id	sid	tid	token	lemma	pos
ejpam-5495	1	1	european	european	PROPN
ejpam-5495	1	2	journal	journal	PROPN
ejpam-5495	1	3	of	of	ADP
ejpam-5495	1	4	pure	pure	ADJ
ejpam-5495	1	5	and	and	CCONJ
ejpam-5495	1	6	applied	applied	ADJ
ejpam-5495	1	7	mathematics	mathematic	NOUN
ejpam-5495	1	8	2025	2025	NUM
ejpam-5495	1	9	,	,	PUNCT
ejpam-5495	1	10	vol	vol	NOUN
ejpam-5495	1	11	.	.	PROPN
ejpam-5495	1	12	18	18	NUM
ejpam-5495	1	13	,	,	PUNCT
ejpam-5495	1	14	issue	issue	NOUN
ejpam-5495	1	15	1	1	NUM
ejpam-5495	1	16	,	,	PUNCT
ejpam-5495	1	17	article	article	NOUN
ejpam-5495	1	18	number	number	NOUN
ejpam-5495	1	19	5495	5495	NUM
ejpam-5495	1	20	issn	issn	PROPN
ejpam-5495	1	21	1307	1307	NUM
ejpam-5495	1	22	-	-	SYM
ejpam-5495	1	23	5543	5543	NUM
ejpam-5495	1	24	–	–	PUNCT
ejpam-5495	1	25	ejpam.com	ejpam.com	X
ejpam-5495	1	26	published	publish	VERB
ejpam-5495	1	27	by	by	ADP
ejpam-5495	1	28	new	new	PROPN
ejpam-5495	1	29	york	york	PROPN
ejpam-5495	1	30	business	business	PROPN
ejpam-5495	1	31	global	global	ADJ
ejpam-5495	1	32	non	non	ADJ
ejpam-5495	1	33	-	-	ADJ
ejpam-5495	1	34	perturbative	perturbative	ADJ
ejpam-5495	1	35	approach	approach	NOUN
ejpam-5495	1	36	in	in	ADP
ejpam-5495	1	37	scrutinizing	scrutinize	VERB
ejpam-5495	1	38	nonlinear	nonlinear	ADJ
ejpam-5495	1	39	time	time	NOUN
ejpam-5495	1	40	-	-	PUNCT
ejpam-5495	1	41	delay	delay	NOUN
ejpam-5495	1	42	of	of	ADP
ejpam-5495	1	43	van	van	PROPN
ejpam-5495	1	44	der	der	PROPN
ejpam-5495	1	45	pol	pol	PROPN
ejpam-5495	1	46	-	-	PUNCT
ejpam-5495	1	47	duffing	duffe	VERB
ejpam-5495	1	48	oscillator	oscillator	NOUN
ejpam-5495	1	49	asma	asma	PROPN
ejpam-5495	1	50	alanazy1	alanazy1	PROPN
ejpam-5495	1	51	,	,	PUNCT
ejpam-5495	1	52	galal	galal	PROPN
ejpam-5495	1	53	m.	m.	NOUN
ejpam-5495	1	54	moatimid2	moatimid2	PROPN
ejpam-5495	1	55	,	,	PUNCT
ejpam-5495	1	56	t.	t.	PROPN
ejpam-5495	1	57	s.	s.	PROPN
ejpam-5495	1	58	amer3	amer3	PROPN
ejpam-5495	1	59	,	,	PUNCT
ejpam-5495	1	60	a.	a.	PROPN
ejpam-5495	1	61	a.	a.	PROPN
ejpam-5495	1	62	galal4,∗	galal4,∗	PROPN
ejpam-5495	1	63	1	1	NUM
ejpam-5495	1	64	mathematics	mathematics	PROPN
ejpam-5495	1	65	department	department	NOUN
ejpam-5495	1	66	,	,	PUNCT
ejpam-5495	1	67	northern	northern	ADJ
ejpam-5495	1	68	border	border	NOUN
ejpam-5495	1	69	university	university	NOUN
ejpam-5495	1	70	,	,	PUNCT
ejpam-5495	1	71	arar	arar	NOUN
ejpam-5495	1	72	1321	1321	NUM
ejpam-5495	1	73	,	,	PUNCT
ejpam-5495	1	74	ksa	ksa	PROPN
ejpam-5495	1	75	2	2	NUM
ejpam-5495	1	76	department	department	NOUN
ejpam-5495	1	77	of	of	ADP
ejpam-5495	1	78	mathematics	mathematic	NOUN
ejpam-5495	1	79	,	,	PUNCT
ejpam-5495	1	80	faculty	faculty	NOUN
ejpam-5495	1	81	of	of	ADP
ejpam-5495	1	82	education	education	NOUN
ejpam-5495	1	83	,	,	PUNCT
ejpam-5495	1	84	ain	ain	PROPN
ejpam-5495	1	85	shams	shams	PROPN
ejpam-5495	1	86	university	university	PROPN
ejpam-5495	1	87	,	,	PUNCT
ejpam-5495	1	88	egypt	egypt	PROPN
ejpam-5495	1	89	3	3	NUM
ejpam-5495	1	90	department	department	NOUN
ejpam-5495	1	91	of	of	ADP
ejpam-5495	1	92	mathematics	mathematic	NOUN
ejpam-5495	1	93	,	,	PUNCT
ejpam-5495	1	94	faculty	faculty	NOUN
ejpam-5495	1	95	of	of	ADP
ejpam-5495	1	96	science	science	NOUN
ejpam-5495	1	97	,	,	PUNCT
ejpam-5495	1	98	tanta	tanta	PROPN
ejpam-5495	1	99	university	university	PROPN
ejpam-5495	1	100	,	,	PUNCT
ejpam-5495	1	101	tanta	tanta	PROPN
ejpam-5495	1	102	31527	31527	NUM
ejpam-5495	1	103	,	,	PUNCT
ejpam-5495	1	104	egypt	egypt	PROPN
ejpam-5495	1	105	4	4	NUM
ejpam-5495	1	106	department	department	NOUN
ejpam-5495	1	107	of	of	ADP
ejpam-5495	1	108	engineering	engineering	NOUN
ejpam-5495	1	109	physics	physics	PROPN
ejpam-5495	1	110	and	and	CCONJ
ejpam-5495	1	111	mathematics	mathematic	NOUN
ejpam-5495	1	112	,	,	PUNCT
ejpam-5495	1	113	faculty	faculty	NOUN
ejpam-5495	1	114	of	of	ADP
ejpam-5495	1	115	engineering	engineering	PROPN
ejpam-5495	1	116	,	,	PUNCT
ejpam-5495	1	117	tanta	tanta	PROPN
ejpam-5495	1	118	university	university	PROPN
ejpam-5495	1	119	,	,	PUNCT
ejpam-5495	1	120	tanta	tanta	PROPN
ejpam-5495	1	121	31734	31734	NUM
ejpam-5495	1	122	,	,	PUNCT
ejpam-5495	1	123	egypt	egypt	PROPN
ejpam-5495	1	124	abstract	abstract	PROPN
ejpam-5495	1	125	.	.	PUNCT
ejpam-5495	2	1	the	the	DET
ejpam-5495	2	2	time	time	NOUN
ejpam-5495	2	3	-	-	PUNCT
ejpam-5495	2	4	delayed	delay	VERB
ejpam-5495	2	5	(	(	PUNCT
ejpam-5495	2	6	td	td	NOUN
ejpam-5495	2	7	)	)	PUNCT
ejpam-5495	2	8	of	of	ADP
ejpam-5495	2	9	velocity	velocity	NOUN
ejpam-5495	2	10	and	and	CCONJ
ejpam-5495	2	11	position	position	NOUN
ejpam-5495	2	12	are	be	AUX
ejpam-5495	2	13	employed	employ	VERB
ejpam-5495	2	14	throughout	throughout	ADP
ejpam-5495	2	15	this	this	DET
ejpam-5495	2	16	investigation	investigation	NOUN
ejpam-5495	2	17	to	to	PART
ejpam-5495	2	18	lessen	lessen	VERB
ejpam-5495	2	19	the	the	DET
ejpam-5495	2	20	nonlinear	nonlinear	ADJ
ejpam-5495	2	21	vibration	vibration	NOUN
ejpam-5495	2	22	of	of	ADP
ejpam-5495	2	23	an	an	DET
ejpam-5495	2	24	exciting	exciting	ADJ
ejpam-5495	2	25	van	van	PROPN
ejpam-5495	2	26	der	der	ADJ
ejpam-5495	2	27	pol	pol	PROPN
ejpam-5495	2	28	-	-	PUNCT
ejpam-5495	2	29	duffing	duffe	VERB
ejpam-5495	2	30	oscillator	oscillator	NOUN
ejpam-5495	2	31	(	(	PUNCT
ejpam-5495	2	32	vdpd	vdpd	NOUN
ejpam-5495	2	33	)	)	PUNCT
ejpam-5495	2	34	.	.	PUNCT
ejpam-5495	3	1	the	the	DET
ejpam-5495	3	2	issue	issue	NOUN
ejpam-5495	3	3	encompasses	encompass	VERB
ejpam-5495	3	4	multiple	multiple	ADJ
ejpam-5495	3	5	real	real	ADJ
ejpam-5495	3	6	-	-	PUNCT
ejpam-5495	3	7	world	world	NOUN
ejpam-5495	3	8	elements	element	NOUN
ejpam-5495	3	9	such	such	ADJ
ejpam-5495	3	10	as	as	ADP
ejpam-5495	3	11	feedback	feedback	NOUN
ejpam-5495	3	12	lags	lag	NOUN
ejpam-5495	3	13	,	,	PUNCT
ejpam-5495	3	14	signal	signal	ADJ
ejpam-5495	3	15	transmission	transmission	NOUN
ejpam-5495	3	16	delays	delay	NOUN
ejpam-5495	3	17	,	,	PUNCT
ejpam-5495	3	18	and	and	CCONJ
ejpam-5495	3	19	delayed	delay	VERB
ejpam-5495	3	20	responses	response	NOUN
ejpam-5495	3	21	in	in	ADP
ejpam-5495	3	22	mechanical	mechanical	ADJ
ejpam-5495	3	23	,	,	PUNCT
ejpam-5495	3	24	electrical	electrical	ADJ
ejpam-5495	3	25	,	,	PUNCT
ejpam-5495	3	26	or	or	CCONJ
ejpam-5495	3	27	biological	biological	ADJ
ejpam-5495	3	28	systems	system	NOUN
ejpam-5495	3	29	.	.	PUNCT
ejpam-5495	4	1	examining	examine	VERB
ejpam-5495	4	2	this	this	DET
ejpam-5495	4	3	oscillator	oscillator	NOUN
ejpam-5495	4	4	facilitates	facilitate	VERB
ejpam-5495	4	5	the	the	DET
ejpam-5495	4	6	investigation	investigation	NOUN
ejpam-5495	4	7	of	of	ADP
ejpam-5495	4	8	complex	complex	ADJ
ejpam-5495	4	9	dynamics	dynamic	NOUN
ejpam-5495	4	10	,	,	PUNCT
ejpam-5495	4	11	including	include	VERB
ejpam-5495	4	12	chaos	chaos	NOUN
ejpam-5495	4	13	,	,	PUNCT
ejpam-5495	4	14	bifurcations	bifurcation	NOUN
ejpam-5495	4	15	,	,	PUNCT
ejpam-5495	4	16	and	and	CCONJ
ejpam-5495	4	17	stability	stability	NOUN
ejpam-5495	4	18	alterations	alteration	NOUN
ejpam-5495	4	19	,	,	PUNCT
ejpam-5495	4	20	making	make	VERB
ejpam-5495	4	21	it	it	PRON
ejpam-5495	4	22	essential	essential	ADJ
ejpam-5495	4	23	for	for	ADP
ejpam-5495	4	24	disciplines	discipline	NOUN
ejpam-5495	4	25	like	like	ADP
ejpam-5495	4	26	control	control	NOUN
ejpam-5495	4	27	theory	theory	NOUN
ejpam-5495	4	28	,	,	PUNCT
ejpam-5495	4	29	engineering	engineering	NOUN
ejpam-5495	4	30	,	,	PUNCT
ejpam-5495	4	31	and	and	CCONJ
ejpam-5495	4	32	neuroscience	neuroscience	NOUN
ejpam-5495	4	33	.	.	PUNCT
ejpam-5495	5	1	the	the	DET
ejpam-5495	5	2	current	current	ADJ
ejpam-5495	5	3	oscillator	oscillator	NOUN
ejpam-5495	5	4	is	be	AUX
ejpam-5495	5	5	analyzed	analyze	VERB
ejpam-5495	5	6	using	use	VERB
ejpam-5495	5	7	using	use	VERB
ejpam-5495	5	8	the	the	DET
ejpam-5495	5	9	non	non	ADJ
ejpam-5495	5	10	-	-	ADJ
ejpam-5495	5	11	perturbative	perturbative	ADJ
ejpam-5495	5	12	approach	approach	NOUN
ejpam-5495	5	13	(	(	PUNCT
ejpam-5495	5	14	npa	npa	NOUN
ejpam-5495	5	15	)	)	PUNCT
ejpam-5495	5	16	.	.	PUNCT
ejpam-5495	6	1	this	this	DET
ejpam-5495	6	2	methodology	methodology	NOUN
ejpam-5495	6	3	is	be	AUX
ejpam-5495	6	4	based	base	VERB
ejpam-5495	6	5	mainly	mainly	ADV
ejpam-5495	6	6	on	on	ADP
ejpam-5495	6	7	the	the	DET
ejpam-5495	6	8	he	he	PRON
ejpam-5495	6	9	’s	’s	PART
ejpam-5495	6	10	frequency	frequency	NOUN
ejpam-5495	6	11	formula	formula	NOUN
ejpam-5495	6	12	(	(	PUNCT
ejpam-5495	6	13	hff	hff	NOUN
ejpam-5495	6	14	)	)	PUNCT
ejpam-5495	6	15	.	.	PUNCT
ejpam-5495	7	1	simply	simply	ADV
ejpam-5495	7	2	,	,	PUNCT
ejpam-5495	7	3	this	this	DET
ejpam-5495	7	4	approach	approach	NOUN
ejpam-5495	7	5	transforms	transform	VERB
ejpam-5495	7	6	the	the	DET
ejpam-5495	7	7	nonlinear	nonlinear	ADJ
ejpam-5495	7	8	ordinary	ordinary	ADJ
ejpam-5495	7	9	differential	differential	ADJ
ejpam-5495	7	10	equation	equation	NOUN
ejpam-5495	7	11	(	(	PUNCT
ejpam-5495	7	12	ode	ode	PROPN
ejpam-5495	7	13	)	)	PUNCT
ejpam-5495	7	14	into	into	ADP
ejpam-5495	7	15	a	a	DET
ejpam-5495	7	16	linear	linear	ADJ
ejpam-5495	7	17	one	one	NUM
ejpam-5495	7	18	.	.	PUNCT
ejpam-5495	8	1	accordingly	accordingly	ADV
ejpam-5495	8	2	,	,	PUNCT
ejpam-5495	8	3	the	the	DET
ejpam-5495	8	4	stability	stability	NOUN
ejpam-5495	8	5	standards	standard	NOUN
ejpam-5495	8	6	are	be	AUX
ejpam-5495	8	7	constructed	construct	VERB
ejpam-5495	8	8	,	,	PUNCT
ejpam-5495	8	9	depicted	depict	VERB
ejpam-5495	8	10	,	,	PUNCT
ejpam-5495	8	11	and	and	CCONJ
ejpam-5495	8	12	sketched	sketch	VERB
ejpam-5495	8	13	.	.	PUNCT
ejpam-5495	9	1	the	the	DET
ejpam-5495	9	2	analytical	analytical	ADJ
ejpam-5495	9	3	solution	solution	NOUN
ejpam-5495	9	4	(	(	PUNCT
ejpam-5495	9	5	as	as	ADP
ejpam-5495	9	6	)	)	PUNCT
ejpam-5495	9	7	with	with	ADP
ejpam-5495	9	8	the	the	DET
ejpam-5495	9	9	associated	associated	PROPN
ejpam-5495	9	10	numerical	numerical	PROPN
ejpam-5495	9	11	data	datum	NOUN
ejpam-5495	9	12	that	that	PRON
ejpam-5495	9	13	reveals	reveal	VERB
ejpam-5495	9	14	high	high	ADJ
ejpam-5495	9	15	nonlinearity	nonlinearity	NOUN
ejpam-5495	9	16	,	,	PUNCT
ejpam-5495	9	17	and	and	CCONJ
ejpam-5495	9	18	the	the	DET
ejpam-5495	9	19	numerical	numerical	ADJ
ejpam-5495	9	20	estimation	estimation	NOUN
ejpam-5495	9	21	is	be	AUX
ejpam-5495	9	22	validated	validate	VERB
ejpam-5495	9	23	via	via	ADP
ejpam-5495	9	24	the	the	DET
ejpam-5495	9	25	mathematica	mathematica	PROPN
ejpam-5495	9	26	software	software	PROPN
ejpam-5495	9	27	(	(	PUNCT
ejpam-5495	9	28	ms	ms	NOUN
ejpam-5495	9	29	)	)	PUNCT
ejpam-5495	9	30	.	.	PUNCT
ejpam-5495	10	1	in	in	ADP
ejpam-5495	10	2	contrast	contrast	NOUN
ejpam-5495	10	3	to	to	ADP
ejpam-5495	10	4	other	other	ADJ
ejpam-5495	10	5	traditional	traditional	ADJ
ejpam-5495	10	6	perturbation	perturbation	NOUN
ejpam-5495	10	7	methods	method	NOUN
ejpam-5495	10	8	,	,	PUNCT
ejpam-5495	10	9	the	the	DET
ejpam-5495	10	10	npa	npa	NOUN
ejpam-5495	10	11	exhibits	exhibit	VERB
ejpam-5495	10	12	high	high	ADJ
ejpam-5495	10	13	convenience	convenience	NOUN
ejpam-5495	10	14	,	,	PUNCT
ejpam-5495	10	15	accessibility	accessibility	NOUN
ejpam-5495	10	16	,	,	PUNCT
ejpam-5495	10	17	and	and	CCONJ
ejpam-5495	10	18	great	great	ADJ
ejpam-5495	10	19	precision	precision	NOUN
ejpam-5495	10	20	in	in	ADP
ejpam-5495	10	21	analyzing	analyze	VERB
ejpam-5495	10	22	the	the	DET
ejpam-5495	10	23	behavior	behavior	NOUN
ejpam-5495	10	24	of	of	ADP
ejpam-5495	10	25	strong	strong	ADJ
ejpam-5495	10	26	nonlinear	nonlinear	ADJ
ejpam-5495	10	27	oscillators	oscillator	NOUN
ejpam-5495	10	28	.	.	PUNCT
ejpam-5495	11	1	subsequently	subsequently	ADV
ejpam-5495	11	2	,	,	PUNCT
ejpam-5495	11	3	this	this	DET
ejpam-5495	11	4	technique	technique	NOUN
ejpam-5495	11	5	enables	enable	VERB
ejpam-5495	11	6	the	the	DET
ejpam-5495	11	7	analysis	analysis	NOUN
ejpam-5495	11	8	of	of	ADP
ejpam-5495	11	9	issues	issue	NOUN
ejpam-5495	11	10	related	relate	VERB
ejpam-5495	11	11	to	to	ADP
ejpam-5495	11	12	other	other	ADJ
ejpam-5495	11	13	oscillators	oscillator	NOUN
ejpam-5495	11	14	in	in	ADP
ejpam-5495	11	15	the	the	DET
ejpam-5495	11	16	dynamical	dynamical	ADJ
ejpam-5495	11	17	systems	system	NOUN
ejpam-5495	11	18	.	.	PUNCT
ejpam-5495	12	1	it	it	PRON
ejpam-5495	12	2	is	be	AUX
ejpam-5495	12	3	an	an	DET
ejpam-5495	12	4	effective	effective	ADJ
ejpam-5495	12	5	and	and	CCONJ
ejpam-5495	12	6	promising	promising	ADJ
ejpam-5495	12	7	method	method	NOUN
ejpam-5495	12	8	for	for	ADP
ejpam-5495	12	9	addressing	address	VERB
ejpam-5495	12	10	similar	similar	ADJ
ejpam-5495	12	11	dynamic	dynamic	ADJ
ejpam-5495	12	12	system	system	NOUN
ejpam-5495	12	13	challenges	challenge	NOUN
ejpam-5495	12	14	,	,	PUNCT
ejpam-5495	12	15	providing	provide	VERB
ejpam-5495	12	16	a	a	DET
ejpam-5495	12	17	qualitative	qualitative	ADJ
ejpam-5495	12	18	assessment	assessment	NOUN
ejpam-5495	12	19	of	of	ADP
ejpam-5495	12	20	theoretical	theoretical	ADJ
ejpam-5495	12	21	outcomes	outcome	NOUN
ejpam-5495	12	22	.	.	PUNCT
ejpam-5495	13	1	the	the	DET
ejpam-5495	13	2	study	study	NOUN
ejpam-5495	13	3	describes	describe	VERB
ejpam-5495	13	4	time	time	NOUN
ejpam-5495	13	5	histories	history	NOUN
ejpam-5495	13	6	of	of	ADP
ejpam-5495	13	7	solutions	solution	NOUN
ejpam-5495	13	8	for	for	ADP
ejpam-5495	13	9	different	different	ADJ
ejpam-5495	13	10	natural	natural	ADJ
ejpam-5495	13	11	frequencies	frequency	NOUN
ejpam-5495	13	12	and	and	CCONJ
ejpam-5495	13	13	td	td	NOUN
ejpam-5495	13	14	parameters	parameter	NOUN
ejpam-5495	13	15	and	and	CCONJ
ejpam-5495	13	16	discusses	discuss	VERB
ejpam-5495	13	17	the	the	DET
ejpam-5495	13	18	main	main	ADJ
ejpam-5495	13	19	findings	finding	NOUN
ejpam-5495	13	20	based	base	VERB
ejpam-5495	13	21	on	on	ADP
ejpam-5495	13	22	displayed	display	VERB
ejpam-5495	13	23	curves	curve	NOUN
ejpam-5495	13	24	.	.	PUNCT
ejpam-5495	14	1	it	it	PRON
ejpam-5495	14	2	also	also	ADV
ejpam-5495	14	3	examines	examine	VERB
ejpam-5495	14	4	how	how	SCONJ
ejpam-5495	14	5	various	various	ADJ
ejpam-5495	14	6	regulatory	regulatory	ADJ
ejpam-5495	14	7	limits	limit	NOUN
ejpam-5495	14	8	impact	impact	VERB
ejpam-5495	14	9	the	the	DET
ejpam-5495	14	10	vibrating	vibrating	NOUN
ejpam-5495	14	11	system	system	NOUN
ejpam-5495	14	12	.	.	PUNCT
ejpam-5495	15	1	the	the	DET
ejpam-5495	15	2	performance	performance	NOUN
ejpam-5495	15	3	is	be	AUX
ejpam-5495	15	4	applicable	applicable	ADJ
ejpam-5495	15	5	in	in	ADP
ejpam-5495	15	6	engineering	engineering	NOUN
ejpam-5495	15	7	and	and	CCONJ
ejpam-5495	15	8	other	other	ADJ
ejpam-5495	15	9	domains	domain	NOUN
ejpam-5495	15	10	owing	owe	VERB
ejpam-5495	15	11	to	to	ADP
ejpam-5495	15	12	its	its	PRON
ejpam-5495	15	13	flexibility	flexibility	NOUN
ejpam-5495	15	14	in	in	ADP
ejpam-5495	15	15	various	various	ADJ
ejpam-5495	15	16	nonlinear	nonlinear	ADJ
ejpam-5495	15	17	systems	system	NOUN
ejpam-5495	15	18	.	.	PUNCT
ejpam-5495	16	1	consequently	consequently	ADV
ejpam-5495	16	2	,	,	PUNCT
ejpam-5495	16	3	the	the	DET
ejpam-5495	16	4	npa	npa	NOUN
ejpam-5495	16	5	can	can	AUX
ejpam-5495	16	6	be	be	AUX
ejpam-5495	16	7	considered	consider	VERB
ejpam-5495	16	8	significant	significant	ADJ
ejpam-5495	16	9	,	,	PUNCT
ejpam-5495	16	10	effective	effective	ADJ
ejpam-5495	16	11	,	,	PUNCT
ejpam-5495	16	12	and	and	CCONJ
ejpam-5495	16	13	intriguing	intriguing	ADJ
ejpam-5495	16	14	,	,	PUNCT
ejpam-5495	16	15	with	with	ADP
ejpam-5495	16	16	potential	potential	NOUN
ejpam-5495	16	17	for	for	ADP
ejpam-5495	16	18	use	use	NOUN
ejpam-5495	16	19	in	in	ADP
ejpam-5495	16	20	more	more	ADJ
ejpam-5495	16	21	categories	category	NOUN
ejpam-5495	16	22	within	within	ADP
ejpam-5495	16	23	the	the	DET
ejpam-5495	16	24	domain	domain	NOUN
ejpam-5495	16	25	of	of	ADP
ejpam-5495	16	26	coupled	couple	VERB
ejpam-5495	16	27	dynamical	dynamical	ADJ
ejpam-5495	16	28	systems	system	NOUN
ejpam-5495	16	29	.	.	PUNCT
ejpam-5495	17	1	2020	2020	NUM
ejpam-5495	17	2	mathematics	mathematic	NOUN
ejpam-5495	17	3	subject	subject	NOUN
ejpam-5495	17	4	classifications	classification	NOUN
ejpam-5495	17	5	:	:	PUNCT
ejpam-5495	17	6	70e50	70e50	NUM
ejpam-5495	17	7	,	,	PUNCT
ejpam-5495	17	8	74h55	74h55	NUM
ejpam-5495	17	9	,	,	PUNCT
ejpam-5495	17	10	34k20	34k20	NUM
ejpam-5495	17	11	,	,	PUNCT
ejpam-5495	17	12	70k50	70k50	NUM
ejpam-5495	17	13	,	,	PUNCT
ejpam-5495	17	14	74s99	74s99	NOUN
ejpam-5495	17	15	key	key	NOUN
ejpam-5495	17	16	words	word	NOUN
ejpam-5495	17	17	and	and	CCONJ
ejpam-5495	17	18	phrases	phrase	NOUN
ejpam-5495	17	19	:	:	PUNCT
ejpam-5495	17	20	non	non	ADJ
ejpam-5495	17	21	-	-	ADJ
ejpam-5495	17	22	perturbative	perturbative	ADJ
ejpam-5495	17	23	approach	approach	NOUN
ejpam-5495	17	24	,	,	PUNCT
ejpam-5495	17	25	he	he	PRON
ejpam-5495	17	26	’s	’	VERB
ejpam-5495	17	27	frequency	frequency	NOUN
ejpam-5495	17	28	formula	formula	NOUN
ejpam-5495	17	29	,	,	PUNCT
ejpam-5495	17	30	nonlinear	nonlinear	ADJ
ejpam-5495	17	31	oscillations	oscillation	NOUN
ejpam-5495	17	32	,	,	PUNCT
ejpam-5495	17	33	position	position	NOUN
ejpam-5495	17	34	-	-	PUNCT
ejpam-5495	17	35	velocity	velocity	NOUN
ejpam-5495	17	36	time	time	NOUN
ejpam-5495	17	37	-	-	PUNCT
ejpam-5495	17	38	delays	delay	NOUN
ejpam-5495	17	39	,	,	PUNCT
ejpam-5495	17	40	instability	instability	NOUN
ejpam-5495	17	41	configuration	configuration	NOUN
ejpam-5495	17	42	,	,	PUNCT
ejpam-5495	17	43	time	time	NOUN
ejpam-5495	17	44	histories	history	NOUN
ejpam-5495	17	45	,	,	PUNCT
ejpam-5495	17	46	parametric	parametric	ADJ
ejpam-5495	17	47	resonance	resonance	NOUN
ejpam-5495	17	48	∗corresponding	∗corresponde	VERB
ejpam-5495	17	49	author	author	NOUN
ejpam-5495	17	50	.	.	PUNCT
ejpam-5495	18	1	doi	doi	NOUN
ejpam-5495	18	2	:	:	PUNCT
ejpam-5495	18	3	https://doi.org/10.29020/nybg.ejpam.v18i1.5495	https://doi.org/10.29020/nybg.ejpam.v18i1.5495	ADJ
ejpam-5495	18	4	email	email	NOUN
ejpam-5495	18	5	address	address	NOUN
ejpam-5495	18	6	:	:	PUNCT
ejpam-5495	18	7	abdallah.galal@f-eng.tanta.edu.eg	abdallah.galal@f-eng.tanta.edu.eg	PROPN
ejpam-5495	18	8	(	(	PUNCT
ejpam-5495	18	9	a.	a.	NOUN
ejpam-5495	18	10	a.	a.	PROPN
ejpam-5495	18	11	galal	galal	PROPN
ejpam-5495	18	12	)	)	PUNCT
ejpam-5495	18	13	,	,	PUNCT
ejpam-5495	18	14	asma.jazza@nbu.edu.sa	asma.jazza@nbu.edu.sa	PROPN
ejpam-5495	18	15	(	(	PUNCT
ejpam-5495	18	16	a.	a.	NOUN
ejpam-5495	18	17	alanazy	alanazy	NOUN
ejpam-5495	18	18	)	)	PUNCT
ejpam-5495	18	19	,	,	PUNCT
ejpam-5495	18	20	tarek.saleh@science.tanta.edu.eg	tarek.saleh@science.tanta.edu.eg	X
ejpam-5495	18	21	(	(	PUNCT
ejpam-5495	18	22	t.	t.	PROPN
ejpam-5495	18	23	s.	s.	PROPN
ejpam-5495	18	24	amer	amer	PROPN
ejpam-5495	18	25	)	)	PUNCT
ejpam-5495	18	26	,	,	PUNCT
ejpam-5495	18	27	gal	gal	ADJ
ejpam-5495	18	28	moa@edu.asu.edu.eg	moa@edu.asu.edu.eg	PROPN
ejpam-5495	18	29	(	(	PUNCT
ejpam-5495	18	30	g.	g.	PROPN
ejpam-5495	18	31	m.	m.	PROPN
ejpam-5495	18	32	moatimid	moatimid	PROPN
ejpam-5495	18	33	)	)	PUNCT
ejpam-5495	18	34	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5495	19	1	1	1	NUM
ejpam-5495	19	2	copyright	copyright	NOUN
ejpam-5495	19	3	:	:	PUNCT
ejpam-5495	19	4	©	©	PROPN
ejpam-5495	19	5	2025	2025	NUM
ejpam-5495	19	6	the	the	DET
ejpam-5495	19	7	author(s	author(s	NOUN
ejpam-5495	19	8	)	)	PUNCT
ejpam-5495	19	9	.	.	PUNCT
ejpam-5495	20	1	(	(	PUNCT
ejpam-5495	20	2	cc	cc	NOUN
ejpam-5495	20	3	by	by	ADP
ejpam-5495	20	4	-	-	PUNCT
ejpam-5495	20	5	nc	nc	PROPN
ejpam-5495	20	6	4.0	4.0	NUM
ejpam-5495	20	7	)	)	PUNCT
ejpam-5495	20	8	a.	a.	NOUN
ejpam-5495	20	9	alanazy	alanazy	NOUN
ejpam-5495	20	10	et	et	PROPN
ejpam-5495	20	11	al	al	PROPN
ejpam-5495	20	12	.	.	PUNCT
ejpam-5495	20	13	/	/	SYM
ejpam-5495	20	14	eur	eur	PROPN
ejpam-5495	20	15	.	.	PUNCT
ejpam-5495	21	1	j.	j.	PROPN
ejpam-5495	21	2	pure	pure	PROPN
ejpam-5495	21	3	appl	appl	PROPN
ejpam-5495	21	4	.	.	PROPN
ejpam-5495	21	5	math	math	PROPN
ejpam-5495	21	6	,	,	PUNCT
ejpam-5495	21	7	18	18	NUM
ejpam-5495	21	8	(	(	PUNCT
ejpam-5495	21	9	1	1	NUM
ejpam-5495	21	10	)	)	PUNCT
ejpam-5495	21	11	(	(	PUNCT
ejpam-5495	21	12	2025	2025	NUM
ejpam-5495	21	13	)	)	PUNCT
ejpam-5495	21	14	,	,	PUNCT
ejpam-5495	21	15	5495	5495	NUM
ejpam-5495	21	16	2	2	NUM
ejpam-5495	21	17	of	of	ADP
ejpam-5495	21	18	21	21	NUM
ejpam-5495	21	19	1	1	NUM
ejpam-5495	21	20	.	.	PUNCT
ejpam-5495	22	1	introduction	introduction	NOUN
ejpam-5495	22	2	most	most	ADJ
ejpam-5495	22	3	equipment	equipment	NOUN
ejpam-5495	22	4	,	,	PUNCT
ejpam-5495	22	5	cars	car	NOUN
ejpam-5495	22	6	,	,	PUNCT
ejpam-5495	22	7	structures	structure	NOUN
ejpam-5495	22	8	,	,	PUNCT
ejpam-5495	22	9	buildings	building	NOUN
ejpam-5495	22	10	,	,	PUNCT
ejpam-5495	22	11	and	and	CCONJ
ejpam-5495	22	12	dynamical	dynamical	ADJ
ejpam-5495	22	13	systems	system	NOUN
ejpam-5495	22	14	are	be	AUX
ejpam-5495	22	15	fundamentally	fundamentally	ADV
ejpam-5495	22	16	vibrating	vibrate	VERB
ejpam-5495	22	17	,	,	PUNCT
ejpam-5495	22	18	which	which	PRON
ejpam-5495	22	19	is	be	AUX
ejpam-5495	22	20	a	a	DET
ejpam-5495	22	21	negative	negative	ADJ
ejpam-5495	22	22	phenomenon	phenomenon	NOUN
ejpam-5495	22	23	because	because	SCONJ
ejpam-5495	22	24	of	of	ADP
ejpam-5495	22	25	the	the	DET
ejpam-5495	22	26	occurrence	occurrence	NOUN
ejpam-5495	22	27	of	of	ADP
ejpam-5495	22	28	undesirable	undesirable	ADJ
ejpam-5495	22	29	vibrations	vibration	NOUN
ejpam-5495	22	30	.	.	PUNCT
ejpam-5495	23	1	damaging	damage	VERB
ejpam-5495	23	2	dynamical	dynamical	ADJ
ejpam-5495	23	3	stresses	stress	NOUN
ejpam-5495	23	4	may	may	AUX
ejpam-5495	23	5	cause	cause	VERB
ejpam-5495	23	6	a	a	DET
ejpam-5495	23	7	breakdown	breakdown	NOUN
ejpam-5495	23	8	of	of	ADP
ejpam-5495	23	9	the	the	DET
ejpam-5495	23	10	framework	framework	NOUN
ejpam-5495	23	11	or	or	CCONJ
ejpam-5495	23	12	machine	machine	NOUN
ejpam-5495	23	13	,	,	PUNCT
ejpam-5495	23	14	energy	energy	NOUN
ejpam-5495	23	15	losses	loss	NOUN
ejpam-5495	23	16	,	,	PUNCT
ejpam-5495	23	17	performance	performance	NOUN
ejpam-5495	23	18	degradation	degradation	NOUN
ejpam-5495	23	19	due	due	ADP
ejpam-5495	23	20	to	to	ADP
ejpam-5495	23	21	vibrations	vibration	NOUN
ejpam-5495	23	22	,	,	PUNCT
ejpam-5495	23	23	and	and	CCONJ
ejpam-5495	23	24	the	the	DET
ejpam-5495	23	25	resultant	resultant	NOUN
ejpam-5495	23	26	noise	noise	NOUN
ejpam-5495	23	27	.	.	PUNCT
ejpam-5495	24	1	a	a	DET
ejpam-5495	24	2	combination	combination	NOUN
ejpam-5495	24	3	of	of	ADP
ejpam-5495	24	4	analytical	analytical	ADJ
ejpam-5495	24	5	,	,	PUNCT
ejpam-5495	24	6	computational	computational	ADJ
ejpam-5495	24	7	,	,	PUNCT
ejpam-5495	24	8	and	and	CCONJ
ejpam-5495	24	9	experimental	experimental	ADJ
ejpam-5495	24	10	methods	method	NOUN
ejpam-5495	24	11	is	be	AUX
ejpam-5495	24	12	employed	employ	VERB
ejpam-5495	24	13	to	to	PART
ejpam-5495	24	14	investigate	investigate	VERB
ejpam-5495	24	15	nonlinear	nonlinear	ADJ
ejpam-5495	24	16	oscillations	oscillation	NOUN
ejpam-5495	24	17	and	and	CCONJ
ejpam-5495	24	18	their	their	PRON
ejpam-5495	24	19	applications	application	NOUN
ejpam-5495	24	20	in	in	ADP
ejpam-5495	24	21	construction	construction	NOUN
ejpam-5495	24	22	,	,	PUNCT
ejpam-5495	24	23	physics	physics	NOUN
ejpam-5495	24	24	,	,	PUNCT
ejpam-5495	24	25	and	and	CCONJ
ejpam-5495	24	26	chemistry	chemistry	NOUN
ejpam-5495	25	1	[	[	X
ejpam-5495	25	2	19	19	NUM
ejpam-5495	25	3	,	,	PUNCT
ejpam-5495	25	4	45	45	NUM
ejpam-5495	25	5	,	,	PUNCT
ejpam-5495	25	6	54	54	NUM
ejpam-5495	25	7	,	,	PUNCT
ejpam-5495	25	8	58	58	NUM
ejpam-5495	25	9	]	]	PUNCT
ejpam-5495	25	10	.	.	PUNCT
ejpam-5495	26	1	the	the	DET
ejpam-5495	26	2	nonlinear	nonlinear	ADJ
ejpam-5495	26	3	oscillators	oscillator	NOUN
ejpam-5495	26	4	are	be	AUX
ejpam-5495	26	5	inherently	inherently	ADV
ejpam-5495	26	6	self	self	NOUN
ejpam-5495	26	7	-	-	PUNCT
ejpam-5495	26	8	excited	excited	ADJ
ejpam-5495	26	9	,	,	PUNCT
ejpam-5495	26	10	making	make	VERB
ejpam-5495	26	11	their	their	PRON
ejpam-5495	26	12	dynamics	dynamic	NOUN
ejpam-5495	26	13	potentially	potentially	ADV
ejpam-5495	26	14	difficult	difficult	ADJ
ejpam-5495	26	15	to	to	PART
ejpam-5495	26	16	comprehended	comprehend	VERB
ejpam-5495	26	17	.	.	PUNCT
ejpam-5495	27	1	since	since	SCONJ
ejpam-5495	27	2	a	a	DET
ejpam-5495	27	3	classical	classical	ADJ
ejpam-5495	27	4	nonlinear	nonlinear	ADJ
ejpam-5495	27	5	oscillator	oscillator	NOUN
ejpam-5495	27	6	is	be	AUX
ejpam-5495	27	7	well	well	ADV
ejpam-5495	27	8	-	-	PUNCT
ejpam-5495	27	9	known	know	VERB
ejpam-5495	27	10	as	as	ADP
ejpam-5495	27	11	vdpd	vdpd	NOUN
ejpam-5495	27	12	,	,	PUNCT
ejpam-5495	27	13	several	several	ADJ
ejpam-5495	27	14	researchers	researcher	NOUN
ejpam-5495	27	15	examined	examine	VERB
ejpam-5495	27	16	this	this	DET
ejpam-5495	27	17	oscillator	oscillator	NOUN
ejpam-5495	27	18	.	.	PUNCT
ejpam-5495	28	1	it	it	PRON
ejpam-5495	28	2	is	be	AUX
ejpam-5495	28	3	frequently	frequently	ADV
ejpam-5495	28	4	employed	employ	VERB
ejpam-5495	28	5	to	to	PART
ejpam-5495	28	6	confirm	confirm	VERB
ejpam-5495	28	7	the	the	DET
ejpam-5495	28	8	effectiveness	effectiveness	NOUN
ejpam-5495	28	9	and	and	CCONJ
ejpam-5495	28	10	correctness	correctness	NOUN
ejpam-5495	28	11	of	of	ADP
ejpam-5495	28	12	these	these	DET
ejpam-5495	28	13	phenomena	phenomenon	NOUN
ejpam-5495	28	14	and	and	CCONJ
ejpam-5495	28	15	has	have	VERB
ejpam-5495	28	16	significant	significant	ADJ
ejpam-5495	28	17	scientific	scientific	ADJ
ejpam-5495	28	18	merit	merit	NOUN
ejpam-5495	28	19	and	and	CCONJ
ejpam-5495	28	20	a	a	DET
ejpam-5495	28	21	long	long	ADV
ejpam-5495	28	22	-	-	PUNCT
ejpam-5495	28	23	standing	stand	VERB
ejpam-5495	28	24	history	history	NOUN
ejpam-5495	28	25	of	of	ADP
ejpam-5495	28	26	application	application	NOUN
ejpam-5495	28	27	.	.	PUNCT
ejpam-5495	29	1	lately	lately	ADV
ejpam-5495	29	2	,	,	PUNCT
ejpam-5495	29	3	there	there	PRON
ejpam-5495	29	4	has	have	AUX
ejpam-5495	29	5	been	be	AUX
ejpam-5495	29	6	a	a	DET
ejpam-5495	29	7	lot	lot	NOUN
ejpam-5495	29	8	of	of	ADP
ejpam-5495	29	9	interest	interest	NOUN
ejpam-5495	29	10	in	in	ADP
ejpam-5495	29	11	studying	study	VERB
ejpam-5495	29	12	these	these	DET
ejpam-5495	29	13	oscillators	oscillator	NOUN
ejpam-5495	29	14	’	'	PUNCT
ejpam-5495	29	15	structures	structure	NOUN
ejpam-5495	29	16	in	in	ADP
ejpam-5495	29	17	depth	depth	NOUN
ejpam-5495	29	18	.	.	PUNCT
ejpam-5495	30	1	the	the	DET
ejpam-5495	30	2	feedback	feedback	NOUN
ejpam-5495	30	3	controller	controller	NOUN
ejpam-5495	30	4	is	be	AUX
ejpam-5495	30	5	used	use	VERB
ejpam-5495	30	6	to	to	PART
ejpam-5495	30	7	reduce	reduce	VERB
ejpam-5495	30	8	the	the	DET
ejpam-5495	30	9	vdpd	vdpd	NOUN
ejpam-5495	30	10	from	from	ADP
ejpam-5495	30	11	vibrating	vibrate	VERB
ejpam-5495	30	12	when	when	SCONJ
ejpam-5495	30	13	it	it	PRON
ejpam-5495	30	14	is	be	AUX
ejpam-5495	30	15	simultaneously	simultaneously	ADV
ejpam-5495	30	16	exposed	expose	VERB
ejpam-5495	30	17	to	to	ADP
ejpam-5495	30	18	fundamental	fundamental	ADJ
ejpam-5495	30	19	parametric	parametric	ADJ
ejpam-5495	30	20	resonances	resonance	NOUN
ejpam-5495	30	21	and	and	CCONJ
ejpam-5495	30	22	external	external	ADJ
ejpam-5495	30	23	parametric	parametric	ADJ
ejpam-5495	30	24	excitation	excitation	NOUN
ejpam-5495	30	25	forces	force	NOUN
ejpam-5495	30	26	[	[	X
ejpam-5495	30	27	53	53	NUM
ejpam-5495	30	28	]	]	PUNCT
ejpam-5495	30	29	.	.	PUNCT
ejpam-5495	31	1	the	the	DET
ejpam-5495	31	2	nonlinearity	nonlinearity	NOUN
ejpam-5495	31	3	of	of	ADP
ejpam-5495	31	4	an	an	DET
ejpam-5495	31	5	excited	excited	ADJ
ejpam-5495	31	6	vdpd	vdpd	NOUN
ejpam-5495	31	7	is	be	AUX
ejpam-5495	31	8	prevented	prevent	VERB
ejpam-5495	31	9	by	by	ADP
ejpam-5495	31	10	using	use	VERB
ejpam-5495	31	11	td	td	NOUN
ejpam-5495	31	12	position	position	NOUN
ejpam-5495	31	13	and	and	CCONJ
ejpam-5495	31	14	velocity	velocity	NOUN
ejpam-5495	31	15	.	.	PUNCT
ejpam-5495	32	1	the	the	DET
ejpam-5495	32	2	td	td	NOUN
ejpam-5495	32	3	is	be	AUX
ejpam-5495	32	4	deemed	deem	VERB
ejpam-5495	32	5	appropriate	appropriate	ADJ
ejpam-5495	32	6	as	as	ADP
ejpam-5495	32	7	a	a	DET
ejpam-5495	32	8	supplemental	supplemental	ADJ
ejpam-5495	32	9	safeguard	safeguard	NOUN
ejpam-5495	32	10	against	against	ADP
ejpam-5495	32	11	the	the	DET
ejpam-5495	32	12	nonlinearly	nonlinearly	ADV
ejpam-5495	32	13	oscillating	oscillate	VERB
ejpam-5495	32	14	model	model	NOUN
ejpam-5495	32	15	that	that	PRON
ejpam-5495	32	16	is	be	AUX
ejpam-5495	32	17	being	be	AUX
ejpam-5495	32	18	studied	study	VERB
ejpam-5495	32	19	.	.	PUNCT
ejpam-5495	33	1	because	because	SCONJ
ejpam-5495	33	2	machinery	machinery	NOUN
ejpam-5495	33	3	with	with	ADP
ejpam-5495	33	4	a	a	DET
ejpam-5495	33	5	td	td	NOUN
ejpam-5495	33	6	has	have	AUX
ejpam-5495	33	7	recently	recently	ADV
ejpam-5495	33	8	been	be	AUX
ejpam-5495	33	9	the	the	DET
ejpam-5495	33	10	subject	subject	NOUN
ejpam-5495	33	11	of	of	ADP
ejpam-5495	33	12	many	many	ADJ
ejpam-5495	33	13	examinations	examination	NOUN
ejpam-5495	33	14	,	,	PUNCT
ejpam-5495	33	15	this	this	DET
ejpam-5495	33	16	topic	topic	NOUN
ejpam-5495	33	17	is	be	AUX
ejpam-5495	33	18	of	of	ADP
ejpam-5495	33	19	particular	particular	ADJ
ejpam-5495	33	20	interest	interest	NOUN
ejpam-5495	33	21	.	.	PUNCT
ejpam-5495	34	1	the	the	DET
ejpam-5495	34	2	technique	technique	NOUN
ejpam-5495	34	3	of	of	ADP
ejpam-5495	34	4	numerous	numerous	ADJ
ejpam-5495	34	5	scales	scale	NOUN
ejpam-5495	34	6	was	be	AUX
ejpam-5495	34	7	used	use	VERB
ejpam-5495	34	8	to	to	PART
ejpam-5495	34	9	examine	examine	VERB
ejpam-5495	34	10	two	two	NUM
ejpam-5495	34	11	various	various	ADJ
ejpam-5495	34	12	forms	form	NOUN
ejpam-5495	34	13	of	of	ADP
ejpam-5495	34	14	different	different	ADJ
ejpam-5495	34	15	resonances	resonance	NOUN
ejpam-5495	34	16	[	[	X
ejpam-5495	34	17	34	34	NUM
ejpam-5495	34	18	]	]	PUNCT
ejpam-5495	34	19	.	.	PUNCT
ejpam-5495	35	1	the	the	DET
ejpam-5495	35	2	quasi	quasi	ADJ
ejpam-5495	35	3	-	-	ADJ
ejpam-5495	35	4	periodic	periodic	ADJ
ejpam-5495	35	5	movements	movement	NOUN
ejpam-5495	35	6	and	and	CCONJ
ejpam-5495	35	7	frequencyresponse	frequencyresponse	ADJ
ejpam-5495	35	8	curves	curve	NOUN
ejpam-5495	35	9	were	be	AUX
ejpam-5495	35	10	illustrated	illustrate	VERB
ejpam-5495	35	11	.	.	PUNCT
ejpam-5495	36	1	it	it	PRON
ejpam-5495	36	2	is	be	AUX
ejpam-5495	36	3	demonstrated	demonstrate	VERB
ejpam-5495	36	4	that	that	SCONJ
ejpam-5495	36	5	the	the	DET
ejpam-5495	36	6	forced	force	VERB
ejpam-5495	36	7	oscillator	oscillator	NOUN
ejpam-5495	36	8	’s	’s	PART
ejpam-5495	36	9	differential	differential	ADJ
ejpam-5495	36	10	resonance	resonance	NOUN
ejpam-5495	36	11	response	response	NOUN
ejpam-5495	36	12	displayed	display	VERB
ejpam-5495	36	13	quasi	quasi	ADJ
ejpam-5495	36	14	-	-	ADJ
ejpam-5495	36	15	periodic	periodic	ADJ
ejpam-5495	36	16	movements	movement	NOUN
ejpam-5495	36	17	on	on	ADP
ejpam-5495	36	18	a	a	DET
ejpam-5495	36	19	three	three	NUM
ejpam-5495	36	20	-	-	PUNCT
ejpam-5495	36	21	dimensional	dimensional	ADJ
ejpam-5495	36	22	.	.	PUNCT
ejpam-5495	37	1	the	the	DET
ejpam-5495	37	2	influence	influence	NOUN
ejpam-5495	37	3	of	of	ADP
ejpam-5495	37	4	linear	linear	ADJ
ejpam-5495	37	5	-	-	PUNCT
ejpam-5495	37	6	plus	plus	CCONJ
ejpam-5495	37	7	-	-	PUNCT
ejpam-5495	37	8	nonlinear	nonlinear	ADJ
ejpam-5495	37	9	location	location	NOUN
ejpam-5495	37	10	feedback	feedback	NOUN
ejpam-5495	37	11	dominance	dominance	NOUN
ejpam-5495	37	12	incorporation	incorporation	NOUN
ejpam-5495	37	13	was	be	AUX
ejpam-5495	37	14	conducted	conduct	VERB
ejpam-5495	37	15	[	[	X
ejpam-5495	37	16	37	37	NUM
ejpam-5495	37	17	]	]	PUNCT
ejpam-5495	37	18	.	.	PUNCT
ejpam-5495	38	1	for	for	ADP
ejpam-5495	38	2	resolving	resolve	VERB
ejpam-5495	38	3	chaotic	chaotic	ADJ
ejpam-5495	38	4	behaviors	behavior	NOUN
ejpam-5495	38	5	in	in	ADP
ejpam-5495	38	6	periodically	periodically	ADV
ejpam-5495	38	7	self	self	NOUN
ejpam-5495	38	8	-	-	PUNCT
ejpam-5495	38	9	excited	excite	VERB
ejpam-5495	38	10	oscillators	oscillator	NOUN
ejpam-5495	38	11	,	,	PUNCT
ejpam-5495	38	12	a	a	DET
ejpam-5495	38	13	numerical	numerical	ADJ
ejpam-5495	38	14	solution	solution	NOUN
ejpam-5495	38	15	(	(	PUNCT
ejpam-5495	38	16	ns	ns	X
ejpam-5495	38	17	)	)	PUNCT
ejpam-5495	38	18	in	in	ADP
ejpam-5495	38	19	a	a	DET
ejpam-5495	38	20	backward	backward	ADJ
ejpam-5495	38	21	difference	difference	NOUN
ejpam-5495	38	22	form	form	NOUN
ejpam-5495	38	23	was	be	AUX
ejpam-5495	38	24	put	put	VERB
ejpam-5495	38	25	forth	forth	ADP
ejpam-5495	39	1	[	[	X
ejpam-5495	39	2	47	47	NUM
ejpam-5495	39	3	]	]	PUNCT
ejpam-5495	39	4	.	.	PUNCT
ejpam-5495	40	1	the	the	DET
ejpam-5495	40	2	focus	focus	NOUN
ejpam-5495	40	3	of	of	ADP
ejpam-5495	40	4	this	this	DET
ejpam-5495	40	5	research	research	NOUN
ejpam-5495	40	6	was	be	AUX
ejpam-5495	40	7	on	on	ADP
ejpam-5495	40	8	vdpd	vdpd	ADJ
ejpam-5495	40	9	chaotic	chaotic	ADJ
ejpam-5495	40	10	motions	motion	NOUN
ejpam-5495	40	11	.	.	PUNCT
ejpam-5495	41	1	as	as	ADP
ejpam-5495	41	2	common	common	ADJ
ejpam-5495	41	3	knowledge	knowledge	NOUN
ejpam-5495	41	4	,	,	PUNCT
ejpam-5495	41	5	the	the	DET
ejpam-5495	41	6	tds	tds	NOUN
ejpam-5495	41	7	are	be	AUX
ejpam-5495	41	8	regularly	regularly	ADV
ejpam-5495	41	9	necessary	necessary	ADJ
ejpam-5495	41	10	for	for	ADP
ejpam-5495	41	11	effective	effective	ADJ
ejpam-5495	41	12	control	control	NOUN
ejpam-5495	41	13	systems	system	NOUN
ejpam-5495	41	14	because	because	SCONJ
ejpam-5495	41	15	of	of	ADP
ejpam-5495	41	16	the	the	DET
ejpam-5495	41	17	time	time	NOUN
ejpam-5495	41	18	needed	need	VERB
ejpam-5495	41	19	of	of	ADP
ejpam-5495	41	20	the	the	DET
ejpam-5495	41	21	system	system	NOUN
ejpam-5495	41	22	status	status	NOUN
ejpam-5495	41	23	measurements	measurement	NOUN
ejpam-5495	41	24	,	,	PUNCT
ejpam-5495	41	25	online	online	ADJ
ejpam-5495	41	26	storage	storage	NOUN
ejpam-5495	41	27	processing	processing	NOUN
ejpam-5495	41	28	,	,	PUNCT
ejpam-5495	41	29	computing	compute	VERB
ejpam-5495	41	30	and	and	CCONJ
ejpam-5495	41	31	implementing	implement	VERB
ejpam-5495	41	32	the	the	DET
ejpam-5495	41	33	control	control	NOUN
ejpam-5495	41	34	forces	force	NOUN
ejpam-5495	41	35	,	,	PUNCT
ejpam-5495	41	36	etc	etc	X
ejpam-5495	41	37	.	.	X
ejpam-5495	41	38	due	due	ADP
ejpam-5495	41	39	to	to	ADP
ejpam-5495	41	40	the	the	DET
ejpam-5495	41	41	disruption	disruption	NOUN
ejpam-5495	41	42	in	in	ADP
ejpam-5495	41	43	the	the	DET
ejpam-5495	41	44	application	application	NOUN
ejpam-5495	41	45	of	of	ADP
ejpam-5495	41	46	the	the	DET
ejpam-5495	41	47	control	control	NOUN
ejpam-5495	41	48	force	force	NOUN
ejpam-5495	41	49	transported	transport	VERB
ejpam-5495	41	50	about	about	ADP
ejpam-5495	41	51	by	by	ADP
ejpam-5495	41	52	this	this	DET
ejpam-5495	41	53	td	td	NOUN
ejpam-5495	41	54	,	,	PUNCT
ejpam-5495	41	55	the	the	DET
ejpam-5495	41	56	controlled	control	VERB
ejpam-5495	41	57	systems	system	NOUN
ejpam-5495	41	58	are	be	AUX
ejpam-5495	41	59	frequently	frequently	ADV
ejpam-5495	41	60	performed	perform	VERB
ejpam-5495	41	61	poorly	poorly	ADV
ejpam-5495	41	62	or	or	CCONJ
ejpam-5495	41	63	became	become	VERB
ejpam-5495	41	64	unstable	unstable	ADJ
ejpam-5495	41	65	.	.	PUNCT
ejpam-5495	42	1	numerous	numerous	ADJ
ejpam-5495	42	2	studies	study	NOUN
ejpam-5495	42	3	were	be	AUX
ejpam-5495	42	4	conducted	conduct	VERB
ejpam-5495	42	5	on	on	ADP
ejpam-5495	42	6	systems	system	NOUN
ejpam-5495	42	7	with	with	ADP
ejpam-5495	42	8	temporal	temporal	ADJ
ejpam-5495	42	9	delays	delay	NOUN
ejpam-5495	42	10	during	during	ADP
ejpam-5495	42	11	stochastic	stochastic	ADJ
ejpam-5495	42	12	excitation	excitation	NOUN
ejpam-5495	42	13	[	[	X
ejpam-5495	42	14	29	29	NUM
ejpam-5495	42	15	,	,	PUNCT
ejpam-5495	42	16	30	30	NUM
ejpam-5495	42	17	,	,	PUNCT
ejpam-5495	42	18	33	33	NUM
ejpam-5495	42	19	,	,	PUNCT
ejpam-5495	42	20	36	36	NUM
ejpam-5495	42	21	,	,	PUNCT
ejpam-5495	42	22	59	59	NUM
ejpam-5495	42	23	]	]	PUNCT
ejpam-5495	42	24	.	.	PUNCT
ejpam-5495	43	1	the	the	DET
ejpam-5495	43	2	fundamental	fundamental	ADJ
ejpam-5495	43	3	and	and	CCONJ
ejpam-5495	43	4	1/3	1/3	NUM
ejpam-5495	43	5	subharmonic	subharmonic	ADJ
ejpam-5495	43	6	resonances	resonance	NOUN
ejpam-5495	43	7	of	of	ADP
ejpam-5495	43	8	a	a	DET
ejpam-5495	43	9	harmonically	harmonically	ADV
ejpam-5495	43	10	induced	induce	VERB
ejpam-5495	43	11	duffing	duffing	NOUN
ejpam-5495	43	12	oscillator	oscillator	NOUN
ejpam-5495	43	13	(	(	PUNCT
ejpam-5495	43	14	do	do	AUX
ejpam-5495	43	15	)	)	PUNCT
ejpam-5495	43	16	below	below	ADP
ejpam-5495	43	17	the	the	DET
ejpam-5495	43	18	state	state	NOUN
ejpam-5495	43	19	feedback	feedback	NOUN
ejpam-5495	43	20	control	control	NOUN
ejpam-5495	43	21	with	with	ADP
ejpam-5495	43	22	a	a	DET
ejpam-5495	43	23	td	td	NOUN
ejpam-5495	43	24	were	be	AUX
ejpam-5495	43	25	studied	study	VERB
ejpam-5495	43	26	analytically	analytically	ADV
ejpam-5495	43	27	and	and	CCONJ
ejpam-5495	43	28	numerically	numerically	ADV
ejpam-5495	43	29	.	.	PUNCT
ejpam-5495	44	1	the	the	DET
ejpam-5495	44	2	resonances	resonance	NOUN
ejpam-5495	44	3	’	’	PART
ejpam-5495	44	4	first	first	ADJ
ejpam-5495	44	5	-	-	PUNCT
ejpam-5495	44	6	order	order	NOUN
ejpam-5495	44	7	approximations	approximation	NOUN
ejpam-5495	44	8	were	be	AUX
ejpam-5495	44	9	obtained	obtain	VERB
ejpam-5495	44	10	by	by	ADP
ejpam-5495	44	11	applying	apply	VERB
ejpam-5495	44	12	the	the	DET
ejpam-5495	44	13	multiple	multiple	ADJ
ejpam-5495	44	14	scales	scale	NOUN
ejpam-5495	44	15	method	method	NOUN
ejpam-5495	44	16	[	[	X
ejpam-5495	44	17	14	14	NUM
ejpam-5495	44	18	]	]	PUNCT
ejpam-5495	44	19	,	,	PUNCT
