id	sid	tid	token	lemma	pos
ejpam-6097	1	1	european	european	PROPN
ejpam-6097	1	2	journal	journal	PROPN
ejpam-6097	1	3	of	of	ADP
ejpam-6097	1	4	pure	pure	ADJ
ejpam-6097	1	5	and	and	CCONJ
ejpam-6097	1	6	applied	applied	ADJ
ejpam-6097	1	7	mathematics	mathematic	NOUN
ejpam-6097	1	8	2025	2025	NUM
ejpam-6097	1	9	,	,	PUNCT
ejpam-6097	1	10	vol	vol	NOUN
ejpam-6097	1	11	.	.	PROPN
ejpam-6097	1	12	18	18	NUM
ejpam-6097	1	13	,	,	PUNCT
ejpam-6097	1	14	issue	issue	NOUN
ejpam-6097	1	15	2	2	NUM
ejpam-6097	1	16	,	,	PUNCT
ejpam-6097	1	17	article	article	NOUN
ejpam-6097	1	18	number	number	NOUN
ejpam-6097	1	19	6097	6097	NUM
ejpam-6097	1	20	issn	issn	VERB
ejpam-6097	1	21	1307	1307	NUM
ejpam-6097	1	22	-	-	SYM
ejpam-6097	1	23	5543	5543	NUM
ejpam-6097	1	24	–	–	PUNCT
ejpam-6097	1	25	ejpam.com	ejpam.com	X
ejpam-6097	1	26	published	publish	VERB
ejpam-6097	1	27	by	by	ADP
ejpam-6097	1	28	new	new	PROPN
ejpam-6097	1	29	york	york	PROPN
ejpam-6097	1	30	business	business	PROPN
ejpam-6097	1	31	global	global	ADJ
ejpam-6097	1	32	1	1	NUM
ejpam-6097	1	33	dynamics	dynamic	NOUN
ejpam-6097	1	34	of	of	ADP
ejpam-6097	1	35	competitive	competitive	ADJ
ejpam-6097	1	36	stochastic	stochastic	ADJ
ejpam-6097	1	37	predator	predator	NOUN
ejpam-6097	1	38	-	-	PUNCT
ejpam-6097	1	39	prey2	prey2	NOUN
ejpam-6097	1	40	model	model	NOUN
ejpam-6097	1	41	with	with	ADP
ejpam-6097	1	42	holling	holle	VERB
ejpam-6097	1	43	type	type	NOUN
ejpam-6097	1	44	ii	ii	PROPN
ejpam-6097	1	45	under	under	ADP
ejpam-6097	1	46	small	small	ADJ
ejpam-6097	1	47	random3	random3	NOUN
ejpam-6097	1	48	immigration4	immigration4	PROPN
ejpam-6097	1	49	mogtaba	mogtaba	PROPN
ejpam-6097	1	50	mohammed1	mohammed1	PROPN
ejpam-6097	1	51	,	,	PUNCT
ejpam-6097	1	52	jawdat	jawdat	PROPN
ejpam-6097	1	53	alebraheem	alebraheem	PROPN
ejpam-6097	1	54	1,∗	1,∗	PROPN
ejpam-6097	1	55	,	,	PUNCT
ejpam-6097	1	56	ismail	ismail	NOUN
ejpam-6097	1	57	m.	m.	NOUN
ejpam-6097	1	58	tayel1,5	tayel1,5	PROPN
ejpam-6097	1	59	muhamad	muhamad	PROPN
ejpam-6097	1	60	hifzhudin	hifzhudin	PROPN
ejpam-6097	1	61	noor	noor	PROPN
ejpam-6097	1	62	aziz26	aziz26	PROPN
ejpam-6097	1	63	1	1	NUM
ejpam-6097	1	64	department	department	NOUN
ejpam-6097	1	65	of	of	ADP
ejpam-6097	1	66	mathematics	mathematic	NOUN
ejpam-6097	1	67	,	,	PUNCT
ejpam-6097	1	68	college	college	NOUN
ejpam-6097	1	69	of	of	ADP
ejpam-6097	1	70	sciences	sciences	PROPN
ejpam-6097	1	71	,	,	PUNCT
ejpam-6097	1	72	majmaah	majmaah	PROPN
ejpam-6097	1	73	university	university	PROPN
ejpam-6097	1	74	,	,	PUNCT
ejpam-6097	1	75	al	al	PROPN
ejpam-6097	1	76	-	-	PUNCT
ejpam-6097	1	77	majmaah	majmaah	PROPN
ejpam-6097	1	78	11952,7	11952,7	NUM
ejpam-6097	1	79	saudi	saudi	ADJ
ejpam-6097	1	80	arabia8	arabia8	NOUN
ejpam-6097	1	81	2	2	NUM
ejpam-6097	1	82	institute	institute	NOUN
ejpam-6097	1	83	of	of	ADP
ejpam-6097	1	84	mathematical	mathematical	ADJ
ejpam-6097	1	85	sciences	science	NOUN
ejpam-6097	1	86	,	,	PUNCT
ejpam-6097	1	87	faculty	faculty	NOUN
ejpam-6097	1	88	of	of	ADP
ejpam-6097	1	89	science	science	PROPN
ejpam-6097	1	90	universiti	universiti	PROPN
ejpam-6097	1	91	malaya	malaya	PROPN
ejpam-6097	1	92	50603,9	50603,9	PROPN
ejpam-6097	1	93	kuala	kuala	PROPN
ejpam-6097	1	94	lumpur	lumpur	PROPN
ejpam-6097	1	95	,	,	PUNCT
ejpam-6097	1	96	malaysia10	malaysia10	NOUN
ejpam-6097	1	97	11	11	NUM
ejpam-6097	1	98	abstract	abstract	NOUN
ejpam-6097	1	99	.	.	PUNCT
ejpam-6097	2	1	in	in	ADP
ejpam-6097	2	2	this	this	DET
ejpam-6097	2	3	paper	paper	NOUN
ejpam-6097	2	4	,	,	PUNCT
ejpam-6097	2	5	we	we	PRON
ejpam-6097	2	6	introduce	introduce	VERB
ejpam-6097	2	7	a	a	DET
ejpam-6097	2	8	novel	novel	ADJ
ejpam-6097	2	9	competitive	competitive	ADJ
ejpam-6097	2	10	stochastic	stochastic	ADJ
ejpam-6097	2	11	predator	predator	NOUN
ejpam-6097	2	12	-	-	PUNCT
ejpam-6097	2	13	prey	prey	NOUN
ejpam-6097	2	14	model	model	NOUN
ejpam-6097	2	15	by	by	ADP
ejpam-6097	2	16	means	mean	NOUN
ejpam-6097	2	17	of	of	ADP
ejpam-6097	2	18	holling	holle	VERB
ejpam-6097	2	19	type	type	NOUN
ejpam-6097	2	20	ii	ii	PROPN
ejpam-6097	2	21	with	with	ADP
ejpam-6097	2	22	small	small	ADJ
ejpam-6097	2	23	random	random	ADJ
ejpam-6097	2	24	immigration	immigration	NOUN
ejpam-6097	2	25	.	.	PUNCT
ejpam-6097	3	1	a	a	DET
ejpam-6097	3	2	series	series	NOUN
ejpam-6097	3	3	of	of	ADP
ejpam-6097	3	4	analytical	analytical	ADJ
ejpam-6097	3	5	results	result	NOUN
ejpam-6097	3	6	are	be	AUX
ejpam-6097	3	7	conducted	conduct	VERB
ejpam-6097	3	8	on	on	ADP
ejpam-6097	3	9	the	the	DET
ejpam-6097	3	10	model	model	NOUN
ejpam-6097	3	11	such	such	ADJ
ejpam-6097	3	12	as	as	ADP
ejpam-6097	3	13	the	the	DET
ejpam-6097	3	14	boundedness	boundedness	NOUN
ejpam-6097	3	15	of	of	ADP
ejpam-6097	3	16	the	the	DET
ejpam-6097	3	17	model	model	NOUN
ejpam-6097	3	18	’s	’s	PART
ejpam-6097	3	19	solution	solution	NOUN
ejpam-6097	3	20	,	,	PUNCT
ejpam-6097	3	21	stochastic	stochastic	ADJ
ejpam-6097	3	22	mean	mean	NOUN
ejpam-6097	3	23	square	square	ADJ
ejpam-6097	3	24	stability	stability	NOUN
ejpam-6097	3	25	,	,	PUNCT
ejpam-6097	3	26	and	and	CCONJ
ejpam-6097	3	27	the	the	DET
ejpam-6097	3	28	conditions	condition	NOUN
ejpam-6097	3	29	of	of	ADP
ejpam-6097	3	30	the	the	DET
ejpam-6097	3	31	persistence	persistence	NOUN
ejpam-6097	3	32	and	and	CCONJ
ejpam-6097	3	33	extinction	extinction	NOUN
ejpam-6097	3	34	of	of	ADP
ejpam-6097	3	35	the	the	DET
ejpam-6097	3	36	predator	predator	NOUN
ejpam-6097	3	37	-	-	PUNCT
ejpam-6097	3	38	prey	prey	NOUN
ejpam-6097	3	39	population	population	NOUN
ejpam-6097	3	40	.	.	PUNCT
ejpam-6097	4	1	all	all	DET
ejpam-6097	4	2	analytical	analytical	ADJ
ejpam-6097	4	3	results	result	NOUN
ejpam-6097	4	4	were	be	AUX
ejpam-6097	4	5	validated	validate	VERB
ejpam-6097	4	6	with	with	ADP
ejpam-6097	4	7	numerical	numerical	ADJ
ejpam-6097	4	8	simulations	simulation	NOUN
ejpam-6097	4	9	by	by	ADP
ejpam-6097	4	10	choosing	choose	VERB
ejpam-6097	4	11	different	different	ADJ
ejpam-6097	4	12	sets	set	NOUN
ejpam-6097	4	13	of	of	ADP
ejpam-6097	4	14	small	small	ADJ
ejpam-6097	4	15	random	random	ADJ
ejpam-6097	4	16	immigration	immigration	NOUN
ejpam-6097	4	17	.	.	PUNCT
ejpam-6097	5	1	conditions	condition	NOUN
ejpam-6097	5	2	on	on	ADP
ejpam-6097	5	3	the	the	DET
ejpam-6097	5	4	random	random	ADJ
ejpam-6097	5	5	immigration	immigration	NOUN
ejpam-6097	5	6	under	under	ADP
ejpam-6097	5	7	which	which	PRON
ejpam-6097	5	8	the	the	DET
ejpam-6097	5	9	system	system	NOUN
ejpam-6097	5	10	is	be	AUX
ejpam-6097	5	11	stochastically	stochastically	ADV
ejpam-6097	5	12	stable	stable	ADJ
ejpam-6097	5	13	are	be	AUX
ejpam-6097	5	14	specified	specify	VERB
ejpam-6097	5	15	.	.	PUNCT
ejpam-6097	6	1	in	in	ADP
ejpam-6097	6	2	addition	addition	NOUN
ejpam-6097	6	3	,	,	PUNCT
ejpam-6097	6	4	small	small	ADJ
ejpam-6097	6	5	immigration	immigration	NOUN
ejpam-6097	6	6	has	have	AUX
ejpam-6097	6	7	been	be	AUX
ejpam-6097	6	8	shown	show	VERB
ejpam-6097	6	9	to	to	PART
ejpam-6097	6	10	have	have	VERB
ejpam-6097	6	11	a	a	DET
ejpam-6097	6	12	great	great	ADJ
ejpam-6097	6	13	impact	impact	NOUN
ejpam-6097	6	14	on	on	ADP
ejpam-6097	6	15	persistence	persistence	NOUN
ejpam-6097	6	16	and	and	CCONJ
ejpam-6097	6	17	extinction	extinction	NOUN
ejpam-6097	6	18	of	of	ADP
ejpam-6097	6	19	the	the	DET
ejpam-6097	6	20	system	system	NOUN
ejpam-6097	6	21	,	,	PUNCT
ejpam-6097	6	22	which	which	PRON
ejpam-6097	6	23	can	can	AUX
ejpam-6097	6	24	play	play	VERB
ejpam-6097	6	25	an	an	DET
ejpam-6097	6	26	important	important	ADJ
ejpam-6097	6	27	role	role	NOUN
ejpam-6097	6	28	in	in	ADP
ejpam-6097	6	29	species	specie	NOUN
ejpam-6097	6	30	conservation	conservation	NOUN
ejpam-6097	6	31	,	,	PUNCT
ejpam-6097	6	32	especially	especially	ADV
ejpam-6097	6	33	by	by	ADP
ejpam-6097	6	34	controlling	control	VERB
ejpam-6097	6	35	the	the	DET
ejpam-6097	6	36	conditions	condition	NOUN
ejpam-6097	6	37	of	of	ADP
ejpam-6097	6	38	stochastic	stochastic	ADJ
ejpam-6097	6	39	small	small	ADJ
ejpam-6097	6	40	immigration	immigration	NOUN
ejpam-6097	6	41	.	.	PUNCT
ejpam-6097	7	1	2020	2020	NUM
ejpam-6097	7	2	mathematics	mathematic	NOUN
ejpam-6097	7	3	subject	subject	NOUN
ejpam-6097	7	4	classifications	classification	NOUN
ejpam-6097	7	5	:	:	PUNCT
ejpam-6097	7	6	92	92	NUM
ejpam-6097	7	7	-	-	SYM
ejpam-6097	7	8	11	11	NUM
ejpam-6097	7	9	,	,	PUNCT
ejpam-6097	7	10	60h10	60h10	NUM
ejpam-6097	7	11	,	,	PUNCT
ejpam-6097	7	12	34d2012	34d2012	NUM
ejpam-6097	7	13	key	key	ADJ
ejpam-6097	7	14	words	word	NOUN
ejpam-6097	7	15	and	and	CCONJ
ejpam-6097	7	16	phrases	phrase	NOUN
ejpam-6097	7	17	:	:	PUNCT
ejpam-6097	7	18	stochastic	stochastic	ADJ
ejpam-6097	7	19	predator	predator	NOUN
ejpam-6097	7	20	-	-	PUNCT
ejpam-6097	7	21	prey	prey	NOUN
ejpam-6097	7	22	model	model	NOUN
ejpam-6097	7	23	,	,	PUNCT
ejpam-6097	7	24	persistence	persistence	NOUN
ejpam-6097	7	25	,	,	PUNCT
ejpam-6097	7	26	extinction	extinction	NOUN
ejpam-6097	7	27	,	,	PUNCT
ejpam-6097	7	28	small	small	ADJ
ejpam-6097	7	29	ran-13	ran-13	PUNCT
ejpam-6097	7	30	dom	dom	NOUN
ejpam-6097	7	31	immigration14	immigration14	NOUN
ejpam-6097	7	32	15	15	NUM
ejpam-6097	7	33	1	1	NUM
ejpam-6097	7	34	.	.	PUNCT
ejpam-6097	7	35	introduction16	introduction16	NOUN
ejpam-6097	7	36	one	one	NUM
ejpam-6097	7	37	of	of	ADP
ejpam-6097	7	38	the	the	DET
ejpam-6097	7	39	most	most	ADV
ejpam-6097	7	40	interesting	interesting	ADJ
ejpam-6097	7	41	topics	topic	NOUN
ejpam-6097	7	42	in	in	ADP
ejpam-6097	7	43	biomathematics	biomathematic	NOUN
ejpam-6097	7	44	is	be	AUX
ejpam-6097	7	45	the	the	DET
ejpam-6097	7	46	study	study	NOUN
ejpam-6097	7	47	of	of	ADP
ejpam-6097	7	48	the	the	DET
ejpam-6097	7	49	dynamical17	dynamical17	NOUN
ejpam-6097	7	50	behavior	behavior	NOUN
ejpam-6097	7	51	of	of	ADP
ejpam-6097	7	52	the	the	DET
ejpam-6097	7	53	so	so	ADV
ejpam-6097	7	54	-	-	PUNCT
ejpam-6097	7	55	called	call	VERB
ejpam-6097	7	56	predator	predator	NOUN
ejpam-6097	7	57	-	-	PUNCT
ejpam-6097	7	58	prey	prey	NOUN
ejpam-6097	7	59	models	model	NOUN
ejpam-6097	7	60	.	.	PUNCT
ejpam-6097	8	1	most	most	ADV
ejpam-6097	8	2	certainly	certainly	ADV
ejpam-6097	8	3	,	,	PUNCT
ejpam-6097	8	4	the	the	DET
ejpam-6097	8	5	initiative	initiative	NOUN
ejpam-6097	8	6	work	work	VERB
ejpam-6097	8	7	in18	in18	PROPN
ejpam-6097	8	8	this	this	DET
ejpam-6097	8	9	direction	direction	NOUN
ejpam-6097	8	10	is	be	AUX
ejpam-6097	8	11	that	that	PRON
ejpam-6097	8	12	of	of	ADP
ejpam-6097	8	13	lotka	lotka	PROPN
ejpam-6097	8	14	[	[	X
ejpam-6097	8	15	1	1	NUM
ejpam-6097	8	16	]	]	PUNCT
ejpam-6097	8	17	and	and	CCONJ
ejpam-6097	8	18	voltera	voltera	NOUN
ejpam-6097	8	19	[	[	X
ejpam-6097	8	20	2	2	NUM
ejpam-6097	8	21	]	]	PUNCT
ejpam-6097	8	22	.	.	PUNCT
ejpam-6097	9	1	however	however	ADV
ejpam-6097	9	2	,	,	PUNCT
ejpam-6097	9	3	some	some	PRON
ejpam-6097	9	4	of	of	ADP
ejpam-6097	9	5	the	the	DET
ejpam-6097	9	6	flaws	flaw	NOUN
ejpam-6097	9	7	with	with	ADP
ejpam-6097	9	8	this19	this19	NOUN
ejpam-6097	9	9	model	model	NOUN
ejpam-6097	9	10	are	be	AUX
ejpam-6097	9	11	that	that	SCONJ
ejpam-6097	9	12	the	the	DET
ejpam-6097	9	13	interaction	interaction	NOUN
ejpam-6097	9	14	between	between	ADP
ejpam-6097	9	15	the	the	DET
ejpam-6097	9	16	prey	prey	NOUN
ejpam-6097	9	17	and	and	CCONJ
ejpam-6097	9	18	predator	predator	NOUN
ejpam-6097	9	19	populations	population	NOUN
ejpam-6097	9	20	is	be	AUX
ejpam-6097	9	21	instantaneous,20	instantaneous,20	NOUN
ejpam-6097	9	22	which	which	PRON
ejpam-6097	9	23	may	may	AUX
ejpam-6097	9	24	not	not	PART
ejpam-6097	9	25	be	be	AUX
ejpam-6097	9	26	the	the	DET
ejpam-6097	9	27	case	case	NOUN
ejpam-6097	9	28	in	in	ADP
ejpam-6097	9	29	many	many	ADJ
ejpam-6097	9	30	natural	natural	ADJ
ejpam-6097	9	31	ecosystems	ecosystem	NOUN
ejpam-6097	9	32	;	;	PUNCT
ejpam-6097	9	33	moreover	moreover	ADV
ejpam-6097	9	34	,	,	PUNCT
ejpam-6097	9	35	the	the	DET
ejpam-6097	9	36	model	model	NOUN
ejpam-6097	9	37	presupposes21	presupposes21	NOUN
ejpam-6097	9	38	that	that	SCONJ
ejpam-6097	9	39	the	the	DET
ejpam-6097	9	40	prey	prey	PROPN
ejpam-6097	9	41	population	population	NOUN
ejpam-6097	9	42	has	have	VERB
ejpam-6097	9	43	infinitely	infinitely	ADV
ejpam-6097	9	44	many	many	ADJ
ejpam-6097	9	45	resources	resource	NOUN
ejpam-6097	9	46	to	to	PART
ejpam-6097	9	47	consume	consume	VERB
ejpam-6097	9	48	.	.	PUNCT
ejpam-6097	10	1	lotka	lotka	PROPN
ejpam-6097	10	2	-	-	PUNCT
ejpam-6097	10	3	voltera	voltera	NOUN
ejpam-6097	10	4	model22	model22	NOUN
ejpam-6097	10	5	has	have	AUX
ejpam-6097	10	6	been	be	AUX
ejpam-6097	10	7	developed	develop	VERB
ejpam-6097	10	8	in	in	ADP
ejpam-6097	10	9	its	its	PRON
ejpam-6097	10	10	structure	structure	NOUN
ejpam-6097	10	11	to	to	PART
ejpam-6097	10	12	display	display	VERB
ejpam-6097	10	13	more	more	ADV
ejpam-6097	10	14	realistic	realistic	ADJ
ejpam-6097	10	15	features	feature	NOUN
ejpam-6097	10	16	of	of	ADP
ejpam-6097	10	17	the	the	DET
ejpam-6097	10	18	dynamics23	dynamics23	NOUN
ejpam-6097	10	19	∗corresponding	∗corresponde	VERB
ejpam-6097	10	20	author	author	NOUN
ejpam-6097	10	21	.	.	PUNCT
ejpam-6097	11	1	doi	doi	NOUN
ejpam-6097	11	2	:	:	PUNCT
ejpam-6097	11	3	https://doi.org/10.29020/nybg.ejpam.v18i2.6097	https://doi.org/10.29020/nybg.ejpam.v18i2.6097	PART
ejpam-6097	11	4	email	email	NOUN
ejpam-6097	11	5	addresses	address	NOUN
ejpam-6097	11	6	:	:	PUNCT
ejpam-6097	11	7	mogtaba.m@mu.edu.sa	mogtaba.m@mu.edu.sa	PROPN
ejpam-6097	11	8	(	(	PUNCT
ejpam-6097	11	9	m.	m.	PROPN
ejpam-6097	11	10	mohammed	mohammed	PROPN
ejpam-6097	11	11	)	)	PUNCT
ejpam-6097	11	12	,	,	PUNCT
ejpam-6097	11	13	j.alebraheem@mu.edu.sa	j.alebraheem@mu.edu.sa	PROPN
ejpam-6097	11	14	(	(	PUNCT
ejpam-6097	11	15	j.	j.	PROPN
ejpam-6097	11	16	alebraheem	alebraheem	PROPN
ejpam-6097	11	17	)	)	PUNCT
ejpam-6097	11	18	,	,	PUNCT
ejpam-6097	11	19	i.tayel.edu.sa	i.tayel.edu.sa	PROPN
ejpam-6097	11	20	(	(	PUNCT
ejpam-6097	11	21	i.	i.	PROPN
ejpam-6097	11	22	m.	m.	PROPN
ejpam-6097	11	23	tayel	tayel	PROPN
ejpam-6097	11	24	)	)	PUNCT
ejpam-6097	11	25	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6097	12	1	1	1	NUM
ejpam-6097	12	2	copyright	copyright	NOUN
ejpam-6097	12	3	:	:	PUNCT
ejpam-6097	12	4	©	©	PROPN
ejpam-6097	12	5	2025	2025	NUM
ejpam-6097	12	6	the	the	DET
ejpam-6097	12	7	author(s	author(s	NOUN
ejpam-6097	12	8	)	)	PUNCT
ejpam-6097	12	9	.	.	PUNCT
ejpam-6097	13	1	(	(	PUNCT
ejpam-6097	13	2	cc	cc	NOUN
ejpam-6097	13	3	by	by	ADP
ejpam-6097	13	4	-	-	PUNCT
ejpam-6097	13	5	nc	nc	PROPN
ejpam-6097	13	6	4.0	4.0	NUM
ejpam-6097	13	7	)	)	PUNCT
ejpam-6097	13	8	m.	m.	NOUN
ejpam-6097	13	9	mohamed	mohamed	PROPN
ejpam-6097	13	10	et	et	PROPN
ejpam-6097	13	11	al	al	PROPN
ejpam-6097	13	12	.	.	PUNCT
ejpam-6097	13	13	/	/	SYM
ejpam-6097	13	14	eur	eur	PROPN
ejpam-6097	13	15	.	.	PUNCT
ejpam-6097	14	1	j.	j.	PROPN
ejpam-6097	14	2	pure	pure	PROPN
ejpam-6097	14	3	appl	appl	PROPN
ejpam-6097	14	4	.	.	PROPN
ejpam-6097	14	5	math	math	PROPN
ejpam-6097	14	6	,	,	PUNCT
ejpam-6097	14	7	18	18	NUM
ejpam-6097	14	8	(	(	PUNCT
ejpam-6097	14	9	2	2	NUM
ejpam-6097	14	10	)	)	PUNCT
ejpam-6097	14	11	(	(	PUNCT
ejpam-6097	14	12	2025	2025	NUM
ejpam-6097	14	13	)	)	PUNCT
ejpam-6097	14	14	,	,	PUNCT
ejpam-6097	14	15	6097	6097	NUM
ejpam-6097	14	16	2	2	NUM
ejpam-6097	14	17	of	of	ADP
ejpam-6097	14	18	19	19	NUM
ejpam-6097	14	19	by	by	ADP
ejpam-6097	14	20	many	many	ADJ
ejpam-6097	14	21	researchers	researcher	NOUN
ejpam-6097	14	22	,	,	PUNCT
ejpam-6097	14	23	see	see	VERB
ejpam-6097	14	24	,	,	PUNCT
ejpam-6097	14	25	for	for	ADP
ejpam-6097	14	26	example	example	NOUN
ejpam-6097	14	27	,	,	PUNCT
ejpam-6097	15	1	[	[	X
ejpam-6097	15	2	3–9	3–9	NUM
ejpam-6097	15	3	]	]	PUNCT
ejpam-6097	15	4	.	.	PUNCT
ejpam-6097	16	1	due	due	ADP
ejpam-6097	16	2	to	to	ADP
ejpam-6097	16	3	many	many	ADJ
ejpam-6097	16	4	questions	question	NOUN
ejpam-6097	16	5	that	that	PRON
ejpam-6097	16	6	come	come	VERB
ejpam-6097	16	7	from24	from24	NOUN
ejpam-6097	16	8	ecological	ecological	ADJ
ejpam-6097	16	9	points	point	NOUN
ejpam-6097	16	10	of	of	ADP
ejpam-6097	16	11	view	view	NOUN
ejpam-6097	16	12	,	,	PUNCT
ejpam-6097	16	13	up	up	ADP
ejpam-6097	16	14	to	to	ADP
ejpam-6097	16	15	date	date	NOUN
ejpam-6097	16	16	many	many	ADJ
ejpam-6097	16	17	researchers	researcher	NOUN
ejpam-6097	16	18	are	be	AUX
ejpam-6097	16	19	still	still	ADV
ejpam-6097	16	20	working	work	VERB
ejpam-6097	16	21	to	to	PART
ejpam-6097	16	22	answer	answer	VERB
ejpam-6097	16	23	such25	such25	NOUN
ejpam-6097	16	24	questions	question	NOUN
ejpam-6097	16	25	,	,	PUNCT
ejpam-6097	16	26	for	for	ADP
ejpam-6097	16	27	some	some	DET
ejpam-6097	16	28	examples	example	NOUN
ejpam-6097	16	29	of	of	ADP
ejpam-6097	16	30	predator	predator	NOUN
ejpam-6097	16	31	-	-	PUNCT
ejpam-6097	16	32	prey	prey	NOUN
ejpam-6097	16	33	models	model	NOUN
ejpam-6097	16	34	include	include	VERB
ejpam-6097	16	35	the	the	DET
ejpam-6097	16	36	allee	allee	PROPN
ejpam-6097	16	37	effect	effect	NOUN
ejpam-6097	16	38	,	,	PUNCT
ejpam-6097	16	39	the	the	DET
ejpam-6097	16	40	fear26	fear26	NOUN
ejpam-6097	16	41	effect	effect	NOUN
ejpam-6097	16	42	,	,	PUNCT
ejpam-6097	16	43	immigration	immigration	NOUN
ejpam-6097	16	44	,	,	PUNCT
ejpam-6097	16	45	prey	prey	NOUN
ejpam-6097	16	46	refuge	refuge	NOUN
ejpam-6097	16	47	,	,	PUNCT
ejpam-6097	16	48	and	and	CCONJ
ejpam-6097	16	49	cannibalism	cannibalism	NOUN
ejpam-6097	16	50	see	see	VERB
ejpam-6097	16	51	,	,	PUNCT
ejpam-6097	16	52	for	for	ADP
ejpam-6097	16	53	example	example	NOUN
ejpam-6097	16	54	,	,	PUNCT
ejpam-6097	17	1	[	[	X
ejpam-6097	17	2	10–13].27	10–13].27	X
ejpam-6097	17	3	one	one	NUM
ejpam-6097	17	4	of	of	ADP
ejpam-6097	17	5	the	the	DET
ejpam-6097	17	6	important	important	ADJ
ejpam-6097	17	7	and	and	CCONJ
ejpam-6097	17	8	recent	recent	ADJ
ejpam-6097	17	9	external	external	ADJ
ejpam-6097	17	10	elements	element	NOUN
ejpam-6097	17	11	that	that	PRON
ejpam-6097	17	12	is	be	AUX
ejpam-6097	17	13	considered	consider	VERB
ejpam-6097	17	14	to	to	PART
ejpam-6097	17	15	play	play	VERB
ejpam-6097	17	16	a	a	DET
ejpam-6097	17	17	crucial28	crucial28	ADJ
ejpam-6097	17	18	role	role	NOUN
ejpam-6097	17	19	in	in	ADP
ejpam-6097	17	20	the	the	DET
ejpam-6097	17	21	dynamics	dynamic	NOUN
ejpam-6097	17	22	of	of	ADP
ejpam-6097	17	23	predator	predator	NOUN
ejpam-6097	17	24	-	-	PUNCT
ejpam-6097	17	25	prey	prey	NOUN
ejpam-6097	17	26	models	model	NOUN
ejpam-6097	17	27	is	be	AUX
ejpam-6097	17	28	immigration	immigration	NOUN
ejpam-6097	17	29	.	.	PUNCT
ejpam-6097	18	1	this	this	DET
ejpam-6097	18	2	factor	factor	NOUN
ejpam-6097	18	3	could	could	AUX
ejpam-6097	18	4	lead	lead	VERB
ejpam-6097	18	5	to29	to29	PROPN
ejpam-6097	18	6	stabilizing	stabilize	VERB
ejpam-6097	18	7	unstable	unstable	ADJ
ejpam-6097	18	8	models	model	NOUN
ejpam-6097	18	9	as	as	ADP
ejpam-6097	18	10	in	in	ADP
ejpam-6097	18	11	[	[	X
ejpam-6097	18	12	14	14	NUM
ejpam-6097	18	13	]	]	PUNCT
ejpam-6097	18	14	,	,	PUNCT
ejpam-6097	18	15	and	and	CCONJ
ejpam-6097	18	16	also	also	ADV
ejpam-6097	18	17	helps	help	VERB
ejpam-6097	18	18	in	in	ADP
ejpam-6097	18	19	understanding	understand	VERB
ejpam-6097	18	20	the	the	DET
ejpam-6097	18	21	persistence	persistence	NOUN
ejpam-6097	18	22	and30	and30	ADJ
ejpam-6097	18	23	extinction	extinction	NOUN
ejpam-6097	18	24	of	of	ADP
ejpam-6097	18	25	some	some	DET
ejpam-6097	18	26	models	model	NOUN
ejpam-6097	18	27	that	that	PRON
ejpam-6097	18	28	were	be	AUX
ejpam-6097	18	29	not	not	PART
ejpam-6097	18	30	clear	clear	ADJ
ejpam-6097	18	31	to	to	PART
ejpam-6097	18	32	explain	explain	VERB
ejpam-6097	18	33	[	[	X
ejpam-6097	18	34	15	15	NUM
ejpam-6097	18	35	,	,	PUNCT
ejpam-6097	18	36	16	16	NUM
ejpam-6097	18	37	]	]	PUNCT
ejpam-6097	18	38	.	.	PUNCT
ejpam-6097	19	1	in	in	ADP
ejpam-6097	19	2	general	general	ADJ
ejpam-6097	19	3	,	,	PUNCT
ejpam-6097	19	4	many	many	ADJ
ejpam-6097	19	5	of	of	ADP
ejpam-6097	19	6	these31	these31	NOUN
ejpam-6097	19	7	elements	element	NOUN
ejpam-6097	19	8	are	be	AUX
ejpam-6097	19	9	described	describe	VERB
ejpam-6097	19	10	by	by	ADP
ejpam-6097	19	11	means	mean	NOUN
ejpam-6097	19	12	of	of	ADP
ejpam-6097	19	13	deterministic	deterministic	ADJ
ejpam-6097	19	14	system	system	NOUN
ejpam-6097	19	15	of	of	ADP
ejpam-6097	19	16	ordinary	ordinary	ADJ
ejpam-6097	19	17	differential	differential	NOUN
ejpam-6097	19	18	equations,32	equations,32	NOUN
ejpam-6097	19	19	which	which	PRON
ejpam-6097	19	20	have	have	VERB
ejpam-6097	19	21	it	it	PRON
ejpam-6097	19	22	is	be	AUX
ejpam-6097	19	23	own	own	ADJ
ejpam-6097	19	24	shortcomings	shortcoming	NOUN
ejpam-6097	19	25	in	in	ADP
ejpam-6097	19	26	considering	consider	VERB
ejpam-6097	19	27	natural	natural	ADJ
ejpam-6097	19	28	fluctuations	fluctuation	NOUN
ejpam-6097	19	29	that	that	PRON
ejpam-6097	19	30	could	could	AUX
ejpam-6097	19	31	affect33	affect33	VERB
ejpam-6097	19	32	the	the	DET
ejpam-6097	19	33	ecological	ecological	ADJ
ejpam-6097	19	34	environment	environment	NOUN
ejpam-6097	19	35	.	.	PUNCT
ejpam-6097	20	1	this	this	DET
ejpam-6097	20	2	constraint	constraint	NOUN
ejpam-6097	20	3	has	have	AUX
ejpam-6097	20	4	increased	increase	VERB
ejpam-6097	20	5	interest	interest	NOUN
ejpam-6097	20	6	in	in	ADP
ejpam-6097	20	7	stochastic	stochastic	ADJ
ejpam-6097	20	8	modeling34	modeling34	NOUN
ejpam-6097	20	9	tools	tool	NOUN
ejpam-6097	20	10	[	[	X
ejpam-6097	20	11	17–21	17–21	NUM
ejpam-6097	20	12	]	]	X
ejpam-6097	20	13	,	,	PUNCT
ejpam-6097	20	14	which	which	PRON
ejpam-6097	20	15	capture	capture	VERB
ejpam-6097	20	16	the	the	DET
ejpam-6097	20	17	natural	natural	ADJ
ejpam-6097	20	18	unpredictability	unpredictability	NOUN
ejpam-6097	20	19	that	that	PRON
ejpam-6097	20	20	affects	affect	VERB
ejpam-6097	20	21	ecological	ecological	ADJ
ejpam-6097	20	22	systems.35	systems.35	NOUN
ejpam-6097	20	23	small	small	ADJ
ejpam-6097	20	24	random	random	ADJ
ejpam-6097	20	25	immigration	immigration	NOUN
ejpam-6097	20	26	has	have	AUX
ejpam-6097	20	27	mostly	mostly	ADV
ejpam-6097	20	28	impacted	impact	VERB
ejpam-6097	20	29	simpler	simple	ADJ
ejpam-6097	20	30	predator	predator	NOUN
ejpam-6097	20	31	-	-	PUNCT
ejpam-6097	20	32	prey	prey	NOUN
ejpam-6097	20	33	interactions	interaction	NOUN
ejpam-6097	20	34	,	,	PUNCT
ejpam-6097	20	35	such36	such36	X
ejpam-6097	20	36	as	as	ADP
ejpam-6097	20	37	holling	holle	VERB
ejpam-6097	20	38	type	type	NOUN
ejpam-6097	20	39	i	i	PRON
ejpam-6097	20	40	models	model	VERB
ejpam-6097	21	1	[	[	X
ejpam-6097	21	2	22	22	NUM
ejpam-6097	21	3	]	]	PUNCT
ejpam-6097	21	4	.	.	PUNCT
ejpam-6097	22	1	these	these	DET
ejpam-6097	22	2	studies	study	NOUN
ejpam-6097	22	3	often	often	ADV
ejpam-6097	22	4	focus	focus	VERB
ejpam-6097	22	5	on	on	ADP
ejpam-6097	22	6	specific	specific	ADJ
ejpam-6097	22	7	elements	element	NOUN
ejpam-6097	22	8	,	,	PUNCT
ejpam-6097	22	9	such	such	ADJ
ejpam-6097	22	10	as37	as37	PROPN
ejpam-6097	22	11	stochastic	stochastic	ADJ
ejpam-6097	22	12	square	square	ADJ
ejpam-6097	22	13	stability	stability	NOUN
ejpam-6097	22	14	,	,	PUNCT
ejpam-6097	22	15	without	without	ADP
ejpam-6097	22	16	completely	completely	ADV
ejpam-6097	22	17	addressing	address	VERB
ejpam-6097	22	18	wider	wide	ADJ
ejpam-6097	22	19	dynamical	dynamical	ADJ
ejpam-6097	22	20	behaviors	behavior	NOUN
ejpam-6097	22	21	like38	like38	VERB
ejpam-6097	22	22	persistence	persistence	NOUN
ejpam-6097	22	23	and	and	CCONJ
ejpam-6097	22	24	extinction	extinction	NOUN
ejpam-6097	22	25	.	.	PUNCT
ejpam-6097	23	1	this	this	PRON
ejpam-6097	23	2	indicates	indicate	VERB
ejpam-6097	23	3	a	a	DET
ejpam-6097	23	4	significant	significant	ADJ
ejpam-6097	23	5	research	research	NOUN
ejpam-6097	23	6	gap	gap	NOUN
ejpam-6097	23	7	:	:	PUNCT
ejpam-6097	23	8	understanding	understand	VERB
ejpam-6097	23	9	how39	how39	VERB
ejpam-6097	23	10	random	random	ADJ
ejpam-6097	23	11	immigration	immigration	NOUN
ejpam-6097	23	12	effects	effect	NOUN
ejpam-6097	23	13	more	more	ADV
ejpam-6097	23	14	complicated	complicated	ADJ
ejpam-6097	23	15	predator	predator	NOUN
ejpam-6097	23	16	-	-	PUNCT
ejpam-6097	23	17	prey	prey	NOUN
ejpam-6097	23	18	systems	system	NOUN
ejpam-6097	23	19	,	,	PUNCT
ejpam-6097	23	20	particularly	particularly	ADV
ejpam-6097	23	21	those40	those40	ADV
ejpam-6097	23	22	regulated	regulate	VERB
ejpam-6097	23	23	by	by	ADP
ejpam-6097	23	24	holling	holle	VERB
ejpam-6097	23	25	type	type	NOUN
ejpam-6097	23	26	ii	ii	PROPN
ejpam-6097	23	27	responses	response	NOUN
ejpam-6097	23	28	,	,	PUNCT
ejpam-6097	23	29	which	which	PRON
ejpam-6097	23	30	better	well	ADV
ejpam-6097	23	31	depict	depict	VERB
ejpam-6097	23	32	predator	predator	NOUN
ejpam-6097	23	33	saturation	saturation	NOUN
ejpam-6097	23	34	and	and	CCONJ
ejpam-6097	23	35	are41	are41	NOUN
ejpam-6097	23	36	ecologically	ecologically	ADV
ejpam-6097	23	37	more	more	ADJ
ejpam-6097	23	38	realistic.42	realistic.42	NOUN
ejpam-6097	23	39	our	our	PRON
ejpam-6097	23	40	goal	goal	NOUN
ejpam-6097	23	41	in	in	ADP
ejpam-6097	23	42	this	this	DET
ejpam-6097	23	43	paper	paper	NOUN
ejpam-6097	23	44	is	be	AUX
ejpam-6097	23	45	to	to	PART
ejpam-6097	23	46	fill	fill	VERB
ejpam-6097	23	47	this	this	DET
ejpam-6097	23	48	gap	gap	NOUN
ejpam-6097	23	49	by	by	ADP
ejpam-6097	23	50	investigating	investigate	VERB
ejpam-6097	23	51	a	a	DET
ejpam-6097	23	52	stochastic	stochastic	ADJ
ejpam-6097	23	53	predator	predator	NOUN
ejpam-6097	23	54	-	-	PUNCT
ejpam-6097	23	55	prey43	prey43	NOUN
ejpam-6097	23	56	model	model	NOUN
ejpam-6097	23	57	with	with	ADP
ejpam-6097	23	58	holling	holle	VERB
ejpam-6097	23	59	type	type	NOUN
ejpam-6097	23	60	ii	ii	NOUN
ejpam-6097	23	61	dynamics	dynamic	NOUN
ejpam-6097	23	62	and	and	CCONJ
ejpam-6097	23	63	extra	extra	ADJ
ejpam-6097	23	64	ecological	ecological	ADJ
ejpam-6097	23	65	interactions	interaction	NOUN
ejpam-6097	23	66	,	,	PUNCT
ejpam-6097	23	67	emphasizing	emphasize	VERB
ejpam-6097	23	68	how44	how44	ADJ
ejpam-6097	23	69	random	random	ADJ
ejpam-6097	23	70	immigration	immigration	NOUN
ejpam-6097	23	71	influences	influence	VERB
ejpam-6097	23	72	the	the	DET
ejpam-6097	23	73	boundedness	boundedness	NOUN
ejpam-6097	23	74	of	of	ADP
ejpam-6097	23	75	solutions	solution	NOUN
ejpam-6097	23	76	,	,	PUNCT
ejpam-6097	23	77	stochastic	stochastic	ADJ
ejpam-6097	23	78	stability	stability	NOUN
ejpam-6097	23	79	,	,	PUNCT
ejpam-6097	23	80	persis-45	persis-45	PROPN
ejpam-6097	23	81	tence	tence	NOUN
ejpam-6097	23	82	,	,	PUNCT
ejpam-6097	23	83	and	and	CCONJ
ejpam-6097	23	84	extinction	extinction	NOUN
ejpam-6097	23	85	of	of	ADP
ejpam-6097	23	86	both	both	DET
ejpam-6097	23	87	prey	prey	NOUN
ejpam-6097	23	88	and	and	CCONJ
ejpam-6097	23	89	predator	predator	NOUN
ejpam-6097	23	90	populations	population	NOUN
ejpam-6097	23	91	.	.	PUNCT
ejpam-6097	24	1	to	to	PART
ejpam-6097	24	2	provide	provide	VERB
ejpam-6097	24	3	a	a	DET
ejpam-6097	24	4	more	more	ADV
ejpam-6097	24	5	complete46	complete46	ADJ
ejpam-6097	24	6	understanding	understanding	NOUN
ejpam-6097	24	7	of	of	ADP
ejpam-6097	24	8	these	these	DET
ejpam-6097	24	9	complex	complex	ADJ
ejpam-6097	24	10	dynamics	dynamic	NOUN
ejpam-6097	24	11	,	,	PUNCT
ejpam-6097	24	12	we	we	PRON
ejpam-6097	24	13	use	use	VERB
ejpam-6097	24	14	both	both	PRON
ejpam-6097	24	15	rigorous	rigorous	ADJ
ejpam-6097	24	16	mathematical	mathematical	ADJ
ejpam-6097	24	17	analysis47	analysis47	NOUN
ejpam-6097	24	18	and	and	CCONJ
ejpam-6097	24	19	numerical	numerical	ADJ
ejpam-6097	24	20	simulation.48	simulation.48	NOUN
ejpam-6097	24	21	2	2	NUM
ejpam-6097	24	22	.	.	PUNCT
ejpam-6097	24	23	problem	problem	NOUN
ejpam-6097	24	24	statement49	statement49	NOUN
ejpam-6097	24	25	we	we	PRON
ejpam-6097	24	26	consider	consider	VERB
ejpam-6097	24	27	a	a	DET
ejpam-6097	24	28	deterministic	deterministic	ADJ
ejpam-6097	24	29	competitive	competitive	ADJ
ejpam-6097	24	30	predator	predator	NOUN
ejpam-6097	24	31	-	-	PUNCT
ejpam-6097	24	32	prey	prey	NOUN
ejpam-6097	24	33	model	model	NOUN
ejpam-6097	24	34	with	with	ADP
ejpam-6097	24	35	holling	holle	VERB
ejpam-6097	24	36	type	type	NOUN
ejpam-6097	24	37	ii50	ii50	PROPN
ejpam-6097	24	38	which	which	PRON
ejpam-6097	24	39	has	have	AUX
ejpam-6097	24	40	been	be	AUX
ejpam-6097	24	41	used	use	VERB
ejpam-6097	24	42	in	in	ADP
ejpam-6097	24	43	earlier	early	ADJ
ejpam-6097	24	44	works	work	NOUN
ejpam-6097	24	45	for	for	ADP
ejpam-6097	24	46	various	various	ADJ
ejpam-6097	24	47	perspectives	perspective	NOUN
ejpam-6097	25	1	[	[	X
ejpam-6097	25	2	23–26	23–26	NUM
ejpam-6097	25	3	]	]	PUNCT
ejpam-6097	25	4	.	.	PUNCT
ejpam-6097	26	1	the	the	DET
ejpam-6097	26	2	model	model	NOUN
ejpam-6097	26	3	equations51	equations51	NOUN
ejpam-6097	26	4	are	be	AUX
ejpam-6097	26	5	defined	define	VERB
ejpam-6097	26	6	below52	below52	ADJ
ejpam-6097	26	7	du	du	X
ejpam-6097	26	8	dt	dt	PROPN
ejpam-6097	27	1	=	=	SYM
ejpam-6097	27	2	ρu	ρu	PROPN
ejpam-6097	27	3	(	(	PUNCT
ejpam-6097	27	4	1−	1−	NUM
ejpam-6097	27	5	u	u	NOUN
ejpam-6097	27	6	k	k	PROPN
ejpam-6097	27	7	)	)	PUNCT
ejpam-6097	27	8	−	−	PROPN
ejpam-6097	27	9	αuv	αuv	ADJ
ejpam-6097	27	10	1	1	NUM
ejpam-6097	28	1	+	+	CCONJ
ejpam-6097	28	2	βu	βu	PUNCT
ejpam-6097	28	3	(	(	PUNCT
ejpam-6097	28	4	1	1	NUM
ejpam-6097	28	5	)	)	PUNCT
ejpam-6097	28	6	53	53	NUM
ejpam-6097	28	7	dv	dv	PROPN
ejpam-6097	28	8	dt	dt	PROPN
ejpam-6097	28	9	=	=	PUNCT
ejpam-6097	28	10	−σv	−σv	PROPN
ejpam-6097	28	11	+	+	CCONJ
ejpam-6097	28	12	γuv	γuv	NUM
ejpam-6097	28	13	1	1	NUM
ejpam-6097	28	14	+	+	NUM
ejpam-6097	28	15	βu	βu	NOUN
ejpam-6097	28	16	−	−	NOUN
ejpam-6097	29	1	λv2	λv2	NOUN
ejpam-6097	29	2	(	(	PUNCT
ejpam-6097	29	3	2	2	NUM
ejpam-6097	29	4	)	)	PUNCT
ejpam-6097	29	5	54	54	NUM
ejpam-6097	29	6	u0	u0	ADJ
ejpam-6097	29	7	=	=	PROPN
ejpam-6097	29	8	u(0	u(0	PROPN
ejpam-6097	29	9	)	)	PUNCT
ejpam-6097	29	10	,	,	PUNCT
ejpam-6097	29	11	v0	v0	NOUN
ejpam-6097	29	12	=	=	SYM
ejpam-6097	29	13	v(0	v(0	PROPN
ejpam-6097	29	14	)	)	PUNCT
ejpam-6097	29	15	(	(	PUNCT
ejpam-6097	29	16	3	3	X
ejpam-6097	29	17	)	)	PUNCT
ejpam-6097	29	18	where	where	SCONJ
ejpam-6097	29	19	u	u	NOUN
ejpam-6097	29	20	and	and	CCONJ
ejpam-6097	29	21	v	v	NOUN
ejpam-6097	29	22	are	be	AUX
ejpam-6097	29	23	the	the	DET
ejpam-6097	29	24	prey	prey	NOUN
ejpam-6097	29	25	and	and	CCONJ
ejpam-6097	29	26	predator	predator	NOUN
ejpam-6097	29	27	populations	population	NOUN
ejpam-6097	29	28	,	,	PUNCT
ejpam-6097	29	29	respectively	respectively	ADV
ejpam-6097	29	30	.	.	PUNCT
