id	sid	tid	token	lemma	pos
cana-1403	1	1	communications	communication	NOUN
cana-1403	1	2	on	on	ADP
cana-1403	1	3	applied	apply	VERB
cana-1403	1	4	nonlinear	nonlinear	ADJ
cana-1403	1	5	analysis	analysis	NOUN
cana-1403	1	6	issn	issn	NOUN
cana-1403	1	7	:	:	PUNCT
cana-1403	1	8	1074	1074	NUM
cana-1403	1	9	-	-	PUNCT
cana-1403	1	10	133x	133x	NUM
cana-1403	1	11	vol	vol	NOUN
cana-1403	1	12	31	31	NUM
cana-1403	1	13	no	no	NOUN
cana-1403	1	14	.	.	PUNCT
cana-1403	2	1	7s	7	NOUN
cana-1403	2	2	(	(	PUNCT
cana-1403	2	3	2024	2024	NUM
cana-1403	2	4	)	)	PUNCT
cana-1403	3	1	631	631	NUM
cana-1403	4	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-1403	4	2	stability	stability	NOUN
cana-1403	4	3	of	of	ADP
cana-1403	4	4	equilibrium	equilibrium	NOUN
cana-1403	4	5	states	state	NOUN
cana-1403	4	6	for	for	ADP
cana-1403	4	7	a	a	DET
cana-1403	4	8	stochastically	stochastically	ADV
cana-1403	4	9	perturbed	perturb	VERB
cana-1403	4	10	pielou	pielou	NOUN
cana-1403	4	11	’s	’s	PART
cana-1403	4	12	equation	equation	NOUN
cana-1403	4	13	[	[	PUNCT
cana-1403	4	14	*	*	PUNCT
cana-1403	4	15	a.	a.	NOUN
cana-1403	4	16	lallouche	lallouche	NOUN
cana-1403	4	17	1	1	NUM
cana-1403	4	18	,	,	PUNCT
cana-1403	4	19	a.	a.	NOUN
cana-1403	4	20	aoufi	aoufi	NOUN
cana-1403	4	21	2	2	NUM
cana-1403	4	22	,	,	PUNCT
cana-1403	4	23	m.	m.	NOUN
cana-1403	4	24	tadjine	tadjine	NOUN
cana-1403	4	25	2	2	NUM
cana-1403	4	26	*	*	SYM
cana-1403	4	27	1	1	NUM
cana-1403	4	28	laboratory	laboratory	NOUN
cana-1403	4	29	of	of	ADP
cana-1403	4	30	applied	apply	VERB
cana-1403	4	31	mathematics	mathematic	NOUN
cana-1403	4	32	and	and	CCONJ
cana-1403	4	33	history	history	NOUN
cana-1403	4	34	and	and	CCONJ
cana-1403	4	35	didactics	didactics	NOUN
cana-1403	4	36	of	of	ADP
cana-1403	4	37	mathematics	mathematics	PROPN
cana-1403	4	38	(	(	PUNCT
cana-1403	4	39	lamahis	lamahis	PROPN
cana-1403	4	40	)	)	PUNCT
cana-1403	4	41	,	,	PUNCT
cana-1403	4	42	20	20	NUM
cana-1403	4	43	august	august	PROPN
cana-1403	4	44	1955	1955	NUM
cana-1403	4	45	,	,	PUNCT
cana-1403	4	46	university	university	NOUN
cana-1403	4	47	of	of	ADP
cana-1403	4	48	skikda	skikda	NOUN
cana-1403	4	49	,	,	PUNCT
cana-1403	4	50	algeria	algeria	PROPN
cana-1403	4	51	.	.	PUNCT
cana-1403	5	1	address	address	NOUN
cana-1403	5	2	:	:	PUNCT
cana-1403	5	3	skikda,21000	skikda,21000	PROPN
cana-1403	5	4	,	,	PUNCT
cana-1403	5	5	algeria	algeria	PROPN
cana-1403	5	6	.	.	PUNCT
cana-1403	6	1	corresponding	correspond	VERB
cana-1403	6	2	author	author	NOUN
cana-1403	6	3	:	:	PUNCT
cana-1403	6	4	e	e	NOUN
cana-1403	6	5	-	-	NOUN
cana-1403	6	6	mail	mail	NOUN
cana-1403	6	7	:	:	PUNCT
cana-1403	6	8	a.lallouche@univ-skikda.dz	a.lallouche@univ-skikda.dz	NOUN
cana-1403	7	1	2	2	NUM
cana-1403	7	2	20	20	NUM
cana-1403	7	3	august	august	PROPN
cana-1403	7	4	1955	1955	NUM
cana-1403	7	5	,	,	PUNCT
cana-1403	7	6	university	university	NOUN
cana-1403	7	7	of	of	ADP
cana-1403	7	8	skikda	skikda	NOUN
cana-1403	7	9	,	,	PUNCT
cana-1403	7	10	algeria	algeria	PROPN
cana-1403	7	11	.	.	PUNCT
cana-1403	8	1	address	address	NOUN
cana-1403	8	2	:	:	PUNCT
cana-1403	8	3	skikda	skikda	NOUN
cana-1403	8	4	,	,	PUNCT
cana-1403	8	5	21000	21000	NUM
cana-1403	8	6	,	,	PUNCT
cana-1403	8	7	algeria	algeria	PROPN
cana-1403	8	8	.	.	PUNCT
cana-1403	9	1	e	e	X
cana-1403	9	2	-	-	NOUN
cana-1403	9	3	mail	mail	NOUN
cana-1403	9	4	:	:	PUNCT
cana-1403	10	1	aoufiamani@gmail.com	aoufiamani@gmail.com	NOUN
cana-1403	10	2	2	2	NUM
cana-1403	10	3	20	20	NUM
cana-1403	10	4	august	august	PROPN
cana-1403	10	5	1955	1955	NUM
cana-1403	10	6	,	,	PUNCT
cana-1403	10	7	university	university	NOUN
cana-1403	10	8	of	of	ADP
cana-1403	10	9	skikda	skikda	NOUN
cana-1403	10	10	,	,	PUNCT
cana-1403	10	11	algeria	algeria	PROPN
cana-1403	10	12	.	.	PUNCT
cana-1403	10	13	address	address	NOUN
cana-1403	10	14	:	:	PUNCT
cana-1403	10	15	skikda	skikda	NOUN
cana-1403	10	16	,	,	PUNCT
cana-1403	10	17	21000	21000	NUM
cana-1403	10	18	,	,	PUNCT
cana-1403	10	19	algeria	algeria	PROPN
cana-1403	10	20	.	.	PUNCT
cana-1403	11	1	e	e	X
cana-1403	11	2	-	-	NOUN
cana-1403	11	3	mail	mail	NOUN
cana-1403	11	4	:	:	PUNCT
cana-1403	11	5	meriem.tedj@gmail.com	meriem.tedj@gmail.com	X
cana-1403	11	6	article	article	NOUN
cana-1403	11	7	history	history	NOUN
cana-1403	11	8	:	:	PUNCT
cana-1403	11	9	received	receive	VERB
cana-1403	11	10	:	:	PUNCT
cana-1403	11	11	04	04	NUM
cana-1403	11	12	-	-	PUNCT
cana-1403	11	13	06	06	NUM
cana-1403	11	14	-	-	PUNCT
cana-1403	11	15	2024	2024	NUM
cana-1403	11	16	revised	revise	VERB
cana-1403	11	17	:	:	PUNCT
cana-1403	11	18	03	03	NUM
cana-1403	11	19	-	-	PUNCT
cana-1403	11	20	07	07	NUM
cana-1403	11	21	-	-	PUNCT
cana-1403	11	22	2024	2024	NUM
cana-1403	11	23	accepted	accept	VERB
cana-1403	11	24	:	:	PUNCT
cana-1403	11	25	30	30	NUM
cana-1403	11	26	-	-	SYM
cana-1403	11	27	07	07	NUM
cana-1403	11	28	-	-	PUNCT
cana-1403	11	29	2024	2024	NUM
cana-1403	11	30	abstract	abstract	NOUN
cana-1403	11	31	:	:	PUNCT
cana-1403	11	32	it	it	PRON
cana-1403	11	33	is	be	AUX
cana-1403	11	34	widely	widely	ADV
cana-1403	11	35	recognized	recognize	VERB
cana-1403	11	36	that	that	SCONJ
cana-1403	11	37	the	the	DET
cana-1403	11	38	theory	theory	NOUN
cana-1403	11	39	of	of	ADP
cana-1403	11	40	stochastic	stochastic	ADJ
cana-1403	11	41	difference	difference	NOUN
cana-1403	11	42	equations	equation	NOUN
cana-1403	11	43	is	be	AUX
cana-1403	11	44	a	a	DET
cana-1403	11	45	mathematical	mathematical	ADJ
cana-1403	11	46	area	area	NOUN
cana-1403	11	47	of	of	ADP
cana-1403	11	48	great	great	ADJ
cana-1403	11	49	interest	interest	NOUN
cana-1403	11	50	.	.	PUNCT
cana-1403	12	1	concrete	concrete	ADJ
cana-1403	12	2	systems	system	NOUN
cana-1403	12	3	and	and	CCONJ
cana-1403	12	4	processes	process	NOUN
cana-1403	12	5	is	be	AUX
cana-1403	12	6	one	one	NUM
cana-1403	12	7	of	of	ADP
cana-1403	12	8	its	its	PRON
cana-1403	12	9	subareas	subarea	NOUN
cana-1403	12	10	,	,	PUNCT
cana-1403	12	11	which	which	PRON
cana-1403	12	12	is	be	AUX
cana-1403	12	13	of	of	ADP
cana-1403	12	14	some	some	DET
cana-1403	12	15	interest	interest	NOUN
cana-1403	12	16	nowadays	nowadays	ADV
cana-1403	12	17	.	.	PUNCT
cana-1403	13	1	specifically	specifically	ADV
cana-1403	13	2	,	,	PUNCT
cana-1403	13	3	in	in	ADP
cana-1403	13	4	fields	field	NOUN
cana-1403	13	5	such	such	ADJ
cana-1403	13	6	as	as	ADP
cana-1403	13	7	systems	system	NOUN
cana-1403	13	8	biology	biology	NOUN
cana-1403	13	9	,	,	PUNCT
cana-1403	13	10	ecology	ecology	NOUN
cana-1403	13	11	,	,	PUNCT
cana-1403	13	12	biochemistry	biochemistry	NOUN
cana-1403	13	13	,	,	PUNCT
cana-1403	13	14	genetics	genetic	NOUN
cana-1403	13	15	,	,	PUNCT
cana-1403	13	16	and	and	CCONJ
cana-1403	13	17	physiology	physiology	NOUN
cana-1403	13	18	dynamics	dynamic	NOUN
cana-1403	13	19	,	,	PUNCT
cana-1403	13	20	numerous	numerous	ADJ
cana-1403	13	21	population	population	NOUN
cana-1403	13	22	models	model	NOUN
cana-1403	13	23	are	be	AUX
cana-1403	13	24	described	describe	VERB
cana-1403	13	25	by	by	ADP
cana-1403	13	26	studying	study	VERB
cana-1403	13	27	linear	linear	ADJ
cana-1403	13	28	and	and	CCONJ
cana-1403	13	29	nonlinear	nonlinear	ADJ
cana-1403	13	30	difference	difference	NOUN
cana-1403	13	31	equations	equation	NOUN
cana-1403	13	32	and	and	CCONJ
cana-1403	13	33	systems	system	NOUN
cana-1403	13	34	.	.	PUNCT
cana-1403	14	1	these	these	DET
cana-1403	14	2	studies	study	NOUN
cana-1403	14	3	have	have	AUX
cana-1403	14	4	been	be	AUX
cana-1403	14	5	very	very	ADV
cana-1403	14	6	productive	productive	ADJ
cana-1403	14	7	and	and	CCONJ
cana-1403	14	8	helpful	helpful	ADJ
cana-1403	14	9	to	to	PART
cana-1403	14	10	develop	develop	VERB
cana-1403	14	11	the	the	DET
cana-1403	14	12	basic	basic	ADJ
cana-1403	14	13	theory	theory	NOUN
cana-1403	14	14	of	of	ADP
cana-1403	14	15	the	the	DET
cana-1403	14	16	qualitative	qualitative	ADJ
cana-1403	14	17	behaviour	behaviour	NOUN
cana-1403	14	18	of	of	ADP
cana-1403	14	19	nonlinear	nonlinear	ADJ
cana-1403	14	20	rational	rational	ADJ
cana-1403	14	21	and	and	CCONJ
cana-1403	14	22	exponential	exponential	ADJ
cana-1403	14	23	difference	difference	NOUN
cana-1403	14	24	equations	equation	NOUN
cana-1403	14	25	and	and	CCONJ
cana-1403	14	26	systems	system	NOUN
cana-1403	14	27	.	.	PUNCT
cana-1403	15	1	in	in	ADP
cana-1403	15	2	this	this	DET
cana-1403	15	3	paper	paper	NOUN
cana-1403	15	4	,	,	PUNCT
cana-1403	15	5	we	we	PRON
cana-1403	15	6	investigate	investigate	VERB
cana-1403	15	7	a	a	DET
cana-1403	15	8	type	type	NOUN
cana-1403	15	9	of	of	ADP
cana-1403	15	10	pielou‟s	pielou‟s	PUNCT
cana-1403	15	11	difference	difference	NOUN
cana-1403	15	12	equation	equation	NOUN
cana-1403	15	13	that	that	PRON
cana-1403	15	14	is	be	AUX
cana-1403	15	15	subject	subject	ADJ
cana-1403	15	16	to	to	ADP
cana-1403	15	17	additive	additive	ADJ
cana-1403	15	18	stochastic	stochastic	ADJ
cana-1403	15	19	perturbations	perturbation	NOUN
cana-1403	15	20	modelled	model	VERB
cana-1403	15	21	as	as	ADP
cana-1403	15	22	a	a	DET
cana-1403	15	23	sequence	sequence	NOUN
cana-1403	15	24	of	of	ADP
cana-1403	15	25	independent	independent	ADJ
cana-1403	15	26	random	random	ADJ
cana-1403	15	27	variables	variable	NOUN
cana-1403	15	28	(	(	PUNCT
cana-1403	15	29	)	)	PUNCT
cana-1403	15	30	with	with	ADP
cana-1403	15	31	zero	zero	NUM
cana-1403	15	32	mean	mean	NOUN
cana-1403	15	33	and	and	CCONJ
cana-1403	15	34	unit	unit	NOUN
cana-1403	15	35	variance	variance	NOUN
cana-1403	15	36	.	.	PUNCT
cana-1403	16	1	these	these	DET
cana-1403	16	2	perturbations	perturbation	NOUN
cana-1403	16	3	are	be	AUX
cana-1403	16	4	proportional	proportional	ADJ
cana-1403	16	5	to	to	ADP
cana-1403	16	6	the	the	DET
cana-1403	16	7	deviation	deviation	NOUN
cana-1403	16	8	of	of	ADP
cana-1403	16	9	the	the	DET
cana-1403	16	10	system	system	NOUN
cana-1403	16	11	state	state	NOUN
cana-1403	16	12	(	(	PUNCT
cana-1403	16	13	)	)	PUNCT
cana-1403	16	14	from	from	ADP
cana-1403	16	15	its	its	PRON
cana-1403	16	16	equilibrium	equilibrium	NOUN
cana-1403	16	17	points	point	NOUN
cana-1403	16	18	,	,	PUNCT
cana-1403	16	19	resulting	result	VERB
cana-1403	16	20	in	in	ADP
cana-1403	16	21	the	the	DET
cana-1403	16	22	following	follow	VERB
cana-1403	16	23	stochastic	stochastic	ADJ
cana-1403	16	24	difference	difference	NOUN
cana-1403	16	25	equation	equation	NOUN
cana-1403	16	26	.	.	PUNCT
cana-1403	17	1	(	(	PUNCT
cana-1403	17	2	)	)	PUNCT
cana-1403	17	3	where	where	SCONJ
cana-1403	17	4	parameters	parameter	NOUN
cana-1403	17	5	have	have	VERB
cana-1403	17	6	arbitrary	arbitrary	ADJ
cana-1403	17	7	values	value	NOUN
cana-1403	17	8	.	.	PUNCT
cana-1403	18	1	utilizing	utilize	VERB
cana-1403	18	2	the	the	DET
cana-1403	18	3	general	general	ADJ
cana-1403	18	4	method	method	NOUN
cana-1403	18	5	of	of	ADP
cana-1403	18	6	constructing	construct	VERB
cana-1403	18	7	lyapunov	lyapunov	NOUN
cana-1403	18	8	functional	functional	ADJ
cana-1403	18	9	for	for	ADP
cana-1403	18	10	stochastic	stochastic	ADJ
cana-1403	18	11	difference	difference	NOUN
cana-1403	18	12	equations	equation	NOUN
cana-1403	18	13	in	in	ADP
cana-1403	18	14	discrete	discrete	ADJ
cana-1403	18	15	time	time	NOUN
cana-1403	18	16	,	,	PUNCT
cana-1403	18	17	we	we	PRON
cana-1403	18	18	establish	establish	VERB
cana-1403	18	19	necessary	necessary	ADJ
cana-1403	18	20	and	and	CCONJ
cana-1403	18	21	sufficient	sufficient	ADJ
cana-1403	18	22	conditions	condition	NOUN
cana-1403	18	23	for	for	ADP
cana-1403	18	24	the	the	DET
cana-1403	18	25	asymptotic	asymptotic	ADJ
cana-1403	18	26	mean	mean	ADJ
cana-1403	18	27	square	square	ADJ
cana-1403	18	28	stability	stability	NOUN
cana-1403	18	29	of	of	ADP
cana-1403	18	30	the	the	DET
cana-1403	18	31	two	two	NUM
cana-1403	18	32	equilibrium	equilibrium	NOUN
cana-1403	18	33	points	point	NOUN
cana-1403	18	34	(	(	PUNCT
cana-1403	18	35	zero	zero	NUM
cana-1403	18	36	and	and	CCONJ
cana-1403	18	37	positive	positive	ADJ
cana-1403	18	38	)	)	PUNCT
cana-1403	18	39	.	.	PUNCT
cana-1403	19	1	these	these	DET
cana-1403	19	2	conditions	condition	NOUN
cana-1403	19	3	also	also	ADV
cana-1403	19	4	serve	serve	VERB
cana-1403	19	5	as	as	ADP
cana-1403	19	6	sufficient	sufficient	ADJ
cana-1403	19	7	conditions	condition	NOUN
cana-1403	19	8	for	for	ADP
cana-1403	19	9	the	the	DET
cana-1403	19	10	stability	stability	NOUN
cana-1403	19	11	in	in	ADP
cana-1403	19	12	probability	probability	NOUN
cana-1403	19	13	of	of	ADP
cana-1403	19	14	the	the	DET
cana-1403	19	15	equilibrium	equilibrium	NOUN
cana-1403	19	16	points	point	NOUN
cana-1403	19	17	of	of	ADP
cana-1403	19	18	the	the	DET
cana-1403	19	19	original	original	ADJ
cana-1403	19	20	nonlinear	nonlinear	ADJ
cana-1403	19	21	equation	equation	NOUN
cana-1403	19	22	.	.	PUNCT
cana-1403	20	1	to	to	PART
cana-1403	20	2	validate	validate	VERB
cana-1403	20	3	the	the	DET
cana-1403	20	4	derived	derive	VERB
cana-1403	20	5	results	result	NOUN
cana-1403	20	6	,	,	PUNCT
cana-1403	20	7	numerical	numerical	ADJ
cana-1403	20	8	examples	example	NOUN
cana-1403	20	9	and	and	CCONJ
cana-1403	20	10	simulations	simulation	NOUN
cana-1403	20	11	of	of	ADP
cana-1403	20	12	equation	equation	NOUN
cana-1403	20	13	solutions	solution	NOUN
cana-1403	20	14	are	be	AUX
cana-1403	20	15	presented	present	VERB
cana-1403	20	16	,	,	PUNCT
cana-1403	20	17	accompanied	accompany	VERB
cana-1403	20	18	by	by	ADP
cana-1403	20	19	numerous	numerous	ADJ
cana-1403	20	20	graphical	graphical	ADJ
cana-1403	20	21	illustrations	illustration	NOUN
cana-1403	20	22	of	of	ADP
cana-1403	20	23	stability	stability	NOUN
cana-1403	20	24	trajectories	trajectory	NOUN
cana-1403	20	25	of	of	ADP
cana-1403	20	26	solutions	solution	NOUN
cana-1403	20	27	.	.	PUNCT
cana-1403	21	1	keywords	keyword	NOUN
cana-1403	21	2	:	:	PUNCT
