id	sid	tid	token	lemma	pos
ejpam-5131	1	1	european	european	PROPN
ejpam-5131	1	2	journal	journal	PROPN
ejpam-5131	1	3	of	of	ADP
ejpam-5131	1	4	pure	pure	ADJ
ejpam-5131	1	5	and	and	CCONJ
ejpam-5131	1	6	applied	apply	VERB
ejpam-5131	1	7	mathematics	mathematic	NOUN
ejpam-5131	1	8	vol	vol	NOUN
ejpam-5131	1	9	.	.	PROPN
ejpam-5131	2	1	17	17	NUM
ejpam-5131	2	2	,	,	PUNCT
ejpam-5131	2	3	no	no	INTJ
ejpam-5131	2	4	.	.	NOUN
ejpam-5131	2	5	2	2	NUM
ejpam-5131	2	6	,	,	PUNCT
ejpam-5131	2	7	2024	2024	NUM
ejpam-5131	2	8	,	,	PUNCT
ejpam-5131	2	9	835	835	NUM
ejpam-5131	2	10	-	-	SYM
ejpam-5131	2	11	851	851	NUM
ejpam-5131	2	12	issn	issn	PROPN
ejpam-5131	2	13	1307	1307	NUM
ejpam-5131	2	14	-	-	SYM
ejpam-5131	2	15	5543	5543	NUM
ejpam-5131	2	16	–	–	PUNCT
ejpam-5131	2	17	ejpam.com	ejpam.com	X
ejpam-5131	2	18	published	publish	VERB
ejpam-5131	2	19	by	by	ADP
ejpam-5131	2	20	new	new	PROPN
ejpam-5131	2	21	york	york	PROPN
ejpam-5131	2	22	business	business	PROPN
ejpam-5131	2	23	global	global	ADJ
ejpam-5131	2	24	analysis	analysis	NOUN
ejpam-5131	2	25	and	and	CCONJ
ejpam-5131	2	26	applications	application	NOUN
ejpam-5131	2	27	of	of	ADP
ejpam-5131	2	28	the	the	DET
ejpam-5131	2	29	chaotic	chaotic	ADJ
ejpam-5131	2	30	hyperbolic	hyperbolic	ADJ
ejpam-5131	2	31	memristor	memristor	NOUN
ejpam-5131	2	32	model	model	NOUN
ejpam-5131	2	33	with	with	ADP
ejpam-5131	2	34	fractional	fractional	ADJ
ejpam-5131	2	35	order	order	NOUN
ejpam-5131	2	36	derivative	derivative	ADJ
ejpam-5131	2	37	ghada	ghada	NOUN
ejpam-5131	2	38	a.	a.	PROPN
ejpam-5131	2	39	ahmed	ahmed	PROPN
ejpam-5131	2	40	department	department	PROPN
ejpam-5131	2	41	of	of	ADP
ejpam-5131	2	42	mathematics	mathematic	NOUN
ejpam-5131	2	43	,	,	PUNCT
ejpam-5131	2	44	faculty	faculty	NOUN
ejpam-5131	2	45	of	of	ADP
ejpam-5131	2	46	science	science	NOUN
ejpam-5131	2	47	,	,	PUNCT
ejpam-5131	2	48	al	al	PROPN
ejpam-5131	2	49	-	-	PUNCT
ejpam-5131	2	50	baha	baha	PROPN
ejpam-5131	2	51	university	university	PROPN
ejpam-5131	2	52	,	,	PUNCT
ejpam-5131	2	53	albaha	albaha	PROPN
ejpam-5131	2	54	,	,	PUNCT
ejpam-5131	2	55	albaha	albaha	PROPN
ejpam-5131	2	56	,	,	PUNCT
ejpam-5131	2	57	saudia	saudia	PROPN
ejpam-5131	2	58	arabia	arabia	PROPN
ejpam-5131	2	59	abstract	abstract	PROPN
ejpam-5131	2	60	.	.	PUNCT
ejpam-5131	3	1	this	this	DET
ejpam-5131	3	2	work	work	NOUN
ejpam-5131	3	3	presents	present	VERB
ejpam-5131	3	4	a	a	DET
ejpam-5131	3	5	new	new	ADJ
ejpam-5131	3	6	five	five	NUM
ejpam-5131	3	7	-	-	PUNCT
ejpam-5131	3	8	dimensional	dimensional	ADJ
ejpam-5131	3	9	fractional	fractional	ADJ
ejpam-5131	3	10	-	-	PUNCT
ejpam-5131	3	11	order	order	NOUN
ejpam-5131	3	12	chaotic	chaotic	ADJ
ejpam-5131	3	13	system	system	NOUN
ejpam-5131	3	14	that	that	PRON
ejpam-5131	3	15	includes	include	VERB
ejpam-5131	3	16	a	a	DET
ejpam-5131	3	17	feedback	feedback	NOUN
ejpam-5131	3	18	memristor	memristor	NOUN
ejpam-5131	3	19	.	.	PUNCT
ejpam-5131	4	1	a	a	DET
ejpam-5131	4	2	lorenz	lorenz	PROPN
ejpam-5131	4	3	-	-	PUNCT
ejpam-5131	4	4	stenflo	stenflo	ADV
ejpam-5131	4	5	-	-	PUNCT
ejpam-5131	4	6	based	base	VERB
ejpam-5131	4	7	fractional	fractional	ADJ
ejpam-5131	4	8	-	-	PUNCT
ejpam-5131	4	9	order	order	NOUN
ejpam-5131	4	10	chaotic	chaotic	ADJ
ejpam-5131	4	11	system	system	NOUN
ejpam-5131	4	12	with	with	ADP
ejpam-5131	4	13	five	five	NUM
ejpam-5131	4	14	dimensions	dimension	NOUN
ejpam-5131	4	15	that	that	PRON
ejpam-5131	4	16	contains	contain	VERB
ejpam-5131	4	17	feedback	feedback	NOUN
ejpam-5131	4	18	memristor	memristor	NOUN
ejpam-5131	4	19	dynamics	dynamic	NOUN
ejpam-5131	4	20	is	be	AUX
ejpam-5131	4	21	used	use	VERB
ejpam-5131	4	22	to	to	PART
ejpam-5131	4	23	do	do	VERB
ejpam-5131	4	24	this	this	PRON
ejpam-5131	4	25	.	.	PUNCT
ejpam-5131	5	1	this	this	DET
ejpam-5131	5	2	work	work	NOUN
ejpam-5131	5	3	focuses	focus	VERB
ejpam-5131	5	4	on	on	ADP
ejpam-5131	5	5	chaotic	chaotic	ADJ
ejpam-5131	5	6	models	model	NOUN
ejpam-5131	5	7	through	through	ADP
ejpam-5131	5	8	the	the	DET
ejpam-5131	5	9	abc	abc	PROPN
ejpam-5131	5	10	fractional	fractional	PROPN
ejpam-5131	5	11	derivative	derivative	NOUN
ejpam-5131	5	12	,	,	PUNCT
ejpam-5131	5	13	a	a	DET
ejpam-5131	5	14	concept	concept	NOUN
ejpam-5131	5	15	we	we	PRON
ejpam-5131	5	16	rigorously	rigorously	ADV
ejpam-5131	5	17	examine	examine	VERB
ejpam-5131	5	18	.	.	PUNCT
ejpam-5131	6	1	we	we	PRON
ejpam-5131	6	2	designed	design	VERB
ejpam-5131	6	3	and	and	CCONJ
ejpam-5131	6	4	used	use	VERB
ejpam-5131	6	5	sophisticated	sophisticated	ADJ
ejpam-5131	6	6	numerical	numerical	ADJ
ejpam-5131	6	7	algorithms	algorithm	NOUN
ejpam-5131	6	8	to	to	PART
ejpam-5131	6	9	model	model	VERB
ejpam-5131	6	10	fractional	fractional	ADJ
ejpam-5131	6	11	-	-	PUNCT
ejpam-5131	6	12	order	order	NOUN
ejpam-5131	6	13	dynamics	dynamic	NOUN
ejpam-5131	6	14	with	with	ADP
ejpam-5131	6	15	the	the	DET
ejpam-5131	6	16	utmost	utmost	ADJ
ejpam-5131	6	17	precision	precision	NOUN
ejpam-5131	6	18	to	to	PART
ejpam-5131	6	19	understand	understand	VERB
ejpam-5131	6	20	this	this	DET
ejpam-5131	6	21	system	system	NOUN
ejpam-5131	6	22	’s	’s	PART
ejpam-5131	6	23	complex	complex	ADJ
ejpam-5131	6	24	characteristics	characteristic	NOUN
ejpam-5131	6	25	.	.	PUNCT
ejpam-5131	7	1	these	these	DET
ejpam-5131	7	2	numerical	numerical	ADJ
ejpam-5131	7	3	approaches	approach	NOUN
ejpam-5131	7	4	excel	excel	VERB
ejpam-5131	7	5	at	at	ADP
ejpam-5131	7	6	noninteger	noninteger	NOUN
ejpam-5131	7	7	order	order	NOUN
ejpam-5131	7	8	differentiation	differentiation	NOUN
ejpam-5131	7	9	,	,	PUNCT
ejpam-5131	7	10	which	which	PRON
ejpam-5131	7	11	standard	standard	ADJ
ejpam-5131	7	12	numerical	numerical	ADJ
ejpam-5131	7	13	methods	method	NOUN
ejpam-5131	7	14	struggle	struggle	VERB
ejpam-5131	7	15	with	with	ADP
ejpam-5131	7	16	.	.	PUNCT
ejpam-5131	8	1	our	our	PRON
ejpam-5131	8	2	research	research	NOUN
ejpam-5131	8	3	uses	use	VERB
ejpam-5131	8	4	fractional	fractional	ADJ
ejpam-5131	8	5	calculus	calculus	NOUN
ejpam-5131	8	6	to	to	PART
ejpam-5131	8	7	increase	increase	VERB
ejpam-5131	8	8	the	the	DET
ejpam-5131	8	9	system	system	NOUN
ejpam-5131	8	10	’s	’s	PART
ejpam-5131	8	11	complexity	complexity	NOUN
ejpam-5131	8	12	and	and	CCONJ
ejpam-5131	8	13	robustness	robustness	NOUN
ejpam-5131	8	14	,	,	PUNCT
ejpam-5131	8	15	revealing	reveal	VERB
ejpam-5131	8	16	its	its	PRON
ejpam-5131	8	17	hyperchaotic	hyperchaotic	ADJ
ejpam-5131	8	18	nature	nature	NOUN
ejpam-5131	8	19	.	.	PUNCT
ejpam-5131	9	1	we	we	PRON
ejpam-5131	9	2	demonstrate	demonstrate	VERB
ejpam-5131	9	3	that	that	SCONJ
ejpam-5131	9	4	the	the	DET
ejpam-5131	9	5	system	system	NOUN
ejpam-5131	9	6	is	be	AUX
ejpam-5131	9	7	chaotic	chaotic	ADJ
ejpam-5131	9	8	and	and	CCONJ
ejpam-5131	9	9	stable	stable	ADJ
ejpam-5131	9	10	over	over	ADP
ejpam-5131	9	11	fractional	fractional	ADJ
ejpam-5131	9	12	orders	order	NOUN
ejpam-5131	9	13	using	use	VERB
ejpam-5131	9	14	eigenvalues	eigenvalue	NOUN
ejpam-5131	9	15	,	,	PUNCT
ejpam-5131	9	16	lyapunov	lyapunov	NOUN
ejpam-5131	9	17	exponents	exponent	NOUN
ejpam-5131	9	18	,	,	PUNCT
ejpam-5131	9	19	kaplan	kaplan	PROPN
ejpam-5131	9	20	-	-	PUNCT
ejpam-5131	9	21	yorke	yorke	PROPN
ejpam-5131	9	22	dimensions	dimension	NOUN
ejpam-5131	9	23	,	,	PUNCT
ejpam-5131	9	24	maximal	maximal	ADJ
ejpam-5131	9	25	exponents	exponent	NOUN
ejpam-5131	9	26	,	,	PUNCT
ejpam-5131	9	27	phase	phase	NOUN
ejpam-5131	9	28	portraits	portrait	NOUN
ejpam-5131	9	29	,	,	PUNCT
ejpam-5131	9	30	and	and	CCONJ
ejpam-5131	9	31	equilibrium	equilibrium	NOUN
ejpam-5131	9	32	points	point	NOUN
ejpam-5131	9	33	.	.	PUNCT
ejpam-5131	10	1	our	our	PRON
ejpam-5131	10	2	conclusions	conclusion	NOUN
ejpam-5131	10	3	are	be	AUX
ejpam-5131	10	4	strengthened	strengthen	VERB
ejpam-5131	10	5	by	by	ADP
ejpam-5131	10	6	using	use	VERB
ejpam-5131	10	7	these	these	DET
ejpam-5131	10	8	numerical	numerical	ADJ
ejpam-5131	10	9	systems	system	NOUN
ejpam-5131	10	10	,	,	PUNCT
ejpam-5131	10	11	intended	intend	VERB
ejpam-5131	10	12	for	for	ADP
ejpam-5131	10	13	this	this	DET
ejpam-5131	10	14	work	work	NOUN
ejpam-5131	10	15	,	,	PUNCT
ejpam-5131	10	16	and	and	CCONJ
ejpam-5131	10	17	analytical	analytical	ADJ
ejpam-5131	10	18	tools	tool	NOUN
ejpam-5131	10	19	.	.	PUNCT
ejpam-5131	11	1	we	we	PRON
ejpam-5131	11	2	improve	improve	VERB
ejpam-5131	11	3	our	our	PRON
ejpam-5131	11	4	understanding	understanding	NOUN
ejpam-5131	11	5	of	of	ADP
ejpam-5131	11	6	fractional	fractional	ADJ
ejpam-5131	11	7	-	-	PUNCT
ejpam-5131	11	8	order	order	NOUN
ejpam-5131	11	9	chaotic	chaotic	ADJ
ejpam-5131	11	10	systems	system	NOUN
ejpam-5131	11	11	with	with	ADP
ejpam-5131	11	12	our	our	PRON
ejpam-5131	11	13	research	research	NOUN
ejpam-5131	11	14	.	.	PUNCT
ejpam-5131	12	1	it	it	PRON
ejpam-5131	12	2	illuminates	illuminate	VERB
ejpam-5131	12	3	how	how	SCONJ
ejpam-5131	12	4	to	to	PART
ejpam-5131	12	5	improve	improve	VERB
ejpam-5131	12	6	electrical	electrical	ADJ
ejpam-5131	12	7	integrations	integration	NOUN
ejpam-5131	12	8	and	and	CCONJ
ejpam-5131	12	9	create	create	VERB
ejpam-5131	12	10	more	more	ADV
ejpam-5131	12	11	sophisticated	sophisticated	ADJ
ejpam-5131	12	12	nonlinear	nonlinear	ADJ
ejpam-5131	12	13	dynamical	dynamical	ADJ
ejpam-5131	12	14	systems	system	NOUN
ejpam-5131	12	15	.	.	PUNCT
ejpam-5131	13	1	this	this	DET
ejpam-5131	13	2	work	work	NOUN
ejpam-5131	13	3	establishes	establish	VERB
ejpam-5131	13	4	the	the	DET
ejpam-5131	13	5	approach	approach	NOUN
ejpam-5131	13	6	and	and	CCONJ
ejpam-5131	13	7	insights	insight	NOUN
ejpam-5131	13	8	for	for	ADP
ejpam-5131	13	9	future	future	ADJ
ejpam-5131	13	10	research	research	NOUN
ejpam-5131	13	11	,	,	PUNCT
ejpam-5131	13	12	guiding	guide	VERB
ejpam-5131	13	13	the	the	DET
ejpam-5131	13	14	development	development	NOUN
ejpam-5131	13	15	of	of	ADP
ejpam-5131	13	16	new	new	ADJ
ejpam-5131	13	17	systems	system	NOUN
ejpam-5131	13	18	with	with	ADP
ejpam-5131	13	19	enhanced	enhanced	ADJ
ejpam-5131	13	20	dynamical	dynamical	ADJ
ejpam-5131	13	21	features	feature	NOUN
ejpam-5131	13	22	2020	2020	NUM
ejpam-5131	13	23	mathematics	mathematic	NOUN
ejpam-5131	13	24	subject	subject	ADJ
ejpam-5131	13	25	classifications	classification	NOUN
ejpam-5131	13	26	:	:	PUNCT
ejpam-5131	13	27	97m40	97m40	NUM
ejpam-5131	13	28	key	key	ADJ
ejpam-5131	13	29	words	word	NOUN
ejpam-5131	13	30	and	and	CCONJ
ejpam-5131	13	31	phrases	phrase	NOUN
ejpam-5131	13	32	:	:	PUNCT
ejpam-5131	13	33	fractional	fractional	ADJ
ejpam-5131	13	34	model	model	NOUN
ejpam-5131	13	35	,	,	PUNCT
ejpam-5131	13	36	lorenz	lorenz	PROPN
ejpam-5131	13	37	-	-	PUNCT
ejpam-5131	13	38	stenflo	stenflo	ADJ
ejpam-5131	13	39	model	model	NOUN
ejpam-5131	13	40	,	,	PUNCT
ejpam-5131	13	41	hyperchaotic	hyperchaotic	ADJ
ejpam-5131	13	42	behavior	behavior	NOUN
ejpam-5131	13	43	,	,	PUNCT
ejpam-5131	13	44	nonlinear	nonlinear	ADJ
ejpam-5131	13	45	dynamical	dynamical	ADJ
ejpam-5131	13	46	systems	system	NOUN
ejpam-5131	13	47	,	,	PUNCT
ejpam-5131	13	48	fractional	fractional	ADJ
ejpam-5131	13	49	derivative	derivative	NOUN
ejpam-5131	13	50	,	,	PUNCT
ejpam-5131	13	51	simulation	simulation	NOUN
ejpam-5131	13	52	.	.	PUNCT
ejpam-5131	14	1	1	1	NUM
ejpam-5131	14	2	.	.	X
ejpam-5131	14	3	introduction	introduction	NOUN
ejpam-5131	14	4	the	the	DET
ejpam-5131	14	5	history	history	NOUN
ejpam-5131	14	6	of	of	ADP
ejpam-5131	14	7	non	non	ADJ
ejpam-5131	14	8	-	-	ADJ
ejpam-5131	14	9	integer	integer	ADJ
ejpam-5131	14	10	order	order	NOUN
ejpam-5131	14	11	systems	system	NOUN
ejpam-5131	14	12	in	in	ADP
ejpam-5131	14	13	science	science	NOUN
ejpam-5131	14	14	and	and	CCONJ
ejpam-5131	14	15	technology	technology	NOUN
ejpam-5131	14	16	,	,	PUNCT
ejpam-5131	14	17	which	which	PRON
ejpam-5131	14	18	has	have	AUX
ejpam-5131	14	19	been	be	AUX
ejpam-5131	14	20	heavily	heavily	ADV
ejpam-5131	14	21	influenced	influence	VERB
ejpam-5131	14	22	by	by	ADP
ejpam-5131	14	23	fractional	fractional	ADJ
ejpam-5131	14	24	derivatives	derivative	NOUN
ejpam-5131	14	25	,	,	PUNCT
ejpam-5131	14	26	has	have	AUX
ejpam-5131	14	27	had	have	VERB
ejpam-5131	14	28	a	a	DET
ejpam-5131	14	29	significant	significant	ADJ
ejpam-5131	14	30	impact	impact	NOUN
ejpam-5131	14	31	on	on	ADP
ejpam-5131	14	32	the	the	DET
ejpam-5131	14	33	emergence	emergence	NOUN
ejpam-5131	14	34	of	of	ADP
ejpam-5131	14	35	chaotic	chaotic	ADJ
ejpam-5131	14	36	systems	system	NOUN
ejpam-5131	14	37	[	[	X
ejpam-5131	14	38	37].fractional	37].fractional	ADJ
ejpam-5131	14	39	derivatives	derivative	NOUN
ejpam-5131	14	40	are	be	AUX
ejpam-5131	14	41	used	use	VERB
ejpam-5131	14	42	to	to	PART
ejpam-5131	14	43	explain	explain	VERB
ejpam-5131	14	44	and	and	CCONJ
ejpam-5131	14	45	resolve	resolve	VERB
ejpam-5131	14	46	integral	integral	ADJ
ejpam-5131	14	47	equations	equation	NOUN
ejpam-5131	14	48	as	as	ADV
ejpam-5131	14	49	well	well	ADV
ejpam-5131	14	50	as	as	ADP
ejpam-5131	14	51	ordinary	ordinary	ADJ
ejpam-5131	14	52	and	and	CCONJ
ejpam-5131	14	53	partial	partial	ADJ
ejpam-5131	14	54	differential	differential	ADJ
ejpam-5131	14	55	equations	equation	NOUN
ejpam-5131	14	56	as	as	ADP
ejpam-5131	14	57	an	an	DET
ejpam-5131	14	58	extension	extension	NOUN
ejpam-5131	14	59	of	of	ADP
ejpam-5131	14	60	classical	classical	ADJ
ejpam-5131	14	61	derivatives	derivative	NOUN
ejpam-5131	14	62	.	.	PUNCT
ejpam-5131	15	1	atangana	atangana	PROPN
ejpam-5131	15	2	-	-	PUNCT
ejpam-5131	15	3	baleanu	baleanu	PROPN
ejpam-5131	15	4	,	,	PUNCT
ejpam-5131	15	5	caputo	caputo	PROPN
ejpam-5131	15	6	,	,	PUNCT
ejpam-5131	15	7	letnikov	letnikov	PROPN
ejpam-5131	15	8	,	,	PUNCT
ejpam-5131	15	9	hadamard	hadamard	ADJ
ejpam-5131	15	10	,	,	PUNCT
ejpam-5131	15	11	marchaud	marchaud	ADV
ejpam-5131	15	12	,	,	PUNCT
ejpam-5131	15	13	weyl	weyl	VERB
ejpam-5131	15	14	,	,	PUNCT
ejpam-5131	15	15	and	and	CCONJ
ejpam-5131	15	16	coimbra	coimbra	PROPN
ejpam-5131	15	17	are	be	AUX
ejpam-5131	15	18	just	just	ADV
ejpam-5131	15	19	a	a	DET
ejpam-5131	15	20	few	few	ADJ
ejpam-5131	15	21	of	of	ADP
ejpam-5131	15	22	the	the	DET
ejpam-5131	15	23	well	well	ADV
ejpam-5131	15	24	-	-	PUNCT
ejpam-5131	15	25	known	know	VERB
ejpam-5131	15	26	definitions	definition	NOUN
ejpam-5131	15	27	of	of	ADP
ejpam-5131	15	28	fractional	fractional	ADJ
ejpam-5131	15	29	derivatives[38	derivatives[38	NOUN
ejpam-5131	15	30	]	]	PUNCT
ejpam-5131	15	31	.	.	PUNCT
ejpam-5131	16	1	doi	doi	NOUN
ejpam-5131	16	2	:	:	PUNCT
ejpam-5131	16	3	https://doi.org/10.29020/nybg.ejpam.v17i2.5131	https://doi.org/10.29020/nybg.ejpam.v17i2.5131	NUM
ejpam-5131	16	4	email	email	NOUN
ejpam-5131	16	5	address	address	NOUN
ejpam-5131	16	6	:	:	PUNCT
ejpam-5131	16	7	gahmed@bu.edu.sa	gahmed@bu.edu.sa	PROPN
ejpam-5131	16	8	(	(	PUNCT
ejpam-5131	16	9	g.	g.	PROPN
ejpam-5131	16	10	a.	a.	PROPN
ejpam-5131	16	11	ahmed	ahmed	PROPN
ejpam-5131	16	12	)	)	PUNCT
ejpam-5131	16	13	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5131	17	1	835	835	NUM
ejpam-5131	17	2	©	©	ADP
ejpam-5131	17	3	2024	2024	NUM
ejpam-5131	17	4	ejpam	ejpam	NOUN
ejpam-5131	17	5	all	all	DET
ejpam-5131	17	6	rights	right	NOUN
ejpam-5131	17	7	reserved	reserve	VERB
ejpam-5131	17	8	.	.	PUNCT
ejpam-5131	18	1	g.	g.	PROPN
ejpam-5131	18	2	a.	a.	PROPN
ejpam-5131	18	3	ahmed	ahmed	PROPN
ejpam-5131	18	4	/	/	SYM
ejpam-5131	18	5	eur	eur	PROPN
ejpam-5131	18	6	.	.	PUNCT
ejpam-5131	19	1	j.	j.	PROPN
ejpam-5131	19	2	pure	pure	PROPN
ejpam-5131	19	3	appl	appl	PROPN
ejpam-5131	19	4	.	.	PROPN
ejpam-5131	19	5	math	math	PROPN
ejpam-5131	19	6	,	,	PUNCT
ejpam-5131	19	7	17	17	NUM
ejpam-5131	19	8	(	(	PUNCT
ejpam-5131	19	9	2	2	NUM
ejpam-5131	19	10	)	)	PUNCT
ejpam-5131	19	11	(	(	PUNCT
ejpam-5131	19	12	2024	2024	NUM
ejpam-5131	19	13	)	)	PUNCT
ejpam-5131	19	14	,	,	PUNCT
ejpam-5131	19	15	835	835	NUM
ejpam-5131	19	16	-	-	SYM
ejpam-5131	19	17	851	851	NUM
ejpam-5131	19	18	836	836	NUM
ejpam-5131	19	19	fractional	fractional	ADJ
ejpam-5131	19	20	derivatives	derivative	NOUN
ejpam-5131	19	21	also	also	ADV
ejpam-5131	19	22	have	have	VERB
ejpam-5131	19	23	a	a	DET
ejpam-5131	19	24	wide	wide	ADJ
ejpam-5131	19	25	range	range	NOUN
ejpam-5131	19	26	of	of	ADP
ejpam-5131	19	27	multidisciplinary	multidisciplinary	ADJ
ejpam-5131	19	28	applications	application	NOUN
ejpam-5131	19	29	.	.	PUNCT
ejpam-5131	20	1	the	the	DET
ejpam-5131	20	2	consequences	consequence	NOUN
ejpam-5131	20	3	of	of	ADP
ejpam-5131	20	4	the	the	DET
ejpam-5131	20	5	modified	modified	PROPN
ejpam-5131	20	6	chua	chua	PROPN
ejpam-5131	20	7	’s	’s	PART
ejpam-5131	20	8	system	system	NOUN
ejpam-5131	20	9	explored	explore	VERB
ejpam-5131	20	10	by	by	ADP
ejpam-5131	20	11	tom	tom	PROPN
ejpam-5131	20	12	et	et	PROPN
ejpam-5131	20	13	al	al	PROPN
ejpam-5131	20	14	.	.	PUNCT
ejpam-5131	20	15	using	use	VERB
ejpam-5131	20	16	fractional	fractional	ADJ
ejpam-5131	20	17	derivatives	derivative	NOUN
ejpam-5131	20	18	are	be	AUX
ejpam-5131	20	19	only	only	ADV
ejpam-5131	20	20	one	one	NUM
ejpam-5131	20	21	example	example	NOUN
ejpam-5131	20	22	of	of	ADP
ejpam-5131	20	23	the	the	DET
ejpam-5131	20	24	various	various	ADJ
ejpam-5131	20	25	current	current	ADJ
ejpam-5131	20	26	contributions	contribution	NOUN
ejpam-5131	20	27	of	of	ADP
ejpam-5131	20	28	fractional	fractional	ADJ
ejpam-5131	20	29	derivatives	derivative	NOUN
ejpam-5131	20	30	in	in	ADP
ejpam-5131	20	31	the	the	DET
ejpam-5131	20	32	field	field	NOUN
ejpam-5131	20	33	of	of	ADP
ejpam-5131	20	34	fractional	fractional	ADJ
ejpam-5131	20	35	index	index	NOUN
ejpam-5131	20	36	chaotic	chaotic	ADJ
ejpam-5131	20	37	systems[18].recently	systems[18].recently	ADV
ejpam-5131	20	38	,	,	PUNCT
ejpam-5131	20	39	chaos	chaos	NOUN
ejpam-5131	20	40	dynamics	dynamic	NOUN
ejpam-5131	20	41	control	control	NOUN
ejpam-5131	20	42	has	have	AUX
ejpam-5131	20	43	been	be	AUX
ejpam-5131	20	44	more	more	ADV
ejpam-5131	20	45	well	well	ADV
ejpam-5131	20	46	-	-	PUNCT
ejpam-5131	20	47	liked	like	VERB
ejpam-5131	20	48	due	due	ADP
ejpam-5131	20	49	to	to	ADP
ejpam-5131	20	50	a	a	DET
ejpam-5131	20	51	new	new	ADJ
ejpam-5131	20	52	trend	trend	NOUN
ejpam-5131	20	53	of	of	ADP
ejpam-5131	20	54	studying	study	VERB
ejpam-5131	20	55	chaotic	chaotic	ADJ
ejpam-5131	20	56	systems	system	NOUN
ejpam-5131	20	57	utilizing	utilize	VERB
ejpam-5131	20	58	various	various	ADJ
ejpam-5131	20	59	mathematical	mathematical	ADJ
ejpam-5131	20	60	and	and	CCONJ
ejpam-5131	20	61	physical	physical	ADJ
ejpam-5131	20	62	models	model	NOUN
ejpam-5131	20	63	,	,	PUNCT
ejpam-5131	20	64	such	such	ADJ
ejpam-5131	20	65	as	as	ADP
ejpam-5131	20	66	the	the	DET
ejpam-5131	20	67	chen	chen	PROPN
ejpam-5131	20	68	system	system	PROPN
ejpam-5131	20	69	with	with	ADP
ejpam-5131	20	70	fractional	fractional	ADJ
ejpam-5131	20	71	order	order	NOUN
ejpam-5131	20	72	investigated	investigate	VERB
ejpam-5131	20	73	by	by	ADP
ejpam-5131	20	74	chunguang	chunguang	PROPN
ejpam-5131	20	75	and	and	CCONJ
ejpam-5131	20	76	guanrong[29].the	guanrong[29].the	PROPN
ejpam-5131	20	77	study	study	NOUN
ejpam-5131	20	78	of	of	ADP
ejpam-5131	20	79	chaotic	chaotic	ADJ
ejpam-5131	20	80	regimes	regime	NOUN
ejpam-5131	20	81	and	and	CCONJ
ejpam-5131	20	82	the	the	DET
ejpam-5131	20	83	creation	creation	NOUN
ejpam-5131	20	84	of	of	ADP
ejpam-5131	20	85	low	low	ADJ
ejpam-5131	20	86	-	-	PUNCT
ejpam-5131	20	87	power	power	NOUN
ejpam-5131	20	88	systems	system	NOUN
ejpam-5131	20	89	with	with	ADP
ejpam-5131	20	90	rapid	rapid	ADJ
ejpam-5131	20	91	processing	processing	NOUN
ejpam-5131	20	92	units	unit	NOUN
ejpam-5131	20	93	both	both	CCONJ
ejpam-5131	20	94	heavily	heavily	ADV
ejpam-5131	20	95	rely	rely	VERB
ejpam-5131	20	96	on	on	ADP
ejpam-5131	20	97	digital	digital	ADJ
ejpam-5131	20	98	/	/	SYM
ejpam-5131	20	99	analogue	analogue	NOUN
ejpam-5131	20	100	electronics	electronic	NOUN
ejpam-5131	20	101	and	and	CCONJ
ejpam-5131	20	102	fractional	fractional	ADJ
ejpam-5131	20	103	index	index	NOUN
ejpam-5131	20	104	systems	system	NOUN
ejpam-5131	20	105	.	.	PUNCT
ejpam-5131	21	1	we	we	PRON
ejpam-5131	21	2	provide	provide	VERB
ejpam-5131	21	3	digital	digital	ADJ
ejpam-5131	21	4	systems	system	NOUN
ejpam-5131	21	5	and	and	CCONJ
ejpam-5131	21	6	their	their	PRON
ejpam-5131	21	7	component	component	NOUN
ejpam-5131	21	8	viewpoints	viewpoint	NOUN
ejpam-5131	21	9	for	for	ADP
ejpam-5131	21	10	a	a	DET
ejpam-5131	21	11	cubic	cubic	ADJ
ejpam-5131	21	12	nonlinear	nonlinear	ADJ
ejpam-5131	21	13	resistor	resistor	NOUN
ejpam-5131	21	14	system	system	NOUN
ejpam-5131	21	15	’s	’s	PART
ejpam-5131	21	16	fractional	fractional	ADJ
ejpam-5131	21	17	index	index	NOUN
ejpam-5131	21	18	,	,	PUNCT
ejpam-5131	21	19	including	include	VERB
ejpam-5131	21	20	adaptive	adaptive	ADJ
ejpam-5131	21	21	controllers	controller	NOUN
ejpam-5131	21	22	with	with	ADP
ejpam-5131	21	23	fpga	fpga	PROPN
ejpam-5131	21	24	implementation	implementation	NOUN
ejpam-5131	21	25	.	.	PUNCT
ejpam-5131	22	1	the	the	DET
ejpam-5131	22	2	novel	novel	ADJ
ejpam-5131	22	3	chaotic	chaotic	ADJ
ejpam-5131	22	4	system	system	NOUN
ejpam-5131	22	5	introduced	introduce	VERB
ejpam-5131	22	6	in	in	ADP
ejpam-5131	22	7	this	this	DET
ejpam-5131	22	8	work	work	NOUN
ejpam-5131	22	9	is	be	AUX
ejpam-5131	22	10	ingeniously	ingeniously	ADV
ejpam-5131	22	11	built	build	VERB
ejpam-5131	22	12	upon	upon	SCONJ
ejpam-5131	22	13	the	the	DET
ejpam-5131	22	14	rich	rich	ADJ
ejpam-5131	22	15	foundation	foundation	NOUN
ejpam-5131	22	16	provided	provide	VERB
ejpam-5131	22	17	by	by	ADP
ejpam-5131	22	18	the	the	DET
ejpam-5131	22	19	lorenz	lorenz	PROPN
ejpam-5131	22	20	-	-	PUNCT
ejpam-5131	22	21	stenflo	stenflo	ADJ
ejpam-5131	22	22	model	model	NOUN
ejpam-5131	22	23	,	,	PUNCT
ejpam-5131	22	24	a	a	DET
ejpam-5131	22	25	model	model	NOUN
ejpam-5131	22	26	that	that	PRON
ejpam-5131	22	27	holds	hold	VERB
ejpam-5131	22	28	a	a	DET
ejpam-5131	22	29	prestigious	prestigious	ADJ
ejpam-5131	22	30	place	place	NOUN
ejpam-5131	22	31	in	in	ADP
ejpam-5131	22	32	the	the	DET
ejpam-5131	22	33	annals	annal	NOUN
ejpam-5131	22	34	of	of	ADP
ejpam-5131	22	35	chaos	chaos	NOUN
ejpam-5131	22	36	theory	theory	NOUN
ejpam-5131	22	37	for	for	ADP
ejpam-5131	22	38	its	its	PRON
ejpam-5131	22	39	profound	profound	ADJ
ejpam-5131	22	40	insights	insight	NOUN
ejpam-5131	22	41	into	into	ADP
ejpam-5131	22	42	the	the	DET
ejpam-5131	22	43	dynamics	dynamic	NOUN
ejpam-5131	22	44	of	of	ADP
ejpam-5131	22	45	complex	complex	ADJ
ejpam-5131	22	46	systems	system	NOUN
ejpam-5131	22	47	.	.	PUNCT
ejpam-5131	23	1	the	the	DET
ejpam-5131	23	2	original	original	ADJ
ejpam-5131	23	3	lorenz	lorenz	PROPN
ejpam-5131	23	4	system	system	NOUN
ejpam-5131	23	5	,	,	PUNCT
ejpam-5131	23	6	from	from	ADP
ejpam-5131	23	7	which	which	PRON
ejpam-5131	23	8	the	the	DET
ejpam-5131	23	9	lorenz	lorenz	PROPN
ejpam-5131	23	10	-	-	PUNCT
ejpam-5131	23	11	stenflo	stenflo	ADJ
ejpam-5131	23	12	model	model	NOUN
ejpam-5131	23	13	evolved	evolve	VERB
ejpam-5131	23	14	,	,	PUNCT
ejpam-5131	23	15	emerged	emerge	VERB
ejpam-5131	23	16	as	as	ADP
ejpam-5131	23	17	a	a	DET
ejpam-5131	23	18	cornerstone	cornerstone	NOUN
ejpam-5131	23	19	in	in	ADP
ejpam-5131	23	20	the	the	DET
ejpam-5131	23	21	study	study	NOUN
ejpam-5131	23	22	of	of	ADP
ejpam-5131	23	23	atmospheric	atmospheric	ADJ
ejpam-5131	23	24	convection	convection	NOUN
ejpam-5131	23	25	,	,	PUNCT
ejpam-5131	23	26	unveiling	unveil	VERB
ejpam-5131	23	27	the	the	DET
ejpam-5131	23	28	intricate	intricate	ADJ
ejpam-5131	23	29	dance	dance	NOUN
ejpam-5131	23	30	of	of	ADP
ejpam-5131	23	31	determinism	determinism	NOUN
ejpam-5131	23	32	and	and	CCONJ
ejpam-5131	23	33	unpredictability	unpredictability	NOUN
ejpam-5131	23	34	that	that	PRON
ejpam-5131	23	35	characterises	characterise	VERB
ejpam-5131	23	36	chaotic	chaotic	ADJ
ejpam-5131	23	37	systems	system	NOUN
ejpam-5131	23	38	.	.	PUNCT
ejpam-5131	24	1	this	this	DET
ejpam-5131	24	2	model	model	NOUN
ejpam-5131	24	3	’s	’s	PART
ejpam-5131	24	4	fame	fame	NOUN
ejpam-5131	24	5	stems	stem	VERB
ejpam-5131	24	6	from	from	ADP
ejpam-5131	24	7	its	its	PRON
ejpam-5131	24	8	vivid	vivid	ADJ
ejpam-5131	24	9	illustration	illustration	NOUN
ejpam-5131	24	10	of	of	ADP
ejpam-5131	24	11	the	the	DET
ejpam-5131	24	12	”	"	PUNCT
ejpam-5131	24	13	butterfly	butterfly	NOUN
ejpam-5131	24	14	effect	effect	NOUN
ejpam-5131	24	15	,	,	PUNCT
ejpam-5131	24	16	”	"	PUNCT
ejpam-5131	24	17	a	a	DET
ejpam-5131	24	18	metaphor	metaphor	NOUN
ejpam-5131	24	19	that	that	PRON
ejpam-5131	24	20	captures	capture	VERB
ejpam-5131	24	21	the	the	DET
ejpam-5131	24	22	essence	essence	NOUN
ejpam-5131	24	23	of	of	ADP
ejpam-5131	24	24	chaos	chaos	NOUN
ejpam-5131	24	25	,	,	PUNCT
ejpam-5131	24	26	where	where	SCONJ
ejpam-5131	24	27	minute	minute	VERB
ejpam-5131	24	28	variations	variation	NOUN
ejpam-5131	24	29	in	in	ADP
ejpam-5131	24	30	initial	initial	ADJ
ejpam-5131	24	31	conditions	condition	NOUN
ejpam-5131	24	32	can	can	AUX
ejpam-5131	24	33	lead	lead	VERB
ejpam-5131	24	34	to	to	ADP
ejpam-5131	24	35	dramatically	dramatically	ADV
ejpam-5131	24	36	divergent	divergent	ADJ
ejpam-5131	24	37	outcomes	outcome	NOUN
ejpam-5131	24	38	,	,	PUNCT
ejpam-5131	24	39	underscoring	underscore	VERB
ejpam-5131	24	40	the	the	DET
ejpam-5131	24	41	inherent	inherent	ADJ
ejpam-5131	24	42	unpredictability	unpredictability	NOUN
ejpam-5131	24	43	of	of	ADP
ejpam-5131	24	44	certain	certain	ADJ
ejpam-5131	24	45	natural	natural	ADJ
ejpam-5131	24	46	systems	system	NOUN
ejpam-5131	24	47	.	.	PUNCT
ejpam-5131	25	1	expanding	expand	VERB
ejpam-5131	25	2	upon	upon	SCONJ
ejpam-5131	25	3	the	the	DET
ejpam-5131	25	4	groundwork	groundwork	NOUN
ejpam-5131	25	5	laid	lay	VERB
ejpam-5131	25	6	by	by	ADP
ejpam-5131	25	7	references	reference	NOUN
ejpam-5131	25	8	[	[	X
ejpam-5131	25	9	36	36	NUM
ejpam-5131	25	10	]	]	PUNCT
ejpam-5131	25	11	,	,	PUNCT
ejpam-5131	25	12	our	our	PRON
ejpam-5131	25	13	investigation	investigation	NOUN
ejpam-5131	25	14	enriches	enrich	VERB
ejpam-5131	25	15	the	the	DET
ejpam-5131	25	16	lorenz	lorenz	PROPN
ejpam-5131	25	17	-	-	PUNCT
ejpam-5131	25	18	stenflo	stenflo	ADJ
ejpam-5131	25	19	framework	framework	NOUN
ejpam-5131	25	20	by	by	ADP
ejpam-5131	25	21	integrating	integrate	VERB
ejpam-5131	25	22	the	the	DET
ejpam-5131	25	23	concept	concept	NOUN
ejpam-5131	25	24	of	of	ADP
ejpam-5131	25	25	fractional	fractional	ADJ
ejpam-5131	25	26	calculus	calculus	NOUN
ejpam-5131	25	27	,	,	PUNCT
ejpam-5131	25	28	a	a	DET
ejpam-5131	25	29	mathematical	mathematical	ADJ
ejpam-5131	25	30	approach	approach	NOUN
ejpam-5131	25	31	that	that	PRON
ejpam-5131	25	32	extends	extend	VERB
ejpam-5131	25	33	the	the	DET
ejpam-5131	25	34	notion	notion	NOUN
ejpam-5131	25	35	of	of	ADP
ejpam-5131	25	36	derivatives	derivative	NOUN
ejpam-5131	25	37	and	and	CCONJ
ejpam-5131	25	38	integrals	integral	NOUN
ejpam-5131	25	39	to	to	ADP
ejpam-5131	25	40	non	non	ADJ
ejpam-5131	25	41	-	-	ADJ
ejpam-5131	25	42	integer	integer	ADJ
ejpam-5131	25	43	orders	order	NOUN
ejpam-5131	25	44	.	.	PUNCT
ejpam-5131	26	1	this	this	DET
ejpam-5131	26	2	extension	extension	NOUN
ejpam-5131	26	3	into	into	ADP
ejpam-5131	26	4	fractional	fractional	ADJ
ejpam-5131	26	5	-	-	PUNCT
ejpam-5131	26	6	order	order	NOUN
ejpam-5131	26	7	systems	system	NOUN
ejpam-5131	26	8	introduces	introduce	VERB
ejpam-5131	26	9	a	a	DET
ejpam-5131	26	10	new	new	ADJ
ejpam-5131	26	11	dimension	dimension	NOUN
ejpam-5131	26	12	of	of	ADP
ejpam-5131	26	13	complexity	complexity	NOUN
ejpam-5131	26	14	and	and	CCONJ
ejpam-5131	26	15	flexibility	flexibility	NOUN
ejpam-5131	26	16	,	,	PUNCT
ejpam-5131	26	17	allowing	allow	VERB
ejpam-5131	26	18	for	for	ADP
ejpam-5131	26	19	a	a	DET
ejpam-5131	26	20	more	more	ADV
ejpam-5131	26	21	nuanced	nuanced	ADJ
ejpam-5131	26	22	exploration	exploration	NOUN
ejpam-5131	26	23	of	of	ADP
ejpam-5131	26	24	dynamical	dynamical	ADJ
ejpam-5131	26	25	behaviours	behaviour	NOUN
ejpam-5131	26	26	that	that	PRON
ejpam-5131	26	27	are	be	AUX
ejpam-5131	26	28	closer	close	ADJ
ejpam-5131	26	29	to	to	ADP
ejpam-5131	26	30	those	those	PRON
ejpam-5131	26	31	observed	observe	VERB
ejpam-5131	26	32	in	in	ADP
ejpam-5131	26	33	natural	natural	ADJ
ejpam-5131	26	34	phenomena	phenomenon	NOUN
ejpam-5131	26	35	.	.	PUNCT
ejpam-5131	27	1	specifically	specifically	ADV
ejpam-5131	27	2	,	,	PUNCT
ejpam-5131	27	3	we	we	PRON
ejpam-5131	27	4	employ	employ	VERB
ejpam-5131	27	5	a	a	DET
ejpam-5131	27	6	generalised	generalise	VERB
ejpam-5131	27	7	liouville	liouville	NOUN
ejpam-5131	27	8	-	-	PUNCT
ejpam-5131	27	9	caputo	caputo	NOUN
ejpam-5131	27	10	-	-	PUNCT
ejpam-5131	27	11	type	type	NOUN
ejpam-5131	27	12	fractional	fractional	ADJ
ejpam-5131	27	13	derivative	derivative	ADJ
ejpam-5131	27	14	operator	operator	NOUN
ejpam-5131	27	15	,	,	PUNCT
ejpam-5131	27	16	marking	mark	VERB
ejpam-5131	27	17	a	a	DET
ejpam-5131	27	18	significant	significant	ADJ
ejpam-5131	27	19	departure	departure	NOUN
ejpam-5131	27	20	from	from	ADP
ejpam-5131	27	21	traditional	traditional	ADJ
ejpam-5131	27	22	integer	integer	NOUN
ejpam-5131	27	23	-	-	PUNCT
ejpam-5131	27	24	order	order	NOUN
ejpam-5131	27	25	models	model	NOUN
ejpam-5131	27	26	.	.	PUNCT
ejpam-5131	28	1	through	through	ADP
ejpam-5131	28	2	a	a	DET
ejpam-5131	28	3	meticulously	meticulously	ADV
ejpam-5131	28	4	formulated	formulate	VERB
ejpam-5131	28	5	system	system	NOUN
ejpam-5131	28	6	of	of	ADP
ejpam-5131	28	7	five	five	NUM
ejpam-5131	28	8	fractional	fractional	ADJ
ejpam-5131	28	9	-	-	PUNCT
