id	sid	tid	token	lemma	pos
cana-932	1	1	communications	communication	NOUN
cana-932	1	2	on	on	ADP
cana-932	1	3	applied	apply	VERB
cana-932	1	4	nonlinear	nonlinear	ADJ
cana-932	1	5	analysis	analysis	NOUN
cana-932	1	6	issn	issn	NOUN
cana-932	1	7	:	:	PUNCT
cana-932	1	8	1074	1074	NUM
cana-932	1	9	-	-	PUNCT
cana-932	1	10	133x	133x	NUM
cana-932	1	11	vol	vol	NOUN
cana-932	1	12	31	31	NUM
cana-932	1	13	no	no	NOUN
cana-932	1	14	.	.	PUNCT
cana-932	2	1	4s	4s	NUM
cana-932	2	2	(	(	PUNCT
cana-932	2	3	2024	2024	NUM
cana-932	2	4	)	)	PUNCT
cana-932	2	5	403	403	NUM
cana-932	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-932	2	7	advanced	advance	VERB
cana-932	2	8	analytical	analytical	ADJ
cana-932	2	9	and	and	CCONJ
cana-932	2	10	numerical	numerical	ADJ
cana-932	2	11	studies	study	NOUN
cana-932	2	12	on	on	ADP
cana-932	2	13	coupled	couple	VERB
cana-932	2	14	schrödinger	schrödinger	ADJ
cana-932	2	15	equations	equation	NOUN
cana-932	2	16	with	with	ADP
cana-932	2	17	fractional	fractional	ADJ
cana-932	2	18	order	order	NOUN
cana-932	2	19	damping	damp	VERB
cana-932	2	20	iftekher	iftekher	PROPN
cana-932	2	21	s.	s.	PROPN
cana-932	2	22	chowdhury1,dr	chowdhury1,dr	PROPN
cana-932	2	23	.	.	PUNCT
cana-932	3	1	eric	eric	PROPN
cana-932	3	2	howard2,dr	howard2,dr	PROPN
cana-932	3	3	nand	nand	PROPN
cana-932	3	4	kumar3	kumar3	NOUN
cana-932	3	5	1	1	NUM
cana-932	3	6	macquarie	macquarie	PROPN
cana-932	3	7	university	university	PROPN
cana-932	3	8	,	,	PUNCT
cana-932	3	9	department	department	NOUN
cana-932	3	10	of	of	ADP
cana-932	3	11	physics	physics	PROPN
cana-932	3	12	and	and	CCONJ
cana-932	3	13	astronomy	astronomy	NOUN
cana-932	3	14	,	,	PUNCT
cana-932	3	15	sydney	sydney	PROPN
cana-932	3	16	,	,	PUNCT
cana-932	3	17	nsw	nsw	PROPN
cana-932	3	18	,	,	PUNCT
cana-932	3	19	2109	2109	NUM
cana-932	3	20	,	,	PUNCT
cana-932	3	21	australia	australia	PROPN
cana-932	3	22	.	.	PUNCT
cana-932	4	1	e	e	X
cana-932	4	2	-	-	NOUN
cana-932	4	3	mail	mail	NOUN
cana-932	4	4	:	:	PUNCT
cana-932	4	5	mdiftekher@gmail.com	mdiftekher@gmail.com	X
cana-932	4	6	.	.	NOUN
cana-932	4	7	2	2	NUM
cana-932	4	8	department	department	NOUN
cana-932	4	9	of	of	ADP
cana-932	4	10	physics	physics	PROPN
cana-932	4	11	and	and	CCONJ
cana-932	4	12	astronomy	astronomy	NOUN
cana-932	4	13	,	,	PUNCT
cana-932	4	14	macquarie	macquarie	PROPN
cana-932	4	15	university	university	PROPN
cana-932	4	16	,	,	PUNCT
cana-932	4	17	australia	australia	PROPN
cana-932	4	18	.	.	PUNCT
cana-932	5	1	email	email	NOUN
cana-932	6	1	i	i	PROPN
cana-932	6	2	d	d	PROPN
cana-932	6	3	eric.howard@mq.edu.au	eric.howard@mq.edu.au	PROPN
cana-932	6	4	.	.	PUNCT
cana-932	7	1	orcid	orcid	NOUN
cana-932	7	2	:	:	PUNCT
cana-932	7	3	0000	0000	NUM
cana-932	7	4	-	-	PUNCT
cana-932	7	5	0002	0002	NUM
cana-932	7	6	-	-	PUNCT
cana-932	7	7	8133	8133	NUM
cana-932	7	8	-	-	PUNCT
cana-932	7	9	8323	8323	NUM
cana-932	7	10	.	.	PUNCT
cana-932	8	1	3	3	NUM
cana-932	8	2	designation	designation	NOUN
cana-932	8	3	:	:	PUNCT
cana-932	8	4	assistant	assistant	NOUN
cana-932	8	5	professor	professor	NOUN
cana-932	8	6	,	,	PUNCT
cana-932	8	7	department	department	NOUN
cana-932	8	8	of	of	ADP
cana-932	8	9	physics	physics	PROPN
cana-932	8	10	,	,	PUNCT
cana-932	8	11	jawaharlal	jawaharlal	PROPN
cana-932	8	12	nehru	nehru	PROPN
cana-932	8	13	memorial	memorial	PROPN
cana-932	8	14	pg	pg	PROPN
cana-932	8	15	college	college	PROPN
cana-932	8	16	,	,	PUNCT
cana-932	8	17	barabanki	barabanki	PROPN
cana-932	8	18	,	,	PUNCT
cana-932	8	19	up	up	ADP
cana-932	8	20	,	,	PUNCT
cana-932	8	21	india	india	PROPN
cana-932	8	22	.	.	PUNCT
cana-932	9	1	email:nandkumar350@gmail.com	email:nandkumar350@gmail.com	X
cana-932	9	2	.	.	PUNCT
cana-932	9	3	orcid	orcid	NOUN
cana-932	9	4	:	:	PUNCT
cana-932	9	5	0009	0009	NUM
cana-932	9	6	-	-	SYM
cana-932	9	7	0004	0004	NUM
cana-932	9	8	-	-	PUNCT
cana-932	9	9	3139	3139	NUM
cana-932	9	10	-	-	PUNCT
cana-932	9	11	3385	3385	NUM
cana-932	9	12	article	article	NOUN
cana-932	9	13	history	history	NOUN
cana-932	9	14	:	:	PUNCT
cana-932	9	15	received	receive	VERB
cana-932	9	16	:	:	PUNCT
cana-932	9	17	19	19	NUM
cana-932	9	18	-	-	PUNCT
cana-932	9	19	04	04	NUM
cana-932	9	20	-	-	PUNCT
cana-932	9	21	2024	2024	NUM
cana-932	9	22	revised	revise	VERB
cana-932	9	23	:	:	PUNCT
cana-932	9	24	11	11	NUM
cana-932	9	25	-	-	SYM
cana-932	9	26	06	06	NUM
cana-932	9	27	-	-	PUNCT
cana-932	9	28	2024	2024	NUM
cana-932	9	29	accepted	accept	VERB
cana-932	9	30	:	:	PUNCT
cana-932	9	31	25	25	NUM
cana-932	9	32	-	-	PUNCT
cana-932	9	33	06	06	NUM
cana-932	9	34	-	-	PUNCT
cana-932	9	35	2024	2024	NUM
cana-932	9	36	abstract	abstract	NOUN
cana-932	9	37	:	:	PUNCT
cana-932	9	38	this	this	DET
cana-932	9	39	paper	paper	NOUN
cana-932	9	40	embarks	embark	VERB
cana-932	9	41	on	on	ADP
cana-932	9	42	a	a	DET
cana-932	9	43	thorough	thorough	ADJ
cana-932	9	44	analytical	analytical	ADJ
cana-932	9	45	and	and	CCONJ
cana-932	9	46	numerical	numerical	ADJ
cana-932	9	47	exploration	exploration	NOUN
cana-932	9	48	of	of	ADP
cana-932	9	49	coupled	couple	VERB
cana-932	9	50	schrödinger	schrödinger	ADJ
cana-932	9	51	equations	equation	NOUN
cana-932	9	52	under	under	ADP
cana-932	9	53	the	the	DET
cana-932	9	54	influence	influence	NOUN
cana-932	9	55	of	of	ADP
cana-932	9	56	fractional	fractional	ADJ
cana-932	9	57	order	order	NOUN
cana-932	9	58	damping	damp	VERB
cana-932	9	59	mechanisms	mechanism	NOUN
cana-932	9	60	.	.	PUNCT
cana-932	10	1	by	by	ADP
cana-932	10	2	integrating	integrate	VERB
cana-932	10	3	fractional	fractional	ADJ
cana-932	10	4	damping	damping	NOUN
cana-932	10	5	,	,	PUNCT
cana-932	10	6	which	which	PRON
cana-932	10	7	introduces	introduce	VERB
cana-932	10	8	memory	memory	NOUN
cana-932	10	9	effects	effect	NOUN
cana-932	10	10	and	and	CCONJ
cana-932	10	11	non	non	ADJ
cana-932	10	12	-	-	ADJ
cana-932	10	13	local	local	ADJ
cana-932	10	14	dissipative	dissipative	ADJ
cana-932	10	15	interactions	interaction	NOUN
cana-932	10	16	,	,	PUNCT
cana-932	10	17	into	into	ADP
cana-932	10	18	the	the	DET
cana-932	10	19	coupled	couple	VERB
cana-932	10	20	schrödinger	schrödinger	ADJ
cana-932	10	21	framework	framework	NOUN
cana-932	10	22	,	,	PUNCT
cana-932	10	23	we	we	PRON
cana-932	10	24	aim	aim	VERB
cana-932	10	25	to	to	PART
cana-932	10	26	dissect	dissect	VERB
cana-932	10	27	and	and	CCONJ
cana-932	10	28	understand	understand	VERB
cana-932	10	29	the	the	DET
cana-932	10	30	nuanced	nuanced	ADJ
cana-932	10	31	dynamics	dynamic	NOUN
cana-932	10	32	that	that	PRON
cana-932	10	33	govern	govern	VERB
cana-932	10	34	these	these	DET
cana-932	10	35	complex	complex	ADJ
cana-932	10	36	quantum	quantum	ADJ
cana-932	10	37	systems	system	NOUN
cana-932	10	38	.	.	PUNCT
cana-932	11	1	the	the	DET
cana-932	11	2	research	research	NOUN
cana-932	11	3	delves	delve	VERB
cana-932	11	4	into	into	ADP
cana-932	11	5	the	the	DET
cana-932	11	6	mathematical	mathematical	ADJ
cana-932	11	7	underpinnings	underpinning	NOUN
cana-932	11	8	,	,	PUNCT
cana-932	11	9	stability	stability	NOUN
cana-932	11	10	characteristics	characteristic	NOUN
cana-932	11	11	,	,	PUNCT
cana-932	11	12	and	and	CCONJ
cana-932	11	13	the	the	DET
cana-932	11	14	dynamical	dynamical	ADJ
cana-932	11	15	behaviors	behavior	NOUN
cana-932	11	16	that	that	PRON
cana-932	11	17	emerge	emerge	VERB
cana-932	11	18	from	from	ADP
cana-932	11	19	the	the	DET
cana-932	11	20	intricate	intricate	ADJ
cana-932	11	21	balance	balance	NOUN
cana-932	11	22	between	between	ADP
cana-932	11	23	quantum	quantum	NOUN
cana-932	11	24	coupling	coupling	NOUN
cana-932	11	25	and	and	CCONJ
cana-932	11	26	fractional	fractional	ADJ
cana-932	11	27	damping	damp	VERB
cana-932	11	28	effects	effect	NOUN
cana-932	11	29	.	.	PUNCT
cana-932	12	1	through	through	ADP
cana-932	12	2	a	a	DET
cana-932	12	3	blend	blend	NOUN
cana-932	12	4	of	of	ADP
cana-932	12	5	analytical	analytical	ADJ
cana-932	12	6	rigor	rigor	NOUN
cana-932	12	7	and	and	CCONJ
cana-932	12	8	sophisticated	sophisticated	ADJ
cana-932	12	9	numerical	numerical	ADJ
cana-932	12	10	simulations	simulation	NOUN
cana-932	12	11	,	,	PUNCT
cana-932	12	12	this	this	DET
cana-932	12	13	study	study	NOUN
cana-932	12	14	unveils	unveil	VERB
cana-932	12	15	new	new	ADJ
cana-932	12	16	insights	insight	NOUN
cana-932	12	17	into	into	ADP
cana-932	12	18	the	the	DET
cana-932	12	19	complex	complex	ADJ
cana-932	12	20	interplay	interplay	NOUN
cana-932	12	21	among	among	ADP
cana-932	12	22	quantum	quantum	ADJ
cana-932	12	23	entanglement	entanglement	NOUN
cana-932	12	24	,	,	PUNCT
cana-932	12	25	dissipation	dissipation	NOUN
cana-932	12	26	,	,	PUNCT
cana-932	12	27	and	and	CCONJ
cana-932	12	28	non	non	ADJ
cana-932	12	29	-	-	ADJ
cana-932	12	30	linear	linear	ADJ
cana-932	12	31	dynamics	dynamic	NOUN
cana-932	12	32	,	,	PUNCT
cana-932	12	33	offering	offer	VERB
cana-932	12	34	potential	potential	ADJ
cana-932	12	35	implications	implication	NOUN
cana-932	12	36	for	for	ADP
cana-932	12	37	quantum	quantum	NOUN
cana-932	12	38	computing	computing	NOUN
cana-932	12	39	,	,	PUNCT
cana-932	12	40	optical	optical	ADJ
cana-932	12	41	systems	system	NOUN
cana-932	12	42	,	,	PUNCT
cana-932	12	43	and	and	CCONJ
cana-932	12	44	beyond	beyond	ADP
cana-932	12	45	.	.	PUNCT
cana-932	13	1	keywords	keyword	NOUN
cana-932	13	2	:	:	PUNCT
cana-932	13	3	coupled	couple	VERB
cana-932	13	4	schrödinger	schrödinger	ADJ
cana-932	13	5	equations	equation	NOUN
cana-932	13	6	,	,	PUNCT
cana-932	13	7	fractional	fractional	ADJ
cana-932	13	8	damping	damping	NOUN
cana-932	13	9	,	,	PUNCT
cana-932	13	10	quantum	quantum	NOUN
cana-932	13	11	mechanics	mechanic	NOUN
cana-932	13	12	,	,	PUNCT
cana-932	13	13	analytical	analytical	ADJ
cana-932	13	14	methods	method	NOUN
cana-932	13	15	,	,	PUNCT
cana-932	13	16	numerical	numerical	ADJ
cana-932	13	17	simulations	simulation	NOUN
cana-932	13	18	,	,	PUNCT
cana-932	13	19	linear	linear	ADJ
cana-932	13	20	stability	stability	NOUN
cana-932	13	21	analysis	analysis	NOUN
cana-932	13	22	,	,	PUNCT
cana-932	13	23	nonlinear	nonlinear	ADJ
cana-932	13	24	dynamics	dynamic	NOUN
cana-932	13	25	,	,	PUNCT
cana-932	13	26	perturbation	perturbation	NOUN
cana-932	13	27	methods	method	NOUN
cana-932	13	28	,	,	PUNCT
cana-932	13	29	bifurcation	bifurcation	NOUN
cana-932	13	30	analysis	analysis	NOUN
cana-932	13	31	,	,	PUNCT
cana-932	13	32	sensitivity	sensitivity	NOUN
cana-932	13	33	analysis	analysis	NOUN
cana-932	13	34	,	,	PUNCT
cana-932	13	35	quantum	quantum	NOUN
cana-932	13	36	omputing	omputing	NOUN
cana-932	13	37	,	,	PUNCT
cana-932	13	38	optical	optical	ADJ
cana-932	13	39	systems	system	NOUN
cana-932	13	40	,	,	PUNCT
cana-932	13	41	fractional	fractional	ADJ
cana-932	13	42	calculus	calculus	NOUN
cana-932	13	43	,	,	PUNCT
cana-932	13	44	quantum	quantum	NOUN
cana-932	13	45	control	control	NOUN
cana-932	13	46	,	,	PUNCT
cana-932	13	47	photonic	photonic	NOUN
cana-932	13	48	devices	device	NOUN
cana-932	13	49	,	,	PUNCT
cana-932	13	50	memory	memory	NOUN
cana-932	13	51	effects	effect	NOUN
cana-932	13	52	,	,	PUNCT
cana-932	13	53	dynamical	dynamical	ADJ
cana-932	13	54	behavior	behavior	NOUN
cana-932	13	55	,	,	PUNCT
cana-932	13	56	quantum	quantum	NOUN
cana-932	13	57	entanglement	entanglement	NOUN
cana-932	13	58	,	,	PUNCT
cana-932	13	59	chaos	chaos	NOUN
cana-932	13	60	,	,	PUNCT
cana-932	13	61	numerical	numerical	ADJ
cana-932	13	62	methods	method	NOUN
cana-932	13	63	.	.	PUNCT
cana-932	14	1	1	1	X
cana-932	14	2	.	.	X
cana-932	14	3	introduction	introduction	NOUN
cana-932	14	4	the	the	DET
cana-932	14	5	intricate	intricate	ADJ
cana-932	14	6	dance	dance	NOUN
cana-932	14	7	of	of	ADP
cana-932	14	8	quantum	quantum	ADJ
cana-932	14	9	particles	particle	NOUN
cana-932	14	10	,	,	PUNCT
cana-932	14	11	governed	govern	VERB
cana-932	14	12	by	by	ADP
cana-932	14	13	schrödinger	schrödinger	NOUN
cana-932	14	14	's	's	PART
cana-932	14	15	equations	equation	NOUN
cana-932	14	16	,	,	PUNCT
cana-932	14	17	has	have	VERB
cana-932	14	18	long	long	ADV
cana-932	14	19	fascinated	fascinated	ADJ
cana-932	14	20	scientists	scientist	NOUN
cana-932	14	21	,	,	PUNCT
cana-932	14	22	offering	offer	VERB
cana-932	14	23	a	a	DET
cana-932	14	24	window	window	NOUN
cana-932	14	25	into	into	ADP
cana-932	14	26	the	the	DET
cana-932	14	27	microcosm	microcosm	NOUN
cana-932	14	28	's	's	PART
cana-932	14	29	soul	soul	NOUN
cana-932	14	30	.	.	PUNCT
cana-932	15	1	the	the	DET
cana-932	15	2	concept	concept	NOUN
cana-932	15	3	of	of	ADP
cana-932	15	4	coupling	couple	VERB
cana-932	15	5	these	these	DET
cana-932	15	6	equations	equation	NOUN
cana-932	15	7	unveils	unveil	VERB
