCT
ejpam-3713	559	34	sars	sars	PROPN
ejpam-3713	559	35	-	-	PUNCT
ejpam-3713	559	36	cov	cov	PROPN
ejpam-3713	559	37	,	,	PUNCT
ejpam-3713	559	38	mers	mer	NOUN
ejpam-3713	559	39	-	-	PUNCT
ejpam-3713	559	40	cov	cov	NOUN
ejpam-3713	559	41	,	,	PUNCT
ejpam-3713	559	42	covid-19	covid-19	PROPN
ejpam-3713	559	43	.	.	PUNCT
ejpam-3713	560	1	especially	especially	ADV
ejpam-3713	560	2	,	,	PUNCT
ejpam-3713	560	3	last	last	ADJ
ejpam-3713	560	4	one	one	NOUN
ejpam-3713	560	5	which	which	PRON
ejpam-3713	560	6	is	be	AUX
ejpam-3713	560	7	the	the	DET
ejpam-3713	560	8	most	most	ADV
ejpam-3713	560	9	deadly	deadly	ADJ
ejpam-3713	560	10	and	and	CCONJ
ejpam-3713	560	11	disastrous	disastrous	ADJ
ejpam-3713	560	12	viruses	virus	NOUN
ejpam-3713	560	13	nowadays	nowadays	ADV
ejpam-3713	560	14	in	in	ADP
ejpam-3713	560	15	the	the	DET
ejpam-3713	560	16	world	world	NOUN
ejpam-3713	560	17	.	.	PUNCT
ejpam-3713	561	1	this	this	DET
ejpam-3713	561	2	viruses	virus	NOUN
ejpam-3713	561	3	is	be	AUX
ejpam-3713	561	4	spread	spread	VERB
ejpam-3713	561	5	in	in	ADP
ejpam-3713	561	6	2019	2019	NUM
ejpam-3713	561	7	,	,	PUNCT
ejpam-3713	561	8	and	and	CCONJ
ejpam-3713	561	9	all	all	PRON
ejpam-3713	561	10	of	of	ADP
ejpam-3713	561	11	the	the	DET
ejpam-3713	561	12	countries	country	NOUN
ejpam-3713	561	13	in	in	ADP
ejpam-3713	561	14	the	the	DET
ejpam-3713	561	15	world	world	NOUN
ejpam-3713	561	16	get	get	AUX
ejpam-3713	561	17	involved	involve	VERB
ejpam-3713	561	18	by	by	ADP
ejpam-3713	561	19	it	it	PRON
ejpam-3713	561	20	.	.	PUNCT
ejpam-3713	562	1	some	some	PRON
ejpam-3713	562	2	of	of	ADP
ejpam-3713	562	3	them	they	PRON
ejpam-3713	562	4	such	such	ADJ
ejpam-3713	562	5	as	as	ADP
ejpam-3713	562	6	corona	corona	NOUN
ejpam-3713	562	7	viruses	virus	NOUN
ejpam-3713	562	8	:	:	PUNCT
ejpam-3713	562	9	covid-19	covid-19	PROPN
ejpam-3713	562	10	are	be	AUX
ejpam-3713	562	11	not	not	PART
ejpam-3713	562	12	only	only	ADV
ejpam-3713	562	13	epidemic	epidemic	NOUN
ejpam-3713	562	14	but	but	CCONJ
ejpam-3713	562	15	also	also	ADV
ejpam-3713	562	16	are	be	AUX
ejpam-3713	562	17	pandemic	pandemic	ADJ
ejpam-3713	562	18	.	.	PUNCT
ejpam-3713	563	1	as	as	ADP
ejpam-3713	563	2	a	a	DET
ejpam-3713	563	3	consequence	consequence	NOUN
ejpam-3713	563	4	in	in	ADP
ejpam-3713	563	5	this	this	DET
ejpam-3713	563	6	research	research	NOUN
ejpam-3713	563	7	,	,	PUNCT
ejpam-3713	563	8	we	we	PRON
ejpam-3713	563	9	worked	work	VERB
ejpam-3713	563	10	out	out	ADP
ejpam-3713	563	11	the	the	DET
ejpam-3713	563	12	series	series	NOUN
ejpam-3713	563	13	solution	solution	NOUN
ejpam-3713	563	14	for	for	ADP