cana-1403	21	3	equilibrium	equilibrium	NOUN
cana-1403	21	4	points	point	NOUN
cana-1403	21	5	;	;	PUNCT
cana-1403	21	6	difference	difference	NOUN
cana-1403	21	7	equation	equation	NOUN
cana-1403	21	8	;	;	PUNCT
cana-1403	21	9	stochastic	stochastic	ADJ
cana-1403	21	10	perturbations	perturbation	NOUN
cana-1403	21	11	;	;	PUNCT
cana-1403	21	12	stability	stability	NOUN
cana-1403	21	13	in	in	ADP
cana-1403	21	14	probability	probability	NOUN
cana-1403	21	15	,	,	PUNCT
cana-1403	21	16	pielou‟s	pielou‟s	PART
cana-1403	21	17	equation	equation	NOUN
cana-1403	21	18	,	,	PUNCT
cana-1403	21	19	.	.	PUNCT
cana-1403	22	1	1	1	X
cana-1403	22	2	.	.	X
cana-1403	22	3	introduction	introduction	NOUN
cana-1403	22	4	stochastic	stochastic	ADJ
cana-1403	22	5	discrete	discrete	ADJ
cana-1403	22	6	dynamical	dynamical	ADJ
cana-1403	22	7	systems	system	NOUN
cana-1403	22	8	is	be	AUX
cana-1403	22	9	a	a	DET
cana-1403	22	10	branch	branch	NOUN
cana-1403	22	11	of	of	ADP
cana-1403	22	12	mathematics	mathematic	NOUN
cana-1403	22	13	that	that	PRON
cana-1403	22	14	deals	deal	VERB
cana-1403	22	15	with	with	ADP
cana-1403	22	16	analyzing	analyze	VERB
cana-1403	22	17	and	and	CCONJ
cana-1403	22	18	modelling	model	VERB
cana-1403	22	19	systems	system	NOUN
cana-1403	22	20	influenced	influence	VERB
cana-1403	22	21	by	by	ADP
cana-1403	22	22	randomness	randomness	NOUN
cana-1403	22	23	.	.	PUNCT
cana-1403	23	1	the	the	DET
cana-1403	23	2	origins	origin	NOUN
cana-1403	23	3	of	of	ADP
cana-1403	23	4	stochastic	stochastic	ADJ
cana-1403	23	5	difference	difference	NOUN
cana-1403	23	6	equations	equation	NOUN
cana-1403	23	7	or	or	CCONJ
cana-1403	23	8	communications	communication	NOUN
cana-1403	23	9	on	on	ADP
cana-1403	23	10	applied	apply	VERB
cana-1403	23	11	nonlinear	nonlinear	ADJ
cana-1403	23	12	analysis	analysis	NOUN
cana-1403	23	13	issn	issn	NOUN
cana-1403	23	14	:	:	PUNCT
cana-1403	23	15	1074	1074	NUM
cana-1403	23	16	-	-	PUNCT
cana-1403	23	17	133x	133x	NUM
cana-1403	23	18	vol	vol	NOUN
cana-1403	23	19	31	31	NUM
cana-1403	23	20	no	no	NOUN
cana-1403	23	21	.	.	PUNCT
cana-1403	24	1	7s	7	NOUN
cana-1403	24	2	(	(	PUNCT
cana-1403	24	3	2024	2024	NUM
cana-1403	24	4	)	)	PUNCT
cana-1403	24	5	632	632	NUM
cana-1403	24	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1403	24	7	stochastic	stochastic	ADJ
cana-1403	24	8	discrete	discrete	ADJ
cana-1403	24	9	dynamical	dynamical	ADJ
cana-1403	24	10	systems	system	NOUN
cana-1403	24	11	trace	trace	VERB
cana-1403	24	12	back	back	ADV
cana-1403	24	13	to	to	ADP
cana-1403	24	14	investigations	investigation	NOUN
cana-1403	24	15	into	into	ADP
cana-1403	24	16	phenomena	phenomenon	NOUN
cana-1403	24	17	characterized	characterize	VERB
cana-1403	24	18	by	by	ADP
cana-1403	24	19	random	random	ADJ
cana-1403	24	20	fluctuations	fluctuation	NOUN
cana-1403	24	21	,	,	PUNCT
cana-1403	24	22	such	such	ADJ
cana-1403	24	23	as	as	ADP
cana-1403	24	24	particle	particle	NOUN
cana-1403	24	25	motion	motion	NOUN
cana-1403	24	26	and	and	CCONJ
cana-1403	24	27	stock	stock	NOUN
cana-1403	24	28	market	market	NOUN
cana-1403	24	29	variability	variability	NOUN
cana-1403	24	30	.	.	PUNCT
cana-1403	25	1	nonlinear	nonlinear	ADJ
cana-1403	25	2	stochastic	stochastic	ADJ
cana-1403	25	3	difference	difference	NOUN
cana-1403	25	4	equations	equation	NOUN
cana-1403	25	5	represent	represent	VERB
cana-1403	25	6	a	a	DET
cana-1403	25	7	significant	significant	ADJ
cana-1403	25	8	category	category	NOUN
cana-1403	25	9	within	within	ADP
cana-1403	25	10	nonlinear	nonlinear	ADJ
cana-1403	25	11	difference	difference	NOUN
cana-1403	25	12	equations	equation	NOUN
cana-1403	25	13	.	.	PUNCT
cana-1403	26	1	unlike	unlike	ADP
cana-1403	26	2	their	their	PRON
cana-1403	26	3	linear	linear	PROPN
cana-1403	26	4	counterparts	counterpart	NOUN
cana-1403	26	5	,	,	PUNCT
cana-1403	26	6	these	these	DET
cana-1403	26	7	equations	equation	NOUN
cana-1403	26	8	are	be	AUX
cana-1403	26	9	inherently	inherently	ADV
cana-1403	26	10	complex	complex	ADJ
cana-1403	26	11	and	and	CCONJ
cana-1403	26	12	do	do	AUX
cana-1403	26	13	not	not	PART
cana-1403	26	14	lend	lend	VERB
cana-1403	26	15	themselves	themselves	PRON
cana-1403	26	16	easily	easily	ADV
cana-1403	26	17	to	to	PART
cana-1403	26	18	exact	exact	VERB
cana-1403	26	19	solutions	solution	NOUN
cana-1403	26	20	or	or	CCONJ
cana-1403	26	21	predictions	prediction	NOUN
cana-1403	26	22	,	,	PUNCT
cana-1403	26	23	occasionally	occasionally	ADV
cana-1403	26	24	exhibiting	exhibit	VERB
cana-1403	26	25	chaotic	chaotic	ADJ
cana-1403	26	26	behaviour	behaviour	NOUN
cana-1403	26	27	under	under	ADP
cana-1403	26	28	certain	certain	ADJ
cana-1403	26	29	conditions	condition	NOUN
cana-1403	26	30	.	.	PUNCT
cana-1403	27	1	recent	recent	ADJ
cana-1403	27	2	interest	interest	NOUN
cana-1403	27	3	in	in	ADP
cana-1403	27	4	these	these	DET
cana-1403	27	5	systems	system	NOUN
cana-1403	27	6	stems	stem	VERB
cana-1403	27	7	from	from	ADP
cana-1403	27	8	their	their	PRON
cana-1403	27	9	relevance	relevance	NOUN
cana-1403	27	10	in	in	ADP
cana-1403	27	11	mathematical	mathematical	ADJ
cana-1403	27	12	models	model	NOUN
cana-1403	27	13	describing	describe	VERB
cana-1403	27	14	realworld	realworld	NOUN
cana-1403	27	15	scenarios	scenario	NOUN
cana-1403	27	16	across	across	ADP
cana-1403	27	17	various	various	ADJ
cana-1403	27	18	fields	field	NOUN
cana-1403	27	19	such	such	ADJ
cana-1403	27	20	as	as	ADP
cana-1403	27	21	probability	probability	NOUN
cana-1403	27	22	theory	theory	NOUN
cana-1403	27	23	,	,	PUNCT
cana-1403	27	24	statistical	statistical	ADJ
cana-1403	27	25	problems	problem	NOUN
cana-1403	27	26	,	,	PUNCT
cana-1403	27	27	stochastic	stochastic	ADJ
cana-1403	27	28	time	time	NOUN
cana-1403	27	29	series	series	NOUN
cana-1403	27	30	,	,	PUNCT
cana-1403	27	31	combinatorial	combinatorial	ADJ
cana-1403	27	32	analysis	analysis	NOUN
cana-1403	27	33	,	,	PUNCT
cana-1403	27	34	number	number	NOUN
cana-1403	27	35	theory	theory	NOUN
cana-1403	27	36	,	,	PUNCT
cana-1403	27	37	geometry	geometry	NOUN
cana-1403	27	38	,	,	PUNCT
cana-1403	27	39	electrical	electrical	ADJ
cana-1403	27	40	networks	network	NOUN
cana-1403	27	41	,	,	PUNCT
cana-1403	27	42	radiation	radiation	NOUN
cana-1403	27	43	quanta	quanta	PROPN
cana-1403	27	44	,	,	PUNCT
cana-1403	27	45	genetics	genetic	NOUN
cana-1403	27	46	,	,	PUNCT
cana-1403	27	47	economics	economic	NOUN
cana-1403	27	48	,	,	PUNCT
cana-1403	27	49	psychology	psychology	NOUN
cana-1403	27	50	,	,	PUNCT
cana-1403	27	51	and	and	CCONJ
cana-1403	27	52	sociology	sociology	NOUN
cana-1403	27	53	.	.	PUNCT
cana-1403	28	1	such	such	ADJ
cana-1403	28	2	equations	equation	NOUN
cana-1403	28	3	also	also	ADV
cana-1403	28	4	arise	arise	VERB
cana-1403	28	5	as	as	ADP
cana-1403	28	6	discrete	discrete	ADJ
cana-1403	28	7	analogs	analog	NOUN
cana-1403	28	8	and	and	CCONJ
cana-1403	28	9	numerical	numerical	ADJ
cana-1403	28	10	solutions	solution	NOUN
cana-1403	28	11	of	of	ADP
cana-1403	28	12	stochastic	stochastic	ADJ
cana-1403	28	13	differential	differential	NOUN
cana-1403	28	14	and	and	CCONJ
cana-1403	28	15	delay	delay	VERB
cana-1403	28	16	differential	differential	ADJ
cana-1403	28	17	equations	equation	NOUN
cana-1403	28	18	,	,	PUNCT
cana-1403	28	19	modelling	model	VERB
cana-1403	28	20	a	a	DET
cana-1403	28	21	wide	wide	ADJ
cana-1403	28	22	array	array	NOUN
cana-1403	28	23	of	of	ADP
cana-1403	28	24	phenomena	phenomenon	NOUN
cana-1403	28	25	.	.	PUNCT
cana-1403	29	1	discrete	discrete	ADJ
cana-1403	29	2	time	time	NOUN
cana-1403	29	3	model	model	NOUN
cana-1403	29	4	is	be	AUX
cana-1403	29	5	the	the	DET
cana-1403	29	6	most	most	ADV
cana-1403	29	7	appropriate	appropriate	ADJ
cana-1403	29	8	mathematical	mathematical	ADJ
cana-1403	29	9	description	description	NOUN
cana-1403	29	10	of	of	ADP
cana-1403	29	11	life	life	NOUN
cana-1403	29	12	histories	history	NOUN
cana-1403	29	13	of	of	ADP
cana-1403	29	14	organism	organism	NOUN
cana-1403	29	15	whose	whose	DET
cana-1403	29	16	reproduction	reproduction	NOUN
cana-1403	29	17	occurs	occur	VERB
cana-1403	29	18	only	only	ADV
cana-1403	29	19	once	once	ADV
cana-1403	29	20	a	a	DET
cana-1403	29	21	year	year	NOUN
cana-1403	29	22	during	during	ADP
cana-1403	29	23	a	a	DET
cana-1403	29	24	very	very	ADV
cana-1403	29	25	short	short	ADJ
cana-1403	29	26	season	season	NOUN
cana-1403	29	27	.	.	PUNCT
cana-1403	30	1	these	these	DET
cana-1403	30	2	models	model	NOUN
cana-1403	30	3	are	be	AUX
cana-1403	30	4	widely	widely	ADV
cana-1403	30	5	used	use	VERB
cana-1403	30	6	in	in	ADP
cana-1403	30	7	fisheries	fishery	NOUN
cana-1403	30	8	and	and	CCONJ
cana-1403	30	9	many	many	ADJ
cana-1403	30	10	organisms	organism	NOUN
cana-1403	30	11	.	.	PUNCT
cana-1403	31	1	in	in	ADP
cana-1403	31	2	1965	1965	NUM
cana-1403	31	3	,	,	PUNCT
cana-1403	31	4	pielou‟s	pielou‟s	PART
cana-1403	31	5	equation	equation	NOUN
cana-1403	31	6	,	,	PUNCT
cana-1403	31	7	as	as	ADP
cana-1403	31	8	a	a	DET
cana-1403	31	9	discrete	discrete	ADJ
cana-1403	31	10	analogue	analogue	NOUN
cana-1403	31	11	of	of	ADP
cana-1403	31	12	the	the	DET
cana-1403	31	13	delay	delay	NOUN
cana-1403	31	14	logistic	logistic	ADJ
cana-1403	31	15	equation	equation	NOUN
cana-1403	31	16	,	,	PUNCT
cana-1403	31	17	was	be	AUX
cana-1403	31	18	proposed	propose	VERB
cana-1403	31	19	by	by	ADP
cana-1403	31	20	pielou	pielou	NOUN
cana-1403	31	21	[	[	X
cana-1403	31	22	8	8	NUM
cana-1403	31	23	,	,	PUNCT
cana-1403	31	24	9	9	NUM
cana-1403	31	25	]	]	PUNCT
cana-1403	31	26	.	.	PUNCT
cana-1403	32	1	(	(	PUNCT
cana-1403	32	2	)	)	PUNCT
cana-1403	32	3	where	where	SCONJ
cana-1403	32	4	a	a	PRON
cana-1403	32	5	is	be	AUX
cana-1403	32	6	a	a	DET
cana-1403	32	7	positive	positive	ADJ
cana-1403	32	8	real	real	ADJ
cana-1403	32	9	number	number	NOUN
cana-1403	32	10	.	.	PUNCT
cana-1403	33	1	in	in	ADP
cana-1403	33	2	order	order	NOUN
cana-1403	33	3	to	to	PART
cana-1403	33	4	find	find	VERB
cana-1403	33	5	equilibrium	equilibrium	NOUN
cana-1403	33	6	points	point	NOUN
cana-1403	33	7	(	(	PUNCT
cana-1403	33	8	fixed	fix	VERB
cana-1403	33	9	points	point	NOUN
cana-1403	33	10	)	)	PUNCT
cana-1403	33	11	of	of	ADP
cana-1403	33	12	the	the	DET
cana-1403	33	13	previous	previous	ADJ
cana-1403	33	14	equation	equation	NOUN
cana-1403	33	15	,	,	PUNCT
cana-1403	33	16	we	we	PRON
cana-1403	33	17	solve	solve	VERB
cana-1403	33	18	the	the	DET
cana-1403	33	19	following	follow	VERB
cana-1403	33	20	algebraic	algebraic	ADJ
cana-1403	33	21	equation	equation	NOUN
cana-1403	33	22	(	(	PUNCT
cana-1403	33	23	)	)	PUNCT
cana-1403	33	24	note	note	VERB
cana-1403	33	25	that	that	SCONJ
cana-1403	33	26	(	(	PUNCT
cana-1403	33	27	)	)	PUNCT
cana-1403	33	28	and	and	CCONJ
cana-1403	33	29	(	(	PUNCT
cana-1403	33	30	)	)	PUNCT
cana-1403	33	31	represent	represent	VERB
cana-1403	33	32	the	the	DET
cana-1403	33	33	solutions	solution	NOUN
cana-1403	33	34	of	of	ADP
cana-1403	33	35	equation	equation	NOUN
cana-1403	33	36	(	(	PUNCT
cana-1403	33	37	1.2	1.2	NUM
cana-1403	33	38	)	)	PUNCT
cana-1403	33	39	which	which	PRON
cana-1403	33	40	simultaneously	simultaneously	ADV
cana-1403	33	41	serve	serve	VERB
cana-1403	33	42	as	as	ADP
cana-1403	33	43	the	the	DET
cana-1403	33	44	equilibrium	equilibrium	NOUN
cana-1403	33	45	points	point	NOUN
cana-1403	33	46	of	of	ADP
cana-1403	33	47	the	the	DET
cana-1403	33	48	equation	equation	NOUN
cana-1403	33	49	(	(	PUNCT
cana-1403	33	50	1.1	1.1	NUM
cana-1403	33	51	)	)	PUNCT
cana-1403	33	52	.	.	PUNCT
cana-1403	34	1	in	in	ADP
cana-1403	34	2	the	the	DET
cana-1403	34	3	following	following	ADJ
cana-1403	34	4	section	section	NOUN
cana-1403	34	5	,	,	PUNCT
cana-1403	34	6	we	we	PRON
cana-1403	34	7	will	will	AUX
cana-1403	34	8	consider	consider	VERB
cana-1403	34	9	that	that	DET
cana-1403	34	10	equation	equation	NOUN
cana-1403	34	11	(	(	PUNCT
cana-1403	34	12	1.1	1.1	NUM
cana-1403	34	13	)	)	PUNCT
cana-1403	34	14	is	be	AUX
cana-1403	34	15	subject	subject	ADJ
cana-1403	34	16	to	to	ADP
cana-1403	34	17	stochastic	stochastic	ADJ
cana-1403	34	18	perturbations	perturbation	NOUN
cana-1403	34	19	that	that	PRON
cana-1403	34	20	are	be	AUX
cana-1403	34	21	directly	directly	ADV
cana-1403	34	22	proportional	proportional	ADJ
cana-1403	34	23	to	to	ADP
cana-1403	34	24	the	the	DET
cana-1403	34	25	deviation	deviation	NOUN
cana-1403	34	26	of	of	ADP
cana-1403	34	27	the	the	DET
cana-1403	34	28	system	system	NOUN
cana-1403	34	29	state	state	NOUN
cana-1403	34	30	from	from	ADP
cana-1403	34	31	the	the	DET
cana-1403	34	32	equilibrium	equilibrium	NOUN
cana-1403	34	33	point	point	NOUN
cana-1403	34	34	.	.	PUNCT
cana-1403	35	1	under	under	ADP
cana-1403	35	2	this	this	DET
cana-1403	35	3	assumption	assumption	NOUN
cana-1403	35	4	,	,	PUNCT
cana-1403	35	5	we	we	PRON
cana-1403	35	6	establish	establish	VERB
cana-1403	35	7	some	some	DET
cana-1403	35	8	sufficient	sufficient	ADJ
cana-1403	35	9	conditions	condition	NOUN
cana-1403	35	10	for	for	ADP
cana-1403	35	11	the	the	DET
cana-1403	35	12	stability	stability	NOUN
cana-1403	35	13	in	in	ADP
cana-1403	35	14	probability	probability	NOUN
cana-1403	35	15	of	of	ADP
cana-1403	35	16	the	the	DET
cana-1403	35	17	equilibrium	equilibrium	NOUN
cana-1403	35	18	points	point	NOUN
cana-1403	35	19	1.2	1.2	NUM
cana-1403	35	20	and	and	CCONJ
cana-1403	35	21	1.3	1.3	NUM
cana-1403	35	22	.	.	PUNCT
cana-1403	36	1	the	the	DET
cana-1403	36	2	results	result	NOUN
cana-1403	36	3	are	be	AUX
cana-1403	36	4	demonstrated	demonstrate	VERB
cana-1403	36	5	through	through	ADP
cana-1403	36	6	the	the	DET
cana-1403	36	7	trajectories	trajectory	NOUN
cana-1403	36	8	of	of	ADP
cana-1403	36	9	the	the	DET
cana-1403	36	10	analyzed	analyze	VERB
cana-1403	36	11	equations	equation	NOUN
cana-1403	36	12	.	.	PUNCT
cana-1403	37	1	the	the	DET