ejpam-6097	30	1	recently	recently	ADV
ejpam-6097	30	2	,	,	PUNCT
ejpam-6097	30	3	jawdat	jawdat	VERB
ejpam-6097	30	4	et55	et55	PROPN
ejpam-6097	30	5	al	al	PROPN
ejpam-6097	30	6	.	.	PUNCT
ejpam-6097	31	1	[	[	X
ejpam-6097	31	2	26	26	NUM
ejpam-6097	31	3	]	]	PUNCT
ejpam-6097	31	4	,	,	PUNCT
ejpam-6097	31	5	studied	study	VERB
ejpam-6097	31	6	system	system	NOUN
ejpam-6097	31	7	(	(	PUNCT
ejpam-6097	31	8	1)-(3	1)-(3	NUM
ejpam-6097	31	9	)	)	PUNCT
ejpam-6097	31	10	with	with	ADP
ejpam-6097	31	11	small	small	ADJ
ejpam-6097	31	12	immigration	immigration	NOUN
ejpam-6097	31	13	in	in	ADP
ejpam-6097	31	14	the	the	DET
ejpam-6097	31	15	prey	prey	NOUN
ejpam-6097	31	16	population	population	NOUN
ejpam-6097	31	17	.	.	PUNCT
ejpam-6097	32	1	the	the	DET
ejpam-6097	32	2	model’s56	model’s56	NOUN
ejpam-6097	32	3	stability	stability	NOUN
ejpam-6097	32	4	and	and	CCONJ
ejpam-6097	32	5	coexistence	coexistence	NOUN
ejpam-6097	32	6	and	and	CCONJ
ejpam-6097	32	7	extinction	extinction	NOUN
ejpam-6097	32	8	conditions	condition	NOUN
ejpam-6097	32	9	between	between	ADP
ejpam-6097	32	10	prey	prey	NOUN
ejpam-6097	32	11	and	and	CCONJ
ejpam-6097	32	12	predator	predator	NOUN
ejpam-6097	32	13	populations57	populations57	NOUN
ejpam-6097	32	14	were	be	AUX
ejpam-6097	32	15	investigated	investigate	VERB
ejpam-6097	32	16	.	.	PUNCT
ejpam-6097	33	1	however	however	ADV
ejpam-6097	33	2	,	,	PUNCT
ejpam-6097	33	3	the	the	DET
ejpam-6097	33	4	effects	effect	NOUN
ejpam-6097	33	5	of	of	ADP
ejpam-6097	33	6	small	small	ADJ
ejpam-6097	33	7	immigration	immigration	NOUN
ejpam-6097	33	8	for	for	ADP
ejpam-6097	33	9	both	both	DET
ejpam-6097	33	10	populations	population	NOUN
ejpam-6097	33	11	were58	were58	ADV
ejpam-6097	33	12	not	not	PART
ejpam-6097	33	13	included	include	VERB
ejpam-6097	33	14	.	.	PUNCT
ejpam-6097	34	1	hence	hence	ADV
ejpam-6097	34	2	,	,	PUNCT
ejpam-6097	34	3	in	in	ADP
ejpam-6097	34	4	this	this	DET
ejpam-6097	34	5	paper	paper	NOUN
ejpam-6097	34	6	,	,	PUNCT
ejpam-6097	34	7	we	we	PRON
ejpam-6097	34	8	aim	aim	VERB
ejpam-6097	34	9	to	to	PART
ejpam-6097	34	10	study	study	VERB
ejpam-6097	34	11	the	the	DET
ejpam-6097	34	12	stochastic	stochastic	ADJ
ejpam-6097	34	13	counterpart	counterpart	NOUN
ejpam-6097	34	14	of	of	ADP
ejpam-6097	34	15	system59	system59	NOUN
ejpam-6097	34	16	m.	m.	PROPN
ejpam-6097	35	1	mohamed	mohamed	PROPN
ejpam-6097	35	2	et	et	PROPN
ejpam-6097	35	3	al	al	PROPN
ejpam-6097	35	4	.	.	PUNCT
ejpam-6097	35	5	/	/	SYM
ejpam-6097	35	6	eur	eur	PROPN
ejpam-6097	35	7	.	.	PUNCT
ejpam-6097	36	1	j.	j.	PROPN
ejpam-6097	36	2	pure	pure	PROPN
ejpam-6097	36	3	appl	appl	PROPN
ejpam-6097	36	4	.	.	PROPN
ejpam-6097	36	5	math	math	PROPN
ejpam-6097	36	6	,	,	PUNCT
ejpam-6097	36	7	18	18	NUM
ejpam-6097	36	8	(	(	PUNCT
ejpam-6097	36	9	2	2	NUM
ejpam-6097	36	10	)	)	PUNCT
ejpam-6097	36	11	(	(	PUNCT
ejpam-6097	36	12	2025	2025	NUM
ejpam-6097	36	13	)	)	PUNCT
ejpam-6097	36	14	,	,	PUNCT
ejpam-6097	36	15	6097	6097	NUM
ejpam-6097	36	16	3	3	NUM
ejpam-6097	36	17	of	of	ADP
ejpam-6097	36	18	19	19	NUM
ejpam-6097	36	19	(	(	PUNCT
ejpam-6097	36	20	1)-(3	1)-(3	NUM
ejpam-6097	36	21	)	)	PUNCT
ejpam-6097	36	22	,	,	PUNCT
ejpam-6097	36	23	more	more	ADV
ejpam-6097	36	24	precisely	precisely	ADV
ejpam-6097	36	25	,	,	PUNCT
ejpam-6097	36	26	we	we	PRON
ejpam-6097	36	27	consider	consider	VERB
ejpam-6097	36	28	small	small	ADJ
ejpam-6097	36	29	random	random	ADJ
ejpam-6097	36	30	immigration	immigration	NOUN
ejpam-6097	36	31	on	on	ADP
ejpam-6097	36	32	both	both	PRON
ejpam-6097	36	33	prey	prey	NOUN
ejpam-6097	36	34	and	and	CCONJ
ejpam-6097	36	35	predator60	predator60	ADJ
ejpam-6097	36	36	populations	population	NOUN
ejpam-6097	36	37	by	by	ADP
ejpam-6097	36	38	means	mean	NOUN
ejpam-6097	36	39	of	of	ADP
ejpam-6097	36	40	the	the	DET
ejpam-6097	36	41	following	follow	VERB
ejpam-6097	36	42	system:61	system:61	X
ejpam-6097	36	43			X
ejpam-6097	36	44	du	du	X
ejpam-6097	37	1	=	=	PUNCT
ejpam-6097	38	1	[	[	PUNCT
ejpam-6097	38	2	ρu	ρu	INTJ
ejpam-6097	38	3	(	(	PUNCT
ejpam-6097	38	4	1−	1−	NUM
ejpam-6097	38	5	u	u	NOUN
ejpam-6097	38	6	k	k	PROPN
ejpam-6097	38	7	)	)	PUNCT
ejpam-6097	38	8	−	−	PROPN
ejpam-6097	38	9	αuv	αuv	ADJ
ejpam-6097	38	10	1	1	NUM
ejpam-6097	38	11	+	+	CCONJ
ejpam-6097	38	12	βu	βu	PART
ejpam-6097	38	13	]	]	PUNCT
ejpam-6097	38	14	dt+	dt+	NOUN
ejpam-6097	38	15	δudb1(t	δudb1(t	PUNCT
ejpam-6097	38	16	)	)	PUNCT
ejpam-6097	38	17	dv	dv	PROPN
ejpam-6097	39	1	=	=	PUNCT
ejpam-6097	39	2	[	[	PUNCT
ejpam-6097	39	3	−σv	−σv	ADP
ejpam-6097	39	4	+	+	CCONJ
ejpam-6097	39	5	γuv	γuv	NUM
ejpam-6097	39	6	1	1	NUM
ejpam-6097	39	7	+	+	NUM
ejpam-6097	39	8	βu	βu	NOUN
ejpam-6097	39	9	−	−	NOUN
ejpam-6097	40	1	λv2	λv2	NOUN
ejpam-6097	40	2	]	]	PUNCT
ejpam-6097	40	3	dt+	dt+	NOUN
ejpam-6097	40	4	ϵvdb2(t	ϵvdb2(t	NOUN
ejpam-6097	40	5	)	)	PUNCT
ejpam-6097	40	6	u0	u0	PROPN
ejpam-6097	40	7	=	=	PROPN
ejpam-6097	40	8	u(0	u(0	PROPN
ejpam-6097	40	9	)	)	PUNCT
ejpam-6097	40	10	,	,	PUNCT
ejpam-6097	40	11	v0	v0	NOUN
ejpam-6097	40	12	=	=	SYM
ejpam-6097	40	13	v(0	v(0	PROPN
ejpam-6097	40	14	)	)	PUNCT
ejpam-6097	40	15	,	,	PUNCT
ejpam-6097	40	16	(	(	PUNCT
ejpam-6097	40	17	4	4	X
ejpam-6097	40	18	)	)	PUNCT
ejpam-6097	40	19	(	(	PUNCT
ejpam-6097	40	20	5	5	NUM
ejpam-6097	40	21	)	)	PUNCT
ejpam-6097	40	22	(	(	PUNCT
ejpam-6097	40	23	6	6	NUM
ejpam-6097	40	24	)	)	PUNCT
ejpam-6097	40	25	in	in	ADP
ejpam-6097	40	26	general	general	ADJ
ejpam-6097	40	27	,	,	PUNCT
ejpam-6097	40	28	the	the	DET
ejpam-6097	40	29	mathematical	mathematical	ADJ
ejpam-6097	40	30	model	model	NOUN
ejpam-6097	40	31	(	(	PUNCT
ejpam-6097	40	32	4)-(6	4)-(6	NUM
ejpam-6097	40	33	)	)	PUNCT
ejpam-6097	40	34	represents	represent	VERB
ejpam-6097	40	35	prey	prey	NOUN
ejpam-6097	40	36	-	-	PUNCT
ejpam-6097	40	37	predator	predator	NOUN
ejpam-6097	40	38	interactions	interaction	NOUN
ejpam-6097	40	39	,	,	PUNCT
ejpam-6097	40	40	where62	where62	NOUN
ejpam-6097	40	41	the	the	DET
ejpam-6097	40	42	term	term	NOUN
ejpam-6097	40	43	ρu	ρu	ADV
ejpam-6097	40	44	(	(	PUNCT
ejpam-6097	40	45	1−	1−	NUM
ejpam-6097	40	46	u	u	NOUN
ejpam-6097	40	47	k	k	PROPN
ejpam-6097	40	48	)	)	PUNCT
ejpam-6097	40	49	is	be	AUX
ejpam-6097	40	50	the	the	DET
ejpam-6097	40	51	logistic	logistic	ADJ
ejpam-6097	40	52	growth	growth	NOUN
ejpam-6097	40	53	rate	rate	NOUN
ejpam-6097	40	54	for	for	ADP
ejpam-6097	40	55	the	the	DET
ejpam-6097	40	56	prey	prey	PROPN
ejpam-6097	40	57	population	population	NOUN
ejpam-6097	40	58	,	,	PUNCT
ejpam-6097	40	59	αuv	αuv	ADJ
ejpam-6097	40	60	1+βu	1+βu	NUM
ejpam-6097	40	61	is	be	AUX
ejpam-6097	40	62	the	the	DET
ejpam-6097	40	63	func-63	func-63	PROPN
ejpam-6097	40	64	tional	tional	ADJ
ejpam-6097	40	65	response	response	NOUN
ejpam-6097	40	66	(	(	PUNCT
ejpam-6097	40	67	which	which	PRON
ejpam-6097	40	68	presents	present	VERB
ejpam-6097	40	69	the	the	DET
ejpam-6097	40	70	prey	prey	NOUN
ejpam-6097	40	71	consumption	consumption	NOUN
ejpam-6097	40	72	rate	rate	NOUN
ejpam-6097	40	73	by	by	ADP
ejpam-6097	40	74	the	the	DET
ejpam-6097	40	75	predator	predator	NOUN
ejpam-6097	40	76	population),64	population),64	NOUN
ejpam-6097	40	77	the	the	DET
ejpam-6097	40	78	term	term	NOUN
ejpam-6097	40	79	−σv	−σv	ADV
ejpam-6097	40	80	is	be	AUX
ejpam-6097	40	81	the	the	DET
ejpam-6097	40	82	loss	loss	NOUN
ejpam-6097	40	83	rate	rate	NOUN
ejpam-6097	40	84	for	for	ADP
ejpam-6097	40	85	the	the	DET
ejpam-6097	40	86	predator	predator	NOUN
ejpam-6097	40	87	population	population	NOUN
ejpam-6097	40	88	,	,	PUNCT
ejpam-6097	40	89	the	the	DET
ejpam-6097	40	90	term	term	NOUN
ejpam-6097	40	91	γuv	γuv	X
ejpam-6097	40	92	1+βu	1+βu	NUM
ejpam-6097	40	93	is	be	AUX
ejpam-6097	40	94	the	the	DET
ejpam-6097	40	95	response65	response65	NOUN
ejpam-6097	40	96	of	of	ADP
ejpam-6097	40	97	predator	predator	NOUN
ejpam-6097	40	98	population	population	NOUN
ejpam-6097	40	99	density	density	NOUN
ejpam-6097	40	100	through	through	ADP
ejpam-6097	40	101	consumption	consumption	NOUN
ejpam-6097	40	102	of	of	ADP
ejpam-6097	40	103	the	the	DET
ejpam-6097	40	104	prey	prey	NOUN
ejpam-6097	40	105	population	population	NOUN
ejpam-6097	40	106	,	,	PUNCT
ejpam-6097	40	107	λv2	λv2	X
ejpam-6097	40	108	is	be	AUX
ejpam-6097	40	109	the66	the66	ADJ
ejpam-6097	40	110	effect	effect	NOUN
ejpam-6097	40	111	of	of	ADP
ejpam-6097	40	112	intraspesific	intraspesific	ADJ
ejpam-6097	40	113	competition	competition	NOUN
ejpam-6097	40	114	for	for	ADP
ejpam-6097	40	115	predator	predator	NOUN
ejpam-6097	40	116	population	population	NOUN
ejpam-6097	40	117	.	.	PUNCT
ejpam-6097	41	1	δudb1(t	δudb1(t	PRON
ejpam-6097	41	2	)	)	PUNCT
ejpam-6097	42	1	and	and	CCONJ
ejpam-6097	42	2	ϵvdb2(t	ϵvdb2(t	NOUN
ejpam-6097	42	3	)	)	PUNCT
ejpam-6097	42	4	refer	refer	VERB
ejpam-6097	42	5	to67	to67	PROPN
ejpam-6097	42	6	low	low	ADJ
ejpam-6097	42	7	-	-	PUNCT
ejpam-6097	42	8	intensity	intensity	NOUN
ejpam-6097	42	9	stochastic	stochastic	NOUN
ejpam-6097	42	10	processes	process	NOUN
ejpam-6097	42	11	that	that	PRON
ejpam-6097	42	12	represent	represent	VERB
ejpam-6097	42	13	small	small	ADJ
ejpam-6097	42	14	random	random	ADJ
ejpam-6097	42	15	immigration	immigration	NOUN
ejpam-6097	42	16	in	in	ADP
ejpam-6097	42	17	the	the	DET
ejpam-6097	42	18	popu-68	popu-68	PROPN
ejpam-6097	42	19	lations	lation	NOUN
ejpam-6097	42	20	(	(	PUNCT
ejpam-6097	42	21	prey	prey	NOUN
ejpam-6097	42	22	and	and	CCONJ
ejpam-6097	42	23	predator	predator	NOUN
ejpam-6097	42	24	)	)	PUNCT
ejpam-6097	42	25	.	.	PUNCT
ejpam-6097	43	1	for	for	ADP
ejpam-6097	43	2	more	more	ADV
ejpam-6097	43	3	detailed	detailed	ADJ
ejpam-6097	43	4	interpretation	interpretation	NOUN
ejpam-6097	43	5	on	on	ADP
ejpam-6097	43	6	the	the	DET
ejpam-6097	43	7	parameters	parameter	NOUN
ejpam-6097	43	8	,	,	PUNCT
ejpam-6097	43	9	we	we	PRON
ejpam-6097	43	10	have69	have69	VERB
ejpam-6097	43	11	the	the	DET
ejpam-6097	43	12	following:70	following:70	NUM
ejpam-6097	43	13	•	•	NOUN
ejpam-6097	43	14	ρ	ρ	NOUN
ejpam-6097	43	15	is	be	AUX
ejpam-6097	43	16	the	the	DET
ejpam-6097	43	17	rate	rate	NOUN
ejpam-6097	43	18	of	of	ADP
ejpam-6097	43	19	growth	growth	NOUN
ejpam-6097	43	20	in	in	ADP
ejpam-6097	43	21	the	the	DET
ejpam-6097	43	22	prey	prey	NOUN
ejpam-6097	43	23	population.71	population.71	VERB
ejpam-6097	44	1	•	•	ADP
ejpam-6097	44	2	k	k	PROPN
ejpam-6097	44	3	is	be	AUX
ejpam-6097	44	4	the	the	DET
ejpam-6097	44	5	carrying	carrying	NOUN
ejpam-6097	44	6	capacity	capacity	NOUN
ejpam-6097	44	7	of	of	ADP
ejpam-6097	44	8	the	the	DET
ejpam-6097	44	9	model.72	model.72	NOUN
ejpam-6097	44	10	•	•	NOUN
ejpam-6097	44	11	α	α	NOUN
ejpam-6097	44	12	is	be	AUX
ejpam-6097	44	13	the	the	DET
ejpam-6097	44	14	rate	rate	NOUN
ejpam-6097	44	15	of	of	ADP
ejpam-6097	44	16	catch	catch	NOUN
ejpam-6097	44	17	prey	prey	NOUN
ejpam-6097	44	18	population	population	NOUN
ejpam-6097	44	19	by	by	ADP
ejpam-6097	44	20	the	the	DET
ejpam-6097	44	21	predator.73	predator.73	NOUN
ejpam-6097	44	22	•	•	ADP
ejpam-6097	44	23	β	β	X
ejpam-6097	44	24	is	be	AUX
ejpam-6097	44	25	the	the	DET
ejpam-6097	44	26	handling	handling	NOUN
ejpam-6097	44	27	rate	rate	NOUN
ejpam-6097	44	28	of	of	ADP
ejpam-6097	44	29	the	the	DET
ejpam-6097	44	30	predator.74	predator.74	NOUN
ejpam-6097	44	31	•	•	NOUN
ejpam-6097	44	32	σ	σ	PROPN
ejpam-6097	44	33	is	be	AUX
ejpam-6097	44	34	the	the	DET
ejpam-6097	44	35	natural	natural	ADJ
ejpam-6097	44	36	death	death	NOUN
ejpam-6097	44	37	rate	rate	NOUN
ejpam-6097	44	38	in	in	ADP
ejpam-6097	44	39	the	the	DET
ejpam-6097	44	40	predator	predator	NOUN
ejpam-6097	44	41	population.75	population.75	ADJ
ejpam-6097	44	42	•	•	NOUN
ejpam-6097	44	43	γ	γ	PROPN
ejpam-6097	44	44	is	be	AUX
ejpam-6097	44	45	the	the	DET
ejpam-6097	44	46	effectiveness	effectiveness	NOUN
ejpam-6097	44	47	of	of	ADP
ejpam-6097	44	48	transforming	transform	VERB
ejpam-6097	44	49	ate	eat	VERB
ejpam-6097	44	50	up	up	ADP
ejpam-6097	44	51	prey	prey	NOUN
ejpam-6097	44	52	into	into	ADP
ejpam-6097	44	53	predator	predator	NOUN
ejpam-6097	44	54	birth.76	birth.76	NOUN
ejpam-6097	44	55	•	•	ADP
ejpam-6097	44	56	λ	λ	PROPN
ejpam-6097	44	57	is	be	AUX
ejpam-6097	44	58	the	the	DET
ejpam-6097	44	59	intraspesific	intraspesific	ADJ
ejpam-6097	44	60	competition	competition	NOUN
ejpam-6097	44	61	between	between	ADP
ejpam-6097	44	62	predators.77	predators.77	NOUN
ejpam-6097	44	63	•	•	NOUN
ejpam-6097	44	64	δdb1	δdb1	PROPN
ejpam-6097	44	65	and	and	CCONJ
ejpam-6097	44	66	ϵdb2	ϵdb2	NOUN
ejpam-6097	44	67	are	be	AUX
ejpam-6097	44	68	the	the	DET
ejpam-6097	44	69	small	small	ADJ
ejpam-6097	44	70	random	random	ADJ
ejpam-6097	44	71	immigration	immigration	NOUN
ejpam-6097	44	72	in	in	ADP
ejpam-6097	44	73	the	the	DET
ejpam-6097	44	74	prey	prey	NOUN
ejpam-6097	44	75	and	and	CCONJ
ejpam-6097	44	76	predator	predator	NOUN
ejpam-6097	44	77	popula-78	popula-78	PROPN
ejpam-6097	44	78	tions	tion	NOUN
ejpam-6097	44	79	,	,	PUNCT
ejpam-6097	44	80	respectively.79	respectively.79	VERB
ejpam-6097	44	81	the	the	DET
ejpam-6097	44	82	stochastic	stochastic	NOUN
ejpam-6097	44	83	processes	process	NOUN
ejpam-6097	44	84	b1(t	b1(t	CCONJ
ejpam-6097	44	85	)	)	PUNCT
ejpam-6097	44	86	and	and	CCONJ
ejpam-6097	44	87	b2(t	b2(t	PROPN
ejpam-6097	44	88	)	)	PUNCT
ejpam-6097	44	89	are	be	AUX
ejpam-6097	44	90	brownian	brownian	ADJ
ejpam-6097	44	91	motions	motion	NOUN
ejpam-6097	44	92	with	with	ADP
ejpam-6097	44	93	the	the	DET
ejpam-6097	44	94	following	follow	VERB
ejpam-6097	44	95	prop-80	prop-80	PROPN
ejpam-6097	44	96	erties:81	erties:81	PROPN
ejpam-6097	44	97	•	•	ADJ
ejpam-6097	44	98	b1(0	b1(0	NOUN
ejpam-6097	44	99	)	)	PUNCT
ejpam-6097	44	100	=	=	SYM
ejpam-6097	44	101	b2(0	b2(0	NOUN
ejpam-6097	44	102	)	)	PUNCT
ejpam-6097	44	103	=	=	PUNCT
ejpam-6097	44	104	0.82	0.82	NUM
ejpam-6097	44	105	•	•	NUM
ejpam-6097	44	106	b1(t	b1(t	SYM
ejpam-6097	44	107	)	)	PUNCT
ejpam-6097	44	108	and	and	CCONJ
ejpam-6097	44	109	b2(t	b2(t	PROPN
ejpam-6097	44	110	)	)	PUNCT
ejpam-6097	44	111	are	be	AUX
ejpam-6097	44	112	continuous	continuous	ADJ
ejpam-6097	44	113	functions	function	NOUN
ejpam-6097	44	114	with	with	ADP
ejpam-6097	44	115	probability	probability	NOUN
ejpam-6097	44	116	1	1	NUM
ejpam-6097	44	117	,	,	PUNCT
ejpam-6097	44	118	for	for	ADP
ejpam-6097	44	119	all	all	DET
ejpam-6097	44	120	t	t	NOUN
ejpam-6097	44	121	∈	∈	PROPN
ejpam-6097	45	1	[	[	X
ejpam-6097	45	2	0	0	NUM
ejpam-6097	45	3	,	,	PUNCT
ejpam-6097	45	4	t	t	X
ejpam-6097	45	5	]	]	X
ejpam-6097	45	6	.83	.83	NUM
ejpam-6097	45	7	•	•	NUM
ejpam-6097	45	8	b1(t	b1(t	SYM
ejpam-6097	45	9	)	)	PUNCT
ejpam-6097	45	10	and	and	CCONJ
ejpam-6097	45	11	b2(t	b2(t	PROPN
ejpam-6097	45	12	)	)	PUNCT
ejpam-6097	45	13	have	have	VERB
ejpam-6097	45	14	stationary	stationary	ADJ
ejpam-6097	45	15	independent	independent	ADJ
ejpam-6097	45	16	increments.84	increments.84	PROPN
ejpam-6097	45	17	•	•	ADP
ejpam-6097	45	18	b1(t+	b1(t+	PROPN
ejpam-6097	45	19	s)−b1(t	s)−b1(t	PRON
ejpam-6097	45	20	)	)	PUNCT
ejpam-6097	45	21	and	and	CCONJ
ejpam-6097	45	22	b2(t+	b2(t+	PROPN
ejpam-6097	45	23	s)−b2(t	s)−b2(t	ADV
ejpam-6097	45	24	)	)	PUNCT
ejpam-6097	45	25	are	be	AUX
ejpam-6097	45	26	normally	normally	ADV
ejpam-6097	45	27	distributed	distribute	VERB
ejpam-6097	45	28	with	with	ADP
ejpam-6097	45	29	zero	zero	NUM
ejpam-6097	45	30	mean	mean	VERB
ejpam-6097	46	1	and85	and85	NOUN
ejpam-6097	46	2	variance	variance	NOUN
ejpam-6097	46	3	t.86	t.86	PROPN
ejpam-6097	46	4	m.	m.	PROPN
ejpam-6097	46	5	mohamed	mohamed	PROPN
ejpam-6097	46	6	et	et	PROPN
ejpam-6097	46	7	al	al	PROPN
ejpam-6097	46	8	.	.	PUNCT
ejpam-6097	46	9	/	/	SYM
ejpam-6097	46	10	eur	eur	PROPN
ejpam-6097	46	11	.	.	PUNCT
ejpam-6097	47	1	j.	j.	PROPN
ejpam-6097	47	2	pure	pure	PROPN
ejpam-6097	47	3	appl	appl	PROPN
ejpam-6097	47	4	.	.	PROPN
ejpam-6097	47	5	math	math	PROPN
ejpam-6097	47	6	,	,	PUNCT
ejpam-6097	47	7	18	18	NUM
ejpam-6097	47	8	(	(	PUNCT
ejpam-6097	47	9	2	2	NUM
ejpam-6097	47	10	)	)	PUNCT
ejpam-6097	47	11	(	(	PUNCT
ejpam-6097	47	12	2025	2025	NUM
ejpam-6097	47	13	)	)	PUNCT
ejpam-6097	47	14	,	,	PUNCT
ejpam-6097	47	15	6097	6097	NUM
ejpam-6097	47	16	4	4	NUM
ejpam-6097	47	17	of	of	ADP
ejpam-6097	47	18	19	19	NUM
ejpam-6097	47	19	3	3	NUM
ejpam-6097	47	20	.	.	PUNCT
ejpam-6097	47	21	model	model	NOUN
ejpam-6097	47	22	boundedness87	boundedness87	NOUN
ejpam-6097	47	23	as	as	SCONJ
ejpam-6097	47	24	it	it	PRON
ejpam-6097	47	25	is	be	AUX
ejpam-6097	47	26	one	one	NUM
ejpam-6097	47	27	of	of	ADP
ejpam-6097	47	28	main	main	ADJ
ejpam-6097	47	29	validations	validation	NOUN
ejpam-6097	47	30	of	of	ADP
ejpam-6097	47	31	the	the	DET
ejpam-6097	47	32	model	model	NOUN
ejpam-6097	47	33	,	,	PUNCT
ejpam-6097	47	34	in	in	ADP
ejpam-6097	47	35	this	this	DET
ejpam-6097	47	36	section	section	NOUN
ejpam-6097	47	37	,	,	PUNCT
ejpam-6097	47	38	we	we	PRON
ejpam-6097	47	39	use	use	VERB
ejpam-6097	47	40	some	some	DET
ejpam-6097	47	41	probabilistic88	probabilistic88	NOUN
ejpam-6097	47	42	and	and	CCONJ
ejpam-6097	47	43	analytic	analytic	ADJ
ejpam-6097	47	44	in	in	ADP
ejpam-6097	47	45	inequalities	inequality	NOUN
ejpam-6097	47	46	to	to	PART
ejpam-6097	47	47	obtain	obtain	VERB
ejpam-6097	47	48	the	the	DET
ejpam-6097	47	49	boundedness	boundedness	NOUN
ejpam-6097	47	50	of	of	ADP
ejpam-6097	47	51	the	the	DET
ejpam-6097	47	52	model	model	NOUN
ejpam-6097	47	53	.	.	PUNCT
ejpam-6097	48	1	system	system	NOUN
ejpam-6097	48	2	(	(	PUNCT
ejpam-6097	48	3	4)-(6	4)-(6	NOUN
ejpam-6097	48	4	)	)	PUNCT
ejpam-6097	48	5	could89	could89	NOUN
ejpam-6097	48	6	be	be	AUX
ejpam-6097	48	7	written	write	VERB
ejpam-6097	48	8	as:90	as:90	PROPN
ejpam-6097	48	9	dx	dx	X
ejpam-6097	48	10	=	=	SYM
ejpam-6097	48	11	m(t	m(t	PROPN
ejpam-6097	48	12	,	,	PUNCT
ejpam-6097	48	13	x)dt+n(t	x)dt+n(t	NUM
ejpam-6097	48	14	,	,	PUNCT
ejpam-6097	48	15	x)db	x)db	PROPN
ejpam-6097	48	16	x0	x0	PROPN
ejpam-6097	49	1	=	=	SYM
ejpam-6097	49	2	x(0	x(0	PROPN
ejpam-6097	49	3	)	)	PUNCT
ejpam-6097	49	4	(	(	PUNCT
ejpam-6097	49	5	7	7	NUM
ejpam-6097	49	6	)	)	PUNCT
ejpam-6097	49	7	(	(	PUNCT
ejpam-6097	49	8	8)	8)	NUM
ejpam-6097	49	9	such	such	ADJ
ejpam-6097	49	10	that91	that91	NOUN
ejpam-6097	49	11	m	m	VERB
ejpam-6097	49	12	:	:	PUNCT
ejpam-6097	49	13	[	[	PUNCT
ejpam-6097	49	14	[	[	X
ejpam-6097	49	15	0	0	NUM
ejpam-6097	49	16	,	,	PUNCT
ejpam-6097	49	17	t	t	X
ejpam-6097	49	18	]	]	PUNCT
ejpam-6097	49	19	×	×	NOUN
ejpam-6097	49	20	r+	r+	NOUN
ejpam-6097	49	21	]	]	X
ejpam-6097	49	22	2	2	NUM
ejpam-6097	49	23	→	→	SYM
ejpam-6097	49	24	r	r	NOUN
ejpam-6097	49	25	n	n	NOUN
ejpam-6097	49	26	:	:	PUNCT
ejpam-6097	49	27	[	[	PUNCT
ejpam-6097	49	28	[	[	X
ejpam-6097	49	29	0	0	NUM
ejpam-6097	49	30	,	,	PUNCT
ejpam-6097	49	31	t	t	X
ejpam-6097	49	32	]	]	PUNCT
ejpam-6097	49	33	×	×	NOUN
ejpam-6097	49	34	r+	r+	NOUN
ejpam-6097	49	35	]	]	X
ejpam-6097	49	36	2	2	NUM
ejpam-6097	49	37	→	→	SYM
ejpam-6097	49	38	r	r	NOUN
ejpam-6097	49	39	m(t	m(t	NOUN
ejpam-6097	49	40	,	,	PUNCT
ejpam-6097	49	41	x	x	NOUN
ejpam-6097	49	42	)	)	PUNCT
ejpam-6097	49	43	and	and	CCONJ
ejpam-6097	49	44	n(t	n(t	PROPN
ejpam-6097	49	45	,	,	PUNCT
ejpam-6097	49	46	x	x	PRON
ejpam-6097	49	47	)	)	PUNCT
ejpam-6097	49	48	are	be	AUX
ejpam-6097	49	49	given	give	VERB
ejpam-6097	49	50	by	by	ADP
ejpam-6097	49	51	m(t	m(t	PROPN
ejpam-6097	49	52	,	,	PUNCT
ejpam-6097	49	53	x	x	X
ejpam-6097	49	54	)	)	PUNCT
ejpam-6097	49	55	=	=	PUNCT
ejpam-6097	50	1	[	[	PUNCT
ejpam-6097	50	2	ρu	ρu	INTJ
ejpam-6097	50	3	(	(	PUNCT
ejpam-6097	50	4	1−	1−	NUM
ejpam-6097	50	5	u	u	NOUN
ejpam-6097	50	6	k	k	PROPN
ejpam-6097	50	7	)	)	PUNCT
ejpam-6097	50	8	−	−	PROPN
ejpam-6097	50	9	αuv	αuv	ADJ
ejpam-6097	50	10	1+βu	1+βu	NUM
ejpam-6097	50	11	−σv	−σv	ADV
ejpam-6097	50	12	+	+	CCONJ
ejpam-6097	50	13	γuv	γuv	NUM
ejpam-6097	50	14	1+βu	1+βu	NUM
ejpam-6097	50	15	−	−	NOUN
ejpam-6097	51	1	λv2	λv2	X
ejpam-6097	51	2	]	]	X
ejpam-6097	51	3	,	,	PUNCT
ejpam-6097	51	4	n(t	n(t	PROPN
ejpam-6097	51	5	,	,	PUNCT
ejpam-6097	51	6	x	x	X
ejpam-6097	51	7	)	)	PUNCT
ejpam-6097	52	1	=	=	NOUN
ejpam-6097	53	1	[	[	PUNCT
ejpam-6097	53	2	δu	δu	X
ejpam-6097	53	3	ϵv	ϵv	INTJ
ejpam-6097	53	4	]	]	PUNCT
ejpam-6097	53	5	x	x	PUNCT
ejpam-6097	54	1	=	=	PUNCT
ejpam-6097	55	1	[	[	PUNCT
ejpam-6097	55	2	u	u	NOUN
ejpam-6097	55	3	v	v	X
ejpam-6097	55	4	]	]	PUNCT
ejpam-6097	55	5	db(t	db(t	NOUN
ejpam-6097	55	6	)	)	PUNCT
ejpam-6097	56	1	=	=	PUNCT
ejpam-6097	56	2	[	[	PUNCT
ejpam-6097	56	3	db1(t	db1(t	PROPN
ejpam-6097	56	4	)	)	PUNCT
ejpam-6097	56	5	db2(t	db2(t	PROPN
ejpam-6097	56	6	)	)	PUNCT
ejpam-6097	56	7	]	]	PUNCT
ejpam-6097	57	1	lemma	lemma	PROPN
ejpam-6097	57	2	1	1	X
ejpam-6097	57	3	.	.	PUNCT
ejpam-6097	58	1	for	for	ADP
ejpam-6097	58	2	some	some	DET
ejpam-6097	58	3	positive	positive	ADJ
ejpam-6097	58	4	constant	constant	ADJ
ejpam-6097	58	5	c	c	NOUN
ejpam-6097	58	6	,	,	PUNCT
ejpam-6097	58	7	the	the	DET
ejpam-6097	58	8	functions	function	NOUN
ejpam-6097	58	9	m(t	m(t	NOUN
ejpam-6097	58	10	,	,	PUNCT
ejpam-6097	58	11	x	x	NOUN
ejpam-6097	58	12	)	)	PUNCT
ejpam-6097	58	13	and	and	CCONJ
ejpam-6097	58	14	n(t	n(t	PROPN
ejpam-6097	58	15	,	,	PUNCT
ejpam-6097	58	16	x	x	NOUN
ejpam-6097	58	17	)	)	PUNCT
ejpam-6097	58	18	in	in	ADP
ejpam-6097	58	19	(	(	PUNCT
ejpam-6097	58	20	7	7	X
ejpam-6097	58	21	)	)	PUNCT
ejpam-6097	58	22	satisfy92	satisfy92	NOUN
ejpam-6097	58	23	the	the	DET
ejpam-6097	58	24	following	follow	VERB
ejpam-6097	58	25	linear	linear	ADJ
ejpam-6097	58	26	growth	growth	NOUN
ejpam-6097	58	27	condition93	condition93	VERB
ejpam-6097	58	28	e∥m(t	e∥m(t	PROPN
ejpam-6097	58	29	,	,	PUNCT
ejpam-6097	58	30	x)∥2	x)∥2	PROPN
ejpam-6097	58	31	+	+	CCONJ
ejpam-6097	59	1	e∥n(t	e∥n(t	PROPN
ejpam-6097	59	2	,	,	PUNCT
ejpam-6097	59	3	x)∥2	x)∥2	PROPN
ejpam-6097	59	4	≤	≤	PROPN
ejpam-6097	60	1	c(1	c(1	PROPN
ejpam-6097	60	2	+	+	CCONJ
ejpam-6097	60	3	e∥x∥2	e∥x∥2	PROPN
ejpam-6097	60	4	)	)	PUNCT
ejpam-6097	60	5	(	(	PUNCT
ejpam-6097	60	6	9	9	X
ejpam-6097	60	7	)	)	PUNCT
ejpam-6097	60	8	proof	proof	NOUN
ejpam-6097	60	9	.	.	PUNCT
ejpam-6097	61	1	from	from	ADP
ejpam-6097	61	2	(	(	PUNCT
ejpam-6097	61	3	4	4	NUM
ejpam-6097	61	4	)	)	PUNCT
ejpam-6097	61	5	and	and	CCONJ
ejpam-6097	61	6	the	the	DET
ejpam-6097	61	7	fact	fact	NOUN
ejpam-6097	61	8	that	that	SCONJ
ejpam-6097	61	9	ρ	ρ	NOUN
ejpam-6097	61	10	,	,	PUNCT
ejpam-6097	61	11	k	k	PROPN
ejpam-6097	61	12	,	,	PUNCT
ejpam-6097	61	13	α	α	PROPN
ejpam-6097	61	14	and	and	CCONJ
ejpam-6097	61	15	β	β	X
ejpam-6097	61	16	are	be	AUX
ejpam-6097	61	17	positive	positive	ADJ
ejpam-6097	61	18	,	,	PUNCT
ejpam-6097	61	19	one	one	PRON
ejpam-6097	61	20	sees	see	VERB
ejpam-6097	61	21	that94	that94	NOUN
ejpam-6097	61	22	u	u	NOUN
ejpam-6097	61	23	≤	≤	X
ejpam-6097	61	24	u0	u0	PROPN
ejpam-6097	61	25	+	+	PROPN
ejpam-6097	61	26	ρ	ρ	PROPN
ejpam-6097	61	27	∫	∫	PROPN
ejpam-6097	61	28	t	t	PROPN
ejpam-6097	61	29	0	0	NUM
ejpam-6097	62	1	uds+	uds+	PROPN
ejpam-6097	62	2	δ	δ	PROPN
ejpam-6097	62	3	∫	∫	PROPN
ejpam-6097	62	4	t	t	PROPN
ejpam-6097	62	5	0	0	NUM
ejpam-6097	62	6	udb1(s	udb1(	NOUN
ejpam-6097	62	7	)	)	PUNCT
ejpam-6097	62	8	.	.	PUNCT
ejpam-6097	63	1	taking	take	VERB
ejpam-6097	63	2	the	the	DET
ejpam-6097	63	3	expectation	expectation	NOUN
ejpam-6097	63	4	on	on	ADP
ejpam-6097	63	5	both	both	DET
ejpam-6097	63	6	sides	side	NOUN
ejpam-6097	63	7	and	and	CCONJ
ejpam-6097	63	8	using	use	VERB
ejpam-6097	63	9	itô	itô	PROPN
ejpam-6097	63	10	’s	’s	PART
ejpam-6097	63	11	isometry	isometry	NOUN
ejpam-6097	63	12	,	,	PUNCT
ejpam-6097	63	13	we	we	PRON
ejpam-6097	63	14	have95	have95	VERB
ejpam-6097	64	1	e|u|	e|u|	ADJ
ejpam-6097	64	2	≤	≤	PROPN
ejpam-6097	64	3	u0	u0	NOUN
ejpam-6097	65	1	+	+	CCONJ
ejpam-6097	65	2	ρe	ρe	PROPN
ejpam-6097	65	3	∫	∫	PROPN
ejpam-6097	65	4	t	t	PROPN
ejpam-6097	65	5	0	0	NUM
ejpam-6097	65	6	|u|ds	|u|ds	PROPN
ejpam-6097	65	7	.	.	PROPN
ejpam-6097	66	1	from	from	ADP
ejpam-6097	66	2	grownall	grownall	PROPN
ejpam-6097	66	3	’s	’s	PART
ejpam-6097	66	4	inequality	inequality	NOUN
ejpam-6097	66	5	,	,	PUNCT
ejpam-6097	66	6	one	one	NUM
ejpam-6097	66	7	gets96	gets96	NOUN
ejpam-6097	66	8	e|u|	e|u|	PROPN
ejpam-6097	66	9	≤	≤	NUM
ejpam-6097	67	1	u0e	u0e	INTJ
ejpam-6097	67	2	ρt	ρt	INTJ
ejpam-6097	67	3	(	(	PUNCT
ejpam-6097	67	4	10	10	NUM
ejpam-6097	67	5	)	)	PUNCT
ejpam-6097	67	6	now,97	now,97	NOUN
ejpam-6097	68	1	e∥m(t	e∥m(t	PROPN
ejpam-6097	68	2	,	,	PUNCT
ejpam-6097	68	3	x)∥2	x)∥2	PROPN
ejpam-6097	68	4	=	=	SYM
ejpam-6097	68	5	e∥ρu	e∥ρu	PROPN
ejpam-6097	68	6	(	(	PUNCT
ejpam-6097	68	7	1−	1−	NUM
ejpam-6097	68	8	u	u	NOUN
ejpam-6097	68	9	k	k	PROPN
ejpam-6097	68	10	)	)	PUNCT
ejpam-6097	68	11	−	−	PROPN
ejpam-6097	68	12	αuv	αuv	ADJ
ejpam-6097	68	13	1	1	NUM
ejpam-6097	68	14	+	+	CCONJ
ejpam-6097	68	15	βu	βu	PUNCT
ejpam-6097	68	16	∥2	∥2	NOUN
ejpam-6097	69	1	+	+	CCONJ
ejpam-6097	69	2	e∥	e∥	NOUN
ejpam-6097	69	3	−	−	NOUN
ejpam-6097	70	1	σv	σv	INTJ
ejpam-6097	70	2	+	+	CCONJ
ejpam-6097	70	3	γuv	γuv	NUM
ejpam-6097	70	4	1	1	NUM
ejpam-6097	70	5	+	+	NUM
ejpam-6097	70	6	βu	βu	NOUN
ejpam-6097	70	7	−	−	NOUN
ejpam-6097	70	8	λv2∥2	λv2∥2	PROPN
ejpam-6097	70	9	≤	≤	NUM
ejpam-6097	70	10	ρ2e∥u∥2	ρ2e∥u∥2	PROPN
ejpam-6097	70	11	+	+	CCONJ
ejpam-6097	70	12	γ2e∥u∥2	γ2e∥u∥2	NOUN
ejpam-6097	70	13	+	+	CCONJ
ejpam-6097	70	14	∥v∥2	∥v∥2	ADJ
ejpam-6097	70	15	≤	≤	NUM
ejpam-6097	70	16	ce∥u∥2(1	ce∥u∥2(1	NOUN
ejpam-6097	70	17	+	+	CCONJ
ejpam-6097	70	18	∥v∥2	∥v∥2	X
ejpam-6097	70	19	)	)	PUNCT
ejpam-6097	70	20	(	(	PUNCT
ejpam-6097	70	21	11	11	NUM
ejpam-6097	70	22	)	)	PUNCT
ejpam-6097	70	23	m.	m.	NOUN
ejpam-6097	70	24	mohamed	mohamed	PROPN
ejpam-6097	70	25	et	et	PROPN
ejpam-6097	70	26	al	al	PROPN
ejpam-6097	70	27	.	.	PUNCT
ejpam-6097	70	28	/	/	SYM
ejpam-6097	70	29	eur	eur	PROPN
ejpam-6097	70	30	.	.	PUNCT
ejpam-6097	71	1	j.	j.	PROPN
ejpam-6097	71	2	pure	pure	PROPN
ejpam-6097	71	3	appl	appl	PROPN
ejpam-6097	71	4	.	.	PROPN
ejpam-6097	71	5	math	math	PROPN
ejpam-6097	71	6	,	,	PUNCT
ejpam-6097	71	7	18	18	NUM
ejpam-6097	71	8	(	(	PUNCT
ejpam-6097	71	9	2	2	NUM
ejpam-6097	71	10	)	)	PUNCT
ejpam-6097	71	11	(	(	PUNCT
ejpam-6097	71	12	2025	2025	NUM
ejpam-6097	71	13	)	)	PUNCT
ejpam-6097	71	14	,	,	PUNCT
ejpam-6097	71	15	6097	6097	NUM
ejpam-6097	71	16	5	5	NUM
ejpam-6097	71	17	of	of	ADP
ejpam-6097	71	18	19	19	NUM
ejpam-6097	71	19	from	from	ADP
ejpam-6097	71	20	(	(	PUNCT
ejpam-6097	71	21	10	10	NUM
ejpam-6097	71	22	)	)	PUNCT
ejpam-6097	71	23	and	and	CCONJ
ejpam-6097	71	24	(	(	PUNCT
ejpam-6097	71	25	11	11	NUM
ejpam-6097	71	26	)	)	PUNCT
ejpam-6097	71	27	we	we	PRON
ejpam-6097	71	28	have98	have98	VERB
ejpam-6097	71	29	e∥m(t	e∥m(t	PROPN
ejpam-6097	71	30	,	,	PUNCT
ejpam-6097	71	31	x)∥2	x)∥2	PROPN
ejpam-6097	71	32	≤	≤	PROPN
ejpam-6097	71	33	c(1	c(1	PROPN
ejpam-6097	71	34	+	+	CCONJ
ejpam-6097	71	35	∥v∥2	∥v∥2	X
ejpam-6097	71	36	)	)	PUNCT
ejpam-6097	71	37	≤	≤	PROPN
ejpam-6097	71	38	c(1	c(1	PROPN
ejpam-6097	71	39	+	+	NUM
ejpam-6097	71	40	∥u∥2	∥u∥2	NOUN
ejpam-6097	71	41	+	+	CCONJ
ejpam-6097	71	42	∥v∥2	∥v∥2	X
ejpam-6097	71	43	)	)	PUNCT
ejpam-6097	71	44	≤	≤	PROPN
ejpam-6097	71	45	c(1	c(1	NOUN
ejpam-6097	71	46	+	+	CCONJ
ejpam-6097	71	47	∥x∥2	∥x∥2	NOUN
ejpam-6097	71	48	)	)	PUNCT
ejpam-6097	71	49	.	.	PUNCT
ejpam-6097	72	1	(	(	PUNCT
ejpam-6097	72	2	12	12	NUM
ejpam-6097	72	3	)	)	PUNCT
ejpam-6097	72	4	it	it	PRON
ejpam-6097	72	5	is	be	AUX
ejpam-6097	72	6	easy	easy	ADJ
ejpam-6097	72	7	to	to	PART
ejpam-6097	72	8	see	see	VERB
ejpam-6097	72	9	that99	that99	NOUN
ejpam-6097	72	10	e∥n(t	e∥n(t	PROPN
ejpam-6097	72	11	,	,	PUNCT
ejpam-6097	72	12	x)∥2	x)∥2	PROPN
ejpam-6097	72	13	=	=	PUNCT
ejpam-6097	72	14	δ2e∥u∥2	δ2e∥u∥2	NOUN
ejpam-6097	73	1	+	+	CCONJ
ejpam-6097	73	2	ϵ2e∥v∥2	ϵ2e∥v∥2	PROPN
ejpam-6097	73	3	≤	≤	PROPN
ejpam-6097	73	4	c(1	c(1	PROPN
ejpam-6097	73	5	+	+	NUM
ejpam-6097	73	6	∥u∥2	∥u∥2	NOUN
ejpam-6097	73	7	+	+	CCONJ
ejpam-6097	73	8	∥v∥2	∥v∥2	X
ejpam-6097	73	9	)	)	PUNCT
ejpam-6097	73	10	≤	≤	PROPN
ejpam-6097	73	11	c(1	c(1	NOUN
ejpam-6097	73	12	+	+	CCONJ
ejpam-6097	73	13	∥x∥2	∥x∥2	NOUN
ejpam-6097	73	14	)	)	PUNCT
ejpam-6097	73	15	.	.	PUNCT
ejpam-6097	74	1	(	(	PUNCT
ejpam-6097	74	2	13	13	NUM
ejpam-6097	74	3	)	)	PUNCT
ejpam-6097	74	4	from	from	ADP
ejpam-6097	74	5	(	(	PUNCT
ejpam-6097	74	6	12	12	NUM
ejpam-6097	74	7	)	)	PUNCT
ejpam-6097	74	8	and	and	CCONJ
ejpam-6097	74	9	(	(	PUNCT
ejpam-6097	74	10	13	13	NUM
ejpam-6097	74	11	)	)	PUNCT
ejpam-6097	74	12	we	we	PRON
ejpam-6097	74	13	conclude	conclude	VERB
ejpam-6097	74	14	the	the	DET
ejpam-6097	74	15	proof.100	proof.100	PROPN
ejpam-6097	74	16	theorem	theorem	NOUN
ejpam-6097	74	17	1	1	NUM
ejpam-6097	74	18	.	.	X
ejpam-6097	75	1	for	for	ADP
ejpam-6097	75	2	all	all	PRON
ejpam-6097	75	3	p	p	X
ejpam-6097	75	4	>	>	X
ejpam-6097	75	5	1	1	NUM
ejpam-6097	75	6	and	and	CCONJ
ejpam-6097	75	7	some	some	PRON
ejpam-6097	75	8	c	c	PROPN
ejpam-6097	75	9	>	>	X
ejpam-6097	75	10	0	0	PROPN
ejpam-6097	75	11	,	,	PUNCT
ejpam-6097	75	12	the	the	DET
ejpam-6097	75	13	following	follow	VERB
ejpam-6097	75	14	condition	condition	NOUN
ejpam-6097	75	15	is	be	AUX
ejpam-6097	75	16	true101	true101	PROPN
ejpam-6097	75	17	e	e	NOUN
ejpam-6097	75	18	sup	sup	NOUN
ejpam-6097	75	19	0≤t≤t	0≤t≤t	NUM
ejpam-6097	75	20	∥x∥p	∥x∥p	NOUN
ejpam-6097	75	21	≤	≤	NUM
ejpam-6097	75	22	c.	c.	NOUN
ejpam-6097	75	23	(	(	PUNCT
ejpam-6097	75	24	14	14	NUM
ejpam-6097	75	25	)	)	PUNCT
ejpam-6097	75	26	proof	proof	NOUN
ejpam-6097	75	27	.	.	PUNCT
ejpam-6097	76	1	from	from	ADP
ejpam-6097	76	2	(	(	PUNCT
ejpam-6097	76	3	7	7	NUM
ejpam-6097	76	4	)	)	PUNCT
ejpam-6097	76	5	,	,	PUNCT
ejpam-6097	76	6	we	we	PRON
ejpam-6097	76	7	have102	have102	VERB
ejpam-6097	76	8	x	x	X
ejpam-6097	76	9	=	=	PUNCT
ejpam-6097	77	1	x0	x0	PROPN
ejpam-6097	78	1	+	+	CCONJ
ejpam-6097	78	2	∫	∫	PROPN
ejpam-6097	78	3	t	t	PROPN
ejpam-6097	78	4	0	0	NUM
ejpam-6097	78	5	m(t	m(t	PROPN
ejpam-6097	78	6	,	,	PUNCT
ejpam-6097	78	7	x)ds+	x)ds+	PROPN
ejpam-6097	78	8	∫	∫	PROPN
ejpam-6097	79	1	t	t	PROPN
ejpam-6097	79	2	0	0	NUM
ejpam-6097	80	1	n(t	n(t	PROPN
ejpam-6097	80	2	,	,	PUNCT
ejpam-6097	80	3	x)db(t	x)db(t	NOUN
ejpam-6097	80	4	)	)	PUNCT
ejpam-6097	80	5	,	,	PUNCT
ejpam-6097	80	6	(	(	PUNCT
ejpam-6097	80	7	15	15	X
ejpam-6097	80	8	)	)	PUNCT
ejpam-6097	80	9	it	it	PRON
ejpam-6097	80	10	is	be	AUX
ejpam-6097	80	11	known	know	VERB
ejpam-6097	80	12	that	that	PRON
ejpam-6097	80	13	see	see	VERB
ejpam-6097	80	14	for	for	ADP
ejpam-6097	80	15	example	example	NOUN
ejpam-6097	80	16	[	[	X