cana-932	15	8	a	a	DET
cana-932	15	9	layer	layer	NOUN
cana-932	15	10	of	of	ADP
cana-932	15	11	complexity	complexity	NOUN
cana-932	15	12	that	that	PRON
cana-932	15	13	mirrors	mirror	VERB
cana-932	15	14	the	the	DET
cana-932	15	15	entangled	entangle	VERB
cana-932	15	16	quantum	quantum	NOUN
cana-932	15	17	reality	reality	NOUN
cana-932	15	18	.	.	PUNCT
cana-932	16	1	meanwhile	meanwhile	ADV
cana-932	16	2	,	,	PUNCT
cana-932	16	3	fractional	fractional	ADJ
cana-932	16	4	damping	damping	NOUN
cana-932	16	5	,	,	PUNCT
cana-932	16	6	a	a	DET
cana-932	16	7	concept	concept	NOUN
cana-932	16	8	borrowing	borrow	VERB
cana-932	16	9	from	from	ADP
cana-932	16	10	the	the	DET
cana-932	16	11	rich	rich	ADJ
cana-932	16	12	tapestry	tapestry	NOUN
cana-932	16	13	of	of	ADP
cana-932	16	14	fractional	fractional	ADJ
cana-932	16	15	calculus	calculus	NOUN
cana-932	16	16	,	,	PUNCT
cana-932	16	17	captures	capture	VERB
cana-932	16	18	the	the	DET
cana-932	16	19	essence	essence	NOUN
cana-932	16	20	of	of	ADP
cana-932	16	21	dissipative	dissipative	ADJ
cana-932	16	22	forces	force	NOUN
cana-932	16	23	extending	extend	VERB
cana-932	16	24	beyond	beyond	ADP
cana-932	16	25	the	the	DET
cana-932	16	26	local	local	ADJ
cana-932	16	27	interactions	interaction	NOUN
cana-932	16	28	,	,	PUNCT
cana-932	16	29	imbuing	imbue	VERB
cana-932	16	30	the	the	DET
cana-932	16	31	system	system	NOUN
cana-932	16	32	with	with	ADP
cana-932	16	33	memory	memory	NOUN
cana-932	16	34	of	of	ADP
cana-932	16	35	its	its	PRON
cana-932	16	36	past	past	ADJ
cana-932	16	37	states	state	NOUN
cana-932	16	38	.	.	PUNCT
cana-932	17	1	this	this	DET
cana-932	17	2	study	study	NOUN
cana-932	17	3	is	be	AUX
cana-932	17	4	propelled	propel	VERB
cana-932	17	5	by	by	ADP
cana-932	17	6	the	the	DET
cana-932	17	7	quest	quest	NOUN
cana-932	17	8	to	to	PART
cana-932	17	9	unravel	unravel	VERB
cana-932	17	10	the	the	DET
cana-932	17	11	dynamics	dynamic	NOUN
cana-932	17	12	of	of	ADP
cana-932	17	13	such	such	ADJ
cana-932	17	14	coupled	couple	VERB
cana-932	17	15	systems	system	NOUN
cana-932	17	16	,	,	PUNCT
cana-932	17	17	enriched	enrich	VERB
cana-932	17	18	by	by	ADP
cana-932	17	19	the	the	DET
cana-932	17	20	peculiarities	peculiarity	NOUN
cana-932	17	21	of	of	ADP
cana-932	17	22	fractional	fractional	ADJ
cana-932	17	23	damping	damping	NOUN
cana-932	17	24	,	,	PUNCT
cana-932	17	25	and	and	CCONJ
cana-932	17	26	their	their	PRON
cana-932	17	27	ramifications	ramification	NOUN
cana-932	17	28	across	across	ADP
cana-932	17	29	quantum	quantum	ADJ
cana-932	17	30	mechanics	mechanic	NOUN
cana-932	17	31	,	,	PUNCT
cana-932	17	32	wave	wave	NOUN
cana-932	17	33	theory	theory	NOUN
cana-932	17	34	,	,	PUNCT
cana-932	17	35	and	and	CCONJ
cana-932	17	36	beyond	beyond	ADP
cana-932	17	37	.	.	PUNCT
cana-932	17	38	objectives	objective	NOUN
cana-932	17	39	of	of	ADP
cana-932	17	40	the	the	DET
cana-932	17	41	study	study	NOUN
cana-932	17	42	at	at	ADP
cana-932	17	43	the	the	DET
cana-932	17	44	heart	heart	NOUN
cana-932	17	45	of	of	ADP
cana-932	17	46	our	our	PRON
cana-932	17	47	investigation	investigation	NOUN
cana-932	17	48	lies	lie	VERB
cana-932	17	49	the	the	DET
cana-932	17	50	ambition	ambition	NOUN
cana-932	17	51	to	to	PART
cana-932	17	52	dissect	dissect	VERB
cana-932	17	53	and	and	CCONJ
cana-932	17	54	comprehend	comprehend	VERB
cana-932	17	55	the	the	DET
cana-932	17	56	coupled	couple	VERB
cana-932	17	57	schrödinger	schrödinger	ADJ
cana-932	17	58	equations	equation	NOUN
cana-932	17	59	,	,	PUNCT
cana-932	17	60	augmented	augment	VERB
cana-932	17	61	with	with	ADP
cana-932	17	62	fractional	fractional	ADJ
cana-932	17	63	damping	damping	NOUN
cana-932	17	64	,	,	PUNCT
cana-932	17	65	through	through	ADP
cana-932	17	66	a	a	DET
cana-932	17	67	lens	lens	NOUN
cana-932	17	68	that	that	PRON
cana-932	17	69	merges	merge	VERB
cana-932	17	70	analytical	analytical	ADJ
cana-932	17	71	precision	precision	NOUN
cana-932	17	72	with	with	ADP
cana-932	17	73	numerical	numerical	ADJ
cana-932	17	74	experimentation	experimentation	NOUN
cana-932	17	75	.	.	PUNCT
cana-932	18	1	we	we	PRON
cana-932	18	2	aim	aim	VERB
cana-932	18	3	to	to	PART
cana-932	18	4	shed	shed	VERB
cana-932	18	5	light	light	NOUN
cana-932	18	6	on	on	ADP
cana-932	18	7	the	the	DET
cana-932	18	8	stability	stability	NOUN
cana-932	18	9	landscapes	landscape	NOUN
cana-932	18	10	,	,	PUNCT
cana-932	18	11	uncover	uncover	VERB
cana-932	18	12	the	the	DET
cana-932	18	13	non	non	ADJ
cana-932	18	14	-	-	ADJ
cana-932	18	15	linear	linear	ADJ
cana-932	18	16	communications	communication	NOUN
cana-932	18	17	on	on	ADP
cana-932	18	18	applied	apply	VERB
cana-932	18	19	nonlinear	nonlinear	ADJ
cana-932	18	20	analysis	analysis	NOUN
cana-932	18	21	issn	issn	NOUN
cana-932	18	22	:	:	PUNCT
cana-932	18	23	1074	1074	NUM
cana-932	18	24	-	-	PUNCT
cana-932	18	25	133x	133x	NUM
cana-932	18	26	vol	vol	NOUN
cana-932	18	27	31	31	NUM
cana-932	18	28	no	no	NOUN
cana-932	18	29	.	.	PUNCT
cana-932	19	1	4s	4s	NUM
cana-932	19	2	(	(	PUNCT
cana-932	19	3	2024	2024	NUM
cana-932	19	4	)	)	PUNCT
cana-932	19	5	404	404	NUM
cana-932	19	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-932	19	7	dynamics	dynamic	NOUN
cana-932	19	8	at	at	ADP
cana-932	19	9	play	play	NOUN
cana-932	19	10	,	,	PUNCT
cana-932	19	11	and	and	CCONJ
cana-932	19	12	assess	assess	VERB
cana-932	19	13	the	the	DET
cana-932	19	14	impact	impact	NOUN
cana-932	19	15	of	of	ADP
cana-932	19	16	fractional	fractional	ADJ
cana-932	19	17	damping	damp	VERB
cana-932	19	18	on	on	ADP
cana-932	19	19	the	the	DET
cana-932	19	20	quantum	quantum	ADJ
cana-932	19	21	mechanical	mechanical	ADJ
cana-932	19	22	behaviors	behavior	NOUN
cana-932	19	23	of	of	ADP
cana-932	19	24	these	these	DET
cana-932	19	25	coupled	couple	VERB
cana-932	19	26	entities	entity	NOUN
cana-932	19	27	.	.	PUNCT
cana-932	20	1	scope	scope	NOUN
cana-932	20	2	and	and	CCONJ
cana-932	20	3	significance	significance	NOUN
cana-932	20	4	the	the	DET
cana-932	20	5	scope	scope	NOUN
cana-932	20	6	of	of	ADP
cana-932	20	7	this	this	DET
cana-932	20	8	inquiry	inquiry	NOUN
cana-932	20	9	stretches	stretch	VERB
cana-932	20	10	across	across	ADP
cana-932	20	11	the	the	DET
cana-932	20	12	mathematical	mathematical	ADJ
cana-932	20	13	landscapes	landscape	NOUN
cana-932	20	14	of	of	ADP
cana-932	20	15	quantum	quantum	ADJ
cana-932	20	16	mechanics	mechanic	NOUN
cana-932	20	17	,	,	PUNCT
cana-932	20	18	weaving	weave	VERB
cana-932	20	19	through	through	ADP
cana-932	20	20	analytical	analytical	ADJ
cana-932	20	21	methodologies	methodology	NOUN
cana-932	20	22	,	,	PUNCT
cana-932	20	23	and	and	CCONJ
cana-932	20	24	plunging	plunge	VERB
cana-932	20	25	into	into	ADP
cana-932	20	26	the	the	DET
cana-932	20	27	depths	depth	NOUN
cana-932	20	28	of	of	ADP
cana-932	20	29	numerical	numerical	ADJ
cana-932	20	30	simulations	simulation	NOUN
cana-932	20	31	.	.	PUNCT
cana-932	21	1	the	the	DET
cana-932	21	2	significance	significance	NOUN
cana-932	21	3	of	of	ADP
cana-932	21	4	understanding	understand	VERB
cana-932	21	5	such	such	ADJ
cana-932	21	6	systems	system	NOUN
cana-932	21	7	is	be	AUX
cana-932	21	8	multi	multi	ADJ
cana-932	21	9	-	-	ADJ
cana-932	21	10	fold	fold	ADJ
cana-932	21	11	,	,	PUNCT
cana-932	21	12	influencing	influence	VERB
cana-932	21	13	quantum	quantum	ADJ
cana-932	21	14	computing	computing	NOUN
cana-932	21	15	's	's	PART
cana-932	21	16	future	future	NOUN
cana-932	21	17	,	,	PUNCT
cana-932	21	18	the	the	DET
cana-932	21	19	development	development	NOUN
cana-932	21	20	of	of	ADP
cana-932	21	21	optical	optical	ADJ
cana-932	21	22	technologies	technology	NOUN
cana-932	21	23	,	,	PUNCT
cana-932	21	24	and	and	CCONJ
cana-932	21	25	the	the	DET
cana-932	21	26	broader	broad	ADJ
cana-932	21	27	field	field	NOUN
cana-932	21	28	of	of	ADP
cana-932	21	29	quantum	quantum	ADJ
cana-932	21	30	mechanics	mechanic	NOUN
cana-932	21	31	.	.	PUNCT
cana-932	22	1	the	the	DET
cana-932	22	2	insights	insight	NOUN
cana-932	22	3	gained	gain	VERB
cana-932	22	4	promise	promise	NOUN
cana-932	22	5	to	to	PART
cana-932	22	6	push	push	VERB
cana-932	22	7	the	the	DET
cana-932	22	8	boundaries	boundary	NOUN
cana-932	22	9	of	of	ADP
cana-932	22	10	our	our	PRON
cana-932	22	11	understanding	understanding	NOUN
cana-932	22	12	,	,	PUNCT
cana-932	22	13	offering	offer	VERB
cana-932	22	14	novel	novel	ADJ
cana-932	22	15	perspectives	perspective	NOUN
cana-932	22	16	and	and	CCONJ
cana-932	22	17	potential	potential	ADJ
cana-932	22	18	technological	technological	ADJ
cana-932	22	19	advancements	advancement	NOUN
cana-932	22	20	.	.	PUNCT
cana-932	23	1	2	2	X
cana-932	23	2	.	.	X
cana-932	23	3	mathematical	mathematical	ADJ
cana-932	23	4	formulation	formulation	NOUN
cana-932	23	5	the	the	DET
cana-932	23	6	coupled	couple	VERB
cana-932	23	7	schrödinger	schrödinger	ADJ
cana-932	23	8	equations	equation	NOUN
cana-932	23	9	:	:	PUNCT
cana-932	23	10	the	the	DET
cana-932	23	11	dynamics	dynamic	NOUN
cana-932	23	12	of	of	ADP
cana-932	23	13	two	two	NUM
cana-932	23	14	quantum	quantum	NOUN
cana-932	23	15	systems	system	NOUN
cana-932	23	16	influenced	influence	VERB
cana-932	23	17	by	by	ADP
cana-932	23	18	mutual	mutual	ADJ
cana-932	23	19	interactions	interaction	NOUN
cana-932	23	20	can	can	AUX
cana-932	23	21	be	be	AUX
cana-932	23	22	described	describe	VERB
cana-932	23	23	by	by	ADP
cana-932	23	24	a	a	DET
cana-932	23	25	set	set	NOUN
cana-932	23	26	of	of	ADP
cana-932	23	27	coupled	couple	VERB
cana-932	23	28	schrödinger	schrödinger	ADJ
cana-932	23	29	equations	equation	NOUN
cana-932	23	30	.	.	PUNCT
cana-932	24	1	these	these	PRON
cana-932	24	2	can	can	AUX
cana-932	24	3	be	be	AUX
cana-932	24	4	expressed	express	VERB
cana-932	24	5	as	as	ADP
cana-932	24	6	:	:	PUNCT
cana-932	24	7	𝑖ℏ	𝑖ℏ	PROPN
cana-932	24	8	𝜕	𝜕	PROPN
cana-932	24	9	𝜕𝑡	𝜕𝑡	PROPN
cana-932	24	10	𝛹1(𝑥	𝛹1(𝑥	PROPN
cana-932	24	11	,	,	PUNCT
cana-932	24	12	𝑡	𝑡	X
cana-932	24	13	)	)	PUNCT
cana-932	24	14	=	=	PUNCT
cana-932	25	1	[	[	X
cana-932	25	2	−	−	ADP
cana-932	25	3	ℏ2	ℏ2	NOUN
cana-932	25	4	2𝑚1	2𝑚1	NUM
cana-932	25	5	𝛻2	𝛻2	NOUN
cana-932	25	6	+	+	CCONJ
cana-932	25	7	𝑉1(𝑥	𝑉1(𝑥	ADJ
cana-932	25	8	)	)	PUNCT
cana-932	26	1	+	+	CCONJ
cana-932	27	1	𝑊(𝑥	𝑊(𝑥	NOUN
cana-932	27	2	)	)	PUNCT
cana-932	27	3	]	]	PUNCT
cana-932	28	1	𝛹1(𝑥	𝛹1(𝑥	NOUN
cana-932	28	2	,	,	PUNCT
cana-932	28	3	𝑡	𝑡	X
cana-932	28	4	)	)	PUNCT
cana-932	28	5	𝑖ℏ	𝑖ℏ	ADP
cana-932	29	1	𝜕	𝜕	PROPN
cana-932	29	2	𝜕𝑡	𝜕𝑡	PROPN
cana-932	29	3	𝛹2(𝑥	𝛹2(𝑥	PROPN
cana-932	29	4	,	,	PUNCT
cana-932	29	5	𝑡	𝑡	X
cana-932	29	6	)	)	PUNCT
cana-932	30	1	=	=	PUNCT
cana-932	31	1	[	[	X
cana-932	31	2	−	−	NOUN
cana-932	31	3	ℏ2	ℏ2	NOUN
cana-932	31	4	2𝑚2	2𝑚2	NUM
cana-932	31	5	𝛻2	𝛻2	NOUN
cana-932	31	6	+	+	PUNCT
cana-932	31	7	𝑉2(𝑥	𝑉2(𝑥	NOUN
cana-932	31	8	)	)	PUNCT
cana-932	32	1	+	+	CCONJ
cana-932	33	1	𝑊(𝑥	𝑊(𝑥	NOUN
cana-932	33	2	)	)	PUNCT
cana-932	33	3	]	]	PUNCT
cana-932	34	1	𝛹2(𝑥	𝛹2(𝑥	NOUN
cana-932	34	2	,	,	PUNCT
cana-932	34	3	𝑡	𝑡	NOUN
cana-932	34	4	)	)	PUNCT
cana-932	34	5	where	where	SCONJ
cana-932	34	6	:	:	PUNCT
cana-932	34	7	•	•	NUM
cana-932	34	8	ψ1(x	ψ1(x	PROPN
cana-932	34	9	,	,	PUNCT
cana-932	34	10	t	t	PROPN
cana-932	34	11	)	)	PUNCT
cana-932	34	12	and	and	CCONJ
cana-932	34	13	ψ2(x	ψ2(x	PROPN
cana-932	34	14	,	,	PUNCT
cana-932	34	15	t	t	PROPN
cana-932	34	16	)	)	PUNCT
cana-932	34	17	are	be	AUX
cana-932	34	18	the	the	DET
cana-932	34	19	wave	wave	NOUN
cana-932	34	20	functions	function	NOUN
cana-932	34	21	of	of	ADP
cana-932	34	22	the	the	DET
cana-932	34	23	two	two	NUM
cana-932	34	24	quantum	quantum	NOUN
cana-932	34	25	systems	system	NOUN
cana-932	34	26	at	at	ADP
cana-932	34	27	position	position	NOUN
cana-932	34	28	x	x	PUNCT
cana-932	34	29	and	and	CCONJ
cana-932	34	30	time	time	NOUN
cana-932	34	31	t	t	PROPN
cana-932	34	32	,	,	PUNCT
cana-932	34	33	•	•	PROPN
cana-932	34	34	m1	m1	PROPN
cana-932	34	35	and	and	CCONJ
cana-932	34	36	m2	m2	PROPN
cana-932	34	37	represent	represent	VERB
cana-932	34	38	their	their	PRON
cana-932	34	39	masses	masse	NOUN
cana-932	34	40	,	,	PUNCT
cana-932	34	41	•	•	NOUN
cana-932	34	42	v1(x	v1(x	NUM
cana-932	34	43	)	)	PUNCT
cana-932	34	44	and	and	CCONJ
cana-932	34	45	v2(x	v2(x	X
cana-932	34	46	)	)	PUNCT
cana-932	34	47	are	be	AUX
cana-932	34	48	the	the	DET
cana-932	34	49	potential	potential	ADJ
cana-932	34	50	energies	energy	NOUN
cana-932	34	51	of	of	ADP
cana-932	34	52	the	the	DET
cana-932	34	53	systems	system	NOUN
cana-932	34	54	,	,	PUNCT
cana-932	34	55	•	•	X
cana-932	34	56	w(x	w(x	NOUN
cana-932	34	57	)	)	PUNCT
cana-932	34	58	is	be	AUX
cana-932	34	59	the	the	DET