cana-1403	37	2	aim	aim	NOUN
cana-1403	37	3	of	of	ADP
cana-1403	37	4	this	this	DET
cana-1403	37	5	paper	paper	NOUN
cana-1403	37	6	is	be	AUX
cana-1403	37	7	to	to	PART
cana-1403	37	8	examine	examine	VERB
cana-1403	37	9	the	the	DET
cana-1403	37	10	stability	stability	NOUN
cana-1403	37	11	in	in	ADP
cana-1403	37	12	probability	probability	NOUN
cana-1403	37	13	of	of	ADP
cana-1403	37	14	the	the	DET
cana-1403	37	15	equilibrium	equilibrium	NOUN
cana-1403	37	16	state	state	NOUN
cana-1403	37	17	of	of	ADP
cana-1403	37	18	pielou„s	pielou„s	NOUN
cana-1403	37	19	equation	equation	NOUN
cana-1403	37	20	type	type	NOUN
cana-1403	37	21	(	(	PUNCT
cana-1403	37	22	1.1	1.1	NUM
cana-1403	37	23	)	)	PUNCT
cana-1403	37	24	affected	affect	VERB
cana-1403	37	25	by	by	ADP
cana-1403	37	26	stochastic	stochastic	ADJ
cana-1403	37	27	perturbations	perturbation	NOUN
cana-1403	37	28	.	.	PUNCT
cana-1403	38	1	2	2	X
cana-1403	38	2	.	.	X
cana-1403	38	3	stochastic	stochastic	ADJ
cana-1403	38	4	perturbations	perturbation	NOUN
cana-1403	38	5	let	let	VERB
cana-1403	38	6	(	(	PUNCT
cana-1403	38	7	)	)	PUNCT
cana-1403	38	8	be	be	AUX
cana-1403	38	9	a	a	DET
cana-1403	38	10	probability	probability	NOUN
cana-1403	38	11	space	space	NOUN
cana-1403	38	12	and	and	CCONJ
cana-1403	38	13	let	let	VERB
cana-1403	38	14	be	be	AUX
cana-1403	38	15	a	a	DET
cana-1403	38	16	family	family	NOUN
cana-1403	38	17	of	of	ADP
cana-1403	38	18	sigma	sigma	PROPN
cana-1403	38	19	-	-	PUNCT
cana-1403	38	20	fields	field	NOUN
cana-1403	38	21	of	of	ADP
cana-1403	38	22	indexed	index	VERB
cana-1403	38	23	by	by	ADP
cana-1403	38	24	*	*	PUNCT
cana-1403	39	1	+	+	CCONJ
cana-1403	39	2	be	be	AUX
cana-1403	39	3	the	the	DET
cana-1403	39	4	mathematical	mathematical	ADJ
cana-1403	39	5	expectation	expectation	NOUN
cana-1403	39	6	,	,	PUNCT
cana-1403	39	7	,	,	PUNCT
cana-1403	39	8	be	be	AUX
cana-1403	39	9	a	a	DET
cana-1403	39	10	sequence	sequence	NOUN
cana-1403	39	11	of	of	ADP
cana-1403	39	12	-adapted	-adapted	ADJ
cana-1403	39	13	random	random	ADJ
cana-1403	39	14	variables	variable	NOUN
cana-1403	39	15	such	such	ADJ
cana-1403	39	16	that	that	PRON
cana-1403	39	17	(	(	PUNCT
cana-1403	39	18	)	)	PUNCT
cana-1403	39	19	,	,	PUNCT
cana-1403	39	20	(	(	PUNCT
cana-1403	39	21	)	)	PUNCT
cana-1403	39	22	.	.	PUNCT
cana-1403	40	1	let	let	VERB
cana-1403	40	2	a	a	DET
cana-1403	40	3	process	process	NOUN
cana-1403	40	4	be	be	AUX
cana-1403	40	5	a	a	DET
cana-1403	40	6	solution	solution	NOUN
cana-1403	40	7	of	of	ADP
cana-1403	40	8	the	the	DET
cana-1403	40	9	equation	equation	NOUN
cana-1403	40	10	communications	communication	NOUN
cana-1403	40	11	on	on	ADP
cana-1403	40	12	applied	apply	VERB
cana-1403	40	13	nonlinear	nonlinear	ADJ
cana-1403	40	14	analysis	analysis	NOUN
cana-1403	40	15	issn	issn	NOUN
cana-1403	40	16	:	:	PUNCT
cana-1403	40	17	1074	1074	NUM
cana-1403	40	18	-	-	PUNCT
cana-1403	40	19	133x	133x	NUM
cana-1403	40	20	vol	vol	NOUN
cana-1403	40	21	31	31	NUM
cana-1403	40	22	no	no	NOUN
cana-1403	40	23	.	.	PUNCT
cana-1403	41	1	7s	7	NOUN
cana-1403	41	2	(	(	PUNCT
cana-1403	41	3	2024	2024	NUM
cana-1403	41	4	)	)	PUNCT
cana-1403	41	5	633	633	NUM
cana-1403	41	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1403	41	7	(	(	PUNCT
cana-1403	41	8	)	)	PUNCT
cana-1403	41	9	(	(	PUNCT
cana-1403	41	10	)	)	PUNCT
cana-1403	41	11	with	with	ADP
cana-1403	41	12	an	an	DET
cana-1403	41	13	-adapted	-adapted	ADJ
cana-1403	41	14	initial	initial	ADJ
cana-1403	41	15	condition	condition	NOUN
cana-1403	41	16	*	*	PUNCT
cana-1403	42	1	+	+	PUNCT
cana-1403	42	2	(	(	PUNCT
cana-1403	42	3	)	)	PUNCT
cana-1403	42	4	here	here	ADV
cana-1403	42	5	is	be	AUX
cana-1403	42	6	an	an	DET
cana-1403	42	7	equilibrium	equilibrium	NOUN
cana-1403	42	8	point	point	NOUN
cana-1403	42	9	(	(	PUNCT
cana-1403	42	10	)	)	PUNCT
cana-1403	42	11	or	or	CCONJ
cana-1403	42	12	(	(	PUNCT
cana-1403	42	13	)	)	PUNCT
cana-1403	42	14	of	of	ADP
cana-1403	42	15	the	the	DET
cana-1403	42	16	equation	equation	NOUN
cana-1403	42	17	(	(	PUNCT
cana-1403	42	18	)	)	PUNCT
cana-1403	42	19	and	and	CCONJ
cana-1403	42	20	is	be	AUX
cana-1403	42	21	an	an	DET
cana-1403	42	22	arbitrary	arbitrary	ADJ
cana-1403	42	23	constant	constant	ADJ
cana-1403	42	24	.	.	PUNCT
cana-1403	43	1	it	it	PRON
cana-1403	43	2	should	should	AUX
cana-1403	43	3	be	be	AUX
cana-1403	43	4	noted	note	VERB
cana-1403	43	5	that	that	SCONJ
cana-1403	43	6	the	the	DET
cana-1403	43	7	equilibrium	equilibrium	NOUN
cana-1403	43	8	point	point	NOUN
cana-1403	43	9	is	be	AUX
cana-1403	43	10	also	also	ADV
cana-1403	43	11	a	a	DET
cana-1403	43	12	solution	solution	NOUN
cana-1403	43	13	of	of	ADP
cana-1403	43	14	equation	equation	NOUN
cana-1403	43	15	(	(	PUNCT
cana-1403	43	16	2.1	2.1	NUM
cana-1403	43	17	)	)	PUNCT
cana-1403	43	18	.	.	PUNCT
cana-1403	44	1	putting	put	VERB
cana-1403	44	2	in	in	ADP
cana-1403	44	3	the	the	DET
cana-1403	44	4	equation	equation	NOUN
cana-1403	44	5	,	,	PUNCT
cana-1403	44	6	(	(	PUNCT
cana-1403	44	7	)	)	PUNCT
cana-1403	44	8	we	we	PRON
cana-1403	44	9	obtain	obtain	VERB
cana-1403	44	10	(	(	PUNCT
cana-1403	44	11	)	)	PUNCT
cana-1403	44	12	(	(	PUNCT
cana-1403	44	13	)	)	PUNCT
cana-1403	44	14	(	(	PUNCT
cana-1403	44	15	)	)	PUNCT
cana-1403	44	16	which	which	PRON
cana-1403	44	17	gives	give	VERB
cana-1403	44	18	the	the	DET
cana-1403	44	19	equation	equation	NOUN
cana-1403	44	20	(	(	PUNCT
cana-1403	44	21	)	)	PUNCT
cana-1403	44	22	.	.	PUNCT
cana-1403	45	1	(	(	PUNCT
cana-1403	45	2	2.3	2.3	NUM
cana-1403	45	3	)	)	PUNCT
cana-1403	45	4	it	it	PRON
cana-1403	45	5	is	be	AUX
cana-1403	45	6	evident	evident	ADJ
cana-1403	45	7	that	that	SCONJ
cana-1403	45	8	the	the	DET
cana-1403	45	9	stability	stability	NOUN
cana-1403	45	10	of	of	ADP
cana-1403	45	11	the	the	DET
cana-1403	45	12	zero	zero	NUM
cana-1403	45	13	solution	solution	NOUN
cana-1403	45	14	of	of	ADP
cana-1403	45	15	equation	equation	NOUN
cana-1403	45	16	(	(	PUNCT
cana-1403	45	17	2.3	2.3	NUM
cana-1403	45	18	)	)	PUNCT
cana-1403	45	19	corresponds	correspond	VERB
cana-1403	45	20	to	to	ADP
cana-1403	45	21	the	the	DET
cana-1403	45	22	stability	stability	NOUN
cana-1403	45	23	of	of	ADP
cana-1403	45	24	the	the	DET
cana-1403	45	25	solution	solution	NOUN
cana-1403	45	26	of	of	ADP
cana-1403	45	27	equation	equation	NOUN
cana-1403	45	28	(	(	PUNCT
cana-1403	45	29	2.1	2.1	NUM
cana-1403	45	30	)	)	PUNCT
cana-1403	45	31	.	.	PUNCT
cana-1403	46	1	note	note	VERB
cana-1403	46	2	that	that	SCONJ
cana-1403	46	3	the	the	DET
cana-1403	46	4	equation	equation	NOUN
cana-1403	46	5	(	(	PUNCT
cana-1403	46	6	)	)	PUNCT
cana-1403	46	7	is	be	AUX
cana-1403	46	8	a	a	DET
cana-1403	46	9	nonlinear	nonlinear	ADJ
cana-1403	46	10	equation	equation	NOUN
cana-1403	46	11	with	with	ADP
cana-1403	46	12	an	an	DET
cana-1403	46	13	order	order	NOUN
cana-1403	46	14	of	of	ADP
cana-1403	46	15	nonlinearity	nonlinearity	NOUN
cana-1403	46	16	higher	high	ADJ
cana-1403	46	17	than	than	ADP
cana-1403	46	18	one	one	NUM
cana-1403	46	19	.	.	PUNCT
cana-1403	47	1	from	from	ADP
cana-1403	47	2	,	,	PUNCT
cana-1403	47	3	-	-	PUNCT
cana-1403	47	4	,	,	PUNCT
cana-1403	47	5	it	it	PRON
cana-1403	47	6	is	be	AUX
cana-1403	47	7	defined	define	VERB
cana-1403	47	8	that	that	SCONJ
cana-1403	47	9	,	,	PUNCT
cana-1403	47	10	in	in	ADP
cana-1403	47	11	this	this	DET
cana-1403	47	12	regard	regard	NOUN
cana-1403	47	13	,	,	PUNCT
cana-1403	47	14	if	if	SCONJ
cana-1403	47	15	the	the	DET
cana-1403	47	16	zero	zero	NUM
cana-1403	47	17	solution	solution	NOUN
cana-1403	47	18	of	of	ADP
cana-1403	47	19	the	the	DET
cana-1403	47	20	linear	linear	ADJ
cana-1403	47	21	approximation	approximation	NOUN
cana-1403	47	22	of	of	ADP
cana-1403	47	23	(	(	PUNCT
cana-1403	47	24	)	)	PUNCT
cana-1403	47	25	is	be	AUX
cana-1403	47	26	asymptotically	asymptotically	ADV
cana-1403	47	27	mean	mean	ADJ
cana-1403	47	28	square	square	ADJ
cana-1403	47	29	stable	stable	ADJ
cana-1403	47	30	,	,	PUNCT
cana-1403	47	31	then	then	ADV
cana-1403	47	32	this	this	DET
cana-1403	47	33	condition	condition	NOUN
cana-1403	47	34	is	be	AUX
cana-1403	47	35	sufficient	sufficient	ADJ
cana-1403	47	36	for	for	ADP
cana-1403	47	37	the	the	DET
cana-1403	47	38	stability	stability	NOUN
cana-1403	47	39	in	in	ADP
cana-1403	47	40	probability	probability	NOUN
cana-1403	47	41	of	of	ADP
cana-1403	47	42	the	the	DET
cana-1403	47	43	zero	zero	NUM
cana-1403	47	44	solution	solution	NOUN
cana-1403	47	45	of	of	ADP
cana-1403	47	46	the	the	DET
cana-1403	47	47	nonlinear	nonlinear	ADJ
cana-1403	47	48	equation	equation	NOUN
cana-1403	47	49	(	(	PUNCT
cana-1403	47	50	)	)	PUNCT
cana-1403	47	51	.	.	PUNCT
cana-1403	48	1	lemma	lemma	PROPN
cana-1403	48	2	1	1	NUM
cana-1403	48	3	:	:	PUNCT
cana-1403	48	4	the	the	DET
cana-1403	48	5	linear	linear	ADJ
cana-1403	48	6	approximation	approximation	NOUN
cana-1403	48	7	of	of	ADP
cana-1403	48	8	(	(	PUNCT
cana-1403	48	9	)	)	PUNCT
cana-1403	48	10	has	have	VERB
cana-1403	48	11	the	the	DET
cana-1403	48	12	form	form	NOUN
cana-1403	48	13	(	(	PUNCT
cana-1403	48	14	)	)	PUNCT
cana-1403	48	15	(	(	PUNCT
cana-1403	48	16	)	)	PUNCT
cana-1403	48	17	(	(	PUNCT
cana-1403	48	18	)	)	PUNCT
cana-1403	48	19	proof	proof	NOUN
cana-1403	48	20	:	:	PUNCT
cana-1403	48	21	using	use	VERB
cana-1403	48	22	the	the	DET
cana-1403	48	23	equality	equality	NOUN
cana-1403	48	24	(	(	PUNCT
cana-1403	48	25	)	)	PUNCT
cana-1403	48	26	,	,	PUNCT
cana-1403	48	27	where	where	SCONJ
cana-1403	48	28	p	p	PRON
cana-1403	48	29	≠	≠	PROPN
cana-1403	48	30	0	0	PUNCT
cana-1403	48	31	and	and	CCONJ
cana-1403	48	32	(	(	PUNCT
cana-1403	48	33	)	)	PUNCT
cana-1403	48	34	we	we	PRON
cana-1403	48	35	have	have	VERB
cana-1403	48	36	(	(	PUNCT
cana-1403	48	37	)	)	PUNCT
cana-1403	48	38	(	(	PUNCT
cana-1403	48	39	)	)	PUNCT
cana-1403	48	40	(	(	PUNCT
cana-1403	48	41	)	)	PUNCT
cana-1403	48	42	substituting	substitute	VERB
cana-1403	48	43	(	(	PUNCT
cana-1403	48	44	2.5	2.5	NUM
cana-1403	48	45	)	)	PUNCT
cana-1403	48	46	in	in	ADP
cana-1403	48	47	(	(	PUNCT
cana-1403	48	48	2.3	2.3	NUM
cana-1403	48	49	)	)	PUNCT
cana-1403	48	50	,	,	PUNCT
cana-1403	48	51	we	we	PRON
cana-1403	48	52	get	get	VERB
cana-1403	48	53	(	(	PUNCT
cana-1403	48	54	2.4	2.4	NUM
cana-1403	48	55	)	)	PUNCT
cana-1403	48	56	now	now	ADV
cana-1403	48	57	putting	put	VERB
cana-1403	48	58	in	in	ADP
cana-1403	48	59	(	(	PUNCT
cana-1403	48	60	)	)	PUNCT
cana-1403	48	61	and	and	CCONJ
cana-1403	48	62	(	(	PUNCT
cana-1403	48	63	)	)	PUNCT
cana-1403	48	64	give	give	VERB
cana-1403	48	65	us	we	PRON
cana-1403	48	66	the	the	DET
cana-1403	48	67	following	follow	VERB
cana-1403	48	68	equations	equation	NOUN
cana-1403	48	69	(	(	PUNCT
cana-1403	48	70	)	)	PUNCT
cana-1403	48	71	(	(	PUNCT
cana-1403	48	72	)	)	PUNCT
cana-1403	48	73	communications	communication	NOUN
cana-1403	48	74	on	on	ADP
cana-1403	48	75	applied	apply	VERB
cana-1403	48	76	nonlinear	nonlinear	ADJ
cana-1403	48	77	analysis	analysis	NOUN
cana-1403	48	78	issn	issn	NOUN
cana-1403	48	79	:	:	PUNCT
cana-1403	48	80	1074	1074	NUM
cana-1403	48	81	-	-	PUNCT
cana-1403	48	82	133x	133x	NUM
cana-1403	48	83	vol	vol	NOUN
cana-1403	48	84	31	31	NUM
cana-1403	48	85	no	no	NOUN
cana-1403	48	86	.	.	PUNCT
cana-1403	49	1	7s	7	NOUN
cana-1403	49	2	(	(	PUNCT
cana-1403	49	3	2024	2024	NUM
cana-1403	49	4	)	)	PUNCT
cana-1403	49	5	634	634	NUM
cana-1403	49	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1403	49	7	and	and	CCONJ
cana-1403	49	8	(	(	PUNCT
cana-1403	49	9	)	)	PUNCT
cana-1403	49	10	.	.	PUNCT
cana-1403	50	1	(	(	PUNCT
cana-1403	50	2	2.7	2.7	NUM
cana-1403	50	3	)	)	PUNCT
cana-1403	50	4	in	in	ADP
cana-1403	50	5	a	a	DET
cana-1403	50	6	similar	similar	ADJ
cana-1403	50	7	way	way	NOUN
cana-1403	50	8	for	for	ADP
cana-1403	50	9	the	the	DET
cana-1403	50	10	equilibrium	equilibrium	NOUN
cana-1403	50	11	point	point	NOUN
cana-1403	50	12	(	(	PUNCT
cana-1403	50	13	)	)	PUNCT
cana-1403	50	14	,	,	PUNCT
cana-1403	50	15	we	we	PRON
cana-1403	50	16	can	can	AUX
cana-1403	50	17	obtain	obtain	VERB
cana-1403	50	18	[	[	PUNCT
cana-1403	50	19	]	]	X
cana-1403	50	20	(	(	PUNCT
cana-1403	50	21	)	)	PUNCT
cana-1403	50	22	(	(	PUNCT
cana-1403	50	23	)	)	PUNCT
cana-1403	50	24	and	and	CCONJ
cana-1403	50	25	.	.	PUNCT
cana-1403	50	26	/	/	PUNCT
cana-1403	51	1	(	(	PUNCT
cana-1403	51	2	)	)	PUNCT
cana-1403	51	3	.	.	PUNCT
cana-1403	52	1	(	(	PUNCT
cana-1403	52	2	2.9	2.9	NUM
cana-1403	52	3	)	)	PUNCT
cana-1403	52	4	next	next	ADV
cana-1403	52	5	,	,	PUNCT
cana-1403	52	6	we	we	PRON
cana-1403	52	7	present	present	VERB
cana-1403	52	8	the	the	DET
cana-1403	52	9	essential	essential	ADJ
cana-1403	52	10	definitions	definition	NOUN
cana-1403	52	11	and	and	CCONJ
cana-1403	52	12	lemmas	lemma	NOUN
cana-1403	52	13	necessary	necessary	ADJ
cana-1403	52	14	for	for	ADP
cana-1403	52	15	deriving	derive	VERB
cana-1403	52	16	our	our	PRON
cana-1403	52	17	main	main	ADJ
cana-1403	52	18	results	result	NOUN
cana-1403	52	19	.	.	PUNCT
cana-1403	53	1	definition	definition	NOUN
cana-1403	53	2	2.1	2.1	NUM
cana-1403	53	3	:	:	PUNCT
cana-1403	53	4	the	the	DET
cana-1403	53	5	zero	zero	NUM
cana-1403	53	6	solution	solution	NOUN
cana-1403	53	7	of	of	ADP
cana-1403	53	8	(	(	PUNCT
cana-1403	53	9	)	)	PUNCT
cana-1403	53	10	,	,	PUNCT
cana-1403	53	11	(	(	PUNCT
cana-1403	53	12	)	)	PUNCT
cana-1403	53	13	is	be	AUX
cana-1403	53	14	called	call	VERB
cana-1403	53	15	stable	stable	ADJ
cana-1403	53	16	in	in	ADP
cana-1403	53	17	probability	probability	NOUN
cana-1403	53	18	if	if	SCONJ
cana-1403	53	19	for	for	ADP
cana-1403	53	20	any	any	PRON
cana-1403	53	21	,	,	PUNCT
cana-1403	53	22	there	there	PRON
cana-1403	53	23	exists	exist	VERB
cana-1403	53	24	a	a	DET
cana-1403	53	25	such	such	ADJ
cana-1403	53	26	that	that	SCONJ
cana-1403	53	27	{	{	PUNCT