ejpam-3713	563	15	exponential	exponential	ADJ
ejpam-3713	563	16	modeling	modeling	NOUN
ejpam-3713	563	17	for	for	ADP
ejpam-3713	563	18	both	both	DET
ejpam-3713	563	19	cases	case	NOUN
ejpam-3713	563	20	of	of	ADP
ejpam-3713	563	21	having	have	VERB
ejpam-3713	563	22	constant	constant	ADJ
ejpam-3713	563	23	harvesting	harvesting	NOUN
ejpam-3713	563	24	factor	factor	NOUN
ejpam-3713	563	25	or	or	CCONJ
ejpam-3713	563	26	simple	simple	ADJ
ejpam-3713	563	27	model	model	NOUN
ejpam-3713	563	28	without	without	ADP
ejpam-3713	563	29	harvesting	harvesting	NOUN
ejpam-3713	563	30	factor	factor	NOUN
ejpam-3713	563	31	.	.	PUNCT
ejpam-3713	564	1	moreover	moreover	ADV
ejpam-3713	564	2	,	,	PUNCT
ejpam-3713	564	3	making	make	VERB
ejpam-3713	564	4	some	some	DET
ejpam-3713	564	5	conditions	condition	NOUN
ejpam-3713	564	6	for	for	ADP
ejpam-3713	564	7	single	single	ADJ
ejpam-3713	564	8	species	specie	NOUN
ejpam-3713	564	9	of	of	ADP
ejpam-3713	564	10	logistic	logistic	ADJ
ejpam-3713	564	11	modeling	modeling	NOUN
ejpam-3713	564	12	,	,	PUNCT
ejpam-3713	564	13	we	we	PRON
ejpam-3713	564	14	find	find	VERB
ejpam-3713	564	15	out	out	ADP
ejpam-3713	564	16	they	they	PRON
ejpam-3713	564	17	have	have	VERB
ejpam-3713	564	18	stable	stable	ADJ
ejpam-3713	564	19	solutions	solution	NOUN
ejpam-3713	564	20	.	.	PUNCT
ejpam-3713	565	1	and	and	CCONJ
ejpam-3713	565	2	also	also	ADV
ejpam-3713	565	3	,	,	PUNCT
ejpam-3713	565	4	their	their	PRON
ejpam-3713	565	5	asymptotical	asymptotical	ADJ
ejpam-3713	565	6	stability	stability	NOUN
ejpam-3713	565	7	is	be	AUX
ejpam-3713	565	8	obtained	obtain	VERB
ejpam-3713	565	9	.	.	PUNCT
ejpam-3713	566	1	making	make	VERB
ejpam-3713	566	2	some	some	DET
ejpam-3713	566	3	various	various	ADJ
ejpam-3713	566	4	simulations	simulation	NOUN
ejpam-3713	566	5	,	,	PUNCT
ejpam-3713	566	6	we	we	PRON
ejpam-3713	566	7	observed	observe	VERB
ejpam-3713	566	8	the	the	DET
ejpam-3713	566	9	obtained	obtain	VERB
ejpam-3713	566	10	results	result	NOUN
ejpam-3713	566	11	which	which	PRON
ejpam-3713	566	12	are	be	AUX
ejpam-3713	566	13	proved	prove	VERB
ejpam-3713	566	14	theorems	theorem	NOUN
ejpam-3713	566	15	are	be	AUX
ejpam-3713	566	16	true	true	ADJ
ejpam-3713	566	17	.	.	PUNCT
ejpam-3713	567	1	the	the	DET
ejpam-3713	567	2	important	important	ADJ
ejpam-3713	567	3	result	result	NOUN
ejpam-3713	567	4	is	be	AUX
ejpam-3713	567	5	:	:	PUNCT
ejpam-3713	567	6	carrying	carry	VERB
ejpam-3713	567	7	capacity	capacity	NOUN
ejpam-3713	567	8	of	of	ADP
ejpam-3713	567	9	the	the	DET
ejpam-3713	567	10	environment	environment	NOUN
ejpam-3713	567	11	,	,	PUNCT
ejpam-3713	567	12	growth	growth	NOUN