ejpam-5131	28	10	order	order	NOUN
ejpam-5131	28	11	differential	differential	ADJ
ejpam-5131	28	12	equations	equation	NOUN
ejpam-5131	28	13	,	,	PUNCT
ejpam-5131	28	14	we	we	PRON
ejpam-5131	28	15	unveil	unveil	VERB
ejpam-5131	28	16	a	a	DET
ejpam-5131	28	17	novel	novel	ADJ
ejpam-5131	28	18	chaotic	chaotic	ADJ
ejpam-5131	28	19	system	system	NOUN
ejpam-5131	28	20	that	that	PRON
ejpam-5131	28	21	not	not	PART
ejpam-5131	28	22	only	only	ADV
ejpam-5131	28	23	inherits	inherit	VERB
ejpam-5131	28	24	the	the	DET
ejpam-5131	28	25	sensitive	sensitive	ADJ
ejpam-5131	28	26	dependence	dependence	NOUN
ejpam-5131	28	27	on	on	ADP
ejpam-5131	28	28	initial	initial	ADJ
ejpam-5131	28	29	conditions	condition	NOUN
ejpam-5131	28	30	characteristic	characteristic	ADJ
ejpam-5131	28	31	of	of	ADP
ejpam-5131	28	32	its	its	PRON
ejpam-5131	28	33	predecessors	predecessor	NOUN
ejpam-5131	28	34	but	but	CCONJ
ejpam-5131	28	35	also	also	ADV
ejpam-5131	28	36	exhibits	exhibit	VERB
ejpam-5131	28	37	a	a	DET
ejpam-5131	28	38	rich	rich	ADJ
ejpam-5131	28	39	tapestry	tapestry	NOUN
ejpam-5131	28	40	of	of	ADP
ejpam-5131	28	41	dynamical	dynamical	ADJ
ejpam-5131	28	42	features	feature	NOUN
ejpam-5131	28	43	unique	unique	ADJ
ejpam-5131	28	44	to	to	ADP
ejpam-5131	28	45	fractional	fractional	ADJ
ejpam-5131	28	46	-	-	PUNCT
ejpam-5131	28	47	order	order	NOUN
ejpam-5131	28	48	systems	system	NOUN
ejpam-5131	28	49	.	.	PUNCT
ejpam-5131	29	1	this	this	DET
ejpam-5131	29	2	innovative	innovative	ADJ
ejpam-5131	29	3	approach	approach	NOUN
ejpam-5131	29	4	to	to	ADP
ejpam-5131	29	5	modelling	model	VERB
ejpam-5131	29	6	chaos	chaos	NOUN
ejpam-5131	29	7	through	through	ADP
ejpam-5131	29	8	fractional	fractional	ADJ
ejpam-5131	29	9	calculus	calculus	NOUN
ejpam-5131	29	10	opens	open	VERB
ejpam-5131	29	11	up	up	ADP
ejpam-5131	29	12	a	a	DET
ejpam-5131	29	13	plethora	plethora	NOUN
ejpam-5131	29	14	of	of	ADP
ejpam-5131	29	15	possibilities	possibility	NOUN
ejpam-5131	29	16	for	for	ADP
ejpam-5131	29	17	capturing	capture	VERB
ejpam-5131	29	18	the	the	DET
ejpam-5131	29	19	subtleties	subtlety	NOUN
ejpam-5131	29	20	of	of	ADP
ejpam-5131	29	21	real	real	ADJ
ejpam-5131	29	22	-	-	PUNCT
ejpam-5131	29	23	world	world	NOUN
ejpam-5131	29	24	systems	system	NOUN
ejpam-5131	29	25	,	,	PUNCT
ejpam-5131	29	26	where	where	SCONJ
ejpam-5131	29	27	the	the	DET
ejpam-5131	29	28	effects	effect	NOUN
ejpam-5131	29	29	of	of	ADP
ejpam-5131	29	30	memory	memory	NOUN
ejpam-5131	29	31	and	and	CCONJ
ejpam-5131	29	32	hereditary	hereditary	ADJ
ejpam-5131	29	33	properties	property	NOUN
ejpam-5131	29	34	are	be	AUX
ejpam-5131	29	35	paramount	paramount	ADJ
ejpam-5131	29	36	.	.	PUNCT
ejpam-5131	30	1	by	by	ADP
ejpam-5131	30	2	venturing	venture	VERB
ejpam-5131	30	3	into	into	ADP
ejpam-5131	30	4	the	the	DET
ejpam-5131	30	5	domain	domain	NOUN
ejpam-5131	30	6	of	of	ADP
ejpam-5131	30	7	fractional	fractional	ADJ
ejpam-5131	30	8	-	-	PUNCT
ejpam-5131	30	9	order	order	NOUN
ejpam-5131	30	10	chaotic	chaotic	ADJ
ejpam-5131	30	11	systems	system	NOUN
ejpam-5131	30	12	,	,	PUNCT
ejpam-5131	30	13	we	we	PRON
ejpam-5131	30	14	aim	aim	VERB
ejpam-5131	30	15	to	to	PART
ejpam-5131	30	16	bridge	bridge	VERB
ejpam-5131	30	17	the	the	DET
ejpam-5131	30	18	gap	gap	NOUN
ejpam-5131	30	19	between	between	ADP
ejpam-5131	30	20	theoretical	theoretical	ADJ
ejpam-5131	30	21	models	model	NOUN
ejpam-5131	30	22	and	and	CCONJ
ejpam-5131	30	23	the	the	DET
ejpam-5131	30	24	complex	complex	ADJ
ejpam-5131	30	25	dynamics	dynamic	NOUN
ejpam-5131	30	26	observed	observe	VERB
ejpam-5131	30	27	in	in	ADP
ejpam-5131	30	28	nature	nature	NOUN
ejpam-5131	30	29	,	,	PUNCT
ejpam-5131	30	30	providing	provide	VERB
ejpam-5131	30	31	a	a	DET
ejpam-5131	30	32	more	more	ADV
ejpam-5131	30	33	accurate	accurate	ADJ
ejpam-5131	30	34	and	and	CCONJ
ejpam-5131	30	35	versatile	versatile	ADJ
ejpam-5131	30	36	framework	framework	NOUN
ejpam-5131	30	37	for	for	ADP
ejpam-5131	30	38	understanding	understanding	NOUN
ejpam-5131	30	39	and	and	CCONJ
ejpam-5131	30	40	harnessing	harness	VERB
ejpam-5131	30	41	the	the	DET
ejpam-5131	30	42	potential	potential	NOUN
ejpam-5131	30	43	of	of	ADP
ejpam-5131	30	44	chaos	chaos	NOUN
ejpam-5131	30	45	.	.	PUNCT
ejpam-5131	31	1	this	this	DET
ejpam-5131	31	2	extended	extend	VERB
ejpam-5131	31	3	introduction	introduction	NOUN
ejpam-5131	31	4	sets	set	VERB
ejpam-5131	31	5	the	the	DET
ejpam-5131	31	6	stage	stage	NOUN
ejpam-5131	31	7	for	for	ADP
ejpam-5131	31	8	a	a	DET
ejpam-5131	31	9	comprehensive	comprehensive	ADJ
ejpam-5131	31	10	exploration	exploration	NOUN
ejpam-5131	31	11	of	of	ADP
ejpam-5131	31	12	the	the	DET
ejpam-5131	31	13	proposed	propose	VERB
ejpam-5131	31	14	system	system	NOUN
ejpam-5131	31	15	,	,	PUNCT
ejpam-5131	31	16	highlighting	highlight	VERB
ejpam-5131	31	17	its	its	PRON
ejpam-5131	31	18	theoretical	theoretical	ADJ
ejpam-5131	31	19	significance	significance	NOUN
ejpam-5131	31	20	,	,	PUNCT
ejpam-5131	31	21	practical	practical	ADJ
ejpam-5131	31	22	implications	implication	NOUN
ejpam-5131	31	23	,	,	PUNCT
ejpam-5131	31	24	and	and	CCONJ
ejpam-5131	31	25	the	the	DET
ejpam-5131	31	26	pioneering	pioneer	VERB
ejpam-5131	31	27	contributions	contribution	NOUN
ejpam-5131	31	28	it	it	PRON
ejpam-5131	31	29	aims	aim	VERB
ejpam-5131	31	30	to	to	PART
ejpam-5131	31	31	make	make	VERB
ejpam-5131	31	32	to	to	ADP
ejpam-5131	31	33	the	the	DET
ejpam-5131	31	34	field	field	NOUN
ejpam-5131	31	35	of	of	ADP
ejpam-5131	31	36	chaos	chaos	NOUN
ejpam-5131	31	37	theory	theory	NOUN
ejpam-5131	31	38	and	and	CCONJ
ejpam-5131	31	39	its	its	PRON
ejpam-5131	31	40	applications	application	NOUN
ejpam-5131	31	41	.	.	PUNCT
ejpam-5131	32	1	the	the	DET
ejpam-5131	32	2	integration	integration	NOUN
ejpam-5131	32	3	of	of	ADP
ejpam-5131	32	4	chaotic	chaotic	ADJ
ejpam-5131	32	5	dynamics	dynamic	NOUN
ejpam-5131	32	6	into	into	ADP
ejpam-5131	32	7	the	the	DET
ejpam-5131	32	8	lorenz	lorenz	PROPN
ejpam-5131	32	9	-	-	PUNCT
ejpam-5131	32	10	stenflo	stenflo	ADJ
ejpam-5131	32	11	model	model	NOUN
ejpam-5131	32	12	represents	represent	VERB
ejpam-5131	32	13	a	a	DET
ejpam-5131	32	14	significant	significant	ADJ
ejpam-5131	32	15	stride	stride	NOUN
ejpam-5131	32	16	in	in	ADP
ejpam-5131	32	17	the	the	DET
ejpam-5131	32	18	exploration	exploration	NOUN
ejpam-5131	32	19	of	of	ADP
ejpam-5131	32	20	complex	complex	ADJ
ejpam-5131	32	21	systems	system	NOUN
ejpam-5131	32	22	within	within	ADP
ejpam-5131	32	23	the	the	DET
ejpam-5131	32	24	realm	realm	NOUN
ejpam-5131	32	25	of	of	ADP
ejpam-5131	32	26	nonlinear	nonlinear	ADJ
ejpam-5131	32	27	dynamics	dynamic	NOUN
ejpam-5131	32	28	and	and	CCONJ
ejpam-5131	32	29	chaos	chaos	NOUN
ejpam-5131	32	30	theory	theory	NOUN
ejpam-5131	32	31	.	.	PUNCT
ejpam-5131	33	1	the	the	DET
ejpam-5131	33	2	lorenz	lorenz	PROPN
ejpam-5131	33	3	-	-	PUNCT
ejpam-5131	33	4	stenflo	stenflo	ADJ
ejpam-5131	33	5	model	model	NOUN
ejpam-5131	33	6	,	,	PUNCT
ejpam-5131	33	7	originally	originally	ADV
ejpam-5131	33	8	derived	derive	VERB
ejpam-5131	33	9	to	to	PART
ejpam-5131	33	10	describe	describe	VERB
ejpam-5131	33	11	atmospheric	atmospheric	ADJ
ejpam-5131	33	12	convection	convection	NOUN
ejpam-5131	33	13	and	and	CCONJ
ejpam-5131	33	14	later	later	ADV
ejpam-5131	33	15	adapted	adapt	VERB
ejpam-5131	33	16	to	to	ADP
ejpam-5131	33	17	various	various	ADJ
ejpam-5131	33	18	physical	physical	ADJ
ejpam-5131	33	19	phenomena	phenomenon	NOUN
ejpam-5131	33	20	,	,	PUNCT
ejpam-5131	33	21	serves	serve	VERB
ejpam-5131	33	22	as	as	ADP
ejpam-5131	33	23	a	a	DET
ejpam-5131	33	24	foundational	foundational	ADJ
ejpam-5131	33	25	framework	framework	NOUN
ejpam-5131	33	26	for	for	ADP
ejpam-5131	33	27	studying	study	VERB
ejpam-5131	33	28	the	the	DET
ejpam-5131	33	29	intricate	intricate	ADJ
ejpam-5131	33	30	behaviour	behaviour	NOUN
ejpam-5131	33	31	of	of	ADP
ejpam-5131	33	32	g.	g.	PROPN
ejpam-5131	33	33	a.	a.	PROPN
ejpam-5131	33	34	ahmed	ahmed	PROPN
ejpam-5131	33	35	/	/	SYM
ejpam-5131	33	36	eur	eur	PROPN
ejpam-5131	33	37	.	.	PUNCT
ejpam-5131	34	1	j.	j.	PROPN
ejpam-5131	34	2	pure	pure	PROPN
ejpam-5131	34	3	appl	appl	PROPN
ejpam-5131	34	4	.	.	PROPN
ejpam-5131	34	5	math	math	PROPN
ejpam-5131	34	6	,	,	PUNCT
ejpam-5131	34	7	17	17	NUM
ejpam-5131	34	8	(	(	PUNCT
ejpam-5131	34	9	2	2	NUM
ejpam-5131	34	10	)	)	PUNCT
ejpam-5131	34	11	(	(	PUNCT
ejpam-5131	34	12	2024	2024	NUM
ejpam-5131	34	13	)	)	PUNCT
ejpam-5131	34	14	,	,	PUNCT
ejpam-5131	34	15	835	835	NUM
ejpam-5131	34	16	-	-	SYM
ejpam-5131	34	17	851	851	NUM
ejpam-5131	34	18	837	837	NUM
ejpam-5131	34	19	dynamical	dynamical	ADJ
ejpam-5131	34	20	systems	system	NOUN
ejpam-5131	34	21	.	.	PUNCT
ejpam-5131	35	1	recent	recent	ADJ
ejpam-5131	35	2	advancements	advancement	NOUN
ejpam-5131	35	3	have	have	AUX
ejpam-5131	35	4	focused	focus	VERB
ejpam-5131	35	5	on	on	ADP
ejpam-5131	35	6	augmenting	augment	VERB
ejpam-5131	35	7	this	this	DET
ejpam-5131	35	8	classic	classic	ADJ
ejpam-5131	35	9	model	model	NOUN
ejpam-5131	35	10	with	with	ADP
ejpam-5131	35	11	memristive	memristive	ADJ
ejpam-5131	35	12	components	component	NOUN
ejpam-5131	35	13	and	and	CCONJ
ejpam-5131	35	14	fractional	fractional	ADJ
ejpam-5131	35	15	-	-	PUNCT
ejpam-5131	35	16	order	order	NOUN
ejpam-5131	35	17	calculus	calculus	NOUN
ejpam-5131	35	18	to	to	PART
ejpam-5131	35	19	introduce	introduce	VERB
ejpam-5131	35	20	novel	novel	ADJ
ejpam-5131	35	21	chaotic	chaotic	ADJ
ejpam-5131	35	22	systems	system	NOUN
ejpam-5131	35	23	that	that	PRON
ejpam-5131	35	24	exhibit	exhibit	VERB
ejpam-5131	35	25	a	a	DET
ejpam-5131	35	26	wider	wide	ADJ
ejpam-5131	35	27	spectrum	spectrum	NOUN
ejpam-5131	35	28	of	of	ADP
ejpam-5131	35	29	dynamical	dynamical	ADJ
ejpam-5131	35	30	behaviors	behavior	NOUN
ejpam-5131	35	31	.	.	PUNCT
ejpam-5131	36	1	this	this	DET
ejpam-5131	36	2	fusion	fusion	NOUN
ejpam-5131	36	3	not	not	PART
ejpam-5131	36	4	only	only	ADV
ejpam-5131	36	5	enriches	enrich	VERB
ejpam-5131	36	6	the	the	DET
ejpam-5131	36	7	model	model	NOUN
ejpam-5131	36	8	’s	’s	PART
ejpam-5131	36	9	capability	capability	NOUN
ejpam-5131	36	10	to	to	PART
ejpam-5131	36	11	mimic	mimic	VERB
ejpam-5131	36	12	real	real	ADJ
ejpam-5131	36	13	-	-	PUNCT
ejpam-5131	36	14	world	world	NOUN
ejpam-5131	36	15	processes	process	NOUN
ejpam-5131	36	16	with	with	ADP
ejpam-5131	36	17	higher	high	ADJ
ejpam-5131	36	18	fidelity	fidelity	NOUN
ejpam-5131	36	19	but	but	CCONJ
ejpam-5131	36	20	also	also	ADV
ejpam-5131	36	21	opens	open	VERB
ejpam-5131	36	22	new	new	ADJ
ejpam-5131	36	23	avenues	avenue	NOUN
ejpam-5131	36	24	for	for	ADP
ejpam-5131	36	25	applications	application	NOUN
ejpam-5131	36	26	in	in	ADP
ejpam-5131	36	27	secure	secure	ADJ
ejpam-5131	36	28	communications	communication	NOUN
ejpam-5131	36	29	,	,	PUNCT
ejpam-5131	36	30	computational	computational	ADJ
ejpam-5131	36	31	neuroscience	neuroscience	NOUN
ejpam-5131	36	32	,	,	PUNCT
ejpam-5131	36	33	and	and	CCONJ
ejpam-5131	36	34	adaptive	adaptive	ADJ
ejpam-5131	36	35	control	control	NOUN
ejpam-5131	36	36	systems	system	NOUN
ejpam-5131	36	37	.	.	PUNCT
ejpam-5131	37	1	studies	study	NOUN
ejpam-5131	37	2	leveraging	leverage	VERB
ejpam-5131	37	3	the	the	DET
ejpam-5131	37	4	lorenz	lorenz	PROPN
ejpam-5131	37	5	-	-	PUNCT
ejpam-5131	37	6	stenflo	stenflo	ADJ
ejpam-5131	37	7	model	model	NOUN
ejpam-5131	37	8	as	as	ADP
ejpam-5131	37	9	a	a	DET
ejpam-5131	37	10	base	base	NOUN
ejpam-5131	37	11	have	have	AUX
ejpam-5131	37	12	revealed	reveal	VERB
ejpam-5131	37	13	that	that	SCONJ
ejpam-5131	37	14	the	the	DET
ejpam-5131	37	15	incorporation	incorporation	NOUN
ejpam-5131	37	16	of	of	ADP
ejpam-5131	37	17	memristors	memristor	NOUN
ejpam-5131	37	18	and	and	CCONJ
ejpam-5131	37	19	fractional	fractional	ADJ
ejpam-5131	37	20	derivatives	derivative	NOUN
ejpam-5131	37	21	can	can	AUX
ejpam-5131	37	22	significantly	significantly	ADV
ejpam-5131	37	23	enhance	enhance	VERB
ejpam-5131	37	24	system	system	NOUN
ejpam-5131	37	25	complexity	complexity	NOUN
ejpam-5131	37	26	,	,	PUNCT
ejpam-5131	37	27	leading	lead	VERB
ejpam-5131	37	28	to	to	ADP
ejpam-5131	37	29	the	the	DET
ejpam-5131	37	30	discovery	discovery	NOUN
ejpam-5131	37	31	of	of	ADP
ejpam-5131	37	32	unique	unique	ADJ
ejpam-5131	37	33	attractors	attractor	NOUN
ejpam-5131	37	34	,	,	PUNCT
ejpam-5131	37	35	bifurcation	bifurcation	NOUN
ejpam-5131	37	36	phenomena	phenomenon	NOUN
ejpam-5131	37	37	,	,	PUNCT
ejpam-5131	37	38	and	and	CCONJ
ejpam-5131	37	39	enhanced	enhance	VERB
ejpam-5131	37	40	sensitivity	sensitivity	NOUN
ejpam-5131	37	41	to	to	ADP
ejpam-5131	37	42	initial	initial	ADJ
ejpam-5131	37	43	conditions	condition	NOUN
ejpam-5131	37	44	.	.	PUNCT
ejpam-5131	38	1	these	these	DET
ejpam-5131	38	2	contributions	contribution	NOUN
ejpam-5131	38	3	highlight	highlight	VERB
ejpam-5131	38	4	the	the	DET
ejpam-5131	38	5	model	model	NOUN
ejpam-5131	38	6	’s	’s	PART
ejpam-5131	38	7	versatility	versatility	NOUN
ejpam-5131	38	8	and	and	CCONJ
ejpam-5131	38	9	its	its	PRON
ejpam-5131	38	10	potential	potential	NOUN
ejpam-5131	38	11	for	for	ADP
ejpam-5131	38	12	pioneering	pioneer	VERB
ejpam-5131	38	13	research	research	NOUN
ejpam-5131	38	14	in	in	ADP
ejpam-5131	38	15	chaos	chaos	NOUN
ejpam-5131	38	16	theory	theory	NOUN
ejpam-5131	38	17	,	,	PUNCT
ejpam-5131	38	18	demonstrating	demonstrate	VERB
ejpam-5131	38	19	a	a	DET
ejpam-5131	38	20	growing	grow	VERB
ejpam-5131	38	21	interest	interest	NOUN
ejpam-5131	38	22	in	in	ADP
ejpam-5131	38	23	developing	develop	VERB
ejpam-5131	38	24	more	more	ADV
ejpam-5131	38	25	sophisticated	sophisticated	ADJ
ejpam-5131	38	26	and	and	CCONJ
ejpam-5131	38	27	applicable	applicable	ADJ
ejpam-5131	38	28	chaotic	chaotic	ADJ
ejpam-5131	38	29	systems	system	NOUN
ejpam-5131	38	30	.	.	PUNCT
ejpam-5131	39	1	in	in	ADP
ejpam-5131	39	2	the	the	DET
ejpam-5131	39	3	exploration	exploration	NOUN
ejpam-5131	39	4	of	of	ADP
ejpam-5131	39	5	nonlinear	nonlinear	ADJ
ejpam-5131	39	6	dynamics	dynamic	NOUN
ejpam-5131	39	7	and	and	CCONJ
ejpam-5131	39	8	chaos	chaos	NOUN
ejpam-5131	39	9	theory	theory	NOUN
ejpam-5131	39	10	,	,	PUNCT
ejpam-5131	39	11	the	the	DET
ejpam-5131	39	12	integration	integration	NOUN
ejpam-5131	39	13	of	of	ADP
ejpam-5131	39	14	chaotic	chaotic	ADJ
ejpam-5131	39	15	dynamics	dynamic	NOUN
ejpam-5131	39	16	into	into	ADP
ejpam-5131	39	17	established	establish	VERB
ejpam-5131	39	18	models	model	NOUN
ejpam-5131	39	19	like	like	ADP
ejpam-5131	39	20	lorenz	lorenz	PROPN
ejpam-5131	39	21	-	-	PUNCT
ejpam-5131	39	22	stenflo	stenflo	PROPN
ejpam-5131	39	23	has	have	AUX
ejpam-5131	39	24	opened	open	VERB
ejpam-5131	39	25	new	new	ADJ
ejpam-5131	39	26	avenues	avenue	NOUN
ejpam-5131	39	27	for	for	ADP
ejpam-5131	39	28	understanding	understand	VERB
ejpam-5131	39	29	the	the	DET
ejpam-5131	39	30	intricate	intricate	ADJ
ejpam-5131	39	31	behaviours	behaviour	NOUN
ejpam-5131	39	32	of	of	ADP
ejpam-5131	39	33	complex	complex	ADJ
ejpam-5131	39	34	systems	system	NOUN
ejpam-5131	39	35	.	.	PUNCT
ejpam-5131	40	1	recent	recent	ADJ
ejpam-5131	40	2	studies	study	NOUN
ejpam-5131	40	3	have	have	AUX
ejpam-5131	40	4	significantly	significantly	ADV
ejpam-5131	40	5	contributed	contribute	VERB
ejpam-5131	40	6	to	to	ADP
ejpam-5131	40	7	this	this	DET
ejpam-5131	40	8	field	field	NOUN
ejpam-5131	40	9	by	by	ADP
ejpam-5131	40	10	introducing	introduce	VERB
ejpam-5131	40	11	memristive	memristive	ADJ
ejpam-5131	40	12	components	component	NOUN
ejpam-5131	40	13	and	and	CCONJ
ejpam-5131	40	14	fractional	fractional	ADJ
ejpam-5131	40	15	-	-	PUNCT
ejpam-5131	40	16	order	order	NOUN
ejpam-5131	40	17	calculus	calculus	NOUN
ejpam-5131	40	18	,	,	PUNCT
ejpam-5131	40	19	thereby	thereby	ADV
ejpam-5131	40	20	expanding	expand	VERB
ejpam-5131	40	21	the	the	DET
ejpam-5131	40	22	traditional	traditional	ADJ
ejpam-5131	40	23	frameworks	framework	NOUN
ejpam-5131	40	24	used	use	VERB
ejpam-5131	40	25	to	to	PART
ejpam-5131	40	26	describe	describe	VERB
ejpam-5131	40	27	such	such	ADJ
ejpam-5131	40	28	phenomena	phenomenon	NOUN
ejpam-5131	40	29	.	.	PUNCT
ejpam-5131	41	1	for	for	ADP
ejpam-5131	41	2	instance	instance	NOUN
ejpam-5131	41	3	,	,	PUNCT
ejpam-5131	41	4	research	research	NOUN
ejpam-5131	41	5	documented	document	VERB
ejpam-5131	41	6	in	in	ADP
ejpam-5131	41	7	[	[	X
ejpam-5131	41	8	20	20	NUM
ejpam-5131	41	9	,	,	PUNCT
ejpam-5131	41	10	22	22	NUM
ejpam-5131	41	11	]	]	PUNCT
ejpam-5131	41	12	delves	delve	VERB
ejpam-5131	41	13	into	into	ADP
ejpam-5131	41	14	the	the	DET
ejpam-5131	41	15	applications	application	NOUN
ejpam-5131	41	16	of	of	ADP
ejpam-5131	41	17	fractional	fractional	ADJ
ejpam-5131	41	18	calculus	calculus	NOUN
ejpam-5131	41	19	to	to	PART
ejpam-5131	41	20	enhance	enhance	VERB
ejpam-5131	41	21	the	the	DET
ejpam-5131	41	22	dynamical	dynamical	ADJ
ejpam-5131	41	23	range	range	NOUN
ejpam-5131	41	24	of	of	ADP
ejpam-5131	41	25	chaotic	chaotic	ADJ
ejpam-5131	41	26	systems	system	NOUN
ejpam-5131	41	27	.	.	PUNCT
ejpam-5131	42	1	similarly	similarly	ADV
ejpam-5131	42	2	,	,	PUNCT
ejpam-5131	42	3	the	the	DET
ejpam-5131	42	4	works	work	NOUN
ejpam-5131	42	5	represented	represent	VERB
ejpam-5131	42	6	by	by	ADP
ejpam-5131	42	7	[	[	X
ejpam-5131	42	8	8	8	NUM
ejpam-5131	42	9	,	,	PUNCT
ejpam-5131	42	10	10	10	NUM
ejpam-5131	42	11	]	]	PUNCT
ejpam-5131	42	12	,	,	PUNCT
ejpam-5131	42	13	along	along	ADP
ejpam-5131	42	14	with	with	ADP
ejpam-5131	42	15	notable	notable	ADJ
ejpam-5131	42	16	contributions	contribution	NOUN
ejpam-5131	42	17	from	from	ADP
ejpam-5131	42	18	hasan	hasan	PROPN
ejpam-5131	42	19	et	et	PROPN
ejpam-5131	42	20	al	al	PROPN
ejpam-5131	42	21	.	.	PUNCT
ejpam-5131	43	1	[	[	X
ejpam-5131	43	2	24	24	NUM
ejpam-5131	43	3	]	]	PUNCT
ejpam-5131	43	4	in	in	ADP
ejpam-5131	43	5	the	the	DET
ejpam-5131	43	6	international	international	ADJ
ejpam-5131	43	7	journal	journal	NOUN
ejpam-5131	43	8	of	of	ADP
ejpam-5131	43	9	mathematical	mathematical	ADJ
ejpam-5131	43	10	engineering	engineering	NOUN
ejpam-5131	43	11	and	and	CCONJ
ejpam-5131	43	12	management	management	NOUN
ejpam-5131	43	13	sciences	science	NOUN
ejpam-5131	43	14	and	and	CCONJ
ejpam-5131	43	15	further	further	ADJ
ejpam-5131	43	16	studies	study	NOUN
ejpam-5131	43	17	by	by	ADP
ejpam-5131	43	18	abdoon	abdoon	PROPN
ejpam-5131	43	19	et	et	PROPN
ejpam-5131	43	20	al	al	PROPN
ejpam-5131	43	21	.	.	PUNCT
ejpam-5131	44	1	[	[	X
ejpam-5131	44	2	2	2	NUM
ejpam-5131	44	3	]	]	PUNCT
ejpam-5131	44	4	in	in	ADP
ejpam-5131	44	5	mathematical	mathematical	ADJ
ejpam-5131	44	6	modelling	modelling	NOUN
ejpam-5131	44	7	of	of	ADP
ejpam-5131	44	8	engineering	engineering	NOUN
ejpam-5131	44	9	problems	problem	NOUN
ejpam-5131	44	10	,	,	PUNCT
ejpam-5131	44	11	highlight	highlight	VERB
ejpam-5131	44	12	the	the	DET
ejpam-5131	44	13	advanced	advanced	ADJ
ejpam-5131	44	14	mathematical	mathematical	ADJ
ejpam-5131	44	15	techniques	technique	NOUN
ejpam-5131	44	16	for	for	ADP
ejpam-5131	44	17	solving	solve	VERB
ejpam-5131	44	18	nonlinear	nonlinear	ADJ
ejpam-5131	44	19	differential	differential	ADJ
ejpam-5131	44	20	equations	equation	NOUN
ejpam-5131	44	21	and	and	CCONJ
ejpam-5131	44	22	their	their	PRON
ejpam-5131	44	23	pivotal	pivotal	ADJ
ejpam-5131	44	24	roles	role	NOUN
ejpam-5131	44	25	in	in	ADP
ejpam-5131	44	26	chaos	chaos	NOUN
ejpam-5131	44	27	theory	theory	NOUN
ejpam-5131	44	28	.	.	PUNCT
ejpam-5131	45	1	these	these	DET
ejpam-5131	45	2	references	reference	NOUN
ejpam-5131	45	3	collectively	collectively	ADV
ejpam-5131	45	4	underscore	underscore	VERB
ejpam-5131	45	5	the	the	DET
ejpam-5131	45	6	evolving	evolve	VERB
ejpam-5131	45	7	complexity	complexity	NOUN
ejpam-5131	45	8	of	of	ADP
ejpam-5131	45	9	modelling	model	VERB
ejpam-5131	45	10	chaotic	chaotic	ADJ
ejpam-5131	45	11	systems	system	NOUN
ejpam-5131	45	12	and	and	CCONJ
ejpam-5131	45	13	the	the	DET
ejpam-5131	45	14	ongoing	ongoing	ADJ
ejpam-5131	45	15	quest	quest	NOUN
ejpam-5131	45	16	for	for	ADP
ejpam-5131	45	17	models	model	NOUN
ejpam-5131	45	18	that	that	PRON
ejpam-5131	45	19	more	more	ADV
ejpam-5131	45	20	accurately	accurately	ADV
ejpam-5131	45	21	reflect	reflect	VERB
ejpam-5131	45	22	the	the	DET
ejpam-5131	45	23	multifaceted	multifaceted	ADJ
ejpam-5131	45	24	nature	nature	NOUN
ejpam-5131	45	25	of	of	ADP
ejpam-5131	45	26	the	the	DET
ejpam-5131	45	27	universe	universe	NOUN
ejpam-5131	45	28	,	,	PUNCT
ejpam-5131	45	29	thus	thus	ADV
ejpam-5131	45	30	paving	pave	VERB
ejpam-5131	45	31	the	the	DET
ejpam-5131	45	32	way	way	NOUN
ejpam-5131	45	33	for	for	ADP
ejpam-5131	45	34	groundbreaking	groundbreake	VERB
ejpam-5131	45	35	applications	application	NOUN
ejpam-5131	45	36	in	in	ADP
ejpam-5131	45	37	science	science	NOUN
ejpam-5131	45	38	and	and	CCONJ
ejpam-5131	45	39	engineering	engineering	NOUN
ejpam-5131	45	40	.	.	PUNCT
ejpam-5131	46	1	in	in	ADP
ejpam-5131	46	2	this	this	DET
ejpam-5131	46	3	research	research	NOUN
ejpam-5131	46	4	,	,	PUNCT
ejpam-5131	46	5	novel	novel	ADJ
ejpam-5131	46	6	chaotic	chaotic	ADJ
ejpam-5131	46	7	attractors	attractor	NOUN
ejpam-5131	46	8	that	that	PRON
ejpam-5131	46	9	are	be	AUX
ejpam-5131	46	10	both	both	PRON
ejpam-5131	46	11	in	in	ADP
ejpam-5131	46	12	excellent	excellent	ADJ
ejpam-5131	46	13	agreement	agreement	NOUN
ejpam-5131	46	14	with	with	ADP
ejpam-5131	46	15	one	one	NUM
ejpam-5131	46	16	another	another	DET
ejpam-5131	46	17	and	and	CCONJ
ejpam-5131	46	18	numerically	numerically	ADV
ejpam-5131	46	19	represented	represent	VERB
ejpam-5131	46	20	using	use	VERB
ejpam-5131	46	21	2d	2d	NUM
ejpam-5131	46	22	phase	phase	NOUN
ejpam-5131	46	23	portrait	portrait	NOUN
ejpam-5131	46	24	diagrams	diagram	NOUN
ejpam-5131	46	25	are	be	AUX
ejpam-5131	46	26	described	describe	VERB
ejpam-5131	46	27	.	.	PUNCT
ejpam-5131	47	1	different	different	ADJ
ejpam-5131	47	2	mathematical	mathematical	ADJ
ejpam-5131	47	3	techniques	technique	NOUN
ejpam-5131	47	4	were	be	AUX
ejpam-5131	47	5	used	use	VERB
ejpam-5131	47	6	to	to	PART
ejpam-5131	47	7	examine	examine	VERB
ejpam-5131	47	8	the	the	DET
ejpam-5131	47	9	system	system	NOUN
ejpam-5131	47	10	dynamics	dynamic	NOUN
ejpam-5131	47	11	for	for	ADP
ejpam-5131	47	12	various	various	ADJ
ejpam-5131	47	13	values	value	NOUN
ejpam-5131	47	14	of	of	ADP
ejpam-5131	47	15	the	the	DET
ejpam-5131	47	16	fractional	fractional	ADJ
ejpam-5131	47	17	order	order	NOUN
ejpam-5131	47	18	q.	q.	VERB
ejpam-5131	47	19	the	the	DET
ejpam-5131	47	20	system	system	NOUN
ejpam-5131	47	21	’s	’s	PART
ejpam-5131	47	22	stability	stability	NOUN
ejpam-5131	47	23	is	be	AUX
ejpam-5131	47	24	examined	examine	VERB
ejpam-5131	47	25	using	use	VERB
ejpam-5131	47	26	equilibrium	equilibrium	NOUN
ejpam-5131	47	27	points	point	NOUN
ejpam-5131	47	28	,	,	PUNCT
ejpam-5131	47	29	eigenvalues	eigenvalue	VERB
ejpam-5131	47	30	,	,	PUNCT
ejpam-5131	47	31	the	the	DET
ejpam-5131	47	32	routh	routh	PROPN
ejpam-5131	47	33	-	-	PUNCT
ejpam-5131	47	34	hurwitz	hurwitz	PROPN
ejpam-5131	47	35	stability	stability	NOUN
ejpam-5131	47	36	criterion	criterion	NOUN
ejpam-5131	47	37	,	,	PUNCT
ejpam-5131	47	38	lyapunov	lyapunov	NOUN
ejpam-5131	47	39	exponents	exponent	NOUN
ejpam-5131	47	40	,	,	PUNCT
ejpam-5131	47	41	and	and	CCONJ
ejpam-5131	47	42	the	the	DET
ejpam-5131	47	43	kaplanyorke	kaplanyorke	PROPN
ejpam-5131	47	44	dimension	dimension	NOUN
ejpam-5131	47	45	.	.	PUNCT
ejpam-5131	48	1	the	the	DET
ejpam-5131	48	2	results	result	NOUN
ejpam-5131	48	3	reveal	reveal	VERB
ejpam-5131	48	4	that	that	SCONJ
ejpam-5131	48	5	the	the	DET
ejpam-5131	48	6	system	system	NOUN
ejpam-5131	48	7	is	be	AUX
ejpam-5131	48	8	chaotic	chaotic	ADJ
ejpam-5131	48	9	in	in	ADP
ejpam-5131	48	10	nature	nature	NOUN
ejpam-5131	48	11	and	and	CCONJ
ejpam-5131	48	12	capable	capable	ADJ
ejpam-5131	48	13	of	of	ADP
ejpam-5131	48	14	producing	produce	VERB
ejpam-5131	48	15	random	random	ADJ
ejpam-5131	48	16	numbers	number	NOUN
ejpam-5131	48	17	.	.	PUNCT
ejpam-5131	49	1	additionally	additionally	ADV
ejpam-5131	49	2	,	,	PUNCT
ejpam-5131	49	3	phase	phase	NOUN
ejpam-5131	49	4	portraits	portrait	NOUN
ejpam-5131	49	5	and	and	CCONJ
ejpam-5131	49	6	three	three	NUM
ejpam-5131	49	7	-	-	PUNCT
ejpam-5131	49	8	dimensional	dimensional	ADJ
ejpam-5131	49	9	graphs	graph	NOUN
ejpam-5131	49	10	are	be	AUX
ejpam-5131	49	11	used	use	VERB
ejpam-5131	49	12	to	to	PART
ejpam-5131	49	13	graphically	graphically	ADV
ejpam-5131	49	14	represent	represent	VERB
ejpam-5131	49	15	the	the	DET
ejpam-5131	49	16	system	system	NOUN
ejpam-5131	49	17	’s	’s	PART
ejpam-5131	49	18	characteristic	characteristic	ADJ
ejpam-5131	49	19	curves.finally	curves.finally	ADV
ejpam-5131	49	20	,	,	PUNCT
ejpam-5131	49	21	lyapunov	lyapunov	NOUN
ejpam-5131	49	22	spectra	spectra	NOUN
ejpam-5131	49	23	and	and	CCONJ
ejpam-5131	49	24	bifurcation	bifurcation	NOUN
ejpam-5131	49	25	graphs	graph	NOUN
ejpam-5131	49	26	are	be	AUX
ejpam-5131	49	27	shown	show	VERB
ejpam-5131	49	28	,	,	PUNCT
ejpam-5131	49	29	correspondingly	correspondingly	ADV
ejpam-5131	49	30	,	,	PUNCT
ejpam-5131	49	31	for	for	ADP
ejpam-5131	49	32	the	the	DET
ejpam-5131	49	33	time	time	NOUN
ejpam-5131	49	34	domain	domain	NOUN
ejpam-5131	49	35	and	and	CCONJ
ejpam-5131	49	36	system	system	NOUN
ejpam-5131	49	37	parameters	parameter	NOUN
ejpam-5131	49	38	.	.	PUNCT
ejpam-5131	50	1	the	the	DET
ejpam-5131	50	2	unique	unique	ADJ
ejpam-5131	50	3	system	system	NOUN
ejpam-5131	50	4	was	be	AUX
ejpam-5131	50	5	implemented	implement	VERB
ejpam-5131	50	6	in	in	ADP
ejpam-5131	50	7	a	a	DET
ejpam-5131	50	8	circuit	circuit	NOUN
ejpam-5131	50	9	after	after	ADP
ejpam-5131	50	10	a	a	DET
ejpam-5131	50	11	thorough	thorough	ADJ
ejpam-5131	50	12	mathematical	mathematical	ADJ
ejpam-5131	50	13	examination	examination	NOUN
ejpam-5131	50	14	of	of	ADP
ejpam-5131	50	15	the	the	DET
ejpam-5131	50	16	system	system	NOUN
ejpam-5131	50	17	.	.	PUNCT
ejpam-5131	51	1	in	in	ADP
ejpam-5131	51	2	the	the	DET
ejpam-5131	51	3	pursuit	pursuit	NOUN
ejpam-5131	51	4	of	of	ADP
ejpam-5131	51	5	advancing	advance	VERB
ejpam-5131	51	6	the	the	DET
ejpam-5131	51	7	study	study	NOUN
ejpam-5131	51	8	of	of	ADP
ejpam-5131	51	9	chaotic	chaotic	ADJ
ejpam-5131	51	10	systems	system	NOUN
ejpam-5131	51	11	,	,	PUNCT
ejpam-5131	51	12	this	this	DET
ejpam-5131	51	13	research	research	NOUN
ejpam-5131	51	14	aims	aim	VERB
ejpam-5131	51	15	to	to	PART
ejpam-5131	51	16	delineate	delineate	VERB
ejpam-5131	51	17	the	the	DET
ejpam-5131	51	18	unique	unique	ADJ
ejpam-5131	51	19	characteristics	characteristic	NOUN
ejpam-5131	51	20	and	and	CCONJ
ejpam-5131	51	21	behaviours	behaviour	NOUN
ejpam-5131	51	22	of	of	ADP
ejpam-5131	51	23	a	a	DET
ejpam-5131	51	24	novel	novel	ADJ
ejpam-5131	51	25	five	five	NUM
ejpam-5131	51	26	-	-	PUNCT
ejpam-5131	51	27	dimensional	dimensional	ADJ
ejpam-5131	51	28	fractional	fractional	ADJ
ejpam-5131	51	29	-	-	PUNCT
ejpam-5131	51	30	order	order	NOUN
ejpam-5131	51	31	chaotic	chaotic	ADJ
ejpam-5131	51	32	system	system	NOUN
ejpam-5131	51	33	.	.	PUNCT
ejpam-5131	52	1	this	this	DET
ejpam-5131	52	2	system	system	NOUN
ejpam-5131	52	3	distinguishes	distinguish	VERB
ejpam-5131	52	4	itself	itself	PRON
ejpam-5131	52	5	by	by	ADP
ejpam-5131	52	6	incorporating	incorporate	VERB
ejpam-5131	52	7	the	the	DET
ejpam-5131	52	8	dynamics	dynamic	NOUN
ejpam-5131	52	9	of	of	ADP
ejpam-5131	52	10	a	a	DET
ejpam-5131	52	11	feedback	feedback	NOUN
ejpam-5131	52	12	memristor	memristor	NOUN
ejpam-5131	52	13	based	base	VERB
ejpam-5131	52	14	on	on	ADP
ejpam-5131	52	15	the	the	DET
ejpam-5131	52	16	lorenz	lorenz	PROPN
ejpam-5131	52	17	-	-	PUNCT
ejpam-5131	52	18	stenflo	stenflo	ADJ
ejpam-5131	52	19	model	model	NOUN
ejpam-5131	52	20	.	.	PUNCT
ejpam-5131	53	1	the	the	DET
ejpam-5131	53	2	primary	primary	ADJ
ejpam-5131	53	3	objective	objective	NOUN
ejpam-5131	53	4	of	of	ADP
ejpam-5131	53	5	our	our	PRON
ejpam-5131	53	6	investigation	investigation	NOUN
ejpam-5131	53	7	is	be	AUX
ejpam-5131	53	8	to	to	PART
ejpam-5131	53	9	dissect	dissect	VERB
ejpam-5131	53	10	the	the	DET
ejpam-5131	53	11	complexities	complexity	NOUN
ejpam-5131	53	12	introduced	introduce	VERB
ejpam-5131	53	13	by	by	ADP
ejpam-5131	53	14	fractional	fractional	ADJ
ejpam-5131	53	15	calculus	calculus	NOUN
ejpam-5131	53	16	in	in	ADP
ejpam-5131	53	17	chaotic	chaotic	ADJ
ejpam-5131	53	18	systems	system	NOUN
ejpam-5131	53	19	,	,	PUNCT
ejpam-5131	53	20	thereby	thereby	ADV
ejpam-5131	53	21	unveiling	unveil	VERB
ejpam-5131	53	22	the	the	DET
ejpam-5131	53	23	hyperchaotic	hyperchaotic	ADJ
ejpam-5131	53	24	nature	nature	NOUN
ejpam-5131	53	25	that	that	PRON
ejpam-5131	53	26	emerges	emerge	VERB
ejpam-5131	53	27	from	from	ADP
ejpam-5131	53	28	such	such	ADJ
ejpam-5131	53	29	intricate	intricate	ADJ
ejpam-5131	53	30	dynamics	dynamic	NOUN
ejpam-5131	53	31	.	.	PUNCT
ejpam-5131	54	1	the	the	DET
ejpam-5131	54	2	g.	g.	PROPN
ejpam-5131	54	3	a.	a.	PROPN
ejpam-5131	54	4	ahmed	ahmed	PROPN
ejpam-5131	54	5	/	/	SYM
ejpam-5131	54	6	eur	eur	PROPN
ejpam-5131	54	7	.	.	PUNCT
ejpam-5131	55	1	j.	j.	PROPN
ejpam-5131	55	2	pure	pure	PROPN
ejpam-5131	55	3	appl	appl	PROPN
ejpam-5131	55	4	.	.	PROPN
ejpam-5131	55	5	math	math	PROPN
ejpam-5131	55	6	,	,	PUNCT
ejpam-5131	55	7	17	17	NUM
ejpam-5131	55	8	(	(	PUNCT
ejpam-5131	55	9	2	2	NUM
ejpam-5131	55	10	)	)	PUNCT
ejpam-5131	55	11	(	(	PUNCT
ejpam-5131	55	12	2024	2024	NUM
ejpam-5131	55	13	)	)	PUNCT
ejpam-5131	55	14	,	,	PUNCT
ejpam-5131	55	15	835	835	NUM