cana-1403	53	28	|	|	ADV
cana-1403	53	29	|	|	ADV
cana-1403	53	30	}	}	PUNCT
cana-1403	53	31	for	for	ADP
cana-1403	53	32	any	any	DET
cana-1403	53	33	initial	initial	ADJ
cana-1403	53	34	function	function	NOUN
cana-1403	53	35	which	which	PRON
cana-1403	53	36	is	be	AUX
cana-1403	53	37	less	less	ADJ
cana-1403	53	38	than	than	ADP
cana-1403	53	39	with	with	ADP
cana-1403	53	40	probability	probability	NOUN
cana-1403	53	41	1	1	NUM
cana-1403	53	42	,	,	PUNCT
cana-1403	53	43	i.e.	i.e.	X
cana-1403	53	44	,	,	PUNCT
cana-1403	53	45	{	{	PUNCT
cana-1403	53	46	|	|	ADV
cana-1403	53	47	|	|	ADV
cana-1403	53	48	}	}	PUNCT
cana-1403	53	49	definition	definition	NOUN
cana-1403	53	50	2.2	2.2	NUM
cana-1403	53	51	:	:	PUNCT
cana-1403	53	52	the	the	DET
cana-1403	53	53	zero	zero	NUM
cana-1403	53	54	solution	solution	NOUN
cana-1403	53	55	of	of	ADP
cana-1403	53	56	(	(	PUNCT
cana-1403	53	57	)	)	PUNCT
cana-1403	53	58	,	,	PUNCT
cana-1403	53	59	(	(	PUNCT
cana-1403	53	60	)	)	PUNCT
cana-1403	53	61	is	be	AUX
cana-1403	53	62	called	call	VERB
cana-1403	53	63	mean	mean	ADJ
cana-1403	53	64	square	square	ADJ
cana-1403	53	65	stable	stable	ADJ
cana-1403	53	66	if	if	SCONJ
cana-1403	53	67	for	for	ADP
cana-1403	53	68	any	any	PRON
cana-1403	53	69	there	there	PRON
cana-1403	53	70	exists	exist	VERB
cana-1403	53	71	a	a	DET
cana-1403	53	72	such	such	ADJ
cana-1403	53	73	that	that	PRON
cana-1403	54	1	|	|	ADV
cana-1403	54	2	|	|	ADV
cana-1403	54	3	,	,	PUNCT
cana-1403	54	4	,	,	PUNCT
cana-1403	54	5	for	for	ADP
cana-1403	54	6	any	any	DET
cana-1403	54	7	initial	initial	ADJ
cana-1403	54	8	function	function	NOUN
cana-1403	54	9	such	such	ADJ
cana-1403	54	10	that	that	SCONJ
cana-1403	54	11	|	|	ADV
cana-1403	54	12	|	|	ADV
cana-1403	54	13	the	the	DET
cana-1403	54	14	zero	zero	NUM
cana-1403	54	15	solution	solution	NOUN
cana-1403	54	16	of	of	ADP
cana-1403	54	17	(	(	PUNCT
cana-1403	54	18	)	)	PUNCT
cana-1403	54	19	,	,	PUNCT
cana-1403	54	20	(	(	PUNCT
cana-1403	54	21	)	)	PUNCT
cana-1403	54	22	is	be	AUX
cana-1403	54	23	called	call	VERB
cana-1403	54	24	asymptotically	asymptotically	ADV
cana-1403	54	25	mean	mean	VERB
cana-1403	54	26	square	square	ADJ
cana-1403	54	27	stable	stable	ADJ
cana-1403	54	28	if	if	SCONJ
cana-1403	54	29	it	it	PRON
cana-1403	54	30	is	be	AUX
cana-1403	54	31	mean	mean	ADJ
cana-1403	54	32	square	square	ADJ
cana-1403	54	33	stable	stable	ADJ
cana-1403	54	34	and	and	CCONJ
cana-1403	54	35	for	for	ADP
cana-1403	54	36	each	each	DET
cana-1403	54	37	initial	initial	ADJ
cana-1403	54	38	function	function	NOUN
cana-1403	54	39	such	such	ADJ
cana-1403	54	40	that	that	SCONJ
cana-1403	54	41	|	|	ADV
cana-1403	54	42	|	|	ADV
cana-1403	54	43	the	the	DET
cana-1403	54	44	solution	solution	NOUN
cana-1403	54	45	of	of	ADP
cana-1403	54	46	(	(	PUNCT
cana-1403	54	47	)	)	PUNCT
cana-1403	54	48	,	,	PUNCT
cana-1403	54	49	(	(	PUNCT
cana-1403	54	50	)	)	PUNCT
cana-1403	54	51	satisfies	satisfy	VERB
cana-1403	54	52	the	the	DET
cana-1403	54	53	condition	condition	NOUN
cana-1403	55	1	|	|	ADV
cana-1403	55	2	|	|	ADV
cana-1403	56	1	3	3	X
cana-1403	56	2	.	.	PUNCT
cana-1403	56	3	stability	stability	NOUN
cana-1403	56	4	of	of	ADP
cana-1403	56	5	equilibruim	equilibruim	ADJ
cana-1403	56	6	points	point	NOUN
cana-1403	56	7	by	by	ADP
cana-1403	56	8	applying	apply	VERB
cana-1403	56	9	equation	equation	NOUN
cana-1403	56	10	(	(	PUNCT
cana-1403	56	11	2.6	2.6	NUM
cana-1403	56	12	)	)	PUNCT
cana-1403	56	13	and	and	CCONJ
cana-1403	56	14	the	the	DET
cana-1403	56	15	inequalities	inequality	NOUN
cana-1403	56	16	derived	derive	VERB
cana-1403	56	17	from	from	ADP
cana-1403	56	18	[	[	X
cana-1403	56	19	22	22	NUM
cana-1403	56	20	]	]	PUNCT
cana-1403	56	21	,	,	PUNCT
cana-1403	56	22	we	we	PRON
cana-1403	56	23	obtain	obtain	VERB
cana-1403	56	24	|	|	ADV
cana-1403	56	25	|	|	ADV
cana-1403	56	26	the	the	DET
cana-1403	56	27	necessary	necessary	ADJ
cana-1403	56	28	and	and	CCONJ
cana-1403	56	29	sufficient	sufficient	ADJ
cana-1403	56	30	conditions	condition	NOUN
cana-1403	56	31	for	for	ADP
cana-1403	56	32	the	the	DET
cana-1403	56	33	asymptotic	asymptotic	ADJ
cana-1403	56	34	mean	mean	ADJ
cana-1403	56	35	square	square	ADJ
cana-1403	56	36	stability	stability	NOUN
cana-1403	56	37	of	of	ADP
cana-1403	56	38	the	the	DET
cana-1403	56	39	zero	zero	NUM
cana-1403	56	40	solution	solution	NOUN
cana-1403	56	41	(	(	PUNCT
cana-1403	56	42	1.4	1.4	NUM
cana-1403	56	43	)	)	PUNCT
cana-1403	56	44	of	of	ADP
cana-1403	56	45	equation	equation	NOUN
cana-1403	56	46	(	(	PUNCT
cana-1403	56	47	2.7	2.7	NUM
cana-1403	56	48	)	)	PUNCT
cana-1403	56	49	.	.	PUNCT
cana-1403	57	1	these	these	DET
cana-1403	57	2	conditions	condition	NOUN
cana-1403	57	3	are	be	AUX
cana-1403	57	4	also	also	ADV
cana-1403	57	5	sufficient	sufficient	ADJ
cana-1403	57	6	for	for	ADP
cana-1403	57	7	the	the	DET
cana-1403	57	8	stability	stability	NOUN
cana-1403	57	9	in	in	ADP
cana-1403	57	10	probability	probability	NOUN
cana-1403	57	11	of	of	ADP
cana-1403	57	12	the	the	DET
cana-1403	57	13	zero	zero	NUM
cana-1403	57	14	solution	solution	NOUN
cana-1403	57	15	of	of	ADP
cana-1403	57	16	equation	equation	NOUN
cana-1403	57	17	(	(	PUNCT
cana-1403	57	18	2.6	2.6	NUM
cana-1403	57	19	)	)	PUNCT
cana-1403	57	20	,	,	PUNCT
cana-1403	57	21	and	and	CCONJ
cana-1403	57	22	consequently	consequently	ADV
cana-1403	57	23	,	,	PUNCT
cana-1403	57	24	for	for	ADP
cana-1403	57	25	the	the	DET
cana-1403	57	26	stability	stability	NOUN
cana-1403	57	27	in	in	ADP
cana-1403	57	28	probability	probability	NOUN
cana-1403	57	29	of	of	ADP
cana-1403	57	30	the	the	DET
cana-1403	57	31	zero	zero	NUM
cana-1403	57	32	equilibrium	equilibrium	NOUN
cana-1403	57	33	point	point	NOUN
cana-1403	57	34	of	of	ADP
cana-1403	57	35	equation	equation	NOUN
cana-1403	57	36	(	(	PUNCT
cana-1403	57	37	2.1	2.1	NUM
cana-1403	57	38	)	)	PUNCT
cana-1403	57	39	.	.	PUNCT
cana-1403	58	1	communications	communication	NOUN
cana-1403	58	2	on	on	ADP
cana-1403	58	3	applied	apply	VERB
cana-1403	58	4	nonlinear	nonlinear	ADJ
cana-1403	58	5	analysis	analysis	NOUN
cana-1403	58	6	issn	issn	NOUN
cana-1403	58	7	:	:	PUNCT
cana-1403	58	8	1074	1074	NUM
cana-1403	58	9	-	-	PUNCT
cana-1403	58	10	133x	133x	NUM
cana-1403	58	11	vol	vol	NOUN
cana-1403	58	12	31	31	NUM
cana-1403	58	13	no	no	NOUN
cana-1403	58	14	.	.	PUNCT
cana-1403	59	1	7s	7	NOUN
cana-1403	59	2	(	(	PUNCT
cana-1403	59	3	2024	2024	NUM
cana-1403	59	4	)	)	PUNCT
cana-1403	59	5	635	635	NUM
cana-1403	59	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1403	59	7	similarly	similarly	ADV
cana-1403	59	8	,	,	PUNCT
cana-1403	59	9	we	we	PRON
cana-1403	59	10	derive	derive	VERB
cana-1403	59	11	the	the	DET
cana-1403	59	12	necessary	necessary	ADJ
cana-1403	59	13	and	and	CCONJ
cana-1403	59	14	sufficient	sufficient	ADJ
cana-1403	59	15	conditions	condition	NOUN
cana-1403	59	16	for	for	ADP
cana-1403	59	17	the	the	DET
cana-1403	59	18	asymptotic	asymptotic	ADJ
cana-1403	59	19	mean	mean	ADJ
cana-1403	59	20	square	square	ADJ
cana-1403	59	21	stability	stability	NOUN
cana-1403	59	22	of	of	ADP
cana-1403	59	23	the	the	DET
cana-1403	59	24	zero	zero	NUM
cana-1403	59	25	solution	solution	NOUN
cana-1403	59	26	of	of	ADP
cana-1403	59	27	equation	equation	NOUN
cana-1403	59	28	(	(	PUNCT
cana-1403	59	29	2.9	2.9	NUM
cana-1403	59	30	)	)	PUNCT
cana-1403	59	31	.	.	PUNCT
cana-1403	60	1	these	these	DET
cana-1403	60	2	conditions	condition	NOUN
cana-1403	60	3	also	also	ADV
cana-1403	60	4	serve	serve	VERB
cana-1403	60	5	as	as	ADP
cana-1403	60	6	sufficient	sufficient	ADJ
cana-1403	60	7	conditions	condition	NOUN
cana-1403	60	8	for	for	ADP
cana-1403	60	9	the	the	DET
cana-1403	60	10	stability	stability	NOUN
cana-1403	60	11	in	in	ADP
cana-1403	60	12	probability	probability	NOUN
cana-1403	60	13	of	of	ADP
cana-1403	60	14	the	the	DET
cana-1403	60	15	zero	zero	NUM
cana-1403	60	16	solution	solution	NOUN
cana-1403	60	17	of	of	ADP
cana-1403	60	18	equation	equation	NOUN
cana-1403	60	19	(	(	PUNCT
cana-1403	60	20	2.8	2.8	NUM
cana-1403	60	21	)	)	PUNCT
cana-1403	60	22	,	,	PUNCT
cana-1403	60	23	and	and	CCONJ
cana-1403	60	24	consequently	consequently	ADV
cana-1403	60	25	,	,	PUNCT
cana-1403	60	26	for	for	ADP
cana-1403	60	27	the	the	DET
cana-1403	60	28	equilibrium	equilibrium	NOUN
cana-1403	60	29	point	point	NOUN
cana-1403	60	30	(	(	PUNCT
cana-1403	60	31	1.5	1.5	NUM
cana-1403	60	32	)	)	PUNCT
cana-1403	60	33	of	of	ADP
cana-1403	60	34	equation	equation	NOUN
cana-1403	60	35	(	(	PUNCT
cana-1403	60	36	2.1	2.1	NUM
cana-1403	60	37	)	)	PUNCT
cana-1403	60	38	.	.	PUNCT
cana-1403	61	1	|	|	ADV
cana-1403	61	2	|	|	ADV
cana-1403	61	3	0	0	NUM
cana-1403	61	4	.	.	PUNCT
cana-1403	61	5	/1	/1	PROPN
cana-1403	62	1	[	[	X
cana-1403	62	2	(	(	PUNCT
cana-1403	62	3	.	.	PUNCT
cana-1403	62	4	/	/	PUNCT
cana-1403	62	5	)	)	PUNCT
cana-1403	62	6	]	]	PUNCT
cana-1403	62	7	.	.	PUNCT
cana-1403	63	1	note	note	VERB
cana-1403	63	2	that	that	SCONJ
cana-1403	63	3	the	the	DET
cana-1403	63	4	stability	stability	NOUN
cana-1403	63	5	conditions	condition	NOUN
cana-1403	63	6	are	be	AUX
cana-1403	63	7	independent	independent	ADJ
cana-1403	63	8	of	of	ADP
cana-1403	63	9	the	the	DET
cana-1403	63	10	parameter	parameter	PROPN
cana-1403	63	11	σ	σ	PROPN
cana-1403	63	12	.	.	PROPN
cana-1403	63	13	4	4	NUM
cana-1403	63	14	.	.	NOUN
cana-1403	63	15	numerical	numerical	ADJ
cana-1403	63	16	examples	example	NOUN
cana-1403	63	17	in	in	ADP
cana-1403	63	18	this	this	DET
cana-1403	63	19	section	section	NOUN
cana-1403	63	20	,	,	PUNCT
cana-1403	63	21	we	we	PRON
cana-1403	63	22	give	give	VERB
cana-1403	63	23	some	some	DET
cana-1403	63	24	numerical	numerical	ADJ
cana-1403	63	25	examples	example	NOUN
cana-1403	63	26	for	for	ADP
cana-1403	63	27	validating	validate	VERB
cana-1403	63	28	the	the	DET
cana-1403	63	29	outcomes	outcome	NOUN
cana-1403	63	30	of	of	ADP
cana-1403	63	31	previous	previous	ADJ
cana-1403	63	32	sections	section	NOUN
cana-1403	63	33	.	.	PUNCT
cana-1403	64	1	all	all	DET
cana-1403	64	2	plots	plot	NOUN
cana-1403	64	3	in	in	ADP
cana-1403	64	4	this	this	DET
cana-1403	64	5	section	section	NOUN
cana-1403	64	6	are	be	AUX
cana-1403	64	7	drawn	draw	VERB
cana-1403	64	8	using	use	VERB
cana-1403	64	9	matlab	matlab	PROPN
cana-1403	64	10	.	.	PUNCT
cana-1403	64	11	example	example	NOUN
cana-1403	65	1	1	1	NUM
cana-1403	65	2	:	:	PUNCT
cana-1403	65	3	we	we	PRON
cana-1403	65	4	let	let	VERB
cana-1403	65	5	,	,	PUNCT
cana-1403	65	6	,	,	PUNCT
cana-1403	65	7	,	,	PUNCT
cana-1403	65	8	.	.	PUNCT
cana-1403	66	1	so	so	ADV
cana-1403	66	2	,	,	PUNCT
cana-1403	66	3	we	we	PRON
cana-1403	66	4	deal	deal	VERB
cana-1403	66	5	with	with	ADP
cana-1403	66	6	the	the	DET
cana-1403	66	7	equation	equation	NOUN
cana-1403	66	8	(	(	PUNCT
cana-1403	66	9	)	)	PUNCT
cana-1403	66	10	(	(	PUNCT
cana-1403	66	11	)	)	PUNCT
cana-1403	66	12	we	we	PRON
cana-1403	66	13	find	find	VERB
cana-1403	66	14	that	that	SCONJ
cana-1403	67	1	|	|	ADV
cana-1403	67	2	|	|	ADV
cana-1403	68	1	|	|	ADV
cana-1403	68	2	|	|	ADV
cana-1403	68	3	.	.	PUNCT
cana-1403	69	1	/	/	PUNCT
cana-1403	70	1	so	so	ADV
cana-1403	70	2	,	,	PUNCT
cana-1403	70	3	the	the	DET
cana-1403	70	4	positive	positive	ADJ
cana-1403	70	5	equilibrium	equilibrium	NOUN
cana-1403	70	6	of	of	ADP
cana-1403	70	7	(	(	PUNCT
cana-1403	70	8	)	)	PUNCT
cana-1403	70	9	is	be	AUX
cana-1403	70	10	stable	stable	ADJ
cana-1403	70	11	in	in	ADP
cana-1403	70	12	probability	probability	NOUN
cana-1403	70	13	.	.	PUNCT
cana-1403	71	1	(	(	PUNCT
cana-1403	71	2	see	see	VERB
cana-1403	71	3	figure	figure	NOUN
cana-1403	71	4	1	1	NUM
cana-1403	71	5	)	)	PUNCT
cana-1403	71	6	.	.	PUNCT
cana-1403	72	1	communications	communication	NOUN
cana-1403	72	2	on	on	ADP
cana-1403	72	3	applied	apply	VERB
cana-1403	72	4	nonlinear	nonlinear	ADJ
cana-1403	72	5	analysis	analysis	NOUN
cana-1403	72	6	issn	issn	NOUN
cana-1403	72	7	:	:	PUNCT
cana-1403	72	8	1074	1074	NUM
cana-1403	72	9	-	-	PUNCT
cana-1403	72	10	133x	133x	NUM
cana-1403	72	11	vol	vol	NOUN
cana-1403	72	12	31	31	NUM
cana-1403	72	13	no	no	NOUN
cana-1403	72	14	.	.	PUNCT
cana-1403	73	1	7s	7	NOUN
cana-1403	73	2	(	(	PUNCT
cana-1403	73	3	2024	2024	NUM
cana-1403	73	4	)	)	PUNCT
cana-1403	73	5	636	636	NUM
cana-1403	73	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1403	73	7	figure	figure	NOUN
cana-1403	73	8	1	1	NUM
cana-1403	73	9	:	:	PUNCT
cana-1403	73	10	300	300	NUM
cana-1403	73	11	trajectories	trajectory	NOUN
cana-1403	73	12	of	of	ADP
cana-1403	73	13	the	the	DET
cana-1403	73	14	equation	equation	NOUN
cana-1403	73	15	(	(	PUNCT
cana-1403	73	16	)	)	PUNCT
cana-1403	73	17	.	.	PUNCT
cana-1403	74	1	in	in	ADP
cana-1403	74	2	figure	figure	NOUN
cana-1403	74	3	1	1	NUM
cana-1403	74	4	,	,	PUNCT
cana-1403	74	5	300	300	NUM
cana-1403	74	6	trajectories	trajectory	NOUN
cana-1403	74	7	of	of	ADP
cana-1403	74	8	the	the	DET
cana-1403	74	9	solutions	solution	NOUN
cana-1403	74	10	of	of	ADP
cana-1403	74	11	equation	equation	NOUN
cana-1403	74	12	(	(	PUNCT
cana-1403	74	13	)	)	PUNCT
cana-1403	74	14	one	one	PRON
cana-1403	74	15	can	can	AUX
cana-1403	74	16	see	see	VERB
cana-1403	74	17	that	that	SCONJ
cana-1403	74	18	all	all	DET
cana-1403	74	19	trajectories	trajectory	NOUN
cana-1403	74	20	converge	converge	VERB
cana-1403	74	21	in	in	ADP
cana-1403	74	22	probability	probability	NOUN
cana-1403	74	23	to	to	ADP
cana-1403	74	24	the	the	DET
cana-1403	74	25	stable	stable	ADJ
cana-1403	74	26	positive	positive	ADJ
cana-1403	74	27	equilibrium	equilibrium	NOUN
cana-1403	74	28	,	,	PUNCT
cana-1403	74	29	so	so	SCONJ
cana-1403	74	30	all	all	DET
cana-1403	74	31	trajectories	trajectory	NOUN
cana-1403	74	32	converge	converge	VERB
cana-1403	74	33	to	to	ADP
cana-1403	74	34	this	this	DET
cana-1403	74	35	equilibrium	equilibrium	NOUN