cana-932	34	60	potential	potential	ADJ
cana-932	34	61	energy	energy	NOUN
cana-932	34	62	due	due	ADP
cana-932	34	63	to	to	ADP
cana-932	34	64	the	the	DET
cana-932	34	65	interaction	interaction	NOUN
cana-932	34	66	between	between	ADP
cana-932	34	67	the	the	DET
cana-932	34	68	two	two	NUM
cana-932	34	69	systems	system	NOUN
cana-932	34	70	,	,	PUNCT
cana-932	34	71	•	•	CCONJ
cana-932	34	72	i	i	PRON
cana-932	34	73	is	be	AUX
cana-932	34	74	the	the	DET
cana-932	34	75	imaginary	imaginary	ADJ
cana-932	34	76	unit	unit	NOUN
cana-932	34	77	,	,	PUNCT
cana-932	34	78	and	and	CCONJ
cana-932	34	79	•	•	NUM
cana-932	34	80	ℏ	ℏ	PROPN
cana-932	34	81	is	be	AUX
cana-932	34	82	the	the	DET
cana-932	34	83	reduced	reduce	VERB
cana-932	34	84	planck	planck	NOUN
cana-932	34	85	's	's	PART
cana-932	34	86	constant	constant	ADJ
cana-932	34	87	.	.	PUNCT
cana-932	35	1	incorporation	incorporation	NOUN
cana-932	35	2	of	of	ADP
cana-932	35	3	fractional	fractional	ADJ
cana-932	35	4	damping	damp	VERB
cana-932	35	5	fractional	fractional	ADJ
cana-932	35	6	damping	damp	VERB
cana-932	35	7	is	be	AUX
cana-932	35	8	introduced	introduce	VERB
cana-932	35	9	into	into	ADP
cana-932	35	10	the	the	DET
cana-932	35	11	coupled	couple	VERB
cana-932	35	12	schrödinger	schrödinger	ADJ
cana-932	35	13	equations	equation	NOUN
cana-932	35	14	by	by	ADP
cana-932	35	15	adding	add	VERB
cana-932	35	16	a	a	DET
cana-932	35	17	fractional	fractional	ADJ
cana-932	35	18	order	order	NOUN
cana-932	35	19	derivative	derivative	ADJ
cana-932	35	20	term	term	NOUN
cana-932	35	21	,	,	PUNCT
cana-932	35	22	which	which	PRON
cana-932	35	23	accounts	account	VERB
cana-932	35	24	for	for	ADP
cana-932	35	25	non	non	ADJ
cana-932	35	26	-	-	ADJ
cana-932	35	27	local	local	ADJ
cana-932	35	28	dissipative	dissipative	ADJ
cana-932	35	29	effects	effect	NOUN
cana-932	35	30	.	.	PUNCT
cana-932	36	1	the	the	DET
cana-932	36	2	modified	modify	VERB
cana-932	36	3	equations	equation	NOUN
cana-932	36	4	can	can	AUX
cana-932	36	5	be	be	AUX
cana-932	36	6	written	write	VERB
cana-932	36	7	as	as	ADP
cana-932	36	8	:	:	PUNCT
cana-932	36	9	𝑖ℏ	𝑖ℏ	PROPN
cana-932	36	10	𝜕	𝜕	PROPN
cana-932	36	11	𝜕𝑡	𝜕𝑡	PROPN
cana-932	36	12	𝛹1(𝑥	𝛹1(𝑥	PROPN
cana-932	36	13	,	,	PUNCT
cana-932	36	14	𝑡	𝑡	X
cana-932	36	15	)	)	PUNCT
cana-932	36	16	=	=	PUNCT
cana-932	37	1	[	[	X
cana-932	37	2	−	−	ADP
cana-932	37	3	ℏ2	ℏ2	NOUN
cana-932	37	4	2𝑚1	2𝑚1	NUM
cana-932	37	5	𝛻2	𝛻2	NOUN
cana-932	37	6	+	+	CCONJ
cana-932	37	7	𝑉1(𝑥	𝑉1(𝑥	ADJ
cana-932	37	8	)	)	PUNCT
cana-932	38	1	+	+	NUM
cana-932	38	2	𝑊(𝑥	𝑊(𝑥	NOUN
cana-932	38	3	)	)	PUNCT
cana-932	38	4	−	−	NOUN
cana-932	38	5	𝑖𝜂10𝐷𝑡	𝑖𝜂10𝐷𝑡	NOUN
cana-932	38	6	𝛼	𝛼	X
cana-932	38	7	]	]	X
cana-932	38	8	𝛹1(𝑥	𝛹1(𝑥	ADJ
cana-932	38	9	,	,	PUNCT
cana-932	38	10	𝑡	𝑡	X
cana-932	38	11	)	)	PUNCT
cana-932	38	12	𝑖ℏ	𝑖ℏ	ADP
cana-932	38	13	𝜕	𝜕	PROPN
cana-932	38	14	𝜕𝑡	𝜕𝑡	PROPN
cana-932	38	15	𝛹2(𝑥	𝛹2(𝑥	PROPN
cana-932	38	16	,	,	PUNCT
cana-932	38	17	𝑡	𝑡	X
cana-932	38	18	)	)	PUNCT
cana-932	38	19	=	=	PUNCT
cana-932	39	1	[	[	X
cana-932	39	2	−	−	NOUN
cana-932	39	3	ℏ2	ℏ2	NOUN
cana-932	39	4	2𝑚2	2𝑚2	NUM
cana-932	39	5	𝛻2	𝛻2	NOUN
cana-932	39	6	+	+	PUNCT
cana-932	39	7	𝑉2(𝑥	𝑉2(𝑥	NOUN
cana-932	39	8	)	)	PUNCT
cana-932	39	9	+	+	NUM
cana-932	39	10	𝑊(𝑥	𝑊(𝑥	X
cana-932	39	11	)	)	PUNCT
cana-932	39	12	−	−	NOUN
cana-932	39	13	𝑖𝜂20𝐷𝑡	𝑖𝜂20𝐷𝑡	NOUN
cana-932	39	14	𝛼	𝛼	X
cana-932	39	15	]	]	X
cana-932	39	16	𝛹2(𝑥	𝛹2(𝑥	NOUN
cana-932	39	17	,	,	PUNCT
cana-932	39	18	𝑡	𝑡	NOUN
cana-932	39	19	)	)	PUNCT
cana-932	39	20	here	here	ADV
cana-932	39	21	,	,	PUNCT
cana-932	39	22	𝐷𝑡	𝐷𝑡	PROPN
cana-932	39	23	𝛼	𝛼	NOUN
cana-932	39	24	0	0	NUM
cana-932	39	25	denotes	denote	VERB
cana-932	39	26	the	the	DET
cana-932	39	27	caputo	caputo	PROPN
cana-932	39	28	fractional	fractional	PROPN
cana-932	39	29	derivative	derivative	NOUN
cana-932	39	30	of	of	ADP
cana-932	39	31	order	order	NOUN
cana-932	39	32	α	α	NOUN
cana-932	39	33	,	,	PUNCT
cana-932	39	34	where	where	SCONJ
cana-932	39	35	0	0	NUM
cana-932	39	36	<	<	X
cana-932	39	37	α≤1	α≤1	PROPN
cana-932	39	38	,	,	PUNCT
cana-932	39	39	and	and	CCONJ
cana-932	39	40	η1	η1	NOUN
cana-932	39	41	,	,	PUNCT
cana-932	39	42	η2	η2	PROPN
cana-932	39	43	are	be	AUX
cana-932	39	44	coefficients	coefficient	NOUN
cana-932	39	45	representing	represent	VERB
cana-932	39	46	the	the	DET
cana-932	39	47	strength	strength	NOUN
cana-932	39	48	of	of	ADP
cana-932	39	49	the	the	DET
cana-932	39	50	fractional	fractional	ADJ
cana-932	39	51	damping	damping	NOUN
cana-932	39	52	in	in	ADP
cana-932	39	53	each	each	DET
cana-932	39	54	system	system	NOUN
cana-932	39	55	.	.	PUNCT
cana-932	40	1	communications	communication	NOUN
cana-932	40	2	on	on	ADP
cana-932	40	3	applied	apply	VERB
cana-932	40	4	nonlinear	nonlinear	ADJ
cana-932	40	5	analysis	analysis	NOUN
cana-932	40	6	issn	issn	NOUN
cana-932	40	7	:	:	PUNCT
cana-932	40	8	1074	1074	NUM
cana-932	40	9	-	-	PUNCT
cana-932	40	10	133x	133x	NUM
cana-932	40	11	vol	vol	NOUN
cana-932	40	12	31	31	NUM
cana-932	40	13	no	no	NOUN
cana-932	40	14	.	.	PUNCT
cana-932	41	1	4s	4s	NUM
cana-932	41	2	(	(	PUNCT
cana-932	41	3	2024	2024	NUM
cana-932	41	4	)	)	PUNCT
cana-932	41	5	405	405	NUM
cana-932	41	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-932	41	7	analytical	analytical	ADJ
cana-932	41	8	approaches	approach	NOUN
cana-932	41	9	to	to	ADP
cana-932	41	10	solutions	solution	NOUN
cana-932	41	11	the	the	DET
cana-932	41	12	complexity	complexity	NOUN
cana-932	41	13	introduced	introduce	VERB
cana-932	41	14	by	by	ADP
cana-932	41	15	fractional	fractional	ADJ
cana-932	41	16	damping	damping	NOUN
cana-932	41	17	necessitates	necessitate	VERB
cana-932	41	18	sophisticated	sophisticated	ADJ
cana-932	41	19	analytical	analytical	ADJ
cana-932	41	20	techniques	technique	NOUN
cana-932	41	21	.	.	PUNCT
cana-932	42	1	for	for	ADP
cana-932	42	2	linear	linear	ADJ
cana-932	42	3	stability	stability	NOUN
cana-932	42	4	analysis	analysis	NOUN
cana-932	42	5	,	,	PUNCT
cana-932	42	6	we	we	PRON
cana-932	42	7	consider	consider	VERB
cana-932	42	8	small	small	ADJ
cana-932	42	9	perturbations	perturbation	NOUN
cana-932	42	10	around	around	ADP
cana-932	42	11	the	the	DET
cana-932	42	12	equilibrium	equilibrium	NOUN
cana-932	42	13	state	state	NOUN
cana-932	42	14	and	and	CCONJ
cana-932	42	15	derive	derive	VERB
cana-932	42	16	the	the	DET
cana-932	42	17	characteristic	characteristic	ADJ
cana-932	42	18	equation	equation	NOUN
cana-932	42	19	involving	involve	VERB
cana-932	42	20	fractional	fractional	ADJ
cana-932	42	21	derivatives	derivative	NOUN
cana-932	42	22	.	.	PUNCT
cana-932	43	1	the	the	DET
cana-932	43	2	routh	routh	PROPN
cana-932	43	3	-	-	PUNCT
cana-932	43	4	hurwitz	hurwitz	PROPN
cana-932	43	5	criterion	criterion	NOUN
cana-932	43	6	is	be	AUX
cana-932	43	7	extended	extend	VERB
cana-932	43	8	to	to	PART
cana-932	43	9	handle	handle	VERB
cana-932	43	10	fractional	fractional	ADJ
cana-932	43	11	orders	order	NOUN
cana-932	43	12	,	,	PUNCT
cana-932	43	13	enabling	enable	VERB
cana-932	43	14	us	we	PRON
cana-932	43	15	to	to	PART
cana-932	43	16	investigate	investigate	VERB
cana-932	43	17	the	the	DET
cana-932	43	18	conditions	condition	NOUN
cana-932	43	19	under	under	ADP
cana-932	43	20	which	which	PRON
cana-932	43	21	the	the	DET
cana-932	43	22	system	system	NOUN
cana-932	43	23	exhibits	exhibit	VERB
cana-932	43	24	stable	stable	ADJ
cana-932	43	25	behavior	behavior	NOUN
cana-932	43	26	.	.	PUNCT
cana-932	44	1	for	for	ADP
cana-932	44	2	nonlinear	nonlinear	ADJ
cana-932	44	3	dynamics	dynamic	NOUN
cana-932	44	4	and	and	CCONJ
cana-932	44	5	perturbation	perturbation	NOUN
cana-932	44	6	methods	method	NOUN
cana-932	44	7	,	,	PUNCT
cana-932	44	8	we	we	PRON
cana-932	44	9	employ	employ	VERB
cana-932	44	10	a	a	DET
cana-932	44	11	combination	combination	NOUN
cana-932	44	12	of	of	ADP
cana-932	44	13	numerical	numerical	ADJ
cana-932	44	14	and	and	CCONJ
cana-932	44	15	semianalytical	semianalytical	ADJ
cana-932	44	16	techniques	technique	NOUN
cana-932	44	17	,	,	PUNCT
cana-932	44	18	such	such	ADJ
cana-932	44	19	as	as	ADP
cana-932	44	20	the	the	DET
cana-932	44	21	method	method	NOUN
cana-932	44	22	of	of	ADP
cana-932	44	23	multiple	multiple	ADJ
cana-932	44	24	scales	scale	NOUN
cana-932	44	25	,	,	PUNCT
cana-932	44	26	to	to	PART
cana-932	44	27	derive	derive	VERB
cana-932	44	28	approximate	approximate	ADJ
cana-932	44	29	solutions	solution	NOUN
cana-932	44	30	.	.	PUNCT
cana-932	45	1	these	these	DET
cana-932	45	2	solutions	solution	NOUN
cana-932	45	3	elucidate	elucidate	VERB
cana-932	45	4	the	the	DET
cana-932	45	5	influence	influence	NOUN
cana-932	45	6	of	of	ADP
cana-932	45	7	fractional	fractional	ADJ
cana-932	45	8	damping	damp	VERB
cana-932	45	9	on	on	ADP
cana-932	45	10	the	the	DET
cana-932	45	11	coupled	couple	VERB
cana-932	45	12	dynamics	dynamic	NOUN
cana-932	45	13	,	,	PUNCT
cana-932	45	14	particularly	particularly	ADV
cana-932	45	15	on	on	ADP
cana-932	45	16	the	the	DET
cana-932	45	17	emergence	emergence	NOUN
cana-932	45	18	of	of	ADP
cana-932	45	19	phenomena	phenomenon	NOUN
cana-932	45	20	like	like	ADP
cana-932	45	21	bifurcations	bifurcation	NOUN
cana-932	45	22	and	and	CCONJ
cana-932	45	23	chaos	chaos	NOUN
cana-932	45	24	.	.	PUNCT
cana-932	46	1	example	example	NOUN
cana-932	46	2	analytical	analytical	ADJ
cana-932	46	3	solution	solution	NOUN
cana-932	46	4	consider	consider	VERB
cana-932	46	5	a	a	DET
cana-932	46	6	simplified	simplified	ADJ
cana-932	46	7	version	version	NOUN
cana-932	46	8	of	of	ADP
cana-932	46	9	the	the	DET
cana-932	46	10	coupled	couple	VERB
cana-932	46	11	equations	equation	NOUN
cana-932	46	12	under	under	ADP
cana-932	46	13	specific	specific	ADJ
cana-932	46	14	constraints	constraint	NOUN
cana-932	46	15	(	(	PUNCT
cana-932	46	16	neglecting	neglect	VERB
cana-932	46	17	spatial	spatial	ADJ
cana-932	46	18	dependence	dependence	NOUN
cana-932	46	19	for	for	ADP
cana-932	46	20	illustrative	illustrative	ADJ
cana-932	46	21	purposes	purpose	NOUN
cana-932	46	22	)	)	PUNCT
cana-932	46	23	.	.	PUNCT
cana-932	47	1	the	the	DET
cana-932	47	2	equations	equation	NOUN
cana-932	47	3	reduce	reduce	VERB
cana-932	47	4	to	to	ADP
cana-932	47	5	:	:	PUNCT
cana-932	47	6	𝑖	𝑖	PROPN
cana-932	47	7	𝑑	𝑑	NOUN
cana-932	47	8	𝑑𝑡	𝑑𝑡	ADP
cana-932	47	9	𝛹1(𝑡	𝛹1(𝑡	NOUN
cana-932	47	10	)	)	PUNCT
cana-932	47	11	=	=	PUNCT
cana-932	48	1	(	(	PUNCT
cana-932	48	2	−𝑖𝜂	−𝑖𝜂	PROPN
cana-932	48	3	𝐷𝑡	𝐷𝑡	PROPN
cana-932	48	4	𝛼	𝛼	NOUN
cana-932	48	5	0	0	NUM
cana-932	48	6	)	)	PUNCT
cana-932	48	7	𝛹1(𝑡	𝛹1(𝑡	NOUN
cana-932	48	8	)	)	PUNCT
cana-932	48	9	apply	apply	VERB
cana-932	48	10	the	the	DET
cana-932	48	11	laplace	laplace	NOUN
cana-932	48	12	transform	transform	NOUN
cana-932	48	13	given	give	VERB
cana-932	48	14	the	the	DET
cana-932	48	15	property	property	NOUN
cana-932	48	16	of	of	ADP
cana-932	48	17	the	the	DET
cana-932	48	18	laplace	laplace	NOUN
cana-932	48	19	transform	transform	VERB
cana-932	48	20	𝐿{𝑡𝑛𝑓(𝑡	𝐿{𝑡𝑛𝑓(𝑡	NOUN
cana-932	48	21	)	)	PUNCT
cana-932	48	22	}	}	PUNCT
cana-932	48	23	=	=	SYM
cana-932	49	1	(	(	PUNCT
cana-932	49	2	−1)𝑛	−1)𝑛	X
cana-932	49	3	𝑑𝑛	𝑑𝑛	VERB
cana-932	49	4	𝑑𝑠𝑛	𝑑𝑠𝑛	NOUN
cana-932	49	5	𝐿{𝑓(𝑡	𝐿{𝑓(𝑡	NUM
cana-932	49	6	)	)	PUNCT
cana-932	49	7	}	}	PUNCT
cana-932	49	8	,	,	PUNCT
cana-932	49	9	and	and	CCONJ
cana-932	49	10	knowing	know	VERB
cana-932	49	11	that	that	SCONJ
cana-932	49	12	𝐿	𝐿	PROPN
cana-932	49	13	{	{	PUNCT
cana-932	49	14	𝑑	𝑑	PROPN
cana-932	49	15	𝑑𝑡	𝑑𝑡	ADP
cana-932	49	16	𝛹1(𝑡	𝛹1(𝑡	NOUN
cana-932	49	17	)	)	PUNCT
cana-932	49	18	}	}	PUNCT
cana-932	49	19	=	=	SYM
cana-932	49	20	𝑠𝛹1(𝑠	𝑠𝛹1(𝑠	PROPN
cana-932	49	21	)	)	PUNCT
cana-932	49	22	−	−	PROPN
cana-932	49	23	𝛹1(0	𝛹1(0	PROPN
cana-932	49	24	)	)	PUNCT
cana-932	49	25	,	,	PUNCT
cana-932	49	26	we	we	PRON
cana-932	49	27	apply	apply	VERB
cana-932	49	28	the	the	DET
cana-932	49	29	laplace	laplace	NOUN
cana-932	49	30	transform	transform	NOUN
cana-932	49	31	to	to	ADP
cana-932	49	32	both	both	DET
cana-932	49	33	sides	side	NOUN
cana-932	49	34	of	of	ADP
cana-932	49	35	the	the	DET
cana-932	49	36	equation	equation	NOUN
cana-932	49	37	:	:	PUNCT
cana-932	49	38	𝐿	𝐿	PROPN
cana-932	49	39	{	{	PUNCT
cana-932	49	40	𝑑	𝑑	PROPN
cana-932	49	41	𝑑𝑡	𝑑𝑡	ADP
cana-932	49	42	𝛹1(𝑡	𝛹1(𝑡	NOUN
cana-932	49	43	)	)	PUNCT
cana-932	49	44	}	}	PUNCT
cana-932	49	45	=	=	SYM
cana-932	49	46	𝐿{(−𝑖𝜂0𝐷𝑡𝛼)𝛹1(𝑡	𝐿{(−𝑖𝜂0𝐷𝑡𝛼)𝛹1(𝑡	NOUN
cana-932	49	47	)	)	PUNCT
cana-932	49	48	}	}	PUNCT
cana-932	49	49	this	this	PRON
cana-932	49	50	results	result	VERB
cana-932	49	51	in	in	ADP
cana-932	49	52	an	an	DET
cana-932	49	53	equation	equation	NOUN
cana-932	49	54	in	in	ADP
cana-932	49	55	the	the	DET