ejpam-5131	55	16	-	-	SYM
ejpam-5131	55	17	851	851	NUM
ejpam-5131	55	18	838	838	NUM
ejpam-5131	55	19	introduction	introduction	NOUN
ejpam-5131	55	20	of	of	ADP
ejpam-5131	55	21	fractional	fractional	ADJ
ejpam-5131	55	22	calculus	calculus	NOUN
ejpam-5131	55	23	not	not	PART
ejpam-5131	55	24	only	only	ADV
ejpam-5131	55	25	intensifies	intensify	VERB
ejpam-5131	55	26	the	the	DET
ejpam-5131	55	27	complexity	complexity	NOUN
ejpam-5131	55	28	but	but	CCONJ
ejpam-5131	55	29	also	also	ADV
ejpam-5131	55	30	augments	augment	VERB
ejpam-5131	55	31	the	the	DET
ejpam-5131	55	32	robustness	robustness	NOUN
ejpam-5131	55	33	against	against	ADP
ejpam-5131	55	34	perturbations	perturbation	NOUN
ejpam-5131	55	35	,	,	PUNCT
ejpam-5131	55	36	offering	offer	VERB
ejpam-5131	55	37	a	a	DET
ejpam-5131	55	38	richer	rich	ADJ
ejpam-5131	55	39	tapestry	tapestry	NOUN
ejpam-5131	55	40	of	of	ADP
ejpam-5131	55	41	dynamical	dynamical	ADJ
ejpam-5131	55	42	behaviours	behaviour	NOUN
ejpam-5131	55	43	to	to	PART
ejpam-5131	55	44	explore	explore	VERB
ejpam-5131	55	45	.	.	PUNCT
ejpam-5131	56	1	the	the	DET
ejpam-5131	56	2	novelty	novelty	NOUN
ejpam-5131	56	3	of	of	ADP
ejpam-5131	56	4	our	our	PRON
ejpam-5131	56	5	approach	approach	NOUN
ejpam-5131	56	6	lies	lie	VERB
ejpam-5131	56	7	in	in	ADP
ejpam-5131	56	8	the	the	DET
ejpam-5131	56	9	integration	integration	NOUN
ejpam-5131	56	10	of	of	ADP
ejpam-5131	56	11	fractional	fractional	ADJ
ejpam-5131	56	12	calculus	calculus	NOUN
ejpam-5131	56	13	within	within	ADP
ejpam-5131	56	14	the	the	DET
ejpam-5131	56	15	five	five	NUM
ejpam-5131	56	16	-	-	PUNCT
ejpam-5131	56	17	dimensional	dimensional	ADJ
ejpam-5131	56	18	framework	framework	NOUN
ejpam-5131	56	19	,	,	PUNCT
ejpam-5131	56	20	a	a	DET
ejpam-5131	56	21	method	method	NOUN
ejpam-5131	56	22	not	not	PART
ejpam-5131	56	23	extensively	extensively	ADV
ejpam-5131	56	24	explored	explore	VERB
ejpam-5131	56	25	in	in	ADP
ejpam-5131	56	26	contemporary	contemporary	ADJ
ejpam-5131	56	27	literature	literature	NOUN
ejpam-5131	56	28	.	.	PUNCT
ejpam-5131	57	1	this	this	DET
ejpam-5131	57	2	innovative	innovative	ADJ
ejpam-5131	57	3	melding	melding	NOUN
ejpam-5131	57	4	of	of	ADP
ejpam-5131	57	5	concepts	concept	NOUN
ejpam-5131	57	6	is	be	AUX
ejpam-5131	57	7	poised	poise	VERB
ejpam-5131	57	8	to	to	PART
ejpam-5131	57	9	yield	yield	VERB
ejpam-5131	57	10	insights	insight	NOUN
ejpam-5131	57	11	into	into	ADP
ejpam-5131	57	12	the	the	DET
ejpam-5131	57	13	stability	stability	NOUN
ejpam-5131	57	14	and	and	CCONJ
ejpam-5131	57	15	chaotic	chaotic	ADJ
ejpam-5131	57	16	behaviour	behaviour	NOUN
ejpam-5131	57	17	of	of	ADP
ejpam-5131	57	18	higher	high	ADJ
ejpam-5131	57	19	-	-	PUNCT
ejpam-5131	57	20	dimensional	dimensional	ADJ
ejpam-5131	57	21	systems	system	NOUN
ejpam-5131	57	22	when	when	SCONJ
ejpam-5131	57	23	subjected	subject	VERB
ejpam-5131	57	24	to	to	ADP
ejpam-5131	57	25	fractional	fractional	ADJ
ejpam-5131	57	26	orders	order	NOUN
ejpam-5131	57	27	.	.	PUNCT
ejpam-5131	58	1	by	by	ADP
ejpam-5131	58	2	deploying	deploy	VERB
ejpam-5131	58	3	a	a	DET
ejpam-5131	58	4	combination	combination	NOUN
ejpam-5131	58	5	of	of	ADP
ejpam-5131	58	6	analytical	analytical	ADJ
ejpam-5131	58	7	and	and	CCONJ
ejpam-5131	58	8	numerical	numerical	ADJ
ejpam-5131	58	9	tools	tool	NOUN
ejpam-5131	58	10	—	—	PUNCT
ejpam-5131	58	11	specifically	specifically	ADV
ejpam-5131	58	12	tailored	tailor	VERB
ejpam-5131	58	13	for	for	ADP
ejpam-5131	58	14	this	this	DET
ejpam-5131	58	15	research	research	NOUN
ejpam-5131	58	16	—	—	PUNCT
ejpam-5131	58	17	we	we	PRON
ejpam-5131	58	18	aim	aim	VERB
ejpam-5131	58	19	to	to	PART
ejpam-5131	58	20	thoroughly	thoroughly	ADV
ejpam-5131	58	21	scrutinize	scrutinize	VERB
ejpam-5131	58	22	the	the	DET
ejpam-5131	58	23	system	system	NOUN
ejpam-5131	58	24	’s	’s	PART
ejpam-5131	58	25	eigenvalues	eigenvalue	NOUN
ejpam-5131	58	26	,	,	PUNCT
ejpam-5131	58	27	lyapunov	lyapunov	NOUN
ejpam-5131	58	28	exponents	exponent	NOUN
ejpam-5131	58	29	,	,	PUNCT
ejpam-5131	58	30	kaplan	kaplan	PROPN
ejpam-5131	58	31	-	-	PUNCT
ejpam-5131	58	32	yorke	yorke	PROPN
ejpam-5131	58	33	dimension	dimension	NOUN
ejpam-5131	58	34	,	,	PUNCT
ejpam-5131	58	35	maximal	maximal	ADJ
ejpam-5131	58	36	lyapunov	lyapunov	ADJ
ejpam-5131	58	37	exponents	exponent	NOUN
ejpam-5131	58	38	,	,	PUNCT
ejpam-5131	58	39	phase	phase	NOUN
ejpam-5131	58	40	portraits	portrait	NOUN
ejpam-5131	58	41	,	,	PUNCT
ejpam-5131	58	42	and	and	CCONJ
ejpam-5131	58	43	equilibrium	equilibrium	NOUN
ejpam-5131	58	44	points	point	NOUN
ejpam-5131	58	45	.	.	PUNCT
ejpam-5131	59	1	the	the	DET
ejpam-5131	59	2	detailed	detailed	ADJ
ejpam-5131	59	3	examination	examination	NOUN
ejpam-5131	59	4	of	of	ADP
ejpam-5131	59	5	these	these	DET
ejpam-5131	59	6	aspects	aspect	NOUN
ejpam-5131	59	7	under	under	ADP
ejpam-5131	59	8	various	various	ADJ
ejpam-5131	59	9	fractional	fractional	ADJ
ejpam-5131	59	10	orders	order	NOUN
ejpam-5131	59	11	will	will	AUX
ejpam-5131	59	12	contribute	contribute	VERB
ejpam-5131	59	13	significantly	significantly	ADV
ejpam-5131	59	14	to	to	ADP
ejpam-5131	59	15	the	the	DET
ejpam-5131	59	16	understanding	understanding	NOUN
ejpam-5131	59	17	of	of	ADP
ejpam-5131	59	18	the	the	DET
ejpam-5131	59	19	system	system	NOUN
ejpam-5131	59	20	’s	’s	PART
ejpam-5131	59	21	stability	stability	NOUN
ejpam-5131	59	22	and	and	CCONJ
ejpam-5131	59	23	chaos	chaos	NOUN
ejpam-5131	59	24	.	.	PUNCT
ejpam-5131	60	1	this	this	DET
ejpam-5131	60	2	study	study	NOUN
ejpam-5131	60	3	is	be	AUX
ejpam-5131	60	4	not	not	PART
ejpam-5131	60	5	merely	merely	ADV
ejpam-5131	60	6	an	an	DET
ejpam-5131	60	7	academic	academic	ADJ
ejpam-5131	60	8	exercise	exercise	NOUN
ejpam-5131	60	9	but	but	CCONJ
ejpam-5131	60	10	a	a	DET
ejpam-5131	60	11	step	step	NOUN
ejpam-5131	60	12	towards	towards	ADP
ejpam-5131	60	13	practical	practical	ADJ
ejpam-5131	60	14	applications	application	NOUN
ejpam-5131	60	15	.	.	PUNCT
ejpam-5131	61	1	by	by	ADP
ejpam-5131	61	2	demonstrating	demonstrate	VERB
ejpam-5131	61	3	the	the	DET
ejpam-5131	61	4	chaotic	chaotic	ADJ
ejpam-5131	61	5	characteristics	characteristic	NOUN
ejpam-5131	61	6	and	and	CCONJ
ejpam-5131	61	7	stability	stability	NOUN
ejpam-5131	61	8	of	of	ADP
ejpam-5131	61	9	the	the	DET
ejpam-5131	61	10	system	system	NOUN
ejpam-5131	61	11	,	,	PUNCT
ejpam-5131	61	12	we	we	PRON
ejpam-5131	61	13	lay	lay	VERB
ejpam-5131	61	14	the	the	DET
ejpam-5131	61	15	groundwork	groundwork	NOUN
ejpam-5131	61	16	for	for	ADP
ejpam-5131	61	17	future	future	ADJ
ejpam-5131	61	18	advancements	advancement	NOUN
ejpam-5131	61	19	in	in	ADP
ejpam-5131	61	20	electronic	electronic	ADJ
ejpam-5131	61	21	integration	integration	NOUN
ejpam-5131	61	22	and	and	CCONJ
ejpam-5131	61	23	the	the	DET
ejpam-5131	61	24	conception	conception	NOUN
ejpam-5131	61	25	of	of	ADP
ejpam-5131	61	26	more	more	ADV
ejpam-5131	61	27	intricate	intricate	ADJ
ejpam-5131	61	28	nonlinear	nonlinear	ADJ
ejpam-5131	61	29	dynamical	dynamical	ADJ
ejpam-5131	61	30	systems	system	NOUN
ejpam-5131	61	31	.	.	PUNCT
ejpam-5131	62	1	as	as	ADP
ejpam-5131	62	2	such	such	ADJ
ejpam-5131	62	3	,	,	PUNCT
ejpam-5131	62	4	the	the	DET
ejpam-5131	62	5	outcomes	outcome	NOUN
ejpam-5131	62	6	of	of	ADP
ejpam-5131	62	7	this	this	DET
ejpam-5131	62	8	research	research	NOUN
ejpam-5131	62	9	are	be	AUX
ejpam-5131	62	10	anticipated	anticipate	VERB
ejpam-5131	62	11	to	to	PART
ejpam-5131	62	12	catalyse	catalyse	VERB
ejpam-5131	62	13	innovation	innovation	NOUN
ejpam-5131	62	14	in	in	ADP
ejpam-5131	62	15	the	the	DET
ejpam-5131	62	16	realm	realm	NOUN
ejpam-5131	62	17	of	of	ADP
ejpam-5131	62	18	chaos	chaos	NOUN
ejpam-5131	62	19	theory	theory	NOUN
ejpam-5131	62	20	and	and	CCONJ
ejpam-5131	62	21	its	its	PRON
ejpam-5131	62	22	applications	application	NOUN
ejpam-5131	62	23	across	across	ADP
ejpam-5131	62	24	diverse	diverse	ADJ
ejpam-5131	62	25	scientific	scientific	ADJ
ejpam-5131	62	26	and	and	CCONJ
ejpam-5131	62	27	engineering	engineering	NOUN
ejpam-5131	62	28	disciplines	discipline	NOUN
ejpam-5131	62	29	.	.	PUNCT
ejpam-5131	63	1	one	one	NUM
ejpam-5131	63	2	of	of	ADP
ejpam-5131	63	3	the	the	DET
ejpam-5131	63	4	primary	primary	ADJ
ejpam-5131	63	5	challenges	challenge	NOUN
ejpam-5131	63	6	lies	lie	VERB
ejpam-5131	63	7	in	in	ADP
ejpam-5131	63	8	the	the	DET
ejpam-5131	63	9	computational	computational	ADJ
ejpam-5131	63	10	domain	domain	NOUN
ejpam-5131	63	11	.	.	PUNCT
ejpam-5131	64	1	future	future	ADJ
ejpam-5131	64	2	work	work	NOUN
ejpam-5131	64	3	could	could	AUX
ejpam-5131	64	4	address	address	VERB
ejpam-5131	64	5	these	these	DET
ejpam-5131	64	6	challenges	challenge	NOUN
ejpam-5131	64	7	by	by	ADP
ejpam-5131	64	8	exploring	explore	VERB
ejpam-5131	64	9	the	the	DET
ejpam-5131	64	10	following	follow	VERB
ejpam-5131	64	11	avenues	avenue	NOUN
ejpam-5131	64	12	:	:	PUNCT
ejpam-5131	64	13	the	the	DET
ejpam-5131	64	14	development	development	NOUN
ejpam-5131	64	15	of	of	ADP
ejpam-5131	64	16	more	more	ADV
ejpam-5131	64	17	advanced	advanced	ADJ
ejpam-5131	64	18	numerical	numerical	ADJ
ejpam-5131	64	19	algorithms	algorithm	NOUN
ejpam-5131	64	20	that	that	PRON
ejpam-5131	64	21	can	can	AUX
ejpam-5131	64	22	reduce	reduce	VERB
ejpam-5131	64	23	approximation	approximation	NOUN
ejpam-5131	64	24	errors	error	NOUN
ejpam-5131	64	25	and	and	CCONJ
ejpam-5131	64	26	enhance	enhance	VERB
ejpam-5131	64	27	the	the	DET
ejpam-5131	64	28	efficiency	efficiency	NOUN
ejpam-5131	64	29	of	of	ADP
ejpam-5131	64	30	simulations	simulation	NOUN
ejpam-5131	64	31	,	,	PUNCT
ejpam-5131	64	32	making	make	VERB
ejpam-5131	64	33	them	they	PRON
ejpam-5131	64	34	more	more	ADV
ejpam-5131	64	35	suitable	suitable	ADJ
ejpam-5131	64	36	for	for	ADP
ejpam-5131	64	37	high	high	ADJ
ejpam-5131	64	38	-	-	PUNCT
ejpam-5131	64	39	dimensional	dimensional	ADJ
ejpam-5131	64	40	systems	system	NOUN
ejpam-5131	64	41	and	and	CCONJ
ejpam-5131	64	42	real	real	ADJ
ejpam-5131	64	43	-	-	PUNCT
ejpam-5131	64	44	time	time	NOUN
ejpam-5131	64	45	analysis	analysis	NOUN
ejpam-5131	64	46	,	,	PUNCT
ejpam-5131	64	47	in	in	ADP
ejpam-5131	64	48	-	-	PUNCT
ejpam-5131	64	49	depth	depth	NOUN
ejpam-5131	64	50	exploration	exploration	NOUN
ejpam-5131	64	51	of	of	ADP
ejpam-5131	64	52	the	the	DET
ejpam-5131	64	53	interactions	interaction	NOUN
ejpam-5131	64	54	between	between	ADP
ejpam-5131	64	55	memristive	memristive	ADJ
ejpam-5131	64	56	properties	property	NOUN
ejpam-5131	64	57	and	and	CCONJ
ejpam-5131	64	58	fractional	fractional	ADJ
ejpam-5131	64	59	-	-	PUNCT
ejpam-5131	64	60	order	order	NOUN
ejpam-5131	64	61	dynamics	dynamic	NOUN
ejpam-5131	64	62	,	,	PUNCT
ejpam-5131	64	63	potentially	potentially	ADV
ejpam-5131	64	64	through	through	ADP
ejpam-5131	64	65	the	the	DET
ejpam-5131	64	66	lens	lens	NOUN
ejpam-5131	64	67	of	of	ADP
ejpam-5131	64	68	other	other	ADJ
ejpam-5131	64	69	non	non	ADJ
ejpam-5131	64	70	-	-	ADJ
ejpam-5131	64	71	integer	integer	ADJ
ejpam-5131	64	72	derivatives	derivative	NOUN
ejpam-5131	64	73	or	or	CCONJ
ejpam-5131	64	74	through	through	ADP
ejpam-5131	64	75	the	the	DET
ejpam-5131	64	76	adoption	adoption	NOUN
ejpam-5131	64	77	of	of	ADP
ejpam-5131	64	78	alternative	alternative	ADJ
ejpam-5131	64	79	memristor	memristor	NOUN
ejpam-5131	64	80	models	model	NOUN
ejpam-5131	64	81	,	,	PUNCT
ejpam-5131	64	82	investigating	investigate	VERB
ejpam-5131	64	83	the	the	DET
ejpam-5131	64	84	impact	impact	NOUN
ejpam-5131	64	85	of	of	ADP
ejpam-5131	64	86	system	system	NOUN
ejpam-5131	64	87	parameters	parameter	NOUN
ejpam-5131	64	88	on	on	ADP
ejpam-5131	64	89	the	the	DET
ejpam-5131	64	90	robustness	robustness	NOUN
ejpam-5131	64	91	and	and	CCONJ
ejpam-5131	64	92	sensitivity	sensitivity	NOUN
ejpam-5131	64	93	of	of	ADP
ejpam-5131	64	94	the	the	DET
ejpam-5131	64	95	chaotic	chaotic	ADJ
ejpam-5131	64	96	behaviours	behaviour	NOUN
ejpam-5131	64	97	observed	observe	VERB
ejpam-5131	64	98	to	to	ADP
ejpam-5131	64	99	better	well	ADJ
ejpam-5131	64	100	control	control	NOUN
ejpam-5131	64	101	and	and	CCONJ
ejpam-5131	64	102	harness	harness	NOUN
ejpam-5131	64	103	these	these	DET
ejpam-5131	64	104	dynamics	dynamic	NOUN
ejpam-5131	64	105	for	for	ADP
ejpam-5131	64	106	practical	practical	ADJ
ejpam-5131	64	107	applications	application	NOUN
ejpam-5131	64	108	see	see	VERB
ejpam-5131	64	109	[	[	X
ejpam-5131	64	110	1	1	NUM
ejpam-5131	64	111	,	,	PUNCT
ejpam-5131	64	112	3	3	NUM
ejpam-5131	64	113	,	,	PUNCT
ejpam-5131	64	114	4	4	NUM
ejpam-5131	64	115	,	,	PUNCT
ejpam-5131	64	116	26–28	26–28	NUM
ejpam-5131	64	117	]	]	PUNCT
ejpam-5131	64	118	.	.	PUNCT
ejpam-5131	65	1	2	2	X
ejpam-5131	65	2	.	.	NUM
ejpam-5131	65	3	basic	basic	ADJ
ejpam-5131	65	4	principles	principle	NOUN
ejpam-5131	65	5	definition	definition	NOUN
ejpam-5131	65	6	1	1	NUM
ejpam-5131	65	7	.	.	PUNCT
ejpam-5131	66	1	the	the	DET
ejpam-5131	66	2	riemann	riemann	PROPN
ejpam-5131	66	3	liouville	liouville	PROPN
ejpam-5131	66	4	integral	integral	ADJ
ejpam-5131	66	5	(	(	PUNCT
ejpam-5131	66	6	rli	rli	NOUN
ejpam-5131	66	7	)	)	PUNCT
ejpam-5131	66	8	order	order	NOUN
ejpam-5131	66	9	of	of	ADP
ejpam-5131	66	10	0	0	NUM
ejpam-5131	66	11	<	<	X
ejpam-5131	66	12	α	α	X
ejpam-5131	66	13	<	<	X
ejpam-5131	66	14	1	1	NUM
ejpam-5131	66	15	and	and	CCONJ
ejpam-5131	66	16	y(τ	y(τ	PROPN
ejpam-5131	66	17	)	)	PUNCT
ejpam-5131	66	18	is	be	AUX
ejpam-5131	66	19	provided	provide	VERB
ejpam-5131	66	20	by	by	ADP
ejpam-5131	66	21	[	[	X
ejpam-5131	66	22	30	30	NUM
ejpam-5131	66	23	]	]	X
ejpam-5131	66	24	:	:	PUNCT
ejpam-5131	66	25	dαy∗	dαy∗	ADJ
ejpam-5131	66	26	(	(	PUNCT
ejpam-5131	66	27	t	t	NOUN
ejpam-5131	66	28	)	)	PUNCT
ejpam-5131	66	29	=	=	SYM
ejpam-5131	66	30	1	1	NUM
ejpam-5131	66	31	γ(n−	γ(n−	PROPN
ejpam-5131	66	32	ζ	ζ	PROPN
ejpam-5131	66	33	)	)	PUNCT
ejpam-5131	66	34	∫	∫	PROPN
ejpam-5131	66	35	t	t	PROPN
ejpam-5131	66	36	0	0	NUM
ejpam-5131	66	37	(	(	PUNCT
ejpam-5131	66	38	t−	t−	PROPN
ejpam-5131	66	39	τ)n−ζ−1y∗n	τ)n−ζ−1y∗n	X
ejpam-5131	66	40	(	(	PUNCT
ejpam-5131	66	41	τ	τ	NOUN
ejpam-5131	66	42	)	)	PUNCT
ejpam-5131	66	43	dτ	dτ	NOUN
ejpam-5131	66	44	=	=	SYM
ejpam-5131	66	45	in−ζy∗n	in−ζy∗n	PROPN
ejpam-5131	66	46	(	(	PUNCT
ejpam-5131	66	47	t	t	PROPN
ejpam-5131	66	48	)	)	PUNCT
ejpam-5131	66	49	,	,	PUNCT
ejpam-5131	66	50	t	t	X
ejpam-5131	66	51	>	>	X
ejpam-5131	66	52	0	0	NUM
ejpam-5131	66	53	.	.	PUNCT
ejpam-5131	67	1	(	(	PUNCT
ejpam-5131	67	2	1	1	X
ejpam-5131	67	3	)	)	PUNCT
ejpam-5131	67	4	definition	definition	NOUN
ejpam-5131	67	5	2	2	NUM
ejpam-5131	67	6	.	.	PUNCT
ejpam-5131	68	1	the	the	DET
ejpam-5131	68	2	riemann	riemann	PROPN
ejpam-5131	68	3	-	-	PUNCT
ejpam-5131	68	4	liouville	liouville	VERB
ejpam-5131	68	5	fractional	fractional	ADJ
ejpam-5131	68	6	integral	integral	ADJ
ejpam-5131	68	7	of	of	ADP
ejpam-5131	68	8	order	order	NOUN
ejpam-5131	68	9	ζ	ζ	NOUN
ejpam-5131	68	10	>	>	X
ejpam-5131	68	11	0	0	NUM
ejpam-5131	68	12	,	,	PUNCT
ejpam-5131	68	13	given	give	VERB
ejpam-5131	68	14	by	by	ADP
ejpam-5131	68	15	[	[	PUNCT
ejpam-5131	68	16	6	6	NUM
ejpam-5131	68	17	]	]	SYM
ejpam-5131	68	18	:	:	PUNCT
ejpam-5131	68	19	iζa+y	iζa+y	NUM
ejpam-5131	68	20	∗(t	∗(t	NOUN
ejpam-5131	68	21	)	)	PUNCT
ejpam-5131	68	22	=	=	SYM
ejpam-5131	68	23	1	1	NUM
ejpam-5131	68	24	γ(ζ	γ(ζ	PROPN
ejpam-5131	68	25	)	)	PUNCT
ejpam-5131	68	26	∫	∫	PROPN
ejpam-5131	69	1	t	t	PROPN
ejpam-5131	69	2	a	a	PRON
ejpam-5131	69	3	(	(	PUNCT
ejpam-5131	69	4	t−	t−	PROPN
ejpam-5131	69	5	s)ζ−1y(s)ds	s)ζ−1y(s)ds	PROPN
ejpam-5131	69	6	,	,	PUNCT
ejpam-5131	69	7	t	t	PROPN
ejpam-5131	69	8	>	>	X
ejpam-5131	69	9	a.	a.	NOUN
ejpam-5131	70	1	(	(	PUNCT
ejpam-5131	70	2	2	2	NUM
ejpam-5131	70	3	)	)	PUNCT
ejpam-5131	70	4	definition	definition	NOUN
ejpam-5131	70	5	3	3	NUM
ejpam-5131	70	6	.	.	PUNCT
ejpam-5131	71	1	for	for	ADP
ejpam-5131	71	2	a	a	DET
ejpam-5131	71	3	function	function	NOUN
ejpam-5131	71	4	y	y	PROPN
ejpam-5131	71	5	(	(	PUNCT
ejpam-5131	71	6	τ	τ	PROPN
ejpam-5131	71	7	)	)	PUNCT
ejpam-5131	71	8	caputo	caputo	PROPN
ejpam-5131	71	9	derivative	derivative	NOUN
ejpam-5131	71	10	of	of	ADP
ejpam-5131	71	11	order	order	NOUN
ejpam-5131	71	12	0	0	PUNCT
ejpam-5131	71	13	<	<	X
ejpam-5131	71	14	ζ	ζ	X
ejpam-5131	71	15	<	<	X
ejpam-5131	71	16	1	1	NUM
ejpam-5131	71	17	is	be	AUX
ejpam-5131	71	18	given	give	VERB
ejpam-5131	71	19	by	by	ADP
ejpam-5131	71	20	[	[	X
ejpam-5131	71	21	19	19	NUM
ejpam-5131	71	22	]	]	X
ejpam-5131	71	23	:	:	PUNCT
ejpam-5131	71	24	iζy	iζy	NOUN
ejpam-5131	71	25	(	(	PUNCT
ejpam-5131	71	26	t	t	NOUN
ejpam-5131	71	27	)	)	PUNCT
ejpam-5131	71	28	=	=	SYM
ejpam-5131	71	29	1	1	NUM
ejpam-5131	71	30	γ	γ	X
ejpam-5131	71	31	(	(	PUNCT
ejpam-5131	71	32	ζ	ζ	NOUN
ejpam-5131	71	33	)	)	PUNCT
ejpam-5131	71	34	∫	∫	PROPN
ejpam-5131	71	35	t	t	PROPN
ejpam-5131	71	36	0	0	NUM
ejpam-5131	71	37	(	(	PUNCT
ejpam-5131	71	38	t−	t−	PROPN
ejpam-5131	71	39	τ)ζ−1	τ)ζ−1	PROPN
ejpam-5131	71	40	y	y	PROPN
ejpam-5131	71	41	(	(	PUNCT
ejpam-5131	71	42	τ	τ	PROPN
ejpam-5131	71	43	)	)	PUNCT
ejpam-5131	71	44	dτ	dτ	PROPN
ejpam-5131	71	45	,	,	PUNCT
ejpam-5131	71	46	t	t	PROPN
ejpam-5131	71	47	>	>	X
ejpam-5131	71	48	0	0	NUM
ejpam-5131	71	49	.	.	PUNCT
ejpam-5131	72	1	(	(	PUNCT
ejpam-5131	72	2	3	3	X
ejpam-5131	72	3	)	)	PUNCT
ejpam-5131	72	4	g.	g.	PROPN
ejpam-5131	72	5	a.	a.	PROPN
ejpam-5131	72	6	ahmed	ahmed	PROPN
ejpam-5131	72	7	/	/	SYM
ejpam-5131	72	8	eur	eur	PROPN
ejpam-5131	72	9	.	.	PUNCT
ejpam-5131	73	1	j.	j.	PROPN
ejpam-5131	73	2	pure	pure	PROPN
ejpam-5131	73	3	appl	appl	PROPN
ejpam-5131	73	4	.	.	PROPN
ejpam-5131	73	5	math	math	PROPN
ejpam-5131	73	6	,	,	PUNCT
ejpam-5131	73	7	17	17	NUM
ejpam-5131	73	8	(	(	PUNCT
ejpam-5131	73	9	2	2	NUM
ejpam-5131	73	10	)	)	PUNCT
ejpam-5131	73	11	(	(	PUNCT
ejpam-5131	73	12	2024	2024	NUM
ejpam-5131	73	13	)	)	PUNCT
ejpam-5131	73	14	,	,	PUNCT
ejpam-5131	73	15	835	835	NUM
ejpam-5131	73	16	-	-	SYM
ejpam-5131	73	17	851	851	NUM
ejpam-5131	73	18	839	839	NUM
ejpam-5131	73	19	definition	definition	NOUN
ejpam-5131	73	20	4	4	NUM
ejpam-5131	73	21	.	.	PUNCT
ejpam-5131	74	1	the	the	DET
ejpam-5131	74	2	mittag	mittag	ADJ
ejpam-5131	74	3	-	-	PUNCT
ejpam-5131	74	4	leffler	leffler	NOUN
ejpam-5131	74	5	function	function	NOUN
ejpam-5131	74	6	can	can	AUX
ejpam-5131	74	7	be	be	AUX
ejpam-5131	74	8	expressed	express	VERB
ejpam-5131	74	9	as	as	SCONJ
ejpam-5131	74	10	follows	follow	VERB
ejpam-5131	74	11	[	[	X
ejpam-5131	74	12	13	13	NUM
ejpam-5131	74	13	]	]	PUNCT
ejpam-5131	74	14	:	:	PUNCT
ejpam-5131	74	15	e∗	e∗	PROPN
ejpam-5131	74	16	α	α	PROPN
ejpam-5131	74	17	(	(	PUNCT
ejpam-5131	74	18	t	t	PROPN
ejpam-5131	74	19	)	)	PUNCT
ejpam-5131	74	20	=	=	NOUN
ejpam-5131	75	1	∞∑	∞∑	NUM
ejpam-5131	75	2	k=0	k=0	PROPN
ejpam-5131	75	3	tk	tk	VERB
ejpam-5131	75	4	γ(ζk	γ(ζk	PRON
ejpam-5131	75	5	+	+	CCONJ
ejpam-5131	75	6	1	1	NUM
ejpam-5131	75	7	)	)	PUNCT
ejpam-5131	75	8	.	.	PUNCT
ejpam-5131	76	1	(	(	PUNCT
ejpam-5131	76	2	4	4	X
ejpam-5131	76	3	)	)	PUNCT
ejpam-5131	76	4	definition	definition	NOUN
ejpam-5131	76	5	5	5	NUM
ejpam-5131	76	6	.	.	PUNCT
ejpam-5131	77	1	the	the	DET
ejpam-5131	77	2	lagrange	lagrange	NOUN
ejpam-5131	77	3	’s	’s	PART
ejpam-5131	77	4	polynomial	polynomial	ADJ
ejpam-5131	77	5	interpolation	interpolation	NOUN
ejpam-5131	77	6	is	be	AUX
ejpam-5131	77	7	defined	define	VERB
ejpam-5131	77	8	by	by	ADP
ejpam-5131	77	9	[	[	X
ejpam-5131	77	10	17	17	NUM
ejpam-5131	77	11	]	]	PUNCT
ejpam-5131	77	12	as	as	ADP
ejpam-5131	77	13	p	p	NOUN
ejpam-5131	77	14	∗	∗	NOUN
ejpam-5131	77	15	n(x	n(x	X
ejpam-5131	77	16	)	)	PUNCT
ejpam-5131	77	17	=	=	SYM
ejpam-5131	77	18	n∑	n∑	PROPN
ejpam-5131	77	19	i=0	i=0	PROPN
ejpam-5131	77	20	f	f	X
ejpam-5131	77	21	(	(	PUNCT
ejpam-5131	77	22	x∗i	x∗i	PROPN
ejpam-5131	77	23	)	)	PUNCT
ejpam-5131	77	24	li(x	li(x	NUM
ejpam-5131	77	25	)	)	PUNCT
ejpam-5131	77	26	,	,	PUNCT
ejpam-5131	77	27	where	where	SCONJ
ejpam-5131	77	28	li	li	PROPN
ejpam-5131	77	29	(	(	PUNCT
ejpam-5131	77	30	x	x	NOUN
ejpam-5131	77	31	∗	∗	NOUN
ejpam-5131	77	32	)	)	PUNCT
ejpam-5131	77	33	=	=	PUNCT
ejpam-5131	77	34	n∏	n∏	NOUN
ejpam-5131	77	35	j=0,j	j=0,j	NOUN
ejpam-5131	77	36	̸=i	̸=i	PROPN
ejpam-5131	77	37	x∗	x∗	PROPN
ejpam-5131	77	38	−	−	PROPN
ejpam-5131	77	39	x∗i	x∗i	PROPN
ejpam-5131	77	40	x∗i	x∗i	PROPN
ejpam-5131	77	41	−	−	PROPN
ejpam-5131	77	42	x∗j	x∗j	PROPN
ejpam-5131	77	43	.	.	PUNCT
ejpam-5131	78	1	definition	definition	NOUN
ejpam-5131	78	2	6	6	NUM
ejpam-5131	78	3	.	.	PUNCT
ejpam-5131	79	1	the	the	DET
ejpam-5131	79	2	abc	abc	PROPN
ejpam-5131	79	3	operator	operator	NOUN
ejpam-5131	79	4	,	,	PUNCT
ejpam-5131	79	5	y	y	PROPN
ejpam-5131	79	6	(	(	PUNCT
ejpam-5131	79	7	t	t	PROPN
ejpam-5131	79	8	)	)	PUNCT
ejpam-5131	79	9	in	in	ADP
ejpam-5131	79	10	the	the	DET
ejpam-5131	79	11	rli	rli	PROPN
ejpam-5131	79	12	is	be	AUX
ejpam-5131	79	13	given	give	VERB
ejpam-5131	79	14	by	by	ADP
ejpam-5131	79	15	[	[	X
ejpam-5131	79	16	16	16	NUM
ejpam-5131	79	17	]	]	X
ejpam-5131	79	18	:	:	PUNCT
ejpam-5131	79	19	abc	abc	PROPN
ejpam-5131	79	20	0	0	PROPN
ejpam-5131	79	21	dζ	dζ	PROPN
ejpam-5131	79	22	t	t	PROPN
ejpam-5131	79	23	y	y	PROPN
ejpam-5131	79	24	(	(	PUNCT
ejpam-5131	79	25	t	t	PROPN
ejpam-5131	79	26	)	)	PUNCT
ejpam-5131	79	27	=	=	SYM
ejpam-5131	79	28	b	b	X
ejpam-5131	79	29	(	(	PUNCT
ejpam-5131	79	30	ζ	ζ	NOUN
ejpam-5131	79	31	)	)	PUNCT
ejpam-5131	79	32	1−	1−	NUM
ejpam-5131	80	1	ζ	ζ	NOUN
ejpam-5131	80	2	d	d	NOUN
ejpam-5131	80	3	dt	dt	X
ejpam-5131	81	1	∫	∫	PROPN
ejpam-5131	81	2	t	t	PROPN
ejpam-5131	81	3	0	0	NUM
ejpam-5131	82	1	y∗	y∗	PROPN
ejpam-5131	82	2	(	(	PUNCT
ejpam-5131	82	3	τ)eζ	τ)eζ	PROPN
ejpam-5131	82	4	(	(	PUNCT
ejpam-5131	82	5	ζ	ζ	PROPN
ejpam-5131	82	6	1−	1−	NUM
ejpam-5131	82	7	ζ	ζ	NOUN
ejpam-5131	82	8	(	(	PUNCT
ejpam-5131	82	9	t−	t−	PROPN
ejpam-5131	82	10	τ)α	τ)α	ADJ
ejpam-5131	82	11	)	)	PUNCT
ejpam-5131	82	12	dτ	dτ	NOUN
ejpam-5131	82	13	,	,	PUNCT
ejpam-5131	82	14	0	0	PUNCT
ejpam-5131	82	15	<	<	X
ejpam-5131	82	16	ζ	ζ	X
ejpam-5131	82	17	<	<	X
ejpam-5131	82	18	1	1	NUM
ejpam-5131	82	19	.	.	PUNCT
ejpam-5131	82	20	(	(	PUNCT
ejpam-5131	82	21	5	5	NUM
ejpam-5131	82	22	)	)	PUNCT
ejpam-5131	82	23	where	where	SCONJ
ejpam-5131	82	24	b∗	b∗	ADJ
ejpam-5131	82	25	(	(	PUNCT
ejpam-5131	82	26	ζ	ζ	NOUN
ejpam-5131	82	27	)	)	PUNCT
ejpam-5131	82	28	satisfies	satisfy	VERB
ejpam-5131	82	29	the	the	DET
ejpam-5131	82	30	condition	condition	NOUN
ejpam-5131	82	31	b∗	b∗	ADJ
ejpam-5131	82	32	(	(	PUNCT
ejpam-5131	82	33	1	1	NUM
ejpam-5131	82	34	)	)	PUNCT
ejpam-5131	82	35	=	=	SYM
ejpam-5131	83	1	b∗	b∗	ADJ
ejpam-5131	83	2	(	(	PUNCT
ejpam-5131	83	3	0	0	NUM
ejpam-5131	83	4	)	)	PUNCT
ejpam-5131	83	5	=	=	SYM
ejpam-5131	84	1	1	1	X
ejpam-5131	84	2	.	.	X
ejpam-5131	84	3	definition	definition	NOUN
ejpam-5131	84	4	7	7	NUM
ejpam-5131	84	5	.	.	PUNCT
ejpam-5131	85	1	the	the	DET
ejpam-5131	85	2	memristor	memristor	NOUN
ejpam-5131	85	3	emulator	emulator	NOUN
ejpam-5131	85	4	is	be	AUX
ejpam-5131	85	5	applied	apply	VERB
ejpam-5131	85	6	to	to	ADP
ejpam-5131	85	7	our	our	PRON
ejpam-5131	85	8	novel	novel	ADJ
ejpam-5131	85	9	system	system	NOUN
ejpam-5131	85	10	which	which	PRON
ejpam-5131	85	11	has	have	VERB
ejpam-5131	85	12	a	a	DET
ejpam-5131	85	13	current	current	ADJ
ejpam-5131	85	14	,	,	PUNCT
ejpam-5131	85	15	voltage	voltage	NOUN
ejpam-5131	85	16	relation	relation	NOUN
ejpam-5131	85	17	as	as	ADP
ejpam-5131	85	18	,	,	PUNCT
ejpam-5131	85	19	i	i	PRON
ejpam-5131	85	20	=	=	VERB
ejpam-5131	85	21	w	w	PROPN
ejpam-5131	85	22	∗	∗	NOUN
ejpam-5131	85	23	(	(	PUNCT
ejpam-5131	85	24	v∗0	v∗0	NOUN
ejpam-5131	85	25	)	)	PUNCT
ejpam-5131	85	26	v	v	NOUN
ejpam-5131	85	27	∗	∗	NOUN
ejpam-5131	85	28	=	=	PUNCT
ejpam-5131	86	1	[	[	X
ejpam-5131	86	2	a−b	a−b	NOUN
ejpam-5131	86	3	tanh	tanh	NOUN
ejpam-5131	86	4	(	(	PUNCT
ejpam-5131	86	5	v∗0	v∗0	NOUN
ejpam-5131	86	6	)	)	PUNCT
ejpam-5131	86	7	]	]	PUNCT
ejpam-5131	86	8	v	v	X
ejpam-5131	86	9	∗.	∗.	PROPN
ejpam-5131	86	10	(	(	PUNCT
ejpam-5131	86	11	6	6	NUM
ejpam-5131	86	12	)	)	PUNCT
ejpam-5131	86	13	3	3	NUM
ejpam-5131	86	14	.	.	PUNCT
ejpam-5131	86	15	numerical	numerical	ADJ
ejpam-5131	86	16	scheme	scheme	NOUN
ejpam-5131	86	17	for	for	ADP
ejpam-5131	86	18	abc	abc	PROPN
ejpam-5131	86	19	the	the	DET
ejpam-5131	86	20	goal	goal	NOUN
ejpam-5131	86	21	of	of	ADP
ejpam-5131	86	22	this	this	DET
ejpam-5131	86	23	section	section	NOUN
ejpam-5131	86	24	is	be	AUX
ejpam-5131	86	25	to	to	PART
ejpam-5131	86	26	investigate	investigate	VERB
ejpam-5131	86	27	chaotic	chaotic	ADJ
ejpam-5131	86	28	models	model	NOUN
ejpam-5131	86	29	in	in	ADP
ejpam-5131	86	30	the	the	DET
ejpam-5131	86	31	sense	sense	NOUN
ejpam-5131	86	32	of	of	ADP
ejpam-5131	86	33	the	the	DET
ejpam-5131	86	34	abc	abc	PROPN
ejpam-5131	86	35	fractional	fractional	PROPN
ejpam-5131	86	36	derivative	derivative	PROPN
ejpam-5131	86	37	.	.	PUNCT
ejpam-5131	87	1	central	central	ADJ
ejpam-5131	87	2	to	to	ADP
ejpam-5131	87	3	this	this	DET
ejpam-5131	87	4	research	research	NOUN
ejpam-5131	87	5	is	be	AUX
ejpam-5131	87	6	the	the	DET
ejpam-5131	87	7	rigorous	rigorous	ADJ
ejpam-5131	87	8	examination	examination	NOUN
ejpam-5131	87	9	of	of	ADP
ejpam-5131	87	10	chaotic	chaotic	ADJ
ejpam-5131	87	11	models	model	NOUN
ejpam-5131	87	12	through	through	ADP
ejpam-5131	87	13	the	the	DET
ejpam-5131	87	14	lens	lens	NOUN
ejpam-5131	87	15	of	of	ADP
ejpam-5131	87	16	the	the	DET
ejpam-5131	87	17	abc	abc	PROPN
ejpam-5131	87	18	fractional	fractional	PROPN
ejpam-5131	87	19	derivative	derivative	NOUN
ejpam-5131	87	20	.	.	PUNCT
ejpam-5131	88	1	to	to	ADP
ejpam-5131	88	2	this	this	DET
ejpam-5131	88	3	end	end	NOUN
ejpam-5131	88	4	,	,	PUNCT
ejpam-5131	88	5	we	we	PRON
ejpam-5131	88	6	have	have	AUX
ejpam-5131	88	7	developed	develop	VERB
ejpam-5131	88	8	and	and	CCONJ
ejpam-5131	88	9	employed	employ	VERB
ejpam-5131	88	10	specialized	specialized	ADJ
ejpam-5131	88	11	numerical	numerical	ADJ
ejpam-5131	88	12	schemes	scheme	NOUN
ejpam-5131	88	13	capable	capable	ADJ
ejpam-5131	88	14	of	of	ADP
ejpam-5131	88	15	simulating	simulate	VERB
ejpam-5131	88	16	the	the	DET
ejpam-5131	88	17	nuanced	nuanced	ADJ
ejpam-5131	88	18	behaviors	behavior	NOUN
ejpam-5131	88	19	of	of	ADP
ejpam-5131	88	20	our	our	PRON
ejpam-5131	88	21	proposed	propose	VERB
ejpam-5131	88	22	fractional	fractional	ADJ
ejpam-5131	88	23	-	-	PUNCT
ejpam-5131	88	24	order	order	NOUN
ejpam-5131	88	25	chaotic	chaotic	ADJ
ejpam-5131	88	26	system	system	NOUN
ejpam-5131	88	27	with	with	ADP
ejpam-5131	88	28	high	high	ADJ
ejpam-5131	88	29	fidelity	fidelity	NOUN
ejpam-5131	88	30	.	.	PUNCT
ejpam-5131	89	1	the	the	DET
ejpam-5131	89	2	numerical	numerical	ADJ
ejpam-5131	89	3	methods	method	NOUN
ejpam-5131	89	4	selected	select	VERB
ejpam-5131	89	5	for	for	ADP
ejpam-5131	89	6	this	this	DET
ejpam-5131	89	7	study	study	NOUN
ejpam-5131	89	8	are	be	AUX
ejpam-5131	89	9	designed	design	VERB
ejpam-5131	89	10	to	to	PART
ejpam-5131	89	11	address	address	VERB
ejpam-5131	89	12	the	the	DET
ejpam-5131	89	13	non	non	ADJ
ejpam-5131	89	14	-	-	ADJ
ejpam-5131	89	15	integer	integer	ADJ
ejpam-5131	89	16	order	order	NOUN
ejpam-5131	89	17	differentiation	differentiation	NOUN
ejpam-5131	89	18	inherent	inherent	ADJ
ejpam-5131	89	19	to	to	ADP
ejpam-5131	89	20	fractional	fractional	ADJ
ejpam-5131	89	21	calculus	calculus	NOUN
ejpam-5131	89	22	,	,	PUNCT
ejpam-5131	89	23	which	which	PRON
ejpam-5131	89	24	standard	standard	ADJ
ejpam-5131	89	25	numerical	numerical	ADJ
ejpam-5131	89	26	approaches	approach	NOUN
ejpam-5131	89	27	may	may	AUX
ejpam-5131	89	28	not	not	PART
ejpam-5131	89	29	handle	handle	VERB
ejpam-5131	89	30	adequately	adequately	ADV
ejpam-5131	89	31	.	.	PUNCT
ejpam-5131	90	1	these	these	DET
ejpam-5131	90	2	methods	method	NOUN
ejpam-5131	90	3	,	,	PUNCT
ejpam-5131	90	4	including	include	VERB
ejpam-5131	90	5	the	the	DET
ejpam-5131	90	6	abc	abc	PROPN
ejpam-5131	90	7	operator	operator	NOUN
ejpam-5131	90	8	approach	approach	NOUN
ejpam-5131	90	9	and	and	CCONJ
ejpam-5131	90	10	the	the	DET
ejpam-5131	90	11	two	two	NUM
ejpam-5131	90	12	-	-	PUNCT
ejpam-5131	90	13	step	step	NOUN
ejpam-5131	90	14	lagrange	lagrange	NOUN
ejpam-5131	90	15	polynomial	polynomial	ADJ
ejpam-5131	90	16	algorithm	algorithm	NOUN
ejpam-5131	90	17	its	its	PRON
ejpam-5131	90	18	renowned	renowned	ADJ
ejpam-5131	90	19	for	for	ADP
ejpam-5131	90	20	their	their	PRON
ejpam-5131	90	21	precision	precision	NOUN
ejpam-5131	90	22	and	and	CCONJ
ejpam-5131	90	23	stability	stability	NOUN
ejpam-5131	90	24	when	when	SCONJ
ejpam-5131	90	25	dealing	deal	VERB
ejpam-5131	90	26	with	with	ADP
ejpam-5131	90	27	fractional	fractional	ADJ
ejpam-5131	90	28	differential	differential	ADJ
ejpam-5131	90	29	equations	equation	NOUN
ejpam-5131	90	30	.	.	PUNCT
ejpam-5131	91	1	the	the	DET
ejpam-5131	91	2	former	former	ADJ
ejpam-5131	91	3	provides	provide	VERB
ejpam-5131	91	4	a	a	DET
ejpam-5131	91	5	direct	direct	ADJ
ejpam-5131	91	6	discretization	discretization	NOUN
ejpam-5131	91	7	of	of	ADP
ejpam-5131	91	8	the	the	DET
ejpam-5131	91	9	fractional	fractional	ADJ
ejpam-5131	91	10	derivative	derivative	NOUN
ejpam-5131	91	11	,	,	PUNCT
ejpam-5131	91	12	while	while	SCONJ
ejpam-5131	91	13	the	the	DET
ejpam-5131	91	14	latter	latter	NOUN
ejpam-5131	91	15	offers	offer	VERB
ejpam-5131	91	16	an	an	DET
ejpam-5131	91	17	iterative	iterative	NOUN
ejpam-5131	91	18	refinement	refinement	NOUN
ejpam-5131	91	19	that	that	PRON
ejpam-5131	91	20	ensures	ensure	VERB
ejpam-5131	91	21	convergence	convergence	NOUN