cana-1403	74	36	,	,	PUNCT
cana-1403	74	37	(	(	PUNCT
cana-1403	74	38	by	by	ADP
cana-1403	74	39	using	use	VERB
cana-1403	74	40	matlab	matlab	PROPN
cana-1403	74	41	)	)	PUNCT
cana-1403	74	42	.	.	PUNCT
cana-1403	75	1	example	example	NOUN
cana-1403	75	2	2	2	NUM
cana-1403	75	3	:	:	PUNCT
cana-1403	75	4	we	we	PRON
cana-1403	75	5	let	let	VERB
cana-1403	75	6	,	,	PUNCT
cana-1403	75	7	,	,	PUNCT
cana-1403	75	8	,	,	PUNCT
cana-1403	75	9	.	.	PUNCT
cana-1403	76	1	so	so	ADV
cana-1403	76	2	,	,	PUNCT
cana-1403	76	3	we	we	PRON
cana-1403	76	4	deal	deal	VERB
cana-1403	76	5	with	with	ADP
cana-1403	76	6	the	the	DET
cana-1403	76	7	equation	equation	NOUN
cana-1403	76	8	(	(	PUNCT
cana-1403	76	9	)	)	PUNCT
cana-1403	76	10	we	we	PRON
cana-1403	76	11	find	find	VERB
cana-1403	76	12	that	that	SCONJ
cana-1403	77	1	|	|	ADV
cana-1403	78	1	|	|	ADV
cana-1403	79	1	|	|	ADV
cana-1403	80	1	|	|	ADV
cana-1403	80	2	(	(	PUNCT
cana-1403	80	3	)	)	PUNCT
cana-1403	80	4	so	so	ADV
cana-1403	80	5	,	,	PUNCT
cana-1403	80	6	the	the	DET
cana-1403	80	7	zero	zero	NUM
cana-1403	80	8	equilibrium	equilibrium	NOUN
cana-1403	80	9	of	of	ADP
cana-1403	80	10	(	(	PUNCT
cana-1403	80	11	)	)	PUNCT
cana-1403	80	12	is	be	AUX
cana-1403	80	13	stable	stable	ADJ
cana-1403	80	14	in	in	ADP
cana-1403	80	15	probability	probability	NOUN
cana-1403	80	16	.	.	PUNCT
cana-1403	81	1	(	(	PUNCT
cana-1403	81	2	see	see	VERB
cana-1403	81	3	figure	figure	NOUN
cana-1403	81	4	2	2	NUM
cana-1403	81	5	)	)	PUNCT
cana-1403	81	6	.	.	PUNCT
cana-1403	82	1	figure	figure	NOUN
cana-1403	82	2	2	2	NUM
cana-1403	82	3	:	:	PUNCT
cana-1403	82	4	300	300	NUM
cana-1403	82	5	trajectories	trajectory	NOUN
cana-1403	82	6	of	of	ADP
cana-1403	82	7	the	the	DET
cana-1403	82	8	equation	equation	NOUN
cana-1403	82	9	(	(	PUNCT
cana-1403	82	10	)	)	PUNCT
cana-1403	82	11	in	in	ADP
cana-1403	82	12	figure	figure	NOUN
cana-1403	82	13	2	2	NUM
cana-1403	82	14	,	,	PUNCT
cana-1403	82	15	300	300	NUM
cana-1403	82	16	trajectories	trajectory	NOUN
cana-1403	82	17	of	of	ADP
cana-1403	82	18	the	the	DET
cana-1403	82	19	solutions	solution	NOUN
cana-1403	82	20	of	of	ADP
cana-1403	82	21	equation	equation	NOUN
cana-1403	82	22	(	(	PUNCT
cana-1403	82	23	)	)	PUNCT
cana-1403	82	24	.	.	PUNCT
cana-1403	83	1	one	one	PRON
cana-1403	83	2	can	can	AUX
cana-1403	83	3	see	see	VERB
cana-1403	83	4	that	that	SCONJ
cana-1403	83	5	all	all	DET
cana-1403	83	6	trajectories	trajectory	NOUN
cana-1403	83	7	converge	converge	VERB
cana-1403	83	8	in	in	ADP
cana-1403	83	9	probability	probability	NOUN
cana-1403	83	10	to	to	ADP
cana-1403	83	11	the	the	DET
cana-1403	83	12	stable	stable	ADJ
cana-1403	83	13	zero	zero	NUM
cana-1403	83	14	equilibrium	equilibrium	NOUN
cana-1403	83	15	,	,	PUNCT
cana-1403	83	16	so	so	SCONJ
cana-1403	83	17	all	all	DET
cana-1403	83	18	trajectories	trajectory	NOUN
cana-1403	83	19	converge	converge	VERB
cana-1403	83	20	to	to	ADP
cana-1403	83	21	this	this	DET
cana-1403	83	22	equilibrium	equilibrium	NOUN
cana-1403	83	23	,	,	PUNCT
cana-1403	83	24	(	(	PUNCT
cana-1403	83	25	by	by	ADP
cana-1403	83	26	using	use	VERB
cana-1403	83	27	matlab	matlab	PROPN
cana-1403	83	28	)	)	PUNCT
cana-1403	83	29	.	.	PUNCT
cana-1403	84	1	example	example	NOUN
cana-1403	85	1	3	3	NUM
cana-1403	85	2	:	:	PUNCT
cana-1403	85	3	we	we	PRON
cana-1403	85	4	let	let	VERB
cana-1403	85	5	,	,	PUNCT
cana-1403	85	6	,	,	PUNCT
cana-1403	85	7	,	,	PUNCT
cana-1403	85	8	.	.	PUNCT
cana-1403	86	1	so	so	ADV
cana-1403	86	2	,	,	PUNCT
cana-1403	86	3	we	we	PRON
cana-1403	86	4	deal	deal	VERB
cana-1403	86	5	with	with	ADP
cana-1403	86	6	the	the	DET
cana-1403	86	7	equation	equation	NOUN
cana-1403	86	8	(	(	PUNCT
cana-1403	86	9	)	)	PUNCT
cana-1403	86	10	thus	thus	ADV
cana-1403	86	11	,	,	PUNCT
cana-1403	86	12	the	the	DET
cana-1403	86	13	zero	zero	NUM
cana-1403	86	14	equilibrium	equilibrium	NOUN
cana-1403	86	15	of	of	ADP
cana-1403	86	16	(	(	PUNCT
cana-1403	86	17	)	)	PUNCT
cana-1403	86	18	is	be	AUX
cana-1403	86	19	unstable	unstable	ADJ
cana-1403	86	20	.	.	PUNCT
cana-1403	87	1	since	since	SCONJ
cana-1403	87	2	,	,	PUNCT
cana-1403	87	3	communications	communication	NOUN
cana-1403	87	4	on	on	ADP
cana-1403	87	5	applied	apply	VERB
cana-1403	87	6	nonlinear	nonlinear	ADJ
cana-1403	87	7	analysis	analysis	NOUN
cana-1403	87	8	issn	issn	NOUN
cana-1403	87	9	:	:	PUNCT
cana-1403	87	10	1074	1074	NUM
cana-1403	87	11	-	-	PUNCT
cana-1403	87	12	133x	133x	NUM
cana-1403	87	13	vol	vol	NOUN
cana-1403	87	14	31	31	NUM
cana-1403	87	15	no	no	NOUN
cana-1403	87	16	.	.	PUNCT
cana-1403	88	1	7s	7	NOUN
cana-1403	88	2	(	(	PUNCT
cana-1403	88	3	2024	2024	NUM
cana-1403	88	4	)	)	PUNCT
cana-1403	88	5	637	637	NUM
cana-1403	88	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1403	88	7	(	(	PUNCT
cana-1403	88	8	)	)	PUNCT
cana-1403	88	9	(	(	PUNCT
cana-1403	88	10	see	see	VERB
cana-1403	88	11	figure	figure	NOUN
cana-1403	88	12	3	3	NUM
cana-1403	88	13	)	)	PUNCT
cana-1403	88	14	.	.	PUNCT
cana-1403	89	1	figure	figure	VERB
cana-1403	89	2	3	3	NUM
cana-1403	89	3	:	:	SYM
cana-1403	89	4	300	300	NUM
cana-1403	89	5	trajectories	trajectory	NOUN
cana-1403	89	6	of	of	ADP
cana-1403	89	7	the	the	DET
cana-1403	89	8	equation	equation	NOUN
cana-1403	89	9	(	(	PUNCT
cana-1403	89	10	)	)	PUNCT
cana-1403	89	11	.	.	PUNCT
cana-1403	90	1	in	in	ADP
cana-1403	90	2	figure	figure	NOUN
cana-1403	90	3	3	3	NUM
cana-1403	90	4	,	,	PUNCT
cana-1403	90	5	300	300	NUM
cana-1403	90	6	trajectories	trajectory	NOUN
cana-1403	90	7	of	of	ADP
cana-1403	90	8	the	the	DET
cana-1403	90	9	solutions	solution	NOUN
cana-1403	90	10	of	of	ADP
cana-1403	90	11	equation	equation	NOUN
cana-1403	90	12	(	(	PUNCT
cana-1403	90	13	)	)	PUNCT
cana-1403	90	14	.	.	PUNCT
cana-1403	91	1	one	one	PRON
cana-1403	91	2	can	can	AUX
cana-1403	91	3	see	see	VERB
cana-1403	91	4	that	that	SCONJ
cana-1403	91	5	all	all	DET
cana-1403	91	6	trajectories	trajectory	NOUN
cana-1403	91	7	go	go	VERB
cana-1403	91	8	out	out	ADP
cana-1403	91	9	of	of	ADP
cana-1403	91	10	the	the	DET
cana-1403	91	11	zero	zero	NUM
cana-1403	91	12	equilibrium	equilibrium	NOUN
cana-1403	91	13	,	,	PUNCT
cana-1403	91	14	(	(	PUNCT
cana-1403	91	15	by	by	ADP
cana-1403	91	16	using	use	VERB
cana-1403	91	17	matlab	matlab	PROPN
cana-1403	91	18	)	)	PUNCT
cana-1403	91	19	.	.	PUNCT
cana-1403	92	1	example	example	NOUN
cana-1403	92	2	4	4	NUM
cana-1403	92	3	:	:	PUNCT
cana-1403	92	4	we	we	PRON
cana-1403	92	5	let	let	VERB
cana-1403	92	6	we	we	PRON
cana-1403	92	7	let	let	VERB
cana-1403	92	8	,	,	PUNCT
cana-1403	92	9	,	,	PUNCT
cana-1403	92	10	,	,	PUNCT
cana-1403	92	11	.	.	PUNCT
cana-1403	93	1	so	so	ADV
cana-1403	93	2	,	,	PUNCT
cana-1403	93	3	we	we	PRON
cana-1403	93	4	deal	deal	VERB
cana-1403	93	5	with	with	ADP
cana-1403	93	6	the	the	DET
cana-1403	93	7	equation	equation	NOUN
cana-1403	93	8	(	(	PUNCT
cana-1403	93	9	)	)	PUNCT
cana-1403	93	10	(	(	PUNCT
cana-1403	93	11	)	)	PUNCT
cana-1403	93	12	thus	thus	ADV
cana-1403	93	13	,	,	PUNCT
cana-1403	93	14	the	the	DET
cana-1403	93	15	positive	positive	ADJ
cana-1403	93	16	equilibrium	equilibrium	NOUN
cana-1403	93	17	of	of	ADP
cana-1403	93	18	(	(	PUNCT
cana-1403	93	19	)	)	PUNCT
cana-1403	93	20	is	be	AUX
cana-1403	93	21	unstable	unstable	ADJ
cana-1403	93	22	.	.	PUNCT
cana-1403	94	1	since	since	SCONJ
cana-1403	94	2	,	,	PUNCT
cana-1403	94	3	.	.	PUNCT
cana-1403	94	4	/	/	PUNCT
cana-1403	94	5	(	(	PUNCT
cana-1403	94	6	see	see	VERB
cana-1403	94	7	figure	figure	NOUN
cana-1403	94	8	4	4	NUM
cana-1403	94	9	)	)	PUNCT
cana-1403	94	10	.	.	PUNCT
cana-1403	95	1	figure	figure	VERB
cana-1403	95	2	4	4	NUM
cana-1403	95	3	:	:	SYM
cana-1403	95	4	300	300	NUM
cana-1403	95	5	trajectories	trajectory	NOUN
cana-1403	95	6	of	of	ADP
cana-1403	95	7	the	the	DET
cana-1403	95	8	equation	equation	NOUN
cana-1403	95	9	(	(	PUNCT
cana-1403	95	10	)	)	PUNCT
cana-1403	95	11	.	.	PUNCT
cana-1403	96	1	communications	communication	NOUN
cana-1403	96	2	on	on	ADP
cana-1403	96	3	applied	apply	VERB
cana-1403	96	4	nonlinear	nonlinear	ADJ
cana-1403	96	5	analysis	analysis	NOUN
cana-1403	96	6	issn	issn	NOUN
cana-1403	96	7	:	:	PUNCT
cana-1403	96	8	1074	1074	NUM
cana-1403	96	9	-	-	PUNCT
cana-1403	96	10	133x	133x	NUM
cana-1403	96	11	vol	vol	NOUN
cana-1403	96	12	31	31	NUM
cana-1403	96	13	no	no	NOUN
cana-1403	96	14	.	.	PUNCT
cana-1403	97	1	7s	7	NOUN
cana-1403	97	2	(	(	PUNCT
cana-1403	97	3	2024	2024	NUM
cana-1403	97	4	)	)	PUNCT
cana-1403	97	5	638	638	NUM
cana-1403	97	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1403	97	7	in	in	ADP
cana-1403	97	8	figure	figure	NOUN
cana-1403	97	9	4	4	NUM
cana-1403	97	10	,	,	PUNCT
cana-1403	97	11	300	300	NUM
cana-1403	97	12	trajectories	trajectory	NOUN
cana-1403	97	13	of	of	ADP
cana-1403	97	14	the	the	DET
cana-1403	97	15	solutions	solution	NOUN
cana-1403	97	16	of	of	ADP
cana-1403	97	17	equation	equation	NOUN
cana-1403	97	18	(	(	PUNCT
cana-1403	97	19	)	)	PUNCT
cana-1403	97	20	one	one	PRON
cana-1403	97	21	can	can	AUX
cana-1403	97	22	see	see	VERB
cana-1403	97	23	that	that	SCONJ
cana-1403	97	24	all	all	DET
cana-1403	97	25	trajectories	trajectory	NOUN
cana-1403	97	26	go	go	VERB
cana-1403	97	27	out	out	ADP
cana-1403	97	28	of	of	ADP
cana-1403	97	29	the	the	DET
cana-1403	97	30	positive	positive	ADJ
cana-1403	97	31	equilibrium	equilibrium	NOUN
cana-1403	97	32	,	,	PUNCT
cana-1403	97	33	(	(	PUNCT
cana-1403	97	34	by	by	ADP
cana-1403	97	35	using	use	VERB
cana-1403	97	36	matlab	matlab	PROPN
cana-1403	97	37	)	)	PUNCT
cana-1403	97	38	.	.	PUNCT
cana-1403	98	1	5	5	X
cana-1403	98	2	.	.	X
cana-1403	98	3	conclusion	conclusion	NOUN
cana-1403	98	4	this	this	DET
cana-1403	98	5	paper	paper	NOUN
cana-1403	98	6	devoted	devote	VERB
cana-1403	98	7	to	to	ADP
cana-1403	98	8	investigation	investigation	NOUN
cana-1403	98	9	of	of	ADP
cana-1403	98	10	the	the	DET
cana-1403	98	11	stability	stability	NOUN
cana-1403	98	12	in	in	ADP
cana-1403	98	13	probability	probability	NOUN
cana-1403	98	14	of	of	ADP
cana-1403	98	15	the	the	DET
cana-1403	98	16	two	two	NUM
cana-1403	98	17	equilibrium	equilibrium	NOUN
cana-1403	98	18	points	point	NOUN
cana-1403	98	19	(	(	PUNCT
cana-1403	98	20	zero	zero	NUM
cana-1403	98	21	and	and	CCONJ
cana-1403	98	22	positive	positive	ADJ
cana-1403	98	23	)	)	PUNCT
cana-1403	98	24	of	of	ADP
cana-1403	98	25	pielou‟s	pielou‟s	PUNCT
cana-1403	98	26	difference	difference	NOUN
cana-1403	98	27	equation	equation	NOUN
cana-1403	98	28	that	that	PRON
cana-1403	98	29	is	be	AUX
cana-1403	98	30	subject	subject	ADJ
cana-1403	98	31	to	to	ADP
cana-1403	98	32	additive	additive	ADJ
cana-1403	98	33	stochastic	stochastic	ADJ
cana-1403	98	34	perturbations	perturbation	NOUN
cana-1403	98	35	(	(	PUNCT
cana-1403	98	36	)	)	PUNCT
cana-1403	98	37	(	(	PUNCT
cana-1403	98	38	)	)	PUNCT
cana-1403	98	39	where	where	SCONJ
cana-1403	98	40	parameters	parameter	NOUN
cana-1403	98	41	and	and	CCONJ
cana-1403	98	42	have	have	VERB
cana-1403	98	43	arbitrary	arbitrary	ADJ
cana-1403	98	44	values	value	NOUN
cana-1403	98	45	,	,	PUNCT
cana-1403	98	46	is	be	AUX
cana-1403	98	47	an	an	DET
cana-1403	98	48	equilibrium	equilibrium	NOUN
cana-1403	98	49	point	point	NOUN
cana-1403	98	50	of	of	ADP
cana-1403	98	51	(	(	PUNCT
cana-1403	98	52	)	)	PUNCT
cana-1403	98	53	,	,	PUNCT
cana-1403	98	54	,	,	PUNCT
cana-1403	98	55	be	be	AUX
cana-1403	98	56	a	a	DET
cana-1403	98	57	sequence	sequence	NOUN
cana-1403	98	58	of	of	ADP
cana-1403	98	59	-adapted	-adapted	ADJ
cana-1403	98	60	random	random	ADJ
cana-1403	98	61	variables	variable	NOUN
cana-1403	98	62	such	such	ADJ
cana-1403	98	63	that	that	SCONJ
cana-1403	98	64	e	e	NOUN
cana-1403	98	65	(	(	PUNCT
cana-1403	98	66	)	)	PUNCT
cana-1403	98	67	(	(	PUNCT
cana-1403	98	68	)	)	PUNCT
cana-1403	98	69	and	and	CCONJ
cana-1403	98	70	the	the	DET
cana-1403	98	71	initials	initial	NOUN
cana-1403	98	72	are	be	AUX
cana-1403	98	73	non	non	ADJ
cana-1403	98	74	-	-	ADJ
cana-1403	98	75	negative	negative	ADJ
cana-1403	98	76	real	real	ADJ
cana-1403	98	77	numbers	number	NOUN
cana-1403	98	78	.	.	PUNCT
cana-1403	99	1	it	it	PRON
cana-1403	99	2	is	be	AUX
cana-1403	99	3	shown	show	VERB
cana-1403	99	4	that	that	SCONJ
cana-1403	99	5	for	for	ADP
cana-1403	99	6	equilibrium	equilibrium	NOUN
cana-1403	99	7	points	point	NOUN
cana-1403	99	8	of	of	ADP
cana-1403	99	9	the	the	DET
cana-1403	99	10	considered	consider	VERB
cana-1403	99	11	equation	equation	NOUN
cana-1403	99	12	it	it	PRON
cana-1403	99	13	is	be	AUX
cana-1403	99	14	possible	possible	ADJ
cana-1403	99	15	to	to	PART
cana-1403	99	16	get	get	VERB
cana-1403	99	17	conditions	condition	NOUN
cana-1403	99	18	for	for	ADP
cana-1403	99	19	stability	stability	NOUN
cana-1403	99	20	in	in	ADP
cana-1403	99	21	probability	probability	NOUN
cana-1403	99	22	in	in	ADP
cana-1403	99	23	an	an	DET
cana-1403	99	24	analytical	analytical	ADJ
cana-1403	99	25	form	form	NOUN
cana-1403	99	26	and	and	CCONJ
cana-1403	99	27	can	can	AUX
cana-1403	99	28	be	be	AUX
cana-1403	99	29	obtained	obtain	VERB
cana-1403	99	30	numerically	numerically	ADV
cana-1403	99	31	via	via	ADP
cana-1403	99	32	matlab	matlab	PROPN
cana-1403	99	33	.	.	PUNCT
cana-1403	100	1	the	the	DET
cana-1403	100	2	obtained	obtain	VERB
cana-1403	100	3	results	result	NOUN
cana-1403	100	4	are	be	AUX
cana-1403	100	5	illustrated	illustrate	VERB
cana-1403	100	6	by	by	ADP
cana-1403	100	7	examples	example	NOUN
cana-1403	100	8	and	and	CCONJ
cana-1403	100	9	figures	figure	NOUN
cana-1403	100	10	with	with	ADP
cana-1403	100	11	stable	stable	ADJ
cana-1403	100	12	and	and	CCONJ
cana-1403	100	13	unstable	unstable	ADJ
cana-1403	100	14	solutions	solution	NOUN
cana-1403	100	15	.	.	PUNCT
cana-1403	101	1	the	the	DET
cana-1403	101	2	authors	author	NOUN
cana-1403	101	3	continues	continue	VERB