ejpam-6097	80	17	27	27	NUM
ejpam-6097	80	18	]	]	PUNCT
ejpam-6097	80	19	for	for	ADP
ejpam-6097	80	20	αk	αk	NOUN
ejpam-6097	80	21	∈	∈	PROPN
ejpam-6097	80	22	r	r	NOUN
ejpam-6097	80	23	,	,	PUNCT
ejpam-6097	80	24	r	r	NOUN
ejpam-6097	80	25	∈	∈	PROPN
ejpam-6097	81	1	[	[	X
ejpam-6097	81	2	0,∞	0,∞	NOUN
ejpam-6097	81	3	)	)	PUNCT
ejpam-6097	81	4	and	and	CCONJ
ejpam-6097	81	5	1	1	NUM
ejpam-6097	81	6	≤	≤	NOUN
ejpam-6097	82	1	p	p	X
ejpam-6097	82	2	<	<	X
ejpam-6097	82	3	∞	∞	PROPN
ejpam-6097	82	4	,	,	PUNCT
ejpam-6097	82	5	that103	that103	NUM
ejpam-6097	82	6	r∑	r∑	NOUN
ejpam-6097	82	7	i=1	i=1	PROPN
ejpam-6097	82	8	αp	αp	NOUN
ejpam-6097	83	1	i	i	NOUN
ejpam-6097	83	2	≤	≤	X
ejpam-6097	83	3	(	(	PUNCT
ejpam-6097	83	4	r∑	r∑	NOUN
ejpam-6097	83	5	i=1	i=1	X
ejpam-6097	83	6	αi	αi	ADV
ejpam-6097	83	7	)	)	PUNCT
ejpam-6097	84	1	p	p	NOUN
ejpam-6097	84	2	≤	≤	PROPN
ejpam-6097	84	3	rp−1	rp−1	NOUN
ejpam-6097	84	4	r∑	r∑	NOUN
ejpam-6097	84	5	i=1	i=1	PROPN
ejpam-6097	84	6	αp	αp	INTJ
ejpam-6097	85	1	i	i	PRON
ejpam-6097	85	2	.	.	PUNCT
ejpam-6097	86	1	(	(	PUNCT
ejpam-6097	86	2	16	16	NUM
ejpam-6097	86	3	)	)	PUNCT
ejpam-6097	86	4	from	from	ADP
ejpam-6097	86	5	(	(	PUNCT
ejpam-6097	86	6	16	16	NUM
ejpam-6097	86	7	)	)	PUNCT
ejpam-6097	86	8	,	,	PUNCT
ejpam-6097	86	9	the	the	DET
ejpam-6097	86	10	sup	sup	NOUN
ejpam-6097	86	11	over	over	ADP
ejpam-6097	86	12	[	[	X
ejpam-6097	86	13	0	0	NUM
ejpam-6097	86	14	,	,	PUNCT
ejpam-6097	86	15	t	t	NOUN
ejpam-6097	86	16	]	]	PUNCT
ejpam-6097	86	17	and	and	CCONJ
ejpam-6097	86	18	the	the	DET
ejpam-6097	86	19	expectation	expectation	NOUN
ejpam-6097	86	20	we	we	PRON
ejpam-6097	86	21	have	have	VERB
ejpam-6097	86	22	the	the	DET
ejpam-6097	86	23	following:104	following:104	NOUN
ejpam-6097	86	24	e	e	NOUN
ejpam-6097	86	25	sup	sup	NOUN
ejpam-6097	86	26	0≤t≤t	0≤t≤t	NUM
ejpam-6097	86	27	∥x∥q	∥x∥q	NOUN
ejpam-6097	86	28	≤3q−1	≤3q−1	NOUN
ejpam-6097	86	29	(	(	PUNCT
ejpam-6097	86	30	|x0|q	|x0|q	VERB
ejpam-6097	86	31	+	+	NUM
ejpam-6097	86	32	e	e	NOUN
ejpam-6097	86	33	sup	sup	NOUN
ejpam-6097	86	34	0≤t≤t	0≤t≤t	NUM
ejpam-6097	86	35	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6097	86	36	∫	∫	PROPN
ejpam-6097	86	37	t	t	PROPN
ejpam-6097	86	38	0	0	SYM
ejpam-6097	86	39	m(t	m(t	PROPN
ejpam-6097	86	40	,	,	PUNCT
ejpam-6097	87	1	x)dt	x)dt	PROPN
ejpam-6097	87	2	∣∣∣∣q	∣∣∣∣q	PROPN
ejpam-6097	88	1	+	+	CCONJ
ejpam-6097	88	2	e	e	PROPN
ejpam-6097	88	3	sup	sup	NOUN
ejpam-6097	88	4	0≤t≤t	0≤t≤t	NUM
ejpam-6097	88	5	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6097	88	6	∫	∫	PROPN
ejpam-6097	88	7	t	t	PROPN
ejpam-6097	88	8	0	0	NUM
ejpam-6097	89	1	n(t	n(t	PROPN
ejpam-6097	89	2	,	,	PUNCT
ejpam-6097	89	3	x)db(t	x)db(t	NUM
ejpam-6097	89	4	)	)	PUNCT
ejpam-6097	89	5	∣∣∣∣q	∣∣∣∣q	PROPN
ejpam-6097	89	6	)	)	PUNCT
ejpam-6097	89	7	.	.	PUNCT
ejpam-6097	90	1	(	(	PUNCT
ejpam-6097	90	2	17	17	NUM
ejpam-6097	90	3	)	)	PUNCT
ejpam-6097	90	4	using	use	VERB
ejpam-6097	90	5	hölder	hölder	NOUN
ejpam-6097	90	6	inequality	inequality	NOUN
ejpam-6097	90	7	for	for	ADP
ejpam-6097	90	8	1	1	NUM
ejpam-6097	90	9	q	q	NOUN
ejpam-6097	91	1	+	+	NUM
ejpam-6097	91	2	1	1	NUM
ejpam-6097	91	3	q	q	NOUN
ejpam-6097	91	4	q−1	q−1	NOUN
ejpam-6097	91	5	=	=	NOUN
ejpam-6097	91	6	1	1	NUM
ejpam-6097	91	7	,	,	PUNCT
ejpam-6097	91	8	we	we	PRON
ejpam-6097	91	9	get105	get105	VERB
ejpam-6097	91	10	e	e	NOUN
ejpam-6097	91	11	sup	sup	NOUN
ejpam-6097	91	12	0≤t≤t	0≤t≤t	NUM
ejpam-6097	91	13	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6097	91	14	∫	∫	PROPN
ejpam-6097	91	15	t	t	PROPN
ejpam-6097	91	16	0	0	SYM
ejpam-6097	91	17	m(t	m(t	PROPN
ejpam-6097	91	18	,	,	PUNCT
ejpam-6097	91	19	x)dt	x)dt	PROPN
ejpam-6097	91	20	∣∣∣∣q	∣∣∣∣q	PROPN
ejpam-6097	91	21	≤	≤	PROPN
ejpam-6097	91	22	e	e	PROPN
ejpam-6097	91	23	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6097	91	24	∫	∫	PROPN
ejpam-6097	91	25	t	t	PROPN
ejpam-6097	91	26	0	0	SYM
ejpam-6097	91	27	m(t	m(t	PROPN
ejpam-6097	91	28	,	,	PUNCT
ejpam-6097	91	29	x)dt	x)dt	PROPN
ejpam-6097	91	30	∣∣∣∣q	∣∣∣∣q	PROPN
ejpam-6097	91	31	≤	≤	PROPN
ejpam-6097	91	32	e	e	X
ejpam-6097	91	33	(	(	PUNCT
ejpam-6097	91	34	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6097	91	35	∫	∫	PROPN
ejpam-6097	91	36	t	t	PROPN
ejpam-6097	91	37	0	0	SYM
ejpam-6097	91	38	m(t	m(t	PROPN
ejpam-6097	91	39	,	,	PUNCT
ejpam-6097	91	40	x)dt	x)dt	PROPN
ejpam-6097	91	41	∣∣∣∣q)q×	∣∣∣∣q)q×	VERB
ejpam-6097	91	42	1	1	NUM
ejpam-6097	91	43	q	q	NOUN
ejpam-6097	91	44	×	×	NOUN
ejpam-6097	91	45	(	(	PUNCT
ejpam-6097	91	46	∫	∫	PROPN
ejpam-6097	91	47	t	t	PROPN
ejpam-6097	91	48	0	0	NUM
ejpam-6097	91	49	(	(	PUNCT
ejpam-6097	91	50	1	1	NUM
ejpam-6097	91	51	)	)	PUNCT
ejpam-6097	91	52	q	q	NOUN
ejpam-6097	92	1	q−1	q−1	PROPN
ejpam-6097	92	2	dt	dt	X
ejpam-6097	92	3	)	)	PUNCT
ejpam-6097	92	4	q×	q×	PROPN
ejpam-6097	93	1	q−1	q−1	PROPN
ejpam-6097	93	2	q	q	PROPN
ejpam-6097	93	3	≤	≤	PROPN
ejpam-6097	93	4	t	t	X
ejpam-6097	93	5	q−1e	q−1e	NOUN
ejpam-6097	93	6	(	(	PUNCT
ejpam-6097	93	7	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6097	93	8	∫	∫	PROPN
ejpam-6097	93	9	t	t	PROPN
ejpam-6097	93	10	0	0	SYM
ejpam-6097	93	11	m(t	m(t	PROPN
ejpam-6097	93	12	,	,	PUNCT
ejpam-6097	93	13	x)dt	x)dt	PROPN
ejpam-6097	93	14	∣∣∣∣q	∣∣∣∣q	PROPN
ejpam-6097	93	15	)	)	PUNCT
ejpam-6097	93	16	.	.	PUNCT
ejpam-6097	94	1	(	(	PUNCT
ejpam-6097	94	2	18	18	NUM
ejpam-6097	94	3	)	)	PUNCT
ejpam-6097	94	4	m.	m.	NOUN
ejpam-6097	94	5	mohamed	mohamed	PROPN
ejpam-6097	94	6	et	et	PROPN
ejpam-6097	94	7	al	al	PROPN
ejpam-6097	94	8	.	.	PUNCT
ejpam-6097	94	9	/	/	SYM
ejpam-6097	94	10	eur	eur	PROPN
ejpam-6097	94	11	.	.	PUNCT
ejpam-6097	95	1	j.	j.	PROPN
ejpam-6097	95	2	pure	pure	PROPN
ejpam-6097	95	3	appl	appl	PROPN
ejpam-6097	95	4	.	.	PROPN
ejpam-6097	95	5	math	math	PROPN
ejpam-6097	95	6	,	,	PUNCT
ejpam-6097	95	7	18	18	NUM
ejpam-6097	95	8	(	(	PUNCT
ejpam-6097	95	9	2	2	NUM
ejpam-6097	95	10	)	)	PUNCT
ejpam-6097	95	11	(	(	PUNCT
ejpam-6097	95	12	2025	2025	NUM
ejpam-6097	95	13	)	)	PUNCT
ejpam-6097	95	14	,	,	PUNCT
ejpam-6097	95	15	6097	6097	NUM
ejpam-6097	95	16	6	6	NUM
ejpam-6097	95	17	of	of	ADP
ejpam-6097	95	18	19	19	NUM
ejpam-6097	95	19	from	from	ADP
ejpam-6097	95	20	lemma	lemma	PROPN
ejpam-6097	95	21	1	1	NUM
ejpam-6097	95	22	and	and	CCONJ
ejpam-6097	95	23	(	(	PUNCT
ejpam-6097	95	24	16	16	NUM
ejpam-6097	95	25	)	)	PUNCT
ejpam-6097	96	1	we	we	PRON
ejpam-6097	96	2	have106	have106	PROPN
ejpam-6097	97	1	e	e	X
ejpam-6097	97	2	∫	∫	PROPN
ejpam-6097	97	3	t	t	PROPN
ejpam-6097	97	4	0	0	NUM
ejpam-6097	97	5	(	(	PUNCT
ejpam-6097	97	6	|m(t	|m(t	PROPN
ejpam-6097	97	7	,	,	PUNCT
ejpam-6097	97	8	x)|2	x)|2	PROPN
ejpam-6097	97	9	)	)	PUNCT
ejpam-6097	98	1	q	q	PROPN
ejpam-6097	98	2	2	2	NUM
ejpam-6097	98	3	dt	dt	NOUN
ejpam-6097	98	4	≤	≤	NUM
ejpam-6097	98	5	ec	ec	PROPN
ejpam-6097	98	6	q	q	PROPN
ejpam-6097	98	7	2	2	NUM
ejpam-6097	98	8	∫	∫	NOUN
ejpam-6097	98	9	t	t	NOUN
ejpam-6097	98	10	0	0	NUM
ejpam-6097	98	11	(	(	PUNCT
ejpam-6097	98	12	1	1	NUM
ejpam-6097	98	13	+	+	CCONJ
ejpam-6097	98	14	∥x∥2	∥x∥2	NOUN
ejpam-6097	98	15	)	)	PUNCT
ejpam-6097	98	16	q	q	PROPN
ejpam-6097	99	1	2	2	NUM
ejpam-6097	99	2	dt	dt	NOUN
ejpam-6097	99	3	≤	≤	NUM
ejpam-6097	99	4	c	c	NOUN
ejpam-6097	99	5	q	q	PROPN
ejpam-6097	99	6	2	2	NUM
ejpam-6097	99	7	2	2	NUM
ejpam-6097	99	8	q	q	NOUN
ejpam-6097	99	9	2	2	NUM
ejpam-6097	99	10	−1e	−1e	NOUN
ejpam-6097	99	11	∫	∫	PROPN
ejpam-6097	99	12	t	t	NOUN
ejpam-6097	99	13	0	0	NUM
ejpam-6097	99	14	(	(	PUNCT
ejpam-6097	99	15	1	1	NUM
ejpam-6097	99	16	+	+	NUM
ejpam-6097	99	17	∥x∥q)dt	∥x∥q)dt	NOUN
ejpam-6097	99	18	≤	≤	NUM
ejpam-6097	99	19	c	c	NOUN
ejpam-6097	99	20	q	q	PROPN
ejpam-6097	99	21	2	2	NUM
ejpam-6097	99	22	2	2	NUM
ejpam-6097	99	23	q	q	NOUN
ejpam-6097	99	24	2	2	NUM
ejpam-6097	99	25	−1	−1	NOUN
ejpam-6097	99	26	(	(	PUNCT
ejpam-6097	99	27	t	t	PROPN
ejpam-6097	99	28	+	+	CCONJ
ejpam-6097	99	29	e	e	PROPN
ejpam-6097	99	30	∫	∫	PROPN
ejpam-6097	99	31	t	t	PROPN
ejpam-6097	99	32	0	0	NUM
ejpam-6097	99	33	∥x∥qdt	∥x∥qdt	PRON
ejpam-6097	99	34	)	)	PUNCT
ejpam-6097	99	35	.	.	PUNCT
ejpam-6097	100	1	(	(	PUNCT
ejpam-6097	100	2	19	19	NUM
ejpam-6097	100	3	)	)	PUNCT
ejpam-6097	100	4	from	from	ADP
ejpam-6097	100	5	the	the	DET
ejpam-6097	100	6	inequality	inequality	NOUN
ejpam-6097	100	7	(	(	PUNCT
ejpam-6097	100	8	18	18	NUM
ejpam-6097	100	9	)	)	PUNCT
ejpam-6097	100	10	and	and	CCONJ
ejpam-6097	100	11	(	(	PUNCT
ejpam-6097	100	12	19	19	NUM
ejpam-6097	100	13	)	)	PUNCT
ejpam-6097	100	14	,	,	PUNCT
ejpam-6097	100	15	we	we	PRON
ejpam-6097	100	16	have107	have107	PROPN
ejpam-6097	100	17	e	e	SYM
ejpam-6097	100	18	sup	sup	NOUN
ejpam-6097	100	19	0≤t≤t	0≤t≤t	NUM
ejpam-6097	100	20	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6097	100	21	∫	∫	PROPN
ejpam-6097	100	22	t	t	PROPN
ejpam-6097	100	23	0	0	SYM
ejpam-6097	100	24	m(t	m(t	PROPN
ejpam-6097	100	25	,	,	PUNCT
ejpam-6097	100	26	x)dt	x)dt	PROPN
ejpam-6097	100	27	∣∣∣∣q	∣∣∣∣q	PROPN
ejpam-6097	100	28	≤	≤	PUNCT
ejpam-6097	101	1	[	[	X
ejpam-6097	101	2	c	c	NOUN
ejpam-6097	101	3	q	q	PROPN
ejpam-6097	101	4	2	2	NUM
ejpam-6097	101	5	2	2	NUM
ejpam-6097	101	6	q	q	NOUN
ejpam-6097	101	7	2	2	NUM
ejpam-6097	101	8	−1	−1	NOUN
ejpam-6097	101	9	t	t	NOUN
ejpam-6097	101	10	q	q	NOUN
ejpam-6097	102	1	+	+	CCONJ
ejpam-6097	102	2	c	c	NOUN
ejpam-6097	102	3	q	q	PROPN
ejpam-6097	102	4	2	2	NUM
ejpam-6097	102	5	2	2	NUM
ejpam-6097	102	6	q	q	NOUN
ejpam-6097	102	7	2	2	NUM
ejpam-6097	102	8	−1	−1	NOUN
ejpam-6097	102	9	t	t	NOUN
ejpam-6097	102	10	q−1	q−1	PROPN
ejpam-6097	102	11	]	]	PUNCT
ejpam-6097	103	1	e	e	X
ejpam-6097	103	2	∫	∫	PROPN
ejpam-6097	103	3	t	t	PROPN
ejpam-6097	103	4	0	0	NUM
ejpam-6097	103	5	∥x∥qdt	∥x∥qdt	PROPN
ejpam-6097	103	6	.	.	PUNCT
ejpam-6097	104	1	(	(	PUNCT
ejpam-6097	104	2	20	20	NUM
ejpam-6097	104	3	)	)	PUNCT
ejpam-6097	104	4	to	to	PART
ejpam-6097	104	5	deal	deal	VERB
ejpam-6097	104	6	with	with	ADP
ejpam-6097	104	7	the	the	DET
ejpam-6097	104	8	stochastic	stochastic	ADJ
ejpam-6097	104	9	term	term	NOUN
ejpam-6097	104	10	,	,	PUNCT
ejpam-6097	104	11	we	we	PRON
ejpam-6097	104	12	employ	employ	VERB
ejpam-6097	104	13	burkholder	burkholder	NOUN
ejpam-6097	104	14	-	-	PUNCT
ejpam-6097	104	15	davis	davis	PROPN
ejpam-6097	104	16	-	-	PUNCT
ejpam-6097	104	17	gundyand	gundyand	NOUN
ejpam-6097	104	18	hölder	hölder	NOUN
ejpam-6097	104	19	inequal-108	inequal-108	ADJ
ejpam-6097	104	20	ities	itie	NOUN
ejpam-6097	104	21	and	and	CCONJ
ejpam-6097	104	22	it	it	PRON
ejpam-6097	104	23	yields109	yields109	PROPN
ejpam-6097	105	1	e	e	PRON
ejpam-6097	105	2	sup	sup	NOUN
ejpam-6097	105	3	0≤t≤t	0≤t≤t	NUM
ejpam-6097	105	4	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6097	105	5	∫	∫	PROPN
ejpam-6097	105	6	t	t	PROPN
ejpam-6097	105	7	0	0	NUM
ejpam-6097	106	1	n(t	n(t	PROPN
ejpam-6097	106	2	,	,	PUNCT
ejpam-6097	106	3	x)db(s	x)db(s	NUM
ejpam-6097	106	4	)	)	PUNCT
ejpam-6097	106	5	∣∣∣∣q	∣∣∣∣q	PROPN
ejpam-6097	106	6	≤	≤	PROPN
ejpam-6097	106	7	cbe	cbe	PROPN
ejpam-6097	106	8	(	(	PUNCT
ejpam-6097	106	9	∫	∫	PROPN
ejpam-6097	106	10	t	t	PROPN
ejpam-6097	106	11	0	0	PROPN
ejpam-6097	106	12	|n(t	|n(t	PROPN
ejpam-6097	106	13	,	,	PUNCT
ejpam-6097	106	14	x)|2dt	x)|2dt	NOUN
ejpam-6097	106	15	)	)	PUNCT
ejpam-6097	106	16	q	q	PROPN
ejpam-6097	106	17	2	2	NUM
ejpam-6097	106	18	cb	cb	X
ejpam-6097	106	19	(	(	PUNCT
ejpam-6097	106	20	e	e	PROPN
ejpam-6097	106	21	∫	∫	PROPN
ejpam-6097	106	22	t	t	PROPN
ejpam-6097	106	23	0	0	PROPN
ejpam-6097	106	24	|n(t	|n(t	PROPN
ejpam-6097	106	25	,	,	PUNCT
ejpam-6097	106	26	x|qdt	x|qdt	PROPN
ejpam-6097	106	27	)	)	PUNCT
ejpam-6097	106	28	(	(	PUNCT
ejpam-6097	106	29	∫	∫	PROPN
ejpam-6097	106	30	t	t	PROPN
ejpam-6097	106	31	0	0	NUM
ejpam-6097	106	32	(	(	PUNCT
ejpam-6097	106	33	1	1	NUM
ejpam-6097	106	34	)	)	PUNCT
ejpam-6097	106	35	q	q	NOUN
ejpam-6097	106	36	q−2dt	q−2dt	NOUN
ejpam-6097	106	37	)	)	PUNCT
ejpam-6097	106	38	q	q	NOUN
ejpam-6097	107	1	2	2	NUM
ejpam-6097	107	2	×	×	NOUN
ejpam-6097	107	3	q−2	q−2	PROPN
ejpam-6097	107	4	q	q	PROPN
ejpam-6097	107	5	≤	≤	NUM
ejpam-6097	107	6	cbt	cbt	NOUN
ejpam-6097	107	7	q−2	q−2	PROPN
ejpam-6097	107	8	2	2	NUM
ejpam-6097	107	9	e	e	NOUN
ejpam-6097	107	10	∫	∫	PROPN
ejpam-6097	107	11	t	t	PROPN
ejpam-6097	107	12	0	0	PROPN
ejpam-6097	108	1	|n(t	|n(t	PROPN
ejpam-6097	108	2	,	,	PUNCT
ejpam-6097	108	3	x)|qdt	x)|qdt	PROPN
ejpam-6097	108	4	.	.	PROPN
ejpam-6097	109	1	(	(	PUNCT
ejpam-6097	109	2	21	21	NUM
ejpam-6097	109	3	)	)	PUNCT
ejpam-6097	109	4	again	again	ADV
ejpam-6097	109	5	we	we	PRON
ejpam-6097	109	6	use	use	VERB
ejpam-6097	109	7	lemma	lemma	PROPN
ejpam-6097	109	8	1	1	NUM
ejpam-6097	109	9	and	and	CCONJ
ejpam-6097	109	10	inequality	inequality	NOUN
ejpam-6097	109	11	(	(	PUNCT
ejpam-6097	109	12	16	16	NUM
ejpam-6097	109	13	)	)	PUNCT
ejpam-6097	109	14	for	for	ADP
ejpam-6097	109	15	p	p	NOUN
ejpam-6097	109	16	=	=	X
ejpam-6097	109	17	q	q	PROPN
ejpam-6097	109	18	2	2	NUM
ejpam-6097	109	19	to	to	ADP
ejpam-6097	109	20	get110	get110	PROPN
ejpam-6097	109	21	e	e	PROPN
ejpam-6097	109	22	sup	sup	NOUN
ejpam-6097	109	23	0≤t≤t	0≤t≤t	NUM
ejpam-6097	109	24	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6097	109	25	∫	∫	PROPN
ejpam-6097	109	26	t	t	PROPN
ejpam-6097	109	27	0	0	NUM
ejpam-6097	109	28	n(s	n(s	PROPN
ejpam-6097	109	29	,	,	PUNCT
ejpam-6097	109	30	x)ds	x)ds	PROPN
ejpam-6097	109	31	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6097	109	32	≤	≤	NUM
ejpam-6097	109	33	cbt	cbt	NOUN
ejpam-6097	109	34	q−2	q−2	PROPN
ejpam-6097	109	35	2	2	NUM
ejpam-6097	109	36	c	c	NOUN
ejpam-6097	109	37	q	q	NOUN
ejpam-6097	109	38	2	2	NUM
ejpam-6097	109	39	2	2	NUM
ejpam-6097	109	40	q	q	NOUN
ejpam-6097	109	41	2	2	NUM
ejpam-6097	109	42	−1e	−1e	NOUN
ejpam-6097	109	43	∫	∫	PROPN
ejpam-6097	109	44	t	t	NOUN
ejpam-6097	109	45	0	0	NUM
ejpam-6097	110	1	(	(	PUNCT
ejpam-6097	110	2	1	1	NUM
ejpam-6097	110	3	+	+	NUM
ejpam-6097	110	4	∥x∥q)dt	∥x∥q)dt	NOUN
ejpam-6097	110	5	≤	≤	NOUN
ejpam-6097	110	6	cbt	cbt	NOUN
ejpam-6097	110	7	q−2	q−2	PROPN
ejpam-6097	110	8	2	2	NUM
ejpam-6097	110	9	c	c	NOUN
ejpam-6097	110	10	q	q	NOUN
ejpam-6097	110	11	2	2	NUM
ejpam-6097	110	12	2	2	NUM
ejpam-6097	110	13	q	q	NOUN
ejpam-6097	110	14	2	2	NUM
ejpam-6097	110	15	−1	−1	NOUN
ejpam-6097	110	16	[	[	PUNCT
ejpam-6097	110	17	t	t	NOUN
ejpam-6097	110	18	+	+	CCONJ
ejpam-6097	110	19	e	e	PROPN
ejpam-6097	110	20	∫	∫	PROPN
ejpam-6097	110	21	t	t	PROPN
ejpam-6097	110	22	0	0	NUM
ejpam-6097	110	23	∥x∥qdt	∥x∥qdt	PRON
ejpam-6097	110	24	]	]	PUNCT
ejpam-6097	110	25	≤	≤	NUM
ejpam-6097	110	26	cbt	cbt	NOUN
ejpam-6097	110	27	q	q	PROPN
ejpam-6097	110	28	2c	2c	PROPN
ejpam-6097	110	29	q	q	NOUN
ejpam-6097	110	30	2	2	NUM
ejpam-6097	110	31	2	2	NUM
ejpam-6097	110	32	q	q	NOUN
ejpam-6097	110	33	2	2	NUM
ejpam-6097	110	34	−1	−1	NOUN
ejpam-6097	110	35	+	+	NOUN
ejpam-6097	110	36	cbt	cbt	NOUN
ejpam-6097	110	37	q−2	q−2	PROPN
ejpam-6097	110	38	2	2	NUM
ejpam-6097	110	39	c	c	NOUN
ejpam-6097	110	40	q	q	NOUN
ejpam-6097	110	41	2	2	NUM
ejpam-6097	110	42	2	2	NUM
ejpam-6097	110	43	q	q	NOUN
ejpam-6097	110	44	2	2	NUM
ejpam-6097	110	45	−1e	−1e	NOUN
ejpam-6097	110	46	∫	∫	PROPN
ejpam-6097	110	47	t	t	NOUN
ejpam-6097	110	48	0	0	NUM
ejpam-6097	110	49	∥x∥qdt	∥x∥qdt	X
ejpam-6097	110	50	.	.	PUNCT
ejpam-6097	111	1	(	(	PUNCT
ejpam-6097	111	2	22	22	NUM
ejpam-6097	111	3	)	)	PUNCT
ejpam-6097	111	4	from	from	ADP
ejpam-6097	111	5	(	(	PUNCT
ejpam-6097	111	6	17	17	NUM
ejpam-6097	111	7	)	)	PUNCT
ejpam-6097	111	8	,	,	PUNCT
ejpam-6097	111	9	(	(	PUNCT
ejpam-6097	111	10	21	21	NUM
ejpam-6097	111	11	)	)	PUNCT
ejpam-6097	111	12	and	and	CCONJ
ejpam-6097	111	13	(	(	PUNCT
ejpam-6097	111	14	22	22	NUM
ejpam-6097	111	15	)	)	PUNCT
ejpam-6097	111	16	one	one	PRON
ejpam-6097	111	17	uses	use	VERB
ejpam-6097	111	18	grownall	grownall	NOUN
ejpam-6097	111	19	’s	’s	PART
ejpam-6097	111	20	inequality	inequality	NOUN
ejpam-6097	111	21	to	to	PART
ejpam-6097	111	22	complete	complete	VERB
ejpam-6097	111	23	the	the	DET
ejpam-6097	111	24	proof.111	proof.111	ADJ
ejpam-6097	111	25	4	4	NUM
ejpam-6097	111	26	.	.	PUNCT
ejpam-6097	111	27	stochastic	stochastic	ADJ
ejpam-6097	111	28	mean	mean	NOUN
ejpam-6097	111	29	square	square	PROPN
ejpam-6097	111	30	stability112	stability112	PROPN
ejpam-6097	111	31	here	here	ADV
ejpam-6097	111	32	,	,	PUNCT
ejpam-6097	111	33	we	we	PRON
ejpam-6097	111	34	investigate	investigate	VERB
ejpam-6097	111	35	the	the	DET
ejpam-6097	111	36	stochastic	stochastic	ADJ
ejpam-6097	111	37	mean	mean	ADJ
ejpam-6097	111	38	square	square	ADJ
ejpam-6097	111	39	stability	stability	NOUN
ejpam-6097	111	40	for	for	ADP
ejpam-6097	111	41	the	the	DET
ejpam-6097	111	42	system	system	NOUN
ejpam-6097	111	43	(	(	PUNCT
ejpam-6097	111	44	4)-(6	4)-(6	NUM
ejpam-6097	111	45	)	)	PUNCT
ejpam-6097	111	46	around113	around113	PROPN
ejpam-6097	111	47	the	the	DET
ejpam-6097	111	48	interior	interior	ADJ
ejpam-6097	111	49	equilibrium	equilibrium	NOUN
ejpam-6097	111	50	point	point	NOUN
ejpam-6097	111	51	of	of	ADP
ejpam-6097	111	52	the	the	DET
ejpam-6097	111	53	deterministic	deterministic	ADJ
ejpam-6097	111	54	version	version	NOUN
ejpam-6097	111	55	(	(	PUNCT
ejpam-6097	111	56	1)-(3	1)-(3	NUM
ejpam-6097	111	57	)	)	PUNCT
ejpam-6097	111	58	.	.	PUNCT
ejpam-6097	112	1	note	note	VERB
ejpam-6097	112	2	that	that	SCONJ
ejpam-6097	112	3	our	our	PRON
ejpam-6097	112	4	system114	system114	PROPN
ejpam-6097	112	5	has	have	VERB
ejpam-6097	112	6	three	three	NUM
ejpam-6097	112	7	non	non	ADJ
ejpam-6097	112	8	-	-	ADJ
ejpam-6097	112	9	negative	negative	ADJ
ejpam-6097	112	10	equilibrium	equilibrium	NOUN
ejpam-6097	112	11	points:115	points:115	PROPN
ejpam-6097	112	12	1	1	NUM
ejpam-6097	112	13	.	.	PUNCT
ejpam-6097	113	1	p0	p0	NOUN
ejpam-6097	113	2	=	=	SYM
ejpam-6097	113	3	(	(	PUNCT
ejpam-6097	113	4	0	0	NUM
ejpam-6097	113	5	,	,	PUNCT
ejpam-6097	113	6	0)116	0)116	NUM
ejpam-6097	113	7	m.	m.	NOUN
ejpam-6097	113	8	mohamed	mohamed	PROPN
ejpam-6097	113	9	et	et	PROPN
ejpam-6097	113	10	al	al	PROPN
ejpam-6097	113	11	.	.	PUNCT
ejpam-6097	113	12	/	/	SYM
ejpam-6097	113	13	eur	eur	PROPN
ejpam-6097	113	14	.	.	PUNCT
ejpam-6097	114	1	j.	j.	PROPN
ejpam-6097	114	2	pure	pure	PROPN
ejpam-6097	114	3	appl	appl	PROPN
ejpam-6097	114	4	.	.	PROPN
ejpam-6097	114	5	math	math	PROPN
ejpam-6097	114	6	,	,	PUNCT
ejpam-6097	114	7	18	18	NUM
ejpam-6097	114	8	(	(	PUNCT
ejpam-6097	114	9	2	2	NUM
ejpam-6097	114	10	)	)	PUNCT
ejpam-6097	114	11	(	(	PUNCT
ejpam-6097	114	12	2025	2025	NUM
ejpam-6097	114	13	)	)	PUNCT
ejpam-6097	114	14	,	,	PUNCT
ejpam-6097	114	15	6097	6097	NUM
ejpam-6097	114	16	7	7	NUM
ejpam-6097	114	17	of	of	ADP
ejpam-6097	114	18	19	19	NUM
ejpam-6097	114	19	2	2	NUM
ejpam-6097	114	20	.	.	PUNCT
ejpam-6097	115	1	p1	p1	NOUN
ejpam-6097	115	2	=	=	SYM
ejpam-6097	115	3	(	(	PUNCT
ejpam-6097	115	4	k	k	X
ejpam-6097	115	5	,	,	PUNCT
ejpam-6097	115	6	0)117	0)117	NUM
ejpam-6097	115	7	3	3	X
ejpam-6097	115	8	.	.	PUNCT
ejpam-6097	116	1	p	p	NOUN
ejpam-6097	116	2	∗	∗	NOUN
ejpam-6097	116	3	=	=	SYM
ejpam-6097	116	4	(	(	PUNCT
ejpam-6097	116	5	u∗	u∗	PROPN
ejpam-6097	116	6	,	,	PUNCT
ejpam-6097	116	7	v∗	v∗	PROPN
ejpam-6097	116	8	)	)	PUNCT
ejpam-6097	116	9	,	,	PUNCT
ejpam-6097	116	10	where	where	SCONJ
ejpam-6097	116	11	(	(	PUNCT
ejpam-6097	116	12	u∗	u∗	ADJ
ejpam-6097	116	13	,	,	PUNCT
ejpam-6097	116	14	v∗	v∗	PROPN
ejpam-6097	116	15	)	)	PUNCT
ejpam-6097	116	16	are	be	AUX
ejpam-6097	116	17	the	the	DET
ejpam-6097	116	18	real	real	ADJ
ejpam-6097	116	19	positive	positive	ADJ
ejpam-6097	116	20	roots	root	NOUN
ejpam-6097	116	21	of	of	ADP
ejpam-6097	116	22	the	the	DET
ejpam-6097	116	23	following	follow	VERB
ejpam-6097	116	24	system:118	system:118	PROPN
ejpam-6097	116	25			PROPN
ejpam-6097	116	26	ρu∗	ρu∗	NOUN
ejpam-6097	116	27	(	(	PUNCT
ejpam-6097	116	28	1−	1−	NUM
ejpam-6097	116	29	u∗	u∗	NOUN
ejpam-6097	116	30	k	k	PROPN
ejpam-6097	116	31	)	)	PUNCT
ejpam-6097	117	1	−	−	NOUN
ejpam-6097	118	1	αu∗v∗	αu∗v∗	NUM
ejpam-6097	118	2	1	1	NUM
ejpam-6097	118	3	+	+	CCONJ
ejpam-6097	118	4	βu∗	βu∗	ADJ
ejpam-6097	118	5	=	=	SYM
ejpam-6097	118	6	0	0	NUM
ejpam-6097	118	7	,	,	PUNCT
ejpam-6097	118	8	−σv∗	−σv∗	PUNCT
ejpam-6097	119	1	+	+	CCONJ
ejpam-6097	119	2	γu∗v∗	γu∗v∗	NOUN
ejpam-6097	119	3	1	1	NUM
ejpam-6097	119	4	+	+	CCONJ
ejpam-6097	119	5	βu∗	βu∗	ADP
ejpam-6097	119	6	−	−	PROPN
ejpam-6097	119	7	λv∗	λv∗	NOUN
ejpam-6097	119	8	2	2	NUM
ejpam-6097	119	9	=	=	SYM
ejpam-6097	119	10	0	0	NUM
ejpam-6097	119	11	.	.	PUNCT
ejpam-6097	120	1	(	(	PUNCT
ejpam-6097	120	2	23	23	NUM
ejpam-6097	120	3	)	)	PUNCT
ejpam-6097	120	4	(	(	PUNCT
ejpam-6097	120	5	24	24	NUM
ejpam-6097	120	6	)	)	PUNCT
ejpam-6097	120	7	the	the	DET
ejpam-6097	120	8	stochastic	stochastic	ADJ
ejpam-6097	120	9	mean	mean	NOUN
ejpam-6097	120	10	square	square	ADJ
ejpam-6097	120	11	stability	stability	NOUN
ejpam-6097	120	12	will	will	AUX
ejpam-6097	120	13	be	be	AUX
ejpam-6097	120	14	studied	study	VERB
ejpam-6097	120	15	around	around	ADP
ejpam-6097	120	16	the	the	DET
ejpam-6097	120	17	interior	interior	ADJ
ejpam-6097	120	18	positive	positive	ADJ
ejpam-6097	120	19	equilib-119	equilib-119	ADJ
ejpam-6097	120	20	rium	rium	NOUN
ejpam-6097	120	21	point	point	NOUN
ejpam-6097	120	22	(	(	PUNCT
ejpam-6097	120	23	u∗	u∗	ADJ
ejpam-6097	120	24	,	,	PUNCT
ejpam-6097	120	25	v∗	v∗	PROPN
ejpam-6097	120	26	)	)	PUNCT
ejpam-6097	120	27	,	,	PUNCT
ejpam-6097	120	28	we	we	PRON
ejpam-6097	120	29	have120	have120	PROPN
ejpam-6097	120	30			X
ejpam-6097	120	31	du	du	X
ejpam-6097	120	32	=	=	PUNCT
ejpam-6097	120	33	(	(	PUNCT
ejpam-6097	120	34	ρu	ρu	INTJ
ejpam-6097	120	35	(	(	PUNCT
ejpam-6097	120	36	1−	1−	NUM
ejpam-6097	120	37	u	u	NOUN
ejpam-6097	120	38	k	k	PROPN
ejpam-6097	120	39	)	)	PUNCT
ejpam-6097	121	1	−	−	PROPN
ejpam-6097	121	2	−αuv	−αuv	ADJ
ejpam-6097	121	3	1	1	NUM
ejpam-6097	122	1	+	+	NUM
ejpam-6097	122	2	βu	βu	X
ejpam-6097	122	3	)	)	PUNCT
ejpam-6097	122	4	dt+	dt+	NOUN
ejpam-6097	122	5	δ(u−	δ(u−	PRON
ejpam-6097	122	6	u∗)db1	u∗)db1	NOUN
ejpam-6097	122	7	,	,	PUNCT
ejpam-6097	122	8	dv	dv	PROPN
ejpam-6097	122	9	=	=	PUNCT
ejpam-6097	122	10	(	(	PUNCT
ejpam-6097	122	11	−σv	−σv	ADP
ejpam-6097	122	12	+	+	CCONJ
ejpam-6097	122	13	γuv	γuv	NUM
ejpam-6097	122	14	1	1	NUM
ejpam-6097	122	15	+	+	NUM
ejpam-6097	122	16	βu	βu	X
ejpam-6097	122	17	)	)	PUNCT
ejpam-6097	122	18	dt−	dt−	NUM
ejpam-6097	122	19	λv2	λv2	X
ejpam-6097	123	1	+	+	CCONJ
ejpam-6097	123	2	ϵ(v	ϵ(v	PROPN
ejpam-6097	123	3	−	−	NUM
ejpam-6097	123	4	v∗)dw2	v∗)dw2	NOUN
ejpam-6097	123	5	.	.	PUNCT
ejpam-6097	124	1	u0	u0	PROPN
ejpam-6097	124	2	=	=	PROPN
ejpam-6097	124	3	u(0	u(0	PROPN
ejpam-6097	124	4	)	)	PUNCT
ejpam-6097	124	5	,	,	PUNCT
ejpam-6097	124	6	v0	v0	NOUN
ejpam-6097	124	7	=	=	SYM
ejpam-6097	124	8	v(0	v(0	PROPN
ejpam-6097	124	9	)	)	PUNCT
ejpam-6097	124	10	.	.	PUNCT
ejpam-6097	125	1	(	(	PUNCT
ejpam-6097	125	2	25	25	NUM
ejpam-6097	125	3	)	)	PUNCT
ejpam-6097	125	4	(	(	PUNCT
ejpam-6097	125	5	26	26	NUM
ejpam-6097	125	6	)	)	PUNCT
ejpam-6097	125	7	(	(	PUNCT
ejpam-6097	125	8	27	27	NUM
ejpam-6097	125	9	)	)	PUNCT
ejpam-6097	125	10	by	by	ADP
ejpam-6097	125	11	setting	set	VERB
ejpam-6097	125	12	x	x	PUNCT
ejpam-6097	125	13	=	=	PUNCT
ejpam-6097	125	14	u−	u−	PROPN
ejpam-6097	125	15	u∗	u∗	NOUN
ejpam-6097	125	16	and	and	CCONJ
ejpam-6097	125	17	y	y	PROPN
ejpam-6097	125	18	=	=	NOUN
ejpam-6097	125	19	v	v	ADP
ejpam-6097	125	20	−	−	PROPN
ejpam-6097	125	21	v∗	v∗	NOUN
ejpam-6097	125	22	,	,	PUNCT
ejpam-6097	125	23	we	we	PRON
ejpam-6097	125	24	transform	transform	VERB
ejpam-6097	125	25	the	the	DET
ejpam-6097	125	26	model	model	NOUN
ejpam-6097	125	27	into:121	into:121	ADP
ejpam-6097	125	28	dx	dx	PROPN
ejpam-6097	125	29	=	=	SYM
ejpam-6097	125	30	f(t	f(t	PROPN
ejpam-6097	125	31	,	,	PUNCT
ejpam-6097	125	32	x)dt+	x)dt+	PROPN
ejpam-6097	125	33	g(t	g(t	PROPN
ejpam-6097	125	34	,	,	PUNCT
ejpam-6097	125	35	x)db	x)db	PROPN
ejpam-6097	125	36	,	,	PUNCT
ejpam-6097	125	37	(	(	PUNCT
ejpam-6097	125	38	28	28	NUM
ejpam-6097	125	39	)	)	PUNCT
ejpam-6097	125	40	where122	where122	X
ejpam-6097	125	41	x	x	PUNCT
ejpam-6097	126	1	=	=	PUNCT
ejpam-6097	127	1	[	[	PUNCT
ejpam-6097	127	2	x	x	X
ejpam-6097	127	3	y	y	PROPN
ejpam-6097	127	4	]	]	PUNCT
ejpam-6097	127	5	,	,	PUNCT
ejpam-6097	127	6	123	123	NUM
ejpam-6097	127	7	f(t	f(t	NOUN
ejpam-6097	127	8	,	,	PUNCT
ejpam-6097	127	9	x	x	X
ejpam-6097	127	10	)	)	PUNCT
ejpam-6097	127	11	=	=	SYM
ejpam-6097	128	1	[	[	PUNCT
ejpam-6097	128	2	u∗	u∗	ADJ
ejpam-6097	128	3	∂k1(u	∂k1(u	ADJ
ejpam-6097	128	4	∗,u∗	∗,u∗	NOUN
ejpam-6097	128	5	)	)	PUNCT
ejpam-6097	128	6	∂u	∂u	NOUN
ejpam-6097	129	1	+	+	CCONJ
ejpam-6097	129	2	k1	k1	PROPN
ejpam-6097	129	3	u∗	u∗	ADJ
ejpam-6097	129	4	∂k1(u	∂k1(u	PROPN
ejpam-6097	129	5	∗,u∗	∗,u∗	ADJ
ejpam-6097	129	6	)	)	PUNCT
ejpam-6097	129	7	∂v	∂v	PROPN
ejpam-6097	129	8	v∗	v∗	PROPN
ejpam-6097	129	9	∂k2(u	∂k2(u	PROPN
ejpam-6097	129	10	∗,v∗	∗,v∗	ADJ
ejpam-6097	129	11	)	)	PUNCT
ejpam-6097	129	12	∂u	∂u	PROPN
ejpam-6097	129	13	v∗∂k2(u∗,v∗	v∗∂k2(u∗,v∗	NOUN
ejpam-6097	129	14	)	)	PUNCT
ejpam-6097	130	1	∂v	∂v	PROPN
ejpam-6097	130	2	+	+	CCONJ
ejpam-6097	130	3	k2	k2	X
ejpam-6097	130	4	]	]	PUNCT
ejpam-6097	131	1	[	[	PUNCT
ejpam-6097	131	2	x	x	X
ejpam-6097	131	3	y	y	PROPN
ejpam-6097	131	4	]	]	PUNCT
ejpam-6097	131	5	,	,	PUNCT
ejpam-6097	131	6	where124	where124	PROPN
ejpam-6097	131	7	k1	k1	PROPN
ejpam-6097	131	8	=	=	SYM
ejpam-6097	131	9	ρ	ρ	PROPN
ejpam-6097	131	10	(	(	PUNCT
ejpam-6097	131	11	1−	1−	NUM
ejpam-6097	131	12	u	u	NOUN
ejpam-6097	131	13	k	k	PROPN
ejpam-6097	131	14	)	)	PUNCT
ejpam-6097	132	1	−	−	ADP
ejpam-6097	132	2	αv	αv	NOUN
ejpam-6097	132	3	1	1	NUM
ejpam-6097	132	4	+	+	NUM
ejpam-6097	132	5	βu	βu	PROPN
ejpam-6097	132	6	,	,	PUNCT
ejpam-6097	132	7	k2	k2	NOUN
ejpam-6097	132	8	=	=	PUNCT
ejpam-6097	132	9	−σ	−σ	NOUN
ejpam-6097	133	1	+	+	CCONJ
ejpam-6097	133	2	γu	γu	INTJ
ejpam-6097	133	3	1	1	NUM
ejpam-6097	134	1	+	+	CCONJ
ejpam-6097	134	2	βu	βu	PUNCT
ejpam-6097	135	1	λv	λv	NOUN
ejpam-6097	135	2	.	.	PUNCT
ejpam-6097	136	1	this	this	DET
ejpam-6097	136	2	gives125	gives125	PROPN
ejpam-6097	136	3	f(t	f(t	PROPN
ejpam-6097	136	4	,	,	PUNCT
ejpam-6097	136	5	x	x	NOUN
ejpam-6097	136	6	)	)	PUNCT
ejpam-6097	137	1	=	=	SYM
ejpam-6097	137	2	u∗	u∗	NOUN
ejpam-6097	137	3	(	(	PUNCT
ejpam-6097	137	4	−ρ	−ρ	NOUN
ejpam-6097	137	5	k	k	X
ejpam-6097	137	6	+	+	PUNCT
ejpam-6097	137	7	αβv∗	αβv∗	NOUN
ejpam-6097	137	8	(	(	PUNCT
ejpam-6097	137	9	1+βu)2	1+βu)2	NUM
ejpam-6097	137	10	)	)	PUNCT
ejpam-6097	137	11	u∗	u∗	INTJ
ejpam-6097	137	12	(	(	PUNCT
ejpam-6097	137	13	−α	−α	PROPN
ejpam-6097	137	14	1+βu∗	1+βu∗	NUM
ejpam-6097	137	15	)	)	PUNCT
ejpam-6097	137	16	v∗	v∗	NOUN
ejpam-6097	137	17	(	(	PUNCT
ejpam-6097	137	18	(	(	PUNCT
ejpam-6097	137	19	1+βu∗)γ−γβu∗	1+βu∗)γ−γβu∗	NUM
ejpam-6097	137	20	(	(	PUNCT
ejpam-6097	137	21	1+βu∗)2	1+βu∗)2	NUM
ejpam-6097	137	22	)	)	PUNCT
ejpam-6097	137	23	−λv∗	−λv∗	X
ejpam-6097	138	1	[x	[x	PROPN
ejpam-6097	138	2	y	y	X
ejpam-6097	138	3	]	]	PUNCT
ejpam-6097	138	4	,	,	PUNCT
ejpam-6097	138	5	and126	and126	PROPN
ejpam-6097	138	6	g(t	g(t	PROPN
ejpam-6097	138	7	,	,	PUNCT
ejpam-6097	138	8	x	x	X
ejpam-6097	138	9	)	)	PUNCT
ejpam-6097	138	10	=	=	NOUN
ejpam-6097	139	1	[	[	PUNCT
ejpam-6097	139	2	δx	δx	NOUN
ejpam-6097	139	3	0	0	NUM
ejpam-6097	139	4	0	0	NUM
ejpam-6097	139	5	ϵy	ϵy	NOUN
ejpam-6097	139	6	]	]	PUNCT
ejpam-6097	140	1	[	[	PUNCT
ejpam-6097	140	2	x	x	X
ejpam-6097	140	3	y	y	PROPN
ejpam-6097	140	4	]	]	PUNCT
ejpam-6097	140	5	.	.	PUNCT
ejpam-6097	141	1	for	for	ADP
ejpam-6097	141	2	strictly	strictly	ADV
ejpam-6097	141	3	positive	positive	ADJ
ejpam-6097	141	4	t0	t0	NOUN
ejpam-6097	141	5	,	,	PUNCT
ejpam-6097	141	6	we	we	PRON
ejpam-6097	141	7	define	define	VERB
ejpam-6097	141	8	the	the	DET
ejpam-6097	141	9	cylindrical	cylindrical	ADJ
ejpam-6097	141	10	domain	domain	NOUN
ejpam-6097	141	11	d	d	NOUN
ejpam-6097	141	12	=	=	SYM
ejpam-6097	141	13	r2	r2	PROPN
ejpam-6097	141	14	×	×	NOUN
ejpam-6097	141	15	[	[	X
ejpam-6097	141	16	t0,∞	t0,∞	NUM
ejpam-6097	141	17	)	)	PUNCT
ejpam-6097	141	18	.	.	PUNCT
ejpam-6097	142	1	hence	hence	ADV
ejpam-6097	142	2	,	,	PUNCT
ejpam-6097	142	3	we127	we127	ADP
ejpam-6097	142	4	introduce	introduce	VERB
ejpam-6097	142	5	the	the	DET
ejpam-6097	142	6	function	function	NOUN
ejpam-6097	142	7	φ	φ	PROPN
ejpam-6097	142	8	∈	∈	PROPN
ejpam-6097	142	9	c2(d	c2(d	PROPN
ejpam-6097	142	10	)	)	PUNCT
ejpam-6097	142	11	as	as	ADP
ejpam-6097	142	12	φ	φ	PROPN
ejpam-6097	142	13	:	:	PUNCT
ejpam-6097	142	14	d	d	X
ejpam-6097	142	15	→	→	SYM
ejpam-6097	142	16	r+	r+	X
ejpam-6097	142	17	.	.	PUNCT
ejpam-6097	143	1	as	as	ADP
ejpam-6097	143	2	in	in	ADP
ejpam-6097	143	3	[	[	X
ejpam-6097	143	4	28	28	NUM
ejpam-6097	143	5	]	]	PUNCT
ejpam-6097	143	6	the	the	DET
ejpam-6097	143	7	generator	generator	NOUN
ejpam-6097	143	8	of	of	ADP
ejpam-6097	143	9	markov128	markov128	PROPN
ejpam-6097	143	10	m.	m.	PROPN
ejpam-6097	143	11	mohamed	mohamed	PROPN
ejpam-6097	143	12	et	et	PROPN
ejpam-6097	143	13	al	al	PROPN
ejpam-6097	143	14	.	.	PUNCT
ejpam-6097	143	15	/	/	SYM
ejpam-6097	143	16	eur	eur	PROPN
ejpam-6097	143	17	.	.	PUNCT
ejpam-6097	144	1	j.	j.	PROPN
ejpam-6097	144	2	pure	pure	PROPN
ejpam-6097	144	3	appl	appl	PROPN
ejpam-6097	144	4	.	.	PROPN
ejpam-6097	144	5	math	math	PROPN
ejpam-6097	144	6	,	,	PUNCT
ejpam-6097	144	7	18	18	NUM
ejpam-6097	144	8	(	(	PUNCT
ejpam-6097	144	9	2	2	NUM
ejpam-6097	144	10	)	)	PUNCT
ejpam-6097	144	11	(	(	PUNCT
ejpam-6097	144	12	2025	2025	NUM
ejpam-6097	144	13	)	)	PUNCT
ejpam-6097	144	14	,	,	PUNCT
ejpam-6097	144	15	6097	6097	NUM
ejpam-6097	144	16	8	8	NUM
ejpam-6097	144	17	of	of	ADP
ejpam-6097	144	18	19	19	NUM
ejpam-6097	144	19	process	process	NOUN
ejpam-6097	144	20	for	for	ADP
ejpam-6097	144	21	equation	equation	NOUN
ejpam-6097	144	22	(	(	PUNCT
ejpam-6097	144	23	28	28	NUM
ejpam-6097	144	24	)	)	PUNCT
ejpam-6097	144	25	is	be	AUX
ejpam-6097	144	26	given	give	VERB
ejpam-6097	144	27	by129	by129	PROPN
ejpam-6097	144	28	lφ(t	lφ(t	NOUN
ejpam-6097	144	29	,	,	PUNCT
ejpam-6097	144	30	x	x	X
ejpam-6097	144	31	)	)	PUNCT
ejpam-6097	144	32	=	=	SYM
ejpam-6097	144	33	∂φ(t	∂φ(t	PROPN
ejpam-6097	144	34	,	,	PUNCT
ejpam-6097	144	35	x	x	NOUN
ejpam-6097	144	36	)	)	PUNCT
ejpam-6097	145	1	∂t	∂t	PROPN
ejpam-6097	145	2	+	+	CCONJ
ejpam-6097	145	3	ft	ft	PROPN
ejpam-6097	145	4	(	(	PUNCT
ejpam-6097	145	5	t	t	PROPN
ejpam-6097	145	6	,	,	PUNCT
ejpam-6097	145	7	x	x	NOUN
ejpam-6097	145	8	)	)	PUNCT