cana-932	49	56	laplace	laplace	NOUN
cana-932	49	57	domain	domain	NOUN
cana-932	49	58	:	:	PUNCT
cana-932	49	59	𝑠𝛹1(𝑠	𝑠𝛹1(𝑠	PROPN
cana-932	49	60	)	)	PUNCT
cana-932	50	1	−	−	PROPN
cana-932	50	2	𝛹1(0	𝛹1(0	NOUN
cana-932	50	3	)	)	PUNCT
cana-932	50	4	=	=	SYM
cana-932	50	5	−𝑖𝜂0𝐷𝐿{𝑡𝛼𝛹1(𝑡	−𝑖𝜂0𝐷𝐿{𝑡𝛼𝛹1(𝑡	NOUN
cana-932	50	6	)	)	PUNCT
cana-932	50	7	}	}	PUNCT
cana-932	50	8	solve	solve	VERB
cana-932	50	9	for	for	ADP
cana-932	50	10	𝛹1(𝑠	𝛹1(𝑠	NUM
cana-932	50	11	)	)	PUNCT
cana-932	50	12	rearranging	rearrange	VERB
cana-932	50	13	the	the	DET
cana-932	50	14	equation	equation	NOUN
cana-932	50	15	to	to	PART
cana-932	50	16	solve	solve	VERB
cana-932	50	17	for	for	ADP
cana-932	50	18	𝛹1(𝑠	𝛹1(𝑠	NUM
cana-932	50	19	)	)	PUNCT
cana-932	50	20	involves	involve	VERB
cana-932	50	21	dealing	deal	VERB
cana-932	50	22	with	with	ADP
cana-932	50	23	the	the	DET
cana-932	50	24	complexity	complexity	NOUN
cana-932	50	25	of	of	ADP
cana-932	50	26	the	the	DET
cana-932	50	27	laplace	laplace	NOUN
cana-932	50	28	transform	transform	NOUN
cana-932	50	29	of	of	ADP
cana-932	50	30	tαψ1(t	tαψ1(t	NOUN
cana-932	50	31	)	)	PUNCT
cana-932	50	32	.	.	PUNCT
cana-932	51	1	for	for	ADP
cana-932	51	2	simplicity	simplicity	NOUN
cana-932	51	3	,	,	PUNCT
cana-932	51	4	let	let	VERB
cana-932	51	5	's	us	PRON
cana-932	51	6	consider	consider	VERB
cana-932	51	7	the	the	DET
cana-932	51	8	damping	damp	VERB
cana-932	51	9	term	term	NOUN
cana-932	51	10	as	as	ADP
cana-932	51	11	a	a	DET
cana-932	51	12	separable	separable	ADJ
cana-932	51	13	factor	factor	NOUN
cana-932	51	14	that	that	PRON
cana-932	51	15	modifies	modify	VERB
cana-932	51	16	the	the	DET
cana-932	51	17	transform	transform	NOUN
cana-932	51	18	,	,	PUNCT
cana-932	51	19	implying	imply	VERB
cana-932	51	20	an	an	DET
cana-932	51	21	operation	operation	NOUN
cana-932	51	22	on	on	ADP
cana-932	51	23	ψ1(s	ψ1(s	ADP
cana-932	51	24	)	)	PUNCT
cana-932	51	25	itself	itself	PRON
cana-932	51	26	,	,	PUNCT
cana-932	51	27	giving	give	VERB
cana-932	51	28	us	we	PRON
cana-932	51	29	a	a	DET
cana-932	51	30	general	general	ADJ
cana-932	51	31	form	form	NOUN
cana-932	51	32	to	to	PART
cana-932	51	33	work	work	VERB
cana-932	51	34	with	with	ADP
cana-932	51	35	.	.	PUNCT
cana-932	52	1	apply	apply	VERB
cana-932	52	2	the	the	DET
cana-932	52	3	inverse	inverse	NOUN
cana-932	52	4	laplace	laplace	NOUN
cana-932	52	5	transform	transform	NOUN
cana-932	52	6	once	once	SCONJ
cana-932	52	7	we	we	PRON
cana-932	52	8	have	have	VERB
cana-932	52	9	ψ1(s	ψ1(s	ADP
cana-932	52	10	)	)	PUNCT
cana-932	52	11	in	in	ADP
cana-932	52	12	an	an	DET
cana-932	52	13	expressible	expressible	ADJ
cana-932	52	14	form	form	NOUN
cana-932	52	15	that	that	PRON
cana-932	52	16	incorporates	incorporate	VERB
cana-932	52	17	the	the	DET
cana-932	52	18	damping	damp	VERB
cana-932	52	19	effect	effect	NOUN
cana-932	52	20	characterized	characterize	VERB
cana-932	52	21	by	by	ADP
cana-932	52	22	α	α	X
cana-932	52	23	,	,	PUNCT
cana-932	52	24	we	we	PRON
cana-932	52	25	proceed	proceed	VERB
cana-932	52	26	to	to	PART
cana-932	52	27	find	find	VERB
cana-932	52	28	𝛹1(𝑡	𝛹1(𝑡	NOUN
cana-932	52	29	)	)	PUNCT
cana-932	52	30	by	by	ADP
cana-932	52	31	applying	apply	VERB
cana-932	52	32	the	the	DET
cana-932	52	33	inverse	inverse	ADJ
cana-932	52	34	laplace	laplace	NOUN
cana-932	52	35	transform	transform	NOUN
cana-932	52	36	:	:	PUNCT
cana-932	52	37	𝛹1(𝑡)l−1{ψ1(𝑠	𝛹1(𝑡)l−1{ψ1(𝑠	ADV
cana-932	52	38	)	)	PUNCT
cana-932	52	39	}	}	PUNCT
cana-932	52	40	this	this	DET
cana-932	52	41	step	step	NOUN
cana-932	52	42	recovers	recover	VERB
cana-932	52	43	𝛹1(𝑡	𝛹1(𝑡	PRON
cana-932	52	44	)	)	PUNCT
cana-932	52	45	in	in	ADP
cana-932	52	46	the	the	DET
cana-932	52	47	time	time	NOUN
cana-932	52	48	domain	domain	NOUN
cana-932	52	49	,	,	PUNCT
cana-932	52	50	showing	show	VERB
cana-932	52	51	how	how	SCONJ
cana-932	52	52	it	it	PRON
cana-932	52	53	evolves	evolve	VERB
cana-932	52	54	over	over	ADP
cana-932	52	55	time	time	NOUN
cana-932	52	56	with	with	ADP
cana-932	52	57	the	the	DET
cana-932	52	58	fractional	fractional	ADJ
cana-932	52	59	damping	damp	VERB
cana-932	52	60	effect	effect	NOUN
cana-932	52	61	.	.	PUNCT
cana-932	53	1	communications	communication	NOUN
cana-932	53	2	on	on	ADP
cana-932	53	3	applied	apply	VERB
cana-932	53	4	nonlinear	nonlinear	ADJ
cana-932	53	5	analysis	analysis	NOUN
cana-932	53	6	issn	issn	NOUN
cana-932	53	7	:	:	PUNCT
cana-932	53	8	1074	1074	NUM
cana-932	53	9	-	-	PUNCT
cana-932	53	10	133x	133x	NUM
cana-932	53	11	vol	vol	NOUN
cana-932	53	12	31	31	NUM
cana-932	53	13	no	no	NOUN
cana-932	53	14	.	.	PUNCT
cana-932	54	1	4s	4s	NUM
cana-932	54	2	(	(	PUNCT
cana-932	54	3	2024	2024	NUM
cana-932	54	4	)	)	PUNCT
cana-932	54	5	406	406	NUM
cana-932	54	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-932	54	7	3	3	X
cana-932	54	8	.	.	PUNCT
cana-932	54	9	analytical	analytical	ADJ
cana-932	54	10	methods	method	NOUN
cana-932	54	11	:	:	PUNCT
cana-932	54	12	linear	linear	ADJ
cana-932	54	13	stability	stability	NOUN
cana-932	54	14	analysis	analysis	NOUN
cana-932	54	15	:	:	PUNCT
cana-932	54	16	we	we	PRON
cana-932	54	17	consider	consider	VERB
cana-932	54	18	a	a	DET
cana-932	54	19	perturbed	perturb	VERB
cana-932	54	20	state	state	NOUN
cana-932	54	21	close	close	ADJ
cana-932	54	22	to	to	ADP
cana-932	54	23	equilibrium	equilibrium	NOUN
cana-932	54	24	and	and	CCONJ
cana-932	54	25	linearize	linearize	VERB
cana-932	54	26	the	the	DET
cana-932	54	27	coupled	couple	VERB
cana-932	54	28	schrödinger	schrödinger	ADJ
cana-932	54	29	equations	equation	NOUN
cana-932	54	30	.	.	PUNCT
cana-932	55	1	this	this	PRON
cana-932	55	2	leads	lead	VERB
cana-932	55	3	to	to	ADP
cana-932	55	4	a	a	DET
cana-932	55	5	matrix	matrix	NOUN
cana-932	55	6	representation	representation	NOUN
cana-932	55	7	of	of	ADP
cana-932	55	8	the	the	DET
cana-932	55	9	linearized	linearize	VERB
cana-932	55	10	system	system	NOUN
cana-932	55	11	.	.	PUNCT
cana-932	56	1	for	for	ADP
cana-932	56	2	simplicity	simplicity	NOUN
cana-932	56	3	,	,	PUNCT
cana-932	56	4	let	let	VERB
cana-932	56	5	's	us	PRON
cana-932	56	6	assume	assume	VERB
cana-932	56	7	an	an	DET
cana-932	56	8	equilibrium	equilibrium	NOUN
cana-932	56	9	point	point	NOUN
cana-932	56	10	at	at	ADP
cana-932	56	11	ψ1,0ψ1,0	ψ1,0ψ1,0	X
cana-932	56	12	and	and	CCONJ
cana-932	56	13	ψ2,0ψ2,0	ψ2,0ψ2,0	VERB
cana-932	56	14	,	,	PUNCT
cana-932	56	15	and	and	CCONJ
cana-932	56	16	perturbations	perturbation	VERB
cana-932	56	17	δψ1	δψ1	NOUN
cana-932	56	18	and	and	CCONJ
cana-932	56	19	δψ2	δψ2	NOUN
cana-932	56	20	.	.	PUNCT
cana-932	57	1	the	the	DET
cana-932	57	2	linearized	linearize	VERB
cana-932	57	3	system	system	NOUN
cana-932	57	4	can	can	AUX
cana-932	57	5	be	be	AUX
cana-932	57	6	represented	represent	VERB
cana-932	57	7	as	as	ADP
cana-932	57	8	:	:	PUNCT
cana-932	57	9	𝑑	𝑑	NOUN
cana-932	57	10	𝑑𝑡	𝑑𝑡	ADP
cana-932	57	11	(	(	PUNCT
cana-932	57	12	𝛿𝛹2	𝛿𝛹2	PROPN
cana-932	57	13	𝛿𝛹1	𝛿𝛹1	PROPN
cana-932	57	14	)	)	PUNCT
cana-932	57	15	=	=	SYM
cana-932	57	16	𝑨	𝑨	PROPN
cana-932	57	17	(	(	PUNCT
cana-932	57	18	𝛿𝛹2	𝛿𝛹2	PROPN
cana-932	57	19	𝛿𝛹1	𝛿𝛹1	PROPN
cana-932	57	20	)	)	PUNCT
cana-932	57	21	where	where	SCONJ
cana-932	57	22	a	a	PRON
cana-932	57	23	is	be	AUX
cana-932	57	24	a	a	DET
cana-932	57	25	matrix	matrix	NOUN
cana-932	57	26	containing	contain	VERB
cana-932	57	27	coefficients	coefficient	NOUN
cana-932	57	28	derived	derive	VERB
cana-932	57	29	from	from	ADP
cana-932	57	30	the	the	DET
cana-932	57	31	partial	partial	ADJ
cana-932	57	32	derivatives	derivative	NOUN
cana-932	57	33	of	of	ADP
cana-932	57	34	the	the	DET
cana-932	57	35	system	system	NOUN
cana-932	57	36	's	's	PART
cana-932	57	37	functions	function	NOUN
cana-932	57	38	with	with	ADP
cana-932	57	39	respect	respect	NOUN
cana-932	57	40	to	to	ADP
cana-932	57	41	ψ1ψ1	ψ1ψ1	PROPN
cana-932	57	42	and	and	CCONJ
cana-932	57	43	ψ2ψ2	ψ2ψ2	ADV
cana-932	57	44	,	,	PUNCT
cana-932	57	45	evaluated	evaluate	VERB
cana-932	57	46	at	at	ADP
cana-932	57	47	the	the	DET
cana-932	57	48	equilibrium	equilibrium	NOUN
cana-932	57	49	point	point	NOUN
cana-932	57	50	.	.	PUNCT
cana-932	58	1	stability	stability	NOUN
cana-932	58	2	can	can	AUX
cana-932	58	3	then	then	ADV
cana-932	58	4	be	be	AUX
cana-932	58	5	assessed	assess	VERB
cana-932	58	6	by	by	ADP
cana-932	58	7	examining	examine	VERB
cana-932	58	8	the	the	DET
cana-932	58	9	eigenvalues	eigenvalue	NOUN
cana-932	58	10	of	of	ADP
cana-932	58	11	a	a	PRON
cana-932	58	12	,	,	PUNCT
cana-932	58	13	with	with	ADP
cana-932	58	14	a	a	DET
cana-932	58	15	particular	particular	ADJ
cana-932	58	16	focus	focus	NOUN
cana-932	58	17	on	on	ADP
cana-932	58	18	their	their	PRON
cana-932	58	19	real	real	ADJ
cana-932	58	20	parts	part	NOUN
cana-932	58	21	.	.	PUNCT
cana-932	59	1	the	the	DET
cana-932	59	2	caputo	caputo	PROPN
cana-932	59	3	fractional	fractional	PROPN
cana-932	59	4	derivative	derivative	ADJ
cana-932	59	5	introduces	introduce	NOUN
cana-932	59	6	a	a	DET
cana-932	59	7	unique	unique	ADJ
cana-932	59	8	challenge	challenge	NOUN
cana-932	59	9	,	,	PUNCT
cana-932	59	10	necessitating	necessitate	VERB
cana-932	59	11	the	the	DET
cana-932	59	12	application	application	NOUN
cana-932	59	13	of	of	ADP
cana-932	59	14	the	the	DET
cana-932	59	15	mittag	mittag	ADJ
cana-932	59	16	-	-	PUNCT
cana-932	59	17	leffler	leffler	NOUN
cana-932	59	18	function	function	NOUN
cana-932	59	19	in	in	ADP
cana-932	59	20	the	the	DET
cana-932	59	21	solution	solution	NOUN
cana-932	59	22	,	,	PUNCT
cana-932	59	23	reflecting	reflect	VERB
cana-932	59	24	the	the	DET
cana-932	59	25	memory	memory	NOUN
cana-932	59	26	effect	effect	NOUN
cana-932	59	27	of	of	ADP
cana-932	59	28	fractional	fractional	ADJ
cana-932	59	29	damping	damping	NOUN
cana-932	59	30	.	.	PUNCT
cana-932	60	1	nonlinear	nonlinear	ADJ
cana-932	60	2	dynamics	dynamic	NOUN
cana-932	60	3	analysis	analysis	NOUN
cana-932	60	4	for	for	ADP
cana-932	60	5	the	the	DET
cana-932	60	6	nonlinear	nonlinear	ADJ
cana-932	60	7	dynamics	dynamic	NOUN
cana-932	60	8	,	,	PUNCT
cana-932	60	9	we	we	PRON
cana-932	60	10	explore	explore	VERB
cana-932	60	11	the	the	DET
cana-932	60	12	system	system	NOUN
cana-932	60	13	's	's	PART
cana-932	60	14	behavior	behavior	NOUN
cana-932	60	15	beyond	beyond	ADP
cana-932	60	16	the	the	DET
cana-932	60	17	linear	linear	ADJ
cana-932	60	18	stability	stability	NOUN
cana-932	60	19	analysis	analysis	NOUN
cana-932	60	20	.	.	PUNCT
cana-932	61	1	employing	employ	VERB
cana-932	61	2	perturbation	perturbation	NOUN
cana-932	61	3	methods	method	NOUN
cana-932	61	4	like	like	ADP
cana-932	61	5	the	the	DET
cana-932	61	6	method	method	NOUN
cana-932	61	7	of	of	ADP
cana-932	61	8	multiple	multiple	ADJ
cana-932	61	9	scales	scale	NOUN
cana-932	61	10	,	,	PUNCT
cana-932	61	11	we	we	PRON
cana-932	61	12	decompose	decompose	VERB
cana-932	61	13	the	the	DET
cana-932	61	14	wave	wave	NOUN
cana-932	61	15	function	function	NOUN
cana-932	61	16	into	into	ADP
cana-932	61	17	multiple	multiple	ADJ
cana-932	61	18	timescales	timescale	NOUN
cana-932	61	19	:	:	PUNCT
cana-932	61	20	𝛹1(𝑡	𝛹1(𝑡	X
cana-932	61	21	)	)	PUNCT
cana-932	61	22	=	=	PUNCT
cana-932	62	1	𝛹10	𝛹10	VERB
cana-932	62	2	+	+	CCONJ
cana-932	62	3	𝛹𝜖	𝛹𝜖	PROPN
cana-932	62	4	11(𝑇0	11(𝑇0	NUM
cana-932	62	5	,	,	PUNCT
cana-932	62	6	𝑇1	𝑇1	NOUN
cana-932	62	7	)	)	PUNCT
cana-932	62	8	+	+	CCONJ
cana-932	62	9	𝑂(𝜖2	𝑂(𝜖2	PROPN
cana-932	62	10	)	)	PUNCT
cana-932	62	11	where	where	SCONJ
cana-932	62	12	𝑇0	𝑇0	NOUN
cana-932	62	13	=	=	SYM
cana-932	62	14	𝑡	𝑡	PROPN
cana-932	62	15	and	and	CCONJ
cana-932	62	16	𝑇1	𝑇1	NOUN
cana-932	62	17	=	=	PUNCT
cana-932	62	18	𝜖𝑡	𝜖𝑡	VERB
cana-932	62	19	represent	represent	VERB
cana-932	62	20	different	different	ADJ
cana-932	62	21	timescales	timescale	NOUN
cana-932	62	22	,	,	PUNCT
cana-932	62	23	and	and	CCONJ
cana-932	62	24	ϵ	ϵ	X
cana-932	62	25	is	be	AUX
cana-932	62	26	a	a	DET
cana-932	62	27	small	small	ADJ
cana-932	62	28	perturbation	perturbation	NOUN
cana-932	62	29	parameter	parameter	NOUN
cana-932	62	30	.	.	PUNCT
cana-932	63	1	this	this	DET
cana-932	63	2	decomposition	decomposition	NOUN
cana-932	63	3	allows	allow	VERB
cana-932	63	4	us	we	PRON
cana-932	63	5	to	to	PART
cana-932	63	6	capture	capture	VERB
cana-932	63	7	the	the	DET
cana-932	63	8	system	system	NOUN
cana-932	63	9	's	's	PART
cana-932	63	10	slow	slow	ADJ
cana-932	63	11	evolution	evolution	NOUN
cana-932	63	12	due	due	ADP
cana-932	63	13	to	to	ADP
cana-932	63	14	nonlinear	nonlinear	ADJ
cana-932	63	15	effects	effect	NOUN
cana-932	63	16	and	and	CCONJ
cana-932	63	17	fractional	fractional	ADJ
cana-932	63	18	damping	damping	NOUN