cana-1403	101	4	this	this	DET
cana-1403	101	5	work	work	NOUN
cana-1403	101	6	and	and	CCONJ
cana-1403	101	7	hopes	hope	VERB
cana-1403	101	8	to	to	PART
cana-1403	101	9	involve	involve	VERB
cana-1403	101	10	all	all	DET
cana-1403	101	11	other	other	ADJ
cana-1403	101	12	interested	interested	ADJ
cana-1403	101	13	researchers	researcher	NOUN
cana-1403	101	14	and	and	CCONJ
cana-1403	101	15	applications	application	NOUN
cana-1403	101	16	in	in	ADP
cana-1403	101	17	it	it	PRON
cana-1403	101	18	.	.	PUNCT
cana-1403	102	1	references	reference	NOUN
cana-1403	102	2	[	[	X
cana-1403	102	3	1	1	NUM
cana-1403	102	4	]	]	SYM
cana-1403	102	5	akrour	akrour	ADJ
cana-1403	102	6	,	,	PUNCT
cana-1403	102	7	y.	y.	PROPN
cana-1403	102	8	,	,	PUNCT
cana-1403	102	9	kara	kara	PROPN
cana-1403	102	10	,	,	PUNCT
cana-1403	102	11	m.	m.	NOUN
cana-1403	102	12	,	,	PUNCT
cana-1403	102	13	touafek	touafek	PROPN
cana-1403	102	14	,	,	PUNCT
cana-1403	102	15	n.	n.	NOUN
cana-1403	102	16	,	,	PUNCT
cana-1403	102	17	&	&	CCONJ
cana-1403	102	18	yazlik	yazlik	PROPN
cana-1403	102	19	,	,	PUNCT
cana-1403	102	20	y.	y.	PROPN
cana-1403	102	21	(	(	PUNCT
cana-1403	102	22	2021	2021	NUM
cana-1403	102	23	)	)	PUNCT
cana-1403	102	24	.	.	PUNCT
cana-1403	103	1	solutions	solution	NOUN
cana-1403	103	2	formulas	formula	NOUN
cana-1403	103	3	for	for	ADP
cana-1403	103	4	some	some	DET
cana-1403	103	5	general	general	ADJ
cana-1403	103	6	systems	system	NOUN
cana-1403	103	7	of	of	ADP
cana-1403	103	8	difference	difference	NOUN
cana-1403	103	9	equations	equation	NOUN
cana-1403	103	10	.	.	PUNCT
cana-1403	104	1	[	[	X
cana-1403	104	2	2	2	NUM
cana-1403	104	3	]	]	X
cana-1403	104	4	aloqeili	aloqeili	NOUN
cana-1403	104	5	,	,	PUNCT
cana-1403	104	6	m.	m.	NOUN
cana-1403	104	7	(	(	PUNCT
cana-1403	104	8	2006	2006	NUM
cana-1403	104	9	)	)	PUNCT
cana-1403	104	10	.	.	PUNCT
cana-1403	105	1	dynamics	dynamic	NOUN
cana-1403	105	2	of	of	ADP
cana-1403	105	3	a	a	DET
cana-1403	105	4	kth	kth	PROPN
cana-1403	105	5	order	order	NOUN
cana-1403	105	6	rational	rational	ADJ
cana-1403	105	7	difference	difference	NOUN
cana-1403	105	8	equation	equation	NOUN
cana-1403	105	9	.	.	PUNCT
cana-1403	106	1	applied	apply	VERB
cana-1403	106	2	mathematics	mathematic	NOUN
cana-1403	106	3	and	and	CCONJ
cana-1403	106	4	computation	computation	NOUN
cana-1403	106	5	,	,	PUNCT
cana-1403	106	6	181(2	181(2	NUM
cana-1403	106	7	)	)	PUNCT
cana-1403	106	8	,	,	PUNCT
cana-1403	106	9	1328	1328	NUM
cana-1403	106	10	-	-	SYM
cana-1403	106	11	1335	1335	NUM
cana-1403	106	12	.	.	PUNCT
cana-1403	107	1	[	[	X
cana-1403	107	2	3	3	NUM
cana-1403	107	3	]	]	X
cana-1403	107	4	appleby	appleby	PROPN
cana-1403	107	5	,	,	PUNCT
cana-1403	107	6	j.	j.	PROPN
cana-1403	107	7	,	,	PUNCT
cana-1403	107	8	berkolaiko	berkolaiko	NOUN
cana-1403	107	9	,	,	PUNCT
cana-1403	107	10	g.	g.	PROPN
cana-1403	107	11	,	,	PUNCT
cana-1403	107	12	rodkina	rodkina	PROPN
cana-1403	107	13	,	,	PUNCT
cana-1403	107	14	a.	a.	NOUN
cana-1403	107	15	(	(	PUNCT
cana-1403	107	16	)	)	PUNCT
cana-1403	107	17	.	.	PUNCT
cana-1403	108	1	on	on	ADP
cana-1403	108	2	local	local	ADJ
cana-1403	108	3	stability	stability	NOUN
cana-1403	108	4	for	for	ADP
cana-1403	108	5	a	a	DET
cana-1403	108	6	nonlinear	nonlinear	ADJ
cana-1403	108	7	difference	difference	NOUN
cana-1403	108	8	equation	equation	NOUN
cana-1403	108	9	with	with	ADP
cana-1403	108	10	a	a	DET
cana-1403	108	11	non	non	ADJ
cana-1403	108	12	-	-	ADJ
cana-1403	108	13	hyperbolic	hyperbolic	ADJ
cana-1403	108	14	equilibrium	equilibrium	NOUN
cana-1403	108	15	and	and	CCONJ
cana-1403	108	16	fading	fade	VERB
cana-1403	108	17	stochastic	stochastic	ADJ
cana-1403	108	18	perturbations	perturbation	NOUN
cana-1403	108	19	.	.	PUNCT
cana-1403	109	1	journal	journal	NOUN
cana-1403	109	2	of	of	ADP
cana-1403	109	3	difference	difference	NOUN
cana-1403	109	4	equations	equation	NOUN
cana-1403	109	5	and	and	CCONJ
cana-1403	109	6	applications	application	NOUN
cana-1403	109	7	,	,	PUNCT
cana-1403	109	8	(	(	PUNCT
cana-1403	109	9	)	)	PUNCT
cana-1403	109	10	.	.	PUNCT
cana-1403	110	1	[	[	X
cana-1403	110	2	4	4	NUM
cana-1403	110	3	]	]	X
cana-1403	110	4	berg	berg	PROPN
cana-1403	110	5	,	,	PUNCT
cana-1403	110	6	l.	l.	PROPN
cana-1403	110	7	,	,	PUNCT
cana-1403	110	8	stević	stević	PROPN
cana-1403	110	9	,	,	PUNCT
cana-1403	110	10	s.	s.	PROPN
cana-1403	110	11	(	(	PUNCT
cana-1403	110	12	2011	2011	NUM
cana-1403	110	13	)	)	PUNCT
cana-1403	110	14	.	.	PUNCT
cana-1403	111	1	on	on	ADP
cana-1403	111	2	the	the	DET
cana-1403	111	3	asymptotics	asymptotic	NOUN
cana-1403	111	4	of	of	ADP
cana-1403	111	5	some	some	DET
cana-1403	111	6	systems	system	NOUN
cana-1403	111	7	of	of	ADP
cana-1403	111	8	difference	difference	NOUN
cana-1403	111	9	equations	equation	NOUN
cana-1403	111	10	.	.	PUNCT
cana-1403	112	1	journal	journal	NOUN
cana-1403	112	2	of	of	ADP
cana-1403	112	3	difference	difference	NOUN
cana-1403	112	4	equations	equation	NOUN
cana-1403	112	5	and	and	CCONJ
cana-1403	112	6	applications	application	NOUN
cana-1403	112	7	,	,	PUNCT
cana-1403	112	8	17(9	17(9	NOUN
cana-1403	112	9	)	)	PUNCT
cana-1403	112	10	,	,	PUNCT
cana-1403	112	11	1291	1291	NUM
cana-1403	112	12	-	-	SYM
cana-1403	112	13	1301	1301	NUM
cana-1403	112	14	.	.	PUNCT
cana-1403	113	1	[	[	X
cana-1403	113	2	5	5	NUM
cana-1403	113	3	]	]	X
cana-1403	113	4	caraballo	caraballo	PROPN
cana-1403	113	5	,	,	PUNCT
cana-1403	113	6	t.	t.	PROPN
cana-1403	113	7	;	;	PUNCT
cana-1403	113	8	colucci	colucci	PROPN
cana-1403	113	9	,	,	PUNCT
cana-1403	113	10	r.	r.	PROPN
cana-1403	113	11	;	;	PUNCT
cana-1403	113	12	lópez	lópez	NOUN
cana-1403	113	13	-	-	PUNCT
cana-1403	113	14	de	de	X
cana-1403	113	15	-	-	ADJ
cana-1403	113	16	la	la	ADJ
cana-1403	113	17	cruz	cruz	PROPN
cana-1403	113	18	,	,	PUNCT
cana-1403	113	19	j.	j.	PROPN
cana-1403	113	20	;	;	PUNCT
cana-1403	113	21	rapaport	rapaport	PROPN
cana-1403	113	22	,	,	PUNCT
cana-1403	113	23	a	a	PRON
cana-1403	113	24	,	,	PUNCT
cana-1403	113	25	(	(	PUNCT
cana-1403	113	26	2019	2019	NUM
cana-1403	113	27	)	)	PUNCT
cana-1403	113	28	.	.	PUNCT
cana-1403	114	1	a	a	DET
cana-1403	114	2	way	way	NOUN
cana-1403	114	3	to	to	PART
cana-1403	114	4	model	model	VERB
cana-1403	114	5	stochastic	stochastic	ADJ
cana-1403	114	6	perturbations	perturbation	NOUN
cana-1403	114	7	in	in	ADP
cana-1403	114	8	population	population	NOUN
cana-1403	114	9	dynamics	dynamic	NOUN
cana-1403	114	10	models	model	NOUN
cana-1403	114	11	with	with	ADP
cana-1403	114	12	bounded	bounded	ADJ
cana-1403	114	13	realizations	realization	NOUN
cana-1403	114	14	.	.	PUNCT
cana-1403	115	1	commun	commun	PROPN
cana-1403	115	2	.	.	PUNCT
cana-1403	116	1	nonlinear	nonlinear	PROPN
cana-1403	116	2	sci	sci	PROPN
cana-1403	116	3	.	.	PUNCT
cana-1403	116	4	numer	numer	PROPN
cana-1403	116	5	.	.	PUNCT
cana-1403	117	1	simul	simul	PROPN
cana-1403	117	2	.	.	PUNCT
cana-1403	118	1	77	77	NUM
cana-1403	118	2	,	,	PUNCT
cana-1403	118	3	239–257	239–257	NUM
cana-1403	118	4	[	[	SYM
cana-1403	118	5	6	6	NUM
cana-1403	118	6	]	]	SYM
cana-1403	118	7	ding	ding	NOUN
cana-1403	118	8	,	,	PUNCT
cana-1403	118	9	x.	x.	PROPN
cana-1403	118	10	,	,	PUNCT
cana-1403	118	11	zhang	zhang	PROPN
cana-1403	118	12	,	,	PUNCT
cana-1403	118	13	r.	r.	PROPN
cana-1403	118	14	(	(	PUNCT
cana-1403	118	15	)	)	PUNCT
cana-1403	118	16	on	on	ADP
cana-1403	118	17	the	the	DET
cana-1403	118	18	difference	difference	NOUN
cana-1403	118	19	equation	equation	NOUN
cana-1403	118	20	.	.	PUNCT
cana-1403	119	1	advances	advance	NOUN
cana-1403	119	2	in	in	ADP
cana-1403	119	3	difference	difference	NOUN
cana-1403	119	4	equations	equation	NOUN
cana-1403	119	5	,	,	PUNCT
cana-1403	119	6	.	.	PUNCT
cana-1403	120	1	[	[	X
cana-1403	120	2	7	7	NUM
cana-1403	120	3	]	]	X
cana-1403	120	4	friedman	friedman	PROPN
cana-1403	120	5	,	,	PUNCT
cana-1403	120	6	a.	a.	NOUN
cana-1403	120	7	(	(	PUNCT
cana-1403	120	8	)	)	PUNCT
cana-1403	120	9	stochastic	stochastic	ADJ
cana-1403	120	10	differential	differential	ADJ
cana-1403	120	11	equations	equation	NOUN
cana-1403	120	12	and	and	CCONJ
cana-1403	120	13	applications	application	NOUN
cana-1403	120	14	.	.	PUNCT
cana-1403	121	1	in	in	ADP
cana-1403	121	2	stochastic	stochastic	ADJ
cana-1403	121	3	differential	differential	ADJ
cana-1403	121	4	equations	equation	NOUN
cana-1403	121	5	(	(	PUNCT
cana-1403	121	6	pp	pp	ADJ
cana-1403	121	7	.	.	PUNCT
cana-1403	121	8	)	)	PUNCT
cana-1403	121	9	.	.	PUNCT
cana-1403	122	1	berlin	berlin	PROPN
cana-1403	122	2	,	,	PUNCT
cana-1403	122	3	heidelberg	heidelberg	PROPN
cana-1403	122	4	:	:	PUNCT
cana-1403	122	5	springer	springer	PROPN
cana-1403	122	6	berlin	berlin	PROPN
cana-1403	122	7	heidelberg	heidelberg	PROPN
cana-1403	122	8	.	.	PUNCT
cana-1403	123	1	[	[	X
cana-1403	123	2	8	8	NUM
cana-1403	123	3	]	]	X
cana-1403	123	4	pielou	pielou	NOUN
cana-1403	123	5	,	,	PUNCT
cana-1403	123	6	e.	e.	PROPN
cana-1403	123	7	c.	c.	PROPN
cana-1403	123	8	(	(	PUNCT
cana-1403	123	9	1969	1969	NUM
cana-1403	123	10	)	)	PUNCT
cana-1403	123	11	.	.	PUNCT
cana-1403	124	1	an	an	DET
cana-1403	124	2	introduction	introduction	NOUN
cana-1403	124	3	to	to	ADP
cana-1403	124	4	mathematical	mathematical	ADJ
cana-1403	124	5	ecology	ecology	NOUN
cana-1403	124	6	.	.	PUNCT
cana-1403	125	1	[	[	X
cana-1403	125	2	9	9	NUM
cana-1403	125	3	]	]	SYM
cana-1403	125	4	pielou	pielou	NOUN
cana-1403	125	5	,	,	PUNCT
cana-1403	125	6	e.	e.	PROPN
cana-1403	125	7	c.	c.	PROPN
cana-1403	125	8	(	(	PUNCT
cana-1403	125	9	1974	1974	NUM
cana-1403	125	10	)	)	PUNCT
cana-1403	125	11	.	.	PUNCT
cana-1403	126	1	population	population	NOUN
cana-1403	126	2	and	and	CCONJ
cana-1403	126	3	community	community	NOUN
cana-1403	126	4	ecology	ecology	NOUN
cana-1403	126	5	:	:	PUNCT
cana-1403	126	6	principles	principle	NOUN
cana-1403	126	7	and	and	CCONJ
cana-1403	126	8	methods	method	NOUN
cana-1403	126	9	.	.	PUNCT
cana-1403	127	1	crc	crc	PROPN
cana-1403	127	2	press	press	PROPN
cana-1403	127	3	.	.	PUNCT
cana-1403	128	1	[	[	X
cana-1403	128	2	10	10	NUM
cana-1403	128	3	]	]	X
cana-1403	128	4	gikhman	gikhman	NOUN
cana-1403	128	5	,	,	PUNCT
cana-1403	128	6	i.	i.	PROPN
cana-1403	128	7	i.	i.	PROPN
cana-1403	128	8	,	,	PUNCT
cana-1403	128	9	skorokhod	skorokhod	PROPN
cana-1403	128	10	,	,	PUNCT
cana-1403	128	11	a.	a.	NOUN
cana-1403	128	12	v.	v.	PROPN
cana-1403	128	13	,	,	PUNCT
cana-1403	128	14	gikhman	gikhman	PROPN
cana-1403	128	15	,	,	PUNCT
cana-1403	128	16	i.	i.	PROPN
cana-1403	128	17	i.	i.	PROPN
cana-1403	128	18	,	,	PUNCT
cana-1403	128	19	&	&	CCONJ
cana-1403	128	20	skorokhod	skorokhod	PROPN
cana-1403	128	21	,	,	PUNCT
cana-1403	128	22	a.	a.	NOUN
cana-1403	128	23	v.	v.	PROPN
cana-1403	128	24	(	(	PUNCT
cana-1403	128	25	)	)	PUNCT
cana-1403	128	26	stochastic	stochastic	ADJ
cana-1403	128	27	differential	differential	ADJ
cana-1403	128	28	equations	equation	NOUN
cana-1403	128	29	(	(	PUNCT
cana-1403	128	30	pp	pp	ADJ
cana-1403	128	31	.	.	PUNCT
cana-1403	128	32	)	)	PUNCT
cana-1403	128	33	.	.	PUNCT
cana-1403	129	1	springer	springer	PROPN
cana-1403	129	2	berlin	berlin	PROPN
cana-1403	129	3	heidelberg	heidelberg	PROPN
cana-1403	129	4	.	.	PUNCT
cana-1403	130	1	[	[	X
cana-1403	130	2	11	11	NUM
cana-1403	130	3	]	]	X
cana-1403	130	4	göcen	göcen	NOUN
cana-1403	130	5	,	,	PUNCT
cana-1403	130	6	m.	m.	NOUN
cana-1403	130	7	(	(	PUNCT
cana-1403	130	8	)	)	PUNCT
cana-1403	130	9	.	.	PUNCT
cana-1403	131	1	on	on	ADP
cana-1403	131	2	some	some	DET
cana-1403	131	3	difference	difference	NOUN
cana-1403	131	4	equations	equation	NOUN
cana-1403	131	5	of	of	ADP
cana-1403	131	6	exponential	exponential	ADJ
cana-1403	131	7	form	form	NOUN
cana-1403	131	8	.	.	PUNCT
cana-1403	132	1	karaelmas	karaelmas	PROPN
cana-1403	132	2	science	science	PROPN
cana-1403	132	3	engineering	engineering	PROPN
cana-1403	132	4	journal	journal	PROPN
cana-1403	132	5	karaelmas	karaelmas	PROPN
cana-1403	132	6	fen	fen	PROPN
cana-1403	132	7	ve	ve	PROPN
cana-1403	132	8	mühendislik	mühendislik	PROPN
cana-1403	132	9	dergisi	dergisi	PROPN
cana-1403	132	10	,	,	PUNCT
cana-1403	132	11	(	(	PUNCT
cana-1403	132	12	)	)	PUNCT
cana-1403	132	13	communications	communication	NOUN
cana-1403	132	14	on	on	ADP
cana-1403	132	15	applied	apply	VERB
cana-1403	132	16	nonlinear	nonlinear	ADJ
cana-1403	132	17	analysis	analysis	NOUN
cana-1403	132	18	issn	issn	NOUN
cana-1403	132	19	:	:	PUNCT
cana-1403	132	20	1074	1074	NUM
cana-1403	132	21	-	-	PUNCT
cana-1403	132	22	133x	133x	NUM
cana-1403	132	23	vol	vol	NOUN
cana-1403	132	24	31	31	NUM
cana-1403	132	25	no	no	NOUN
cana-1403	132	26	.	.	PUNCT
cana-1403	133	1	7s	7	NOUN
cana-1403	133	2	(	(	PUNCT
cana-1403	133	3	2024	2024	NUM
cana-1403	133	4	)	)	PUNCT
cana-1403	133	5	639	639	NUM
cana-1403	133	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1403	134	1	[	[	X
cana-1403	134	2	12	12	NUM
cana-1403	134	3	]	]	X
cana-1403	134	4	ibrahim	ibrahim	PROPN
cana-1403	134	5	,	,	PUNCT
cana-1403	134	6	t.	t.	PROPN
cana-1403	134	7	f.	f.	PROPN
cana-1403	134	8	,	,	PUNCT
cana-1403	134	9	khan	khan	PROPN
cana-1403	134	10	,	,	PUNCT
cana-1403	134	11	a.	a.	PROPN
cana-1403	134	12	q.	q.	PROPN
cana-1403	134	13	,	,	PUNCT
cana-1403	134	14	alshehri	alshehri	PROPN
cana-1403	134	15	,	,	PUNCT
cana-1403	134	16	f.	f.	PROPN
cana-1403	134	17	m.	m.	PROPN
cana-1403	134	18	,	,	PUNCT
cana-1403	134	19	el	el	PROPN
cana-1403	134	20	-	-	PUNCT
cana-1403	134	21	moneam	moneam	PROPN
cana-1403	134	22	,	,	PUNCT
cana-1403	134	23	m.	m.	NOUN
cana-1403	134	24	a.	a.	NOUN
cana-1403	134	25	(	(	PUNCT
cana-1403	134	26	)	)	PUNCT
cana-1403	134	27	.	.	PUNCT
cana-1403	135	1	global	global	ADJ
cana-1403	135	2	stability	stability	NOUN
cana-1403	135	3	of	of	ADP
cana-1403	135	4	a	a	DET
cana-1403	135	5	second	second	ADJ