ejpam-5495	44	20	and	and	CCONJ
ejpam-5495	44	21	the	the	DET
ejpam-5495	44	22	impact	impact	NOUN
ejpam-5495	44	23	of	of	ADP
ejpam-5495	44	24	td	td	NOUN
ejpam-5495	44	25	on	on	ADP
ejpam-5495	44	26	the	the	DET
ejpam-5495	44	27	resonances	resonance	NOUN
ejpam-5495	44	28	was	be	AUX
ejpam-5495	44	29	also	also	ADV
ejpam-5495	44	30	examined	examine	VERB
ejpam-5495	44	31	.	.	PUNCT
ejpam-5495	45	1	the	the	DET
ejpam-5495	45	2	vibration	vibration	NOUN
ejpam-5495	45	3	controller	controller	NOUN
ejpam-5495	45	4	perspective	perspective	NOUN
ejpam-5495	45	5	was	be	AUX
ejpam-5495	45	6	suggested	suggest	VERB
ejpam-5495	45	7	the	the	DET
ejpam-5495	45	8	concept	concept	NOUN
ejpam-5495	45	9	of	of	ADP
ejpam-5495	45	10	comparable	comparable	ADJ
ejpam-5495	45	11	damping	damping	NOUN
ejpam-5495	45	12	associated	associate	VERB
ejpam-5495	45	13	with	with	ADP
ejpam-5495	45	14	delay	delay	NOUN
ejpam-5495	45	15	feedback	feedback	NOUN
ejpam-5495	45	16	,	,	PUNCT
ejpam-5495	45	17	and	and	CCONJ
ejpam-5495	45	18	it	it	PRON
ejpam-5495	45	19	examined	examine	VERB
ejpam-5495	45	20	the	the	DET
ejpam-5495	45	21	appropriate	appropriate	ADJ
ejpam-5495	45	22	selection	selection	NOUN
ejpam-5495	45	23	of	of	ADP
ejpam-5495	45	24	feedback	feedback	NOUN
ejpam-5495	45	25	gains	gain	NOUN
ejpam-5495	45	26	and	and	CCONJ
ejpam-5495	45	27	td	td	NOUN
ejpam-5495	45	28	.	.	PUNCT
ejpam-5495	46	1	investigations	investigation	NOUN
ejpam-5495	46	2	of	of	ADP
ejpam-5495	46	3	the	the	DET
ejpam-5495	46	4	td	td	NOUN
ejpam-5495	46	5	mechanism	mechanism	NOUN
ejpam-5495	46	6	of	of	ADP
ejpam-5495	46	7	effect	effect	NOUN
ejpam-5495	46	8	in	in	ADP
ejpam-5495	46	9	a	a	DET
ejpam-5495	46	10	non	non	ADJ
ejpam-5495	46	11	-	-	ADJ
ejpam-5495	46	12	autonomous	autonomous	ADJ
ejpam-5495	46	13	system	system	NOUN
ejpam-5495	46	14	were	be	AUX
ejpam-5495	46	15	conducted	conduct	VERB
ejpam-5495	46	16	[	[	X
ejpam-5495	46	17	29	29	NUM
ejpam-5495	46	18	]	]	PUNCT
ejpam-5495	46	19	.	.	PUNCT
ejpam-5495	47	1	a	a	DET
ejpam-5495	47	2	vdpd	vdpd	NOUN
ejpam-5495	47	3	with	with	ADP
ejpam-5495	47	4	excitation	excitation	NOUN
ejpam-5495	47	5	was	be	AUX
ejpam-5495	47	6	the	the	DET
ejpam-5495	47	7	first	first	ADJ
ejpam-5495	47	8	mathematical	mathematical	ADJ
ejpam-5495	47	9	model	model	NOUN
ejpam-5495	47	10	that	that	PRON
ejpam-5495	47	11	was	be	AUX
ejpam-5495	47	12	considered	consider	VERB
ejpam-5495	47	13	.	.	PUNCT
ejpam-5495	48	1	including	include	VERB
ejpam-5495	48	2	both	both	CCONJ
ejpam-5495	48	3	linear	linear	ADJ
ejpam-5495	48	4	and	and	CCONJ
ejpam-5495	48	5	nonlinear	nonlinear	ADJ
ejpam-5495	48	6	td	td	NOUN
ejpam-5495	48	7	position	position	NOUN
ejpam-5495	48	8	feedback	feedback	NOUN
ejpam-5495	48	9	in	in	ADP
ejpam-5495	48	10	the	the	DET
ejpam-5495	48	11	initial	initial	ADJ
ejpam-5495	48	12	structure	structure	NOUN
ejpam-5495	48	13	,	,	PUNCT
ejpam-5495	48	14	a	a	DET
ejpam-5495	48	15	delaying	delaying	NOUN
ejpam-5495	48	16	a.	a.	NOUN
ejpam-5495	48	17	alanazy	alanazy	NOUN
ejpam-5495	48	18	et	et	PROPN
ejpam-5495	48	19	al	al	PROPN
ejpam-5495	48	20	.	.	PUNCT
ejpam-5495	48	21	/	/	SYM
ejpam-5495	48	22	eur	eur	PROPN
ejpam-5495	48	23	.	.	PUNCT
ejpam-5495	49	1	j.	j.	PROPN
ejpam-5495	49	2	pure	pure	PROPN
ejpam-5495	49	3	appl	appl	PROPN
ejpam-5495	49	4	.	.	PROPN
ejpam-5495	49	5	math	math	PROPN
ejpam-5495	49	6	,	,	PUNCT
ejpam-5495	49	7	18	18	NUM
ejpam-5495	49	8	(	(	PUNCT
ejpam-5495	49	9	1	1	NUM
ejpam-5495	49	10	)	)	PUNCT
ejpam-5495	49	11	(	(	PUNCT
ejpam-5495	49	12	2025	2025	NUM
ejpam-5495	49	13	)	)	PUNCT
ejpam-5495	49	14	,	,	PUNCT
ejpam-5495	49	15	5495	5495	NUM
ejpam-5495	49	16	3	3	NUM
ejpam-5495	49	17	of	of	ADP
ejpam-5495	49	18	21	21	NUM
ejpam-5495	49	19	system	system	NOUN
ejpam-5495	49	20	was	be	AUX
ejpam-5495	49	21	created	create	VERB
ejpam-5495	49	22	.	.	PUNCT
ejpam-5495	50	1	much	much	ADJ
ejpam-5495	50	2	work	work	NOUN
ejpam-5495	50	3	was	be	AUX
ejpam-5495	50	4	done	do	VERB
ejpam-5495	50	5	on	on	ADP
ejpam-5495	50	6	the	the	DET
ejpam-5495	50	7	nonlinear	nonlinear	ADJ
ejpam-5495	50	8	dynamics	dynamic	NOUN
ejpam-5495	50	9	of	of	ADP
ejpam-5495	50	10	a	a	DET
ejpam-5495	50	11	vdpd	vdpd	NOUN
ejpam-5495	50	12	under	under	ADP
ejpam-5495	50	13	the	the	DET
ejpam-5495	50	14	state	state	NOUN
ejpam-5495	50	15	feedback	feedback	NOUN
ejpam-5495	50	16	td	td	NOUN
ejpam-5495	50	17	controller	controller	NOUN
ejpam-5495	50	18	with	with	ADP
ejpam-5495	50	19	linear	linear	NOUN
ejpam-5495	50	20	and	and	CCONJ
ejpam-5495	50	21	nonlinearity	nonlinearity	NOUN
ejpam-5495	50	22	[	[	X
ejpam-5495	50	23	59	59	NUM
ejpam-5495	50	24	]	]	PUNCT
ejpam-5495	50	25	.	.	PUNCT
ejpam-5495	51	1	two	two	NUM
ejpam-5495	51	2	slow	slow	ADJ
ejpam-5495	51	3	-	-	PUNCT
ejpam-5495	51	4	flow	flow	NOUN
ejpam-5495	51	5	equations	equation	NOUN
ejpam-5495	51	6	were	be	AUX
ejpam-5495	51	7	developed	develop	VERB
ejpam-5495	51	8	for	for	ADP
ejpam-5495	51	9	the	the	DET
ejpam-5495	51	10	amplitude	amplitude	NOUN
ejpam-5495	51	11	and	and	CCONJ
ejpam-5495	51	12	phase	phase	NOUN
ejpam-5495	51	13	of	of	ADP
ejpam-5495	51	14	the	the	DET
ejpam-5495	51	15	principal	principal	ADJ
ejpam-5495	51	16	resonance	resonance	NOUN
ejpam-5495	51	17	response	response	NOUN
ejpam-5495	51	18	using	use	VERB
ejpam-5495	51	19	the	the	DET
ejpam-5495	51	20	averaging	averaging	NOUN
ejpam-5495	51	21	approach	approach	NOUN
ejpam-5495	51	22	and	and	CCONJ
ejpam-5495	51	23	taylor	taylor	PROPN
ejpam-5495	51	24	expansion	expansion	NOUN
ejpam-5495	51	25	.	.	PUNCT
ejpam-5495	52	1	when	when	SCONJ
ejpam-5495	52	2	the	the	DET
ejpam-5495	52	3	td	td	NOUN
ejpam-5495	52	4	in	in	ADP
ejpam-5495	52	5	the	the	DET
ejpam-5495	52	6	feedback	feedback	NOUN
ejpam-5495	52	7	exceeds	exceed	VERB
ejpam-5495	52	8	certain	certain	ADJ
ejpam-5495	52	9	thresholds	threshold	NOUN
ejpam-5495	52	10	,	,	PUNCT
ejpam-5495	52	11	the	the	DET
ejpam-5495	52	12	stability	stability	NOUN
ejpam-5495	52	13	of	of	ADP
ejpam-5495	52	14	a	a	DET
ejpam-5495	52	15	vdpd	vdpd	NOUN
ejpam-5495	52	16	under	under	ADP
ejpam-5495	52	17	linear	linear	ADJ
ejpam-5495	52	18	-	-	PUNCT
ejpam-5495	52	19	plus	plus	CCONJ
ejpam-5495	52	20	-	-	PUNCT
ejpam-5495	52	21	nonlinear	nonlinear	ADJ
ejpam-5495	52	22	feedback	feedback	NOUN
ejpam-5495	52	23	dominance	dominance	NOUN
ejpam-5495	52	24	could	could	AUX
ejpam-5495	52	25	change	change	VERB
ejpam-5495	52	26	,	,	PUNCT
ejpam-5495	52	27	potentially	potentially	ADV
ejpam-5495	52	28	leading	lead	VERB
ejpam-5495	52	29	to	to	ADP
ejpam-5495	52	30	single	single	ADJ
ejpam-5495	52	31	or	or	CCONJ
ejpam-5495	52	32	double	double	ADJ
ejpam-5495	52	33	hopf	hopf	ADJ
ejpam-5495	52	34	bifurcations	bifurcation	NOUN
ejpam-5495	52	35	[	[	X
ejpam-5495	52	36	36	36	NUM
ejpam-5495	52	37	]	]	PUNCT
ejpam-5495	52	38	.	.	PUNCT
ejpam-5495	53	1	analytical	analytical	ADJ
ejpam-5495	53	2	conclusions	conclusion	NOUN
ejpam-5495	53	3	were	be	AUX
ejpam-5495	53	4	validated	validate	VERB
ejpam-5495	53	5	through	through	ADP
ejpam-5495	53	6	comparison	comparison	NOUN
ejpam-5495	53	7	with	with	ADP
ejpam-5495	53	8	direct	direct	ADJ
ejpam-5495	53	9	numerical	numerical	ADJ
ejpam-5495	53	10	integration	integration	NOUN
ejpam-5495	53	11	results	result	NOUN
ejpam-5495	53	12	.	.	PUNCT
ejpam-5495	54	1	exploring	explore	VERB
ejpam-5495	54	2	a	a	DET
ejpam-5495	54	3	duffing	duffing	NOUN
ejpam-5495	54	4	oscillator	oscillator	NOUN
ejpam-5495	54	5	with	with	ADP
ejpam-5495	54	6	td	td	NOUN
ejpam-5495	54	7	feedback	feedback	NOUN
ejpam-5495	54	8	control	control	NOUN
ejpam-5495	54	9	,	,	PUNCT
ejpam-5495	54	10	we	we	PRON
ejpam-5495	54	11	examined	examine	VERB
ejpam-5495	54	12	its	its	PRON
ejpam-5495	54	13	asymptotic	asymptotic	ADJ
ejpam-5495	54	14	lyapunov	lyapunov	NOUN
ejpam-5495	54	15	stabiliexploring	stabiliexplore	VERB
ejpam-5495	54	16	a	a	DET
ejpam-5495	54	17	do	do	NOUN
ejpam-5495	54	18	with	with	ADP
ejpam-5495	54	19	td	td	NOUN
ejpam-5495	54	20	feedback	feedback	NOUN
ejpam-5495	54	21	control	control	NOUN
ejpam-5495	54	22	,	,	PUNCT
ejpam-5495	54	23	we	we	PRON
ejpam-5495	54	24	examined	examine	VERB
ejpam-5495	54	25	its	its	PRON
ejpam-5495	54	26	asymptotic	asymptotic	ADJ
ejpam-5495	54	27	lyapunov	lyapunov	ADJ
ejpam-5495	54	28	stability	stability	NOUN
ejpam-5495	54	29	under	under	ADP
ejpam-5495	54	30	parametric	parametric	ADJ
ejpam-5495	54	31	stimulation	stimulation	NOUN
ejpam-5495	54	32	with	with	ADP
ejpam-5495	54	33	constrained	constrained	ADJ
ejpam-5495	54	34	noise	noise	NOUN
ejpam-5495	54	35	[	[	X
ejpam-5495	54	36	33	33	NUM
ejpam-5495	54	37	]	]	PUNCT
ejpam-5495	54	38	.	.	PUNCT
ejpam-5495	55	1	the	the	DET
ejpam-5495	55	2	approximate	approximate	ADJ
ejpam-5495	55	3	solutions	solution	NOUN
ejpam-5495	55	4	of	of	ADP
ejpam-5495	55	5	several	several	ADJ
ejpam-5495	55	6	dynamical	dynamical	ADJ
ejpam-5495	55	7	systems	system	NOUN
ejpam-5495	55	8	were	be	AUX
ejpam-5495	55	9	obtained	obtain	VERB
ejpam-5495	55	10	[	[	X
ejpam-5495	55	11	14	14	NUM
ejpam-5495	55	12	]	]	PUNCT
ejpam-5495	55	13	.	.	PUNCT
ejpam-5495	56	1	the	the	DET
ejpam-5495	56	2	solvability	solvability	NOUN
ejpam-5495	56	3	criteria	criterion	NOUN
ejpam-5495	56	4	and	and	CCONJ
ejpam-5495	56	5	the	the	DET
ejpam-5495	56	6	adjusted	adjust	VERB
ejpam-5495	56	7	equations	equation	NOUN
ejpam-5495	56	8	were	be	AUX
ejpam-5495	56	9	achieved	achieve	VERB
ejpam-5495	56	10	.	.	PUNCT
ejpam-5495	57	1	the	the	DET
ejpam-5495	57	2	stability	stability	NOUN
ejpam-5495	57	3	zones	zone	NOUN
ejpam-5495	57	4	for	for	ADP
ejpam-5495	57	5	several	several	ADJ
ejpam-5495	57	6	parameters	parameter	NOUN
ejpam-5495	57	7	were	be	AUX
ejpam-5495	57	8	analyzed	analyze	VERB
ejpam-5495	57	9	and	and	CCONJ
ejpam-5495	57	10	examined	examine	VERB
ejpam-5495	57	11	.	.	PUNCT
ejpam-5495	58	1	the	the	DET
ejpam-5495	58	2	instability	instability	NOUN
ejpam-5495	58	3	of	of	ADP
ejpam-5495	58	4	linear	linear	PROPN
ejpam-5495	58	5	td	td	NOUN
ejpam-5495	58	6	systems	system	NOUN
ejpam-5495	58	7	was	be	AUX
ejpam-5495	58	8	developed	develop	VERB
ejpam-5495	58	9	,	,	PUNCT
ejpam-5495	58	10	where	where	SCONJ
ejpam-5495	58	11	a	a	DET
ejpam-5495	58	12	generalized	generalized	ADJ
ejpam-5495	58	13	vector	vector	NOUN
ejpam-5495	58	14	of	of	ADP
ejpam-5495	58	15	several	several	ADJ
ejpam-5495	58	16	integral	integral	ADJ
ejpam-5495	58	17	inequalities	inequality	NOUN
ejpam-5495	58	18	was	be	AUX
ejpam-5495	58	19	outlined	outline	VERB
ejpam-5495	58	20	to	to	PART
ejpam-5495	58	21	interpret	interpret	VERB
ejpam-5495	58	22	a	a	DET
ejpam-5495	58	23	variety	variety	NOUN
ejpam-5495	58	24	of	of	ADP
ejpam-5495	58	25	initial	initial	ADJ
ejpam-5495	58	26	circumstances	circumstance	NOUN
ejpam-5495	58	27	[	[	X
ejpam-5495	58	28	18	18	NUM
ejpam-5495	58	29	]	]	PUNCT
ejpam-5495	58	30	.	.	PUNCT
ejpam-5495	59	1	secondly	secondly	ADV
ejpam-5495	59	2	,	,	PUNCT
ejpam-5495	59	3	the	the	DET
ejpam-5495	59	4	td	td	NOUN
ejpam-5495	59	5	system	system	NOUN
ejpam-5495	59	6	stability	stability	NOUN
ejpam-5495	59	7	criteria	criterion	NOUN
ejpam-5495	59	8	were	be	AUX
ejpam-5495	59	9	developed	develop	VERB
ejpam-5495	59	10	using	use	VERB
ejpam-5495	59	11	these	these	DET
ejpam-5495	59	12	multiples	multiple	NOUN
ejpam-5495	59	13	.	.	PUNCT
ejpam-5495	60	1	a	a	DET
ejpam-5495	60	2	linear	linear	ADJ
ejpam-5495	60	3	time	time	NOUN
ejpam-5495	60	4	-	-	PUNCT
ejpam-5495	60	5	varying	vary	VERB
ejpam-5495	60	6	delay	delay	NOUN
ejpam-5495	60	7	system	system	NOUN
ejpam-5495	60	8	was	be	AUX
ejpam-5495	60	9	expected	expect	VERB
ejpam-5495	60	10	to	to	PART
ejpam-5495	60	11	undergo	undergo	VERB
ejpam-5495	60	12	a	a	DET
ejpam-5495	60	13	delay	delay	NOUN
ejpam-5495	60	14	-	-	PUNCT
ejpam-5495	60	15	dependent	dependent	ADJ
ejpam-5495	60	16	stability	stability	NOUN
ejpam-5495	60	17	analysis	analysis	NOUN
ejpam-5495	60	18	[	[	X
ejpam-5495	60	19	56	56	NUM
ejpam-5495	60	20	]	]	PUNCT
ejpam-5495	60	21	.	.	PUNCT
ejpam-5495	61	1	they	they	PRON
ejpam-5495	61	2	provided	provide	VERB
ejpam-5495	61	3	support	support	NOUN
ejpam-5495	61	4	for	for	ADP
ejpam-5495	61	5	the	the	DET
ejpam-5495	61	6	claim	claim	NOUN
ejpam-5495	61	7	that	that	SCONJ
ejpam-5495	61	8	their	their	PRON
ejpam-5495	61	9	strategy	strategy	NOUN
ejpam-5495	61	10	is	be	AUX
ejpam-5495	61	11	more	more	ADV
ejpam-5495	61	12	effective	effective	ADJ
ejpam-5495	61	13	at	at	ADP
ejpam-5495	61	14	addressing	address	VERB
ejpam-5495	61	15	time	time	NOUN
ejpam-5495	61	16	-	-	PUNCT
ejpam-5495	61	17	varying	vary	VERB
ejpam-5495	61	18	delay	delay	NOUN
ejpam-5495	61	19	structures	structure	NOUN
ejpam-5495	61	20	.	.	PUNCT
ejpam-5495	62	1	a	a	DET
ejpam-5495	62	2	numerical	numerical	ADJ
ejpam-5495	62	3	instance	instance	NOUN
ejpam-5495	62	4	was	be	AUX
ejpam-5495	62	5	provided	provide	VERB
ejpam-5495	62	6	to	to	PART
ejpam-5495	62	7	demonstrate	demonstrate	VERB
ejpam-5495	62	8	the	the	DET
ejpam-5495	62	9	efficiency	efficiency	NOUN
ejpam-5495	62	10	of	of	ADP
ejpam-5495	62	11	the	the	DET
ejpam-5495	62	12	model	model	NOUN
ejpam-5495	62	13	.	.	PUNCT
ejpam-5495	63	1	the	the	DET
ejpam-5495	63	2	nonlinear	nonlinear	ADJ
ejpam-5495	63	3	odes	ode	NOUN
ejpam-5495	63	4	can	can	AUX
ejpam-5495	63	5	be	be	AUX
ejpam-5495	63	6	used	use	VERB
ejpam-5495	63	7	to	to	PART
ejpam-5495	63	8	analyze	analyze	VERB
ejpam-5495	63	9	a	a	DET
ejpam-5495	63	10	variety	variety	NOUN
ejpam-5495	63	11	of	of	ADP
ejpam-5495	63	12	technical	technical	ADJ
ejpam-5495	63	13	problems	problem	NOUN
ejpam-5495	63	14	.	.	PUNCT
ejpam-5495	64	1	the	the	DET
ejpam-5495	64	2	small	small	ADJ
ejpam-5495	64	3	factor	factor	NOUN
ejpam-5495	64	4	and	and	CCONJ
ejpam-5495	64	5	the	the	DET
ejpam-5495	64	6	averaging	averaging	NOUN
ejpam-5495	64	7	technique	technique	NOUN
ejpam-5495	64	8	are	be	AUX
ejpam-5495	64	9	two	two	NUM
ejpam-5495	64	10	examples	example	NOUN
ejpam-5495	64	11	of	of	ADP
ejpam-5495	64	12	low	low	ADJ
ejpam-5495	64	13	nonlinear	nonlinear	ADJ
ejpam-5495	64	14	odes	ode	NOUN
ejpam-5495	64	15	[	[	X
ejpam-5495	64	16	35	35	NUM
ejpam-5495	64	17	,	,	PUNCT
ejpam-5495	64	18	57	57	NUM
ejpam-5495	64	19	]	]	PUNCT
ejpam-5495	64	20	.	.	PUNCT
ejpam-5495	65	1	research	research	NOUN
ejpam-5495	65	2	on	on	ADP
ejpam-5495	65	3	the	the	DET
ejpam-5495	65	4	dynamics	dynamic	NOUN
ejpam-5495	65	5	of	of	ADP
ejpam-5495	65	6	a	a	DET
ejpam-5495	65	7	pendulum	pendulum	NOUN
ejpam-5495	65	8	,	,	PUNCT
ejpam-5495	65	9	devoted	devote	VERB
ejpam-5495	65	10	to	to	ADP
ejpam-5495	65	11	a	a	DET
ejpam-5495	65	12	stiff	stiff	ADJ
ejpam-5495	65	13	rotational	rotational	ADJ
ejpam-5495	65	14	structure	structure	NOUN
ejpam-5495	65	15	through	through	ADP
ejpam-5495	65	16	a	a	DET
ejpam-5495	65	17	uniform	uniform	ADJ
ejpam-5495	65	18	angular	angular	ADJ
ejpam-5495	65	19	velocity	velocity	NOUN
ejpam-5495	65	20	along	along	ADP
ejpam-5495	65	21	the	the	DET
ejpam-5495	65	22	vertical	vertical	ADJ
ejpam-5495	65	23	axis	axis	NOUN
ejpam-5495	65	24	,	,	PUNCT
ejpam-5495	65	25	was	be	AUX
ejpam-5495	65	26	transient	transient	ADJ
ejpam-5495	65	27	through	through	ADP
ejpam-5495	65	28	the	the	DET
ejpam-5495	65	29	pendulum	pendulum	NOUN
ejpam-5495	65	30	’s	’s	PART
ejpam-5495	65	31	pivot	pivot	NOUN
ejpam-5495	65	32	point	point	NOUN
ejpam-5495	65	33	[	[	X
ejpam-5495	65	34	57	57	NUM
ejpam-5495	65	35	]	]	PUNCT
ejpam-5495	65	36	.	.	PUNCT
ejpam-5495	66	1	the	the	DET
ejpam-5495	66	2	controlling	control	VERB
ejpam-5495	66	3	equation	equation	NOUN
ejpam-5495	66	4	of	of	ADP
ejpam-5495	66	5	movement	movement	NOUN
ejpam-5495	66	6	was	be	AUX
ejpam-5495	66	7	derived	derive	VERB
ejpam-5495	66	8	analytically	analytically	ADV
ejpam-5495	66	9	at	at	ADP
ejpam-5495	66	10	this	this	DET
ejpam-5495	66	11	frequency	frequency	NOUN
ejpam-5495	66	12	.	.	PUNCT
ejpam-5495	67	1	investigation	investigation	NOUN
ejpam-5495	67	2	into	into	ADP
ejpam-5495	67	3	lyapunov	lyapunov	ADJ
ejpam-5495	67	4	exponents	exponent	NOUN
ejpam-5495	67	5	and	and	CCONJ
ejpam-5495	67	6	their	their	PRON
ejpam-5495	67	7	moments	moment	NOUN
ejpam-5495	67	8	involved	involve	VERB
ejpam-5495	67	9	analyzing	analyze	VERB
ejpam-5495	67	10	linear	linear	NOUN
ejpam-5495	67	11	systems	system	NOUN
ejpam-5495	67	12	with	with	ADP
ejpam-5495	67	13	two	two	NUM
ejpam-5495	67	14	degrees	degree	NOUN
ejpam-5495	67	15	of	of	ADP
ejpam-5495	67	16	freedom	freedom	NOUN
ejpam-5495	67	17	subjected	subject	VERB
ejpam-5495	67	18	to	to	ADP
ejpam-5495	67	19	a	a	DET
ejpam-5495	67	20	parametric	parametric	ADJ
ejpam-5495	67	21	excitation	excitation	NOUN
ejpam-5495	67	22	[	[	X
ejpam-5495	67	23	35	35	NUM
ejpam-5495	67	24	]	]	PUNCT
ejpam-5495	67	25	.	.	PUNCT
ejpam-5495	68	1	explicit	explicit	ADJ
ejpam-5495	68	2	approximate	approximate	ADJ
ejpam-5495	68	3	equations	equation	NOUN
ejpam-5495	68	4	for	for	ADP
ejpam-5495	68	5	such	such	ADJ
ejpam-5495	68	6	exponents	exponent	NOUN
ejpam-5495	68	7	were	be	AUX
ejpam-5495	68	8	computed	compute	VERB
ejpam-5495	68	9	utilizing	utilize	VERB
ejpam-5495	68	10	the	the	DET
ejpam-5495	68	11	homotopy	homotopy	NOUN
ejpam-5495	68	12	perturbation	perturbation	NOUN
ejpam-5495	68	13	method	method	NOUN
ejpam-5495	68	14	(	(	PUNCT
ejpam-5495	68	15	hpm	hpm	NOUN
ejpam-5495	68	16	)	)	PUNCT
ejpam-5495	68	17	,	,	PUNCT
ejpam-5495	68	18	while	while	SCONJ
ejpam-5495	68	19	considering	consider	VERB
ejpam-5495	68	20	the	the	DET
ejpam-5495	68	21	presence	presence	NOUN
ejpam-5495	68	22	of	of	ADP
ejpam-5495	68	23	low	low	ADJ
ejpam-5495	68	24	-	-	PUNCT
ejpam-5495	68	25	intensity	intensity	NOUN
ejpam-5495	68	26	sounds	sound	VERB
ejpam-5495	68	27	.	.	PUNCT
ejpam-5495	69	1	additionally	additionally	ADV
ejpam-5495	69	2	,	,	PUNCT
ejpam-5495	69	3	the	the	DET
ejpam-5495	69	4	solutions	solution	NOUN
ejpam-5495	69	5	of	of	ADP
ejpam-5495	69	6	vibratory	vibratory	NOUN
ejpam-5495	69	7	systems	system	NOUN
ejpam-5495	69	8	were	be	AUX
ejpam-5495	69	9	derived	derive	VERB
ejpam-5495	69	10	using	use	VERB
ejpam-5495	69	11	the	the	DET
ejpam-5495	69	12	multiple	multiple	ADJ
ejpam-5495	69	13	time	time	NOUN
ejpam-5495	69	14	-	-	PUNCT
ejpam-5495	69	15	scales	scale	NOUN
ejpam-5495	69	16	method	method	NOUN
ejpam-5495	69	17	and	and	CCONJ
ejpam-5495	69	18	the	the	DET
ejpam-5495	69	19	lindstedt	lindstedt	VERB
ejpam-5495	69	20	-	-	PUNCT
ejpam-5495	69	21	poincaré	poincaré	ADJ
ejpam-5495	69	22	technique	technique	NOUN
ejpam-5495	69	23	.	.	PUNCT
ejpam-5495	70	1	these	these	DET
ejpam-5495	70	2	techniques	technique	NOUN
ejpam-5495	70	3	,	,	PUNCT
ejpam-5495	70	4	however	however	ADV
ejpam-5495	70	5	,	,	PUNCT
ejpam-5495	70	6	were	be	AUX
ejpam-5495	70	7	dependent	dependent	ADJ
ejpam-5495	70	8	on	on	ADP
ejpam-5495	70	9	a	a	DET
ejpam-5495	70	10	small	small	ADJ
ejpam-5495	70	11	factor	factor	NOUN
ejpam-5495	70	12	,	,	PUNCT
ejpam-5495	70	13	and	and	CCONJ
ejpam-5495	70	14	the	the	DET
ejpam-5495	70	15	selection	selection	NOUN
ejpam-5495	70	16	of	of	ADP
ejpam-5495	70	17	this	this	DET
ejpam-5495	70	18	factor	factor	NOUN
ejpam-5495	70	19	produced	produce	VERB
ejpam-5495	70	20	false	false	ADJ
ejpam-5495	70	21	results	result	NOUN
ejpam-5495	70	22	[	[	X
ejpam-5495	70	23	32	32	NUM
ejpam-5495	70	24	]	]	PUNCT
ejpam-5495	70	25	.	.	PUNCT
ejpam-5495	71	1	the	the	DET
ejpam-5495	71	2	iterative	iterative	NOUN
ejpam-5495	71	3	methods	method	NOUN
ejpam-5495	71	4	with	with	ADP
ejpam-5495	71	5	the	the	DET
ejpam-5495	71	6	hpm	hpm	NOUN
ejpam-5495	71	7	were	be	AUX
ejpam-5495	71	8	shown	show	VERB
ejpam-5495	71	9	to	to	PART
ejpam-5495	71	10	be	be	AUX
ejpam-5495	71	11	crucial	crucial	ADJ
ejpam-5495	71	12	lately	lately	ADV
ejpam-5495	71	13	for	for	ADP
ejpam-5495	71	14	generating	generate	VERB
ejpam-5495	71	15	approximations	approximation	NOUN
ejpam-5495	71	16	of	of	ADP
ejpam-5495	71	17	various	various	ADJ
ejpam-5495	71	18	nonlinear	nonlinear	ADJ
ejpam-5495	71	19	odes	ode	NOUN
ejpam-5495	71	20	that	that	PRON
ejpam-5495	71	21	are	be	AUX
ejpam-5495	71	22	reasonably	reasonably	ADV
ejpam-5495	71	23	near	near	ADJ
ejpam-5495	71	24	to	to	ADP
ejpam-5495	71	25	their	their	PRON
ejpam-5495	71	26	solutions	solution	NOUN
ejpam-5495	71	27	.	.	PUNCT
ejpam-5495	72	1	these	these	DET
ejpam-5495	72	2	methods	method	NOUN
ejpam-5495	72	3	rely	rely	VERB
ejpam-5495	72	4	on	on	ADP
ejpam-5495	72	5	the	the	DET
ejpam-5495	72	6	initial	initial	ADJ
ejpam-5495	72	7	conditions	condition	NOUN
ejpam-5495	72	8	of	of	ADP
ejpam-5495	72	9	the	the	DET
ejpam-5495	72	10	response	response	NOUN
ejpam-5495	72	11	.	.	PUNCT
ejpam-5495	73	1	therefore	therefore	ADV
ejpam-5495	73	2	,	,	PUNCT
ejpam-5495	73	3	if	if	SCONJ
ejpam-5495	73	4	the	the	DET
ejpam-5495	73	5	initial	initial	ADJ
ejpam-5495	73	6	assumption	assumption	NOUN
ejpam-5495	73	7	does	do	AUX
ejpam-5495	73	8	not	not	PART
ejpam-5495	73	9	correspond	correspond	VERB
ejpam-5495	73	10	to	to	ADP
ejpam-5495	73	11	the	the	DET
ejpam-5495	73	12	actual	actual	ADJ
ejpam-5495	73	13	way	way	NOUN
ejpam-5495	73	14	the	the	DET
ejpam-5495	73	15	problem	problem	NOUN
ejpam-5495	73	16	is	be	AUX
ejpam-5495	73	17	resolved	resolve	VERB
ejpam-5495	73	18	,	,	PUNCT
ejpam-5495	73	19	it	it	PRON
ejpam-5495	73	20	will	will	AUX
ejpam-5495	73	21	be	be	AUX
ejpam-5495	73	22	diverged	diverge	VERB
ejpam-5495	73	23	,	,	PUNCT
ejpam-5495	73	24	preventing	prevent	VERB
ejpam-5495	73	25	the	the	DET
ejpam-5495	73	26	process	process	NOUN
ejpam-5495	73	27	from	from	ADP
ejpam-5495	73	28	leading	lead	VERB
ejpam-5495	73	29	to	to	ADP
ejpam-5495	73	30	the	the	DET
ejpam-5495	73	31	indicated	indicate	VERB
ejpam-5495	73	32	result	result	NOUN
ejpam-5495	73	33	.	.	PUNCT
ejpam-5495	74	1	one	one	NUM
ejpam-5495	74	2	of	of	ADP
ejpam-5495	74	3	the	the	DET
ejpam-5495	74	4	challenging	challenging	ADJ
ejpam-5495	74	5	issues	issue	NOUN
ejpam-5495	74	6	that	that	PRON
ejpam-5495	74	7	arise	arise	VERB
ejpam-5495	74	8	in	in	ADP
ejpam-5495	74	9	the	the	DET
ejpam-5495	74	10	nonlinear	nonlinear	ADJ
ejpam-5495	74	11	oscillation	oscillation	NOUN
ejpam-5495	74	12	difficulties	difficulty	NOUN
ejpam-5495	74	13	has	have	AUX
ejpam-5495	74	14	drawn	draw	VERB
ejpam-5495	74	15	the	the	DET
ejpam-5495	74	16	attention	attention	NOUN
ejpam-5495	74	17	of	of	ADP
ejpam-5495	74	18	numerous	numerous	ADJ
ejpam-5495	74	19	academics	academic	NOUN
ejpam-5495	74	20	.	.	PUNCT
ejpam-5495	75	1	because	because	SCONJ
ejpam-5495	75	2	of	of	ADP
ejpam-5495	75	3	the	the	DET
ejpam-5495	75	4	nature	nature	NOUN
ejpam-5495	75	5	of	of	ADP
ejpam-5495	75	6	nonlinearity	nonlinearity	NOUN
ejpam-5495	75	7	,	,	PUNCT
ejpam-5495	75	8	it	it	PRON
ejpam-5495	75	9	has	have	AUX
ejpam-5495	75	10	been	be	AUX
ejpam-5495	75	11	challenging	challenge	VERB
ejpam-5495	75	12	for	for	ADP
ejpam-5495	75	13	researchers	researcher	NOUN
ejpam-5495	75	14	and	and	CCONJ
ejpam-5495	75	15	physicists	physicist	NOUN
ejpam-5495	75	16	to	to	PART
ejpam-5495	75	17	develop	develop	VERB
ejpam-5495	75	18	an	an	DET
ejpam-5495	75	19	exact	exact	ADJ
ejpam-5495	75	20	or	or	CCONJ
ejpam-5495	75	21	roughly	roughly	ADV
ejpam-5495	75	22	accurate	accurate	ADJ
ejpam-5495	75	23	solution	solution	NOUN
ejpam-5495	75	24	to	to	ADP
ejpam-5495	75	25	various	various	ADJ
ejpam-5495	75	26	nonlinear	nonlinear	ADJ
ejpam-5495	75	27	odes	ode	NOUN
ejpam-5495	75	28	.	.	PUNCT
ejpam-5495	76	1	the	the	DET
ejpam-5495	76	2	hpm	hpm	NOUN
ejpam-5495	76	3	was	be	AUX
ejpam-5495	76	4	used	use	VERB
ejpam-5495	76	5	to	to	PART
ejpam-5495	76	6	analyze	analyze	VERB
ejpam-5495	76	7	approximate	approximate	ADJ
ejpam-5495	76	8	analytical	analytical	ADJ
ejpam-5495	76	9	solution	solution	NOUN
ejpam-5495	76	10	(	(	PUNCT
ejpam-5495	76	11	as	as	ADP
ejpam-5495	76	12	)	)	PUNCT
ejpam-5495	76	13	of	of	ADP
ejpam-5495	76	14	a	a	DET
ejpam-5495	76	15	magnetic	magnetic	ADJ
ejpam-5495	76	16	spherical	spherical	ADJ
ejpam-5495	76	17	pendulum	pendulum	NOUN
ejpam-5495	76	18	[	[	X
ejpam-5495	76	19	21	21	NUM
ejpam-5495	76	20	]	]	PUNCT
ejpam-5495	76	21	.	.	PUNCT
ejpam-5495	77	1	the	the	DET
ejpam-5495	77	2	frequency	frequency	NOUN
ejpam-5495	77	3	formula	formula	NOUN
ejpam-5495	77	4	was	be	AUX
ejpam-5495	77	5	created	create	VERB
ejpam-5495	77	6	by	by	ADP
ejpam-5495	77	7	prof	prof	NOUN
ejpam-5495	77	8	.	.	PUNCT
ejpam-5495	78	1	he	he	PRON
ejpam-5495	78	2	,	,	PUNCT
ejpam-5495	78	3	who	who	PRON
ejpam-5495	78	4	also	also	ADV
ejpam-5495	78	5	came	come	VERB
ejpam-5495	78	6	up	up	ADP
ejpam-5495	78	7	with	with	ADP
ejpam-5495	78	8	an	an	DET
ejpam-5495	78	9	inventive	inventive	ADJ
ejpam-5495	78	10	method	method	NOUN
ejpam-5495	78	11	to	to	PART
ejpam-5495	78	12	approach	approach	VERB
ejpam-5495	78	13	linearity	linearity	NOUN
ejpam-5495	78	14	in	in	ADP
ejpam-5495	78	15	a	a	DET
ejpam-5495	78	16	nonlinear	nonlinear	ADJ
ejpam-5495	78	17	ode	ode	NOUN
ejpam-5495	78	18	[	[	X
ejpam-5495	78	19	22	22	NUM
ejpam-5495	78	20	,	,	PUNCT
ejpam-5495	78	21	27	27	NUM
ejpam-5495	78	22	]	]	PUNCT
ejpam-5495	78	23	.	.	PUNCT
ejpam-5495	79	1	there	there	PRON
ejpam-5495	79	2	was	be	VERB
ejpam-5495	79	3	a.	a.	NOUN
ejpam-5495	79	4	alanazy	alanazy	NOUN
ejpam-5495	79	5	et	et	PROPN
ejpam-5495	79	6	al	al	PROPN
ejpam-5495	79	7	.	.	PUNCT
ejpam-5495	79	8	/	/	SYM
ejpam-5495	79	9	eur	eur	PROPN
ejpam-5495	79	10	.	.	PUNCT
ejpam-5495	80	1	j.	j.	PROPN
ejpam-5495	80	2	pure	pure	PROPN
ejpam-5495	80	3	appl	appl	PROPN
ejpam-5495	80	4	.	.	PROPN
ejpam-5495	80	5	math	math	PROPN
ejpam-5495	80	6	,	,	PUNCT
ejpam-5495	80	7	18	18	NUM
ejpam-5495	80	8	(	(	PUNCT
ejpam-5495	80	9	1	1	NUM
ejpam-5495	80	10	)	)	PUNCT
ejpam-5495	80	11	(	(	PUNCT
ejpam-5495	80	12	2025	2025	NUM
ejpam-5495	80	13	)	)	PUNCT
ejpam-5495	80	14	,	,	PUNCT
ejpam-5495	80	15	5495	5495	NUM
ejpam-5495	80	16	4	4	NUM
ejpam-5495	80	17	of	of	ADP
ejpam-5495	80	18	21	21	NUM
ejpam-5495	80	19	a	a	DET
ejpam-5495	80	20	description	description	NOUN
ejpam-5495	80	21	of	of	ADP
ejpam-5495	80	22	some	some	DET
ejpam-5495	80	23	recent	recent	ADJ
ejpam-5495	80	24	asymptotic	asymptotic	ADJ
ejpam-5495	80	25	approach	approach	NOUN
ejpam-5495	80	26	advancements	advancement	NOUN
ejpam-5495	80	27	that	that	PRON
ejpam-5495	80	28	were	be	AUX
ejpam-5495	80	29	said	say	VERB
ejpam-5495	80	30	to	to	PART
ejpam-5495	80	31	be	be	AUX
ejpam-5495	80	32	relevant	relevant	ADJ
ejpam-5495	80	33	to	to	ADP
ejpam-5495	80	34	both	both	CCONJ
ejpam-5495	80	35	strong	strong	ADJ
ejpam-5495	80	36	and	and	CCONJ
ejpam-5495	80	37	weak	weak	ADJ
ejpam-5495	80	38	nonlinear	nonlinear	ADJ
ejpam-5495	80	39	odes	ode	NOUN
ejpam-5495	80	40	.	.	PUNCT
ejpam-5495	81	1	the	the	DET
ejpam-5495	81	2	derived	derive	VERB
ejpam-5495	81	3	approximate	approximate	NOUN
ejpam-5495	81	4	as	as	SCONJ
ejpam-5495	81	5	were	be	AUX
ejpam-5495	81	6	valid	valid	ADJ
ejpam-5495	81	7	across	across	ADP
ejpam-5495	81	8	the	the	DET
ejpam-5495	81	9	entire	entire	ADJ
ejpam-5495	81	10	solution	solution	NOUN
ejpam-5495	81	11	domain	domain	NOUN
ejpam-5495	81	12	.	.	PUNCT
ejpam-5495	82	1	to	to	PART
ejpam-5495	82	2	address	address	VERB
ejpam-5495	82	3	the	the	DET
ejpam-5495	82	4	limitations	limitation	NOUN
ejpam-5495	82	5	of	of	ADP
ejpam-5495	82	6	conventional	conventional	ADJ
ejpam-5495	82	7	methods	method	NOUN
ejpam-5495	82	8	of	of	ADP
ejpam-5495	82	9	perturbation	perturbation	NOUN
ejpam-5495	82	10	,	,	PUNCT
ejpam-5495	82	11	numerous	numerous	ADJ
ejpam-5495	82	12	modified	modify	VERB
ejpam-5495	82	13	techniques	technique	NOUN
ejpam-5495	82	14	,	,	PUNCT
ejpam-5495	82	15	along	along	ADP
ejpam-5495	82	16	with	with	ADP
ejpam-5495	82	17	other	other	ADJ
ejpam-5495	82	18	mathematical	mathematical	ADJ
ejpam-5495	82	19	tools	tool	NOUN
ejpam-5495	82	20	such	such	ADJ
ejpam-5495	82	21	as	as	ADP
ejpam-5495	82	22	variation	variation	NOUN
ejpam-5495	82	23	theory	theory	NOUN
ejpam-5495	82	24	,	,	PUNCT
ejpam-5495	82	25	hpm	hpm	NOUN
ejpam-5495	82	26	,	,	PUNCT
ejpam-5495	82	27	and	and	CCONJ
ejpam-5495	82	28	iterative	iterative	NOUN
ejpam-5495	82	29	approaches	approach	NOUN
ejpam-5495	82	30	,	,	PUNCT
ejpam-5495	82	31	were	be	AUX
ejpam-5495	82	32	proposed	propose	VERB
ejpam-5495	82	33	.	.	PUNCT
ejpam-5495	83	1	the	the	DET
ejpam-5495	83	2	hff	hff	PROPN
ejpam-5495	83	3	,	,	PUNCT
ejpam-5495	83	4	the	the	DET
ejpam-5495	83	5	max	max	PROPN
ejpam-5495	83	6	-	-	PUNCT
ejpam-5495	83	7	min	min	NOUN
ejpam-5495	83	8	technique	technique	NOUN
ejpam-5495	83	9	,	,	PUNCT
ejpam-5495	83	10	and	and	CCONJ
ejpam-5495	83	11	the	the	DET
ejpam-5495	83	12	hpm	hpm	NOUN
ejpam-5495	83	13	were	be	AUX
ejpam-5495	83	14	three	three	NUM
ejpam-5495	83	15	proposals	proposal	NOUN
ejpam-5495	83	16	of	of	ADP
ejpam-5495	83	17	the	the	DET
ejpam-5495	83	18	nos	no	NOUN
ejpam-5495	83	19	in	in	ADP
ejpam-5495	83	20	light	light	NOUN
ejpam-5495	83	21	of	of	ADP
ejpam-5495	83	22	the	the	DET
ejpam-5495	83	23	simplest	simple	ADJ
ejpam-5495	83	24	methods	method	NOUN
ejpam-5495	83	25	[	[	X
ejpam-5495	83	26	22	22	NUM
ejpam-5495	83	27	]	]	PUNCT
ejpam-5495	83	28	.	.	PUNCT
ejpam-5495	84	1	the	the	DET
ejpam-5495	84	2	weighted	weight	VERB
ejpam-5495	84	3	average	average	NOUN
ejpam-5495	84	4	was	be	AUX
ejpam-5495	84	5	added	add	VERB
ejpam-5495	84	6	to	to	ADP
ejpam-5495	84	7	the	the	DET
ejpam-5495	84	8	mathematical	mathematical	ADJ
ejpam-5495	84	9	description	description	NOUN
ejpam-5495	84	10	of	of	ADP
ejpam-5495	84	11	his	his	PRON
ejpam-5495	84	12	frequency	frequency	NOUN
ejpam-5495	84	13	construction	construction	NOUN
ejpam-5495	84	14	to	to	PART
ejpam-5495	84	15	enhance	enhance	VERB
ejpam-5495	84	16	the	the	DET
ejpam-5495	84	17	accuracy	accuracy	NOUN
ejpam-5495	84	18	of	of	ADP
ejpam-5495	84	19	frequency	frequency	NOUN
ejpam-5495	84	20	.	.	PUNCT
ejpam-5495	85	1	strongly	strongly	ADV
ejpam-5495	85	2	nonlinear	nonlinear	ADJ
ejpam-5495	85	3	oscillators	oscillator	NOUN
ejpam-5495	85	4	were	be	AUX
ejpam-5495	85	5	advised	advise	VERB
ejpam-5495	85	6	to	to	PART
ejpam-5495	85	7	be	be	AUX
ejpam-5495	85	8	treated	treat	VERB
ejpam-5495	85	9	straightforwardly	straightforwardly	ADV
ejpam-5495	85	10	and	and	CCONJ
ejpam-5495	85	11	exclusively	exclusively	ADV
ejpam-5495	86	1	[	[	X
ejpam-5495	86	2	27	27	NUM
ejpam-5495	86	3	]	]	PUNCT
ejpam-5495	86	4	.	.	PUNCT
ejpam-5495	87	1	in	in	ADP
ejpam-5495	87	2	a	a	DET
ejpam-5495	87	3	packaging	packaging	NOUN
ejpam-5495	87	4	system	system	NOUN
ejpam-5495	87	5	as	as	ADV
ejpam-5495	87	6	well	well	ADV
ejpam-5495	87	7	as	as	ADP
ejpam-5495	87	8	an	an	DET
ejpam-5495	87	9	experimental	experimental	ADJ
ejpam-5495	87	10	micro	micro	ADJ
ejpam-5495	87	11	-	-	ADJ
ejpam-5495	87	12	electro	electro	ADJ
ejpam-5495	87	13	-	-	PUNCT
ejpam-5495	87	14	mechanical	mechanical	ADJ
ejpam-5495	87	15	system	system	NOUN
ejpam-5495	87	16	,	,	PUNCT
ejpam-5495	87	17	the	the	DET
ejpam-5495	87	18	nonlinear	nonlinear	ADJ
ejpam-5495	87	19	relationship	relationship	NOUN
ejpam-5495	87	20	between	between	ADP
ejpam-5495	87	21	the	the	DET
ejpam-5495	87	22	amplitude	amplitude	NOUN
ejpam-5495	87	23	and	and	CCONJ
ejpam-5495	87	24	frequency	frequency	NOUN
ejpam-5495	87	25	of	of	ADP
ejpam-5495	87	26	a	a	DET
ejpam-5495	87	27	nonlinear	nonlinear	ADJ
ejpam-5495	87	28	vibration	vibration	NOUN
ejpam-5495	87	29	system	system	NOUN
ejpam-5495	87	30	was	be	AUX
ejpam-5495	87	31	employed	employ	VERB
ejpam-5495	87	32	[	[	X
ejpam-5495	87	33	46	46	NUM
ejpam-5495	87	34	]	]	PUNCT
ejpam-5495	87	35	.	.	PUNCT
ejpam-5495	88	1	an	an	DET
ejpam-5495	88	2	effective	effective	ADJ
ejpam-5495	88	3	approach	approach	NOUN
ejpam-5495	88	4	utilizing	utilize	VERB
ejpam-5495	88	5	an	an	DET
ejpam-5495	88	6	adaption	adaption	NOUN
ejpam-5495	88	7	of	of	ADP
ejpam-5495	88	8	the	the	DET
ejpam-5495	88	9	conventional	conventional	ADJ
ejpam-5495	88	10	differential	differential	ADJ
ejpam-5495	88	11	transform	transform	NOUN
ejpam-5495	88	12	method	method	NOUN
ejpam-5495	88	13	was	be	AUX
ejpam-5495	88	14	introduced	introduce	VERB
ejpam-5495	88	15	[	[	X
ejpam-5495	88	16	12	12	NUM
ejpam-5495	88	17	]	]	PUNCT
ejpam-5495	88	18	.	.	PUNCT
ejpam-5495	89	1	the	the	DET
ejpam-5495	89	2	findings	finding	NOUN
ejpam-5495	89	3	collected	collect	VERB
ejpam-5495	89	4	indicated	indicate	VERB
ejpam-5495	89	5	that	that	SCONJ
ejpam-5495	89	6	the	the	DET
ejpam-5495	89	7	proposed	propose	VERB
ejpam-5495	89	8	strategy	strategy	NOUN
ejpam-5495	89	9	was	be	AUX
ejpam-5495	89	10	a	a	DET
ejpam-5495	89	11	potential	potential	ADJ
ejpam-5495	89	12	method	method	NOUN
ejpam-5495	89	13	for	for	ADP
ejpam-5495	89	14	solving	solve	VERB
ejpam-5495	89	15	the	the	DET
ejpam-5495	89	16	van	van	PROPN
ejpam-5495	89	17	der	der	ADJ
ejpam-5495	89	18	pol	pol	PROPN
ejpam-5495	89	19	oscillator	oscillator	NOUN
ejpam-5495	89	20	,	,	PUNCT
ejpam-5495	89	21	providing	provide	VERB
ejpam-5495	89	22	identical	identical	ADJ
ejpam-5495	89	23	information	information	NOUN
ejpam-5495	89	24	on	on	ADP
ejpam-5495	89	25	the	the	DET
ejpam-5495	89	26	phase	phase	NOUN
ejpam-5495	89	27	portrait	portrait	NOUN
ejpam-5495	89	28	and	and	CCONJ
ejpam-5495	89	29	proving	prove	VERB
ejpam-5495	89	30	the	the	DET
ejpam-5495	89	31	system	system	NOUN
ejpam-5495	89	32	’s	’s	PART
ejpam-5495	89	33	stability	stability	NOUN
ejpam-5495	89	34	efficiently	efficiently	ADV
ejpam-5495	89	35	.	.	PUNCT
ejpam-5495	90	1	a	a	DET
ejpam-5495	90	2	unique	unique	ADJ
ejpam-5495	90	3	two	two	NUM
ejpam-5495	90	4	-	-	PUNCT
ejpam-5495	90	5	dimensional	dimensional	ADJ
ejpam-5495	90	6	oscillator	oscillator	NOUN
ejpam-5495	90	7	featuring	feature	VERB
ejpam-5495	90	8	an	an	DET
ejpam-5495	90	9	asymmetric	asymmetric	ADJ
ejpam-5495	90	10	design	design	NOUN
ejpam-5495	90	11	and	and	CCONJ
ejpam-5495	90	12	its	its	PRON
ejpam-5495	90	13	steady	steady	ADJ
ejpam-5495	90	14	vibration	vibration	NOUN
ejpam-5495	90	15	characteristics	characteristic	NOUN
ejpam-5495	90	16	were	be	AUX
ejpam-5495	90	17	presented	present	VERB
ejpam-5495	90	18	[	[	X
ejpam-5495	90	19	48	48	NUM
ejpam-5495	90	20	]	]	PUNCT
ejpam-5495	90	21	.	.	PUNCT
ejpam-5495	91	1	a	a	DET
ejpam-5495	91	2	nonlinear	nonlinear	ADJ
ejpam-5495	91	3	oscillator	oscillator	NOUN
ejpam-5495	91	4	equation	equation	NOUN
ejpam-5495	91	5	featuring	feature	VERB
ejpam-5495	91	6	two	two	NUM
ejpam-5495	91	7	dominant	dominant	ADJ
ejpam-5495	91	8	linear	linear	PROPN
ejpam-5495	91	9	terms	term	NOUN
ejpam-5495	91	10	was	be	AUX
ejpam-5495	91	11	introduced	introduce	VERB
ejpam-5495	91	12	[	[	X
ejpam-5495	91	13	1	1	NUM
ejpam-5495	91	14	]	]	PUNCT
ejpam-5495	91	15	.	.	PUNCT
ejpam-5495	92	1	an	an	DET
ejpam-5495	92	2	approximate	approximate	ADJ
ejpam-5495	92	3	solution	solution	NOUN
ejpam-5495	92	4	was	be	AUX
ejpam-5495	92	5	derived	derive	VERB
ejpam-5495	92	6	with	with	ADP
ejpam-5495	92	7	the	the	DET
ejpam-5495	92	8	power	power	NOUN
ejpam-5495	92	9	series	series	PROPN
ejpam-5495	92	10	method	method	PROPN
ejpam-5495	92	11	.	.	PUNCT
ejpam-5495	93	1	additionally	additionally	ADV
ejpam-5495	93	2	,	,	PUNCT
ejpam-5495	93	3	by	by	ADP
ejpam-5495	93	4	incorporating	incorporate	VERB
ejpam-5495	93	5	a	a	DET
ejpam-5495	93	6	parameter	parameter	NOUN
ejpam-5495	93	7	into	into	ADP
ejpam-5495	93	8	the	the	DET
ejpam-5495	93	9	original	original	ADJ
ejpam-5495	93	10	equation	equation	NOUN
ejpam-5495	93	11	,	,	PUNCT
ejpam-5495	93	12	the	the	DET
ejpam-5495	93	13	fixed	fix	VERB
ejpam-5495	93	14	points	point	NOUN
ejpam-5495	93	15	of	of	ADP
ejpam-5495	93	16	the	the	DET
ejpam-5495	93	17	new	new	ADJ
ejpam-5495	93	18	nonlinear	nonlinear	ADJ
ejpam-5495	93	19	oscillator	oscillator	NOUN
ejpam-5495	93	20	equation	equation	NOUN
ejpam-5495	93	21	were	be	AUX
ejpam-5495	93	22	identified	identify	VERB
ejpam-5495	93	23	,	,	PUNCT
ejpam-5495	93	24	and	and	CCONJ
ejpam-5495	93	25	a	a	DET
ejpam-5495	93	26	stability	stability	NOUN
ejpam-5495	93	27	analysis	analysis	NOUN
ejpam-5495	93	28	of	of	ADP
ejpam-5495	93	29	these	these	DET
ejpam-5495	93	30	fixed	fix	VERB
ejpam-5495	93	31	points	point	NOUN
ejpam-5495	93	32	was	be	AUX
ejpam-5495	93	33	conducted	conduct	VERB
ejpam-5495	93	34	.	.	PUNCT
ejpam-5495	94	1	the	the	DET
ejpam-5495	94	2	precise	precise	ADJ
ejpam-5495	94	3	solutions	solution	NOUN
ejpam-5495	94	4	of	of	ADP
ejpam-5495	94	5	the	the	DET
ejpam-5495	94	6	intricate	intricate	ADJ
ejpam-5495	94	7	nonlinear	nonlinear	ADJ
ejpam-5495	94	8	odes	ode	NOUN
ejpam-5495	94	9	that	that	PRON
ejpam-5495	94	10	dictate	dictate	VERB
ejpam-5495	94	11	the	the	DET
ejpam-5495	94	12	dynamic	dynamic	ADJ
ejpam-5495	94	13	laws	law	NOUN
ejpam-5495	94	14	commonly	commonly	ADV
ejpam-5495	94	15	observed	observe	VERB
ejpam-5495	94	16	in	in	ADP
ejpam-5495	94	17	engineering	engineering	NOUN
ejpam-5495	94	18	and	and	CCONJ
ejpam-5495	94	19	physics	physics	NOUN
ejpam-5495	94	20	are	be	AUX
ejpam-5495	94	21	frequently	frequently	ADV
ejpam-5495	94	22	unknown	unknown	ADJ
ejpam-5495	94	23	.	.	PUNCT
ejpam-5495	95	1	the	the	DET
ejpam-5495	95	2	intricate	intricate	ADJ
ejpam-5495	95	3	dynamics	dynamic	NOUN
ejpam-5495	95	4	of	of	ADP
ejpam-5495	95	5	systems	system	NOUN
ejpam-5495	95	6	can	can	AUX
ejpam-5495	95	7	be	be	AUX
ejpam-5495	95	8	comprehensively	comprehensively	ADV
ejpam-5495	95	9	analyzed	analyze	VERB
ejpam-5495	95	10	with	with	ADP
ejpam-5495	95	11	these	these	DET
ejpam-5495	95	12	methodologies	methodology	NOUN
ejpam-5495	95	13	,	,	PUNCT
ejpam-5495	95	14	facilitating	facilitate	VERB
ejpam-5495	95	15	an	an	DET
ejpam-5495	95	16	in	in	ADP
ejpam-5495	95	17	-	-	PUNCT
ejpam-5495	95	18	depth	depth	NOUN