ejpam-6097	145	9	∂φ(t	∂φ(t	PROPN
ejpam-6097	145	10	,	,	PUNCT
ejpam-6097	145	11	x	x	NOUN
ejpam-6097	145	12	)	)	PUNCT
ejpam-6097	145	13	∂x	∂x	NOUN
ejpam-6097	146	1	+	+	CCONJ
ejpam-6097	146	2	1	1	NUM
ejpam-6097	146	3	2	2	NUM
ejpam-6097	146	4	trace	trace	NOUN
ejpam-6097	146	5	[	[	PUNCT
ejpam-6097	146	6	gt	gt	PROPN
ejpam-6097	146	7	(	(	PUNCT
ejpam-6097	146	8	t	t	PROPN
ejpam-6097	146	9	,	,	PUNCT
ejpam-6097	146	10	x	x	NOUN
ejpam-6097	146	11	)	)	PUNCT
ejpam-6097	146	12	∂2φ(t	∂2φ(t	NUM
ejpam-6097	146	13	,	,	PUNCT
ejpam-6097	146	14	x	x	X
ejpam-6097	146	15	)	)	PUNCT
ejpam-6097	146	16	∂x2	∂x2	PROPN
ejpam-6097	146	17	g(t	g(t	PROPN
ejpam-6097	146	18	,	,	PUNCT
ejpam-6097	146	19	x	x	X
ejpam-6097	146	20	)	)	PUNCT
ejpam-6097	146	21	]	]	PUNCT
ejpam-6097	146	22	.	.	PUNCT
ejpam-6097	147	1	(	(	PUNCT
ejpam-6097	147	2	29	29	NUM
ejpam-6097	147	3	)	)	PUNCT
ejpam-6097	147	4	the	the	DET
ejpam-6097	147	5	following	follow	VERB
ejpam-6097	147	6	theorem	theorem	ADJ
ejpam-6097	147	7	states	state	NOUN
ejpam-6097	147	8	the	the	DET
ejpam-6097	147	9	mean	mean	ADJ
ejpam-6097	147	10	-	-	PUNCT
ejpam-6097	147	11	square	square	ADJ
ejpam-6097	147	12	stability	stability	NOUN
ejpam-6097	147	13	for	for	ADP
ejpam-6097	147	14	our	our	PRON
ejpam-6097	147	15	system	system	NOUN
ejpam-6097	147	16	(	(	PUNCT
ejpam-6097	147	17	28)130	28)130	NUM
ejpam-6097	147	18	theorem	theorem	NOUN
ejpam-6097	147	19	2	2	NUM
ejpam-6097	147	20	.	.	X
ejpam-6097	147	21	assume	assume	VERB
ejpam-6097	147	22	that131	that131	PUNCT
ejpam-6097	148	1	ρu∗	ρu∗	VERB
ejpam-6097	148	2	k	k	PROPN
ejpam-6097	148	3	>	>	X
ejpam-6097	148	4	αβu∗v∗	αβu∗v∗	PROPN
ejpam-6097	148	5	(	(	PUNCT
ejpam-6097	148	6	1	1	NUM
ejpam-6097	148	7	+	+	CCONJ
ejpam-6097	148	8	βu∗)2	βu∗)2	ADJ
ejpam-6097	148	9	+	+	CCONJ
ejpam-6097	148	10	δ2	δ2	ADJ
ejpam-6097	148	11	2	2	NUM
ejpam-6097	148	12	,	,	PUNCT
ejpam-6097	148	13	λv∗	λv∗	NOUN
ejpam-6097	148	14	>	>	X
ejpam-6097	148	15	ϵ2	ϵ2	PROPN
ejpam-6097	148	16	2	2	NUM
ejpam-6097	148	17	,	,	PUNCT
ejpam-6097	148	18	(	(	PUNCT
ejpam-6097	148	19	30	30	NUM
ejpam-6097	148	20	)	)	PUNCT
ejpam-6097	148	21	(	(	PUNCT
ejpam-6097	148	22	31	31	NUM
ejpam-6097	148	23	)	)	PUNCT
ejpam-6097	148	24	then	then	ADV
ejpam-6097	148	25	,	,	PUNCT
ejpam-6097	148	26	system	system	NOUN
ejpam-6097	148	27	(	(	PUNCT
ejpam-6097	148	28	23)-(27	23)-(27	NUM
ejpam-6097	148	29	)	)	PUNCT
ejpam-6097	148	30	is	be	AUX
ejpam-6097	148	31	mean	mean	ADJ
ejpam-6097	148	32	-	-	PUNCT
ejpam-6097	148	33	square	square	ADJ
ejpam-6097	148	34	asymptotically	asymptotically	ADV
ejpam-6097	148	35	stable.132	stable.132	NOUN
ejpam-6097	148	36	proof	proof	NOUN
ejpam-6097	148	37	.	.	PUNCT
ejpam-6097	149	1	let133	let133	PROPN
ejpam-6097	149	2	φ(t	φ(t	PROPN
ejpam-6097	149	3	,	,	PUNCT
ejpam-6097	149	4	x	x	X
ejpam-6097	149	5	)	)	PUNCT
ejpam-6097	149	6	=	=	SYM
ejpam-6097	149	7	1	1	NUM
ejpam-6097	149	8	2	2	NUM
ejpam-6097	149	9	(	(	PUNCT
ejpam-6097	149	10	a1x	a1x	X
ejpam-6097	149	11	2	2	NUM
ejpam-6097	149	12	+	+	NUM
ejpam-6097	149	13	a2y	a2y	X
ejpam-6097	149	14	2	2	NUM
ejpam-6097	149	15	)	)	PUNCT
ejpam-6097	149	16	,	,	PUNCT
ejpam-6097	149	17	be	be	AUX
ejpam-6097	149	18	the	the	DET
ejpam-6097	149	19	markovian	markovian	ADJ
ejpam-6097	149	20	process	process	NOUN
ejpam-6097	149	21	generator	generator	NOUN
ejpam-6097	149	22	,	,	PUNCT
ejpam-6097	149	23	where	where	SCONJ
ejpam-6097	149	24	ai(i	ai(i	X
ejpam-6097	149	25	=	=	SYM
ejpam-6097	149	26	1	1	NUM
ejpam-6097	149	27	,	,	PUNCT
ejpam-6097	149	28	2	2	NUM
ejpam-6097	149	29	)	)	PUNCT
ejpam-6097	149	30	are	be	AUX
ejpam-6097	149	31	some	some	DET
ejpam-6097	149	32	parameters	parameter	NOUN
ejpam-6097	149	33	to	to	PART
ejpam-6097	149	34	be	be	AUX
ejpam-6097	149	35	deter-134	deter-134	NOUN
ejpam-6097	149	36	mined	mine	VERB
ejpam-6097	149	37	later	later	ADV
ejpam-6097	149	38	.	.	PUNCT
ejpam-6097	150	1	then	then	ADV
ejpam-6097	150	2	we	we	PRON
ejpam-6097	150	3	have	have	VERB
ejpam-6097	150	4	the	the	DET
ejpam-6097	150	5	following135	following135	PROPN
ejpam-6097	150	6	∂φ	∂φ	PROPN
ejpam-6097	150	7	∂t	∂t	PROPN
ejpam-6097	151	1	=	=	SYM
ejpam-6097	151	2	0	0	PROPN
ejpam-6097	151	3	,	,	PUNCT
ejpam-6097	151	4	∂φ	∂φ	NOUN
ejpam-6097	152	1	∂x	∂x	PROPN
ejpam-6097	152	2	=	=	SYM
ejpam-6097	152	3	(	(	PUNCT
ejpam-6097	152	4	a1x	a1x	PROPN
ejpam-6097	152	5	,	,	PUNCT
ejpam-6097	152	6	a2y	a2y	NOUN
ejpam-6097	152	7	)	)	PUNCT
ejpam-6097	152	8	,	,	PUNCT
ejpam-6097	152	9	(	(	PUNCT
ejpam-6097	152	10	32	32	NUM
ejpam-6097	152	11	)	)	PUNCT
ejpam-6097	152	12	136	136	NUM
ejpam-6097	152	13	f	f	NOUN
ejpam-6097	152	14	t(t	t(t	NOUN
ejpam-6097	152	15	,	,	PUNCT
ejpam-6097	152	16	x	x	X
ejpam-6097	152	17	)	)	PUNCT
ejpam-6097	152	18	∂φ	∂φ	PROPN
ejpam-6097	153	1	∂x	∂x	PROPN
ejpam-6097	153	2	=	=	SYM
ejpam-6097	153	3	a1u	a1u	PROPN
ejpam-6097	153	4	2	2	NUM
ejpam-6097	153	5	(	(	PUNCT
ejpam-6097	153	6	−ρ	−ρ	NOUN
ejpam-6097	153	7	k	k	X
ejpam-6097	153	8	+	+	PUNCT
ejpam-6097	153	9	αβv∗	αβv∗	NOUN
ejpam-6097	153	10	(	(	PUNCT
ejpam-6097	153	11	1	1	NUM
ejpam-6097	153	12	+	+	NOUN
ejpam-6097	153	13	bu∗)2	bu∗)2	NUM
ejpam-6097	153	14	)	)	PUNCT
ejpam-6097	153	15	−	−	PROPN
ejpam-6097	153	16	a1αu	a1αu	PUNCT
ejpam-6097	153	17	∗	∗	NOUN
ejpam-6097	153	18	1	1	NUM
ejpam-6097	153	19	+	+	CCONJ
ejpam-6097	153	20	βu∗	βu∗	ADJ
ejpam-6097	153	21	uv	uv	NOUN
ejpam-6097	153	22	+	+	CCONJ
ejpam-6097	153	23	a2αv	a2αv	NOUN
ejpam-6097	153	24	∗	∗	NOUN
ejpam-6097	153	25	(	(	PUNCT
ejpam-6097	153	26	1	1	NUM
ejpam-6097	153	27	+	+	CCONJ
ejpam-6097	153	28	βu∗)2	βu∗)2	ADJ
ejpam-6097	153	29	uv	uv	NOUN
ejpam-6097	153	30	−	−	NOUN
ejpam-6097	153	31	a2λv	a2λv	PUNCT
ejpam-6097	153	32	∗v∗	∗v∗	NUM
ejpam-6097	153	33	,	,	PUNCT
ejpam-6097	153	34	(	(	PUNCT
ejpam-6097	153	35	33	33	NUM
ejpam-6097	153	36	)	)	PUNCT
ejpam-6097	153	37	and137	and137	NOUN
ejpam-6097	153	38	1	1	NUM
ejpam-6097	153	39	2	2	NUM
ejpam-6097	153	40	trace	trace	NOUN
ejpam-6097	153	41	[	[	PUNCT
ejpam-6097	153	42	gt	gt	PROPN
ejpam-6097	153	43	(	(	PUNCT
ejpam-6097	153	44	t	t	PROPN
ejpam-6097	153	45	,	,	PUNCT
ejpam-6097	153	46	x	x	NOUN
ejpam-6097	153	47	)	)	PUNCT
ejpam-6097	153	48	∂2φ(t	∂2φ(t	NUM
ejpam-6097	153	49	,	,	PUNCT
ejpam-6097	153	50	x	x	X
ejpam-6097	153	51	)	)	PUNCT
ejpam-6097	153	52	∂x2	∂x2	PROPN
ejpam-6097	153	53	t	t	PROPN
ejpam-6097	153	54	g(t	g(t	PROPN
ejpam-6097	153	55	,	,	PUNCT
ejpam-6097	153	56	x	x	X
ejpam-6097	153	57	)	)	PUNCT
ejpam-6097	153	58	]	]	PUNCT
ejpam-6097	154	1	=	=	SYM
ejpam-6097	154	2	1	1	NUM
ejpam-6097	154	3	2	2	NUM
ejpam-6097	154	4	a1u	a1u	PROPN
ejpam-6097	154	5	2	2	NUM
ejpam-6097	154	6	+	+	CCONJ
ejpam-6097	154	7	1	1	NUM
ejpam-6097	154	8	2	2	NUM
ejpam-6097	154	9	a2v	a2v	X
ejpam-6097	154	10	2ϵ2	2ϵ2	NUM
ejpam-6097	154	11	.	.	PUNCT
ejpam-6097	155	1	(	(	PUNCT
ejpam-6097	155	2	34	34	NUM
ejpam-6097	155	3	)	)	PUNCT
ejpam-6097	155	4	substituting	substituting	NOUN
ejpam-6097	155	5	(	(	PUNCT
ejpam-6097	155	6	32)-(34	32)-(34	NUM
ejpam-6097	155	7	)	)	PUNCT
ejpam-6097	155	8	into	into	ADP
ejpam-6097	155	9	(	(	PUNCT
ejpam-6097	155	10	29	29	NUM
ejpam-6097	155	11	)	)	PUNCT
ejpam-6097	155	12	,	,	PUNCT
ejpam-6097	155	13	we	we	PRON
ejpam-6097	155	14	get138	get138	PROPN
ejpam-6097	155	15	l(φ(t	l(φ(t	PROPN
ejpam-6097	155	16	,	,	PUNCT
ejpam-6097	155	17	x	x	NOUN
ejpam-6097	155	18	)	)	PUNCT
ejpam-6097	155	19	)	)	PUNCT
ejpam-6097	156	1	=	=	PUNCT
ejpam-6097	156	2	u∗	u∗	INTJ
ejpam-6097	156	3	(	(	PUNCT
ejpam-6097	156	4	−ρ	−ρ	NOUN
ejpam-6097	156	5	k	k	X
ejpam-6097	157	1	+	+	PUNCT
ejpam-6097	158	1	αβv∗	αβv∗	NOUN
ejpam-6097	158	2	(	(	PUNCT
ejpam-6097	158	3	1	1	NUM
ejpam-6097	158	4	+	+	NOUN
ejpam-6097	158	5	bu∗)2	bu∗)2	NUM
ejpam-6097	158	6	)	)	PUNCT
ejpam-6097	158	7	u2a1	u2a1	ADP
ejpam-6097	158	8	−	−	ADP
ejpam-6097	158	9	αu∗	αu∗	ADJ
ejpam-6097	158	10	1	1	NUM
ejpam-6097	158	11	+	+	CCONJ
ejpam-6097	158	12	βu∗	βu∗	ADJ
ejpam-6097	158	13	uva1	uva1	PROPN
ejpam-6097	158	14	+	+	CCONJ
ejpam-6097	158	15	αv∗	αv∗	ADJ
ejpam-6097	158	16	(	(	PUNCT
ejpam-6097	158	17	1	1	NUM
ejpam-6097	158	18	+	+	CCONJ
ejpam-6097	158	19	βu∗)2	βu∗)2	NOUN
ejpam-6097	158	20	uva2	uva2	NOUN
ejpam-6097	158	21	−	−	NOUN
ejpam-6097	159	1	λv∗v∗a2	λv∗v∗a2	ADV
ejpam-6097	159	2	+	+	CCONJ
ejpam-6097	159	3	1	1	NUM
ejpam-6097	159	4	2	2	NUM
ejpam-6097	159	5	a1δ	a1δ	PROPN
ejpam-6097	159	6	2u2	2u2	NUM
ejpam-6097	160	1	+	+	CCONJ
ejpam-6097	160	2	1	1	NUM
ejpam-6097	160	3	2	2	NUM
ejpam-6097	160	4	a2ϵ	a2ϵ	NOUN
ejpam-6097	160	5	2v2	2v2	NUM
ejpam-6097	160	6	=	=	SYM
ejpam-6097	160	7	(	(	PUNCT
ejpam-6097	160	8	−ρ	−ρ	NOUN
ejpam-6097	160	9	k	k	PROPN
ejpam-6097	160	10	u∗	u∗	PROPN
ejpam-6097	160	11	−	−	PROPN
ejpam-6097	160	12	αβu∗v∗	αβu∗v∗	PROPN
ejpam-6097	160	13	(	(	PUNCT
ejpam-6097	160	14	1	1	NUM
ejpam-6097	160	15	+	+	NOUN
ejpam-6097	160	16	bu∗)2	bu∗)2	ADJ
ejpam-6097	160	17	−	−	NUM
ejpam-6097	160	18	1	1	NUM
ejpam-6097	160	19	2	2	NUM
ejpam-6097	160	20	δ2	δ2	ADJ
ejpam-6097	160	21	)	)	PUNCT
ejpam-6097	160	22	a1u	a1u	PROPN
ejpam-6097	160	23	2	2	NUM
ejpam-6097	160	24	−	−	PROPN
ejpam-6097	160	25	(	(	PUNCT
ejpam-6097	160	26	λv∗	λv∗	NOUN
ejpam-6097	160	27	−	−	PROPN
ejpam-6097	160	28	1	1	NUM
ejpam-6097	160	29	2	2	NUM
ejpam-6097	160	30	ϵ2	ϵ2	NOUN
ejpam-6097	160	31	)	)	PUNCT
ejpam-6097	160	32	a2v	a2v	ADV
ejpam-6097	160	33	2	2	NUM
ejpam-6097	160	34	−	−	PROPN
ejpam-6097	160	35	(	(	PUNCT
ejpam-6097	160	36	αu∗	αu∗	NOUN
ejpam-6097	160	37	1	1	NUM
ejpam-6097	160	38	+	+	CCONJ
ejpam-6097	160	39	βu∗	βu∗	ADJ
ejpam-6097	160	40	a1	a1	NOUN
ejpam-6097	160	41	−	−	PROPN
ejpam-6097	160	42	αv∗	αv∗	NOUN
ejpam-6097	160	43	(	(	PUNCT
ejpam-6097	160	44	1	1	NUM
ejpam-6097	160	45	+	+	CCONJ
ejpam-6097	160	46	βu∗)2	βu∗)2	PROPN
ejpam-6097	160	47	a2	a2	PROPN
ejpam-6097	160	48	)	)	PUNCT
ejpam-6097	160	49	uv	uv	NOUN
ejpam-6097	160	50	.	.	PUNCT
ejpam-6097	161	1	(	(	PUNCT
ejpam-6097	161	2	35	35	NUM
ejpam-6097	161	3	)	)	PUNCT
ejpam-6097	161	4	m.	m.	NOUN
ejpam-6097	161	5	mohamed	mohamed	PROPN
ejpam-6097	161	6	et	et	PROPN
ejpam-6097	161	7	al	al	PROPN
ejpam-6097	161	8	.	.	PUNCT
ejpam-6097	161	9	/	/	SYM
ejpam-6097	161	10	eur	eur	PROPN
ejpam-6097	161	11	.	.	PUNCT
ejpam-6097	162	1	j.	j.	PROPN
ejpam-6097	162	2	pure	pure	PROPN
ejpam-6097	162	3	appl	appl	PROPN
ejpam-6097	162	4	.	.	PROPN
ejpam-6097	162	5	math	math	PROPN
ejpam-6097	162	6	,	,	PUNCT
ejpam-6097	162	7	18	18	NUM
ejpam-6097	162	8	(	(	PUNCT
ejpam-6097	162	9	2	2	NUM
ejpam-6097	162	10	)	)	PUNCT
ejpam-6097	162	11	(	(	PUNCT
ejpam-6097	162	12	2025	2025	NUM
ejpam-6097	162	13	)	)	PUNCT
ejpam-6097	162	14	,	,	PUNCT
ejpam-6097	162	15	6097	6097	NUM
ejpam-6097	162	16	9	9	NUM
ejpam-6097	162	17	of	of	ADP
ejpam-6097	162	18	19	19	NUM
ejpam-6097	162	19	let	let	VERB
ejpam-6097	162	20	αu∗a1	αu∗a1	NOUN
ejpam-6097	162	21	=	=	SYM
ejpam-6097	162	22	γv∗	γv∗	ADJ
ejpam-6097	162	23	1+βu∗a2	1+βu∗a2	NOUN
ejpam-6097	162	24	,	,	PUNCT
ejpam-6097	162	25	this	this	DET
ejpam-6097	162	26	implies139	implies139	PROPN
ejpam-6097	162	27	l(φ(t	l(φ(t	PROPN
ejpam-6097	162	28	,	,	PUNCT
ejpam-6097	162	29	x	x	NOUN
ejpam-6097	162	30	)	)	PUNCT
ejpam-6097	162	31	)	)	PUNCT
ejpam-6097	163	1	=	=	PUNCT
ejpam-6097	164	1	(	(	PUNCT
ejpam-6097	164	2	−ρu∗	−ρu∗	INTJ
ejpam-6097	164	3	k	k	NOUN
ejpam-6097	164	4	−	−	PROPN
ejpam-6097	164	5	αβu∗v∗	αβu∗v∗	PROPN
ejpam-6097	164	6	(	(	PUNCT
ejpam-6097	164	7	1	1	NUM
ejpam-6097	164	8	+	+	NOUN
ejpam-6097	164	9	bu∗)2	bu∗)2	ADJ
ejpam-6097	164	10	−	−	NUM
ejpam-6097	164	11	1	1	NUM
ejpam-6097	164	12	2	2	NUM
ejpam-6097	164	13	δ2	δ2	ADJ
ejpam-6097	164	14	)	)	PUNCT
ejpam-6097	164	15	a1u	a1u	PROPN
ejpam-6097	164	16	2	2	NUM
ejpam-6097	164	17	−	−	PROPN
ejpam-6097	164	18	(	(	PUNCT
ejpam-6097	164	19	λv∗	λv∗	NOUN
ejpam-6097	164	20	−	−	PROPN
ejpam-6097	164	21	1	1	NUM
ejpam-6097	164	22	2	2	NUM
ejpam-6097	164	23	ϵ2	ϵ2	NOUN
ejpam-6097	164	24	)	)	PUNCT
ejpam-6097	164	25	a2v	a2v	ADP
ejpam-6097	165	1	2	2	X
ejpam-6097	165	2	.	.	PUNCT
ejpam-6097	165	3	(	(	PUNCT
ejpam-6097	165	4	36	36	NUM
ejpam-6097	165	5	)	)	PUNCT
ejpam-6097	165	6	for	for	ADP
ejpam-6097	165	7	l(φ(t	l(φ(t	PROPN
ejpam-6097	165	8	,	,	PUNCT
ejpam-6097	165	9	x	x	NOUN
ejpam-6097	165	10	)	)	PUNCT
ejpam-6097	165	11	)	)	PUNCT
ejpam-6097	165	12	<	<	X
ejpam-6097	165	13	0	0	NUM
ejpam-6097	165	14	,	,	PUNCT
ejpam-6097	166	1	then140	then140	PROPN
ejpam-6097	166	2	−ρu∗	−ρu∗	X
ejpam-6097	166	3	k	k	X
ejpam-6097	166	4	>	>	X
ejpam-6097	166	5	αβu∗v∗	αβu∗v∗	PROPN
ejpam-6097	166	6	(	(	PUNCT
ejpam-6097	166	7	1	1	NUM
ejpam-6097	166	8	+	+	CCONJ
ejpam-6097	166	9	βu∗)2	βu∗)2	ADJ
ejpam-6097	166	10	+	+	NUM
ejpam-6097	166	11	1	1	NUM
ejpam-6097	166	12	2	2	NUM
ejpam-6097	166	13	δ2	δ2	VERB
ejpam-6097	166	14	,	,	PUNCT
ejpam-6097	166	15	λv∗	λv∗	NOUN
ejpam-6097	166	16	>	>	X
ejpam-6097	166	17	1	1	NUM
ejpam-6097	166	18	2	2	NUM
ejpam-6097	166	19	ϵ2	ϵ2	NOUN
ejpam-6097	166	20	.	.	PUNCT
ejpam-6097	167	1	this	this	PRON
ejpam-6097	167	2	completes	complete	VERB
ejpam-6097	167	3	the	the	DET
ejpam-6097	167	4	proof.141	proof.141	NOUN
ejpam-6097	167	5	corollary	corollary	ADJ
ejpam-6097	167	6	1	1	NUM
ejpam-6097	167	7	.	.	PUNCT
ejpam-6097	168	1	when	when	SCONJ
ejpam-6097	168	2	conditions	condition	NOUN
ejpam-6097	168	3	(	(	PUNCT
ejpam-6097	168	4	30	30	NUM
ejpam-6097	168	5	)	)	PUNCT
ejpam-6097	168	6	and	and	CCONJ
ejpam-6097	168	7	(	(	PUNCT
ejpam-6097	168	8	31	31	NUM
ejpam-6097	168	9	)	)	PUNCT
ejpam-6097	168	10	are	be	AUX
ejpam-6097	168	11	not	not	PART
ejpam-6097	168	12	satisfied	satisfied	ADJ
ejpam-6097	168	13	,	,	PUNCT
ejpam-6097	168	14	then	then	ADV
ejpam-6097	168	15	the	the	DET
ejpam-6097	168	16	system	system	NOUN
ejpam-6097	168	17	(	(	PUNCT
ejpam-6097	168	18	4)-(6	4)-(6	NUM
ejpam-6097	168	19	)	)	PUNCT
ejpam-6097	168	20	is142	is142	PROPN
ejpam-6097	168	21	unstable.143	unstable.143	PROPN
ejpam-6097	168	22	remark	remark	NOUN
ejpam-6097	168	23	1	1	NUM
ejpam-6097	168	24	.	.	PUNCT
ejpam-6097	169	1	the	the	DET
ejpam-6097	169	2	main	main	ADJ
ejpam-6097	169	3	factors	factor	NOUN
ejpam-6097	169	4	that	that	PRON
ejpam-6097	169	5	affect	affect	VERB
ejpam-6097	169	6	the	the	DET
ejpam-6097	169	7	system	system	NOUN
ejpam-6097	169	8	’s	’s	PART
ejpam-6097	169	9	stability	stability	NOUN
ejpam-6097	169	10	are	be	AUX
ejpam-6097	169	11	the	the	DET
ejpam-6097	169	12	rate	rate	NOUN
ejpam-6097	169	13	of	of	ADP
ejpam-6097	169	14	growth	growth	NOUN
ejpam-6097	169	15	in	in	ADP
ejpam-6097	169	16	the144	the144	PROPN
ejpam-6097	169	17	prey	prey	PROPN
ejpam-6097	169	18	population	population	NOUN
ejpam-6097	169	19	,	,	PUNCT
ejpam-6097	169	20	the	the	DET
ejpam-6097	169	21	carrying	carry	VERB
ejpam-6097	169	22	capacity	capacity	NOUN
ejpam-6097	169	23	of	of	ADP
ejpam-6097	169	24	the	the	DET
ejpam-6097	169	25	model	model	NOUN
ejpam-6097	169	26	,	,	PUNCT
ejpam-6097	169	27	the	the	DET
ejpam-6097	169	28	rate	rate	NOUN
ejpam-6097	169	29	of	of	ADP
ejpam-6097	169	30	catching	catch	VERB
ejpam-6097	169	31	prey	prey	NOUN
ejpam-6097	169	32	population	population	NOUN
ejpam-6097	169	33	by145	by145	PROPN
ejpam-6097	169	34	the	the	DET
ejpam-6097	169	35	predator	predator	NOUN
ejpam-6097	169	36	,	,	PUNCT
ejpam-6097	169	37	the	the	DET
ejpam-6097	169	38	handling	handling	NOUN
ejpam-6097	169	39	rate	rate	NOUN
ejpam-6097	169	40	of	of	ADP
ejpam-6097	169	41	the	the	DET
ejpam-6097	169	42	predator	predator	NOUN
ejpam-6097	169	43	,	,	PUNCT
ejpam-6097	169	44	intraspecific	intraspecific	NOUN
ejpam-6097	169	45	competition	competition	NOUN
ejpam-6097	169	46	between	between	ADP
ejpam-6097	169	47	predators,146	predators,146	PROPN
ejpam-6097	169	48	and	and	CCONJ
ejpam-6097	169	49	the	the	DET
ejpam-6097	169	50	small	small	ADJ
ejpam-6097	169	51	random	random	ADJ
ejpam-6097	169	52	immigration	immigration	NOUN
ejpam-6097	169	53	in	in	ADP
ejpam-6097	169	54	the	the	DET
ejpam-6097	169	55	prey	prey	NOUN
ejpam-6097	169	56	and	and	CCONJ
ejpam-6097	169	57	predator	predator	NOUN
ejpam-6097	169	58	populations.147	populations.147	NOUN
ejpam-6097	169	59	5	5	NUM
ejpam-6097	169	60	.	.	PUNCT
ejpam-6097	169	61	persistence	persistence	NOUN
ejpam-6097	169	62	and	and	CCONJ
ejpam-6097	169	63	extinction148	extinction148	PROPN
ejpam-6097	169	64	in	in	ADP
ejpam-6097	169	65	this	this	DET
ejpam-6097	169	66	section	section	NOUN
ejpam-6097	169	67	,	,	PUNCT
ejpam-6097	169	68	we	we	PRON
ejpam-6097	169	69	will	will	AUX
ejpam-6097	169	70	study	study	VERB
ejpam-6097	169	71	the	the	DET
ejpam-6097	169	72	persistence	persistence	NOUN
ejpam-6097	169	73	for	for	ADP
ejpam-6097	169	74	both	both	CCONJ
ejpam-6097	169	75	prey	prey	NOUN
ejpam-6097	169	76	and	and	CCONJ
ejpam-6097	169	77	predator	predator	NOUN
ejpam-6097	169	78	populations149	populations149	PROPN
ejpam-6097	169	79	and	and	CCONJ
ejpam-6097	169	80	the	the	DET
ejpam-6097	169	81	extinction	extinction	NOUN
ejpam-6097	169	82	for	for	ADP
ejpam-6097	169	83	the	the	DET
ejpam-6097	169	84	prey	prey	NOUN
ejpam-6097	169	85	population.150	population.150	ADV
ejpam-6097	169	86	5.1	5.1	NUM
ejpam-6097	169	87	.	.	PUNCT
ejpam-6097	170	1	persistence	persistence	NOUN
ejpam-6097	170	2	of	of	ADP
ejpam-6097	170	3	the	the	DET
ejpam-6097	170	4	prey	prey	NOUN
ejpam-6097	170	5	population151	population151	PROPN
ejpam-6097	170	6	the	the	DET
ejpam-6097	170	7	following	follow	VERB
ejpam-6097	170	8	lemma	lemma	PROPN
ejpam-6097	170	9	was	be	AUX
ejpam-6097	170	10	collected	collect	VERB
ejpam-6097	170	11	from	from	ADP
ejpam-6097	170	12	[	[	PUNCT
ejpam-6097	170	13	29].152	29].152	NUM
ejpam-6097	170	14	lemma	lemma	PROPN
ejpam-6097	170	15	2	2	X
ejpam-6097	170	16	.	.	PUNCT
ejpam-6097	171	1	lim	lim	PROPN
ejpam-6097	171	2	sup	sup	VERB
ejpam-6097	171	3	t→∞	t→∞	NUM
ejpam-6097	171	4	0≤t≤t	0≤t≤t	NUM
ejpam-6097	171	5	1	1	NUM
ejpam-6097	171	6	t	t	NOUN
ejpam-6097	171	7	lnu	lnu	NOUN
ejpam-6097	171	8	≤	≤	NOUN
ejpam-6097	171	9	0	0	NUM
ejpam-6097	172	1	a.s	a.s	PROPN
ejpam-6097	172	2	..	..	PUNCT
ejpam-6097	172	3	(	(	PUNCT
ejpam-6097	172	4	37	37	NUM
ejpam-6097	172	5	)	)	PUNCT
ejpam-6097	172	6	theorem	theorem	NOUN
ejpam-6097	172	7	3	3	NUM
ejpam-6097	172	8	.	.	PUNCT
ejpam-6097	173	1	the	the	DET
ejpam-6097	173	2	prey	prey	PROPN
ejpam-6097	173	3	population	population	NOUN
ejpam-6097	173	4	u	u	PROPN
ejpam-6097	173	5	admits	admit	VERB
ejpam-6097	173	6	weak	weak	ADJ
ejpam-6097	173	7	persistence	persistence	NOUN
ejpam-6097	173	8	in	in	ADP
ejpam-6097	173	9	the	the	DET
ejpam-6097	173	10	average	average	NOUN
ejpam-6097	173	11	with	with	ADP
ejpam-6097	173	12	probability153	probability153	NOUN
ejpam-6097	173	13	almost	almost	ADV
ejpam-6097	173	14	if154	if154	NOUN
ejpam-6097	173	15	ρ−	ρ−	NOUN
ejpam-6097	173	16	δ2	δ2	VERB
ejpam-6097	173	17	2	2	NUM
ejpam-6097	173	18	>	>	SYM
ejpam-6097	173	19	0	0	NUM
ejpam-6097	173	20	.	.	PUNCT
ejpam-6097	174	1	proof	proof	NOUN
ejpam-6097	174	2	.	.	PUNCT
ejpam-6097	175	1	to	to	PART
ejpam-6097	175	2	prove	prove	VERB
ejpam-6097	175	3	this	this	PRON
ejpam-6097	175	4	,	,	PUNCT
ejpam-6097	175	5	we	we	PRON
ejpam-6097	175	6	need	need	VERB
ejpam-6097	175	7	to	to	PART
ejpam-6097	175	8	show	show	VERB
ejpam-6097	175	9	that	that	SCONJ
ejpam-6097	175	10	ul	ul	INTJ
ejpam-6097	175	11	>	>	X
ejpam-6097	175	12	a	a	DET
ejpam-6097	175	13	>	>	X
ejpam-6097	175	14	0	0	NUM
ejpam-6097	175	15	,	,	PUNCT
ejpam-6097	175	16	where155	where155	PROPN
ejpam-6097	175	17	ul	ul	INTJ
ejpam-6097	175	18	:	:	PUNCT
ejpam-6097	175	19	=	=	SYM
ejpam-6097	175	20	lim	lim	PROPN
ejpam-6097	175	21	sup	sup	NOUN
ejpam-6097	175	22	t→∞	t→∞	NUM
ejpam-6097	175	23	1	1	NUM
ejpam-6097	175	24	t	t	NOUN
ejpam-6097	175	25	∫	∫	PROPN
ejpam-6097	175	26	t	t	PROPN
ejpam-6097	175	27	0	0	NUM
ejpam-6097	175	28	uds	uds	PROPN
ejpam-6097	175	29	,	,	PUNCT
ejpam-6097	175	30	(	(	PUNCT
ejpam-6097	175	31	38	38	NUM
ejpam-6097	175	32	)	)	PUNCT
ejpam-6097	175	33	we	we	PRON
ejpam-6097	175	34	prove	prove	VERB
ejpam-6097	175	35	this	this	PRON
ejpam-6097	175	36	by	by	ADP
ejpam-6097	175	37	contradiction	contradiction	NOUN
ejpam-6097	175	38	.	.	PUNCT
ejpam-6097	176	1	assume	assume	VERB
ejpam-6097	176	2	that	that	SCONJ
ejpam-6097	176	3	ϱ1	ϱ1	NOUN
ejpam-6097	176	4	be	be	AUX
ejpam-6097	176	5	small	small	ADJ
ejpam-6097	176	6	enough	enough	ADV
ejpam-6097	176	7	such	such	ADJ
ejpam-6097	176	8	that156	that156	PROPN
ejpam-6097	176	9	−σ	−σ	NOUN
ejpam-6097	176	10	−	−	PROPN
ejpam-6097	176	11	1	1	NUM
ejpam-6097	176	12	2	2	NUM
ejpam-6097	176	13	ϵ2	ϵ2	NOUN
ejpam-6097	176	14	+	+	CCONJ
ejpam-6097	177	1	γϱ1	γϱ1	VERB
ejpam-6097	177	2	<	<	X
ejpam-6097	177	3	0	0	NUM
ejpam-6097	177	4	,	,	PUNCT
ejpam-6097	177	5	(	(	PUNCT
ejpam-6097	177	6	39	39	NUM
ejpam-6097	177	7	)	)	PUNCT
ejpam-6097	177	8	m.	m.	NOUN
ejpam-6097	177	9	mohamed	mohamed	PROPN
ejpam-6097	177	10	et	et	PROPN
ejpam-6097	177	11	al	al	PROPN
ejpam-6097	177	12	.	.	PUNCT
ejpam-6097	177	13	/	/	SYM
ejpam-6097	177	14	eur	eur	PROPN
ejpam-6097	177	15	.	.	PUNCT
ejpam-6097	178	1	j.	j.	PROPN
ejpam-6097	178	2	pure	pure	PROPN
ejpam-6097	178	3	appl	appl	PROPN
ejpam-6097	178	4	.	.	PROPN
ejpam-6097	178	5	math	math	PROPN
ejpam-6097	178	6	,	,	PUNCT
ejpam-6097	178	7	18	18	NUM
ejpam-6097	178	8	(	(	PUNCT
ejpam-6097	178	9	2	2	NUM
ejpam-6097	178	10	)	)	PUNCT
ejpam-6097	178	11	(	(	PUNCT
ejpam-6097	178	12	2025	2025	NUM
ejpam-6097	178	13	)	)	PUNCT
ejpam-6097	178	14	,	,	PUNCT
ejpam-6097	178	15	6097	6097	NUM
ejpam-6097	178	16	10	10	NUM
ejpam-6097	178	17	of	of	ADP
ejpam-6097	178	18	19	19	NUM
ejpam-6097	178	19	and157	and157	PROPN
ejpam-6097	178	20	ρ−	ρ−	NOUN
ejpam-6097	178	21	1	1	NUM
ejpam-6097	178	22	2	2	NUM
ejpam-6097	178	23	δ2	δ2	VERB
ejpam-6097	178	24	−	−	PROPN
ejpam-6097	178	25	ρ	ρ	NOUN
ejpam-6097	178	26	k	k	PROPN
ejpam-6097	178	27	ϱ1	ϱ1	PROPN
ejpam-6097	178	28	>	>	PUNCT
ejpam-6097	178	29	0	0	NUM
ejpam-6097	178	30	,	,	PUNCT
ejpam-6097	178	31	for	for	ADP
ejpam-6097	178	32	each	each	DET
ejpam-6097	178	33	ϱ1	ϱ1	PROPN
ejpam-6097	178	34	>	>	PUNCT
ejpam-6097	178	35	0	0	NUM
ejpam-6097	179	1	,	,	PUNCT
ejpam-6097	179	2	there	there	PRON
ejpam-6097	179	3	exists	exist	VERB
ejpam-6097	179	4	a	a	DET
ejpam-6097	179	5	solution	solution	NOUN
ejpam-6097	179	6	(	(	PUNCT
ejpam-6097	179	7	û	û	NUM
ejpam-6097	179	8	,	,	PUNCT
ejpam-6097	179	9	v̂	v̂	NOUN
ejpam-6097	179	10	)	)	PUNCT
ejpam-6097	179	11	where158	where158	PROPN
ejpam-6097	179	12	p{ul	p{ul	PROPN
ejpam-6097	179	13	<	<	X
ejpam-6097	179	14	ϱ1	ϱ1	NOUN
ejpam-6097	179	15	}	}	PUNCT
ejpam-6097	179	16	.	.	PUNCT
ejpam-6097	180	1	(	(	PUNCT
ejpam-6097	180	2	40	40	NUM
ejpam-6097	180	3	)	)	PUNCT
ejpam-6097	180	4	therefore159	therefore159	PROPN
ejpam-6097	181	1	d	d	NOUN
ejpam-6097	181	2	ln	ln	ADV
ejpam-6097	181	3	v̂	v̂	X
ejpam-6097	181	4	≤	≤	NOUN
ejpam-6097	182	1	[	[	X
ejpam-6097	182	2	−σ	−σ	NOUN
ejpam-6097	182	3	−	−	PROPN
ejpam-6097	182	4	ϵ2	ϵ2	NOUN
ejpam-6097	182	5	2	2	NUM
ejpam-6097	182	6	+	+	CCONJ
ejpam-6097	182	7	γû]dt+	γû]dt+	PROPN
ejpam-6097	182	8	ϵdb2	ϵdb2	NOUN
ejpam-6097	182	9	.	.	PUNCT
ejpam-6097	183	1	once	once	ADV
ejpam-6097	183	2	again	again	ADV
ejpam-6097	183	3	,	,	PUNCT
ejpam-6097	183	4	we	we	PRON
ejpam-6097	183	5	apply	apply	VERB
ejpam-6097	183	6	the	the	DET
ejpam-6097	183	7	integration	integration	NOUN
ejpam-6097	183	8	over	over	ADP
ejpam-6097	183	9	(	(	PUNCT
ejpam-6097	183	10	0	0	NUM
ejpam-6097	183	11	,	,	PUNCT
ejpam-6097	183	12	t	t	PROPN
ejpam-6097	183	13	)	)	PUNCT
ejpam-6097	183	14	and	and	CCONJ
ejpam-6097	183	15	divide	divide	VERB
ejpam-6097	183	16	by	by	ADP
ejpam-6097	183	17	t	t	PROPN
ejpam-6097	183	18	,	,	PUNCT
ejpam-6097	183	19	we	we	PRON
ejpam-6097	183	20	get160	get160	PROPN
ejpam-6097	183	21	ln	ln	ADV
ejpam-6097	183	22	v̂	v̂	ADJ
ejpam-6097	183	23	−	−	PROPN
ejpam-6097	183	24	ln	ln	ADJ
ejpam-6097	183	25	v̂0	v̂0	NOUN
ejpam-6097	183	26	t	t	NOUN
ejpam-6097	183	27	≤	≤	NOUN
ejpam-6097	183	28	1	1	NUM
ejpam-6097	183	29	t	t	NOUN
ejpam-6097	183	30	∫	∫	PROPN
ejpam-6097	183	31	t	t	PROPN
ejpam-6097	183	32	0	0	NUM
ejpam-6097	183	33	(	(	PUNCT
ejpam-6097	183	34	−σ	−σ	NOUN
ejpam-6097	183	35	−	−	PROPN
ejpam-6097	183	36	ϵ2	ϵ2	PROPN
ejpam-6097	183	37	2	2	NUM
ejpam-6097	183	38	)	)	PUNCT
ejpam-6097	183	39	ds+	ds+	NOUN
ejpam-6097	183	40	1	1	NUM
ejpam-6097	183	41	t	t	NOUN
ejpam-6097	183	42	∫	∫	PROPN
ejpam-6097	183	43	t	t	PROPN
ejpam-6097	183	44	0	0	NUM
ejpam-6097	184	1	γûds+	γûds+	PRON
ejpam-6097	184	2	1	1	NUM
ejpam-6097	184	3	t	t	NOUN
ejpam-6097	184	4	∫	∫	PROPN
ejpam-6097	184	5	t	t	PROPN
ejpam-6097	184	6	0	0	NUM
ejpam-6097	184	7	ϵdb2(s	ϵdb2(s	NUM
ejpam-6097	184	8	)	)	PUNCT
ejpam-6097	184	9	,	,	PUNCT
ejpam-6097	184	10	=	=	SYM
ejpam-6097	184	11	−σ	−σ	NOUN
ejpam-6097	185	1	−	−	PROPN
ejpam-6097	185	2	ϵ2	ϵ2	NOUN
ejpam-6097	185	3	2	2	NUM
ejpam-6097	185	4	+	+	CCONJ
ejpam-6097	185	5	γ	γ	PROPN
ejpam-6097	185	6	t	t	PROPN
ejpam-6097	185	7	1	1	NUM
ejpam-6097	185	8	t	t	NOUN
ejpam-6097	185	9	∫	∫	PROPN
ejpam-6097	185	10	t	t	PROPN
ejpam-6097	185	11	0	0	NUM
ejpam-6097	185	12	γûds+	γûds+	PRON
ejpam-6097	186	1	1	1	NUM
ejpam-6097	186	2	t	t	NOUN
ejpam-6097	186	3	∫	∫	PROPN
ejpam-6097	186	4	t	t	PROPN
ejpam-6097	186	5	0	0	NUM
ejpam-6097	186	6	ϵdb2(s	ϵdb2(s	NUM
ejpam-6097	186	7	)	)	PUNCT
ejpam-6097	186	8	.	.	PUNCT
ejpam-6097	187	1	(	(	PUNCT
ejpam-6097	187	2	41	41	NUM
ejpam-6097	187	3	)	)	PUNCT
ejpam-6097	187	4	as	as	ADP
ejpam-6097	187	5	before	before	ADV
ejpam-6097	187	6	,	,	PUNCT
ejpam-6097	187	7	from	from	ADP
ejpam-6097	187	8	the	the	DET
ejpam-6097	187	9	strong	strong	ADJ
ejpam-6097	187	10	law	law	NOUN
ejpam-6097	187	11	of	of	ADP
ejpam-6097	187	12	large	large	ADJ
ejpam-6097	187	13	number	number	NOUN
ejpam-6097	187	14	,	,	PUNCT
ejpam-6097	187	15	we	we	PRON
ejpam-6097	187	16	get161	get161	VERB
ejpam-6097	187	17	lim	lim	NOUN
ejpam-6097	187	18	sup	sup	NOUN
ejpam-6097	187	19	t→∞	t→∞	ADV
ejpam-6097	187	20	ln	ln	NOUN
ejpam-6097	187	21	v̂	v̂	ADP
ejpam-6097	187	22	t	t	NOUN
ejpam-6097	187	23	≤	≤	NUM
ejpam-6097	187	24	−σ	−σ	NOUN
ejpam-6097	187	25	−	−	PROPN
ejpam-6097	187	26	ϵ2	ϵ2	NOUN
ejpam-6097	187	27	2	2	NUM
ejpam-6097	187	28	+	+	CCONJ
ejpam-6097	187	29	γϱ1	γϱ1	VERB
ejpam-6097	187	30	<	<	X
ejpam-6097	187	31	0	0	NUM
ejpam-6097	187	32	,	,	PUNCT
ejpam-6097	187	33	(	(	PUNCT
ejpam-6097	187	34	42	42	NUM
ejpam-6097	187	35	)	)	PUNCT
ejpam-6097	187	36	this	this	PRON
ejpam-6097	187	37	implies	imply	VERB
ejpam-6097	187	38	that	that	SCONJ
ejpam-6097	187	39	lim	lim	PROPN
ejpam-6097	187	40	v̂	v̂	ADP
ejpam-6097	187	41	=	=	NOUN
ejpam-6097	188	1	0	0	X
ejpam-6097	188	2	.	.	PUNCT
ejpam-6097	188	3	therefore,162	therefore,162	INTJ
ejpam-6097	189	1	d	d	X
ejpam-6097	189	2	ln(û	ln(û	PROPN
ejpam-6097	189	3	)	)	PUNCT
ejpam-6097	189	4	=	=	PUNCT
ejpam-6097	190	1	[	[	PUNCT
ejpam-6097	190	2	ρ−	ρ−	NOUN
ejpam-6097	190	3	ρ	ρ	X
ejpam-6097	190	4	k	k	X
ejpam-6097	190	5	û−	û−	NOUN
ejpam-6097	190	6	αûv̂	αûv̂	NUM
ejpam-6097	190	7	1	1	NUM
ejpam-6097	190	8	+	+	CCONJ
ejpam-6097	190	9	βû	βû	NUM
ejpam-6097	190	10	−	−	NUM
ejpam-6097	190	11	1	1	NUM
ejpam-6097	190	12	2	2	NUM
ejpam-6097	190	13	δ2	δ2	VERB
ejpam-6097	190	14	]	]	PUNCT
ejpam-6097	190	15	dt+	dt+	NOUN
ejpam-6097	190	16	δdb1(t	δdb1(t	NOUN
ejpam-6097	190	17	)	)	PUNCT
ejpam-6097	190	18	.	.	PUNCT
ejpam-6097	191	1	(	(	PUNCT
ejpam-6097	191	2	43	43	NUM
ejpam-6097	191	3	)	)	PUNCT
ejpam-6097	191	4	integration	integration	NOUN
ejpam-6097	191	5	followed	follow	VERB
ejpam-6097	191	6	by	by	ADP
ejpam-6097	191	7	division	division	NOUN
ejpam-6097	191	8	by	by	ADP
ejpam-6097	191	9	t	t	PROPN
ejpam-6097	191	10	,	,	PUNCT
ejpam-6097	191	11	give163	give163	PROPN
ejpam-6097	191	12	ln	ln	ADP
ejpam-6097	191	13	û−	û−	PROPN
ejpam-6097	191	14	ln	ln	X
ejpam-6097	191	15	û0	û0	PROPN
ejpam-6097	191	16	t	t	PROPN
ejpam-6097	191	17	=	=	SYM
ejpam-6097	192	1	1	1	NUM
ejpam-6097	192	2	t	t	NOUN
ejpam-6097	192	3	∫	∫	PROPN
ejpam-6097	192	4	t	t	PROPN
ejpam-6097	192	5	0	0	NUM
ejpam-6097	193	1	(	(	PUNCT
ejpam-6097	193	2	ρ−	ρ−	NOUN
ejpam-6097	193	3	1	1	NUM
ejpam-6097	193	4	2	2	NUM
ejpam-6097	193	5	δ2	δ2	ADJ
ejpam-6097	193	6	)	)	PUNCT
ejpam-6097	193	7	ds−	ds−	PROPN
ejpam-6097	193	8	ρ	ρ	X
ejpam-6097	193	9	kt	kt	PROPN
ejpam-6097	193	10	∫	∫	PROPN
ejpam-6097	193	11	t	t	PROPN
ejpam-6097	193	12	0	0	NUM
ejpam-6097	193	13	ûds−	ûds−	PROPN
ejpam-6097	193	14	α	α	NOUN
ejpam-6097	193	15	t	t	NOUN
ejpam-6097	193	16	∫	∫	PROPN
ejpam-6097	193	17	t	t	PROPN
ejpam-6097	193	18	0	0	NUM
ejpam-6097	193	19	ûv̂	ûv̂	ADP
ejpam-6097	193	20	1	1	NUM
ejpam-6097	193	21	+	+	CCONJ
ejpam-6097	193	22	βû	βû	NUM
ejpam-6097	193	23	ds+	ds+	PROPN
ejpam-6097	193	24	δ	δ	PROPN
ejpam-6097	194	1	t	t	PROPN
ejpam-6097	194	2	∫	∫	PROPN
ejpam-6097	194	3	t	t	PROPN
ejpam-6097	194	4	0	0	NUM
ejpam-6097	194	5	db1(s	db1(s	PROPN
ejpam-6097	194	6	)	)	PUNCT
ejpam-6097	194	7	,	,	PUNCT
ejpam-6097	195	1	=	=	PUNCT
ejpam-6097	195	2	ρ−	ρ−	NOUN
ejpam-6097	195	3	1	1	NUM
ejpam-6097	195	4	2	2	NUM
ejpam-6097	195	5	δ2	δ2	VERB
ejpam-6097	195	6	−	−	PROPN
ejpam-6097	195	7	ρ	ρ	PROPN
ejpam-6097	195	8	kt	kt	PROPN
ejpam-6097	195	9	∫	∫	PROPN
ejpam-6097	195	10	t	t	PROPN
ejpam-6097	195	11	0	0	NUM
ejpam-6097	195	12	ûds−	ûds−	PROPN
ejpam-6097	195	13	α	α	NOUN
ejpam-6097	195	14	t	t	NOUN
ejpam-6097	195	15	∫	∫	PROPN
ejpam-6097	195	16	t	t	PROPN
ejpam-6097	195	17	0	0	NUM
ejpam-6097	195	18	ûv̂	ûv̂	ADP
ejpam-6097	196	1	1	1	NUM
ejpam-6097	196	2	+	+	CCONJ
ejpam-6097	196	3	βû	βû	NUM
ejpam-6097	196	4	ds+	ds+	PROPN
ejpam-6097	196	5	δ	δ	PROPN
ejpam-6097	196	6	t	t	PROPN
ejpam-6097	196	7	∫	∫	PROPN
ejpam-6097	196	8	t	t	PROPN
ejpam-6097	196	9	0	0	NUM
ejpam-6097	196	10	db1(s	db1(s	PROPN
ejpam-6097	196	11	)	)	PUNCT
ejpam-6097	196	12	.	.	PUNCT
ejpam-6097	197	1	taking	take	VERB
ejpam-6097	197	2	the	the	DET
ejpam-6097	197	3	lim	lim	PROPN
ejpam-6097	197	4	supt→∞	supt→∞	PROPN
ejpam-6097	197	5	in	in	ADP
ejpam-6097	197	6	both	both	DET
ejpam-6097	197	7	sides	side	NOUN
ejpam-6097	197	8	with	with	ADP
ejpam-6097	197	9	(	(	PUNCT
ejpam-6097	197	10	39	39	NUM
ejpam-6097	197	11	)	)	PUNCT
ejpam-6097	197	12	,	,	PUNCT
ejpam-6097	197	13	(	(	PUNCT
ejpam-6097	197	14	40	40	NUM
ejpam-6097	197	15	)	)	PUNCT
ejpam-6097	197	16	and	and	CCONJ
ejpam-6097	197	17	the	the	DET
ejpam-6097	197	18	law	law	NOUN
ejpam-6097	197	19	of	of	ADP
ejpam-6097	197	20	large	large	ADJ
ejpam-6097	197	21	number	number	NOUN
ejpam-6097	197	22	,	,	PUNCT
ejpam-6097	197	23	we164	we164	PROPN
ejpam-6097	197	24	obtain165	obtain165	PROPN
ejpam-6097	197	25	lim	lim	PROPN
ejpam-6097	197	26	sup	sup	NOUN
ejpam-6097	197	27	1	1	NUM