cana-1403	135	6	-	-	PUNCT
cana-1403	135	7	order	order	NOUN
cana-1403	135	8	exponential	exponential	ADJ
cana-1403	135	9	-	-	PUNCT
cana-1403	135	10	type	type	NOUN
cana-1403	135	11	difference	difference	NOUN
cana-1403	135	12	equation	equation	NOUN
cana-1403	135	13	.	.	PUNCT
cana-1403	136	1	symmetry	symmetry	NOUN
cana-1403	136	2	,	,	PUNCT
cana-1403	136	3	(	(	PUNCT
cana-1403	136	4	)	)	PUNCT
cana-1403	136	5	.	.	PUNCT
cana-1403	137	1	[	[	X
cana-1403	137	2	13	13	NUM
cana-1403	137	3	]	]	SYM
cana-1403	137	4	karatas	karata	NOUN
cana-1403	137	5	,	,	PUNCT
cana-1403	137	6	r.	r.	PROPN
cana-1403	137	7	(	(	PUNCT
cana-1403	137	8	2010	2010	NUM
cana-1403	137	9	)	)	PUNCT
cana-1403	137	10	.	.	PUNCT
cana-1403	138	1	global	global	ADJ
cana-1403	138	2	behavior	behavior	NOUN
cana-1403	138	3	of	of	ADP
cana-1403	138	4	a	a	DET
cana-1403	138	5	higher	high	ADJ
cana-1403	138	6	order	order	NOUN
cana-1403	138	7	difference	difference	NOUN
cana-1403	138	8	equation	equation	NOUN
cana-1403	138	9	.	.	PUNCT
cana-1403	139	1	computers	computer	NOUN
cana-1403	139	2	and	and	CCONJ
cana-1403	139	3	mathematics	mathematic	NOUN
cana-1403	139	4	with	with	ADP
cana-1403	139	5	applications	application	NOUN
cana-1403	139	6	,	,	PUNCT
cana-1403	139	7	60(3	60(3	NOUN
cana-1403	139	8	)	)	PUNCT
cana-1403	139	9	,	,	PUNCT
cana-1403	139	10	830	830	NUM
cana-1403	139	11	-	-	SYM
cana-1403	139	12	839	839	NUM
cana-1403	139	13	.	.	PUNCT
cana-1403	140	1	[	[	X
cana-1403	140	2	14	14	NUM
cana-1403	140	3	]	]	X
cana-1403	140	4	khasminskii	khasminskii	PROPN
cana-1403	140	5	,	,	PUNCT
cana-1403	140	6	r.	r.	PROPN
cana-1403	140	7	(	(	PUNCT
cana-1403	140	8	)	)	PUNCT
cana-1403	140	9	stochastic	stochastic	ADJ
cana-1403	140	10	stability	stability	NOUN
cana-1403	140	11	of	of	ADP
cana-1403	140	12	differential	differential	ADJ
cana-1403	140	13	equations	equation	NOUN
cana-1403	140	14	.	.	PUNCT
cana-1403	141	1	springer	springer	NOUN
cana-1403	141	2	.	.	PUNCT
cana-1403	142	1	[	[	X
cana-1403	142	2	15	15	NUM
cana-1403	142	3	]	]	X
cana-1403	142	4	kolmanovskii	kolmanovskii	PROPN
cana-1403	142	5	,	,	PUNCT
cana-1403	142	6	v.b	v.b	PROPN
cana-1403	142	7	.	.	PROPN
cana-1403	142	8	,	,	PUNCT
cana-1403	142	9	and	and	CCONJ
cana-1403	142	10	shaikhet	shaikhet	NOUN
cana-1403	142	11	,	,	PUNCT
cana-1403	142	12	l.e	l.e	PROPN
cana-1403	142	13	.	.	PROPN
cana-1403	142	14	(	(	PUNCT
cana-1403	142	15	1995	1995	NUM
cana-1403	142	16	)	)	PUNCT
cana-1403	142	17	.	.	PUNCT
cana-1403	143	1	general	general	ADJ
cana-1403	143	2	method	method	NOUN
cana-1403	143	3	of	of	ADP
cana-1403	143	4	lyapunov	lyapunov	PROPN
cana-1403	143	5	functionals	functional	VERB
cana-1403	143	6	construction	construction	NOUN
cana-1403	143	7	for	for	ADP
cana-1403	143	8	stability	stability	NOUN
cana-1403	143	9	investigations	investigation	NOUN
cana-1403	143	10	of	of	ADP
cana-1403	143	11	stochastic	stochastic	ADJ
cana-1403	143	12	difference	difference	NOUN
cana-1403	143	13	equations	equation	NOUN
cana-1403	143	14	.	.	PUNCT
cana-1403	144	1	in	in	ADP
cana-1403	144	2	dynamical	dynamical	ADJ
cana-1403	144	3	systems	system	NOUN
cana-1403	144	4	and	and	CCONJ
cana-1403	144	5	applications	application	NOUN
cana-1403	144	6	.	.	PUNCT
cana-1403	145	1	world	world	NOUN
cana-1403	145	2	scientific	scientific	ADJ
cana-1403	145	3	series	series	NOUN
cana-1403	145	4	in	in	ADP
cana-1403	145	5	applicable	applicable	ADJ
cana-1403	145	6	analysis	analysis	NOUN
cana-1403	145	7	4	4	NUM
cana-1403	145	8	.	.	PUNCT
cana-1403	145	9	world	world	PROPN
cana-1403	145	10	sci	sci	PROPN
cana-1403	145	11	.	.	PROPN
cana-1403	145	12	publ	publ	PROPN
cana-1403	145	13	.	.	PUNCT
cana-1403	145	14	,	,	PUNCT
cana-1403	145	15	river	river	NOUN
cana-1403	145	16	edge	edge	NOUN
cana-1403	145	17	,	,	PUNCT
cana-1403	145	18	nj	nj	PROPN
cana-1403	145	19	.	.	PUNCT
cana-1403	146	1	[	[	X
cana-1403	146	2	16	16	NUM
cana-1403	146	3	]	]	X
cana-1403	146	4	kulenovic	kulenovic	PROPN
cana-1403	146	5	,	,	PUNCT
cana-1403	146	6	m.	m.	PROPN
cana-1403	146	7	r.	r.	PROPN
cana-1403	146	8	,	,	PUNCT
cana-1403	146	9	&	&	CCONJ
cana-1403	146	10	ladas	ladas	PROPN
cana-1403	146	11	,	,	PUNCT
cana-1403	146	12	g.	g.	PROPN
cana-1403	146	13	(	(	PUNCT
cana-1403	146	14	2001	2001	NUM
cana-1403	146	15	)	)	PUNCT
cana-1403	146	16	.	.	PUNCT
cana-1403	147	1	dynamics	dynamic	NOUN
cana-1403	147	2	of	of	ADP
cana-1403	147	3	second	second	ADJ
cana-1403	147	4	order	order	NOUN
cana-1403	147	5	rational	rational	ADJ
cana-1403	147	6	difference	difference	NOUN
cana-1403	147	7	equations	equation	NOUN
cana-1403	147	8	:	:	PUNCT
cana-1403	147	9	with	with	ADP
cana-1403	147	10	open	open	ADJ
cana-1403	147	11	problems	problem	NOUN
cana-1403	147	12	and	and	CCONJ
cana-1403	147	13	conjectures	conjecture	VERB
cana-1403	147	14	.	.	PUNCT
cana-1403	148	1	chapman	chapman	NOUN
cana-1403	148	2	and	and	CCONJ
cana-1403	148	3	hall	hall	PROPN
cana-1403	148	4	/	/	SYM
cana-1403	148	5	crc	crc	NOUN
cana-1403	148	6	.	.	PUNCT
cana-1403	149	1	[	[	X
cana-1403	149	2	17	17	NUM
cana-1403	149	3	]	]	X
cana-1403	149	4	markov	markov	NOUN
cana-1403	149	5	,	,	PUNCT
cana-1403	149	6	a.	a.	NOUN
cana-1403	149	7	a.	a.	NOUN
cana-1403	149	8	(	(	PUNCT
cana-1403	149	9	)	)	PUNCT
cana-1403	149	10	.	.	PUNCT
cana-1403	150	1	extension	extension	NOUN
cana-1403	150	2	of	of	ADP
cana-1403	150	3	the	the	DET
cana-1403	150	4	law	law	NOUN
cana-1403	150	5	of	of	ADP
cana-1403	150	6	large	large	ADJ
cana-1403	150	7	numbers	number	NOUN
cana-1403	150	8	to	to	ADP
cana-1403	150	9	dependent	dependent	ADJ
cana-1403	150	10	quantities	quantity	NOUN
cana-1403	150	11	.	.	PUNCT
cana-1403	151	1	izv	izv	PROPN
cana-1403	151	2	.	.	PUNCT
cana-1403	152	1	fiz.-matem	fiz.-matem	PROPN
cana-1403	152	2	.	.	PUNCT
cana-1403	153	1	obsch	obsch	PROPN
cana-1403	153	2	.	.	PUNCT
cana-1403	154	1	kazan	kazan	PROPN
cana-1403	154	2	univ.(2nd	univ.(2nd	PROPN
cana-1403	154	3	ser	ser	PROPN
cana-1403	154	4	)	)	PUNCT
cana-1403	154	5	,	,	PUNCT
cana-1403	154	6	(	(	PUNCT
cana-1403	154	7	)	)	PUNCT
cana-1403	155	1	[	[	X
cana-1403	155	2	18	18	NUM
cana-1403	155	3	]	]	PUNCT
cana-1403	155	4	mohammed	mohammed	PROPN
cana-1403	155	5	,	,	PUNCT
cana-1403	155	6	p.	p.	PROPN
cana-1403	155	7	o.	o.	PROPN
cana-1403	155	8	,	,	PUNCT
cana-1403	155	9	baleanu	baleanu	PROPN
cana-1403	155	10	,	,	PUNCT
cana-1403	155	11	d.	d.	PROPN
cana-1403	155	12	,	,	PUNCT
cana-1403	155	13	abdeljawad	abdeljawad	NOUN
cana-1403	155	14	,	,	PUNCT
cana-1403	155	15	t.	t.	PROPN
cana-1403	155	16	,	,	PUNCT
cana-1403	155	17	sahoo	sahoo	PROPN
cana-1403	155	18	,	,	PUNCT
cana-1403	155	19	s.	s.	PROPN
cana-1403	155	20	k.	k.	PROPN
cana-1403	155	21	,	,	PUNCT
cana-1403	155	22	&	&	CCONJ
cana-1403	155	23	abualnaja	abualnaja	PROPN
cana-1403	155	24	,	,	PUNCT
cana-1403	155	25	k.	k.	PROPN
cana-1403	155	26	m.	m.	PROPN
cana-1403	155	27	(	(	PUNCT
cana-1403	155	28	2023	2023	NUM
cana-1403	155	29	)	)	PUNCT
cana-1403	155	30	.	.	PUNCT
cana-1403	156	1	positivity	positivity	NOUN
cana-1403	156	2	analysis	analysis	NOUN
cana-1403	156	3	for	for	ADP
cana-1403	156	4	mixed	mixed	ADJ
cana-1403	156	5	order	order	NOUN
cana-1403	156	6	sequential	sequential	ADJ
cana-1403	156	7	fractional	fractional	ADJ
cana-1403	156	8	difference	difference	NOUN
cana-1403	156	9	operators	operator	NOUN
cana-1403	156	10	.	.	PUNCT
cana-1403	157	1	[	[	X
cana-1403	157	2	19	19	NUM
cana-1403	157	3	]	]	X
cana-1403	157	4	n.	n.	NOUN
cana-1403	157	5	bradul	bradul	NOUN
cana-1403	157	6	and	and	CCONJ
cana-1403	157	7	l.	l.	PROPN
cana-1403	157	8	shaikhet,(2007	shaikhet,(2007	NOUN
cana-1403	157	9	)	)	PUNCT
cana-1403	157	10	“	"	PUNCT
cana-1403	157	11	stability	stability	NOUN
cana-1403	157	12	of	of	ADP
cana-1403	157	13	the	the	DET
cana-1403	157	14	positive	positive	ADJ
cana-1403	157	15	point	point	NOUN
cana-1403	157	16	of	of	ADP
cana-1403	157	17	equilibrium	equilibrium	NOUN
cana-1403	157	18	of	of	ADP
cana-1403	157	19	nicholson‟s	nicholson‟s	X
cana-1403	157	20	blowflies	blowfly	NOUN
cana-1403	157	21	equation	equation	NOUN
cana-1403	157	22	with	with	ADP
cana-1403	157	23	stochastic	stochastic	ADJ
cana-1403	157	24	perturbations	perturbation	NOUN
cana-1403	157	25	:	:	PUNCT
cana-1403	157	26	numerical	numerical	ADJ
cana-1403	157	27	analysis	analysis	NOUN
cana-1403	157	28	,	,	PUNCT
cana-1403	157	29	”	"	PUNCT
cana-1403	157	30	discrete	discrete	ADJ
cana-1403	157	31	dynamics	dynamic	NOUN
cana-1403	157	32	in	in	ADP
cana-1403	157	33	nature	nature	NOUN
cana-1403	157	34	and	and	CCONJ
cana-1403	157	35	society	society	NOUN
cana-1403	157	36	,	,	PUNCT
cana-1403	157	37	article	article	NOUN
cana-1403	157	38	i	i	PROPN
cana-1403	157	39	d	d	PROPN
cana-1403	157	40	92959	92959	NUM
cana-1403	157	41	,	,	PUNCT
cana-1403	157	42	25	25	NUM
cana-1403	157	43	pages	page	NOUN
cana-1403	157	44	.	.	PUNCT
cana-1403	158	1	[	[	X
cana-1403	158	2	20	20	NUM
cana-1403	158	3	]	]	SYM
cana-1403	158	4	ozturk	ozturk	PROPN
cana-1403	158	5	,	,	PUNCT
cana-1403	158	6	i.	i.	PROPN
cana-1403	158	7	,	,	PUNCT
cana-1403	158	8	bozkurt	bozkurt	PROPN
cana-1403	158	9	,	,	PUNCT
cana-1403	158	10	f.	f.	PROPN
cana-1403	158	11	,	,	PUNCT
cana-1403	158	12	ozen	ozen	PROPN
cana-1403	158	13	,	,	PUNCT
cana-1403	158	14	s.	s.	PROPN
cana-1403	158	15	(	(	PUNCT
cana-1403	158	16	)	)	PUNCT
cana-1403	158	17	.	.	PUNCT
cana-1403	159	1	on	on	ADP
cana-1403	159	2	the	the	DET
cana-1403	159	3	difference	difference	NOUN
cana-1403	159	4	equation	equation	NOUN
cana-1403	159	5	(	(	PUNCT
cana-1403	159	6	)	)	PUNCT
cana-1403	159	7	(	(	PUNCT
cana-1403	159	8	)	)	PUNCT
cana-1403	159	9	.	.	PUNCT
cana-1403	160	1	applied	apply	VERB
cana-1403	160	2	mathematics	mathematic	NOUN
cana-1403	160	3	and	and	CCONJ
cana-1403	160	4	computation	computation	NOUN
cana-1403	160	5	,	,	PUNCT
cana-1403	160	6	(	(	PUNCT
cana-1403	160	7	)	)	PUNCT
cana-1403	160	8	.	.	PUNCT
cana-1403	161	1	[	[	X
cana-1403	161	2	21	21	NUM
cana-1403	161	3	]	]	PUNCT
cana-1403	161	4	papaschinopoulos	papaschinopoulo	NOUN
cana-1403	161	5	,	,	PUNCT
cana-1403	161	6	g.	g.	PROPN
cana-1403	161	7	,	,	PUNCT
cana-1403	161	8	ellina	ellina	PROPN
cana-1403	161	9	,	,	PUNCT
cana-1403	161	10	g.	g.	PROPN
cana-1403	161	11	,	,	PUNCT
cana-1403	161	12	papadopoulos	papadopoulos	PROPN
cana-1403	161	13	,	,	PUNCT
cana-1403	161	14	k.	k.	PROPN
cana-1403	161	15	b.	b.	PROPN
cana-1403	161	16	(	(	PUNCT
cana-1403	161	17	)	)	PUNCT
cana-1403	161	18	.	.	PUNCT
cana-1403	162	1	asymptotic	asymptotic	ADJ
cana-1403	162	2	behavior	behavior	NOUN
cana-1403	162	3	of	of	ADP
cana-1403	162	4	the	the	DET
cana-1403	162	5	positive	positive	ADJ
cana-1403	162	6	solutions	solution	NOUN
cana-1403	162	7	of	of	ADP
cana-1403	162	8	an	an	DET
cana-1403	162	9	exponential	exponential	ADJ
cana-1403	162	10	type	type	NOUN
cana-1403	162	11	system	system	NOUN
cana-1403	162	12	of	of	ADP
cana-1403	162	13	difference	difference	NOUN
cana-1403	162	14	equations	equation	NOUN
cana-1403	162	15	.	.	PUNCT
cana-1403	163	1	applied	apply	VERB
cana-1403	163	2	mathematics	mathematic	NOUN
cana-1403	163	3	and	and	CCONJ
cana-1403	163	4	computation	computation	NOUN
cana-1403	163	5	,	,	PUNCT
cana-1403	163	6	.	.	PUNCT
cana-1403	164	1	[	[	X
cana-1403	164	2	22	22	NUM
cana-1403	164	3	]	]	SYM
cana-1403	164	4	paternoster	paternoster	PROPN
cana-1403	164	5	,	,	PUNCT
cana-1403	164	6	b.	b.	PROPN
cana-1403	164	7	,	,	PUNCT
cana-1403	164	8	and	and	CCONJ
cana-1403	164	9	shaikhet	shaikhet	NOUN
cana-1403	164	10	,	,	PUNCT
cana-1403	164	11	l.	l.	PROPN
cana-1403	164	12	(	(	PUNCT
cana-1403	164	13	2000	2000	NUM
cana-1403	164	14	)	)	PUNCT
cana-1403	164	15	.	.	PUNCT
cana-1403	165	1	about	about	ADP
cana-1403	165	2	stability	stability	NOUN
cana-1403	165	3	of	of	ADP
cana-1403	165	4	nonlinear	nonlinear	ADJ
cana-1403	165	5	stochastic	stochastic	ADJ
cana-1403	165	6	difference	difference	NOUN
cana-1403	165	7	equations	equation	NOUN
cana-1403	165	8	.	.	PUNCT
cana-1403	166	1	applied	apply	VERB
cana-1403	166	2	mathematics	mathematics	NOUN
cana-1403	166	3	letters	letter	NOUN
cana-1403	166	4	13:27–32	13:27–32	NUM
cana-1403	166	5	.	.	PUNCT
cana-1403	167	1	[	[	X
cana-1403	167	2	23	23	NUM
cana-1403	167	3	]	]	SYM
cana-1403	167	4	paternoster	paternoster	PROPN
cana-1403	167	5	,	,	PUNCT
cana-1403	167	6	b.	b.	PROPN
cana-1403	167	7	,	,	PUNCT
cana-1403	167	8	shaikhet	shaikhet	PROPN
cana-1403	167	9	,	,	PUNCT
cana-1403	167	10	l.	l.	PROPN
cana-1403	167	11	(	(	PUNCT
cana-1403	167	12	)	)	PUNCT
cana-1403	167	13	.	.	PUNCT
cana-1403	168	1	stability	stability	NOUN
cana-1403	168	2	of	of	ADP
cana-1403	168	3	equilibrium	equilibrium	NOUN
cana-1403	168	4	points	point	NOUN
cana-1403	168	5	of	of	ADP
cana-1403	168	6	fractional	fractional	ADJ
cana-1403	168	7	difference	difference	NOUN
cana-1403	168	8	equations	equation	NOUN
cana-1403	168	9	with	with	ADP
cana-1403	168	10	stochastic	stochastic	ADJ
cana-1403	168	11	perturbations	perturbation	NOUN
cana-1403	168	12	.	.	PUNCT
cana-1403	169	1	advances	advance	NOUN
cana-1403	169	2	in	in	ADP
cana-1403	169	3	difference	difference	NOUN
cana-1403	169	4	equations	equation	NOUN
cana-1403	169	5	,	,	PUNCT
cana-1403	169	6	.	.	PUNCT
cana-1403	170	1	[	[	X
cana-1403	170	2	24	24	NUM
cana-1403	170	3	]	]	X
cana-1403	170	4	p.	p.	NOUN
cana-1403	170	5	borne	borne	NOUN
cana-1403	170	6	,	,	PUNCT
cana-1403	170	7	v.	v.	PROPN
cana-1403	170	8	kolmanovskii	kolmanovskii	PROPN
cana-1403	170	9	,	,	PUNCT
cana-1403	170	10	and	and	CCONJ
cana-1403	170	11	l.	l.	PROPN
cana-1403	170	12	shaikhet	shaikhet	PROPN
cana-1403	170	13	,	,	PUNCT
cana-1403	170	14	(	(	PUNCT
cana-1403	170	15	2000	2000	NUM
cana-1403	170	16	)	)	PUNCT
cana-1403	170	17	.	.	PUNCT
cana-1403	171	1	stabilization	stabilization	NOUN
cana-1403	171	2	of	of	ADP
cana-1403	171	3	inverted	inverted	ADJ