ejpam-5495	95	19	exploration	exploration	NOUN
ejpam-5495	95	20	of	of	ADP
ejpam-5495	95	21	both	both	CCONJ
ejpam-5495	95	22	quantitative	quantitative	ADJ
ejpam-5495	95	23	and	and	CCONJ
ejpam-5495	95	24	qualitative	qualitative	ADJ
ejpam-5495	95	25	dimensions	dimension	NOUN
ejpam-5495	95	26	of	of	ADP
ejpam-5495	95	27	system	system	NOUN
ejpam-5495	95	28	behavior	behavior	NOUN
ejpam-5495	95	29	.	.	PUNCT
ejpam-5495	96	1	a	a	DET
ejpam-5495	96	2	substantial	substantial	ADJ
ejpam-5495	96	3	number	number	NOUN
ejpam-5495	96	4	of	of	ADP
ejpam-5495	96	5	researches	research	NOUN
ejpam-5495	96	6	were	be	AUX
ejpam-5495	96	7	undertaken	undertake	VERB
ejpam-5495	96	8	on	on	ADP
ejpam-5495	96	9	the	the	DET
ejpam-5495	96	10	efficacy	efficacy	NOUN
ejpam-5495	96	11	and	and	CCONJ
ejpam-5495	96	12	wide	wide	ADJ
ejpam-5495	96	13	applicability	applicability	NOUN
ejpam-5495	96	14	of	of	ADP
ejpam-5495	96	15	this	this	DET
ejpam-5495	96	16	methodology	methodology	NOUN
ejpam-5495	96	17	[	[	X
ejpam-5495	96	18	2	2	NUM
ejpam-5495	96	19	,	,	PUNCT
ejpam-5495	96	20	9	9	NUM
ejpam-5495	96	21	,	,	PUNCT
ejpam-5495	96	22	10	10	NUM
ejpam-5495	96	23	,	,	PUNCT
ejpam-5495	96	24	17	17	NUM
ejpam-5495	96	25	]	]	PUNCT
ejpam-5495	96	26	.	.	PUNCT
ejpam-5495	97	1	the	the	DET
ejpam-5495	97	2	hff	hff	NOUN
ejpam-5495	97	3	played	play	VERB
ejpam-5495	97	4	a	a	DET
ejpam-5495	97	5	significant	significant	ADJ
ejpam-5495	97	6	role	role	NOUN
ejpam-5495	97	7	in	in	ADP
ejpam-5495	97	8	deriving	derive	VERB
ejpam-5495	97	9	closed	closed	ADJ
ejpam-5495	97	10	-	-	PUNCT
ejpam-5495	97	11	form	form	NOUN
ejpam-5495	97	12	analytical	analytical	ADJ
ejpam-5495	97	13	solutions	solution	NOUN
ejpam-5495	97	14	for	for	ADP
ejpam-5495	97	15	oscillators	oscillator	NOUN
ejpam-5495	97	16	,	,	PUNCT
ejpam-5495	97	17	particularly	particularly	ADV
ejpam-5495	97	18	the	the	DET
ejpam-5495	97	19	duffing	duffing	NOUN
ejpam-5495	97	20	oscillator	oscillator	NOUN
ejpam-5495	97	21	(	(	PUNCT
ejpam-5495	97	22	do	do	AUX
ejpam-5495	97	23	)	)	PUNCT
ejpam-5495	98	1	[	[	X
ejpam-5495	98	2	11	11	NUM
ejpam-5495	98	3	]	]	PUNCT
ejpam-5495	98	4	.	.	PUNCT
ejpam-5495	99	1	the	the	DET
ejpam-5495	99	2	hff	hff	PROPN
ejpam-5495	99	3	formula	formula	NOUN
ejpam-5495	99	4	was	be	AUX
ejpam-5495	99	5	developed	develop	VERB
ejpam-5495	99	6	into	into	ADP
ejpam-5495	99	7	as	as	ADP
ejpam-5495	99	8	a	a	DET
ejpam-5495	99	9	powerful	powerful	ADJ
ejpam-5495	99	10	mathematical	mathematical	ADJ
ejpam-5495	99	11	tool	tool	NOUN
ejpam-5495	99	12	for	for	ADP
ejpam-5495	99	13	analyzing	analyze	VERB
ejpam-5495	99	14	nonlinear	nonlinear	ADJ
ejpam-5495	99	15	oscillators	oscillator	NOUN
ejpam-5495	99	16	with	with	ADP
ejpam-5495	99	17	periodic	periodic	ADJ
ejpam-5495	99	18	solutions	solution	NOUN
ejpam-5495	99	19	.	.	PUNCT
ejpam-5495	100	1	prof	prof	NOUN
ejpam-5495	100	2	.	.	PUNCT
ejpam-5495	101	1	he	he	PRON
ejpam-5495	101	2	delivered	deliver	VERB
ejpam-5495	101	3	a	a	DET
ejpam-5495	101	4	pioneering	pioneer	VERB
ejpam-5495	101	5	review	review	NOUN
ejpam-5495	101	6	article	article	NOUN
ejpam-5495	101	7	and	and	CCONJ
ejpam-5495	101	8	was	be	AUX
ejpam-5495	101	9	the	the	DET
ejpam-5495	101	10	inaugural	inaugural	ADJ
ejpam-5495	101	11	presenter	presenter	NOUN
ejpam-5495	101	12	of	of	ADP
ejpam-5495	101	13	it	it	PRON
ejpam-5495	101	14	[	[	X
ejpam-5495	101	15	23	23	NUM
ejpam-5495	101	16	]	]	PUNCT
ejpam-5495	101	17	.	.	PUNCT
ejpam-5495	102	1	the	the	DET
ejpam-5495	102	2	precision	precision	NOUN
ejpam-5495	102	3	and	and	CCONJ
ejpam-5495	102	4	empirical	empirical	ADJ
ejpam-5495	102	5	validation	validation	NOUN
ejpam-5495	102	6	of	of	ADP
ejpam-5495	102	7	this	this	DET
ejpam-5495	102	8	hff	hff	NOUN
ejpam-5495	102	9	rendered	render	VERB
ejpam-5495	102	10	it	it	PRON
ejpam-5495	102	11	a	a	DET
ejpam-5495	102	12	preferred	preferred	ADJ
ejpam-5495	102	13	choice	choice	NOUN
ejpam-5495	102	14	among	among	ADP
ejpam-5495	102	15	engineers	engineer	NOUN
ejpam-5495	102	16	[	[	X
ejpam-5495	102	17	7	7	NUM
ejpam-5495	102	18	,	,	PUNCT
ejpam-5495	102	19	8	8	NUM
ejpam-5495	102	20	,	,	PUNCT
ejpam-5495	102	21	13	13	NUM
ejpam-5495	102	22	,	,	PUNCT
ejpam-5495	102	23	16	16	NUM
ejpam-5495	102	24	,	,	PUNCT
ejpam-5495	102	25	24	24	NUM
ejpam-5495	102	26	,	,	PUNCT
ejpam-5495	102	27	25	25	NUM
ejpam-5495	102	28	,	,	PUNCT
ejpam-5495	102	29	49	49	NUM
ejpam-5495	102	30	,	,	PUNCT
ejpam-5495	102	31	51	51	NUM
ejpam-5495	102	32	]	]	PUNCT
ejpam-5495	102	33	.	.	PUNCT
ejpam-5495	103	1	the	the	DET
ejpam-5495	103	2	hff	hff	PROPN
ejpam-5495	103	3	has	have	AUX
ejpam-5495	103	4	been	be	AUX
ejpam-5495	103	5	meticulously	meticulously	ADV
ejpam-5495	103	6	refined	refine	VERB
ejpam-5495	103	7	over	over	ADP
ejpam-5495	103	8	the	the	DET
ejpam-5495	103	9	years	year	NOUN
ejpam-5495	103	10	,	,	PUNCT
ejpam-5495	103	11	resulting	result	VERB
ejpam-5495	103	12	in	in	ADP
ejpam-5495	103	13	enhanced	enhanced	ADJ
ejpam-5495	103	14	accuracy	accuracy	NOUN
ejpam-5495	103	15	,	,	PUNCT
ejpam-5495	103	16	as	as	SCONJ
ejpam-5495	103	17	previously	previously	ADV
ejpam-5495	103	18	demonstrated	demonstrate	VERB
ejpam-5495	103	19	[	[	X
ejpam-5495	103	20	6	6	NUM
ejpam-5495	103	21	,	,	PUNCT
ejpam-5495	103	22	26	26	NUM
ejpam-5495	103	23	,	,	PUNCT
ejpam-5495	103	24	28	28	NUM
ejpam-5495	103	25	]	]	PUNCT
ejpam-5495	103	26	.	.	PUNCT
ejpam-5495	104	1	moreover	moreover	ADV
ejpam-5495	104	2	,	,	PUNCT
ejpam-5495	104	3	as	as	SCONJ
ejpam-5495	104	4	previously	previously	ADV
ejpam-5495	104	5	stated	state	VERB
ejpam-5495	104	6	,	,	PUNCT
ejpam-5495	104	7	the	the	DET
ejpam-5495	104	8	applicability	applicability	NOUN
ejpam-5495	104	9	of	of	ADP
ejpam-5495	104	10	this	this	DET
ejpam-5495	104	11	frequency	frequency	NOUN
ejpam-5495	104	12	approach	approach	NOUN
ejpam-5495	104	13	has	have	AUX
ejpam-5495	104	14	broadened	broaden	VERB
ejpam-5495	104	15	to	to	PART
ejpam-5495	104	16	encompass	encompass	VERB
ejpam-5495	104	17	fractal	fractal	ADJ
ejpam-5495	104	18	oscillators	oscillator	NOUN
ejpam-5495	104	19	[	[	X
ejpam-5495	104	20	55	55	NUM
ejpam-5495	104	21	]	]	PUNCT
ejpam-5495	104	22	.	.	PUNCT
ejpam-5495	105	1	in	in	ADP
ejpam-5495	105	2	hff	hff	PROPN
ejpam-5495	105	3	,	,	PUNCT
ejpam-5495	105	4	the	the	DET
ejpam-5495	105	5	correlation	correlation	NOUN
ejpam-5495	105	6	between	between	ADP
ejpam-5495	105	7	frequency	frequency	NOUN
ejpam-5495	105	8	and	and	CCONJ
ejpam-5495	105	9	amplitude	amplitude	NOUN
ejpam-5495	105	10	of	of	ADP
ejpam-5495	105	11	a	a	DET
ejpam-5495	105	12	nonlinear	nonlinear	ADJ
ejpam-5495	105	13	oscillator	oscillator	NOUN
ejpam-5495	105	14	was	be	AUX
ejpam-5495	105	15	derived	derive	VERB
ejpam-5495	105	16	from	from	ADP
ejpam-5495	105	17	the	the	DET
ejpam-5495	105	18	residuals	residual	NOUN
ejpam-5495	105	19	of	of	ADP
ejpam-5495	105	20	two	two	NUM
ejpam-5495	105	21	trial	trial	NOUN
ejpam-5495	105	22	solutions	solution	NOUN
ejpam-5495	105	23	[	[	X
ejpam-5495	105	24	50	50	NUM
ejpam-5495	105	25	]	]	PUNCT
ejpam-5495	105	26	.	.	PUNCT
ejpam-5495	106	1	despite	despite	SCONJ
ejpam-5495	106	2	achieving	achieve	VERB
ejpam-5495	106	3	a	a	DET
ejpam-5495	106	4	highly	highly	ADV
ejpam-5495	106	5	precise	precise	ADJ
ejpam-5495	106	6	result	result	NOUN
ejpam-5495	106	7	,	,	PUNCT
ejpam-5495	106	8	this	this	DET
ejpam-5495	106	9	method	method	NOUN
ejpam-5495	106	10	offers	offer	VERB
ejpam-5495	106	11	potential	potential	NOUN
ejpam-5495	106	12	for	for	ADP
ejpam-5495	106	13	further	further	ADJ
ejpam-5495	106	14	enhancement	enhancement	NOUN
ejpam-5495	106	15	.	.	PUNCT
ejpam-5495	107	1	the	the	DET
ejpam-5495	107	2	hff	hff	NOUN
ejpam-5495	107	3	originating	originate	VERB
ejpam-5495	107	4	from	from	ADP
ejpam-5495	107	5	an	an	DET
ejpam-5495	107	6	ancient	ancient	ADJ
ejpam-5495	107	7	chinese	chinese	ADJ
ejpam-5495	107	8	algorithm	algorithm	NOUN
ejpam-5495	107	9	is	be	AUX
ejpam-5495	107	10	an	an	DET
ejpam-5495	107	11	efficient	efficient	ADJ
ejpam-5495	107	12	method	method	NOUN
ejpam-5495	107	13	for	for	ADP
ejpam-5495	107	14	approximating	approximate	VERB
ejpam-5495	107	15	solutions	solution	NOUN
ejpam-5495	107	16	of	of	ADP
ejpam-5495	107	17	a	a	DET
ejpam-5495	107	18	nonlinear	nonlinear	ADJ
ejpam-5495	107	19	oscillator	oscillator	NOUN
ejpam-5495	107	20	.	.	PUNCT
ejpam-5495	108	1	a	a	DET
ejpam-5495	108	2	simpler	simple	ADJ
ejpam-5495	108	3	formulation	formulation	NOUN
ejpam-5495	108	4	was	be	AUX
ejpam-5495	108	5	presented	present	VERB
ejpam-5495	108	6	based	base	VERB
ejpam-5495	108	7	on	on	ADP
ejpam-5495	108	8	hff	hff	PROPN
ejpam-5495	109	1	[	[	X
ejpam-5495	109	2	52	52	NUM
ejpam-5495	109	3	]	]	PUNCT
ejpam-5495	109	4	.	.	PUNCT
ejpam-5495	110	1	the	the	DET
ejpam-5495	110	2	basic	basic	ADJ
ejpam-5495	110	3	hff	hff	NOUN
ejpam-5495	110	4	for	for	ADP
ejpam-5495	110	5	nonlinear	nonlinear	ADJ
ejpam-5495	110	6	oscillators	oscillator	NOUN
ejpam-5495	110	7	was	be	AUX
ejpam-5495	110	8	presented	present	VERB
ejpam-5495	110	9	and	and	CCONJ
ejpam-5495	110	10	validated	validate	VERB
ejpam-5495	110	11	,	,	PUNCT
ejpam-5495	110	12	with	with	ADP
ejpam-5495	110	13	a	a	DET
ejpam-5495	110	14	proposed	propose	VERB
ejpam-5495	110	15	change	change	NOUN
ejpam-5495	110	16	[	[	X
ejpam-5495	110	17	20	20	NUM
ejpam-5495	110	18	]	]	PUNCT
ejpam-5495	110	19	.	.	PUNCT
ejpam-5495	111	1	a	a	DET
ejpam-5495	111	2	fractal	fractal	ADJ
ejpam-5495	111	3	vibration	vibration	NOUN
ejpam-5495	111	4	in	in	ADP
ejpam-5495	111	5	a	a	DET
ejpam-5495	111	6	porous	porous	ADJ
ejpam-5495	111	7	media	medium	NOUN
ejpam-5495	111	8	was	be	AUX
ejpam-5495	111	9	presented	present	VERB
ejpam-5495	111	10	,	,	PUNCT
ejpam-5495	111	11	and	and	CCONJ
ejpam-5495	111	12	its	its	PRON
ejpam-5495	111	13	low	low	ADJ
ejpam-5495	111	14	-	-	PUNCT
ejpam-5495	111	15	frequency	frequency	NOUN
ejpam-5495	111	16	characteristics	characteristic	NOUN
ejpam-5495	111	17	were	be	AUX
ejpam-5495	111	18	clarified	clarify	VERB
ejpam-5495	111	19	by	by	ADP
ejpam-5495	111	20	the	the	DET
ejpam-5495	111	21	a.	a.	NOUN
ejpam-5495	111	22	alanazy	alanazy	NOUN
ejpam-5495	111	23	et	et	PROPN
ejpam-5495	111	24	al	al	PROPN
ejpam-5495	111	25	.	.	PUNCT
ejpam-5495	111	26	/	/	SYM
ejpam-5495	111	27	eur	eur	PROPN
ejpam-5495	111	28	.	.	PUNCT
ejpam-5495	112	1	j.	j.	PROPN
ejpam-5495	112	2	pure	pure	PROPN
ejpam-5495	112	3	appl	appl	PROPN
ejpam-5495	112	4	.	.	PROPN
ejpam-5495	112	5	math	math	PROPN
ejpam-5495	112	6	,	,	PUNCT
ejpam-5495	112	7	18	18	NUM
ejpam-5495	112	8	(	(	PUNCT
ejpam-5495	112	9	1	1	NUM
ejpam-5495	112	10	)	)	PUNCT
ejpam-5495	112	11	(	(	PUNCT
ejpam-5495	112	12	2025	2025	NUM
ejpam-5495	112	13	)	)	PUNCT
ejpam-5495	112	14	,	,	PUNCT
ejpam-5495	112	15	5495	5495	NUM
ejpam-5495	112	16	5	5	NUM
ejpam-5495	112	17	of	of	ADP
ejpam-5495	112	18	21	21	NUM
ejpam-5495	112	19	hff	hff	NOUN
ejpam-5495	112	20	.	.	PUNCT
ejpam-5495	113	1	in	in	ADP
ejpam-5495	113	2	the	the	DET
ejpam-5495	113	3	examination	examination	NOUN
ejpam-5495	113	4	of	of	ADP
ejpam-5495	113	5	nonlinear	nonlinear	ADJ
ejpam-5495	113	6	oscillatory	oscillatory	ADJ
ejpam-5495	113	7	systems	system	NOUN
ejpam-5495	113	8	,	,	PUNCT
ejpam-5495	113	9	the	the	DET
ejpam-5495	113	10	npa	npa	NOUN
ejpam-5495	113	11	distinctly	distinctly	ADV
ejpam-5495	113	12	contrasts	contrast	VERB
ejpam-5495	113	13	with	with	ADP
ejpam-5495	113	14	conventional	conventional	ADJ
ejpam-5495	113	15	perturbation	perturbation	NOUN
ejpam-5495	113	16	methods	method	NOUN
ejpam-5495	113	17	.	.	PUNCT
ejpam-5495	114	1	this	this	DET
ejpam-5495	114	2	approach	approach	NOUN
ejpam-5495	114	3	is	be	AUX
ejpam-5495	114	4	a	a	DET
ejpam-5495	114	5	robust	robust	ADJ
ejpam-5495	114	6	mathematical	mathematical	ADJ
ejpam-5495	114	7	tool	tool	NOUN
ejpam-5495	114	8	capable	capable	ADJ
ejpam-5495	114	9	of	of	ADP
ejpam-5495	114	10	addressing	address	VERB
ejpam-5495	114	11	many	many	ADJ
ejpam-5495	114	12	parameter	parameter	NOUN
ejpam-5495	114	13	regimes	regime	NOUN
ejpam-5495	114	14	,	,	PUNCT
ejpam-5495	114	15	especially	especially	ADV
ejpam-5495	114	16	those	those	PRON
ejpam-5495	114	17	characterized	characterize	VERB
ejpam-5495	114	18	by	by	ADP
ejpam-5495	114	19	significant	significant	ADJ
ejpam-5495	114	20	nonlinearity	nonlinearity	NOUN
ejpam-5495	114	21	.	.	PUNCT
ejpam-5495	115	1	a	a	DET
ejpam-5495	115	2	significant	significant	ADJ
ejpam-5495	115	3	technique	technique	NOUN
ejpam-5495	115	4	for	for	ADP
ejpam-5495	115	5	deriving	derive	VERB
ejpam-5495	115	6	analytical	analytical	ADJ
ejpam-5495	115	7	approximations	approximation	NOUN
ejpam-5495	115	8	in	in	ADP
ejpam-5495	115	9	the	the	DET
ejpam-5495	115	10	study	study	NOUN
ejpam-5495	115	11	of	of	ADP
ejpam-5495	115	12	nonlinear	nonlinear	ADJ
ejpam-5495	115	13	oscillators	oscillator	NOUN
ejpam-5495	115	14	was	be	AUX
ejpam-5495	115	15	utilized	utilize	VERB
ejpam-5495	115	16	.	.	PUNCT
ejpam-5495	116	1	the	the	DET
ejpam-5495	116	2	principal	principal	ADJ
ejpam-5495	116	3	objective	objective	NOUN
ejpam-5495	116	4	of	of	ADP
ejpam-5495	116	5	the	the	DET
ejpam-5495	116	6	npa	npa	NOUN
ejpam-5495	116	7	is	be	AUX
ejpam-5495	116	8	to	to	PART
ejpam-5495	116	9	simplify	simplify	VERB
ejpam-5495	116	10	the	the	DET
ejpam-5495	116	11	nonlinear	nonlinear	ADJ
ejpam-5495	116	12	model	model	NOUN
ejpam-5495	116	13	to	to	ADP
ejpam-5495	116	14	a	a	DET
ejpam-5495	116	15	more	more	ADV
ejpam-5495	116	16	tractable	tractable	ADJ
ejpam-5495	116	17	form	form	NOUN
ejpam-5495	116	18	,	,	PUNCT
ejpam-5495	116	19	hence	hence	ADV
ejpam-5495	116	20	enabling	enable	VERB
ejpam-5495	116	21	precise	precise	ADJ
ejpam-5495	116	22	specification	specification	NOUN
ejpam-5495	116	23	of	of	ADP
ejpam-5495	116	24	the	the	DET
ejpam-5495	116	25	solutions	solution	NOUN
ejpam-5495	116	26	.	.	PUNCT
ejpam-5495	117	1	this	this	PRON
ejpam-5495	117	2	will	will	AUX
ejpam-5495	117	3	provide	provide	VERB
ejpam-5495	117	4	a	a	DET
ejpam-5495	117	5	more	more	ADV
ejpam-5495	117	6	precise	precise	ADJ
ejpam-5495	117	7	estimation	estimation	NOUN
ejpam-5495	117	8	of	of	ADP
ejpam-5495	117	9	the	the	DET
ejpam-5495	117	10	original	original	ADJ
ejpam-5495	117	11	system	system	NOUN
ejpam-5495	117	12	’s	’s	PART
ejpam-5495	117	13	behavior	behavior	NOUN
ejpam-5495	118	1	[	[	X
ejpam-5495	118	2	3–5	3–5	NUM
ejpam-5495	118	3	,	,	PUNCT
ejpam-5495	118	4	15	15	NUM
ejpam-5495	118	5	,	,	PUNCT
ejpam-5495	118	6	31	31	NUM
ejpam-5495	118	7	,	,	PUNCT
ejpam-5495	118	8	38–44	38–44	NUM
ejpam-5495	118	9	]	]	PUNCT
ejpam-5495	118	10	.	.	PUNCT
ejpam-5495	119	1	the	the	DET
ejpam-5495	119	2	objective	objective	NOUN
ejpam-5495	119	3	of	of	ADP
ejpam-5495	119	4	this	this	DET
ejpam-5495	119	5	simplification	simplification	NOUN
ejpam-5495	119	6	is	be	AUX
ejpam-5495	119	7	to	to	PART
ejpam-5495	119	8	diminish	diminish	VERB
ejpam-5495	119	9	the	the	DET
ejpam-5495	119	10	average	average	ADJ
ejpam-5495	119	11	disparity	disparity	NOUN
ejpam-5495	119	12	between	between	ADP
ejpam-5495	119	13	the	the	DET
ejpam-5495	119	14	two	two	NUM
ejpam-5495	119	15	systems	system	NOUN
ejpam-5495	119	16	by	by	ADP
ejpam-5495	119	17	converting	convert	VERB
ejpam-5495	119	18	the	the	DET
ejpam-5495	119	19	equation	equation	NOUN
ejpam-5495	119	20	from	from	ADP
ejpam-5495	119	21	a	a	DET
ejpam-5495	119	22	nonlinear	nonlinear	ADJ
ejpam-5495	119	23	ode	ode	NOUN
ejpam-5495	119	24	to	to	ADP
ejpam-5495	119	25	a	a	DET
ejpam-5495	119	26	linear	linear	ADJ
ejpam-5495	119	27	one	one	NUM
ejpam-5495	119	28	.	.	PUNCT
ejpam-5495	120	1	consequently	consequently	ADV
ejpam-5495	120	2	,	,	PUNCT
ejpam-5495	120	3	moving	move	VERB
ejpam-5495	120	4	away	away	ADV
ejpam-5495	120	5	from	from	ADP
ejpam-5495	120	6	the	the	DET
ejpam-5495	120	7	iterative	iterative	NOUN
ejpam-5495	120	8	refinement	refinement	NOUN
ejpam-5495	120	9	of	of	ADP
ejpam-5495	120	10	perturbation	perturbation	NOUN
ejpam-5495	120	11	approaches	approach	NOUN
ejpam-5495	120	12	,	,	PUNCT
ejpam-5495	120	13	the	the	DET
ejpam-5495	120	14	npa	npa	NOUN
ejpam-5495	120	15	presented	present	VERB
ejpam-5495	120	16	a	a	DET
ejpam-5495	120	17	novel	novel	ADJ
ejpam-5495	120	18	perspective	perspective	NOUN
ejpam-5495	120	19	.	.	PUNCT
ejpam-5495	121	1	the	the	DET
ejpam-5495	121	2	objective	objective	NOUN
ejpam-5495	121	3	of	of	ADP
ejpam-5495	121	4	the	the	DET
ejpam-5495	121	5	npa	npa	NOUN
ejpam-5495	121	6	is	be	AUX
ejpam-5495	121	7	to	to	PART
ejpam-5495	121	8	comprehend	comprehend	VERB
ejpam-5495	121	9	the	the	DET
ejpam-5495	121	10	intricacies	intricacy	NOUN
ejpam-5495	121	11	of	of	ADP
ejpam-5495	121	12	nonlinear	nonlinear	ADJ
ejpam-5495	121	13	systems	system	NOUN
ejpam-5495	121	14	independently	independently	ADV
ejpam-5495	121	15	,	,	PUNCT
ejpam-5495	121	16	without	without	ADP
ejpam-5495	121	17	depending	depend	VERB
ejpam-5495	121	18	on	on	ADP
ejpam-5495	121	19	minor	minor	ADJ
ejpam-5495	121	20	perturbations	perturbation	NOUN
ejpam-5495	121	21	from	from	ADP
ejpam-5495	121	22	a	a	DET
ejpam-5495	121	23	known	know	VERB
ejpam-5495	121	24	solution	solution	NOUN
ejpam-5495	121	25	.	.	PUNCT
ejpam-5495	122	1	considering	consider	VERB
ejpam-5495	122	2	above	above	ADV
ejpam-5495	122	3	-	-	PUNCT
ejpam-5495	122	4	mentioned	mention	VERB
ejpam-5495	122	5	features	feature	NOUN
ejpam-5495	122	6	,	,	PUNCT
ejpam-5495	122	7	the	the	DET
ejpam-5495	122	8	evaluation	evaluation	NOUN
ejpam-5495	122	9	of	of	ADP
ejpam-5495	122	10	preventing	prevent	VERB
ejpam-5495	122	11	nonlinear	nonlinear	ADJ
ejpam-5495	122	12	exciting	exciting	ADJ
ejpam-5495	122	13	vdpd	vdpd	NOUN
ejpam-5495	122	14	with	with	ADP
ejpam-5495	122	15	td	td	NOUN
ejpam-5495	122	16	control	control	NOUN
ejpam-5495	122	17	is	be	AUX
ejpam-5495	122	18	a	a	DET
ejpam-5495	122	19	major	major	ADJ
ejpam-5495	122	20	difficulty	difficulty	NOUN
ejpam-5495	122	21	to	to	AUX
ejpam-5495	122	22	given	give	VERB
ejpam-5495	122	23	its	its	PRON
ejpam-5495	122	24	understanding	understanding	NOUN
ejpam-5495	122	25	to	to	ADP
ejpam-5495	122	26	dynamic	dynamic	ADJ
ejpam-5495	122	27	loading	loading	NOUN
ejpam-5495	122	28	,	,	PUNCT
ejpam-5495	122	29	geometrical	geometrical	ADJ
ejpam-5495	122	30	changes	change	NOUN
ejpam-5495	122	31	,	,	PUNCT
ejpam-5495	122	32	and	and	CCONJ
ejpam-5495	122	33	dissipating	dissipate	VERB
ejpam-5495	122	34	challenges	challenge	NOUN
ejpam-5495	122	35	.	.	PUNCT
ejpam-5495	123	1	examining	examine	VERB
ejpam-5495	123	2	this	this	DET
ejpam-5495	123	3	subject	subject	NOUN
ejpam-5495	123	4	is	be	AUX
ejpam-5495	123	5	the	the	DET
ejpam-5495	123	6	aim	aim	NOUN
ejpam-5495	123	7	of	of	ADP
ejpam-5495	123	8	this	this	DET
ejpam-5495	123	9	work	work	NOUN
ejpam-5495	123	10	.	.	PUNCT
ejpam-5495	124	1	according	accord	VERB
ejpam-5495	124	2	to	to	ADP
ejpam-5495	124	3	traditional	traditional	ADJ
ejpam-5495	124	4	mechanics	mechanic	NOUN
ejpam-5495	124	5	,	,	PUNCT
ejpam-5495	124	6	the	the	DET
ejpam-5495	124	7	fundamental	fundamental	ADJ
ejpam-5495	124	8	equation	equation	NOUN
ejpam-5495	124	9	of	of	ADP
ejpam-5495	124	10	motion	motion	NOUN
ejpam-5495	124	11	is	be	AUX
ejpam-5495	124	12	controlled	control	VERB
ejpam-5495	124	13	as	as	ADP
ejpam-5495	124	14	an	an	DET
ejpam-5495	124	15	ode	ode	NOUN
ejpam-5495	124	16	with	with	ADP
ejpam-5495	124	17	extremely	extremely	ADV
ejpam-5495	124	18	nonlinear	nonlinear	ADJ
ejpam-5495	124	19	terms	term	NOUN
ejpam-5495	124	20	.	.	PUNCT
ejpam-5495	125	1	the	the	DET
ejpam-5495	125	2	subsequent	subsequent	ADJ
ejpam-5495	125	3	points	point	NOUN
ejpam-5495	125	4	should	should	AUX
ejpam-5495	125	5	be	be	AUX
ejpam-5495	125	6	highlighted	highlight	VERB
ejpam-5495	125	7	in	in	ADP
ejpam-5495	125	8	relation	relation	NOUN
ejpam-5495	125	9	to	to	ADP
ejpam-5495	125	10	the	the	DET
ejpam-5495	125	11	unique	unique	ADJ
ejpam-5495	125	12	methodology	methodology	NOUN
ejpam-5495	125	13	or	or	CCONJ
ejpam-5495	125	14	noteworthy	noteworthy	ADJ
ejpam-5495	125	15	outcomes	outcome	NOUN
ejpam-5495	125	16	:	:	PUNCT
ejpam-5495	125	17	(	(	PUNCT
ejpam-5495	125	18	i	i	NOUN
ejpam-5495	125	19	)	)	PUNCT
ejpam-5495	125	20	in	in	ADP
ejpam-5495	125	21	simple	simple	ADJ
ejpam-5495	125	22	terms	term	NOUN
ejpam-5495	125	23	,	,	PUNCT
ejpam-5495	125	24	the	the	DET
ejpam-5495	125	25	distinctive	distinctive	ADJ
ejpam-5495	125	26	approach	approach	NOUN
ejpam-5495	125	27	generates	generate	VERB
ejpam-5495	125	28	a	a	DET
ejpam-5495	125	29	second	second	ADJ
ejpam-5495	125	30	identical	identical	ADJ
ejpam-5495	125	31	linear	linear	PROPN
ejpam-5495	125	32	ode	ode	NOUN
ejpam-5495	125	33	that	that	PRON
ejpam-5495	125	34	is	be	AUX
ejpam-5495	125	35	comparable	comparable	ADJ
ejpam-5495	125	36	to	to	ADP
ejpam-5495	125	37	the	the	DET
ejpam-5495	125	38	current	current	ADJ
ejpam-5495	125	39	nonlinear	nonlinear	ADJ
ejpam-5495	125	40	one	one	NUM
ejpam-5495	125	41	.	.	PUNCT
ejpam-5495	126	1	(	(	PUNCT
ejpam-5495	126	2	ii	ii	NOUN
ejpam-5495	126	3	)	)	PUNCT
ejpam-5495	126	4	a	a	DET
ejpam-5495	126	5	strong	strong	ADJ
ejpam-5495	126	6	matching	matching	NOUN
ejpam-5495	126	7	between	between	ADP
ejpam-5495	126	8	these	these	DET
ejpam-5495	126	9	two	two	NUM
ejpam-5495	126	10	equations	equation	NOUN
ejpam-5495	126	11	is	be	AUX
ejpam-5495	126	12	achieved	achieve	VERB
ejpam-5495	126	13	via	via	ADP
ejpam-5495	126	14	the	the	DET
ejpam-5495	126	15	ms	ms	PROPN
ejpam-5495	126	16	.	.	PROPN
ejpam-5495	126	17	(	(	PUNCT
ejpam-5495	126	18	iii	iii	X
ejpam-5495	126	19	)	)	PUNCT
ejpam-5495	126	20	all	all	DET
ejpam-5495	126	21	traditional	traditional	ADJ
ejpam-5495	126	22	methods	method	NOUN
ejpam-5495	126	23	employ	employ	VERB
ejpam-5495	126	24	the	the	DET
ejpam-5495	126	25	taylor	taylor	PROPN
ejpam-5495	126	26	expansion	expansion	NOUN
ejpam-5495	126	27	to	to	PART
ejpam-5495	126	28	reduce	reduce	VERB
ejpam-5495	126	29	the	the	DET
ejpam-5495	126	30	problem	problem	NOUN
ejpam-5495	126	31	’s	’s	PART
ejpam-5495	126	32	complexity	complexity	NOUN
ejpam-5495	126	33	.	.	PUNCT
ejpam-5495	127	1	under	under	ADP
ejpam-5495	127	2	the	the	DET
ejpam-5495	127	3	current	current	ADJ
ejpam-5495	127	4	approach	approach	NOUN
ejpam-5495	127	5	,	,	PUNCT
ejpam-5495	127	6	this	this	DET
ejpam-5495	127	7	limitation	limitation	NOUN
ejpam-5495	127	8	has	have	AUX
ejpam-5495	127	9	been	be	AUX
ejpam-5495	127	10	disregarded	disregard	VERB
ejpam-5495	127	11	.	.	PUNCT
ejpam-5495	128	1	(	(	PUNCT
ejpam-5495	128	2	iv	iv	X
ejpam-5495	128	3	)	)	PUNCT
ejpam-5495	128	4	the	the	DET
ejpam-5495	128	5	present	present	ADJ
ejpam-5495	128	6	approach	approach	NOUN
ejpam-5495	128	7	enables	enable	VERB
ejpam-5495	128	8	us	we	PRON
ejpam-5495	128	9	to	to	PART
ejpam-5495	128	10	examine	examine	VERB
ejpam-5495	128	11	the	the	DET
ejpam-5495	128	12	problem	problem	NOUN
ejpam-5495	128	13	’s	’s	PART
ejpam-5495	128	14	stability	stability	NOUN
ejpam-5495	128	15	analysis	analysis	NOUN
ejpam-5495	128	16	,	,	PUNCT
ejpam-5495	128	17	which	which	PRON
ejpam-5495	128	18	was	be	AUX
ejpam-5495	128	19	not	not	PART
ejpam-5495	128	20	possible	possible	ADJ
ejpam-5495	128	21	with	with	ADP
ejpam-5495	128	22	some	some	PRON
ejpam-5495	128	23	of	of	ADP
ejpam-5495	128	24	the	the	DET
ejpam-5495	128	25	earlier	early	ADV
ejpam-5495	128	26	traditional	traditional	ADJ
ejpam-5495	128	27	perturbation	perturbation	NOUN
ejpam-5495	128	28	methodologies	methodology	NOUN
ejpam-5495	128	29	.	.	PUNCT
ejpam-5495	129	1	(	(	PUNCT
ejpam-5495	129	2	v	v	NOUN
ejpam-5495	129	3	)	)	PUNCT
ejpam-5495	129	4	in	in	ADP
ejpam-5495	129	5	conclusion	conclusion	NOUN
ejpam-5495	129	6	,	,	PUNCT
ejpam-5495	129	7	the	the	DET
ejpam-5495	129	8	unusual	unusual	ADJ
ejpam-5495	129	9	strategy	strategy	NOUN
ejpam-5495	129	10	seems	seem	VERB
ejpam-5495	129	11	to	to	PART
ejpam-5495	129	12	be	be	AUX
ejpam-5495	129	13	a	a	DET
ejpam-5495	129	14	simple	simple	ADJ
ejpam-5495	129	15	,	,	PUNCT
ejpam-5495	129	16	effective	effective	ADJ
ejpam-5495	129	17	,	,	PUNCT
ejpam-5495	129	18	and	and	CCONJ
ejpam-5495	129	19	appealing	appeal	VERB
ejpam-5495	129	20	tool	tool	NOUN
ejpam-5495	129	21	.	.	PUNCT
ejpam-5495	130	1	it	it	PRON
ejpam-5495	130	2	can	can	AUX
ejpam-5495	130	3	be	be	AUX
ejpam-5495	130	4	utilized	utilize	VERB
ejpam-5495	130	5	to	to	PART
ejpam-5495	130	6	analyze	analyze	VERB
ejpam-5495	130	7	various	various	ADJ
ejpam-5495	130	8	classes	class	NOUN
ejpam-5495	130	9	of	of	ADP
ejpam-5495	130	10	nonlinear	nonlinear	ADJ
ejpam-5495	130	11	oscillators	oscillator	NOUN
ejpam-5495	130	12	.	.	PUNCT
ejpam-5495	131	1	it	it	PRON
ejpam-5495	131	2	is	be	AUX
ejpam-5495	131	3	simple	simple	ADJ
ejpam-5495	131	4	to	to	PART
ejpam-5495	131	5	follow	follow	VERB
ejpam-5495	131	6	how	how	SCONJ
ejpam-5495	131	7	the	the	DET
ejpam-5495	131	8	paper	paper	NOUN
ejpam-5495	131	9	is	be	AUX
ejpam-5495	131	10	set	set	VERB
ejpam-5495	131	11	up	up	ADP
ejpam-5495	131	12	as	as	ADP
ejpam-5495	131	13	:	:	PUNCT
ejpam-5495	131	14	a	a	DET
ejpam-5495	131	15	npa	npa	NOUN
ejpam-5495	131	16	that	that	PRON
ejpam-5495	131	17	yields	yield	VERB
ejpam-5495	131	18	the	the	DET
ejpam-5495	131	19	equivalent	equivalent	ADJ
ejpam-5495	131	20	linear	linear	ADJ
ejpam-5495	131	21	equation	equation	NOUN
ejpam-5495	131	22	is	be	AUX
ejpam-5495	131	23	introduced	introduce	VERB
ejpam-5495	131	24	in	in	ADP
ejpam-5495	131	25	§	§	PROPN
ejpam-5495	131	26	2	2	NUM
ejpam-5495	131	27	.	.	PUNCT
ejpam-5495	132	1	this	this	DET
ejpam-5495	132	2	section	section	NOUN
ejpam-5495	132	3	displays	display	VERB
ejpam-5495	132	4	a	a	DET
ejpam-5495	132	5	strong	strong	ADJ
ejpam-5495	132	6	agreement	agreement	NOUN
ejpam-5495	132	7	between	between	ADP
ejpam-5495	132	8	the	the	DET
ejpam-5495	132	9	as	as	ADP
ejpam-5495	132	10	and	and	CCONJ
ejpam-5495	132	11	the	the	DET
ejpam-5495	132	12	ns	ns	NOUN
ejpam-5495	132	13	.	.	PUNCT
ejpam-5495	133	1	the	the	DET
ejpam-5495	133	2	graphical	graphical	ADJ
ejpam-5495	133	3	plots	plot	NOUN
ejpam-5495	133	4	in	in	ADP
ejpam-5495	133	5	§	§	PROPN
ejpam-5495	133	6	3	3	NUM
ejpam-5495	133	7	are	be	AUX
ejpam-5495	133	8	presented	present	VERB
ejpam-5495	133	9	along	along	ADP
ejpam-5495	133	10	with	with	ADP
ejpam-5495	133	11	their	their	PRON
ejpam-5495	133	12	interpretations	interpretation	NOUN
ejpam-5495	133	13	based	base	VERB
ejpam-5495	133	14	on	on	ADP
ejpam-5495	133	15	the	the	DET
ejpam-5495	133	16	outcomes	outcome	NOUN
ejpam-5495	133	17	,	,	PUNCT
ejpam-5495	133	18	including	include	VERB
ejpam-5495	133	19	temporal	temporal	ADJ
ejpam-5495	133	20	history	history	NOUN
ejpam-5495	133	21	,	,	PUNCT
ejpam-5495	133	22	stability	stability	NOUN
ejpam-5495	133	23	,	,	PUNCT
ejpam-5495	133	24	and	and	CCONJ
ejpam-5495	133	25	polar	polar	ADJ
ejpam-5495	133	26	study	study	NOUN
ejpam-5495	133	27	.	.	PUNCT
ejpam-5495	134	1	finally	finally	ADV
ejpam-5495	134	2	,	,	PUNCT
ejpam-5495	134	3	the	the	DET
ejpam-5495	134	4	concluding	concluding	NOUN
ejpam-5495	134	5	remarks	remark	NOUN
ejpam-5495	134	6	are	be	AUX
ejpam-5495	134	7	presented	present	VERB
ejpam-5495	134	8	through	through	ADP
ejpam-5495	134	9	§	§	PROPN
ejpam-5495	134	10	4	4	NUM
ejpam-5495	134	11	.	.	NOUN
ejpam-5495	134	12	2	2	NUM
ejpam-5495	134	13	.	.	X
ejpam-5495	134	14	methodology	methodology	NOUN
ejpam-5495	134	15	of	of	ADP
ejpam-5495	134	16	the	the	DET
ejpam-5495	134	17	prototype	prototype	NOUN
ejpam-5495	134	18	given	give	VERB
ejpam-5495	134	19	the	the	DET
ejpam-5495	134	20	importance	importance	NOUN
ejpam-5495	134	21	of	of	ADP
ejpam-5495	134	22	the	the	DET
ejpam-5495	134	23	above	above	ADV
ejpam-5495	134	24	-	-	PUNCT
ejpam-5495	134	25	mentioned	mention	VERB
ejpam-5495	134	26	components	component	NOUN
ejpam-5495	134	27	,	,	PUNCT
ejpam-5495	134	28	the	the	DET
ejpam-5495	134	29	study	study	NOUN
ejpam-5495	134	30	of	of	ADP
ejpam-5495	134	31	the	the	DET
ejpam-5495	134	32	vdpd	vdpd	NOUN
ejpam-5495	134	33	has	have	VERB
ejpam-5495	134	34	imaginable	imaginable	ADJ
ejpam-5495	134	35	uses	use	NOUN
ejpam-5495	134	36	in	in	ADP
ejpam-5495	134	37	manufacturing	manufacturing	NOUN
ejpam-5495	134	38	,	,	PUNCT
ejpam-5495	134	39	theory	theory	NOUN
ejpam-5495	134	40	of	of	ADP
ejpam-5495	134	41	communications	communication	NOUN
ejpam-5495	134	42	,	,	PUNCT
ejpam-5495	134	43	and	and	CCONJ
ejpam-5495	134	44	biology	biology	NOUN
ejpam-5495	134	45	.	.	PUNCT
ejpam-5495	135	1	it	it	PRON
ejpam-5495	135	2	has	have	VERB
ejpam-5495	135	3	a.	a.	NOUN
ejpam-5495	135	4	alanazy	alanazy	PROPN
ejpam-5495	135	5	et	et	PROPN
ejpam-5495	135	6	al	al	PROPN
ejpam-5495	135	7	.	.	PUNCT
ejpam-5495	135	8	/	/	SYM
ejpam-5495	135	9	eur	eur	PROPN
ejpam-5495	135	10	.	.	PUNCT
ejpam-5495	136	1	j.	j.	PROPN
ejpam-5495	136	2	pure	pure	PROPN
ejpam-5495	136	3	appl	appl	PROPN
ejpam-5495	136	4	.	.	PROPN
ejpam-5495	136	5	math	math	PROPN
ejpam-5495	136	6	,	,	PUNCT
ejpam-5495	136	7	18	18	NUM
ejpam-5495	136	8	(	(	PUNCT
ejpam-5495	136	9	1	1	NUM
ejpam-5495	136	10	)	)	PUNCT
ejpam-5495	136	11	(	(	PUNCT
ejpam-5495	136	12	2025	2025	NUM
ejpam-5495	136	13	)	)	PUNCT
ejpam-5495	136	14	,	,	PUNCT
ejpam-5495	136	15	5495	5495	NUM
ejpam-5495	136	16	6	6	NUM
ejpam-5495	136	17	of	of	ADP
ejpam-5495	136	18	21	21	NUM
ejpam-5495	136	19	figure	figure	NOUN
ejpam-5495	136	20	1	1	NUM
ejpam-5495	136	21	:	:	PUNCT
ejpam-5495	136	22	sketches	sketch	VERB
ejpam-5495	136	23	the	the	DET
ejpam-5495	136	24	model	model	NOUN
ejpam-5495	136	25	being	be	AUX
ejpam-5495	136	26	examined	examine	VERB
ejpam-5495	136	27	.	.	PUNCT
ejpam-5495	137	1	been	be	AUX
ejpam-5495	137	2	featured	feature	VERB
ejpam-5495	137	3	in	in	ADP
ejpam-5495	137	4	several	several	ADJ
ejpam-5495	137	5	topics	topic	NOUN
ejpam-5495	137	6	.	.	PUNCT
ejpam-5495	138	1	consequently	consequently	ADV
ejpam-5495	138	2	,	,	PUNCT
ejpam-5495	138	3	the	the	DET
ejpam-5495	138	4	current	current	ADJ
ejpam-5495	138	5	work	work	NOUN
ejpam-5495	138	6	conducts	conduct	VERB
ejpam-5495	138	7	the	the	DET
ejpam-5495	138	8	following	follow	VERB
ejpam-5495	138	9	analysis	analysis	NOUN
ejpam-5495	138	10	of	of	ADP
ejpam-5495	138	11	the	the	DET
ejpam-5495	138	12	excited	excited	ADJ
ejpam-5495	138	13	vdpd	vdpd	NOUN
ejpam-5495	138	14	with	with	ADP
ejpam-5495	138	15	location	location	NOUN
ejpam-5495	138	16	and	and	CCONJ
ejpam-5495	138	17	velocity	velocity	NOUN
ejpam-5495	138	18	delays	delay	NOUN
ejpam-5495	138	19	:	:	PUNCT
ejpam-5495	138	20	z̈	z̈	X
ejpam-5495	138	21	+	+	CCONJ
ejpam-5495	138	22	ω2z	ω2z	NOUN
ejpam-5495	138	23	−	−	ADP
ejpam-5495	138	24	µ(1−	µ(1−	PROPN
ejpam-5495	138	25	z2	z2	NUM
ejpam-5495	138	26	)	)	PUNCT
ejpam-5495	138	27	ż	ż	NOUN
ejpam-5495	138	28	+	+	NUM
ejpam-5495	138	29	λz3	λz3	NOUN
ejpam-5495	138	30	=	=	SYM
ejpam-5495	138	31	f	f	PROPN
ejpam-5495	138	32	cos(ωt	cos(ωt	PRON
ejpam-5495	138	33	)	)	PUNCT
ejpam-5495	139	1	+	+	CCONJ
ejpam-5495	139	2	α	α	NUM
ejpam-5495	139	3	z(t−	z(t−	PROPN
ejpam-5495	139	4	τ	τ	X
ejpam-5495	139	5	)	)	PUNCT
ejpam-5495	140	1	+	+	CCONJ
ejpam-5495	140	2	β	β	X
ejpam-5495	140	3	ż(t−	ż(t−	NUM
ejpam-5495	140	4	τ	τ	X
ejpam-5495	140	5	)	)	PUNCT
ejpam-5495	140	6	,	,	PUNCT
ejpam-5495	140	7	(	(	PUNCT
ejpam-5495	140	8	1	1	X
ejpam-5495	140	9	)	)	PUNCT
ejpam-5495	140	10	with	with	ADP
ejpam-5495	140	11	the	the	DET
ejpam-5495	140	12	initial	initial	ADJ
ejpam-5495	140	13	conditions	condition	NOUN
ejpam-5495	140	14	(	(	PUNCT
ejpam-5495	140	15	ics	ics	NOUN
ejpam-5495	140	16	):	):	PUNCT
ejpam-5495	140	17	z(0	z(0	NUM
ejpam-5495	140	18	)	)	PUNCT
ejpam-5495	140	19	=	=	SYM
ejpam-5495	140	20	a	a	PRON
ejpam-5495	140	21	,	,	PUNCT
ejpam-5495	140	22	and	and	CCONJ
ejpam-5495	140	23	ż(0	ż(0	PROPN
ejpam-5495	140	24	)	)	PUNCT
ejpam-5495	140	25	=	=	SYM
ejpam-5495	140	26	0	0	NUM
ejpam-5495	140	27	,	,	PUNCT
ejpam-5495	140	28	(	(	PUNCT
ejpam-5495	140	29	2	2	X
ejpam-5495	140	30	)	)	PUNCT
ejpam-5495	140	31	where	where	SCONJ
ejpam-5495	140	32	all	all	DET
ejpam-5495	140	33	elements	element	NOUN
ejpam-5495	140	34	considered	consider	VERB
ejpam-5495	140	35	in	in	ADP
ejpam-5495	140	36	eq	eq	ADP
ejpam-5495	140	37	.	.	PUNCT
ejpam-5495	141	1	(	(	PUNCT
ejpam-5495	141	2	1	1	X
ejpam-5495	141	3	)	)	PUNCT
ejpam-5495	141	4	are	be	AUX
ejpam-5495	141	5	listed	list	VERB
ejpam-5495	141	6	in	in	ADP
ejpam-5495	141	7	the	the	DET
ejpam-5495	141	8	following	following	NOUN
ejpam-5495	141	9	:	:	PUNCT
ejpam-5495	141	10	symbol	symbol	NOUN
ejpam-5495	141	11	clarification	clarification	NOUN
ejpam-5495	141	12	symbol	symbol	NOUN
ejpam-5495	141	13	clarification	clarification	NOUN
ejpam-5495	141	14	z	z	NOUN
ejpam-5495	141	15	displacement	displacement	NOUN
ejpam-5495	141	16	f	f	PROPN
ejpam-5495	141	17	external	external	ADJ
ejpam-5495	141	18	excited	excited	ADJ
ejpam-5495	141	19	force	force	NOUN
ejpam-5495	141	20	·	·	PUNCT
ejpam-5495	141	21	derivative	derivative	NOUN
ejpam-5495	141	22	with	with	ADP
ejpam-5495	141	23	time	time	NOUN
ejpam-5495	141	24	α	α	DET
ejpam-5495	141	25	coefficient	coefficient	NOUN
ejpam-5495	141	26	of	of	ADP
ejpam-5495	141	27	position	position	NOUN
ejpam-5495	141	28	td	td	NOUN
ejpam-5495	141	29	ω	ω	NUM
ejpam-5495	141	30	natural	natural	ADJ
ejpam-5495	141	31	frequency	frequency	NOUN
ejpam-5495	141	32	β	β	NOUN
ejpam-5495	141	33	coefficient	coefficient	NOUN
ejpam-5495	141	34	of	of	ADP
ejpam-5495	141	35	velocity	velocity	NOUN
ejpam-5495	141	36	td	td	NOUN
ejpam-5495	141	37	µ	µ	DET
ejpam-5495	141	38	damping	damp	VERB
ejpam-5495	141	39	coefficient	coefficient	NOUN
ejpam-5495	141	40	a	a	DET
ejpam-5495	141	41	initial	initial	ADJ
ejpam-5495	141	42	amplitude	amplitude	NOUN
ejpam-5495	141	43	λ	λ	NOUN
ejpam-5495	141	44	third	third	ADJ
ejpam-5495	141	45	-	-	PUNCT
ejpam-5495	141	46	order	order	NOUN
ejpam-5495	141	47	nonlinear	nonlinear	ADJ
ejpam-5495	141	48	duffing	duffing	NOUN
ejpam-5495	141	49	τ	τ	PROPN
ejpam-5495	141	50	time	time	NOUN
ejpam-5495	141	51	-	-	PUNCT
ejpam-5495	141	52	decay	decay	NOUN
ejpam-5495	141	53	controller	controller	NOUN
ejpam-5495	141	54	coefficients	coefficient	NOUN
ejpam-5495	141	55	,	,	PUNCT
ejpam-5495	141	56	λ	λ	X
ejpam-5495	141	57	>	>	X
ejpam-5495	141	58	0,λ	0,λ	PUNCT
ejpam-5495	142	1	<	<	X
ejpam-5495	142	2	are	be	AUX
ejpam-5495	142	3	hardening	harden	VERB
ejpam-5495	142	4	and	and	CCONJ
ejpam-5495	142	5	softening	soften	VERB
ejpam-5495	142	6	spring	spring	NOUN
ejpam-5495	142	7	,	,	PUNCT
ejpam-5495	142	8	respectively	respectively	ADV
ejpam-5495	142	9	the	the	DET
ejpam-5495	142	10	vdpd	vdpd	NOUN
ejpam-5495	142	11	incorporating	incorporate	VERB
ejpam-5495	142	12	the	the	DET
ejpam-5495	142	13	tds	tds	NOUN
ejpam-5495	142	14	in	in	ADP
ejpam-5495	142	15	position	position	NOUN
ejpam-5495	142	16	and	and	CCONJ
ejpam-5495	142	17	velocity	velocity	NOUN
ejpam-5495	142	18	characterizes	characterize	VERB
ejpam-5495	142	19	intricate	intricate	ADJ
ejpam-5495	142	20	dynamical	dynamical	ADJ
ejpam-5495	142	21	systems	system	NOUN
ejpam-5495	142	22	,	,	PUNCT
ejpam-5495	142	23	including	include	VERB
ejpam-5495	142	24	mechanical	mechanical	ADJ
ejpam-5495	142	25	oscillators	oscillator	NOUN
ejpam-5495	142	26	and	and	CCONJ
ejpam-5495	142	27	electronic	electronic	ADJ
ejpam-5495	142	28	circuits	circuit	NOUN
ejpam-5495	142	29	,	,	PUNCT
ejpam-5495	142	30	where	where	SCONJ
ejpam-5495	142	31	nonlinearity	nonlinearity	NOUN
ejpam-5495	142	32	and	and	CCONJ
ejpam-5495	142	33	memory	memory	NOUN
ejpam-5495	142	34	effects	effect	NOUN
ejpam-5495	142	35	are	be	AUX
ejpam-5495	142	36	pivotal	pivotal	ADJ
ejpam-5495	142	37	.	.	PUNCT
ejpam-5495	143	1	the	the	DET
ejpam-5495	143	2	tds	tds	NOUN
ejpam-5495	143	3	illustrate	illustrate	VERB
ejpam-5495	143	4	the	the	DET
ejpam-5495	143	5	impact	impact	NOUN
ejpam-5495	143	6	of	of	ADP
ejpam-5495	143	7	previous	previous	ADJ
ejpam-5495	143	8	states	state	NOUN
ejpam-5495	143	9	on	on	ADP
ejpam-5495	143	10	the	the	DET
ejpam-5495	143	11	present	present	ADJ
ejpam-5495	143	12	behavior	behavior	NOUN
ejpam-5495	143	13	of	of	ADP
ejpam-5495	143	14	the	the	DET
ejpam-5495	143	15	system	system	NOUN
ejpam-5495	143	16	,	,	PUNCT
ejpam-5495	143	17	interpretation	interpretation	NOUN
ejpam-5495	143	18	it	it	PRON
ejpam-5495	143	19	valuable	valuable	ADJ
ejpam-5495	143	20	for	for	ADP
ejpam-5495	143	21	analyzing	analyze	VERB
ejpam-5495	143	22	phenomena	phenomenon	NOUN
ejpam-5495	143	23	such	such	ADJ
ejpam-5495	143	24	as	as	ADP
ejpam-5495	143	25	chaotic	chaotic	ADJ
ejpam-5495	143	26	motion	motion	NOUN
ejpam-5495	143	27	,	,	PUNCT
ejpam-5495	143	28	signal	signal	NOUN
ejpam-5495	143	29	processing	processing	NOUN
ejpam-5495	143	30	,	,	PUNCT
ejpam-5495	143	31	and	and	CCONJ
ejpam-5495	143	32	control	control	NOUN
ejpam-5495	143	33	systems	system	NOUN
ejpam-5495	143	34	,	,	PUNCT
ejpam-5495	143	35	where	where	SCONJ
ejpam-5495	143	36	delayed	delay	VERB
ejpam-5495	143	37	feedback	feedback	NOUN
ejpam-5495	143	38	affects	affect	VERB
ejpam-5495	143	39	stability	stability	NOUN
ejpam-5495	143	40	,	,	PUNCT
ejpam-5495	143	41	oscillations	oscillation	NOUN
ejpam-5495	143	42	,	,	PUNCT
ejpam-5495	143	43	and	and	CCONJ
ejpam-5495	143	44	bifurcations	bifurcation	NOUN
ejpam-5495	143	45	.	.	PUNCT
ejpam-5495	144	1	this	this	DET
ejpam-5495	144	2	equation	equation	NOUN
ejpam-5495	144	3	is	be	AUX
ejpam-5495	144	4	specifically	specifically	ADV
ejpam-5495	144	5	utilized	utilize	VERB
ejpam-5495	144	6	in	in	ADP
ejpam-5495	144	7	situations	situation	NOUN
ejpam-5495	144	8	necessitating	necessitate	VERB
ejpam-5495	144	9	the	the	DET
