id	sid	tid	token	lemma	pos
ajrhss-3200	1	1	american	american	PROPN
ajrhss-3200	1	2	journal	journal	PROPN
ajrhss-3200	1	3	of	of	ADP
ajrhss-3200	1	4	research	research	NOUN
ajrhss-3200	1	5	in	in	ADP
ajrhss-3200	1	6	humanities	humanity	NOUN
ajrhss-3200	1	7	and	and	CCONJ
ajrhss-3200	1	8	social	social	ADJ
ajrhss-3200	1	9	sciences	science	NOUN
ajrhss-3200	1	10	issn	issn	PROPN
ajrhss-3200	1	11	(	(	PUNCT
ajrhss-3200	1	12	e	e	NOUN
ajrhss-3200	1	13	):	):	PUNCT
ajrhss-3200	1	14	2832	2832	NUM
ajrhss-3200	1	15	-	-	SYM
ajrhss-3200	1	16	8019	8019	NUM
ajrhss-3200	1	17	volume	volume	NOUN
ajrhss-3200	1	18	43	43	NUM
ajrhss-3200	1	19	,	,	PUNCT
ajrhss-3200	1	20	|	|	ADV
ajrhss-3200	1	21	december	december	PROPN
ajrhss-3200	1	22	2025	2025	NUM
ajrhss-3200	2	1	p	p	NOUN
ajrhss-3200	2	2	a	a	DET
ajrhss-3200	2	3	g	g	NOUN
ajrhss-3200	2	4	e	e	NOUN
ajrhss-3200	2	5	|	|	ADV
ajrhss-3200	2	6	4	4	NUM
ajrhss-3200	2	7	www.americanjournal.org	www.americanjournal.org	NOUN
ajrhss-3200	2	8	properties	property	NOUN
ajrhss-3200	2	9	of	of	ADP
ajrhss-3200	2	10	nonlinear	nonlinear	ADJ
ajrhss-3200	2	11	oscillations	oscillation	NOUN
ajrhss-3200	2	12	of	of	ADP
ajrhss-3200	2	13	dissipative	dissipative	ADJ
ajrhss-3200	2	14	mechanical	mechanical	ADJ
ajrhss-3200	2	15	systems	system	NOUN
ajrhss-3200	2	16	with	with	ADP
ajrhss-3200	2	17	a	a	DET
ajrhss-3200	2	18	limited	limited	ADJ
ajrhss-3200	2	19	number	number	NOUN
ajrhss-3200	2	20	of	of	ADP
ajrhss-3200	2	21	degrees	degree	NOUN
ajrhss-3200	2	22	of	of	ADP
ajrhss-3200	2	23	freedom	freedom	NOUN
ajrhss-3200	2	24	turaeyv	turaeyv	PROPN
ajrhss-3200	2	25	qahramon	qahramon	PROPN
ajrhss-3200	2	26	nortojiyevich	nortojiyevich	PROPN
ajrhss-3200	2	27	terdu	terdu	PROPN
ajrhss-3200	2	28	is	be	AUX
ajrhss-3200	2	29	a	a	DET
ajrhss-3200	2	30	senior	senior	ADJ
ajrhss-3200	2	31	lecturer	lecturer	NOUN
ajrhss-3200	2	32	at	at	ADP
ajrhss-3200	2	33	the	the	DET
ajrhss-3200	2	34	department	department	NOUN
ajrhss-3200	2	35	of	of	ADP
ajrhss-3200	2	36	mathematical	mathematical	ADJ
ajrhss-3200	2	37	analysis	analysis	NOUN
ajrhss-3200	2	38	a	a	DET
ajrhss-3200	2	39	b	b	NOUN
ajrhss-3200	2	40	s	s	ADP
ajrhss-3200	2	41	t	t	PROPN
ajrhss-3200	2	42	r	r	NOUN
ajrhss-3200	2	43	a	a	DET
ajrhss-3200	2	44	c	c	NOUN
ajrhss-3200	2	45	t	t	NOUN
ajrhss-3200	2	46	k	k	X
ajrhss-3200	2	47	e	e	PROPN
ajrhss-3200	2	48	y	y	PROPN