ejpam-5131	91	22	to	to	ADP
ejpam-5131	91	23	the	the	DET
ejpam-5131	91	24	true	true	ADJ
ejpam-5131	91	25	solution	solution	NOUN
ejpam-5131	91	26	.	.	PUNCT
ejpam-5131	92	1	moreover	moreover	ADV
ejpam-5131	92	2	,	,	PUNCT
ejpam-5131	92	3	the	the	DET
ejpam-5131	92	4	analysis	analysis	NOUN
ejpam-5131	92	5	of	of	ADP
ejpam-5131	92	6	the	the	DET
ejpam-5131	92	7	system	system	NOUN
ejpam-5131	92	8	’s	’s	PART
ejpam-5131	92	9	dynamics	dynamic	NOUN
ejpam-5131	92	10	is	be	AUX
ejpam-5131	92	11	bolstered	bolster	VERB
ejpam-5131	92	12	by	by	ADP
ejpam-5131	92	13	the	the	DET
ejpam-5131	92	14	use	use	NOUN
ejpam-5131	92	15	of	of	ADP
ejpam-5131	92	16	robust	robust	ADJ
ejpam-5131	92	17	analytical	analytical	ADJ
ejpam-5131	92	18	tools	tool	NOUN
ejpam-5131	92	19	.	.	PUNCT
ejpam-5131	93	1	eigenvalue	eigenvalue	VERB
ejpam-5131	93	2	analysis	analysis	NOUN
ejpam-5131	93	3	serves	serve	VERB
ejpam-5131	93	4	as	as	ADP
ejpam-5131	93	5	the	the	DET
ejpam-5131	93	6	cornerstone	cornerstone	NOUN
ejpam-5131	93	7	for	for	ADP
ejpam-5131	93	8	assessing	assess	VERB
ejpam-5131	93	9	the	the	DET
ejpam-5131	93	10	stability	stability	NOUN
ejpam-5131	93	11	of	of	ADP
ejpam-5131	93	12	the	the	DET
ejpam-5131	93	13	equilibrium	equilibrium	NOUN
ejpam-5131	93	14	points	point	NOUN
ejpam-5131	93	15	,	,	PUNCT
ejpam-5131	93	16	offering	offer	VERB
ejpam-5131	93	17	a	a	DET
ejpam-5131	93	18	clear	clear	ADJ
ejpam-5131	93	19	view	view	NOUN
ejpam-5131	93	20	of	of	ADP
ejpam-5131	93	21	the	the	DET
ejpam-5131	93	22	system	system	NOUN
ejpam-5131	93	23	’s	’s	PART
ejpam-5131	93	24	response	response	NOUN
ejpam-5131	93	25	to	to	ADP
ejpam-5131	93	26	infinitesimal	infinitesimal	ADJ
ejpam-5131	93	27	perturbations	perturbation	NOUN
ejpam-5131	93	28	.	.	PUNCT
ejpam-5131	94	1	concurrently	concurrently	ADV
ejpam-5131	94	2	,	,	PUNCT
ejpam-5131	94	3	lyapunov	lyapunov	PROPN
ejpam-5131	94	4	exponents	exponent	NOUN
ejpam-5131	94	5	provide	provide	VERB
ejpam-5131	94	6	a	a	DET
ejpam-5131	94	7	quantitative	quantitative	ADJ
ejpam-5131	94	8	measure	measure	NOUN
ejpam-5131	94	9	of	of	ADP
ejpam-5131	94	10	the	the	DET
ejpam-5131	94	11	exponential	exponential	ADJ
ejpam-5131	94	12	divergence	divergence	NOUN
ejpam-5131	94	13	or	or	CCONJ
ejpam-5131	94	14	convergence	convergence	NOUN
ejpam-5131	94	15	of	of	ADP
ejpam-5131	94	16	nearby	nearby	ADJ
ejpam-5131	94	17	trajectories	trajectory	NOUN
ejpam-5131	94	18	,	,	PUNCT
ejpam-5131	94	19	a	a	DET
ejpam-5131	94	20	hallmark	hallmark	NOUN
ejpam-5131	94	21	of	of	ADP
ejpam-5131	94	22	chaotic	chaotic	ADJ
ejpam-5131	94	23	behavior	behavior	NOUN
ejpam-5131	94	24	.	.	PUNCT
ejpam-5131	95	1	the	the	DET
ejpam-5131	95	2	maximal	maximal	ADJ
ejpam-5131	95	3	lyapunov	lyapunov	ADJ
ejpam-5131	95	4	exponent	exponent	NOUN
ejpam-5131	95	5	,	,	PUNCT
ejpam-5131	95	6	in	in	ADP
ejpam-5131	95	7	particular	particular	ADJ
ejpam-5131	95	8	,	,	PUNCT
ejpam-5131	95	9	is	be	AUX
ejpam-5131	95	10	indicative	indicative	ADJ
ejpam-5131	95	11	of	of	ADP
ejpam-5131	95	12	the	the	DET
ejpam-5131	95	13	presence	presence	NOUN
ejpam-5131	95	14	of	of	ADP
ejpam-5131	95	15	g.	g.	PROPN
ejpam-5131	95	16	a.	a.	PROPN
ejpam-5131	95	17	ahmed	ahmed	PROPN
ejpam-5131	95	18	/	/	SYM
ejpam-5131	95	19	eur	eur	PROPN
ejpam-5131	95	20	.	.	PUNCT
ejpam-5131	96	1	j.	j.	PROPN
ejpam-5131	96	2	pure	pure	PROPN
ejpam-5131	96	3	appl	appl	PROPN
ejpam-5131	96	4	.	.	PROPN
ejpam-5131	96	5	math	math	PROPN
ejpam-5131	96	6	,	,	PUNCT
ejpam-5131	96	7	17	17	NUM
ejpam-5131	96	8	(	(	PUNCT
ejpam-5131	96	9	2	2	NUM
ejpam-5131	96	10	)	)	PUNCT
ejpam-5131	96	11	(	(	PUNCT
ejpam-5131	96	12	2024	2024	NUM
ejpam-5131	96	13	)	)	PUNCT
ejpam-5131	96	14	,	,	PUNCT
ejpam-5131	96	15	835	835	NUM
ejpam-5131	96	16	-	-	SYM
ejpam-5131	96	17	851	851	NUM
ejpam-5131	96	18	840	840	NUM
ejpam-5131	96	19	chaos	chaos	NOUN
ejpam-5131	96	20	when	when	SCONJ
ejpam-5131	96	21	it	it	PRON
ejpam-5131	96	22	is	be	AUX
ejpam-5131	96	23	positive	positive	ADJ
ejpam-5131	96	24	,	,	PUNCT
ejpam-5131	96	25	while	while	SCONJ
ejpam-5131	96	26	a	a	DET
ejpam-5131	96	27	spectrum	spectrum	NOUN
ejpam-5131	96	28	of	of	ADP
ejpam-5131	96	29	lyapunov	lyapunov	ADJ
ejpam-5131	96	30	exponents	exponent	NOUN
ejpam-5131	96	31	gives	give	VERB
ejpam-5131	96	32	a	a	DET
ejpam-5131	96	33	broader	broad	ADJ
ejpam-5131	96	34	picture	picture	NOUN
ejpam-5131	96	35	of	of	ADP
ejpam-5131	96	36	the	the	DET
ejpam-5131	96	37	system	system	NOUN
ejpam-5131	96	38	’s	’s	PART
ejpam-5131	96	39	dynamical	dynamical	ADJ
ejpam-5131	96	40	stability	stability	NOUN
ejpam-5131	96	41	.	.	PUNCT
ejpam-5131	97	1	these	these	DET
ejpam-5131	97	2	analytical	analytical	ADJ
ejpam-5131	97	3	instruments	instrument	NOUN
ejpam-5131	97	4	are	be	AUX
ejpam-5131	97	5	invaluable	invaluable	ADJ
ejpam-5131	97	6	for	for	ADP
ejpam-5131	97	7	the	the	DET
ejpam-5131	97	8	characterization	characterization	NOUN
ejpam-5131	97	9	of	of	ADP
ejpam-5131	97	10	chaos	chaos	NOUN
ejpam-5131	97	11	,	,	PUNCT
ejpam-5131	97	12	as	as	SCONJ
ejpam-5131	97	13	they	they	PRON
ejpam-5131	97	14	allow	allow	VERB
ejpam-5131	97	15	for	for	ADP
ejpam-5131	97	16	a	a	DET
ejpam-5131	97	17	detailed	detailed	ADJ
ejpam-5131	97	18	exploration	exploration	NOUN
ejpam-5131	97	19	of	of	ADP
ejpam-5131	97	20	the	the	DET
ejpam-5131	97	21	system	system	NOUN
ejpam-5131	97	22	’s	’s	PART
ejpam-5131	97	23	response	response	NOUN
ejpam-5131	97	24	under	under	ADP
ejpam-5131	97	25	varying	vary	VERB
ejpam-5131	97	26	initial	initial	ADJ
ejpam-5131	97	27	conditions	condition	NOUN
ejpam-5131	97	28	and	and	CCONJ
ejpam-5131	97	29	parameter	parameter	NOUN
ejpam-5131	97	30	values	value	NOUN
ejpam-5131	97	31	.	.	PUNCT
ejpam-5131	98	1	the	the	DET
ejpam-5131	98	2	combination	combination	NOUN
ejpam-5131	98	3	of	of	ADP
ejpam-5131	98	4	these	these	DET
ejpam-5131	98	5	carefully	carefully	ADV
ejpam-5131	98	6	chosen	choose	VERB
ejpam-5131	98	7	numerical	numerical	ADJ
ejpam-5131	98	8	schemes	scheme	NOUN
ejpam-5131	98	9	and	and	CCONJ
ejpam-5131	98	10	analytical	analytical	ADJ
ejpam-5131	98	11	tools	tool	NOUN
ejpam-5131	98	12	constitutes	constitute	VERB
ejpam-5131	98	13	a	a	DET
ejpam-5131	98	14	robust	robust	ADJ
ejpam-5131	98	15	framework	framework	NOUN
ejpam-5131	98	16	for	for	ADP
ejpam-5131	98	17	capturing	capture	VERB
ejpam-5131	98	18	the	the	DET
ejpam-5131	98	19	dynamic	dynamic	ADJ
ejpam-5131	98	20	complexities	complexity	NOUN
ejpam-5131	98	21	of	of	ADP
ejpam-5131	98	22	the	the	DET
ejpam-5131	98	23	proposed	propose	VERB
ejpam-5131	98	24	chaotic	chaotic	ADJ
ejpam-5131	98	25	system	system	NOUN
ejpam-5131	98	26	.	.	PUNCT
ejpam-5131	99	1	through	through	ADP
ejpam-5131	99	2	this	this	DET
ejpam-5131	99	3	dual	dual	ADJ
ejpam-5131	99	4	approach	approach	NOUN
ejpam-5131	99	5	,	,	PUNCT
ejpam-5131	99	6	the	the	DET
ejpam-5131	99	7	study	study	NOUN
ejpam-5131	99	8	not	not	PART
ejpam-5131	99	9	only	only	ADV
ejpam-5131	99	10	ensures	ensure	VERB
ejpam-5131	99	11	the	the	DET
ejpam-5131	99	12	accurate	accurate	ADJ
ejpam-5131	99	13	portrayal	portrayal	NOUN
ejpam-5131	99	14	of	of	ADP
ejpam-5131	99	15	the	the	DET
ejpam-5131	99	16	system	system	NOUN
ejpam-5131	99	17	’s	’s	PART
ejpam-5131	99	18	behavior	behavior	NOUN
ejpam-5131	99	19	but	but	CCONJ
ejpam-5131	99	20	also	also	ADV
ejpam-5131	99	21	underscores	underscore	VERB
ejpam-5131	99	22	the	the	DET
ejpam-5131	99	23	intricate	intricate	ADJ
ejpam-5131	99	24	interplay	interplay	NOUN
ejpam-5131	99	25	between	between	ADP
ejpam-5131	99	26	stability	stability	NOUN
ejpam-5131	99	27	and	and	CCONJ
ejpam-5131	99	28	chaos	chaos	NOUN
ejpam-5131	99	29	in	in	ADP
ejpam-5131	99	30	fractional	fractional	ADJ
ejpam-5131	99	31	-	-	PUNCT
ejpam-5131	99	32	order	order	NOUN
ejpam-5131	99	33	environments	environment	NOUN
ejpam-5131	99	34	,	,	PUNCT
ejpam-5131	99	35	to	to	PART
ejpam-5131	99	36	expand	expand	VERB
ejpam-5131	99	37	on	on	ADP
ejpam-5131	99	38	the	the	DET
ejpam-5131	99	39	given	give	VERB
ejpam-5131	99	40	statement	statement	NOUN
ejpam-5131	99	41	and	and	CCONJ
ejpam-5131	99	42	provide	provide	VERB
ejpam-5131	99	43	more	more	ADJ
ejpam-5131	99	44	detail	detail	NOUN
ejpam-5131	99	45	as	as	SCONJ
ejpam-5131	99	46	requested	request	VERB
ejpam-5131	99	47	,	,	PUNCT
ejpam-5131	99	48	you	you	PRON
ejpam-5131	99	49	might	might	AUX
ejpam-5131	99	50	consider	consider	VERB
ejpam-5131	99	51	the	the	DET
ejpam-5131	99	52	following	follow	VERB
ejpam-5131	99	53	elaboration	elaboration	NOUN
ejpam-5131	99	54	:	:	PUNCT
ejpam-5131	99	55	abc	abc	PROPN
ejpam-5131	99	56	0	0	NUM
ejpam-5131	99	57	dζ	dζ	PROPN
ejpam-5131	99	58	0v	0v	PROPN
ejpam-5131	99	59	∗	∗	PROPN
ejpam-5131	99	60	(	(	PUNCT
ejpam-5131	99	61	t	t	PROPN
ejpam-5131	99	62	)	)	PUNCT
ejpam-5131	100	1	=	=	SYM
ejpam-5131	100	2	f	f	PROPN
ejpam-5131	100	3	(	(	PUNCT
ejpam-5131	100	4	t	t	PROPN
ejpam-5131	100	5	,	,	PUNCT
ejpam-5131	100	6	v∗	v∗	PROPN
ejpam-5131	100	7	(	(	PUNCT
ejpam-5131	100	8	t	t	PROPN
ejpam-5131	100	9	)	)	PUNCT
ejpam-5131	100	10	)	)	PUNCT
ejpam-5131	100	11	,	,	PUNCT
ejpam-5131	100	12	v∗	v∗	PROPN
ejpam-5131	100	13	(	(	PUNCT
ejpam-5131	100	14	0	0	NUM
ejpam-5131	100	15	)	)	PUNCT
ejpam-5131	100	16	=	=	NOUN
ejpam-5131	100	17	v∗0	v∗0	NOUN
ejpam-5131	100	18	.	.	PUNCT
ejpam-5131	101	1	(	(	PUNCT
ejpam-5131	101	2	7	7	X
ejpam-5131	101	3	)	)	PUNCT
ejpam-5131	101	4	a	a	DET
ejpam-5131	101	5	fractional	fractional	ADJ
ejpam-5131	101	6	integral	integral	ADJ
ejpam-5131	101	7	equation	equation	NOUN
ejpam-5131	101	8	can	can	AUX
ejpam-5131	101	9	be	be	AUX
ejpam-5131	101	10	derived	derive	VERB
ejpam-5131	101	11	from	from	ADP
ejpam-5131	101	12	the	the	DET
ejpam-5131	101	13	equation	equation	NOUN
ejpam-5131	101	14	above	above	ADP
ejpam-5131	101	15	v∗(t)−	v∗(t)−	PROPN
ejpam-5131	101	16	v∗(0	v∗(0	NOUN
ejpam-5131	101	17	)	)	PUNCT
ejpam-5131	101	18	=	=	SYM
ejpam-5131	101	19	(	(	PUNCT
ejpam-5131	101	20	1−	1−	NUM
ejpam-5131	101	21	ζ)f(t	ζ)f(t	NOUN
ejpam-5131	101	22	,	,	PUNCT
ejpam-5131	101	23	v∗(t	v∗(t	NOUN
ejpam-5131	101	24	)	)	PUNCT
ejpam-5131	101	25	)	)	PUNCT
ejpam-5131	102	1	abc(ζ	abc(ζ	PROPN
ejpam-5131	102	2	)	)	PUNCT
ejpam-5131	103	1	+	+	NUM
ejpam-5131	103	2	ζ	ζ	PROPN
ejpam-5131	103	3	γ(ζ	γ(ζ	PROPN
ejpam-5131	103	4	+	+	CCONJ
ejpam-5131	103	5	1)×abc(ζ	1)×abc(ζ	NUM
ejpam-5131	103	6	)	)	PUNCT
ejpam-5131	103	7	∫	∫	PROPN
ejpam-5131	103	8	t	t	PROPN
ejpam-5131	103	9	0	0	NUM
ejpam-5131	103	10	f(τ	f(τ	PROPN
ejpam-5131	103	11	,	,	PUNCT
ejpam-5131	103	12	v∗(τ))(t−	v∗(τ))(t−	PROPN
ejpam-5131	103	13	τ)ζ−1dτ	τ)ζ−1dτ	VERB
ejpam-5131	103	14	,	,	PUNCT
ejpam-5131	103	15	(	(	PUNCT
ejpam-5131	103	16	8)	8)	NUM
ejpam-5131	103	17	where	where	SCONJ
ejpam-5131	103	18	n	n	NOUN
ejpam-5131	103	19	=	=	SYM
ejpam-5131	103	20	0	0	NUM
ejpam-5131	103	21	,	,	PUNCT
ejpam-5131	103	22	1	1	NUM
ejpam-5131	103	23	,	,	PUNCT
ejpam-5131	103	24	2	2	NUM
ejpam-5131	103	25	,	,	PUNCT
ejpam-5131	103	26	3	3	NUM
ejpam-5131	103	27	.	.	PUNCT
ejpam-5131	103	28	.	.	PUNCT
ejpam-5131	103	29	.	.	PUNCT
ejpam-5131	104	1	,	,	PUNCT
ejpam-5131	104	2	reformulated	reformulate	VERB
ejpam-5131	104	3	as	as	ADP
ejpam-5131	104	4	v∗(tn+1)−	v∗(tn+1)−	PROPN
ejpam-5131	104	5	v∗(0	v∗(0	NOUN
ejpam-5131	104	6	)	)	PUNCT
ejpam-5131	105	1	=	=	SYM
ejpam-5131	105	2	(	(	PUNCT
ejpam-5131	105	3	1−	1−	NUM
ejpam-5131	105	4	ζ)f(tn	ζ)f(tn	NUM
ejpam-5131	105	5	,	,	PUNCT
ejpam-5131	105	6	v	v	ADP
ejpam-5131	105	7	∗(tn	∗(tn	PROPN
ejpam-5131	105	8	)	)	PUNCT
ejpam-5131	105	9	)	)	PUNCT
ejpam-5131	105	10	abc(ζ	abc(ζ	PROPN
ejpam-5131	105	11	)	)	PUNCT
ejpam-5131	105	12	+	+	NUM
ejpam-5131	105	13	ζ	ζ	PROPN
ejpam-5131	105	14	abc(ζ)×	abc(ζ)×	PROPN
ejpam-5131	105	15	γ(ζ	γ(ζ	PROPN
ejpam-5131	105	16	+	+	CCONJ
ejpam-5131	105	17	1	1	X
ejpam-5131	105	18	)	)	PUNCT
ejpam-5131	105	19	∫	∫	PROPN
ejpam-5131	105	20	tn+1	tn+1	NOUN
ejpam-5131	105	21	0	0	NUM
ejpam-5131	106	1	g	g	PROPN
ejpam-5131	106	2	(	(	PUNCT
ejpam-5131	106	3	τ	τ	PROPN
ejpam-5131	106	4	,	,	PUNCT
ejpam-5131	106	5	v∗	v∗	PROPN
ejpam-5131	106	6	(	(	PUNCT
ejpam-5131	106	7	τ	τ	PROPN
ejpam-5131	106	8	)	)	PUNCT
ejpam-5131	106	9	)	)	PUNCT
ejpam-5131	106	10	(	(	PUNCT
ejpam-5131	106	11	tn+1	tn+1	NUM
ejpam-5131	106	12	−	−	NOUN
ejpam-5131	106	13	τ)ζ−1	τ)ζ−1	X
ejpam-5131	106	14	dτ	dτ	NOUN
ejpam-5131	106	15	=	=	SYM
ejpam-5131	106	16	(	(	PUNCT
ejpam-5131	106	17	1−	1−	NUM
ejpam-5131	106	18	ζ)g(tn	ζ)g(tn	NUM
ejpam-5131	106	19	,	,	PUNCT
ejpam-5131	106	20	v	v	X
ejpam-5131	106	21	∗(tn	∗(tn	PROPN
ejpam-5131	106	22	)	)	PUNCT
ejpam-5131	106	23	)	)	PUNCT
ejpam-5131	106	24	abc(ζ	abc(ζ	PROPN
ejpam-5131	106	25	)	)	PUNCT
ejpam-5131	107	1	+	+	CCONJ
ejpam-5131	107	2	ζ	ζ	PROPN
ejpam-5131	107	3	abc(ζ)×	abc(ζ)×	PROPN
ejpam-5131	107	4	γ(ζ	γ(ζ	PROPN
ejpam-5131	107	5	)	)	PUNCT
ejpam-5131	107	6	n∑	n∑	PART
ejpam-5131	108	1	k=0	k=0	PROPN
ejpam-5131	108	2	∫	∫	PROPN
ejpam-5131	108	3	tk+1	tk+1	PROPN
ejpam-5131	108	4	tk	tk	PROPN
ejpam-5131	108	5	g(τ	g(τ	PROPN
ejpam-5131	108	6	,	,	PUNCT
ejpam-5131	108	7	v∗(τ	v∗(τ	NOUN
ejpam-5131	108	8	)	)	PUNCT
ejpam-5131	108	9	)	)	PUNCT
ejpam-5131	108	10	(	(	PUNCT
ejpam-5131	108	11	tn+1	tn+1	NUM
ejpam-5131	108	12	−	−	PROPN
ejpam-5131	108	13	τ)ζ−1	τ)ζ−1	SYM
ejpam-5131	108	14	dτ	dτ	PROPN
ejpam-5131	108	15	.	.	PROPN
ejpam-5131	108	16	(	(	PUNCT
ejpam-5131	108	17	9	9	X
ejpam-5131	108	18	)	)	PUNCT
ejpam-5131	108	19	the	the	DET
ejpam-5131	108	20	following	follow	VERB
ejpam-5131	108	21	can	can	AUX
ejpam-5131	108	22	be	be	AUX
ejpam-5131	108	23	approximated	approximate	VERB
ejpam-5131	108	24	using	use	VERB
ejpam-5131	108	25	two	two	NUM
ejpam-5131	108	26	-	-	PUNCT
ejpam-5131	108	27	step	step	NOUN
ejpam-5131	108	28	lagrange	lagrange	NOUN
ejpam-5131	108	29	polynomial	polynomial	ADJ
ejpam-5131	108	30	interpolation	interpolation	NOUN
ejpam-5131	108	31	:	:	PUNCT
ejpam-5131	109	1	p	p	X
ejpam-5131	109	2	∗	∗	X
ejpam-5131	109	3	k	k	PROPN
ejpam-5131	109	4	(	(	PUNCT
ejpam-5131	109	5	τ	τ	X
ejpam-5131	109	6	)	)	PUNCT
ejpam-5131	109	7	=	=	SYM
ejpam-5131	109	8	(	(	PUNCT
ejpam-5131	109	9	τ	τ	X
ejpam-5131	109	10	−	−	PROPN
ejpam-5131	109	11	tk−1)f	tk−1)f	NUM
ejpam-5131	109	12	(	(	PUNCT
ejpam-5131	109	13	tk	tk	PROPN
ejpam-5131	109	14	,	,	PUNCT
ejpam-5131	109	15	v	v	NOUN
ejpam-5131	109	16	∗	∗	NOUN
ejpam-5131	109	17	(	(	PUNCT
ejpam-5131	109	18	tk	tk	PROPN
ejpam-5131	109	19	)	)	PUNCT
ejpam-5131	109	20	)	)	PUNCT
ejpam-5131	109	21	tk	tk	PROPN
ejpam-5131	109	22	−	−	PROPN
ejpam-5131	109	23	tk−1	tk−1	PROPN
ejpam-5131	109	24	−	−	PROPN
ejpam-5131	110	1	(	(	PUNCT
ejpam-5131	110	2	τ	τ	PROPN
ejpam-5131	110	3	−	−	PROPN
ejpam-5131	110	4	tk)f	tk)f	PROPN
ejpam-5131	110	5	(	(	PUNCT
ejpam-5131	110	6	tk−1	tk−1	PROPN
ejpam-5131	110	7	,	,	PUNCT
ejpam-5131	110	8	v	v	NOUN
ejpam-5131	110	9	∗	∗	NOUN
ejpam-5131	110	10	(	(	PUNCT
ejpam-5131	110	11	tk−1	tk−1	PROPN
ejpam-5131	110	12	)	)	PUNCT
ejpam-5131	110	13	)	)	PUNCT
ejpam-5131	110	14	tk	tk	PROPN
ejpam-5131	111	1	−	−	PROPN
ejpam-5131	111	2	tk−1	tk−1	PROPN
ejpam-5131	111	3	=	=	SYM
ejpam-5131	111	4	f	f	PROPN
ejpam-5131	111	5	(	(	PUNCT
ejpam-5131	111	6	tk	tk	PROPN
ejpam-5131	111	7	,	,	PUNCT
ejpam-5131	111	8	v	v	NOUN
ejpam-5131	111	9	∗	∗	NOUN
ejpam-5131	111	10	(	(	PUNCT
ejpam-5131	111	11	tk	tk	PROPN
ejpam-5131	111	12	)	)	PUNCT
ejpam-5131	111	13	)	)	PUNCT
ejpam-5131	112	1	(	(	PUNCT
ejpam-5131	112	2	τ	τ	PROPN
ejpam-5131	112	3	−	−	PROPN
ejpam-5131	112	4	tk−1	tk−1	PROPN
ejpam-5131	112	5	)	)	PUNCT
ejpam-5131	112	6	h	h	NOUN
ejpam-5131	113	1	−	−	PROPN
ejpam-5131	113	2	f	f	PROPN
ejpam-5131	113	3	(	(	PUNCT
ejpam-5131	113	4	tk−1	tk−1	PROPN
ejpam-5131	113	5	,	,	PUNCT
ejpam-5131	113	6	v	v	NOUN
ejpam-5131	113	7	(	(	PUNCT
ejpam-5131	113	8	tk−1	tk−1	PROPN
ejpam-5131	113	9	)	)	PUNCT
ejpam-5131	113	10	)	)	PUNCT
ejpam-5131	114	1	(	(	PUNCT
ejpam-5131	114	2	τ	τ	PROPN
ejpam-5131	114	3	−	−	PROPN
ejpam-5131	114	4	tk	tk	PROPN
ejpam-5131	114	5	)	)	PUNCT
ejpam-5131	114	6	h	h	NOUN
ejpam-5131	114	7	≃	≃	PROPN
ejpam-5131	114	8	f	f	PROPN
ejpam-5131	114	9	(	(	PUNCT
ejpam-5131	114	10	tk	tk	PROPN
ejpam-5131	114	11	,	,	PUNCT
ejpam-5131	114	12	v	v	NOUN
ejpam-5131	114	13	∗	∗	X
ejpam-5131	114	14	k	k	NOUN
ejpam-5131	114	15	)	)	PUNCT
ejpam-5131	114	16	(	(	PUNCT
ejpam-5131	114	17	τ	τ	PROPN
ejpam-5131	114	18	−	−	PROPN
ejpam-5131	114	19	tk−1	tk−1	PROPN
ejpam-5131	114	20	)	)	PUNCT
ejpam-5131	114	21	h	h	NOUN
ejpam-5131	114	22	−	−	PROPN
ejpam-5131	114	23	f	f	PROPN
ejpam-5131	115	1	(	(	PUNCT
ejpam-5131	115	2	tk−1	tk−1	PROPN
ejpam-5131	115	3	,	,	PUNCT
ejpam-5131	115	4	v	v	NOUN
ejpam-5131	115	5	∗	∗	NOUN
ejpam-5131	115	6	k−1	k−1	PROPN
ejpam-5131	115	7	)	)	PUNCT
ejpam-5131	115	8	(	(	PUNCT
ejpam-5131	115	9	τ	τ	PROPN
ejpam-5131	115	10	−	−	PROPN
ejpam-5131	115	11	tk	tk	PROPN
ejpam-5131	115	12	)	)	PUNCT
ejpam-5131	115	13	h	h	NOUN
ejpam-5131	115	14	,	,	PUNCT
ejpam-5131	115	15	(	(	PUNCT
ejpam-5131	115	16	10	10	NUM
ejpam-5131	115	17	)	)	PUNCT
ejpam-5131	115	18	v∗n+1	v∗n+1	NOUN
ejpam-5131	115	19	=	=	NOUN
ejpam-5131	115	20	v∗0	v∗0	NOUN
ejpam-5131	115	21	+	+	CCONJ
ejpam-5131	115	22	(	(	PUNCT
ejpam-5131	115	23	1−	1−	NUM
ejpam-5131	115	24	ζ	ζ	NOUN
ejpam-5131	115	25	)	)	PUNCT
ejpam-5131	115	26	abc(ζ	abc(ζ	PROPN
ejpam-5131	115	27	)	)	PUNCT
ejpam-5131	115	28	g(tn	g(tn	PROPN
ejpam-5131	115	29	,	,	PUNCT
ejpam-5131	115	30	v	v	ADP
ejpam-5131	115	31	∗(tn	∗(tn	PROPN
ejpam-5131	115	32	)	)	PUNCT
ejpam-5131	115	33	)	)	PUNCT
ejpam-5131	116	1	+	+	CCONJ
ejpam-5131	116	2	ζ	ζ	X
ejpam-5131	116	3	abc(α)×	abc(α)×	ADP
ejpam-5131	116	4	γ(ζ	γ(ζ	NOUN
ejpam-5131	116	5	)	)	PUNCT
ejpam-5131	117	1	n∑	n∑	PART
ejpam-5131	117	2	k=0	k=0	PROPN
ejpam-5131	117	3	(	(	PUNCT
ejpam-5131	117	4	f(tk	f(tk	NOUN
ejpam-5131	117	5	,	,	PUNCT
ejpam-5131	117	6	v	v	NOUN
ejpam-5131	117	7	∗	∗	X
ejpam-5131	117	8	k	k	NOUN
ejpam-5131	117	9	)	)	PUNCT
ejpam-5131	118	1	h	h	NOUN
ejpam-5131	118	2	∫	∫	PROPN
ejpam-5131	119	1	tk+1	tk+1	NUM
ejpam-5131	119	2	tk	tk	PROPN
ejpam-5131	119	3	(	(	PUNCT
ejpam-5131	119	4	τ	τ	PROPN
ejpam-5131	119	5	+	+	NUM
ejpam-5131	119	6	tk−1t)(tn+1	tk−1t)(tn+1	PROPN
ejpam-5131	119	7	−	−	PROPN
ejpam-5131	119	8	τ)ζ−1dτ	τ)ζ−1dτ	VERB
ejpam-5131	119	9	−	−	NOUN
ejpam-5131	119	10	f(tk−1	f(tk−1	NOUN
ejpam-5131	119	11	,	,	PUNCT
ejpam-5131	119	12	v	v	NOUN
ejpam-5131	119	13	∗	∗	NOUN
ejpam-5131	119	14	k−1	k−1	PROPN
ejpam-5131	119	15	)	)	PUNCT
ejpam-5131	120	1	h	h	NOUN
ejpam-5131	120	2	∫	∫	PROPN
ejpam-5131	121	1	tk+1	tk+1	NUM
ejpam-5131	121	2	tk	tk	PROPN
ejpam-5131	121	3	(	(	PUNCT
ejpam-5131	121	4	τ	τ	PROPN
ejpam-5131	121	5	−	−	PROPN
ejpam-5131	121	6	tk)(tn+1	tk)(tn+1	PROPN
ejpam-5131	121	7	−	−	PROPN
ejpam-5131	121	8	τ)ζ−1dτ	τ)ζ−1dτ	VERB
ejpam-5131	121	9	)	)	PUNCT
ejpam-5131	121	10	.	.	PUNCT
ejpam-5131	122	1	(	(	PUNCT
ejpam-5131	122	2	11	11	NUM
ejpam-5131	122	3	)	)	PUNCT
ejpam-5131	122	4	g.	g.	PROPN
ejpam-5131	122	5	a.	a.	PROPN
ejpam-5131	122	6	ahmed	ahmed	PROPN
ejpam-5131	122	7	/	/	SYM
ejpam-5131	122	8	eur	eur	PROPN
ejpam-5131	122	9	.	.	PUNCT
ejpam-5131	123	1	j.	j.	PROPN
ejpam-5131	123	2	pure	pure	PROPN
ejpam-5131	123	3	appl	appl	PROPN
ejpam-5131	123	4	.	.	PROPN
ejpam-5131	123	5	math	math	PROPN
ejpam-5131	123	6	,	,	PUNCT
ejpam-5131	123	7	17	17	NUM
ejpam-5131	123	8	(	(	PUNCT
ejpam-5131	123	9	2	2	NUM
ejpam-5131	123	10	)	)	PUNCT
ejpam-5131	123	11	(	(	PUNCT
ejpam-5131	123	12	2024	2024	NUM
ejpam-5131	123	13	)	)	PUNCT
ejpam-5131	123	14	,	,	PUNCT
ejpam-5131	123	15	835	835	NUM
ejpam-5131	123	16	-	-	SYM
ejpam-5131	123	17	851	851	NUM
ejpam-5131	123	18	841	841	NUM
ejpam-5131	123	19	for	for	ADP
ejpam-5131	123	20	simplicity	simplicity	NOUN
ejpam-5131	123	21	a∗	a∗	PROPN
ejpam-5131	123	22	ζ	ζ	NOUN
ejpam-5131	123	23	,	,	PUNCT
ejpam-5131	123	24	k,1	k,1	PROPN
ejpam-5131	123	25	=	=	SYM
ejpam-5131	123	26	∫	∫	PROPN
ejpam-5131	123	27	tk+1	tk+1	NUM
ejpam-5131	123	28	tk	tk	PROPN
ejpam-5131	123	29	(	(	PUNCT
ejpam-5131	123	30	τ	τ	PROPN
ejpam-5131	123	31	−	−	PROPN
ejpam-5131	123	32	tk−1)(tn+1	tk−1)(tn+1	NUM
ejpam-5131	123	33	−	−	NOUN
ejpam-5131	123	34	τ)ζ−1dτ	τ)ζ−1dτ	VERB
ejpam-5131	123	35	,	,	PUNCT
ejpam-5131	123	36	(	(	PUNCT
ejpam-5131	123	37	12	12	NUM
ejpam-5131	123	38	)	)	PUNCT
ejpam-5131	123	39	a∗	a∗	PROPN
ejpam-5131	123	40	ζ	ζ	NOUN
ejpam-5131	123	41	,	,	PUNCT
ejpam-5131	123	42	k,2	k,2	X
ejpam-5131	123	43	=	=	SYM
ejpam-5131	123	44	∫	∫	PROPN
ejpam-5131	123	45	tk+1	tk+1	NUM
ejpam-5131	123	46	tk	tk	PROPN
ejpam-5131	123	47	(	(	PUNCT
ejpam-5131	123	48	τ	τ	PROPN
ejpam-5131	123	49	−	−	PROPN
ejpam-5131	123	50	tk)(tn+2	tk)(tn+2	PROPN
ejpam-5131	124	1	−	−	PROPN
ejpam-5131	124	2	τ)ζ−1dτ	τ)ζ−1dτ	VERB
ejpam-5131	124	3	a∗	a∗	PROPN
ejpam-5131	124	4	ζ	ζ	NOUN
ejpam-5131	124	5	,	,	PUNCT
ejpam-5131	124	6	k,1	k,1	PROPN
ejpam-5131	124	7	=	=	SYM
ejpam-5131	124	8	hζ+1	hζ+1	PROPN
ejpam-5131	124	9	(	(	PUNCT
ejpam-5131	124	10	n+	n+	NUM
ejpam-5131	124	11	1−	1−	NUM
ejpam-5131	124	12	k)ζ(n−	k)ζ(n−	PROPN
ejpam-5131	124	13	k	k	PROPN
ejpam-5131	125	1	+	+	CCONJ
ejpam-5131	125	2	2	2	NUM
ejpam-5131	125	3	+	+	CCONJ
ejpam-5131	125	4	ζ)−	ζ)−	PROPN
ejpam-5131	125	5	(	(	PUNCT
ejpam-5131	125	6	n−	n−	NOUN
ejpam-5131	125	7	k)ζ(n−	k)ζ(n−	VERB
ejpam-5131	125	8	k	k	PROPN
ejpam-5131	126	1	+	+	CCONJ
ejpam-5131	126	2	2	2	NUM
ejpam-5131	126	3	+	+	CCONJ
ejpam-5131	126	4	2ζ	2ζ	NUM
ejpam-5131	126	5	)	)	PUNCT
ejpam-5131	126	6	ζ(ζ	ζ(ζ	PROPN
ejpam-5131	126	7	+	+	CCONJ
ejpam-5131	126	8	1	1	X
ejpam-5131	126	9	)	)	PUNCT
ejpam-5131	126	10	a∗	a∗	PROPN
ejpam-5131	126	11	ζ	ζ	NOUN
ejpam-5131	126	12	,	,	PUNCT
ejpam-5131	126	13	k,2	k,2	X
ejpam-5131	126	14	=	=	SYM
ejpam-5131	126	15	(	(	PUNCT
ejpam-5131	126	16	hζ+1	hζ+1	NUM
ejpam-5131	126	17	)	)	PUNCT
ejpam-5131	126	18	(	(	PUNCT
ejpam-5131	126	19	n+	n+	NUM
ejpam-5131	126	20	1−	1−	NUM
ejpam-5131	126	21	k)ζ+1	k)ζ+1	NOUN
ejpam-5131	126	22	−	−	PROPN
ejpam-5131	126	23	(	(	PUNCT
ejpam-5131	126	24	n−	n−	NOUN
ejpam-5131	126	25	k)ζ(n−	k)ζ(n−	VERB
ejpam-5131	126	26	k	k	PROPN
ejpam-5131	127	1	+	+	CCONJ
ejpam-5131	127	2	1	1	NUM
ejpam-5131	127	3	+	+	CCONJ
ejpam-5131	127	4	ζ	ζ	NOUN
ejpam-5131	127	5	)	)	PUNCT
ejpam-5131	127	6	ζ(ζ	ζ(ζ	PROPN
ejpam-5131	127	7	+	+	CCONJ
ejpam-5131	127	8	1	1	NUM
ejpam-5131	127	9	)	)	PUNCT
ejpam-5131	127	10	.	.	PUNCT
ejpam-5131	128	1	(	(	PUNCT
ejpam-5131	128	2	13	13	NUM
ejpam-5131	128	3	)	)	PUNCT
ejpam-5131	128	4	by	by	ADP
ejpam-5131	128	5	combining	combine	VERB
ejpam-5131	128	6	equations	equation	NOUN
ejpam-5131	128	7	(	(	PUNCT
ejpam-5131	128	8	12	12	NUM
ejpam-5131	128	9	)	)	PUNCT
ejpam-5131	128	10	and	and	CCONJ
ejpam-5131	128	11	(	(	PUNCT
ejpam-5131	128	12	13	13	NUM
ejpam-5131	128	13	)	)	PUNCT
ejpam-5131	128	14	and	and	CCONJ
ejpam-5131	128	15	substituting	substitute	VERB
ejpam-5131	128	16	in	in	ADP
ejpam-5131	128	17	(	(	PUNCT
ejpam-5131	128	18	11	11	NUM
ejpam-5131	128	19	)	)	PUNCT
ejpam-5131	128	20	,	,	PUNCT
ejpam-5131	128	21	v∗n+1	v∗n+1	VERB
ejpam-5131	128	22	=	=	SYM
ejpam-5131	128	23	v∗(1	v∗(1	NOUN
ejpam-5131	128	24	)	)	PUNCT
ejpam-5131	129	1	+	+	CCONJ
ejpam-5131	129	2	(	(	PUNCT
ejpam-5131	129	3	1−	1−	NUM
ejpam-5131	129	4	ζ	ζ	NOUN
ejpam-5131	129	5	)	)	PUNCT
ejpam-5131	129	6	abc(ζ	abc(ζ	PROPN
ejpam-5131	129	7	)	)	PUNCT
ejpam-5131	129	8	f	f	PROPN
ejpam-5131	129	9	(	(	PUNCT
ejpam-5131	129	10	tn	tn	PROPN
ejpam-5131	129	11	,	,	PUNCT
ejpam-5131	129	12	v	v	NOUN
ejpam-5131	129	13	∗	∗	NOUN
ejpam-5131	129	14	(	(	PUNCT
ejpam-5131	129	15	tn	tn	NOUN
ejpam-5131	129	16	)	)	PUNCT
ejpam-5131	129	17	)	)	PUNCT
ejpam-5131	130	1	+	+	CCONJ
ejpam-5131	130	2	ζ	ζ	PROPN
ejpam-5131	130	3	abc(ζ	abc(ζ	PROPN
ejpam-5131	130	4	)	)	PUNCT
ejpam-5131	130	5	n∑	n∑	NOUN
ejpam-5131	130	6	j=0	j=0	PROPN
ejpam-5131	130	7	(	(	PUNCT
ejpam-5131	130	8	hζf	hζf	PROPN
ejpam-5131	130	9	(	(	PUNCT
ejpam-5131	130	10	tk	tk	PROPN
ejpam-5131	130	11	,	,	PUNCT
ejpam-5131	130	12	v	v	NOUN
ejpam-5131	130	13	∗	∗	X
ejpam-5131	130	14	k	k	NOUN
ejpam-5131	130	15	)	)	PUNCT
ejpam-5131	130	16	γ(ζ	γ(ζ	PROPN
ejpam-5131	130	17	+	+	CCONJ
ejpam-5131	130	18	1	1	NUM
ejpam-5131	130	19	)	)	PUNCT
ejpam-5131	130	20	(	(	PUNCT
ejpam-5131	130	21	(	(	PUNCT
ejpam-5131	130	22	1	1	NUM
ejpam-5131	130	23	+	+	NUM
ejpam-5131	130	24	n−	n−	NOUN
ejpam-5131	130	25	j)ζ	j)ζ	NOUN
ejpam-5131	130	26	(	(	PUNCT
ejpam-5131	130	27	2	2	NUM
ejpam-5131	130	28	+	+	CCONJ
ejpam-5131	130	29	ζ	ζ	NOUN
ejpam-5131	130	30	+	+	NUM
ejpam-5131	130	31	n−	n−	PROPN
ejpam-5131	130	32	k	k	NOUN
ejpam-5131	130	33	)	)	PUNCT
ejpam-5131	131	1	+	+	CCONJ
ejpam-5131	131	2	(	(	PUNCT
ejpam-5131	131	3	j	j	PROPN
ejpam-5131	131	4	−	−	PROPN
ejpam-5131	132	1	n)ζ(2	n)ζ(2	PROPN
ejpam-5131	133	1	+	+	CCONJ
ejpam-5131	133	2	n−	n−	PROPN
ejpam-5131	133	3	k	k	NOUN
ejpam-5131	133	4	+	+	CCONJ
ejpam-5131	133	5	2ζ	2ζ	NUM
ejpam-5131	133	6	)	)	PUNCT
ejpam-5131	133	7	)	)	PUNCT
ejpam-5131	134	1	−	−	PROPN
ejpam-5131	134	2	hζf	hζf	ADV
ejpam-5131	134	3	(	(	PUNCT
ejpam-5131	134	4	tj−1	tj−1	PROPN
ejpam-5131	134	5	,	,	PUNCT
ejpam-5131	134	6	v	v	NOUN
ejpam-5131	134	7	∗	∗	NOUN
ejpam-5131	134	8	j−1	j−1	PROPN
ejpam-5131	134	9	)	)	PUNCT
ejpam-5131	135	1	γ(1	γ(1	PROPN
ejpam-5131	135	2	+	+	CCONJ
ejpam-5131	135	3	ζ	ζ	NOUN
ejpam-5131	135	4	)	)	PUNCT
ejpam-5131	135	5	(	(	PUNCT
ejpam-5131	135	6	(	(	PUNCT
ejpam-5131	135	7	n−	n−	NOUN
ejpam-5131	135	8	j	j	PROPN
ejpam-5131	135	9	+	+	CCONJ
ejpam-5131	135	10	1)ζ+1	1)ζ+1	NUM
ejpam-5131	136	1	+	+	CCONJ
ejpam-5131	136	2	(	(	PUNCT
ejpam-5131	136	3	j	j	PROPN
ejpam-5131	136	4	−	−	PROPN
ejpam-5131	136	5	n)ζ(n−	n)ζ(n−	PROPN
ejpam-5131	136	6	j	j	PROPN
ejpam-5131	137	1	+	+	CCONJ
ejpam-5131	137	2	1	1	NUM
ejpam-5131	137	3	+	+	NUM
ejpam-5131	137	4	ζ	ζ	NOUN
ejpam-5131	137	5	)	)	PUNCT
ejpam-5131	137	6	)	)	PUNCT
ejpam-5131	138	1			PROPN
ejpam-5131	138	2	.	.	PUNCT
ejpam-5131	139	1	(	(	PUNCT
ejpam-5131	139	2	14	14	NUM
ejpam-5131	139	3	)	)	SYM
ejpam-5131	139	4	4	4	NUM
ejpam-5131	139	5	.	.	PUNCT
ejpam-5131	139	6	model	model	NOUN
ejpam-5131	139	7	of	of	ADP
ejpam-5131	139	8	a	a	DET
ejpam-5131	139	9	novel	novel	ADJ
ejpam-5131	139	10	chaotic	chaotic	ADJ
ejpam-5131	139	11	system	system	NOUN
ejpam-5131	139	12	the	the	DET
ejpam-5131	139	13	created	create	VERB
ejpam-5131	139	14	system	system	NOUN
ejpam-5131	139	15	mainly	mainly	ADV
ejpam-5131	139	16	consists	consist	VERB
ejpam-5131	139	17	of	of	ADP
ejpam-5131	139	18	a	a	DET
ejpam-5131	139	19	five	five	NUM
ejpam-5131	139	20	-	-	PUNCT
ejpam-5131	139	21	dimensional	dimensional	ADJ
ejpam-5131	139	22	system	system	NOUN
ejpam-5131	139	23	with	with	ADP
ejpam-5131	139	24	eleven	eleven	NUM
ejpam-5131	139	25	terms	term	NOUN
ejpam-5131	139	26	and	and	CCONJ
ejpam-5131	139	27	the	the	DET
ejpam-5131	139	28	following	follow	VERB
ejpam-5131	139	29	state	state	NOUN
ejpam-5131	139	30	variables	variable	NOUN
ejpam-5131	139	31	:	:	PUNCT
ejpam-5131	139	32			NUM
ejpam-5131	139	33	abc	abc	PROPN
ejpam-5131	139	34	0	0	PROPN
ejpam-5131	139	35	dζ	dζ	PROPN
ejpam-5131	139	36	t	t	PROPN
ejpam-5131	139	37	η1(t	η1(t	PROPN
ejpam-5131	139	38	)	)	PUNCT
ejpam-5131	139	39	=	=	SYM
ejpam-5131	139	40	k	k	X
ejpam-5131	139	41	(	(	PUNCT
ejpam-5131	139	42	α+	α+	X
ejpam-5131	139	43	β	β	X
ejpam-5131	139	44	tanh	tanh	PROPN
ejpam-5131	139	45	η5	η5	PROPN
ejpam-5131	139	46	)	)	PUNCT
ejpam-5131	139	47	η2	η2	PROPN
ejpam-5131	139	48	+	+	CCONJ
ejpam-5131	139	49	a(η2	a(η2	ADJ
ejpam-5131	139	50	+	+	CCONJ
ejpam-5131	139	51	η1	η1	NOUN
ejpam-5131	139	52	)	)	PUNCT
ejpam-5131	139	53	+	+	CCONJ
ejpam-5131	140	1	rη4	rη4	PROPN
ejpam-5131	140	2	,	,	PUNCT
ejpam-5131	140	3	abc	abc	PROPN
ejpam-5131	140	4	0	0	NUM
ejpam-5131	140	5	dζ	dζ	PROPN
ejpam-5131	140	6	t	t	PROPN
ejpam-5131	140	7	η2(t	η2(t	PROPN
ejpam-5131	140	8	)	)	PUNCT
ejpam-5131	140	9	=	=	PUNCT
ejpam-5131	141	1	cη1	cη1	X
ejpam-5131	142	1	−	−	NOUN
ejpam-5131	142	2	η2	η2	PROPN
ejpam-5131	142	3	−	−	PROPN
ejpam-5131	142	4	η1η3	η1η3	PROPN
ejpam-5131	142	5	,	,	PUNCT
ejpam-5131	142	6	abc	abc	PROPN
ejpam-5131	142	7	0	0	PROPN
ejpam-5131	142	8	dζ	dζ	PROPN
ejpam-5131	142	9	t	t	PROPN
ejpam-5131	142	10	η3(t	η3(t	PROPN
ejpam-5131	142	11	)	)	PUNCT
ejpam-5131	142	12	=	=	PUNCT
ejpam-5131	142	13	η1η2	η1η2	NOUN
ejpam-5131	142	14	−	−	NOUN
ejpam-5131	142	15	bη3	bη3	NOUN
ejpam-5131	142	16	,	,	PUNCT
ejpam-5131	142	17	abc	abc	PROPN
ejpam-5131	142	18	0	0	PROPN
ejpam-5131	142	19	dζ	dζ	PROPN
ejpam-5131	142	20	t	t	PROPN
ejpam-5131	142	21	η4(t	η4(t	PROPN
ejpam-5131	142	22	)	)	PUNCT
ejpam-5131	142	23	=	=	PROPN
ejpam-5131	142	24	−η1	−η1	PROPN
ejpam-5131	142	25	−	−	PROPN
ejpam-5131	142	26	aη4	aη4	PROPN
ejpam-5131	142	27	,	,	PUNCT
ejpam-5131	142	28	abc	abc	PROPN
ejpam-5131	142	29	0	0	PROPN
ejpam-5131	142	30	dζ	dζ	PROPN
ejpam-5131	142	31	t	t	PROPN
ejpam-5131	142	32	η5(t	η5(t	PROPN
ejpam-5131	142	33	)	)	PUNCT
ejpam-5131	142	34	=	=	SYM
ejpam-5131	142	35	η2	η2	PROPN
ejpam-5131	142	36	,	,	PUNCT
ejpam-5131	142	37	(	(	PUNCT
ejpam-5131	142	38	15	15	NUM
ejpam-5131	142	39	)	)	PUNCT
ejpam-5131	142	40	with	with	ADP
ejpam-5131	142	41	initial	initial	ADJ
ejpam-5131	142	42	conditions	condition	NOUN
ejpam-5131	142	43	:	:	PUNCT
ejpam-5131	142	44	η1	η1	NOUN
ejpam-5131	142	45	(	(	PUNCT
ejpam-5131	142	46	0	0	NUM
ejpam-5131	142	47	)	)	PUNCT
ejpam-5131	142	48	=	=	SYM
ejpam-5131	142	49	0.2	0.2	NUM
ejpam-5131	142	50	,	,	PUNCT
ejpam-5131	142	51	η2	η2	PROPN
ejpam-5131	142	52	(	(	PUNCT
ejpam-5131	142	53	0	0	NUM
ejpam-5131	142	54	)	)	PUNCT
ejpam-5131	142	55	=	=	SYM
ejpam-5131	142	56	0.2	0.2	NUM
ejpam-5131	142	57	,	,	PUNCT
ejpam-5131	142	58	η3	η3	NOUN
ejpam-5131	142	59	(	(	PUNCT
ejpam-5131	142	60	0	0	NUM
ejpam-5131	142	61	)	)	PUNCT
ejpam-5131	142	62	=	=	SYM
ejpam-5131	142	63	0.2	0.2	NUM