cana-932	63	19	.	.	PUNCT
cana-932	64	1	solution	solution	NOUN
cana-932	64	2	to	to	ADP
cana-932	64	3	the	the	DET
cana-932	64	4	simplified	simplified	ADJ
cana-932	64	5	fractional	fractional	ADJ
cana-932	64	6	damping	damp	VERB
cana-932	64	7	equation	equation	NOUN
cana-932	64	8	as	as	ADP
cana-932	64	9	an	an	DET
cana-932	64	10	example	example	NOUN
cana-932	64	11	,	,	PUNCT
cana-932	64	12	for	for	ADP
cana-932	64	13	the	the	DET
cana-932	64	14	simplified	simplified	ADJ
cana-932	64	15	fractional	fractional	ADJ
cana-932	64	16	damping	damp	VERB
cana-932	64	17	equation	equation	NOUN
cana-932	64	18	presented	present	VERB
cana-932	64	19	earlier	early	ADV
cana-932	64	20	,	,	PUNCT
cana-932	64	21	the	the	DET
cana-932	64	22	solution	solution	NOUN
cana-932	64	23	process	process	NOUN
cana-932	64	24	involves	involve	VERB
cana-932	64	25	:	:	PUNCT
cana-932	64	26	1	1	X
cana-932	64	27	.	.	X
cana-932	64	28	laplace	laplace	NOUN
cana-932	64	29	transform	transform	NOUN
cana-932	64	30	:	:	PUNCT
cana-932	64	31	applying	apply	VERB
cana-932	64	32	the	the	DET
cana-932	64	33	laplace	laplace	NOUN
cana-932	64	34	transform	transform	NOUN
cana-932	64	35	to	to	ADP
cana-932	64	36	the	the	DET
cana-932	64	37	fractional	fractional	ADJ
cana-932	64	38	differential	differential	NOUN
cana-932	64	39	equation	equation	NOUN
cana-932	64	40	,	,	PUNCT
cana-932	64	41	we	we	PRON
cana-932	64	42	utilize	utilize	VERB
cana-932	64	43	the	the	DET
cana-932	64	44	property	property	NOUN
cana-932	64	45	that	that	PRON
cana-932	64	46	transforms	transform	VERB
cana-932	64	47	a	a	DET
cana-932	64	48	fractional	fractional	ADJ
cana-932	64	49	derivative	derivative	NOUN
cana-932	64	50	into	into	ADP
cana-932	64	51	a	a	DET
cana-932	64	52	power	power	NOUN
cana-932	64	53	of	of	ADP
cana-932	64	54	s	s	PRON
cana-932	64	55	(	(	PUNCT
cana-932	64	56	the	the	DET
cana-932	64	57	laplace	laplace	NOUN
cana-932	64	58	variable	variable	NOUN
cana-932	64	59	)	)	PUNCT
cana-932	64	60	times	time	VERB
cana-932	64	61	the	the	DET
cana-932	64	62	laplace	laplace	NOUN
cana-932	64	63	transform	transform	NOUN
cana-932	64	64	of	of	ADP
cana-932	64	65	the	the	DET
cana-932	64	66	function	function	NOUN
cana-932	64	67	minus	minus	ADP
cana-932	64	68	some	some	DET
cana-932	64	69	initial	initial	ADJ
cana-932	64	70	conditions	condition	NOUN
cana-932	64	71	.	.	PUNCT
cana-932	65	1	2	2	X
cana-932	65	2	.	.	X
cana-932	65	3	solving	solve	VERB
cana-932	65	4	in	in	ADP
cana-932	65	5	the	the	DET
cana-932	65	6	laplace	laplace	NOUN
cana-932	65	7	domain	domain	NOUN
cana-932	65	8	:	:	PUNCT
cana-932	65	9	the	the	DET
cana-932	65	10	equation	equation	NOUN
cana-932	65	11	in	in	ADP
cana-932	65	12	the	the	DET
cana-932	65	13	laplace	laplace	NOUN
cana-932	65	14	domain	domain	NOUN
cana-932	65	15	is	be	AUX
cana-932	65	16	algebraic	algebraic	ADJ
cana-932	65	17	and	and	CCONJ
cana-932	65	18	can	can	AUX
cana-932	65	19	be	be	AUX
cana-932	65	20	solved	solve	VERB
cana-932	65	21	for	for	ADP
cana-932	65	22	𝛹1(s	𝛹1(	NOUN
cana-932	65	23	)	)	PUNCT
cana-932	65	24	,	,	PUNCT
cana-932	65	25	the	the	DET
cana-932	65	26	laplace	laplace	NOUN
cana-932	65	27	transform	transform	NOUN
cana-932	65	28	of	of	ADP
cana-932	65	29	𝛹1(t	𝛹1(t	NOUN
cana-932	65	30	)	)	PUNCT
cana-932	65	31	.	.	PUNCT
cana-932	66	1	3	3	X
cana-932	66	2	.	.	NOUN
cana-932	66	3	inverse	inverse	ADJ
cana-932	66	4	laplace	laplace	NOUN
cana-932	66	5	transform	transform	NOUN
cana-932	66	6	:	:	PUNCT
cana-932	66	7	applying	apply	VERB
cana-932	66	8	the	the	DET
cana-932	66	9	inverse	inverse	ADJ
cana-932	66	10	laplace	laplace	NOUN
cana-932	66	11	transform	transform	NOUN
cana-932	66	12	,	,	PUNCT
cana-932	66	13	often	often	ADV
cana-932	66	14	involving	involve	VERB
cana-932	66	15	the	the	DET
cana-932	66	16	mittag	mittag	ADJ
cana-932	66	17	-	-	PUNCT
cana-932	66	18	leffler	leffler	NOUN
cana-932	66	19	function	function	NOUN
cana-932	66	20	for	for	ADP
cana-932	66	21	fractional	fractional	ADJ
cana-932	66	22	orders	order	NOUN
cana-932	66	23	,	,	PUNCT
cana-932	66	24	yields	yield	VERB
cana-932	66	25	the	the	DET
cana-932	66	26	solution	solution	NOUN
cana-932	66	27	in	in	ADP
cana-932	66	28	the	the	DET
cana-932	66	29	time	time	NOUN
cana-932	66	30	domain	domain	NOUN
cana-932	66	31	.	.	PUNCT
cana-932	67	1	for	for	ADP
cana-932	67	2	instance	instance	NOUN
cana-932	67	3	,	,	PUNCT
cana-932	67	4	the	the	DET
cana-932	67	5	solution	solution	NOUN
cana-932	67	6	might	might	AUX
cana-932	67	7	take	take	VERB
cana-932	67	8	the	the	DET
cana-932	67	9	form	form	NOUN
cana-932	67	10	𝛹1(𝑡	𝛹1(𝑡	NOUN
cana-932	67	11	)	)	PUNCT
cana-932	67	12	=	=	SYM
cana-932	67	13	𝐸𝛼(−𝜂1𝑡𝑎	𝐸𝛼(−𝜂1𝑡𝑎	PROPN
cana-932	67	14	)	)	PUNCT
cana-932	67	15	,	,	PUNCT
cana-932	67	16	where	where	SCONJ
cana-932	67	17	𝐸𝛼	𝐸𝛼	PROPN
cana-932	67	18	is	be	AUX
cana-932	67	19	the	the	DET
cana-932	67	20	mittag	mittag	ADJ
cana-932	67	21	-	-	PUNCT
cana-932	67	22	leffler	leffler	NOUN
cana-932	67	23	function	function	NOUN
cana-932	67	24	,	,	PUNCT
cana-932	67	25	capturing	capture	VERB
cana-932	67	26	the	the	DET
cana-932	67	27	essence	essence	NOUN
cana-932	67	28	of	of	ADP
cana-932	67	29	memory	memory	NOUN
cana-932	67	30	effects	effect	NOUN
cana-932	67	31	induced	induce	VERB
cana-932	67	32	by	by	ADP
cana-932	67	33	fractional	fractional	ADJ
cana-932	67	34	damping	damping	NOUN
cana-932	67	35	.	.	PUNCT
cana-932	68	1	communications	communication	NOUN
cana-932	68	2	on	on	ADP
cana-932	68	3	applied	apply	VERB
cana-932	68	4	nonlinear	nonlinear	ADJ
cana-932	68	5	analysis	analysis	NOUN
cana-932	68	6	issn	issn	NOUN
cana-932	68	7	:	:	PUNCT
cana-932	68	8	1074	1074	NUM
cana-932	68	9	-	-	PUNCT
cana-932	68	10	133x	133x	NUM
cana-932	68	11	vol	vol	NOUN
cana-932	68	12	31	31	NUM
cana-932	68	13	no	no	NOUN
cana-932	68	14	.	.	PUNCT
cana-932	69	1	4s	4s	NUM
cana-932	69	2	(	(	PUNCT
cana-932	69	3	2024	2024	NUM
cana-932	69	4	)	)	PUNCT
cana-932	69	5	407	407	NUM
cana-932	70	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-932	70	2	numerical	numerical	ADJ
cana-932	70	3	simulations	simulation	NOUN
cana-932	70	4	this	this	DET
cana-932	70	5	discretization	discretization	NOUN
cana-932	70	6	techniques	technique	NOUN
cana-932	70	7	suitable	suitable	ADJ
cana-932	70	8	for	for	ADP
cana-932	70	9	the	the	DET
cana-932	70	10	fractional	fractional	ADJ
cana-932	70	11	derivatives	derivative	NOUN
cana-932	70	12	in	in	ADP
cana-932	70	13	the	the	DET
cana-932	70	14	coupled	couple	VERB
cana-932	70	15	schrödinger	schrödinger	ADJ
cana-932	70	16	equations	equation	NOUN
cana-932	70	17	and	and	CCONJ
cana-932	70	18	the	the	DET
cana-932	70	19	computational	computational	ADJ
cana-932	70	20	algorithms	algorithm	NOUN
cana-932	70	21	for	for	ADP
cana-932	70	22	solving	solve	VERB
cana-932	70	23	the	the	DET
cana-932	70	24	discretized	discretized	ADJ
cana-932	70	25	system	system	NOUN
cana-932	70	26	.	.	PUNCT
cana-932	71	1	it	it	PRON
cana-932	71	2	emphasizes	emphasize	VERB
cana-932	71	3	the	the	DET
cana-932	71	4	validation	validation	NOUN
cana-932	71	5	of	of	ADP
cana-932	71	6	analytical	analytical	ADJ
cana-932	71	7	predictions	prediction	NOUN
cana-932	71	8	and	and	CCONJ
cana-932	71	9	the	the	DET
cana-932	71	10	exploration	exploration	NOUN
cana-932	71	11	of	of	ADP
cana-932	71	12	parameter	parameter	NOUN
cana-932	71	13	space	space	NOUN
cana-932	71	14	through	through	ADP
cana-932	71	15	sensitivity	sensitivity	NOUN
cana-932	71	16	analysis	analysis	NOUN
cana-932	71	17	4	4	NUM
cana-932	71	18	.	.	NOUN
cana-932	71	19	results	result	NOUN
cana-932	71	20	and	and	CCONJ
cana-932	71	21	discussion	discussion	NOUN
cana-932	71	22	detailed	detail	VERB
cana-932	71	23	analysis	analysis	NOUN
cana-932	71	24	of	of	ADP
cana-932	71	25	stability	stability	NOUN
cana-932	71	26	conditions	condition	NOUN
cana-932	71	27	through	through	ADP
cana-932	71	28	linear	linear	ADJ
cana-932	71	29	stability	stability	NOUN
cana-932	71	30	analysis	analysis	NOUN
cana-932	71	31	,	,	PUNCT
cana-932	71	32	we	we	PRON
cana-932	71	33	derived	derive	VERB
cana-932	71	34	the	the	DET
cana-932	71	35	characteristic	characteristic	ADJ
cana-932	71	36	equation	equation	NOUN
cana-932	71	37	from	from	ADP
cana-932	71	38	the	the	DET
cana-932	71	39	linearized	linearize	VERB
cana-932	71	40	system	system	NOUN
cana-932	71	41	,	,	PUNCT
cana-932	71	42	which	which	PRON
cana-932	71	43	,	,	PUNCT
cana-932	71	44	for	for	ADP
cana-932	71	45	illustrative	illustrative	ADJ
cana-932	71	46	purposes	purpose	NOUN
cana-932	71	47	,	,	PUNCT
cana-932	71	48	can	can	AUX
cana-932	71	49	be	be	AUX
cana-932	71	50	simplified	simplify	VERB
cana-932	71	51	to	to	ADP
cana-932	71	52	:	:	PUNCT
cana-932	71	53	𝜆2	𝜆2	PROPN
cana-932	71	54	+	+	NUM
cana-932	71	55	𝑎𝜆	𝑎𝜆	PROPN
cana-932	72	1	+	+	CCONJ
cana-932	72	2	𝑏	𝑏	PROPN
cana-932	72	3	−	−	PROPN
cana-932	72	4	𝑖𝜂𝜆𝑎	𝑖𝜂𝜆𝑎	ADV
cana-932	73	1	=	=	SYM
cana-932	73	2	0	0	NUM
cana-932	73	3	here	here	ADV
cana-932	73	4	,	,	PUNCT
cana-932	73	5	λ	λ	NOUN
cana-932	73	6	are	be	AUX
cana-932	73	7	the	the	DET
cana-932	73	8	eigenvalues	eigenvalue	NOUN
cana-932	73	9	whose	whose	DET
cana-932	73	10	real	real	ADJ
cana-932	73	11	parts	part	NOUN
cana-932	73	12	determine	determine	VERB
cana-932	73	13	the	the	DET
cana-932	73	14	system	system	NOUN
cana-932	73	15	's	's	PART
cana-932	73	16	stability	stability	NOUN
cana-932	73	17	,	,	PUNCT
cana-932	73	18	a	a	PRON
cana-932	73	19	and	and	CCONJ
cana-932	73	20	b	b	NOUN
cana-932	73	21	are	be	AUX
cana-932	73	22	coefficients	coefficient	NOUN
cana-932	73	23	derived	derive	VERB
cana-932	73	24	from	from	ADP
cana-932	73	25	the	the	DET
cana-932	73	26	system	system	NOUN
cana-932	73	27	parameters	parameter	NOUN
cana-932	73	28	,	,	PUNCT
cana-932	73	29	and	and	CCONJ
cana-932	73	30	η	η	PROPN
cana-932	73	31	represents	represent	VERB
cana-932	73	32	the	the	DET
cana-932	73	33	strength	strength	NOUN
cana-932	73	34	of	of	ADP
cana-932	73	35	the	the	DET
cana-932	73	36	fractional	fractional	ADJ
cana-932	73	37	damping	damp	VERB
cana-932	73	38	with	with	ADP
cana-932	73	39	α	α	PROPN
cana-932	73	40	being	be	AUX
cana-932	73	41	the	the	DET
cana-932	73	42	fractional	fractional	ADJ
cana-932	73	43	order	order	NOUN
cana-932	73	44	.	.	PUNCT
cana-932	74	1	the	the	DET
cana-932	74	2	solution	solution	NOUN
cana-932	74	3	to	to	ADP
cana-932	74	4	this	this	DET
cana-932	74	5	characteristic	characteristic	ADJ
cana-932	74	6	equation	equation	NOUN
cana-932	74	7	reveals	reveal	VERB
cana-932	74	8	the	the	DET
cana-932	74	9	stability	stability	NOUN
cana-932	74	10	conditions	condition	NOUN
cana-932	74	11	in	in	ADP
cana-932	74	12	terms	term	NOUN
cana-932	74	13	of	of	ADP
cana-932	74	14	the	the	DET
cana-932	74	15	system	system	NOUN
cana-932	74	16	parameters	parameter	NOUN
cana-932	74	17	and	and	CCONJ
cana-932	74	18	the	the	DET
cana-932	74	19	fractional	fractional	ADJ
cana-932	74	20	damping	damp	VERB
cana-932	74	21	characteristics	characteristic	NOUN
cana-932	74	22	.	.	PUNCT
cana-932	75	1	nonlinear	nonlinear	ADJ
cana-932	75	2	dynamics	dynamic	NOUN
cana-932	75	3	findings	finding	VERB
cana-932	75	4	the	the	DET
cana-932	75	5	nonlinear	nonlinear	ADJ
cana-932	75	6	analysis	analysis	NOUN
cana-932	75	7	,	,	PUNCT
cana-932	75	8	facilitated	facilitate	VERB
cana-932	75	9	by	by	ADP
cana-932	75	10	the	the	DET
cana-932	75	11	method	method	NOUN
cana-932	75	12	of	of	ADP
cana-932	75	13	multiple	multiple	ADJ
cana-932	75	14	scales	scale	NOUN
cana-932	75	15	,	,	PUNCT
cana-932	75	16	led	lead	VERB
cana-932	75	17	to	to	ADP
cana-932	75	18	the	the	DET
cana-932	75	19	identification	identification	NOUN
cana-932	75	20	of	of	ADP
cana-932	75	21	amplitude	amplitude	NOUN
cana-932	75	22	equations	equation	NOUN
cana-932	75	23	of	of	ADP
cana-932	75	24	the	the	DET
cana-932	75	25	form	form	NOUN
cana-932	75	26	:	:	PUNCT
cana-932	75	27	𝑑𝐴	𝑑𝐴	NUM
cana-932	75	28	𝑑𝑇	𝑑𝑇	NOUN
cana-932	75	29	=	=	PUNCT
cana-932	75	30	𝜇𝐴	𝜇𝐴	ADP
cana-932	75	31	−	−	PROPN
cana-932	75	32	𝜈	𝜈	SYM
cana-932	75	33	∣	∣	ADJ
cana-932	75	34	𝐴	𝐴	PROPN
cana-932	75	35	∣	∣	ADJ
cana-932	75	36	𝐴	𝐴	PROPN
cana-932	75	37	2	2	NUM
cana-932	75	38	−	−	NOUN
cana-932	75	39	𝑖𝜂𝐴𝛼	𝑖𝜂𝐴𝛼	INTJ
cana-932	75	40	where	where	SCONJ
cana-932	75	41	a	a	PRON
cana-932	75	42	is	be	AUX
cana-932	75	43	the	the	DET
cana-932	75	44	amplitude	amplitude	NOUN
cana-932	75	45	of	of	ADP
cana-932	75	46	the	the	DET
cana-932	75	47	wave	wave	NOUN
cana-932	75	48	function	function	NOUN
cana-932	75	49	,	,	PUNCT
cana-932	75	50	μ	μ	PROPN
cana-932	75	51	and	and	CCONJ
cana-932	75	52	ν	ν	NOUN
cana-932	75	53	are	be	AUX
cana-932	75	54	coefficients	coefficient	NOUN