ajrhss-3200	2	49	w	w	NOUN
ajrhss-3200	2	50	o	o	NOUN
ajrhss-3200	2	51	r	r	NOUN
ajrhss-3200	2	52	d	d	X
ajrhss-3200	2	53	s	s	VERB
ajrhss-3200	2	54	this	this	DET
ajrhss-3200	2	55	article	article	NOUN
ajrhss-3200	2	56	studies	study	VERB
ajrhss-3200	2	57	nonlinear	nonlinear	ADJ
ajrhss-3200	2	58	oscillation	oscillation	NOUN
ajrhss-3200	2	59	processes	process	NOUN
ajrhss-3200	2	60	of	of	ADP
ajrhss-3200	2	61	dissipative	dissipative	ADJ
ajrhss-3200	2	62	mechanical	mechanical	ADJ
ajrhss-3200	2	63	systems	system	NOUN
ajrhss-3200	2	64	with	with	ADP
ajrhss-3200	2	65	a	a	DET
ajrhss-3200	2	66	limited	limited	ADJ
ajrhss-3200	2	67	number	number	NOUN
ajrhss-3200	2	68	of	of	ADP
ajrhss-3200	2	69	degrees	degree	NOUN
ajrhss-3200	2	70	of	of	ADP
ajrhss-3200	2	71	freedom	freedom	NOUN
ajrhss-3200	2	72	.	.	PUNCT
ajrhss-3200	3	1	the	the	DET
ajrhss-3200	3	2	properties	property	NOUN
ajrhss-3200	3	3	of	of	ADP
ajrhss-3200	3	4	dissipative	dissipative	ADJ
ajrhss-3200	3	5	forces	force	NOUN
ajrhss-3200	3	6	,	,	PUNCT
ajrhss-3200	3	7	how	how	SCONJ
ajrhss-3200	3	8	they	they	PRON
ajrhss-3200	3	9	affect	affect	VERB
ajrhss-3200	3	10	nonlinear	nonlinear	ADJ
ajrhss-3200	3	11	oscillations	oscillation	NOUN
ajrhss-3200	3	12	,	,	PUNCT
ajrhss-3200	3	13	the	the	DET
ajrhss-3200	3	14	stability	stability	NOUN
ajrhss-3200	3	15	of	of	ADP
ajrhss-3200	3	16	oscillations	oscillation	NOUN
ajrhss-3200	3	17	,	,	PUNCT
ajrhss-3200	3	18	the	the	DET
ajrhss-3200	3	19	formation	formation	NOUN
ajrhss-3200	3	20	of	of	ADP
ajrhss-3200	3	21	limit	limit	NOUN
ajrhss-3200	3	22	cycles	cycle	NOUN
ajrhss-3200	3	23	,	,	PUNCT
ajrhss-3200	3	24	subharmonic	subharmonic	ADJ
ajrhss-3200	3	25	and	and	CCONJ
ajrhss-3200	3	26	superharmonic	superharmonic	ADJ
ajrhss-3200	3	27	resonance	resonance	NOUN
ajrhss-3200	3	28	phenomena	phenomenon	NOUN
ajrhss-3200	3	29	are	be	AUX
ajrhss-3200	3	30	analyzed	analyze	VERB
ajrhss-3200	3	31	.	.	PUNCT
ajrhss-3200	4	1	also	also	ADV
ajrhss-3200	4	2	,	,	PUNCT
ajrhss-3200	4	3	the	the	DET
ajrhss-3200	4	4	main	main	ADJ
ajrhss-3200	4	5	mechanisms	mechanism	NOUN
ajrhss-3200	4	6	of	of	ADP
ajrhss-3200	4	7	nonlinear	nonlinear	ADJ
ajrhss-3200	4	8	oscillations	oscillation	NOUN
ajrhss-3200	4	9	are	be	AUX
ajrhss-3200	4	10	considered	consider	VERB
ajrhss-3200	4	11	using	use	VERB
ajrhss-3200	4	12	spatial	spatial	ADJ