ejpam-5131	142	64	,	,	PUNCT
ejpam-5131	142	65	η4	η4	VERB
ejpam-5131	142	66	(	(	PUNCT
ejpam-5131	142	67	0	0	NUM
ejpam-5131	142	68	)	)	PUNCT
ejpam-5131	142	69	=	=	SYM
ejpam-5131	142	70	0.2	0.2	NUM
ejpam-5131	142	71	,	,	PUNCT
ejpam-5131	142	72	η5	η5	PROPN
ejpam-5131	142	73	(	(	PUNCT
ejpam-5131	142	74	0	0	NUM
ejpam-5131	142	75	)	)	PUNCT
ejpam-5131	142	76	=	=	NOUN
ejpam-5131	142	77	0.2	0.2	NUM
ejpam-5131	142	78	here	here	ADV
ejpam-5131	142	79	,	,	PUNCT
ejpam-5131	142	80	the	the	DET
ejpam-5131	142	81	values	value	NOUN
ejpam-5131	142	82	of	of	ADP
ejpam-5131	142	83	constants	constant	NOUN
ejpam-5131	142	84	are	be	AUX
ejpam-5131	142	85	a	a	DET
ejpam-5131	142	86	=	=	ADJ
ejpam-5131	142	87	1	1	NUM
ejpam-5131	142	88	,	,	PUNCT
ejpam-5131	142	89	α	α	NOUN
ejpam-5131	142	90	=	=	SYM
ejpam-5131	142	91	20	20	NUM
ejpam-5131	142	92	,	,	PUNCT
ejpam-5131	142	93	β	β	X
ejpam-5131	142	94	=	=	SYM
ejpam-5131	142	95	0.02	0.02	NUM
ejpam-5131	142	96	,	,	PUNCT
ejpam-5131	142	97	c	c	NOUN
ejpam-5131	142	98	=	=	SYM
ejpam-5131	142	99	23	23	NUM
ejpam-5131	142	100	,	,	PUNCT
ejpam-5131	142	101	b	b	X
ejpam-5131	142	102	=	=	SYM
ejpam-5131	142	103	0.7	0.7	NUM
ejpam-5131	142	104	,	,	PUNCT
ejpam-5131	142	105	ρ	ρ	NOUN
ejpam-5131	142	106	=	=	SYM
ejpam-5131	142	107	1.5	1.5	NUM
ejpam-5131	142	108	,	,	PUNCT
ejpam-5131	142	109	k	k	NOUN
ejpam-5131	142	110	=	=	NOUN
ejpam-5131	142	111	4	4	NUM
ejpam-5131	142	112	5	5	NUM
ejpam-5131	142	113	.	.	PUNCT
ejpam-5131	142	114	analysis	analysis	NOUN
ejpam-5131	142	115	of	of	ADP
ejpam-5131	142	116	a	a	DET
ejpam-5131	142	117	nonlinear	nonlinear	ADJ
ejpam-5131	142	118	chaotic	chaotic	ADJ
ejpam-5131	142	119	dynamical	dynamical	ADJ
ejpam-5131	142	120	system	system	NOUN
ejpam-5131	142	121	in	in	ADP
ejpam-5131	142	122	this	this	DET
ejpam-5131	142	123	section	section	NOUN
ejpam-5131	142	124	,	,	PUNCT
ejpam-5131	142	125	we	we	PRON
ejpam-5131	142	126	delve	delve	VERB
ejpam-5131	142	127	into	into	ADP
ejpam-5131	142	128	the	the	DET
ejpam-5131	142	129	meticulous	meticulous	ADJ
ejpam-5131	142	130	evaluation	evaluation	NOUN
ejpam-5131	142	131	of	of	ADP
ejpam-5131	142	132	equilibrium	equilibrium	NOUN
ejpam-5131	142	133	points	point	NOUN
ejpam-5131	142	134	for	for	ADP
ejpam-5131	142	135	system	system	NOUN
ejpam-5131	142	136	(	(	PUNCT
ejpam-5131	142	137	5	5	NUM
ejpam-5131	142	138	)	)	PUNCT
ejpam-5131	142	139	by	by	ADP
ejpam-5131	142	140	considering	consider	VERB
ejpam-5131	142	141	varying	vary	VERB
ejpam-5131	142	142	fractional	fractional	ADJ
ejpam-5131	142	143	order	order	NOUN
ejpam-5131	142	144	values	value	NOUN
ejpam-5131	142	145	.	.	PUNCT
ejpam-5131	143	1	this	this	DET
ejpam-5131	143	2	exploration	exploration	NOUN
ejpam-5131	143	3	is	be	AUX
ejpam-5131	143	4	critical	critical	ADJ
ejpam-5131	143	5	as	as	SCONJ
ejpam-5131	143	6	equilibrium	equilibrium	NOUN
ejpam-5131	143	7	points	point	NOUN
ejpam-5131	143	8	serve	serve	VERB
ejpam-5131	143	9	as	as	ADP
ejpam-5131	143	10	the	the	DET
ejpam-5131	143	11	cornerstone	cornerstone	NOUN
ejpam-5131	143	12	for	for	ADP
ejpam-5131	143	13	understanding	understand	VERB
ejpam-5131	143	14	the	the	DET
ejpam-5131	143	15	long	long	ADJ
ejpam-5131	143	16	-	-	PUNCT
ejpam-5131	143	17	term	term	NOUN
ejpam-5131	143	18	behavior	behavior	NOUN
ejpam-5131	143	19	of	of	ADP
ejpam-5131	143	20	g.	g.	PROPN
ejpam-5131	143	21	a.	a.	PROPN
ejpam-5131	143	22	ahmed	ahmed	PROPN
ejpam-5131	143	23	/	/	SYM
ejpam-5131	143	24	eur	eur	PROPN
ejpam-5131	143	25	.	.	PUNCT
ejpam-5131	144	1	j.	j.	PROPN
ejpam-5131	144	2	pure	pure	PROPN
ejpam-5131	144	3	appl	appl	PROPN
ejpam-5131	144	4	.	.	PROPN
ejpam-5131	144	5	math	math	PROPN
ejpam-5131	144	6	,	,	PUNCT
ejpam-5131	144	7	17	17	NUM
ejpam-5131	144	8	(	(	PUNCT
ejpam-5131	144	9	2	2	NUM
ejpam-5131	144	10	)	)	PUNCT
ejpam-5131	144	11	(	(	PUNCT
ejpam-5131	144	12	2024	2024	NUM
ejpam-5131	144	13	)	)	PUNCT
ejpam-5131	144	14	,	,	PUNCT
ejpam-5131	144	15	835	835	NUM
ejpam-5131	144	16	-	-	SYM
ejpam-5131	144	17	851	851	NUM
ejpam-5131	144	18	842	842	NUM
ejpam-5131	144	19	dynamical	dynamical	ADJ
ejpam-5131	144	20	systems	system	NOUN
ejpam-5131	144	21	.	.	PUNCT
ejpam-5131	145	1	by	by	ADP
ejpam-5131	145	2	setting	set	VERB
ejpam-5131	145	3	the	the	DET
ejpam-5131	145	4	right	right	ADJ
ejpam-5131	145	5	-	-	PUNCT
ejpam-5131	145	6	hand	hand	NOUN
ejpam-5131	145	7	side	side	NOUN
ejpam-5131	145	8	of	of	ADP
ejpam-5131	145	9	the	the	DET
ejpam-5131	145	10	equation	equation	NOUN
ejpam-5131	145	11	to	to	ADP
ejpam-5131	145	12	zero	zero	NUM
ejpam-5131	145	13	,	,	PUNCT
ejpam-5131	145	14	we	we	PRON
ejpam-5131	145	15	embark	embark	VERB
ejpam-5131	145	16	on	on	ADP
ejpam-5131	145	17	a	a	DET
ejpam-5131	145	18	systematic	systematic	ADJ
ejpam-5131	145	19	journey	journey	NOUN
ejpam-5131	145	20	to	to	PART
ejpam-5131	145	21	solve	solve	VERB
ejpam-5131	145	22	the	the	DET
ejpam-5131	145	23	system	system	NOUN
ejpam-5131	145	24	,	,	PUNCT
ejpam-5131	145	25	revealing	reveal	VERB
ejpam-5131	145	26	the	the	DET
ejpam-5131	145	27	complex	complex	ADJ
ejpam-5131	145	28	interplay	interplay	NOUN
ejpam-5131	145	29	between	between	ADP
ejpam-5131	145	30	the	the	DET
ejpam-5131	145	31	system	system	NOUN
ejpam-5131	145	32	’s	’s	PART
ejpam-5131	145	33	inherent	inherent	ADJ
ejpam-5131	145	34	properties	property	NOUN
ejpam-5131	145	35	and	and	CCONJ
ejpam-5131	145	36	the	the	DET
ejpam-5131	145	37	fractional	fractional	ADJ
ejpam-5131	145	38	order	order	NOUN
ejpam-5131	145	39	values	value	NOUN
ejpam-5131	145	40	.	.	PUNCT
ejpam-5131	146	1	theorem.1	theorem.1	PROPN
ejpam-5131	146	2	the	the	DET
ejpam-5131	146	3	equilibrium	equilibrium	NOUN
ejpam-5131	146	4	point	point	NOUN
ejpam-5131	146	5	e0of	e0of	PUNCT
ejpam-5131	146	6	the	the	DET
ejpam-5131	146	7	system(15	system(15	NOUN
ejpam-5131	146	8	)	)	PUNCT
ejpam-5131	146	9	is	be	AUX
ejpam-5131	146	10	las	las	PROPN
ejpam-5131	146	11	if	if	SCONJ
ejpam-5131	146	12	all	all	DET
ejpam-5131	146	13	the	the	DET
ejpam-5131	146	14	eigenvaluesλ	eigenvaluesλ	NOUN
ejpam-5131	146	15	of	of	ADP
ejpam-5131	146	16	the	the	DET
ejpam-5131	146	17	matrix	matrix	NOUN
ejpam-5131	146	18	je	je	X
ejpam-5131	146	19	satisfy	satisfy	PROPN
ejpam-5131	146	20	.	.	PUNCT
ejpam-5131	147	1	α	α	PRON
ejpam-5131	147	2	<	<	X
ejpam-5131	147	3	2	2	NUM
ejpam-5131	147	4	π	π	NOUN
ejpam-5131	147	5	|	|	ADV
ejpam-5131	147	6	arg(λm)|,m	arg(λm)|,m	NOUN
ejpam-5131	147	7	=	=	NOUN
ejpam-5131	147	8	1	1	NUM
ejpam-5131	147	9	,	,	PUNCT
ejpam-5131	147	10	.	.	PUNCT
ejpam-5131	147	11	.	.	PUNCT
ejpam-5131	148	1	.	.	PUNCT
ejpam-5131	149	1	,	,	PUNCT
ejpam-5131	149	2	n	n	CCONJ
ejpam-5131	149	3	,	,	PUNCT
ejpam-5131	149	4	(	(	PUNCT
ejpam-5131	149	5	16	16	NUM
ejpam-5131	149	6	)	)	PUNCT
ejpam-5131	149	7	another	another	DET
ejpam-5131	149	8	basic	basic	ADJ
ejpam-5131	149	9	lemma	lemma	PROPN
ejpam-5131	149	10	for	for	ADP
ejpam-5131	149	11	the	the	DET
ejpam-5131	149	12	stability	stability	NOUN
ejpam-5131	149	13	of	of	ADP
ejpam-5131	149	14	fractional	fractional	ADJ
ejpam-5131	149	15	-	-	PUNCT
ejpam-5131	149	16	order	order	NOUN
ejpam-5131	149	17	system(15)is	system(15)is	NOUN
ejpam-5131	149	18	also	also	ADV
ejpam-5131	149	19	given	give	VERB
ejpam-5131	149	20	as	as	ADP
ejpam-5131	149	21	.	.	PUNCT
ejpam-5131	150	1	lemma.1	lemma.1	NOUN
ejpam-5131	150	2	assume	assume	VERB
ejpam-5131	150	3	that	that	SCONJ
ejpam-5131	150	4	defines	define	VERB
ejpam-5131	150	5	continuous	continuous	ADJ
ejpam-5131	150	6	and	and	CCONJ
ejpam-5131	150	7	differentiable	differentiable	ADJ
ejpam-5131	150	8	function.let	function.let	NOUN
ejpam-5131	150	9	t	t	PROPN
ejpam-5131	150	10	be	be	AUX
ejpam-5131	150	11	a	a	DET
ejpam-5131	150	12	specific	specific	ADJ
ejpam-5131	150	13	instant	instant	NOUN
ejpam-5131	150	14	of	of	ADP
ejpam-5131	150	15	time	time	NOUN
ejpam-5131	150	16	,	,	PUNCT
ejpam-5131	150	17	then	then	ADV
ejpam-5131	150	18	for	for	ADP
ejpam-5131	150	19	any	any	PRON
ejpam-5131	150	20	then	then	ADV
ejpam-5131	150	21			NOUN
ejpam-5131	150	22	0	0	NUM
ejpam-5131	151	1	=	=	SYM
ejpam-5131	151	2	k	k	X
ejpam-5131	151	3	(	(	PUNCT
ejpam-5131	151	4	α+	α+	X
ejpam-5131	151	5	β	β	X
ejpam-5131	151	6	tanh	tanh	PROPN
ejpam-5131	151	7	η5	η5	PROPN
ejpam-5131	151	8	)	)	PUNCT
ejpam-5131	151	9	η2	η2	PROPN
ejpam-5131	151	10	+	+	NOUN
ejpam-5131	151	11	a(η2	a(η2	ADJ
ejpam-5131	151	12	+	+	CCONJ
ejpam-5131	151	13	η1	η1	NOUN
ejpam-5131	151	14	)	)	PUNCT
ejpam-5131	151	15	+	+	X
ejpam-5131	151	16	rη4	rη4	ADJ
ejpam-5131	151	17	,	,	PUNCT
ejpam-5131	151	18	0	0	NUM
ejpam-5131	151	19	=	=	SYM
ejpam-5131	152	1	cη1	cη1	PROPN
ejpam-5131	152	2	−	−	NOUN
ejpam-5131	152	3	η2	η2	PROPN
ejpam-5131	152	4	−	−	PROPN
ejpam-5131	152	5	η1η3	η1η3	PROPN
ejpam-5131	152	6	,	,	PUNCT
ejpam-5131	152	7	0	0	PUNCT
ejpam-5131	153	1	=	=	PUNCT
ejpam-5131	154	1	η1η2	η1η2	NOUN
ejpam-5131	154	2	−	−	NOUN
ejpam-5131	154	3	bη3	bη3	NOUN
ejpam-5131	154	4	,	,	PUNCT
ejpam-5131	154	5	0	0	NUM
ejpam-5131	154	6	=	=	SYM
ejpam-5131	154	7	−η1	−η1	PROPN
ejpam-5131	154	8	−	−	PROPN
ejpam-5131	154	9	aη4	aη4	PROPN
ejpam-5131	154	10	,	,	PUNCT
ejpam-5131	154	11	0	0	NUM
ejpam-5131	154	12	=	=	SYM
ejpam-5131	154	13	η2	η2	PROPN
ejpam-5131	154	14	,	,	PUNCT
ejpam-5131	154	15	(	(	PUNCT
ejpam-5131	154	16	17	17	NUM
ejpam-5131	154	17	)	)	PUNCT
ejpam-5131	154	18	solving	solve	VERB
ejpam-5131	154	19	above	above	ADV
ejpam-5131	154	20	gives	give	VERB
ejpam-5131	154	21	us	we	PRON
ejpam-5131	154	22	the	the	DET
ejpam-5131	154	23	equilibrium	equilibrium	NOUN
ejpam-5131	154	24	points	point	NOUN
ejpam-5131	154	25	for	for	ADP
ejpam-5131	154	26	integer	integer	NOUN
ejpam-5131	154	27	and	and	CCONJ
ejpam-5131	154	28	non	non	ADJ
ejpam-5131	154	29	integer	integer	NOUN
ejpam-5131	154	30	or	or	CCONJ
ejpam-5131	154	31	der	der	NOUN
ejpam-5131	154	32	i.e.	i.e.	X
ejpam-5131	154	33	,	,	PUNCT
ejpam-5131	154	34	e	e	X
ejpam-5131	154	35	(	(	PUNCT
ejpam-5131	154	36	η∗1	η∗1	PROPN
ejpam-5131	154	37	,	,	PUNCT
ejpam-5131	154	38	η	η	PROPN
ejpam-5131	154	39	∗	∗	PROPN
ejpam-5131	154	40	2	2	NUM
ejpam-5131	154	41	,	,	PUNCT
ejpam-5131	154	42	η	η	PROPN
ejpam-5131	154	43	∗	∗	PROPN
ejpam-5131	154	44	3	3	NUM
ejpam-5131	154	45	,	,	PUNCT
ejpam-5131	154	46	η	η	PROPN
ejpam-5131	154	47	∗	∗	PROPN
ejpam-5131	154	48	4	4	NUM
ejpam-5131	154	49	,	,	PUNCT
ejpam-5131	154	50	η	η	PROPN
ejpam-5131	154	51	∗	∗	X
ejpam-5131	154	52	5	5	NUM
ejpam-5131	154	53	)	)	PUNCT
ejpam-5131	154	54	,	,	PUNCT
ejpam-5131	154	55	where	where	SCONJ
ejpam-5131	154	56	all	all	DET
ejpam-5131	154	57	the	the	DET
ejpam-5131	154	58	calculated	calculated	ADJ
ejpam-5131	154	59	values	value	NOUN
ejpam-5131	154	60	of	of	ADP
ejpam-5131	154	61	equilibrium	equilibrium	NOUN
ejpam-5131	154	62	points	point	NOUN
ejpam-5131	154	63	for	for	ADP
ejpam-5131	154	64	different	different	ADJ
ejpam-5131	154	65	α	α	NOUN
ejpam-5131	154	66	values	value	NOUN
ejpam-5131	154	67	.	.	PUNCT
ejpam-5131	155	1	further	far	ADV
ejpam-5131	155	2	the	the	DET
ejpam-5131	155	3	jacobian	jacobian	ADJ
ejpam-5131	155	4	matrix	matrix	NOUN
ejpam-5131	155	5	of	of	ADP
ejpam-5131	155	6	(	(	PUNCT
ejpam-5131	155	7	18	18	NUM
ejpam-5131	155	8	)	)	PUNCT
ejpam-5131	155	9	for	for	ADP
ejpam-5131	155	10	equilibrium	equilibrium	NOUN
ejpam-5131	155	11	point	point	NOUN
ejpam-5131	155	12	α	α	NOUN
ejpam-5131	156	1	=	=	NOUN
ejpam-5131	156	2	1	1	NUM
ejpam-5131	156	3	is	be	AUX
ejpam-5131	156	4	presented	present	VERB
ejpam-5131	156	5	which	which	PRON
ejpam-5131	156	6	is	be	AUX
ejpam-5131	156	7	:	:	PUNCT
ejpam-5131	156	8	je	je	X
ejpam-5131	156	9	=	=	PROPN
ejpam-5131	156	10			NOUN
ejpam-5131	156	11	a	a	DET
ejpam-5131	156	12	2	2	NUM
ejpam-5131	156	13	+	+	NOUN
ejpam-5131	156	14	a	a	DET
ejpam-5131	156	15	0	0	NUM
ejpam-5131	156	16	r	r	NOUN
ejpam-5131	156	17	0	0	NUM
ejpam-5131	156	18	c	c	NOUN
ejpam-5131	156	19	−1	−1	NOUN
ejpam-5131	156	20	0	0	NUM
ejpam-5131	156	21	0	0	NUM
ejpam-5131	156	22	0	0	NUM
ejpam-5131	156	23	0	0	NUM
ejpam-5131	156	24	0	0	NUM
ejpam-5131	157	1	−b	−b	NOUN
ejpam-5131	157	2	0	0	NUM
ejpam-5131	157	3	0	0	NUM
ejpam-5131	157	4	−1	−1	NOUN
ejpam-5131	157	5	0	0	NUM
ejpam-5131	157	6	0	0	NUM
ejpam-5131	157	7	−a	−a	NOUN
ejpam-5131	157	8	0	0	NUM
ejpam-5131	157	9	0	0	NUM
ejpam-5131	157	10	1	1	NUM
ejpam-5131	157	11	0	0	NUM
ejpam-5131	157	12	0	0	NUM
ejpam-5131	157	13	0	0	NUM
ejpam-5131	157	14			NOUN
ejpam-5131	157	15	(	(	PUNCT
ejpam-5131	157	16	18	18	NUM
ejpam-5131	157	17	)	)	PUNCT
ejpam-5131	157	18	the	the	DET
ejpam-5131	157	19	calculated	calculate	VERB
ejpam-5131	157	20	characteristic	characteristic	ADJ
ejpam-5131	157	21	equation	equation	NOUN
ejpam-5131	157	22	of	of	ADP
ejpam-5131	157	23	jacobian	jacobian	ADJ
ejpam-5131	157	24	matrix	matrix	NOUN
ejpam-5131	157	25	at	at	ADP
ejpam-5131	157	26	e	e	PROPN
ejpam-5131	157	27	is	be	AUX
ejpam-5131	157	28	a0λ	a0λ	PRON
ejpam-5131	157	29	5	5	NUM
ejpam-5131	158	1	+	+	ADJ
ejpam-5131	158	2	a1λ	a1λ	PROPN
ejpam-5131	158	3	4	4	NUM
ejpam-5131	158	4	+	+	NOUN
ejpam-5131	158	5	a2λ	a2λ	NOUN
ejpam-5131	158	6	3	3	NUM
ejpam-5131	158	7	+	+	NOUN
ejpam-5131	158	8	a3λ	a3λ	NOUN
ejpam-5131	158	9	2	2	NUM
ejpam-5131	158	10	+	+	NOUN
ejpam-5131	158	11	a4λ+a5	a4λ+a5	NOUN
ejpam-5131	158	12	=	=	SYM
ejpam-5131	158	13	0	0	NUM
ejpam-5131	158	14	,	,	PUNCT
ejpam-5131	158	15	(	(	PUNCT
ejpam-5131	158	16	19	19	NUM
ejpam-5131	158	17	)	)	PUNCT
ejpam-5131	158	18	from	from	ADP
ejpam-5131	158	19	eq.(19	eq.(19	NOUN
ejpam-5131	158	20	)	)	PUNCT
ejpam-5131	158	21	,	,	PUNCT
ejpam-5131	158	22	the	the	DET
ejpam-5131	158	23	coeficients	coeficient	NOUN
ejpam-5131	158	24	of	of	ADP
ejpam-5131	158	25	the	the	DET
ejpam-5131	158	26	polynomial	polynomial	NOUN
ejpam-5131	158	27	can	can	AUX
ejpam-5131	158	28	be	be	AUX
ejpam-5131	158	29	obtained	obtain	VERB
ejpam-5131	158	30	,	,	PUNCT
ejpam-5131	158	31	which	which	PRON
ejpam-5131	158	32	are	be	AUX
ejpam-5131	158	33	a0	a0	NOUN
ejpam-5131	158	34	=	=	SYM
ejpam-5131	158	35	2	2	NUM
ejpam-5131	158	36	,	,	PUNCT
ejpam-5131	158	37	a1	a1	NOUN
ejpam-5131	158	38	=	=	SYM
ejpam-5131	158	39	a	a	PROPN
ejpam-5131	158	40	,	,	PUNCT
ejpam-5131	158	41	a2	a2	PROPN
ejpam-5131	158	42	=	=	SYM
ejpam-5131	158	43	−3.0561a+	−3.0561a+	PROPN
ejpam-5131	158	44	4c+	4c+	NUM
ejpam-5131	158	45	6.1591	6.1591	NUM
ejpam-5131	158	46	,	,	PUNCT
ejpam-5131	158	47	a3	a3	NOUN
ejpam-5131	158	48	=	=	SYM
ejpam-5131	158	49	2.5646ab+	2.5646ab+	NUM
ejpam-5131	158	50	4ac+	4ac+	NUM
ejpam-5131	158	51	15.095a+	15.095a+	NUM
ejpam-5131	158	52	117.8545b+	117.8545b+	NUM
ejpam-5131	158	53	9.2433c+	9.2433c+	NUM
ejpam-5131	158	54	11.8625	11.8625	NUM
ejpam-5131	158	55	,	,	PUNCT
ejpam-5131	158	56	a4	a4	NOUN
ejpam-5131	158	57	=	=	SYM
ejpam-5131	158	58	464.610ab+	464.610ab+	NOUN
ejpam-5131	158	59	19.835ac+	19.835ac+	NUM
ejpam-5131	158	60	14.674a+	14.674a+	NUM
ejpam-5131	158	61	422.890b+	422.890b+	NOUN
ejpam-5131	158	62	20.7693c	20.7693c	NUM
ejpam-5131	158	63	+	+	CCONJ
ejpam-5131	158	64	6.3831	6.3831	NUM
ejpam-5131	158	65	,	,	PUNCT
ejpam-5131	158	66	a5	a5	PROPN
ejpam-5131	158	67	=	=	SYM
ejpam-5131	158	68	0	0	X
ejpam-5131	158	69	.	.	PUNCT
ejpam-5131	159	1	from	from	ADP
ejpam-5131	159	2	(	(	PUNCT
ejpam-5131	159	3	19	19	NUM
ejpam-5131	159	4	)	)	PUNCT
ejpam-5131	159	5	,	,	PUNCT
ejpam-5131	159	6	the	the	DET
ejpam-5131	159	7	calculated	calculate	VERB
ejpam-5131	159	8	eigenvalues	eigenvalue	NOUN
ejpam-5131	159	9	are	be	AUX
ejpam-5131	159	10	λ1	λ1	ADJ
ejpam-5131	159	11	=	=	SYM
ejpam-5131	159	12	0	0	NUM
ejpam-5131	159	13	,	,	PUNCT
ejpam-5131	159	14	λ2,3	λ2,3	NOUN
ejpam-5131	159	15	=	=	SYM
ejpam-5131	159	16	4.044±8.156j	4.044±8.156j	X
ejpam-5131	159	17	.	.	PUNCT
ejpam-5131	160	1	λ4	λ4	PROPN
ejpam-5131	160	2	=	=	PUNCT
ejpam-5131	161	1	−9.1137	−9.1137	NOUN
ejpam-5131	161	2	and	and	CCONJ
ejpam-5131	161	3	λ5	λ5	NOUN
ejpam-5131	161	4	=	=	SYM
ejpam-5131	161	5	−5.247	−5.247	PROPN
ejpam-5131	161	6	and	and	CCONJ
ejpam-5131	161	7	the	the	DET
ejpam-5131	161	8	jacobian	jacobian	ADJ
ejpam-5131	161	9	matrix	matrix	NOUN
ejpam-5131	161	10	analysis	analysis	NOUN
ejpam-5131	161	11	for	for	ADP
ejpam-5131	161	12	system	system	NOUN
ejpam-5131	161	13	(	(	PUNCT
ejpam-5131	161	14	3.3	3.3	NUM
ejpam-5131	161	15	)	)	PUNCT
ejpam-5131	161	16	reveals	reveal	VERB
ejpam-5131	161	17	three	three	NUM
ejpam-5131	161	18	negative	negative	ADJ
ejpam-5131	161	19	,	,	PUNCT
ejpam-5131	161	20	one	one	NUM
ejpam-5131	161	21	zero	zero	NUM
ejpam-5131	161	22	,	,	PUNCT
ejpam-5131	161	23	and	and	CCONJ
ejpam-5131	161	24	two	two	NUM
ejpam-5131	161	25	complex	complex	ADJ
ejpam-5131	161	26	eigenvalues	eigenvalue	NOUN
ejpam-5131	161	27	,	,	PUNCT
ejpam-5131	161	28	indicating	indicate	VERB
ejpam-5131	161	29	the	the	DET
ejpam-5131	161	30	equilibrium	equilibrium	NOUN
ejpam-5131	161	31	points	point	NOUN
ejpam-5131	161	32	p1	p1	NOUN
ejpam-5131	161	33	as	as	ADP
ejpam-5131	161	34	unstable	unstable	ADJ
ejpam-5131	161	35	saddlefocus	saddlefocus	NOUN
ejpam-5131	161	36	points	point	NOUN
ejpam-5131	161	37	.	.	PUNCT
ejpam-5131	162	1	utilizing	utilize	VERB
ejpam-5131	162	2	the	the	DET
ejpam-5131	162	3	routh	routh	PROPN
ejpam-5131	162	4	-	-	PUNCT
ejpam-5131	162	5	hurwitz	hurwitz	PROPN
ejpam-5131	162	6	criterion	criterion	NOUN
ejpam-5131	162	7	for	for	ADP
ejpam-5131	162	8	a	a	DET
ejpam-5131	162	9	deeper	deep	ADJ
ejpam-5131	162	10	stability	stability	NOUN
ejpam-5131	162	11	assessment	assessment	NOUN
ejpam-5131	162	12	,	,	PUNCT
ejpam-5131	162	13	this	this	DET
ejpam-5131	162	14	g.	g.	PROPN
ejpam-5131	162	15	a.	a.	PROPN
ejpam-5131	162	16	ahmed	ahmed	PROPN
ejpam-5131	162	17	/	/	SYM
ejpam-5131	162	18	eur	eur	PROPN
ejpam-5131	162	19	.	.	PUNCT
ejpam-5131	163	1	j.	j.	PROPN
ejpam-5131	163	2	pure	pure	PROPN
ejpam-5131	163	3	appl	appl	PROPN
ejpam-5131	163	4	.	.	PROPN
ejpam-5131	163	5	math	math	PROPN
ejpam-5131	163	6	,	,	PUNCT
ejpam-5131	163	7	17	17	NUM
ejpam-5131	163	8	(	(	PUNCT
ejpam-5131	163	9	2	2	NUM
ejpam-5131	163	10	)	)	PUNCT
ejpam-5131	163	11	(	(	PUNCT
ejpam-5131	163	12	2024	2024	NUM
ejpam-5131	163	13	)	)	PUNCT
ejpam-5131	163	14	,	,	PUNCT
ejpam-5131	163	15	835	835	NUM
ejpam-5131	163	16	-	-	SYM
ejpam-5131	163	17	851	851	NUM
ejpam-5131	163	18	843	843	NUM
ejpam-5131	163	19	mathematical	mathematical	ADJ
ejpam-5131	163	20	approach	approach	NOUN
ejpam-5131	163	21	bypasses	bypass	VERB
ejpam-5131	163	22	direct	direct	ADJ
ejpam-5131	163	23	eigenvalue	eigenvalue	NOUN
ejpam-5131	163	24	calculation	calculation	NOUN
ejpam-5131	163	25	to	to	PART
ejpam-5131	163	26	confirm	confirm	VERB
ejpam-5131	163	27	the	the	DET
ejpam-5131	163	28	system	system	NOUN
ejpam-5131	163	29	’s	’s	PART
ejpam-5131	163	30	instability	instability	NOUN
ejpam-5131	163	31	,	,	PUNCT
ejpam-5131	163	32	showcasing	showcase	VERB
ejpam-5131	163	33	the	the	DET
ejpam-5131	163	34	blend	blend	NOUN
ejpam-5131	163	35	of	of	ADP
ejpam-5131	163	36	theoretical	theoretical	ADJ
ejpam-5131	163	37	insight	insight	NOUN
ejpam-5131	163	38	and	and	CCONJ
ejpam-5131	163	39	analytical	analytical	ADJ
ejpam-5131	163	40	rigor	rigor	NOUN
ejpam-5131	163	41	in	in	ADP
ejpam-5131	163	42	examining	examine	VERB
ejpam-5131	163	43	dynamical	dynamical	ADJ
ejpam-5131	163	44	stability	stability	NOUN
ejpam-5131	163	45	.	.	PUNCT
ejpam-5131	164	1	∆1	∆1	PUNCT
ejpam-5131	165	1	=	=	PUNCT
ejpam-5131	165	2	a1,∆2	a1,∆2	PROPN
ejpam-5131	165	3	=	=	PUNCT
ejpam-5131	165	4	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5131	165	5	a1	a1	NOUN
ejpam-5131	165	6	a3	a3	NOUN
ejpam-5131	165	7	a0	a0	PROPN
ejpam-5131	165	8	a2	a2	PROPN
ejpam-5131	165	9	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5131	165	10	,	,	PUNCT
ejpam-5131	165	11	∆3	∆3	PROPN
ejpam-5131	165	12	=	=	SYM
ejpam-5131	165	13	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ejpam-5131	165	14	a1	a1	NOUN
ejpam-5131	165	15	a3	a3	NOUN
ejpam-5131	165	16	a5	a5	PROPN
ejpam-5131	165	17	a0	a0	PROPN
ejpam-5131	165	18	a2	a2	PROPN
ejpam-5131	165	19	a4	a4	PROPN
ejpam-5131	165	20	0	0	NUM
ejpam-5131	165	21	a1	a1	NOUN
ejpam-5131	165	22	a3	a3	NOUN
ejpam-5131	165	23	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ejpam-5131	165	24	,	,	PUNCT
ejpam-5131	165	25	∆4	∆4	NOUN
ejpam-5131	165	26	=	=	SYM
ejpam-5131	165	27	∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣	PROPN
ejpam-5131	165	28	a1	a1	NOUN
ejpam-5131	165	29	a3	a3	NOUN
ejpam-5131	165	30	a5	a5	PROPN
ejpam-5131	165	31	a7	a7	PROPN
ejpam-5131	165	32	a0	a0	PROPN
ejpam-5131	165	33	a2	a2	PROPN
ejpam-5131	165	34	a4	a4	PROPN
ejpam-5131	165	35	a6	a6	NOUN
ejpam-5131	165	36	0	0	NUM
ejpam-5131	165	37	a1	a1	NOUN
ejpam-5131	165	38	a3	a3	NOUN
ejpam-5131	165	39	a5	a5	PROPN
ejpam-5131	165	40	0	0	NUM
ejpam-5131	165	41	a0	a0	PROPN
ejpam-5131	165	42	a2	a2	PROPN
ejpam-5131	165	43	a4	a4	PROPN
ejpam-5131	165	44	∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣	PROPN
ejpam-5131	165	45	,	,	PUNCT
ejpam-5131	165	46	∆5	∆5	PROPN
ejpam-5131	165	47	=	=	PUNCT
ejpam-5131	165	48	∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣	PROPN
ejpam-5131	165	49	a1	a1	NOUN
ejpam-5131	165	50	a3	a3	NOUN
ejpam-5131	165	51	a5	a5	PROPN
ejpam-5131	165	52	a7	a7	PROPN
ejpam-5131	165	53	a9	a9	PROPN
ejpam-5131	165	54	a0	a0	PROPN
ejpam-5131	165	55	a2	a2	PROPN
ejpam-5131	165	56	a4	a4	PROPN
ejpam-5131	165	57	a6	a6	NOUN
ejpam-5131	165	58	a8	a8	PROPN
ejpam-5131	165	59	0	0	NUM
ejpam-5131	165	60	a1	a1	NOUN
ejpam-5131	165	61	a3	a3	NOUN
ejpam-5131	165	62	a5	a5	PROPN
ejpam-5131	165	63	a7	a7	PROPN
ejpam-5131	165	64	0	0	NUM
ejpam-5131	165	65	a0	a0	PROPN
ejpam-5131	165	66	a2	a2	PROPN
ejpam-5131	165	67	a4	a4	PROPN
ejpam-5131	165	68	a6	a6	NOUN
ejpam-5131	165	69	0	0	SYM
ejpam-5131	165	70	0	0	NUM
ejpam-5131	165	71	a1	a1	NOUN
ejpam-5131	165	72	a3	a3	NOUN
ejpam-5131	165	73	a5	a5	PROPN
ejpam-5131	165	74	∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣	PROPN
ejpam-5131	165	75	.	.	PUNCT
ejpam-5131	166	1	when	when	SCONJ
ejpam-5131	166	2	the	the	DET
ejpam-5131	166	3	parameters	parameter	NOUN
ejpam-5131	166	4	a	a	PRON
ejpam-5131	166	5	=	=	SYM
ejpam-5131	166	6	9	9	NUM
ejpam-5131	166	7	,	,	PUNCT
ejpam-5131	166	8	b	b	NOUN
ejpam-5131	166	9	=	=	SYM
ejpam-5131	166	10	1.5	1.5	NUM
ejpam-5131	166	11	,	,	PUNCT
ejpam-5131	166	12	c	c	NOUN
ejpam-5131	166	13	=	=	SYM
ejpam-5131	166	14	11	11	NUM
ejpam-5131	166	15	and	and	CCONJ
ejpam-5131	166	16	d	d	NOUN
ejpam-5131	166	17	=	=	SYM
ejpam-5131	166	18	4	4	NUM
ejpam-5131	166	19	are	be	AUX
ejpam-5131	166	20	plugged	plug	VERB
ejpam-5131	166	21	in	in	ADP
ejpam-5131	166	22	eq.(4.4	eq.(4.4	PROPN
ejpam-5131	166	23	)	)	PUNCT
ejpam-5131	166	24	to	to	PART
ejpam-5131	166	25	calculate	calculate	VERB
ejpam-5131	166	26	the	the	DET
ejpam-5131	166	27	eq.(4.5	eq.(4.5	PROPN
ejpam-5131	166	28	)	)	PUNCT
ejpam-5131	166	29	determinants	determinant	NOUN
ejpam-5131	166	30	,	,	PUNCT
ejpam-5131	166	31	we	we	PRON
ejpam-5131	166	32	get	get	VERB
ejpam-5131	166	33	some	some	DET
ejpam-5131	166	34	negative	negative	ADJ
ejpam-5131	166	35	and	and	CCONJ
ejpam-5131	166	36	some	some	DET
ejpam-5131	166	37	positive	positive	ADJ
ejpam-5131	166	38	values	value	NOUN
ejpam-5131	166	39	.	.	PUNCT
ejpam-5131	167	1	the	the	DET
ejpam-5131	167	2	criterion	criterion	NOUN
ejpam-5131	167	3	suggests	suggest	VERB
ejpam-5131	167	4	that	that	SCONJ
ejpam-5131	167	5	if	if	SCONJ
ejpam-5131	167	6	∆1,∆2,∆3,∆4	∆1,∆2,∆3,∆4	PROPN
ejpam-5131	167	7	,	,	PUNCT
ejpam-5131	167	8	and	and	CCONJ
ejpam-5131	167	9	∆5	∆5	NUM
ejpam-5131	167	10	all	all	PRON
ejpam-5131	167	11	eigenvalues	eigenvalue	NOUN
ejpam-5131	167	12	are	be	AUX
ejpam-5131	167	13	positive	positive	ADJ
ejpam-5131	167	14	,	,	PUNCT
ejpam-5131	167	15	the	the	DET
ejpam-5131	167	16	system	system	NOUN
ejpam-5131	167	17	is	be	AUX
ejpam-5131	167	18	stable	stable	ADJ
ejpam-5131	167	19	with	with	ADP
ejpam-5131	167	20	no	no	DET
ejpam-5131	167	21	chaos	chaos	NOUN
ejpam-5131	167	22	.	.	PUNCT
ejpam-5131	168	1	a	a	DET
ejpam-5131	168	2	negative	negative	ADJ
ejpam-5131	168	3	eigenvalue	eigenvalue	NOUN
ejpam-5131	168	4	,	,	PUNCT
ejpam-5131	168	5	however	however	ADV
ejpam-5131	168	6	,	,	PUNCT
ejpam-5131	168	7	indicates	indicate	VERB
ejpam-5131	168	8	potential	potential	ADJ
ejpam-5131	168	9	for	for	ADP
ejpam-5131	168	10	chaotic	chaotic	ADJ
ejpam-5131	168	11	behavior	behavior	NOUN
ejpam-5131	168	12	.	.	PUNCT
ejpam-5131	169	1	5.1	5.1	NUM
ejpam-5131	169	2	.	.	PUNCT
ejpam-5131	170	1	lyapunov	lyapunov	PROPN
ejpam-5131	170	2	exponent	exponent	VERB
ejpam-5131	170	3	the	the	DET
ejpam-5131	170	4	determination	determination	NOUN
ejpam-5131	170	5	of	of	ADP
ejpam-5131	170	6	a	a	DET
ejpam-5131	170	7	system	system	NOUN
ejpam-5131	170	8	’s	’s	PART
ejpam-5131	170	9	lyapunov	lyapunov	ADJ
ejpam-5131	170	10	exponents	exponent	NOUN
ejpam-5131	170	11	(	(	PUNCT
ejpam-5131	170	12	les	les	X
ejpam-5131	170	13	)	)	PUNCT
ejpam-5131	170	14	is	be	AUX
ejpam-5131	170	15	of	of	ADP
ejpam-5131	170	16	paramount	paramount	ADJ
ejpam-5131	170	17	importance	importance	NOUN
ejpam-5131	170	18	in	in	ADP
ejpam-5131	170	19	discerning	discern	VERB
ejpam-5131	170	20	the	the	DET
ejpam-5131	170	21	presence	presence	NOUN
ejpam-5131	170	22	of	of	ADP
ejpam-5131	170	23	chaos	chaos	NOUN
ejpam-5131	170	24	inside	inside	ADP
ejpam-5131	170	25	the	the	DET
ejpam-5131	170	26	system.the	system.the	DET
ejpam-5131	170	27	jacobian	jacobian	ADJ
ejpam-5131	170	28	approach	approach	NOUN
ejpam-5131	170	29	is	be	AUX
ejpam-5131	170	30	among	among	ADP
ejpam-5131	170	31	the	the	DET
ejpam-5131	170	32	methodologies	methodology	NOUN
ejpam-5131	170	33	used	use	VERB
ejpam-5131	170	34	in	in	ADP
ejpam-5131	170	35	the	the	DET
ejpam-5131	170	36	computation	computation	NOUN
ejpam-5131	170	37	of	of	ADP
ejpam-5131	170	38	lyapunov	lyapunov	NOUN
ejpam-5131	170	39	exponents.methods	exponents.method	NOUN
ejpam-5131	170	40	for	for	ADP
ejpam-5131	170	41	computing	compute	VERB
ejpam-5131	170	42	time	time	NOUN
ejpam-5131	170	43	series	series	NOUN
ejpam-5131	170	44	-	-	PUNCT
ejpam-5131	170	45	based	base	VERB
ejpam-5131	170	46	lyapunov	lyapunov	ADJ
ejpam-5131	170	47	exponents	exponent	NOUN
ejpam-5131	170	48	(	(	PUNCT
ejpam-5131	170	49	les	les	PROPN
ejpam-5131	170	50	)	)	PUNCT
ejpam-5131	170	51	,	,	PUNCT
ejpam-5131	170	52	such	such	ADJ
ejpam-5131	170	53	as	as	ADP
ejpam-5131	170	54	wolf	wolf	PROPN
ejpam-5131	170	55	’s	’s	PART
ejpam-5131	170	56	technique	technique	NOUN
ejpam-5131	170	57	,	,	PUNCT
ejpam-5131	170	58	may	may	AUX
ejpam-5131	170	59	be	be	AUX
ejpam-5131	170	60	used	use	VERB
ejpam-5131	170	61	to	to	PART
ejpam-5131	170	62	determine	determine	VERB
ejpam-5131	170	63	the	the	DET
ejpam-5131	170	64	rate	rate	NOUN
ejpam-5131	170	65	of	of	ADP
ejpam-5131	170	66	divergence	divergence	NOUN
ejpam-5131	170	67	of	of	ADP
ejpam-5131	170	68	nearby	nearby	ADJ
ejpam-5131	170	69	trajectories	trajectory	NOUN
ejpam-5131	170	70	in	in	ADP
ejpam-5131	170	71	a	a	DET
ejpam-5131	170	72	dynamical	dynamical	ADJ
ejpam-5131	170	73	system	system	NOUN
ejpam-5131	170	74	.	.	PUNCT
ejpam-5131	171	1	[	[	X
ejpam-5131	171	2	15].the	15].the	DET
ejpam-5131	171	3	use	use	NOUN
ejpam-5131	171	4	of	of	ADP
ejpam-5131	171	5	other	other	ADJ
ejpam-5131	171	6	methods	method	NOUN
ejpam-5131	171	7	is	be	AUX
ejpam-5131	171	8	often	often	ADV
ejpam-5131	171	9	seen	see	VERB
ejpam-5131	171	10	in	in	ADP
ejpam-5131	171	11	the	the	DET
ejpam-5131	171	12	computation	computation	NOUN
ejpam-5131	171	13	of	of	ADP
ejpam-5131	171	14	lyapunov	lyapunov	ADJ
ejpam-5131	171	15	exponents	exponent	NOUN
ejpam-5131	171	16	for	for	ADP
ejpam-5131	171	17	systems	system	NOUN
ejpam-5131	171	18	characterized	characterize	VERB
ejpam-5131	171	19	by	by	ADP
ejpam-5131	171	20	both	both	DET
ejpam-5131	171	21	integer	integer	NOUN
ejpam-5131	171	22	and	and	CCONJ
ejpam-5131	171	23	fractional	fractional	ADJ
ejpam-5131	171	24	orders.[39	orders.[39	PROPN
ejpam-5131	171	25	]	]	PUNCT
ejpam-5131	171	26	.	.	PUNCT
ejpam-5131	172	1	in	in	ADP
ejpam-5131	172	2	this	this	DET
ejpam-5131	172	3	study	study	NOUN
ejpam-5131	172	4	,	,	PUNCT
ejpam-5131	172	5	we	we	PRON
ejpam-5131	172	6	used	use	VERB
ejpam-5131	172	7	wolf	wolf	PROPN
ejpam-5131	172	8	’s	’s	PART
ejpam-5131	172	9	algorithm	algorithm	NOUN
ejpam-5131	172	10	to	to	PART
ejpam-5131	172	11	calculate	calculate	VERB
ejpam-5131	172	12	les	le	NOUN
ejpam-5131	172	13	.	.	PUNCT
ejpam-5131	173	1	the	the	DET
ejpam-5131	173	2	lyapunov	lyapunov	ADJ
ejpam-5131	173	3	exponents	exponent	NOUN
ejpam-5131	173	4	are	be	AUX
ejpam-5131	173	5	calculated	calculate	VERB
ejpam-5131	173	6	for	for	ADP
ejpam-5131	173	7	system	system	NOUN
ejpam-5131	173	8	(	(	PUNCT
ejpam-5131	173	9	5	5	NUM
ejpam-5131	173	10	)	)	PUNCT
ejpam-5131	173	11	with	with	ADP
ejpam-5131	173	12	integer	integer	NOUN
ejpam-5131	173	13	and	and	CCONJ
ejpam-5131	173	14	fractional	fractional	ADJ
ejpam-5131	173	15	order	order	NOUN
ejpam-5131	173	16	ζ	ζ	NOUN
ejpam-5131	173	17	=	=	SYM
ejpam-5131	173	18	1	1	NUM
ejpam-5131	173	19	and	and	CCONJ
ejpam-5131	173	20	ζ	ζ	NOUN
ejpam-5131	173	21	=	=	SYM
ejpam-5131	173	22	0.99	0.99	NUM
ejpam-5131	173	23	respectively	respectively	ADV
ejpam-5131	173	24	.	.	PUNCT
ejpam-5131	174	1	the	the	DET
ejpam-5131	174	2	values	value	NOUN
ejpam-5131	174	3	at	at	ADP
ejpam-5131	174	4	integer	integer	NOUN
ejpam-5131	174	5	order	order	NOUN
ejpam-5131	174	6	ζ	ζ	NOUN
ejpam-5131	174	7	=	=	SYM
ejpam-5131	174	8	1	1	NUM
ejpam-5131	174	9	are	be	AUX
ejpam-5131	174	10	0.0796	0.0796	NUM
ejpam-5131	174	11	,	,	PUNCT