cana-1403	171	4	pendulum	pendulum	NOUN
cana-1403	171	5	by	by	ADP
cana-1403	171	6	control	control	NOUN
cana-1403	171	7	with	with	ADP
cana-1403	171	8	delay	delay	NOUN
cana-1403	171	9	,	,	PUNCT
cana-1403	171	10	dynam	dynam	NOUN
cana-1403	171	11	.	.	PUNCT
cana-1403	172	1	systems	system	NOUN
cana-1403	172	2	appl	appl	PROPN
cana-1403	172	3	.	.	PROPN
cana-1403	172	4	,	,	PUNCT
cana-1403	172	5	9	9	NUM
cana-1403	172	6	,	,	PUNCT
cana-1403	172	7	pp	pp	ADJ
cana-1403	172	8	.	.	PUNCT
cana-1403	173	1	501–514	501–514	NUM
cana-1403	173	2	.	.	PUNCT
cana-1403	174	1	[	[	X
cana-1403	174	2	25	25	NUM
cana-1403	174	3	]	]	PUNCT
cana-1403	174	4	psarros	psarro	NOUN
cana-1403	174	5	,	,	PUNCT
cana-1403	174	6	n.	n.	NOUN
cana-1403	174	7	,	,	PUNCT
cana-1403	174	8	papaschinopoulos	papaschinopoulo	NOUN
cana-1403	174	9	,	,	PUNCT
cana-1403	174	10	g.	g.	PROPN
cana-1403	174	11	,	,	PUNCT
cana-1403	174	12	schinas	schinas	PROPN
cana-1403	174	13	,	,	PUNCT
cana-1403	174	14	c.	c.	PROPN
cana-1403	174	15	j.	j.	PROPN
cana-1403	174	16	(	(	PUNCT
cana-1403	174	17	)	)	PUNCT
cana-1403	174	18	.	.	PUNCT
cana-1403	175	1	on	on	ADP
cana-1403	175	2	the	the	DET
cana-1403	175	3	stability	stability	NOUN
cana-1403	175	4	of	of	ADP
cana-1403	175	5	some	some	DET
cana-1403	175	6	systems	system	NOUN
cana-1403	175	7	of	of	ADP
cana-1403	175	8	exponential	exponential	ADJ
cana-1403	175	9	difference	difference	NOUN
cana-1403	175	10	equations	equation	NOUN
cana-1403	175	11	.	.	PUNCT
cana-1403	176	1	opuscula	opuscula	PROPN
cana-1403	176	2	mathematica	mathematica	PROPN
cana-1403	176	3	,	,	PUNCT
cana-1403	176	4	(	(	PUNCT
cana-1403	176	5	)	)	PUNCT
cana-1403	176	6	.	.	PUNCT
cana-1403	177	1	[	[	X
cana-1403	177	2	26	26	NUM
cana-1403	177	3	]	]	X
cana-1403	177	4	saleh	saleh	NOUN
cana-1403	177	5	,	,	PUNCT
cana-1403	177	6	m.	m.	NOUN
cana-1403	177	7	,	,	PUNCT
cana-1403	177	8	&	&	CCONJ
cana-1403	177	9	hirzallah	hirzallah	PROPN
cana-1403	177	10	,	,	PUNCT
cana-1403	177	11	s.	s.	PROPN
cana-1403	177	12	(	(	PUNCT
cana-1403	177	13	2021	2021	NUM
cana-1403	177	14	)	)	PUNCT
cana-1403	177	15	.	.	PUNCT
cana-1403	178	1	dynamics	dynamic	NOUN
cana-1403	178	2	and	and	CCONJ
cana-1403	178	3	bifurcation	bifurcation	NOUN
cana-1403	178	4	of	of	ADP
cana-1403	178	5	a	a	DET
cana-1403	178	6	second	second	ADJ
cana-1403	178	7	order	order	NOUN
cana-1403	178	8	rational	rational	ADJ
cana-1403	178	9	difference	difference	NOUN
cana-1403	178	10	equation	equation	NOUN
cana-1403	178	11	with	with	ADP
cana-1403	178	12	quadratic	quadratic	ADJ
cana-1403	178	13	terms	term	NOUN
cana-1403	178	14	.	.	PUNCT
cana-1403	179	1	[	[	X
cana-1403	179	2	27	27	NUM
cana-1403	179	3	]	]	PUNCT
cana-1403	179	4	shaikhet	shaikhet	NOUN
cana-1403	179	5	,	,	PUNCT
cana-1403	179	6	l.	l.	PROPN
cana-1403	179	7	(	(	PUNCT
cana-1403	179	8	)	)	PUNCT
cana-1403	179	9	.	.	PUNCT
cana-1403	180	1	about	about	ADP
cana-1403	180	2	an	an	DET
cana-1403	180	3	unsolved	unsolved	ADJ
cana-1403	180	4	problem	problem	NOUN
cana-1403	180	5	of	of	ADP
cana-1403	180	6	stabilization	stabilization	NOUN
cana-1403	180	7	by	by	ADP
cana-1403	180	8	noise	noise	NOUN
cana-1403	180	9	for	for	ADP
cana-1403	180	10	difference	difference	NOUN
cana-1403	180	11	equations	equation	NOUN
cana-1403	180	12	.	.	PUNCT
cana-1403	181	1	mathematics	mathematic	NOUN
cana-1403	181	2	,	,	PUNCT
cana-1403	181	3	(	(	PUNCT
cana-1403	181	4	)	)	PUNCT
cana-1403	181	5	.	.	PUNCT
cana-1403	182	1	[	[	X
cana-1403	182	2	28	28	NUM
cana-1403	182	3	]	]	PUNCT
cana-1403	182	4	shaikhet	shaikhet	NOUN
cana-1403	182	5	,	,	PUNCT
cana-1403	182	6	l.	l.	PROPN
cana-1403	182	7	(	(	PUNCT
cana-1403	182	8	)	)	PUNCT
cana-1403	182	9	.	.	PUNCT
cana-1403	183	1	about	about	ADP
cana-1403	183	2	stability	stability	NOUN
cana-1403	183	3	of	of	ADP
cana-1403	183	4	difference	difference	NOUN
cana-1403	183	5	equations	equation	NOUN
cana-1403	183	6	with	with	ADP
cana-1403	183	7	square	square	ADJ
cana-1403	183	8	summable	summable	ADJ
cana-1403	183	9	level	level	NOUN
cana-1403	183	10	of	of	ADP
cana-1403	183	11	stochastic	stochastic	ADJ
cana-1403	183	12	perturbations	perturbation	NOUN
cana-1403	183	13	.	.	PUNCT
cana-1403	184	1	journal	journal	NOUN
cana-1403	184	2	of	of	ADP
cana-1403	184	3	difference	difference	NOUN
cana-1403	184	4	equations	equation	NOUN
cana-1403	184	5	and	and	CCONJ
cana-1403	184	6	applications	application	NOUN
cana-1403	184	7	,	,	PUNCT
cana-1403	184	8	(	(	PUNCT
cana-1403	184	9	)	)	PUNCT
cana-1403	184	10	.	.	PUNCT
cana-1403	185	1	[	[	X
cana-1403	185	2	29	29	NUM
cana-1403	185	3	]	]	PUNCT
cana-1403	185	4	shaikhet	shaikhet	NOUN
cana-1403	185	5	,	,	PUNCT
cana-1403	185	6	l.	l.	PROPN
cana-1403	185	7	(	(	PUNCT
cana-1403	185	8	)	)	PUNCT
cana-1403	185	9	.	.	PUNCT
cana-1403	186	1	lyapunov	lyapunov	NOUN
cana-1403	186	2	functionals	functional	NOUN
cana-1403	186	3	and	and	CCONJ
cana-1403	186	4	stability	stability	NOUN
cana-1403	186	5	of	of	ADP
cana-1403	186	6	stochastic	stochastic	ADJ
cana-1403	186	7	difference	difference	NOUN
cana-1403	186	8	equations	equation	NOUN
cana-1403	186	9	.	.	PUNCT
cana-1403	187	1	springer	springer	NOUN
cana-1403	187	2	science	science	PROPN
cana-1403	187	3	business	business	NOUN
cana-1403	187	4	media	medium	NOUN
cana-1403	187	5	.	.	PUNCT
cana-1403	188	1	communications	communication	NOUN
cana-1403	188	2	on	on	ADP
cana-1403	188	3	applied	apply	VERB
cana-1403	188	4	nonlinear	nonlinear	ADJ
cana-1403	188	5	analysis	analysis	NOUN
cana-1403	188	6	issn	issn	NOUN
cana-1403	188	7	:	:	PUNCT
cana-1403	188	8	1074	1074	NUM
cana-1403	188	9	-	-	PUNCT
cana-1403	188	10	133x	133x	NUM
cana-1403	188	11	vol	vol	NOUN
cana-1403	188	12	31	31	NUM
cana-1403	188	13	no	no	NOUN
cana-1403	188	14	.	.	PUNCT
cana-1403	189	1	7s	7	NOUN
cana-1403	189	2	(	(	PUNCT
cana-1403	189	3	2024	2024	NUM
cana-1403	189	4	)	)	PUNCT
cana-1403	189	5	640	640	NUM
cana-1403	189	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1403	189	7	[	[	X
cana-1403	189	8	30	30	NUM
cana-1403	189	9	]	]	PUNCT
cana-1403	189	10	shaikhet	shaikhet	NOUN
cana-1403	189	11	,	,	PUNCT
cana-1403	189	12	l.	l.	PROPN
cana-1403	189	13	(	(	PUNCT
cana-1403	189	14	)	)	PUNCT
cana-1403	189	15	.	.	PUNCT
cana-1403	190	1	lyapunov	lyapunov	NOUN
cana-1403	190	2	functionals	functional	NOUN
cana-1403	190	3	and	and	CCONJ
cana-1403	190	4	stability	stability	NOUN
cana-1403	190	5	of	of	ADP
cana-1403	190	6	stochastic	stochastic	ADJ
cana-1403	190	7	functional	functional	ADJ
cana-1403	190	8	differencial	differencial	ADJ
cana-1403	190	9	equations	equation	NOUN
cana-1403	190	10	.	.	PUNCT
cana-1403	191	1	springer	springer	PROPN
cana-1403	191	2	,	,	PUNCT
cana-1403	191	3	dordrecht	dordrecht	PROPN
cana-1403	191	4	,	,	PUNCT
cana-1403	191	5	heidelberg	heidelberg	PROPN
cana-1403	191	6	,	,	PUNCT
cana-1403	191	7	new	new	PROPN
cana-1403	191	8	york	york	PROPN
cana-1403	191	9	,	,	PUNCT
cana-1403	191	10	london	london	PROPN
cana-1403	191	11	.	.	PUNCT
cana-1403	192	1	[	[	X
cana-1403	192	2	31	31	NUM
cana-1403	192	3	]	]	PUNCT
cana-1403	192	4	shaikhet	shaikhet	NOUN
cana-1403	192	5	,	,	PUNCT
cana-1403	192	6	l.	l.	PROPN
cana-1403	192	7	(	(	PUNCT
cana-1403	192	8	)	)	PUNCT
cana-1403	192	9	.	.	PUNCT
cana-1403	193	1	stability	stability	NOUN
cana-1403	193	2	of	of	ADP
cana-1403	193	3	equilibrium	equilibrium	NOUN
cana-1403	193	4	states	state	NOUN
cana-1403	193	5	for	for	ADP
cana-1403	193	6	a	a	DET
cana-1403	193	7	stochastically	stochastically	ADV
cana-1403	193	8	perturbed	perturb	VERB
cana-1403	193	9	exponential	exponential	ADJ
cana-1403	193	10	type	type	NOUN
cana-1403	193	11	system	system	NOUN
cana-1403	193	12	of	of	ADP
cana-1403	193	13	difference	difference	NOUN
cana-1403	193	14	equations	equation	NOUN
cana-1403	193	15	.	.	PUNCT
cana-1403	194	1	journal	journal	NOUN
cana-1403	194	2	of	of	ADP
cana-1403	194	3	computational	computational	ADJ
cana-1403	194	4	and	and	CCONJ
cana-1403	194	5	applied	applied	ADJ
cana-1403	194	6	mathematics	mathematic	NOUN
cana-1403	194	7	,	,	PUNCT
cana-1403	194	8	.	.	PUNCT
cana-1403	195	1	[	[	X
cana-1403	195	2	32	32	NUM
cana-1403	195	3	]	]	PUNCT
cana-1403	195	4	shaikhet	shaikhet	NOUN
cana-1403	195	5	,	,	PUNCT
cana-1403	195	6	l.	l.	PROPN
cana-1403	195	7	(	(	PUNCT
cana-1403	195	8	2014	2014	NUM
cana-1403	195	9	)	)	PUNCT
cana-1403	195	10	.	.	PUNCT
cana-1403	196	1	stability	stability	NOUN
cana-1403	196	2	of	of	ADP
cana-1403	196	3	equilibrium	equilibrium	NOUN
cana-1403	196	4	states	state	NOUN
cana-1403	196	5	for	for	ADP
cana-1403	196	6	a	a	DET
cana-1403	196	7	stochastically	stochastically	ADV
cana-1403	196	8	perturbed	perturb	VERB
cana-1403	196	9	mosquito	mosquito	ADJ
cana-1403	196	10	population	population	NOUN
cana-1403	196	11	equation	equation	NOUN
cana-1403	196	12	.	.	PUNCT
cana-1403	197	1	dyn	dyn	NOUN
cana-1403	197	2	.	.	PUNCT
cana-1403	198	1	contin	contin	AUX
cana-1403	198	2	.	.	PUNCT
cana-1403	199	1	discrete	discrete	ADJ
cana-1403	199	2	impuls	impul	NOUN
cana-1403	199	3	.	.	PUNCT
cana-1403	200	1	syst	syst	PROPN
cana-1403	200	2	.	.	PUNCT
cana-1403	200	3	ser	ser	PROPN
cana-1403	200	4	.	.	PUNCT
cana-1403	201	1	b	b	X
cana-1403	201	2	appl	appl	PROPN
cana-1403	201	3	.	.	PUNCT
cana-1403	202	1	algorithms	algorithm	NOUN
cana-1403	202	2	,	,	PUNCT
cana-1403	202	3	21(2–3	21(2–3	NUM
cana-1403	202	4	)	)	PUNCT
cana-1403	202	5	,	,	PUNCT
cana-1403	202	6	185	185	NUM
cana-1403	202	7	-	-	SYM
cana-1403	202	8	196	196	NUM
cana-1403	202	9	.	.	PUNCT
cana-1403	203	1	[	[	X
cana-1403	203	2	33	33	NUM
cana-1403	203	3	]	]	PUNCT
cana-1403	203	4	shaikhet	shaikhet	NOUN
cana-1403	203	5	,	,	PUNCT
cana-1403	203	6	l	l	PROPN
cana-1403	203	7	(	(	PUNCT
cana-1403	203	8	2019	2019	NUM
cana-1403	203	9	)	)	PUNCT
cana-1403	203	10	.	.	PUNCT
cana-1403	204	1	stability	stability	NOUN
cana-1403	204	2	of	of	ADP
cana-1403	204	3	the	the	DET
cana-1403	204	4	zero	zero	NUM
cana-1403	204	5	and	and	CCONJ
cana-1403	204	6	positive	positive	ADJ
cana-1403	204	7	equilibria	equilibrium	NOUN
cana-1403	204	8	of	of	ADP
cana-1403	204	9	two	two	NUM
cana-1403	204	10	connected	connected	ADJ
cana-1403	204	11	neoclassical	neoclassical	ADJ
cana-1403	204	12	growth	growth	NOUN
cana-1403	204	13	models	model	NOUN
cana-1403	204	14	under	under	ADP
cana-1403	204	15	stochastic	stochastic	ADJ
cana-1403	204	16	perturbations	perturbation	NOUN
cana-1403	204	17	.	.	PUNCT
cana-1403	205	1	commun	commun	PROPN
cana-1403	205	2	.	.	PUNCT
cana-1403	206	1	nonlinear	nonlinear	PROPN
cana-1403	206	2	sci	sci	PROPN
cana-1403	206	3	.	.	PUNCT
cana-1403	206	4	numer	numer	PROPN
cana-1403	206	5	.	.	PUNCT
cana-1403	207	1	simul	simul	PROPN
cana-1403	207	2	.	.	PROPN
cana-1403	208	1	2019	2019	NUM
cana-1403	208	2	,	,	PUNCT
cana-1403	208	3	68	68	NUM
cana-1403	208	4	,	,	PUNCT
cana-1403	208	5	86–93	86–93	NUM
cana-1403	208	6	.	.	PUNCT
cana-1403	209	1	[	[	X
cana-1403	209	2	34	34	NUM
cana-1403	209	3	]	]	X
cana-1403	209	4	v.	v.	CCONJ
cana-1403	209	5	lakshmikantham	lakshmikantham	PROPN
cana-1403	209	6	,	,	PUNCT
cana-1403	209	7	d.	d.	PROPN
cana-1403	209	8	trigiante	trigiante	PROPN
cana-1403	209	9	,	,	PUNCT
cana-1403	209	10	(	(	PUNCT
cana-1403	209	11	1988	1988	NUM
cana-1403	209	12	)	)	PUNCT
cana-1403	209	13	theory	theory	NOUN
cana-1403	209	14	of	of	ADP
cana-1403	209	15	difference	difference	NOUN
cana-1403	209	16	equations	equation	NOUN
cana-1403	209	17	academic	academic	ADJ
cana-1403	209	18	press	press	NOUN
cana-1403	209	19	,	,	PUNCT
cana-1403	209	20	san	san	PROPN
cana-1403	209	21	diego	diego	PROPN
cana-1403	209	22	.	.	PUNCT
cana-1403	210	1	[	[	X
cana-1403	210	2	35	35	NUM
cana-1403	210	3	]	]	X
cana-1403	210	4	zhang	zhang	PROPN
cana-1403	210	5	,	,	PUNCT
cana-1403	210	6	c.	c.	PROPN
cana-1403	210	7	,	,	PUNCT
cana-1403	210	8	li	li	PROPN
cana-1403	210	9	,	,	PUNCT
cana-1403	210	10	h.	h.	PROPN
cana-1403	210	11	x.	x.	PROPN
cana-1403	210	12	(	(	PUNCT
cana-1403	210	13	2009	2009	NUM
cana-1403	210	14	)	)	PUNCT
cana-1403	210	15	.	.	PUNCT
cana-1403	211	1	dynamics	dynamic	NOUN
cana-1403	211	2	of	of	ADP
cana-1403	211	3	a	a	DET
cana-1403	211	4	rational	rational	ADJ
cana-1403	211	5	difference	difference	NOUN
cana-1403	211	6	equation	equation	NOUN
cana-1403	211	7	of	of	ADP
cana-1403	211	8	higher	high	ADJ
cana-1403	211	9	order	order	NOUN
cana-1403	211	10	.	.	PUNCT
cana-1403	212	1	applied	apply	VERB
cana-1403	212	2	mathematics	mathematics	PROPN
cana-1403	212	3	enotes	enote	NOUN
cana-1403	212	4	,	,	PUNCT
cana-1403	212	5	9	9	NUM
cana-1403	212	6	,	,	PUNCT
cana-1403	212	7	80	80	NUM
cana-1403	212	8	-	-	SYM
cana-1403	212	9	88	88	NUM
cana-1403	212	10	.	.	PUNCT
cana-1403	213	1	[	[	X
cana-1403	213	2	36	36	NUM
cana-1403	213	3	]	]	X
cana-1403	213	4	zhao	zhao	X
cana-1403	213	5	,	,	PUNCT
cana-1403	213	6	houyu	houyu	VERB
cana-1403	213	7	(	(	PUNCT
cana-1403	213	8	2013	2013	NUM
cana-1403	213	9	)	)	PUNCT
cana-1403	213	10	.	.	PUNCT
cana-1403	214	1	analytic	analytic	ADJ
cana-1403	214	2	invariant	invariant	ADJ
cana-1403	214	3	curves	curve	NOUN
cana-1403	214	4	for	for	ADP
cana-1403	214	5	an	an	DET
cana-1403	214	6	iterative	iterative	NOUN
cana-1403	214	7	equation	equation	NOUN
cana-1403	214	8	related	relate	VERB
cana-1403	214	9	to	to	ADP
cana-1403	214	10	pielou‟s	pielou‟s	PUNCT
cana-1403	214	11	equation	equation	NOUN
cana-1403	214	12	,	,	PUNCT
cana-1403	214	13	j.	j.	PROPN
cana-1403	214	14	difference	difference	PROPN
cana-1403	214	15	equ	equ	PROPN
cana-1403	214	16	.	.	PUNCT
cana-1403	214	17	appl	appl	PROPN
cana-1403	214	18	.	.	PROPN
cana-1403	215	1	19	19	NUM
cana-1403	215	2	no	no	NOUN
cana-1403	215	3	.	.	NOUN
cana-1403	215	4	7	7	NUM
cana-1403	215	5	,	,	PUNCT
cana-1403	215	6	1082	1082	NUM
cana-1403	215	7	-	-	SYM
cana-1403	215	8	1092	1092	NUM
cana-1403	215	9	.	.	PUNCT