ejpam-3713	567	13	rate	rate	NOUN
ejpam-3713	567	14	of	of	ADP
ejpam-3713	567	15	population	population	NOUN
ejpam-3713	567	16	,	,	PUNCT
ejpam-3713	567	17	harvesting	harvesting	NOUN
ejpam-3713	567	18	factor	factor	NOUN
ejpam-3713	567	19	are	be	AUX
ejpam-3713	567	20	so	so	ADV
ejpam-3713	567	21	important	important	ADJ
ejpam-3713	567	22	to	to	PART
ejpam-3713	567	23	stability	stability	VERB
ejpam-3713	567	24	the	the	DET
ejpam-3713	567	25	equilibria	equilibrium	NOUN
ejpam-3713	567	26	.	.	PUNCT
ejpam-3713	568	1	references	reference	NOUN
ejpam-3713	568	2	[	[	X
ejpam-3713	568	3	1	1	NUM
ejpam-3713	568	4	]	]	PUNCT
ejpam-3713	568	5	r.	r.	PROPN
ejpam-3713	568	6	aarthee	aarthee	PROPN
ejpam-3713	568	7	,	,	PUNCT
ejpam-3713	568	8	d.	d.	PROPN
ejpam-3713	568	9	ezhilmaran	ezhilmaran	PROPN
ejpam-3713	568	10	,	,	PUNCT
ejpam-3713	568	11	a	a	DET
ejpam-3713	568	12	logistic	logistic	ADJ
ejpam-3713	568	13	model	model	NOUN
ejpam-3713	568	14	for	for	ADP
ejpam-3713	568	15	the	the	DET
ejpam-3713	568	16	population	population	NOUN
ejpam-3713	568	17	of	of	ADP
ejpam-3713	568	18	virus	virus	NOUN
ejpam-3713	568	19	growth	growth	NOUN
ejpam-3713	568	20	in	in	ADP
ejpam-3713	568	21	local	local	ADJ
ejpam-3713	568	22	area	area	NOUN
ejpam-3713	568	23	network	network	NOUN
ejpam-3713	568	24	,	,	PUNCT
ejpam-3713	568	25	international	international	ADJ
ejpam-3713	568	26	journal	journal	NOUN
ejpam-3713	568	27	of	of	ADP
ejpam-3713	568	28	pure	pure	ADJ
ejpam-3713	568	29	and	and	CCONJ
ejpam-3713	568	30	applied	applied	ADJ
ejpam-3713	568	31	mathematics	mathematic	NOUN
ejpam-3713	568	32	,	,	PUNCT
ejpam-3713	568	33	115(9):401	115(9):401	NUM
ejpam-3713	568	34	-	-	SYM
ejpam-3713	568	35	409	409	NUM
ejpam-3713	568	36	,	,	PUNCT
ejpam-3713	568	37	2017	2017	NUM
ejpam-3713	568	38	.	.	PUNCT
ejpam-3713	569	1	[	[	X
ejpam-3713	569	2	2	2	NUM
ejpam-3713	569	3	]	]	X
ejpam-3713	569	4	k.c	k.c	PROPN
ejpam-3713	569	5	.	.	PROPN
ejpam-3713	569	6	abbott	abbott	PROPN
ejpam-3713	569	7	,	,	PUNCT
ejpam-3713	569	8	j.	j.	PROPN
ejpam-3713	569	9	ripa	ripa	PROPN
ejpam-3713	569	10	,	,	PUNCT
ejpam-3713	569	11	a.r	a.r	PROPN
ejpam-3713	569	12	.	.	PROPN
ejpam-3713	569	13	ives	ive	NOUN
ejpam-3713	569	14	,	,	PUNCT
ejpam-3713	569	15	environmental	environmental	ADJ
ejpam-3713	569	16	variation	variation	NOUN
ejpam-3713	569	17	in	in	ADP
ejpam-3713	569	18	ecological	ecological	ADJ
ejpam-3713	569	19	communities	community	NOUN
ejpam-3713	569	20	and	and	CCONJ
ejpam-3713	569	21	inferences	inference	NOUN
ejpam-3713	569	22	from	from	ADP
ejpam-3713	569	23	single	single	ADJ
ejpam-3713	569	24	species	specie	NOUN