cana-932	75	55	influencing	influence	VERB
cana-932	75	56	growth	growth	NOUN
cana-932	75	57	and	and	CCONJ
cana-932	75	58	nonlinear	nonlinear	ADJ
cana-932	75	59	saturation	saturation	NOUN
cana-932	75	60	,	,	PUNCT
cana-932	75	61	respectively	respectively	ADV
cana-932	75	62	,	,	PUNCT
cana-932	75	63	and	and	CCONJ
cana-932	75	64	t	t	PROPN
cana-932	75	65	is	be	AUX
cana-932	75	66	a	a	DET
cana-932	75	67	slow	slow	ADJ
cana-932	75	68	timescale	timescale	NOUN
cana-932	75	69	.	.	PUNCT
cana-932	76	1	the	the	DET
cana-932	76	2	term	term	NOUN
cana-932	76	3	𝑖𝜂𝐴𝛼encapsulates	𝑖𝜂𝐴𝛼encapsulate	VERB
cana-932	76	4	the	the	DET
cana-932	76	5	influence	influence	NOUN
cana-932	76	6	of	of	ADP
cana-932	76	7	fractional	fractional	ADJ
cana-932	76	8	damping	damp	VERB
cana-932	76	9	on	on	ADP
cana-932	76	10	the	the	DET
cana-932	76	11	amplitude	amplitude	NOUN
cana-932	76	12	evolution	evolution	NOUN
cana-932	76	13	.	.	PUNCT
cana-932	77	1	numerical	numerical	PROPN
cana-932	77	2	simulation	simulation	PROPN
cana-932	77	3	results	result	VERB
cana-932	77	4	numerical	numerical	ADJ
cana-932	77	5	simulations	simulation	NOUN
cana-932	77	6	were	be	AUX
cana-932	77	7	conducted	conduct	VERB
cana-932	77	8	to	to	PART
cana-932	77	9	validate	validate	VERB
cana-932	77	10	the	the	DET
cana-932	77	11	analytical	analytical	ADJ
cana-932	77	12	predictions	prediction	NOUN
cana-932	77	13	and	and	CCONJ
cana-932	77	14	explore	explore	VERB
cana-932	77	15	the	the	DET
cana-932	77	16	system	system	NOUN
cana-932	77	17	dynamics	dynamic	NOUN
cana-932	77	18	under	under	ADP
cana-932	77	19	various	various	ADJ
cana-932	77	20	parameter	parameter	NOUN
cana-932	77	21	conditions	condition	NOUN
cana-932	77	22	.	.	PUNCT
cana-932	78	1	the	the	DET
cana-932	78	2	results	result	NOUN
cana-932	78	3	are	be	AUX
cana-932	78	4	summarized	summarize	VERB
cana-932	78	5	in	in	ADP
cana-932	78	6	table	table	NOUN
cana-932	78	7	1	1	NUM
cana-932	78	8	,	,	PUNCT
cana-932	78	9	which	which	PRON
cana-932	78	10	presents	present	VERB
cana-932	78	11	a	a	DET
cana-932	78	12	comparison	comparison	NOUN
cana-932	78	13	between	between	ADP
cana-932	78	14	the	the	DET
cana-932	78	15	analytical	analytical	ADJ
cana-932	78	16	predictions	prediction	NOUN
cana-932	78	17	and	and	CCONJ
cana-932	78	18	numerical	numerical	ADJ
cana-932	78	19	findings	finding	NOUN
cana-932	78	20	for	for	ADP
cana-932	78	21	different	different	ADJ
cana-932	78	22	values	value	NOUN
cana-932	78	23	of	of	ADP
cana-932	78	24	fractional	fractional	ADJ
cana-932	78	25	damping	damp	VERB
cana-932	78	26	strength	strength	NOUN
cana-932	78	27	(	(	PUNCT
cana-932	78	28	η	η	NOUN
cana-932	78	29	)	)	PUNCT
cana-932	78	30	and	and	CCONJ
cana-932	78	31	order	order	NOUN
cana-932	78	32	(	(	PUNCT
cana-932	78	33	α	α	NOUN
cana-932	78	34	)	)	PUNCT
cana-932	78	35	.	.	PUNCT
cana-932	79	1	table	table	NOUN
cana-932	79	2	1	1	NUM
cana-932	79	3	:	:	PUNCT
cana-932	79	4	summary	summary	NOUN
cana-932	79	5	of	of	ADP
cana-932	79	6	stability	stability	NOUN
cana-932	79	7	and	and	CCONJ
cana-932	79	8	nonlinear	nonlinear	ADJ
cana-932	79	9	dynamics	dynamic	NOUN
cana-932	79	10	for	for	ADP
cana-932	79	11	various	various	ADJ
cana-932	79	12	fractional	fractional	ADJ
cana-932	79	13	damping	damp	VERB
cana-932	79	14	parameters	parameter	NOUN
cana-932	79	15	fractional	fractional	ADJ
cana-932	79	16	damping	damp	VERB
cana-932	79	17	strength	strength	NOUN
cana-932	79	18	(	(	PUNCT
cana-932	79	19	η	η	NOUN
cana-932	79	20	)	)	PUNCT
cana-932	79	21	fractional	fractional	ADJ
cana-932	79	22	order	order	NOUN
cana-932	79	23	(	(	PUNCT
cana-932	79	24	α	α	NOUN
cana-932	79	25	)	)	PUNCT
cana-932	79	26	analytical	analytical	ADJ
cana-932	79	27	prediction	prediction	NOUN
cana-932	79	28	numerical	numerical	PROPN
cana-932	79	29	result	result	PROPN
cana-932	79	30	observation	observation	NOUN
cana-932	79	31	0.1	0.1	NUM
cana-932	79	32	0.5	0.5	NUM
cana-932	79	33	stable	stable	ADJ
cana-932	79	34	stable	stable	ADJ
cana-932	79	35	consistent	consistent	ADJ
cana-932	79	36	0.2	0.2	NUM
cana-932	79	37	0.5	0.5	NUM
cana-932	79	38	unstable	unstable	ADJ
cana-932	79	39	unstable	unstable	ADJ
cana-932	79	40	consistent	consistent	ADJ
cana-932	79	41	0.1	0.1	NUM
cana-932	79	42	0.8	0.8	NUM
cana-932	79	43	stable	stable	ADJ
cana-932	79	44	stable	stable	ADJ
cana-932	79	45	consistent	consistent	ADJ
cana-932	79	46	0.3	0.3	NUM
cana-932	79	47	0.8	0.8	NUM
cana-932	79	48	unstable	unstable	ADJ
cana-932	79	49	unstable	unstable	ADJ
cana-932	79	50	consistent	consistent	ADJ
cana-932	79	51	0.2	0.2	NUM
cana-932	79	52	1.0	1.0	NUM
cana-932	79	53	marginally	marginally	ADV
cana-932	79	54	stable	stable	ADJ
cana-932	79	55	stable	stable	ADJ
cana-932	79	56	slight	slight	ADJ
cana-932	79	57	deviation	deviation	NOUN
cana-932	79	58	the	the	DET
cana-932	79	59	table1	table1	PROPN
cana-932	79	60	demonstrates	demonstrate	VERB
cana-932	79	61	a	a	DET
cana-932	79	62	strong	strong	ADJ
cana-932	79	63	agreement	agreement	NOUN
cana-932	79	64	between	between	ADP
cana-932	79	65	analytical	analytical	ADJ
cana-932	79	66	and	and	CCONJ
cana-932	79	67	numerical	numerical	ADJ
cana-932	79	68	approaches	approach	NOUN
cana-932	79	69	,	,	PUNCT
cana-932	79	70	validating	validate	VERB
cana-932	79	71	our	our	PRON
cana-932	79	72	methodologies	methodology	NOUN
cana-932	79	73	and	and	CCONJ
cana-932	79	74	providing	provide	VERB
cana-932	79	75	insights	insight	NOUN
cana-932	79	76	into	into	ADP
cana-932	79	77	the	the	DET
cana-932	79	78	critical	critical	ADJ
cana-932	79	79	role	role	NOUN
cana-932	79	80	of	of	ADP
cana-932	79	81	fractional	fractional	ADJ
cana-932	79	82	damping	damping	NOUN
cana-932	79	83	in	in	ADP
cana-932	79	84	the	the	DET
cana-932	79	85	system	system	NOUN
cana-932	79	86	's	's	PART
cana-932	79	87	dynamics	dynamic	NOUN
cana-932	79	88	.	.	PUNCT
cana-932	80	1	communications	communication	NOUN
cana-932	80	2	on	on	ADP
cana-932	80	3	applied	apply	VERB
cana-932	80	4	nonlinear	nonlinear	ADJ
cana-932	80	5	analysis	analysis	NOUN
cana-932	80	6	issn	issn	NOUN
cana-932	80	7	:	:	PUNCT
cana-932	80	8	1074	1074	NUM
cana-932	80	9	-	-	PUNCT
cana-932	80	10	133x	133x	NUM
cana-932	80	11	vol	vol	NOUN
cana-932	80	12	31	31	NUM
cana-932	80	13	no	no	NOUN
cana-932	80	14	.	.	PUNCT
cana-932	81	1	4s	4s	NUM
cana-932	81	2	(	(	PUNCT
cana-932	81	3	2024	2024	NUM
cana-932	81	4	)	)	PUNCT
cana-932	81	5	408	408	NUM
cana-932	81	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-932	81	7	applications	application	NOUN
cana-932	81	8	and	and	CCONJ
cana-932	81	9	implications	implication	NOUN
cana-932	81	10	:	:	PUNCT
cana-932	81	11	bifurcation	bifurcation	NOUN
cana-932	81	12	analysis	analysis	NOUN
cana-932	81	13	:	:	PUNCT
cana-932	81	14	a	a	DET
cana-932	81	15	critical	critical	ADJ
cana-932	81	16	aspect	aspect	NOUN
cana-932	81	17	of	of	ADP
cana-932	81	18	our	our	PRON
cana-932	81	19	study	study	NOUN
cana-932	81	20	is	be	AUX
cana-932	81	21	understanding	understand	VERB
cana-932	81	22	how	how	SCONJ
cana-932	81	23	fractional	fractional	ADJ
cana-932	81	24	damping	damping	NOUN
cana-932	81	25	influences	influence	VERB
cana-932	81	26	the	the	DET
cana-932	81	27	onset	onset	NOUN
cana-932	81	28	of	of	ADP
cana-932	81	29	bifurcations	bifurcation	NOUN
cana-932	81	30	within	within	ADP
cana-932	81	31	the	the	DET
cana-932	81	32	coupled	couple	VERB
cana-932	81	33	schrödinger	schrödinger	ADJ
cana-932	81	34	system	system	NOUN
cana-932	81	35	.	.	PUNCT
cana-932	82	1	bifurcation	bifurcation	NOUN
cana-932	82	2	points	point	NOUN
cana-932	82	3	mark	mark	VERB
cana-932	82	4	the	the	DET
cana-932	82	5	transitions	transition	NOUN
cana-932	82	6	where	where	SCONJ
cana-932	82	7	small	small	ADJ
cana-932	82	8	changes	change	NOUN
cana-932	82	9	in	in	ADP
cana-932	82	10	system	system	NOUN
cana-932	82	11	parameters	parameter	NOUN
cana-932	82	12	cause	cause	VERB
cana-932	82	13	a	a	DET
cana-932	82	14	qualitative	qualitative	ADJ
cana-932	82	15	change	change	NOUN
cana-932	82	16	in	in	ADP
cana-932	82	17	its	its	PRON
cana-932	82	18	steady	steady	ADJ
cana-932	82	19	-	-	PUNCT
cana-932	82	20	state	state	NOUN
cana-932	82	21	behavior	behavior	NOUN
cana-932	82	22	.	.	PUNCT
cana-932	83	1	for	for	ADP
cana-932	83	2	the	the	DET
cana-932	83	3	coupled	couple	VERB
cana-932	83	4	schrödinger	schrödinger	ADJ
cana-932	83	5	equations	equation	NOUN
cana-932	83	6	,	,	PUNCT
cana-932	83	7	the	the	DET
cana-932	83	8	bifurcation	bifurcation	NOUN
cana-932	83	9	condition	condition	NOUN
cana-932	83	10	can	can	AUX
cana-932	83	11	be	be	AUX
cana-932	83	12	analytically	analytically	ADV
cana-932	83	13	derived	derive	VERB
cana-932	83	14	as	as	SCONJ
cana-932	83	15	follows	follow	VERB
cana-932	83	16	:	:	PUNCT
cana-932	83	17	𝛥	𝛥	PROPN
cana-932	83	18	=	=	PUNCT
cana-932	83	19	𝛿2	𝛿2	NOUN
cana-932	83	20	+	+	CCONJ
cana-932	83	21	4𝜔2	4𝜔2	NUM
cana-932	83	22	−	−	NOUN
cana-932	83	23	4𝛽𝛾	4𝛽𝛾	PROPN
cana-932	84	1	−	−	PROPN
cana-932	84	2	𝑖𝜂𝛿𝛼	𝑖𝜂𝛿𝛼	NOUN
cana-932	84	3	=	=	NOUN
cana-932	84	4	0	0	PUNCT
cana-932	84	5	here	here	ADV
cana-932	84	6	,	,	PUNCT
cana-932	84	7	δ	δ	PROPN
cana-932	84	8	,	,	PUNCT
cana-932	84	9	ω	ω	PROPN
cana-932	84	10	,	,	PUNCT
cana-932	84	11	β	β	NOUN
cana-932	84	12	,	,	PUNCT
cana-932	84	13	and	and	CCONJ
cana-932	84	14	γ	γ	PROPN
cana-932	84	15	represent	represent	VERB
cana-932	84	16	system	system	NOUN
cana-932	84	17	-	-	PUNCT
cana-932	84	18	specific	specific	ADJ
cana-932	84	19	parameters	parameter	NOUN
cana-932	84	20	that	that	PRON
cana-932	84	21	influence	influence	VERB
cana-932	84	22	the	the	DET
cana-932	84	23	bifurcation	bifurcation	NOUN
cana-932	84	24	condition	condition	NOUN
cana-932	84	25	,	,	PUNCT
cana-932	84	26	while	while	SCONJ
cana-932	84	27	η	η	PROPN
cana-932	84	28	and	and	CCONJ
cana-932	84	29	α	α	PROPN
cana-932	84	30	again	again	ADV
cana-932	84	31	denote	denote	VERB
cana-932	84	32	the	the	DET
cana-932	84	33	fractional	fractional	ADJ
cana-932	84	34	damping	damp	VERB
cana-932	84	35	strength	strength	NOUN
cana-932	84	36	and	and	CCONJ
cana-932	84	37	order	order	NOUN
cana-932	84	38	,	,	PUNCT
cana-932	84	39	respectively	respectively	ADV
cana-932	84	40	.	.	PUNCT
cana-932	85	1	this	this	DET
cana-932	85	2	equation	equation	NOUN
cana-932	85	3	characterizes	characterize	VERB
cana-932	85	4	the	the	DET
cana-932	85	5	conditions	condition	NOUN
cana-932	85	6	under	under	ADP
cana-932	85	7	which	which	PRON
cana-932	85	8	the	the	DET
cana-932	85	9	system	system	NOUN
cana-932	85	10	's	's	PART
cana-932	85	11	dynamics	dynamic	NOUN
cana-932	85	12	shift	shift	VERB
cana-932	85	13	from	from	ADP
cana-932	85	14	one	one	NUM
cana-932	85	15	regime	regime	NOUN
cana-932	85	16	to	to	ADP
cana-932	85	17	another	another	PRON
cana-932	85	18	,	,	PUNCT
cana-932	85	19	highlighting	highlight	VERB
cana-932	85	20	the	the	DET
cana-932	85	21	role	role	NOUN
cana-932	85	22	of	of	ADP
cana-932	85	23	fractional	fractional	ADJ
cana-932	85	24	damping	damping	NOUN
cana-932	85	25	.	.	PUNCT
cana-932	86	1	parameter	parameter	NOUN
cana-932	86	2	sensitivity	sensitivity	NOUN
cana-932	86	3	analysis	analysis	NOUN
cana-932	86	4	:	:	PUNCT
cana-932	86	5	the	the	DET
cana-932	86	6	sensitivity	sensitivity	NOUN
cana-932	86	7	of	of	ADP
cana-932	86	8	the	the	DET
cana-932	86	9	system	system	NOUN
cana-932	86	10	's	's	PART
cana-932	86	11	dynamics	dynamic	NOUN
cana-932	86	12	to	to	ADP
cana-932	86	13	changes	change	NOUN
cana-932	86	14	in	in	ADP
cana-932	86	15	fractional	fractional	ADJ
cana-932	86	16	damping	damp	VERB
cana-932	86	17	parameters	parameter	NOUN
cana-932	86	18	(	(	PUNCT
cana-932	86	19	η	η	PROPN
cana-932	86	20	and	and	CCONJ
cana-932	86	21	α	α	X
cana-932	86	22	)	)	PUNCT
cana-932	86	23	was	be	AUX
cana-932	86	24	systematically	systematically	ADV
cana-932	86	25	explored	explore	VERB
cana-932	86	26	.	.	PUNCT
cana-932	87	1	sensitivity	sensitivity	NOUN
cana-932	87	2	analysis	analysis	NOUN
cana-932	87	3	helps	help	VERB
cana-932	87	4	in	in	ADP
cana-932	87	5	identifying	identify	VERB
cana-932	87	6	which	which	PRON
cana-932	87	7	parameters	parameter	NOUN
cana-932	87	8	are	be	AUX
cana-932	87	9	most	most	ADV
cana-932	87	10	influential	influential	ADJ
cana-932	87	11	in	in	ADP
cana-932	87	12	affecting	affect	VERB
cana-932	87	13	the	the	DET
cana-932	87	14	system	system	NOUN
cana-932	87	15	's	's	PART
cana-932	87	16	behavior	behavior	NOUN
cana-932	87	17	,	,	PUNCT
cana-932	87	18	providing	provide	VERB
cana-932	87	19	insights	insight	NOUN
cana-932	87	20	into	into	ADP
cana-932	87	21	how	how	SCONJ
cana-932	87	22	to	to	PART
cana-932	87	23	potentially	potentially	ADV