ajrhss-3200	4	13	portraits	portrait	NOUN
ajrhss-3200	4	14	,	,	PUNCT
ajrhss-3200	4	15	lyapunov	lyapunov	ADJ
ajrhss-3200	4	16	stability	stability	NOUN
ajrhss-3200	4	17	criteria	criterion	NOUN
ajrhss-3200	4	18	,	,	PUNCT
ajrhss-3200	4	19	parametric	parametric	ADJ
ajrhss-3200	4	20	oscillations	oscillation	NOUN
ajrhss-3200	4	21	,	,	PUNCT
ajrhss-3200	4	22	duffing	duffing	NOUN
ajrhss-3200	4	23	,	,	PUNCT
ajrhss-3200	4	24	van	van	PROPN
ajrhss-3200	4	25	der	der	ADJ
ajrhss-3200	4	26	pol	pol	PROPN
ajrhss-3200	4	27	and	and	CCONJ
ajrhss-3200	4	28	rayleigh	rayleigh	ADJ
ajrhss-3200	4	29	-	-	PUNCT
ajrhss-3200	4	30	type	type	NOUN
ajrhss-3200	4	31	models	model	NOUN
ajrhss-3200	4	32	.	.	PUNCT
ajrhss-3200	5	1	the	the	DET
ajrhss-3200	5	2	energy	energy	NOUN
ajrhss-3200	5	3	balance	balance	NOUN
ajrhss-3200	5	4	of	of	ADP
ajrhss-3200	5	5	systems	system	NOUN
ajrhss-3200	5	6	,	,	PUNCT
ajrhss-3200	5	7	the	the	DET
ajrhss-3200	5	8	effect	effect	NOUN
ajrhss-3200	5	9	of	of	ADP
ajrhss-3200	5	10	the	the	DET
ajrhss-3200	5	11	dissipation	dissipation	NOUN
ajrhss-3200	5	12	level	level	NOUN
ajrhss-3200	5	13	on	on	ADP
ajrhss-3200	5	14	the	the	DET
ajrhss-3200	5	15	time	time	NOUN
ajrhss-3200	5	16	evolution	evolution	NOUN
ajrhss-3200	5	17	of	of	ADP
ajrhss-3200	5	18	the	the	DET
ajrhss-3200	5	19	oscillation	oscillation	NOUN
ajrhss-3200	5	20	amplitude	amplitude	NOUN
ajrhss-3200	5	21	are	be	AUX
ajrhss-3200	5	22	also	also	ADV
ajrhss-3200	5	23	covered	cover	VERB
ajrhss-3200	5	24	from	from	ADP
ajrhss-3200	5	25	a	a	DET
ajrhss-3200	5	26	mathematical	mathematical	ADJ
ajrhss-3200	5	27	point	point	NOUN
ajrhss-3200	5	28	of	of	ADP
ajrhss-3200	5	29	view	view	NOUN
ajrhss-3200	5	30	.	.	PUNCT
ajrhss-3200	6	1	nonlinear	nonlinear	ADJ
ajrhss-3200	6	2	oscillations	oscillation	NOUN
ajrhss-3200	6	3	,	,	PUNCT
ajrhss-3200	6	4	dissipative	dissipative	ADJ
ajrhss-3200	6	5	system	system	NOUN
ajrhss-3200	6	6	,	,	PUNCT
ajrhss-3200	6	7	degree	degree	NOUN
ajrhss-3200	6	8	of	of	ADP
ajrhss-3200	6	9	freedom	freedom	NOUN
ajrhss-3200	6	10	,	,	PUNCT
ajrhss-3200	6	11	stability	stability	NOUN
ajrhss-3200	6	12	,	,	PUNCT
ajrhss-3200	6	13	spatial	spatial	ADJ
ajrhss-3200	6	14	portrait	portrait	NOUN
ajrhss-3200	6	15	,	,	PUNCT
ajrhss-3200	6	16	resonance	resonance	NOUN
ajrhss-3200	6	17	,	,	PUNCT
ajrhss-3200	6	18	limit	limit	VERB
ajrhss-3200	6	19	cycle	cycle	NOUN