ejpam-3713	569	25	data	datum	NOUN
ejpam-3713	569	26	,	,	PUNCT
ejpam-3713	569	27	ecology	ecology	NOUN
ejpam-3713	569	28	,	,	PUNCT
ejpam-3713	569	29	(	(	PUNCT
ejpam-3713	569	30	2009	2009	NUM
ejpam-3713	569	31	)	)	PUNCT
ejpam-3713	569	32	.	.	PUNCT
ejpam-3713	570	1	[	[	X
ejpam-3713	570	2	3	3	X
ejpam-3713	570	3	]	]	PUNCT
ejpam-3713	570	4	j.	j.	PROPN
ejpam-3713	570	5	barlow	barlow	PROPN
ejpam-3713	570	6	,	,	PUNCT
ejpam-3713	570	7	nonlinear	nonlinear	ADJ
ejpam-3713	570	8	and	and	CCONJ
ejpam-3713	570	9	logistic	logistic	ADJ
ejpam-3713	570	10	growth	growth	NOUN
ejpam-3713	570	11	in	in	ADP
ejpam-3713	570	12	experimental	experimental	ADJ
ejpam-3713	570	13	populations	population	NOUN
ejpam-3713	570	14	of	of	ADP
ejpam-3713	570	15	guppies	guppy	NOUN
ejpam-3713	570	16	,	,	PUNCT
ejpam-3713	570	17	ecology	ecology	NOUN
ejpam-3713	570	18	,	,	PUNCT
ejpam-3713	570	19	(	(	PUNCT
ejpam-3713	570	20	1992	1992	NUM
ejpam-3713	570	21	)	)	PUNCT
ejpam-3713	570	22	.	.	PUNCT
ejpam-3713	571	1	[	[	X
ejpam-3713	571	2	4	4	NUM
ejpam-3713	571	3	]	]	X
ejpam-3713	571	4	d.a	d.a	PROPN
ejpam-3713	571	5	.	.	PROPN
ejpam-3713	571	6	charlebois	charlebois	ADJ
ejpam-3713	571	7	,	,	PUNCT
ejpam-3713	571	8	g.balazsi	g.balazsi	NOUN
ejpam-3713	571	9	,	,	PUNCT
ejpam-3713	571	10	modeling	model	VERB
ejpam-3713	571	11	cell	cell	NOUN
ejpam-3713	571	12	population	population	NOUN
ejpam-3713	571	13	dynamics	dynamic	NOUN
ejpam-3713	571	14	,	,	PUNCT
ejpam-3713	571	15	in	in	ADP
ejpam-3713	571	16	silico	silico	NOUN
ejpam-3713	571	17	biology	biology	NOUN
ejpam-3713	571	18	,	,	PUNCT
ejpam-3713	571	19	13:21	13:21	NUM
ejpam-3713	571	20	-	-	SYM
ejpam-3713	571	21	39	39	NUM
ejpam-3713	571	22	,	,	PUNCT
ejpam-3713	571	23	2019	2019	NUM
ejpam-3713	571	24	.	.	PUNCT
ejpam-3713	572	1	[	[	X
ejpam-3713	572	2	5	5	X
ejpam-3713	572	3	]	]	PUNCT
ejpam-3713	572	4	s.	s.	PROPN
ejpam-3713	572	5	chauhan	chauhan	PROPN
ejpam-3713	572	6	,	,	PUNCT
ejpam-3713	572	7	o.p	o.p	PROPN
ejpam-3713	572	8	.	.	PROPN
ejpam-3713	572	9	misra	misra	PROPN
ejpam-3713	572	10	,	,	PUNCT
ejpam-3713	572	11	modeling	modeling	NOUN
ejpam-3713	572	12	and	and	CCONJ
ejpam-3713	572	13	analysis	analysis	NOUN
ejpam-3713	572	14	of	of	ADP
ejpam-3713	572	15	a	a	DET
ejpam-3713	572	16	single	single	ADJ
ejpam-3713	572	17	species	specie	NOUN
ejpam-3713	572	18	population	population	NOUN
ejpam-3713	572	19	with	with	ADP
ejpam-3713	572	20	viral	viral	ADJ
ejpam-3713	572	21	infection	infection	NOUN
ejpam-3713	572	22	in	in	ADP
ejpam-3713	572	23	polluted	polluted	ADJ
ejpam-3713	572	24	environment	environment	NOUN
ejpam-3713	572	25	,	,	PUNCT