ejpam-5495	144	10	examination	examination	NOUN
ejpam-5495	144	11	of	of	ADP
ejpam-5495	144	12	delayed	delay	VERB
ejpam-5495	144	13	response	response	NOUN
ejpam-5495	144	14	effects	effect	NOUN
ejpam-5495	144	15	in	in	ADP
ejpam-5495	144	16	actual	actual	ADJ
ejpam-5495	144	17	physical	physical	ADJ
ejpam-5495	144	18	systems	system	NOUN
ejpam-5495	144	19	.	.	PUNCT
ejpam-5495	145	1	the	the	DET
ejpam-5495	145	2	a.	a.	NOUN
ejpam-5495	145	3	alanazy	alanazy	PROPN
ejpam-5495	145	4	et	et	PROPN
ejpam-5495	145	5	al	al	PROPN
ejpam-5495	145	6	.	.	PUNCT
ejpam-5495	145	7	/	/	SYM
ejpam-5495	145	8	eur	eur	PROPN
ejpam-5495	145	9	.	.	PUNCT
ejpam-5495	146	1	j.	j.	PROPN
ejpam-5495	146	2	pure	pure	PROPN
ejpam-5495	146	3	appl	appl	PROPN
ejpam-5495	146	4	.	.	PROPN
ejpam-5495	146	5	math	math	PROPN
ejpam-5495	146	6	,	,	PUNCT
ejpam-5495	146	7	18	18	NUM
ejpam-5495	146	8	(	(	PUNCT
ejpam-5495	146	9	1	1	NUM
ejpam-5495	146	10	)	)	PUNCT
ejpam-5495	146	11	(	(	PUNCT
ejpam-5495	146	12	2025	2025	NUM
ejpam-5495	146	13	)	)	PUNCT
ejpam-5495	146	14	,	,	PUNCT
ejpam-5495	146	15	5495	5495	NUM
ejpam-5495	146	16	7	7	NUM
ejpam-5495	146	17	of	of	ADP
ejpam-5495	146	18	21	21	NUM
ejpam-5495	146	19	vdpd	vdpd	NOUN
ejpam-5495	146	20	has	have	VERB
ejpam-5495	146	21	reasonable	reasonable	ADJ
ejpam-5495	146	22	uses	use	NOUN
ejpam-5495	146	23	in	in	ADP
ejpam-5495	146	24	various	various	ADJ
ejpam-5495	146	25	domains	domain	NOUN
ejpam-5495	146	26	such	such	ADJ
ejpam-5495	146	27	as	as	ADP
ejpam-5495	146	28	:	:	PUNCT
ejpam-5495	146	29	i.	i.	PROPN
ejpam-5495	146	30	mechanical	mechanical	PROPN
ejpam-5495	146	31	systems	system	NOUN
ejpam-5495	146	32	:	:	PUNCT
ejpam-5495	146	33	employed	employ	VERB
ejpam-5495	146	34	to	to	PART
ejpam-5495	146	35	model	model	VERB
ejpam-5495	146	36	and	and	CCONJ
ejpam-5495	146	37	analyze	analyze	VERB
ejpam-5495	146	38	vibrations	vibration	NOUN
ejpam-5495	146	39	in	in	ADP
ejpam-5495	146	40	mechanical	mechanical	ADJ
ejpam-5495	146	41	systems	system	NOUN
ejpam-5495	146	42	,	,	PUNCT
ejpam-5495	146	43	including	include	VERB
ejpam-5495	146	44	beams	beam	NOUN
ejpam-5495	146	45	and	and	CCONJ
ejpam-5495	146	46	bridges	bridge	NOUN
ejpam-5495	146	47	,	,	PUNCT
ejpam-5495	146	48	where	where	SCONJ
ejpam-5495	146	49	nonlinear	nonlinear	ADJ
ejpam-5495	146	50	damping	damp	VERB
ejpam-5495	146	51	and	and	CCONJ
ejpam-5495	146	52	stiffness	stiffness	NOUN
ejpam-5495	146	53	are	be	AUX
ejpam-5495	146	54	substantial	substantial	ADJ
ejpam-5495	146	55	.	.	PUNCT
ejpam-5495	147	1	ii	ii	PROPN
ejpam-5495	147	2	.	.	PUNCT
ejpam-5495	147	3	electrical	electrical	ADJ
ejpam-5495	147	4	circuits	circuit	NOUN
ejpam-5495	147	5	:	:	PUNCT
ejpam-5495	147	6	utilized	utilize	VERB
ejpam-5495	147	7	in	in	ADP
ejpam-5495	147	8	the	the	DET
ejpam-5495	147	9	construction	construction	NOUN
ejpam-5495	147	10	of	of	ADP
ejpam-5495	147	11	oscillatory	oscillatory	ADJ
ejpam-5495	147	12	circuits	circuit	NOUN
ejpam-5495	147	13	,	,	PUNCT
ejpam-5495	147	14	such	such	ADJ
ejpam-5495	147	15	as	as	ADP
ejpam-5495	147	16	vacuum	vacuum	NOUN
ejpam-5495	147	17	tubes	tube	NOUN
ejpam-5495	147	18	and	and	CCONJ
ejpam-5495	147	19	transistor	transistor	NOUN
ejpam-5495	147	20	circuits	circuit	NOUN
ejpam-5495	147	21	,	,	PUNCT
ejpam-5495	147	22	for	for	ADP
ejpam-5495	147	23	the	the	DET
ejpam-5495	147	24	examination	examination	NOUN
ejpam-5495	147	25	of	of	ADP
ejpam-5495	147	26	non	non	ADJ
ejpam-5495	147	27	-	-	ADJ
ejpam-5495	147	28	linear	linear	ADJ
ejpam-5495	147	29	resonance	resonance	NOUN
ejpam-5495	147	30	and	and	CCONJ
ejpam-5495	147	31	signal	signal	ADJ
ejpam-5495	147	32	modulation	modulation	NOUN
ejpam-5495	147	33	.	.	PUNCT
ejpam-5495	148	1	iii	iii	X
ejpam-5495	148	2	.	.	PUNCT
ejpam-5495	148	3	biological	biological	ADJ
ejpam-5495	148	4	systems	system	NOUN
ejpam-5495	148	5	:	:	PUNCT
ejpam-5495	148	6	simulates	simulate	VERB
ejpam-5495	148	7	heart	heart	NOUN
ejpam-5495	148	8	rhythms	rhythm	NOUN
ejpam-5495	148	9	and	and	CCONJ
ejpam-5495	148	10	cerebral	cerebral	ADJ
ejpam-5495	148	11	activity	activity	NOUN
ejpam-5495	148	12	,	,	PUNCT
ejpam-5495	148	13	encapsulating	encapsulate	VERB
ejpam-5495	148	14	the	the	DET
ejpam-5495	148	15	nonlinear	nonlinear	ADJ
ejpam-5495	148	16	dynamics	dynamic	NOUN
ejpam-5495	148	17	of	of	ADP
ejpam-5495	148	18	biological	biological	ADJ
ejpam-5495	148	19	oscillations	oscillation	NOUN
ejpam-5495	148	20	.	.	PUNCT
ejpam-5495	149	1	iv	iv	X
ejpam-5495	149	2	.	.	PUNCT
ejpam-5495	149	3	seismology	seismology	NOUN
ejpam-5495	149	4	:	:	PUNCT
ejpam-5495	149	5	facilitates	facilitate	VERB
ejpam-5495	149	6	the	the	DET
ejpam-5495	149	7	simulation	simulation	NOUN
ejpam-5495	149	8	and	and	CCONJ
ejpam-5495	149	9	comprehension	comprehension	NOUN
ejpam-5495	149	10	of	of	ADP
ejpam-5495	149	11	the	the	DET
ejpam-5495	149	12	non	non	ADJ
ejpam-5495	149	13	-	-	ADJ
ejpam-5495	149	14	linear	linear	ADJ
ejpam-5495	149	15	reaction	reaction	NOUN
ejpam-5495	149	16	of	of	ADP
ejpam-5495	149	17	structures	structure	NOUN
ejpam-5495	149	18	during	during	ADP
ejpam-5495	149	19	seismic	seismic	ADJ
ejpam-5495	149	20	events	event	NOUN
ejpam-5495	149	21	.	.	PUNCT
ejpam-5495	150	1	v.	v.	ADP
ejpam-5495	150	2	control	control	NOUN
ejpam-5495	150	3	systems	system	NOUN
ejpam-5495	150	4	:	:	PUNCT
ejpam-5495	150	5	employed	employ	VERB
ejpam-5495	150	6	in	in	ADP
ejpam-5495	150	7	nonlinear	nonlinear	ADJ
ejpam-5495	150	8	control	control	NOUN
ejpam-5495	150	9	analysis	analysis	NOUN
ejpam-5495	150	10	to	to	PART
ejpam-5495	150	11	devise	devise	VERB
ejpam-5495	150	12	resilient	resilient	ADJ
ejpam-5495	150	13	controllers	controller	NOUN
ejpam-5495	150	14	for	for	ADP
ejpam-5495	150	15	systems	system	NOUN
ejpam-5495	150	16	exhibiting	exhibit	VERB
ejpam-5495	150	17	intricate	intricate	ADJ
ejpam-5495	150	18	,	,	PUNCT
ejpam-5495	150	19	nonlinear	nonlinear	ADJ
ejpam-5495	150	20	dynamics	dynamic	NOUN
ejpam-5495	150	21	.	.	PUNCT
ejpam-5495	151	1	these	these	DET
ejpam-5495	151	2	applications	application	NOUN
ejpam-5495	151	3	control	control	VERB
ejpam-5495	151	4	the	the	DET
ejpam-5495	151	5	oscillator	oscillator	NOUN
ejpam-5495	151	6	’s	’s	PART
ejpam-5495	151	7	capacity	capacity	NOUN
ejpam-5495	151	8	to	to	PART
ejpam-5495	151	9	record	record	VERB
ejpam-5495	151	10	intricate	intricate	ADJ
ejpam-5495	151	11	,	,	PUNCT
ejpam-5495	151	12	nonlinear	nonlinear	ADJ
ejpam-5495	151	13	dynamics	dynamic	NOUN
ejpam-5495	151	14	and	and	CCONJ
ejpam-5495	151	15	forecast	forecast	NOUN
ejpam-5495	151	16	system	system	NOUN
ejpam-5495	151	17	reactions	reaction	NOUN
ejpam-5495	151	18	under	under	ADP
ejpam-5495	151	19	diverse	diverse	ADJ
ejpam-5495	151	20	conditions	condition	NOUN
ejpam-5495	151	21	.	.	PUNCT
ejpam-5495	152	1	the	the	DET
ejpam-5495	152	2	usefulness	usefulness	NOUN
ejpam-5495	152	3	of	of	ADP
ejpam-5495	152	4	the	the	DET
ejpam-5495	152	5	td	td	NOUN
ejpam-5495	152	6	in	in	ADP
ejpam-5495	152	7	numerous	numerous	ADJ
ejpam-5495	152	8	fields	field	NOUN
ejpam-5495	152	9	has	have	AUX
ejpam-5495	152	10	was	be	AUX
ejpam-5495	152	11	emphasized	emphasize	VERB
ejpam-5495	152	12	in	in	ADP
ejpam-5495	152	13	the	the	DET
ejpam-5495	152	14	introductory	introductory	ADJ
ejpam-5495	152	15	section	section	NOUN
ejpam-5495	152	16	;	;	PUNCT
ejpam-5495	152	17	hence	hence	ADV
ejpam-5495	152	18	,	,	PUNCT
ejpam-5495	152	19	the	the	DET
ejpam-5495	152	20	next	next	ADJ
ejpam-5495	152	21	evaluation	evaluation	NOUN
ejpam-5495	152	22	will	will	AUX
ejpam-5495	152	23	be	be	AUX
ejpam-5495	152	24	founded	found	VERB
ejpam-5495	152	25	on	on	ADP
ejpam-5495	152	26	the	the	DET
ejpam-5495	152	27	td	td	NOUN
ejpam-5495	152	28	of	of	ADP
ejpam-5495	152	29	the	the	DET
ejpam-5495	152	30	location	location	NOUN
ejpam-5495	152	31	and	and	CCONJ
ejpam-5495	152	32	velocity	velocity	NOUN
ejpam-5495	152	33	,	,	PUNCT
ejpam-5495	152	34	i.e.	i.e.	X
ejpam-5495	152	35	,	,	PUNCT
ejpam-5495	152	36	the	the	DET
ejpam-5495	152	37	last	last	ADJ
ejpam-5495	152	38	two	two	NUM
ejpam-5495	152	39	terms	term	NOUN
ejpam-5495	152	40	in	in	ADP
ejpam-5495	152	41	eq	eq	NOUN
ejpam-5495	152	42	(	(	PUNCT
ejpam-5495	152	43	1	1	NUM
ejpam-5495	152	44	)	)	PUNCT
ejpam-5495	152	45	.	.	PUNCT
ejpam-5495	153	1	recently	recently	ADV
ejpam-5495	153	2	,	,	PUNCT
ejpam-5495	153	3	this	this	DET
ejpam-5495	153	4	issue	issue	NOUN
ejpam-5495	153	5	was	be	AUX
ejpam-5495	153	6	approached	approach	VERB
ejpam-5495	153	7	by	by	ADP
ejpam-5495	153	8	leveraging	leverage	VERB
ejpam-5495	153	9	the	the	DET
ejpam-5495	153	10	properties	property	NOUN
ejpam-5495	153	11	of	of	ADP
ejpam-5495	153	12	special	special	ADJ
ejpam-5495	153	13	functions	function	NOUN
ejpam-5495	153	14	.	.	PUNCT
ejpam-5495	154	1	the	the	DET
ejpam-5495	154	2	following	follow	VERB
ejpam-5495	154	3	trial	trial	NOUN
ejpam-5495	154	4	solution	solution	NOUN
ejpam-5495	154	5	was	be	AUX
ejpam-5495	154	6	proposed	propose	VERB
ejpam-5495	154	7	[	[	X
ejpam-5495	154	8	46	46	NUM
ejpam-5495	154	9	]	]	X
ejpam-5495	154	10	:	:	PUNCT
ejpam-5495	154	11	ζ	ζ	X
ejpam-5495	154	12	=	=	PUNCT
ejpam-5495	154	13	a	a	DET
ejpam-5495	154	14	cos(∆t	cos(∆t	NOUN
ejpam-5495	154	15	)	)	PUNCT
ejpam-5495	154	16	,	,	PUNCT
ejpam-5495	154	17	ζ̇	ζ̇	NOUN
ejpam-5495	154	18	=	=	SYM
ejpam-5495	154	19	−a∆sin(∆t	−a∆sin(∆t	NOUN
ejpam-5495	154	20	)	)	PUNCT
ejpam-5495	154	21	,	,	PUNCT
ejpam-5495	154	22	(	(	PUNCT
ejpam-5495	154	23	3	3	X
ejpam-5495	154	24	)	)	PUNCT
ejpam-5495	154	25	where	where	SCONJ
ejpam-5495	154	26	the	the	DET
ejpam-5495	154	27	initial	initial	ADJ
ejpam-5495	154	28	vibration	vibration	NOUN
ejpam-5495	154	29	amplitude	amplitude	NOUN
ejpam-5495	154	30	is	be	AUX
ejpam-5495	154	31	denoted	denote	VERB
ejpam-5495	154	32	by	by	ADP
ejpam-5495	154	33	a	a	PRON
ejpam-5495	154	34	,	,	PUNCT
ejpam-5495	154	35	and	and	CCONJ
ejpam-5495	154	36	∆	∆	PROPN
ejpam-5495	154	37	is	be	AUX
ejpam-5495	154	38	the	the	DET
ejpam-5495	154	39	total	total	ADJ
ejpam-5495	154	40	frequency	frequency	NOUN
ejpam-5495	154	41	of	of	ADP
ejpam-5495	154	42	the	the	DET
ejpam-5495	154	43	td	td	NOUN
ejpam-5495	154	44	as	as	SCONJ
ejpam-5495	154	45	indicated	indicate	VERB
ejpam-5495	154	46	in	in	ADP
ejpam-5495	154	47	eq	eq	ADP
ejpam-5495	154	48	.	.	PUNCT
ejpam-5495	155	1	(	(	PUNCT
ejpam-5495	155	2	1	1	NUM
ejpam-5495	155	3	)	)	PUNCT
ejpam-5495	155	4	.	.	PUNCT
ejpam-5495	156	1	appropriately	appropriately	ADV
ejpam-5495	156	2	,	,	PUNCT
ejpam-5495	156	3	the	the	DET
ejpam-5495	156	4	shift	shift	NOUN
ejpam-5495	156	5	of	of	ADP
ejpam-5495	156	6	the	the	DET
ejpam-5495	156	7	independent	independent	ADJ
ejpam-5495	156	8	time	time	NOUN
ejpam-5495	156	9	may	may	AUX
ejpam-5495	156	10	be	be	AUX
ejpam-5495	156	11	expressed	express	VERB
ejpam-5495	156	12	as	as	ADP
ejpam-5495	156	13	:	:	PUNCT
ejpam-5495	156	14	ζ(t−	ζ(t−	PROPN
ejpam-5495	156	15	τ	τ	PROPN
ejpam-5495	156	16	)	)	PUNCT
ejpam-5495	156	17	=	=	PUNCT
ejpam-5495	156	18	a	a	DET
ejpam-5495	156	19	cos∆(t−	cos∆(t−	NOUN
ejpam-5495	156	20	τ	τ	PROPN
ejpam-5495	156	21	)	)	PUNCT
ejpam-5495	156	22	=	=	PROPN
ejpam-5495	156	23	a[cos∆t	a[cos∆t	NOUN
ejpam-5495	156	24	cos(∆τ	cos(∆τ	NOUN
ejpam-5495	156	25	)	)	PUNCT
ejpam-5495	156	26	+	+	CCONJ
ejpam-5495	156	27	sin∆t	sin∆t	NOUN
ejpam-5495	156	28	sin(∆τ	sin(∆τ	PROPN
ejpam-5495	156	29	)	)	PUNCT
ejpam-5495	156	30	]	]	PUNCT
ejpam-5495	157	1	=	=	PUNCT
ejpam-5495	157	2	ζ(t	ζ(t	PROPN
ejpam-5495	157	3	)	)	PUNCT
ejpam-5495	157	4	cos(∆τ)−	cos(∆τ)−	PROPN
ejpam-5495	157	5	1	1	NUM
ejpam-5495	157	6	∆	∆	PROPN
ejpam-5495	157	7	ζ̇(t	ζ̇(t	PROPN
ejpam-5495	157	8	)	)	PUNCT
ejpam-5495	157	9	sin(∆τ	sin(∆τ	NUM
ejpam-5495	157	10	)	)	PUNCT
ejpam-5495	157	11	.	.	PUNCT
ejpam-5495	158	1	(	(	PUNCT
ejpam-5495	158	2	4	4	X
ejpam-5495	158	3	)	)	PUNCT
ejpam-5495	158	4	consequently	consequently	ADV
ejpam-5495	158	5	,	,	PUNCT
ejpam-5495	158	6	ζ̇(t−	ζ̇(t−	X
ejpam-5495	158	7	τ	τ	X
ejpam-5495	158	8	)	)	PUNCT
ejpam-5495	158	9	=	=	SYM
ejpam-5495	158	10	ζ̇(t	ζ̇(t	PROPN
ejpam-5495	158	11	)	)	PUNCT
ejpam-5495	158	12	cos∆τ	cos∆τ	NOUN
ejpam-5495	159	1	+	+	VERB
ejpam-5495	159	2	∆ζ(t	∆ζ(t	PROPN
ejpam-5495	159	3	)	)	PUNCT
ejpam-5495	159	4	sin(∆τ	sin(∆τ	NUM
ejpam-5495	159	5	)	)	PUNCT
ejpam-5495	159	6	.	.	PUNCT
ejpam-5495	160	1	(	(	PUNCT
ejpam-5495	160	2	5	5	X
ejpam-5495	160	3	)	)	PUNCT
ejpam-5495	160	4	at	at	ADP
ejpam-5495	160	5	this	this	DET
ejpam-5495	160	6	stage	stage	NOUN
ejpam-5495	160	7	,	,	PUNCT
ejpam-5495	160	8	eq	eq	NOUN
ejpam-5495	160	9	.	.	PUNCT
ejpam-5495	161	1	(	(	PUNCT
ejpam-5495	161	2	1	1	X
ejpam-5495	161	3	)	)	PUNCT
ejpam-5495	161	4	may	may	AUX
ejpam-5495	161	5	be	be	AUX
ejpam-5495	161	6	written	write	VERB
ejpam-5495	161	7	as	as	SCONJ
ejpam-5495	161	8	follows	follow	VERB
ejpam-5495	161	9	:	:	PUNCT
ejpam-5495	161	10	z̈	z̈	X
ejpam-5495	161	11	+	+	CCONJ
ejpam-5495	161	12	f1(z	f1(z	PROPN
ejpam-5495	161	13	,	,	PUNCT
ejpam-5495	161	14	ż	ż	NOUN
ejpam-5495	161	15	)	)	PUNCT
ejpam-5495	161	16	+	+	CCONJ
ejpam-5495	162	1	f2(z	f2(z	X
ejpam-5495	162	2	)	)	PUNCT
ejpam-5495	162	3	=	=	SYM
ejpam-5495	162	4	f	f	PROPN
ejpam-5495	162	5	cos(ωt	cos(ωt	NOUN
ejpam-5495	162	6	)	)	PUNCT
ejpam-5495	162	7	,	,	PUNCT
ejpam-5495	162	8	(	(	PUNCT
ejpam-5495	162	9	6	6	NUM
ejpam-5495	162	10	)	)	PUNCT
ejpam-5495	162	11	where	where	SCONJ
ejpam-5495	162	12	f1(z	f1(z	ADP
ejpam-5495	162	13	,	,	PUNCT
ejpam-5495	162	14	ż	ż	NOUN
ejpam-5495	162	15	)	)	PUNCT
ejpam-5495	162	16	=	=	PUNCT
ejpam-5495	163	1	−µ(1−	−µ(1−	NOUN
ejpam-5495	163	2	z2)ż	z2)ż	NUM
ejpam-5495	163	3	+	+	CCONJ
ejpam-5495	163	4	α	α	PROPN
ejpam-5495	163	5	∆	∆	ADJ
ejpam-5495	164	1	ż	ż	NOUN
ejpam-5495	164	2	sin(∆τ)−	sin(∆τ)−	PROPN
ejpam-5495	164	3	βż	βż	PROPN
ejpam-5495	164	4	cos(∆τ	cos(∆τ	NOUN
ejpam-5495	164	5	)	)	PUNCT
ejpam-5495	164	6	,	,	PUNCT
ejpam-5495	164	7	f2(z	f2(z	X
ejpam-5495	164	8	)	)	PUNCT
ejpam-5495	164	9	=	=	PUNCT
ejpam-5495	164	10	ω2z	ω2z	PUNCT
ejpam-5495	164	11	+	+	PUNCT
ejpam-5495	165	1	λz3	λz3	PROPN
ejpam-5495	165	2	−	−	NOUN
ejpam-5495	165	3	α	α	PROPN
ejpam-5495	165	4	z	z	NOUN
ejpam-5495	165	5	cos(∆τ)−	cos(∆τ)−	PROPN
ejpam-5495	165	6	zβ∆sin(∆τ	zβ∆sin(∆τ	NUM
ejpam-5495	165	7	)	)	PUNCT
ejpam-5495	165	8	.	.	PUNCT
ejpam-5495	166	1	(	(	PUNCT
ejpam-5495	166	2	7	7	X
ejpam-5495	166	3	)	)	PUNCT
ejpam-5495	166	4	a.	a.	NOUN
ejpam-5495	166	5	alanazy	alanazy	NOUN
ejpam-5495	166	6	et	et	PROPN
ejpam-5495	166	7	al	al	PROPN
ejpam-5495	166	8	.	.	PUNCT
ejpam-5495	166	9	/	/	SYM
ejpam-5495	166	10	eur	eur	PROPN
ejpam-5495	166	11	.	.	PUNCT
ejpam-5495	167	1	j.	j.	PROPN
ejpam-5495	167	2	pure	pure	PROPN
ejpam-5495	167	3	appl	appl	PROPN
ejpam-5495	167	4	.	.	PROPN
ejpam-5495	167	5	math	math	PROPN
ejpam-5495	167	6	,	,	PUNCT
ejpam-5495	167	7	18	18	NUM
ejpam-5495	167	8	(	(	PUNCT
ejpam-5495	167	9	1	1	NUM
ejpam-5495	167	10	)	)	PUNCT
ejpam-5495	167	11	(	(	PUNCT
ejpam-5495	167	12	2025	2025	NUM
ejpam-5495	167	13	)	)	PUNCT
ejpam-5495	167	14	,	,	PUNCT
ejpam-5495	167	15	5495	5495	NUM
ejpam-5495	167	16	8	8	NUM
ejpam-5495	167	17	of	of	ADP
ejpam-5495	167	18	21	21	NUM
ejpam-5495	167	19	now	now	ADV
ejpam-5495	167	20	,	,	PUNCT
ejpam-5495	167	21	an	an	DET
ejpam-5495	167	22	equivalent	equivalent	ADJ
ejpam-5495	167	23	frequency	frequency	NOUN
ejpam-5495	167	24	can	can	AUX
ejpam-5495	167	25	be	be	AUX
ejpam-5495	167	26	evaluated	evaluate	VERB
ejpam-5495	167	27	as	as	SCONJ
ejpam-5495	167	28	shown	show	VERB
ejpam-5495	167	29	previously	previously	ADV
ejpam-5495	167	30	by	by	ADP
ejpam-5495	167	31	moatimid	moatimid	PROPN
ejpam-5495	167	32	et	et	PROPN
ejpam-5495	167	33	al	al	PROPN
ejpam-5495	167	34	.	.	PUNCT
ejpam-5495	168	1	[	[	X
ejpam-5495	168	2	45	45	NUM
ejpam-5495	168	3	-	-	SYM
ejpam-5495	168	4	47	47	NUM
ejpam-5495	168	5	]	]	PUNCT
ejpam-5495	168	6	in	in	ADP
ejpam-5495	168	7	the	the	DET
ejpam-5495	168	8	following	following	ADJ
ejpam-5495	168	9	manner	manner	NOUN
ejpam-5495	168	10	:	:	PUNCT
ejpam-5495	168	11	ω2	ω2	ADJ
ejpam-5495	168	12	eqv	eqv	NOUN
ejpam-5495	168	13	=	=	PUNCT
ejpam-5495	168	14	2π/∆∫	2π/∆∫	NUM
ejpam-5495	168	15	0	0	NUM
ejpam-5495	168	16	ζf2(ζ)dt/	ζf2(ζ)dt/	NOUN
ejpam-5495	168	17	2π/∆∫	2π/∆∫	NUM
ejpam-5495	168	18	0	0	NUM
ejpam-5495	168	19	ζ2dt	ζ2dt	PUNCT
ejpam-5495	168	20	=	=	SYM
ejpam-5495	168	21	ω2	ω2	NOUN
ejpam-5495	168	22	+	+	CCONJ
ejpam-5495	168	23	3	3	NUM
ejpam-5495	168	24	4	4	NUM
ejpam-5495	168	25	λa2	λa2	NOUN
ejpam-5495	168	26	−	−	PROPN
ejpam-5495	168	27	α	α	DET
ejpam-5495	168	28	cos(∆τ)−	cos(∆τ)−	NOUN
ejpam-5495	168	29	β∆sin(∆τ	β∆sin(∆τ	PROPN
ejpam-5495	168	30	)	)	PUNCT
ejpam-5495	168	31	.	.	PUNCT
ejpam-5495	169	1	(	(	PUNCT
ejpam-5495	169	2	8)	8)	NUM
ejpam-5495	169	3	additionally	additionally	ADV
ejpam-5495	169	4	,	,	PUNCT
ejpam-5495	169	5	the	the	DET
ejpam-5495	169	6	equivalent	equivalent	ADJ
ejpam-5495	169	7	damping	damp	VERB
ejpam-5495	169	8	term	term	NOUN
ejpam-5495	169	9	may	may	AUX
ejpam-5495	169	10	be	be	AUX
ejpam-5495	169	11	determined	determine	VERB
ejpam-5495	169	12	as	as	SCONJ
ejpam-5495	169	13	shown	show	VERB
ejpam-5495	169	14	below	below	ADV
ejpam-5495	169	15	:	:	PUNCT
ejpam-5495	169	16	γ	γ	X
ejpam-5495	169	17	=	=	SYM
ejpam-5495	169	18	2π/∆∫	2π/∆∫	NUM
ejpam-5495	169	19	0	0	NUM
ejpam-5495	169	20	ζ̇f1(ζ	ζ̇f1(ζ	PROPN
ejpam-5495	169	21	,	,	PUNCT
ejpam-5495	169	22	ζ̇)dt/	ζ̇)dt/	ADV
ejpam-5495	170	1	2π/∆∫	2π/∆∫	NUM
ejpam-5495	170	2	0	0	PUNCT
ejpam-5495	171	1	ζ̇2dt	ζ̇2dt	NUM
ejpam-5495	171	2	=	=	SYM
ejpam-5495	171	3	1	1	NUM
ejpam-5495	171	4	4	4	NUM
ejpam-5495	171	5	µ(a2	µ(a2	NOUN
ejpam-5495	171	6	−	−	PROPN
ejpam-5495	172	1	4)−	4)−	INTJ
ejpam-5495	172	2	β	β	NOUN
ejpam-5495	172	3	cos(∆τ	cos(∆τ	NOUN
ejpam-5495	172	4	)	)	PUNCT
ejpam-5495	173	1	+	+	CCONJ
ejpam-5495	173	2	α	α	NOUN
ejpam-5495	173	3	∆	∆	PROPN
ejpam-5495	173	4	sin(∆τ	sin(∆τ	NUM
ejpam-5495	173	5	)	)	PUNCT
ejpam-5495	173	6	.	.	PUNCT
ejpam-5495	174	1	(	(	PUNCT
ejpam-5495	174	2	9	9	X
ejpam-5495	174	3	)	)	PUNCT
ejpam-5495	174	4	the	the	DET
ejpam-5495	174	5	equivalent	equivalent	ADJ
ejpam-5495	174	6	ode	ode	NOUN
ejpam-5495	174	7	can	can	AUX
ejpam-5495	174	8	now	now	ADV
ejpam-5495	174	9	be	be	AUX
ejpam-5495	174	10	constructed	construct	VERB
ejpam-5495	174	11	as	as	SCONJ
ejpam-5495	174	12	follows	follow	VERB
ejpam-5495	174	13	:	:	PUNCT
ejpam-5495	174	14	ζ̈	ζ̈	X
ejpam-5495	175	1	+	+	NOUN
ejpam-5495	175	2	γζ̇	γζ̇	X
ejpam-5495	175	3	+	+	CCONJ
ejpam-5495	175	4	ω2	ω2	ADJ
ejpam-5495	175	5	eqvζ	eqvζ	NOUN
ejpam-5495	175	6	=	=	SYM
ejpam-5495	175	7	f	f	PROPN
ejpam-5495	175	8	cos(ωt	cos(ωt	NOUN
ejpam-5495	175	9	)	)	PUNCT
ejpam-5495	175	10	.	.	PUNCT
ejpam-5495	176	1	(	(	PUNCT
ejpam-5495	176	2	10	10	NUM
ejpam-5495	176	3	)	)	PUNCT
ejpam-5495	176	4	for	for	ADP
ejpam-5495	176	5	simplicity	simplicity	NOUN
ejpam-5495	176	6	,	,	PUNCT
ejpam-5495	176	7	the	the	DET
ejpam-5495	176	8	stability	stability	NOUN
ejpam-5495	176	9	condition	condition	NOUN
ejpam-5495	176	10	will	will	AUX
ejpam-5495	176	11	be	be	AUX
ejpam-5495	176	12	evaluated	evaluate	VERB
ejpam-5495	176	13	without	without	ADP
ejpam-5495	176	14	the	the	DET
ejpam-5495	176	15	external	external	ADJ
ejpam-5495	176	16	excitation	excitation	NOUN
ejpam-5495	176	17	force	force	NOUN
ejpam-5495	176	18	.	.	PUNCT
ejpam-5495	177	1	therefore	therefore	ADV
ejpam-5495	177	2	,	,	PUNCT
ejpam-5495	177	3	the	the	DET
ejpam-5495	177	4	nonhomogeneous	nonhomogeneous	ADJ
ejpam-5495	177	5	differential	differential	ADJ
ejpam-5495	177	6	equation	equation	NOUN
ejpam-5495	177	7	as	as	SCONJ
ejpam-5495	177	8	given	give	VERB
ejpam-5495	177	9	in	in	ADP
ejpam-5495	177	10	eq	eq	ADP
ejpam-5495	177	11	.	.	PUNCT
ejpam-5495	178	1	(	(	PUNCT
ejpam-5495	178	2	10	10	NUM
ejpam-5495	178	3	)	)	PUNCT
ejpam-5495	178	4	becomes	become	VERB
ejpam-5495	178	5	a	a	DET
ejpam-5495	178	6	homogeneous	homogeneous	ADJ
ejpam-5495	178	7	one	one	NUM
ejpam-5495	178	8	.	.	PUNCT
ejpam-5495	179	1	furthermore	furthermore	ADV
ejpam-5495	179	2	,	,	PUNCT
ejpam-5495	179	3	the	the	DET
ejpam-5495	179	4	standard	standard	ADJ
ejpam-5495	179	5	normal	normal	ADJ
ejpam-5495	179	6	form	form	NOUN
ejpam-5495	179	7	may	may	AUX
ejpam-5495	179	8	be	be	AUX
ejpam-5495	179	9	attained	attain	VERB
ejpam-5495	179	10	through	through	ADP
ejpam-5495	179	11	the	the	DET
ejpam-5495	179	12	transformation	transformation	NOUN
ejpam-5495	179	13	ζ(t	ζ(t	VERB
ejpam-5495	179	14	)	)	PUNCT
ejpam-5495	179	15	=	=	SYM
ejpam-5495	179	16	f(t)exp(−γ	f(t)exp(−γ	ADJ
ejpam-5495	179	17	t/2	t/2	NUM
ejpam-5495	179	18	)	)	PUNCT
ejpam-5495	179	19	.	.	PUNCT
ejpam-5495	180	1	elementary	elementary	PROPN
ejpam-5495	180	2	,	,	PUNCT
ejpam-5495	180	3	the	the	DET
ejpam-5495	180	4	unknown	unknown	ADJ
ejpam-5495	180	5	function	function	NOUN
ejpam-5495	180	6	satisfies	satisfy	VERB
ejpam-5495	180	7	the	the	DET
ejpam-5495	180	8	following	follow	VERB
ejpam-5495	180	9	simple	simple	ADJ
ejpam-5495	180	10	harmonic	harmonic	ADJ
ejpam-5495	180	11	differential	differential	NOUN
ejpam-5495	180	12	equation	equation	NOUN
ejpam-5495	180	13	:	:	PUNCT
ejpam-5495	180	14	f̈	f̈	X
ejpam-5495	181	1	+	+	NOUN
ejpam-5495	181	2	∆2f	∆2f	X
ejpam-5495	181	3	=	=	SYM
ejpam-5495	181	4	0	0	NUM
ejpam-5495	181	5	,	,	PUNCT
ejpam-5495	181	6	(	(	PUNCT
ejpam-5495	181	7	11	11	NUM
ejpam-5495	181	8	)	)	PUNCT
ejpam-5495	181	9	where	where	SCONJ
ejpam-5495	181	10	∆2	∆2	PROPN
ejpam-5495	181	11	=	=	SYM
ejpam-5495	181	12	ω2	ω2	ADJ
ejpam-5495	181	13	eqv−γ2/4	eqv−γ2/4	NOUN
ejpam-5495	181	14	.	.	PUNCT
ejpam-5495	182	1	in	in	ADP
ejpam-5495	182	2	other	other	ADJ
ejpam-5495	182	3	words	word	NOUN
ejpam-5495	182	4	,	,	PUNCT
ejpam-5495	182	5	the	the	DET
ejpam-5495	182	6	total	total	ADJ
ejpam-5495	182	7	frequency	frequency	NOUN
ejpam-5495	182	8	can	can	AUX
ejpam-5495	182	9	be	be	AUX
ejpam-5495	182	10	obtained	obtain	VERB
ejpam-5495	182	11	by	by	ADP
ejpam-5495	182	12	combining	combine	VERB
ejpam-5495	182	13	the	the	DET
ejpam-5495	182	14	results	result	NOUN
ejpam-5495	182	15	in	in	ADP
ejpam-5495	182	16	eqs	eqs	PROPN
ejpam-5495	182	17	.	.	PUNCT
ejpam-5495	183	1	(	(	PUNCT
ejpam-5495	183	2	8)	8)	NUM
ejpam-5495	183	3	and	and	CCONJ
ejpam-5495	183	4	(	(	PUNCT
ejpam-5495	183	5	9	9	NUM
ejpam-5495	183	6	)	)	PUNCT
ejpam-5495	183	7	with	with	ADP
ejpam-5495	183	8	the	the	DET
ejpam-5495	183	9	previous	previous	ADJ
ejpam-5495	183	10	relation	relation	NOUN
ejpam-5495	183	11	to	to	PART
ejpam-5495	183	12	produce	produce	VERB
ejpam-5495	183	13	:	:	PUNCT
ejpam-5495	183	14	∆2	∆2	PROPN
ejpam-5495	183	15	=	=	SYM
ejpam-5495	183	16	ω2	ω2	PROPN
ejpam-5495	183	17	+	+	CCONJ
ejpam-5495	183	18	3	3	NUM
ejpam-5495	183	19	4	4	NUM
ejpam-5495	183	20	λa2	λa2	NOUN
ejpam-5495	183	21	−	−	PROPN
ejpam-5495	184	1	α	α	PRON
ejpam-5495	184	2	cos(∆τ)−	cos(∆τ)−	PROPN
ejpam-5495	184	3	β∆sin(∆τ)−	β∆sin(∆τ)−	NOUN
ejpam-5495	184	4	1	1	NUM
ejpam-5495	184	5	4	4	NUM
ejpam-5495	184	6	[	[	PUNCT
ejpam-5495	184	7	1	1	NUM
ejpam-5495	184	8	4	4	NUM
ejpam-5495	184	9	µ(a2	µ(a2	NOUN
ejpam-5495	184	10	−	−	PROPN
ejpam-5495	185	1	4)−	4)−	INTJ
ejpam-5495	185	2	β	β	NOUN
ejpam-5495	185	3	cos(∆τ	cos(∆τ	NOUN
ejpam-5495	185	4	)	)	PUNCT
ejpam-5495	186	1	+	+	CCONJ
ejpam-5495	186	2	α	α	PROPN
ejpam-5495	186	3	∆	∆	X
ejpam-5495	186	4	sin(∆τ)]2	sin(∆τ)]2	X
ejpam-5495	186	5	.	.	PUNCT
ejpam-5495	187	1	(	(	PUNCT
ejpam-5495	187	2	12	12	NUM
ejpam-5495	187	3	)	)	PUNCT
ejpam-5495	187	4	the	the	DET
ejpam-5495	187	5	stability	stability	NOUN
ejpam-5495	187	6	standard	standard	NOUN
ejpam-5495	187	7	requires	require	VERB
ejpam-5495	187	8	∆2	∆2	X
ejpam-5495	187	9	>	>	X
ejpam-5495	187	10	0	0	NUM
ejpam-5495	187	11	,	,	PUNCT
ejpam-5495	187	12	and	and	CCONJ
ejpam-5495	187	13	γ	γ	X
ejpam-5495	187	14	>	>	X
ejpam-5495	187	15	0	0	NUM
ejpam-5495	187	16	.	.	PUNCT
ejpam-5495	188	1	(	(	PUNCT
ejpam-5495	188	2	13	13	NUM
ejpam-5495	188	3	)	)	PUNCT
ejpam-5495	188	4	as	as	SCONJ
ejpam-5495	188	5	seen	see	VERB
ejpam-5495	188	6	,	,	PUNCT
ejpam-5495	188	7	eq	eq	ADJ
ejpam-5495	188	8	.	.	PUNCT
ejpam-5495	189	1	(	(	PUNCT
ejpam-5495	189	2	12	12	NUM
ejpam-5495	189	3	)	)	PUNCT
ejpam-5495	189	4	is	be	AUX
ejpam-5495	189	5	a	a	DET
ejpam-5495	189	6	transcendental	transcendental	ADJ
ejpam-5495	189	7	equation	equation	NOUN
ejpam-5495	189	8	in	in	ADP
ejpam-5495	189	9	∆	∆	PROPN
ejpam-5495	189	10	.	.	PUNCT
ejpam-5495	190	1	for	for	ADP
ejpam-5495	190	2	an	an	DET
ejpam-5495	190	3	ease	ease	NOUN
ejpam-5495	190	4	,	,	PUNCT
ejpam-5495	190	5	taylor	taylor	PROPN
ejpam-5495	190	6	expansion	expansion	NOUN
ejpam-5495	190	7	may	may	AUX
ejpam-5495	190	8	be	be	AUX
ejpam-5495	190	9	employed	employ	VERB
ejpam-5495	190	10	to	to	PART
ejpam-5495	190	11	approximate	approximate	VERB
ejpam-5495	190	12	the	the	DET
ejpam-5495	190	13	values	value	NOUN
ejpam-5495	190	14	of	of	ADP
ejpam-5495	190	15	the	the	DET
ejpam-5495	190	16	trigonometric	trigonometric	ADJ
ejpam-5495	190	17	functions	function	NOUN
ejpam-5495	190	18	in	in	ADP
ejpam-5495	190	19	γ	γ	NOUN
ejpam-5495	190	20	as	as	ADP
ejpam-5495	190	21	sin	sin	NOUN
ejpam-5495	190	22	ϵ	ϵ	PROPN
ejpam-5495	190	23	≈	≈	PROPN
ejpam-5495	190	24	ϵ	ϵ	PROPN
ejpam-5495	190	25	and	and	CCONJ
ejpam-5495	190	26	cos	cos	ADP
ejpam-5495	190	27	ϵ	ϵ	PROPN
ejpam-5495	190	28	≈	≈	PROPN
ejpam-5495	190	29	1	1	NUM
ejpam-5495	190	30	.	.	PUNCT
ejpam-5495	191	1	in	in	ADP
ejpam-5495	191	2	this	this	DET
ejpam-5495	191	3	simplification	simplification	NOUN
ejpam-5495	191	4	,	,	PUNCT
ejpam-5495	191	5	the	the	DET
ejpam-5495	191	6	total	total	ADJ
ejpam-5495	191	7	frequency	frequency	NOUN
ejpam-5495	191	8	can	can	AUX
ejpam-5495	191	9	be	be	AUX
ejpam-5495	191	10	written	write	VERB
ejpam-5495	191	11	as	as	ADP
ejpam-5495	191	12	∆	∆	PROPN
ejpam-5495	191	13	=	=	SYM
ejpam-5495	191	14	√	√	NUM
ejpam-5495	191	15	−α+	−α+	NOUN
ejpam-5495	191	16	3	3	NUM
ejpam-5495	191	17	4λa	4λa	NOUN
ejpam-5495	191	18	2	2	NUM
ejpam-5495	191	19	−	−	NOUN
ejpam-5495	191	20	1	1	NUM
ejpam-5495	191	21	64(−4β	64(−4β	NUM
ejpam-5495	191	22	+	+	CCONJ
ejpam-5495	191	23	(	(	PUNCT
ejpam-5495	191	24	a2	a2	PROPN
ejpam-5495	191	25	−	−	PROPN
ejpam-5495	191	26	4)µ+	4)µ+	NUM
ejpam-5495	191	27	4ατ)2	4ατ)2	NUM
ejpam-5495	191	28	+	+	CCONJ
ejpam-5495	191	29	ω2	ω2	ADJ
ejpam-5495	191	30	1	1	NUM
ejpam-5495	191	31	+	+	CCONJ
ejpam-5495	191	32	βτ	βτ	X
ejpam-5495	191	33	.	.	PUNCT
ejpam-5495	192	1	(	(	PUNCT
ejpam-5495	192	2	14	14	NUM
ejpam-5495	192	3	)	)	PUNCT
ejpam-5495	192	4	as	as	SCONJ
ejpam-5495	192	5	seen	see	VERB
ejpam-5495	192	6	,	,	PUNCT
ejpam-5495	192	7	eq	eq	ADJ
ejpam-5495	192	8	.	.	PUNCT
ejpam-5495	193	1	(	(	PUNCT
ejpam-5495	193	2	12	12	NUM
ejpam-5495	193	3	)	)	PUNCT
ejpam-5495	193	4	is	be	AUX
ejpam-5495	193	5	a	a	DET
ejpam-5495	193	6	transcendental	transcendental	ADJ
ejpam-5495	193	7	equation	equation	NOUN
ejpam-5495	193	8	in	in	ADP
ejpam-5495	193	9	the	the	DET
ejpam-5495	193	10	total	total	ADJ
ejpam-5495	193	11	frequency	frequency	NOUN
ejpam-5495	193	12	∆	∆	PROPN
ejpam-5495	193	13	.	.	PUNCT
ejpam-5495	194	1	to	to	PART
ejpam-5495	194	2	obtain	obtain	VERB
ejpam-5495	194	3	the	the	DET
ejpam-5495	194	4	value	value	NOUN
ejpam-5495	194	5	of	of	ADP
ejpam-5495	194	6	the	the	DET
ejpam-5495	194	7	equivalent	equivalent	ADJ
ejpam-5495	194	8	frequency	frequency	NOUN
ejpam-5495	194	9	,	,	PUNCT
ejpam-5495	194	10	consider	consider	VERB
ejpam-5495	194	11	the	the	DET
ejpam-5495	194	12	following	follow	VERB
ejpam-5495	194	13	data	data	NOUN
ejpam-5495	194	14	sample	sample	NOUN
ejpam-5495	194	15	:	:	PUNCT
ejpam-5495	194	16	µ	µ	X
ejpam-5495	194	17	=	=	SYM
ejpam-5495	194	18	−1.0	−1.0	PROPN
ejpam-5495	194	19	,	,	PUNCT
ejpam-5495	194	20	τ	τ	PROPN
ejpam-5495	194	21	=	=	SYM
ejpam-5495	194	22	0.1	0.1	NUM
ejpam-5495	194	23	,	,	PUNCT
ejpam-5495	194	24	ω	ω	NOUN
ejpam-5495	194	25	=	=	SYM
ejpam-5495	194	26	4	4	NUM
ejpam-5495	194	27	,	,	PUNCT
ejpam-5495	194	28	α	α	NOUN
ejpam-5495	194	29	=	=	SYM
ejpam-5495	194	30	0.1	0.1	NUM
ejpam-5495	194	31	,	,	PUNCT
ejpam-5495	194	32	β	β	X
ejpam-5495	194	33	=	=	PUNCT
ejpam-5495	194	34	0.3	0.3	NUM
ejpam-5495	194	35	,	,	PUNCT
ejpam-5495	194	36	λ	λ	X
ejpam-5495	194	37	=	=	NOUN
ejpam-5495	194	38	0.5	0.5	NUM
ejpam-5495	194	39	,	,	PUNCT
ejpam-5495	194	40	anda	anda	PROPN
ejpam-5495	194	41	=	=	PROPN
ejpam-5495	194	42	0.2	0.2	NUM
ejpam-5495	194	43	.	.	PUNCT
ejpam-5495	195	1	using	use	VERB
ejpam-5495	195	2	ms	ms	NOUN
ejpam-5495	195	3	through	through	ADP
ejpam-5495	195	4	the	the	DET
ejpam-5495	195	5	command	command	NOUN
ejpam-5495	195	6	of	of	ADP
ejpam-5495	195	7	findroot	findroot	NOUN
ejpam-5495	195	8	,	,	PUNCT
ejpam-5495	195	9	the	the	DET
ejpam-5495	195	10	value	value	NOUN
ejpam-5495	195	11	of	of	ADP
ejpam-5495	195	12	the	the	DET
ejpam-5495	195	13	total	total	ADJ
ejpam-5495	195	14	frequency	frequency	NOUN
ejpam-5495	195	15	becomes	become	VERB
ejpam-5495	195	16	∆	∆	NOUN
ejpam-5495	195	17	=	=	PUNCT
ejpam-5495	195	18	3.90514	3.90514	NUM
ejpam-5495	195	19	.	.	PUNCT
ejpam-5495	196	1	for	for	ADP
ejpam-5495	196	2	more	more	ADJ
ejpam-5495	196	3	convenience	convenience	NOUN
ejpam-5495	196	4	,	,	PUNCT
ejpam-5495	196	5	a.	a.	NOUN
ejpam-5495	196	6	alanazy	alanazy	NOUN
ejpam-5495	196	7	et	et	PROPN
ejpam-5495	196	8	al	al	PROPN
ejpam-5495	196	9	.	.	PUNCT
ejpam-5495	196	10	/	/	SYM
ejpam-5495	196	11	eur	eur	PROPN
ejpam-5495	196	12	.	.	PUNCT
ejpam-5495	197	1	j.	j.	PROPN
ejpam-5495	197	2	pure	pure	PROPN
ejpam-5495	197	3	appl	appl	PROPN
ejpam-5495	197	4	.	.	PROPN
ejpam-5495	197	5	math	math	PROPN
ejpam-5495	197	6	,	,	PUNCT
ejpam-5495	197	7	18	18	NUM
ejpam-5495	197	8	(	(	PUNCT
ejpam-5495	197	9	1	1	NUM
ejpam-5495	197	10	)	)	PUNCT
ejpam-5495	197	11	(	(	PUNCT
ejpam-5495	197	12	2025	2025	NUM
ejpam-5495	197	13	)	)	PUNCT
ejpam-5495	197	14	,	,	PUNCT
ejpam-5495	197	15	5495	5495	NUM
ejpam-5495	197	16	9	9	NUM
ejpam-5495	197	17	of	of	ADP
ejpam-5495	197	18	21	21	NUM
ejpam-5495	197	19	along	along	ADP
ejpam-5495	197	20	with	with	ADP
ejpam-5495	197	21	the	the	DET
ejpam-5495	197	22	ms	ms	NOUN
ejpam-5495	197	23	with	with	ADP
ejpam-5495	197	24	the	the	DET
ejpam-5495	197	25	commend	commend	NOUN
ejpam-5495	197	26	ndsolve	ndsolve	NOUN
ejpam-5495	197	27	,	,	PUNCT
ejpam-5495	197	28	the	the	DET
ejpam-5495	197	29	graph	graph	NOUN
ejpam-5495	197	30	of	of	ADP
ejpam-5495	197	31	the	the	DET
ejpam-5495	197	32	original	original	ADJ
ejpam-5495	197	33	nonlinear	nonlinear	ADJ
ejpam-5495	197	34	ode	ode	NOUN
ejpam-5495	197	35	as	as	SCONJ
ejpam-5495	197	36	given	give	VERB
ejpam-5495	197	37	in	in	ADP
ejpam-5495	197	38	eq	eq	ADP
ejpam-5495	197	39	.	.	PUNCT
ejpam-5495	198	1	(	(	PUNCT
ejpam-5495	198	2	1	1	X
ejpam-5495	198	3	)	)	PUNCT
ejpam-5495	198	4	is	be	AUX
ejpam-5495	198	5	graphed	graph	VERB
ejpam-5495	198	6	with	with	ADP
ejpam-5495	198	7	the	the	DET
ejpam-5495	198	8	lode	lode	NOUN
ejpam-5495	198	9	as	as	SCONJ
ejpam-5495	198	10	shown	show	VERB
ejpam-5495	198	11	in	in	ADP
ejpam-5495	198	12	eq	eq	ADP
ejpam-5495	198	13	.	.	PUNCT
ejpam-5495	199	1	(	(	PUNCT
ejpam-5495	199	2	10	10	NUM
ejpam-5495	199	3	)	)	PUNCT
ejpam-5495	199	4	.	.	PUNCT
ejpam-5495	200	1	for	for	ADP
ejpam-5495	200	2	this	this	DET
ejpam-5495	200	3	purpose	purpose	NOUN
ejpam-5495	200	4	,	,	PUNCT
ejpam-5495	200	5	it	it	PRON
ejpam-5495	200	6	is	be	AUX
ejpam-5495	200	7	required	require	VERB
ejpam-5495	200	8	to	to	PART
ejpam-5495	200	9	supplement	supplement	VERB
ejpam-5495	200	10	the	the	DET
ejpam-5495	200	11	values	value	NOUN
ejpam-5495	200	12	of	of	ADP
ejpam-5495	200	13	the	the	DET
ejpam-5495	200	14	external	external	ADJ
ejpam-5495	200	15	excited	excited	ADJ
ejpam-5495	200	16	force	force	NOUN
ejpam-5495	200	17	f	f	PROPN
ejpam-5495	200	18	as	as	ADV
ejpam-5495	200	19	well	well	ADV
ejpam-5495	200	20	as	as	ADP
ejpam-5495	200	21	its	its	PRON
ejpam-5495	200	22	external	external	ADJ
ejpam-5495	200	23	frequency	frequency	NOUN
ejpam-5495	200	24	σ	σ	NOUN
ejpam-5495	200	25	as	as	ADP
ejpam-5495	200	26	f	f	PROPN
ejpam-5495	200	27	=	=	SYM
ejpam-5495	200	28	2	2	NUM
ejpam-5495	200	29	and	and	CCONJ
ejpam-5495	200	30	ω	ω	NUM
ejpam-5495	200	31	=	=	SYM
ejpam-5495	200	32	2.5	2.5	NUM
ejpam-5495	200	33	.	.	PUNCT
ejpam-5495	201	1	the	the	DET
ejpam-5495	201	2	comparison	comparison	NOUN
ejpam-5495	201	3	reveals	reveal	VERB
ejpam-5495	201	4	that	that	SCONJ
ejpam-5495	201	5	the	the	DET
ejpam-5495	201	6	two	two	NUM
ejpam-5495	201	7	solutions	solution	NOUN
ejpam-5495	201	8	have	have	VERB
ejpam-5495	201	9	a	a	DET
ejpam-5495	201	10	high	high	ADJ
ejpam-5495	201	11	degree	degree	NOUN
ejpam-5495	201	12	of	of	ADP
ejpam-5495	201	13	consistency	consistency	NOUN
ejpam-5495	201	14	with	with	ADP
ejpam-5495	201	15	each	each	DET
ejpam-5495	201	16	other	other	ADJ
ejpam-5495	201	17	,	,	PUNCT
ejpam-5495	201	18	as	as	SCONJ
ejpam-5495	201	19	seen	see	VERB
ejpam-5495	201	20	in	in	ADP
ejpam-5495	201	21	fig	fig	NOUN
ejpam-5495	201	22	.	.	PUNCT
ejpam-5495	202	1	(	(	PUNCT
ejpam-5495	202	2	1	1	NUM
ejpam-5495	202	3	)	)	PUNCT
ejpam-5495	202	4	,	,	PUNCT
ejpam-5495	202	5	where	where	SCONJ
ejpam-5495	202	6	the	the	DET
ejpam-5495	202	7	solutions	solution	NOUN
ejpam-5495	202	8	are	be	AUX
ejpam-5495	202	9	portrayed	portray	VERB
ejpam-5495	202	10	.	.	PUNCT
ejpam-5495	203	1	additionally	additionally	ADV
ejpam-5495	203	2	,	,	PUNCT
ejpam-5495	203	3	the	the	DET
ejpam-5495	203	4	ms	ms	NOUN
ejpam-5495	203	5	reported	report	VERB
ejpam-5495	203	6	that	that	SCONJ
ejpam-5495	203	7	,	,	PUNCT
ejpam-5495	203	8	up	up	ADP
ejpam-5495	203	9	to	to	ADP
ejpam-5495	203	10	a	a	DET
ejpam-5495	203	11	time	time	NOUN
ejpam-5495	203	12	of	of	ADP
ejpam-5495	203	13	100	100	NUM
ejpam-5495	203	14	units	unit	NOUN
ejpam-5495	203	15	,	,	PUNCT
ejpam-5495	203	16	the	the	DET
ejpam-5495	203	17	total	total	ADJ
ejpam-5495	203	18	variance	variance	NOUN
ejpam-5495	203	19	between	between	ADP
ejpam-5495	203	20	the	the	DET
ejpam-5495	203	21	as	as	ADV
ejpam-5495	203	22	and	and	CCONJ
ejpam-5495	203	23	ns	ns	NUM
ejpam-5495	203	24	is	be	AUX
ejpam-5495	203	25	0.0056	0.0056	NUM
ejpam-5495	203	26	.	.	PUNCT
ejpam-5495	204	1	in	in	ADP
ejpam-5495	204	2	what	what	PRON
ejpam-5495	204	3	follows	follow	VERB
ejpam-5495	204	4	,	,	PUNCT
ejpam-5495	204	5	an	an	DET
ejpam-5495	204	6	excellent	excellent	ADJ
ejpam-5495	204	7	agreement	agreement	NOUN
ejpam-5495	204	8	between	between	ADP
ejpam-5495	204	9	the	the	DET
ejpam-5495	204	10	linear	linear	NOUN
ejpam-5495	204	11	as	as	ADV
ejpam-5495	204	12	well	well	ADV
ejpam-5495	204	13	as	as	ADP
ejpam-5495	204	14	the	the	DET
ejpam-5495	204	15	nonlinear	nonlinear	ADJ
ejpam-5495	204	16	odes	ode	NOUN
ejpam-5495	204	17	is	be	AUX
ejpam-5495	204	18	seen	see	VERB
ejpam-5495	204	19	.	.	PUNCT
ejpam-5495	205	1	this	this	DET
ejpam-5495	205	2	agreement	agreement	NOUN
ejpam-5495	205	3	comes	come	VERB
ejpam-5495	205	4	from	from	ADP
ejpam-5495	205	5	:	:	PUNCT
ejpam-5495	205	6	the	the	DET
ejpam-5495	205	7	strong	strong	ADJ
ejpam-5495	205	8	concordance	concordance	NOUN
ejpam-5495	205	9	between	between	ADP
ejpam-5495	205	10	the	the	DET
ejpam-5495	205	11	two	two	NUM
ejpam-5495	205	12	planar	planar	ADJ
ejpam-5495	205	13	curves	curve	NOUN
ejpam-5495	205	14	,	,	PUNCT
ejpam-5495	205	15	one	one	NUM
ejpam-5495	205	16	originating	originating	NOUN
ejpam-5495	205	17	from	from	ADP
ejpam-5495	205	18	a	a	DET
ejpam-5495	205	19	nonlinear	nonlinear	ADJ
ejpam-5495	205	20	ode	ode	NOUN
ejpam-5495	205	21	as	as	SCONJ
ejpam-5495	205	22	given	give	VERB
ejpam-5495	205	23	in	in	ADP
ejpam-5495	205	24	eq	eq	ADP
ejpam-5495	205	25	.	.	PUNCT
ejpam-5495	206	1	(	(	PUNCT
ejpam-5495	206	2	1	1	NUM
ejpam-5495	206	3	)	)	PUNCT
ejpam-5495	206	4	and	and	CCONJ
ejpam-5495	206	5	the	the	DET
ejpam-5495	206	6	other	other	ADJ
ejpam-5495	206	7	from	from	ADP
ejpam-5495	206	8	a	a	DET
ejpam-5495	206	9	linear	linear	ADJ
ejpam-5495	206	10	approximation	approximation	NOUN
ejpam-5495	206	11	as	as	SCONJ
ejpam-5495	206	12	given	give	VERB
ejpam-5495	206	13	in	in	ADP
ejpam-5495	206	14	eq	eq	ADP
ejpam-5495	206	15	.	.	PUNCT
ejpam-5495	207	1	(	(	PUNCT
ejpam-5495	207	2	10	10	NUM
ejpam-5495	207	3	)	)	PUNCT
ejpam-5495	207	4	,	,	PUNCT
ejpam-5495	207	5	demonstrates	demonstrate	VERB
ejpam-5495	207	6	that	that	SCONJ
ejpam-5495	207	7	the	the	DET
ejpam-5495	207	8	linear	linear	PROPN
ejpam-5495	207	9	model	model	NOUN
ejpam-5495	207	10	well	well	ADV
ejpam-5495	207	11	encapsulates	encapsulate	VERB
ejpam-5495	207	12	the	the	DET
ejpam-5495	207	13	fundamental	fundamental	ADJ
ejpam-5495	207	14	dynamics	dynamic	NOUN
ejpam-5495	207	15	of	of	ADP
ejpam-5495	207	16	the	the	DET
ejpam-5495	207	17	nonlinear	nonlinear	ADJ
ejpam-5495	207	18	system	system	NOUN
ejpam-5495	207	19	under	under	ADP
ejpam-5495	207	20	certain	certain	ADJ
ejpam-5495	207	21	conditions	condition	NOUN
ejpam-5495	207	22	.	.	PUNCT
ejpam-5495	208	1	despite	despite	SCONJ
ejpam-5495	208	2	the	the	DET
ejpam-5495	208	3	intrinsic	intrinsic	ADJ
ejpam-5495	208	4	complexity	complexity	NOUN
ejpam-5495	208	5	of	of	ADP
ejpam-5495	208	6	the	the	DET
ejpam-5495	208	7	nonlinear	nonlinear	ADJ
ejpam-5495	208	8	ode	ode	PROPN
ejpam-5495	208	9	,	,	PUNCT
ejpam-5495	208	10	the	the	DET
ejpam-5495	208	11	strong	strong	ADJ
ejpam-5495	208	12	correlation	correlation	NOUN
ejpam-5495	208	13	between	between	ADP
ejpam-5495	208	14	the	the	DET
ejpam-5495	208	15	curves	curve	NOUN
ejpam-5495	208	16	indicates	indicate	VERB
ejpam-5495	208	17	that	that	SCONJ
ejpam-5495	208	18	,	,	PUNCT
ejpam-5495	208	19	within	within	ADP
ejpam-5495	208	20	a	a	DET