ejpam-6097	197	28	t	t	NOUN
ejpam-6097	197	29	ln	ln	NOUN
ejpam-6097	197	30	û	û	PROPN
ejpam-6097	197	31	=	=	PUNCT
ejpam-6097	197	32	ρ−	ρ−	NOUN
ejpam-6097	197	33	δ2	δ2	VERB
ejpam-6097	197	34	2	2	NUM
ejpam-6097	197	35	−	−	PROPN
ejpam-6097	197	36	ρ	ρ	NUM
ejpam-6097	197	37	k	k	PROPN
ejpam-6097	197	38	ϱ1	ϱ1	PROPN
ejpam-6097	197	39	>	>	PUNCT
ejpam-6097	197	40	0	0	X
ejpam-6097	197	41	.	.	PUNCT
ejpam-6097	198	1	(	(	PUNCT
ejpam-6097	198	2	44	44	NUM
ejpam-6097	198	3	)	)	PUNCT
ejpam-6097	198	4	this	this	PRON
ejpam-6097	198	5	contradicts	contradict	VERB
ejpam-6097	198	6	the	the	DET
ejpam-6097	198	7	lemma	lemma	PROPN
ejpam-6097	198	8	(	(	PUNCT
ejpam-6097	198	9	2	2	NUM
ejpam-6097	198	10	)	)	PUNCT
ejpam-6097	198	11	.	.	PUNCT
ejpam-6097	199	1	therefore	therefore	ADV
ejpam-6097	199	2	,	,	PUNCT
ejpam-6097	199	3	ul	ul	INTJ
ejpam-6097	199	4	>	>	X
ejpam-6097	199	5	0	0	X
ejpam-6097	199	6	.	.	PUNCT
ejpam-6097	200	1	this	this	PRON
ejpam-6097	200	2	completes	complete	VERB
ejpam-6097	200	3	the	the	DET
ejpam-6097	200	4	proof.166	proof.166	NOUN
ejpam-6097	200	5	5.2	5.2	NUM
ejpam-6097	200	6	.	.	PUNCT
ejpam-6097	201	1	extinction	extinction	NOUN
ejpam-6097	201	2	of	of	ADP
ejpam-6097	201	3	the	the	DET
ejpam-6097	201	4	prey	prey	NOUN
ejpam-6097	201	5	population167	population167	PROPN
ejpam-6097	201	6	theorem	theorem	VERB
ejpam-6097	201	7	4	4	NUM
ejpam-6097	201	8	.	.	PUNCT
ejpam-6097	202	1	the	the	DET
ejpam-6097	202	2	prey	prey	PROPN
ejpam-6097	202	3	population	population	NOUN
ejpam-6097	202	4	u	u	PROPN
ejpam-6097	202	5	goes	go	VERB
ejpam-6097	202	6	to	to	PART
ejpam-6097	202	7	extinct	extinct	VERB
ejpam-6097	202	8	with	with	ADP
ejpam-6097	202	9	probability	probability	NOUN
ejpam-6097	202	10	almost	almost	ADV
ejpam-6097	202	11	surely	surely	ADV
ejpam-6097	202	12	when168	when168	AUX
ejpam-6097	202	13	ρ−	ρ−	NOUN
ejpam-6097	202	14	δ2	δ2	VERB
ejpam-6097	202	15	2	2	NUM
ejpam-6097	202	16	≤	≤	NUM
ejpam-6097	202	17	0	0	NUM
ejpam-6097	202	18	.	.	PUNCT
ejpam-6097	203	1	(	(	PUNCT
ejpam-6097	203	2	45	45	NUM
ejpam-6097	203	3	)	)	PUNCT
ejpam-6097	203	4	m.	m.	NOUN
ejpam-6097	203	5	mohamed	mohamed	PROPN
ejpam-6097	203	6	et	et	PROPN
ejpam-6097	203	7	al	al	PROPN
ejpam-6097	203	8	.	.	PUNCT
ejpam-6097	203	9	/	/	SYM
ejpam-6097	203	10	eur	eur	PROPN
ejpam-6097	203	11	.	.	PUNCT
ejpam-6097	204	1	j.	j.	PROPN
ejpam-6097	204	2	pure	pure	PROPN
ejpam-6097	204	3	appl	appl	PROPN
ejpam-6097	204	4	.	.	PROPN
ejpam-6097	204	5	math	math	PROPN
ejpam-6097	204	6	,	,	PUNCT
ejpam-6097	204	7	18	18	NUM
ejpam-6097	204	8	(	(	PUNCT
ejpam-6097	204	9	2	2	NUM
ejpam-6097	204	10	)	)	PUNCT
ejpam-6097	204	11	(	(	PUNCT
ejpam-6097	204	12	2025	2025	NUM
ejpam-6097	204	13	)	)	PUNCT
ejpam-6097	204	14	,	,	PUNCT
ejpam-6097	204	15	6097	6097	NUM
ejpam-6097	204	16	11	11	NUM
ejpam-6097	204	17	of	of	ADP
ejpam-6097	204	18	19	19	NUM
ejpam-6097	204	19	proof	proof	NOUN
ejpam-6097	204	20	.	.	PUNCT
ejpam-6097	205	1	let	let	VERB
ejpam-6097	205	2	us	we	PRON
ejpam-6097	205	3	construct	construct	VERB
ejpam-6097	205	4	the	the	DET
ejpam-6097	205	5	following	follow	VERB
ejpam-6097	205	6	comparison	comparison	NOUN
ejpam-6097	205	7	system;169	system;169	PROPN
ejpam-6097	205	8	du	du	VERB
ejpam-6097	205	9	≤	≤	X
ejpam-6097	205	10	u	u	NOUN
ejpam-6097	205	11	(	(	PUNCT
ejpam-6097	205	12	ρ−	ρ−	NOUN
ejpam-6097	205	13	ρu	ρu	INTJ
ejpam-6097	205	14	k	k	NOUN
ejpam-6097	205	15	)	)	PUNCT
ejpam-6097	205	16	dt+	dt+	NOUN
ejpam-6097	205	17	δudb1(t	δudb1(t	VERB
ejpam-6097	205	18	)	)	PUNCT
ejpam-6097	205	19	,	,	PUNCT
ejpam-6097	205	20	u0	u0	ADJ
ejpam-6097	205	21	=	=	SYM
ejpam-6097	205	22	u0	u0	PROPN
ejpam-6097	205	23	.	.	PROPN
ejpam-6097	205	24	from	from	ADP
ejpam-6097	205	25	itô	itô	PROPN
ejpam-6097	205	26	’s	’s	PART
ejpam-6097	205	27	lemma	lemma	PROPN
ejpam-6097	205	28	for	for	ADP
ejpam-6097	205	29	the	the	DET
ejpam-6097	205	30	function	function	NOUN
ejpam-6097	205	31	φ(t	φ(t	PROPN
ejpam-6097	205	32	,	,	PUNCT
ejpam-6097	205	33	u	u	NOUN
ejpam-6097	205	34	)	)	PUNCT
ejpam-6097	205	35	=	=	SYM
ejpam-6097	205	36	lnu	lnu	NOUN
ejpam-6097	205	37	,	,	PUNCT
ejpam-6097	205	38	we	we	PRON
ejpam-6097	205	39	get170	get170	VERB
ejpam-6097	205	40	d	d	NOUN
ejpam-6097	205	41	lnu	lnu	NOUN
ejpam-6097	205	42	=	=	PUNCT
ejpam-6097	206	1	[	[	PUNCT
ejpam-6097	206	2	ρ−	ρ−	NOUN
ejpam-6097	206	3	ρu	ρu	INTJ
ejpam-6097	206	4	k	k	NOUN
ejpam-6097	206	5	−	−	NOUN
ejpam-6097	206	6	1	1	NUM
ejpam-6097	206	7	2	2	NUM
ejpam-6097	206	8	δ2	δ2	VERB
ejpam-6097	206	9	]	]	PUNCT
ejpam-6097	206	10	dt+	dt+	NOUN
ejpam-6097	206	11	δdb1(t	δdb1(t	NOUN
ejpam-6097	206	12	)	)	PUNCT
ejpam-6097	206	13	.	.	PUNCT
ejpam-6097	207	1	(	(	PUNCT
ejpam-6097	207	2	46	46	X
ejpam-6097	207	3	)	)	PUNCT
ejpam-6097	207	4	applying	apply	VERB
ejpam-6097	207	5	integration	integration	NOUN
ejpam-6097	207	6	on	on	ADP
ejpam-6097	207	7	the	the	DET
ejpam-6097	207	8	interval	interval	NOUN
ejpam-6097	207	9	(	(	PUNCT
ejpam-6097	207	10	0	0	NUM
ejpam-6097	207	11	,	,	PUNCT
ejpam-6097	207	12	t	t	PROPN
ejpam-6097	207	13	)	)	PUNCT
ejpam-6097	207	14	followed	follow	VERB
ejpam-6097	207	15	by	by	ADP
ejpam-6097	207	16	division	division	NOUN
ejpam-6097	207	17	by	by	ADP
ejpam-6097	207	18	t	t	PROPN
ejpam-6097	207	19	to	to	ADP
ejpam-6097	207	20	get171	get171	PROPN
ejpam-6097	207	21	lnu	lnu	PROPN
ejpam-6097	207	22	−	−	PROPN
ejpam-6097	207	23	lnu0	lnu0	PROPN
ejpam-6097	207	24	t	t	NOUN
ejpam-6097	207	25	=	=	SYM
ejpam-6097	207	26	1	1	NUM
ejpam-6097	207	27	t	t	NOUN
ejpam-6097	207	28	∫	∫	PROPN
ejpam-6097	207	29	t	t	PROPN
ejpam-6097	207	30	0	0	NUM
ejpam-6097	208	1	(	(	PUNCT
ejpam-6097	208	2	ρ−	ρ−	NOUN
ejpam-6097	208	3	ρu	ρu	INTJ
ejpam-6097	208	4	k	k	NOUN
ejpam-6097	208	5	−	−	NOUN
ejpam-6097	208	6	1	1	NUM
ejpam-6097	208	7	2	2	NUM
ejpam-6097	208	8	δ2	δ2	ADJ
ejpam-6097	208	9	)	)	PUNCT
ejpam-6097	208	10	ds+	ds+	NOUN
ejpam-6097	208	11	1	1	NUM
ejpam-6097	208	12	t	t	NOUN
ejpam-6097	208	13	∫	∫	PROPN
ejpam-6097	208	14	t	t	PROPN
ejpam-6097	208	15	0	0	NUM
ejpam-6097	208	16	δdb1(s	δdb1(	NOUN
ejpam-6097	208	17	)	)	PUNCT
ejpam-6097	208	18	.	.	PUNCT
ejpam-6097	209	1	(	(	PUNCT
ejpam-6097	209	2	47	47	NUM
ejpam-6097	209	3	)	)	PUNCT
ejpam-6097	209	4	let	let	VERB
ejpam-6097	209	5	us	we	PRON
ejpam-6097	209	6	note	note	VERB
ejpam-6097	209	7	that	that	SCONJ
ejpam-6097	209	8	from	from	ADP
ejpam-6097	209	9	the	the	DET
ejpam-6097	209	10	strong	strong	ADJ
ejpam-6097	209	11	law	law	NOUN
ejpam-6097	209	12	of	of	ADP
ejpam-6097	209	13	large	large	ADJ
ejpam-6097	209	14	number	number	NOUN
ejpam-6097	209	15	,	,	PUNCT
ejpam-6097	209	16	one	one	NUM
ejpam-6097	209	17	gets172	gets172	PROPN
ejpam-6097	209	18	lim	lim	PROPN
ejpam-6097	209	19	sup	sup	NOUN
ejpam-6097	209	20	t→∞	t→∞	NUM
ejpam-6097	209	21	1	1	NUM
ejpam-6097	209	22	t	t	NOUN
ejpam-6097	209	23	∫	∫	PROPN
ejpam-6097	209	24	t	t	PROPN
ejpam-6097	209	25	0	0	NUM
ejpam-6097	209	26	δdb1(s	δdb1(	NOUN
ejpam-6097	209	27	)	)	PUNCT
ejpam-6097	209	28	=	=	SYM
ejpam-6097	209	29	0	0	NUM
ejpam-6097	209	30	,	,	PUNCT
ejpam-6097	209	31	(	(	PUNCT
ejpam-6097	209	32	48	48	NUM
ejpam-6097	209	33	)	)	PUNCT
ejpam-6097	209	34	and	and	CCONJ
ejpam-6097	209	35	this	this	PRON
ejpam-6097	209	36	implies	imply	VERB
ejpam-6097	209	37	that173	that173	PROPN
ejpam-6097	209	38	lim	lim	PROPN
ejpam-6097	209	39	sup	sup	NOUN
ejpam-6097	209	40	t→∞	t→∞	NUM
ejpam-6097	209	41	lnu	lnu	NOUN
ejpam-6097	209	42	t	t	PROPN
ejpam-6097	209	43	≤	≤	NUM
ejpam-6097	209	44	ρ−	ρ−	NOUN
ejpam-6097	209	45	1	1	NUM
ejpam-6097	209	46	2	2	NUM
ejpam-6097	209	47	δ2	δ2	VERB
ejpam-6097	210	1	<	<	X
ejpam-6097	210	2	0	0	NUM
ejpam-6097	210	3	a.s	a.s	PROPN
ejpam-6097	210	4	.	.	PROPN
ejpam-6097	210	5	(	(	PUNCT
ejpam-6097	210	6	49	49	NUM
ejpam-6097	210	7	)	)	PUNCT
ejpam-6097	210	8	using	use	VERB
ejpam-6097	210	9	the	the	DET
ejpam-6097	210	10	comparison	comparison	NOUN
ejpam-6097	210	11	theorem	theorem	VERB
ejpam-6097	210	12	for	for	ADP
ejpam-6097	210	13	sdes	sde	NOUN
ejpam-6097	210	14	,	,	PUNCT
ejpam-6097	210	15	we	we	PRON
ejpam-6097	210	16	have174	have174	PROPN
ejpam-6097	210	17	lim	lim	PROPN
ejpam-6097	210	18	sup	sup	NOUN
ejpam-6097	210	19	t→∞	t→∞	NUM
ejpam-6097	210	20	1	1	NUM
ejpam-6097	210	21	t	t	NOUN
ejpam-6097	210	22	lnu	lnu	NOUN
ejpam-6097	210	23	<	<	X
ejpam-6097	210	24	0	0	PROPN
ejpam-6097	210	25	,	,	PUNCT
ejpam-6097	210	26	thus175	thus175	PROPN
ejpam-6097	210	27	lim	lim	PROPN
ejpam-6097	210	28	t→∞	t→∞	NUM
ejpam-6097	210	29	u	u	NOUN
ejpam-6097	210	30	=	=	NOUN
ejpam-6097	210	31	0	0	NUM
ejpam-6097	210	32	.	.	NOUN
ejpam-6097	210	33	5.3	5.3	NUM
ejpam-6097	210	34	.	.	PUNCT
ejpam-6097	210	35	extinction	extinction	NOUN
ejpam-6097	210	36	for	for	ADP
ejpam-6097	210	37	the	the	DET
ejpam-6097	210	38	predator	predator	NOUN
ejpam-6097	210	39	population176	population176	PROPN
ejpam-6097	210	40	theorem	theorem	VERB
ejpam-6097	210	41	5	5	NUM
ejpam-6097	210	42	.	.	PUNCT
ejpam-6097	211	1	if177	if177	PROPN
ejpam-6097	211	2	γk	γk	PROPN
ejpam-6097	211	3	(	(	PUNCT
ejpam-6097	211	4	ρ−	ρ−	PROPN
ejpam-6097	211	5	δ2	δ2	VERB
ejpam-6097	211	6	2	2	NUM
ejpam-6097	211	7	)	)	PUNCT
ejpam-6097	211	8	<	<	X
ejpam-6097	211	9	ρ	ρ	PROPN
ejpam-6097	211	10	(	(	PUNCT
ejpam-6097	211	11	δ	δ	PROPN
ejpam-6097	211	12	+	+	CCONJ
ejpam-6097	211	13	ϵ2	ϵ2	PROPN
ejpam-6097	211	14	2	2	NUM
ejpam-6097	211	15	)	)	PUNCT
ejpam-6097	211	16	,	,	PUNCT
ejpam-6097	211	17	(	(	PUNCT
ejpam-6097	211	18	50	50	NUM
ejpam-6097	211	19	)	)	PUNCT
ejpam-6097	211	20	then	then	ADV
ejpam-6097	211	21	the	the	DET
ejpam-6097	211	22	predator	predator	NOUN
ejpam-6097	211	23	population	population	NOUN
ejpam-6097	211	24	goes	go	VERB
ejpam-6097	211	25	to	to	PART
ejpam-6097	211	26	extinct	extinct	VERB
ejpam-6097	211	27	with	with	ADP
ejpam-6097	211	28	probability	probability	NOUN
ejpam-6097	211	29	almost	almost	ADV
ejpam-6097	211	30	surely.178	surely.178	NUM
ejpam-6097	211	31	proof	proof	NOUN
ejpam-6097	211	32	.	.	PUNCT
ejpam-6097	212	1	let	let	VERB
ejpam-6097	212	2	us	we	PRON
ejpam-6097	212	3	consider	consider	VERB
ejpam-6097	212	4	the	the	DET
ejpam-6097	212	5	following	follow	VERB
ejpam-6097	212	6	two	two	NUM
ejpam-6097	212	7	cases179	cases179	PROPN
ejpam-6097	212	8	(	(	PUNCT
ejpam-6097	212	9	i	i	NOUN
ejpam-6097	212	10	)	)	PUNCT
ejpam-6097	212	11	ρ−	ρ−	NOUN
ejpam-6097	212	12	δ2	δ2	VERB
ejpam-6097	212	13	2	2	NUM
ejpam-6097	212	14	<	<	X
ejpam-6097	212	15	0	0	NUM
ejpam-6097	212	16	.	.	PUNCT
ejpam-6097	213	1	it	it	PRON
ejpam-6097	213	2	is	be	AUX
ejpam-6097	213	3	clear	clear	ADJ
ejpam-6097	213	4	that	that	SCONJ
ejpam-6097	213	5	this	this	PRON
ejpam-6097	213	6	will	will	AUX
ejpam-6097	213	7	imply	imply	VERB
ejpam-6097	213	8	ul	ul	INTJ
ejpam-6097	213	9	<	<	X
ejpam-6097	213	10	0	0	NUM
ejpam-6097	213	11	.	.	PUNCT
ejpam-6097	214	1	as	as	ADP
ejpam-6097	214	2	in	in	ADP
ejpam-6097	214	3	(	(	PUNCT
ejpam-6097	214	4	41	41	NUM
ejpam-6097	214	5	)	)	PUNCT
ejpam-6097	214	6	,	,	PUNCT
ejpam-6097	214	7	we	we	PRON
ejpam-6097	214	8	have180	have180	PROPN
ejpam-6097	214	9	ln	ln	NOUN
ejpam-6097	214	10	v	v	NOUN
ejpam-6097	214	11	−	−	PROPN
ejpam-6097	214	12	ln	ln	ADJ
ejpam-6097	214	13	v0	v0	PROPN
ejpam-6097	214	14	t	t	PROPN
ejpam-6097	214	15	≤	≤	NUM
ejpam-6097	214	16	−σ	−σ	NOUN
ejpam-6097	214	17	−	−	PROPN
ejpam-6097	214	18	ϵ2	ϵ2	NOUN
ejpam-6097	214	19	2	2	NUM
ejpam-6097	214	20	+	+	CCONJ
ejpam-6097	214	21	γ	γ	PROPN
ejpam-6097	214	22	t	t	PROPN
ejpam-6097	214	23	∫	∫	PROPN
ejpam-6097	214	24	t	t	PROPN
ejpam-6097	214	25	0	0	NUM
ejpam-6097	214	26	uds+	uds+	PROPN
ejpam-6097	214	27	ϵb2(t	ϵb2(t	PROPN
ejpam-6097	214	28	)	)	PUNCT
ejpam-6097	214	29	t	t	PROPN
ejpam-6097	214	30	.	.	PUNCT
ejpam-6097	215	1	(	(	PUNCT
ejpam-6097	215	2	51	51	NUM
ejpam-6097	215	3	)	)	PUNCT
ejpam-6097	215	4	from	from	ADP
ejpam-6097	215	5	this	this	PRON
ejpam-6097	215	6	and	and	CCONJ
ejpam-6097	215	7	the	the	DET
ejpam-6097	215	8	fact	fact	NOUN
ejpam-6097	215	9	that	that	SCONJ
ejpam-6097	215	10	ul	ul	INTJ
ejpam-6097	215	11	<	<	X
ejpam-6097	215	12	0	0	NUM
ejpam-6097	215	13	,	,	PUNCT
ejpam-6097	215	14	then181	then181	PROPN
ejpam-6097	215	15	lim	lim	PROPN
ejpam-6097	215	16	sup	sup	VERB
ejpam-6097	215	17	t→∞	t→∞	NUM
ejpam-6097	215	18	ln	ln	ADJ
ejpam-6097	215	19	v	v	ADP
ejpam-6097	215	20	t	t	PROPN
ejpam-6097	215	21	≤	≤	NUM
ejpam-6097	215	22	−σ	−σ	NOUN
ejpam-6097	216	1	−	−	PROPN
ejpam-6097	216	2	ϵ2	ϵ2	NOUN
ejpam-6097	216	3	2	2	NUM
ejpam-6097	216	4	<	<	X
ejpam-6097	216	5	0	0	NUM
ejpam-6097	216	6	,	,	PUNCT
ejpam-6097	216	7	then	then	ADV
ejpam-6097	216	8	limt→∞v	limt→∞v	PROPN
ejpam-6097	216	9	=	=	PROPN
ejpam-6097	216	10	0	0	PROPN
ejpam-6097	216	11	,	,	PUNCT
ejpam-6097	216	12	which	which	PRON
ejpam-6097	216	13	means	mean	VERB
ejpam-6097	216	14	the	the	DET
ejpam-6097	216	15	extinction	extinction	NOUN
ejpam-6097	216	16	of	of	ADP
ejpam-6097	216	17	predator	predator	NOUN
ejpam-6097	216	18	population	population	NOUN
ejpam-6097	216	19	v	v	NOUN
ejpam-6097	216	20	(	(	PUNCT
ejpam-6097	216	21	t).182	t).182	PROPN
ejpam-6097	216	22	m.	m.	NOUN
ejpam-6097	216	23	mohamed	mohamed	PROPN
ejpam-6097	216	24	et	et	PROPN
ejpam-6097	216	25	al	al	PROPN
ejpam-6097	216	26	.	.	PUNCT
ejpam-6097	216	27	/	/	SYM
ejpam-6097	216	28	eur	eur	PROPN
ejpam-6097	216	29	.	.	PUNCT
ejpam-6097	217	1	j.	j.	PROPN
ejpam-6097	217	2	pure	pure	PROPN
ejpam-6097	217	3	appl	appl	PROPN
ejpam-6097	217	4	.	.	PROPN
ejpam-6097	217	5	math	math	PROPN
ejpam-6097	217	6	,	,	PUNCT
ejpam-6097	217	7	18	18	NUM
ejpam-6097	217	8	(	(	PUNCT
ejpam-6097	217	9	2	2	NUM
ejpam-6097	217	10	)	)	PUNCT
ejpam-6097	217	11	(	(	PUNCT
ejpam-6097	217	12	2025	2025	NUM
ejpam-6097	217	13	)	)	PUNCT
ejpam-6097	217	14	,	,	PUNCT
ejpam-6097	217	15	6097	6097	NUM
ejpam-6097	217	16	12	12	NUM
ejpam-6097	217	17	of	of	ADP
ejpam-6097	217	18	19	19	NUM
ejpam-6097	217	19	(	(	PUNCT
ejpam-6097	217	20	ii	ii	NOUN
ejpam-6097	217	21	)	)	PUNCT
ejpam-6097	217	22	ρ	ρ	NOUN
ejpam-6097	217	23	−	−	PROPN
ejpam-6097	217	24	δ2	δ2	ADJ
ejpam-6097	217	25	2	2	NUM
ejpam-6097	217	26	>	>	X
ejpam-6097	217	27	0	0	NUM
ejpam-6097	217	28	.	.	PUNCT
ejpam-6097	218	1	in	in	ADP
ejpam-6097	218	2	this	this	DET
ejpam-6097	218	3	case	case	NOUN
ejpam-6097	218	4	,	,	PUNCT
ejpam-6097	218	5	one	one	PRON
ejpam-6097	218	6	can	can	AUX
ejpam-6097	218	7	always	always	ADV
ejpam-6097	218	8	ϱ2	ϱ2	VERB
ejpam-6097	218	9	>	>	X
ejpam-6097	218	10	0	0	PUNCT
ejpam-6097	219	1	at	at	ADP
ejpam-6097	219	2	a	a	DET
ejpam-6097	219	3	time	time	NOUN
ejpam-6097	219	4	t1	t1	NOUN
ejpam-6097	219	5	such	such	ADJ
ejpam-6097	219	6	that	that	PRON
ejpam-6097	219	7	for	for	ADP
ejpam-6097	219	8	t	t	PROPN
ejpam-6097	219	9	>	>	PUNCT
ejpam-6097	219	10	t1183	t1183	ADV
ejpam-6097	219	11	and	and	CCONJ
ejpam-6097	219	12	has	have	VERB
ejpam-6097	219	13	b1(t	b1(t	NUM
ejpam-6097	219	14	)	)	PUNCT
ejpam-6097	219	15	t	t	PROPN
ejpam-6097	219	16	<	<	X
ejpam-6097	219	17	ϱ2	ϱ2	PROPN
ejpam-6097	219	18	.	.	PUNCT
ejpam-6097	220	1	thus	thus	ADV
ejpam-6097	220	2	,	,	PUNCT
ejpam-6097	220	3	we	we	PRON
ejpam-6097	220	4	have184	have184	PROPN
ejpam-6097	220	5	lnu−	lnu−	NOUN
ejpam-6097	220	6	lnu0	lnu0	VERB
ejpam-6097	220	7	≤	≤	ADJ
ejpam-6097	220	8	∫	∫	PROPN
ejpam-6097	220	9	t	t	NOUN
ejpam-6097	220	10	0	0	NUM
ejpam-6097	221	1	(	(	PUNCT
ejpam-6097	221	2	ρ−	ρ−	NOUN
ejpam-6097	221	3	δ2	δ2	VERB
ejpam-6097	221	4	2	2	NUM
ejpam-6097	221	5	)	)	PUNCT
ejpam-6097	221	6	ds−	ds−	PROPN
ejpam-6097	221	7	ρ	ρ	X
ejpam-6097	221	8	k	k	PROPN
ejpam-6097	222	1	∫	∫	PROPN
ejpam-6097	223	1	t	t	PROPN
ejpam-6097	223	2	0	0	NUM
ejpam-6097	224	1	uds+	uds+	PROPN
ejpam-6097	224	2	δb1(t	δb1(t	PROPN
ejpam-6097	224	3	)	)	PUNCT
ejpam-6097	224	4	.	.	PUNCT
ejpam-6097	225	1	≤	≤	NUM
ejpam-6097	225	2	(	(	PUNCT
ejpam-6097	225	3	ρ−	ρ−	NOUN
ejpam-6097	225	4	δ2	δ2	VERB
ejpam-6097	225	5	2	2	NUM
ejpam-6097	225	6	+	+	CCONJ
ejpam-6097	225	7	ϱ2	ϱ2	NOUN
ejpam-6097	225	8	)	)	PUNCT
ejpam-6097	225	9	t−	t−	PROPN
ejpam-6097	225	10	ρ	ρ	PROPN
ejpam-6097	225	11	k	k	PROPN
ejpam-6097	225	12	∫	∫	PROPN
ejpam-6097	225	13	t	t	PROPN
ejpam-6097	225	14	0	0	NUM
ejpam-6097	225	15	uds	uds	PROPN
ejpam-6097	225	16	.	.	PROPN
ejpam-6097	226	1	from	from	ADP
ejpam-6097	226	2	[	[	X
ejpam-6097	226	3	30	30	NUM
ejpam-6097	226	4	,	,	PUNCT
ejpam-6097	226	5	lemma	lemma	PROPN
ejpam-6097	226	6	2.2	2.2	NUM
ejpam-6097	226	7	]	]	PUNCT
ejpam-6097	226	8	,	,	PUNCT
ejpam-6097	226	9	one	one	PRON
ejpam-6097	226	10	obtains	obtain	VERB
ejpam-6097	226	11	ul	ul	INTJ
ejpam-6097	227	1	≤	≤	ADJ
ejpam-6097	227	2	k	k	PRON
ejpam-6097	227	3	(	(	PUNCT
ejpam-6097	227	4	ρ−	ρ−	NOUN
ejpam-6097	227	5	δ2	δ2	VERB
ejpam-6097	227	6	2	2	NUM
ejpam-6097	227	7	+	+	CCONJ
ejpam-6097	227	8	ϱ2	ϱ2	NOUN
ejpam-6097	227	9	)	)	PUNCT
ejpam-6097	227	10	ρ	ρ	PROPN
ejpam-6097	227	11	now	now	ADV
ejpam-6097	227	12	,	,	PUNCT
ejpam-6097	227	13	since	since	SCONJ
ejpam-6097	227	14	ϱ2	ϱ2	PROPN
ejpam-6097	227	15	→	→	SYM
ejpam-6097	227	16	0	0	PUNCT
ejpam-6097	227	17	as	as	ADP
ejpam-6097	227	18	t	t	PROPN
ejpam-6097	227	19	→	→	SYM
ejpam-6097	227	20	∞	∞	PROPN
ejpam-6097	227	21	,	,	PUNCT
ejpam-6097	227	22	then	then	ADV
ejpam-6097	227	23	we	we	PRON
ejpam-6097	227	24	have	have	VERB
ejpam-6097	227	25	ul	ul	INTJ
ejpam-6097	228	1	≤	≤	ADJ
ejpam-6097	228	2	k	k	PROPN
ejpam-6097	229	1	(	(	PUNCT
ejpam-6097	229	2	ρ−	ρ−	NOUN
ejpam-6097	229	3	δ2	δ2	VERB
ejpam-6097	229	4	2	2	X
ejpam-6097	229	5	)	)	PUNCT
ejpam-6097	229	6	ρ	ρ	NOUN
ejpam-6097	229	7	.	.	PUNCT
ejpam-6097	230	1	from	from	ADP
ejpam-6097	230	2	(	(	PUNCT
ejpam-6097	230	3	17	17	NUM
ejpam-6097	230	4	)	)	PUNCT
ejpam-6097	230	5	,	,	PUNCT
ejpam-6097	230	6	one	one	PRON
ejpam-6097	230	7	sees	see	VERB
ejpam-6097	230	8	that185	that185	PROPN
ejpam-6097	230	9	lim	lim	NOUN
ejpam-6097	230	10	sup	sup	NOUN
ejpam-6097	230	11	t→∞	t→∞	NUM
ejpam-6097	230	12	1	1	NUM
ejpam-6097	230	13	t	t	NOUN
ejpam-6097	230	14	ln	ln	NOUN
ejpam-6097	230	15	v	v	NOUN
ejpam-6097	230	16	≤	≤	NUM
ejpam-6097	230	17	−σ	−σ	NOUN
ejpam-6097	230	18	−	−	PROPN
ejpam-6097	230	19	ϵ2	ϵ2	NOUN
ejpam-6097	230	20	2	2	NUM
ejpam-6097	230	21	+	+	CCONJ
ejpam-6097	230	22	γul	γul	ADJ
ejpam-6097	230	23	≤	≤	NUM
ejpam-6097	230	24	−σ	−σ	NOUN
ejpam-6097	230	25	−	−	PROPN
ejpam-6097	230	26	ϵ2	ϵ2	NOUN
ejpam-6097	230	27	2	2	NUM
ejpam-6097	231	1	+	+	CCONJ
ejpam-6097	231	2	k	k	X
ejpam-6097	231	3	(	(	PUNCT
ejpam-6097	231	4	ρ−	ρ−	NOUN
ejpam-6097	231	5	δ2	δ2	VERB
ejpam-6097	231	6	2	2	NUM
ejpam-6097	231	7	)	)	PUNCT
ejpam-6097	231	8	ρ	ρ	NOUN
ejpam-6097	231	9	<	<	X
ejpam-6097	231	10	0	0	NUM
ejpam-6097	231	11	.	.	PUNCT
ejpam-6097	232	1	thus	thus	ADV
ejpam-6097	232	2	limt→∞	limt→∞	ADP
ejpam-6097	232	3	v	v	NOUN
ejpam-6097	232	4	=	=	SYM
ejpam-6097	232	5	0.186	0.186	NUM
ejpam-6097	232	6	corollary	corollary	ADJ
ejpam-6097	232	7	2	2	NUM
ejpam-6097	232	8	.	.	PUNCT
ejpam-6097	233	1	the	the	DET
ejpam-6097	233	2	persistence	persistence	NOUN
ejpam-6097	233	3	of	of	ADP
ejpam-6097	233	4	the	the	DET
ejpam-6097	233	5	predator	predator	NOUN
ejpam-6097	233	6	population	population	NOUN
ejpam-6097	233	7	is	be	AUX
ejpam-6097	233	8	obtained	obtain	VERB
ejpam-6097	233	9	by	by	ADP
ejpam-6097	233	10	reversing	reverse	VERB
ejpam-6097	233	11	the	the	DET
ejpam-6097	233	12	con-187	con-187	NOUN
ejpam-6097	233	13	dition	dition	NOUN
ejpam-6097	233	14	(	(	PUNCT
ejpam-6097	233	15	50).188	50).188	NUM
ejpam-6097	233	16	6	6	NUM
ejpam-6097	233	17	.	.	PUNCT
ejpam-6097	234	1	numerical	numerical	ADJ
ejpam-6097	234	2	simulations	simulation	NOUN
ejpam-6097	234	3	and	and	CCONJ
ejpam-6097	234	4	discussion189	discussion189	PROPN
ejpam-6097	234	5	to	to	PART
ejpam-6097	234	6	validate	validate	VERB
ejpam-6097	234	7	our	our	PRON
ejpam-6097	234	8	theoretical	theoretical	ADJ
ejpam-6097	234	9	results	result	NOUN
ejpam-6097	234	10	presented	present	VERB
ejpam-6097	234	11	in	in	ADP
ejpam-6097	234	12	the	the	DET
ejpam-6097	234	13	previous	previous	ADJ
ejpam-6097	234	14	sections	section	NOUN
ejpam-6097	235	1	,	,	PUNCT
ejpam-6097	235	2	we	we	PRON
ejpam-6097	235	3	performed	perform	VERB
ejpam-6097	235	4	several	several	ADJ
ejpam-6097	235	5	numerical	numerical	ADJ
ejpam-6097	235	6	simulations	simulation	NOUN
ejpam-6097	235	7	in	in	ADP
ejpam-6097	235	8	this	this	DET
ejpam-6097	235	9	section	section	NOUN
ejpam-6097	235	10	.	.	PUNCT
ejpam-6097	236	1	we	we	PRON
ejpam-6097	236	2	employ	employ	VERB
ejpam-6097	236	3	the	the	DET
ejpam-6097	236	4	“	"	PUNCT
ejpam-6097	236	5	stochasticrungekuttascalarnoise	stochasticrungekuttascalarnoise	NOUN
ejpam-6097	236	6	”	"	PUNCT
ejpam-6097	236	7	command	command	NOUN
ejpam-6097	236	8	in	in	ADP
ejpam-6097	236	9	mathematica	mathematica	PROPN
ejpam-6097	236	10	11.1	11.1	NUM
ejpam-6097	236	11	to	to	PART
ejpam-6097	236	12	perform	perform	VERB
ejpam-6097	236	13	numerical	numerical	ADJ
ejpam-6097	236	14	simulations	simulation	NOUN
ejpam-6097	236	15	,	,	PUNCT
ejpam-6097	236	16	as	as	SCONJ
ejpam-6097	236	17	described	describe	VERB
ejpam-6097	236	18	on	on	ADP
ejpam-6097	236	19	the	the	DET
ejpam-6097	236	20	wolfram	wolfram	PROPN
ejpam-6097	236	21	website	website	NOUN
ejpam-6097	236	22	.	.	PUNCT
ejpam-6097	237	1	the	the	DET
ejpam-6097	237	2	initial	initial	ADJ
ejpam-6097	237	3	populations	population	NOUN
ejpam-6097	237	4	values	value	NOUN
ejpam-6097	237	5	are	be	AUX
ejpam-6097	237	6	chosen	choose	VERB
ejpam-6097	237	7	to	to	PART
ejpam-6097	237	8	be	be	AUX
ejpam-6097	237	9	u0	u0	ADJ
ejpam-6097	237	10	=	=	ADJ
ejpam-6097	237	11	0.9	0.9	NUM
ejpam-6097	237	12	,	,	PUNCT
ejpam-6097	237	13	v0	v0	NOUN
ejpam-6097	237	14	=	=	PUNCT
ejpam-6097	237	15	0.8	0.8	NUM
ejpam-6097	237	16	.	.	PUNCT
ejpam-6097	238	1	and	and	CCONJ
ejpam-6097	238	2	the	the	DET
ejpam-6097	238	3	set	set	NOUN
ejpam-6097	238	4	of	of	ADP
ejpam-6097	238	5	parameters	parameter	NOUN
ejpam-6097	238	6	are	be	AUX
ejpam-6097	238	7	chosen	choose	VERB
ejpam-6097	238	8	such	such	ADJ
ejpam-6097	238	9	that	that	SCONJ
ejpam-6097	238	10	the	the	DET
ejpam-6097	238	11	stability	stability	NOUN
ejpam-6097	238	12	and	and	CCONJ
ejpam-6097	238	13	coexistence	coexistence	NOUN
ejpam-6097	238	14	between	between	ADP
ejpam-6097	238	15	prey190	prey190	PROPN
ejpam-6097	238	16	and	and	CCONJ
ejpam-6097	238	17	predator	predator	NOUN
ejpam-6097	238	18	populations	population	NOUN
ejpam-6097	238	19	hold	hold	VERB
ejpam-6097	238	20	for	for	ADP
ejpam-6097	238	21	the	the	DET
ejpam-6097	238	22	deterministic	deterministic	ADJ
ejpam-6097	238	23	model	model	NOUN
ejpam-6097	238	24	(	(	PUNCT
ejpam-6097	238	25	1)-(3	1)-(3	NUM
ejpam-6097	238	26	)	)	PUNCT
ejpam-6097	238	27	in	in	ADP
ejpam-6097	238	28	order	order	NOUN
ejpam-6097	238	29	to	to	PART
ejpam-6097	238	30	check	check	VERB
ejpam-6097	238	31	the191	the191	PROPN
ejpam-6097	238	32	effect	effect	NOUN
ejpam-6097	238	33	of	of	ADP
ejpam-6097	238	34	the	the	DET
ejpam-6097	238	35	random	random	ADJ
ejpam-6097	238	36	immigration	immigration	NOUN
ejpam-6097	238	37	of	of	ADP
ejpam-6097	238	38	the	the	DET
ejpam-6097	238	39	system	system	NOUN
ejpam-6097	238	40	as	as	ADP
ejpam-6097	238	41	follows:192	follows:192	X
ejpam-6097	238	42	ρ	ρ	NOUN
ejpam-6097	238	43	=	=	SYM
ejpam-6097	238	44	0.4	0.4	NUM
ejpam-6097	238	45	,	,	PUNCT
ejpam-6097	238	46	k	k	X
ejpam-6097	238	47	=	=	SYM
ejpam-6097	238	48	2.0	2.0	NUM
ejpam-6097	238	49	,	,	PUNCT
ejpam-6097	238	50	α	α	NOUN
ejpam-6097	238	51	=	=	SYM
ejpam-6097	238	52	0.75	0.75	NUM
ejpam-6097	238	53	,	,	PUNCT
ejpam-6097	238	54	β	β	X
ejpam-6097	238	55	=	=	SYM
ejpam-6097	238	56	0.5	0.5	NUM
ejpam-6097	238	57	,	,	PUNCT
ejpam-6097	238	58	σ	σ	NOUN
ejpam-6097	238	59	=	=	SYM
ejpam-6097	238	60	0.2	0.2	NUM
ejpam-6097	238	61	,	,	PUNCT
ejpam-6097	238	62	γ	γ	X
ejpam-6097	238	63	=	=	SYM
ejpam-6097	238	64	0.6	0.6	NUM
ejpam-6097	238	65	,	,	PUNCT
ejpam-6097	238	66	λ	λ	X
ejpam-6097	238	67	=	=	NOUN
ejpam-6097	238	68	0.1	0.1	NUM
ejpam-6097	238	69	.	.	PUNCT
ejpam-6097	239	1	(	(	PUNCT
ejpam-6097	239	2	52	52	NUM
ejpam-6097	239	3	)	)	PUNCT
ejpam-6097	239	4	m.	m.	NOUN
ejpam-6097	239	5	mohamed	mohamed	PROPN
ejpam-6097	239	6	et	et	PROPN
ejpam-6097	239	7	al	al	PROPN
ejpam-6097	239	8	.	.	PUNCT
ejpam-6097	239	9	/	/	SYM
ejpam-6097	239	10	eur	eur	PROPN
ejpam-6097	239	11	.	.	PUNCT
ejpam-6097	240	1	j.	j.	PROPN
ejpam-6097	240	2	pure	pure	PROPN
ejpam-6097	240	3	appl	appl	PROPN
ejpam-6097	240	4	.	.	PROPN
ejpam-6097	240	5	math	math	PROPN
ejpam-6097	240	6	,	,	PUNCT
ejpam-6097	240	7	18	18	NUM
ejpam-6097	240	8	(	(	PUNCT
ejpam-6097	240	9	2	2	NUM
ejpam-6097	240	10	)	)	PUNCT
ejpam-6097	240	11	(	(	PUNCT
ejpam-6097	240	12	2025	2025	NUM
ejpam-6097	240	13	)	)	PUNCT
ejpam-6097	240	14	,	,	PUNCT
ejpam-6097	240	15	6097	6097	NUM
ejpam-6097	240	16	13	13	NUM
ejpam-6097	240	17	of	of	ADP
ejpam-6097	240	18	19	19	NUM
ejpam-6097	240	19	since	since	SCONJ
ejpam-6097	240	20	the	the	DET
ejpam-6097	240	21	model	model	NOUN
ejpam-6097	240	22	equations	equation	NOUN
ejpam-6097	240	23	in	in	ADP
ejpam-6097	240	24	(	(	PUNCT
ejpam-6097	240	25	4)-(6	4)-(6	NUM
ejpam-6097	240	26	)	)	PUNCT
ejpam-6097	240	27	are	be	AUX
ejpam-6097	240	28	taken	take	VERB
ejpam-6097	240	29	to	to	PART
ejpam-6097	240	30	be	be	AUX
ejpam-6097	240	31	dimensionless	dimensionless	NOUN
ejpam-6097	240	32	,	,	PUNCT
ejpam-6097	240	33	the	the	DET
ejpam-6097	240	34	parameters	parameter	NOUN
ejpam-6097	240	35	were193	were193	PROPN
ejpam-6097	240	36	freely	freely	ADV
ejpam-6097	240	37	chosen	choose	VERB
ejpam-6097	240	38	.	.	PUNCT
ejpam-6097	241	1	with	with	ADP
ejpam-6097	241	2	these	these	DET
ejpam-6097	241	3	selections	selection	NOUN
ejpam-6097	241	4	,	,	PUNCT
ejpam-6097	241	5	our	our	PRON
ejpam-6097	241	6	persistence	persistence	NOUN
ejpam-6097	241	7	equilibrium	equilibrium	NOUN
ejpam-6097	241	8	point	point	NOUN
ejpam-6097	241	9	is	be	AUX
ejpam-6097	241	10	(	(	PUNCT
ejpam-6097	241	11	u∗	u∗	ADJ
ejpam-6097	241	12	,	,	PUNCT
ejpam-6097	241	13	v∗	v∗	PROPN
ejpam-6097	241	14	)	)	PUNCT
ejpam-6097	241	15	≈194	≈194	NOUN
ejpam-6097	241	16	(	(	PUNCT
ejpam-6097	241	17	0.5254	0.5254	NUM
ejpam-6097	241	18	,	,	PUNCT
ejpam-6097	241	19	0.4965	0.4965	NUM
ejpam-6097	241	20	)	)	PUNCT
ejpam-6097	241	21	.	.	PUNCT
ejpam-6097	242	1	now	now	ADV
ejpam-6097	242	2	,	,	PUNCT
ejpam-6097	242	3	to	to	PART
ejpam-6097	242	4	study	study	VERB
ejpam-6097	242	5	the	the	DET
ejpam-6097	242	6	impact	impact	NOUN
ejpam-6097	242	7	of	of	ADP
ejpam-6097	242	8	small	small	ADJ
ejpam-6097	242	9	random	random	ADJ
ejpam-6097	242	10	immigration	immigration	NOUN
ejpam-6097	242	11	on	on	ADP
ejpam-6097	242	12	the	the	DET
ejpam-6097	242	13	prey-195	prey-195	ADJ
ejpam-6097	242	14	predator	predator	NOUN
ejpam-6097	242	15	populations	population	NOUN
ejpam-6097	242	16	(	(	PUNCT
ejpam-6097	242	17	u	u	NOUN
ejpam-6097	242	18	,	,	PUNCT
ejpam-6097	242	19	v	v	NOUN
ejpam-6097	242	20	)	)	PUNCT
ejpam-6097	242	21	,	,	PUNCT
ejpam-6097	242	22	several	several	ADJ
ejpam-6097	242	23	considerations	consideration	NOUN
ejpam-6097	242	24	of	of	ADP
ejpam-6097	242	25	δ	δ	PROPN
ejpam-6097	242	26	and	and	CCONJ
ejpam-6097	242	27	ϵ	ϵ	PROPN
ejpam-6097	242	28	were	be	AUX
ejpam-6097	242	29	taken	take	VERB
ejpam-6097	242	30	into	into	ADP
ejpam-6097	242	31	account196	account196	PROPN
ejpam-6097	242	32	(	(	PUNCT
ejpam-6097	242	33	δ	δ	PROPN
ejpam-6097	242	34	=	=	SYM
ejpam-6097	242	35	0	0	NUM
ejpam-6097	242	36	,	,	PUNCT
ejpam-6097	242	37	ϵ	ϵ	X
ejpam-6097	242	38	=	=	SYM
ejpam-6097	242	39	0	0	NUM
ejpam-6097	242	40	)	)	PUNCT
ejpam-6097	242	41	,	,	PUNCT
ejpam-6097	242	42	(	(	PUNCT
ejpam-6097	242	43	δ	δ	X
ejpam-6097	242	44	=	=	NOUN
ejpam-6097	242	45	0.05	0.05	NUM
ejpam-6097	242	46	,	,	PUNCT
ejpam-6097	242	47	ϵ	ϵ	X
ejpam-6097	242	48	=	=	NOUN
ejpam-6097	242	49	0.05	0.05	NUM
ejpam-6097	242	50	)	)	PUNCT
ejpam-6097	242	51	,	,	PUNCT
ejpam-6097	242	52	(	(	PUNCT
ejpam-6097	242	53	δ	δ	NOUN
ejpam-6097	242	54	=	=	PUNCT
ejpam-6097	242	55	0.4	0.4	NUM
ejpam-6097	242	56	,	,	PUNCT
ejpam-6097	242	57	ϵ	ϵ	X
ejpam-6097	242	58	=	=	SYM
ejpam-6097	242	59	0.4	0.4	NUM
ejpam-6097	242	60	)	)	PUNCT
ejpam-6097	242	61	,	,	PUNCT
ejpam-6097	242	62	(	(	PUNCT
ejpam-6097	242	63	δ	δ	NOUN
ejpam-6097	242	64	=	=	PUNCT
ejpam-6097	242	65	0.4	0.4	NUM
ejpam-6097	242	66	,	,	PUNCT
ejpam-6097	242	67	ϵ	ϵ	X
ejpam-6097	242	68	=	=	SYM
ejpam-6097	242	69	1.2	1.2	NUM
ejpam-6097	242	70	)	)	PUNCT
ejpam-6097	242	71	and197	and197	PROPN
ejpam-6097	242	72	(	(	PUNCT
ejpam-6097	242	73	δ	δ	X
ejpam-6097	242	74	=	=	SYM
ejpam-6097	242	75	1.0	1.0	NUM
ejpam-6097	242	76	,	,	PUNCT
ejpam-6097	242	77	ϵ	ϵ	X
ejpam-6097	242	78	=	=	SYM
ejpam-6097	242	79	0.1).198	0.1).198	PROPN
ejpam-6097	242	80	199	199	NUM
ejpam-6097	242	81	0	0	NUM
ejpam-6097	242	82	20	20	NUM
ejpam-6097	242	83	40	40	NUM
ejpam-6097	242	84	60	60	NUM
ejpam-6097	242	85	80	80	NUM
ejpam-6097	242	86	100	100	NUM
ejpam-6097	242	87	0.0	0.0	NUM
ejpam-6097	242	88	0.2	0.2	NUM
ejpam-6097	242	89	0.4	0.4	NUM
ejpam-6097	242	90	0.6	0.6	NUM
ejpam-6097	242	91	0.8	0.8	NUM
ejpam-6097	242	92	1.0	1.0	NUM
ejpam-6097	242	93	1.2	1.2	NUM
ejpam-6097	242	94	1.4	1.4	NUM
ejpam-6097	242	95	time	time	NOUN
ejpam-6097	242	96	p	p	X
ejpam-6097	242	97	o	o	X
ejpam-6097	242	98	p	p	X
ejpam-6097	242	99	u	u	X
ejpam-6097	242	100	la	la	X
ejpam-6097	242	101	ti	ti	X
ejpam-6097	242	102	o	o	VERB
ejpam-6097	242	103	n	n	ADP
ejpam-6097	242	104	prey	prey	NOUN
ejpam-6097	242	105	predator	predator	NOUN
ejpam-6097	242	106	(	(	PUNCT
ejpam-6097	242	107	a	a	DET
ejpam-6097	242	108	)	)	PUNCT
ejpam-6097	242	109	time	time	NOUN
ejpam-6097	242	110	series	series	NOUN
ejpam-6097	242	111	0.0	0.0	NUM
ejpam-6097	242	112	0.2	0.2	NUM
ejpam-6097	242	113	0.4	0.4	NUM
ejpam-6097	242	114	0.6	0.6	NUM
ejpam-6097	242	115	0.8	0.8	NUM
ejpam-6097	242	116	1.0	1.0	NUM
ejpam-6097	242	117	1.2	1.2	NUM
ejpam-6097	242	118	1.4	1.4	NUM
ejpam-6097	242	119	0.0	0.0	NUM
ejpam-6097	242	120	0.2	0.2	NUM
ejpam-6097	242	121	0.4	0.4	NUM
ejpam-6097	242	122	0.6	0.6	NUM
ejpam-6097	242	123	0.8	0.8	NUM
ejpam-6097	242	124	1.0	1.0	NUM
ejpam-6097	242	125	1.2	1.2	NUM
ejpam-6097	242	126	1.4	1.4	NUM
ejpam-6097	242	127	prey	prey	NOUN
ejpam-6097	242	128	p	p	PROPN
ejpam-6097	242	129	re	re	PROPN
ejpam-6097	242	130	d	d	X
ejpam-6097	242	131	a	a	PRON
ejpam-6097	242	132	to	to	ADP
ejpam-6097	242	133	r	r	NOUN
ejpam-6097	242	134	(	(	PUNCT
ejpam-6097	242	135	b	b	NOUN
ejpam-6097	242	136	)	)	PUNCT
ejpam-6097	242	137	phase	phase	NOUN
ejpam-6097	242	138	plane	plane	NOUN
ejpam-6097	242	139	figure	figure	NOUN