ejpam-3713	572	26	applied	apply	VERB
ejpam-3713	572	27	mathematics	mathematic	NOUN
ejpam-3713	572	28	,	,	PUNCT
ejpam-3713	572	29	3	3	NUM
ejpam-3713	572	30	:	:	SYM
ejpam-3713	572	31	662	662	NUM
ejpam-3713	572	32	-	-	PUNCT
ejpam-3713	572	33	672(2012	672(2012	NUM
ejpam-3713	572	34	)	)	PUNCT
ejpam-3713	572	35	.	.	PUNCT
ejpam-3713	573	1	[	[	X
ejpam-3713	573	2	6	6	NUM
ejpam-3713	573	3	]	]	PUNCT
ejpam-3713	573	4	i.	i.	PROPN
ejpam-3713	573	5	hanski	hanski	PROPN
ejpam-3713	573	6	,	,	PUNCT
ejpam-3713	573	7	single	single	ADJ
ejpam-3713	573	8	species	specie	NOUN
ejpam-3713	573	9	spatial	spatial	ADJ
ejpam-3713	573	10	dynamics	dynamic	NOUN
ejpam-3713	573	11	may	may	AUX
ejpam-3713	573	12	contribute	contribute	VERB
ejpam-3713	573	13	to	to	ADP
ejpam-3713	573	14	long?term	long?term	PROPN
ejpam-3713	573	15	rarity	rarity	NOUN
ejpam-3713	573	16	and	and	CCONJ
ejpam-3713	573	17	commonness	commonness	NOUN
ejpam-3713	573	18	,	,	PUNCT
ejpam-3713	573	19	ecology	ecology	NOUN
ejpam-3713	573	20	,	,	PUNCT
ejpam-3713	573	21	(	(	PUNCT
ejpam-3713	573	22	1985	1985	NUM
ejpam-3713	573	23	)	)	PUNCT
ejpam-3713	573	24	.	.	PUNCT
ejpam-3713	574	1	[	[	X
ejpam-3713	574	2	7	7	X
ejpam-3713	574	3	]	]	X
ejpam-3713	574	4	r.	r.	PROPN
ejpam-3713	574	5	law	law	PROPN
ejpam-3713	574	6	,	,	PUNCT
ejpam-3713	574	7	d.j	d.j	PROPN
ejpam-3713	574	8	.	.	PROPN
ejpam-3713	574	9	murrell	murrell	PROPN
ejpam-3713	574	10	,	,	PUNCT
ejpam-3713	574	11	u.	u.	PROPN
ejpam-3713	574	12	dieckmann	dieckmann	PROPN
ejpam-3713	574	13	,	,	PUNCT
ejpam-3713	574	14	population	population	NOUN
ejpam-3713	574	15	growth	growth	NOUN
ejpam-3713	574	16	in	in	ADP
ejpam-3713	574	17	space	space	NOUN
ejpam-3713	574	18	and	and	CCONJ
ejpam-3713	574	19	time	time	NOUN
ejpam-3713	574	20	:	:	PUNCT
ejpam-3713	574	21	spatial	spatial	ADJ
ejpam-3713	574	22	logistic	logistic	ADJ
ejpam-3713	574	23	equations	equation	NOUN
ejpam-3713	574	24	,	,	PUNCT
ejpam-3713	574	25	ecology	ecology	NOUN
ejpam-3713	574	26	,	,	PUNCT
ejpam-3713	574	27	(	(	PUNCT
ejpam-3713	574	28	2003	2003	NUM
ejpam-3713	574	29	)	)	PUNCT
ejpam-3713	574	30	.	.	PUNCT
ejpam-3713	575	1	[	[	X
ejpam-3713	575	2	8	8	NUM
ejpam-3713	575	3	]	]	X
ejpam-3713	575	4	l.d	l.d	PROPN
ejpam-3713	575	5	.	.	PROPN
ejpam-3713	575	6	mueller	mueller	PROPN
ejpam-3713	575	7	,	,	PUNCT
ejpam-3713	575	8	f.j	f.j	PROPN
ejpam-3713	575	9	.	.	PROPN
ejpam-3713	575	10	ayala	ayala	PROPN
ejpam-3713	575	11	,	,	PUNCT
ejpam-3713	575	12	dynamics	dynamic	NOUN
ejpam-3713	575	13	of	of	ADP
ejpam-3713	575	14	single	single	ADJ
ejpam-3713	575	15	species	specie	NOUN
ejpam-3713	575	16	population	population	NOUN