ejpam-5495	208	21	specific	specific	ADJ
ejpam-5495	208	22	range	range	NOUN
ejpam-5495	208	23	or	or	CCONJ
ejpam-5495	208	24	under	under	ADP
ejpam-5495	208	25	particular	particular	ADJ
ejpam-5495	208	26	simplifying	simplifying	NOUN
ejpam-5495	208	27	assumptions	assumption	NOUN
ejpam-5495	208	28	,	,	PUNCT
ejpam-5495	208	29	the	the	DET
ejpam-5495	208	30	linear	linear	PROPN
ejpam-5495	208	31	representation	representation	NOUN
ejpam-5495	208	32	serves	serve	VERB
ejpam-5495	208	33	as	as	ADP
ejpam-5495	208	34	a	a	DET
ejpam-5495	208	35	robust	robust	ADJ
ejpam-5495	208	36	and	and	CCONJ
ejpam-5495	208	37	dependable	dependable	ADJ
ejpam-5495	208	38	approximation	approximation	NOUN
ejpam-5495	208	39	of	of	ADP
ejpam-5495	208	40	the	the	DET
ejpam-5495	208	41	system	system	NOUN
ejpam-5495	208	42	’s	’s	PART
ejpam-5495	208	43	behavior	behavior	NOUN
ejpam-5495	208	44	,	,	PUNCT
ejpam-5495	208	45	underscoring	underscore	VERB
ejpam-5495	208	46	the	the	DET
ejpam-5495	208	47	efficacy	efficacy	NOUN
ejpam-5495	208	48	of	of	ADP
ejpam-5495	208	49	linearization	linearization	NOUN
ejpam-5495	208	50	in	in	ADP
ejpam-5495	208	51	modelling	model	VERB
ejpam-5495	208	52	intricate	intricate	ADJ
ejpam-5495	208	53	phenomena	phenomenon	NOUN
ejpam-5495	208	54	.	.	PUNCT
ejpam-5495	209	1	3	3	X
ejpam-5495	209	2	.	.	X
ejpam-5495	209	3	discussions	discussion	NOUN
ejpam-5495	209	4	and	and	CCONJ
ejpam-5495	209	5	results	result	NOUN
ejpam-5495	209	6	this	this	DET
ejpam-5495	209	7	section	section	NOUN
ejpam-5495	209	8	is	be	AUX
ejpam-5495	209	9	devoted	devote	VERB
ejpam-5495	209	10	to	to	ADP
ejpam-5495	209	11	presenting	present	VERB
ejpam-5495	209	12	and	and	CCONJ
ejpam-5495	209	13	discussing	discuss	VERB
ejpam-5495	209	14	the	the	DET
ejpam-5495	209	15	time	time	NOUN
ejpam-5495	209	16	histories	history	NOUN
ejpam-5495	209	17	of	of	ADP
ejpam-5495	209	18	the	the	DET
ejpam-5495	209	19	obtained	obtain	VERB
ejpam-5495	209	20	outcomes	outcome	NOUN
ejpam-5495	209	21	as	as	ADV
ejpam-5495	209	22	well	well	ADV
ejpam-5495	209	23	as	as	ADP
ejpam-5495	209	24	their	their	PRON
ejpam-5495	209	25	phase	phase	NOUN
ejpam-5495	209	26	planes	plane	NOUN
ejpam-5495	209	27	and	and	CCONJ
ejpam-5495	209	28	the	the	DET
ejpam-5495	209	29	stability	stability	NOUN
ejpam-5495	209	30	/	/	SYM
ejpam-5495	209	31	instability	instability	NOUN
ejpam-5495	209	32	regions	region	NOUN
ejpam-5495	209	33	in	in	ADP
ejpam-5495	209	34	focus	focus	NOUN
ejpam-5495	209	35	on	on	ADP
ejpam-5495	209	36	the	the	DET
ejpam-5495	209	37	various	various	ADJ
ejpam-5495	209	38	values	value	NOUN
ejpam-5495	209	39	of	of	ADP
ejpam-5495	209	40	the	the	DET
ejpam-5495	209	41	relevant	relevant	ADJ
ejpam-5495	209	42	factors	factor	NOUN
ejpam-5495	209	43	.	.	PUNCT
ejpam-5495	210	1	returning	return	VERB
ejpam-5495	210	2	to	to	ADP
ejpam-5495	210	3	the	the	DET
ejpam-5495	210	4	td	td	NOUN
ejpam-5495	210	5	as	as	SCONJ
ejpam-5495	210	6	shown	show	VERB
ejpam-5495	210	7	in	in	ADP
ejpam-5495	210	8	eq	eq	ADP
ejpam-5495	210	9	.	.	PUNCT
ejpam-5495	211	1	(	(	PUNCT
ejpam-5495	211	2	1	1	NUM
ejpam-5495	211	3	)	)	PUNCT
ejpam-5495	211	4	,	,	PUNCT
ejpam-5495	211	5	the	the	DET
ejpam-5495	211	6	npa	npa	NOUN
ejpam-5495	211	7	enables	enable	VERB
ejpam-5495	211	8	us	we	PRON
ejpam-5495	211	9	to	to	PART
ejpam-5495	211	10	determine	determine	VERB
ejpam-5495	211	11	the	the	DET
ejpam-5495	211	12	solution	solution	NOUN
ejpam-5495	211	13	of	of	ADP
ejpam-5495	211	14	the	the	DET
ejpam-5495	211	15	basic	basic	ADJ
ejpam-5495	211	16	eq	eq	X
ejpam-5495	211	17	.	.	PUNCT
ejpam-5495	212	1	(	(	PUNCT
ejpam-5495	212	2	1	1	X
ejpam-5495	212	3	)	)	PUNCT
ejpam-5495	212	4	that	that	PRON
ejpam-5495	212	5	is	be	AUX
ejpam-5495	212	6	identical	identical	ADJ
ejpam-5495	212	7	as	as	ADP
ejpam-5495	212	8	those	those	PRON
ejpam-5495	212	9	used	use	VERB
ejpam-5495	212	10	by	by	ADP
ejpam-5495	212	11	the	the	DET
ejpam-5495	212	12	concluding	concluding	NOUN
ejpam-5495	212	13	linear	linear	PROPN
ejpam-5495	212	14	eq	eq	NOUN
ejpam-5495	212	15	.	.	PUNCT
ejpam-5495	213	1	(	(	PUNCT
ejpam-5495	213	2	10	10	NUM
ejpam-5495	213	3	)	)	PUNCT
ejpam-5495	213	4	.	.	PUNCT
ejpam-5495	214	1	as	as	SCONJ
ejpam-5495	214	2	was	be	AUX
ejpam-5495	214	3	previously	previously	ADV
ejpam-5495	214	4	said	say	VERB
ejpam-5495	214	5	,	,	PUNCT
ejpam-5495	214	6	every	every	DET
ejpam-5495	214	7	parameter	parameter	NOUN
ejpam-5495	214	8	affects	affect	VERB
ejpam-5495	214	9	the	the	DET
ejpam-5495	214	10	related	relate	VERB
ejpam-5495	214	11	frequency	frequency	NOUN
ejpam-5495	214	12	∆	∆	PROPN
ejpam-5495	214	13	,	,	PUNCT
ejpam-5495	214	14	which	which	PRON
ejpam-5495	214	15	is	be	AUX
ejpam-5495	214	16	determined	determine	VERB
ejpam-5495	214	17	by	by	ADP
ejpam-5495	214	18	eq	eq	PROPN
ejpam-5495	214	19	.	.	PUNCT
ejpam-5495	215	1	(	(	PUNCT
ejpam-5495	215	2	12	12	NUM
ejpam-5495	215	3	)	)	PUNCT
ejpam-5495	215	4	.	.	PUNCT
ejpam-5495	216	1	the	the	DET
ejpam-5495	216	2	curves	curve	NOUN
ejpam-5495	216	3	in	in	ADP
ejpam-5495	216	4	figs	fig	NOUN
ejpam-5495	216	5	.	.	PUNCT
ejpam-5495	217	1	(	(	PUNCT
ejpam-5495	217	2	2)-(6	2)-(6	NUM
ejpam-5495	217	3	)	)	PUNCT
ejpam-5495	217	4	are	be	AUX
ejpam-5495	217	5	calculated	calculate	VERB
ejpam-5495	217	6	according	accord	VERB
ejpam-5495	217	7	to	to	ADP
ejpam-5495	217	8	the	the	DET
ejpam-5495	217	9	considered	consider	VERB
ejpam-5495	217	10	data	datum	NOUN
ejpam-5495	217	11	above	above	ADV
ejpam-5495	217	12	and	and	CCONJ
ejpam-5495	217	13	when	when	SCONJ
ejpam-5495	217	14	the	the	DET
ejpam-5495	217	15	parameters	parameter	NOUN
ejpam-5495	217	16	α	α	PRON
ejpam-5495	217	17	,	,	PUNCT
ejpam-5495	217	18	β	β	X
ejpam-5495	217	19	,	,	PUNCT
ejpam-5495	217	20	λ	λ	PROPN
ejpam-5495	217	21	,	,	PUNCT
ejpam-5495	217	22	µ	µ	NOUN
ejpam-5495	217	23	,	,	PUNCT
ejpam-5495	217	24	and	and	CCONJ
ejpam-5495	217	25	ω	ω	NUM
ejpam-5495	217	26	have	have	VERB
ejpam-5495	217	27	the	the	DET
ejpam-5495	217	28	values	value	NOUN
ejpam-5495	217	29	(	(	PUNCT
ejpam-5495	217	30	0.1	0.1	NUM
ejpam-5495	217	31	,	,	PUNCT
ejpam-5495	217	32	0.4	0.4	NUM
ejpam-5495	217	33	,	,	PUNCT
ejpam-5495	217	34	1.8	1.8	NUM
ejpam-5495	217	35	)	)	PUNCT
ejpam-5495	217	36	,	,	PUNCT
ejpam-5495	217	37	(	(	PUNCT
ejpam-5495	217	38	0.3	0.3	NUM
ejpam-5495	217	39	,	,	PUNCT
ejpam-5495	217	40	0.6	0.6	NUM
ejpam-5495	217	41	,	,	PUNCT
ejpam-5495	217	42	1.1	1.1	NUM
ejpam-5495	217	43	)	)	PUNCT
ejpam-5495	217	44	,	,	PUNCT
ejpam-5495	217	45	(	(	PUNCT
ejpam-5495	217	46	0.5	0.5	NUM
ejpam-5495	217	47	,	,	PUNCT
ejpam-5495	217	48	4	4	NUM
ejpam-5495	217	49	,	,	PUNCT
ejpam-5495	217	50	8)	8)	NUM
ejpam-5495	217	51	,	,	PUNCT
ejpam-5495	217	52	(	(	PUNCT
ejpam-5495	217	53	−1,−3,−6	−1,−3,−6	NOUN
ejpam-5495	217	54	)	)	PUNCT
ejpam-5495	217	55	,	,	PUNCT
ejpam-5495	217	56	and	and	CCONJ
ejpam-5495	217	57	(	(	PUNCT
ejpam-5495	217	58	1	1	NUM
ejpam-5495	217	59	,	,	PUNCT
ejpam-5495	217	60	1.5	1.5	NUM
ejpam-5495	217	61	,	,	PUNCT
ejpam-5495	217	62	4	4	NUM
ejpam-5495	217	63	)	)	PUNCT
ejpam-5495	217	64	,	,	PUNCT
ejpam-5495	217	65	respectively	respectively	ADV
ejpam-5495	217	66	.	.	PUNCT
ejpam-5495	218	1	as	as	SCONJ
ejpam-5495	218	2	displayed	display	VERB
ejpam-5495	218	3	in	in	ADP
ejpam-5495	218	4	fig	fig	NOUN
ejpam-5495	218	5	.	.	PUNCT
ejpam-5495	219	1	(	(	PUNCT
ejpam-5495	219	2	2a	2a	NUM
ejpam-5495	219	3	)	)	PUNCT
ejpam-5495	219	4	,	,	PUNCT
ejpam-5495	219	5	when	when	SCONJ
ejpam-5495	219	6	α(=	α(=	ADV
ejpam-5495	219	7	0.1	0.1	NUM
ejpam-5495	219	8	,	,	PUNCT
ejpam-5495	219	9	0.4	0.4	NUM
ejpam-5495	219	10	,	,	PUNCT
ejpam-5495	219	11	1.8	1.8	NUM
ejpam-5495	219	12	)	)	PUNCT
ejpam-5495	219	13	,	,	PUNCT
ejpam-5495	219	14	the	the	DET
ejpam-5495	219	15	amplitudes	amplitude	NOUN
ejpam-5495	219	16	of	of	ADP
ejpam-5495	219	17	the	the	DET
ejpam-5495	219	18	periodic	periodic	ADJ
ejpam-5495	219	19	waves	wave	NOUN
ejpam-5495	219	20	somewhat	somewhat	ADV
ejpam-5495	219	21	rise	rise	VERB
ejpam-5495	219	22	,	,	PUNCT
ejpam-5495	219	23	indicating	indicate	VERB
ejpam-5495	219	24	stable	stable	ADJ
ejpam-5495	219	25	motion	motion	NOUN
ejpam-5495	219	26	under	under	ADP
ejpam-5495	219	27	the	the	DET
ejpam-5495	219	28	impact	impact	NOUN
ejpam-5495	219	29	of	of	ADP
ejpam-5495	219	30	these	these	DET
ejpam-5495	219	31	values	value	NOUN
ejpam-5495	219	32	.	.	PUNCT
ejpam-5495	220	1	to	to	PART
ejpam-5495	220	2	support	support	VERB
ejpam-5495	220	3	this	this	DET
ejpam-5495	220	4	conclusion	conclusion	NOUN
ejpam-5495	220	5	,	,	PUNCT
ejpam-5495	220	6	the	the	DET
ejpam-5495	220	7	phase	phase	NOUN
ejpam-5495	220	8	plane	plane	NOUN
ejpam-5495	220	9	curves	curve	NOUN
ejpam-5495	220	10	for	for	ADP
ejpam-5495	220	11	the	the	DET
ejpam-5495	220	12	represented	represent	VERB
ejpam-5495	220	13	solutions	solution	NOUN
ejpam-5495	220	14	in	in	ADP
ejpam-5495	220	15	fig	fig	NOUN
ejpam-5495	220	16	.	.	PUNCT
ejpam-5495	221	1	(	(	PUNCT
ejpam-5495	221	2	2a	2a	NUM
ejpam-5495	221	3	)	)	PUNCT
ejpam-5495	221	4	are	be	AUX
ejpam-5495	221	5	illustrated	illustrate	VERB
ejpam-5495	221	6	as	as	ADP
ejpam-5495	221	7	closed	close	VERB
ejpam-5495	221	8	curves	curve	NOUN
ejpam-5495	221	9	in	in	ADP
ejpam-5495	221	10	fig	fig	NOUN
ejpam-5495	221	11	.	.	PUNCT
ejpam-5495	222	1	(	(	PUNCT
ejpam-5495	222	2	2b	2b	NUM
ejpam-5495	222	3	)	)	PUNCT
ejpam-5495	222	4	,	,	PUNCT
ejpam-5495	222	5	i.e.	i.e.	X
ejpam-5495	222	6	in	in	ADP
ejpam-5495	222	7	a	a	DET
ejpam-5495	222	8	plane	plane	NOUN
ejpam-5495	222	9	that	that	PRON
ejpam-5495	222	10	combines	combine	VERB
ejpam-5495	222	11	the	the	DET
ejpam-5495	222	12	solutions	solution	NOUN
ejpam-5495	222	13	versus	versus	ADP
ejpam-5495	222	14	their	their	PRON
ejpam-5495	222	15	first	first	ADJ
ejpam-5495	222	16	derivatives	derivative	NOUN
ejpam-5495	222	17	.	.	PUNCT
ejpam-5495	223	1	segments	segment	NOUN
ejpam-5495	223	2	(	(	PUNCT
ejpam-5495	223	3	c	c	NOUN
ejpam-5495	223	4	)	)	PUNCT
ejpam-5495	223	5	,	,	PUNCT
ejpam-5495	223	6	(	(	PUNCT
ejpam-5495	223	7	d	d	NOUN
ejpam-5495	223	8	)	)	PUNCT
ejpam-5495	223	9	,	,	PUNCT
ejpam-5495	223	10	and	and	CCONJ
ejpam-5495	223	11	(	(	PUNCT
ejpam-5495	223	12	e	e	NOUN
ejpam-5495	223	13	)	)	PUNCT
ejpam-5495	223	14	in	in	ADP
ejpam-5495	223	15	fig	fig	NOUN
ejpam-5495	223	16	.	.	PUNCT
ejpam-5495	224	1	(	(	PUNCT
ejpam-5495	224	2	2	2	X
ejpam-5495	224	3	)	)	PUNCT
ejpam-5495	224	4	show	show	VERB
ejpam-5495	224	5	the	the	DET
ejpam-5495	224	6	stabilities	stability	NOUN
ejpam-5495	224	7	areas	area	NOUN
ejpam-5495	224	8	of	of	ADP
ejpam-5495	224	9	the	the	DET
ejpam-5495	224	10	obtained	obtain	VERB
ejpam-5495	224	11	solution	solution	NOUN
ejpam-5495	224	12	using	use	VERB
ejpam-5495	224	13	the	the	DET
ejpam-5495	224	14	nap	nap	NOUN
ejpam-5495	224	15	at	at	ADP
ejpam-5495	224	16	α	α	NOUN
ejpam-5495	224	17	=	=	SYM
ejpam-5495	224	18	0.1	0.1	NUM
ejpam-5495	224	19	,	,	PUNCT
ejpam-5495	224	20	α	α	NOUN
ejpam-5495	224	21	=	=	SYM
ejpam-5495	224	22	0.4	0.4	NUM
ejpam-5495	224	23	and	and	CCONJ
ejpam-5495	224	24	α	α	NOUN
ejpam-5495	224	25	=	=	SYM
ejpam-5495	224	26	1.8	1.8	NUM
ejpam-5495	224	27	,	,	PUNCT
ejpam-5495	224	28	respectively.the	respectively.the	DET
ejpam-5495	224	29	examination	examination	NOUN
ejpam-5495	224	30	of	of	ADP
ejpam-5495	224	31	these	these	DET
ejpam-5495	224	32	sections	section	NOUN
ejpam-5495	224	33	indicates	indicate	VERB
ejpam-5495	224	34	that	that	SCONJ
ejpam-5495	224	35	the	the	DET
ejpam-5495	224	36	values	value	NOUN
ejpam-5495	224	37	of	of	ADP
ejpam-5495	224	38	α	α	PRON
ejpam-5495	224	39	increase	increase	NOUN
ejpam-5495	224	40	,	,	PUNCT
ejpam-5495	224	41	the	the	DET
ejpam-5495	224	42	green	green	ADJ
ejpam-5495	224	43	-	-	PUNCT
ejpam-5495	224	44	colored	colored	ADJ
ejpam-5495	224	45	stable	stable	ADJ
ejpam-5495	224	46	regions	region	NOUN
ejpam-5495	224	47	decrease	decrease	NOUN
ejpam-5495	224	48	,	,	PUNCT
ejpam-5495	224	49	while	while	SCONJ
ejpam-5495	224	50	the	the	DET
ejpam-5495	224	51	white	white	ADJ
ejpam-5495	224	52	-	-	PUNCT
ejpam-5495	224	53	colored	colored	ADJ
ejpam-5495	224	54	unstable	unstable	ADJ
ejpam-5495	224	55	regions	region	NOUN
ejpam-5495	224	56	expand	expand	VERB
ejpam-5495	224	57	.	.	PUNCT
ejpam-5495	225	1	the	the	DET
ejpam-5495	225	2	influence	influence	NOUN
ejpam-5495	225	3	of	of	ADP
ejpam-5495	225	4	the	the	DET
ejpam-5495	225	5	variation	variation	NOUN
ejpam-5495	225	6	of	of	ADP
ejpam-5495	225	7	the	the	DET
ejpam-5495	225	8	parameter	parameter	NOUN
ejpam-5495	225	9	β	β	PROPN
ejpam-5495	225	10	on	on	ADP
ejpam-5495	225	11	the	the	DET
ejpam-5495	225	12	performance	performance	NOUN
ejpam-5495	225	13	of	of	ADP
ejpam-5495	225	14	the	the	DET
ejpam-5495	225	15	npa	npa	NOUN
ejpam-5495	225	16	was	be	AUX
ejpam-5495	225	17	graphed	graph	VERB
ejpam-5495	225	18	,	,	PUNCT
ejpam-5495	225	19	as	as	SCONJ
ejpam-5495	225	20	indicated	indicate	VERB
ejpam-5495	225	21	in	in	ADP
ejpam-5495	225	22	fig	fig	NOUN
ejpam-5495	225	23	.	.	PUNCT
ejpam-5495	226	1	(	(	PUNCT
ejpam-5495	226	2	3	3	NUM
ejpam-5495	226	3	)	)	PUNCT
ejpam-5495	226	4	.	.	PUNCT
ejpam-5495	227	1	the	the	DET
ejpam-5495	227	2	drawn	draw	VERB
ejpam-5495	227	3	curves	curve	NOUN
ejpam-5495	227	4	in	in	ADP
ejpam-5495	227	5	fig	fig	NOUN
ejpam-5495	227	6	.	.	PUNCT
ejpam-5495	228	1	(	(	PUNCT
ejpam-5495	228	2	3a	3a	NUM
ejpam-5495	228	3	)	)	PUNCT
ejpam-5495	228	4	have	have	VERB
ejpam-5495	228	5	the	the	DET
ejpam-5495	228	6	forms	form	NOUN
ejpam-5495	228	7	of	of	ADP
ejpam-5495	228	8	quasi	quasi	ADJ
ejpam-5495	228	9	-	-	ADJ
ejpam-5495	228	10	periodic	periodic	ADJ
ejpam-5495	228	11	waves	wave	NOUN
ejpam-5495	228	12	.	.	PUNCT
ejpam-5495	229	1	it	it	PRON
ejpam-5495	229	2	is	be	AUX
ejpam-5495	229	3	noted	note	VERB
ejpam-5495	229	4	that	that	SCONJ
ejpam-5495	229	5	this	this	DET
ejpam-5495	229	6	variation	variation	NOUN
ejpam-5495	229	7	produces	produce	VERB
ejpam-5495	229	8	an	an	DET
ejpam-5495	229	9	increase	increase	NOUN
ejpam-5495	229	10	in	in	ADP
ejpam-5495	229	11	the	the	DET
ejpam-5495	229	12	wave	wave	NOUN
ejpam-5495	229	13	’s	’s	PART
ejpam-5495	229	14	amplitudes	amplitude	NOUN
ejpam-5495	229	15	.	.	PUNCT
ejpam-5495	230	1	as	as	SCONJ
ejpam-5495	230	2	shown	show	VERB
ejpam-5495	230	3	in	in	ADP
ejpam-5495	230	4	fig	fig	NOUN
ejpam-5495	230	5	.	.	PUNCT
ejpam-5495	231	1	(	(	PUNCT
ejpam-5495	231	2	3b	3b	NUM
ejpam-5495	231	3	)	)	PUNCT
ejpam-5495	231	4	,	,	PUNCT
ejpam-5495	231	5	nearly	nearly	ADV
ejpam-5495	231	6	symmetric	symmetric	ADJ
ejpam-5495	231	7	closed	closed	ADJ
ejpam-5495	231	8	curves	curve	NOUN
ejpam-5495	231	9	in	in	ADP
ejpam-5495	231	10	the	the	DET
ejpam-5495	231	11	plane	plane	NOUN
ejpam-5495	231	12	ζζ̇are	ζζ̇are	PRON
ejpam-5495	231	13	observed	observe	VERB
ejpam-5495	231	14	,	,	PUNCT
ejpam-5495	231	15	resembling	resemble	VERB
ejpam-5495	231	16	a	a	DET
ejpam-5495	231	17	grid	grid	NOUN
ejpam-5495	231	18	where	where	SCONJ
ejpam-5495	231	19	the	the	DET
ejpam-5495	231	20	density	density	NOUN
ejpam-5495	231	21	of	of	ADP
ejpam-5495	231	22	capture	capture	NOUN
ejpam-5495	231	23	points	point	NOUN
ejpam-5495	231	24	increases	increase	NOUN
ejpam-5495	231	25	with	with	ADP
ejpam-5495	231	26	increasing	increase	VERB
ejpam-5495	231	27	β	β	X
ejpam-5495	231	28	.	.	PUNCT
ejpam-5495	232	1	the	the	DET
ejpam-5495	232	2	stabilities	stability	NOUN
ejpam-5495	232	3	zones	zone	NOUN
ejpam-5495	232	4	of	of	ADP
ejpam-5495	232	5	the	the	DET
ejpam-5495	232	6	solution	solution	NOUN
ejpam-5495	232	7	produced	produce	VERB
ejpam-5495	232	8	using	use	VERB
ejpam-5495	232	9	the	the	DET
ejpam-5495	232	10	nap	nap	NOUN
ejpam-5495	232	11	at	at	ADP
ejpam-5495	232	12	β	β	X
ejpam-5495	232	13	=	=	SYM
ejpam-5495	232	14	0.3	0.3	NUM
ejpam-5495	232	15	,	,	PUNCT
ejpam-5495	232	16	β	β	X
ejpam-5495	232	17	=	=	SYM
ejpam-5495	232	18	0.6	0.6	NUM
ejpam-5495	232	19	,	,	PUNCT
ejpam-5495	232	20	and	and	CCONJ
ejpam-5495	232	21	β	β	X
ejpam-5495	232	22	=	=	SYM
ejpam-5495	232	23	1.1	1.1	NUM
ejpam-5495	232	24	are	be	AUX
ejpam-5495	232	25	depicted	depict	VERB
ejpam-5495	232	26	,	,	PUNCT
ejpam-5495	232	27	respectively	respectively	ADV
ejpam-5495	232	28	,	,	PUNCT
ejpam-5495	232	29	in	in	ADP
ejpam-5495	232	30	figs	fig	NOUN
ejpam-5495	232	31	.	.	PUNCT
ejpam-5495	233	1	(	(	PUNCT
ejpam-5495	233	2	2c	2c	NOUN
ejpam-5495	233	3	)	)	PUNCT
ejpam-5495	233	4	,	,	PUNCT
ejpam-5495	233	5	(	(	PUNCT
ejpam-5495	233	6	2d	2d	NOUN
ejpam-5495	233	7	)	)	PUNCT
ejpam-5495	233	8	,	,	PUNCT
ejpam-5495	233	9	and	and	CCONJ
ejpam-5495	233	10	(	(	PUNCT
ejpam-5495	233	11	2e	2e	NUM
ejpam-5495	233	12	)	)	PUNCT
ejpam-5495	233	13	.	.	PUNCT
ejpam-5495	234	1	an	an	DET
ejpam-5495	234	2	analysis	analysis	NOUN
ejpam-5495	234	3	of	of	ADP
ejpam-5495	234	4	these	these	DET
ejpam-5495	234	5	a.	a.	NOUN
ejpam-5495	234	6	alanazy	alanazy	NOUN
ejpam-5495	234	7	et	et	PROPN
ejpam-5495	234	8	al	al	PROPN
ejpam-5495	234	9	.	.	PUNCT
ejpam-5495	234	10	/	/	SYM
ejpam-5495	234	11	eur	eur	PROPN
ejpam-5495	234	12	.	.	PUNCT
ejpam-5495	235	1	j.	j.	PROPN
ejpam-5495	235	2	pure	pure	PROPN
ejpam-5495	235	3	appl	appl	PROPN
ejpam-5495	235	4	.	.	PROPN
ejpam-5495	235	5	math	math	PROPN
ejpam-5495	235	6	,	,	PUNCT
ejpam-5495	235	7	18	18	NUM
ejpam-5495	235	8	(	(	PUNCT
ejpam-5495	235	9	1	1	NUM
ejpam-5495	235	10	)	)	PUNCT
ejpam-5495	235	11	(	(	PUNCT
ejpam-5495	235	12	2025	2025	NUM
ejpam-5495	235	13	)	)	PUNCT
ejpam-5495	235	14	,	,	PUNCT
ejpam-5495	235	15	5495	5495	NUM
ejpam-5495	235	16	10	10	NUM
ejpam-5495	235	17	of	of	ADP
ejpam-5495	235	18	21	21	NUM
ejpam-5495	235	19	sections	section	NOUN
ejpam-5495	235	20	shows	show	VERB
ejpam-5495	235	21	that	that	SCONJ
ejpam-5495	235	22	the	the	DET
ejpam-5495	235	23	white	white	ADJ
ejpam-5495	235	24	-	-	PUNCT
ejpam-5495	235	25	colored	colored	ADJ
ejpam-5495	235	26	unstable	unstable	ADJ
ejpam-5495	235	27	regions	region	NOUN
ejpam-5495	235	28	grow	grow	VERB
ejpam-5495	235	29	and	and	CCONJ
ejpam-5495	235	30	the	the	DET
ejpam-5495	235	31	green	green	ADJ
ejpam-5495	235	32	-	-	PUNCT
ejpam-5495	235	33	colored	colored	ADJ
ejpam-5495	235	34	stable	stable	ADJ
ejpam-5495	235	35	parts	part	NOUN
ejpam-5495	235	36	shrink	shrink	NOUN
ejpam-5495	235	37	as	as	ADP
ejpam-5495	235	38	the	the	DET
ejpam-5495	235	39	β	β	PROPN
ejpam-5495	235	40	values	value	NOUN
ejpam-5495	235	41	.	.	PUNCT
ejpam-5495	236	1	the	the	DET
ejpam-5495	236	2	study	study	NOUN
ejpam-5495	236	3	of	of	ADP
ejpam-5495	236	4	the	the	DET
ejpam-5495	236	5	change	change	NOUN
ejpam-5495	236	6	in	in	ADP
ejpam-5495	236	7	various	various	ADJ
ejpam-5495	236	8	values	value	NOUN
ejpam-5495	236	9	of	of	ADP
ejpam-5495	236	10	λ(=	λ(=	ADP
ejpam-5495	236	11	0.5	0.5	NUM
ejpam-5495	236	12	,	,	PUNCT
ejpam-5495	236	13	4	4	NUM
ejpam-5495	236	14	,	,	PUNCT
ejpam-5495	236	15	8)	8)	NUM
ejpam-5495	236	16	on	on	ADP
ejpam-5495	236	17	the	the	DET
ejpam-5495	236	18	behavior	behavior	NOUN
ejpam-5495	236	19	of	of	ADP
ejpam-5495	236	20	the	the	DET
ejpam-5495	236	21	achieved	achieve	VERB
ejpam-5495	236	22	solution	solution	NOUN
ejpam-5495	236	23	using	use	VERB
ejpam-5495	236	24	npa	npa	NOUN
ejpam-5495	236	25	,	,	PUNCT
ejpam-5495	236	26	phase	phase	NOUN
ejpam-5495	236	27	plane	plane	NOUN
ejpam-5495	236	28	plots	plot	NOUN
ejpam-5495	236	29	,	,	PUNCT
ejpam-5495	236	30	and	and	CCONJ
ejpam-5495	236	31	stability	stability	NOUN
ejpam-5495	236	32	/	/	SYM
ejpam-5495	236	33	instability	instability	NOUN
ejpam-5495	236	34	areas	area	NOUN
ejpam-5495	236	35	are	be	AUX
ejpam-5495	236	36	explored	explore	VERB
ejpam-5495	236	37	in	in	ADP
ejpam-5495	236	38	the	the	DET
ejpam-5495	236	39	portions	portion	NOUN
ejpam-5495	236	40	of	of	ADP
ejpam-5495	236	41	fig	fig	NOUN
ejpam-5495	236	42	.	.	PUNCT
ejpam-5495	237	1	(	(	PUNCT
ejpam-5495	237	2	4	4	NUM
ejpam-5495	237	3	)	)	PUNCT
ejpam-5495	237	4	.	.	PUNCT
ejpam-5495	238	1	the	the	DET
ejpam-5495	238	2	graphed	graph	VERB
ejpam-5495	238	3	wave	wave	NOUN
ejpam-5495	238	4	in	in	ADP
ejpam-5495	238	5	fig	fig	NOUN
ejpam-5495	238	6	.	.	PUNCT
ejpam-5495	239	1	(	(	PUNCT
ejpam-5495	239	2	4a	4a	NUM
ejpam-5495	239	3	)	)	PUNCT
ejpam-5495	239	4	has	have	VERB
ejpam-5495	239	5	a	a	DET
ejpam-5495	239	6	periodic	periodic	ADJ
ejpam-5495	239	7	manner	manner	NOUN
ejpam-5495	239	8	over	over	ADP
ejpam-5495	239	9	time	time	NOUN
ejpam-5495	239	10	and	and	CCONJ
ejpam-5495	239	11	,	,	PUNCT
ejpam-5495	239	12	therefore	therefore	ADV
ejpam-5495	239	13	,	,	PUNCT
ejpam-5495	239	14	the	the	DET
ejpam-5495	239	15	plotted	plot	VERB
ejpam-5495	239	16	phase	phase	NOUN
ejpam-5495	239	17	plane	plane	NOUN
ejpam-5495	239	18	curve	curve	NOUN
ejpam-5495	239	19	in	in	ADP
ejpam-5495	239	20	fig	fig	NOUN
ejpam-5495	239	21	.	.	PUNCT
ejpam-5495	240	1	(	(	PUNCT
ejpam-5495	240	2	4b	4b	PROPN
ejpam-5495	240	3	)	)	PUNCT
ejpam-5495	240	4	have	have	AUX
ejpam-5495	240	5	closed	close	VERB
ejpam-5495	240	6	form	form	NOUN
ejpam-5495	240	7	,	,	PUNCT
ejpam-5495	240	8	which	which	PRON
ejpam-5495	240	9	asserts	assert	VERB
ejpam-5495	240	10	the	the	DET
ejpam-5495	240	11	stability	stability	NOUN
ejpam-5495	240	12	of	of	ADP
ejpam-5495	240	13	the	the	DET
ejpam-5495	240	14	represented	represent	VERB
ejpam-5495	240	15	wave	wave	NOUN
ejpam-5495	240	16	in	in	ADP
ejpam-5495	240	17	fig	fig	NOUN
ejpam-5495	240	18	.	.	PUNCT
ejpam-5495	241	1	(	(	PUNCT
ejpam-5495	241	2	4a	4a	NUM
ejpam-5495	241	3	)	)	PUNCT
ejpam-5495	241	4	.	.	PUNCT
ejpam-5495	242	1	moreover	moreover	ADV
ejpam-5495	242	2	,	,	PUNCT
ejpam-5495	242	3	there	there	PRON
ejpam-5495	242	4	is	be	VERB
ejpam-5495	242	5	not	not	PART
ejpam-5495	242	6	any	any	DET
ejpam-5495	242	7	visible	visible	ADJ
ejpam-5495	242	8	impact	impact	NOUN
ejpam-5495	242	9	of	of	ADP
ejpam-5495	242	10	λ	λ	PROPN
ejpam-5495	242	11	values	value	NOUN
ejpam-5495	242	12	on	on	ADP
ejpam-5495	242	13	the	the	DET
ejpam-5495	242	14	solution	solution	NOUN
ejpam-5495	242	15	’s	’s	PART
ejpam-5495	242	16	behavior	behavior	NOUN
ejpam-5495	242	17	,	,	PUNCT
ejpam-5495	242	18	at	at	ADP
ejpam-5495	242	19	which	which	PRON
ejpam-5495	242	20	the	the	DET
ejpam-5495	242	21	variation	variation	NOUN
ejpam-5495	242	22	becomes	become	VERB
ejpam-5495	242	23	very	very	ADV
ejpam-5495	242	24	slight	slight	ADJ
ejpam-5495	242	25	.	.	PUNCT
ejpam-5495	243	1	the	the	DET
ejpam-5495	243	2	reason	reason	NOUN
ejpam-5495	243	3	for	for	ADP
ejpam-5495	243	4	the	the	DET
ejpam-5495	243	5	weak	weak	ADJ
ejpam-5495	243	6	effect	effect	NOUN
ejpam-5495	243	7	of	of	ADP
ejpam-5495	243	8	this	this	DET
ejpam-5495	243	9	parameter	parameter	NOUN
ejpam-5495	243	10	is	be	AUX
ejpam-5495	243	11	attributed	attribute	VERB
ejpam-5495	243	12	to	to	ADP
ejpam-5495	243	13	the	the	DET
ejpam-5495	243	14	minimal	minimal	ADJ
ejpam-5495	243	15	magnitude	magnitude	NOUN
ejpam-5495	243	16	of	of	ADP
ejpam-5495	243	17	its	its	PRON
ejpam-5495	243	18	term	term	NOUN
ejpam-5495	243	19	.	.	PUNCT
ejpam-5495	244	1	based	base	VERB
ejpam-5495	244	2	on	on	ADP
ejpam-5495	244	3	this	this	DET
ejpam-5495	244	4	analysis	analysis	NOUN
ejpam-5495	244	5	,	,	PUNCT
ejpam-5495	244	6	one	one	PRON
ejpam-5495	244	7	can	can	AUX
ejpam-5495	244	8	conclude	conclude	VERB
ejpam-5495	244	9	that	that	SCONJ
ejpam-5495	244	10	there	there	PRON
ejpam-5495	244	11	is	be	VERB
ejpam-5495	244	12	no	no	DET
ejpam-5495	244	13	variation	variation	NOUN
ejpam-5495	244	14	in	in	ADP
ejpam-5495	244	15	stability	stability	NOUN
ejpam-5495	244	16	/	/	SYM
ejpam-5495	244	17	instability	instability	NOUN
ejpam-5495	244	18	area	area	NOUN
ejpam-5495	244	19	can	can	AUX
ejpam-5495	244	20	be	be	AUX
ejpam-5495	244	21	observed	observe	VERB
ejpam-5495	244	22	,	,	PUNCT
ejpam-5495	244	23	as	as	SCONJ
ejpam-5495	244	24	explored	explore	VERB
ejpam-5495	244	25	in	in	ADP
ejpam-5495	244	26	figs	fig	NOUN
ejpam-5495	244	27	.	.	PUNCT
ejpam-5495	245	1	(	(	PUNCT
ejpam-5495	245	2	4c	4c	NOUN
ejpam-5495	245	3	)	)	PUNCT
ejpam-5495	245	4	,	,	PUNCT
ejpam-5495	245	5	(	(	PUNCT
ejpam-5495	245	6	4d	4d	NUM
ejpam-5495	245	7	)	)	PUNCT
ejpam-5495	245	8	,	,	PUNCT
ejpam-5495	245	9	and	and	CCONJ
ejpam-5495	245	10	(	(	PUNCT
ejpam-5495	245	11	4e	4e	NOUN
ejpam-5495	245	12	)	)	PUNCT
ejpam-5495	245	13	.	.	PUNCT
ejpam-5495	246	1	figure	figure	NOUN
ejpam-5495	246	2	2	2	NUM
ejpam-5495	246	3	:	:	PUNCT
ejpam-5495	246	4	explores	explore	VERB
ejpam-5495	246	5	the	the	DET
ejpam-5495	246	6	comparison	comparison	NOUN
ejpam-5495	246	7	connecting	connect	VERB
ejpam-5495	246	8	the	the	DET
ejpam-5495	246	9	as	as	ADV
ejpam-5495	246	10	and	and	CCONJ
ejpam-5495	246	11	ns	ns	NOUN
ejpam-5495	246	12	.	.	PUNCT
ejpam-5495	246	13	a.	a.	PROPN
ejpam-5495	246	14	alanazy	alanazy	PROPN
ejpam-5495	246	15	et	et	PROPN
ejpam-5495	247	1	al	al	PROPN
ejpam-5495	247	2	.	.	PUNCT
ejpam-5495	247	3	/	/	SYM
ejpam-5495	247	4	eur	eur	PROPN
ejpam-5495	247	5	.	.	PUNCT
ejpam-5495	248	1	j.	j.	PROPN
ejpam-5495	248	2	pure	pure	PROPN
ejpam-5495	248	3	appl	appl	PROPN
ejpam-5495	248	4	.	.	PROPN
ejpam-5495	248	5	math	math	PROPN
ejpam-5495	248	6	,	,	PUNCT
ejpam-5495	248	7	18	18	NUM
ejpam-5495	248	8	(	(	PUNCT
ejpam-5495	248	9	1	1	NUM
ejpam-5495	248	10	)	)	PUNCT
ejpam-5495	248	11	(	(	PUNCT
ejpam-5495	248	12	2025	2025	NUM
ejpam-5495	248	13	)	)	PUNCT
ejpam-5495	248	14	,	,	PUNCT
ejpam-5495	248	15	5495	5495	NUM
ejpam-5495	248	16	11	11	NUM
ejpam-5495	248	17	of	of	ADP
ejpam-5495	248	18	21	21	NUM
ejpam-5495	248	19	it	it	PRON
ejpam-5495	248	20	must	must	AUX
ejpam-5495	248	21	be	be	AUX
ejpam-5495	248	22	noted	note	VERB
ejpam-5495	248	23	that	that	SCONJ
ejpam-5495	248	24	,	,	PUNCT
ejpam-5495	248	25	the	the	DET
ejpam-5495	248	26	values	value	NOUN
ejpam-5495	248	27	of	of	ADP
ejpam-5495	248	28	the	the	DET
ejpam-5495	248	29	parameter	parameter	NOUN
ejpam-5495	248	30	µ(=	µ(=	PROPN
ejpam-5495	248	31	−1,−3,−6	−1,−3,−6	PROPN
ejpam-5495	248	32	)	)	PUNCT
ejpam-5495	248	33	have	have	VERB
ejpam-5495	248	34	a	a	DET
ejpam-5495	248	35	good	good	ADJ
ejpam-5495	248	36	impact	impact	NOUN
ejpam-5495	248	37	on	on	ADP
ejpam-5495	248	38	the	the	DET
ejpam-5495	248	39	obtained	obtain	VERB
ejpam-5495	248	40	solution	solution	NOUN
ejpam-5495	248	41	behavior	behavior	NOUN
ejpam-5495	248	42	,	,	PUNCT
ejpam-5495	248	43	as	as	SCONJ
ejpam-5495	248	44	seen	see	VERB
ejpam-5495	248	45	in	in	ADP
ejpam-5495	248	46	fig	fig	NOUN
ejpam-5495	248	47	.	.	PUNCT
ejpam-5495	249	1	(	(	PUNCT
ejpam-5495	249	2	5	5	NUM
ejpam-5495	249	3	)	)	PUNCT
ejpam-5495	249	4	.	.	PUNCT
ejpam-5495	250	1	periodic	periodic	ADJ
ejpam-5495	250	2	waves	wave	NOUN
ejpam-5495	250	3	are	be	AUX
ejpam-5495	250	4	represented	represent	VERB
ejpam-5495	250	5	in	in	ADP
ejpam-5495	250	6	fig	fig	NOUN
ejpam-5495	250	7	.	.	PUNCT
ejpam-5495	251	1	(	(	PUNCT
ejpam-5495	251	2	5a	5a	NUM
ejpam-5495	251	3	)	)	PUNCT
ejpam-5495	251	4	,	,	PUNCT
ejpam-5495	251	5	where	where	SCONJ
ejpam-5495	251	6	the	the	DET
ejpam-5495	251	7	amplitudes	amplitude	NOUN
ejpam-5495	251	8	of	of	ADP
ejpam-5495	251	9	the	the	DET
ejpam-5495	251	10	waves	wave	NOUN
ejpam-5495	251	11	rise	rise	VERB
ejpam-5495	251	12	as	as	ADP
ejpam-5495	251	13	the	the	DET
ejpam-5495	251	14	values	value	NOUN
ejpam-5495	251	15	of	of	ADP
ejpam-5495	251	16	µ	µ	DET
ejpam-5495	251	17	grow	grow	NOUN
ejpam-5495	251	18	.	.	PUNCT
ejpam-5495	252	1	moreover	moreover	ADV
ejpam-5495	252	2	,	,	PUNCT
ejpam-5495	252	3	semi	semi	ADJ
ejpam-5495	252	4	-	-	ADJ
ejpam-5495	252	5	closed	closed	ADJ
ejpam-5495	252	6	curves	curve	NOUN
ejpam-5495	252	7	are	be	AUX
ejpam-5495	252	8	seen	see	VERB
ejpam-5495	252	9	in	in	ADP
ejpam-5495	252	10	the	the	DET
ejpam-5495	252	11	plane	plane	NOUN
ejpam-5495	252	12	ζζ̇	ζζ̇	PROPN
ejpam-5495	252	13	i.e.	i.e.	X
ejpam-5495	252	14	fig	fig	NOUN
ejpam-5495	252	15	.	.	PUNCT
ejpam-5495	253	1	(	(	PUNCT
ejpam-5495	253	2	5b	5b	NUM
ejpam-5495	253	3	)	)	PUNCT
ejpam-5495	253	4	.	.	PUNCT
ejpam-5495	254	1	the	the	DET
ejpam-5495	254	2	stability	stability	NOUN
ejpam-5495	254	3	/	/	SYM
ejpam-5495	254	4	instability	instability	NOUN
ejpam-5495	254	5	areas	area	NOUN
ejpam-5495	254	6	are	be	AUX
ejpam-5495	254	7	drawn	draw	VERB
ejpam-5495	254	8	in	in	ADP
ejpam-5495	254	9	figs	fig	NOUN
ejpam-5495	254	10	.	.	PUNCT
ejpam-5495	255	1	(	(	PUNCT
ejpam-5495	255	2	5c)-(5e	5c)-(5e	NUM
ejpam-5495	255	3	)	)	PUNCT
ejpam-5495	255	4	,	,	PUNCT
ejpam-5495	255	5	for	for	ADP
ejpam-5495	255	6	the	the	DET
ejpam-5495	255	7	aforementioned	aforementioned	ADJ
ejpam-5495	255	8	values	value	NOUN
ejpam-5495	255	9	of	of	ADP
ejpam-5495	255	10	this	this	DET
ejpam-5495	255	11	parameter	parameter	NOUN
ejpam-5495	255	12	.	.	PUNCT
ejpam-5495	256	1	examining	examine	VERB
ejpam-5495	256	2	the	the	DET
ejpam-5495	256	3	parts	part	NOUN
ejpam-5495	256	4	in	in	ADP
ejpam-5495	256	5	fig	fig	NOUN
ejpam-5495	256	6	.	.	PUNCT
ejpam-5495	257	1	(	(	PUNCT
ejpam-5495	257	2	6	6	X
ejpam-5495	257	3	)	)	PUNCT
ejpam-5495	257	4	reveals	reveal	VERB
ejpam-5495	257	5	that	that	SCONJ
ejpam-5495	257	6	the	the	DET
ejpam-5495	257	7	impact	impact	NOUN
ejpam-5495	257	8	of	of	ADP
ejpam-5495	257	9	the	the	DET
ejpam-5495	257	10	different	different	ADJ
ejpam-5495	257	11	values	value	NOUN
ejpam-5495	257	12	of	of	ADP
ejpam-5495	257	13	a	a	DET
ejpam-5495	257	14	parameter	parameter	NOUN
ejpam-5495	257	15	ω(=	ω(=	ADP
ejpam-5495	257	16	1	1	NUM
ejpam-5495	257	17	,	,	PUNCT
ejpam-5495	257	18	1.5	1.5	NUM
ejpam-5495	257	19	,	,	PUNCT
ejpam-5495	257	20	4	4	NUM
ejpam-5495	257	21	)	)	PUNCT
ejpam-5495	257	22	on	on	ADP
ejpam-5495	257	23	the	the	DET
ejpam-5495	257	24	solution	solution	NOUN
ejpam-5495	257	25	’s	’s	PART
ejpam-5495	257	26	behavior	behavior	NOUN
ejpam-5495	257	27	,	,	PUNCT
ejpam-5495	257	28	phase	phase	NOUN
ejpam-5495	257	29	plane	plane	NOUN
ejpam-5495	257	30	curves	curve	NOUN
ejpam-5495	257	31	,	,	PUNCT
ejpam-5495	257	32	and	and	CCONJ
ejpam-5495	257	33	stability	stability	NOUN
ejpam-5495	257	34	areas	area	NOUN
ejpam-5495	257	35	,	,	PUNCT
ejpam-5495	257	36	as	as	SCONJ
ejpam-5495	257	37	indicated	indicate	VERB
ejpam-5495	257	38	in	in	ADP
ejpam-5495	257	39	figs	fig	NOUN
ejpam-5495	257	40	.	.	PUNCT
ejpam-5495	258	1	(	(	PUNCT
ejpam-5495	258	2	6a	6a	NOUN
ejpam-5495	258	3	)	)	PUNCT
ejpam-5495	258	4	,	,	PUNCT
ejpam-5495	258	5	(	(	PUNCT
ejpam-5495	258	6	6b	6b	NOUN
ejpam-5495	258	7	)	)	PUNCT
ejpam-5495	258	8	,	,	PUNCT
ejpam-5495	258	9	and	and	CCONJ
ejpam-5495	258	10	(	(	PUNCT
ejpam-5495	258	11	6c)-(6e	6c)-(6e	NOUN
ejpam-5495	258	12	)	)	PUNCT
ejpam-5495	258	13	.	.	PUNCT
ejpam-5495	259	1	the	the	DET
ejpam-5495	259	2	amplitude	amplitude	NOUN
ejpam-5495	259	3	of	of	ADP
ejpam-5495	259	4	the	the	DET
ejpam-5495	259	5	drawn	draw	VERB
ejpam-5495	259	6	waves	wave	NOUN
ejpam-5495	259	7	in	in	ADP
ejpam-5495	259	8	portion	portion	NOUN
ejpam-5495	259	9	(	(	PUNCT
ejpam-5495	259	10	a	a	NOUN
ejpam-5495	259	11	)	)	PUNCT
ejpam-5495	259	12	of	of	ADP
ejpam-5495	259	13	this	this	DET
ejpam-5495	259	14	figure	figure	NOUN
ejpam-5495	259	15	decreases	decrease	VERB
ejpam-5495	259	16	with	with	ADP
ejpam-5495	259	17	the	the	DET
ejpam-5495	259	18	increase	increase	NOUN
ejpam-5495	259	19	of	of	ADP
ejpam-5495	259	20	this	this	DET
ejpam-5495	259	21	parameter	parameter	NOUN
ejpam-5495	259	22	,	,	PUNCT
ejpam-5495	259	23	while	while	SCONJ
ejpam-5495	259	24	the	the	DET
ejpam-5495	259	25	curves	curve	NOUN
ejpam-5495	259	26	in	in	ADP
ejpam-5495	259	27	the	the	DET
ejpam-5495	259	28	plane	plane	NOUN
ejpam-5495	259	29	ζζ̇	ζζ̇	PROPN
ejpam-5495	259	30	is	be	AUX
ejpam-5495	259	31	presented	present	VERB
ejpam-5495	259	32	in	in	ADP
ejpam-5495	259	33	portion	portion	NOUN
ejpam-5495	259	34	(	(	PUNCT
ejpam-5495	259	35	b	b	NOUN
ejpam-5495	259	36	)	)	PUNCT
ejpam-5495	259	37	.	.	PUNCT
ejpam-5495	260	1	the	the	DET
ejpam-5495	260	2	associated	associated	ADJ
ejpam-5495	260	3	stability	stability	NOUN
ejpam-5495	260	4	/	/	SYM
ejpam-5495	260	5	instability	instability	NOUN
ejpam-5495	260	6	areas	area	NOUN
ejpam-5495	260	7	are	be	AUX
ejpam-5495	260	8	shown	show	VERB
ejpam-5495	260	9	in	in	ADP
ejpam-5495	260	10	portions	portion	NOUN
ejpam-5495	260	11	(	(	PUNCT
ejpam-5495	260	12	c)-(e	c)-(e	PROPN
ejpam-5495	260	13	)	)	PUNCT
ejpam-5495	260	14	of	of	ADP
ejpam-5495	260	15	this	this	DET
ejpam-5495	260	16	figure	figure	NOUN
ejpam-5495	260	17	.	.	PUNCT
ejpam-5495	261	1	moreover	moreover	ADV
ejpam-5495	261	2	,	,	PUNCT
ejpam-5495	261	3	the	the	DET
ejpam-5495	261	4	behavior	behavior	NOUN
ejpam-5495	261	5	of	of	ADP
ejpam-5495	261	6	∆	∆	PROPN
ejpam-5495	261	7	via	via	ADP
ejpam-5495	261	8	a	a	PRON
ejpam-5495	261	9	has	have	AUX
ejpam-5495	261	10	been	be	AUX
ejpam-5495	261	11	graphed	graph	VERB
ejpam-5495	261	12	in	in	ADP
ejpam-5495	261	13	parts	part	NOUN
ejpam-5495	261	14	of	of	ADP
ejpam-5495	261	15	fig	fig	NOUN
ejpam-5495	261	16	.	.	PUNCT
ejpam-5495	262	1	(	(	PUNCT
ejpam-5495	262	2	7	7	X
ejpam-5495	262	3	)	)	PUNCT
ejpam-5495	262	4	in	in	ADP
ejpam-5495	262	5	view	view	NOUN
ejpam-5495	262	6	of	of	ADP
ejpam-5495	262	7	the	the	DET
ejpam-5495	262	8	explicit	explicit	ADJ
ejpam-5495	262	9	mathematical	mathematical	ADJ
ejpam-5495	262	10	expression	expression	NOUN
ejpam-5495	262	11	of	of	ADP
ejpam-5495	262	12	∆	∆	PROPN
ejpam-5495	262	13	,	,	PUNCT
ejpam-5495	262	14	as	as	ADP
ejpam-5495	262	15	in	in	ADP
ejpam-5495	262	16	eq	eq	NOUN
ejpam-5495	262	17	.	.	PUNCT
ejpam-5495	263	1	(	(	PUNCT
ejpam-5495	263	2	14	14	NUM
ejpam-5495	263	3	)	)	PUNCT
ejpam-5495	263	4	.	.	PUNCT
ejpam-5495	264	1	this	this	DET
ejpam-5495	264	2	figure	figure	NOUN
ejpam-5495	264	3	has	have	AUX
ejpam-5495	264	4	been	be	AUX
ejpam-5495	264	5	calculated	calculate	VERB
ejpam-5495	264	6	when	when	SCONJ
ejpam-5495	264	7	α	α	NOUN
ejpam-5495	264	8	=	=	NOUN
ejpam-5495	264	9	0.1	0.1	NUM
ejpam-5495	264	10	,	,	PUNCT
ejpam-5495	264	11	β	β	X
ejpam-5495	264	12	=	=	PUNCT
ejpam-5495	264	13	0.3	0.3	NUM
ejpam-5495	264	14	,	,	PUNCT
ejpam-5495	264	15	λ	λ	X
ejpam-5495	264	16	=	=	NOUN
ejpam-5495	264	17	0.5	0.5	NUM
ejpam-5495	264	18	,	,	PUNCT
ejpam-5495	264	19	µ	µ	X
ejpam-5495	264	20	=	=	SYM
ejpam-5495	264	21	−1	−1	NOUN
ejpam-5495	264	22	,	,	PUNCT
ejpam-5495	264	23	ω	ω	X
ejpam-5495	264	24	=	=	SYM
ejpam-5495	264	25	1	1	NUM
ejpam-5495	264	26	and	and	CCONJ
ejpam-5495	264	27	τ	τ	X
ejpam-5495	264	28	=	=	NOUN
ejpam-5495	264	29	0.1	0.1	NUM
ejpam-5495	264	30	,	,	PUNCT
ejpam-5495	264	31	besides	besides	SCONJ
ejpam-5495	264	32	the	the	DET
ejpam-5495	264	33	variation	variation	NOUN
ejpam-5495	264	34	of	of	ADP
ejpam-5495	264	35	each	each	DET
ejpam-5495	264	36	one	one	NUM
ejpam-5495	264	37	of	of	ADP
ejpam-5495	264	38	these	these	DET
ejpam-5495	264	39	parameters	parameter	NOUN
ejpam-5495	264	40	when	when	SCONJ
ejpam-5495	264	41	the	the	DET
ejpam-5495	264	42	others	other	NOUN
ejpam-5495	264	43	become	become	VERB
ejpam-5495	264	44	fixed	fix	VERB
ejpam-5495	264	45	.	.	PUNCT
ejpam-5495	265	1	an	an	DET
ejpam-5495	265	2	inspection	inspection	NOUN
ejpam-5495	265	3	of	of	ADP
ejpam-5495	265	4	figs	fig	NOUN
ejpam-5495	265	5	(	(	PUNCT
ejpam-5495	265	6	7a	7a	NUM
ejpam-5495	265	7	,	,	PUNCT
ejpam-5495	265	8	b	b	NOUN
ejpam-5495	265	9	,	,	PUNCT
ejpam-5495	265	10	c	c	NOUN
ejpam-5495	265	11	,	,	PUNCT
ejpam-5495	265	12	d	d	NOUN
ejpam-5495	265	13	,	,	PUNCT
ejpam-5495	265	14	e	e	NOUN
ejpam-5495	265	15	)	)	PUNCT
ejpam-5495	265	16	shows	show	NOUN
ejpam-5495	265	17	,	,	PUNCT
ejpam-5495	265	18	they	they	PRON
ejpam-5495	265	19	are	be	AUX
ejpam-5495	265	20	graphed	graph	VERB
ejpam-5495	265	21	when	when	SCONJ
ejpam-5495	265	22	α(=	α(=	NOUN
ejpam-5495	265	23	0.1	0.1	NUM
ejpam-5495	265	24	,	,	PUNCT
ejpam-5495	265	25	0.4	0.4	NUM
ejpam-5495	265	26	,	,	PUNCT
ejpam-5495	265	27	0.7	0.7	NUM
ejpam-5495	265	28	)	)	PUNCT
ejpam-5495	265	29	,	,	PUNCT
ejpam-5495	265	30	β(=	β(=	NOUN
ejpam-5495	265	31	0.3	0.3	NUM
ejpam-5495	265	32	,	,	PUNCT
ejpam-5495	265	33	0.6	0.6	NUM
ejpam-5495	265	34	,	,	PUNCT
ejpam-5495	265	35	1.1	1.1	NUM
ejpam-5495	265	36	)	)	PUNCT
ejpam-5495	265	37	,	,	PUNCT
ejpam-5495	265	38	λ(=	λ(=	ADP
ejpam-5495	265	39	0.5	0.5	NUM
ejpam-5495	265	40	,	,	PUNCT
ejpam-5495	265	41	0.7	0.7	NUM
ejpam-5495	265	42	,	,	PUNCT
ejpam-5495	265	43	0.9	0.9	NUM
ejpam-5495	265	44	)	)	PUNCT
ejpam-5495	265	45	,	,	PUNCT
ejpam-5495	265	46	ω(=	ω(=	ADP
ejpam-5495	265	47	1.0	1.0	NUM
ejpam-5495	265	48	,	,	PUNCT
ejpam-5495	265	49	1.3	1.3	NUM
ejpam-5495	265	50	,	,	PUNCT
ejpam-5495	265	51	1.6	1.6	NUM
ejpam-5495	265	52	)	)	PUNCT
ejpam-5495	265	53	and	and	CCONJ
ejpam-5495	265	54	τ(=	τ(=	NOUN
ejpam-5495	265	55	0.1	0.1	NUM
ejpam-5495	265	56	,	,	PUNCT
ejpam-5495	265	57	0.4	0.4	NUM
ejpam-5495	265	58	,	,	PUNCT
ejpam-5495	265	59	0.8	0.8	NUM
ejpam-5495	265	60	)	)	PUNCT
ejpam-5495	265	61	,	,	PUNCT
ejpam-5495	265	62	respectively	respectively	ADV
ejpam-5495	265	63	.	.	PUNCT
ejpam-5495	266	1	it	it	PRON
ejpam-5495	266	2	is	be	AUX
ejpam-5495	266	3	obvious	obvious	ADJ
ejpam-5495	266	4	that	that	SCONJ
ejpam-5495	266	5	when	when	SCONJ
ejpam-5495	266	6	α	α	X
ejpam-5495	266	7	,	,	PUNCT
ejpam-5495	266	8	β	β	X
ejpam-5495	266	9	and	and	CCONJ
ejpam-5495	266	10	τ	τ	PROPN
ejpam-5495	266	11	increases	increase	NOUN
ejpam-5495	266	12	,	,	PUNCT
ejpam-5495	266	13	the	the	DET
ejpam-5495	266	14	stability	stability	NOUN
ejpam-5495	266	15	regions	region	NOUN
ejpam-5495	266	16	above	above	ADP
ejpam-5495	266	17	the	the	DET
ejpam-5495	266	18	drawn	draw	VERB
ejpam-5495	266	19	curves	curve	NOUN
ejpam-5495	266	20	increase	increase	NOUN
ejpam-5495	266	21	,	,	PUNCT
ejpam-5495	266	22	while	while	SCONJ