ejpam-5131	174	12	0,−0.838	0,−0.838	PUNCT
ejpam-5131	174	13	and	and	CCONJ
ejpam-5131	174	14	at	at	ADP
ejpam-5131	174	15	ζ	ζ	NOUN
ejpam-5131	174	16	=	=	SYM
ejpam-5131	174	17	0.99	0.99	NUM
ejpam-5131	174	18	the	the	DET
ejpam-5131	174	19	values	value	NOUN
ejpam-5131	174	20	are	be	AUX
ejpam-5131	174	21	0.0520,−0.05266,−0.92940	0.0520,−0.05266,−0.92940	PRON
ejpam-5131	174	22	.	.	PUNCT
ejpam-5131	175	1	lyapunov	lyapunov	ADJ
ejpam-5131	175	2	exponents	exponent	NOUN
ejpam-5131	175	3	are	be	AUX
ejpam-5131	175	4	presented	present	VERB
ejpam-5131	175	5	in	in	ADP
ejpam-5131	175	6	fig	fig	NOUN
ejpam-5131	175	7	.	.	PUNCT
ejpam-5131	176	1	10a	10a	PROPN
ejpam-5131	176	2	–	–	PUNCT
ejpam-5131	176	3	b.	b.	PROPN
ejpam-5131	176	4	figure	figure	NOUN
ejpam-5131	176	5	10a	10a	PROPN
ejpam-5131	176	6	shows	show	VERB
ejpam-5131	176	7	the	the	DET
ejpam-5131	176	8	lyapunov	lyapunov	ADJ
ejpam-5131	176	9	exponents	exponent	NOUN
ejpam-5131	176	10	for	for	ADP
ejpam-5131	176	11	ζ	ζ	NOUN
ejpam-5131	176	12	=	=	SYM
ejpam-5131	176	13	1	1	NUM
ejpam-5131	176	14	while	while	SCONJ
ejpam-5131	176	15	fig	fig	NOUN
ejpam-5131	176	16	.	.	PUNCT
ejpam-5131	177	1	10b	10b	NOUN
ejpam-5131	177	2	illustrates	illustrate	VERB
ejpam-5131	177	3	the	the	DET
ejpam-5131	177	4	lyapunov	lyapunov	ADJ
ejpam-5131	177	5	exponents	exponent	NOUN
ejpam-5131	177	6	for	for	ADP
ejpam-5131	177	7	ζ	ζ	NOUN
ejpam-5131	177	8	=	=	SYM
ejpam-5131	177	9	0.99	0.99	NUM
ejpam-5131	177	10	.	.	PUNCT
ejpam-5131	178	1	les	le	NOUN
ejpam-5131	178	2	at	at	ADP
ejpam-5131	178	3	ζ	ζ	NOUN
ejpam-5131	178	4	=	=	SYM
ejpam-5131	178	5	1	1	NUM
ejpam-5131	178	6	and	and	CCONJ
ejpam-5131	178	7	ζ	ζ	NOUN
ejpam-5131	178	8	=	=	SYM
ejpam-5131	178	9	0.99	0.99	NUM
ejpam-5131	178	10	show	show	VERB
ejpam-5131	178	11	that	that	SCONJ
ejpam-5131	178	12	the	the	DET
ejpam-5131	178	13	system	system	NOUN
ejpam-5131	178	14	(	(	PUNCT
ejpam-5131	178	15	4	4	X
ejpam-5131	178	16	)	)	PUNCT
ejpam-5131	178	17	is	be	AUX
ejpam-5131	178	18	chaotic	chaotic	ADJ
ejpam-5131	178	19	because	because	SCONJ
ejpam-5131	178	20	each	each	PRON
ejpam-5131	178	21	of	of	ADP
ejpam-5131	178	22	them	they	PRON
ejpam-5131	178	23	consists	consist	VERB
ejpam-5131	178	24	of	of	ADP
ejpam-5131	178	25	one	one	NUM
ejpam-5131	178	26	positive	positive	ADJ
ejpam-5131	178	27	,	,	PUNCT
ejpam-5131	178	28	one	one	NUM
ejpam-5131	178	29	negative	negative	ADJ
ejpam-5131	178	30	and	and	CCONJ
ejpam-5131	178	31	one	one	NUM
ejpam-5131	178	32	which	which	PRON
ejpam-5131	178	33	is	be	AUX
ejpam-5131	178	34	almost	almost	ADV
ejpam-5131	178	35	zero	zero	NUM
ejpam-5131	178	36	.	.	PUNCT
ejpam-5131	179	1	g.	g.	PROPN
ejpam-5131	179	2	a.	a.	PROPN
ejpam-5131	179	3	ahmed	ahmed	PROPN
ejpam-5131	179	4	/	/	SYM
ejpam-5131	179	5	eur	eur	PROPN
ejpam-5131	179	6	.	.	PUNCT
ejpam-5131	180	1	j.	j.	PROPN
ejpam-5131	180	2	pure	pure	PROPN
ejpam-5131	180	3	appl	appl	PROPN
ejpam-5131	180	4	.	.	PROPN
ejpam-5131	180	5	math	math	PROPN
ejpam-5131	180	6	,	,	PUNCT
ejpam-5131	180	7	17	17	NUM
ejpam-5131	180	8	(	(	PUNCT
ejpam-5131	180	9	2	2	NUM
ejpam-5131	180	10	)	)	PUNCT
ejpam-5131	180	11	(	(	PUNCT
ejpam-5131	180	12	2024	2024	NUM
ejpam-5131	180	13	)	)	PUNCT
ejpam-5131	180	14	,	,	PUNCT
ejpam-5131	180	15	835	835	NUM
ejpam-5131	180	16	-	-	SYM
ejpam-5131	180	17	851	851	NUM
ejpam-5131	180	18	844	844	NUM
ejpam-5131	180	19	figure	figure	NOUN
ejpam-5131	180	20	1	1	NUM
ejpam-5131	180	21	:	:	PUNCT
ejpam-5131	180	22	exponents	exponent	NOUN
ejpam-5131	180	23	of	of	ADP
ejpam-5131	180	24	the	the	DET
ejpam-5131	180	25	system	system	NOUN
ejpam-5131	180	26	(	(	PUNCT
ejpam-5131	180	27	4	4	NUM
ejpam-5131	180	28	)	)	PUNCT
ejpam-5131	180	29	.	.	PUNCT
ejpam-5131	181	1	6	6	X
ejpam-5131	181	2	.	.	X
ejpam-5131	181	3	the	the	DET
ejpam-5131	181	4	implementation	implementation	NOUN
ejpam-5131	181	5	of	of	ADP
ejpam-5131	181	6	a	a	DET
ejpam-5131	181	7	circuit	circuit	NOUN
ejpam-5131	181	8	for	for	ADP
ejpam-5131	181	9	a	a	DET
ejpam-5131	181	10	chaotic	chaotic	ADJ
ejpam-5131	181	11	system	system	NOUN
ejpam-5131	181	12	this	this	DET
ejpam-5131	181	13	segment	segment	NOUN
ejpam-5131	181	14	of	of	ADP
ejpam-5131	181	15	our	our	PRON
ejpam-5131	181	16	research	research	NOUN
ejpam-5131	181	17	extends	extend	VERB
ejpam-5131	181	18	into	into	ADP
ejpam-5131	181	19	the	the	DET
ejpam-5131	181	20	practical	practical	ADJ
ejpam-5131	181	21	domain	domain	NOUN
ejpam-5131	181	22	by	by	ADP
ejpam-5131	181	23	detailing	detail	VERB
ejpam-5131	181	24	the	the	DET
ejpam-5131	181	25	intricate	intricate	ADJ
ejpam-5131	181	26	process	process	NOUN
ejpam-5131	181	27	of	of	ADP
ejpam-5131	181	28	constructing	construct	VERB
ejpam-5131	181	29	analog	analog	NOUN
ejpam-5131	181	30	circuits	circuit	NOUN
ejpam-5131	181	31	that	that	PRON
ejpam-5131	181	32	embody	embody	VERB
ejpam-5131	181	33	our	our	PRON
ejpam-5131	181	34	chaotic	chaotic	ADJ
ejpam-5131	181	35	system	system	NOUN
ejpam-5131	181	36	,	,	PUNCT
ejpam-5131	181	37	thereby	thereby	ADV
ejpam-5131	181	38	allowing	allow	VERB
ejpam-5131	181	39	for	for	ADP
ejpam-5131	181	40	empirical	empirical	ADJ
ejpam-5131	181	41	verification	verification	NOUN
ejpam-5131	181	42	.	.	PUNCT
ejpam-5131	182	1	initially	initially	ADV
ejpam-5131	182	2	,	,	PUNCT
ejpam-5131	182	3	beginning	begin	VERB
ejpam-5131	182	4	with	with	ADP
ejpam-5131	182	5	the	the	DET
ejpam-5131	182	6	theoretical	theoretical	ADJ
ejpam-5131	182	7	foundations	foundation	NOUN
ejpam-5131	182	8	laid	lay	VERB
ejpam-5131	182	9	out	out	ADP
ejpam-5131	182	10	by	by	ADP
ejpam-5131	182	11	system	system	NOUN
ejpam-5131	182	12	(	(	PUNCT
ejpam-5131	182	13	1	1	NUM
ejpam-5131	182	14	)	)	PUNCT
ejpam-5131	182	15	,	,	PUNCT
ejpam-5131	182	16	we	we	PRON
ejpam-5131	182	17	embarked	embark	VERB
ejpam-5131	182	18	on	on	ADP
ejpam-5131	182	19	a	a	DET
ejpam-5131	182	20	methodical	methodical	ADJ
ejpam-5131	182	21	transformation	transformation	NOUN
ejpam-5131	182	22	of	of	ADP
ejpam-5131	182	23	these	these	DET
ejpam-5131	182	24	abstract	abstract	ADJ
ejpam-5131	182	25	equations	equation	NOUN
ejpam-5131	182	26	into	into	ADP
ejpam-5131	182	27	tangible	tangible	ADJ
ejpam-5131	182	28	circuit	circuit	NOUN
ejpam-5131	182	29	representations	representation	NOUN
ejpam-5131	182	30	.	.	PUNCT
ejpam-5131	183	1	this	this	DET
ejpam-5131	183	2	translation	translation	NOUN
ejpam-5131	183	3	from	from	ADP
ejpam-5131	183	4	mathematical	mathematical	ADJ
ejpam-5131	183	5	models	model	NOUN
ejpam-5131	183	6	to	to	ADP
ejpam-5131	183	7	physical	physical	ADJ
ejpam-5131	183	8	circuits	circuit	NOUN
ejpam-5131	183	9	necessitates	necessitate	VERB
ejpam-5131	183	10	meticulous	meticulous	ADJ
ejpam-5131	183	11	consideration	consideration	NOUN
ejpam-5131	183	12	of	of	ADP
ejpam-5131	183	13	the	the	DET
ejpam-5131	183	14	system	system	NOUN
ejpam-5131	183	15	’s	’s	PART
ejpam-5131	183	16	dynamical	dynamical	ADJ
ejpam-5131	183	17	properties	property	NOUN
ejpam-5131	183	18	,	,	PUNCT
ejpam-5131	183	19	ensuring	ensure	VERB
ejpam-5131	183	20	that	that	SCONJ
ejpam-5131	183	21	the	the	DET
ejpam-5131	183	22	resultant	resultant	NOUN
ejpam-5131	183	23	hardware	hardware	NOUN
ejpam-5131	183	24	not	not	PART
ejpam-5131	183	25	only	only	ADV
ejpam-5131	183	26	captures	capture	VERB
ejpam-5131	183	27	the	the	DET
ejpam-5131	183	28	essence	essence	NOUN
ejpam-5131	183	29	of	of	ADP
ejpam-5131	183	30	the	the	DET
ejpam-5131	183	31	theoretical	theoretical	ADJ
ejpam-5131	183	32	model	model	NOUN
ejpam-5131	183	33	but	but	CCONJ
ejpam-5131	183	34	also	also	ADV
ejpam-5131	183	35	faithfully	faithfully	ADV
ejpam-5131	183	36	reproduces	reproduce	VERB
ejpam-5131	183	37	its	its	PRON
ejpam-5131	183	38	chaotic	chaotic	ADJ
ejpam-5131	183	39	behavior	behavior	NOUN
ejpam-5131	183	40	.	.	PUNCT
ejpam-5131	184	1	the	the	DET
ejpam-5131	184	2	conversion	conversion	NOUN
ejpam-5131	184	3	process	process	NOUN
ejpam-5131	184	4	involves	involve	VERB
ejpam-5131	184	5	selecting	select	VERB
ejpam-5131	184	6	appropriate	appropriate	ADJ
ejpam-5131	184	7	electronic	electronic	ADJ
ejpam-5131	184	8	components	component	NOUN
ejpam-5131	184	9	that	that	PRON
ejpam-5131	184	10	mirror	mirror	VERB
ejpam-5131	184	11	the	the	DET
ejpam-5131	184	12	system	system	NOUN
ejpam-5131	184	13	’s	’s	PART
ejpam-5131	184	14	parameters	parameter	NOUN
ejpam-5131	184	15	and	and	CCONJ
ejpam-5131	184	16	operational	operational	ADJ
ejpam-5131	184	17	amplifiers	amplifier	NOUN
ejpam-5131	184	18	that	that	PRON
ejpam-5131	184	19	enforce	enforce	VERB
ejpam-5131	184	20	the	the	DET
ejpam-5131	184	21	nonlinearity	nonlinearity	NOUN
ejpam-5131	184	22	central	central	ADJ
ejpam-5131	184	23	to	to	ADP
ejpam-5131	184	24	chaotic	chaotic	ADJ
ejpam-5131	184	25	dynamics	dynamic	NOUN
ejpam-5131	184	26	.	.	PUNCT
ejpam-5131	185	1	by	by	ADP
ejpam-5131	185	2	doing	do	VERB
ejpam-5131	185	3	so	so	ADV
ejpam-5131	185	4	,	,	PUNCT
ejpam-5131	185	5	we	we	PRON
ejpam-5131	185	6	aim	aim	VERB
ejpam-5131	185	7	to	to	PART
ejpam-5131	185	8	bridge	bridge	VERB
ejpam-5131	185	9	the	the	DET
ejpam-5131	185	10	gap	gap	NOUN
ejpam-5131	185	11	between	between	ADP
ejpam-5131	185	12	simulation	simulation	NOUN
ejpam-5131	185	13	and	and	CCONJ
ejpam-5131	185	14	real	real	ADJ
ejpam-5131	185	15	-	-	PUNCT
ejpam-5131	185	16	world	world	NOUN
ejpam-5131	185	17	application	application	NOUN
ejpam-5131	185	18	,	,	PUNCT
ejpam-5131	185	19	providing	provide	VERB
ejpam-5131	185	20	a	a	DET
ejpam-5131	185	21	robust	robust	ADJ
ejpam-5131	185	22	platform	platform	NOUN
ejpam-5131	185	23	for	for	ADP
ejpam-5131	185	24	observing	observe	VERB
ejpam-5131	185	25	and	and	CCONJ
ejpam-5131	185	26	analyzing	analyze	VERB
ejpam-5131	185	27	the	the	DET
ejpam-5131	185	28	nuanced	nuanced	ADJ
ejpam-5131	185	29	behaviors	behavior	NOUN
ejpam-5131	185	30	of	of	ADP
ejpam-5131	185	31	the	the	DET
ejpam-5131	185	32	chaotic	chaotic	ADJ
ejpam-5131	185	33	system	system	NOUN
ejpam-5131	185	34	within	within	ADP
ejpam-5131	185	35	a	a	DET
ejpam-5131	185	36	controlled	control	VERB
ejpam-5131	185	37	experimental	experimental	ADJ
ejpam-5131	185	38	environment	environment	NOUN
ejpam-5131	185	39	.	.	PUNCT
ejpam-5131	186	1	in	in	ADP
ejpam-5131	186	2	this	this	DET
ejpam-5131	186	3	part	part	NOUN
ejpam-5131	186	4	of	of	ADP
ejpam-5131	186	5	the	the	DET
ejpam-5131	186	6	process	process	NOUN
ejpam-5131	186	7	,	,	PUNCT
ejpam-5131	186	8	the	the	DET
ejpam-5131	186	9	analog	analog	NOUN
ejpam-5131	186	10	circuits	circuit	NOUN
ejpam-5131	186	11	are	be	AUX
ejpam-5131	186	12	constructed	construct	VERB
ejpam-5131	186	13	such	such	ADJ
ejpam-5131	186	14	that	that	SCONJ
ejpam-5131	186	15	the	the	DET
ejpam-5131	186	16	system	system	NOUN
ejpam-5131	186	17	can	can	AUX
ejpam-5131	186	18	be	be	AUX
ejpam-5131	186	19	verified	verify	VERB
ejpam-5131	186	20	(	(	PUNCT
ejpam-5131	186	21	1	1	NUM
ejpam-5131	186	22	)	)	PUNCT
ejpam-5131	186	23	.	.	PUNCT
ejpam-5131	187	1	in	in	ADP
ejpam-5131	187	2	the	the	DET
ejpam-5131	187	3	first	first	ADJ
ejpam-5131	187	4	step	step	NOUN
ejpam-5131	187	5	g.	g.	PROPN
ejpam-5131	187	6	a.	a.	PROPN
ejpam-5131	187	7	ahmed	ahmed	PROPN
ejpam-5131	187	8	/	/	SYM
ejpam-5131	187	9	eur	eur	PROPN
ejpam-5131	187	10	.	.	PUNCT
ejpam-5131	188	1	j.	j.	PROPN
ejpam-5131	188	2	pure	pure	PROPN
ejpam-5131	188	3	appl	appl	PROPN
ejpam-5131	188	4	.	.	PROPN
ejpam-5131	188	5	math	math	PROPN
ejpam-5131	188	6	,	,	PUNCT
ejpam-5131	188	7	17	17	NUM
ejpam-5131	188	8	(	(	PUNCT
ejpam-5131	188	9	2	2	NUM
ejpam-5131	188	10	)	)	PUNCT
ejpam-5131	188	11	(	(	PUNCT
ejpam-5131	188	12	2024	2024	NUM
ejpam-5131	188	13	)	)	PUNCT
ejpam-5131	188	14	,	,	PUNCT
ejpam-5131	188	15	835	835	NUM
ejpam-5131	188	16	-	-	SYM
ejpam-5131	188	17	851	851	NUM
ejpam-5131	188	18	845	845	NUM
ejpam-5131	188	19	of	of	ADP
ejpam-5131	188	20	this	this	DET
ejpam-5131	188	21	process	process	NOUN
ejpam-5131	189	1	,	,	PUNCT
ejpam-5131	189	2	we	we	PRON
ejpam-5131	189	3	started	start	VERB
ejpam-5131	189	4	with	with	ADP
ejpam-5131	189	5	the	the	DET
ejpam-5131	189	6	system	system	NOUN
ejpam-5131	189	7	(	(	PUNCT
ejpam-5131	189	8	1	1	NUM
ejpam-5131	189	9	)	)	PUNCT
ejpam-5131	189	10	and	and	CCONJ
ejpam-5131	189	11	transformed	transform	VERB
ejpam-5131	189	12	it	it	PRON
ejpam-5131	189	13	into	into	ADP
ejpam-5131	189	14	circuit	circuit	NOUN
ejpam-5131	189	15	equations	equation	NOUN
ejpam-5131	189	16	.	.	PUNCT
ejpam-5131	190	1	d0.95η1	d0.95η1	VERB
ejpam-5131	190	2	=	=	SYM
ejpam-5131	190	3	1	1	NUM
ejpam-5131	190	4	r1c	r1c	NOUN
ejpam-5131	190	5	η2	η2	VERB
ejpam-5131	190	6	−	−	PROPN
ejpam-5131	190	7	1	1	NUM
ejpam-5131	190	8	r2c	r2c	NOUN
ejpam-5131	190	9	η1	η1	NOUN
ejpam-5131	190	10	+	+	CCONJ
ejpam-5131	190	11	1	1	NUM
ejpam-5131	190	12	r3c	r3c	ADP
ejpam-5131	190	13	η4	η4	VERB
ejpam-5131	190	14	+	+	CCONJ
ejpam-5131	190	15	1	1	NUM
ejpam-5131	190	16	r4c	r4c	X
ejpam-5131	190	17	(	(	PUNCT
ejpam-5131	190	18	r13	r13	NOUN
ejpam-5131	190	19	r14	r14	NOUN
ejpam-5131	190	20	+	+	CCONJ
ejpam-5131	190	21	r13	r13	NOUN
ejpam-5131	190	22	r15	r15	NOUN
ejpam-5131	190	23	η25	η25	NOUN
ejpam-5131	190	24	)	)	PUNCT
ejpam-5131	190	25	η2	η2	VERB
ejpam-5131	190	26	d0.95η2	d0.95η2	NOUN
ejpam-5131	190	27	=	=	NOUN
ejpam-5131	190	28	1	1	NUM
ejpam-5131	190	29	r5c	r5c	NOUN
ejpam-5131	190	30	η1	η1	NOUN
ejpam-5131	190	31	−	−	PROPN
ejpam-5131	190	32	1	1	NUM
ejpam-5131	190	33	r6c	r6c	NOUN
ejpam-5131	190	34	η1	η1	NOUN
ejpam-5131	190	35	−	−	PROPN
ejpam-5131	190	36	1	1	NUM
ejpam-5131	190	37	r7c	r7c	VERB
ejpam-5131	190	38	xη1	xη1	X
ejpam-5131	191	1	d0.95η3	d0.95η3	NOUN
ejpam-5131	192	1	=	=	NOUN
ejpam-5131	192	2	1	1	NUM
ejpam-5131	192	3	r8c	r8c	NOUN
ejpam-5131	192	4	η1η2	η1η2	NOUN
ejpam-5131	192	5	−	−	PROPN
ejpam-5131	192	6	1	1	NUM
ejpam-5131	192	7	r9c	r9c	PROPN
ejpam-5131	192	8	η3	η3	NOUN
ejpam-5131	192	9	d0.95η4	d0.95η4	NOUN
ejpam-5131	192	10	=	=	PUNCT
ejpam-5131	192	11	−	−	PROPN
ejpam-5131	192	12	1	1	NUM
ejpam-5131	192	13	r10c	r10c	NOUN
ejpam-5131	192	14	η1	η1	NOUN
ejpam-5131	192	15	−	−	NOUN
ejpam-5131	192	16	1	1	NUM
ejpam-5131	192	17	r11c	r11c	NOUN
ejpam-5131	192	18	η4	η4	VERB
ejpam-5131	192	19	d0.95η5	d0.95η5	VERB
ejpam-5131	192	20	=	=	SYM
ejpam-5131	192	21	1	1	X
ejpam-5131	192	22	r12c	r12c	NUM
ejpam-5131	192	23	η5	η5	PROPN
ejpam-5131	192	24	(	(	PUNCT
ejpam-5131	192	25	20	20	NUM
ejpam-5131	192	26	)	)	PUNCT
ejpam-5131	192	27	figure	figure	NOUN
ejpam-5131	192	28	2	2	NUM
ejpam-5131	192	29	:	:	PUNCT
ejpam-5131	192	30	circuit	circuit	NOUN
ejpam-5131	192	31	realization	realization	NOUN
ejpam-5131	192	32	of	of	ADP
ejpam-5131	192	33	chaotic	chaotic	ADJ
ejpam-5131	192	34	system	system	NOUN
ejpam-5131	192	35	.	.	PUNCT
ejpam-5131	193	1	g.	g.	PROPN
ejpam-5131	193	2	a.	a.	PROPN
ejpam-5131	193	3	ahmed	ahmed	PROPN
ejpam-5131	193	4	/	/	SYM
ejpam-5131	193	5	eur	eur	PROPN
ejpam-5131	193	6	.	.	PUNCT
ejpam-5131	194	1	j.	j.	PROPN
ejpam-5131	194	2	pure	pure	PROPN
ejpam-5131	194	3	appl	appl	PROPN
ejpam-5131	194	4	.	.	PROPN
ejpam-5131	194	5	math	math	PROPN
ejpam-5131	194	6	,	,	PUNCT
ejpam-5131	194	7	17	17	NUM
ejpam-5131	194	8	(	(	PUNCT
ejpam-5131	194	9	2	2	NUM
ejpam-5131	194	10	)	)	PUNCT
ejpam-5131	194	11	(	(	PUNCT
ejpam-5131	194	12	2024	2024	NUM
ejpam-5131	194	13	)	)	PUNCT
ejpam-5131	194	14	,	,	PUNCT
ejpam-5131	194	15	835	835	NUM
ejpam-5131	194	16	-	-	SYM
ejpam-5131	194	17	851	851	NUM
ejpam-5131	194	18	846	846	NUM
ejpam-5131	194	19	figure	figure	NOUN
ejpam-5131	194	20	3	3	NUM
ejpam-5131	194	21	:	:	PUNCT
ejpam-5131	194	22	circuit	circuit	NOUN
ejpam-5131	194	23	realization	realization	NOUN
ejpam-5131	194	24	of	of	ADP
ejpam-5131	194	25	chaotic	chaotic	ADJ
ejpam-5131	194	26	system	system	NOUN
ejpam-5131	194	27	figure	figure	NOUN
ejpam-5131	194	28	4	4	NUM
ejpam-5131	194	29	:	:	PUNCT
ejpam-5131	194	30	numerical	numerical	ADJ
ejpam-5131	194	31	simulated	simulate	VERB
ejpam-5131	194	32	and	and	CCONJ
ejpam-5131	194	33	circuital	circuital	PROPN
ejpam-5131	194	34	generated	generate	VERB
ejpam-5131	194	35	results	result	NOUN
ejpam-5131	194	36	for	for	ADP
ejpam-5131	194	37	system	system	NOUN
ejpam-5131	194	38	α=0.99	α=0.99	NOUN
ejpam-5131	194	39	.	.	PUNCT
ejpam-5131	195	1	figure	figure	NOUN
ejpam-5131	195	2	5	5	NUM
ejpam-5131	195	3	:	:	PUNCT
ejpam-5131	195	4	numerical	numerical	ADJ
ejpam-5131	195	5	simulated	simulate	VERB
ejpam-5131	195	6	and	and	CCONJ
ejpam-5131	195	7	circuital	circuital	PROPN
ejpam-5131	195	8	generated	generate	VERB
ejpam-5131	195	9	results	result	NOUN
ejpam-5131	195	10	for	for	ADP
ejpam-5131	195	11	system	system	NOUN
ejpam-5131	195	12	α=0.99	α=0.99	NOUN
ejpam-5131	195	13	.	.	PUNCT
ejpam-5131	196	1	figure	figure	VERB
ejpam-5131	196	2	6	6	NUM
ejpam-5131	196	3	:	:	PUNCT
ejpam-5131	196	4	numerical	numerical	ADJ
ejpam-5131	196	5	simulated	simulate	VERB
ejpam-5131	196	6	and	and	CCONJ
ejpam-5131	196	7	circuital	circuital	PROPN
ejpam-5131	196	8	generated	generate	VERB
ejpam-5131	196	9	results	result	NOUN
ejpam-5131	196	10	for	for	ADP
ejpam-5131	196	11	system	system	NOUN
ejpam-5131	196	12	α=0.99	α=0.99	NOUN
ejpam-5131	196	13	.	.	PUNCT
ejpam-5131	197	1	g.	g.	PROPN
ejpam-5131	197	2	a.	a.	PROPN
ejpam-5131	197	3	ahmed	ahmed	PROPN
ejpam-5131	197	4	/	/	SYM
ejpam-5131	197	5	eur	eur	PROPN
ejpam-5131	197	6	.	.	PUNCT
ejpam-5131	198	1	j.	j.	PROPN
ejpam-5131	198	2	pure	pure	PROPN
ejpam-5131	198	3	appl	appl	PROPN
ejpam-5131	198	4	.	.	PROPN
ejpam-5131	198	5	math	math	PROPN
ejpam-5131	198	6	,	,	PUNCT
ejpam-5131	198	7	17	17	NUM
ejpam-5131	198	8	(	(	PUNCT
ejpam-5131	198	9	2	2	NUM
ejpam-5131	198	10	)	)	PUNCT
ejpam-5131	198	11	(	(	PUNCT
ejpam-5131	198	12	2024	2024	NUM
ejpam-5131	198	13	)	)	PUNCT
ejpam-5131	198	14	,	,	PUNCT
ejpam-5131	198	15	835	835	NUM
ejpam-5131	198	16	-	-	SYM
ejpam-5131	198	17	851	851	NUM
ejpam-5131	198	18	847	847	NUM
ejpam-5131	198	19	figure	figure	NOUN
ejpam-5131	198	20	7	7	NUM
ejpam-5131	198	21	:	:	PUNCT
ejpam-5131	198	22	numerical	numerical	ADJ
ejpam-5131	198	23	simulated	simulate	VERB
ejpam-5131	198	24	and	and	CCONJ
ejpam-5131	198	25	circuital	circuital	PROPN
ejpam-5131	198	26	generated	generate	VERB
ejpam-5131	198	27	results	result	NOUN
ejpam-5131	198	28	for	for	ADP
ejpam-5131	198	29	system	system	NOUN
ejpam-5131	198	30	α=0.98	α=0.98	NOUN
ejpam-5131	198	31	.	.	PUNCT
ejpam-5131	199	1	figure	figure	VERB
ejpam-5131	199	2	8	8	NUM
ejpam-5131	199	3	:	:	PUNCT
ejpam-5131	199	4	numerical	numerical	ADJ
ejpam-5131	199	5	simulated	simulate	VERB
ejpam-5131	199	6	and	and	CCONJ
ejpam-5131	199	7	circuital	circuital	PROPN
ejpam-5131	199	8	generated	generate	VERB
ejpam-5131	199	9	results	result	NOUN
ejpam-5131	199	10	for	for	ADP
ejpam-5131	199	11	system	system	NOUN
ejpam-5131	199	12	α=0.99	α=0.99	NOUN
ejpam-5131	199	13	.	.	PUNCT
ejpam-5131	200	1	in	in	ADP
ejpam-5131	200	2	figures	figure	NOUN
ejpam-5131	200	3	2	2	NUM
ejpam-5131	200	4	through	through	ADP
ejpam-5131	200	5	5	5	NUM
ejpam-5131	200	6	,	,	PUNCT
ejpam-5131	200	7	we	we	PRON
ejpam-5131	200	8	delve	delve	VERB
ejpam-5131	200	9	into	into	ADP
ejpam-5131	200	10	the	the	DET
ejpam-5131	200	11	intricate	intricate	ADJ
ejpam-5131	200	12	dynamics	dynamic	NOUN
ejpam-5131	200	13	of	of	ADP
ejpam-5131	200	14	a	a	DET
ejpam-5131	200	15	chaotic	chaotic	ADJ
ejpam-5131	200	16	system	system	NOUN
ejpam-5131	200	17	through	through	ADP
ejpam-5131	200	18	both	both	DET
ejpam-5131	200	19	circuit	circuit	NOUN
ejpam-5131	200	20	realization	realization	NOUN
ejpam-5131	200	21	and	and	CCONJ
ejpam-5131	200	22	numerical	numerical	ADJ
ejpam-5131	200	23	simulations	simulation	NOUN
ejpam-5131	200	24	,	,	PUNCT
ejpam-5131	200	25	specifically	specifically	ADV
ejpam-5131	200	26	focusing	focus	VERB
ejpam-5131	200	27	on	on	ADP
ejpam-5131	200	28	the	the	DET
ejpam-5131	200	29	system	system	NOUN
ejpam-5131	200	30	with	with	ADP
ejpam-5131	200	31	α	α	NOUN
ejpam-5131	200	32	=	=	NOUN
ejpam-5131	200	33	0.99	0.99	NUM
ejpam-5131	200	34	.	.	PUNCT
ejpam-5131	201	1	figure	figure	NOUN
ejpam-5131	201	2	2	2	NUM
ejpam-5131	201	3	showcases	showcase	VERB
ejpam-5131	201	4	the	the	DET
ejpam-5131	201	5	physical	physical	ADJ
ejpam-5131	201	6	circuitry	circuitry	NOUN
ejpam-5131	201	7	that	that	PRON
ejpam-5131	201	8	underpins	underpin	VERB
ejpam-5131	201	9	the	the	DET
ejpam-5131	201	10	chaotic	chaotic	ADJ
ejpam-5131	201	11	behavior	behavior	NOUN
ejpam-5131	201	12	,	,	PUNCT
ejpam-5131	201	13	serving	serve	VERB
ejpam-5131	201	14	as	as	ADP
ejpam-5131	201	15	a	a	DET
ejpam-5131	201	16	tangible	tangible	ADJ
ejpam-5131	201	17	foundation	foundation	NOUN
ejpam-5131	201	18	for	for	ADP
ejpam-5131	201	19	the	the	DET
ejpam-5131	201	20	theoretical	theoretical	ADJ
ejpam-5131	201	21	models	model	NOUN
ejpam-5131	201	22	.	.	PUNCT
ejpam-5131	202	1	subsequently	subsequently	ADV
ejpam-5131	202	2	,	,	PUNCT
ejpam-5131	202	3	figures	figure	NOUN
ejpam-5131	202	4	2	2	NUM
ejpam-5131	202	5	to	to	PART
ejpam-5131	202	6	5	5	NUM
ejpam-5131	202	7	present	present	ADJ
ejpam-5131	202	8	a	a	DET
ejpam-5131	202	9	detailed	detailed	ADJ
ejpam-5131	202	10	examination	examination	NOUN
ejpam-5131	202	11	of	of	ADP
ejpam-5131	202	12	the	the	DET
ejpam-5131	202	13	system	system	NOUN
ejpam-5131	202	14	’s	’s	PART
ejpam-5131	202	15	behavior	behavior	NOUN
ejpam-5131	202	16	through	through	ADP
ejpam-5131	202	17	numerical	numerical	ADJ
ejpam-5131	202	18	simulations	simulation	NOUN
ejpam-5131	202	19	that	that	PRON
ejpam-5131	202	20	corroborate	corroborate	VERB
ejpam-5131	202	21	the	the	DET
ejpam-5131	202	22	circuit	circuit	NOUN
ejpam-5131	202	23	-	-	PUNCT
ejpam-5131	202	24	generated	generate	VERB
ejpam-5131	202	25	outcomes	outcome	NOUN
ejpam-5131	202	26	,	,	PUNCT
ejpam-5131	202	27	illustrating	illustrate	VERB
ejpam-5131	202	28	the	the	DET
ejpam-5131	202	29	system	system	NOUN
ejpam-5131	202	30	’s	’s	PART
ejpam-5131	202	31	response	response	NOUN
ejpam-5131	202	32	at	at	ADP
ejpam-5131	202	33	α	α	NOUN
ejpam-5131	202	34	=	=	NOUN
ejpam-5131	202	35	0.99	0.99	NUM
ejpam-5131	202	36	.	.	PUNCT
ejpam-5131	203	1	these	these	DET
ejpam-5131	203	2	figures	figure	NOUN
ejpam-5131	203	3	collectively	collectively	ADV
ejpam-5131	203	4	highlight	highlight	VERB
ejpam-5131	203	5	the	the	DET
ejpam-5131	203	6	consistency	consistency	NOUN
ejpam-5131	203	7	between	between	ADP
ejpam-5131	203	8	theoretical	theoretical	ADJ
ejpam-5131	203	9	predictions	prediction	NOUN
ejpam-5131	203	10	and	and	CCONJ
ejpam-5131	203	11	experimental	experimental	ADJ
ejpam-5131	203	12	observations	observation	NOUN
ejpam-5131	203	13	,	,	PUNCT
ejpam-5131	203	14	demonstrating	demonstrate	VERB
ejpam-5131	203	15	the	the	DET
ejpam-5131	203	16	robustness	robustness	NOUN
ejpam-5131	203	17	of	of	ADP
ejpam-5131	203	18	the	the	DET
ejpam-5131	203	19	chaotic	chaotic	ADJ
ejpam-5131	203	20	system	system	NOUN
ejpam-5131	203	21	under	under	ADP
ejpam-5131	203	22	study	study	NOUN
ejpam-5131	203	23	.	.	PUNCT
ejpam-5131	204	1	the	the	DET
ejpam-5131	204	2	nuanced	nuanced	ADJ
ejpam-5131	204	3	differences	difference	NOUN
ejpam-5131	204	4	in	in	ADP
ejpam-5131	204	5	the	the	DET
ejpam-5131	204	6	simulated	simulate	VERB
ejpam-5131	204	7	results	result	NOUN
ejpam-5131	204	8	,	,	PUNCT
ejpam-5131	204	9	despite	despite	SCONJ
ejpam-5131	204	10	the	the	DET
ejpam-5131	204	11	same	same	ADJ
ejpam-5131	204	12	α	α	NOUN
ejpam-5131	204	13	value	value	NOUN
ejpam-5131	204	14	,	,	PUNCT
ejpam-5131	204	15	underline	underline	VERB
ejpam-5131	204	16	the	the	DET
ejpam-5131	204	17	sensitivity	sensitivity	NOUN
ejpam-5131	204	18	to	to	ADP
ejpam-5131	204	19	initial	initial	ADJ
ejpam-5131	204	20	conditions	condition	NOUN
ejpam-5131	204	21	—	—	PUNCT
ejpam-5131	204	22	a	a	DET
ejpam-5131	204	23	hallmark	hallmark	NOUN
ejpam-5131	204	24	of	of	ADP
ejpam-5131	204	25	chaotic	chaotic	ADJ
ejpam-5131	204	26	systems	system	NOUN
ejpam-5131	204	27	.	.	PUNCT
ejpam-5131	205	1	this	this	DET
ejpam-5131	205	2	alignment	alignment	NOUN
ejpam-5131	205	3	between	between	ADP
ejpam-5131	205	4	experimental	experimental	ADJ
ejpam-5131	205	5	and	and	CCONJ
ejpam-5131	205	6	simulated	simulated	ADJ
ejpam-5131	205	7	data	datum	NOUN
ejpam-5131	205	8	not	not	PART
ejpam-5131	205	9	only	only	ADV
ejpam-5131	205	10	validates	validate	VERB
ejpam-5131	205	11	our	our	PRON
ejpam-5131	205	12	approach	approach	NOUN
ejpam-5131	205	13	but	but	CCONJ
ejpam-5131	205	14	also	also	ADV
ejpam-5131	205	15	offers	offer	VERB
ejpam-5131	205	16	insights	insight	NOUN
ejpam-5131	205	17	into	into	ADP
ejpam-5131	205	18	the	the	DET
ejpam-5131	205	19	practical	practical	ADJ
ejpam-5131	205	20	implementation	implementation	NOUN
ejpam-5131	205	21	and	and	CCONJ
ejpam-5131	205	22	potential	potential	ADJ
ejpam-5131	205	23	applications	application	NOUN
ejpam-5131	205	24	of	of	ADP
ejpam-5131	205	25	such	such	ADJ
ejpam-5131	205	26	chaotic	chaotic	ADJ
ejpam-5131	205	27	systems	system	NOUN
ejpam-5131	205	28	in	in	ADP
ejpam-5131	205	29	real	real	ADJ
ejpam-5131	205	30	-	-	PUNCT
ejpam-5131	205	31	world	world	NOUN
ejpam-5131	205	32	scenarios	scenario	NOUN
ejpam-5131	205	33	.	.	PUNCT
ejpam-5131	206	1	7	7	X
ejpam-5131	206	2	.	.	X
ejpam-5131	206	3	conclusion	conclusion	NOUN
ejpam-5131	206	4	the	the	DET
ejpam-5131	206	5	exploration	exploration	NOUN
ejpam-5131	206	6	into	into	ADP
ejpam-5131	206	7	a	a	DET
ejpam-5131	206	8	memristor	memristor	NOUN
ejpam-5131	206	9	fused	fuse	VERB
ejpam-5131	206	10	five	five	NUM
ejpam-5131	206	11	-	-	PUNCT
ejpam-5131	206	12	dimensional	dimensional	ADJ
ejpam-5131	206	13	fractional	fractional	ADJ
ejpam-5131	206	14	-	-	PUNCT
ejpam-5131	206	15	order	order	NOUN
ejpam-5131	206	16	chaotic	chaotic	ADJ
ejpam-5131	206	17	system	system	NOUN
ejpam-5131	206	18	delineates	delineate	VERB
ejpam-5131	206	19	a	a	DET
ejpam-5131	206	20	significant	significant	ADJ
ejpam-5131	206	21	advancement	advancement	NOUN
ejpam-5131	206	22	in	in	ADP
ejpam-5131	206	23	the	the	DET
ejpam-5131	206	24	study	study	NOUN
ejpam-5131	206	25	of	of	ADP
ejpam-5131	206	26	chaotic	chaotic	ADJ
ejpam-5131	206	27	systems	system	NOUN
ejpam-5131	206	28	.	.	PUNCT
ejpam-5131	207	1	incorporating	incorporate	VERB
ejpam-5131	207	2	fractional	fractional	ADJ
ejpam-5131	207	3	calculus	calculus	NOUN
ejpam-5131	207	4	,	,	PUNCT
ejpam-5131	207	5	this	this	DET
ejpam-5131	207	6	research	research	NOUN
ejpam-5131	207	7	unveils	unveil	VERB
ejpam-5131	207	8	a	a	DET
ejpam-5131	207	9	more	more	ADV
ejpam-5131	207	10	intricate	intricate	ADJ
ejpam-5131	207	11	and	and	CCONJ
ejpam-5131	207	12	robust	robust	ADJ
ejpam-5131	207	13	hyperchaotic	hyperchaotic	ADJ
ejpam-5131	207	14	behavior	behavior	NOUN
ejpam-5131	207	15	,	,	PUNCT
ejpam-5131	207	16	verified	verify	VERB
ejpam-5131	207	17	through	through	ADP
ejpam-5131	207	18	comprehensive	comprehensive	ADJ
ejpam-5131	207	19	simulations	simulation	NOUN
ejpam-5131	207	20	and	and	CCONJ
ejpam-5131	207	21	analytical	analytical	ADJ
ejpam-5131	207	22	validations	validation	NOUN
ejpam-5131	207	23	.	.	PUNCT
ejpam-5131	208	1	the	the	DET
ejpam-5131	208	2	findings	finding	NOUN
ejpam-5131	208	3	affirm	affirm	VERB
ejpam-5131	208	4	the	the	DET
ejpam-5131	208	5	potential	potential	NOUN
ejpam-5131	208	6	of	of	ADP
ejpam-5131	208	7	fractional	fractional	ADJ
ejpam-5131	208	8	-	-	PUNCT
ejpam-5131	208	9	order	order	NOUN
ejpam-5131	208	10	systems	system	NOUN
ejpam-5131	208	11	in	in	ADP
ejpam-5131	208	12	enhancing	enhance	VERB
ejpam-5131	208	13	the	the	DET
ejpam-5131	208	14	dynamics	dynamic	NOUN
ejpam-5131	208	15	and	and	CCONJ
ejpam-5131	208	16	stability	stability	NOUN
ejpam-5131	208	17	of	of	ADP
ejpam-5131	208	18	chaotic	chaotic	ADJ
ejpam-5131	208	19	systems	system	NOUN
ejpam-5131	208	20	,	,	PUNCT
ejpam-5131	208	21	as	as	SCONJ
ejpam-5131	208	22	evidenced	evidence	VERB
ejpam-5131	208	23	by	by	ADP
ejpam-5131	208	24	the	the	DET
ejpam-5131	208	25	alignment	alignment	NOUN
ejpam-5131	208	26	between	between	ADP
ejpam-5131	208	27	the	the	DET
ejpam-5131	208	28	circuit	circuit	NOUN
ejpam-5131	208	29	and	and	CCONJ
ejpam-5131	208	30	numerical	numerical	ADJ
ejpam-5131	208	31	simulations	simulation	NOUN
ejpam-5131	208	32	.	.	PUNCT
ejpam-5131	209	1	the	the	DET
ejpam-5131	209	2	study	study	NOUN
ejpam-5131	209	3	not	not	PART
ejpam-5131	209	4	only	only	ADV
ejpam-5131	209	5	deepens	deepen	VERB
ejpam-5131	209	6	the	the	DET
ejpam-5131	209	7	understanding	understanding	NOUN
ejpam-5131	209	8	of	of	ADP
ejpam-5131	209	9	chaotic	chaotic	ADJ
ejpam-5131	209	10	systems	system	NOUN
ejpam-5131	209	11	but	but	CCONJ
ejpam-5131	209	12	also	also	ADV
ejpam-5131	209	13	paves	pave	VERB
ejpam-5131	209	14	the	the	DET
ejpam-5131	209	15	way	way	NOUN
ejpam-5131	209	16	for	for	ADP
ejpam-5131	209	17	future	future	ADJ
ejpam-5131	209	18	innovations	innovation	NOUN
ejpam-5131	209	19	in	in	ADP
ejpam-5131	209	20	electronic	electronic	ADJ
ejpam-5131	209	21	circuit	circuit	NOUN
ejpam-5131	209	22	design	design	NOUN
ejpam-5131	209	23	and	and	CCONJ
ejpam-5131	209	24	the	the	DET
ejpam-5131	209	25	broader	broad	ADJ
ejpam-5131	209	26	application	application	NOUN
ejpam-5131	209	27	of	of	ADP
ejpam-5131	209	28	chaos	chaos	NOUN
ejpam-5131	209	29	theory	theory	NOUN
ejpam-5131	209	30	.	.	PUNCT
ejpam-5131	210	1	as	as	SCONJ
ejpam-5131	210	2	we	we	PRON
ejpam-5131	210	3	embark	embark	VERB
ejpam-5131	210	4	on	on	ADP
ejpam-5131	210	5	the	the	DET
ejpam-5131	210	6	next	next	ADJ
ejpam-5131	210	7	phase	phase	NOUN
ejpam-5131	210	8	of	of	ADP
ejpam-5131	210	9	research	research	NOUN