ejpam-3713	575	17	growth	growth	NOUN
ejpam-3713	575	18	:	:	PUNCT
ejpam-3713	575	19	stability	stability	NOUN
ejpam-3713	575	20	or	or	CCONJ
ejpam-3713	575	21	chaos	chaos	NOUN
ejpam-3713	575	22	?	?	PUNCT
ejpam-3713	575	23	,	,	PUNCT
ejpam-3713	575	24	ecology	ecology	NOUN
ejpam-3713	575	25	,	,	PUNCT
ejpam-3713	575	26	(	(	PUNCT
ejpam-3713	575	27	1981	1981	NUM
ejpam-3713	575	28	)	)	PUNCT
ejpam-3713	575	29	.	.	PUNCT
ejpam-3713	576	1	references	reference	NOUN
ejpam-3713	576	2	1198	1198	NUM
ejpam-3713	577	1	[	[	X
ejpam-3713	577	2	9	9	NUM
ejpam-3713	577	3	]	]	SYM
ejpam-3713	577	4	j.d	j.d	PROPN
ejpam-3713	577	5	.	.	PROPN
ejpam-3713	577	6	murrray	murrray	PROPN
ejpam-3713	577	7	,	,	PUNCT
ejpam-3713	577	8	mathematical	mathematical	ADJ
ejpam-3713	577	9	biology	biology	NOUN
ejpam-3713	577	10	i.	i.	NOUN
ejpam-3713	577	11	an	an	DET
ejpam-3713	577	12	introduction	introduction	NOUN
ejpam-3713	577	13	,	,	PUNCT
ejpam-3713	577	14	springer	springer	NOUN
ejpam-3713	577	15	,	,	PUNCT
ejpam-3713	577	16	new	new	PROPN
ejpam-3713	577	17	york	york	PROPN
ejpam-3713	577	18	,	,	PUNCT
ejpam-3713	577	19	(	(	PUNCT
ejpam-3713	577	20	2002	2002	NUM
ejpam-3713	577	21	)	)	PUNCT
ejpam-3713	577	22	.	.	PUNCT
ejpam-3713	578	1	[	[	X
ejpam-3713	578	2	10	10	NUM
ejpam-3713	578	3	]	]	SYM
ejpam-3713	578	4	c.pao	c.pao	NOUN
ejpam-3713	578	5	,	,	PUNCT
ejpam-3713	578	6	c.hao	c.hao	PROPN
ejpam-3713	578	7	lin	lin	PROPN
ejpam-3713	578	8	,	,	PUNCT
ejpam-3713	578	9	a	a	DET
ejpam-3713	578	10	new	new	ADJ
ejpam-3713	578	11	approach	approach	NOUN
ejpam-3713	578	12	to	to	ADP
ejpam-3713	578	13	the	the	DET
ejpam-3713	578	14	logistic	logistic	ADJ
ejpam-3713	578	15	modeling	modeling	NOUN
ejpam-3713	578	16	population	population	NOUN
ejpam-3713	578	17	;	;	PUNCT
ejpam-3713	578	18	having	have	VERB
ejpam-3713	578	19	harvesting	harvesting	NOUN
ejpam-3713	578	20	factor	factor	NOUN
ejpam-3713	578	21	,	,	PUNCT
ejpam-3713	578	22	yugoslav	yugoslav	ADJ
ejpam-3713	578	23	journal	journal	PROPN
ejpam-3713	578	24	of	of	ADP
ejpam-3713	578	25	operations	operation	NOUN
ejpam-3713	578	26	research	research	NOUN
ejpam-3713	578	27	,	,	PUNCT
ejpam-3713	578	28	26(3):381	26(3):381	PROPN
ejpam-3713	578	29	-	-	PUNCT
ejpam-3713	578	30	392,2016	392,2016	NUM
ejpam-3713	578	31	.	.	PUNCT
ejpam-3713	579	1	[	[	X
ejpam-3713	579	2	11	11	NUM
ejpam-3713	579	3	]	]	X
ejpam-3713	579	4	m.h	m.h	PROPN
ejpam-3713	579	5	.	.	PROPN
ejpam-3713	579	6	rahmani	rahmani	PROPN
ejpam-3713	579	7	doust	doust	PROPN
ejpam-3713	579	8	,	,	PUNCT
ejpam-3713	579	9	m.	m.	NOUN
ejpam-3713	579	10	saraj	saraj	PROPN
ejpam-3713	579	11	,	,	PUNCT