ejpam-6097	242	140	1	1	NUM
ejpam-6097	242	141	:	:	PUNCT
ejpam-6097	242	142	dynamical	dynamical	ADJ
ejpam-6097	242	143	behaviour	behaviour	NOUN
ejpam-6097	242	144	for	for	ADP
ejpam-6097	242	145	the	the	DET
ejpam-6097	242	146	deterministic	deterministic	ADJ
ejpam-6097	242	147	model	model	NOUN
ejpam-6097	242	148	(	(	PUNCT
ejpam-6097	242	149	1)-(3	1)-(3	NUM
ejpam-6097	242	150	)	)	PUNCT
ejpam-6097	242	151	with	with	ADP
ejpam-6097	242	152	initial	initial	ADJ
ejpam-6097	242	153	values	value	NOUN
ejpam-6097	242	154	(	(	PUNCT
ejpam-6097	242	155	u0	u0	ADJ
ejpam-6097	242	156	=	=	ADJ
ejpam-6097	242	157	0.9	0.9	NUM
ejpam-6097	242	158	,	,	PUNCT
ejpam-6097	242	159	v0	v0	NOUN
ejpam-6097	242	160	=	=	PUNCT
ejpam-6097	242	161	0.8	0.8	NUM
ejpam-6097	242	162	.	.	PUNCT
ejpam-6097	242	163	)	)	PUNCT
ejpam-6097	243	1	and	and	CCONJ
ejpam-6097	243	2	parameters	parameter	NOUN
ejpam-6097	243	3	values	value	NOUN
ejpam-6097	243	4	are	be	AUX
ejpam-6097	243	5	given	give	VERB
ejpam-6097	243	6	in	in	ADP
ejpam-6097	243	7	(	(	PUNCT
ejpam-6097	243	8	52	52	NUM
ejpam-6097	243	9	)	)	PUNCT
ejpam-6097	243	10	.	.	PUNCT
ejpam-6097	244	1	figure1	figure1	PROPN
ejpam-6097	244	2	represents	represent	VERB
ejpam-6097	244	3	the	the	DET
ejpam-6097	244	4	dynamical	dynamical	ADJ
ejpam-6097	244	5	behavior	behavior	NOUN
ejpam-6097	244	6	of	of	ADP
ejpam-6097	244	7	the	the	DET
ejpam-6097	244	8	deterministic	deterministic	ADJ
ejpam-6097	244	9	model	model	NOUN
ejpam-6097	244	10	(	(	PUNCT
ejpam-6097	244	11	1)-(3	1)-(3	NUM
ejpam-6097	244	12	)	)	PUNCT
ejpam-6097	244	13	at	at	ADP
ejpam-6097	244	14	the200	the200	PROPN
ejpam-6097	244	15	equilibrium	equilibrium	NOUN
ejpam-6097	244	16	point	point	NOUN
ejpam-6097	244	17	(	(	PUNCT
ejpam-6097	244	18	u∗	u∗	ADJ
ejpam-6097	244	19	,	,	PUNCT
ejpam-6097	244	20	v∗	v∗	PROPN
ejpam-6097	244	21	)	)	PUNCT
ejpam-6097	244	22	≈	≈	PROPN
ejpam-6097	244	23	(	(	PUNCT
ejpam-6097	244	24	0.5254	0.5254	NUM
ejpam-6097	244	25	,	,	PUNCT
ejpam-6097	244	26	0.4965	0.4965	NUM
ejpam-6097	244	27	)	)	PUNCT
ejpam-6097	244	28	,	,	PUNCT
ejpam-6097	244	29	in	in	ADP
ejpam-6097	244	30	which	which	PRON
ejpam-6097	244	31	the	the	DET
ejpam-6097	244	32	system	system	NOUN
ejpam-6097	244	33	is	be	AUX
ejpam-6097	244	34	stable	stable	ADJ
ejpam-6097	244	35	and	and	CCONJ
ejpam-6097	244	36	persist.201	persist.201	VERB
ejpam-6097	244	37	for	for	ADP
ejpam-6097	244	38	more	more	ADV
ejpam-6097	244	39	detailed	detailed	ADJ
ejpam-6097	244	40	analysis	analysis	NOUN
ejpam-6097	244	41	of	of	ADP
ejpam-6097	244	42	this	this	DET
ejpam-6097	244	43	model	model	NOUN
ejpam-6097	244	44	,	,	PUNCT
ejpam-6097	244	45	we	we	PRON
ejpam-6097	244	46	refer	refer	VERB
ejpam-6097	244	47	to	to	ADP
ejpam-6097	244	48	[	[	X
ejpam-6097	244	49	25].202	25].202	PROPN
ejpam-6097	244	50	203	203	NUM
ejpam-6097	244	51	0	0	NUM
ejpam-6097	244	52	20	20	NUM
ejpam-6097	244	53	40	40	NUM
ejpam-6097	244	54	60	60	NUM
ejpam-6097	244	55	80	80	NUM
ejpam-6097	244	56	100	100	NUM
ejpam-6097	244	57	0.0	0.0	NUM
ejpam-6097	244	58	0.2	0.2	NUM
ejpam-6097	244	59	0.4	0.4	NUM
ejpam-6097	244	60	0.6	0.6	NUM
ejpam-6097	244	61	0.8	0.8	NUM
ejpam-6097	244	62	1.0	1.0	NUM
ejpam-6097	244	63	1.2	1.2	NUM
ejpam-6097	244	64	1.4	1.4	NUM
ejpam-6097	244	65	time	time	NOUN
ejpam-6097	244	66	p	p	X
ejpam-6097	244	67	o	o	X
ejpam-6097	244	68	p	p	X
ejpam-6097	244	69	u	u	X
ejpam-6097	244	70	la	la	X
ejpam-6097	244	71	ti	ti	X
ejpam-6097	244	72	o	o	VERB
ejpam-6097	244	73	n	n	ADP
ejpam-6097	244	74	prey	prey	NOUN
ejpam-6097	244	75	predator	predator	NOUN
ejpam-6097	244	76	(	(	PUNCT
ejpam-6097	244	77	a	a	DET
ejpam-6097	244	78	)	)	PUNCT
ejpam-6097	244	79	time	time	NOUN
ejpam-6097	244	80	series	series	NOUN
ejpam-6097	244	81	0.0	0.0	NUM
ejpam-6097	244	82	0.2	0.2	NUM
ejpam-6097	244	83	0.4	0.4	NUM
ejpam-6097	244	84	0.6	0.6	NUM
ejpam-6097	244	85	0.8	0.8	NUM
ejpam-6097	244	86	1.0	1.0	NUM
ejpam-6097	244	87	1.2	1.2	NUM
ejpam-6097	244	88	1.4	1.4	NUM
ejpam-6097	244	89	0.0	0.0	NUM
ejpam-6097	244	90	0.2	0.2	NUM
ejpam-6097	244	91	0.4	0.4	NUM
ejpam-6097	244	92	0.6	0.6	NUM
ejpam-6097	244	93	0.8	0.8	NUM
ejpam-6097	244	94	1.0	1.0	NUM
ejpam-6097	244	95	1.2	1.2	NUM
ejpam-6097	244	96	1.4	1.4	NUM
ejpam-6097	244	97	prey	prey	NOUN
ejpam-6097	244	98	p	p	PROPN
ejpam-6097	244	99	re	re	PROPN
ejpam-6097	244	100	d	d	X
ejpam-6097	244	101	a	a	PRON
ejpam-6097	244	102	to	to	ADP
ejpam-6097	244	103	r	r	NOUN
ejpam-6097	244	104	(	(	PUNCT
ejpam-6097	244	105	b	b	NOUN
ejpam-6097	244	106	)	)	PUNCT
ejpam-6097	244	107	phase	phase	NOUN
ejpam-6097	244	108	plane	plane	NOUN
ejpam-6097	244	109	figure	figure	NOUN
ejpam-6097	244	110	2	2	NUM
ejpam-6097	244	111	:	:	PUNCT
ejpam-6097	244	112	dynamical	dynamical	ADJ
ejpam-6097	244	113	behaviour	behaviour	NOUN
ejpam-6097	244	114	for	for	ADP
ejpam-6097	244	115	the	the	DET
ejpam-6097	244	116	stochastic	stochastic	ADJ
ejpam-6097	244	117	model	model	NOUN
ejpam-6097	244	118	(	(	PUNCT
ejpam-6097	244	119	4)-(6	4)-(6	NUM
ejpam-6097	244	120	)	)	PUNCT
ejpam-6097	244	121	with	with	ADP
ejpam-6097	244	122	initial	initial	ADJ
ejpam-6097	244	123	values	value	NOUN
ejpam-6097	244	124	(	(	PUNCT
ejpam-6097	244	125	u0	u0	ADJ
ejpam-6097	244	126	=	=	ADJ
ejpam-6097	244	127	0.9	0.9	NUM
ejpam-6097	244	128	,	,	PUNCT
ejpam-6097	244	129	v0	v0	NOUN
ejpam-6097	244	130	=	=	PUNCT
ejpam-6097	244	131	0.8	0.8	NUM
ejpam-6097	244	132	.	.	PUNCT
ejpam-6097	244	133	)	)	PUNCT
ejpam-6097	244	134	,	,	PUNCT
ejpam-6097	244	135	(	(	PUNCT
ejpam-6097	244	136	δ	δ	X
ejpam-6097	244	137	=	=	NOUN
ejpam-6097	244	138	0.05	0.05	NUM
ejpam-6097	244	139	,	,	PUNCT
ejpam-6097	244	140	ϵ	ϵ	X
ejpam-6097	244	141	=	=	NOUN
ejpam-6097	244	142	0.05	0.05	NUM
ejpam-6097	244	143	)	)	PUNCT
ejpam-6097	244	144	and	and	CCONJ
ejpam-6097	244	145	parameters	parameter	NOUN
ejpam-6097	244	146	values	value	NOUN
ejpam-6097	244	147	are	be	AUX
ejpam-6097	244	148	given	give	VERB
ejpam-6097	244	149	in	in	ADP
ejpam-6097	244	150	(	(	PUNCT
ejpam-6097	244	151	52	52	NUM
ejpam-6097	244	152	)	)	PUNCT
ejpam-6097	244	153	.	.	PUNCT
ejpam-6097	245	1	figure	figure	NOUN
ejpam-6097	245	2	2	2	NUM
ejpam-6097	245	3	represents	represent	VERB
ejpam-6097	245	4	the	the	DET
ejpam-6097	245	5	stochastic	stochastic	ADJ
ejpam-6097	245	6	model	model	NOUN
ejpam-6097	245	7	(	(	PUNCT
ejpam-6097	245	8	4)-(6	4)-(6	NUM
ejpam-6097	245	9	)	)	PUNCT
ejpam-6097	245	10	with	with	ADP
ejpam-6097	245	11	(	(	PUNCT
ejpam-6097	245	12	δ	δ	NOUN
ejpam-6097	245	13	=	=	NOUN
ejpam-6097	245	14	0.05	0.05	NUM
ejpam-6097	245	15	,	,	PUNCT
ejpam-6097	245	16	ϵ	ϵ	X
ejpam-6097	245	17	=	=	NOUN
ejpam-6097	245	18	0.05	0.05	NUM
ejpam-6097	245	19	)	)	PUNCT
ejpam-6097	245	20	,	,	PUNCT
ejpam-6097	245	21	in	in	ADP
ejpam-6097	245	22	which	which	PRON
ejpam-6097	245	23	the204	the204	PROPN
ejpam-6097	245	24	calculations	calculation	NOUN
ejpam-6097	245	25	give	give	VERB
ejpam-6097	245	26	the	the	DET
ejpam-6097	245	27	following:205	following:205	PUNCT
ejpam-6097	245	28	•	•	NOUN
ejpam-6097	245	29	ρu∗	ρu∗	PUNCT
ejpam-6097	245	30	k	k	PROPN
ejpam-6097	245	31	−	−	PROPN
ejpam-6097	245	32	αβu∗v∗	αβu∗v∗	PROPN
ejpam-6097	245	33	(	(	PUNCT
ejpam-6097	245	34	1+bu∗)2	1+bu∗)2	ADV
ejpam-6097	245	35	−	−	PROPN
ejpam-6097	246	1	δ2	δ2	ADJ
ejpam-6097	246	2	2	2	NUM
ejpam-6097	246	3	≈	≈	PROPN
ejpam-6097	246	4	0.0425	0.0425	NUM
ejpam-6097	246	5	>	>	SYM
ejpam-6097	246	6	0.206	0.206	NUM
ejpam-6097	246	7	m.	m.	NOUN
ejpam-6097	246	8	mohamed	mohamed	PROPN
ejpam-6097	246	9	et	et	PROPN
ejpam-6097	246	10	al	al	PROPN
ejpam-6097	246	11	.	.	PUNCT
ejpam-6097	246	12	/	/	SYM
ejpam-6097	246	13	eur	eur	PROPN
ejpam-6097	246	14	.	.	PUNCT
ejpam-6097	247	1	j.	j.	PROPN
ejpam-6097	247	2	pure	pure	PROPN
ejpam-6097	247	3	appl	appl	PROPN
ejpam-6097	247	4	.	.	PROPN
ejpam-6097	247	5	math	math	PROPN
ejpam-6097	247	6	,	,	PUNCT
ejpam-6097	247	7	18	18	NUM
ejpam-6097	247	8	(	(	PUNCT
ejpam-6097	247	9	2	2	NUM
ejpam-6097	247	10	)	)	PUNCT
ejpam-6097	247	11	(	(	PUNCT
ejpam-6097	247	12	2025	2025	NUM
ejpam-6097	247	13	)	)	PUNCT
ejpam-6097	247	14	,	,	PUNCT
ejpam-6097	247	15	6097	6097	NUM
ejpam-6097	247	16	14	14	NUM
ejpam-6097	247	17	of	of	ADP
ejpam-6097	247	18	19	19	NUM
ejpam-6097	247	19	•	•	NOUN
ejpam-6097	247	20	λv∗	λv∗	NOUN
ejpam-6097	248	1	−	−	PROPN
ejpam-6097	249	1	ϵ2	ϵ2	NOUN
ejpam-6097	249	2	2	2	NUM
ejpam-6097	250	1	≈	≈	PROPN
ejpam-6097	250	2	0.0484	0.0484	NUM
ejpam-6097	250	3	>	>	SYM
ejpam-6097	250	4	0.207	0.207	NUM
ejpam-6097	250	5	•	•	NOUN
ejpam-6097	250	6	ρ−	ρ−	NOUN
ejpam-6097	250	7	δ2	δ2	VERB
ejpam-6097	250	8	2	2	NUM
ejpam-6097	250	9	≈	≈	PROPN
ejpam-6097	250	10	0.3988	0.3988	NUM
ejpam-6097	250	11	>	>	SYM
ejpam-6097	250	12	0.208	0.208	NUM
ejpam-6097	250	13	•	•	NOUN
ejpam-6097	250	14	γk	γk	NOUN
ejpam-6097	251	1	(	(	PUNCT
ejpam-6097	251	2	ρ−	ρ−	PROPN
ejpam-6097	251	3	δ2	δ2	VERB
ejpam-6097	251	4	2	2	NUM
ejpam-6097	251	5	)	)	PUNCT
ejpam-6097	251	6	−	−	PROPN
ejpam-6097	251	7	ρ	ρ	PROPN
ejpam-6097	251	8	(	(	PUNCT
ejpam-6097	251	9	δ	δ	PROPN
ejpam-6097	251	10	+	+	CCONJ
ejpam-6097	251	11	ϵ2	ϵ2	PROPN
ejpam-6097	251	12	2	2	NUM
ejpam-6097	251	13	)	)	PUNCT
ejpam-6097	252	1	≈	≈	PROPN
ejpam-6097	252	2	0.4478	0.4478	NUM
ejpam-6097	252	3	>	>	PUNCT
ejpam-6097	252	4	0.209	0.209	NUM
ejpam-6097	252	5	thus	thus	ADV
ejpam-6097	252	6	,	,	PUNCT
ejpam-6097	252	7	the	the	DET
ejpam-6097	252	8	conditions	condition	NOUN
ejpam-6097	252	9	of	of	ADP
ejpam-6097	252	10	theorems	theorem	NOUN
ejpam-6097	252	11	2	2	NUM
ejpam-6097	252	12	and	and	CCONJ
ejpam-6097	252	13	3	3	NUM
ejpam-6097	252	14	are	be	AUX
ejpam-6097	252	15	satisfied	satisfied	ADJ
ejpam-6097	252	16	,	,	PUNCT
ejpam-6097	252	17	which	which	PRON
ejpam-6097	252	18	means	mean	VERB
ejpam-6097	252	19	the	the	DET
ejpam-6097	252	20	system	system	NOUN
ejpam-6097	252	21	(	(	PUNCT
ejpam-6097	252	22	4)-(6)210	4)-(6)210	NOUN
ejpam-6097	252	23	is	be	AUX
ejpam-6097	252	24	stochastically	stochastically	ADV
ejpam-6097	252	25	stable	stable	ADJ
ejpam-6097	252	26	and	and	CCONJ
ejpam-6097	252	27	the	the	DET
ejpam-6097	252	28	prey	prey	NOUN
ejpam-6097	252	29	population	population	NOUN
ejpam-6097	252	30	u	u	PROPN
ejpam-6097	252	31	is	be	AUX
ejpam-6097	252	32	weakly	weakly	ADJ
ejpam-6097	252	33	persistence	persistence	NOUN
ejpam-6097	252	34	in	in	ADP
ejpam-6097	252	35	average	average	ADJ
ejpam-6097	252	36	with211	with211	NOUN
ejpam-6097	252	37	probability	probability	NOUN
ejpam-6097	252	38	almost	almost	ADV
ejpam-6097	252	39	surely	surely	ADV
ejpam-6097	252	40	and	and	CCONJ
ejpam-6097	252	41	the	the	DET
ejpam-6097	252	42	predator	predator	NOUN
ejpam-6097	252	43	population	population	NOUN
ejpam-6097	252	44	v	v	X
ejpam-6097	252	45	achieved	achieve	VERB
ejpam-6097	252	46	the	the	DET
ejpam-6097	252	47	persistence	persistence	NOUN
ejpam-6097	252	48	through212	through212	PROPN
ejpam-6097	252	49	simulation	simulation	NOUN
ejpam-6097	252	50	under	under	ADP
ejpam-6097	252	51	the	the	DET
ejpam-6097	252	52	same	same	ADJ
ejpam-6097	252	53	condition.213	condition.213	NOUN
ejpam-6097	252	54	214	214	NUM
ejpam-6097	252	55	0	0	NUM
ejpam-6097	252	56	20	20	NUM
ejpam-6097	252	57	40	40	NUM
ejpam-6097	252	58	60	60	NUM
ejpam-6097	252	59	80	80	NUM
ejpam-6097	252	60	100	100	NUM
ejpam-6097	252	61	0	0	NUM
ejpam-6097	252	62	1	1	NUM
ejpam-6097	252	63	2	2	NUM
ejpam-6097	252	64	3	3	NUM
ejpam-6097	252	65	4	4	NUM
ejpam-6097	252	66	time	time	NOUN
ejpam-6097	253	1	p	p	X
ejpam-6097	253	2	o	o	X
ejpam-6097	253	3	p	p	X
ejpam-6097	253	4	u	u	X
ejpam-6097	253	5	la	la	X
ejpam-6097	253	6	ti	ti	X
ejpam-6097	253	7	o	o	VERB
ejpam-6097	253	8	n	n	ADP
ejpam-6097	253	9	prey	prey	NOUN
ejpam-6097	253	10	predator	predator	NOUN
ejpam-6097	253	11	(	(	PUNCT
ejpam-6097	253	12	a	a	DET
ejpam-6097	253	13	)	)	PUNCT
ejpam-6097	253	14	time	time	NOUN
ejpam-6097	253	15	series	series	NOUN
ejpam-6097	253	16	0.0	0.0	NUM
ejpam-6097	253	17	0.5	0.5	NUM
ejpam-6097	253	18	1.0	1.0	NUM
ejpam-6097	253	19	1.5	1.5	NUM
ejpam-6097	253	20	2.0	2.0	NUM
ejpam-6097	253	21	2.5	2.5	NUM
ejpam-6097	253	22	3.0	3.0	NUM
ejpam-6097	253	23	0.0	0.0	NUM
ejpam-6097	253	24	0.5	0.5	NUM
ejpam-6097	253	25	1.0	1.0	NUM
ejpam-6097	253	26	1.5	1.5	NUM
ejpam-6097	253	27	2.0	2.0	NUM
ejpam-6097	253	28	2.5	2.5	NUM
ejpam-6097	253	29	3.0	3.0	NUM
ejpam-6097	253	30	prey	prey	NOUN
ejpam-6097	253	31	p	p	PROPN
ejpam-6097	253	32	re	re	PROPN
ejpam-6097	253	33	d	d	X
ejpam-6097	253	34	a	a	PRON
ejpam-6097	253	35	to	to	ADP
ejpam-6097	253	36	r	r	NOUN
ejpam-6097	253	37	(	(	PUNCT
ejpam-6097	253	38	b	b	NOUN
ejpam-6097	253	39	)	)	PUNCT
ejpam-6097	253	40	phase	phase	NOUN
ejpam-6097	253	41	plane	plane	NOUN
ejpam-6097	253	42	figure	figure	NOUN
ejpam-6097	253	43	3	3	NUM
ejpam-6097	253	44	:	:	PUNCT
ejpam-6097	253	45	dynamical	dynamical	ADJ
ejpam-6097	253	46	behaviour	behaviour	NOUN
ejpam-6097	253	47	for	for	ADP
ejpam-6097	253	48	the	the	DET
ejpam-6097	253	49	stochastic	stochastic	ADJ
ejpam-6097	253	50	model	model	NOUN
ejpam-6097	253	51	(	(	PUNCT
ejpam-6097	253	52	4)-(6	4)-(6	NUM
ejpam-6097	253	53	)	)	PUNCT
ejpam-6097	253	54	with	with	ADP
ejpam-6097	253	55	initial	initial	ADJ
ejpam-6097	253	56	values	value	NOUN
ejpam-6097	253	57	(	(	PUNCT
ejpam-6097	253	58	u0	u0	ADJ
ejpam-6097	253	59	=	=	ADJ
ejpam-6097	253	60	0.9	0.9	NUM
ejpam-6097	253	61	,	,	PUNCT
ejpam-6097	253	62	v0	v0	NOUN
ejpam-6097	253	63	=	=	PUNCT
ejpam-6097	253	64	0.8	0.8	NUM
ejpam-6097	253	65	.	.	PUNCT
ejpam-6097	253	66	)	)	PUNCT
ejpam-6097	253	67	,	,	PUNCT
ejpam-6097	253	68	(	(	PUNCT
ejpam-6097	253	69	δ	δ	NOUN
ejpam-6097	253	70	=	=	PUNCT
ejpam-6097	253	71	0.4	0.4	NUM
ejpam-6097	253	72	,	,	PUNCT
ejpam-6097	253	73	ϵ	ϵ	X
ejpam-6097	253	74	=	=	SYM
ejpam-6097	253	75	0.4	0.4	NUM
ejpam-6097	253	76	)	)	PUNCT
ejpam-6097	253	77	and	and	CCONJ
ejpam-6097	253	78	parameters	parameter	NOUN
ejpam-6097	253	79	values	value	NOUN
ejpam-6097	253	80	are	be	AUX
ejpam-6097	253	81	given	give	VERB
ejpam-6097	253	82	in	in	ADP
ejpam-6097	253	83	(	(	PUNCT
ejpam-6097	253	84	52	52	NUM
ejpam-6097	253	85	)	)	PUNCT
ejpam-6097	253	86	.	.	PUNCT
ejpam-6097	254	1	figure	figure	NOUN
ejpam-6097	254	2	3	3	NUM
ejpam-6097	254	3	indicates	indicate	VERB
ejpam-6097	254	4	the	the	DET
ejpam-6097	254	5	stochastic	stochastic	ADJ
ejpam-6097	254	6	model	model	NOUN
ejpam-6097	254	7	(	(	PUNCT
ejpam-6097	254	8	4)-(6	4)-(6	NUM
ejpam-6097	254	9	)	)	PUNCT
ejpam-6097	254	10	with	with	ADP
ejpam-6097	254	11	(	(	PUNCT
ejpam-6097	254	12	δ	δ	X
ejpam-6097	254	13	=	=	PUNCT
ejpam-6097	254	14	0.4	0.4	NUM
ejpam-6097	254	15	,	,	PUNCT
ejpam-6097	254	16	ϵ	ϵ	X
ejpam-6097	254	17	=	=	SYM
ejpam-6097	254	18	0.4	0.4	NUM
ejpam-6097	254	19	)	)	PUNCT
ejpam-6097	254	20	,	,	PUNCT
ejpam-6097	254	21	in	in	ADP
ejpam-6097	254	22	which	which	PRON
ejpam-6097	254	23	the215	the215	NOUN
ejpam-6097	254	24	calculations	calculation	NOUN
ejpam-6097	254	25	give	give	VERB
ejpam-6097	254	26	the	the	DET
ejpam-6097	254	27	following:216	following:216	NOUN
ejpam-6097	254	28	•	•	NOUN
ejpam-6097	254	29	ρu∗	ρu∗	VERB
ejpam-6097	254	30	k	k	PROPN
ejpam-6097	254	31	−	−	PROPN
ejpam-6097	254	32	αβu∗v∗	αβu∗v∗	PROPN
ejpam-6097	254	33	(	(	PUNCT
ejpam-6097	254	34	1+bu∗)2	1+bu∗)2	ADV
ejpam-6097	254	35	−	−	PROPN
ejpam-6097	255	1	δ2	δ2	ADJ
ejpam-6097	255	2	2	2	NUM
ejpam-6097	255	3	≈	≈	NUM
ejpam-6097	255	4	−0.0363	−0.0363	NOUN
ejpam-6097	255	5	<	<	X
ejpam-6097	255	6	0.217	0.217	NUM
ejpam-6097	255	7	•	•	NOUN
ejpam-6097	255	8	λv∗	λv∗	NOUN
ejpam-6097	255	9	−	−	PROPN
ejpam-6097	255	10	ϵ2	ϵ2	NOUN
ejpam-6097	255	11	2	2	NUM
ejpam-6097	255	12	≈	≈	NOUN
ejpam-6097	255	13	0−	0−	NUM
ejpam-6097	255	14	0.0305	0.0305	NUM
ejpam-6097	255	15	<	<	X
ejpam-6097	255	16	0.218	0.218	NUM
ejpam-6097	255	17	•	•	NOUN
ejpam-6097	255	18	ρ−	ρ−	NOUN
ejpam-6097	255	19	δ2	δ2	VERB
ejpam-6097	255	20	2	2	NUM
ejpam-6097	255	21	≈	≈	PROPN
ejpam-6097	255	22	0.32	0.32	NUM
ejpam-6097	255	23	>	>	SYM
ejpam-6097	255	24	0.219	0.219	NUM
ejpam-6097	255	25	•	•	NOUN
ejpam-6097	255	26	γk	γk	PROPN
ejpam-6097	256	1	(	(	PUNCT
ejpam-6097	256	2	ρ−	ρ−	PROPN
ejpam-6097	256	3	δ2	δ2	VERB
ejpam-6097	256	4	2	2	NUM
ejpam-6097	256	5	)	)	PUNCT
ejpam-6097	256	6	−	−	PROPN
ejpam-6097	256	7	ρ	ρ	PROPN
ejpam-6097	256	8	(	(	PUNCT
ejpam-6097	256	9	δ	δ	PROPN
ejpam-6097	256	10	+	+	CCONJ
ejpam-6097	256	11	ϵ2	ϵ2	PROPN
ejpam-6097	256	12	2	2	NUM
ejpam-6097	256	13	)	)	PUNCT
ejpam-6097	256	14	≈	≈	PROPN
ejpam-6097	256	15	0.096	0.096	NUM
ejpam-6097	256	16	>	>	X
ejpam-6097	256	17	0.220	0.220	NUM
ejpam-6097	256	18	from	from	ADP
ejpam-6097	256	19	the	the	DET
ejpam-6097	256	20	above	above	ADJ
ejpam-6097	256	21	calculations	calculation	NOUN
ejpam-6097	256	22	,	,	PUNCT
ejpam-6097	256	23	one	one	PRON
ejpam-6097	256	24	can	can	AUX
ejpam-6097	256	25	see	see	VERB
ejpam-6097	256	26	that	that	SCONJ
ejpam-6097	256	27	the	the	DET
ejpam-6097	256	28	conditions	condition	NOUN
ejpam-6097	256	29	of	of	ADP
ejpam-6097	256	30	theorem	theorem	ADJ
ejpam-6097	256	31	2	2	NUM
ejpam-6097	256	32	are	be	AUX
ejpam-6097	256	33	not	not	PART
ejpam-6097	256	34	met,221	met,221	NOUN
ejpam-6097	256	35	and	and	CCONJ
ejpam-6097	256	36	therefore	therefore	ADV
ejpam-6097	256	37	the	the	DET
ejpam-6097	256	38	system	system	NOUN
ejpam-6097	256	39	is	be	AUX
ejpam-6097	256	40	unstable	unstable	ADJ
ejpam-6097	256	41	.	.	PUNCT
ejpam-6097	257	1	the	the	DET
ejpam-6097	257	2	condition	condition	NOUN
ejpam-6097	257	3	of	of	ADP
ejpam-6097	257	4	theorem	theorem	ADJ
ejpam-6097	257	5	3	3	NUM
ejpam-6097	257	6	is	be	AUX
ejpam-6097	257	7	satisfied	satisfied	ADJ
ejpam-6097	257	8	,	,	PUNCT
ejpam-6097	257	9	therefore222	therefore222	PROPN
ejpam-6097	257	10	the	the	DET
ejpam-6097	257	11	prey	prey	NOUN
ejpam-6097	257	12	population	population	NOUN
ejpam-6097	257	13	is	be	AUX
ejpam-6097	257	14	weakly	weakly	ADV
ejpam-6097	257	15	persistent	persistent	ADJ
ejpam-6097	257	16	in	in	ADP
ejpam-6097	257	17	average	average	NOUN
ejpam-6097	257	18	with	with	ADP
ejpam-6097	257	19	probability	probability	NOUN
ejpam-6097	257	20	almost	almost	ADV
ejpam-6097	257	21	surely	surely	ADV
ejpam-6097	257	22	.	.	PUNCT
ejpam-6097	258	1	in223	in223	VERB
ejpam-6097	258	2	the	the	DET
ejpam-6097	258	3	meanwhile	meanwhile	ADJ
ejpam-6097	258	4	,	,	PUNCT
ejpam-6097	258	5	condition	condition	NOUN
ejpam-6097	258	6	of	of	ADP
ejpam-6097	258	7	theorem	theorem	NOUN
ejpam-6097	258	8	5	5	NUM
ejpam-6097	258	9	does	do	AUX
ejpam-6097	258	10	not	not	PART
ejpam-6097	258	11	satisfied	satisfied	ADJ
ejpam-6097	258	12	,	,	PUNCT
ejpam-6097	258	13	which	which	PRON
ejpam-6097	258	14	means	mean	VERB
ejpam-6097	258	15	that	that	SCONJ
ejpam-6097	258	16	the	the	DET
ejpam-6097	258	17	predator224	predator224	PROPN
ejpam-6097	258	18	population	population	NOUN
ejpam-6097	258	19	also	also	ADV
ejpam-6097	258	20	persist	persist	VERB
ejpam-6097	258	21	.	.	PUNCT
ejpam-6097	259	1	however	however	ADV
ejpam-6097	259	2	,	,	PUNCT
ejpam-6097	259	3	one	one	PRON
ejpam-6097	259	4	can	can	AUX
ejpam-6097	259	5	see	see	VERB
ejpam-6097	259	6	that	that	SCONJ
ejpam-6097	259	7	the	the	DET
ejpam-6097	259	8	destabilization	destabilization	NOUN
ejpam-6097	259	9	of	of	ADP
ejpam-6097	259	10	the	the	DET
ejpam-6097	259	11	system	system	NOUN
ejpam-6097	259	12	has225	has225	ADP
ejpam-6097	259	13	the	the	DET
ejpam-6097	259	14	potential	potential	NOUN
ejpam-6097	259	15	to	to	PART
ejpam-6097	259	16	affect	affect	VERB
ejpam-6097	259	17	its	its	PRON
ejpam-6097	259	18	persistence.226	persistence.226	PROPN
ejpam-6097	259	19	227	227	NUM
ejpam-6097	259	20	m.	m.	NOUN
ejpam-6097	259	21	mohamed	mohamed	PROPN
ejpam-6097	259	22	et	et	PROPN
ejpam-6097	259	23	al	al	PROPN
ejpam-6097	259	24	.	.	PUNCT
ejpam-6097	259	25	/	/	SYM
ejpam-6097	259	26	eur	eur	PROPN
ejpam-6097	259	27	.	.	PUNCT
ejpam-6097	260	1	j.	j.	PROPN
ejpam-6097	260	2	pure	pure	PROPN
ejpam-6097	260	3	appl	appl	PROPN
ejpam-6097	260	4	.	.	PROPN
ejpam-6097	260	5	math	math	PROPN
ejpam-6097	260	6	,	,	PUNCT
ejpam-6097	260	7	18	18	NUM
ejpam-6097	260	8	(	(	PUNCT
ejpam-6097	260	9	2	2	NUM
ejpam-6097	260	10	)	)	PUNCT
ejpam-6097	260	11	(	(	PUNCT
ejpam-6097	260	12	2025	2025	NUM
ejpam-6097	260	13	)	)	PUNCT
ejpam-6097	260	14	,	,	PUNCT
ejpam-6097	260	15	6097	6097	NUM
ejpam-6097	260	16	15	15	NUM
ejpam-6097	260	17	of	of	ADP
ejpam-6097	260	18	19	19	NUM
ejpam-6097	260	19	0	0	NUM
ejpam-6097	260	20	20	20	NUM
ejpam-6097	260	21	40	40	NUM
ejpam-6097	260	22	60	60	NUM
ejpam-6097	260	23	80	80	NUM
ejpam-6097	260	24	100	100	NUM
ejpam-6097	260	25	0	0	NUM
ejpam-6097	260	26	1	1	NUM
ejpam-6097	260	27	2	2	NUM
ejpam-6097	260	28	3	3	NUM
ejpam-6097	260	29	4	4	NUM
ejpam-6097	260	30	5	5	NUM
ejpam-6097	260	31	time	time	NOUN
ejpam-6097	260	32	p	p	X
ejpam-6097	260	33	o	o	X
ejpam-6097	260	34	p	p	X
ejpam-6097	260	35	u	u	X
ejpam-6097	260	36	la	la	X
ejpam-6097	260	37	ti	ti	X
ejpam-6097	260	38	o	o	VERB
ejpam-6097	260	39	n	n	ADP
ejpam-6097	260	40	prey	prey	NOUN
ejpam-6097	260	41	predator	predator	NOUN
ejpam-6097	260	42	(	(	PUNCT
ejpam-6097	260	43	a	a	PRON
ejpam-6097	260	44	)	)	PUNCT
ejpam-6097	260	45	time	time	NOUN
ejpam-6097	260	46	series	series	NOUN
ejpam-6097	260	47	0	0	NUM
ejpam-6097	260	48	1	1	NUM
ejpam-6097	260	49	2	2	NUM
ejpam-6097	260	50	3	3	NUM
ejpam-6097	260	51	4	4	NUM
ejpam-6097	260	52	5	5	NUM
ejpam-6097	260	53	0.0	0.0	NUM
ejpam-6097	260	54	0.5	0.5	NUM
ejpam-6097	260	55	1.0	1.0	NUM
ejpam-6097	260	56	1.5	1.5	NUM
ejpam-6097	260	57	2.0	2.0	NUM
ejpam-6097	260	58	2.5	2.5	NUM
ejpam-6097	260	59	3.0	3.0	NUM
ejpam-6097	260	60	prey	prey	NOUN
ejpam-6097	260	61	p	p	PROPN
ejpam-6097	260	62	re	re	PROPN
ejpam-6097	260	63	d	d	X
ejpam-6097	260	64	a	a	PRON
ejpam-6097	260	65	to	to	ADP
ejpam-6097	260	66	r	r	NOUN
ejpam-6097	260	67	(	(	PUNCT
ejpam-6097	260	68	b	b	NOUN
ejpam-6097	260	69	)	)	PUNCT
ejpam-6097	260	70	phase	phase	NOUN
ejpam-6097	260	71	plane	plane	NOUN
ejpam-6097	260	72	figure	figure	NOUN
ejpam-6097	260	73	4	4	NUM
ejpam-6097	260	74	:	:	PUNCT
ejpam-6097	260	75	dynamical	dynamical	ADJ
ejpam-6097	260	76	behaviour	behaviour	NOUN
ejpam-6097	260	77	for	for	ADP
ejpam-6097	260	78	the	the	DET
ejpam-6097	260	79	stochastic	stochastic	ADJ
ejpam-6097	260	80	model	model	NOUN
ejpam-6097	260	81	(	(	PUNCT
ejpam-6097	260	82	4)-(6	4)-(6	NUM
ejpam-6097	260	83	)	)	PUNCT
ejpam-6097	260	84	with	with	ADP
ejpam-6097	260	85	initial	initial	ADJ
ejpam-6097	260	86	values	value	NOUN
ejpam-6097	260	87	(	(	PUNCT
ejpam-6097	260	88	u0	u0	ADJ
ejpam-6097	260	89	=	=	ADJ
ejpam-6097	260	90	0.9	0.9	NUM
ejpam-6097	260	91	,	,	PUNCT
ejpam-6097	260	92	v0	v0	NOUN
ejpam-6097	260	93	=	=	PUNCT
ejpam-6097	260	94	0.8	0.8	NUM
ejpam-6097	260	95	.	.	PUNCT
ejpam-6097	260	96	)	)	PUNCT
ejpam-6097	260	97	,	,	PUNCT
ejpam-6097	260	98	(	(	PUNCT
ejpam-6097	260	99	δ	δ	NOUN
ejpam-6097	260	100	=	=	PUNCT
ejpam-6097	260	101	0.4	0.4	NUM
ejpam-6097	260	102	,	,	PUNCT
ejpam-6097	260	103	ϵ	ϵ	X
ejpam-6097	260	104	=	=	SYM
ejpam-6097	260	105	1.2	1.2	NUM
ejpam-6097	260	106	)	)	PUNCT
ejpam-6097	260	107	and	and	CCONJ
ejpam-6097	260	108	parameters	parameter	NOUN
ejpam-6097	260	109	values	value	NOUN
ejpam-6097	260	110	are	be	AUX
ejpam-6097	260	111	given	give	VERB
ejpam-6097	260	112	in	in	ADP
ejpam-6097	260	113	(	(	PUNCT
ejpam-6097	260	114	52	52	NUM
ejpam-6097	260	115	)	)	PUNCT
ejpam-6097	260	116	.	.	PUNCT
ejpam-6097	261	1	figure	figure	NOUN
ejpam-6097	261	2	4	4	NUM
ejpam-6097	261	3	represents	represent	VERB
ejpam-6097	261	4	the	the	DET
ejpam-6097	261	5	stochastic	stochastic	ADJ
ejpam-6097	261	6	model	model	NOUN
ejpam-6097	261	7	(	(	PUNCT
ejpam-6097	261	8	4)-(6	4)-(6	NUM
ejpam-6097	261	9	)	)	PUNCT
ejpam-6097	261	10	with	with	ADP
ejpam-6097	261	11	(	(	PUNCT
ejpam-6097	261	12	δ	δ	X
ejpam-6097	261	13	=	=	PUNCT
ejpam-6097	261	14	0.4	0.4	NUM
ejpam-6097	261	15	,	,	PUNCT
ejpam-6097	261	16	ϵ	ϵ	X
ejpam-6097	261	17	=	=	SYM
ejpam-6097	261	18	1.2	1.2	NUM
ejpam-6097	261	19	)	)	PUNCT
ejpam-6097	261	20	,	,	PUNCT
ejpam-6097	261	21	in	in	ADP
ejpam-6097	261	22	which	which	PRON
ejpam-6097	261	23	the228	the228	PROPN
ejpam-6097	261	24	calculations	calculation	NOUN
ejpam-6097	261	25	shows	show	VERB
ejpam-6097	261	26	the	the	DET
ejpam-6097	261	27	following:229	following:229	PROPN
ejpam-6097	261	28	•	•	ADP
ejpam-6097	261	29	ρu∗	ρu∗	VERB
ejpam-6097	262	1	k	k	PROPN
ejpam-6097	262	2	−	−	PROPN
ejpam-6097	262	3	αβu∗v∗	αβu∗v∗	PROPN
ejpam-6097	262	4	(	(	PUNCT
ejpam-6097	262	5	1+bu∗)2	1+bu∗)2	ADV
ejpam-6097	262	6	−	−	PROPN
ejpam-6097	263	1	δ2	δ2	ADJ
ejpam-6097	263	2	2	2	NUM
ejpam-6097	263	3	≈	≈	NUM
ejpam-6097	263	4	−0.0363	−0.0363	NOUN
ejpam-6097	263	5	<	<	X
ejpam-6097	263	6	0.230	0.230	NUM
ejpam-6097	263	7	•	•	NOUN
ejpam-6097	263	8	λv∗	λv∗	NOUN
ejpam-6097	263	9	−	−	PROPN
ejpam-6097	263	10	ϵ2	ϵ2	PROPN
ejpam-6097	263	11	2	2	NUM
ejpam-6097	263	12	≈	≈	NOUN
ejpam-6097	263	13	0−	0−	NUM
ejpam-6097	263	14	0.6704	0.6704	NUM
ejpam-6097	263	15	<	<	X
ejpam-6097	263	16	0.231	0.231	NUM
ejpam-6097	263	17	•	•	NOUN
ejpam-6097	263	18	ρ−	ρ−	NOUN
ejpam-6097	263	19	δ2	δ2	VERB
ejpam-6097	263	20	2	2	NUM
ejpam-6097	263	21	≈	≈	PROPN
ejpam-6097	263	22	0.32	0.32	NUM
ejpam-6097	263	23	>	>	SYM
ejpam-6097	263	24	0.232	0.232	NUM
ejpam-6097	263	25	•	•	NOUN
ejpam-6097	263	26	γk	γk	NOUN
ejpam-6097	263	27	(	(	PUNCT
ejpam-6097	263	28	ρ−	ρ−	PROPN
ejpam-6097	263	29	δ2	δ2	VERB
ejpam-6097	263	30	2	2	NUM
ejpam-6097	263	31	)	)	PUNCT
ejpam-6097	263	32	−	−	PROPN
ejpam-6097	263	33	ρ	ρ	PROPN
ejpam-6097	263	34	(	(	PUNCT
ejpam-6097	263	35	δ	δ	PROPN
ejpam-6097	263	36	+	+	CCONJ
ejpam-6097	263	37	ϵ2	ϵ2	PROPN
ejpam-6097	263	38	2	2	NUM
ejpam-6097	263	39	)	)	PUNCT
ejpam-6097	264	1	≈	≈	PROPN
ejpam-6097	264	2	−0.288	−0.288	ADJ
ejpam-6097	264	3	<	<	X
ejpam-6097	264	4	0.233	0.233	NUM
ejpam-6097	264	5	from	from	ADP
ejpam-6097	264	6	the	the	DET
ejpam-6097	264	7	above	above	ADJ
ejpam-6097	264	8	calculations	calculation	NOUN
ejpam-6097	264	9	,	,	PUNCT
ejpam-6097	264	10	one	one	PRON
ejpam-6097	264	11	can	can	AUX
ejpam-6097	264	12	see	see	VERB
ejpam-6097	264	13	that	that	SCONJ
ejpam-6097	264	14	the	the	DET
ejpam-6097	264	15	conditions	condition	NOUN
ejpam-6097	264	16	of	of	ADP
ejpam-6097	264	17	the	the	DET
ejpam-6097	264	18	mean	mean	ADJ
ejpam-6097	264	19	square	square	ADJ
ejpam-6097	264	20	stochas-234	stochas-234	ADJ
ejpam-6097	264	21	tic	tic	ADJ
ejpam-6097	264	22	stability	stability	NOUN
ejpam-6097	264	23	theorem	theorem	VERB
ejpam-6097	264	24	2	2	NUM
ejpam-6097	264	25	are	be	AUX
ejpam-6097	264	26	not	not	PART
ejpam-6097	264	27	satisfied	satisfied	ADJ
ejpam-6097	264	28	,	,	PUNCT
ejpam-6097	264	29	so	so	ADV
ejpam-6097	264	30	the	the	DET
ejpam-6097	264	31	system	system	NOUN
ejpam-6097	264	32	is	be	AUX
ejpam-6097	264	33	unstable	unstable	ADJ
ejpam-6097	264	34	.	.	PUNCT
ejpam-6097	265	1	also	also	ADV
ejpam-6097	265	2	,	,	PUNCT
ejpam-6097	265	3	conditions	condition	NOUN
ejpam-6097	265	4	of235	of235	PRON
ejpam-6097	265	5	theorems	theorem	NOUN
ejpam-6097	265	6	3	3	NUM
ejpam-6097	265	7	and	and	CCONJ
ejpam-6097	265	8	5	5	NUM
ejpam-6097	265	9	are	be	AUX
ejpam-6097	265	10	satisfied	satisfied	ADJ
ejpam-6097	265	11	,	,	PUNCT
ejpam-6097	265	12	which	which	PRON
ejpam-6097	265	13	imply	imply	VERB
ejpam-6097	265	14	that	that	SCONJ
ejpam-6097	265	15	the	the	DET
ejpam-6097	265	16	prey	prey	NOUN
ejpam-6097	265	17	population	population	NOUN
ejpam-6097	265	18	u	u	PROPN
ejpam-6097	265	19	is	be	AUX
ejpam-6097	265	20	weakly	weakly	ADJ
ejpam-6097	265	21	persist236	persist236	PROPN
ejpam-6097	265	22	in	in	ADP
ejpam-6097	265	23	average	average	ADJ
ejpam-6097	265	24	,	,	PUNCT
ejpam-6097	265	25	while	while	SCONJ
ejpam-6097	265	26	the	the	DET
ejpam-6097	265	27	predator	predator	NOUN
ejpam-6097	265	28	population	population	NOUN
ejpam-6097	265	29	v	v	PART
ejpam-6097	265	30	go	go	VERB
ejpam-6097	265	31	to	to	ADP
ejpam-6097	265	32	extinct.237	extinct.237	PROPN
ejpam-6097	265	33	238	238	NUM
ejpam-6097	265	34	0	0	NUM
ejpam-6097	265	35	20	20	NUM
ejpam-6097	265	36	40	40	NUM
ejpam-6097	265	37	60	60	NUM
ejpam-6097	265	38	80	80	NUM
ejpam-6097	265	39	100	100	NUM
ejpam-6097	265	40	0	0	NUM
ejpam-6097	265	41	1	1	NUM
ejpam-6097	265	42	2	2	NUM
ejpam-6097	265	43	3	3	NUM
ejpam-6097	265	44	4	4	NUM
ejpam-6097	265	45	5	5	NUM
ejpam-6097	265	46	time	time	NOUN
ejpam-6097	265	47	p	p	X
ejpam-6097	265	48	o	o	X
ejpam-6097	265	49	p	p	X
ejpam-6097	265	50	u	u	X
ejpam-6097	265	51	la	la	X
ejpam-6097	265	52	ti	ti	X
ejpam-6097	265	53	o	o	VERB
ejpam-6097	265	54	n	n	ADP
ejpam-6097	265	55	prey	prey	NOUN
ejpam-6097	265	56	predator	predator	NOUN
ejpam-6097	265	57	(	(	PUNCT
ejpam-6097	265	58	a	a	DET
ejpam-6097	265	59	)	)	PUNCT
ejpam-6097	265	60	time	time	NOUN
ejpam-6097	265	61	series	series	NOUN
ejpam-6097	265	62	0.0	0.0	NUM
ejpam-6097	265	63	0.2	0.2	NUM
ejpam-6097	265	64	0.4	0.4	NUM
ejpam-6097	265	65	0.6	0.6	NUM
ejpam-6097	265	66	0.8	0.8	NUM
ejpam-6097	265	67	1.0	1.0	NUM
ejpam-6097	265	68	1.2	1.2	NUM
ejpam-6097	265	69	1.4	1.4	NUM
ejpam-6097	265	70	0.0	0.0	NUM
ejpam-6097	265	71	0.2	0.2	NUM
ejpam-6097	265	72	0.4	0.4	NUM
ejpam-6097	265	73	0.6	0.6	NUM
ejpam-6097	265	74	0.8	0.8	NUM
ejpam-6097	265	75	1.0	1.0	NUM
ejpam-6097	265	76	1.2	1.2	NUM
ejpam-6097	265	77	1.4	1.4	NUM
ejpam-6097	265	78	prey	prey	NOUN
ejpam-6097	265	79	p	p	PROPN
ejpam-6097	265	80	re	re	PROPN
ejpam-6097	265	81	d	d	X
ejpam-6097	265	82	a	a	PRON
ejpam-6097	265	83	to	to	ADP
ejpam-6097	265	84	r	r	NOUN
ejpam-6097	265	85	(	(	PUNCT
ejpam-6097	265	86	b	b	NOUN
ejpam-6097	265	87	)	)	PUNCT
ejpam-6097	265	88	phase	phase	NOUN
ejpam-6097	265	89	plane	plane	NOUN
ejpam-6097	265	90	figure	figure	NOUN
ejpam-6097	265	91	5	5	NUM
ejpam-6097	265	92	:	:	PUNCT
ejpam-6097	265	93	dynamical	dynamical	ADJ
ejpam-6097	265	94	behaviour	behaviour	NOUN
ejpam-6097	265	95	for	for	ADP
ejpam-6097	265	96	the	the	DET
ejpam-6097	265	97	stochastic	stochastic	ADJ
ejpam-6097	265	98	model	model	NOUN
ejpam-6097	265	99	(	(	PUNCT
ejpam-6097	265	100	4)-(6	4)-(6	NUM
ejpam-6097	265	101	)	)	PUNCT
ejpam-6097	265	102	with	with	ADP
ejpam-6097	265	103	initial	initial	ADJ
ejpam-6097	265	104	values	value	NOUN
ejpam-6097	265	105	(	(	PUNCT
ejpam-6097	265	106	u0	u0	ADJ
ejpam-6097	265	107	=	=	ADJ
ejpam-6097	265	108	0.9	0.9	NUM
ejpam-6097	265	109	,	,	PUNCT
ejpam-6097	265	110	v0	v0	NOUN
ejpam-6097	265	111	=	=	PUNCT
ejpam-6097	265	112	0.8	0.8	NUM
ejpam-6097	265	113	.	.	PUNCT