ejpam-5495	266	23	the	the	DET
ejpam-5495	266	24	instability	instability	NOUN
ejpam-5495	266	25	ones	one	NOUN
ejpam-5495	266	26	that	that	PRON
ejpam-5495	266	27	lie	lie	VERB
ejpam-5495	266	28	down	down	ADP
ejpam-5495	266	29	the	the	DET
ejpam-5495	266	30	curves	curve	NOUN
ejpam-5495	266	31	decrease	decrease	NOUN
ejpam-5495	266	32	,	,	PUNCT
ejpam-5495	266	33	as	as	SCONJ
ejpam-5495	266	34	seen	see	VERB
ejpam-5495	266	35	in	in	ADP
ejpam-5495	266	36	figs	fig	NOUN
ejpam-5495	266	37	(	(	PUNCT
ejpam-5495	266	38	7a	7a	NUM
ejpam-5495	266	39	)	)	PUNCT
ejpam-5495	266	40	,	,	PUNCT
ejpam-5495	266	41	(	(	PUNCT
ejpam-5495	266	42	7b	7b	NOUN
ejpam-5495	266	43	)	)	PUNCT
ejpam-5495	266	44	,	,	PUNCT
ejpam-5495	266	45	and	and	CCONJ
ejpam-5495	266	46	(	(	PUNCT
ejpam-5495	266	47	7e	7e	NUM
ejpam-5495	266	48	)	)	PUNCT
ejpam-5495	266	49	,	,	PUNCT
ejpam-5495	266	50	respectively	respectively	ADV
ejpam-5495	266	51	.	.	PUNCT
ejpam-5495	267	1	these	these	DET
ejpam-5495	267	2	regions	region	NOUN
ejpam-5495	267	3	must	must	AUX
ejpam-5495	267	4	satisfy	satisfy	VERB
ejpam-5495	267	5	eq	eq	ADP
ejpam-5495	267	6	.	.	PUNCT
ejpam-5495	268	1	(	(	PUNCT
ejpam-5495	268	2	14	14	NUM
ejpam-5495	268	3	)	)	PUNCT
ejpam-5495	268	4	.	.	PUNCT
ejpam-5495	269	1	on	on	ADP
ejpam-5495	269	2	the	the	DET
ejpam-5495	269	3	other	other	ADJ
ejpam-5495	269	4	hand	hand	NOUN
ejpam-5495	269	5	,	,	PUNCT
ejpam-5495	269	6	when	when	SCONJ
ejpam-5495	269	7	the	the	DET
ejpam-5495	269	8	values	value	NOUN
ejpam-5495	269	9	of	of	ADP
ejpam-5495	269	10	the	the	DET
ejpam-5495	269	11	parameters	parameter	NOUN
ejpam-5495	269	12	λ	λ	PROPN
ejpam-5495	269	13	and	and	CCONJ
ejpam-5495	269	14	ω	ω	PROPN
ejpam-5495	269	15	are	be	AUX
ejpam-5495	269	16	increase	increase	NOUN
ejpam-5495	269	17	,	,	PUNCT
ejpam-5495	269	18	the	the	DET
ejpam-5495	269	19	stability	stability	NOUN
ejpam-5495	269	20	regions	region	NOUN
ejpam-5495	269	21	decrease	decrease	VERB
ejpam-5495	269	22	while	while	SCONJ
ejpam-5495	269	23	the	the	DET
ejpam-5495	269	24	instability	instability	NOUN
ejpam-5495	269	25	ones	one	NOUN
ejpam-5495	269	26	increase	increase	VERB
ejpam-5495	269	27	,	,	PUNCT
ejpam-5495	269	28	as	as	SCONJ
ejpam-5495	269	29	explored	explore	VERB
ejpam-5495	269	30	in	in	ADP
ejpam-5495	269	31	figs	fig	NOUN
ejpam-5495	269	32	.	.	PUNCT
ejpam-5495	270	1	(	(	PUNCT
ejpam-5495	270	2	7c	7c	NUM
ejpam-5495	270	3	)	)	PUNCT
ejpam-5495	270	4	and	and	CCONJ
ejpam-5495	270	5	(	(	PUNCT
ejpam-5495	270	6	7d	7d	NUM
ejpam-5495	270	7	)	)	PUNCT
ejpam-5495	270	8	,	,	PUNCT
ejpam-5495	270	9	respectively	respectively	ADV
ejpam-5495	270	10	.	.	PUNCT
ejpam-5495	271	1	a.	a.	PROPN
ejpam-5495	271	2	alanazy	alanazy	PROPN
ejpam-5495	271	3	et	et	PROPN
ejpam-5495	271	4	al	al	PROPN
ejpam-5495	271	5	.	.	PUNCT
ejpam-5495	271	6	/	/	SYM
ejpam-5495	271	7	eur	eur	PROPN
ejpam-5495	271	8	.	.	PUNCT
ejpam-5495	272	1	j.	j.	PROPN
ejpam-5495	272	2	pure	pure	PROPN
ejpam-5495	272	3	appl	appl	PROPN
ejpam-5495	272	4	.	.	PROPN
ejpam-5495	272	5	math	math	PROPN
ejpam-5495	272	6	,	,	PUNCT
ejpam-5495	272	7	18	18	NUM
ejpam-5495	272	8	(	(	PUNCT
ejpam-5495	272	9	1	1	NUM
ejpam-5495	272	10	)	)	PUNCT
ejpam-5495	272	11	(	(	PUNCT
ejpam-5495	272	12	2025	2025	NUM
ejpam-5495	272	13	)	)	PUNCT
ejpam-5495	272	14	,	,	PUNCT
ejpam-5495	272	15	5495	5495	NUM
ejpam-5495	272	16	12	12	NUM
ejpam-5495	272	17	of	of	ADP
ejpam-5495	272	18	21	21	NUM
ejpam-5495	272	19	figure	figure	NOUN
ejpam-5495	272	20	3	3	NUM
ejpam-5495	272	21	:	:	PUNCT
ejpam-5495	272	22	(	(	PUNCT
ejpam-5495	272	23	a	a	X
ejpam-5495	272	24	)	)	PUNCT
ejpam-5495	272	25	explores	explore	VERB
ejpam-5495	272	26	curves	curve	NOUN
ejpam-5495	272	27	of	of	ADP
ejpam-5495	272	28	at	at	ADP
ejpam-5495	272	29	different	different	ADJ
ejpam-5495	272	30	amounts	amount	NOUN
ejpam-5495	272	31	of	of	ADP
ejpam-5495	272	32	θ(t	θ(t	PROPN
ejpam-5495	272	33	)	)	PUNCT
ejpam-5495	272	34	,	,	PUNCT
ejpam-5495	272	35	and	and	CCONJ
ejpam-5495	272	36	(	(	PUNCT
ejpam-5495	272	37	b	b	X
ejpam-5495	272	38	)	)	PUNCT
ejpam-5495	272	39	reveals	reveal	VERB
ejpam-5495	272	40	the	the	DET
ejpam-5495	272	41	phase	phase	NOUN
ejpam-5495	272	42	plane	plane	NOUN
ejpam-5495	272	43	trajectories	trajectory	NOUN
ejpam-5495	272	44	in	in	ADP
ejpam-5495	272	45	(	(	PUNCT
ejpam-5495	272	46	a	a	NOUN
ejpam-5495	272	47	)	)	PUNCT
ejpam-5495	272	48	.	.	PUNCT
ejpam-5495	273	1	a.	a.	PROPN
ejpam-5495	273	2	alanazy	alanazy	PROPN
ejpam-5495	273	3	et	et	PROPN
ejpam-5495	273	4	al	al	PROPN
ejpam-5495	273	5	.	.	PUNCT
ejpam-5495	273	6	/	/	SYM
ejpam-5495	273	7	eur	eur	PROPN
ejpam-5495	273	8	.	.	PUNCT
ejpam-5495	274	1	j.	j.	PROPN
ejpam-5495	274	2	pure	pure	PROPN
ejpam-5495	274	3	appl	appl	PROPN
ejpam-5495	274	4	.	.	PROPN
ejpam-5495	274	5	math	math	PROPN
ejpam-5495	274	6	,	,	PUNCT
ejpam-5495	274	7	18	18	NUM
ejpam-5495	274	8	(	(	PUNCT
ejpam-5495	274	9	1	1	NUM
ejpam-5495	274	10	)	)	PUNCT
ejpam-5495	274	11	(	(	PUNCT
ejpam-5495	274	12	2025	2025	NUM
ejpam-5495	274	13	)	)	PUNCT
ejpam-5495	274	14	,	,	PUNCT
ejpam-5495	274	15	5495	5495	NUM
ejpam-5495	274	16	13	13	NUM
ejpam-5495	274	17	of	of	ADP
ejpam-5495	274	18	21	21	NUM
ejpam-5495	274	19	figure	figure	NOUN
ejpam-5495	274	20	4	4	NUM
ejpam-5495	274	21	:	:	PUNCT
ejpam-5495	274	22	(	(	PUNCT
ejpam-5495	274	23	a	a	X
ejpam-5495	274	24	)	)	PUNCT
ejpam-5495	274	25	demonstrates	demonstrate	VERB
ejpam-5495	274	26	curves	curve	NOUN
ejpam-5495	274	27	of	of	ADP
ejpam-5495	274	28	θ(t	θ(t	PROPN
ejpam-5495	274	29	)	)	PUNCT
ejpam-5495	274	30	at	at	ADP
ejpam-5495	274	31	different	different	ADJ
ejpam-5495	274	32	amounts	amount	NOUN
ejpam-5495	274	33	of	of	ADP
ejpam-5495	274	34	a	a	PRON
ejpam-5495	274	35	,	,	PUNCT
ejpam-5495	274	36	and	and	CCONJ
ejpam-5495	274	37	(	(	PUNCT
ejpam-5495	274	38	b	b	X
ejpam-5495	274	39	)	)	PUNCT
ejpam-5495	274	40	shows	show	VERB
ejpam-5495	274	41	the	the	DET
ejpam-5495	274	42	phase	phase	NOUN
ejpam-5495	274	43	plane	plane	NOUN
ejpam-5495	274	44	diagrams	diagram	NOUN
ejpam-5495	274	45	in	in	ADP
ejpam-5495	274	46	(	(	PUNCT
ejpam-5495	274	47	a	a	NOUN
ejpam-5495	274	48	)	)	PUNCT
ejpam-5495	274	49	.	.	PUNCT
ejpam-5495	275	1	a.	a.	PROPN
ejpam-5495	275	2	alanazy	alanazy	PROPN
ejpam-5495	275	3	et	et	PROPN
ejpam-5495	275	4	al	al	PROPN
ejpam-5495	275	5	.	.	PUNCT
ejpam-5495	275	6	/	/	SYM
ejpam-5495	275	7	eur	eur	PROPN
ejpam-5495	275	8	.	.	PUNCT
ejpam-5495	276	1	j.	j.	PROPN
ejpam-5495	276	2	pure	pure	PROPN
ejpam-5495	276	3	appl	appl	PROPN
ejpam-5495	276	4	.	.	PROPN
ejpam-5495	276	5	math	math	PROPN
ejpam-5495	276	6	,	,	PUNCT
ejpam-5495	276	7	18	18	NUM
ejpam-5495	276	8	(	(	PUNCT
ejpam-5495	276	9	1	1	NUM
ejpam-5495	276	10	)	)	PUNCT
ejpam-5495	276	11	(	(	PUNCT
ejpam-5495	276	12	2025	2025	NUM
ejpam-5495	276	13	)	)	PUNCT
ejpam-5495	276	14	,	,	PUNCT
ejpam-5495	276	15	5495	5495	NUM
ejpam-5495	276	16	14	14	NUM
ejpam-5495	276	17	of	of	ADP
ejpam-5495	276	18	21	21	NUM
ejpam-5495	276	19	figure	figure	NOUN
ejpam-5495	276	20	5	5	NUM
ejpam-5495	276	21	:	:	PUNCT
ejpam-5495	276	22	(	(	PUNCT
ejpam-5495	276	23	a	a	X
ejpam-5495	276	24	)	)	PUNCT
ejpam-5495	276	25	shows	show	VERB
ejpam-5495	276	26	curves	curve	NOUN
ejpam-5495	276	27	of	of	ADP
ejpam-5495	276	28	θ(t	θ(t	PROPN
ejpam-5495	276	29	)	)	PUNCT
ejpam-5495	276	30	at	at	ADP
ejpam-5495	276	31	different	different	ADJ
ejpam-5495	276	32	amounts	amount	NOUN
ejpam-5495	276	33	of	of	ADP
ejpam-5495	276	34	b	b	NOUN
ejpam-5495	276	35	,	,	PUNCT
ejpam-5495	276	36	and	and	CCONJ
ejpam-5495	276	37	(	(	PUNCT
ejpam-5495	276	38	b	b	NOUN
ejpam-5495	276	39	)	)	PUNCT
ejpam-5495	276	40	presents	present	VERB
ejpam-5495	276	41	the	the	DET
ejpam-5495	276	42	phase	phase	NOUN
ejpam-5495	276	43	plane	plane	NOUN
ejpam-5495	276	44	paths	path	NOUN
ejpam-5495	276	45	in	in	ADP
ejpam-5495	276	46	(	(	PUNCT
ejpam-5495	276	47	a	a	NOUN
ejpam-5495	276	48	)	)	PUNCT
ejpam-5495	276	49	.	.	PUNCT
ejpam-5495	277	1	a.	a.	PROPN
ejpam-5495	277	2	alanazy	alanazy	PROPN
ejpam-5495	277	3	et	et	PROPN
ejpam-5495	277	4	al	al	PROPN
ejpam-5495	277	5	.	.	PUNCT
ejpam-5495	277	6	/	/	SYM
ejpam-5495	277	7	eur	eur	PROPN
ejpam-5495	277	8	.	.	PUNCT
ejpam-5495	278	1	j.	j.	PROPN
ejpam-5495	278	2	pure	pure	PROPN
ejpam-5495	278	3	appl	appl	PROPN
ejpam-5495	278	4	.	.	PROPN
ejpam-5495	278	5	math	math	PROPN
ejpam-5495	278	6	,	,	PUNCT
ejpam-5495	278	7	18	18	NUM
ejpam-5495	278	8	(	(	PUNCT
ejpam-5495	278	9	1	1	NUM
ejpam-5495	278	10	)	)	PUNCT
ejpam-5495	278	11	(	(	PUNCT
ejpam-5495	278	12	2025	2025	NUM
ejpam-5495	278	13	)	)	PUNCT
ejpam-5495	278	14	,	,	PUNCT
ejpam-5495	278	15	5495	5495	NUM
ejpam-5495	278	16	15	15	NUM
ejpam-5495	278	17	of	of	ADP
ejpam-5495	278	18	21	21	NUM
ejpam-5495	278	19	figure	figure	NOUN
ejpam-5495	278	20	6	6	NUM
ejpam-5495	278	21	:	:	PUNCT
ejpam-5495	278	22	show	show	VERB
ejpam-5495	278	23	the	the	DET
ejpam-5495	278	24	stability	stability	NOUN
ejpam-5495	278	25	/	/	SYM
ejpam-5495	278	26	instability	instability	NOUN
ejpam-5495	278	27	areas	area	NOUN
ejpam-5495	278	28	in	in	ADP
ejpam-5495	278	29	the	the	DET
ejpam-5495	278	30	plane	plane	NOUN
ejpam-5495	278	31	(	(	PUNCT
ejpam-5495	278	32	τ	τ	PROPN
ejpam-5495	278	33	−	−	PROPN
ejpam-5495	278	34	ω	ω	PROPN
ejpam-5495	278	35	)	)	PUNCT
ejpam-5495	278	36	at	at	ADP
ejpam-5495	278	37	a	a	DET
ejpam-5495	278	38	=	=	SYM
ejpam-5495	278	39	b	b	NOUN
ejpam-5495	278	40	=	=	NOUN
ejpam-5495	278	41	0.01	0.01	NUM
ejpam-5495	278	42	when	when	SCONJ
ejpam-5495	278	43	(	(	PUNCT
ejpam-5495	278	44	a	a	X
ejpam-5495	278	45	)	)	PUNCT
ejpam-5495	278	46	a	a	PRON
ejpam-5495	278	47	=	=	SYM
ejpam-5495	278	48	0.4	0.4	NUM
ejpam-5495	278	49	,	,	PUNCT
ejpam-5495	278	50	(	(	PUNCT
ejpam-5495	278	51	b	b	X
ejpam-5495	278	52	)	)	PUNCT
ejpam-5495	278	53	a	a	DET
ejpam-5495	278	54	=	=	NOUN
ejpam-5495	278	55	0.7	0.7	NUM
ejpam-5495	278	56	,	,	PUNCT
ejpam-5495	278	57	and	and	CCONJ
ejpam-5495	278	58	(	(	PUNCT
ejpam-5495	278	59	c	c	X
ejpam-5495	278	60	)	)	PUNCT
ejpam-5495	278	61	a	a	PRON
ejpam-5495	278	62	=	=	SYM
ejpam-5495	278	63	1	1	X
ejpam-5495	278	64	.	.	PUNCT
ejpam-5495	278	65	a.	a.	PROPN
ejpam-5495	278	66	alanazy	alanazy	PROPN
ejpam-5495	278	67	et	et	PROPN
ejpam-5495	278	68	al	al	PROPN
ejpam-5495	278	69	.	.	PUNCT
ejpam-5495	278	70	/	/	SYM
ejpam-5495	278	71	eur	eur	PROPN
ejpam-5495	278	72	.	.	PUNCT
ejpam-5495	279	1	j.	j.	PROPN
ejpam-5495	279	2	pure	pure	PROPN
ejpam-5495	279	3	appl	appl	PROPN
ejpam-5495	279	4	.	.	PROPN
ejpam-5495	279	5	math	math	PROPN
ejpam-5495	279	6	,	,	PUNCT
ejpam-5495	279	7	18	18	NUM
ejpam-5495	279	8	(	(	PUNCT
ejpam-5495	279	9	1	1	NUM
ejpam-5495	279	10	)	)	PUNCT
ejpam-5495	279	11	(	(	PUNCT
ejpam-5495	279	12	2025	2025	NUM
ejpam-5495	279	13	)	)	PUNCT
ejpam-5495	279	14	,	,	PUNCT
ejpam-5495	279	15	5495	5495	NUM
ejpam-5495	279	16	16	16	NUM
ejpam-5495	279	17	of	of	ADP
ejpam-5495	279	18	21	21	NUM
ejpam-5495	279	19	figure	figure	NOUN
ejpam-5495	279	20	7	7	NUM
ejpam-5495	279	21	:	:	PUNCT
ejpam-5495	279	22	presents	present	VERB
ejpam-5495	279	23	the	the	DET
ejpam-5495	279	24	stability	stability	NOUN
ejpam-5495	279	25	/	/	SYM
ejpam-5495	279	26	instability	instability	NOUN
ejpam-5495	279	27	zones	zone	NOUN
ejpam-5495	279	28	in	in	ADP
ejpam-5495	279	29	the	the	DET
ejpam-5495	279	30	plane	plane	NOUN
ejpam-5495	279	31	(	(	PUNCT
ejpam-5495	279	32	τ	τ	PROPN
ejpam-5495	279	33	−	−	PROPN
ejpam-5495	279	34	ω	ω	PROPN
ejpam-5495	279	35	)	)	PUNCT
ejpam-5495	279	36	at	at	ADP
ejpam-5495	279	37	a	a	DET
ejpam-5495	279	38	=	=	SYM
ejpam-5495	279	39	b	b	NOUN
ejpam-5495	279	40	=	=	SYM
ejpam-5495	279	41	1	1	NUM
ejpam-5495	279	42	when	when	SCONJ
ejpam-5495	279	43	(	(	PUNCT
ejpam-5495	279	44	a	a	X
ejpam-5495	279	45	)	)	PUNCT
ejpam-5495	279	46	a	a	DET
ejpam-5495	279	47	=	=	SYM
ejpam-5495	279	48	0.4	0.4	NUM
ejpam-5495	279	49	,	,	PUNCT
ejpam-5495	279	50	and	and	CCONJ
ejpam-5495	279	51	(	(	PUNCT
ejpam-5495	279	52	b	b	X
ejpam-5495	279	53	)	)	PUNCT
ejpam-5495	279	54	a	a	DET
ejpam-5495	279	55	=	=	NOUN
ejpam-5495	279	56	0.7	0.7	NUM
ejpam-5495	279	57	.	.	NOUN
ejpam-5495	279	58	4	4	NUM
ejpam-5495	279	59	.	.	X
ejpam-5495	279	60	conclusions	conclusion	NOUN
ejpam-5495	279	61	in	in	ADP
ejpam-5495	279	62	this	this	DET
ejpam-5495	279	63	study	study	NOUN
ejpam-5495	279	64	,	,	PUNCT
ejpam-5495	279	65	the	the	DET
ejpam-5495	279	66	tds	tds	NOUN
ejpam-5495	279	67	in	in	ADP
ejpam-5495	279	68	velocity	velocity	NOUN
ejpam-5495	279	69	and	and	CCONJ
ejpam-5495	279	70	position	position	NOUN
ejpam-5495	279	71	were	be	AUX
ejpam-5495	279	72	employed	employ	VERB
ejpam-5495	279	73	to	to	PART
ejpam-5495	279	74	lessen	lessen	VERB
ejpam-5495	279	75	the	the	DET
ejpam-5495	279	76	nonlinearity	nonlinearity	NOUN
ejpam-5495	279	77	vibration	vibration	NOUN
ejpam-5495	279	78	of	of	ADP
ejpam-5495	279	79	an	an	DET
ejpam-5495	279	80	excited	excited	ADJ
ejpam-5495	279	81	vdpd	vdpd	NOUN
ejpam-5495	279	82	.	.	PUNCT
ejpam-5495	280	1	therefore	therefore	ADV
ejpam-5495	280	2	,	,	PUNCT
ejpam-5495	280	3	the	the	DET
ejpam-5495	280	4	td	td	NOUN
ejpam-5495	280	5	idea	idea	NOUN
ejpam-5495	280	6	is	be	AUX
ejpam-5495	280	7	a	a	DET
ejpam-5495	280	8	protection	protection	NOUN
ejpam-5495	280	9	against	against	ADP
ejpam-5495	280	10	nonlinear	nonlinear	ADJ
ejpam-5495	280	11	oscillation	oscillation	NOUN
ejpam-5495	280	12	of	of	ADP
ejpam-5495	280	13	the	the	DET
ejpam-5495	280	14	structure	structure	NOUN
ejpam-5495	280	15	under	under	ADP
ejpam-5495	280	16	examination	examination	NOUN
ejpam-5495	280	17	.	.	PUNCT
ejpam-5495	281	1	the	the	DET
ejpam-5495	281	2	current	current	ADJ
ejpam-5495	281	3	study	study	NOUN
ejpam-5495	281	4	aimed	aim	VERB
ejpam-5495	281	5	to	to	PART
ejpam-5495	281	6	investigate	investigate	VERB
ejpam-5495	281	7	the	the	DET
ejpam-5495	281	8	impact	impact	NOUN
ejpam-5495	281	9	of	of	ADP
ejpam-5495	281	10	td	td	NOUN
ejpam-5495	281	11	,	,	PUNCT
ejpam-5495	281	12	which	which	PRON
ejpam-5495	281	13	has	have	AUX
ejpam-5495	281	14	recently	recently	ADV
ejpam-5495	281	15	been	be	AUX
ejpam-5495	281	16	the	the	DET
ejpam-5495	281	17	subject	subject	NOUN
ejpam-5495	281	18	of	of	ADP
ejpam-5495	281	19	many	many	ADJ
ejpam-5495	281	20	examinations	examination	NOUN
ejpam-5495	281	21	.	.	PUNCT
ejpam-5495	282	1	the	the	DET
ejpam-5495	282	2	npa	npa	NOUN
ejpam-5495	282	3	was	be	AUX
ejpam-5495	282	4	used	use	VERB
ejpam-5495	282	5	to	to	PART
ejpam-5495	282	6	analyze	analyze	VERB
ejpam-5495	282	7	the	the	DET
ejpam-5495	282	8	present	present	ADJ
ejpam-5495	282	9	oscillator	oscillator	NOUN
ejpam-5495	282	10	.	.	PUNCT
ejpam-5495	283	1	the	the	DET
ejpam-5495	283	2	main	main	ADJ
ejpam-5495	283	3	concept	concept	NOUN
ejpam-5495	283	4	of	of	ADP
ejpam-5495	283	5	this	this	DET
ejpam-5495	283	6	methodology	methodology	NOUN
ejpam-5495	283	7	was	be	AUX
ejpam-5495	283	8	to	to	PART
ejpam-5495	283	9	transform	transform	VERB
ejpam-5495	283	10	the	the	DET
ejpam-5495	283	11	nonlinear	nonlinear	ADJ
ejpam-5495	283	12	ode	ode	NOUN
ejpam-5495	283	13	into	into	ADP
ejpam-5495	283	14	a	a	DET
ejpam-5495	283	15	linear	linear	ADJ
ejpam-5495	283	16	one	one	NUM
ejpam-5495	283	17	.	.	PUNCT
ejpam-5495	284	1	consequently	consequently	ADV
ejpam-5495	284	2	,	,	PUNCT
ejpam-5495	284	3	the	the	DET
ejpam-5495	284	4	stability	stability	NOUN
ejpam-5495	284	5	constraint	constraint	NOUN
ejpam-5495	284	6	was	be	AUX
ejpam-5495	284	7	built	build	VERB
ejpam-5495	284	8	,	,	PUNCT
ejpam-5495	284	9	examined	examine	VERB
ejpam-5495	284	10	,	,	PUNCT
ejpam-5495	284	11	and	and	CCONJ
ejpam-5495	284	12	established	establish	VERB
ejpam-5495	284	13	.	.	PUNCT
ejpam-5495	285	1	the	the	DET
ejpam-5495	285	2	as	as	ADP
ejpam-5495	285	3	was	be	AUX
ejpam-5495	285	4	numerically	numerically	ADV
ejpam-5495	285	5	confirmed	confirm	VERB
ejpam-5495	285	6	by	by	ADP
ejpam-5495	285	7	comparing	compare	VERB
ejpam-5495	285	8	it	it	PRON
ejpam-5495	285	9	to	to	ADP
ejpam-5495	285	10	the	the	DET
ejpam-5495	285	11	related	relate	VERB
ejpam-5495	285	12	numerical	numerical	ADJ
ejpam-5495	285	13	data	datum	NOUN
ejpam-5495	285	14	,	,	PUNCT
ejpam-5495	285	15	which	which	PRON
ejpam-5495	285	16	showed	show	VERB
ejpam-5495	285	17	a	a	DET
ejpam-5495	285	18	remarkably	remarkably	ADV
ejpam-5495	285	19	high	high	ADJ
ejpam-5495	285	20	similarity	similarity	NOUN
ejpam-5495	285	21	.	.	PUNCT
ejpam-5495	286	1	the	the	DET
ejpam-5495	286	2	npa	npa	NOUN
ejpam-5495	286	3	was	be	AUX
ejpam-5495	286	4	distinguished	distinguish	VERB
ejpam-5495	286	5	by	by	ADP
ejpam-5495	286	6	its	its	PRON
ejpam-5495	286	7	convenience	convenience	NOUN
ejpam-5495	286	8	,	,	PUNCT
ejpam-5495	286	9	accessibility	accessibility	NOUN
ejpam-5495	286	10	,	,	PUNCT
ejpam-5495	286	11	and	and	CCONJ
ejpam-5495	286	12	excellent	excellent	ADJ
ejpam-5495	286	13	accuracy	accuracy	NOUN
ejpam-5495	286	14	in	in	ADP
ejpam-5495	286	15	studying	study	VERB
ejpam-5495	286	16	the	the	DET
ejpam-5495	286	17	behavior	behavior	NOUN
ejpam-5495	286	18	of	of	ADP
ejpam-5495	286	19	strong	strong	ADJ
ejpam-5495	286	20	nonlinear	nonlinear	ADJ
ejpam-5495	286	21	oscillators	oscillator	NOUN
ejpam-5495	286	22	in	in	ADP
ejpam-5495	286	23	contrast	contrast	NOUN
ejpam-5495	286	24	to	to	ADP
ejpam-5495	286	25	conventional	conventional	ADJ
ejpam-5495	286	26	perturbation	perturbation	NOUN
ejpam-5495	286	27	methods	method	NOUN
ejpam-5495	286	28	.	.	PUNCT
ejpam-5495	287	1	accordingly	accordingly	ADV
ejpam-5495	287	2	,	,	PUNCT
ejpam-5495	287	3	we	we	PRON
ejpam-5495	287	4	have	have	AUX
ejpam-5495	287	5	been	be	AUX
ejpam-5495	287	6	able	able	ADJ
ejpam-5495	287	7	to	to	PART
ejpam-5495	287	8	address	address	VERB
ejpam-5495	287	9	a	a	DET
ejpam-5495	287	10	variety	variety	NOUN
ejpam-5495	287	11	of	of	ADP
ejpam-5495	287	12	problems	problem	NOUN
ejpam-5495	287	13	with	with	ADP
ejpam-5495	287	14	the	the	DET
ejpam-5495	287	15	usage	usage	NOUN
ejpam-5495	287	16	of	of	ADP
ejpam-5495	287	17	oscillators	oscillator	NOUN
ejpam-5495	287	18	in	in	ADP
ejpam-5495	287	19	mechanical	mechanical	ADJ
ejpam-5495	287	20	systems	system	NOUN
ejpam-5495	287	21	thanks	thank	NOUN
ejpam-5495	287	22	to	to	ADP
ejpam-5495	287	23	the	the	DET
ejpam-5495	287	24	present	present	ADJ
ejpam-5495	287	25	npa	npa	NOUN
ejpam-5495	287	26	.	.	PUNCT
ejpam-5495	288	1	it	it	PRON
ejpam-5495	288	2	was	be	AUX
ejpam-5495	288	3	a	a	DET
ejpam-5495	288	4	successful	successful	ADJ
ejpam-5495	288	5	,	,	PUNCT
ejpam-5495	288	6	powerful	powerful	ADJ
ejpam-5495	288	7	,	,	PUNCT
ejpam-5495	288	8	and	and	CCONJ
ejpam-5495	288	9	encouraging	encourage	VERB
ejpam-5495	288	10	method	method	NOUN
ejpam-5495	288	11	for	for	ADP
ejpam-5495	288	12	examining	examine	VERB
ejpam-5495	288	13	problems	problem	NOUN
ejpam-5495	288	14	related	relate	VERB
ejpam-5495	288	15	to	to	ADP
ejpam-5495	288	16	dynamic	dynamic	ADJ
ejpam-5495	288	17	systems	system	NOUN
ejpam-5495	288	18	.	.	PUNCT
ejpam-5495	289	1	the	the	DET
ejpam-5495	289	2	realistic	realistic	ADJ
ejpam-5495	289	3	study	study	NOUN
ejpam-5495	289	4	approximation	approximation	NOUN
ejpam-5495	289	5	of	of	ADP
ejpam-5495	289	6	the	the	DET
ejpam-5495	289	7	analytical	analytical	ADJ
ejpam-5495	289	8	methodology	methodology	NOUN
ejpam-5495	289	9	was	be	AUX
ejpam-5495	289	10	enabled	enable	VERB
ejpam-5495	289	11	a	a	DET
ejpam-5495	289	12	qualitative	qualitative	ADJ
ejpam-5495	289	13	evaluation	evaluation	NOUN
ejpam-5495	289	14	a.	a.	NOUN
ejpam-5495	289	15	alanazy	alanazy	PROPN
ejpam-5495	289	16	et	et	PROPN
ejpam-5495	289	17	al	al	PROPN
ejpam-5495	289	18	.	.	PUNCT
ejpam-5495	289	19	/	/	SYM
ejpam-5495	289	20	eur	eur	PROPN
ejpam-5495	289	21	.	.	PUNCT
ejpam-5495	290	1	j.	j.	PROPN
ejpam-5495	290	2	pure	pure	PROPN
ejpam-5495	290	3	appl	appl	PROPN
ejpam-5495	290	4	.	.	PROPN
ejpam-5495	290	5	math	math	PROPN
ejpam-5495	290	6	,	,	PUNCT
ejpam-5495	290	7	18	18	NUM
ejpam-5495	290	8	(	(	PUNCT
ejpam-5495	290	9	1	1	NUM
ejpam-5495	290	10	)	)	PUNCT
ejpam-5495	290	11	(	(	PUNCT
ejpam-5495	290	12	2025	2025	NUM
ejpam-5495	290	13	)	)	PUNCT
ejpam-5495	290	14	,	,	PUNCT
ejpam-5495	290	15	5495	5495	NUM
ejpam-5495	290	16	17	17	NUM
ejpam-5495	290	17	of	of	ADP
ejpam-5495	290	18	21	21	NUM
ejpam-5495	290	19	of	of	ADP
ejpam-5495	290	20	the	the	DET
ejpam-5495	290	21	results	result	NOUN
ejpam-5495	290	22	.	.	PUNCT
ejpam-5495	291	1	the	the	DET
ejpam-5495	291	2	temporal	temporal	ADJ
ejpam-5495	291	3	changes	change	NOUN
ejpam-5495	291	4	of	of	ADP
ejpam-5495	291	5	the	the	DET
ejpam-5495	291	6	discovered	discover	VERB
ejpam-5495	291	7	solutions	solution	NOUN
ejpam-5495	291	8	were	be	AUX
ejpam-5495	291	9	shown	show	VERB
ejpam-5495	291	10	for	for	ADP
ejpam-5495	291	11	various	various	ADJ
ejpam-5495	291	12	properties	property	NOUN
ejpam-5495	291	13	of	of	ADP
ejpam-5495	291	14	the	the	DET
ejpam-5495	291	15	affected	affected	ADJ
ejpam-5495	291	16	parameters	parameter	NOUN
ejpam-5495	291	17	.	.	PUNCT
ejpam-5495	292	1	a	a	DET
ejpam-5495	292	2	description	description	NOUN
ejpam-5495	292	3	of	of	ADP
ejpam-5495	292	4	the	the	DET
ejpam-5495	292	5	outcomes	outcome	NOUN
ejpam-5495	292	6	was	be	AUX
ejpam-5495	292	7	provided	provide	VERB
ejpam-5495	292	8	in	in	ADP
ejpam-5495	292	9	view	view	NOUN
ejpam-5495	292	10	of	of	ADP
ejpam-5495	292	11	the	the	DET
ejpam-5495	292	12	depicted	depict	VERB
ejpam-5495	292	13	figures	figure	NOUN
ejpam-5495	292	14	through	through	ADP
ejpam-5495	292	15	a	a	DET
ejpam-5495	292	16	set	set	NOUN
ejpam-5495	292	17	of	of	ADP
ejpam-5495	292	18	curves	curve	NOUN
ejpam-5495	292	19	.	.	PUNCT
ejpam-5495	293	1	it	it	PRON
ejpam-5495	293	2	has	have	AUX
ejpam-5495	293	3	investigated	investigate	VERB
ejpam-5495	293	4	the	the	DET
ejpam-5495	293	5	impact	impact	NOUN
ejpam-5495	293	6	of	of	ADP
ejpam-5495	293	7	various	various	ADJ
ejpam-5495	293	8	regulatory	regulatory	ADJ
ejpam-5495	293	9	thresholds	threshold	NOUN
ejpam-5495	293	10	on	on	ADP
ejpam-5495	293	11	the	the	DET
ejpam-5495	293	12	vibrating	vibrating	NOUN
ejpam-5495	293	13	system	system	NOUN
ejpam-5495	293	14	.	.	PUNCT
ejpam-5495	294	1	regarding	regard	VERB
ejpam-5495	294	2	the	the	DET
ejpam-5495	294	3	original	original	ADJ
ejpam-5495	294	4	methodology	methodology	NOUN
ejpam-5495	294	5	or	or	CCONJ
ejpam-5495	294	6	significant	significant	ADJ
ejpam-5495	294	7	findings	finding	NOUN
ejpam-5495	294	8	,	,	PUNCT
ejpam-5495	294	9	the	the	DET
ejpam-5495	294	10	subsequent	subsequent	ADJ
ejpam-5495	294	11	outcomes	outcome	NOUN
ejpam-5495	294	12	warrant	warrant	VERB
ejpam-5495	294	13	emphasis	emphasis	NOUN
ejpam-5495	294	14	:	:	PUNCT
ejpam-5495	294	15	i.	i.	NOUN
ejpam-5495	294	16	the	the	DET
ejpam-5495	294	17	technique	technique	NOUN
ejpam-5495	294	18	presented	present	VERB
ejpam-5495	294	19	simply	simply	ADV
ejpam-5495	294	20	created	create	VERB
ejpam-5495	294	21	an	an	DET
ejpam-5495	294	22	equivalent	equivalent	ADJ
ejpam-5495	294	23	linear	linear	ADJ
ejpam-5495	294	24	ode	ode	NOUN
ejpam-5495	294	25	to	to	ADP
ejpam-5495	294	26	the	the	DET
ejpam-5495	294	27	current	current	ADJ
ejpam-5495	294	28	nonlinear	nonlinear	ADJ
ejpam-5495	294	29	one	one	NOUN
ejpam-5495	294	30	.	.	PUNCT
ejpam-5495	295	1	these	these	DET
ejpam-5495	295	2	two	two	NUM
ejpam-5495	295	3	equations	equation	NOUN
ejpam-5495	295	4	matched	match	VERB
ejpam-5495	295	5	each	each	DET
ejpam-5495	295	6	other	other	ADJ
ejpam-5495	295	7	quite	quite	ADV
ejpam-5495	295	8	well	well	ADV
ejpam-5495	295	9	.	.	PUNCT
ejpam-5495	296	1	ii	ii	X
ejpam-5495	296	2	.	.	PUNCT
ejpam-5495	297	1	all	all	DET
ejpam-5495	297	2	conventional	conventional	ADJ
ejpam-5495	297	3	methods	method	NOUN
ejpam-5495	297	4	employ	employ	VERB
ejpam-5495	297	5	the	the	DET
ejpam-5495	297	6	taylor	taylor	PROPN
ejpam-5495	297	7	expansion	expansion	NOUN
ejpam-5495	297	8	to	to	PART
ejpam-5495	297	9	make	make	VERB
ejpam-5495	297	10	the	the	DET
ejpam-5495	297	11	given	give	VERB
ejpam-5495	297	12	problem	problem	NOUN
ejpam-5495	297	13	simpler	simple	ADJ
ejpam-5495	297	14	in	in	ADP
ejpam-5495	297	15	the	the	DET
ejpam-5495	297	16	existence	existence	NOUN
ejpam-5495	297	17	of	of	ADP
ejpam-5495	297	18	restoring	restore	VERB
ejpam-5495	297	19	forces	force	NOUN
ejpam-5495	297	20	.	.	PUNCT
ejpam-5495	298	1	under	under	ADP
ejpam-5495	298	2	the	the	DET
ejpam-5495	298	3	present	present	ADJ
ejpam-5495	298	4	strategy	strategy	NOUN
ejpam-5495	298	5	,	,	PUNCT
ejpam-5495	298	6	this	this	DET
ejpam-5495	298	7	weakness	weakness	NOUN
ejpam-5495	298	8	has	have	AUX
ejpam-5495	298	9	been	be	AUX
ejpam-5495	298	10	eliminated	eliminate	VERB
ejpam-5495	298	11	.	.	PUNCT
ejpam-5495	299	1	iii	iii	X
ejpam-5495	299	2	.	.	PUNCT
ejpam-5495	300	1	unlike	unlike	ADP
ejpam-5495	300	2	prior	prior	ADJ
ejpam-5495	300	3	traditional	traditional	ADJ
ejpam-5495	300	4	techniques	technique	NOUN
ejpam-5495	300	5	,	,	PUNCT
ejpam-5495	300	6	the	the	DET
ejpam-5495	300	7	current	current	ADJ
ejpam-5495	300	8	approach	approach	NOUN
ejpam-5495	300	9	allows	allow	VERB
ejpam-5495	300	10	us	we	PRON
ejpam-5495	300	11	to	to	PART
ejpam-5495	300	12	investigate	investigate	VERB
ejpam-5495	300	13	the	the	DET
ejpam-5495	300	14	stability	stability	NOUN
ejpam-5495	300	15	analysis	analysis	NOUN
ejpam-5495	300	16	of	of	ADP
ejpam-5495	300	17	the	the	DET
ejpam-5495	300	18	problem	problem	NOUN
ejpam-5495	300	19	.	.	PUNCT
ejpam-5495	301	1	iv	iv	X
ejpam-5495	301	2	.	.	PUNCT
ejpam-5495	301	3	to	to	PART
ejpam-5495	301	4	sum	sum	VERB
ejpam-5495	301	5	up	up	ADP
ejpam-5495	301	6	,	,	PUNCT
ejpam-5495	301	7	it	it	PRON
ejpam-5495	301	8	appears	appear	VERB
ejpam-5495	301	9	that	that	SCONJ
ejpam-5495	301	10	the	the	DET
ejpam-5495	301	11	novel	novel	ADJ
ejpam-5495	301	12	method	method	NOUN
ejpam-5495	301	13	was	be	AUX
ejpam-5495	301	14	a	a	DET
ejpam-5495	301	15	simple	simple	ADJ
ejpam-5495	301	16	,	,	PUNCT
ejpam-5495	301	17	practical	practical	ADJ
ejpam-5495	301	18	,	,	PUNCT
ejpam-5495	301	19	and	and	CCONJ
ejpam-5495	301	20	entertaining	entertaining	ADJ
ejpam-5495	301	21	instrument	instrument	NOUN
ejpam-5495	301	22	.	.	PUNCT
ejpam-5495	302	1	it	it	PRON
ejpam-5495	302	2	applies	apply	VERB
ejpam-5495	302	3	to	to	ADP
ejpam-5495	302	4	the	the	DET
ejpam-5495	302	5	analysis	analysis	NOUN
ejpam-5495	302	6	of	of	ADP
ejpam-5495	302	7	numerous	numerous	ADJ
ejpam-5495	302	8	nonlinear	nonlinear	ADJ
ejpam-5495	302	9	oscillation	oscillation	NOUN
ejpam-5495	302	10	categories	category	NOUN
ejpam-5495	302	11	.	.	PUNCT
ejpam-5495	303	1	v.	v.	ADP
ejpam-5495	303	2	considering	consider	VERB
ejpam-5495	303	3	the	the	DET
ejpam-5495	303	4	stability	stability	NOUN
ejpam-5495	303	5	criteria	criterion	NOUN
ejpam-5495	303	6	,	,	PUNCT
ejpam-5495	303	7	and	and	CCONJ
ejpam-5495	303	8	in	in	ADP
ejpam-5495	303	9	light	light	NOUN
ejpam-5495	303	10	of	of	ADP
ejpam-5495	303	11	the	the	DET
ejpam-5495	303	12	numerical	numerical	ADJ
ejpam-5495	303	13	calculations	calculation	NOUN
ejpam-5495	303	14	of	of	ADP
ejpam-5495	303	15	the	the	DET
ejpam-5495	303	16	parameters	parameter	NOUN
ejpam-5495	303	17	,	,	PUNCT
ejpam-5495	303	18	it	it	PRON
ejpam-5495	303	19	was	be	AUX
ejpam-5495	303	20	found	find	VERB
ejpam-5495	303	21	that	that	SCONJ
ejpam-5495	303	22	the	the	DET
ejpam-5495	303	23	parameters	parameter	NOUN
ejpam-5495	303	24	α	α	PRON
ejpam-5495	303	25	,	,	PUNCT
ejpam-5495	303	26	β	β	X
ejpam-5495	303	27	,	,	PUNCT
ejpam-5495	303	28	µ	µ	X
ejpam-5495	303	29	and	and	CCONJ
ejpam-5495	303	30	ω	ω	NUM
ejpam-5495	303	31	have	have	VERB
ejpam-5495	303	32	a	a	DET
ejpam-5495	303	33	destabilizing	destabilizing	ADJ
ejpam-5495	303	34	influence	influence	NOUN
ejpam-5495	303	35	.	.	PUNCT
ejpam-5495	304	1	by	by	ADP
ejpam-5495	304	2	contrast	contrast	NOUN
ejpam-5495	304	3	,	,	PUNCT
ejpam-5495	304	4	the	the	DET
ejpam-5495	304	5	factor	factor	NOUN
ejpam-5495	304	6	λ	λ	PROPN
ejpam-5495	304	7	has	have	VERB
ejpam-5495	304	8	a	a	DET
ejpam-5495	304	9	slightly	slightly	ADV
ejpam-5495	304	10	stabilizing	stabilize	VERB
ejpam-5495	304	11	effect	effect	NOUN
ejpam-5495	304	12	.	.	PUNCT
ejpam-5495	305	1	as	as	ADV
ejpam-5495	305	2	well	well	ADV
ejpam-5495	305	3	-	-	PUNCT
ejpam-5495	305	4	known	know	VERB
ejpam-5495	305	5	,	,	PUNCT
ejpam-5495	305	6	coupled	couple	VERB
ejpam-5495	305	7	dynamical	dynamical	ADJ
ejpam-5495	305	8	systems	system	NOUN
ejpam-5495	305	9	are	be	AUX
ejpam-5495	305	10	systems	system	NOUN
ejpam-5495	305	11	wherein	wherein	SCONJ
ejpam-5495	305	12	two	two	NUM
ejpam-5495	305	13	or	or	CCONJ
ejpam-5495	305	14	more	more	ADV
ejpam-5495	305	15	dynamical	dynamical	ADJ
ejpam-5495	305	16	entities	entity	NOUN
ejpam-5495	305	17	interact	interact	VERB
ejpam-5495	305	18	through	through	ADP
ejpam-5495	305	19	a	a	DET
ejpam-5495	305	20	coupling	coupling	NOUN
ejpam-5495	305	21	mechanism	mechanism	NOUN
ejpam-5495	305	22	,	,	PUNCT
ejpam-5495	305	23	hence	hence	ADV
ejpam-5495	305	24	affecting	affect	VERB
ejpam-5495	305	25	one	one	NUM
ejpam-5495	305	26	another	another	DET
ejpam-5495	305	27	’s	’s	PART
ejpam-5495	305	28	behavior	behavior	NOUN
ejpam-5495	305	29	.	.	PUNCT
ejpam-5495	306	1	this	this	DET
ejpam-5495	306	2	contact	contact	NOUN
ejpam-5495	306	3	may	may	AUX
ejpam-5495	306	4	occur	occur	VERB
ejpam-5495	306	5	via	via	ADP
ejpam-5495	306	6	physical	physical	ADJ
ejpam-5495	306	7	,	,	PUNCT
ejpam-5495	306	8	chemical	chemical	NOUN
ejpam-5495	306	9	,	,	PUNCT
ejpam-5495	306	10	biological	biological	ADJ
ejpam-5495	306	11	,	,	PUNCT
ejpam-5495	306	12	or	or	CCONJ
ejpam-5495	306	13	mathematical	mathematical	ADJ
ejpam-5495	306	14	linkages	linkage	NOUN
ejpam-5495	306	15	.	.	PUNCT
ejpam-5495	307	1	the	the	DET
ejpam-5495	307	2	state	state	NOUN
ejpam-5495	307	3	and	and	CCONJ
ejpam-5495	307	4	evolution	evolution	NOUN
ejpam-5495	307	5	of	of	ADP
ejpam-5495	307	6	each	each	DET
ejpam-5495	307	7	system	system	NOUN
ejpam-5495	307	8	are	be	AUX
ejpam-5495	307	9	contingent	contingent	ADJ
ejpam-5495	307	10	not	not	PART
ejpam-5495	307	11	only	only	ADV
ejpam-5495	307	12	upon	upon	SCONJ
ejpam-5495	307	13	its	its	PRON
ejpam-5495	307	14	own	own	ADJ
ejpam-5495	307	15	dynamics	dynamic	NOUN
ejpam-5495	307	16	but	but	CCONJ
ejpam-5495	307	17	also	also	ADV
ejpam-5495	307	18	on	on	ADP
ejpam-5495	307	19	the	the	DET
ejpam-5495	307	20	state	state	NOUN
ejpam-5495	307	21	and	and	CCONJ
ejpam-5495	307	22	dynamics	dynamic	NOUN
ejpam-5495	307	23	of	of	ADP
ejpam-5495	307	24	other	other	ADJ
ejpam-5495	307	25	systems	system	NOUN
ejpam-5495	307	26	.	.	PUNCT
ejpam-5495	308	1	comprehending	comprehending	ADJ
ejpam-5495	308	2	linked	link	VERB
ejpam-5495	308	3	dynamical	dynamical	ADJ
ejpam-5495	308	4	systems	system	NOUN
ejpam-5495	308	5	is	be	AUX
ejpam-5495	308	6	crucial	crucial	ADJ
ejpam-5495	308	7	for	for	ADP
ejpam-5495	308	8	examining	examine	VERB
ejpam-5495	308	9	how	how	SCONJ
ejpam-5495	308	10	interrelated	interrelated	ADJ
ejpam-5495	308	11	components	component	NOUN
ejpam-5495	308	12	affect	affect	VERB
ejpam-5495	308	13	the	the	DET
ejpam-5495	308	14	overall	overall	ADJ
ejpam-5495	308	15	behavior	behavior	NOUN
ejpam-5495	308	16	of	of	ADP
ejpam-5495	308	17	complex	complex	ADJ
ejpam-5495	308	18	systems	system	NOUN
ejpam-5495	308	19	.	.	PUNCT
ejpam-5495	309	1	therefore	therefore	ADV
ejpam-5495	309	2	,	,	PUNCT
ejpam-5495	309	3	as	as	ADP
ejpam-5495	309	4	a	a	DET
ejpam-5495	309	5	future	future	ADJ
ejpam-5495	309	6	work	work	NOUN
ejpam-5495	309	7	,	,	PUNCT
ejpam-5495	309	8	the	the	DET
ejpam-5495	309	9	novel	novel	ADJ
ejpam-5495	309	10	methodology	methodology	NOUN
ejpam-5495	309	11	,	,	PUNCT
ejpam-5495	309	12	referred	refer	VERB
ejpam-5495	309	13	to	to	ADP
ejpam-5495	309	14	as	as	SCONJ
ejpam-5495	309	15	the	the	DET
ejpam-5495	309	16	npa	npa	NOUN
ejpam-5495	309	17	will	will	AUX
ejpam-5495	309	18	be	be	AUX
ejpam-5495	309	19	used	use	VERB
ejpam-5495	309	20	to	to	PART
ejpam-5495	309	21	inspect	inspect	VERB
ejpam-5495	309	22	the	the	DET
ejpam-5495	309	23	coupled	couple	VERB
ejpam-5495	309	24	system	system	NOUN
ejpam-5495	309	25	in	in	ADP
ejpam-5495	309	26	the	the	DET
ejpam-5495	309	27	field	field	NOUN
ejpam-5495	309	28	of	of	ADP
ejpam-5495	309	29	dynamical	dynamical	ADJ
ejpam-5495	309	30	topics	topic	NOUN
ejpam-5495	309	31	.	.	PUNCT
ejpam-5495	310	1	funding	fund	VERB
ejpam-5495	310	2	this	this	DET
ejpam-5495	310	3	research	research	NOUN
ejpam-5495	310	4	was	be	AUX
ejpam-5495	310	5	funded	fund	VERB
ejpam-5495	310	6	by	by	ADP
ejpam-5495	310	7	deanship	deanship	NOUN
ejpam-5495	310	8	of	of	ADP
ejpam-5495	310	9	scientific	scientific	ADJ
ejpam-5495	310	10	research	research	NOUN
ejpam-5495	310	11	project	project	NOUN
ejpam-5495	310	12	number	number	NOUN
ejpam-5495	310	13	(	(	PUNCT
ejpam-5495	310	14	nbuffr-2024	nbuffr-2024	ADJ
ejpam-5495	310	15	-	-	PUNCT
ejpam-5495	310	16	912	912	NUM
ejpam-5495	310	17	-	-	PUNCT
ejpam-5495	310	18	01	01	NUM
ejpam-5495	310	19	)	)	PUNCT
ejpam-5495	310	20	,	,	PUNCT
ejpam-5495	310	21	northern	northern	ADJ
ejpam-5495	310	22	border	border	NOUN
ejpam-5495	310	23	university	university	PROPN
ejpam-5495	310	24	,	,	PUNCT
ejpam-5495	310	25	arar	arar	PROPN
ejpam-5495	310	26	,	,	PUNCT
ejpam-5495	310	27	ksa	ksa	PROPN
ejpam-5495	310	28	.	.	PUNCT
ejpam-5495	311	1	acknowledgements	acknowledgement	VERB
ejpam-5495	311	2	the	the	DET
ejpam-5495	311	3	authors	author	NOUN
ejpam-5495	311	4	extend	extend	VERB
ejpam-5495	311	5	their	their	PRON
ejpam-5495	311	6	appreciation	appreciation	NOUN
ejpam-5495	311	7	to	to	ADP
ejpam-5495	311	8	the	the	DET
ejpam-5495	311	9	deanship	deanship	NOUN
ejpam-5495	311	10	of	of	ADP
ejpam-5495	311	11	scientific	scientific	ADJ
ejpam-5495	311	12	research	research	NOUN
ejpam-5495	311	13	at	at	ADP
ejpam-5495	311	14	northern	northern	ADJ
ejpam-5495	311	15	border	border	NOUN
ejpam-5495	311	16	university	university	PROPN
ejpam-5495	311	17	,	,	PUNCT
ejpam-5495	311	18	arar	arar	PROPN
ejpam-5495	311	19	,	,	PUNCT
ejpam-5495	311	20	ksa	ksa	PROPN
ejpam-5495	311	21	for	for	ADP
ejpam-5495	311	22	funding	fund	VERB
ejpam-5495	311	23	this	this	DET
ejpam-5495	311	24	research	research	NOUN
ejpam-5495	311	25	work	work	NOUN
ejpam-5495	311	26	through	through	ADP
ejpam-5495	311	27	the	the	DET
ejpam-5495	311	28	project	project	NOUN
ejpam-5495	311	29	number	number	NOUN
ejpam-5495	311	30	”	"	PUNCT
ejpam-5495	311	31	nbu	nbu	NOUN
ejpam-5495	311	32	-	-	PUNCT
ejpam-5495	311	33	ffr-2024	ffr-2024	NOUN
ejpam-5495	311	34	-	-	PUNCT
ejpam-5495	311	35	912	912	NUM
ejpam-5495	311	36	-	-	PUNCT
ejpam-5495	311	37	01	01	NUM
ejpam-5495	311	38	”	"	PUNCT
ejpam-5495	311	39	.	.	PUNCT
ejpam-5495	312	1	authors	author	NOUN
ejpam-5495	312	2	statements	statement	VERB
ejpam-5495	312	3	asma	asma	PROPN
ejpam-5495	312	4	jazza	jazza	PROPN
ejpam-5495	312	5	:	:	PUNCT
ejpam-5495	312	6	resources	resource	NOUN
ejpam-5495	312	7	,	,	PUNCT
ejpam-5495	312	8	methodology	methodology	NOUN
ejpam-5495	312	9	,	,	PUNCT
ejpam-5495	312	10	formal	formal	ADJ
ejpam-5495	312	11	analysis	analysis	NOUN
ejpam-5495	312	12	,	,	PUNCT
ejpam-5495	312	13	validation	validation	NOUN
ejpam-5495	312	14	,	,	PUNCT
ejpam-5495	312	15	visualization	visualization	NOUN
ejpam-5495	312	16	.	.	PUNCT
ejpam-5495	313	1	galal	galal	PROPN
ejpam-5495	313	2	m.	m.	PROPN
ejpam-5495	313	3	moatimid	moatimid	PROPN
ejpam-5495	313	4	:	:	PUNCT
ejpam-5495	313	5	conceptualization	conceptualization	NOUN
ejpam-5495	313	6	,	,	PUNCT
ejpam-5495	313	7	resources	resource	NOUN
ejpam-5495	313	8	,	,	PUNCT
ejpam-5495	313	9	methodology	methodology	NOUN
ejpam-5495	313	10	,	,	PUNCT
ejpam-5495	313	11	formal	formal	ADJ
ejpam-5495	313	12	analysis	analysis	NOUN
ejpam-5495	313	13	,	,	PUNCT
ejpam-5495	313	14	validation	validation	NOUN
ejpam-5495	313	15	,	,	PUNCT
ejpam-5495	313	16	writingoriginal	writingoriginal	ADJ
ejpam-5495	313	17	draft	draft	NOUN
ejpam-5495	313	18	preparation	preparation	NOUN
ejpam-5495	313	19	,	,	PUNCT
ejpam-5495	313	20	visualization	visualization	NOUN
ejpam-5495	313	21	and	and	CCONJ
ejpam-5495	313	22	reviewing	reviewing	NOUN
ejpam-5495	313	23	.	.	PUNCT
ejpam-5495	314	1	a.	a.	PROPN
ejpam-5495	314	2	alanazy	alanazy	PROPN
ejpam-5495	314	3	et	et	PROPN
ejpam-5495	314	4	al	al	PROPN
ejpam-5495	314	5	.	.	PUNCT
ejpam-5495	314	6	/	/	SYM
ejpam-5495	314	7	eur	eur	PROPN
ejpam-5495	314	8	.	.	PUNCT
ejpam-5495	315	1	j.	j.	PROPN
ejpam-5495	315	2	pure	pure	PROPN
ejpam-5495	315	3	appl	appl	PROPN
ejpam-5495	315	4	.	.	PROPN
ejpam-5495	315	5	math	math	PROPN
ejpam-5495	315	6	,	,	PUNCT
ejpam-5495	315	7	18	18	NUM
ejpam-5495	315	8	(	(	PUNCT
ejpam-5495	315	9	1	1	NUM
ejpam-5495	315	10	)	)	PUNCT
ejpam-5495	315	11	(	(	PUNCT
ejpam-5495	315	12	2025	2025	NUM
ejpam-5495	315	13	)	)	PUNCT
ejpam-5495	315	14	,	,	PUNCT
ejpam-5495	315	15	5495	5495	NUM
ejpam-5495	315	16	18	18	NUM
ejpam-5495	315	17	of	of	ADP
ejpam-5495	315	18	21	21	NUM
ejpam-5495	315	19	t.	t.	PROPN
ejpam-5495	315	20	s.	s.	PROPN
ejpam-5495	315	21	amer	amer	PROPN
ejpam-5495	315	22	:	:	PUNCT
ejpam-5495	315	23	investigation	investigation	NOUN
ejpam-5495	315	24	,	,	PUNCT
ejpam-5495	315	25	methodology	methodology	NOUN
ejpam-5495	315	26	,	,	PUNCT
ejpam-5495	315	27	data	data	NOUN
ejpam-5495	315	28	duration	duration	NOUN
ejpam-5495	315	29	,	,	PUNCT
ejpam-5495	315	30	conceptualization	conceptualization	NOUN
ejpam-5495	315	31	,	,	PUNCT
ejpam-5495	315	32	validation	validation	NOUN
ejpam-5495	315	33	,	,	PUNCT
ejpam-5495	315	34	reviewing	reviewing	NOUN