ejpam-5131	210	10	,	,	PUNCT
ejpam-5131	210	11	the	the	DET
ejpam-5131	210	12	focus	focus	NOUN
ejpam-5131	210	13	will	will	AUX
ejpam-5131	210	14	shift	shift	VERB
ejpam-5131	210	15	towards	towards	ADP
ejpam-5131	210	16	the	the	DET
ejpam-5131	210	17	deployment	deployment	ADJ
ejpam-5131	210	18	and	and	CCONJ
ejpam-5131	210	19	electronic	electronic	ADJ
ejpam-5131	210	20	integration	integration	NOUN
ejpam-5131	210	21	of	of	ADP
ejpam-5131	210	22	this	this	DET
ejpam-5131	210	23	innovative	innovative	ADJ
ejpam-5131	210	24	system	system	NOUN
ejpam-5131	210	25	,	,	PUNCT
ejpam-5131	210	26	promising	promise	VERB
ejpam-5131	210	27	new	new	ADJ
ejpam-5131	210	28	avreferences	avreference	NOUN
ejpam-5131	210	29	848	848	NUM
ejpam-5131	210	30	enues	enue	NOUN
ejpam-5131	210	31	for	for	ADP
ejpam-5131	210	32	exploration	exploration	NOUN
ejpam-5131	210	33	in	in	ADP
ejpam-5131	210	34	the	the	DET
ejpam-5131	210	35	field	field	NOUN
ejpam-5131	210	36	of	of	ADP
ejpam-5131	210	37	nonlinear	nonlinear	ADJ
ejpam-5131	210	38	dynamical	dynamical	ADJ
ejpam-5131	210	39	systems	system	NOUN
ejpam-5131	210	40	.	.	PUNCT
ejpam-5131	211	1	this	this	DET
ejpam-5131	211	2	work	work	NOUN
ejpam-5131	211	3	lays	lay	VERB
ejpam-5131	211	4	the	the	DET
ejpam-5131	211	5	groundwork	groundwork	NOUN
ejpam-5131	211	6	for	for	ADP
ejpam-5131	211	7	future	future	ADJ
ejpam-5131	211	8	research	research	NOUN
ejpam-5131	211	9	,	,	PUNCT
ejpam-5131	211	10	highlighting	highlight	VERB
ejpam-5131	211	11	the	the	DET
ejpam-5131	211	12	potential	potential	NOUN
ejpam-5131	211	13	for	for	ADP
ejpam-5131	211	14	further	further	ADJ
ejpam-5131	211	15	advancements	advancement	NOUN
ejpam-5131	211	16	in	in	ADP
ejpam-5131	211	17	the	the	DET
ejpam-5131	211	18	domain	domain	NOUN
ejpam-5131	211	19	of	of	ADP
ejpam-5131	211	20	fractional	fractional	ADJ
ejpam-5131	211	21	-	-	PUNCT
ejpam-5131	211	22	order	order	NOUN
ejpam-5131	211	23	chaotic	chaotic	ADJ
ejpam-5131	211	24	systems	system	NOUN
ejpam-5131	211	25	and	and	CCONJ
ejpam-5131	211	26	their	their	PRON
ejpam-5131	211	27	practical	practical	ADJ
ejpam-5131	211	28	applications.we	applications.we	NOUN
ejpam-5131	211	29	proposed	propose	VERB
ejpam-5131	211	30	to	to	PART
ejpam-5131	211	31	compare	compare	VERB
ejpam-5131	211	32	numerical	numerical	ADJ
ejpam-5131	211	33	solutions	solution	NOUN
ejpam-5131	211	34	with	with	ADP
ejpam-5131	211	35	other	other	ADJ
ejpam-5131	211	36	ways	way	NOUN
ejpam-5131	211	37	[	[	X
ejpam-5131	211	38	5	5	NUM
ejpam-5131	211	39	,	,	PUNCT
ejpam-5131	211	40	33	33	NUM
ejpam-5131	211	41	,	,	PUNCT
ejpam-5131	211	42	35	35	NUM
ejpam-5131	211	43	]	]	PUNCT
ejpam-5131	211	44	and	and	CCONJ
ejpam-5131	211	45	use	use	VERB
ejpam-5131	211	46	this	this	DET
ejpam-5131	211	47	method	method	NOUN
ejpam-5131	211	48	to	to	PART
ejpam-5131	211	49	solve	solve	VERB
ejpam-5131	211	50	novel	novel	ADJ
ejpam-5131	211	51	fractional	fractional	ADJ
ejpam-5131	211	52	issues	issue	NOUN
ejpam-5131	211	53	[	[	X
ejpam-5131	211	54	7	7	NUM
ejpam-5131	211	55	,	,	PUNCT
ejpam-5131	211	56	9	9	NUM
ejpam-5131	211	57	,	,	PUNCT
ejpam-5131	211	58	11	11	NUM
ejpam-5131	211	59	,	,	PUNCT
ejpam-5131	211	60	12	12	NUM
ejpam-5131	211	61	,	,	PUNCT
ejpam-5131	211	62	14	14	NUM
ejpam-5131	211	63	,	,	PUNCT
ejpam-5131	211	64	21	21	NUM
ejpam-5131	211	65	,	,	PUNCT
ejpam-5131	211	66	23	23	NUM
ejpam-5131	211	67	,	,	PUNCT
ejpam-5131	211	68	25	25	NUM
ejpam-5131	211	69	,	,	PUNCT
ejpam-5131	211	70	31	31	NUM
ejpam-5131	211	71	,	,	PUNCT
ejpam-5131	211	72	32	32	NUM
ejpam-5131	211	73	,	,	PUNCT
ejpam-5131	211	74	34	34	NUM
ejpam-5131	211	75	]	]	PUNCT
ejpam-5131	211	76	acknowledgements	acknowledgement	VERB
ejpam-5131	211	77	the	the	DET
ejpam-5131	211	78	author	author	NOUN
ejpam-5131	211	79	thank	thank	VERB
ejpam-5131	211	80	the	the	DET
ejpam-5131	211	81	editor	editor	NOUN
ejpam-5131	211	82	in	in	ADP
ejpam-5131	211	83	chief	chief	NOUN
ejpam-5131	211	84	of	of	ADP
ejpam-5131	211	85	european	european	PROPN
ejpam-5131	211	86	journal	journal	PROPN
ejpam-5131	211	87	of	of	ADP
ejpam-5131	211	88	pure	pure	ADJ
ejpam-5131	211	89	and	and	CCONJ
ejpam-5131	211	90	applied	applied	ADJ
ejpam-5131	211	91	mathematics	mathematic	NOUN
ejpam-5131	211	92	and	and	CCONJ
ejpam-5131	211	93	the	the	DET
ejpam-5131	211	94	referees	referee	NOUN
ejpam-5131	211	95	for	for	ADP
ejpam-5131	211	96	their	their	PRON
ejpam-5131	211	97	critical	critical	ADJ
ejpam-5131	211	98	reviews	review	NOUN
ejpam-5131	211	99	and	and	CCONJ
ejpam-5131	211	100	valuable	valuable	ADJ
ejpam-5131	211	101	comments	comment	NOUN
ejpam-5131	211	102	which	which	PRON
ejpam-5131	211	103	thoroughly	thoroughly	ADV
ejpam-5131	211	104	improved	improve	VERB
ejpam-5131	211	105	the	the	DET
ejpam-5131	211	106	paper	paper	NOUN
ejpam-5131	211	107	.	.	PUNCT
ejpam-5131	212	1	references	reference	NOUN
ejpam-5131	212	2	[	[	X
ejpam-5131	212	3	1	1	NUM
ejpam-5131	212	4	]	]	PUNCT
ejpam-5131	212	5	mohamed	mohame	VERB
ejpam-5131	212	6	a	a	DET
ejpam-5131	212	7	abdoon	abdoon	NOUN
ejpam-5131	212	8	.	.	PUNCT
ejpam-5131	213	1	first	first	ADJ
ejpam-5131	213	2	integral	integral	ADJ
ejpam-5131	213	3	method	method	NOUN
ejpam-5131	213	4	:	:	PUNCT
ejpam-5131	213	5	a	a	DET
ejpam-5131	213	6	general	general	ADJ
ejpam-5131	213	7	formula	formula	NOUN
ejpam-5131	213	8	for	for	ADP
ejpam-5131	213	9	nonlinear	nonlinear	ADJ
ejpam-5131	213	10	fractional	fractional	PROPN
ejpam-5131	213	11	klein	klein	PROPN
ejpam-5131	213	12	-	-	PUNCT
ejpam-5131	213	13	gordon	gordon	PROPN
ejpam-5131	213	14	equation	equation	NOUN
ejpam-5131	213	15	using	use	VERB
ejpam-5131	213	16	advanced	advanced	ADJ
ejpam-5131	213	17	computing	computing	NOUN
ejpam-5131	213	18	language	language	NOUN
ejpam-5131	213	19	.	.	PUNCT
ejpam-5131	214	1	american	american	PROPN
ejpam-5131	214	2	journal	journal	PROPN
ejpam-5131	214	3	of	of	ADP
ejpam-5131	214	4	computational	computational	ADJ
ejpam-5131	214	5	mathematics	mathematic	NOUN
ejpam-5131	214	6	,	,	PUNCT
ejpam-5131	214	7	5(02):127–134	5(02):127–134	NUM
ejpam-5131	214	8	,	,	PUNCT
ejpam-5131	214	9	2015	2015	NUM
ejpam-5131	214	10	.	.	PUNCT
ejpam-5131	215	1	[	[	X
ejpam-5131	215	2	2	2	NUM
ejpam-5131	215	3	]	]	PUNCT
ejpam-5131	215	4	mohamed	mohame	VERB
ejpam-5131	215	5	a	a	DET
ejpam-5131	215	6	abdoon	abdoon	NOUN
ejpam-5131	215	7	et	et	PROPN
ejpam-5131	215	8	al	al	PROPN
ejpam-5131	215	9	.	.	PROPN
ejpam-5131	216	1	programming	program	VERB
ejpam-5131	216	2	first	first	ADJ
ejpam-5131	216	3	integral	integral	ADJ
ejpam-5131	216	4	method	method	NOUN
ejpam-5131	216	5	general	general	ADJ
ejpam-5131	216	6	formula	formula	NOUN
ejpam-5131	216	7	for	for	ADP
ejpam-5131	216	8	the	the	DET
ejpam-5131	216	9	solving	solve	VERB
ejpam-5131	216	10	linear	linear	NOUN
ejpam-5131	216	11	and	and	CCONJ
ejpam-5131	216	12	nonlinear	nonlinear	ADJ
ejpam-5131	216	13	equations	equation	NOUN
ejpam-5131	216	14	.	.	PUNCT
ejpam-5131	217	1	applied	apply	VERB
ejpam-5131	217	2	mathematics	mathematic	NOUN
ejpam-5131	217	3	,	,	PUNCT
ejpam-5131	217	4	6(03):568	6(03):568	PROPN
ejpam-5131	217	5	,	,	PUNCT
ejpam-5131	217	6	2015	2015	NUM
ejpam-5131	217	7	.	.	PUNCT
ejpam-5131	218	1	[	[	X
ejpam-5131	218	2	3	3	NUM
ejpam-5131	218	3	]	]	PUNCT
ejpam-5131	218	4	mohamed	mohame	VERB
ejpam-5131	218	5	a	a	DET
ejpam-5131	218	6	abdoon	abdoon	NOUN
ejpam-5131	218	7	and	and	CCONJ
ejpam-5131	218	8	faeza	faeza	PROPN
ejpam-5131	218	9	lafta	lafta	PROPN
ejpam-5131	218	10	hasan	hasan	PROPN
ejpam-5131	218	11	.	.	PUNCT
ejpam-5131	219	1	advantages	advantage	NOUN
ejpam-5131	219	2	of	of	ADP
ejpam-5131	219	3	the	the	DET
ejpam-5131	219	4	differential	differential	ADJ
ejpam-5131	219	5	equations	equation	NOUN
ejpam-5131	219	6	for	for	ADP
ejpam-5131	219	7	solving	solve	VERB
ejpam-5131	219	8	problems	problem	NOUN
ejpam-5131	219	9	in	in	ADP
ejpam-5131	219	10	mathematical	mathematical	ADJ
ejpam-5131	219	11	physics	physics	NOUN
ejpam-5131	219	12	with	with	ADP
ejpam-5131	219	13	symbolic	symbolic	ADJ
ejpam-5131	219	14	computation	computation	NOUN
ejpam-5131	219	15	.	.	PUNCT
ejpam-5131	220	1	mathematical	mathematical	ADJ
ejpam-5131	220	2	modelling	modelling	NOUN
ejpam-5131	220	3	of	of	ADP
ejpam-5131	220	4	engineering	engineering	NOUN
ejpam-5131	220	5	problems	problem	NOUN
ejpam-5131	220	6	,	,	PUNCT
ejpam-5131	220	7	9(1	9(1	NUM
ejpam-5131	220	8	)	)	PUNCT
ejpam-5131	220	9	,	,	PUNCT
ejpam-5131	220	10	2022	2022	NUM
ejpam-5131	220	11	.	.	PUNCT
ejpam-5131	221	1	[	[	X
ejpam-5131	221	2	4	4	NUM
ejpam-5131	221	3	]	]	PUNCT
ejpam-5131	221	4	mohamed	mohame	VERB
ejpam-5131	221	5	a	a	DET
ejpam-5131	221	6	abdoon	abdoon	NOUN
ejpam-5131	221	7	and	and	CCONJ
ejpam-5131	221	8	faeza	faeza	PROPN
ejpam-5131	221	9	lafta	lafta	PROPN
ejpam-5131	221	10	hasan	hasan	PROPN
ejpam-5131	221	11	.	.	PUNCT
ejpam-5131	222	1	advantages	advantage	NOUN
ejpam-5131	222	2	of	of	ADP
ejpam-5131	222	3	the	the	DET
ejpam-5131	222	4	differential	differential	ADJ
ejpam-5131	222	5	equations	equation	NOUN
ejpam-5131	222	6	for	for	ADP
ejpam-5131	222	7	solving	solve	VERB
ejpam-5131	222	8	problems	problem	NOUN
ejpam-5131	222	9	in	in	ADP
ejpam-5131	222	10	mathematical	mathematical	ADJ
ejpam-5131	222	11	physics	physics	NOUN
ejpam-5131	222	12	with	with	ADP
ejpam-5131	222	13	symbolic	symbolic	ADJ
ejpam-5131	222	14	computation	computation	NOUN
ejpam-5131	222	15	.	.	PUNCT
ejpam-5131	223	1	mathematical	mathematical	ADJ
ejpam-5131	223	2	modelling	modelling	NOUN
ejpam-5131	223	3	of	of	ADP
ejpam-5131	223	4	engineering	engineering	NOUN
ejpam-5131	223	5	problems	problem	NOUN
ejpam-5131	223	6	,	,	PUNCT
ejpam-5131	223	7	9(1	9(1	NUM
ejpam-5131	223	8	)	)	PUNCT
ejpam-5131	223	9	,	,	PUNCT
ejpam-5131	223	10	2022	2022	NUM
ejpam-5131	223	11	.	.	PUNCT
ejpam-5131	224	1	[	[	X
ejpam-5131	224	2	5	5	NUM
ejpam-5131	224	3	]	]	X
ejpam-5131	224	4	ghada	ghada	NOUN
ejpam-5131	224	5	a	a	DET
ejpam-5131	224	6	ahmed	ahmed	PROPN
ejpam-5131	224	7	.	.	PUNCT
ejpam-5131	225	1	on	on	ADP
ejpam-5131	225	2	the	the	DET
ejpam-5131	225	3	fractional	fractional	ADJ
ejpam-5131	225	4	-	-	PUNCT
ejpam-5131	225	5	order	order	NOUN
ejpam-5131	225	6	glucose	glucose	NOUN
ejpam-5131	225	7	-	-	PUNCT
ejpam-5131	225	8	insulin	insulin	NOUN
ejpam-5131	225	9	interaction	interaction	NOUN
ejpam-5131	225	10	,	,	PUNCT
ejpam-5131	225	11	journal	journal	NOUN
ejpam-5131	225	12	=	=	SYM
ejpam-5131	225	13	aims	aim	VERB
ejpam-5131	225	14	mathematics	mathematic	NOUN
ejpam-5131	225	15	.	.	PUNCT
ejpam-5131	226	1	8(7):15824–15843	8(7):15824–15843	NUM
ejpam-5131	226	2	,	,	PUNCT
ejpam-5131	226	3	2023	2023	NUM
ejpam-5131	226	4	.	.	PUNCT
ejpam-5131	227	1	[	[	X
ejpam-5131	227	2	6	6	NUM
ejpam-5131	227	3	]	]	PUNCT
ejpam-5131	227	4	kilbas	kilbas	PROPN
ejpam-5131	227	5	anatolĭı	anatolĭı	PROPN
ejpam-5131	227	6	aleksandrovich	aleksandrovich	PROPN
ejpam-5131	227	7	,	,	PUNCT
ejpam-5131	227	8	srivastava	srivastava	PROPN
ejpam-5131	227	9	hari	hari	PROPN
ejpam-5131	227	10	m	m	PROPN
ejpam-5131	227	11	,	,	PUNCT
ejpam-5131	227	12	and	and	CCONJ
ejpam-5131	227	13	trujillo	trujillo	PROPN
ejpam-5131	227	14	juan	juan	PROPN
ejpam-5131	227	15	j.	j.	PROPN
ejpam-5131	227	16	theory	theory	PROPN
ejpam-5131	227	17	and	and	CCONJ
ejpam-5131	227	18	applications	application	NOUN
ejpam-5131	227	19	of	of	ADP
ejpam-5131	227	20	fractional	fractional	ADJ
ejpam-5131	227	21	differential	differential	ADJ
ejpam-5131	227	22	equations	equation	NOUN
ejpam-5131	227	23	.	.	PUNCT
ejpam-5131	228	1	elsevier	elsevier	NOUN
ejpam-5131	228	2	,	,	PUNCT
ejpam-5131	228	3	2006	2006	NUM
ejpam-5131	228	4	.	.	PUNCT
ejpam-5131	229	1	[	[	X
ejpam-5131	229	2	7	7	X
ejpam-5131	229	3	]	]	X
ejpam-5131	229	4	dalal	dalal	PROPN
ejpam-5131	229	5	khalid	khalid	PROPN
ejpam-5131	229	6	almutairi	almutairi	PROPN
ejpam-5131	229	7	,	,	PUNCT
ejpam-5131	229	8	mohamed	mohame	VERB
ejpam-5131	229	9	a	a	DET
ejpam-5131	229	10	abdoon	abdoon	NOUN
ejpam-5131	229	11	,	,	PUNCT
ejpam-5131	229	12	mohammed	mohammed	PROPN
ejpam-5131	229	13	berir	berir	PROPN
ejpam-5131	229	14	,	,	PUNCT
ejpam-5131	229	15	rania	rania	PROPN
ejpam-5131	229	16	saadeh	saadeh	PROPN
ejpam-5131	229	17	,	,	PUNCT
ejpam-5131	229	18	and	and	CCONJ
ejpam-5131	229	19	ahmad	ahmad	PROPN
ejpam-5131	229	20	qazza	qazza	PROPN
ejpam-5131	229	21	.	.	PUNCT
ejpam-5131	230	1	a	a	DET
ejpam-5131	230	2	numerical	numerical	ADJ
ejpam-5131	230	3	confirmation	confirmation	NOUN
ejpam-5131	230	4	of	of	ADP
ejpam-5131	230	5	a	a	DET
ejpam-5131	230	6	fractional	fractional	ADJ
ejpam-5131	230	7	seitr	seitr	NOUN
ejpam-5131	230	8	for	for	ADP
ejpam-5131	230	9	influenza	influenza	NOUN
ejpam-5131	230	10	model	model	NOUN
ejpam-5131	230	11	efficiency	efficiency	NOUN
ejpam-5131	230	12	.	.	PUNCT
ejpam-5131	231	1	appl	appl	PROPN
ejpam-5131	231	2	.	.	PROPN
ejpam-5131	231	3	math	math	PROPN
ejpam-5131	231	4	,	,	PUNCT
ejpam-5131	231	5	17(5):741–749	17(5):741–749	NUM
ejpam-5131	231	6	,	,	PUNCT
ejpam-5131	231	7	2023	2023	NUM
ejpam-5131	231	8	.	.	PUNCT
ejpam-5131	232	1	[	[	X
ejpam-5131	232	2	8	8	NUM
ejpam-5131	232	3	]	]	PUNCT
ejpam-5131	232	4	abdulrahman	abdulrahman	PROPN
ejpam-5131	232	5	bm	bm	PROPN
ejpam-5131	232	6	alzahrani	alzahrani	PROPN
ejpam-5131	232	7	,	,	PUNCT
ejpam-5131	232	8	mohamed	mohame	VERB
ejpam-5131	232	9	a	a	DET
ejpam-5131	232	10	abdoon	abdoon	NOUN
ejpam-5131	232	11	,	,	PUNCT
ejpam-5131	232	12	mohamed	mohamed	PROPN
ejpam-5131	232	13	elbadri	elbadri	PROPN
ejpam-5131	232	14	,	,	PUNCT
ejpam-5131	232	15	mohammed	mohammed	PROPN
ejpam-5131	232	16	berir	berir	NOUN
ejpam-5131	232	17	,	,	PUNCT
ejpam-5131	232	18	and	and	CCONJ
ejpam-5131	232	19	diaa	diaa	VERB
ejpam-5131	232	20	eldin	eldin	PROPN
ejpam-5131	232	21	elgezouli	elgezouli	PROPN
ejpam-5131	232	22	.	.	PUNCT
ejpam-5131	233	1	a	a	DET
ejpam-5131	233	2	comparative	comparative	ADJ
ejpam-5131	233	3	numerical	numerical	ADJ
ejpam-5131	233	4	study	study	NOUN
ejpam-5131	233	5	of	of	ADP
ejpam-5131	233	6	the	the	DET
ejpam-5131	233	7	symmetry	symmetry	NOUN
ejpam-5131	233	8	chaotic	chaotic	ADJ
ejpam-5131	233	9	jerk	jerk	NOUN
ejpam-5131	233	10	system	system	NOUN
ejpam-5131	233	11	with	with	ADP
ejpam-5131	233	12	a	a	DET
ejpam-5131	233	13	hyperbolic	hyperbolic	ADJ
ejpam-5131	233	14	sine	sine	NOUN
ejpam-5131	233	15	function	function	NOUN
ejpam-5131	233	16	via	via	ADP
ejpam-5131	233	17	two	two	NUM
ejpam-5131	233	18	different	different	ADJ
ejpam-5131	233	19	methods	method	NOUN
ejpam-5131	233	20	.	.	PUNCT
ejpam-5131	234	1	symmetry	symmetry	NOUN
ejpam-5131	234	2	,	,	PUNCT
ejpam-5131	234	3	15(11):1991	15(11):1991	NUM
ejpam-5131	234	4	,	,	PUNCT
ejpam-5131	234	5	2023	2023	NUM
ejpam-5131	234	6	.	.	PUNCT
ejpam-5131	235	1	[	[	X
ejpam-5131	235	2	9	9	NUM
ejpam-5131	235	3	]	]	PUNCT
ejpam-5131	235	4	abdulrahman	abdulrahman	PROPN
ejpam-5131	235	5	bm	bm	PROPN
ejpam-5131	235	6	alzahrani	alzahrani	PROPN
ejpam-5131	235	7	,	,	PUNCT
ejpam-5131	235	8	mohamed	mohame	VERB
ejpam-5131	235	9	a	a	DET
ejpam-5131	235	10	abdoon	abdoon	NOUN
ejpam-5131	235	11	,	,	PUNCT
ejpam-5131	235	12	mohamed	mohamed	PROPN
ejpam-5131	235	13	elbadri	elbadri	PROPN
ejpam-5131	235	14	,	,	PUNCT
ejpam-5131	235	15	mohammed	mohammed	PROPN
ejpam-5131	235	16	berir	berir	NOUN
ejpam-5131	235	17	,	,	PUNCT
ejpam-5131	235	18	and	and	CCONJ
ejpam-5131	235	19	diaa	diaa	VERB
ejpam-5131	235	20	eldin	eldin	PROPN
ejpam-5131	235	21	elgezouli	elgezouli	PROPN
ejpam-5131	235	22	.	.	PUNCT
ejpam-5131	236	1	a	a	DET
ejpam-5131	236	2	comparative	comparative	ADJ
ejpam-5131	236	3	numerical	numerical	ADJ
ejpam-5131	236	4	study	study	NOUN
ejpam-5131	236	5	of	of	ADP
ejpam-5131	236	6	the	the	DET
ejpam-5131	236	7	symmetry	symmetry	NOUN
ejpam-5131	236	8	references	reference	VERB
ejpam-5131	236	9	849	849	NUM
ejpam-5131	236	10	chaotic	chaotic	ADJ
ejpam-5131	236	11	jerk	jerk	NOUN
ejpam-5131	236	12	system	system	NOUN
ejpam-5131	236	13	with	with	ADP
ejpam-5131	236	14	a	a	DET
ejpam-5131	236	15	hyperbolic	hyperbolic	ADJ
ejpam-5131	236	16	sine	sine	NOUN
ejpam-5131	236	17	function	function	NOUN
ejpam-5131	236	18	via	via	ADP
ejpam-5131	236	19	two	two	NUM
ejpam-5131	236	20	different	different	ADJ
ejpam-5131	236	21	methods	method	NOUN
ejpam-5131	236	22	.	.	PUNCT
ejpam-5131	237	1	symmetry	symmetry	NOUN
ejpam-5131	237	2	,	,	PUNCT
ejpam-5131	237	3	15(11):1991	15(11):1991	NUM
ejpam-5131	237	4	,	,	PUNCT
ejpam-5131	237	5	2023	2023	NUM
ejpam-5131	237	6	.	.	PUNCT
ejpam-5131	238	1	[	[	X
ejpam-5131	238	2	10	10	NUM
ejpam-5131	238	3	]	]	X
ejpam-5131	238	4	abdulrahman	abdulrahman	NOUN
ejpam-5131	238	5	bmalzahrani	bmalzahrani	PROPN
ejpam-5131	238	6	,	,	PUNCT
ejpam-5131	238	7	rania	rania	PROPN
ejpam-5131	238	8	saadeh	saadeh	PROPN
ejpam-5131	238	9	,	,	PUNCT
ejpam-5131	238	10	mohamed	mohame	VERB
ejpam-5131	238	11	a	a	DET
ejpam-5131	238	12	abdoon	abdoon	NOUN
ejpam-5131	238	13	,	,	PUNCT
ejpam-5131	238	14	mohamed	mohamed	PROPN
ejpam-5131	238	15	elbadri	elbadri	PROPN
ejpam-5131	238	16	,	,	PUNCT
ejpam-5131	238	17	mohammed	mohammed	PROPN
ejpam-5131	238	18	berir	berir	PROPN
ejpam-5131	238	19	,	,	PUNCT
ejpam-5131	238	20	and	and	CCONJ
ejpam-5131	238	21	ahmad	ahmad	PROPN
ejpam-5131	238	22	qazza	qazza	PROPN
ejpam-5131	238	23	.	.	PUNCT
ejpam-5131	239	1	effective	effective	ADJ
ejpam-5131	239	2	methods	method	NOUN
ejpam-5131	239	3	for	for	ADP
ejpam-5131	239	4	numerical	numerical	ADJ
ejpam-5131	239	5	analysis	analysis	NOUN
ejpam-5131	239	6	of	of	ADP
ejpam-5131	239	7	the	the	DET
ejpam-5131	239	8	simplest	simple	ADJ
ejpam-5131	239	9	chaotic	chaotic	ADJ
ejpam-5131	239	10	circuit	circuit	NOUN
ejpam-5131	239	11	model	model	NOUN
ejpam-5131	239	12	with	with	ADP
ejpam-5131	239	13	atangana	atangana	PROPN
ejpam-5131	239	14	–	–	PUNCT
ejpam-5131	239	15	baleanu	baleanu	PROPN
ejpam-5131	239	16	caputo	caputo	PROPN
ejpam-5131	239	17	fractional	fractional	PROPN
ejpam-5131	239	18	derivative	derivative	PROPN
ejpam-5131	239	19	.	.	PUNCT
ejpam-5131	240	1	journal	journal	PROPN
ejpam-5131	240	2	of	of	ADP
ejpam-5131	240	3	engineering	engineering	NOUN
ejpam-5131	240	4	mathematics	mathematic	NOUN
ejpam-5131	240	5	,	,	PUNCT
ejpam-5131	240	6	144(1):9	144(1):9	NUM
ejpam-5131	240	7	,	,	PUNCT
ejpam-5131	240	8	2024	2024	NUM
ejpam-5131	240	9	.	.	PUNCT
ejpam-5131	241	1	[	[	X
ejpam-5131	241	2	11	11	NUM
ejpam-5131	241	3	]	]	PUNCT
ejpam-5131	241	4	abdulrahman	abdulrahman	NOUN
ejpam-5131	241	5	bmalzahrani	bmalzahrani	PROPN
ejpam-5131	241	6	,	,	PUNCT
ejpam-5131	241	7	rania	rania	PROPN
ejpam-5131	241	8	saadeh	saadeh	PROPN
ejpam-5131	241	9	,	,	PUNCT
ejpam-5131	241	10	mohamed	mohame	VERB
ejpam-5131	241	11	a	a	DET
ejpam-5131	241	12	abdoon	abdoon	NOUN
ejpam-5131	241	13	,	,	PUNCT
ejpam-5131	241	14	mohamed	mohamed	PROPN
ejpam-5131	241	15	elbadri	elbadri	PROPN
ejpam-5131	241	16	,	,	PUNCT
ejpam-5131	241	17	mohammed	mohammed	PROPN
ejpam-5131	241	18	berir	berir	PROPN
ejpam-5131	241	19	,	,	PUNCT
ejpam-5131	241	20	and	and	CCONJ
ejpam-5131	241	21	ahmad	ahmad	PROPN
ejpam-5131	241	22	qazza	qazza	PROPN
ejpam-5131	241	23	.	.	PUNCT
ejpam-5131	242	1	effective	effective	ADJ
ejpam-5131	242	2	methods	method	NOUN
ejpam-5131	242	3	for	for	ADP
ejpam-5131	242	4	numerical	numerical	ADJ
ejpam-5131	242	5	analysis	analysis	NOUN
ejpam-5131	242	6	of	of	ADP
ejpam-5131	242	7	the	the	DET
ejpam-5131	242	8	simplest	simple	ADJ
ejpam-5131	242	9	chaotic	chaotic	ADJ
ejpam-5131	242	10	circuit	circuit	NOUN
ejpam-5131	242	11	model	model	NOUN
ejpam-5131	242	12	with	with	ADP
ejpam-5131	242	13	atangana	atangana	PROPN
ejpam-5131	242	14	–	–	PUNCT
ejpam-5131	242	15	baleanu	baleanu	PROPN
ejpam-5131	242	16	caputo	caputo	PROPN
ejpam-5131	242	17	fractional	fractional	PROPN
ejpam-5131	242	18	derivative	derivative	PROPN
ejpam-5131	242	19	.	.	PUNCT
ejpam-5131	243	1	journal	journal	PROPN
ejpam-5131	243	2	of	of	ADP
ejpam-5131	243	3	engineering	engineering	NOUN
ejpam-5131	243	4	mathematics	mathematic	NOUN
ejpam-5131	243	5	,	,	PUNCT
ejpam-5131	243	6	144:9	144:9	NUM
ejpam-5131	243	7	,	,	PUNCT
ejpam-5131	243	8	2024	2024	NUM
ejpam-5131	243	9	.	.	PUNCT
ejpam-5131	244	1	[	[	X
ejpam-5131	244	2	12	12	NUM
ejpam-5131	244	3	]	]	PUNCT
ejpam-5131	244	4	salem	salem	PROPN
ejpam-5131	244	5	mubarak	mubarak	PROPN
ejpam-5131	244	6	alzahrani	alzahrani	PROPN
ejpam-5131	244	7	,	,	PUNCT
ejpam-5131	244	8	rania	rania	PROPN
ejpam-5131	244	9	saadeh	saadeh	PROPN
ejpam-5131	244	10	,	,	PUNCT
ejpam-5131	244	11	mohamed	mohame	VERB
ejpam-5131	244	12	a	a	DET
ejpam-5131	244	13	abdoon	abdoon	NOUN
ejpam-5131	244	14	,	,	PUNCT
ejpam-5131	244	15	ahmad	ahmad	PROPN
ejpam-5131	244	16	qazza	qazza	PROPN
ejpam-5131	244	17	,	,	PUNCT
ejpam-5131	244	18	fathelrhman	fathelrhman	NOUN
ejpam-5131	244	19	el	el	PROPN
ejpam-5131	244	20	guma	guma	PROPN
ejpam-5131	244	21	,	,	PUNCT
ejpam-5131	244	22	and	and	CCONJ
ejpam-5131	244	23	mohammed	mohammed	PROPN
ejpam-5131	244	24	berir	berir	PROPN
ejpam-5131	244	25	.	.	PUNCT
ejpam-5131	245	1	numerical	numerical	PROPN
ejpam-5131	245	2	simulation	simulation	PROPN
ejpam-5131	245	3	of	of	ADP
ejpam-5131	245	4	an	an	DET
ejpam-5131	245	5	influenza	influenza	NOUN
ejpam-5131	245	6	epidemic	epidemic	NOUN
ejpam-5131	245	7	:	:	PUNCT
ejpam-5131	245	8	prediction	prediction	NOUN
ejpam-5131	245	9	with	with	ADP
ejpam-5131	245	10	fractional	fractional	ADJ
ejpam-5131	245	11	seir	seir	NOUN
ejpam-5131	245	12	and	and	CCONJ
ejpam-5131	245	13	the	the	DET
ejpam-5131	245	14	arima	arima	PROPN
ejpam-5131	245	15	model	model	NOUN
ejpam-5131	245	16	.	.	PUNCT
ejpam-5131	246	1	appl	appl	PROPN
ejpam-5131	246	2	.	.	PROPN
ejpam-5131	246	3	math	math	PROPN
ejpam-5131	246	4	,	,	PUNCT
ejpam-5131	246	5	18(1):1–12	18(1):1–12	NUM
ejpam-5131	246	6	,	,	PUNCT
ejpam-5131	246	7	2024	2024	NUM
ejpam-5131	246	8	.	.	PUNCT
ejpam-5131	247	1	[	[	X
ejpam-5131	247	2	13	13	NUM
ejpam-5131	247	3	]	]	PUNCT
ejpam-5131	247	4	abdon	abdon	NOUN
ejpam-5131	247	5	atangana	atangana	PROPN
ejpam-5131	247	6	and	and	CCONJ
ejpam-5131	247	7	dumitru	dumitru	PROPN
ejpam-5131	247	8	baleanu	baleanu	NOUN
ejpam-5131	247	9	.	.	PUNCT
ejpam-5131	248	1	new	new	ADJ
ejpam-5131	248	2	fractional	fractional	ADJ
ejpam-5131	248	3	derivatives	derivative	NOUN
ejpam-5131	248	4	with	with	ADP
ejpam-5131	248	5	nonlocal	nonlocal	ADJ
ejpam-5131	248	6	and	and	CCONJ
ejpam-5131	248	7	non	non	ADJ
ejpam-5131	248	8	-	-	ADJ
ejpam-5131	248	9	singular	singular	ADJ
ejpam-5131	248	10	kerne	kerne	NOUN
ejpam-5131	248	11	.	.	PUNCT
ejpam-5131	249	1	arxiv	arxiv	PROPN
ejpam-5131	249	2	preprint	preprint	VERB
ejpam-5131	249	3	arxiv:1602.03408	arxiv:1602.03408	PROPN
ejpam-5131	249	4	,	,	PUNCT
ejpam-5131	249	5	2016	2016	NUM
ejpam-5131	249	6	.	.	PUNCT
ejpam-5131	250	1	[	[	X
ejpam-5131	250	2	14	14	NUM
ejpam-5131	250	3	]	]	PUNCT
ejpam-5131	250	4	abdon	abdon	NOUN
ejpam-5131	250	5	atangana	atangana	PROPN
ejpam-5131	250	6	and	and	CCONJ
ejpam-5131	250	7	dumitru	dumitru	PROPN
ejpam-5131	250	8	baleanu	baleanu	NOUN
ejpam-5131	250	9	.	.	PUNCT
ejpam-5131	251	1	new	new	ADJ
ejpam-5131	251	2	fractional	fractional	ADJ
ejpam-5131	251	3	derivatives	derivative	NOUN
ejpam-5131	251	4	with	with	ADP
ejpam-5131	251	5	nonlocal	nonlocal	ADJ
ejpam-5131	251	6	and	and	CCONJ
ejpam-5131	251	7	non	non	ADJ
ejpam-5131	251	8	-	-	ADJ
ejpam-5131	251	9	singular	singular	ADJ
ejpam-5131	251	10	kernel	kernel	NOUN
ejpam-5131	251	11	:	:	PUNCT
ejpam-5131	251	12	theory	theory	NOUN
ejpam-5131	251	13	and	and	CCONJ
ejpam-5131	251	14	application	application	NOUN
ejpam-5131	251	15	to	to	PART
ejpam-5131	251	16	heat	heat	NOUN
ejpam-5131	251	17	transfer	transfer	NOUN
ejpam-5131	251	18	model	model	NOUN
ejpam-5131	251	19	.	.	PUNCT
ejpam-5131	252	1	arxiv	arxiv	PROPN
ejpam-5131	252	2	preprint	preprint	VERB
ejpam-5131	252	3	arxiv:1602.03408	arxiv:1602.03408	PROPN
ejpam-5131	252	4	,	,	PUNCT
ejpam-5131	252	5	2016	2016	NUM
ejpam-5131	252	6	.	.	PUNCT
ejpam-5131	253	1	[	[	X
ejpam-5131	253	2	15	15	NUM
ejpam-5131	253	3	]	]	X
ejpam-5131	253	4	giancarlo	giancarlo	PROPN
ejpam-5131	253	5	benettin	benettin	PROPN
ejpam-5131	253	6	,	,	PUNCT
ejpam-5131	253	7	luigi	luigi	PROPN
ejpam-5131	253	8	galgani	galgani	PROPN
ejpam-5131	253	9	,	,	PUNCT
ejpam-5131	253	10	antonio	antonio	PROPN
ejpam-5131	253	11	giorgilli	giorgilli	PROPN
ejpam-5131	253	12	,	,	PUNCT
ejpam-5131	253	13	and	and	CCONJ
ejpam-5131	253	14	jean	jean	PROPN
ejpam-5131	253	15	-	-	PUNCT
ejpam-5131	253	16	marie	marie	PROPN
ejpam-5131	253	17	strelcyn	strelcyn	PROPN
ejpam-5131	253	18	.	.	PUNCT
ejpam-5131	254	1	lyapunov	lyapunov	ADJ
ejpam-5131	254	2	characteristic	characteristic	ADJ
ejpam-5131	254	3	exponents	exponent	NOUN
ejpam-5131	254	4	for	for	ADP
ejpam-5131	254	5	smooth	smooth	ADJ
ejpam-5131	254	6	dynamical	dynamical	ADJ
ejpam-5131	254	7	systems	system	NOUN
ejpam-5131	254	8	and	and	CCONJ
ejpam-5131	254	9	for	for	ADP
ejpam-5131	254	10	hamiltonian	hamiltonian	ADJ
ejpam-5131	254	11	systems	system	NOUN
ejpam-5131	254	12	;	;	PUNCT
ejpam-5131	254	13	a	a	DET
ejpam-5131	254	14	method	method	NOUN
ejpam-5131	254	15	for	for	ADP
ejpam-5131	254	16	computing	compute	VERB
ejpam-5131	254	17	all	all	PRON
ejpam-5131	254	18	of	of	ADP
ejpam-5131	254	19	them	they	PRON
ejpam-5131	254	20	.	.	PUNCT
ejpam-5131	255	1	part	part	NOUN
ejpam-5131	255	2	1	1	NUM
ejpam-5131	255	3	:	:	PUNCT
ejpam-5131	255	4	theory	theory	NOUN
ejpam-5131	255	5	.	.	PUNCT
ejpam-5131	256	1	meccanica	meccanica	PROPN
ejpam-5131	256	2	,	,	PUNCT
ejpam-5131	256	3	15:9–20	15:9–20	NUM
ejpam-5131	256	4	,	,	PUNCT
ejpam-5131	256	5	1980	1980	NUM
ejpam-5131	256	6	.	.	PUNCT
ejpam-5131	257	1	[	[	X
ejpam-5131	257	2	16	16	NUM
ejpam-5131	257	3	]	]	X
ejpam-5131	257	4	jakob	jakob	PROPN
ejpam-5131	257	5	bernoulli	bernoulli	PROPN
ejpam-5131	257	6	,	,	PUNCT
ejpam-5131	257	7	jean	jean	PROPN
ejpam-5131	257	8	bernoulli	bernoulli	PROPN
ejpam-5131	257	9	,	,	PUNCT
ejpam-5131	257	10	herman	herman	PROPN
ejpam-5131	257	11	h	h	PROPN
ejpam-5131	257	12	goldstine	goldstine	PROPN
ejpam-5131	257	13	,	,	PUNCT
ejpam-5131	257	14	patricia	patricia	PROPN
ejpam-5131	257	15	radelet	radelet	NOUN
ejpam-5131	257	16	-	-	PUNCT
ejpam-5131	257	17	de	de	X
ejpam-5131	257	18	grave	grave	NOUN
ejpam-5131	257	19	,	,	PUNCT
ejpam-5131	257	20	david	david	PROPN
ejpam-5131	257	21	speiser	speiser	PROPN
ejpam-5131	257	22	,	,	PUNCT
ejpam-5131	257	23	et	et	PROPN
ejpam-5131	257	24	al	al	PROPN
ejpam-5131	257	25	.	.	PROPN
ejpam-5131	257	26	die	die	PROPN
ejpam-5131	257	27	streitschriften	streitschriften	VERB
ejpam-5131	257	28	von	von	PROPN
ejpam-5131	257	29	jacob	jacob	PROPN
ejpam-5131	257	30	und	und	PROPN
ejpam-5131	257	31	johann	johann	PROPN
ejpam-5131	257	32	bernoulli	bernoulli	PROPN
ejpam-5131	257	33	:	:	PUNCT
ejpam-5131	257	34	variationsrechnung	variationsrechnung	VERB
ejpam-5131	257	35	.	.	PUNCT
ejpam-5131	258	1	no	no	DET
ejpam-5131	258	2	title	title	NOUN
ejpam-5131	258	3	,	,	PUNCT
ejpam-5131	258	4	1991	1991	NUM
ejpam-5131	258	5	.	.	PUNCT
ejpam-5131	259	1	[	[	X
ejpam-5131	259	2	17	17	NUM
ejpam-5131	259	3	]	]	X
ejpam-5131	259	4	jean	jean	PROPN
ejpam-5131	259	5	-	-	PUNCT
ejpam-5131	259	6	paul	paul	PROPN
ejpam-5131	259	7	berrut	berrut	PROPN
ejpam-5131	259	8	and	and	CCONJ
ejpam-5131	259	9	lloyd	lloyd	PROPN
ejpam-5131	259	10	n	n	PROPN
ejpam-5131	259	11	trefethen	trefethen	NOUN
ejpam-5131	259	12	.	.	PUNCT
ejpam-5131	260	1	barycentric	barycentric	ADJ
ejpam-5131	260	2	lagrange	lagrange	PROPN
ejpam-5131	260	3	interpolation	interpolation	NOUN
ejpam-5131	260	4	.	.	PUNCT
ejpam-5131	261	1	siam	siam	PROPN
ejpam-5131	261	2	review	review	PROPN
ejpam-5131	261	3	,	,	PUNCT
ejpam-5131	261	4	46(3):501–517	46(3):501–517	PROPN
ejpam-5131	261	5	,	,	PUNCT
ejpam-5131	261	6	2004	2004	NUM
ejpam-5131	261	7	.	.	PUNCT
ejpam-5131	262	1	[	[	X
ejpam-5131	262	2	18	18	NUM
ejpam-5131	262	3	]	]	PUNCT
ejpam-5131	262	4	donato	donato	NOUN
ejpam-5131	262	5	cafagna	cafagna	PROPN
ejpam-5131	262	6	and	and	CCONJ
ejpam-5131	262	7	giuseppe	giuseppe	PROPN
ejpam-5131	262	8	grassi	grassi	PROPN
ejpam-5131	262	9	.	.	PUNCT
ejpam-5131	263	1	on	on	ADP
ejpam-5131	263	2	the	the	DET
ejpam-5131	263	3	simplest	simple	ADJ
ejpam-5131	263	4	fractional	fractional	ADJ
ejpam-5131	263	5	-	-	PUNCT
ejpam-5131	263	6	order	order	NOUN
ejpam-5131	263	7	memristorbased	memristorbase	VERB
ejpam-5131	263	8	chaotic	chaotic	ADJ
ejpam-5131	263	9	system	system	NOUN
ejpam-5131	263	10	.	.	PUNCT
ejpam-5131	264	1	nonlinear	nonlinear	ADJ
ejpam-5131	264	2	dynamics	dynamic	NOUN
ejpam-5131	264	3	,	,	PUNCT
ejpam-5131	264	4	70:1185–1197	70:1185–1197	NUM
ejpam-5131	264	5	,	,	PUNCT
ejpam-5131	264	6	2012	2012	NUM
ejpam-5131	264	7	.	.	PUNCT
ejpam-5131	265	1	[	[	X
ejpam-5131	265	2	19	19	NUM
ejpam-5131	265	3	]	]	X
ejpam-5131	265	4	michele	michele	PROPN
ejpam-5131	265	5	caputo	caputo	PROPN
ejpam-5131	265	6	and	and	CCONJ
ejpam-5131	265	7	mauro	mauro	PROPN
ejpam-5131	265	8	fabrizio	fabrizio	PROPN
ejpam-5131	265	9	.	.	PUNCT
ejpam-5131	266	1	a	a	DET
ejpam-5131	266	2	new	new	ADJ
ejpam-5131	266	3	definition	definition	NOUN
ejpam-5131	266	4	of	of	ADP
ejpam-5131	266	5	fractional	fractional	ADJ
ejpam-5131	266	6	derivative	derivative	NOUN
ejpam-5131	266	7	without	without	ADP
ejpam-5131	266	8	singular	singular	ADJ
ejpam-5131	266	9	kernel	kernel	PROPN
ejpam-5131	266	10	.	.	PUNCT
ejpam-5131	267	1	progress	progress	NOUN
ejpam-5131	267	2	in	in	ADP
ejpam-5131	267	3	fractional	fractional	ADJ
ejpam-5131	267	4	differentiation	differentiation	NOUN