ajrhss-3200	6	20	,	,	PUNCT
ajrhss-3200	6	21	lyapunov	lyapunov	NOUN
ajrhss-3200	6	22	function	function	NOUN
ajrhss-3200	6	23	,	,	PUNCT
ajrhss-3200	6	24	duffing	duffe	VERB
ajrhss-3200	6	25	model	model	NOUN
ajrhss-3200	6	26	,	,	PUNCT
ajrhss-3200	6	27	van	van	PROPN
ajrhss-3200	6	28	der	der	ADJ
ajrhss-3200	6	29	pol	pol	PROPN
ajrhss-3200	6	30	oscillations	oscillation	NOUN
ajrhss-3200	6	31	.	.	PUNCT
ajrhss-3200	7	1	introduction	introduction	NOUN
ajrhss-3200	7	2	oscillation	oscillation	NOUN
ajrhss-3200	7	3	processes	process	NOUN
ajrhss-3200	7	4	of	of	ADP
ajrhss-3200	7	5	mechanical	mechanical	ADJ
ajrhss-3200	7	6	systems	system	NOUN
ajrhss-3200	7	7	are	be	AUX
ajrhss-3200	7	8	a	a	DET
ajrhss-3200	7	9	fundamental	fundamental	ADJ
ajrhss-3200	7	10	component	component	NOUN
ajrhss-3200	7	11	of	of	ADP
ajrhss-3200	7	12	many	many	ADJ
ajrhss-3200	7	13	natural	natural	ADJ
ajrhss-3200	7	14	and	and	CCONJ
ajrhss-3200	7	15	technical	technical	ADJ
ajrhss-3200	7	16	systems	system	NOUN
ajrhss-3200	7	17	.	.	PUNCT
ajrhss-3200	8	1	real	real	ADJ
ajrhss-3200	8	2	mechanical	mechanical	ADJ
ajrhss-3200	8	3	systems	system	NOUN
ajrhss-3200	8	4	are	be	AUX
ajrhss-3200	8	5	often	often	ADV
ajrhss-3200	8	6	not	not	PART
ajrhss-3200	8	7	ideal	ideal	ADJ
ajrhss-3200	8	8	and	and	CCONJ
ajrhss-3200	8	9	have	have	VERB
ajrhss-3200	8	10	energy	energy	NOUN
ajrhss-3200	8	11	losses	loss	NOUN
ajrhss-3200	8	12	,	,	PUNCT
ajrhss-3200	8	13	i.e.	i.e.	X
ajrhss-3200	8	14	dissipation	dissipation	NOUN
ajrhss-3200	8	15	.	.	PUNCT
ajrhss-3200	9	1	in	in	ADP
ajrhss-3200	9	2	addition	addition	NOUN
ajrhss-3200	9	3	,	,	PUNCT
ajrhss-3200	9	4	in	in	ADP
ajrhss-3200	9	5	many	many	ADJ
ajrhss-3200	9	6	processes	process	NOUN
ajrhss-3200	9	7	,	,	PUNCT
ajrhss-3200	9	8	forces	force	NOUN
ajrhss-3200	9	9	obey	obey	VERB
ajrhss-3200	9	10	not	not	PART
ajrhss-3200	9	11	linear	linear	ADJ
ajrhss-3200	9	12	laws	law	NOUN
ajrhss-3200	9	13	,	,	PUNCT
ajrhss-3200	9	14	but	but	CCONJ
ajrhss-3200	9	15	nonlinear	nonlinear	ADJ
ajrhss-3200	9	16	laws	law	NOUN
ajrhss-3200	9	17	.	.	PUNCT
ajrhss-3200	10	1	therefore	therefore	ADV
ajrhss-3200	10	2	,	,	PUNCT
ajrhss-3200	10	3	the	the	DET
ajrhss-3200	10	4	use	use	NOUN
ajrhss-3200	10	5	of	of	ADP
ajrhss-3200	10	6	nonlinear	nonlinear	ADJ
ajrhss-3200	10	7	and	and	CCONJ
ajrhss-3200	10	8	dissipative	dissipative	ADJ