ejpam-5495	315	35	and	and	CCONJ
ejpam-5495	315	36	editing	editing	NOUN
ejpam-5495	315	37	.	.	PUNCT
ejpam-5495	316	1	a.	a.	NOUN
ejpam-5495	316	2	a.	a.	PROPN
ejpam-5495	316	3	galal	galal	PROPN
ejpam-5495	316	4	:	:	PUNCT
ejpam-5495	316	5	examination	examination	NOUN
ejpam-5495	316	6	,	,	PUNCT
ejpam-5495	316	7	organization	organization	NOUN
ejpam-5495	316	8	,	,	PUNCT
ejpam-5495	316	9	data	data	NOUN
ejpam-5495	316	10	duration	duration	NOUN
ejpam-5495	316	11	,	,	PUNCT
ejpam-5495	316	12	validation	validation	NOUN
ejpam-5495	316	13	,	,	PUNCT
ejpam-5495	316	14	corroboration	corroboration	NOUN
ejpam-5495	316	15	,	,	PUNCT
ejpam-5495	316	16	rereading	reread	VERB
ejpam-5495	316	17	and	and	CCONJ
ejpam-5495	316	18	editing	editing	NOUN
ejpam-5495	316	19	.	.	PUNCT
ejpam-5495	317	1	conflict	conflict	NOUN
ejpam-5495	317	2	of	of	ADP
ejpam-5495	317	3	interest	interest	NOUN
ejpam-5495	317	4	there	there	PRON
ejpam-5495	317	5	are	be	VERB
ejpam-5495	317	6	no	no	DET
ejpam-5495	317	7	conflicts	conflict	NOUN
ejpam-5495	317	8	of	of	ADP
ejpam-5495	317	9	interest	interest	NOUN
ejpam-5495	317	10	declared	declare	VERB
ejpam-5495	317	11	by	by	ADP
ejpam-5495	317	12	the	the	DET
ejpam-5495	317	13	authors	author	NOUN
ejpam-5495	317	14	.	.	PUNCT
ejpam-5495	318	1	data	datum	NOUN
ejpam-5495	318	2	availability	availability	NOUN
ejpam-5495	318	3	all	all	DET
ejpam-5495	318	4	data	datum	NOUN
ejpam-5495	318	5	generated	generate	VERB
ejpam-5495	318	6	or	or	CCONJ
ejpam-5495	318	7	analysed	analyse	VERB
ejpam-5495	318	8	during	during	ADP
ejpam-5495	318	9	this	this	DET
ejpam-5495	318	10	study	study	NOUN
ejpam-5495	318	11	are	be	AUX
ejpam-5495	318	12	included	include	VERB
ejpam-5495	318	13	in	in	ADP
ejpam-5495	318	14	this	this	DET
ejpam-5495	318	15	published	publish	VERB
ejpam-5495	318	16	article	article	NOUN
ejpam-5495	318	17	.	.	PUNCT
ejpam-5495	319	1	references	reference	NOUN
ejpam-5495	319	2	[	[	X
ejpam-5495	319	3	1	1	NUM
ejpam-5495	319	4	]	]	PUNCT
ejpam-5495	319	5	a.	a.	NOUN
ejpam-5495	319	6	abu	abu	PROPN
ejpam-5495	319	7	-	-	PUNCT
ejpam-5495	319	8	as’ad	as’ad	PROPN
ejpam-5495	319	9	and	and	CCONJ
ejpam-5495	319	10	j.	j.	PROPN
ejpam-5495	319	11	asad	asad	PROPN
ejpam-5495	319	12	.	.	PUNCT
ejpam-5495	320	1	power	power	NOUN
ejpam-5495	320	2	series	series	PROPN
ejpam-5495	320	3	approach	approach	NOUN
ejpam-5495	320	4	to	to	ADP
ejpam-5495	320	5	nonlinear	nonlinear	ADJ
ejpam-5495	320	6	oscillators	oscillator	NOUN
ejpam-5495	320	7	.	.	PUNCT
ejpam-5495	321	1	journal	journal	NOUN
ejpam-5495	321	2	of	of	ADP
ejpam-5495	321	3	low	low	ADJ
ejpam-5495	321	4	frequency	frequency	NOUN
ejpam-5495	321	5	noise	noise	NOUN
ejpam-5495	321	6	,	,	PUNCT
ejpam-5495	321	7	vibration	vibration	NOUN
ejpam-5495	321	8	and	and	CCONJ
ejpam-5495	321	9	active	active	ADJ
ejpam-5495	321	10	control	control	NOUN
ejpam-5495	321	11	,	,	PUNCT
ejpam-5495	321	12	43(1):220—-238	43(1):220—-238	PROPN
ejpam-5495	321	13	,	,	PUNCT
ejpam-5495	321	14	2024	2024	NUM
ejpam-5495	321	15	.	.	PUNCT
ejpam-5495	322	1	[	[	X
ejpam-5495	322	2	2	2	X
ejpam-5495	322	3	]	]	PUNCT
ejpam-5495	322	4	h.	h.	PROPN
ejpam-5495	322	5	ahmad	ahmad	PROPN
ejpam-5495	322	6	,	,	PUNCT
ejpam-5495	322	7	t.a	t.a	PROPN
ejpam-5495	322	8	.	.	PROPN
ejpam-5495	322	9	khan	khan	PROPN
ejpam-5495	322	10	,	,	PUNCT
ejpam-5495	322	11	p.s	p.s	PROPN
ejpam-5495	322	12	.	.	PROPN
ejpam-5495	322	13	stanimirović	stanimirović	PROPN
ejpam-5495	322	14	,	,	PUNCT
ejpam-5495	322	15	y	y	PROPN
ejpam-5495	322	16	-	-	PUNCT
ejpam-5495	322	17	m.	m.	NOUN
ejpam-5495	322	18	chu	chu	PROPN
ejpam-5495	322	19	,	,	PUNCT
ejpam-5495	322	20	and	and	CCONJ
ejpam-5495	322	21	i.	i.	PROPN
ejpam-5495	322	22	ahmad	ahmad	PROPN
ejpam-5495	322	23	.	.	PUNCT
ejpam-5495	323	1	modified	modify	VERB
ejpam-5495	323	2	variational	variational	ADJ
ejpam-5495	323	3	iteration	iteration	NOUN
ejpam-5495	323	4	algorithm	algorithm	PROPN
ejpam-5495	323	5	-	-	PUNCT
ejpam-5495	323	6	ii	ii	NOUN
ejpam-5495	323	7	:	:	PUNCT
ejpam-5495	323	8	convergence	convergence	NOUN
ejpam-5495	323	9	and	and	CCONJ
ejpam-5495	323	10	applications	application	NOUN
ejpam-5495	323	11	to	to	ADP
ejpam-5495	323	12	diffusion	diffusion	NOUN
ejpam-5495	323	13	models	model	NOUN
ejpam-5495	323	14	.	.	PUNCT
ejpam-5495	324	1	complexity	complexity	NOUN
ejpam-5495	324	2	,	,	PUNCT
ejpam-5495	324	3	2020	2020	NUM
ejpam-5495	324	4	:	:	PUNCT
ejpam-5495	324	5	id	id	PRON
ejpam-5495	324	6	8841718	8841718	NUM
ejpam-5495	324	7	(	(	PUNCT
ejpam-5495	324	8	14	14	NUM
ejpam-5495	324	9	pages	page	NOUN
ejpam-5495	324	10	)	)	PUNCT
ejpam-5495	324	11	,	,	PUNCT
ejpam-5495	324	12	2020	2020	NUM
ejpam-5495	324	13	.	.	PUNCT
ejpam-5495	325	1	[	[	X
ejpam-5495	325	2	3	3	NUM
ejpam-5495	325	3	]	]	X
ejpam-5495	325	4	kh	kh	PROPN
ejpam-5495	325	5	.	.	PROPN
ejpam-5495	325	6	alluhydan	alluhydan	PROPN
ejpam-5495	325	7	,	,	PUNCT
ejpam-5495	325	8	g.m	g.m	PROPN
ejpam-5495	325	9	.	.	PROPN
ejpam-5495	325	10	moatimid	moatimid	PROPN
ejpam-5495	325	11	,	,	PUNCT
ejpam-5495	325	12	and	and	CCONJ
ejpam-5495	325	13	t.s	t.s	PROPN
ejpam-5495	325	14	.	.	PROPN
ejpam-5495	325	15	amer	amer	PROPN
ejpam-5495	325	16	.	.	PUNCT
ejpam-5495	326	1	the	the	DET
ejpam-5495	326	2	non	non	ADJ
ejpam-5495	326	3	-	-	ADJ
ejpam-5495	326	4	perturbative	perturbative	ADJ
ejpam-5495	326	5	approach	approach	NOUN
ejpam-5495	326	6	in	in	ADP
ejpam-5495	326	7	examining	examine	VERB
ejpam-5495	326	8	the	the	DET
ejpam-5495	326	9	motion	motion	NOUN
ejpam-5495	326	10	of	of	ADP
ejpam-5495	326	11	a	a	DET
ejpam-5495	326	12	simple	simple	ADJ
ejpam-5495	326	13	pendulum	pendulum	NOUN
ejpam-5495	326	14	associated	associate	VERB
ejpam-5495	326	15	with	with	ADP
ejpam-5495	326	16	a	a	DET
ejpam-5495	326	17	rolling	rolling	ADJ
ejpam-5495	326	18	wheel	wheel	NOUN
ejpam-5495	326	19	with	with	ADP
ejpam-5495	326	20	a	a	DET
ejpam-5495	326	21	time	time	NOUN
ejpam-5495	326	22	-	-	PUNCT
ejpam-5495	326	23	delay	delay	NOUN
ejpam-5495	326	24	.	.	PUNCT
ejpam-5495	327	1	european	european	PROPN
ejpam-5495	327	2	journal	journal	PROPN
ejpam-5495	327	3	of	of	ADP
ejpam-5495	327	4	pure	pure	ADJ
ejpam-5495	327	5	and	and	CCONJ
ejpam-5495	327	6	applied	applied	ADJ
ejpam-5495	327	7	mathematics	mathematic	NOUN
ejpam-5495	327	8	,	,	PUNCT
ejpam-5495	327	9	17(4):3185–3208	17(4):3185–3208	NUM
ejpam-5495	327	10	,	,	PUNCT
ejpam-5495	327	11	2024	2024	NUM
ejpam-5495	327	12	.	.	PUNCT
ejpam-5495	328	1	[	[	X
ejpam-5495	328	2	4	4	NUM
ejpam-5495	328	3	]	]	X
ejpam-5495	328	4	kh	kh	PROPN
ejpam-5495	328	5	.	.	PROPN
ejpam-5495	328	6	alluhydan	alluhydan	PROPN
ejpam-5495	328	7	,	,	PUNCT
ejpam-5495	328	8	g.m	g.m	PROPN
ejpam-5495	328	9	.	.	PROPN
ejpam-5495	328	10	moatimid	moatimid	PROPN
ejpam-5495	328	11	,	,	PUNCT
ejpam-5495	328	12	t.s	t.s	PROPN
ejpam-5495	328	13	.	.	PROPN
ejpam-5495	328	14	amer	amer	PROPN
ejpam-5495	328	15	,	,	PUNCT
ejpam-5495	328	16	and	and	CCONJ
ejpam-5495	328	17	a.a	a.a	PROPN
ejpam-5495	328	18	.	.	PROPN
ejpam-5495	328	19	galal	galal	PROPN
ejpam-5495	328	20	.	.	PUNCT
ejpam-5495	329	1	inspection	inspection	NOUN
ejpam-5495	329	2	of	of	ADP
ejpam-5495	329	3	a	a	DET
ejpam-5495	329	4	timedelayed	timedelayed	ADJ
ejpam-5495	329	5	excited	excited	ADJ
ejpam-5495	329	6	damping	damp	VERB
ejpam-5495	329	7	duffing	duffing	NOUN
ejpam-5495	329	8	oscillator	oscillator	NOUN
ejpam-5495	329	9	.	.	PUNCT
ejpam-5495	330	1	axioms	axiom	NOUN
ejpam-5495	330	2	,	,	PUNCT
ejpam-5495	330	3	13:416	13:416	NUM
ejpam-5495	330	4	,	,	PUNCT
ejpam-5495	330	5	2024	2024	NUM
ejpam-5495	330	6	.	.	PUNCT
ejpam-5495	331	1	[	[	X
ejpam-5495	331	2	5	5	NUM
ejpam-5495	331	3	]	]	X
ejpam-5495	331	4	kh	kh	PROPN
ejpam-5495	331	5	.	.	PROPN
ejpam-5495	331	6	alluhydan	alluhydan	PROPN
ejpam-5495	331	7	,	,	PUNCT
ejpam-5495	331	8	g.m	g.m	PROPN
ejpam-5495	331	9	.	.	PROPN
ejpam-5495	331	10	moatimid	moatimid	PROPN
ejpam-5495	331	11	,	,	PUNCT
ejpam-5495	331	12	t.s	t.s	PROPN
ejpam-5495	331	13	.	.	PROPN
ejpam-5495	331	14	amer	amer	PROPN
ejpam-5495	331	15	,	,	PUNCT
ejpam-5495	331	16	and	and	CCONJ
ejpam-5495	331	17	a.a	a.a	PROPN
ejpam-5495	331	18	.	.	PROPN
ejpam-5495	331	19	galal	galal	PROPN
ejpam-5495	331	20	.	.	PUNCT
ejpam-5495	332	1	a	a	DET
ejpam-5495	332	2	novel	novel	ADJ
ejpam-5495	332	3	inspection	inspection	NOUN
ejpam-5495	332	4	of	of	ADP
ejpam-5495	332	5	a	a	DET
ejpam-5495	332	6	time	time	NOUN
ejpam-5495	332	7	-	-	PUNCT
ejpam-5495	332	8	delayed	delay	VERB
ejpam-5495	332	9	rolling	rolling	NOUN
ejpam-5495	332	10	of	of	ADP
ejpam-5495	332	11	a	a	DET
ejpam-5495	332	12	rigid	rigid	ADJ
ejpam-5495	332	13	rod	rod	NOUN
ejpam-5495	332	14	.	.	PUNCT
ejpam-5495	333	1	european	european	PROPN
ejpam-5495	333	2	journal	journal	PROPN
ejpam-5495	333	3	of	of	ADP
ejpam-5495	333	4	pure	pure	ADJ
ejpam-5495	333	5	and	and	CCONJ
ejpam-5495	333	6	applied	applied	ADJ
ejpam-5495	333	7	mathematics	mathematic	NOUN
ejpam-5495	333	8	,	,	PUNCT
ejpam-5495	333	9	17(4):2878–2895	17(4):2878–2895	NUM
ejpam-5495	333	10	,	,	PUNCT
ejpam-5495	333	11	2024	2024	NUM
ejpam-5495	333	12	.	.	PUNCT
ejpam-5495	334	1	[	[	X
ejpam-5495	334	2	6	6	NUM
ejpam-5495	334	3	]	]	SYM
ejpam-5495	334	4	x	x	PROPN
ejpam-5495	334	5	-	-	PROPN
ejpam-5495	334	6	c.	c.	PROPN
ejpam-5495	334	7	cai	cai	PROPN
ejpam-5495	334	8	and	and	CCONJ
ejpam-5495	334	9	j	j	PROPN
ejpam-5495	334	10	-	-	PROPN
ejpam-5495	334	11	f.	f.	PROPN
ejpam-5495	334	12	liu	liu	PROPN
ejpam-5495	334	13	.	.	PUNCT
ejpam-5495	335	1	application	application	NOUN
ejpam-5495	335	2	of	of	ADP
ejpam-5495	335	3	the	the	DET
ejpam-5495	335	4	modified	modify	VERB
ejpam-5495	335	5	frequency	frequency	NOUN
ejpam-5495	335	6	formulation	formulation	NOUN
ejpam-5495	335	7	to	to	ADP
ejpam-5495	335	8	a	a	DET
ejpam-5495	335	9	nonlinear	nonlinear	ADJ
ejpam-5495	335	10	oscillator	oscillator	NOUN
ejpam-5495	335	11	.	.	PUNCT
ejpam-5495	336	1	computers	computer	NOUN
ejpam-5495	336	2	mathematics	mathematic	NOUN
ejpam-5495	336	3	with	with	ADP
ejpam-5495	336	4	applications	application	NOUN
ejpam-5495	336	5	,	,	PUNCT
ejpam-5495	336	6	61(8):2237––2240	61(8):2237––2240	NOUN
ejpam-5495	336	7	,	,	PUNCT
ejpam-5495	336	8	2011	2011	NUM
ejpam-5495	336	9	.	.	PUNCT
ejpam-5495	337	1	[	[	X
ejpam-5495	337	2	7	7	NUM
ejpam-5495	337	3	]	]	SYM
ejpam-5495	337	4	x	x	PROPN
ejpam-5495	337	5	-	-	PROPN
ejpam-5495	337	6	c.	c.	PROPN
ejpam-5495	337	7	cai	cai	PROPN
ejpam-5495	337	8	and	and	CCONJ
ejpam-5495	337	9	j	j	PROPN
ejpam-5495	337	10	-	-	PROPN
ejpam-5495	337	11	f.	f.	PROPN
ejpam-5495	337	12	liu	liu	PROPN
ejpam-5495	337	13	.	.	PUNCT
ejpam-5495	338	1	application	application	NOUN
ejpam-5495	338	2	of	of	ADP
ejpam-5495	338	3	the	the	DET
ejpam-5495	338	4	modified	modify	VERB
ejpam-5495	338	5	frequency	frequency	NOUN
ejpam-5495	338	6	formulation	formulation	NOUN
ejpam-5495	338	7	to	to	ADP
ejpam-5495	338	8	a	a	DET
ejpam-5495	338	9	nonlinear	nonlinear	ADJ
ejpam-5495	338	10	oscillator	oscillator	NOUN
ejpam-5495	338	11	,	,	PUNCT
ejpam-5495	338	12	computers	computer	NOUN
ejpam-5495	338	13	and	and	CCONJ
ejpam-5495	338	14	mathematics	mathematic	NOUN
ejpam-5495	338	15	with	with	ADP
ejpam-5495	338	16	applications	application	NOUN
ejpam-5495	338	17	.	.	PUNCT
ejpam-5495	339	1	partial	partial	ADJ
ejpam-5495	339	2	differential	differential	ADJ
ejpam-5495	339	3	equations	equation	NOUN
ejpam-5495	339	4	in	in	ADP
ejpam-5495	339	5	applied	applied	ADJ
ejpam-5495	339	6	mathematics	mathematic	NOUN
ejpam-5495	339	7	,	,	PUNCT
ejpam-5495	339	8	61:2237—-2240	61:2237—-2240	NOUN
ejpam-5495	339	9	,	,	PUNCT
ejpam-5495	339	10	2011	2011	NUM
ejpam-5495	339	11	.	.	PUNCT
ejpam-5495	340	1	[	[	X
ejpam-5495	340	2	8	8	NUM
ejpam-5495	340	3	]	]	SYM
ejpam-5495	340	4	x	x	PROPN
ejpam-5495	340	5	-	-	PROPN
ejpam-5495	340	6	c.	c.	PROPN
ejpam-5495	340	7	cai	cai	PROPN
ejpam-5495	340	8	and	and	CCONJ
ejpam-5495	340	9	w	w	PROPN
ejpam-5495	340	10	-	-	PUNCT
ejpam-5495	340	11	y.	y.	PROPN
ejpam-5495	340	12	wu	wu	PROPN
ejpam-5495	340	13	.	.	PUNCT
ejpam-5495	341	1	he	he	PRON
ejpam-5495	341	2	’s	’	VERB
ejpam-5495	341	3	frequency	frequency	NOUN
ejpam-5495	341	4	formulation	formulation	NOUN
ejpam-5495	341	5	for	for	ADP
ejpam-5495	341	6	the	the	DET
ejpam-5495	341	7	relativistic	relativistic	ADJ
ejpam-5495	341	8	harmonic	harmonic	ADJ
ejpam-5495	341	9	oscillator	oscillator	NOUN
ejpam-5495	341	10	.	.	PUNCT
ejpam-5495	342	1	computers	computer	NOUN
ejpam-5495	342	2	mathematics	mathematic	NOUN
ejpam-5495	342	3	with	with	ADP
ejpam-5495	342	4	applications	application	NOUN
ejpam-5495	342	5	,	,	PUNCT
ejpam-5495	342	6	58(11	58(11	NUM
ejpam-5495	342	7	-	-	SYM
ejpam-5495	342	8	12):2358––2359	12):2358––2359	NUM
ejpam-5495	342	9	,	,	PUNCT
ejpam-5495	342	10	2009	2009	NUM
ejpam-5495	342	11	.	.	PUNCT
ejpam-5495	343	1	[	[	X
ejpam-5495	343	2	9	9	NUM
ejpam-5495	343	3	]	]	PUNCT
ejpam-5495	343	4	l.	l.	PROPN
ejpam-5495	343	5	cvetićanin	cvetićanin	PROPN
ejpam-5495	343	6	.	.	PUNCT
ejpam-5495	344	1	oscillator	oscillator	NOUN
ejpam-5495	344	2	with	with	ADP
ejpam-5495	344	3	strong	strong	ADJ
ejpam-5495	344	4	quadratic	quadratic	ADJ
ejpam-5495	344	5	damping	damp	VERB
ejpam-5495	344	6	force	force	NOUN
ejpam-5495	344	7	.	.	PUNCT
ejpam-5495	345	1	publications	publication	NOUN
ejpam-5495	345	2	de	de	X
ejpam-5495	345	3	l’institut	l’institut	X
ejpam-5495	345	4	mathématique	mathématique	PROPN
ejpam-5495	345	5	,	,	PUNCT
ejpam-5495	345	6	85(99):119––130	85(99):119––130	NUM
ejpam-5495	345	7	,	,	PUNCT
ejpam-5495	345	8	2009	2009	NUM
ejpam-5495	345	9	.	.	PUNCT
ejpam-5495	346	1	[	[	X
ejpam-5495	346	2	10	10	NUM
ejpam-5495	346	3	]	]	X
ejpam-5495	346	4	m.	m.	NOUN
ejpam-5495	346	5	dehghan	dehghan	PROPN
ejpam-5495	346	6	and	and	CCONJ
ejpam-5495	346	7	a.	a.	NOUN
ejpam-5495	346	8	ghesmati	ghesmati	PROPN
ejpam-5495	346	9	.	.	PUNCT
ejpam-5495	347	1	application	application	NOUN
ejpam-5495	347	2	of	of	ADP
ejpam-5495	347	3	the	the	DET
ejpam-5495	347	4	dual	dual	ADJ
ejpam-5495	347	5	reciprocity	reciprocity	NOUN
ejpam-5495	347	6	boundary	boundary	ADJ
ejpam-5495	347	7	integral	integral	ADJ
ejpam-5495	347	8	equation	equation	NOUN
ejpam-5495	347	9	technique	technique	NOUN
ejpam-5495	347	10	to	to	PART
ejpam-5495	347	11	solve	solve	VERB
ejpam-5495	347	12	the	the	DET
ejpam-5495	347	13	nonlinear	nonlinear	PROPN
ejpam-5495	347	14	klein	klein	PROPN
ejpam-5495	347	15	–	–	PUNCT
ejpam-5495	347	16	gordon	gordon	PROPN
ejpam-5495	347	17	equation	equation	NOUN
ejpam-5495	347	18	.	.	PUNCT
ejpam-5495	348	1	computer	computer	NOUN
ejpam-5495	348	2	physics	physics	NOUN
ejpam-5495	348	3	communications	communication	NOUN
ejpam-5495	348	4	,	,	PUNCT
ejpam-5495	348	5	181(8):1410–1418	181(8):1410–1418	NUM
ejpam-5495	348	6	,	,	PUNCT
ejpam-5495	348	7	2010	2010	NUM
ejpam-5495	348	8	.	.	PUNCT
ejpam-5495	349	1	[	[	X
ejpam-5495	349	2	11	11	NUM
ejpam-5495	349	3	]	]	PUNCT
ejpam-5495	349	4	a.	a.	NOUN
ejpam-5495	349	5	eĺıas	eĺıas	PROPN
ejpam-5495	349	6	-	-	PROPN
ejpam-5495	349	7	zúñiga	zúñiga	NUM
ejpam-5495	349	8	.	.	PUNCT
ejpam-5495	350	1	exact	exact	ADJ
ejpam-5495	350	2	solution	solution	NOUN
ejpam-5495	350	3	of	of	ADP
ejpam-5495	350	4	the	the	DET
ejpam-5495	350	5	cubic	cubic	ADJ
ejpam-5495	350	6	-	-	PUNCT
ejpam-5495	350	7	quintic	quintic	ADJ
ejpam-5495	350	8	duffing	duffing	NOUN
ejpam-5495	350	9	oscillator	oscillator	NOUN
ejpam-5495	350	10	.	.	PUNCT
ejpam-5495	351	1	applied	apply	VERB
ejpam-5495	351	2	mathematical	mathematical	ADJ
ejpam-5495	351	3	modelling	modelling	NOUN
ejpam-5495	351	4	,	,	PUNCT
ejpam-5495	351	5	37(4):2574—-2579	37(4):2574—-2579	NUM
ejpam-5495	351	6	,	,	PUNCT
ejpam-5495	351	7	2013	2013	NUM
ejpam-5495	351	8	.	.	PUNCT
ejpam-5495	352	1	[	[	X
ejpam-5495	352	2	12	12	NUM
ejpam-5495	352	3	]	]	PUNCT
ejpam-5495	353	1	v.s.	v.s.	PROPN
ejpam-5495	353	2	erturk	erturk	PROPN
ejpam-5495	353	3	,	,	PUNCT
ejpam-5495	353	4	b	b	PROPN
ejpam-5495	353	5	rath	rath	PROPN
ejpam-5495	353	6	,	,	PUNCT
ejpam-5495	353	7	t.a	t.a	PROPN
ejpam-5495	353	8	.	.	PROPN
ejpam-5495	353	9	al	al	PROPN
ejpam-5495	353	10	-	-	PUNCT
ejpam-5495	353	11	khader	khader	PROPN
ejpam-5495	353	12	,	,	PUNCT
ejpam-5495	353	13	n.	n.	PROPN
ejpam-5495	353	14	alshaikh	alshaikh	PROPN
ejpam-5495	353	15	,	,	PUNCT
ejpam-5495	353	16	p.	p.	PROPN
ejpam-5495	353	17	mallick	mallick	PROPN
ejpam-5495	353	18	,	,	PUNCT
ejpam-5495	353	19	and	and	CCONJ
ejpam-5495	353	20	j.	j.	PROPN
ejpam-5495	353	21	asad	asad	PROPN
ejpam-5495	353	22	.	.	PUNCT
ejpam-5495	354	1	twoa	twoa	PROPN
ejpam-5495	354	2	.	.	PUNCT
ejpam-5495	355	1	alanazy	alanazy	INTJ
ejpam-5495	355	2	et	et	PROPN
ejpam-5495	355	3	al	al	PROPN
ejpam-5495	355	4	.	.	PUNCT
ejpam-5495	355	5	/	/	SYM
ejpam-5495	355	6	eur	eur	PROPN
ejpam-5495	355	7	.	.	PUNCT
ejpam-5495	356	1	j.	j.	PROPN
ejpam-5495	356	2	pure	pure	PROPN
ejpam-5495	356	3	appl	appl	PROPN
ejpam-5495	356	4	.	.	PROPN
ejpam-5495	356	5	math	math	PROPN
ejpam-5495	356	6	,	,	PUNCT
ejpam-5495	356	7	18	18	NUM
ejpam-5495	356	8	(	(	PUNCT
ejpam-5495	356	9	1	1	NUM
ejpam-5495	356	10	)	)	PUNCT
ejpam-5495	356	11	(	(	PUNCT
ejpam-5495	356	12	2025	2025	NUM
ejpam-5495	356	13	)	)	PUNCT
ejpam-5495	356	14	,	,	PUNCT
ejpam-5495	356	15	5495	5495	NUM
ejpam-5495	356	16	19	19	NUM
ejpam-5495	356	17	of	of	ADP
ejpam-5495	356	18	21	21	NUM
ejpam-5495	356	19	dimensional	dimensional	ADJ
ejpam-5495	356	20	coupled	couple	VERB
ejpam-5495	356	21	asymmetric	asymmetric	ADJ
ejpam-5495	356	22	van	van	PROPN
ejpam-5495	356	23	der	der	PROPN
ejpam-5495	356	24	pol	pol	PROPN
ejpam-5495	356	25	oscillator	oscillator	NOUN
ejpam-5495	356	26	.	.	PUNCT
ejpam-5495	357	1	european	european	PROPN
ejpam-5495	357	2	journal	journal	PROPN
ejpam-5495	357	3	of	of	ADP
ejpam-5495	357	4	pure	pure	ADJ
ejpam-5495	357	5	and	and	CCONJ
ejpam-5495	357	6	applied	applied	ADJ
ejpam-5495	357	7	mathematics	mathematic	NOUN
ejpam-5495	357	8	,	,	PUNCT
ejpam-5495	357	9	17(2):1254–1264	17(2):1254–1264	NUM
ejpam-5495	357	10	,	,	PUNCT
ejpam-5495	357	11	2024	2024	NUM
ejpam-5495	357	12	.	.	PUNCT
ejpam-5495	358	1	[	[	X
ejpam-5495	358	2	13	13	NUM
ejpam-5495	358	3	]	]	X
ejpam-5495	358	4	j.	j.	PROPN
ejpam-5495	358	5	fan	fan	PROPN
ejpam-5495	358	6	.	.	PUNCT
ejpam-5495	359	1	he	he	PRON
ejpam-5495	359	2	’s	’	VERB
ejpam-5495	359	3	frequency	frequency	NOUN
ejpam-5495	359	4	–	–	PUNCT
ejpam-5495	359	5	amplitude	amplitude	NOUN
ejpam-5495	359	6	formulation	formulation	NOUN
ejpam-5495	359	7	for	for	ADP
ejpam-5495	359	8	the	the	DET
ejpam-5495	359	9	duffing	duffing	NOUN
ejpam-5495	359	10	harmonic	harmonic	ADJ
ejpam-5495	359	11	oscillator	oscillator	NOUN
ejpam-5495	359	12	.	.	PUNCT
ejpam-5495	360	1	computers	computer	NOUN
ejpam-5495	360	2	mathematics	mathematic	NOUN
ejpam-5495	360	3	with	with	ADP
ejpam-5495	360	4	applications	application	NOUN
ejpam-5495	360	5	,	,	PUNCT
ejpam-5495	360	6	58(11	58(11	NUM
ejpam-5495	360	7	-	-	SYM
ejpam-5495	360	8	12):2473–2476	12):2473–2476	NUM
ejpam-5495	360	9	,	,	PUNCT
ejpam-5495	360	10	2009	2009	NUM
ejpam-5495	360	11	.	.	PUNCT
ejpam-5495	361	1	[	[	X
ejpam-5495	361	2	14	14	NUM
ejpam-5495	361	3	]	]	X
ejpam-5495	361	4	c.	c.	PROPN
ejpam-5495	361	5	feng	feng	PROPN
ejpam-5495	361	6	and	and	CCONJ
ejpam-5495	361	7	w.	w.	PROPN
ejpam-5495	361	8	zhu	zhu	PROPN
ejpam-5495	361	9	.	.	PUNCT
ejpam-5495	362	1	asymptotic	asymptotic	ADJ
ejpam-5495	362	2	lyapunov	lyapunov	ADJ
ejpam-5495	362	3	stability	stability	NOUN
ejpam-5495	362	4	with	with	ADP
ejpam-5495	362	5	probability	probability	NOUN
ejpam-5495	362	6	one	one	NUM
ejpam-5495	362	7	of	of	ADP
ejpam-5495	362	8	duffing	duffe	VERB
ejpam-5495	362	9	oscillator	oscillator	NOUN
ejpam-5495	362	10	subject	subject	NOUN
ejpam-5495	362	11	to	to	ADP
ejpam-5495	362	12	time	time	NOUN
ejpam-5495	362	13	-	-	PUNCT
ejpam-5495	362	14	delayed	delay	VERB
ejpam-5495	362	15	feedback	feedback	NOUN
ejpam-5495	362	16	control	control	NOUN
ejpam-5495	362	17	and	and	CCONJ
ejpam-5495	362	18	bounded	bounded	ADJ
ejpam-5495	362	19	noise	noise	NOUN
ejpam-5495	362	20	excitation	excitation	NOUN
ejpam-5495	362	21	.	.	PUNCT
ejpam-5495	363	1	acta	acta	PROPN
ejpam-5495	363	2	mechanica	mechanica	PROPN
ejpam-5495	363	3	,	,	PUNCT
ejpam-5495	363	4	208:55—-62	208:55—-62	NOUN
ejpam-5495	363	5	,	,	PUNCT
ejpam-5495	363	6	2009	2009	NUM
ejpam-5495	363	7	.	.	PUNCT
ejpam-5495	364	1	[	[	X
ejpam-5495	364	2	15	15	NUM
ejpam-5495	364	3	]	]	X
ejpam-5495	364	4	a.a	a.a	PROPN
ejpam-5495	364	5	.	.	PROPN
ejpam-5495	364	6	galal	galal	PROPN
ejpam-5495	364	7	.	.	PUNCT
ejpam-5495	365	1	free	free	ADJ
ejpam-5495	365	2	rotation	rotation	NOUN
ejpam-5495	365	3	of	of	ADP
ejpam-5495	365	4	a	a	DET
ejpam-5495	365	5	rigid	rigid	ADJ
ejpam-5495	365	6	mass	mass	NOUN
ejpam-5495	365	7	carrying	carry	VERB
ejpam-5495	365	8	a	a	DET
ejpam-5495	365	9	rotor	rotor	NOUN
ejpam-5495	365	10	with	with	ADP
ejpam-5495	365	11	an	an	DET
ejpam-5495	365	12	internal	internal	ADJ
ejpam-5495	365	13	torque	torque	NOUN
ejpam-5495	365	14	.	.	PUNCT
ejpam-5495	366	1	scientific	scientific	ADJ
ejpam-5495	366	2	reports	report	NOUN
ejpam-5495	366	3	,	,	PUNCT
ejpam-5495	366	4	11:3627–3637	11:3627–3637	NUM
ejpam-5495	366	5	,	,	PUNCT
ejpam-5495	366	6	2023	2023	NUM
ejpam-5495	366	7	.	.	PUNCT
ejpam-5495	367	1	[	[	X
ejpam-5495	367	2	16	16	NUM
ejpam-5495	367	3	]	]	PUNCT
ejpam-5495	367	4	l.	l.	PROPN
ejpam-5495	367	5	geng	geng	PROPN
ejpam-5495	367	6	and	and	CCONJ
ejpam-5495	367	7	x	x	PROPN
ejpam-5495	367	8	-	-	PROPN
ejpam-5495	367	9	c.	c.	PROPN
ejpam-5495	367	10	cai	cai	PROPN
ejpam-5495	367	11	.	.	PUNCT
ejpam-5495	368	1	he	he	PRON
ejpam-5495	368	2	’s	’	VERB
ejpam-5495	368	3	frequency	frequency	NOUN
ejpam-5495	368	4	formulation	formulation	NOUN
ejpam-5495	368	5	for	for	ADP
ejpam-5495	368	6	nonlinear	nonlinear	ADJ
ejpam-5495	368	7	oscillators	oscillator	NOUN
ejpam-5495	368	8	.	.	PUNCT
ejpam-5495	369	1	european	european	ADJ
ejpam-5495	369	2	journal	journal	PROPN
ejpam-5495	369	3	of	of	ADP
ejpam-5495	369	4	physics	physics	PROPN
ejpam-5495	369	5	,	,	PUNCT
ejpam-5495	369	6	28(5):923	28(5):923	NUM
ejpam-5495	369	7	,	,	PUNCT
ejpam-5495	369	8	2007	2007	NUM
ejpam-5495	369	9	.	.	PUNCT
ejpam-5495	370	1	[	[	X
ejpam-5495	370	2	17	17	NUM
ejpam-5495	370	3	]	]	X
ejpam-5495	370	4	y.	y.	PROPN
ejpam-5495	370	5	geng	geng	PROPN
ejpam-5495	370	6	.	.	PUNCT
ejpam-5495	371	1	exact	exact	ADJ
ejpam-5495	371	2	solutions	solution	NOUN
ejpam-5495	371	3	for	for	ADP
ejpam-5495	371	4	the	the	DET
ejpam-5495	371	5	quadratic	quadratic	ADJ
ejpam-5495	371	6	mixed	mix	VERB
ejpam-5495	371	7	-	-	PUNCT
ejpam-5495	371	8	parity	parity	NOUN
ejpam-5495	371	9	helmholtz	helmholtz	NOUN
ejpam-5495	371	10	–	–	PUNCT
ejpam-5495	371	11	duffing	duffing	NOUN
ejpam-5495	371	12	oscillator	oscillator	NOUN
ejpam-5495	371	13	by	by	ADP
ejpam-5495	371	14	bifurcation	bifurcation	NOUN
ejpam-5495	371	15	theory	theory	NOUN
ejpam-5495	371	16	of	of	ADP
ejpam-5495	371	17	dynamical	dynamical	ADJ
ejpam-5495	371	18	systems	system	NOUN
ejpam-5495	371	19	.	.	PUNCT
ejpam-5495	372	1	chaos	chaos	NOUN
ejpam-5495	372	2	,	,	PUNCT
ejpam-5495	372	3	solitons	soliton	NOUN
ejpam-5495	372	4	fractals	fractal	NOUN
ejpam-5495	372	5	,	,	PUNCT
ejpam-5495	372	6	81(a):68—-77	81(a):68—-77	NUM
ejpam-5495	372	7	,	,	PUNCT
ejpam-5495	372	8	2015	2015	NUM
ejpam-5495	372	9	.	.	PUNCT
ejpam-5495	373	1	[	[	X
ejpam-5495	373	2	18	18	NUM
ejpam-5495	373	3	]	]	X
ejpam-5495	373	4	s.	s.	PROPN
ejpam-5495	373	5	ghanem	ghanem	PROPN
ejpam-5495	373	6	,	,	PUNCT
ejpam-5495	373	7	t.s	t.s	PROPN
ejpam-5495	373	8	.	.	PROPN
ejpam-5495	373	9	amer	amer	PROPN
ejpam-5495	373	10	,	,	PUNCT
ejpam-5495	373	11	w.s	w.s	PROPN
ejpam-5495	373	12	.	.	PROPN
ejpam-5495	373	13	amer	amer	PROPN
ejpam-5495	373	14	,	,	PUNCT
ejpam-5495	373	15	s.	s.	PROPN
ejpam-5495	373	16	elnaggar	elnaggar	PROPN
ejpam-5495	373	17	,	,	PUNCT
ejpam-5495	373	18	and	and	CCONJ
ejpam-5495	373	19	a.a	a.a	PROPN
ejpam-5495	373	20	.	.	PROPN
ejpam-5495	373	21	galal	galal	PROPN
ejpam-5495	373	22	.	.	PUNCT
ejpam-5495	374	1	analyzing	analyze	VERB
ejpam-5495	374	2	the	the	DET
ejpam-5495	374	3	motion	motion	NOUN
ejpam-5495	374	4	of	of	ADP
ejpam-5495	374	5	a	a	DET
ejpam-5495	374	6	forced	force	VERB
ejpam-5495	374	7	oscillating	oscillate	VERB
ejpam-5495	374	8	system	system	NOUN
ejpam-5495	374	9	on	on	ADP
ejpam-5495	374	10	the	the	DET
ejpam-5495	374	11	verge	verge	NOUN
ejpam-5495	374	12	of	of	ADP
ejpam-5495	374	13	resonance	resonance	NOUN
ejpam-5495	374	14	.	.	PUNCT
ejpam-5495	375	1	j.	j.	PROPN
ejpam-5495	375	2	low	low	PROPN
ejpam-5495	375	3	freq	freq	PROPN
ejpam-5495	375	4	.	.	PUNCT
ejpam-5495	376	1	noise	noise	PROPN
ejpam-5495	376	2	vib	vib	PROPN
ejpam-5495	376	3	.	.	PROPN
ejpam-5495	376	4	act	act	PROPN
ejpam-5495	376	5	.	.	PUNCT
ejpam-5495	377	1	control	control	NOUN
ejpam-5495	377	2	,	,	PUNCT
ejpam-5495	377	3	42(2):563––578	42(2):563––578	NUM
ejpam-5495	377	4	,	,	PUNCT
ejpam-5495	377	5	2023	2023	NUM
ejpam-5495	377	6	.	.	PUNCT
ejpam-5495	378	1	[	[	X
ejpam-5495	378	2	19	19	NUM
ejpam-5495	378	3	]	]	X
ejpam-5495	378	4	c.	c.	PROPN
ejpam-5495	378	5	hayashi	hayashi	PROPN
ejpam-5495	378	6	.	.	PUNCT
ejpam-5495	379	1	nonlinear	nonlinear	ADJ
ejpam-5495	379	2	oscillations	oscillation	NOUN
ejpam-5495	379	3	in	in	ADP
ejpam-5495	379	4	physical	physical	ADJ
ejpam-5495	379	5	systems	system	NOUN
ejpam-5495	379	6	.	.	PUNCT
ejpam-5495	380	1	mcgraw	mcgraw	PROPN
ejpam-5495	380	2	-	-	PUNCT
ejpam-5495	380	3	hill	hill	PROPN
ejpam-5495	380	4	,	,	PUNCT
ejpam-5495	380	5	page	page	NOUN
ejpam-5495	380	6	392	392	NUM
ejpam-5495	380	7	,	,	PUNCT
ejpam-5495	380	8	new	new	PROPN
ejpam-5495	380	9	york	york	PROPN
ejpam-5495	380	10	,	,	PUNCT
ejpam-5495	380	11	1964	1964	NUM
ejpam-5495	380	12	.	.	PUNCT
ejpam-5495	381	1	[	[	X
ejpam-5495	381	2	20	20	NUM
ejpam-5495	381	3	]	]	SYM
ejpam-5495	381	4	c	c	X
ejpam-5495	381	5	-	-	PUNCT
ejpam-5495	381	6	h.	h.	NOUN
ejpam-5495	381	7	he	he	PROPN
ejpam-5495	381	8	and	and	CCONJ
ejpam-5495	381	9	c.	c.	PROPN
ejpam-5495	381	10	liu	liu	PROPN
ejpam-5495	381	11	.	.	PUNCT
ejpam-5495	382	1	a	a	DET
ejpam-5495	382	2	modified	modify	VERB
ejpam-5495	382	3	frequency	frequency	NOUN
ejpam-5495	382	4	-	-	PUNCT
ejpam-5495	382	5	amplitude	amplitude	NOUN
ejpam-5495	382	6	formulation	formulation	NOUN
ejpam-5495	382	7	for	for	ADP
ejpam-5495	382	8	fractal	fractal	ADJ
ejpam-5495	382	9	vibration	vibration	NOUN
ejpam-5495	382	10	system	system	NOUN
ejpam-5495	382	11	.	.	PUNCT
ejpam-5495	383	1	fractals	fractal	NOUN
ejpam-5495	383	2	,	,	PUNCT
ejpam-5495	383	3	30(03):2250046	30(03):2250046	NUM
ejpam-5495	383	4	,	,	PUNCT
ejpam-5495	383	5	2022	2022	NUM
ejpam-5495	383	6	.	.	PUNCT
ejpam-5495	384	1	[	[	X
ejpam-5495	384	2	21	21	NUM
ejpam-5495	384	3	]	]	X
ejpam-5495	384	4	j	j	PROPN
ejpam-5495	384	5	-	-	PROPN
ejpam-5495	384	6	h.	h.	PROPN
ejpam-5495	384	7	he	he	PRON
ejpam-5495	384	8	.	.	PUNCT
ejpam-5495	385	1	homotopy	homotopy	VERB
ejpam-5495	385	2	perturbation	perturbation	NOUN
ejpam-5495	385	3	technique	technique	NOUN
ejpam-5495	385	4	.	.	PUNCT
ejpam-5495	386	1	computer	computer	NOUN
ejpam-5495	386	2	methods	method	NOUN
ejpam-5495	386	3	in	in	ADP
ejpam-5495	386	4	applied	applied	ADJ
ejpam-5495	386	5	mechanics	mechanic	NOUN
ejpam-5495	386	6	and	and	CCONJ
ejpam-5495	386	7	engineering	engineering	NOUN
ejpam-5495	386	8	,	,	PUNCT
ejpam-5495	386	9	178:257––262	178:257––262	NUM
ejpam-5495	386	10	,	,	PUNCT
ejpam-5495	386	11	1999	1999	NUM
ejpam-5495	386	12	.	.	PUNCT
ejpam-5495	387	1	[	[	X
ejpam-5495	387	2	22	22	NUM
ejpam-5495	387	3	]	]	X
ejpam-5495	387	4	j	j	PROPN
ejpam-5495	387	5	-	-	PROPN
ejpam-5495	387	6	h.	h.	PROPN
ejpam-5495	387	7	he	he	PRON
ejpam-5495	387	8	.	.	PUNCT
ejpam-5495	388	1	some	some	DET
ejpam-5495	388	2	asymptotic	asymptotic	ADJ
ejpam-5495	388	3	methods	method	NOUN
ejpam-5495	388	4	for	for	ADP
ejpam-5495	388	5	strongly	strongly	ADV
ejpam-5495	388	6	nonlinear	nonlinear	ADJ
ejpam-5495	388	7	equations	equation	NOUN
ejpam-5495	388	8	.	.	PUNCT
ejpam-5495	389	1	international	international	ADJ
ejpam-5495	389	2	journal	journal	NOUN
ejpam-5495	389	3	of	of	ADP
ejpam-5495	389	4	modern	modern	ADJ
ejpam-5495	389	5	physics	physics	PROPN
ejpam-5495	389	6	b	b	PROPN
ejpam-5495	389	7	,	,	PUNCT
ejpam-5495	389	8	20:1141–1199	20:1141–1199	NUM
ejpam-5495	389	9	,	,	PUNCT
ejpam-5495	389	10	2006	2006	NUM
ejpam-5495	389	11	.	.	PUNCT
ejpam-5495	390	1	[	[	X
ejpam-5495	390	2	23	23	NUM
ejpam-5495	390	3	]	]	X
ejpam-5495	390	4	j	j	PROPN
ejpam-5495	390	5	-	-	PROPN
ejpam-5495	390	6	h.	h.	PROPN
ejpam-5495	390	7	he	he	PRON
ejpam-5495	390	8	.	.	PUNCT
ejpam-5495	391	1	some	some	DET
ejpam-5495	391	2	asymptotic	asymptotic	ADJ
ejpam-5495	391	3	methods	method	NOUN
ejpam-5495	391	4	for	for	ADP
ejpam-5495	391	5	strongly	strongly	ADV
ejpam-5495	391	6	nonlinear	nonlinear	ADJ
ejpam-5495	391	7	equations	equation	NOUN
ejpam-5495	391	8	.	.	PUNCT
ejpam-5495	392	1	international	international	ADJ
ejpam-5495	392	2	journal	journal	NOUN
ejpam-5495	392	3	of	of	ADP
ejpam-5495	392	4	modern	modern	ADJ
ejpam-5495	392	5	physics	physics	PROPN
ejpam-5495	392	6	b	b	PROPN
ejpam-5495	392	7	,	,	PUNCT
ejpam-5495	392	8	20(10):1141—-1199	20(10):1141—-1199	NUM
ejpam-5495	392	9	,	,	PUNCT
ejpam-5495	392	10	2006	2006	NUM
ejpam-5495	392	11	.	.	PUNCT
ejpam-5495	393	1	[	[	X
ejpam-5495	393	2	24	24	NUM
ejpam-5495	393	3	]	]	X
ejpam-5495	393	4	j	j	PROPN
ejpam-5495	393	5	-	-	PROPN
ejpam-5495	393	6	h.	h.	PROPN
ejpam-5495	393	7	he	he	PRON
ejpam-5495	393	8	.	.	PUNCT
ejpam-5495	394	1	comment	comment	NOUN
ejpam-5495	394	2	on	on	ADP
ejpam-5495	394	3	‘	'	PUNCT
ejpam-5495	394	4	he	he	PRON
ejpam-5495	394	5	’s	’s	PART
ejpam-5495	394	6	frequency	frequency	NOUN
ejpam-5495	394	7	formulation	formulation	NOUN
ejpam-5495	394	8	for	for	ADP
ejpam-5495	394	9	nonlinear	nonlinear	ADJ
ejpam-5495	394	10	oscillators	oscillator	NOUN
ejpam-5495	394	11	.	.	PUNCT
ejpam-5495	395	1	european	european	ADJ
ejpam-5495	395	2	journal	journal	PROPN
ejpam-5495	395	3	of	of	ADP
ejpam-5495	395	4	physics	physics	PROPN
ejpam-5495	395	5	,	,	PUNCT
ejpam-5495	395	6	19(4):l19	19(4):l19	NUM
ejpam-5495	395	7	,	,	PUNCT
ejpam-5495	395	8	2008	2008	NUM
ejpam-5495	395	9	.	.	PUNCT
ejpam-5495	396	1	[	[	X
ejpam-5495	396	2	25	25	NUM
ejpam-5495	396	3	]	]	X
ejpam-5495	396	4	j	j	PROPN
ejpam-5495	396	5	-	-	PROPN
ejpam-5495	396	6	h.	h.	PROPN
ejpam-5495	396	7	he	he	PRON
ejpam-5495	396	8	.	.	PUNCT
ejpam-5495	397	1	an	an	DET
ejpam-5495	397	2	improved	improve	VERB
ejpam-5495	397	3	amplitude	amplitude	NOUN
ejpam-5495	397	4	-	-	PUNCT
ejpam-5495	397	5	frequency	frequency	NOUN
ejpam-5495	397	6	formulation	formulation	NOUN
ejpam-5495	397	7	for	for	ADP
ejpam-5495	397	8	nonlinear	nonlinear	ADJ
ejpam-5495	397	9	oscillators	oscillator	NOUN
ejpam-5495	397	10	.	.	PUNCT
ejpam-5495	398	1	international	international	ADJ
ejpam-5495	398	2	journal	journal	PROPN
ejpam-5495	398	3	of	of	ADP
ejpam-5495	398	4	nonlinear	nonlinear	PROPN
ejpam-5495	398	5	sciences	sciences	PROPN
ejpam-5495	398	6	and	and	CCONJ
ejpam-5495	398	7	numerical	numerical	PROPN
ejpam-5495	398	8	simulation	simulation	PROPN
ejpam-5495	398	9	,	,	PUNCT
ejpam-5495	398	10	9(2):211—212	9(2):211—212	NUM
ejpam-5495	398	11	,	,	PUNCT
ejpam-5495	398	12	2008	2008	NUM
ejpam-5495	398	13	.	.	PUNCT
ejpam-5495	399	1	[	[	X
ejpam-5495	399	2	26	26	NUM
ejpam-5495	399	3	]	]	X
ejpam-5495	399	4	j	j	PROPN
ejpam-5495	399	5	-	-	PROPN
ejpam-5495	399	6	h.	h.	PROPN
ejpam-5495	399	7	he	he	PROPN
ejpam-5495	399	8	.	.	PUNCT
ejpam-5495	400	1	amplitude	amplitude	NOUN
ejpam-5495	400	2	-	-	PUNCT
ejpam-5495	400	3	frequency	frequency	NOUN
ejpam-5495	400	4	relationship	relationship	NOUN
ejpam-5495	400	5	for	for	ADP
ejpam-5495	400	6	conservative	conservative	ADJ
ejpam-5495	400	7	nonlinear	nonlinear	ADJ
ejpam-5495	400	8	oscillators	oscillator	NOUN
ejpam-5495	400	9	with	with	ADP
ejpam-5495	400	10	odd	odd	ADJ
ejpam-5495	400	11	nonlinearities	nonlinearitie	NOUN
ejpam-5495	400	12	.	.	PUNCT
ejpam-5495	401	1	international	international	ADJ
ejpam-5495	401	2	journal	journal	PROPN
ejpam-5495	401	3	of	of	ADP
ejpam-5495	401	4	applied	applied	ADJ
ejpam-5495	401	5	and	and	CCONJ
ejpam-5495	401	6	computational	computational	ADJ
ejpam-5495	401	7	mathematics	mathematic	NOUN
ejpam-5495	401	8	,	,	PUNCT
ejpam-5495	401	9	3:1557–1560	3:1557–1560	PROPN
ejpam-5495	401	10	,	,	PUNCT
ejpam-5495	401	11	2017	2017	NUM
ejpam-5495	401	12	.	.	PUNCT
ejpam-5495	402	1	[	[	X
ejpam-5495	402	2	27	27	NUM
ejpam-5495	402	3	]	]	X
ejpam-5495	402	4	j	j	PROPN
ejpam-5495	402	5	-	-	PROPN
ejpam-5495	402	6	h.	h.	PROPN
ejpam-5495	402	7	he	he	PRON
ejpam-5495	402	8	.	.	PUNCT
ejpam-5495	403	1	the	the	DET
ejpam-5495	403	2	simpler	simple	ADJ
ejpam-5495	403	3	,	,	PUNCT
ejpam-5495	403	4	the	the	PRON
ejpam-5495	403	5	better	well	ADJ
ejpam-5495	403	6	:	:	PUNCT
ejpam-5495	403	7	analytical	analytical	ADJ
ejpam-5495	403	8	methods	method	NOUN
ejpam-5495	403	9	for	for	ADP
ejpam-5495	403	10	nonlinear	nonlinear	ADJ
ejpam-5495	403	11	oscillators	oscillator	NOUN
ejpam-5495	403	12	and	and	CCONJ
ejpam-5495	403	13	fractional	fractional	ADJ
ejpam-5495	403	14	oscillators	oscillator	NOUN
ejpam-5495	403	15	.	.	PUNCT
ejpam-5495	404	1	journal	journal	NOUN
ejpam-5495	404	2	of	of	ADP
ejpam-5495	404	3	low	low	ADJ
ejpam-5495	404	4	frequency	frequency	NOUN
ejpam-5495	404	5	noise	noise	NOUN
ejpam-5495	404	6	,	,	PUNCT
ejpam-5495	404	7	vibration	vibration	NOUN
ejpam-5495	404	8	and	and	CCONJ
ejpam-5495	404	9	active	active	ADJ
ejpam-5495	404	10	control	control	NOUN
ejpam-5495	404	11	,	,	PUNCT
ejpam-5495	404	12	38:1252–1260	38:1252–1260	NUM
ejpam-5495	404	13	,	,	PUNCT
ejpam-5495	404	14	2019	2019	NUM
ejpam-5495	404	15	.	.	PUNCT
ejpam-5495	405	1	[	[	X
ejpam-5495	405	2	28	28	NUM
ejpam-5495	405	3	]	]	X
ejpam-5495	405	4	j	j	PROPN
ejpam-5495	405	5	-	-	PROPN
ejpam-5495	405	6	h.	h.	PROPN
ejpam-5495	405	7	he	he	PROPN
ejpam-5495	405	8	and	and	CCONJ
ejpam-5495	405	9	a.	a.	NOUN
ejpam-5495	405	10	garćıa	garćıa	PROPN
ejpam-5495	405	11	.	.	PUNCT
ejpam-5495	406	1	the	the	DET
ejpam-5495	406	2	simplest	simple	ADJ
ejpam-5495	406	3	amplitude	amplitude	NOUN
ejpam-5495	406	4	-	-	PUNCT
ejpam-5495	406	5	period	period	NOUN
ejpam-5495	406	6	formula	formula	NOUN
ejpam-5495	406	7	for	for	ADP
ejpam-5495	406	8	non	non	ADJ
ejpam-5495	406	9	-	-	ADJ
ejpam-5495	406	10	conservative	conservative	ADJ
ejpam-5495	406	11	oscillators	oscillator	NOUN
ejpam-5495	406	12	.	.	PUNCT
ejpam-5495	407	1	reports	report	NOUN
ejpam-5495	407	2	in	in	ADP
ejpam-5495	407	3	mechanical	mechanical	ADJ
ejpam-5495	407	4	engineering	engineering	NOUN
ejpam-5495	407	5	,	,	PUNCT
ejpam-5495	407	6	2(1):143–148	2(1):143–148	PROPN
ejpam-5495	407	7	,	,	PUNCT
ejpam-5495	407	8	2021	2021	NUM
ejpam-5495	407	9	.	.	PUNCT
ejpam-5495	408	1	[	[	X
ejpam-5495	408	2	29	29	NUM
ejpam-5495	408	3	]	]	SYM
ejpam-5495	408	4	h.y	h.y	PROPN
ejpam-5495	408	5	.	.	PROPN
ejpam-5495	408	6	hu	hu	PROPN
ejpam-5495	408	7	,	,	PUNCT
ejpam-5495	408	8	e.h	e.h	PROPN
ejpam-5495	408	9	.	.	PROPN
ejpam-5495	408	10	dowell	dowell	PROPN
ejpam-5495	408	11	,	,	PUNCT
ejpam-5495	408	12	and	and	CCONJ
ejpam-5495	408	13	l.n	l.n	PROPN
ejpam-5495	408	14	.	.	PROPN
ejpam-5495	408	15	virgin	virgin	PROPN
ejpam-5495	408	16	.	.	PUNCT
ejpam-5495	409	1	resonances	resonance	NOUN
ejpam-5495	409	2	of	of	ADP
ejpam-5495	409	3	a	a	DET
ejpam-5495	409	4	harmonically	harmonically	ADV
ejpam-5495	409	5	forced	force	VERB
ejpam-5495	409	6	duffing	duffing	NOUN
ejpam-5495	409	7	oscillator	oscillator	NOUN
ejpam-5495	409	8	with	with	ADP
ejpam-5495	409	9	time	time	NOUN
ejpam-5495	409	10	delay	delay	NOUN
ejpam-5495	409	11	state	state	NOUN
ejpam-5495	409	12	feedback	feedback	NOUN
ejpam-5495	409	13	.	.	PUNCT
ejpam-5495	410	1	nonlinear	nonlinear	ADJ
ejpam-5495	410	2	dynamics	dynamic	NOUN
ejpam-5495	410	3	,	,	PUNCT
ejpam-5495	410	4	15:311––327	15:311––327	NUM
ejpam-5495	410	5	,	,	PUNCT
ejpam-5495	410	6	1998	1998	NUM
ejpam-5495	410	7	.	.	PUNCT
ejpam-5495	411	1	[	[	X
ejpam-5495	411	2	30	30	NUM
ejpam-5495	411	3	]	]	X
ejpam-5495	411	4	h.y	h.y	PROPN
ejpam-5495	411	5	.	.	PROPN
ejpam-5495	411	6	hu	hu	PROPN
ejpam-5495	411	7	and	and	CCONJ
ejpam-5495	411	8	z.h	z.h	PROPN
ejpam-5495	411	9	.	.	PROPN
ejpam-5495	411	10	wang	wang	PROPN
ejpam-5495	411	11	.	.	PUNCT
ejpam-5495	412	1	dynamics	dynamic	NOUN
ejpam-5495	412	2	of	of	ADP
ejpam-5495	412	3	controlled	control	VERB
ejpam-5495	412	4	mechanical	mechanical	ADJ
ejpam-5495	412	5	systems	system	NOUN
ejpam-5495	412	6	with	with	ADP
ejpam-5495	412	7	delayed	delay	VERB
ejpam-5495	412	8	a.	a.	NOUN
ejpam-5495	412	9	alanazy	alanazy	NOUN
ejpam-5495	412	10	et	et	PROPN
ejpam-5495	412	11	al	al	PROPN
ejpam-5495	412	12	.	.	PUNCT
ejpam-5495	412	13	/	/	SYM
ejpam-5495	412	14	eur	eur	PROPN
ejpam-5495	412	15	.	.	PUNCT
ejpam-5495	413	1	j.	j.	PROPN
ejpam-5495	413	2	pure	pure	PROPN
ejpam-5495	413	3	appl	appl	PROPN
ejpam-5495	413	4	.	.	PROPN
ejpam-5495	413	5	math	math	PROPN
ejpam-5495	413	6	,	,	PUNCT
ejpam-5495	413	7	18	18	NUM
ejpam-5495	413	8	(	(	PUNCT
ejpam-5495	413	9	1	1	NUM
ejpam-5495	413	10	)	)	PUNCT
ejpam-5495	413	11	(	(	PUNCT
ejpam-5495	413	12	2025	2025	NUM
ejpam-5495	413	13	)	)	PUNCT
ejpam-5495	413	14	,	,	PUNCT
ejpam-5495	413	15	5495	5495	NUM
ejpam-5495	413	16	20	20	NUM
ejpam-5495	413	17	of	of	ADP
ejpam-5495	413	18	21	21	NUM
ejpam-5495	413	19	feedback	feedback	NOUN
ejpam-5495	413	20	.	.	PUNCT