ejpam-6097	265	114	)	)	PUNCT
ejpam-6097	265	115	,	,	PUNCT
ejpam-6097	265	116	(	(	PUNCT
ejpam-6097	265	117	δ	δ	X
ejpam-6097	265	118	=	=	SYM
ejpam-6097	265	119	1.0	1.0	NUM
ejpam-6097	265	120	,	,	PUNCT
ejpam-6097	265	121	ϵ	ϵ	X
ejpam-6097	265	122	=	=	SYM
ejpam-6097	265	123	0.1	0.1	NUM
ejpam-6097	265	124	)	)	PUNCT
ejpam-6097	265	125	and	and	CCONJ
ejpam-6097	265	126	parameters	parameter	NOUN
ejpam-6097	265	127	values	value	NOUN
ejpam-6097	265	128	are	be	AUX
ejpam-6097	265	129	given	give	VERB
ejpam-6097	265	130	in	in	ADP
ejpam-6097	265	131	(	(	PUNCT
ejpam-6097	265	132	52	52	NUM
ejpam-6097	265	133	)	)	PUNCT
ejpam-6097	265	134	.	.	PUNCT
ejpam-6097	266	1	m.	m.	PROPN
ejpam-6097	266	2	mohamed	mohamed	PROPN
ejpam-6097	266	3	et	et	PROPN
ejpam-6097	266	4	al	al	PROPN
ejpam-6097	266	5	.	.	PUNCT
ejpam-6097	266	6	/	/	SYM
ejpam-6097	266	7	eur	eur	PROPN
ejpam-6097	266	8	.	.	PUNCT
ejpam-6097	267	1	j.	j.	PROPN
ejpam-6097	267	2	pure	pure	PROPN
ejpam-6097	267	3	appl	appl	PROPN
ejpam-6097	267	4	.	.	PROPN
ejpam-6097	267	5	math	math	PROPN
ejpam-6097	267	6	,	,	PUNCT
ejpam-6097	267	7	18	18	NUM
ejpam-6097	267	8	(	(	PUNCT
ejpam-6097	267	9	2	2	NUM
ejpam-6097	267	10	)	)	PUNCT
ejpam-6097	267	11	(	(	PUNCT
ejpam-6097	267	12	2025	2025	NUM
ejpam-6097	267	13	)	)	PUNCT
ejpam-6097	267	14	,	,	PUNCT
ejpam-6097	267	15	6097	6097	NUM
ejpam-6097	267	16	16	16	NUM
ejpam-6097	267	17	of	of	ADP
ejpam-6097	267	18	19	19	NUM
ejpam-6097	267	19	figure	figure	NOUN
ejpam-6097	267	20	5	5	NUM
ejpam-6097	267	21	represents	represent	VERB
ejpam-6097	267	22	the	the	DET
ejpam-6097	267	23	stochastic	stochastic	ADJ
ejpam-6097	267	24	model	model	NOUN
ejpam-6097	267	25	(	(	PUNCT
ejpam-6097	267	26	4)-(6	4)-(6	NUM
ejpam-6097	267	27	)	)	PUNCT
ejpam-6097	267	28	with	with	ADP
ejpam-6097	267	29	(	(	PUNCT
ejpam-6097	267	30	δ	δ	X
ejpam-6097	267	31	=	=	SYM
ejpam-6097	267	32	1.0	1.0	NUM
ejpam-6097	267	33	,	,	PUNCT
ejpam-6097	267	34	ϵ	ϵ	X
ejpam-6097	267	35	=	=	SYM
ejpam-6097	267	36	0.1	0.1	NUM
ejpam-6097	267	37	)	)	PUNCT
ejpam-6097	267	38	,	,	PUNCT
ejpam-6097	267	39	in	in	ADP
ejpam-6097	267	40	which	which	PRON
ejpam-6097	267	41	the239	the239	PROPN
ejpam-6097	267	42	calculations	calculation	NOUN
ejpam-6097	267	43	shows	show	VERB
ejpam-6097	267	44	the	the	DET
ejpam-6097	267	45	following:240	following:240	NOUN
ejpam-6097	267	46	•	•	NOUN
ejpam-6097	267	47	ρu∗	ρu∗	VERB
ejpam-6097	267	48	k	k	PROPN
ejpam-6097	267	49	−	−	PROPN
ejpam-6097	267	50	αβu∗v∗	αβu∗v∗	PROPN
ejpam-6097	267	51	(	(	PUNCT
ejpam-6097	267	52	1+bu∗)2	1+bu∗)2	ADV
ejpam-6097	267	53	−	−	PROPN
ejpam-6097	268	1	δ2	δ2	ADJ
ejpam-6097	268	2	2	2	NUM
ejpam-6097	268	3	≈	≈	NUM
ejpam-6097	268	4	−0.4563	−0.4563	NOUN
ejpam-6097	268	5	<	<	X
ejpam-6097	268	6	0.241	0.241	NUM
ejpam-6097	268	7	•	•	NOUN
ejpam-6097	268	8	λv∗	λv∗	NOUN
ejpam-6097	268	9	−	−	PROPN
ejpam-6097	268	10	ϵ2	ϵ2	NOUN
ejpam-6097	268	11	2	2	NUM
ejpam-6097	268	12	≈	≈	PROPN
ejpam-6097	268	13	00.0447	00.0447	NOUN
ejpam-6097	268	14	>	>	X
ejpam-6097	268	15	0.242	0.242	NUM
ejpam-6097	268	16	•	•	NOUN
ejpam-6097	268	17	ρ−	ρ−	NOUN
ejpam-6097	268	18	δ2	δ2	VERB
ejpam-6097	268	19	2	2	NUM
ejpam-6097	269	1	≈	≈	NOUN
ejpam-6097	269	2	−0.1	−0.1	PROPN
ejpam-6097	269	3	<	<	X
ejpam-6097	269	4	0.243	0.243	NUM
ejpam-6097	269	5	•	•	NOUN
ejpam-6097	269	6	γk	γk	PROPN
ejpam-6097	269	7	(	(	PUNCT
ejpam-6097	269	8	ρ−	ρ−	PROPN
ejpam-6097	269	9	δ2	δ2	VERB
ejpam-6097	269	10	2	2	NUM
ejpam-6097	269	11	)	)	PUNCT
ejpam-6097	269	12	−	−	PROPN
ejpam-6097	269	13	ρ	ρ	PROPN
ejpam-6097	269	14	(	(	PUNCT
ejpam-6097	269	15	δ	δ	PROPN
ejpam-6097	269	16	+	+	CCONJ
ejpam-6097	269	17	ϵ2	ϵ2	PROPN
ejpam-6097	269	18	2	2	NUM
ejpam-6097	269	19	)	)	PUNCT
ejpam-6097	270	1	≈	≈	PROPN
ejpam-6097	270	2	−0.723	−0.723	PROPN
ejpam-6097	270	3	<	<	X
ejpam-6097	270	4	0.244	0.244	NUM
ejpam-6097	270	5	here	here	ADV
ejpam-6097	270	6	,	,	PUNCT
ejpam-6097	270	7	the	the	DET
ejpam-6097	270	8	calculations	calculation	NOUN
ejpam-6097	270	9	show	show	VERB
ejpam-6097	270	10	that	that	SCONJ
ejpam-6097	270	11	the	the	DET
ejpam-6097	270	12	conditions	condition	NOUN
ejpam-6097	270	13	of	of	ADP
ejpam-6097	270	14	theorems	theorem	NOUN
ejpam-6097	270	15	2	2	NUM
ejpam-6097	270	16	and	and	CCONJ
ejpam-6097	270	17	3	3	NUM
ejpam-6097	270	18	are	be	AUX
ejpam-6097	270	19	not	not	PART
ejpam-6097	270	20	satisfied	satisfied	ADJ
ejpam-6097	270	21	,	,	PUNCT
ejpam-6097	270	22	while245	while245	PROPN
ejpam-6097	270	23	the	the	DET
ejpam-6097	270	24	condition	condition	NOUN
ejpam-6097	270	25	of	of	ADP
ejpam-6097	270	26	theorem	theorem	ADJ
ejpam-6097	270	27	5	5	NUM
ejpam-6097	270	28	is	be	AUX
ejpam-6097	270	29	satisfied	satisfied	ADJ
ejpam-6097	270	30	,	,	PUNCT
ejpam-6097	270	31	which	which	PRON
ejpam-6097	270	32	means	mean	VERB
ejpam-6097	270	33	that	that	SCONJ
ejpam-6097	270	34	neither	neither	CCONJ
ejpam-6097	270	35	stability	stability	NOUN
ejpam-6097	270	36	nor	nor	CCONJ
ejpam-6097	270	37	persistence246	persistence246	PROPN
ejpam-6097	270	38	of	of	ADP
ejpam-6097	270	39	the	the	DET
ejpam-6097	270	40	stochastic	stochastic	ADJ
ejpam-6097	270	41	system	system	NOUN
ejpam-6097	270	42	took	take	VERB
ejpam-6097	270	43	place	place	NOUN
ejpam-6097	270	44	,	,	PUNCT
ejpam-6097	270	45	but	but	CCONJ
ejpam-6097	270	46	the	the	DET
ejpam-6097	270	47	system	system	NOUN
ejpam-6097	270	48	collapsed	collapse	VERB
ejpam-6097	270	49	for	for	ADP
ejpam-6097	270	50	both	both	CCONJ
ejpam-6097	270	51	prey	prey	NOUN
ejpam-6097	270	52	and	and	CCONJ
ejpam-6097	270	53	predator247	predator247	NOUN
ejpam-6097	270	54	populations	population	NOUN
ejpam-6097	270	55	.	.	PUNCT
ejpam-6097	271	1	in	in	ADP
ejpam-6097	271	2	this	this	DET
ejpam-6097	271	3	figure	figure	NOUN
ejpam-6097	271	4	,	,	PUNCT
ejpam-6097	271	5	high	high	ADJ
ejpam-6097	271	6	prey	prey	PROPN
ejpam-6097	271	7	immigration	immigration	NOUN
ejpam-6097	271	8	results	result	NOUN
ejpam-6097	271	9	in	in	ADP
ejpam-6097	271	10	species	specie	NOUN
ejpam-6097	271	11	extinction	extinction	NOUN
ejpam-6097	271	12	,	,	PUNCT
ejpam-6097	271	13	which248	which248	PROPN
ejpam-6097	271	14	contradicts	contradict	VERB
ejpam-6097	271	15	the	the	DET
ejpam-6097	271	16	immigration	immigration	NOUN
ejpam-6097	271	17	argument	argument	NOUN
ejpam-6097	271	18	.	.	PUNCT
ejpam-6097	272	1	this	this	DET
ejpam-6097	272	2	phenomenon	phenomenon	NOUN
ejpam-6097	272	3	illustrates	illustrate	VERB
ejpam-6097	272	4	a	a	DET
ejpam-6097	272	5	case	case	NOUN
ejpam-6097	272	6	of	of	ADP
ejpam-6097	272	7	destabiliza-249	destabiliza-249	PROPN
ejpam-6097	272	8	tion	tion	NOUN
ejpam-6097	272	9	within	within	ADP
ejpam-6097	272	10	the	the	DET
ejpam-6097	272	11	ecological	ecological	ADJ
ejpam-6097	272	12	system	system	NOUN
ejpam-6097	272	13	due	due	ADP
ejpam-6097	272	14	to	to	ADP
ejpam-6097	272	15	the	the	DET
ejpam-6097	272	16	stochastic	stochastic	ADJ
ejpam-6097	272	17	intensity	intensity	NOUN
ejpam-6097	272	18	of	of	ADP
ejpam-6097	272	19	immigration	immigration	NOUN
ejpam-6097	272	20	,	,	PUNCT
ejpam-6097	272	21	which250	which250	PROPN
ejpam-6097	272	22	prevents	prevent	VERB
ejpam-6097	272	23	the	the	DET
ejpam-6097	272	24	system	system	NOUN
ejpam-6097	272	25	from	from	ADP
ejpam-6097	272	26	self	self	NOUN
ejpam-6097	272	27	-	-	PUNCT
ejpam-6097	272	28	regulating	regulating	NOUN
ejpam-6097	272	29	.	.	PUNCT
ejpam-6097	273	1	in	in	ADP
ejpam-6097	273	2	practice	practice	NOUN
ejpam-6097	273	3	,	,	PUNCT
ejpam-6097	273	4	this	this	PRON
ejpam-6097	273	5	is	be	AUX
ejpam-6097	273	6	referred	refer	VERB
ejpam-6097	273	7	to	to	ADP
ejpam-6097	273	8	as	as	ADP
ejpam-6097	273	9	the	the	DET
ejpam-6097	273	10	”	"	PUNCT
ejpam-6097	273	11	paradox251	paradox251	PROPN
ejpam-6097	273	12	of	of	ADP
ejpam-6097	273	13	enrichment”.252	enrichment”.252	PROPN
ejpam-6097	273	14	7	7	NUM
ejpam-6097	273	15	.	.	PUNCT
ejpam-6097	274	1	conclusion253	conclusion253	VERB
ejpam-6097	274	2	in	in	ADP
ejpam-6097	274	3	this	this	DET
ejpam-6097	274	4	paper	paper	NOUN
ejpam-6097	274	5	,	,	PUNCT
ejpam-6097	274	6	we	we	PRON
ejpam-6097	274	7	investigated	investigate	VERB
ejpam-6097	274	8	the	the	DET
ejpam-6097	274	9	effects	effect	NOUN
ejpam-6097	274	10	of	of	ADP
ejpam-6097	274	11	small	small	ADJ
ejpam-6097	274	12	random	random	ADJ
ejpam-6097	274	13	immigration	immigration	NOUN
ejpam-6097	274	14	in	in	ADP
ejpam-6097	274	15	competitive254	competitive254	PROPN
ejpam-6097	274	16	predatorprey	predatorprey	PROPN
ejpam-6097	274	17	model	model	NOUN
ejpam-6097	274	18	with	with	ADP
ejpam-6097	274	19	holling	holle	VERB
ejpam-6097	274	20	type	type	NOUN
ejpam-6097	274	21	ii	ii	PROPN
ejpam-6097	274	22	.	.	PUNCT
ejpam-6097	275	1	we	we	PRON
ejpam-6097	275	2	obtained	obtain	VERB
ejpam-6097	275	3	boundedness	boundedness	NOUN
ejpam-6097	275	4	of	of	ADP
ejpam-6097	275	5	the	the	DET
ejpam-6097	275	6	model	model	NOUN
ejpam-6097	275	7	’s	’s	PART
ejpam-6097	275	8	solu-255	solu-255	PROPN
ejpam-6097	275	9	tion	tion	NOUN
ejpam-6097	275	10	using	use	VERB
ejpam-6097	275	11	both	both	CCONJ
ejpam-6097	275	12	probabilistic	probabilistic	ADJ
ejpam-6097	275	13	and	and	CCONJ
ejpam-6097	275	14	analytics	analytic	NOUN
ejpam-6097	275	15	inequalities	inequality	NOUN
ejpam-6097	275	16	.	.	PUNCT
ejpam-6097	276	1	the	the	DET
ejpam-6097	276	2	conditions	condition	NOUN
ejpam-6097	276	3	of	of	ADP
ejpam-6097	276	4	stochastic	stochastic	ADJ
ejpam-6097	276	5	mean256	mean256	PROPN
ejpam-6097	276	6	square	square	ADJ
ejpam-6097	276	7	stability	stability	NOUN
ejpam-6097	276	8	were	be	AUX
ejpam-6097	276	9	derived	derive	VERB
ejpam-6097	276	10	(	(	PUNCT
ejpam-6097	276	11	theorem	theorem	ADJ
ejpam-6097	276	12	2	2	NUM
ejpam-6097	276	13	and	and	CCONJ
ejpam-6097	276	14	corollary	corollary	ADJ
ejpam-6097	276	15	1	1	NUM
ejpam-6097	276	16	)	)	PUNCT
ejpam-6097	276	17	.	.	PUNCT
ejpam-6097	277	1	a	a	DET
ejpam-6097	277	2	series	series	NOUN
ejpam-6097	277	3	of	of	ADP
ejpam-6097	277	4	results	result	NOUN
ejpam-6097	277	5	on	on	ADP
ejpam-6097	277	6	persis-257	persis-257	NOUN
ejpam-6097	277	7	tence	tence	NOUN
ejpam-6097	277	8	and	and	CCONJ
ejpam-6097	277	9	extinction	extinction	NOUN
ejpam-6097	277	10	for	for	ADP
ejpam-6097	277	11	both	both	PRON
ejpam-6097	277	12	prey	prey	NOUN
ejpam-6097	277	13	and	and	CCONJ
ejpam-6097	277	14	predator	predator	NOUN
ejpam-6097	277	15	populations	population	NOUN
ejpam-6097	277	16	was	be	AUX
ejpam-6097	277	17	obtained	obtain	VERB
ejpam-6097	277	18	(	(	PUNCT
ejpam-6097	277	19	theorems	theorem	NOUN
ejpam-6097	277	20	3	3	NUM
ejpam-6097	277	21	-258	-258	NUM
ejpam-6097	277	22	5	5	NUM
ejpam-6097	277	23	and	and	CCONJ
ejpam-6097	277	24	corollary	corollary	ADJ
ejpam-6097	277	25	2	2	NUM
ejpam-6097	277	26	)	)	PUNCT
ejpam-6097	277	27	.	.	PUNCT
ejpam-6097	278	1	all	all	DET
ejpam-6097	278	2	theoretical	theoretical	ADJ
ejpam-6097	278	3	results	result	NOUN
ejpam-6097	278	4	were	be	AUX
ejpam-6097	278	5	numerically	numerically	ADV
ejpam-6097	278	6	verified	verify	VERB
ejpam-6097	278	7	in	in	ADP
ejpam-6097	278	8	figures	figure	NOUN
ejpam-6097	278	9	1	1	NUM
ejpam-6097	278	10	-	-	SYM
ejpam-6097	278	11	5	5	NUM
ejpam-6097	278	12	.	.	PUNCT
ejpam-6097	279	1	from259	from259	NOUN
ejpam-6097	279	2	this	this	DET
ejpam-6097	279	3	work	work	NOUN
ejpam-6097	279	4	,	,	PUNCT
ejpam-6097	279	5	we	we	PRON
ejpam-6097	279	6	conclude	conclude	VERB
ejpam-6097	279	7	the	the	DET
ejpam-6097	279	8	following:260	following:260	NOUN
ejpam-6097	279	9	•	•	NOUN
ejpam-6097	279	10	for	for	ADP
ejpam-6097	279	11	fixed	fix	VERB
ejpam-6097	279	12	values	value	NOUN
ejpam-6097	279	13	of	of	ADP
ejpam-6097	279	14	the	the	DET
ejpam-6097	279	15	parameters	parameter	NOUN
ejpam-6097	279	16	set	set	VERB
ejpam-6097	279	17	(	(	PUNCT
ejpam-6097	279	18	52	52	NUM
ejpam-6097	279	19	)	)	PUNCT
ejpam-6097	279	20	,	,	PUNCT
ejpam-6097	279	21	the	the	DET
ejpam-6097	279	22	stochastic	stochastic	ADJ
ejpam-6097	279	23	stability	stability	NOUN
ejpam-6097	279	24	of	of	ADP
ejpam-6097	279	25	the	the	DET
ejpam-6097	279	26	model	model	NOUN
ejpam-6097	279	27	de-261	de-261	NOUN
ejpam-6097	279	28	pends	pend	VERB
ejpam-6097	279	29	on	on	ADP
ejpam-6097	279	30	the	the	DET
ejpam-6097	279	31	intensities	intensity	NOUN
ejpam-6097	279	32	of	of	ADP
ejpam-6097	279	33	random	random	ADJ
ejpam-6097	279	34	immigration	immigration	NOUN
ejpam-6097	279	35	.	.	PUNCT
ejpam-6097	280	1	when	when	SCONJ
ejpam-6097	280	2	random	random	ADJ
ejpam-6097	280	3	immigration	immigration	NOUN
ejpam-6097	280	4	is	be	AUX
ejpam-6097	280	5	small262	small262	PROPN
ejpam-6097	280	6	enough	enough	ADV
ejpam-6097	280	7	,	,	PUNCT
ejpam-6097	280	8	the	the	DET
ejpam-6097	280	9	system	system	NOUN
ejpam-6097	280	10	becomes	become	VERB
ejpam-6097	280	11	stochastically	stochastically	ADV
ejpam-6097	280	12	stable	stable	ADJ
ejpam-6097	280	13	.	.	PUNCT
ejpam-6097	281	1	however	however	ADV
ejpam-6097	281	2	,	,	PUNCT
ejpam-6097	281	3	as	as	ADP
ejpam-6097	281	4	random	random	ADJ
ejpam-6097	281	5	immigration263	immigration263	PROPN
ejpam-6097	281	6	increases	increase	NOUN
ejpam-6097	281	7	,	,	PUNCT
ejpam-6097	281	8	the	the	DET
ejpam-6097	281	9	system	system	NOUN
ejpam-6097	281	10	is	be	AUX
ejpam-6097	281	11	destabilized	destabilize	VERB
ejpam-6097	281	12	with	with	ADP
ejpam-6097	281	13	high	high	ADJ
ejpam-6097	281	14	oscillations.264	oscillations.264	ADJ
ejpam-6097	281	15	•	•	NOUN
ejpam-6097	281	16	the	the	DET
ejpam-6097	281	17	persistence	persistence	NOUN
ejpam-6097	281	18	of	of	ADP
ejpam-6097	281	19	the	the	DET
ejpam-6097	281	20	prey	prey	NOUN
ejpam-6097	281	21	population	population	NOUN
ejpam-6097	281	22	u	u	NOUN
ejpam-6097	281	23	clearly	clearly	ADV
ejpam-6097	281	24	affected	affect	VERB
ejpam-6097	281	25	by	by	ADP
ejpam-6097	281	26	δ	δ	PROPN
ejpam-6097	281	27	;	;	PUNCT
ejpam-6097	281	28	where	where	SCONJ
ejpam-6097	281	29	δ	δ	PROPN
ejpam-6097	281	30	was	be	AUX
ejpam-6097	281	31	small265	small265	VERB
ejpam-6097	281	32	enough	enough	ADV
ejpam-6097	281	33	,	,	PUNCT
ejpam-6097	281	34	that	that	ADV
ejpam-6097	281	35	is	is	ADV
ejpam-6097	281	36	,	,	PUNCT
ejpam-6097	281	37	ρ−	ρ−	PROPN
ejpam-6097	281	38	δ2	δ2	VERB
ejpam-6097	281	39	2	2	NUM
ejpam-6097	281	40	,	,	PUNCT
ejpam-6097	281	41	the	the	DET
ejpam-6097	281	42	prey	prey	NOUN
ejpam-6097	281	43	population	population	NOUN
ejpam-6097	281	44	u	u	PROPN
ejpam-6097	281	45	would	would	AUX
ejpam-6097	281	46	persist	persist	VERB
ejpam-6097	281	47	with	with	ADP
ejpam-6097	281	48	probability	probability	NOUN
ejpam-6097	281	49	almost266	almost266	X
ejpam-6097	281	50	surely	surely	ADV
ejpam-6097	281	51	.	.	PUNCT
ejpam-6097	282	1	as	as	ADP
ejpam-6097	282	2	in	in	ADP
ejpam-6097	282	3	condition	condition	NOUN
ejpam-6097	282	4	(	(	PUNCT
ejpam-6097	282	5	50	50	NUM
ejpam-6097	282	6	)	)	PUNCT
ejpam-6097	282	7	when	when	SCONJ
ejpam-6097	282	8	ϵ	ϵ	PROPN
ejpam-6097	282	9	was	be	AUX
ejpam-6097	282	10	large	large	ADJ
ejpam-6097	282	11	enough	enough	ADV
ejpam-6097	282	12	,	,	PUNCT
ejpam-6097	282	13	the	the	DET
ejpam-6097	282	14	predator	predator	NOUN
ejpam-6097	282	15	population	population	NOUN
ejpam-6097	282	16	will267	will267	PROPN
ejpam-6097	282	17	extinct	extinct	VERB
ejpam-6097	282	18	with	with	ADP
ejpam-6097	282	19	probability	probability	NOUN
ejpam-6097	282	20	almost	almost	ADV
ejpam-6097	282	21	surely	surely	ADV
ejpam-6097	282	22	.	.	PUNCT
ejpam-6097	283	1	however	however	ADV
ejpam-6097	283	2	,	,	PUNCT
ejpam-6097	283	3	conditions	condition	NOUN
ejpam-6097	283	4	(	(	PUNCT
ejpam-6097	283	5	45	45	NUM
ejpam-6097	283	6	)	)	PUNCT
ejpam-6097	283	7	and	and	CCONJ
ejpam-6097	283	8	(	(	PUNCT
ejpam-6097	283	9	50)together268	50)together268	NUM
ejpam-6097	283	10	emphasize	emphasize	VERB
ejpam-6097	283	11	that	that	SCONJ
ejpam-6097	283	12	when	when	SCONJ
ejpam-6097	283	13	δ	δ	PROPN
ejpam-6097	283	14	was	be	AUX
ejpam-6097	283	15	large	large	ADJ
ejpam-6097	283	16	enough	enough	ADV
ejpam-6097	283	17	(	(	PUNCT
ejpam-6097	283	18	the	the	DET
ejpam-6097	283	19	immigration	immigration	NOUN
ejpam-6097	283	20	on	on	ADP
ejpam-6097	283	21	the	the	DET
ejpam-6097	283	22	prey	prey	NOUN
ejpam-6097	283	23	population269	population269	PROPN
ejpam-6097	283	24	was	be	AUX
ejpam-6097	283	25	large	large	ADJ
ejpam-6097	283	26	enough	enough	ADV
ejpam-6097	283	27	)	)	PUNCT
ejpam-6097	283	28	,	,	PUNCT
ejpam-6097	283	29	the	the	DET
ejpam-6097	283	30	whole	whole	ADJ
ejpam-6097	283	31	system	system	NOUN
ejpam-6097	283	32	would	would	AUX
ejpam-6097	283	33	extinct	extinct	VERB
ejpam-6097	283	34	.	.	PUNCT
ejpam-6097	284	1	this	this	DET
ejpam-6097	284	2	case	case	NOUN
ejpam-6097	284	3	is	be	AUX
ejpam-6097	284	4	demonstrated	demonstrate	VERB
ejpam-6097	284	5	in270	in270	PROPN
ejpam-6097	284	6	figure	figure	NOUN
ejpam-6097	284	7	5.271	5.271	NUM
ejpam-6097	284	8	to	to	ADP
ejpam-6097	284	9	the	the	DET
ejpam-6097	284	10	best	good	ADJ
ejpam-6097	284	11	of	of	ADP
ejpam-6097	284	12	the	the	DET
ejpam-6097	284	13	authors	author	NOUN
ejpam-6097	284	14	’	’	PART
ejpam-6097	284	15	knowledge	knowledge	NOUN
ejpam-6097	284	16	,	,	PUNCT
ejpam-6097	284	17	the	the	DET
ejpam-6097	284	18	first	first	ADJ
ejpam-6097	284	19	study	study	NOUN
ejpam-6097	284	20	to	to	PART
ejpam-6097	284	21	examine	examine	VERB
ejpam-6097	284	22	a	a	DET
ejpam-6097	284	23	competitive	competitive	ADJ
ejpam-6097	284	24	stochastic272	stochastic272	PROPN
ejpam-6097	284	25	predator	predator	NOUN
ejpam-6097	284	26	-	-	PUNCT
ejpam-6097	284	27	prey	prey	NOUN
ejpam-6097	284	28	model	model	NOUN
ejpam-6097	284	29	under	under	ADP
ejpam-6097	284	30	the	the	DET
ejpam-6097	284	31	influence	influence	NOUN
ejpam-6097	284	32	of	of	ADP
ejpam-6097	284	33	small	small	ADJ
ejpam-6097	284	34	random	random	ADJ
ejpam-6097	284	35	immigration	immigration	NOUN
ejpam-6097	284	36	was	be	AUX
ejpam-6097	284	37	[	[	X
ejpam-6097	284	38	22	22	NUM
ejpam-6097	284	39	]	]	PUNCT
ejpam-6097	284	40	,	,	PUNCT
ejpam-6097	284	41	where273	where273	PROPN
ejpam-6097	284	42	m.	m.	PROPN
ejpam-6097	284	43	mohamed	mohame	VERB
ejpam-6097	284	44	et	et	PROPN
ejpam-6097	284	45	al	al	PROPN
ejpam-6097	284	46	.	.	PUNCT
ejpam-6097	284	47	/	/	SYM
ejpam-6097	284	48	eur	eur	PROPN
ejpam-6097	284	49	.	.	PUNCT
ejpam-6097	285	1	j.	j.	PROPN
ejpam-6097	285	2	pure	pure	PROPN
ejpam-6097	285	3	appl	appl	PROPN
ejpam-6097	285	4	.	.	PROPN
ejpam-6097	285	5	math	math	PROPN
ejpam-6097	285	6	,	,	PUNCT
ejpam-6097	285	7	18	18	NUM
ejpam-6097	285	8	(	(	PUNCT
ejpam-6097	285	9	2	2	NUM
ejpam-6097	285	10	)	)	PUNCT
ejpam-6097	285	11	(	(	PUNCT
ejpam-6097	285	12	2025	2025	NUM
ejpam-6097	285	13	)	)	PUNCT
ejpam-6097	285	14	,	,	PUNCT
ejpam-6097	285	15	6097	6097	NUM
ejpam-6097	285	16	17	17	NUM
ejpam-6097	285	17	of	of	ADP
ejpam-6097	285	18	19	19	NUM
ejpam-6097	285	19	the	the	DET
ejpam-6097	285	20	analysis	analysis	NOUN
ejpam-6097	285	21	focused	focus	VERB
ejpam-6097	285	22	on	on	ADP
ejpam-6097	285	23	stochastic	stochastic	ADJ
ejpam-6097	285	24	stability	stability	NOUN
ejpam-6097	285	25	using	use	VERB
ejpam-6097	285	26	a	a	DET
ejpam-6097	285	27	simpler	simple	ADJ
ejpam-6097	285	28	model	model	NOUN
ejpam-6097	285	29	with	with	ADP
ejpam-6097	285	30	a	a	DET
ejpam-6097	285	31	holling	holle	VERB
ejpam-6097	285	32	type	type	NOUN
ejpam-6097	285	33	i274	i274	PRON
ejpam-6097	285	34	functional	functional	ADJ
ejpam-6097	285	35	response	response	NOUN
ejpam-6097	285	36	.	.	PUNCT
ejpam-6097	286	1	in	in	ADP
ejpam-6097	286	2	this	this	DET
ejpam-6097	286	3	paper	paper	NOUN
ejpam-6097	286	4	,	,	PUNCT
ejpam-6097	286	5	we	we	PRON
ejpam-6097	286	6	present	present	VERB
ejpam-6097	286	7	a	a	DET
ejpam-6097	286	8	comprehensive	comprehensive	ADJ
ejpam-6097	286	9	study	study	NOUN
ejpam-6097	286	10	of	of	ADP
ejpam-6097	286	11	a	a	DET
ejpam-6097	286	12	more	more	ADV
ejpam-6097	286	13	general275	general275	PROPN
ejpam-6097	286	14	and	and	CCONJ
ejpam-6097	286	15	realistic	realistic	ADJ
ejpam-6097	286	16	competitive	competitive	ADJ
ejpam-6097	286	17	stochastic	stochastic	ADJ
ejpam-6097	286	18	predator	predator	NOUN
ejpam-6097	286	19	-	-	PUNCT
ejpam-6097	286	20	prey	prey	NOUN
ejpam-6097	286	21	model	model	NOUN
ejpam-6097	286	22	incorporating	incorporate	VERB
ejpam-6097	286	23	a	a	DET
ejpam-6097	286	24	holling	holle	VERB
ejpam-6097	286	25	type	type	NOUN
ejpam-6097	286	26	ii276	ii276	PROPN
ejpam-6097	286	27	functional	functional	ADJ
ejpam-6097	286	28	response	response	NOUN
ejpam-6097	286	29	,	,	PUNCT
ejpam-6097	286	30	also	also	ADV
ejpam-6097	286	31	subject	subject	ADJ
ejpam-6097	286	32	to	to	ADP
ejpam-6097	286	33	small	small	ADJ
ejpam-6097	286	34	random	random	ADJ
ejpam-6097	286	35	immigration	immigration	NOUN
ejpam-6097	286	36	.	.	PUNCT
ejpam-6097	287	1	we	we	PRON
ejpam-6097	287	2	investigate	investigate	VERB
ejpam-6097	287	3	stochastic277	stochastic277	NOUN
ejpam-6097	287	4	mean	mean	ADJ
ejpam-6097	287	5	square	square	ADJ
ejpam-6097	287	6	stability	stability	NOUN
ejpam-6097	287	7	and	and	CCONJ
ejpam-6097	287	8	establish	establish	VERB
ejpam-6097	287	9	conditions	condition	NOUN
ejpam-6097	287	10	for	for	ADP
ejpam-6097	287	11	persistence	persistence	NOUN
ejpam-6097	287	12	and	and	CCONJ
ejpam-6097	287	13	extinction	extinction	NOUN
ejpam-6097	287	14	of	of	ADP
ejpam-6097	287	15	the	the	DET
ejpam-6097	287	16	species.278	species.278	NOUN
ejpam-6097	287	17	in	in	ADP
ejpam-6097	287	18	addition	addition	NOUN
ejpam-6097	287	19	,	,	PUNCT
ejpam-6097	287	20	our	our	PRON
ejpam-6097	287	21	theoretical	theoretical	ADJ
ejpam-6097	287	22	results	result	NOUN
ejpam-6097	287	23	are	be	AUX
ejpam-6097	287	24	reinforced	reinforce	VERB
ejpam-6097	287	25	through	through	ADP
ejpam-6097	287	26	numerical	numerical	ADJ
ejpam-6097	287	27	simulations	simulation	NOUN
ejpam-6097	287	28	,	,	PUNCT
ejpam-6097	287	29	which279	which279	PROPN
ejpam-6097	287	30	illustrate	illustrate	VERB
ejpam-6097	287	31	and	and	CCONJ
ejpam-6097	287	32	validate	validate	VERB
ejpam-6097	287	33	the	the	DET
ejpam-6097	287	34	analytical	analytical	ADJ
ejpam-6097	287	35	findings.280	findings.280	NOUN
ejpam-6097	287	36	acknowledgements281	acknowledgements281	PROPN
ejpam-6097	287	37	the	the	DET
ejpam-6097	287	38	authors	author	NOUN
ejpam-6097	287	39	extend	extend	VERB
ejpam-6097	287	40	the	the	DET
ejpam-6097	287	41	appreciation	appreciation	NOUN
ejpam-6097	287	42	to	to	ADP
ejpam-6097	287	43	the	the	DET
ejpam-6097	287	44	deanship	deanship	NOUN
ejpam-6097	287	45	of	of	ADP
ejpam-6097	287	46	postgraduate	postgraduate	ADJ
ejpam-6097	287	47	studies	study	NOUN
ejpam-6097	287	48	and282	and282	PROPN
ejpam-6097	287	49	scientific	scientific	ADJ
ejpam-6097	287	50	research	research	NOUN
ejpam-6097	287	51	at	at	ADP
ejpam-6097	287	52	majmaah	majmaah	PROPN
ejpam-6097	287	53	university	university	PROPN
ejpam-6097	287	54	for	for	ADP
ejpam-6097	287	55	funding	fund	VERB
ejpam-6097	287	56	this	this	DET
ejpam-6097	287	57	research	research	NOUN
ejpam-6097	287	58	work	work	NOUN
ejpam-6097	287	59	through	through	ADP
ejpam-6097	287	60	the283	the283	PROPN
ejpam-6097	287	61	project	project	NOUN
ejpam-6097	287	62	number	number	NOUN
ejpam-6097	287	63	(	(	PUNCT
ejpam-6097	287	64	icr-2025	icr-2025	NOUN
ejpam-6097	287	65	-	-	PUNCT
ejpam-6097	287	66	1724).284	1724).284	NOUN
ejpam-6097	287	67	references285	references285	PUNCT
ejpam-6097	288	1	[	[	X
ejpam-6097	288	2	1	1	X
ejpam-6097	288	3	]	]	PUNCT
ejpam-6097	288	4	alfred	alfred	PROPN
ejpam-6097	288	5	james	james	PROPN
ejpam-6097	288	6	lotka	lotka	PROPN
ejpam-6097	288	7	.	.	PUNCT
ejpam-6097	289	1	elements	element	NOUN
ejpam-6097	289	2	of	of	ADP
ejpam-6097	289	3	physical	physical	ADJ
ejpam-6097	289	4	biology	biology	NOUN
ejpam-6097	289	5	.	.	PUNCT
ejpam-6097	290	1	williams	williams	PROPN
ejpam-6097	290	2	&	&	CCONJ
ejpam-6097	290	3	wilkins	wilkins	PROPN
ejpam-6097	290	4	,	,	PUNCT
ejpam-6097	290	5	1925.286	1925.286	PROPN
ejpam-6097	290	6	[	[	X
ejpam-6097	290	7	2	2	NUM
ejpam-6097	290	8	]	]	PUNCT
ejpam-6097	290	9	vito	vito	PROPN
ejpam-6097	290	10	volterra	volterra	PROPN
ejpam-6097	290	11	.	.	PUNCT
ejpam-6097	291	1	variazioni	variazioni	PROPN
ejpam-6097	291	2	e	e	X
ejpam-6097	291	3	fluttuazioni	fluttuazioni	X
ejpam-6097	291	4	del	del	X
ejpam-6097	291	5	numero	numero	PROPN
ejpam-6097	291	6	d’individui	d’individui	PROPN
ejpam-6097	291	7	in	in	ADP
ejpam-6097	291	8	specie	specie	PROPN
ejpam-6097	291	9	animali287	animali287	PROPN
ejpam-6097	291	10	conviventi	conviventi	PROPN
ejpam-6097	291	11	.	.	PUNCT
ejpam-6097	292	1	società	società	ADJ
ejpam-6097	292	2	anonima	anonima	PROPN
ejpam-6097	292	3	tipografica	tipografica	PROPN
ejpam-6097	292	4	”	"	PUNCT
ejpam-6097	292	5	leonardo	leonardo	PROPN
ejpam-6097	292	6	da	da	PROPN
ejpam-6097	292	7	vinci	vinci	PROPN
ejpam-6097	292	8	”	"	PUNCT
ejpam-6097	292	9	,	,	PUNCT
ejpam-6097	292	10	1926.288	1926.288	NUM
ejpam-6097	292	11	[	[	X
ejpam-6097	292	12	3	3	NUM
ejpam-6097	292	13	]	]	X
ejpam-6097	292	14	patrick	patrick	PROPN
ejpam-6097	292	15	h	h	PROPN
ejpam-6097	292	16	leslie	leslie	PROPN
ejpam-6097	292	17	.	.	PUNCT
ejpam-6097	293	1	some	some	DET
ejpam-6097	293	2	further	further	ADJ
ejpam-6097	293	3	notes	note	NOUN
ejpam-6097	293	4	on	on	ADP
ejpam-6097	293	5	the	the	DET
ejpam-6097	293	6	use	use	NOUN
ejpam-6097	293	7	of	of	ADP
ejpam-6097	293	8	matrices	matrix	NOUN
ejpam-6097	293	9	in	in	ADP
ejpam-6097	293	10	population	population	NOUN
ejpam-6097	293	11	mathematics.289	mathematics.289	NOUN
ejpam-6097	293	12	biometrika	biometrika	NOUN
ejpam-6097	293	13	,	,	PUNCT
ejpam-6097	293	14	35(3/4):213–245	35(3/4):213–245	NUM
ejpam-6097	293	15	,	,	PUNCT
ejpam-6097	293	16	1948.290	1948.290	NUM
ejpam-6097	293	17	[	[	X
ejpam-6097	293	18	4	4	NUM
ejpam-6097	293	19	]	]	X
ejpam-6097	293	20	crawford	crawford	PROPN
ejpam-6097	293	21	s	s	PART
ejpam-6097	293	22	holling	holling	NOUN
ejpam-6097	293	23	.	.	PUNCT
ejpam-6097	294	1	some	some	DET
ejpam-6097	294	2	characteristics	characteristic	NOUN
ejpam-6097	294	3	of	of	ADP
ejpam-6097	294	4	simple	simple	ADJ
ejpam-6097	294	5	types	type	NOUN
ejpam-6097	294	6	of	of	ADP
ejpam-6097	294	7	predation	predation	NOUN
ejpam-6097	294	8	and	and	CCONJ
ejpam-6097	294	9	parasitism1.291	parasitism1.291	VERB
ejpam-6097	294	10	the	the	DET
ejpam-6097	294	11	canadian	canadian	ADJ
ejpam-6097	294	12	entomologist	entomologist	NOUN
ejpam-6097	294	13	,	,	PUNCT
ejpam-6097	294	14	91(7):385–398	91(7):385–398	PROPN
ejpam-6097	294	15	,	,	PUNCT
ejpam-6097	294	16	1959.292	1959.292	NUM
ejpam-6097	294	17	[	[	X
ejpam-6097	294	18	5	5	NUM
ejpam-6097	294	19	]	]	PUNCT
ejpam-6097	294	20	michael	michael	PROPN
ejpam-6097	294	21	l	l	PROPN
ejpam-6097	294	22	rosenzweig	rosenzweig	PROPN
ejpam-6097	294	23	and	and	CCONJ
ejpam-6097	294	24	robert	robert	PROPN
ejpam-6097	294	25	h	h	PROPN
ejpam-6097	294	26	macarthur	macarthur	PROPN
ejpam-6097	294	27	.	.	PUNCT
ejpam-6097	295	1	graphical	graphical	ADJ
ejpam-6097	295	2	representation	representation	NOUN
ejpam-6097	295	3	and	and	CCONJ
ejpam-6097	295	4	stabil-293	stabil-293	NOUN
ejpam-6097	295	5	ity	ity	PROPN
ejpam-6097	295	6	conditions	condition	NOUN
ejpam-6097	295	7	of	of	ADP
ejpam-6097	295	8	predator	predator	NOUN
ejpam-6097	295	9	-	-	PUNCT
ejpam-6097	295	10	prey	prey	NOUN
ejpam-6097	295	11	interactions	interaction	NOUN
ejpam-6097	295	12	.	.	PUNCT
ejpam-6097	296	1	the	the	DET
ejpam-6097	296	2	american	american	PROPN
ejpam-6097	296	3	naturalist	naturalist	PROPN
ejpam-6097	296	4	,	,	PUNCT
ejpam-6097	296	5	97(895):209–294	97(895):209–294	PROPN
ejpam-6097	296	6	223	223	NUM
ejpam-6097	296	7	,	,	PUNCT
ejpam-6097	296	8	1963.295	1963.295	NUM
ejpam-6097	296	9	[	[	SYM
ejpam-6097	296	10	6	6	NUM
ejpam-6097	296	11	]	]	X
ejpam-6097	296	12	robert	robert	PROPN
ejpam-6097	296	13	m	m	PROPN
ejpam-6097	296	14	may	may	AUX
ejpam-6097	296	15	.	.	PUNCT
ejpam-6097	297	1	limit	limit	VERB
ejpam-6097	297	2	cycles	cycle	NOUN
ejpam-6097	297	3	in	in	ADP
ejpam-6097	297	4	predator	predator	NOUN
ejpam-6097	297	5	-	-	PUNCT
ejpam-6097	297	6	prey	prey	NOUN
ejpam-6097	297	7	communities	community	NOUN
ejpam-6097	297	8	.	.	PUNCT
ejpam-6097	298	1	science	science	NOUN
ejpam-6097	298	2	,	,	PUNCT
ejpam-6097	298	3	177(4052):900–296	177(4052):900–296	NUM
ejpam-6097	298	4	902	902	NUM
ejpam-6097	298	5	,	,	PUNCT
ejpam-6097	298	6	1972.297	1972.297	PROPN
ejpam-6097	298	7	[	[	X
ejpam-6097	298	8	7	7	NUM
ejpam-6097	298	9	]	]	X
ejpam-6097	298	10	herbert	herbert	PROPN
ejpam-6097	298	11	i	i	PROPN
ejpam-6097	298	12	freedman	freedman	PROPN
ejpam-6097	298	13	.	.	PUNCT
ejpam-6097	299	1	deterministic	deterministic	ADJ
ejpam-6097	299	2	mathematical	mathematical	ADJ
ejpam-6097	299	3	models	model	NOUN
ejpam-6097	299	4	in	in	ADP
ejpam-6097	299	5	population	population	NOUN
ejpam-6097	299	6	ecology	ecology	NOUN
ejpam-6097	299	7	.	.	PUNCT
ejpam-6097	300	1	m.298	m.298	PROPN
ejpam-6097	300	2	dekker	dekker	PROPN
ejpam-6097	300	3	,	,	PUNCT
ejpam-6097	300	4	1980.299	1980.299	NUM
ejpam-6097	301	1	[	[	X
ejpam-6097	301	2	8	8	NUM
ejpam-6097	301	3	]	]	X
ejpam-6097	301	4	yang	yang	PROPN
ejpam-6097	301	5	kuang	kuang	PROPN
ejpam-6097	301	6	.	.	PUNCT
ejpam-6097	302	1	basic	basic	ADJ
ejpam-6097	302	2	properties	property	NOUN
ejpam-6097	302	3	of	of	ADP
ejpam-6097	302	4	mathematical	mathematical	ADJ
ejpam-6097	302	5	population	population	NOUN
ejpam-6097	302	6	models	model	NOUN
ejpam-6097	302	7	.	.	PUNCT
ejpam-6097	303	1	j.	j.	PROPN
ejpam-6097	303	2	biomath,300	biomath,300	PUNCT
ejpam-6097	304	1	17(2):129–142	17(2):129–142	PROPN
ejpam-6097	304	2	,	,	PUNCT
ejpam-6097	304	3	2002.301	2002.301	NUM
ejpam-6097	304	4	[	[	X
ejpam-6097	304	5	9	9	NUM
ejpam-6097	304	6	]	]	PUNCT
ejpam-6097	304	7	seda	seda	PROPN
ejpam-6097	304	8	igret	igret	PROPN
ejpam-6097	304	9	araz	araz	PROPN
ejpam-6097	304	10	and	and	CCONJ
ejpam-6097	304	11	salah	salah	PROPN
ejpam-6097	304	12	boulaaras	boulaaras	NOUN
ejpam-6097	304	13	.	.	PUNCT
ejpam-6097	305	1	fractional	fractional	ADJ
ejpam-6097	305	2	modelling	modelling	NOUN
ejpam-6097	305	3	of	of	ADP
ejpam-6097	305	4	gradual	gradual	ADJ
ejpam-6097	305	5	incorporation	incorporation	NOUN
ejpam-6097	305	6	of302	of302	NOUN
ejpam-6097	305	7	infected	infect	VERB
ejpam-6097	305	8	prey	prey	NOUN
ejpam-6097	305	9	into	into	ADP
ejpam-6097	305	10	the	the	DET