ajrhss-3200	10	9	models	model	NOUN
ajrhss-3200	10	10	in	in	ADP
ajrhss-3200	10	11	the	the	DET
ajrhss-3200	10	12	study	study	NOUN
ajrhss-3200	10	13	of	of	ADP
ajrhss-3200	10	14	oscillations	oscillation	NOUN
ajrhss-3200	10	15	of	of	ADP
ajrhss-3200	10	16	real	real	ADJ
ajrhss-3200	10	17	systems	system	NOUN
ajrhss-3200	10	18	is	be	AUX
ajrhss-3200	10	19	important	important	ADJ
ajrhss-3200	10	20	.	.	PUNCT
ajrhss-3200	11	1	systems	system	NOUN
ajrhss-3200	11	2	with	with	ADP
ajrhss-3200	11	3	a	a	DET
ajrhss-3200	11	4	limited	limited	ADJ
ajrhss-3200	11	5	number	number	NOUN
ajrhss-3200	11	6	of	of	ADP
ajrhss-3200	11	7	degrees	degree	NOUN
ajrhss-3200	11	8	of	of	ADP
ajrhss-3200	11	9	freedom	freedom	NOUN
ajrhss-3200	11	10	constitute	constitute	VERB
ajrhss-3200	11	11	a	a	DET
ajrhss-3200	11	12	separate	separate	ADJ
ajrhss-3200	11	13	section	section	NOUN
ajrhss-3200	11	14	of	of	ADP
ajrhss-3200	11	15	the	the	DET
ajrhss-3200	11	16	theory	theory	NOUN
ajrhss-3200	11	17	of	of	ADP
ajrhss-3200	11	18	oscillations	oscillation	NOUN
ajrhss-3200	11	19	.	.	PUNCT
ajrhss-3200	12	1	such	such	ADJ
ajrhss-3200	12	2	systems	system	NOUN
ajrhss-3200	12	3	include	include	VERB
ajrhss-3200	12	4	mechanical	mechanical	ADJ
ajrhss-3200	12	5	oscillators	oscillator	NOUN
ajrhss-3200	12	6	,	,	PUNCT
ajrhss-3200	12	7	robot	robot	NOUN
ajrhss-3200	12	8	manipulator	manipulator	NOUN
ajrhss-3200	12	9	joints	joint	NOUN
ajrhss-3200	12	10	,	,	PUNCT
ajrhss-3200	12	11	mechanical	mechanical	ADJ
ajrhss-3200	12	12	structures	structure	NOUN
ajrhss-3200	12	13	connected	connect	VERB
ajrhss-3200	12	14	by	by	ADP
ajrhss-3200	12	15	elastic	elastic	ADJ
ajrhss-3200	12	16	elements	element	NOUN
ajrhss-3200	12	17	,	,	PUNCT
ajrhss-3200	12	18	and	and	CCONJ
ajrhss-3200	12	19	actuators	actuator	NOUN
ajrhss-3200	12	20	of	of	ADP
ajrhss-3200	12	21	automatic	automatic	ADJ
ajrhss-3200	12	22	control	control	NOUN
ajrhss-3200	12	23	systems	system	NOUN
ajrhss-3200	12	24	.	.	PUNCT
ajrhss-3200	13	1	the	the	DET
ajrhss-3200	13	2	behavior	behavior	NOUN
ajrhss-3200	13	3	of	of	ADP
ajrhss-3200	13	4	these	these	DET
ajrhss-3200	13	5	systems	system	NOUN
ajrhss-3200	13	6	is	be	AUX
ajrhss-3200	13	7	often	often	ADV
ajrhss-3200	13	8	described	describe	VERB
ajrhss-3200	13	9	not	not	PART
ajrhss-3200	13	10	by	by	ADP
ajrhss-3200	13	11	simple	simple	ADJ