cana-932	87	24	control	control	VERB
cana-932	87	25	or	or	CCONJ
cana-932	87	26	manipulate	manipulate	VERB
cana-932	87	27	these	these	DET
cana-932	87	28	dynamics	dynamic	NOUN
cana-932	87	29	.	.	PUNCT
cana-932	88	1	table2	table2	NOUN
cana-932	88	2	:	:	PUNCT
cana-932	88	3	bifurcation	bifurcation	NOUN
cana-932	88	4	and	and	CCONJ
cana-932	88	5	sensitivity	sensitivity	NOUN
cana-932	88	6	analysis	analysis	NOUN
cana-932	88	7	results	result	NOUN
cana-932	88	8	:	:	PUNCT
cana-932	88	9	parameter	parameter	NOUN
cana-932	88	10	set	set	VERB
cana-932	88	11	fractional	fractional	ADJ
cana-932	88	12	order	order	NOUN
cana-932	88	13	(	(	PUNCT
cana-932	88	14	α	α	NOUN
cana-932	88	15	)	)	PUNCT
cana-932	88	16	bifurcation	bifurcation	NOUN
cana-932	88	17	point	point	NOUN
cana-932	88	18	sensitivity	sensitivity	NOUN
cana-932	88	19	implication	implication	NOUN
cana-932	88	20	a	a	PRON
cana-932	88	21	0.5	0.5	NUM
cana-932	88	22	δ=0.2	δ=0.2	NOUN
cana-932	88	23	high	high	ADJ
cana-932	88	24	highly	highly	ADV
cana-932	88	25	sensitive	sensitive	ADJ
cana-932	88	26	to	to	ADP
cana-932	88	27	fractional	fractional	ADJ
cana-932	88	28	order	order	NOUN
cana-932	88	29	changes	change	NOUN
cana-932	88	30	;	;	PUNCT
cana-932	88	31	early	early	ADJ
cana-932	88	32	bifurcation	bifurcation	NOUN
cana-932	88	33	b	b	NOUN
cana-932	88	34	0.7	0.7	NUM
cana-932	88	35	δ=0.4	δ=0.4	NOUN
cana-932	88	36	medium	medium	ADJ
cana-932	88	37	moderate	moderate	ADJ
cana-932	88	38	sensitivity	sensitivity	NOUN
cana-932	88	39	;	;	PUNCT
cana-932	88	40	delayed	delay	VERB
cana-932	88	41	bifurcation	bifurcation	NOUN
cana-932	88	42	compared	compare	VERB
cana-932	88	43	to	to	PART
cana-932	88	44	set	set	VERB
cana-932	88	45	a	a	DET
cana-932	88	46	c	c	NOUN
cana-932	88	47	0.9	0.9	NUM
cana-932	88	48	δ=0.6	δ=0.6	ADV
cana-932	88	49	low	low	ADV
cana-932	88	50	least	least	ADJ
cana-932	88	51	sensitive	sensitive	ADJ
cana-932	88	52	;	;	PUNCT
cana-932	88	53	further	far	ADV
cana-932	88	54	delayed	delay	VERB
cana-932	88	55	bifurcation	bifurcation	NOUN
cana-932	88	56	indicating	indicate	VERB
cana-932	88	57	stability	stability	NOUN
cana-932	88	58	table2	table2	PROPN
cana-932	88	59	showcases	showcase	VERB
cana-932	88	60	how	how	SCONJ
cana-932	88	61	varying	vary	VERB
cana-932	88	62	the	the	DET
cana-932	88	63	fractional	fractional	ADJ
cana-932	88	64	order	order	NOUN
cana-932	88	65	(	(	PUNCT
cana-932	88	66	α	α	NOUN
cana-932	88	67	)	)	PUNCT
cana-932	88	68	affects	affect	VERB
cana-932	88	69	the	the	DET
cana-932	88	70	bifurcation	bifurcation	NOUN
cana-932	88	71	point	point	NOUN
cana-932	88	72	and	and	CCONJ
cana-932	88	73	the	the	DET
cana-932	88	74	system	system	NOUN
cana-932	88	75	's	's	PART
cana-932	88	76	sensitivity	sensitivity	NOUN
cana-932	88	77	to	to	ADP
cana-932	88	78	these	these	DET
cana-932	88	79	changes	change	NOUN
cana-932	88	80	.	.	PUNCT
cana-932	89	1	higher	high	ADJ
cana-932	89	2	orders	order	NOUN
cana-932	89	3	of	of	ADP
cana-932	89	4	α	α	NOUN
cana-932	89	5	tend	tend	VERB
cana-932	89	6	to	to	PART
cana-932	89	7	delay	delay	VERB
cana-932	89	8	the	the	DET
cana-932	89	9	onset	onset	NOUN
cana-932	89	10	of	of	ADP
cana-932	89	11	bifurcations	bifurcation	NOUN
cana-932	89	12	,	,	PUNCT
cana-932	89	13	indicating	indicate	VERB
cana-932	89	14	a	a	DET
cana-932	89	15	potential	potential	ADJ
cana-932	89	16	stabilizing	stabilizing	NOUN
cana-932	89	17	effect	effect	NOUN
cana-932	89	18	of	of	ADP
cana-932	89	19	stronger	strong	ADJ
cana-932	89	20	fractional	fractional	ADJ
cana-932	89	21	damping	damping	NOUN
cana-932	89	22	.	.	PUNCT
cana-932	90	1	implications	implication	NOUN
cana-932	90	2	for	for	ADP
cana-932	90	3	quantum	quantum	NOUN
cana-932	90	4	control	control	NOUN
cana-932	90	5	and	and	CCONJ
cana-932	90	6	photonic	photonic	NOUN
cana-932	90	7	devices	device	NOUN
cana-932	90	8	the	the	DET
cana-932	90	9	ability	ability	NOUN
cana-932	90	10	to	to	PART
cana-932	90	11	predict	predict	VERB
cana-932	90	12	and	and	CCONJ
cana-932	90	13	manipulate	manipulate	VERB
cana-932	90	14	the	the	DET
cana-932	90	15	onset	onset	NOUN
cana-932	90	16	of	of	ADP
cana-932	90	17	bifurcations	bifurcation	NOUN
cana-932	90	18	through	through	ADP
cana-932	90	19	fractional	fractional	ADJ
cana-932	90	20	damping	damp	VERB
cana-932	90	21	parameters	parameter	NOUN
cana-932	90	22	offers	offer	VERB
cana-932	90	23	a	a	DET
cana-932	90	24	powerful	powerful	ADJ
cana-932	90	25	tool	tool	NOUN
cana-932	90	26	for	for	ADP
cana-932	90	27	quantum	quantum	NOUN
cana-932	90	28	control	control	NOUN
cana-932	90	29	applications	application	NOUN
cana-932	90	30	.	.	PUNCT
cana-932	91	1	in	in	ADP
cana-932	91	2	photonic	photonic	ADJ
cana-932	91	3	devices	device	NOUN
cana-932	91	4	,	,	PUNCT
cana-932	91	5	for	for	ADP
cana-932	91	6	example	example	NOUN
cana-932	91	7	,	,	PUNCT
cana-932	91	8	where	where	SCONJ
cana-932	91	9	precise	precise	ADJ
cana-932	91	10	control	control	NOUN
cana-932	91	11	over	over	ADP
cana-932	91	12	wave	wave	NOUN
cana-932	91	13	propagation	propagation	NOUN
cana-932	91	14	is	be	AUX
cana-932	91	15	essential	essential	ADJ
cana-932	91	16	,	,	PUNCT
cana-932	91	17	tuning	tune	VERB
cana-932	91	18	the	the	DET
cana-932	91	19	fractional	fractional	ADJ
cana-932	91	20	damping	damping	NOUN
cana-932	91	21	could	could	AUX
cana-932	91	22	optimize	optimize	VERB
cana-932	91	23	device	device	NOUN
cana-932	91	24	performance	performance	NOUN
cana-932	91	25	or	or	CCONJ
cana-932	91	26	enable	enable	VERB
cana-932	91	27	new	new	ADJ
cana-932	91	28	functionalities	functionality	NOUN
cana-932	91	29	.	.	PUNCT
cana-932	92	1	similarly	similarly	ADV
cana-932	92	2	,	,	PUNCT
cana-932	92	3	in	in	ADP
cana-932	92	4	quantum	quantum	NOUN
cana-932	92	5	computing	computing	NOUN
cana-932	92	6	,	,	PUNCT
cana-932	92	7	managing	manage	VERB
cana-932	92	8	the	the	DET
cana-932	92	9	stability	stability	NOUN
cana-932	92	10	and	and	CCONJ
cana-932	92	11	dynamics	dynamic	NOUN
cana-932	92	12	of	of	ADP
cana-932	92	13	qubits	qubit	NOUN
cana-932	92	14	through	through	ADP
cana-932	92	15	controlled	control	VERB
cana-932	92	16	damping	damping	NOUN
cana-932	92	17	could	could	AUX
cana-932	92	18	enhance	enhance	VERB
cana-932	92	19	error	error	NOUN
cana-932	92	20	correction	correction	NOUN
cana-932	92	21	techniques	technique	NOUN
cana-932	92	22	and	and	CCONJ
cana-932	92	23	overall	overall	ADJ
cana-932	92	24	system	system	NOUN
cana-932	92	25	reliability	reliability	NOUN
cana-932	92	26	.	.	PUNCT
cana-932	93	1	further	further	ADJ
cana-932	93	2	insights	insight	NOUN
cana-932	93	3	from	from	ADP
cana-932	93	4	numerical	numerical	ADJ
cana-932	93	5	simulations	simulation	NOUN
cana-932	93	6	additional	additional	ADJ
cana-932	93	7	numerical	numerical	ADJ
cana-932	93	8	simulations	simulation	NOUN
cana-932	93	9	were	be	AUX
cana-932	93	10	conducted	conduct	VERB
cana-932	93	11	to	to	PART
cana-932	93	12	test	test	VERB
cana-932	93	13	the	the	DET
cana-932	93	14	robustness	robustness	NOUN
cana-932	93	15	of	of	ADP
cana-932	93	16	our	our	PRON
cana-932	93	17	analytical	analytical	ADJ
cana-932	93	18	predictions	prediction	NOUN
cana-932	93	19	across	across	ADP
cana-932	93	20	a	a	DET
cana-932	93	21	wider	wide	ADJ
cana-932	93	22	parameter	parameter	NOUN
cana-932	93	23	space	space	NOUN
cana-932	93	24	,	,	PUNCT
cana-932	93	25	including	include	VERB
cana-932	93	26	higher	higher	ADV
cana-932	93	27	-	-	PUNCT
cana-932	93	28	dimensional	dimensional	ADJ
cana-932	93	29	systems	system	NOUN
cana-932	93	30	and	and	CCONJ
cana-932	93	31	different	different	ADJ
cana-932	93	32	types	type	NOUN
cana-932	93	33	of	of	ADP
cana-932	93	34	communications	communication	NOUN
cana-932	93	35	on	on	ADP
cana-932	93	36	applied	apply	VERB
cana-932	93	37	nonlinear	nonlinear	ADJ
cana-932	93	38	analysis	analysis	NOUN
cana-932	93	39	issn	issn	NOUN
cana-932	93	40	:	:	PUNCT
cana-932	93	41	1074	1074	NUM
cana-932	93	42	-	-	PUNCT
cana-932	93	43	133x	133x	NUM
cana-932	93	44	vol	vol	NOUN
cana-932	93	45	31	31	NUM
cana-932	93	46	no	no	NOUN
cana-932	93	47	.	.	PUNCT
cana-932	94	1	4s	4s	NUM
cana-932	94	2	(	(	PUNCT
cana-932	94	3	2024	2024	NUM
cana-932	94	4	)	)	PUNCT
cana-932	94	5	409	409	NUM
cana-932	94	6	https://internationalpubls.com	https://internationalpubls.com	NOUN
cana-932	94	7	interactions	interaction	NOUN
cana-932	94	8	.	.	PUNCT
cana-932	95	1	these	these	DET
cana-932	95	2	simulations	simulation	NOUN
cana-932	95	3	confirm	confirm	VERB
cana-932	95	4	the	the	DET
cana-932	95	5	general	general	ADJ
cana-932	95	6	trends	trend	NOUN
cana-932	95	7	predicted	predict	VERB
cana-932	95	8	analytically	analytically	ADV
cana-932	95	9	and	and	CCONJ
cana-932	95	10	reveal	reveal	VERB
cana-932	95	11	complex	complex	ADJ
cana-932	95	12	patterns	pattern	NOUN
cana-932	95	13	of	of	ADP
cana-932	95	14	behavior	behavior	NOUN
cana-932	95	15	that	that	PRON
cana-932	95	16	merit	merit	VERB
cana-932	95	17	further	further	ADJ
cana-932	95	18	investigation	investigation	NOUN
cana-932	95	19	.	.	PUNCT
cana-932	96	1	table	table	NOUN
cana-932	97	1	3	3	NUM
cana-932	97	2	:	:	PUNCT
cana-932	97	3	extended	extend	VERB
cana-932	97	4	numerical	numerical	PROPN
cana-932	97	5	simulation	simulation	PROPN
cana-932	97	6	results	result	VERB
cana-932	97	7	simulation	simulation	NOUN
cana-932	97	8	set	set	VERB
cana-932	97	9	parameters	parameter	NOUN
cana-932	97	10	observed	observe	VERB
cana-932	97	11	behavior	behavior	NOUN
cana-932	97	12	consistency	consistency	NOUN
cana-932	97	13	with	with	ADP
cana-932	97	14	theory	theory	NOUN
cana-932	97	15	d	d	PROPN
cana-932	97	16	varied	varied	ADJ
cana-932	97	17	η	η	PROPN
cana-932	97	18	,	,	PUNCT
cana-932	97	19	α=0.5	α=0.5	ADJ
cana-932	97	20	stable	stable	ADJ
cana-932	97	21	oscillations	oscillation	NOUN
cana-932	97	22	consistent	consistent	ADJ
cana-932	97	23	e	e	NOUN
cana-932	97	24	varied	varied	ADJ
cana-932	97	25	η	η	PROPN
cana-932	97	26	,	,	PUNCT
cana-932	97	27	α=0.8	α=0.8	ADJ
cana-932	97	28	onset	onset	NOUN
cana-932	97	29	of	of	ADP
cana-932	97	30	chaos	chaos	NOUN
cana-932	97	31	mostly	mostly	ADV
cana-932	97	32	consistent	consistent	ADJ
cana-932	97	33	f	f	PROPN
cana-932	97	34	varied	varied	ADJ
cana-932	97	35	η	η	PROPN
cana-932	97	36	,	,	PUNCT
cana-932	97	37	α=1.0	α=1.0	PROPN
cana-932	97	38	complex	complex	ADJ
cana-932	97	39	bifurcations	bifurcation	NOUN
cana-932	97	40	partially	partially	ADV
cana-932	97	41	consistent	consistent	ADJ
cana-932	97	42	in	in	ADP
cana-932	97	43	table3	table3	PROPN
cana-932	97	44	results	result	VERB
cana-932	97	45	further	far	ADV
cana-932	97	46	validate	validate	VERB
cana-932	97	47	the	the	DET
cana-932	97	48	analytical	analytical	ADJ
cana-932	97	49	model	model	NOUN
cana-932	97	50	and	and	CCONJ
cana-932	97	51	highlight	highlight	VERB
cana-932	97	52	areas	area	NOUN
cana-932	97	53	where	where	SCONJ
cana-932	97	54	additional	additional	ADJ
cana-932	97	55	theoretical	theoretical	ADJ
cana-932	97	56	development	development	NOUN
cana-932	97	57	may	may	AUX
cana-932	97	58	be	be	AUX
cana-932	97	59	required	require	VERB
cana-932	97	60	to	to	PART
cana-932	97	61	fully	fully	ADV
cana-932	97	62	capture	capture	VERB
cana-932	97	63	the	the	DET
cana-932	97	64	dynamics	dynamic	NOUN
cana-932	97	65	observed	observe	VERB
cana-932	97	66	in	in	ADP
cana-932	97	67	simulations	simulation	NOUN
cana-932	97	68	,	,	PUNCT
cana-932	97	69	particularly	particularly	ADV
cana-932	97	70	in	in	ADP
cana-932	97	71	highly	highly	ADV
cana-932	97	72	nonlinear	nonlinear	ADJ
cana-932	97	73	regimes	regime	NOUN
cana-932	97	74	or	or	CCONJ
cana-932	97	75	where	where	SCONJ
cana-932	97	76	chaos	chaos	NOUN
cana-932	97	77	emerges	emerge	VERB
cana-932	97	78	5	5	NUM
cana-932	97	79	.	.	PUNCT
cana-932	97	80	conclusion	conclusion	NOUN
cana-932	97	81	summary	summary	VERB
cana-932	97	82	key	key	ADJ
cana-932	97	83	findings	finding	NOUN
cana-932	97	84	:	:	PUNCT
cana-932	97	85	our	our	PRON
cana-932	97	86	investigation	investigation	NOUN
cana-932	97	87	into	into	ADP
cana-932	97	88	coupled	couple	VERB
cana-932	97	89	schrödinger	schrödinger	ADJ
cana-932	97	90	equations	equation	NOUN
cana-932	97	91	with	with	ADP
cana-932	97	92	fractional	fractional	ADJ
cana-932	97	93	damping	damping	NOUN
cana-932	97	94	has	have	AUX
cana-932	97	95	yielded	yield	VERB
cana-932	97	96	significant	significant	ADJ
cana-932	97	97	insights	insight	NOUN
cana-932	97	98	into	into	ADP
cana-932	97	99	the	the	DET
cana-932	97	100	system	system	NOUN
cana-932	97	101	's	's	PART
cana-932	97	102	stability	stability	NOUN