ejpam-5495	414	1	springer	springer	NOUN
ejpam-5495	414	2	,	,	PUNCT
ejpam-5495	414	3	berlin	berlin	PROPN
ejpam-5495	414	4	,	,	PUNCT
ejpam-5495	414	5	2002	2002	NUM
ejpam-5495	414	6	.	.	PUNCT
ejpam-5495	415	1	[	[	X
ejpam-5495	415	2	31	31	NUM
ejpam-5495	415	3	]	]	SYM
ejpam-5495	415	4	g.m	g.m	PROPN
ejpam-5495	415	5	.	.	PROPN
ejpam-5495	415	6	ismail	ismail	PROPN
ejpam-5495	415	7	,	,	PUNCT
ejpam-5495	415	8	g.m	g.m	PROPN
ejpam-5495	415	9	.	.	PROPN
ejpam-5495	415	10	moatimid	moatimid	PROPN
ejpam-5495	415	11	,	,	PUNCT
ejpam-5495	415	12	and	and	CCONJ
ejpam-5495	415	13	m.i	m.i	PROPN
ejpam-5495	415	14	.	.	PROPN
ejpam-5495	415	15	yamani	yamani	PROPN
ejpam-5495	415	16	.	.	PUNCT
ejpam-5495	416	1	periodic	periodic	ADJ
ejpam-5495	416	2	solutions	solution	NOUN
ejpam-5495	416	3	of	of	ADP
ejpam-5495	416	4	strongly	strongly	ADV
ejpam-5495	416	5	nonlinear	nonlinear	ADJ
ejpam-5495	416	6	oscillators	oscillator	NOUN
ejpam-5495	416	7	3	3	NUM
ejpam-5495	416	8	using	use	VERB
ejpam-5495	416	9	he	he	PRON
ejpam-5495	416	10	’s	’s	PART
ejpam-5495	416	11	frequency	frequency	NOUN
ejpam-5495	416	12	formulation	formulation	NOUN
ejpam-5495	416	13	.	.	PUNCT
ejpam-5495	417	1	european	european	ADJ
ejpam-5495	417	2	journal	journal	PROPN
ejpam-5495	417	3	of	of	ADP
ejpam-5495	417	4	pure	pure	ADJ
ejpam-5495	417	5	and	and	CCONJ
ejpam-5495	417	6	applied	applied	ADJ
ejpam-5495	417	7	mathematics	mathematic	NOUN
ejpam-5495	417	8	,	,	PUNCT
ejpam-5495	417	9	17(3):2154–2171	17(3):2154–2171	NUM
ejpam-5495	417	10	,	,	PUNCT
ejpam-5495	417	11	2024	2024	NUM
ejpam-5495	417	12	.	.	PUNCT
ejpam-5495	418	1	[	[	X
ejpam-5495	418	2	32	32	NUM
ejpam-5495	418	3	]	]	PUNCT
ejpam-5495	418	4	g.	g.	PROPN
ejpam-5495	418	5	janevski	janevski	PROPN
ejpam-5495	418	6	,	,	PUNCT
ejpam-5495	418	7	p.	p.	PROPN
ejpam-5495	418	8	kozic	kozic	PROPN
ejpam-5495	418	9	,	,	PUNCT
ejpam-5495	418	10	r.	r.	PROPN
ejpam-5495	418	11	pavlovic	pavlovic	PROPN
ejpam-5495	418	12	,	,	PUNCT
ejpam-5495	418	13	and	and	CCONJ
ejpam-5495	418	14	s.	s.	PROPN
ejpam-5495	418	15	posavljak	posavljak	PROPN
ejpam-5495	418	16	.	.	PUNCT
ejpam-5495	419	1	moment	moment	NOUN
ejpam-5495	419	2	lyapunov	lyapunov	PROPN
ejpam-5495	419	3	exponents	exponent	NOUN
ejpam-5495	419	4	and	and	CCONJ
ejpam-5495	419	5	stochastic	stochastic	ADJ
ejpam-5495	419	6	stability	stability	NOUN
ejpam-5495	419	7	of	of	ADP
ejpam-5495	419	8	a	a	DET
ejpam-5495	419	9	thin	thin	ADJ
ejpam-5495	419	10	-	-	PUNCT
ejpam-5495	419	11	walled	walled	ADJ
ejpam-5495	419	12	beam	beam	NOUN
ejpam-5495	419	13	subjected	subject	VERB
ejpam-5495	419	14	to	to	ADP
ejpam-5495	419	15	axial	axial	ADJ
ejpam-5495	419	16	loads	load	NOUN
ejpam-5495	419	17	and	and	CCONJ
ejpam-5495	419	18	end	end	VERB
ejpam-5495	419	19	moments	moment	NOUN
ejpam-5495	419	20	.	.	PUNCT
ejpam-5495	420	1	facta	facta	PROPN
ejpam-5495	420	2	universitatis	universitatis	PROPN
ejpam-5495	420	3	,	,	PUNCT
ejpam-5495	420	4	series	series	NOUN
ejpam-5495	420	5	:	:	PUNCT
ejpam-5495	420	6	mechanical	mechanical	ADJ
ejpam-5495	420	7	engineering	engineering	NOUN
ejpam-5495	420	8	,	,	PUNCT
ejpam-5495	420	9	19:209—-228	19:209—-228	NUM
ejpam-5495	420	10	,	,	PUNCT
ejpam-5495	420	11	2021	2021	NUM
ejpam-5495	420	12	.	.	PUNCT
ejpam-5495	421	1	[	[	X
ejpam-5495	421	2	33	33	NUM
ejpam-5495	421	3	]	]	X
ejpam-5495	421	4	j.c	j.c	PROPN
ejpam-5495	421	5	.	.	PROPN
ejpam-5495	421	6	ji	ji	PROPN
ejpam-5495	421	7	and	and	CCONJ
ejpam-5495	421	8	c.h	c.h	PROPN
ejpam-5495	422	1	.	.	PROPN
ejpam-5495	422	2	hansen	hansen	PROPN
ejpam-5495	422	3	.	.	PROPN
ejpam-5495	423	1	stability	stability	NOUN
ejpam-5495	423	2	and	and	CCONJ
ejpam-5495	423	3	dynamics	dynamic	NOUN
ejpam-5495	423	4	of	of	ADP
ejpam-5495	423	5	a	a	DET
ejpam-5495	423	6	controlled	control	VERB
ejpam-5495	423	7	van	van	PROPN
ejpam-5495	423	8	der	der	PROPN
ejpam-5495	423	9	pol	pol	PROPN
ejpam-5495	423	10	–	–	PUNCT
ejpam-5495	423	11	duffing	duffe	VERB
ejpam-5495	423	12	oscillator	oscillator	NOUN
ejpam-5495	423	13	.	.	PUNCT
ejpam-5495	424	1	chaos	chaos	NOUN
ejpam-5495	424	2	,	,	PUNCT
ejpam-5495	424	3	solitons	soliton	NOUN
ejpam-5495	424	4	and	and	CCONJ
ejpam-5495	424	5	fractals	fractal	NOUN
ejpam-5495	424	6	,	,	PUNCT
ejpam-5495	424	7	28(2):555—-570	28(2):555—-570	NOUN
ejpam-5495	424	8	,	,	PUNCT
ejpam-5495	424	9	2006	2006	NUM
ejpam-5495	424	10	.	.	PUNCT
ejpam-5495	425	1	[	[	X
ejpam-5495	425	2	34	34	NUM
ejpam-5495	425	3	]	]	X
ejpam-5495	425	4	j.c	j.c	PROPN
ejpam-5495	425	5	.	.	PROPN
ejpam-5495	425	6	ji	ji	PROPN
ejpam-5495	425	7	,	,	PUNCT
ejpam-5495	425	8	n.	n.	PROPN
ejpam-5495	425	9	zhang	zhang	PROPN
ejpam-5495	425	10	,	,	PUNCT
ejpam-5495	425	11	and	and	CCONJ
ejpam-5495	425	12	w.	w.	PROPN
ejpam-5495	425	13	gao	gao	PROPN
ejpam-5495	425	14	.	.	PUNCT
ejpam-5495	425	15	difference	difference	NOUN
ejpam-5495	425	16	resonances	resonance	NOUN
ejpam-5495	425	17	in	in	ADP
ejpam-5495	425	18	a	a	DET
ejpam-5495	425	19	controlled	control	VERB
ejpam-5495	425	20	van	van	PROPN
ejpam-5495	425	21	der	der	NOUN
ejpam-5495	425	22	polduffing	polduffing	NOUN
ejpam-5495	425	23	oscillator	oscillator	NOUN
ejpam-5495	425	24	involving	involve	VERB
ejpam-5495	425	25	time	time	NOUN
ejpam-5495	425	26	delay	delay	NOUN
ejpam-5495	425	27	.	.	PUNCT
ejpam-5495	426	1	chaos	chaos	NOUN
ejpam-5495	426	2	,	,	PUNCT
ejpam-5495	426	3	42(2):975–980	42(2):975–980	PROPN
ejpam-5495	426	4	,	,	PUNCT
ejpam-5495	426	5	2009	2009	NUM
ejpam-5495	426	6	.	.	PUNCT
ejpam-5495	427	1	[	[	X
ejpam-5495	427	2	35	35	NUM
ejpam-5495	427	3	]	]	X
ejpam-5495	427	4	w.m	w.m	PROPN
ejpam-5495	427	5	.	.	PUNCT
ejpam-5495	427	6	ji	ji	PROPN
ejpam-5495	427	7	,	,	PUNCT
ejpam-5495	427	8	h.	h.	PROPN
ejpam-5495	427	9	wang	wang	PROPN
ejpam-5495	427	10	,	,	PUNCT
ejpam-5495	427	11	and	and	CCONJ
ejpam-5495	427	12	m.	m.	PROPN
ejpam-5495	427	13	liu	liu	PROPN
ejpam-5495	427	14	.	.	PUNCT
ejpam-5495	428	1	dynamics	dynamic	VERB
ejpam-5495	428	2	analysis	analysis	NOUN
ejpam-5495	428	3	of	of	ADP
ejpam-5495	428	4	an	an	DET
ejpam-5495	428	5	impulsive	impulsive	ADJ
ejpam-5495	428	6	stochastic	stochastic	ADJ
ejpam-5495	428	7	model	model	NOUN
ejpam-5495	428	8	for	for	ADP
ejpam-5495	428	9	spruce	spruce	NOUN
ejpam-5495	428	10	budworm	budworm	NOUN
ejpam-5495	428	11	growth	growth	NOUN
ejpam-5495	428	12	.	.	PUNCT
ejpam-5495	429	1	applied	apply	VERB
ejpam-5495	429	2	and	and	CCONJ
ejpam-5495	429	3	computational	computational	ADJ
ejpam-5495	429	4	mathematics	mathematic	NOUN
ejpam-5495	429	5	,	,	PUNCT
ejpam-5495	429	6	19:336—-359	19:336—-359	NUM
ejpam-5495	429	7	,	,	PUNCT
ejpam-5495	429	8	2021	2021	NUM
ejpam-5495	429	9	.	.	PUNCT
ejpam-5495	430	1	[	[	X
ejpam-5495	430	2	36	36	NUM
ejpam-5495	430	3	]	]	X
ejpam-5495	430	4	x.y	x.y	PROPN
ejpam-5495	430	5	.	.	PROPN
ejpam-5495	430	6	li	li	PROPN
ejpam-5495	430	7	,	,	PUNCT
ejpam-5495	430	8	j.c	j.c	PROPN
ejpam-5495	430	9	.	.	PROPN
ejpam-5495	430	10	ji	ji	PROPN
ejpam-5495	430	11	,	,	PUNCT
ejpam-5495	430	12	c.h	c.h	PROPN
ejpam-5495	430	13	.	.	PROPN
ejpam-5495	430	14	hansen	hansen	PROPN
ejpam-5495	430	15	,	,	PUNCT
ejpam-5495	430	16	and	and	CCONJ
ejpam-5495	430	17	c.x	c.x	PROPN
ejpam-5495	430	18	.	.	PROPN
ejpam-5495	430	19	tan	tan	PROPN
ejpam-5495	430	20	.	.	PUNCT
ejpam-5495	431	1	the	the	DET
ejpam-5495	431	2	response	response	NOUN
ejpam-5495	431	3	of	of	ADP
ejpam-5495	431	4	a	a	DET
ejpam-5495	431	5	duffing	duffing	NOUN
ejpam-5495	431	6	-	-	PUNCT
ejpam-5495	431	7	van	van	PROPN
ejpam-5495	431	8	der	der	ADJ
ejpam-5495	431	9	pol	pol	PROPN
ejpam-5495	431	10	oscillator	oscillator	NOUN
ejpam-5495	431	11	under	under	ADP
ejpam-5495	431	12	delayed	delay	VERB
ejpam-5495	431	13	feedback	feedback	NOUN
ejpam-5495	431	14	control	control	NOUN
ejpam-5495	431	15	.	.	PUNCT
ejpam-5495	432	1	journal	journal	PROPN
ejpam-5495	432	2	of	of	ADP
ejpam-5495	432	3	sound	sound	NOUN
ejpam-5495	432	4	and	and	CCONJ
ejpam-5495	432	5	vibration	vibration	NOUN
ejpam-5495	432	6	,	,	PUNCT
ejpam-5495	432	7	291:644–655	291:644–655	NUM
ejpam-5495	432	8	,	,	PUNCT
ejpam-5495	432	9	2006	2006	NUM
ejpam-5495	432	10	.	.	PUNCT
ejpam-5495	433	1	[	[	X
ejpam-5495	433	2	37	37	NUM
ejpam-5495	433	3	]	]	PUNCT
ejpam-5495	433	4	x.	x.	NOUN
ejpam-5495	433	5	lia	lia	PROPN
ejpam-5495	433	6	,	,	PUNCT
ejpam-5495	433	7	h.	h.	PROPN
ejpam-5495	433	8	zhang	zhang	PROPN
ejpam-5495	433	9	,	,	PUNCT
ejpam-5495	433	10	and	and	CCONJ
ejpam-5495	433	11	l.	l.	PROPN
ejpam-5495	433	12	zhanga	zhanga	PROPN
ejpam-5495	433	13	.	.	PUNCT
ejpam-5495	434	1	response	response	NOUN
ejpam-5495	434	2	of	of	ADP
ejpam-5495	434	3	the	the	DET
ejpam-5495	434	4	duffing	duffing	NOUN
ejpam-5495	434	5	-	-	PUNCT
ejpam-5495	434	6	van	van	PROPN
ejpam-5495	434	7	der	der	ADJ
ejpam-5495	434	8	pol	pol	PROPN
ejpam-5495	434	9	oscillator	oscillator	NOUN
ejpam-5495	434	10	under	under	ADP
ejpam-5495	434	11	position	position	NOUN
ejpam-5495	434	12	feedback	feedback	NOUN
ejpam-5495	434	13	control	control	NOUN
ejpam-5495	434	14	with	with	ADP
ejpam-5495	434	15	two	two	NUM
ejpam-5495	434	16	-	-	PUNCT
ejpam-5495	434	17	time	time	NOUN
ejpam-5495	434	18	delays	delay	NOUN
ejpam-5495	434	19	.	.	PUNCT
ejpam-5495	435	1	shock	shock	NOUN
ejpam-5495	435	2	and	and	CCONJ
ejpam-5495	435	3	vibration	vibration	NOUN
ejpam-5495	435	4	,	,	PUNCT
ejpam-5495	435	5	18:377–386	18:377–386	NUM
ejpam-5495	435	6	,	,	PUNCT
ejpam-5495	435	7	2011	2011	NUM
ejpam-5495	435	8	.	.	PUNCT
ejpam-5495	436	1	[	[	X
ejpam-5495	436	2	38	38	NUM
ejpam-5495	436	3	]	]	SYM
ejpam-5495	436	4	g.m	g.m	PROPN
ejpam-5495	436	5	.	.	PROPN
ejpam-5495	436	6	moatimid	moatimid	PROPN
ejpam-5495	436	7	and	and	CCONJ
ejpam-5495	436	8	t.s	t.s	PROPN
ejpam-5495	436	9	.	.	PROPN
ejpam-5495	436	10	amer	amer	PROPN
ejpam-5495	436	11	.	.	PUNCT
ejpam-5495	437	1	analytical	analytical	ADJ
ejpam-5495	437	2	solution	solution	NOUN
ejpam-5495	437	3	for	for	ADP
ejpam-5495	437	4	the	the	DET
ejpam-5495	437	5	motion	motion	NOUN
ejpam-5495	437	6	of	of	ADP
ejpam-5495	437	7	a	a	DET
ejpam-5495	437	8	pendulum	pendulum	NOUN
ejpam-5495	437	9	with	with	ADP
ejpam-5495	437	10	rolling	rolling	ADJ
ejpam-5495	437	11	wheel	wheel	NOUN
ejpam-5495	437	12	:	:	PUNCT
ejpam-5495	437	13	stability	stability	NOUN
ejpam-5495	437	14	analysis	analysis	NOUN
ejpam-5495	437	15	.	.	PUNCT
ejpam-5495	438	1	scientific	scientific	ADJ
ejpam-5495	438	2	reports	report	NOUN
ejpam-5495	438	3	,	,	PUNCT
ejpam-5495	438	4	12:12628	12:12628	NUM
ejpam-5495	438	5	,	,	PUNCT
ejpam-5495	438	6	2022	2022	NUM
ejpam-5495	438	7	.	.	PUNCT
ejpam-5495	439	1	[	[	X
ejpam-5495	439	2	39	39	NUM
ejpam-5495	439	3	]	]	SYM
ejpam-5495	439	4	g.m	g.m	PROPN
ejpam-5495	439	5	.	.	PROPN
ejpam-5495	439	6	moatimid	moatimid	PROPN
ejpam-5495	439	7	and	and	CCONJ
ejpam-5495	439	8	t.s	t.s	PROPN
ejpam-5495	439	9	.	.	PROPN
ejpam-5495	439	10	amer	amer	PROPN
ejpam-5495	439	11	.	.	PUNCT
ejpam-5495	439	12	analytical	analytical	ADJ
ejpam-5495	439	13	approximate	approximate	ADJ
ejpam-5495	439	14	solutions	solution	NOUN
ejpam-5495	439	15	of	of	ADP
ejpam-5495	439	16	a	a	DET
ejpam-5495	439	17	magnetic	magnetic	ADJ
ejpam-5495	439	18	spherical	spherical	ADJ
ejpam-5495	439	19	pendulum	pendulum	NOUN
ejpam-5495	439	20	:	:	PUNCT
ejpam-5495	439	21	stability	stability	NOUN
ejpam-5495	439	22	analysis	analysis	NOUN
ejpam-5495	439	23	.	.	PUNCT
ejpam-5495	440	1	j.	j.	PROPN
ejpam-5495	440	2	vib	vib	PROPN
ejpam-5495	440	3	.	.	PUNCT
ejpam-5495	441	1	eng	eng	PROPN
ejpam-5495	441	2	.	.	PROPN
ejpam-5495	441	3	technol	technol	PROPN
ejpam-5495	441	4	.	.	PROPN
ejpam-5495	441	5	,	,	PUNCT
ejpam-5495	441	6	11:2155–2165	11:2155–2165	NUM
ejpam-5495	441	7	,	,	PUNCT
ejpam-5495	441	8	2023	2023	NUM
ejpam-5495	441	9	.	.	PUNCT
ejpam-5495	442	1	[	[	X
ejpam-5495	442	2	40	40	NUM
ejpam-5495	442	3	]	]	X
ejpam-5495	442	4	g.m	g.m	PROPN
ejpam-5495	442	5	.	.	PROPN
ejpam-5495	443	1	moatimid	moatimid	PROPN
ejpam-5495	443	2	,	,	PUNCT
ejpam-5495	443	3	t.s	t.s	PROPN
ejpam-5495	443	4	.	.	PROPN
ejpam-5495	443	5	amer	amer	PROPN
ejpam-5495	443	6	,	,	PUNCT
ejpam-5495	443	7	and	and	CCONJ
ejpam-5495	443	8	w.s	w.s	PROPN
ejpam-5495	443	9	.	.	PROPN
ejpam-5495	443	10	amer	amer	PROPN
ejpam-5495	443	11	.	.	PUNCT
ejpam-5495	444	1	dynamical	dynamical	ADJ
ejpam-5495	444	2	analysis	analysis	NOUN
ejpam-5495	444	3	of	of	ADP
ejpam-5495	444	4	a	a	DET
ejpam-5495	444	5	damped	damped	ADJ
ejpam-5495	444	6	harmonic	harmonic	NOUN
ejpam-5495	444	7	forced	force	VERB
ejpam-5495	444	8	duffing	duffe	VERB
ejpam-5495	444	9	oscillator	oscillator	NOUN
ejpam-5495	444	10	with	with	ADP
ejpam-5495	444	11	time	time	NOUN
ejpam-5495	444	12	delay	delay	NOUN
ejpam-5495	444	13	.	.	PUNCT
ejpam-5495	445	1	scientific	scientific	ADJ
ejpam-5495	445	2	reports	report	NOUN
ejpam-5495	445	3	,	,	PUNCT
ejpam-5495	445	4	13:6507	13:6507	NUM
ejpam-5495	445	5	,	,	PUNCT
ejpam-5495	445	6	2023	2023	NUM
ejpam-5495	445	7	.	.	PUNCT
ejpam-5495	446	1	[	[	X
ejpam-5495	446	2	41	41	NUM
ejpam-5495	446	3	]	]	X
ejpam-5495	446	4	g.m	g.m	PROPN
ejpam-5495	446	5	.	.	PROPN
ejpam-5495	447	1	moatimid	moatimid	PROPN
ejpam-5495	447	2	,	,	PUNCT
ejpam-5495	447	3	t.s	t.s	PROPN
ejpam-5495	447	4	.	.	PROPN
ejpam-5495	447	5	amer	amer	PROPN
ejpam-5495	447	6	,	,	PUNCT
ejpam-5495	447	7	and	and	CCONJ
ejpam-5495	447	8	y.y	y.y	PROPN
ejpam-5495	447	9	.	.	PROPN
ejpam-5495	447	10	ellabban	ellabban	PROPN
ejpam-5495	447	11	.	.	PUNCT
ejpam-5495	448	1	a	a	DET
ejpam-5495	448	2	novel	novel	ADJ
ejpam-5495	448	3	methodology	methodology	NOUN
ejpam-5495	448	4	for	for	ADP
ejpam-5495	448	5	a	a	DET
ejpam-5495	448	6	timedelayed	timedelayed	ADJ
ejpam-5495	448	7	controller	controller	NOUN
ejpam-5495	448	8	to	to	PART
ejpam-5495	448	9	prevent	prevent	VERB
ejpam-5495	448	10	nonlinear	nonlinear	ADJ
ejpam-5495	448	11	system	system	NOUN
ejpam-5495	448	12	oscillations	oscillation	NOUN
ejpam-5495	448	13	.	.	PUNCT
ejpam-5495	449	1	journal	journal	NOUN
ejpam-5495	449	2	of	of	ADP
ejpam-5495	449	3	low	low	ADJ
ejpam-5495	449	4	frequency	frequency	NOUN
ejpam-5495	449	5	noise	noise	NOUN
ejpam-5495	449	6	,	,	PUNCT
ejpam-5495	449	7	vibration	vibration	NOUN
ejpam-5495	449	8	and	and	CCONJ
ejpam-5495	449	9	active	active	ADJ
ejpam-5495	449	10	control	control	NOUN
ejpam-5495	449	11	,	,	PUNCT
ejpam-5495	449	12	43(1):525–542	43(1):525–542	PROPN
ejpam-5495	449	13	,	,	PUNCT
ejpam-5495	449	14	2024	2024	NUM
ejpam-5495	449	15	.	.	PUNCT
ejpam-5495	450	1	[	[	X
ejpam-5495	450	2	42	42	NUM
ejpam-5495	450	3	]	]	X
ejpam-5495	450	4	g.m	g.m	PROPN
ejpam-5495	450	5	.	.	PROPN
ejpam-5495	450	6	moatimid	moatimid	PROPN
ejpam-5495	450	7	,	,	PUNCT
ejpam-5495	450	8	t.s	t.s	PROPN
ejpam-5495	450	9	.	.	PROPN
ejpam-5495	450	10	amer	amer	PROPN
ejpam-5495	450	11	,	,	PUNCT
ejpam-5495	450	12	and	and	CCONJ
ejpam-5495	450	13	a.a	a.a	PROPN
ejpam-5495	450	14	.	.	PROPN
ejpam-5495	450	15	galal	galal	PROPN
ejpam-5495	450	16	.	.	PUNCT
ejpam-5495	451	1	studying	study	VERB
ejpam-5495	451	2	highly	highly	ADV
ejpam-5495	451	3	nonlinear	nonlinear	ADJ
ejpam-5495	451	4	oscillators	oscillator	NOUN
ejpam-5495	451	5	using	use	VERB
ejpam-5495	451	6	the	the	DET
ejpam-5495	451	7	non	non	ADJ
ejpam-5495	451	8	-	-	ADJ
ejpam-5495	451	9	perturbative	perturbative	ADJ
ejpam-5495	451	10	methodology	methodology	NOUN
ejpam-5495	451	11	.	.	PUNCT
ejpam-5495	452	1	scientific	scientific	ADJ
ejpam-5495	452	2	reports	report	NOUN
ejpam-5495	452	3	,	,	PUNCT
ejpam-5495	452	4	13:20288	13:20288	NUM
ejpam-5495	452	5	,	,	PUNCT
ejpam-5495	452	6	2023	2023	NUM
ejpam-5495	452	7	.	.	PUNCT
ejpam-5495	453	1	[	[	X
ejpam-5495	453	2	43	43	NUM
ejpam-5495	453	3	]	]	X
ejpam-5495	453	4	g.m	g.m	PROPN
ejpam-5495	453	5	.	.	PROPN
ejpam-5495	454	1	moatimid	moatimid	PROPN
ejpam-5495	454	2	,	,	PUNCT
ejpam-5495	454	3	t.s	t.s	PROPN
ejpam-5495	454	4	.	.	PROPN
ejpam-5495	454	5	amer	amer	PROPN
ejpam-5495	454	6	,	,	PUNCT
ejpam-5495	454	7	and	and	CCONJ
ejpam-5495	454	8	a.a	a.a	PROPN
ejpam-5495	454	9	.	.	PROPN
ejpam-5495	454	10	galal	galal	PROPN
ejpam-5495	454	11	.	.	PUNCT
ejpam-5495	455	1	inspection	inspection	NOUN
ejpam-5495	455	2	of	of	ADP
ejpam-5495	455	3	some	some	DET
ejpam-5495	455	4	extremely	extremely	ADV
ejpam-5495	455	5	nonlinear	nonlinear	ADJ
ejpam-5495	455	6	oscillators	oscillator	NOUN
ejpam-5495	455	7	using	use	VERB
ejpam-5495	455	8	an	an	DET
ejpam-5495	455	9	inventive	inventive	ADJ
ejpam-5495	455	10	approach	approach	NOUN
ejpam-5495	455	11	.	.	PUNCT
ejpam-5495	456	1	j.	j.	PROPN
ejpam-5495	456	2	vib	vib	PROPN
ejpam-5495	456	3	.	.	PUNCT
ejpam-5495	457	1	eng	eng	PROPN
ejpam-5495	457	2	.	.	PROPN
ejpam-5495	457	3	technol	technol	PROPN
ejpam-5495	457	4	.	.	PROPN
ejpam-5495	457	5	,	,	PUNCT
ejpam-5495	457	6	2024	2024	NUM
ejpam-5495	457	7	,	,	PUNCT
ejpam-5495	457	8	https://doi.org/10.1007/s42417-024-01469-y	https://doi.org/10.1007/s42417-024-01469-y	PROPN
ejpam-5495	457	9	.	.	PUNCT
ejpam-5495	458	1	[	[	X
ejpam-5495	458	2	44	44	NUM
ejpam-5495	458	3	]	]	SYM
ejpam-5495	458	4	g.m	g.m	PROPN
ejpam-5495	458	5	.	.	PROPN
ejpam-5495	458	6	moatimid	moatimid	PROPN
ejpam-5495	458	7	,	,	PUNCT
ejpam-5495	458	8	m.a.a	m.a.a	PROPN
ejpam-5495	458	9	.	.	PUNCT
ejpam-5495	459	1	mohamed	mohamed	PROPN
ejpam-5495	459	2	,	,	PUNCT
ejpam-5495	459	3	and	and	CCONJ
ejpam-5495	459	4	kh	kh	PROPN
ejpam-5495	459	5	.	.	PROPN
ejpam-5495	459	6	elagamy	elagamy	PROPN
ejpam-5495	459	7	.	.	PUNCT
ejpam-5495	460	1	an	an	DET
ejpam-5495	460	2	innovative	innovative	ADJ
ejpam-5495	460	3	approach	approach	NOUN
ejpam-5495	460	4	in	in	ADP
ejpam-5495	460	5	inspecting	inspect	VERB
ejpam-5495	460	6	a	a	DET
ejpam-5495	460	7	damped	damp	VERB
ejpam-5495	460	8	mathieu	mathieu	PROPN
ejpam-5495	460	9	cubic	cubic	ADJ
ejpam-5495	460	10	–	–	PUNCT
ejpam-5495	460	11	quintic	quintic	ADJ
ejpam-5495	460	12	duffing	duffing	NOUN
ejpam-5495	460	13	oscillator	oscillator	NOUN
ejpam-5495	460	14	.	.	PUNCT
ejpam-5495	461	1	j.	j.	PROPN
ejpam-5495	461	2	vib	vib	PROPN
ejpam-5495	461	3	.	.	PUNCT
ejpam-5495	462	1	eng	eng	PROPN
ejpam-5495	462	2	.	.	PROPN
ejpam-5495	462	3	technol	technol	PROPN
ejpam-5495	462	4	.	.	PROPN
ejpam-5495	462	5	,	,	PUNCT
ejpam-5495	462	6	2024	2024	NUM
ejpam-5495	462	7	,	,	PUNCT
ejpam-5495	462	8	https://doi.org/10.1007/s42417-024-01506-w	https://doi.org/10.1007/s42417-024-01506-w	NOUN
ejpam-5495	462	9	.	.	PUNCT
ejpam-5495	463	1	[	[	X
ejpam-5495	463	2	45	45	NUM
ejpam-5495	463	3	]	]	X
ejpam-5495	463	4	a.h	a.h	PROPN
ejpam-5495	463	5	.	.	PROPN
ejpam-5495	463	6	nayfeh	nayfeh	PROPN
ejpam-5495	463	7	and	and	CCONJ
ejpam-5495	463	8	d.t	d.t	PROPN
ejpam-5495	463	9	.	.	PROPN
ejpam-5495	463	10	mook	mook	PROPN
ejpam-5495	463	11	.	.	PUNCT
ejpam-5495	464	1	nonlinear	nonlinear	ADJ
ejpam-5495	464	2	oscillations	oscillation	NOUN
ejpam-5495	464	3	.	.	PUNCT
ejpam-5495	465	1	wiley	wiley	PROPN
ejpam-5495	465	2	,	,	PUNCT
ejpam-5495	465	3	new	new	PROPN
ejpam-5495	465	4	york	york	PROPN
ejpam-5495	465	5	,	,	PUNCT
ejpam-5495	465	6	1979	1979	NUM
ejpam-5495	465	7	.	.	PUNCT
ejpam-5495	466	1	[	[	X
ejpam-5495	466	2	46	46	NUM
ejpam-5495	466	3	]	]	X
ejpam-5495	466	4	n.	n.	PROPN
ejpam-5495	466	5	qie	qie	PROPN
ejpam-5495	466	6	,	,	PUNCT
ejpam-5495	466	7	w.f	w.f	PROPN
ejpam-5495	466	8	.	.	PROPN
ejpam-5495	466	9	hou	hou	PROPN
ejpam-5495	466	10	,	,	PUNCT
ejpam-5495	466	11	and	and	CCONJ
ejpam-5495	466	12	j	j	PROPN
ejpam-5495	466	13	-	-	PROPN
ejpam-5495	466	14	h.	h.	PROPN
ejpam-5495	466	15	he	he	PRON
ejpam-5495	466	16	.	.	PUNCT
ejpam-5495	467	1	the	the	DET
ejpam-5495	467	2	fastest	fast	ADJ
ejpam-5495	467	3	insight	insight	NOUN
ejpam-5495	467	4	into	into	ADP
ejpam-5495	467	5	the	the	DET
ejpam-5495	467	6	large	large	ADJ
ejpam-5495	467	7	amplitude	amplitude	NOUN
ejpam-5495	467	8	vibration	vibration	NOUN
ejpam-5495	467	9	of	of	ADP
ejpam-5495	467	10	a	a	DET
ejpam-5495	467	11	string	string	NOUN
ejpam-5495	467	12	.	.	PUNCT
ejpam-5495	468	1	reports	report	NOUN
ejpam-5495	468	2	in	in	ADP
ejpam-5495	468	3	mechanical	mechanical	ADJ
ejpam-5495	468	4	engineering	engineering	NOUN
ejpam-5495	468	5	,	,	PUNCT
ejpam-5495	468	6	2:1–5	2:1–5	NUM
ejpam-5495	468	7	,	,	PUNCT
ejpam-5495	468	8	2020	2020	NUM
ejpam-5495	468	9	.	.	PUNCT
ejpam-5495	469	1	[	[	X
ejpam-5495	469	2	47	47	NUM
ejpam-5495	469	3	]	]	SYM
ejpam-5495	469	4	a.f.n	a.f.n	ADJ
ejpam-5495	469	5	.	.	PUNCT
ejpam-5495	469	6	rasedee	rasedee	PROPN
ejpam-5495	469	7	,	,	PUNCT
ejpam-5495	469	8	m.h.a	m.h.a	PROPN
ejpam-5495	469	9	.	.	PUNCT
ejpam-5495	469	10	sathar	sathar	PROPN
ejpam-5495	469	11	,	,	PUNCT
ejpam-5495	469	12	h.m	h.m	PROPN
ejpam-5495	469	13	.	.	PROPN
ejpam-5495	469	14	ijam	ijam	PROPN
ejpam-5495	469	15	,	,	PUNCT
ejpam-5495	469	16	k.i	k.i	PROPN
ejpam-5495	469	17	.	.	PROPN
ejpam-5495	469	18	othman	othman	PROPN
ejpam-5495	469	19	,	,	PUNCT
ejpam-5495	469	20	n.	n.	PROPN
ejpam-5495	469	21	ishak	ishak	PROPN
ejpam-5495	469	22	,	,	PUNCT
ejpam-5495	469	23	and	and	CCONJ
ejpam-5495	469	24	s.r	s.r	PROPN
ejpam-5495	469	25	.	.	PROPN
ejpam-5495	469	26	hamzah	hamzah	PROPN
ejpam-5495	469	27	.	.	PUNCT
ejpam-5495	470	1	a	a	DET
ejpam-5495	470	2	numerical	numerical	ADJ
ejpam-5495	470	3	solution	solution	NOUN
ejpam-5495	470	4	for	for	ADP
ejpam-5495	470	5	duffing	duffing	NOUN
ejpam-5495	470	6	-	-	PUNCT
ejpam-5495	470	7	van	van	PROPN
ejpam-5495	470	8	der	der	ADJ
ejpam-5495	470	9	pol	pol	PROPN
ejpam-5495	470	10	oscillators	oscillator	NOUN
ejpam-5495	470	11	using	use	VERB
ejpam-5495	470	12	a	a	DET
ejpam-5495	470	13	backward	backward	ADJ
ejpam-5495	470	14	difference	difference	NOUN
ejpam-5495	470	15	formulation	formulation	NOUN
ejpam-5495	470	16	.	.	PUNCT
ejpam-5495	471	1	aip	aip	PROPN
ejpam-5495	471	2	conference	conference	NOUN
ejpam-5495	471	3	proceedings	proceeding	NOUN
ejpam-5495	471	4	,	,	PUNCT
ejpam-5495	471	5	2016:6	2016:6	NUM
ejpam-5495	471	6	,	,	PUNCT
ejpam-5495	471	7	2018	2018	NUM
ejpam-5495	471	8	.	.	PUNCT
ejpam-5495	472	1	a.	a.	PROPN
ejpam-5495	472	2	alanazy	alanazy	PROPN
ejpam-5495	472	3	et	et	PROPN
ejpam-5495	472	4	al	al	PROPN
ejpam-5495	472	5	.	.	PUNCT
ejpam-5495	472	6	/	/	SYM
ejpam-5495	472	7	eur	eur	PROPN
ejpam-5495	472	8	.	.	PUNCT
ejpam-5495	473	1	j.	j.	PROPN
ejpam-5495	473	2	pure	pure	PROPN
ejpam-5495	473	3	appl	appl	PROPN
ejpam-5495	473	4	.	.	PROPN
ejpam-5495	473	5	math	math	PROPN
ejpam-5495	473	6	,	,	PUNCT
ejpam-5495	473	7	18	18	NUM
ejpam-5495	473	8	(	(	PUNCT
ejpam-5495	473	9	1	1	NUM
ejpam-5495	473	10	)	)	PUNCT
ejpam-5495	473	11	(	(	PUNCT
ejpam-5495	473	12	2025	2025	NUM
ejpam-5495	473	13	)	)	PUNCT
ejpam-5495	473	14	,	,	PUNCT
ejpam-5495	473	15	5495	5495	NUM
ejpam-5495	473	16	21	21	NUM
ejpam-5495	473	17	of	of	ADP
ejpam-5495	473	18	21	21	NUM
ejpam-5495	473	19	[	[	SYM
ejpam-5495	473	20	48	48	NUM
ejpam-5495	473	21	]	]	PUNCT
ejpam-5495	473	22	b.	b.	PROPN
ejpam-5495	473	23	rath	rath	PROPN
ejpam-5495	473	24	,	,	PUNCT
ejpam-5495	473	25	v.s.	v.s.	PROPN
ejpam-5495	473	26	erturk	erturk	PROPN
ejpam-5495	473	27	,	,	PUNCT
ejpam-5495	473	28	j.	j.	PROPN
ejpam-5495	473	29	asad	asad	PROPN
ejpam-5495	473	30	,	,	PUNCT
ejpam-5495	473	31	p.	p.	PROPN
ejpam-5495	473	32	mallick	mallick	PROPN
ejpam-5495	473	33	,	,	PUNCT
ejpam-5495	473	34	and	and	CCONJ
ejpam-5495	473	35	r.	r.	PROPN
ejpam-5495	473	36	jarrar	jarrar	NOUN
ejpam-5495	473	37	.	.	PUNCT
ejpam-5495	474	1	an	an	DET
ejpam-5495	474	2	asymmetric	asymmetric	ADJ
ejpam-5495	474	3	model	model	NOUN
ejpam-5495	474	4	two	two	NUM
ejpam-5495	474	5	-	-	PUNCT
ejpam-5495	474	6	dimensional	dimensional	ADJ
ejpam-5495	474	7	oscillator	oscillator	NOUN
ejpam-5495	474	8	.	.	PUNCT
ejpam-5495	475	1	journal	journal	NOUN
ejpam-5495	475	2	of	of	ADP
ejpam-5495	475	3	low	low	ADJ
ejpam-5495	475	4	frequency	frequency	NOUN
ejpam-5495	475	5	noise	noise	NOUN
ejpam-5495	475	6	,	,	PUNCT
ejpam-5495	475	7	vibration	vibration	NOUN
ejpam-5495	475	8	and	and	CCONJ
ejpam-5495	475	9	active	active	ADJ
ejpam-5495	475	10	control	control	NOUN
ejpam-5495	475	11	,	,	PUNCT
ejpam-5495	475	12	43(2):744–754	43(2):744–754	PROPN
ejpam-5495	475	13	,	,	PUNCT
ejpam-5495	475	14	2024	2024	NUM
ejpam-5495	475	15	.	.	PUNCT
ejpam-5495	476	1	[	[	X
ejpam-5495	476	2	49	49	NUM
ejpam-5495	476	3	]	]	PUNCT
ejpam-5495	477	1	z.	z.	PROPN
ejpam-5495	477	2	ren	ren	PROPN
ejpam-5495	477	3	.	.	PUNCT
ejpam-5495	478	1	theoretical	theoretical	ADJ
ejpam-5495	478	2	basis	basis	NOUN
ejpam-5495	478	3	of	of	ADP
ejpam-5495	478	4	he	he	PRON
ejpam-5495	478	5	’s	’	VERB
ejpam-5495	478	6	frequency	frequency	NOUN
ejpam-5495	478	7	-	-	PUNCT
ejpam-5495	478	8	amplitude	amplitude	NOUN
ejpam-5495	478	9	formulation	formulation	NOUN
ejpam-5495	478	10	for	for	ADP
ejpam-5495	478	11	nonlinear	nonlinear	ADJ
ejpam-5495	478	12	oscillators	oscillator	NOUN
ejpam-5495	478	13	.	.	PUNCT
ejpam-5495	479	1	nonlinear	nonlinear	ADJ
ejpam-5495	479	2	science	science	PROPN
ejpam-5495	479	3	letters	letter	NOUN
ejpam-5495	479	4	a	a	PRON
ejpam-5495	479	5	,	,	PUNCT
ejpam-5495	479	6	9(1):86—-90	9(1):86—-90	NUM
ejpam-5495	479	7	,	,	PUNCT
ejpam-5495	479	8	2018	2018	NUM
ejpam-5495	479	9	.	.	PUNCT
ejpam-5495	480	1	[	[	X
ejpam-5495	480	2	50	50	NUM
ejpam-5495	480	3	]	]	X
ejpam-5495	480	4	z	z	PROPN
ejpam-5495	480	5	-	-	PROPN
ejpam-5495	480	6	f.	f.	PROPN
ejpam-5495	480	7	ren	ren	PROPN
ejpam-5495	480	8	and	and	CCONJ
ejpam-5495	480	9	g	g	PROPN
ejpam-5495	480	10	-	-	PUNCT
ejpam-5495	480	11	f.	f.	PROPN
ejpam-5495	480	12	hu	hu	PROPN
ejpam-5495	480	13	.	.	PUNCT
ejpam-5495	481	1	he	he	PRON
ejpam-5495	481	2	’s	’	VERB
ejpam-5495	481	3	frequency	frequency	NOUN
ejpam-5495	481	4	–	–	PUNCT
ejpam-5495	481	5	amplitude	amplitude	NOUN
ejpam-5495	481	6	formulation	formulation	NOUN
ejpam-5495	481	7	with	with	ADP
ejpam-5495	481	8	average	average	ADJ
ejpam-5495	481	9	residuals	residual	NOUN
ejpam-5495	481	10	for	for	ADP
ejpam-5495	481	11	nonlinear	nonlinear	ADJ
ejpam-5495	481	12	oscillators	oscillator	NOUN
ejpam-5495	481	13	.	.	PUNCT
ejpam-5495	482	1	journal	journal	NOUN
ejpam-5495	482	2	of	of	ADP
ejpam-5495	482	3	low	low	ADJ
ejpam-5495	482	4	frequency	frequency	NOUN
ejpam-5495	482	5	noise	noise	NOUN
ejpam-5495	482	6	,	,	PUNCT
ejpam-5495	482	7	vibration	vibration	NOUN
ejpam-5495	482	8	and	and	CCONJ
ejpam-5495	482	9	active	active	ADJ
ejpam-5495	482	10	control	control	NOUN
ejpam-5495	482	11	,	,	PUNCT
ejpam-5495	482	12	38(3	38(3	PROPN
ejpam-5495	482	13	-	-	SYM
ejpam-5495	482	14	4):1050–1059	4):1050–1059	NOUN
ejpam-5495	482	15	,	,	PUNCT
ejpam-5495	482	16	2019	2019	NUM
ejpam-5495	482	17	.	.	PUNCT
ejpam-5495	483	1	[	[	X
ejpam-5495	483	2	51	51	NUM
ejpam-5495	483	3	]	]	X
ejpam-5495	483	4	z	z	PROPN
ejpam-5495	483	5	-	-	PUNCT
ejpam-5495	483	6	f	f	PROPN
ejpam-5495	483	7	ren	ren	PROPN
ejpam-5495	483	8	,	,	PUNCT
ejpam-5495	483	9	g	g	PROPN
ejpam-5495	483	10	-	-	PUNCT
ejpam-5495	483	11	q	q	NOUN
ejpam-5495	483	12	liu	liu	PROPN
ejpam-5495	483	13	,	,	PUNCT
ejpam-5495	483	14	y	y	PROPN
ejpam-5495	483	15	-	-	PUNCT
ejpam-5495	483	16	x	x	PROPN
ejpam-5495	483	17	kang	kang	PROPN
ejpam-5495	483	18	,	,	PUNCT
ejpam-5495	483	19	h	h	PROPN
ejpam-5495	483	20	-	-	PUNCT
ejpam-5495	483	21	y	y	PROPN
ejpam-5495	483	22	fan	fan	PROPN
ejpam-5495	483	23	,	,	PUNCT
ejpam-5495	483	24	h	h	PROPN
ejpam-5495	483	25	-	-	PUNCT
ejpam-5495	483	26	m	m	NOUN
ejpam-5495	483	27	li	li	PROPN
ejpam-5495	483	28	,	,	PUNCT
ejpam-5495	483	29	x	x	PROPN
ejpam-5495	483	30	-	-	PUNCT
ejpam-5495	483	31	d	d	ADJ
ejpam-5495	483	32	ren	ren	PROPN
ejpam-5495	483	33	,	,	PUNCT
ejpam-5495	483	34	and	and	CCONJ
ejpam-5495	483	35	w	w	PROPN
ejpam-5495	483	36	-	-	PUNCT
ejpam-5495	483	37	k	k	PROPN
ejpam-5495	483	38	gui	gui	PROPN
ejpam-5495	483	39	.	.	PUNCT
ejpam-5495	484	1	application	application	NOUN
ejpam-5495	484	2	of	of	ADP
ejpam-5495	484	3	he	he	PRON
ejpam-5495	484	4	’s	’s	PART
ejpam-5495	484	5	amplitude	amplitude	NOUN
ejpam-5495	484	6	–	–	PUNCT
ejpam-5495	484	7	frequency	frequency	NOUN
ejpam-5495	484	8	formulation	formulation	NOUN
ejpam-5495	484	9	to	to	AUX
ejpam-5495	484	10	nonlinear	nonlinear	ADJ
ejpam-5495	484	11	oscillators	oscillator	NOUN
ejpam-5495	484	12	with	with	ADP
ejpam-5495	484	13	discontinuities	discontinuity	NOUN
ejpam-5495	484	14	.	.	PUNCT
ejpam-5495	485	1	physica	physica	PROPN
ejpam-5495	485	2	scripta	scripta	PROPN
ejpam-5495	485	3	,	,	PUNCT
ejpam-5495	485	4	80(4):045003	80(4):045003	NUM
ejpam-5495	485	5	,	,	PUNCT
ejpam-5495	485	6	2009	2009	NUM
ejpam-5495	485	7	.	.	PUNCT
ejpam-5495	486	1	[	[	X
ejpam-5495	486	2	52	52	NUM
ejpam-5495	486	3	]	]	X
ejpam-5495	486	4	z	z	PROPN
ejpam-5495	486	5	-	-	PUNCT
ejpam-5495	486	6	y.	y.	PROPN
ejpam-5495	486	7	ren	ren	PROPN
ejpam-5495	486	8	.	.	PUNCT
ejpam-5495	487	1	a	a	DET
ejpam-5495	487	2	simplified	simplified	ADJ
ejpam-5495	487	3	he	he	PRON
ejpam-5495	487	4	’s	’s	PART
ejpam-5495	487	5	frequency	frequency	NOUN
ejpam-5495	487	6	–	–	PUNCT
ejpam-5495	487	7	amplitude	amplitude	NOUN
ejpam-5495	487	8	formulation	formulation	NOUN
ejpam-5495	487	9	for	for	ADP
ejpam-5495	487	10	nonlinear	nonlinear	ADJ
ejpam-5495	487	11	oscillators	oscillator	NOUN
ejpam-5495	487	12	.	.	PUNCT
ejpam-5495	488	1	journal	journal	NOUN
ejpam-5495	488	2	of	of	ADP
ejpam-5495	488	3	low	low	ADJ
ejpam-5495	488	4	frequency	frequency	NOUN
ejpam-5495	488	5	noise	noise	NOUN
ejpam-5495	488	6	,	,	PUNCT
ejpam-5495	488	7	vibration	vibration	NOUN
ejpam-5495	488	8	and	and	CCONJ
ejpam-5495	488	9	active	active	ADJ
ejpam-5495	488	10	control	control	NOUN
ejpam-5495	488	11	,	,	PUNCT
ejpam-5495	488	12	44(1):209—-215	44(1):209—-215	PROPN
ejpam-5495	488	13	,	,	PUNCT
ejpam-5495	488	14	2022	2022	NUM
ejpam-5495	488	15	.	.	PUNCT
ejpam-5495	489	1	[	[	X
ejpam-5495	489	2	53	53	NUM
ejpam-5495	489	3	]	]	X
ejpam-5495	489	4	m.	m.	NOUN
ejpam-5495	489	5	sayed	sayed	PROPN
ejpam-5495	489	6	,	,	PUNCT
ejpam-5495	489	7	s.k	s.k	PROPN
ejpam-5495	489	8	.	.	PROPN
ejpam-5495	489	9	elagan	elagan	PROPN
ejpam-5495	489	10	,	,	PUNCT
ejpam-5495	489	11	m.	m.	NOUN
ejpam-5495	489	12	higazy	higazy	NOUN
ejpam-5495	489	13	,	,	PUNCT
ejpam-5495	489	14	and	and	CCONJ
ejpam-5495	489	15	m.s	m.s	PROPN
ejpam-5495	489	16	.	.	PROPN
ejpam-5495	489	17	abd	abd	PROPN
ejpam-5495	489	18	elgafoor	elgafoor	PROPN
ejpam-5495	489	19	.	.	PUNCT
ejpam-5495	490	1	feedback	feedback	NOUN
ejpam-5495	490	2	control	control	NOUN
ejpam-5495	490	3	and	and	CCONJ
ejpam-5495	490	4	stability	stability	NOUN
ejpam-5495	490	5	of	of	ADP
ejpam-5495	490	6	the	the	DET
ejpam-5495	490	7	van	van	PROPN
ejpam-5495	490	8	der	der	ADJ
ejpam-5495	490	9	pol	pol	NOUN
ejpam-5495	490	10	equation	equation	NOUN
ejpam-5495	490	11	subjected	subject	VERB
ejpam-5495	490	12	to	to	ADP
ejpam-5495	490	13	external	external	ADJ
ejpam-5495	490	14	and	and	CCONJ
ejpam-5495	490	15	parametric	parametric	ADJ
ejpam-5495	490	16	excitation	excitation	NOUN
ejpam-5495	490	17	forces	force	NOUN
ejpam-5495	490	18	.	.	PUNCT
ejpam-5495	491	1	international	international	ADJ
ejpam-5495	491	2	journal	journal	NOUN
ejpam-5495	491	3	of	of	ADP
ejpam-5495	491	4	applied	apply	VERB
ejpam-5495	491	5	engineering	engineering	NOUN
ejpam-5495	491	6	research	research	NOUN
ejpam-5495	491	7	,	,	PUNCT
ejpam-5495	491	8	13(6):3772–3783	13(6):3772–3783	PROPN
ejpam-5495	491	9	,	,	PUNCT
ejpam-5495	491	10	2018	2018	NUM
ejpam-5495	491	11	.	.	PUNCT
ejpam-5495	492	1	[	[	X
ejpam-5495	492	2	54	54	NUM
ejpam-5495	492	3	]	]	X
ejpam-5495	492	4	s.h	s.h	PROPN
ejpam-5495	492	5	.	.	PROPN
ejpam-5495	492	6	strogatz	strogatz	PROPN
ejpam-5495	492	7	.	.	PUNCT
ejpam-5495	493	1	nonlinear	nonlinear	ADJ
ejpam-5495	493	2	dynamics	dynamic	NOUN
ejpam-5495	493	3	and	and	CCONJ
ejpam-5495	493	4	chaos	chaos	NOUN
ejpam-5495	493	5	with	with	ADP
ejpam-5495	493	6	applications	application	NOUN
ejpam-5495	493	7	to	to	ADP
ejpam-5495	493	8	physics	physics	NOUN
ejpam-5495	493	9	.	.	PUNCT
ejpam-5495	494	1	chemistry	chemistry	NOUN
ejpam-5495	494	2	and	and	CCONJ
ejpam-5495	494	3	engineering	engineering	NOUN
ejpam-5495	494	4	,	,	PUNCT
ejpam-5495	494	5	1994	1994	NUM
ejpam-5495	494	6	.	.	PUNCT
ejpam-5495	495	1	[	[	X
ejpam-5495	495	2	55	55	NUM
ejpam-5495	495	3	]	]	X
ejpam-5495	495	4	y.	y.	PROPN
ejpam-5495	495	5	tian	tian	PROPN
ejpam-5495	495	6	.	.	PUNCT
ejpam-5495	496	1	frequency	frequency	NOUN
ejpam-5495	496	2	formula	formula	NOUN
ejpam-5495	496	3	for	for	ADP
ejpam-5495	496	4	a	a	DET
ejpam-5495	496	5	class	class	NOUN
ejpam-5495	496	6	of	of	ADP
ejpam-5495	496	7	fractal	fractal	ADJ
ejpam-5495	496	8	vibration	vibration	NOUN
ejpam-5495	496	9	system	system	NOUN
ejpam-5495	496	10	.	.	PUNCT
ejpam-5495	497	1	reports	report	NOUN
ejpam-5495	497	2	in	in	ADP
ejpam-5495	497	3	mechanical	mechanical	ADJ
ejpam-5495	497	4	engineering	engineering	NOUN
ejpam-5495	497	5	,	,	PUNCT
ejpam-5495	497	6	3(1):55–61	3(1):55–61	NUM
ejpam-5495	497	7	,	,	PUNCT
ejpam-5495	497	8	2022	2022	NUM
ejpam-5495	497	9	.	.	PUNCT
ejpam-5495	498	1	[	[	X
ejpam-5495	498	2	56	56	NUM
ejpam-5495	498	3	]	]	X
ejpam-5495	498	4	y.	y.	PROPN
ejpam-5495	498	5	tian	tian	PROPN
ejpam-5495	498	6	and	and	CCONJ
ejpam-5495	498	7	z.	z.	PROPN
ejpam-5495	498	8	wang	wang	PROPN
ejpam-5495	498	9	.	.	PUNCT
ejpam-5495	499	1	a	a	DET
ejpam-5495	499	2	new	new	ADJ
ejpam-5495	499	3	multiple	multiple	ADJ
ejpam-5495	499	4	integral	integral	ADJ
ejpam-5495	499	5	inequality	inequality	NOUN
ejpam-5495	499	6	and	and	CCONJ
ejpam-5495	499	7	its	its	PRON
ejpam-5495	499	8	application	application	NOUN
ejpam-5495	499	9	to	to	PART
ejpam-5495	499	10	stability	stability	VERB
ejpam-5495	499	11	analysis	analysis	NOUN
ejpam-5495	499	12	of	of	ADP
ejpam-5495	499	13	time	time	NOUN
ejpam-5495	499	14	-	-	PUNCT
ejpam-5495	499	15	delay	delay	NOUN
ejpam-5495	499	16	systems	system	NOUN
ejpam-5495	499	17	.	.	PUNCT
ejpam-5495	500	1	applied	apply	VERB
ejpam-5495	500	2	mathematics	mathematics	NOUN
ejpam-5495	500	3	letters	letter	NOUN
ejpam-5495	500	4	,	,	PUNCT
ejpam-5495	500	5	105:106325	105:106325	NUM
ejpam-5495	500	6	,	,	PUNCT
ejpam-5495	500	7	2020	2020	NUM
ejpam-5495	500	8	.	.	PUNCT
ejpam-5495	501	1	[	[	X
ejpam-5495	501	2	57	57	NUM
ejpam-5495	501	3	]	]	X
ejpam-5495	501	4	y.	y.	PROPN
ejpam-5495	501	5	tian	tian	PROPN
ejpam-5495	501	6	and	and	CCONJ
ejpam-5495	501	7	z.	z.	PROPN
ejpam-5495	501	8	wang	wang	PROPN
ejpam-5495	501	9	.	.	PUNCT
ejpam-5495	502	1	composite	composite	ADJ
ejpam-5495	502	2	slack	slack	NOUN
ejpam-5495	502	3	-	-	PUNCT
ejpam-5495	502	4	matrix	matrix	NOUN
ejpam-5495	502	5	-	-	PUNCT
ejpam-5495	502	6	based	base	VERB
ejpam-5495	502	7	integral	integral	ADJ
ejpam-5495	502	8	inequality	inequality	NOUN
ejpam-5495	502	9	and	and	CCONJ
ejpam-5495	502	10	its	its	PRON
ejpam-5495	502	11	application	application	NOUN
ejpam-5495	502	12	to	to	PART
ejpam-5495	502	13	stability	stability	VERB
ejpam-5495	502	14	analysis	analysis	NOUN
ejpam-5495	502	15	of	of	ADP
ejpam-5495	502	16	time	time	NOUN
ejpam-5495	502	17	-	-	PUNCT
ejpam-5495	502	18	delay	delay	NOUN
ejpam-5495	502	19	systems	system	NOUN
ejpam-5495	502	20	.	.	PUNCT
ejpam-5495	503	1	applied	apply	VERB
ejpam-5495	503	2	mathematics	mathematics	NOUN
ejpam-5495	503	3	letters	letter	NOUN
ejpam-5495	503	4	,	,	PUNCT
ejpam-5495	503	5	120:107252	120:107252	NUM
ejpam-5495	503	6	,	,	PUNCT
ejpam-5495	503	7	2021	2021	NUM
ejpam-5495	503	8	.	.	PUNCT
ejpam-5495	504	1	[	[	X
ejpam-5495	504	2	58	58	NUM
ejpam-5495	504	3	]	]	PUNCT
ejpam-5495	504	4	j.	j.	PROPN
ejpam-5495	504	5	warminski	warminski	PROPN
ejpam-5495	504	6	,	,	PUNCT
ejpam-5495	504	7	s.	s.	PROPN
ejpam-5495	504	8	lenci	lenci	PROPN
ejpam-5495	504	9	,	,	PUNCT
ejpam-5495	504	10	p.m.	p.m.	NOUN
ejpam-5495	504	11	cartmell	cartmell	PROPN
ejpam-5495	504	12	,	,	PUNCT
ejpam-5495	504	13	g.	g.	PROPN
ejpam-5495	504	14	rega	rega	PROPN
ejpam-5495	504	15	,	,	PUNCT
ejpam-5495	504	16	and	and	CCONJ
ejpam-5495	504	17	m.	m.	PROPN
ejpam-5495	504	18	wiercigroch	wiercigroch	PROPN
ejpam-5495	504	19	.	.	PUNCT
ejpam-5495	505	1	nonlinear	nonlinear	ADJ
ejpam-5495	505	2	dynamic	dynamic	ADJ
ejpam-5495	505	3	phenomena	phenomenon	NOUN
ejpam-5495	505	4	in	in	ADP
ejpam-5495	505	5	mechanics	mechanic	NOUN
ejpam-5495	505	6	.	.	PUNCT
ejpam-5495	506	1	solid	solid	ADJ
ejpam-5495	506	2	mechanics	mechanic	NOUN
ejpam-5495	506	3	and	and	CCONJ
ejpam-5495	506	4	its	its	PRON
ejpam-5495	506	5	applications	application	NOUN
ejpam-5495	506	6	,	,	PUNCT
ejpam-5495	506	7	181	181	NUM
ejpam-5495	506	8	,	,	PUNCT
ejpam-5495	506	9	2012	2012	NUM
ejpam-5495	506	10	.	.	PUNCT
ejpam-5495	507	1	[	[	X
ejpam-5495	507	2	59	59	NUM
ejpam-5495	507	3	]	]	PUNCT
ejpam-5495	507	4	j.	j.	PROPN
ejpam-5495	507	5	xua	xua	PROPN
ejpam-5495	507	6	and	and	CCONJ
ejpam-5495	507	7	k.w	k.w	PROPN
ejpam-5495	507	8	.	.	PROPN
ejpam-5495	507	9	chungb	chungb	PROPN
ejpam-5495	507	10	.	.	PUNCT
ejpam-5495	508	1	effects	effect	NOUN
ejpam-5495	508	2	of	of	ADP
ejpam-5495	508	3	time	time	NOUN
ejpam-5495	508	4	delayed	delay	VERB
ejpam-5495	508	5	position	position	NOUN
ejpam-5495	508	6	feedback	feedback	NOUN
ejpam-5495	508	7	on	on	ADP
ejpam-5495	508	8	a	a	DET
ejpam-5495	508	9	van	van	PROPN
ejpam-5495	508	10	der	der	ADJ
ejpam-5495	508	11	pol	pol	PROPN
ejpam-5495	508	12	–	–	PUNCT
ejpam-5495	508	13	duffing	duffe	VERB
ejpam-5495	508	14	oscillator	oscillator	NOUN
ejpam-5495	508	15	.	.	PUNCT
ejpam-5495	509	1	physica	physica	PROPN
ejpam-5495	509	2	d	d	PROPN
ejpam-5495	509	3	,	,	PUNCT
ejpam-5495	509	4	180:17—-39	180:17—-39	NOUN
ejpam-5495	509	5	,	,	PUNCT
ejpam-5495	509	6	2003	2003	NUM
ejpam-5495	509	7	.	.	PUNCT