ajrhss-3200	13	12	linear	linear	ADJ
ajrhss-3200	13	13	models	model	NOUN
ajrhss-3200	13	14	,	,	PUNCT
ajrhss-3200	13	15	but	but	CCONJ
ajrhss-3200	13	16	by	by	ADP
ajrhss-3200	13	17	complex	complex	ADJ
ajrhss-3200	13	18	nonlinear	nonlinear	ADJ
ajrhss-3200	13	19	equations	equation	NOUN
ajrhss-3200	13	20	.	.	PUNCT
ajrhss-3200	14	1	the	the	DET
ajrhss-3200	14	2	purpose	purpose	NOUN
ajrhss-3200	14	3	of	of	ADP
ajrhss-3200	14	4	this	this	DET
ajrhss-3200	14	5	article	article	NOUN
ajrhss-3200	14	6	is	be	AUX
ajrhss-3200	14	7	to	to	PART
ajrhss-3200	14	8	analyze	analyze	VERB
ajrhss-3200	14	9	dissipative	dissipative	ADJ
ajrhss-3200	14	10	and	and	CCONJ
ajrhss-3200	14	11	nonlinear	nonlinear	ADJ
ajrhss-3200	14	12	vibrations	vibration	NOUN
ajrhss-3200	14	13	from	from	ADP
ajrhss-3200	14	14	a	a	DET
ajrhss-3200	14	15	mathematical	mathematical	ADJ
ajrhss-3200	14	16	and	and	CCONJ
ajrhss-3200	14	17	physical	physical	ADJ
ajrhss-3200	14	18	point	point	NOUN
ajrhss-3200	14	19	of	of	ADP
ajrhss-3200	14	20	view	view	NOUN
ajrhss-3200	14	21	,	,	PUNCT
ajrhss-3200	14	22	to	to	PART
ajrhss-3200	14	23	study	study	VERB
ajrhss-3200	14	24	important	important	ADJ
ajrhss-3200	14	25	mechanisms	mechanism	NOUN
ajrhss-3200	14	26	such	such	ADJ
ajrhss-3200	14	27	as	as	ADP
ajrhss-3200	14	28	their	their	PRON
ajrhss-3200	14	29	stability	stability	NOUN
ajrhss-3200	14	30	properties	property	NOUN
ajrhss-3200	14	31	,	,	PUNCT
ajrhss-3200	14	32	resonance	resonance	NOUN
ajrhss-3200	14	33	processes	process	NOUN
ajrhss-3200	14	34	,	,	PUNCT
ajrhss-3200	14	35	and	and	CCONJ
ajrhss-3200	14	36	the	the	DET
ajrhss-3200	14	37	formation	formation	NOUN
ajrhss-3200	14	38	of	of	ADP
ajrhss-3200	14	39	limit	limit	NOUN
ajrhss-3200	14	40	cycles	cycle	NOUN
ajrhss-3200	14	41	.	.	PUNCT
ajrhss-3200	15	1	main	main	ADJ
ajrhss-3200	15	2	part	part	NOUN
ajrhss-3200	15	3	general	general	ADJ
ajrhss-3200	15	4	description	description	NOUN
ajrhss-3200	15	5	of	of	ADP
ajrhss-3200	15	6	dissipative	dissipative	ADJ
ajrhss-3200	15	7	systems	system	NOUN
ajrhss-3200	15	8	a	a	DET
ajrhss-3200	15	9	dissipative	dissipative	ADJ
ajrhss-3200	15	10	system	system	NOUN
ajrhss-3200	15	11	is	be	AUX
ajrhss-3200	15	12	a	a	DET
ajrhss-3200	15	13	system	system	NOUN
ajrhss-3200	15	14	in	in	ADP
ajrhss-3200	15	15	which	which	PRON
ajrhss-3200	15	16	the	the	DET