ejpam-5131	267	5	&	&	CCONJ
ejpam-5131	267	6	applications	application	NOUN
ejpam-5131	267	7	,	,	PUNCT
ejpam-5131	267	8	1(2):73–85	1(2):73–85	NUM
ejpam-5131	267	9	,	,	PUNCT
ejpam-5131	267	10	2015	2015	NUM
ejpam-5131	267	11	.	.	PUNCT
ejpam-5131	268	1	[	[	X
ejpam-5131	268	2	20	20	NUM
ejpam-5131	268	3	]	]	PUNCT
ejpam-5131	268	4	mohamed	mohamed	PROPN
ejpam-5131	268	5	elbadri	elbadri	PROPN
ejpam-5131	268	6	,	,	PUNCT
ejpam-5131	268	7	mohamed	mohame	VERB
ejpam-5131	268	8	a	a	DET
ejpam-5131	268	9	abdoon	abdoon	NOUN
ejpam-5131	268	10	,	,	PUNCT
ejpam-5131	268	11	mohammed	mohammed	PROPN
ejpam-5131	268	12	berir	berir	PROPN
ejpam-5131	268	13	,	,	PUNCT
ejpam-5131	268	14	and	and	CCONJ
ejpam-5131	268	15	dalal	dalal	PROPN
ejpam-5131	268	16	khalid	khalid	PROPN
ejpam-5131	268	17	almutairi	almutairi	PROPN
ejpam-5131	268	18	.	.	PUNCT
ejpam-5131	269	1	a	a	DET
ejpam-5131	269	2	numerical	numerical	ADJ
ejpam-5131	269	3	solution	solution	NOUN
ejpam-5131	269	4	and	and	CCONJ
ejpam-5131	269	5	comparative	comparative	ADJ
ejpam-5131	269	6	study	study	NOUN
ejpam-5131	269	7	of	of	ADP
ejpam-5131	269	8	the	the	DET
ejpam-5131	269	9	symmetric	symmetric	ADJ
ejpam-5131	269	10	rossler	rossler	NOUN
ejpam-5131	269	11	attractor	attractor	NOUN
ejpam-5131	269	12	with	with	ADP
ejpam-5131	269	13	the	the	DET
ejpam-5131	269	14	generalized	generalize	VERB
ejpam-5131	269	15	caputo	caputo	PROPN
ejpam-5131	269	16	fractional	fractional	PROPN
ejpam-5131	269	17	derivative	derivative	NOUN
ejpam-5131	269	18	via	via	ADP
ejpam-5131	269	19	two	two	NUM
ejpam-5131	269	20	different	different	ADJ
ejpam-5131	269	21	methods	method	NOUN
ejpam-5131	269	22	.	.	PUNCT
ejpam-5131	270	1	mathematics	mathematic	NOUN
ejpam-5131	270	2	,	,	PUNCT
ejpam-5131	270	3	11(13):2997	11(13):2997	NUM
ejpam-5131	270	4	,	,	PUNCT
ejpam-5131	270	5	2023	2023	NUM
ejpam-5131	270	6	.	.	PUNCT
ejpam-5131	271	1	references	reference	NOUN
ejpam-5131	271	2	850	850	NUM
ejpam-5131	271	3	[	[	X
ejpam-5131	271	4	21	21	NUM
ejpam-5131	271	5	]	]	X
ejpam-5131	271	6	mohamed	mohamed	PROPN
ejpam-5131	271	7	elbadri	elbadri	PROPN
ejpam-5131	271	8	,	,	PUNCT
ejpam-5131	271	9	mohamed	mohame	VERB
ejpam-5131	271	10	a	a	DET
ejpam-5131	271	11	abdoon	abdoon	NOUN
ejpam-5131	271	12	,	,	PUNCT
ejpam-5131	271	13	mohammed	mohammed	PROPN
ejpam-5131	271	14	berir	berir	PROPN
ejpam-5131	271	15	,	,	PUNCT
ejpam-5131	271	16	and	and	CCONJ
ejpam-5131	271	17	dalal	dalal	PROPN
ejpam-5131	271	18	khalid	khalid	PROPN
ejpam-5131	271	19	almutairi	almutairi	PROPN
ejpam-5131	271	20	.	.	PUNCT
ejpam-5131	272	1	a	a	DET
ejpam-5131	272	2	numerical	numerical	ADJ
ejpam-5131	272	3	solution	solution	NOUN
ejpam-5131	272	4	and	and	CCONJ
ejpam-5131	272	5	comparative	comparative	ADJ
ejpam-5131	272	6	study	study	NOUN
ejpam-5131	272	7	of	of	ADP
ejpam-5131	272	8	the	the	DET
ejpam-5131	272	9	symmetric	symmetric	ADJ
ejpam-5131	272	10	rossler	rossler	NOUN
ejpam-5131	272	11	attractor	attractor	NOUN
ejpam-5131	272	12	with	with	ADP
ejpam-5131	272	13	the	the	DET
ejpam-5131	272	14	generalized	generalize	VERB
ejpam-5131	272	15	caputo	caputo	PROPN
ejpam-5131	272	16	fractional	fractional	PROPN
ejpam-5131	272	17	derivative	derivative	NOUN
ejpam-5131	272	18	via	via	ADP
ejpam-5131	272	19	two	two	NUM
ejpam-5131	272	20	different	different	ADJ
ejpam-5131	272	21	methods	method	NOUN
ejpam-5131	272	22	.	.	PUNCT
ejpam-5131	273	1	mathematics	mathematic	NOUN
ejpam-5131	273	2	,	,	PUNCT
ejpam-5131	273	3	11(13):2997	11(13):2997	NUM
ejpam-5131	273	4	,	,	PUNCT
ejpam-5131	273	5	2023	2023	NUM
ejpam-5131	273	6	.	.	PUNCT
ejpam-5131	274	1	[	[	X
ejpam-5131	274	2	22	22	NUM
ejpam-5131	274	3	]	]	PUNCT
ejpam-5131	274	4	mohamed	mohamed	PROPN
ejpam-5131	274	5	elbadri	elbadri	PROPN
ejpam-5131	274	6	,	,	PUNCT
ejpam-5131	274	7	mohamed	mohame	VERB
ejpam-5131	274	8	a	a	DET
ejpam-5131	274	9	abdoon	abdoon	NOUN
ejpam-5131	274	10	,	,	PUNCT
ejpam-5131	274	11	mohammed	mohammed	PROPN
ejpam-5131	274	12	berir	berir	PROPN
ejpam-5131	274	13	,	,	PUNCT
ejpam-5131	274	14	and	and	CCONJ
ejpam-5131	274	15	dalal	dalal	PROPN
ejpam-5131	274	16	khalid	khalid	PROPN
ejpam-5131	274	17	almutairi	almutairi	PROPN
ejpam-5131	274	18	.	.	PUNCT
ejpam-5131	275	1	a	a	DET
ejpam-5131	275	2	symmetry	symmetry	NOUN
ejpam-5131	275	3	chaotic	chaotic	ADJ
ejpam-5131	275	4	model	model	NOUN
ejpam-5131	275	5	with	with	ADP
ejpam-5131	275	6	fractional	fractional	ADJ
ejpam-5131	275	7	derivative	derivative	ADJ
ejpam-5131	275	8	order	order	NOUN
ejpam-5131	275	9	via	via	ADP
ejpam-5131	275	10	two	two	NUM
ejpam-5131	275	11	different	different	ADJ
ejpam-5131	275	12	methods	method	NOUN
ejpam-5131	275	13	.	.	PUNCT
ejpam-5131	276	1	symmetry	symmetry	NOUN
ejpam-5131	276	2	,	,	PUNCT
ejpam-5131	276	3	15(6):1151	15(6):1151	NUM
ejpam-5131	276	4	,	,	PUNCT
ejpam-5131	276	5	2023	2023	NUM
ejpam-5131	276	6	.	.	PUNCT
ejpam-5131	277	1	[	[	X
ejpam-5131	277	2	23	23	NUM
ejpam-5131	277	3	]	]	PUNCT
ejpam-5131	277	4	mohamed	mohamed	PROPN
ejpam-5131	277	5	elbadri	elbadri	PROPN
ejpam-5131	277	6	,	,	PUNCT
ejpam-5131	277	7	mohamed	mohame	VERB
ejpam-5131	277	8	a	a	DET
ejpam-5131	277	9	abdoon	abdoon	NOUN
ejpam-5131	277	10	,	,	PUNCT
ejpam-5131	277	11	mohammed	mohammed	PROPN
ejpam-5131	277	12	berir	berir	PROPN
ejpam-5131	277	13	,	,	PUNCT
ejpam-5131	277	14	and	and	CCONJ
ejpam-5131	277	15	dalal	dalal	PROPN
ejpam-5131	277	16	khalid	khalid	PROPN
ejpam-5131	277	17	almutairi	almutairi	PROPN
ejpam-5131	277	18	.	.	PUNCT
ejpam-5131	278	1	a	a	DET
ejpam-5131	278	2	symmetry	symmetry	NOUN
ejpam-5131	278	3	chaotic	chaotic	ADJ
ejpam-5131	278	4	model	model	NOUN
ejpam-5131	278	5	with	with	ADP
ejpam-5131	278	6	fractional	fractional	ADJ
ejpam-5131	278	7	derivative	derivative	ADJ
ejpam-5131	278	8	order	order	NOUN
ejpam-5131	278	9	via	via	ADP
ejpam-5131	278	10	two	two	NUM
ejpam-5131	278	11	different	different	ADJ
ejpam-5131	278	12	methods	method	NOUN
ejpam-5131	278	13	.	.	PUNCT
ejpam-5131	279	1	symmetry	symmetry	NOUN
ejpam-5131	279	2	,	,	PUNCT
ejpam-5131	279	3	15(6):1151	15(6):1151	NUM
ejpam-5131	279	4	,	,	PUNCT
ejpam-5131	279	5	2023	2023	NUM
ejpam-5131	279	6	.	.	PUNCT
ejpam-5131	280	1	[	[	X
ejpam-5131	280	2	24	24	NUM
ejpam-5131	280	3	]	]	X
ejpam-5131	280	4	elsayed	elsaye	VERB
ejpam-5131	280	5	elshoubary	elshoubary	NOUN
ejpam-5131	280	6	,	,	PUNCT
ejpam-5131	280	7	mohamed	mohame	VERB
ejpam-5131	280	8	a	a	DET
ejpam-5131	280	9	abdoon	abdoon	NOUN
ejpam-5131	280	10	,	,	PUNCT
ejpam-5131	280	11	abdulgader	abdulgader	ADJ
ejpam-5131	280	12	bahatheg	bahatheg	NOUN
ejpam-5131	280	13	,	,	PUNCT
ejpam-5131	280	14	and	and	CCONJ
ejpam-5131	280	15	mousa	mousa	PROPN
ejpam-5131	280	16	mubarak	mubarak	PROPN
ejpam-5131	280	17	albeladi	albeladi	PROPN
ejpam-5131	280	18	.	.	PUNCT
ejpam-5131	281	1	stability	stability	NOUN
ejpam-5131	281	2	analysis	analysis	NOUN
ejpam-5131	281	3	and	and	CCONJ
ejpam-5131	281	4	numerical	numerical	PROPN
ejpam-5131	281	5	simulation	simulation	NOUN
ejpam-5131	281	6	of	of	ADP
ejpam-5131	281	7	fractional	fractional	ADJ
ejpam-5131	281	8	model	model	NOUN
ejpam-5131	281	9	of	of	ADP
ejpam-5131	281	10	leishmaniasis	leishmaniasis	NOUN
ejpam-5131	281	11	.	.	PUNCT
ejpam-5131	282	1	results	result	NOUN
ejpam-5131	282	2	in	in	ADP
ejpam-5131	282	3	nonlinear	nonlinear	ADJ
ejpam-5131	282	4	analysis	analysis	NOUN
ejpam-5131	282	5	,	,	PUNCT
ejpam-5131	282	6	6(2):9–17	6(2):9–17	NUM
ejpam-5131	282	7	,	,	PUNCT
ejpam-5131	282	8	2023	2023	NUM
ejpam-5131	282	9	.	.	PUNCT
ejpam-5131	283	1	[	[	X
ejpam-5131	283	2	25	25	NUM
ejpam-5131	283	3	]	]	PUNCT
ejpam-5131	283	4	fathelrhman	fathelrhman	NOUN
ejpam-5131	283	5	el	el	PROPN
ejpam-5131	283	6	guma	guma	PROPN
ejpam-5131	283	7	,	,	PUNCT
ejpam-5131	283	8	ossama	ossama	NOUN
ejpam-5131	283	9	m	m	PROPN
ejpam-5131	283	10	badawy	badawy	PROPN
ejpam-5131	283	11	,	,	PUNCT
ejpam-5131	283	12	mohammed	mohammed	PROPN
ejpam-5131	283	13	berir	berir	PROPN
ejpam-5131	283	14	,	,	PUNCT
ejpam-5131	283	15	and	and	CCONJ
ejpam-5131	283	16	mohamed	mohame	VERB
ejpam-5131	283	17	a	a	DET
ejpam-5131	283	18	abdoon	abdoon	NOUN
ejpam-5131	283	19	.	.	PUNCT
ejpam-5131	284	1	numerical	numerical	ADJ
ejpam-5131	284	2	analysis	analysis	NOUN
ejpam-5131	284	3	of	of	ADP
ejpam-5131	284	4	fractional	fractional	ADJ
ejpam-5131	284	5	-	-	PUNCT
ejpam-5131	284	6	order	order	NOUN
ejpam-5131	284	7	dynamic	dynamic	ADJ
ejpam-5131	284	8	dengue	dengue	NOUN
ejpam-5131	284	9	disease	disease	NOUN
ejpam-5131	284	10	epidemic	epidemic	NOUN
ejpam-5131	284	11	in	in	ADP
ejpam-5131	284	12	sudan	sudan	PROPN
ejpam-5131	284	13	.	.	PUNCT
ejpam-5131	285	1	journal	journal	PROPN
ejpam-5131	285	2	of	of	ADP
ejpam-5131	285	3	the	the	DET
ejpam-5131	285	4	nigerian	nigerian	ADJ
ejpam-5131	285	5	society	society	NOUN
ejpam-5131	285	6	of	of	ADP
ejpam-5131	285	7	physical	physical	ADJ
ejpam-5131	285	8	sciences	science	NOUN
ejpam-5131	285	9	,	,	PUNCT
ejpam-5131	285	10	pages	page	NOUN
ejpam-5131	285	11	1464–1464	1464–1464	NUM
ejpam-5131	285	12	,	,	PUNCT
ejpam-5131	285	13	2023	2023	NUM
ejpam-5131	285	14	.	.	PUNCT
ejpam-5131	286	1	[	[	X
ejpam-5131	286	2	26	26	NUM
ejpam-5131	286	3	]	]	X
ejpam-5131	286	4	tareq	tareq	PROPN
ejpam-5131	286	5	hamadneh	hamadneh	PROPN
ejpam-5131	286	6	,	,	PUNCT
ejpam-5131	286	7	amel	amel	PROPN
ejpam-5131	286	8	hioual	hioual	PROPN
ejpam-5131	286	9	,	,	PUNCT
ejpam-5131	286	10	rania	rania	PROPN
ejpam-5131	286	11	saadeh	saadeh	PROPN
ejpam-5131	286	12	,	,	PUNCT
ejpam-5131	286	13	mohamed	mohame	VERB
ejpam-5131	286	14	a	a	DET
ejpam-5131	286	15	abdoon	abdoon	NOUN
ejpam-5131	286	16	,	,	PUNCT
ejpam-5131	286	17	dalal	dalal	PROPN
ejpam-5131	286	18	khalid	khalid	PROPN
ejpam-5131	286	19	almutairi	almutairi	PROPN
ejpam-5131	286	20	,	,	PUNCT
ejpam-5131	286	21	thwiba	thwiba	PROPN
ejpam-5131	286	22	a	a	DET
ejpam-5131	286	23	khalid	khalid	PROPN
ejpam-5131	286	24	,	,	PUNCT
ejpam-5131	286	25	and	and	CCONJ
ejpam-5131	286	26	adel	adel	PROPN
ejpam-5131	286	27	ouannas	ouannas	PROPN
ejpam-5131	286	28	.	.	PUNCT
ejpam-5131	287	1	general	general	ADJ
ejpam-5131	287	2	methods	method	NOUN
ejpam-5131	287	3	to	to	PART
ejpam-5131	287	4	synchronize	synchronize	VERB
ejpam-5131	287	5	fractional	fractional	ADJ
ejpam-5131	287	6	discrete	discrete	ADJ
ejpam-5131	287	7	reaction	reaction	NOUN
ejpam-5131	287	8	–	–	PUNCT
ejpam-5131	287	9	diffusion	diffusion	NOUN
ejpam-5131	287	10	systems	system	NOUN
ejpam-5131	287	11	applied	apply	VERB
ejpam-5131	287	12	to	to	ADP
ejpam-5131	287	13	the	the	DET
ejpam-5131	287	14	glycolysis	glycolysis	NOUN
ejpam-5131	287	15	model	model	NOUN
ejpam-5131	287	16	.	.	PUNCT
ejpam-5131	288	1	fractal	fractal	PROPN
ejpam-5131	288	2	and	and	CCONJ
ejpam-5131	288	3	fractional	fractional	ADJ
ejpam-5131	288	4	,	,	PUNCT
ejpam-5131	288	5	7(11):828	7(11):828	PROPN
ejpam-5131	288	6	,	,	PUNCT
ejpam-5131	288	7	2023	2023	NUM
ejpam-5131	288	8	.	.	PUNCT
ejpam-5131	289	1	[	[	X
ejpam-5131	289	2	27	27	NUM
ejpam-5131	289	3	]	]	PUNCT
ejpam-5131	289	4	faeza	faeza	PROPN
ejpam-5131	289	5	hasan	hasan	PROPN
ejpam-5131	289	6	,	,	PUNCT
ejpam-5131	289	7	mohamed	mohame	VERB
ejpam-5131	289	8	a	a	DET
ejpam-5131	289	9	abdoon	abdoon	NOUN
ejpam-5131	289	10	,	,	PUNCT
ejpam-5131	289	11	rania	rania	PROPN
ejpam-5131	289	12	saadeh	saadeh	PROPN
ejpam-5131	289	13	,	,	PUNCT
ejpam-5131	289	14	mohammed	mohammed	PROPN
ejpam-5131	289	15	berir	berir	PROPN
ejpam-5131	289	16	,	,	PUNCT
ejpam-5131	289	17	and	and	CCONJ
ejpam-5131	289	18	ahmad	ahmad	PROPN
ejpam-5131	289	19	qazza	qazza	PROPN
ejpam-5131	289	20	.	.	PUNCT
ejpam-5131	290	1	a	a	DET
ejpam-5131	290	2	new	new	ADJ
ejpam-5131	290	3	perspective	perspective	NOUN
ejpam-5131	290	4	on	on	ADP
ejpam-5131	290	5	the	the	DET
ejpam-5131	290	6	stochastic	stochastic	ADJ
ejpam-5131	290	7	fractional	fractional	ADJ
ejpam-5131	290	8	order	order	NOUN
ejpam-5131	290	9	materialized	materialize	VERB
ejpam-5131	290	10	by	by	ADP
ejpam-5131	290	11	the	the	DET
ejpam-5131	290	12	exact	exact	ADJ
ejpam-5131	290	13	solutions	solution	NOUN
ejpam-5131	290	14	of	of	ADP
ejpam-5131	290	15	allen	allen	ADJ
ejpam-5131	290	16	-	-	PUNCT
ejpam-5131	290	17	cahn	cahn	NOUN
ejpam-5131	290	18	equation	equation	NOUN
ejpam-5131	290	19	.	.	PUNCT
ejpam-5131	291	1	international	international	ADJ
ejpam-5131	291	2	journal	journal	PROPN
ejpam-5131	291	3	of	of	ADP
ejpam-5131	291	4	mathematical	mathematical	ADJ
ejpam-5131	291	5	,	,	PUNCT
ejpam-5131	291	6	engineering	engineering	NOUN
ejpam-5131	291	7	and	and	CCONJ
ejpam-5131	291	8	management	management	NOUN
ejpam-5131	291	9	sciences	science	NOUN
ejpam-5131	291	10	,	,	PUNCT
ejpam-5131	291	11	8(5):912	8(5):912	NUM
ejpam-5131	291	12	,	,	PUNCT
ejpam-5131	291	13	2023	2023	NUM
ejpam-5131	291	14	.	.	PUNCT
ejpam-5131	292	1	[	[	X
ejpam-5131	292	2	28	28	NUM
ejpam-5131	292	3	]	]	PUNCT
ejpam-5131	292	4	faeza	faeza	ADP
ejpam-5131	292	5	l	l	PROPN
ejpam-5131	292	6	hasan	hasan	PROPN
ejpam-5131	292	7	and	and	CCONJ
ejpam-5131	292	8	mohamed	mohame	VERB
ejpam-5131	292	9	a	a	DET
ejpam-5131	292	10	abdoon	abdoon	NOUN
ejpam-5131	292	11	.	.	PUNCT
ejpam-5131	293	1	the	the	DET
ejpam-5131	293	2	generalized	generalized	ADJ
ejpam-5131	293	3	(	(	PUNCT
ejpam-5131	293	4	2	2	NUM
ejpam-5131	293	5	+	+	NUM
ejpam-5131	293	6	1	1	NUM
ejpam-5131	293	7	)	)	PUNCT
ejpam-5131	293	8	and	and	CCONJ
ejpam-5131	293	9	(	(	PUNCT
ejpam-5131	293	10	3	3	NUM
ejpam-5131	293	11	+	+	NOUN
ejpam-5131	293	12	1)dimensional	1)dimensional	NUM
ejpam-5131	293	13	with	with	ADP
ejpam-5131	293	14	advanced	advanced	ADJ
ejpam-5131	293	15	analytical	analytical	ADJ
ejpam-5131	293	16	wave	wave	NOUN
ejpam-5131	293	17	solutions	solution	NOUN
ejpam-5131	293	18	via	via	ADP
ejpam-5131	293	19	computational	computational	ADJ
ejpam-5131	293	20	applications	application	NOUN
ejpam-5131	293	21	.	.	PUNCT
ejpam-5131	294	1	international	international	ADJ
ejpam-5131	294	2	journal	journal	PROPN
ejpam-5131	294	3	of	of	ADP
ejpam-5131	294	4	nonlinear	nonlinear	ADJ
ejpam-5131	294	5	analysis	analysis	NOUN
ejpam-5131	294	6	and	and	CCONJ
ejpam-5131	294	7	applications	application	NOUN
ejpam-5131	294	8	,	,	PUNCT
ejpam-5131	294	9	12(2):1213–1241	12(2):1213–1241	NUM
ejpam-5131	294	10	,	,	PUNCT
ejpam-5131	294	11	2021	2021	NUM
ejpam-5131	294	12	.	.	PUNCT
ejpam-5131	295	1	[	[	X
ejpam-5131	295	2	29	29	NUM
ejpam-5131	295	3	]	]	X
ejpam-5131	295	4	ivo	ivo	PROPN
ejpam-5131	295	5	petráš.	petráš.	PROPN
ejpam-5131	295	6	fractional	fractional	ADJ
ejpam-5131	295	7	-	-	PUNCT
ejpam-5131	295	8	order	order	NOUN
ejpam-5131	295	9	nonlinear	nonlinear	ADJ
ejpam-5131	295	10	systems	system	NOUN
ejpam-5131	295	11	:	:	PUNCT
ejpam-5131	295	12	modeling	modeling	NOUN
ejpam-5131	295	13	,	,	PUNCT
ejpam-5131	295	14	analysis	analysis	NOUN
ejpam-5131	295	15	and	and	CCONJ
ejpam-5131	295	16	simulation	simulation	NOUN
ejpam-5131	295	17	.	.	PUNCT
ejpam-5131	296	1	springer	springer	PROPN
ejpam-5131	296	2	science	science	PROPN
ejpam-5131	296	3	&	&	CCONJ
ejpam-5131	296	4	business	business	NOUN
ejpam-5131	296	5	media	medium	NOUN
ejpam-5131	296	6	,	,	PUNCT
ejpam-5131	296	7	ann	ann	PROPN
ejpam-5131	296	8	arbor	arbor	PROPN
ejpam-5131	296	9	,	,	PUNCT
ejpam-5131	296	10	michigan	michigan	PROPN
ejpam-5131	296	11	,	,	PUNCT
ejpam-5131	296	12	2011	2011	NUM
ejpam-5131	296	13	.	.	PUNCT
ejpam-5131	297	1	[	[	X
ejpam-5131	297	2	30	30	NUM
ejpam-5131	297	3	]	]	X
ejpam-5131	297	4	igor	igor	NOUN
ejpam-5131	297	5	podlubny	podlubny	PROPN
ejpam-5131	297	6	.	.	PUNCT
ejpam-5131	298	1	fractional	fractional	ADJ
ejpam-5131	298	2	differential	differential	ADJ
ejpam-5131	298	3	equations	equation	NOUN
ejpam-5131	298	4	:	:	PUNCT
ejpam-5131	298	5	an	an	DET
ejpam-5131	298	6	introduction	introduction	NOUN
ejpam-5131	298	7	to	to	ADP
ejpam-5131	298	8	fractional	fractional	ADJ
ejpam-5131	298	9	derivatives	derivative	NOUN
ejpam-5131	298	10	,	,	PUNCT
ejpam-5131	298	11	fractional	fractional	ADJ
ejpam-5131	298	12	differential	differential	ADJ
ejpam-5131	298	13	equations	equation	NOUN
ejpam-5131	298	14	,	,	PUNCT
ejpam-5131	298	15	to	to	ADP
ejpam-5131	298	16	methods	method	NOUN
ejpam-5131	298	17	of	of	ADP
ejpam-5131	298	18	their	their	PRON
ejpam-5131	298	19	solution	solution	NOUN
ejpam-5131	298	20	and	and	CCONJ
ejpam-5131	298	21	some	some	PRON
ejpam-5131	298	22	of	of	ADP
ejpam-5131	298	23	their	their	PRON
ejpam-5131	298	24	applications	application	NOUN
ejpam-5131	298	25	.	.	PUNCT
ejpam-5131	299	1	elsevier	elsevier	NOUN
ejpam-5131	299	2	,	,	PUNCT
ejpam-5131	299	3	1998	1998	NUM
ejpam-5131	299	4	.	.	PUNCT
ejpam-5131	300	1	[	[	X
ejpam-5131	300	2	31	31	NUM
ejpam-5131	300	3	]	]	X
ejpam-5131	300	4	ahmad	ahmad	PROPN
ejpam-5131	300	5	qazza	qazza	PROPN
ejpam-5131	300	6	,	,	PUNCT
ejpam-5131	300	7	mohamed	mohamed	PROPN
ejpam-5131	300	8	abdoon	abdoon	PROPN
ejpam-5131	300	9	,	,	PUNCT
ejpam-5131	300	10	rania	rania	PROPN
ejpam-5131	300	11	saadeh	saadeh	PROPN
ejpam-5131	300	12	,	,	PUNCT
ejpam-5131	300	13	and	and	CCONJ
ejpam-5131	300	14	mohammed	mohammed	PROPN
ejpam-5131	300	15	berir	berir	PROPN
ejpam-5131	300	16	.	.	PUNCT
ejpam-5131	301	1	a	a	DET
ejpam-5131	301	2	new	new	ADJ
ejpam-5131	301	3	scheme	scheme	NOUN
ejpam-5131	301	4	for	for	ADP
ejpam-5131	301	5	solving	solve	VERB
ejpam-5131	301	6	a	a	DET
ejpam-5131	301	7	fractional	fractional	ADJ
ejpam-5131	301	8	differential	differential	ADJ
ejpam-5131	301	9	equation	equation	NOUN
ejpam-5131	301	10	and	and	CCONJ
ejpam-5131	301	11	a	a	DET
ejpam-5131	301	12	chaotic	chaotic	ADJ
ejpam-5131	301	13	system	system	NOUN
ejpam-5131	301	14	.	.	PUNCT
ejpam-5131	302	1	european	european	PROPN
ejpam-5131	302	2	journal	journal	PROPN
ejpam-5131	302	3	of	of	ADP
ejpam-5131	302	4	pure	pure	ADJ
ejpam-5131	302	5	and	and	CCONJ
ejpam-5131	302	6	applied	applied	ADJ
ejpam-5131	302	7	mathematics	mathematic	NOUN
ejpam-5131	302	8	,	,	PUNCT
ejpam-5131	302	9	16(2):1128–1139	16(2):1128–1139	NUM
ejpam-5131	302	10	,	,	PUNCT
ejpam-5131	302	11	2023	2023	NUM
ejpam-5131	302	12	.	.	PUNCT
ejpam-5131	303	1	references	reference	NOUN
ejpam-5131	303	2	851	851	NUM
ejpam-5131	303	3	[	[	X
ejpam-5131	303	4	32	32	NUM
ejpam-5131	303	5	]	]	X
ejpam-5131	303	6	rania	rania	PROPN
ejpam-5131	303	7	saadeh	saadeh	PROPN
ejpam-5131	303	8	,	,	PUNCT
ejpam-5131	303	9	mohamed	mohamed	PROPN
ejpam-5131	303	10	a.	a.	PROPN
ejpam-5131	303	11	abdoon	abdoon	PROPN
ejpam-5131	303	12	,	,	PUNCT
ejpam-5131	303	13	ahmad	ahmad	PROPN
ejpam-5131	303	14	qazza	qazza	PROPN
ejpam-5131	303	15	,	,	PUNCT
ejpam-5131	303	16	and	and	CCONJ
ejpam-5131	303	17	mohammed	mohammed	PROPN
ejpam-5131	303	18	berir	berir	PROPN
ejpam-5131	303	19	.	.	PUNCT
ejpam-5131	304	1	a	a	DET
ejpam-5131	304	2	numerical	numerical	ADJ
ejpam-5131	304	3	solution	solution	NOUN
ejpam-5131	304	4	of	of	ADP
ejpam-5131	304	5	generalized	generalized	ADJ
ejpam-5131	304	6	caputo	caputo	PROPN
ejpam-5131	304	7	fractional	fractional	ADJ
ejpam-5131	304	8	initial	initial	ADJ
ejpam-5131	304	9	value	value	NOUN
ejpam-5131	304	10	problems	problem	NOUN
ejpam-5131	304	11	.	.	PUNCT
ejpam-5131	305	1	fractal	fractal	ADJ
ejpam-5131	305	2	and	and	CCONJ
ejpam-5131	305	3	fractional	fractional	ADJ
ejpam-5131	305	4	,	,	PUNCT
ejpam-5131	305	5	7(4):332	7(4):332	NUM
ejpam-5131	305	6	,	,	PUNCT
ejpam-5131	305	7	2023	2023	NUM
ejpam-5131	305	8	.	.	PUNCT
ejpam-5131	306	1	[	[	X
ejpam-5131	306	2	33	33	NUM
ejpam-5131	306	3	]	]	X
ejpam-5131	306	4	rania	rania	PROPN
ejpam-5131	306	5	saadeh	saadeh	PROPN
ejpam-5131	306	6	,	,	PUNCT
ejpam-5131	306	7	mohamed	mohame	VERB
ejpam-5131	306	8	a	a	DET
ejpam-5131	306	9	abdoon	abdoon	NOUN
ejpam-5131	306	10	,	,	PUNCT
ejpam-5131	306	11	ahmad	ahmad	PROPN
ejpam-5131	306	12	qazza	qazza	PROPN
ejpam-5131	306	13	,	,	PUNCT
ejpam-5131	306	14	mohammed	mohammed	PROPN
ejpam-5131	306	15	berir	berir	PROPN
ejpam-5131	306	16	,	,	PUNCT
ejpam-5131	306	17	fathelrhman	fathelrhman	NOUN
ejpam-5131	306	18	el	el	PROPN
ejpam-5131	306	19	guma	guma	PROPN
ejpam-5131	306	20	,	,	PUNCT
ejpam-5131	306	21	naseam	naseam	PROPN
ejpam-5131	306	22	al	al	PROPN
ejpam-5131	306	23	-	-	PUNCT
ejpam-5131	306	24	kuleab	kuleab	PROPN
ejpam-5131	306	25	,	,	PUNCT
ejpam-5131	306	26	and	and	CCONJ
ejpam-5131	306	27	abdoelnaser	abdoelnaser	PROPN
ejpam-5131	306	28	m	m	PROPN
ejpam-5131	306	29	degoot	degoot	PROPN
ejpam-5131	306	30	.	.	PUNCT
ejpam-5131	307	1	mathematical	mathematical	ADJ
ejpam-5131	307	2	modeling	modeling	NOUN
ejpam-5131	307	3	and	and	CCONJ
ejpam-5131	307	4	stability	stability	NOUN
ejpam-5131	307	5	analysis	analysis	NOUN
ejpam-5131	307	6	of	of	ADP
ejpam-5131	307	7	the	the	DET
ejpam-5131	307	8	novel	novel	ADJ
ejpam-5131	307	9	fractional	fractional	ADJ
ejpam-5131	307	10	model	model	NOUN
ejpam-5131	307	11	in	in	ADP
ejpam-5131	307	12	the	the	DET
ejpam-5131	307	13	caputo	caputo	PROPN
ejpam-5131	307	14	derivative	derivative	ADJ
ejpam-5131	307	15	operator	operator	NOUN
ejpam-5131	307	16	:	:	PUNCT
ejpam-5131	307	17	a	a	DET
ejpam-5131	307	18	case	case	NOUN
ejpam-5131	307	19	study	study	NOUN
ejpam-5131	307	20	.	.	PUNCT
ejpam-5131	308	1	heliyon	heliyon	NOUN
ejpam-5131	308	2	,	,	PUNCT
ejpam-5131	308	3	2024	2024	NUM
ejpam-5131	308	4	.	.	PUNCT
ejpam-5131	309	1	[	[	X
ejpam-5131	309	2	34	34	NUM
ejpam-5131	309	3	]	]	X
ejpam-5131	309	4	rania	rania	PROPN
ejpam-5131	309	5	saadeh	saadeh	PROPN
ejpam-5131	309	6	,	,	PUNCT
ejpam-5131	309	7	mohamed	mohamed	PROPN
ejpam-5131	309	8	a.	a.	PROPN
ejpam-5131	309	9	abdoon	abdoon	PROPN
ejpam-5131	309	10	,	,	PUNCT
ejpam-5131	309	11	ahmad	ahmad	PROPN
ejpam-5131	309	12	qazza	qazza	PROPN
ejpam-5131	309	13	,	,	PUNCT
ejpam-5131	309	14	fathelrhman	fathelrhman	NOUN
ejpam-5131	309	15	el	el	PROPN
ejpam-5131	309	16	guma	guma	PROPN
ejpam-5131	309	17	,	,	PUNCT
ejpam-5131	309	18	naseam	naseam	PROPN
ejpam-5131	309	19	al	al	PROPN
ejpam-5131	309	20	-	-	PUNCT
ejpam-5131	309	21	kuleab	kuleab	PROPN
ejpam-5131	309	22	,	,	PUNCT
ejpam-5131	309	23	and	and	CCONJ
ejpam-5131	309	24	abdoelnaser	abdoelnaser	PROPN
ejpam-5131	309	25	m.	m.	NOUN
ejpam-5131	309	26	degoot	degoot	PROPN
ejpam-5131	309	27	.	.	PUNCT
ejpam-5131	310	1	mathematical	mathematical	ADJ
ejpam-5131	310	2	modeling	modeling	NOUN
ejpam-5131	310	3	and	and	CCONJ
ejpam-5131	310	4	stability	stability	NOUN
ejpam-5131	310	5	analysis	analysis	NOUN
ejpam-5131	310	6	of	of	ADP
ejpam-5131	310	7	the	the	DET
ejpam-5131	310	8	novel	novel	ADJ
ejpam-5131	310	9	fractional	fractional	ADJ
ejpam-5131	310	10	model	model	NOUN
ejpam-5131	310	11	in	in	ADP
ejpam-5131	310	12	the	the	DET
ejpam-5131	310	13	caputo	caputo	PROPN
ejpam-5131	310	14	derivative	derivative	ADJ
ejpam-5131	310	15	operator	operator	NOUN
ejpam-5131	310	16	:	:	PUNCT
ejpam-5131	310	17	a	a	DET
ejpam-5131	310	18	case	case	NOUN
ejpam-5131	310	19	study	study	NOUN
ejpam-5131	310	20	.	.	PUNCT
ejpam-5131	311	1	heliyon	heliyon	NOUN
ejpam-5131	311	2	,	,	PUNCT
ejpam-5131	311	3	e26611(1):1	e26611(1):1	PROPN
ejpam-5131	311	4	,	,	PUNCT
ejpam-5131	311	5	2024	2024	NUM
ejpam-5131	311	6	.	.	PUNCT
ejpam-5131	312	1	[	[	X
ejpam-5131	312	2	35	35	NUM
ejpam-5131	312	3	]	]	PUNCT
ejpam-5131	312	4	sayed	say	VERB
ejpam-5131	312	5	saber	saber	PROPN
ejpam-5131	312	6	,	,	PUNCT
ejpam-5131	312	7	azza	azza	PROPN
ejpam-5131	312	8	m	m	PROPN
ejpam-5131	312	9	alghamdi	alghamdi	NOUN
ejpam-5131	312	10	,	,	PUNCT
ejpam-5131	312	11	ghada	ghada	NOUN
ejpam-5131	312	12	a	a	DET
ejpam-5131	312	13	ahmed	ahmed	PROPN
ejpam-5131	312	14	,	,	PUNCT
ejpam-5131	312	15	and	and	CCONJ
ejpam-5131	312	16	khulud	khulud	PROPN
ejpam-5131	312	17	m	m	PROPN
ejpam-5131	312	18	alshehri	alshehri	PROPN
ejpam-5131	312	19	.	.	PUNCT
ejpam-5131	313	1	mathematical	mathematical	ADJ
ejpam-5131	313	2	modelling	modelling	NOUN
ejpam-5131	313	3	and	and	CCONJ
ejpam-5131	313	4	optimal	optimal	ADJ
ejpam-5131	313	5	control	control	NOUN
ejpam-5131	313	6	of	of	ADP
ejpam-5131	313	7	pneumonia	pneumonia	NOUN
ejpam-5131	313	8	disease	disease	NOUN
ejpam-5131	313	9	in	in	ADP
ejpam-5131	313	10	sheep	sheep	NOUN
ejpam-5131	313	11	and	and	CCONJ
ejpam-5131	313	12	goats	goat	NOUN
ejpam-5131	313	13	in	in	ADP
ejpam-5131	313	14	al	al	PROPN
ejpam-5131	313	15	-	-	PUNCT
ejpam-5131	313	16	baha	baha	PROPN
ejpam-5131	313	17	region	region	NOUN
ejpam-5131	313	18	with	with	ADP
ejpam-5131	313	19	cost	cost	NOUN
ejpam-5131	313	20	-	-	PUNCT
ejpam-5131	313	21	effective	effective	ADJ
ejpam-5131	313	22	strategies	strategy	NOUN
ejpam-5131	313	23	.	.	PUNCT
ejpam-5131	314	1	aims	aim	VERB
ejpam-5131	314	2	mathematics	mathematic	NOUN
ejpam-5131	314	3	,	,	PUNCT
ejpam-5131	314	4	7(8):12011–12049	7(8):12011–12049	PROPN
ejpam-5131	314	5	,	,	PUNCT
ejpam-5131	314	6	2022	2022	NUM
ejpam-5131	314	7	.	.	PUNCT
ejpam-5131	315	1	[	[	X
ejpam-5131	315	2	36	36	NUM
ejpam-5131	315	3	]	]	X
ejpam-5131	315	4	l	l	NOUN
ejpam-5131	315	5	stenflo	stenflo	ADJ
ejpam-5131	315	6	.	.	PUNCT
ejpam-5131	316	1	generalized	generalize	VERB
ejpam-5131	316	2	lorenz	lorenz	PROPN
ejpam-5131	316	3	equations	equation	NOUN
ejpam-5131	316	4	for	for	ADP
ejpam-5131	316	5	acoustic	acoustic	ADJ
ejpam-5131	316	6	-	-	PUNCT
ejpam-5131	316	7	gravity	gravity	NOUN
ejpam-5131	316	8	waves	wave	NOUN
ejpam-5131	316	9	in	in	ADP
ejpam-5131	316	10	the	the	DET
ejpam-5131	316	11	atmosphere	atmosphere	NOUN
ejpam-5131	316	12	.	.	PUNCT
ejpam-5131	317	1	physica	physica	PROPN
ejpam-5131	317	2	scripta	scripta	PROPN
ejpam-5131	317	3	,	,	PUNCT
ejpam-5131	317	4	53(1):83	53(1):83	NUM
ejpam-5131	317	5	,	,	PUNCT
ejpam-5131	317	6	1996	1996	NUM
ejpam-5131	317	7	.	.	PUNCT
ejpam-5131	318	1	[	[	X
ejpam-5131	318	2	37	37	NUM
ejpam-5131	318	3	]	]	X
ejpam-5131	318	4	junwei	junwei	PROPN
ejpam-5131	318	5	sun	sun	PROPN
ejpam-5131	318	6	,	,	PUNCT
ejpam-5131	318	7	xingtong	xingtong	PROPN
ejpam-5131	318	8	zhao	zhao	PROPN
ejpam-5131	318	9	,	,	PUNCT
ejpam-5131	318	10	jie	jie	PROPN
ejpam-5131	318	11	fang	fang	PROPN
ejpam-5131	318	12	,	,	PUNCT
ejpam-5131	318	13	and	and	CCONJ
ejpam-5131	318	14	yanfeng	yanfeng	PROPN
ejpam-5131	318	15	wang	wang	PROPN
ejpam-5131	318	16	.	.	PUNCT
ejpam-5131	318	17	autonomous	autonomous	ADJ
ejpam-5131	318	18	memristor	memristor	PROPN
ejpam-5131	318	19	chaotic	chaotic	ADJ
ejpam-5131	318	20	systems	system	NOUN
ejpam-5131	318	21	of	of	ADP
ejpam-5131	318	22	infinite	infinite	ADJ
ejpam-5131	318	23	chaotic	chaotic	ADJ
ejpam-5131	318	24	attractors	attractor	NOUN
ejpam-5131	318	25	and	and	CCONJ
ejpam-5131	318	26	circuitry	circuitry	NOUN
ejpam-5131	318	27	realization	realization	NOUN
ejpam-5131	318	28	.	.	PUNCT
ejpam-5131	319	1	nonlinear	nonlinear	ADJ
ejpam-5131	319	2	dynamics	dynamic	NOUN
ejpam-5131	319	3	,	,	PUNCT
ejpam-5131	319	4	94:2879–2887	94:2879–2887	NUM
ejpam-5131	319	5	,	,	PUNCT
ejpam-5131	319	6	2018	2018	NUM
ejpam-5131	319	7	.	.	PUNCT
ejpam-5131	320	1	[	[	X
ejpam-5131	320	2	38	38	NUM
ejpam-5131	320	3	]	]	PUNCT
ejpam-5131	320	4	leimin	leimin	NOUN
ejpam-5131	320	5	wang	wang	PROPN
ejpam-5131	320	6	,	,	PUNCT
ejpam-5131	320	7	tiandu	tiandu	NOUN
ejpam-5131	320	8	dong	dong	PROPN
ejpam-5131	320	9	,	,	PUNCT
ejpam-5131	320	10	and	and	CCONJ
ejpam-5131	320	11	ming	ming	PROPN
ejpam-5131	320	12	-	-	PUNCT
ejpam-5131	320	13	feng	feng	PROPN
ejpam-5131	320	14	ge	ge	PROPN
ejpam-5131	320	15	.	.	PUNCT
ejpam-5131	321	1	finite	finite	ADJ
ejpam-5131	321	2	-	-	PUNCT
ejpam-5131	321	3	time	time	NOUN
ejpam-5131	321	4	synchronization	synchronization	NOUN
ejpam-5131	321	5	of	of	ADP
ejpam-5131	321	6	memristor	memristor	NOUN
ejpam-5131	321	7	chaotic	chaotic	ADJ
ejpam-5131	321	8	systems	system	NOUN
ejpam-5131	321	9	and	and	CCONJ
ejpam-5131	321	10	its	its	PRON
ejpam-5131	321	11	application	application	NOUN
ejpam-5131	321	12	in	in	ADP
ejpam-5131	321	13	image	image	NOUN
ejpam-5131	321	14	encryption	encryption	NOUN
ejpam-5131	321	15	.	.	PUNCT
ejpam-5131	322	1	applied	apply	VERB
ejpam-5131	322	2	mathematics	mathematic	NOUN
ejpam-5131	322	3	and	and	CCONJ
ejpam-5131	322	4	computation	computation	NOUN
ejpam-5131	322	5	,	,	PUNCT
ejpam-5131	322	6	347:293–305	347:293–305	NUM
ejpam-5131	322	7	,	,	PUNCT
ejpam-5131	322	8	2019	2019	NUM
ejpam-5131	322	9	.	.	PUNCT
ejpam-5131	323	1	[	[	X
ejpam-5131	323	2	39	39	NUM
ejpam-5131	323	3	]	]	PUNCT
ejpam-5131	323	4	shuang	shuang	PROPN
ejpam-5131	323	5	zhou	zhou	PROPN
ejpam-5131	323	6	and	and	CCONJ
ejpam-5131	323	7	xingyuan	xingyuan	PROPN
ejpam-5131	323	8	wang	wang	PROPN
ejpam-5131	323	9	.	.	PUNCT
ejpam-5131	324	1	simple	simple	ADJ
ejpam-5131	324	2	estimation	estimation	NOUN
ejpam-5131	324	3	method	method	NOUN
ejpam-5131	324	4	for	for	ADP
ejpam-5131	324	5	the	the	DET
ejpam-5131	324	6	largest	large	ADJ
ejpam-5131	324	7	lyapunov	lyapunov	ADJ
ejpam-5131	324	8	exponent	exponent	NOUN
ejpam-5131	324	9	of	of	ADP
ejpam-5131	324	10	continuous	continuous	ADJ
ejpam-5131	324	11	fractional	fractional	ADJ
ejpam-5131	324	12	-	-	PUNCT
ejpam-5131	324	13	order	order	NOUN
ejpam-5131	324	14	differential	differential	ADJ
ejpam-5131	324	15	equations	equation	NOUN
ejpam-5131	324	16	.	.	PUNCT
ejpam-5131	325	1	physica	physica	VERB
ejpam-5131	325	2	a	a	DET
ejpam-5131	325	3	:	:	PUNCT
ejpam-5131	325	4	statistical	statistical	ADJ
ejpam-5131	325	5	mechanics	mechanic	NOUN
ejpam-5131	325	6	and	and	CCONJ
ejpam-5131	325	7	its	its	PRON
ejpam-5131	325	8	applications	application	NOUN
ejpam-5131	325	9	,	,	PUNCT
ejpam-5131	325	10	563:125478	563:125478	NUM
ejpam-5131	325	11	,	,	PUNCT
ejpam-5131	325	12	2021	2021	NUM
ejpam-5131	325	13	.	.	PUNCT