ejpam-3713	579	12	the	the	DET
ejpam-3713	579	13	logistic	logistic	ADJ
ejpam-3713	579	14	modeling	model	VERB
ejpam-3713	579	15	population	population	NOUN
ejpam-3713	579	16	;	;	PUNCT
ejpam-3713	579	17	having	have	VERB
ejpam-3713	579	18	harvesting	harvesting	NOUN
ejpam-3713	579	19	factor	factor	NOUN
ejpam-3713	579	20	,	,	PUNCT
ejpam-3713	579	21	yugoslav	yugoslav	ADJ
ejpam-3713	579	22	journal	journal	PROPN
ejpam-3713	579	23	of	of	ADP
ejpam-3713	579	24	operations	operation	NOUN
ejpam-3713	579	25	research	research	VERB
ejpam-3713	579	26	25(1):107	25(1):107	NOUN
ejpam-3713	579	27	-	-	SYM
ejpam-3713	579	28	115	115	NUM
ejpam-3713	579	29	,	,	PUNCT
ejpam-3713	579	30	2013	2013	NUM
ejpam-3713	579	31	.	.	PUNCT
ejpam-3713	580	1	[	[	X
ejpam-3713	580	2	12	12	NUM
ejpam-3713	580	3	]	]	X
ejpam-3713	580	4	s.	s.	PROPN
ejpam-3713	580	5	ruan	ruan	PROPN
ejpam-3713	580	6	,	,	PUNCT
ejpam-3713	580	7	delay	delay	NOUN
ejpam-3713	580	8	differential	differential	ADJ
ejpam-3713	580	9	equation	equation	NOUN
ejpam-3713	580	10	in	in	ADP
ejpam-3713	580	11	single	single	ADJ
ejpam-3713	580	12	species	specie	NOUN
ejpam-3713	580	13	dynamics	dynamic	NOUN
ejpam-3713	580	14	,	,	PUNCT
ejpam-3713	580	15	university	university	NOUN
ejpam-3713	580	16	of	of	ADP
ejpam-3713	580	17	miami	miami	PROPN
ejpam-3713	580	18	,	,	PUNCT
ejpam-3713	580	19	(	(	PUNCT
ejpam-3713	580	20	2006	2006	NUM
ejpam-3713	580	21	)	)	PUNCT
ejpam-3713	580	22	.	.	PUNCT
ejpam-3713	581	1	[	[	X
ejpam-3713	581	2	13	13	NUM
ejpam-3713	581	3	]	]	X
ejpam-3713	581	4	e.	e.	PROPN
ejpam-3713	581	5	sorouri	sorouri	PROPN
ejpam-3713	581	6	,	,	PUNCT
ejpam-3713	581	7	m.	m.	PROPN
ejpam-3713	581	8	eshaghi	eshaghi	PROPN
ejpam-3713	581	9	gourji	gourji	PROPN
ejpam-3713	581	10	,	,	PUNCT
ejpam-3713	581	11	r.memarbashi	r.memarbashi	X
ejpam-3713	581	12	,	,	PUNCT
ejpam-3713	581	13	an	an	DET
ejpam-3713	581	14	ajnalysis	ajnalysis	NOUN
ejpam-3713	581	15	of	of	ADP
ejpam-3713	581	16	a	a	DET
ejpam-3713	581	17	model	model	NOUN
ejpam-3713	581	18	with	with	ADP
ejpam-3713	581	19	nonlinear	nonlinear	ADJ
ejpam-3713	581	20	harvesting	harvesting	NOUN
ejpam-3713	581	21	function	function	NOUN
ejpam-3713	581	22	,	,	PUNCT
ejpam-3713	581	23	int	int	NOUN
ejpam-3713	581	24	.	.	PUNCT
ejpam-3713	582	1	j.	j.	PROPN
ejpam-3713	582	2	nonlinear	nonlinear	PROPN
ejpam-3713	582	3	anal	anal	PROPN
ejpam-3713	582	4	appl	appl	PROPN
ejpam-3713	582	5	.	.	PROPN
ejpam-3713	582	6	,	,	PUNCT
ejpam-3713	582	7	11(1):,37	11(1):,37	NUM
ejpam-3713	582	8	-	-	SYM
ejpam-3713	582	9	80	80	NUM
ejpam-3713	582	10	,	,	PUNCT
ejpam-3713	582	11	2020	2020	NUM
ejpam-3713	582	12	.	.	PUNCT