ajrhss-3200	15	17	energy	energy	NOUN
ajrhss-3200	15	18	decays	decay	VERB
ajrhss-3200	15	19	over	over	ADP
ajrhss-3200	15	20	time	time	NOUN
ajrhss-3200	15	21	,	,	PUNCT
ajrhss-3200	15	22	the	the	DET
ajrhss-3200	15	23	amplitude	amplitude	NOUN
ajrhss-3200	15	24	of	of	ADP
ajrhss-3200	15	25	oscillations	oscillation	NOUN
ajrhss-3200	15	26	decreases	decrease	VERB
ajrhss-3200	15	27	even	even	ADV
ajrhss-3200	15	28	in	in	ADP
ajrhss-3200	15	29	the	the	DET
ajrhss-3200	15	30	absence	absence	NOUN
ajrhss-3200	15	31	of	of	ADP
ajrhss-3200	15	32	external	external	ADJ
ajrhss-3200	15	33	influences	influence	NOUN
ajrhss-3200	15	34	.	.	PUNCT
ajrhss-3200	16	1	dissipation	dissipation	NOUN
ajrhss-3200	16	2	often	often	ADV
ajrhss-3200	16	3	arises	arise	VERB
ajrhss-3200	16	4	from	from	ADP
ajrhss-3200	16	5	the	the	DET
ajrhss-3200	16	6	following	follow	VERB
ajrhss-3200	16	7	sources	source	NOUN
ajrhss-3200	16	8	:	:	PUNCT
ajrhss-3200	16	9	american	american	PROPN
ajrhss-3200	16	10	journal	journal	PROPN
ajrhss-3200	16	11	of	of	ADP
ajrhss-3200	16	12	research	research	NOUN
ajrhss-3200	16	13	in	in	ADP
ajrhss-3200	16	14	humanities	humanity	NOUN
ajrhss-3200	16	15	and	and	CCONJ
ajrhss-3200	16	16	social	social	ADJ
ajrhss-3200	16	17	sciences	science	NOUN
ajrhss-3200	16	18	volume	volume	NOUN
ajrhss-3200	16	19	43	43	NUM
ajrhss-3200	16	20	december	december	PROPN
ajrhss-3200	16	21	2025	2025	NUM
ajrhss-3200	17	1	p	p	NOUN
ajrhss-3200	17	2	a	a	DET
ajrhss-3200	17	3	g	g	NOUN
ajrhss-3200	17	4	e	e	NOUN
ajrhss-3200	17	5	|	|	ADV
ajrhss-3200	17	6	5	5	NUM
ajrhss-3200	17	7	www.americanjournal.org	www.americanjournal.org	NOUN
ajrhss-3200	17	8	1	1	NUM
ajrhss-3200	17	9	.	.	PUNCT
ajrhss-3200	18	1	internal	internal	ADJ
ajrhss-3200	18	2	resistance	resistance	NOUN
ajrhss-3200	18	3	(	(	PUNCT
ajrhss-3200	18	4	internal	internal	ADJ
ajrhss-3200	18	5	friction	friction	NOUN
ajrhss-3200	18	6	of	of	ADP
ajrhss-3200	18	7	the	the	DET
ajrhss-3200	18	8	material	material	NOUN
ajrhss-3200	18	9	)	)	PUNCT
ajrhss-3200	18	10	.	.	PUNCT
ajrhss-3200	19	1	2	2	X
ajrhss-3200	19	2	.	.	X
ajrhss-3200	19	3	external	external	ADJ
ajrhss-3200	19	4	friction	friction	NOUN
ajrhss-3200	19	5	(	(	PUNCT
ajrhss-3200	19	6	air	air	NOUN
ajrhss-3200	19	7	resistance	resistance	NOUN
ajrhss-3200	19	8	,	,	PUNCT
ajrhss-3200	19	9	mechanical	mechanical	ADJ
ajrhss-3200	19	10	friction	friction	NOUN