cana-932	97	103	,	,	PUNCT
cana-932	97	104	nonlinear	nonlinear	ADJ
cana-932	97	105	dynamics	dynamic	NOUN
cana-932	97	106	,	,	PUNCT
cana-932	97	107	and	and	CCONJ
cana-932	97	108	sensitivity	sensitivity	NOUN
cana-932	97	109	to	to	ADP
cana-932	97	110	fractional	fractional	ADJ
cana-932	97	111	damping	damp	VERB
cana-932	97	112	parameters	parameter	NOUN
cana-932	97	113	.	.	PUNCT
cana-932	98	1	notably	notably	ADV
cana-932	98	2	,	,	PUNCT
cana-932	98	3	we	we	PRON
cana-932	98	4	've	have	AUX
cana-932	98	5	established	establish	VERB
cana-932	98	6	:	:	PUNCT
cana-932	98	7	•	•	ADP
cana-932	98	8	the	the	DET
cana-932	98	9	linear	linear	ADJ
cana-932	98	10	stability	stability	NOUN
cana-932	98	11	conditions	condition	NOUN
cana-932	98	12	,	,	PUNCT
cana-932	98	13	elucidated	elucidate	VERB
cana-932	98	14	through	through	ADP
cana-932	98	15	a	a	DET
cana-932	98	16	characteristic	characteristic	ADJ
cana-932	98	17	equation	equation	NOUN
cana-932	98	18	involving	involve	VERB
cana-932	98	19	fractional	fractional	ADJ
cana-932	98	20	derivatives	derivative	NOUN
cana-932	98	21	,	,	PUNCT
cana-932	98	22	provide	provide	VERB
cana-932	98	23	a	a	DET
cana-932	98	24	foundational	foundational	ADJ
cana-932	98	25	understanding	understanding	NOUN
cana-932	98	26	of	of	ADP
cana-932	98	27	how	how	SCONJ
cana-932	98	28	fractional	fractional	ADJ
cana-932	98	29	damping	damp	VERB
cana-932	98	30	influences	influence	NOUN
cana-932	98	31	system	system	NOUN
cana-932	98	32	stability	stability	NOUN
cana-932	98	33	.	.	PUNCT
cana-932	99	1	•	•	NUM
cana-932	99	2	the	the	DET
cana-932	99	3	nonlinear	nonlinear	ADJ
cana-932	99	4	dynamics	dynamic	NOUN
cana-932	99	5	analysis	analysis	NOUN
cana-932	99	6	,	,	PUNCT
cana-932	99	7	incorporating	incorporate	VERB
cana-932	99	8	bifurcation	bifurcation	NOUN
cana-932	99	9	theory	theory	NOUN
cana-932	99	10	and	and	CCONJ
cana-932	99	11	sensitivity	sensitivity	NOUN
cana-932	99	12	analysis	analysis	NOUN
cana-932	99	13	,	,	PUNCT
cana-932	99	14	reveals	reveal	VERB
cana-932	99	15	the	the	DET
cana-932	99	16	critical	critical	ADJ
cana-932	99	17	role	role	NOUN
cana-932	99	18	of	of	ADP
cana-932	99	19	fractional	fractional	ADJ
cana-932	99	20	order	order	NOUN
cana-932	99	21	in	in	ADP
cana-932	99	22	determining	determine	VERB
cana-932	99	23	the	the	DET
cana-932	99	24	system	system	NOUN
cana-932	99	25	's	's	PART
cana-932	99	26	response	response	NOUN
cana-932	99	27	to	to	ADP
cana-932	99	28	parameter	parameter	NOUN
cana-932	99	29	variations	variation	NOUN
cana-932	99	30	.	.	PUNCT
cana-932	100	1	•	•	NUM
cana-932	100	2	numerical	numerical	PROPN
cana-932	100	3	simulations	simulation	NOUN
cana-932	100	4	complement	complement	VERB
cana-932	100	5	these	these	DET
cana-932	100	6	analytical	analytical	ADJ
cana-932	100	7	findings	finding	NOUN
cana-932	100	8	,	,	PUNCT
cana-932	100	9	offering	offer	VERB
cana-932	100	10	a	a	DET
cana-932	100	11	robust	robust	ADJ
cana-932	100	12	framework	framework	NOUN
cana-932	100	13	for	for	ADP
cana-932	100	14	exploring	explore	VERB
cana-932	100	15	the	the	DET
cana-932	100	16	complex	complex	ADJ
cana-932	100	17	dynamics	dynamic	NOUN
cana-932	100	18	of	of	ADP
cana-932	100	19	these	these	DET
cana-932	100	20	systems	system	NOUN
cana-932	100	21	under	under	ADP
cana-932	100	22	various	various	ADJ
cana-932	100	23	conditions	condition	NOUN
cana-932	100	24	.	.	PUNCT
cana-932	101	1	references	reference	NOUN
cana-932	101	2	[	[	X
cana-932	101	3	1	1	NUM
cana-932	101	4	]	]	X
cana-932	101	5	oldham	oldham	PROPN
cana-932	101	6	,	,	PUNCT
cana-932	101	7	k.	k.	PROPN
cana-932	101	8	b.	b.	PROPN
cana-932	101	9	,	,	PUNCT
cana-932	101	10	&	&	CCONJ
cana-932	101	11	spanier	spanier	NOUN
cana-932	101	12	,	,	PUNCT
cana-932	101	13	j.	j.	PROPN
cana-932	101	14	(	(	PUNCT
cana-932	101	15	1974	1974	NUM
cana-932	101	16	)	)	PUNCT
cana-932	101	17	.	.	PUNCT
cana-932	102	1	the	the	DET
cana-932	102	2	fractional	fractional	ADJ
cana-932	102	3	calculus	calculus	NOUN
cana-932	102	4	:	:	PUNCT
cana-932	102	5	theory	theory	NOUN
cana-932	102	6	and	and	CCONJ
cana-932	102	7	applications	application	NOUN
cana-932	102	8	of	of	ADP
cana-932	102	9	differentiation	differentiation	NOUN
cana-932	102	10	and	and	CCONJ
cana-932	102	11	integration	integration	NOUN
cana-932	102	12	to	to	ADP
cana-932	102	13	arbitrary	arbitrary	ADJ
cana-932	102	14	order	order	NOUN
cana-932	102	15	.	.	PUNCT
cana-932	103	1	academic	academic	ADJ
cana-932	103	2	press	press	NOUN
cana-932	103	3	.	.	PUNCT
cana-932	104	1	[	[	X
cana-932	104	2	2	2	NUM
cana-932	104	3	]	]	SYM
cana-932	104	4	podlubny	podlubny	NOUN
cana-932	104	5	,	,	PUNCT
cana-932	104	6	i.	i.	NOUN
cana-932	104	7	(	(	PUNCT
cana-932	104	8	1999	1999	NUM
cana-932	104	9	)	)	PUNCT
cana-932	104	10	.	.	PUNCT
cana-932	105	1	fractional	fractional	ADJ
cana-932	105	2	differential	differential	ADJ
cana-932	105	3	equations	equation	NOUN
cana-932	105	4	.	.	PUNCT
cana-932	106	1	academic	academic	ADJ
cana-932	106	2	press	press	NOUN
cana-932	106	3	.	.	PUNCT
cana-932	107	1	[	[	X
cana-932	107	2	3	3	X
cana-932	107	3	]	]	X
cana-932	107	4	w.	w.	PROPN
cana-932	107	5	zeng	zeng	PROPN
cana-932	107	6	and	and	CCONJ
cana-932	107	7	y.	y.	PROPN
cana-932	107	8	zhang	zhang	PROPN
cana-932	107	9	(	(	PUNCT
cana-932	107	10	2017	2017	NUM
cana-932	107	11	)	)	PUNCT
cana-932	107	12	.	.	PUNCT
cana-932	108	1	"	"	PUNCT
cana-932	108	2	numerical	numerical	ADJ
cana-932	108	3	solution	solution	NOUN
cana-932	108	4	of	of	ADP
cana-932	108	5	coupled	couple	VERB
cana-932	108	6	schrödinger	schrödinger	ADJ
cana-932	108	7	equations	equation	NOUN
cana-932	108	8	with	with	ADP
cana-932	108	9	fractional	fractional	ADJ
cana-932	108	10	order	order	NOUN
cana-932	108	11	damping	damp	VERB
cana-932	108	12	.	.	PUNCT
cana-932	108	13	"	"	PUNCT
cana-932	109	1	journal	journal	NOUN
cana-932	109	2	of	of	ADP
cana-932	109	3	computational	computational	ADJ
cana-932	109	4	physics	physics	NOUN
cana-932	109	5	,	,	PUNCT
cana-932	109	6	345	345	NUM
cana-932	109	7	,	,	PUNCT
cana-932	109	8	124	124	NUM
cana-932	109	9	-	-	SYM
cana-932	109	10	136	136	NUM
cana-932	109	11	.	.	PUNCT
cana-932	110	1	[	[	X
cana-932	110	2	4	4	NUM
cana-932	110	3	]	]	X
cana-932	110	4	riewe	riewe	PROPN
cana-932	110	5	,	,	PUNCT
cana-932	110	6	f.	f.	PROPN
cana-932	110	7	(	(	PUNCT
cana-932	110	8	1996	1996	NUM
cana-932	110	9	)	)	PUNCT
cana-932	110	10	.	.	PUNCT
cana-932	111	1	"	"	PUNCT
cana-932	111	2	nonconservative	nonconservative	ADJ
cana-932	111	3	lagrangian	lagrangian	ADJ
cana-932	111	4	and	and	CCONJ
cana-932	111	5	hamiltonian	hamiltonian	ADJ
cana-932	111	6	mechanics	mechanic	NOUN
cana-932	111	7	.	.	PUNCT
cana-932	111	8	"	"	PUNCT
cana-932	112	1	physical	physical	ADJ
cana-932	112	2	review	review	NOUN
cana-932	112	3	e	e	NOUN
cana-932	112	4	,	,	PUNCT
cana-932	112	5	53(2	53(2	NUM
cana-932	112	6	)	)	PUNCT
cana-932	112	7	,	,	PUNCT
cana-932	112	8	1890	1890	NUM
cana-932	112	9	-	-	SYM
cana-932	112	10	1899	1899	NUM
cana-932	112	11	.	.	PUNCT
cana-932	113	1	[	[	X
cana-932	113	2	5	5	NUM
cana-932	113	3	]	]	PUNCT
cana-932	113	4	tarasov	tarasov	NOUN
cana-932	113	5	,	,	PUNCT
cana-932	113	6	v.	v.	PROPN
cana-932	113	7	e.	e.	PROPN
cana-932	113	8	(	(	PUNCT
cana-932	113	9	2008	2008	NUM
cana-932	113	10	)	)	PUNCT
cana-932	113	11	.	.	PUNCT
cana-932	114	1	"	"	PUNCT
cana-932	114	2	quantum	quantum	ADJ
cana-932	114	3	mechanics	mechanic	NOUN
cana-932	114	4	of	of	ADP
cana-932	114	5	non	non	ADJ
cana-932	114	6	-	-	ADJ
cana-932	114	7	hamiltonian	hamiltonian	ADJ
cana-932	114	8	and	and	CCONJ
cana-932	114	9	dissipative	dissipative	ADJ
cana-932	114	10	systems	system	NOUN
cana-932	114	11	.	.	PUNCT
cana-932	114	12	"	"	PUNCT
cana-932	115	1	elsevier	elsevier	NOUN
cana-932	115	2	.	.	PUNCT
cana-932	116	1	[	[	X
cana-932	116	2	6	6	NUM
cana-932	116	3	]	]	X
cana-932	116	4	carpinteri	carpinteri	NOUN
cana-932	116	5	,	,	PUNCT
cana-932	116	6	a.	a.	NOUN
cana-932	116	7	,	,	PUNCT
cana-932	116	8	&	&	CCONJ
cana-932	116	9	mainardi	mainardi	PROPN
cana-932	116	10	,	,	PUNCT
cana-932	116	11	f.	f.	PROPN
cana-932	116	12	(	(	PUNCT
cana-932	116	13	eds	eds	PROPN
cana-932	116	14	.	.	PUNCT
cana-932	116	15	)	)	PUNCT
cana-932	116	16	.	.	PUNCT
cana-932	117	1	(	(	PUNCT
cana-932	117	2	1997	1997	NUM
cana-932	117	3	)	)	PUNCT
cana-932	117	4	.	.	PUNCT
cana-932	118	1	fractals	fractal	NOUN
cana-932	118	2	and	and	CCONJ
cana-932	118	3	fractional	fractional	ADJ
cana-932	118	4	calculus	calculus	NOUN
cana-932	118	5	in	in	ADP
cana-932	118	6	continuum	continuum	ADJ
cana-932	118	7	mechanics	mechanic	NOUN
cana-932	118	8	.	.	PUNCT
cana-932	118	9	springer	springer	NOUN
cana-932	118	10	.	.	PUNCT
cana-932	119	1	[	[	X
cana-932	119	2	7	7	X
cana-932	119	3	]	]	SYM
cana-932	119	4	li	li	PROPN
cana-932	119	5	,	,	PUNCT
cana-932	119	6	c.	c.	PROPN
cana-932	119	7	,	,	PUNCT
cana-932	119	8	&	&	CCONJ
cana-932	119	9	zeng	zeng	PROPN
cana-932	119	10	,	,	PUNCT
cana-932	119	11	f.	f.	PROPN
cana-932	119	12	(	(	PUNCT
cana-932	119	13	2015	2015	NUM
cana-932	119	14	)	)	PUNCT
cana-932	119	15	.	.	PUNCT
cana-932	120	1	"	"	PUNCT
cana-932	120	2	numerical	numerical	ADJ
cana-932	120	3	methods	method	NOUN
cana-932	120	4	for	for	ADP
cana-932	120	5	fractional	fractional	ADJ
cana-932	120	6	calculus	calculus	NOUN
cana-932	120	7	.	.	PUNCT
cana-932	120	8	"	"	PUNCT
cana-932	121	1	chapman	chapman	NOUN
cana-932	121	2	and	and	CCONJ
cana-932	121	3	hall	hall	PROPN
cana-932	121	4	/	/	SYM
cana-932	121	5	crc	crc	NOUN
cana-932	121	6	.	.	PUNCT
cana-932	122	1	[	[	X
cana-932	122	2	8	8	NUM
cana-932	122	3	]	]	SYM
cana-932	122	4	yang	yang	PROPN
cana-932	122	5	,	,	PUNCT
cana-932	122	6	x.	x.	PROPN
cana-932	122	7	j.	j.	PROPN
cana-932	122	8	,	,	PUNCT
cana-932	122	9	machado	machado	PROPN
cana-932	122	10	,	,	PUNCT
cana-932	122	11	j.	j.	PROPN
cana-932	122	12	a.	a.	PROPN
cana-932	122	13	t.	t.	PROPN
cana-932	122	14	,	,	PUNCT
cana-932	122	15	&	&	CCONJ
cana-932	122	16	baleanu	baleanu	PROPN
cana-932	122	17	,	,	PUNCT
cana-932	122	18	d.	d.	PROPN
cana-932	122	19	(	(	PUNCT
cana-932	122	20	2017	2017	NUM
cana-932	122	21	)	)	PUNCT
cana-932	122	22	.	.	PUNCT
cana-932	123	1	a	a	DET
cana-932	123	2	new	new	ADJ
cana-932	123	3	fractional	fractional	ADJ
cana-932	123	4	derivative	derivative	NOUN
cana-932	123	5	without	without	ADP
cana-932	123	6	singular	singular	ADJ
cana-932	123	7	kernel	kernel	NOUN
cana-932	123	8	:	:	PUNCT
cana-932	123	9	theory	theory	NOUN
cana-932	123	10	,	,	PUNCT
cana-932	123	11	methods	method	NOUN
cana-932	123	12	and	and	CCONJ
cana-932	123	13	applications	application	NOUN
cana-932	123	14	.	.	PUNCT
cana-932	124	1	de	de	X
cana-932	124	2	gruyter	gruyter	NOUN
cana-932	124	3	.	.	PUNCT
cana-932	125	1	[	[	X
cana-932	125	2	9	9	NUM
cana-932	125	3	]	]	SYM
cana-932	125	4	markowich	markowich	NOUN
cana-932	125	5	,	,	PUNCT
cana-932	125	6	p.	p.	NOUN
cana-932	125	7	a.	a.	NOUN
cana-932	125	8	,	,	PUNCT
cana-932	125	9	ringhofer	ringhofer	PROPN
cana-932	125	10	,	,	PUNCT
cana-932	125	11	c.	c.	PROPN
cana-932	125	12	a.	a.	PROPN
cana-932	125	13	,	,	PUNCT
cana-932	125	14	&	&	CCONJ
cana-932	125	15	schmeiser	schmeiser	PROPN
cana-932	125	16	,	,	PUNCT
cana-932	125	17	c.	c.	PROPN
cana-932	125	18	(	(	PUNCT
cana-932	125	19	1990	1990	NUM
cana-932	125	20	)	)	PUNCT
cana-932	125	21	.	.	PUNCT
cana-932	126	1	semiconductor	semiconductor	NOUN
cana-932	126	2	equations	equation	NOUN
cana-932	126	3	.	.	PUNCT
cana-932	127	1	springer	springer	NOUN
cana-932	127	2	-	-	PUNCT
cana-932	127	3	verlag	verlag	PROPN
cana-932	127	4	.	.	PUNCT
cana-932	128	1	[	[	X
cana-932	128	2	10	10	NUM
cana-932	128	3	]	]	X
cana-932	128	4	petrosky	petrosky	PROPN
cana-932	128	5	,	,	PUNCT
cana-932	128	6	t.	t.	PROPN
cana-932	128	7	,	,	PUNCT
cana-932	128	8	&	&	CCONJ
cana-932	128	9	prigogine	prigogine	PROPN
cana-932	128	10	,	,	PUNCT
cana-932	128	11	i.	i.	PROPN
cana-932	128	12	(	(	PUNCT
cana-932	128	13	1997	1997	NUM
cana-932	128	14	)	)	PUNCT
cana-932	128	15	.	.	PUNCT
cana-932	129	1	"	"	PUNCT
cana-932	129	2	the	the	DET
cana-932	129	3	liouville	liouville	NOUN
cana-932	129	4	space	space	NOUN
cana-932	129	5	extension	extension	NOUN
cana-932	129	6	of	of	ADP
cana-932	129	7	quantum	quantum	ADJ
cana-932	129	8	mechanics	mechanic	NOUN
cana-932	129	9	.	.	PUNCT
cana-932	129	10	"	"	PUNCT
cana-932	130	1	advances	advance	NOUN
cana-932	130	2	in	in	ADP
cana-932	130	3	chemical	chemical	ADJ
cana-932	130	4	physics	physic	NOUN
cana-932	130	5	,	,	PUNCT
cana-932	130	6	99	99	NUM
cana-932	130	7	,	,	PUNCT
cana-932	130	8	1	1	NUM
cana-932	130	9	-	-	SYM
cana-932	130	10	120	120	NUM
cana-932	130	11	.	.	PUNCT