ejpam-6097	305	11	predator	predator	NOUN
ejpam-6097	305	12	-	-	PUNCT
ejpam-6097	305	13	prey	prey	NOUN
ejpam-6097	305	14	system	system	NOUN
ejpam-6097	305	15	with	with	ADP
ejpam-6097	305	16	consideration	consideration	NOUN
ejpam-6097	305	17	of	of	ADP
ejpam-6097	305	18	seasonality	seasonality	NOUN
ejpam-6097	305	19	.	.	PUNCT
ejpam-6097	306	1	applied303	applied303	PROPN
ejpam-6097	306	2	mathematics	mathematic	NOUN
ejpam-6097	306	3	in	in	ADP
ejpam-6097	306	4	science	science	NOUN
ejpam-6097	306	5	and	and	CCONJ
ejpam-6097	306	6	engineering	engineering	NOUN
ejpam-6097	306	7	,	,	PUNCT
ejpam-6097	306	8	33(1):2483728	33(1):2483728	NUM
ejpam-6097	306	9	,	,	PUNCT
ejpam-6097	306	10	2025.304	2025.304	NUM
ejpam-6097	306	11	[	[	X
ejpam-6097	306	12	10	10	NUM
ejpam-6097	306	13	]	]	PUNCT
ejpam-6097	306	14	zhihui	zhihui	PROPN
ejpam-6097	306	15	ma	ma	PROPN
ejpam-6097	306	16	,	,	PUNCT
ejpam-6097	306	17	shufan	shufan	PROPN
ejpam-6097	306	18	wang	wang	PROPN
ejpam-6097	306	19	,	,	PUNCT
ejpam-6097	306	20	weide	weide	PROPN
ejpam-6097	306	21	li	li	PROPN
ejpam-6097	306	22	,	,	PUNCT
ejpam-6097	306	23	and	and	CCONJ
ejpam-6097	306	24	zizhen	zizhen	PROPN
ejpam-6097	306	25	li	li	PROPN
ejpam-6097	306	26	.	.	PUNCT
ejpam-6097	307	1	the	the	DET
ejpam-6097	307	2	effect	effect	NOUN
ejpam-6097	307	3	of	of	ADP
ejpam-6097	307	4	prey	prey	ADJ
ejpam-6097	307	5	refuge	refuge	NOUN
ejpam-6097	307	6	in	in	ADP
ejpam-6097	307	7	a305	a305	PROPN
ejpam-6097	307	8	patchy	patchy	ADJ
ejpam-6097	307	9	predator	predator	NOUN
ejpam-6097	307	10	–	–	PUNCT
ejpam-6097	307	11	prey	prey	NOUN
ejpam-6097	307	12	system	system	NOUN
ejpam-6097	307	13	.	.	PUNCT
ejpam-6097	308	1	mathematical	mathematical	ADJ
ejpam-6097	308	2	biosciences	bioscience	NOUN
ejpam-6097	308	3	,	,	PUNCT
ejpam-6097	308	4	243(1):126–130	243(1):126–130	PROPN
ejpam-6097	308	5	,	,	PUNCT
ejpam-6097	308	6	2013.306	2013.306	NUM
ejpam-6097	309	1	[	[	X
ejpam-6097	309	2	11	11	NUM
ejpam-6097	309	3	]	]	PUNCT
ejpam-6097	309	4	sahabuddin	sahabuddin	VERB
ejpam-6097	309	5	sarwardi	sarwardi	PROPN
ejpam-6097	309	6	,	,	PUNCT
ejpam-6097	309	7	prashanta	prashanta	NOUN
ejpam-6097	309	8	kumar	kumar	PROPN
ejpam-6097	309	9	mandal	mandal	PROPN
ejpam-6097	309	10	,	,	PUNCT
ejpam-6097	309	11	and	and	CCONJ
ejpam-6097	309	12	santanu	santanu	VERB
ejpam-6097	309	13	ray	ray	NOUN
ejpam-6097	309	14	.	.	PUNCT
ejpam-6097	310	1	analysis	analysis	NOUN
ejpam-6097	310	2	of	of	ADP
ejpam-6097	310	3	a307	a307	NUM
ejpam-6097	310	4	competitive	competitive	ADJ
ejpam-6097	310	5	prey	prey	NOUN
ejpam-6097	310	6	–	–	PUNCT
ejpam-6097	310	7	predator	predator	NOUN
ejpam-6097	310	8	system	system	NOUN
ejpam-6097	310	9	with	with	ADP
ejpam-6097	310	10	a	a	DET
ejpam-6097	310	11	prey	prey	NOUN
ejpam-6097	310	12	refuge	refuge	NOUN
ejpam-6097	310	13	.	.	PUNCT
ejpam-6097	311	1	biosystems	biosystem	NOUN
ejpam-6097	311	2	,	,	PUNCT
ejpam-6097	311	3	110(3):133–148,308	110(3):133–148,308	NUM
ejpam-6097	311	4	2012.309	2012.309	NUM
ejpam-6097	312	1	[	[	X
ejpam-6097	312	2	12	12	NUM
ejpam-6097	312	3	]	]	PUNCT
ejpam-6097	312	4	xiaoying	xiaoye	VERB
ejpam-6097	312	5	wang	wang	PROPN
ejpam-6097	312	6	,	,	PUNCT
ejpam-6097	312	7	liana	liana	PROPN
ejpam-6097	312	8	zanette	zanette	PROPN
ejpam-6097	312	9	,	,	PUNCT
ejpam-6097	312	10	and	and	CCONJ
ejpam-6097	312	11	xingfu	xingfu	PROPN
ejpam-6097	312	12	zou	zou	PROPN
ejpam-6097	312	13	.	.	PUNCT
ejpam-6097	313	1	modelling	model	VERB
ejpam-6097	313	2	the	the	DET
ejpam-6097	313	3	fear	fear	ADJ
ejpam-6097	313	4	effect	effect	NOUN
ejpam-6097	313	5	in	in	ADP
ejpam-6097	313	6	predator–310	predator–310	NOUN
ejpam-6097	313	7	prey	prey	VERB
ejpam-6097	313	8	interactions	interaction	NOUN
ejpam-6097	313	9	.	.	PUNCT
ejpam-6097	314	1	journal	journal	NOUN
ejpam-6097	314	2	of	of	ADP
ejpam-6097	314	3	mathematical	mathematical	ADJ
ejpam-6097	314	4	biology	biology	NOUN
ejpam-6097	314	5	,	,	PUNCT
ejpam-6097	314	6	73(5):1179–1204	73(5):1179–1204	NUM
ejpam-6097	314	7	,	,	PUNCT
ejpam-6097	314	8	2016.311	2016.311	NUM
ejpam-6097	314	9	m.	m.	NOUN
ejpam-6097	314	10	mohamed	mohamed	PROPN
ejpam-6097	314	11	et	et	PROPN
ejpam-6097	314	12	al	al	PROPN
ejpam-6097	314	13	.	.	PUNCT
ejpam-6097	314	14	/	/	SYM
ejpam-6097	314	15	eur	eur	PROPN
ejpam-6097	314	16	.	.	PUNCT
ejpam-6097	315	1	j.	j.	PROPN
ejpam-6097	315	2	pure	pure	PROPN
ejpam-6097	315	3	appl	appl	PROPN
ejpam-6097	315	4	.	.	PROPN
ejpam-6097	315	5	math	math	PROPN
ejpam-6097	315	6	,	,	PUNCT
ejpam-6097	315	7	18	18	NUM
ejpam-6097	315	8	(	(	PUNCT
ejpam-6097	315	9	2	2	NUM
ejpam-6097	315	10	)	)	PUNCT
ejpam-6097	315	11	(	(	PUNCT
ejpam-6097	315	12	2025	2025	NUM
ejpam-6097	315	13	)	)	PUNCT
ejpam-6097	315	14	,	,	PUNCT
ejpam-6097	315	15	6097	6097	NUM
ejpam-6097	315	16	18	18	NUM
ejpam-6097	315	17	of	of	ADP
ejpam-6097	315	18	19	19	NUM
ejpam-6097	315	19	[	[	SYM
ejpam-6097	315	20	13	13	NUM
ejpam-6097	315	21	]	]	SYM
ejpam-6097	315	22	hang	hang	PROPN
ejpam-6097	315	23	deng	deng	PROPN
ejpam-6097	315	24	,	,	PUNCT
ejpam-6097	315	25	fengde	fengde	PROPN
ejpam-6097	315	26	chen	chen	PROPN
ejpam-6097	315	27	,	,	PUNCT
ejpam-6097	315	28	zhenliang	zhenliang	PROPN
ejpam-6097	315	29	zhu	zhu	PROPN
ejpam-6097	315	30	,	,	PUNCT
ejpam-6097	315	31	and	and	CCONJ
ejpam-6097	315	32	zhong	zhong	PROPN
ejpam-6097	315	33	li	li	PROPN
ejpam-6097	315	34	.	.	PROPN
ejpam-6097	316	1	modelling	model	VERB
ejpam-6097	316	2	the	the	DET
ejpam-6097	316	3	fear	fear	NOUN
ejpam-6097	316	4	effect	effect	NOUN
ejpam-6097	316	5	in312	in312	PROPN
ejpam-6097	316	6	predator	predator	NOUN
ejpam-6097	316	7	–	–	PUNCT
ejpam-6097	316	8	prey	prey	NOUN
ejpam-6097	316	9	interactions	interaction	NOUN
ejpam-6097	316	10	.	.	PUNCT
ejpam-6097	317	1	advances	advance	NOUN
ejpam-6097	317	2	in	in	ADP
ejpam-6097	317	3	difference	difference	NOUN
ejpam-6097	317	4	equations	equation	NOUN
ejpam-6097	317	5	,	,	PUNCT
ejpam-6097	317	6	2019:1–17	2019:1–17	NUM
ejpam-6097	317	7	,	,	PUNCT
ejpam-6097	317	8	2019.313	2019.313	NUM
ejpam-6097	318	1	[	[	X
ejpam-6097	318	2	14	14	NUM
ejpam-6097	318	3	]	]	PUNCT
ejpam-6097	318	4	takeru	takeru	PROPN
ejpam-6097	318	5	tahara	tahara	PROPN
ejpam-6097	318	6	,	,	PUNCT
ejpam-6097	318	7	maica	maica	PROPN
ejpam-6097	318	8	krizna	krizna	PROPN
ejpam-6097	318	9	areja	areja	PROPN
ejpam-6097	318	10	gavina	gavina	PROPN
ejpam-6097	318	11	,	,	PUNCT
ejpam-6097	318	12	takenori	takenori	PROPN
ejpam-6097	318	13	kawano	kawano	PROPN
ejpam-6097	318	14	,	,	PUNCT
ejpam-6097	318	15	jerrold	jerrold	PROPN
ejpam-6097	318	16	m	m	PROPN
ejpam-6097	318	17	tubay,314	tubay,314	PROPN
ejpam-6097	318	18	jomar	jomar	PROPN
ejpam-6097	318	19	f	f	PROPN
ejpam-6097	318	20	rabajante	rabajante	PROPN
ejpam-6097	318	21	,	,	PUNCT
ejpam-6097	318	22	hiromu	hiromu	PROPN
ejpam-6097	318	23	ito	ito	PROPN
ejpam-6097	318	24	,	,	PUNCT
ejpam-6097	318	25	satoru	satoru	PROPN
ejpam-6097	318	26	morita	morita	PROPN
ejpam-6097	318	27	,	,	PUNCT
ejpam-6097	318	28	genki	genki	PROPN
ejpam-6097	318	29	ichinose	ichinose	PROPN
ejpam-6097	318	30	,	,	PUNCT
ejpam-6097	318	31	takuya	takuya	PROPN
ejpam-6097	318	32	okabe,315	okabe,315	PROPN
ejpam-6097	318	33	tatsuya	tatsuya	PROPN
ejpam-6097	318	34	togashi	togashi	PROPN
ejpam-6097	318	35	,	,	PUNCT
ejpam-6097	318	36	et	et	PROPN
ejpam-6097	318	37	al	al	PROPN
ejpam-6097	318	38	.	.	PUNCT
ejpam-6097	318	39	asymptotic	asymptotic	ADJ
ejpam-6097	318	40	stability	stability	NOUN
ejpam-6097	318	41	of	of	ADP
ejpam-6097	318	42	a	a	DET
ejpam-6097	318	43	modified	modify	VERB
ejpam-6097	318	44	lotka	lotka	PROPN
ejpam-6097	318	45	-	-	PUNCT
ejpam-6097	318	46	volterra	volterra	PROPN
ejpam-6097	318	47	model	model	NOUN
ejpam-6097	318	48	with316	with316	VERB
ejpam-6097	318	49	small	small	ADJ
ejpam-6097	318	50	immigrations	immigration	NOUN
ejpam-6097	318	51	.	.	PUNCT
ejpam-6097	319	1	scientific	scientific	ADJ
ejpam-6097	319	2	reports	report	NOUN
ejpam-6097	319	3	,	,	PUNCT
ejpam-6097	319	4	8(1):7029	8(1):7029	NUM
ejpam-6097	319	5	,	,	PUNCT
ejpam-6097	319	6	2018.317	2018.317	NUM
ejpam-6097	319	7	[	[	X
ejpam-6097	319	8	15	15	NUM
ejpam-6097	319	9	]	]	PUNCT
ejpam-6097	319	10	debasis	debasis	NOUN
ejpam-6097	319	11	mukherjee	mukherjee	NOUN
ejpam-6097	319	12	.	.	PUNCT
ejpam-6097	320	1	the	the	DET
ejpam-6097	320	2	effect	effect	NOUN
ejpam-6097	320	3	of	of	ADP
ejpam-6097	320	4	refuge	refuge	NOUN
ejpam-6097	320	5	and	and	CCONJ
ejpam-6097	320	6	immigration	immigration	NOUN
ejpam-6097	320	7	in	in	ADP
ejpam-6097	320	8	a	a	DET
ejpam-6097	320	9	predator	predator	NOUN
ejpam-6097	320	10	–	–	PUNCT
ejpam-6097	320	11	prey	prey	NOUN
ejpam-6097	320	12	sys-318	sys-318	PROPN
ejpam-6097	320	13	tem	tem	PROPN
ejpam-6097	320	14	in	in	ADP
ejpam-6097	320	15	the	the	DET
ejpam-6097	320	16	presence	presence	NOUN
ejpam-6097	320	17	of	of	ADP
ejpam-6097	320	18	a	a	DET
ejpam-6097	320	19	competitor	competitor	NOUN
ejpam-6097	320	20	for	for	ADP
ejpam-6097	320	21	the	the	DET
ejpam-6097	320	22	prey	prey	NOUN
ejpam-6097	320	23	.	.	PUNCT
ejpam-6097	321	1	nonlinear	nonlinear	ADJ
ejpam-6097	321	2	analysis	analysis	NOUN
ejpam-6097	321	3	:	:	PUNCT
ejpam-6097	321	4	real	real	ADJ
ejpam-6097	321	5	world319	world319	PROPN
ejpam-6097	321	6	applications	application	NOUN
ejpam-6097	321	7	,	,	PUNCT
ejpam-6097	321	8	31:277–287	31:277–287	NUM
ejpam-6097	321	9	,	,	PUNCT
ejpam-6097	321	10	2016.320	2016.320	NUM
ejpam-6097	322	1	[	[	X
ejpam-6097	322	2	16	16	NUM
ejpam-6097	322	3	]	]	PUNCT
ejpam-6097	322	4	jawdat	jawdat	PROPN
ejpam-6097	322	5	alebraheem	alebraheem	PROPN
ejpam-6097	322	6	.	.	PUNCT
ejpam-6097	323	1	dynamics	dynamic	NOUN
ejpam-6097	323	2	of	of	ADP
ejpam-6097	323	3	a	a	DET
ejpam-6097	323	4	predator	predator	NOUN
ejpam-6097	323	5	–	–	PUNCT
ejpam-6097	323	6	prey	prey	NOUN
ejpam-6097	323	7	model	model	NOUN
ejpam-6097	323	8	with	with	ADP
ejpam-6097	323	9	the	the	DET
ejpam-6097	323	10	effect	effect	NOUN
ejpam-6097	323	11	of	of	ADP
ejpam-6097	323	12	oscillation321	oscillation321	PROPN
ejpam-6097	323	13	of	of	ADP
ejpam-6097	323	14	immigration	immigration	NOUN
ejpam-6097	323	15	of	of	ADP
ejpam-6097	323	16	the	the	DET
ejpam-6097	323	17	prey	prey	NOUN
ejpam-6097	323	18	.	.	PUNCT
ejpam-6097	324	1	diversity	diversity	NOUN
ejpam-6097	324	2	,	,	PUNCT
ejpam-6097	324	3	13(1):23	13(1):23	NUM
ejpam-6097	324	4	,	,	PUNCT
ejpam-6097	324	5	2021.322	2021.322	PROPN
ejpam-6097	324	6	[	[	X
ejpam-6097	324	7	17	17	NUM
ejpam-6097	324	8	]	]	X
ejpam-6097	324	9	leonid	leonid	PROPN
ejpam-6097	324	10	shaikhet	shaikhet	PROPN
ejpam-6097	324	11	and	and	CCONJ
ejpam-6097	324	12	andrei	andrei	PROPN
ejpam-6097	324	13	korobeinikov	korobeinikov	PROPN
ejpam-6097	324	14	.	.	PUNCT
ejpam-6097	325	1	persistence	persistence	NOUN
ejpam-6097	325	2	and	and	CCONJ
ejpam-6097	325	3	stochastic	stochastic	ADJ
ejpam-6097	325	4	extinction323	extinction323	PROPN
ejpam-6097	325	5	in	in	ADP
ejpam-6097	325	6	a	a	DET
ejpam-6097	325	7	lotka	lotka	PROPN
ejpam-6097	325	8	–	–	PUNCT
ejpam-6097	325	9	volterra	volterra	NOUN
ejpam-6097	325	10	predator	predator	NOUN
ejpam-6097	325	11	–	–	PUNCT
ejpam-6097	325	12	prey	prey	PROPN
ejpam-6097	325	13	stochastically	stochastically	ADV
ejpam-6097	325	14	perturbed	perturb	VERB
ejpam-6097	325	15	model	model	NOUN
ejpam-6097	325	16	.	.	PUNCT
ejpam-6097	326	1	mathematics,324	mathematics,324	PROPN
ejpam-6097	326	2	12(10):1588	12(10):1588	NUM
ejpam-6097	326	3	,	,	PUNCT
ejpam-6097	326	4	2024.325	2024.325	PROPN
ejpam-6097	326	5	[	[	X
ejpam-6097	326	6	18	18	NUM
ejpam-6097	326	7	]	]	PUNCT
ejpam-6097	326	8	qiuyue	qiuyue	NOUN
ejpam-6097	326	9	zhao	zhao	PROPN
ejpam-6097	326	10	and	and	CCONJ
ejpam-6097	326	11	xinglong	xinglong	PROPN
ejpam-6097	326	12	niu	niu	PROPN
ejpam-6097	326	13	.	.	PUNCT
ejpam-6097	327	1	dynamics	dynamic	NOUN
ejpam-6097	327	2	of	of	ADP
ejpam-6097	327	3	a	a	DET
ejpam-6097	327	4	stochastic	stochastic	ADJ
ejpam-6097	327	5	predator	predator	NOUN
ejpam-6097	327	6	–	–	PUNCT
ejpam-6097	327	7	prey	prey	NOUN
ejpam-6097	327	8	model	model	NOUN
ejpam-6097	327	9	with326	with326	PROPN
ejpam-6097	327	10	smith	smith	PROPN
ejpam-6097	327	11	growth	growth	NOUN
ejpam-6097	327	12	rate	rate	NOUN
ejpam-6097	327	13	and	and	CCONJ
ejpam-6097	327	14	cooperative	cooperative	ADJ
ejpam-6097	327	15	defense	defense	NOUN
ejpam-6097	327	16	.	.	PUNCT
ejpam-6097	328	1	mathematics	mathematic	NOUN
ejpam-6097	328	2	,	,	PUNCT
ejpam-6097	328	3	12(12):1796	12(12):1796	NUM
ejpam-6097	328	4	,	,	PUNCT
ejpam-6097	328	5	2024.327	2024.327	NUM
ejpam-6097	328	6	[	[	X
ejpam-6097	328	7	19	19	NUM
ejpam-6097	328	8	]	]	X
ejpam-6097	328	9	feng	feng	PROPN
ejpam-6097	328	10	rao	rao	PROPN
ejpam-6097	328	11	and	and	CCONJ
ejpam-6097	328	12	yun	yun	PROPN
ejpam-6097	328	13	kang	kang	PROPN
ejpam-6097	328	14	.	.	PUNCT
ejpam-6097	329	1	dynamics	dynamic	NOUN
ejpam-6097	329	2	of	of	ADP
ejpam-6097	329	3	a	a	DET
ejpam-6097	329	4	stochastic	stochastic	ADJ
ejpam-6097	329	5	prey	prey	NOUN
ejpam-6097	329	6	–	–	PUNCT
ejpam-6097	329	7	predator	predator	NOUN
ejpam-6097	329	8	system	system	NOUN
ejpam-6097	329	9	with328	with328	PROPN
ejpam-6097	329	10	prey	prey	NOUN
ejpam-6097	329	11	refuge	refuge	PROPN
ejpam-6097	329	12	,	,	PUNCT
ejpam-6097	329	13	predation	predation	NOUN
ejpam-6097	329	14	fear	fear	NOUN
ejpam-6097	329	15	and	and	CCONJ
ejpam-6097	329	16	its	its	PRON
ejpam-6097	329	17	carry	carry	VERB
ejpam-6097	329	18	-	-	PUNCT
ejpam-6097	329	19	over	over	ADP
ejpam-6097	329	20	effects	effect	NOUN
ejpam-6097	329	21	.	.	PUNCT
ejpam-6097	330	1	chaos	chaos	NOUN
ejpam-6097	330	2	,	,	PUNCT
ejpam-6097	330	3	solitons	soliton	NOUN
ejpam-6097	330	4	&	&	CCONJ
ejpam-6097	330	5	fractals,329	fractals,329	PROPN
ejpam-6097	330	6	175:113935	175:113935	NUM
ejpam-6097	330	7	,	,	PUNCT
ejpam-6097	330	8	2023.330	2023.330	NUM
ejpam-6097	330	9	[	[	X
ejpam-6097	330	10	20	20	NUM
ejpam-6097	330	11	]	]	X
ejpam-6097	330	12	jaouad	jaouad	PROPN
ejpam-6097	330	13	danane	danane	PROPN
ejpam-6097	330	14	,	,	PUNCT
ejpam-6097	330	15	karam	karam	PROPN
ejpam-6097	330	16	allali	allali	PROPN
ejpam-6097	330	17	,	,	PUNCT
ejpam-6097	330	18	zakia	zakia	NOUN
ejpam-6097	330	19	hammouch	hammouch	NOUN
ejpam-6097	330	20	,	,	PUNCT
ejpam-6097	330	21	and	and	CCONJ
ejpam-6097	330	22	kottakkaran	kottakkaran	VERB
ejpam-6097	330	23	sooppy	sooppy	ADJ
ejpam-6097	330	24	nisar.331	nisar.331	NOUN
ejpam-6097	330	25	mathematical	mathematical	ADJ
ejpam-6097	330	26	analysis	analysis	NOUN
ejpam-6097	330	27	and	and	CCONJ
ejpam-6097	330	28	simulation	simulation	NOUN
ejpam-6097	330	29	of	of	ADP
ejpam-6097	330	30	a	a	DET
ejpam-6097	330	31	stochastic	stochastic	ADJ
ejpam-6097	330	32	covid-19	covid-19	PROPN
ejpam-6097	330	33	lévy	lévy	X
ejpam-6097	330	34	jump	jump	VERB
ejpam-6097	330	35	model332	model332	PROPN
ejpam-6097	330	36	with	with	ADP
ejpam-6097	330	37	isolation	isolation	NOUN
ejpam-6097	330	38	strategy	strategy	NOUN
ejpam-6097	330	39	.	.	PUNCT
ejpam-6097	331	1	results	result	NOUN
ejpam-6097	331	2	in	in	ADP
ejpam-6097	331	3	physics	physics	NOUN
ejpam-6097	331	4	,	,	PUNCT
ejpam-6097	331	5	23:103994	23:103994	NUM
ejpam-6097	331	6	,	,	PUNCT
ejpam-6097	331	7	2021.333	2021.333	NUM
ejpam-6097	331	8	[	[	SYM
ejpam-6097	331	9	21	21	NUM
ejpam-6097	331	10	]	]	X
ejpam-6097	331	11	mudhafar	mudhafar	PROPN
ejpam-6097	331	12	f	f	PROPN
ejpam-6097	331	13	hama	hama	PROPN
ejpam-6097	331	14	,	,	PUNCT
ejpam-6097	331	15	rando	rando	PROPN
ejpam-6097	331	16	rq	rq	X
ejpam-6097	331	17	rasul	rasul	PROPN
ejpam-6097	331	18	,	,	PUNCT
ejpam-6097	331	19	zakia	zakia	NOUN
ejpam-6097	331	20	hammouch	hammouch	PROPN
ejpam-6097	331	21	,	,	PUNCT
ejpam-6097	331	22	kawa	kawa	PROPN
ejpam-6097	331	23	ah	ah	INTJ
ejpam-6097	331	24	rasul	rasul	PROPN
ejpam-6097	331	25	,	,	PUNCT
ejpam-6097	331	26	and	and	CCONJ
ejpam-6097	331	27	jaouad334	jaouad334	PROPN
ejpam-6097	331	28	danane	danane	PROPN
ejpam-6097	331	29	.	.	PUNCT
ejpam-6097	332	1	analysis	analysis	NOUN
ejpam-6097	332	2	of	of	ADP
ejpam-6097	332	3	a	a	DET
ejpam-6097	332	4	stochastic	stochastic	ADJ
ejpam-6097	332	5	seis	seis	NOUN
ejpam-6097	332	6	epidemic	epidemic	NOUN
ejpam-6097	332	7	model	model	NOUN
ejpam-6097	332	8	with	with	ADP
ejpam-6097	332	9	the	the	DET
ejpam-6097	332	10	standard	standard	ADJ
ejpam-6097	332	11	brownian335	brownian335	PROPN
ejpam-6097	332	12	motion	motion	NOUN
ejpam-6097	332	13	and	and	CCONJ
ejpam-6097	332	14	lévy	lévy	NOUN
ejpam-6097	332	15	jump	jump	NOUN
ejpam-6097	332	16	.	.	PUNCT
ejpam-6097	333	1	results	result	NOUN
ejpam-6097	333	2	in	in	ADP
ejpam-6097	333	3	physics	physics	NOUN
ejpam-6097	333	4	,	,	PUNCT
ejpam-6097	333	5	37:105477	37:105477	NUM
ejpam-6097	333	6	,	,	PUNCT
ejpam-6097	333	7	2022.336	2022.336	NUM
ejpam-6097	334	1	[	[	X
ejpam-6097	334	2	22	22	NUM
ejpam-6097	334	3	]	]	PUNCT
ejpam-6097	334	4	jawdat	jawdat	PROPN
ejpam-6097	334	5	alebraheem	alebraheem	PROPN
ejpam-6097	334	6	,	,	PUNCT
ejpam-6097	334	7	mogtaba	mogtaba	PROPN
ejpam-6097	334	8	mohammed	mohammed	PROPN
ejpam-6097	334	9	,	,	PUNCT
ejpam-6097	334	10	ismail	ismail	PROPN
ejpam-6097	334	11	m	m	VERB
ejpam-6097	334	12	tayel	tayel	PROPN
ejpam-6097	334	13	,	,	PUNCT
ejpam-6097	334	14	and	and	CCONJ
ejpam-6097	334	15	muhamad337	muhamad337	PROPN
ejpam-6097	334	16	hifzhudin	hifzhudin	PROPN
ejpam-6097	334	17	noor	noor	PROPN
ejpam-6097	334	18	aziz	aziz	PROPN
ejpam-6097	334	19	.	.	PUNCT
ejpam-6097	335	1	stochastic	stochastic	ADJ
ejpam-6097	335	2	prey	prey	NOUN
ejpam-6097	335	3	-	-	PUNCT
ejpam-6097	335	4	predator	predator	NOUN
ejpam-6097	335	5	model	model	NOUN
ejpam-6097	335	6	with	with	ADP
ejpam-6097	335	7	small	small	ADJ
ejpam-6097	335	8	random	random	ADJ
ejpam-6097	335	9	immigra-338	immigra-338	ADJ
ejpam-6097	335	10	tion	tion	NOUN
ejpam-6097	335	11	.	.	PUNCT
ejpam-6097	336	1	aims	aim	VERB
ejpam-6097	336	2	mathematics	mathematic	NOUN
ejpam-6097	336	3	,	,	PUNCT
ejpam-6097	336	4	9(6):14982–14996	9(6):14982–14996	PROPN
ejpam-6097	336	5	,	,	PUNCT
ejpam-6097	336	6	2024.339	2024.339	PROPN
ejpam-6097	336	7	[	[	X
ejpam-6097	336	8	23	23	NUM
ejpam-6097	336	9	]	]	PUNCT
ejpam-6097	336	10	hamlet	hamlet	PROPN
ejpam-6097	336	11	castillo	castillo	PROPN
ejpam-6097	336	12	-	-	PUNCT
ejpam-6097	336	13	alvino	alvino	PROPN
ejpam-6097	336	14	and	and	CCONJ
ejpam-6097	336	15	marcos	marcos	PROPN
ejpam-6097	336	16	marvá.	marvá.	PROPN
ejpam-6097	336	17	the	the	DET
ejpam-6097	336	18	competition	competition	NOUN
ejpam-6097	336	19	model	model	NOUN
ejpam-6097	336	20	with	with	ADP
ejpam-6097	336	21	holling340	holling340	PROPN
ejpam-6097	336	22	type	type	NOUN
ejpam-6097	336	23	ii	ii	NOUN
ejpam-6097	336	24	competitive	competitive	ADJ
ejpam-6097	336	25	response	response	NOUN
ejpam-6097	336	26	to	to	ADP
ejpam-6097	336	27	interfering	interfere	VERB
ejpam-6097	336	28	time	time	NOUN
ejpam-6097	336	29	.	.	PUNCT
ejpam-6097	337	1	journal	journal	NOUN
ejpam-6097	337	2	of	of	ADP
ejpam-6097	337	3	biological	biological	ADJ
ejpam-6097	337	4	dynamics,341	dynamics,341	PROPN
ejpam-6097	337	5	14(1):222–244	14(1):222–244	PROPN
ejpam-6097	337	6	,	,	PUNCT
ejpam-6097	337	7	2020.342	2020.342	PROPN
ejpam-6097	338	1	[	[	X
ejpam-6097	338	2	24	24	NUM
ejpam-6097	338	3	]	]	SYM
ejpam-6097	338	4	s	s	PART
ejpam-6097	338	5	toaha	toaha	NOUN
ejpam-6097	338	6	et	et	PROPN
ejpam-6097	338	7	al	al	PROPN
ejpam-6097	338	8	.	.	PROPN
ejpam-6097	339	1	stability	stability	NOUN
ejpam-6097	339	2	analysis	analysis	NOUN
ejpam-6097	339	3	of	of	ADP
ejpam-6097	339	4	prey	prey	PROPN
ejpam-6097	339	5	predator	predator	NOUN
ejpam-6097	339	6	model	model	NOUN
ejpam-6097	339	7	with	with	ADP
ejpam-6097	339	8	holling	holling	PROPN
ejpam-6097	339	9	ii	ii	PROPN
ejpam-6097	339	10	functional343	functional343	PROPN
ejpam-6097	339	11	response	response	NOUN
ejpam-6097	339	12	and	and	CCONJ
ejpam-6097	339	13	threshold	threshold	NOUN
ejpam-6097	339	14	harvesting	harvesting	NOUN
ejpam-6097	339	15	for	for	ADP
ejpam-6097	339	16	the	the	DET
ejpam-6097	339	17	predator	predator	NOUN
ejpam-6097	339	18	.	.	PUNCT
ejpam-6097	340	1	in	in	ADP
ejpam-6097	340	2	journal	journal	PROPN
ejpam-6097	340	3	of	of	ADP
ejpam-6097	340	4	physics	physics	PROPN
ejpam-6097	340	5	:	:	PUNCT
ejpam-6097	340	6	conference344	conference344	PROPN
ejpam-6097	340	7	series	series	PROPN
ejpam-6097	340	8	.	.	PUNCT
ejpam-6097	340	9	,	,	PUNCT
ejpam-6097	340	10	page	page	NOUN
ejpam-6097	340	11	062025	062025	NUM
ejpam-6097	340	12	.	.	PUNCT
ejpam-6097	341	1	iop	iop	PROPN
ejpam-6097	341	2	publishing	publishing	NOUN
ejpam-6097	341	3	,	,	PUNCT
ejpam-6097	341	4	2019.345	2019.345	NUM
ejpam-6097	342	1	[	[	X
ejpam-6097	342	2	25	25	NUM
ejpam-6097	342	3	]	]	PUNCT
ejpam-6097	342	4	jawdat	jawdat	PROPN
ejpam-6097	342	5	alebraheem	alebraheem	PROPN
ejpam-6097	342	6	.	.	PUNCT
ejpam-6097	343	1	relationship	relationship	NOUN
ejpam-6097	343	2	between	between	ADP
ejpam-6097	343	3	the	the	DET
ejpam-6097	343	4	paradox	paradox	NOUN
ejpam-6097	343	5	of	of	ADP
ejpam-6097	343	6	enrichment	enrichment	NOUN
ejpam-6097	343	7	and	and	CCONJ
ejpam-6097	343	8	the	the	DET
ejpam-6097	343	9	dy-346	dy-346	ADJ
ejpam-6097	343	10	namics	namic	NOUN
ejpam-6097	343	11	of	of	ADP
ejpam-6097	343	12	persistence	persistence	NOUN
ejpam-6097	343	13	and	and	CCONJ
ejpam-6097	343	14	extinction	extinction	NOUN
ejpam-6097	343	15	in	in	ADP
ejpam-6097	343	16	prey	prey	NOUN
ejpam-6097	343	17	-	-	PUNCT
ejpam-6097	343	18	predator	predator	NOUN
ejpam-6097	343	19	systems	system	NOUN
ejpam-6097	343	20	.	.	PUNCT
ejpam-6097	344	1	symmetry	symmetry	NOUN
ejpam-6097	344	2	,	,	PUNCT
ejpam-6097	344	3	10(10):532,347	10(10):532,347	PROPN
ejpam-6097	345	1	2018.348	2018.348	NUM
ejpam-6097	346	1	[	[	X
ejpam-6097	346	2	26	26	NUM
ejpam-6097	346	3	]	]	PUNCT
ejpam-6097	346	4	jawdat	jawdat	PROPN
ejpam-6097	346	5	alebraheem	alebraheem	PROPN
ejpam-6097	346	6	,	,	PUNCT
ejpam-6097	346	7	tabarek	tabarek	PROPN
ejpam-6097	346	8	qasim	qasim	PROPN
ejpam-6097	346	9	ibrahim	ibrahim	PROPN
ejpam-6097	346	10	,	,	PUNCT
ejpam-6097	346	11	ghassan	ghassan	PROPN
ejpam-6097	346	12	ezzulddin	ezzulddin	PROPN
ejpam-6097	346	13	arif	arif	PROPN
ejpam-6097	346	14	,	,	PUNCT
ejpam-6097	346	15	aws	aws	NOUN
ejpam-6097	346	16	asaad349	asaad349	PRON
ejpam-6097	346	17	hamdi	hamdi	PROPN
ejpam-6097	346	18	,	,	PUNCT
ejpam-6097	346	19	omar	omar	PROPN
ejpam-6097	346	20	bazighifan	bazighifan	PROPN
ejpam-6097	346	21	,	,	PUNCT
ejpam-6097	346	22	and	and	CCONJ
ejpam-6097	346	23	ali	ali	PROPN
ejpam-6097	346	24	hasan	hasan	PROPN
ejpam-6097	346	25	ali	ali	PROPN
ejpam-6097	346	26	.	.	PUNCT
ejpam-6097	347	1	the	the	DET
ejpam-6097	347	2	stabilizing	stabilize	VERB
ejpam-6097	347	3	effect	effect	NOUN
ejpam-6097	347	4	of	of	ADP
ejpam-6097	347	5	small	small	ADJ
ejpam-6097	347	6	prey350	prey350	PROPN
ejpam-6097	347	7	immigration	immigration	NOUN
ejpam-6097	347	8	on	on	ADP
ejpam-6097	347	9	competitive	competitive	ADJ
ejpam-6097	347	10	predator	predator	NOUN
ejpam-6097	347	11	-	-	PUNCT
ejpam-6097	347	12	prey	prey	NOUN
ejpam-6097	347	13	dynamics	dynamic	NOUN
ejpam-6097	347	14	.	.	PUNCT
ejpam-6097	348	1	mathematical	mathematical	ADJ
ejpam-6097	348	2	and	and	CCONJ
ejpam-6097	348	3	computer351	computer351	PROPN
ejpam-6097	348	4	modelling	modelling	NOUN
ejpam-6097	348	5	of	of	ADP
ejpam-6097	348	6	dynamical	dynamical	ADJ
ejpam-6097	348	7	systems	system	NOUN
ejpam-6097	348	8	,	,	PUNCT
ejpam-6097	348	9	30(1):605–625	30(1):605–625	NUM
ejpam-6097	348	10	,	,	PUNCT
ejpam-6097	348	11	2024.352	2024.352	NUM
ejpam-6097	348	12	[	[	SYM
ejpam-6097	348	13	27	27	NUM
ejpam-6097	348	14	]	]	PUNCT
ejpam-6097	348	15	doina	doina	NOUN
ejpam-6097	348	16	cioranescu	cioranescu	PROPN
ejpam-6097	348	17	,	,	PUNCT
ejpam-6097	348	18	patrizia	patrizia	PROPN
ejpam-6097	348	19	donato	donato	NOUN
ejpam-6097	348	20	,	,	PUNCT
ejpam-6097	348	21	and	and	CCONJ
ejpam-6097	348	22	marian	marian	PROPN
ejpam-6097	348	23	p	p	PROPN
ejpam-6097	348	24	roque	roque	PROPN
ejpam-6097	348	25	.	.	PUNCT
ejpam-6097	349	1	an	an	DET
ejpam-6097	349	2	introduction	introduction	NOUN
ejpam-6097	349	3	to	to	ADP
ejpam-6097	349	4	sec-353	sec-353	PROPN
ejpam-6097	349	5	ond	ond	NOUN
ejpam-6097	349	6	order	order	NOUN
ejpam-6097	349	7	partial	partial	ADJ
ejpam-6097	349	8	differential	differential	NOUN
ejpam-6097	349	9	equations	equation	NOUN
ejpam-6097	349	10	:	:	PUNCT
ejpam-6097	349	11	classical	classical	ADJ
ejpam-6097	349	12	and	and	CCONJ
ejpam-6097	349	13	variational	variational	ADJ
ejpam-6097	349	14	solutions	solution	NOUN
ejpam-6097	349	15	.	.	PUNCT
ejpam-6097	350	1	world354	world354	PROPN
ejpam-6097	350	2	m.	m.	NOUN
ejpam-6097	350	3	mohamed	mohamed	PROPN
ejpam-6097	350	4	et	et	PROPN
ejpam-6097	350	5	al	al	PROPN
ejpam-6097	350	6	.	.	PUNCT
ejpam-6097	350	7	/	/	SYM
ejpam-6097	350	8	eur	eur	PROPN
ejpam-6097	350	9	.	.	PUNCT
ejpam-6097	351	1	j.	j.	PROPN
ejpam-6097	351	2	pure	pure	PROPN
ejpam-6097	351	3	appl	appl	PROPN
ejpam-6097	351	4	.	.	PROPN
ejpam-6097	351	5	math	math	PROPN
ejpam-6097	351	6	,	,	PUNCT
ejpam-6097	351	7	18	18	NUM
ejpam-6097	351	8	(	(	PUNCT
ejpam-6097	351	9	2	2	NUM
ejpam-6097	351	10	)	)	PUNCT
ejpam-6097	351	11	(	(	PUNCT
ejpam-6097	351	12	2025	2025	NUM
ejpam-6097	351	13	)	)	PUNCT
ejpam-6097	351	14	,	,	PUNCT
ejpam-6097	351	15	6097	6097	NUM
ejpam-6097	351	16	19	19	NUM
ejpam-6097	351	17	of	of	ADP
ejpam-6097	351	18	19	19	NUM
ejpam-6097	351	19	scientific	scientific	ADJ
ejpam-6097	351	20	,	,	PUNCT
ejpam-6097	351	21	2018.355	2018.355	NUM
ejpam-6097	352	1	[	[	X
ejpam-6097	352	2	28	28	NUM
ejpam-6097	352	3	]	]	PUNCT
ejpam-6097	352	4	valerii	valerii	PROPN
ejpam-6097	352	5	nikolaevich	nikolaevich	PROPN
ejpam-6097	352	6	afanasiev	afanasiev	PROPN
ejpam-6097	352	7	,	,	PUNCT
ejpam-6097	352	8	v	v	NOUN
ejpam-6097	352	9	kolmanovskii	kolmanovskii	PROPN
ejpam-6097	352	10	,	,	PUNCT
ejpam-6097	352	11	and	and	CCONJ
ejpam-6097	352	12	valerij	valerij	ADV
ejpam-6097	352	13	romanovič	romanovič	NOUN
ejpam-6097	352	14	nosov	nosov	NOUN
ejpam-6097	352	15	.	.	PUNCT
ejpam-6097	353	1	math-356	math-356	NOUN
ejpam-6097	353	2	ematical	ematical	ADJ
ejpam-6097	353	3	theory	theory	NOUN
ejpam-6097	353	4	of	of	ADP
ejpam-6097	353	5	control	control	NOUN
ejpam-6097	353	6	systems	system	NOUN
ejpam-6097	353	7	design	design	NOUN
ejpam-6097	353	8	.	.	PUNCT
ejpam-6097	354	1	springer	springer	NOUN
ejpam-6097	354	2	science	science	PROPN
ejpam-6097	354	3	&	&	CCONJ
ejpam-6097	354	4	business	business	NOUN
ejpam-6097	354	5	media	medium	NOUN
ejpam-6097	354	6	,	,	PUNCT
ejpam-6097	354	7	2013.357	2013.357	NUM
ejpam-6097	354	8	[	[	X
ejpam-6097	354	9	29	29	NUM
ejpam-6097	354	10	]	]	X
ejpam-6097	354	11	youlin	youlin	PROPN
ejpam-6097	354	12	huang	huang	PROPN
ejpam-6097	354	13	,	,	PUNCT
ejpam-6097	354	14	wanying	wanye	VERB
ejpam-6097	354	15	shi	shi	PROPN
ejpam-6097	354	16	,	,	PUNCT
ejpam-6097	354	17	chunjin	chunjin	PROPN
ejpam-6097	354	18	wei	wei	PROPN
ejpam-6097	354	19	,	,	PUNCT
ejpam-6097	354	20	and	and	CCONJ
ejpam-6097	354	21	shuwen	shuwen	PROPN
ejpam-6097	354	22	zhang	zhang	PROPN
ejpam-6097	354	23	.	.	PUNCT
ejpam-6097	355	1	a	a	DET
ejpam-6097	355	2	stochastic	stochastic	ADJ
ejpam-6097	355	3	predator–358	predator–358	NOUN
ejpam-6097	355	4	prey	prey	NOUN
ejpam-6097	355	5	model	model	NOUN
ejpam-6097	355	6	with	with	ADP
ejpam-6097	355	7	holling	holle	VERB
ejpam-6097	355	8	ii	ii	NOUN
ejpam-6097	355	9	increasing	increase	VERB
ejpam-6097	355	10	function	function	NOUN
ejpam-6097	355	11	in	in	ADP
ejpam-6097	355	12	the	the	DET
ejpam-6097	355	13	predator	predator	NOUN
ejpam-6097	355	14	.	.	PUNCT
ejpam-6097	356	1	journal	journal	PROPN
ejpam-6097	356	2	of	of	ADP
ejpam-6097	356	3	biological359	biological359	PROPN
ejpam-6097	356	4	dynamics	dynamic	NOUN
ejpam-6097	356	5	,	,	PUNCT
ejpam-6097	356	6	15(1):1–18	15(1):1–18	NUM
ejpam-6097	356	7	,	,	PUNCT
ejpam-6097	356	8	2021.360	2021.360	NUM
ejpam-6097	356	9	[	[	SYM
ejpam-6097	356	10	30	30	NUM
ejpam-6097	356	11	]	]	X
ejpam-6097	356	12	nirav	nirav	PROPN
ejpam-6097	356	13	dalal	dalal	PROPN
ejpam-6097	356	14	,	,	PUNCT
ejpam-6097	356	15	david	david	PROPN
ejpam-6097	356	16	greenhalgh	greenhalgh	PROPN
ejpam-6097	356	17	,	,	PUNCT
ejpam-6097	356	18	and	and	CCONJ
ejpam-6097	356	19	xuerong	xuerong	PROPN
ejpam-6097	356	20	mao	mao	PROPN
ejpam-6097	356	21	.	.	PUNCT
ejpam-6097	357	1	a	a	DET
ejpam-6097	357	2	stochastic	stochastic	ADJ
ejpam-6097	357	3	model	model	NOUN
ejpam-6097	357	4	for	for	ADP
ejpam-6097	357	5	internal361	internal361	NOUN
ejpam-6097	357	6	hiv	hiv	PROPN
ejpam-6097	357	7	dynamics	dynamic	NOUN
ejpam-6097	357	8	.	.	PUNCT
ejpam-6097	358	1	journal	journal	PROPN
ejpam-6097	358	2	of	of	ADP
ejpam-6097	358	3	mathematical	mathematical	ADJ
ejpam-6097	358	4	analysis	analysis	NOUN
ejpam-6097	358	5	and	and	CCONJ
ejpam-6097	358	6	applications	application	NOUN
ejpam-6097	358	7	,	,	PUNCT
ejpam-6097	358	8	341(2):1084–362	341(2):1084–362	NUM
ejpam-6097	358	9	1101	1101	NUM
ejpam-6097	358	10	,	,	PUNCT
ejpam-6097	358	11	2008.363	2008.363	NUM
ejpam-6097	358	12	introduction	introduction	NOUN
ejpam-6097	358	13	problem	problem	NOUN
ejpam-6097	358	14	statement	statement	NOUN
ejpam-6097	358	15	model	model	NOUN
ejpam-6097	358	16	boundedness	boundedness	PROPN
ejpam-6097	358	17	stochastic	stochastic	ADJ
ejpam-6097	358	18	mean	mean	NOUN
ejpam-6097	358	19	square	square	ADJ
ejpam-6097	358	20	stability	stability	NOUN
ejpam-6097	358	21	persistence	persistence	NOUN
ejpam-6097	358	22	and	and	CCONJ
ejpam-6097	358	23	extinction	extinction	NOUN
ejpam-6097	358	24	persistence	persistence	NOUN
ejpam-6097	358	25	of	of	ADP
ejpam-6097	358	26	the	the	DET
ejpam-6097	358	27	prey	prey	NOUN
ejpam-6097	358	28	population	population	NOUN
ejpam-6097	358	29	extinction	extinction	NOUN
ejpam-6097	358	30	of	of	ADP
ejpam-6097	358	31	the	the	DET
ejpam-6097	358	32	prey	prey	NOUN
ejpam-6097	358	33	population	population	NOUN
ejpam-6097	358	34	extinction	extinction	NOUN
ejpam-6097	358	35	for	for	ADP
ejpam-6097	358	36	the	the	DET
ejpam-6097	358	37	predator	predator	NOUN
ejpam-6097	358	38	population	population	NOUN
ejpam-6097	358	39	numerical	numerical	ADJ
ejpam-6097	358	40	simulations	simulation	NOUN
ejpam-6097	358	41	and	and	CCONJ
ejpam-6097	358	42	discussion	discussion	NOUN
ejpam-6097	358	43	conclusion	conclusion	NOUN