ajrhss-3200	19	11	)	)	PUNCT
ajrhss-3200	19	12	.	.	PUNCT
ajrhss-3200	20	1	3	3	X
ajrhss-3200	20	2	.	.	X
ajrhss-3200	20	3	energy	energy	NOUN
ajrhss-3200	20	4	consumption	consumption	NOUN
ajrhss-3200	20	5	of	of	ADP
ajrhss-3200	20	6	active	active	ADJ
ajrhss-3200	20	7	control	control	NOUN
ajrhss-3200	20	8	systems	system	NOUN
ajrhss-3200	20	9	.	.	PUNCT
ajrhss-3200	21	1	the	the	DET
ajrhss-3200	21	2	classical	classical	ADJ
ajrhss-3200	21	3	model	model	NOUN
ajrhss-3200	21	4	for	for	ADP
ajrhss-3200	21	5	a	a	DET
ajrhss-3200	21	6	simple	simple	ADJ
ajrhss-3200	21	7	one	one	NUM
ajrhss-3200	21	8	-	-	PUNCT
ajrhss-3200	21	9	degree	degree	NOUN
ajrhss-3200	21	10	-	-	PUNCT
ajrhss-3200	21	11	of	of	ADP
ajrhss-3200	21	12	-	-	PUNCT
ajrhss-3200	21	13	freedom	freedom	NOUN
ajrhss-3200	21	14	system	system	NOUN
ajrhss-3200	21	15	is	be	AUX
ajrhss-3200	21	16	:	:	PUNCT
ajrhss-3200	21	17	m\ddot{x	m\ddot{x	ADJ
ajrhss-3200	21	18	}	}	PUNCT
ajrhss-3200	21	19	+	+	CCONJ
ajrhss-3200	21	20	c\dot{x	c\dot{x	NOUN
ajrhss-3200	21	21	}	}	PUNCT
ajrhss-3200	21	22	+	+	NUM
ajrhss-3200	21	23	kx	kx	X
ajrhss-3200	21	24	=	=	NOUN
ajrhss-3200	21	25	0	0	PROPN
ajrhss-3200	22	1	this	this	PRON
ajrhss-3200	22	2	is	be	AUX
ajrhss-3200	22	3	a	a	DET
ajrhss-3200	22	4	linear	linear	ADJ
ajrhss-3200	22	5	model	model	NOUN
ajrhss-3200	22	6	,	,	PUNCT
ajrhss-3200	22	7	and	and	CCONJ
ajrhss-3200	22	8	in	in	ADP
ajrhss-3200	22	9	real	real	ADJ
ajrhss-3200	22	10	systems	system	NOUN
ajrhss-3200	22	11	the	the	DET
ajrhss-3200	22	12	following	follow	VERB
ajrhss-3200	22	13	nonlinear	nonlinear	ADJ
ajrhss-3200	22	14	additions	addition	NOUN
ajrhss-3200	22	15	are	be	AUX
ajrhss-3200	22	16	often	often	ADV
ajrhss-3200	22	17	introduced	introduce	VERB
ajrhss-3200	22	18	:	:	PUNCT
ajrhss-3200	22	19	m\ddot{x	m\ddot{x	ADJ
ajrhss-3200	22	20	}	}	PUNCT
ajrhss-3200	22	21	+	+	CCONJ
ajrhss-3200	22	22	c\dot{x	c\dot{x	NOUN
ajrhss-3200	22	23	}	}	PUNCT
ajrhss-3200	22	24	+	+	NUM
ajrhss-3200	22	25	kx	kx	X
ajrhss-3200	23	1	+	+	PROPN
ajrhss-3200	23	2	\alpha	\alpha	PROPN
ajrhss-3200	23	3	x^3	x^3	PROPN
ajrhss-3200	24	1	=	=	PUNCT
ajrhss-3200	24	2	0	0	NUM
ajrhss-3200	25	1	this	this	PRON
ajrhss-3200	25	2	is	be	AUX
ajrhss-3200	25	3	a	a	DET
ajrhss-3200	25	4	duffing	duffing	NOUN
ajrhss-3200	25	5	-	-	PUNCT
ajrhss-3200	25	6	type	type	NOUN
ajrhss-3200	25	7	nonlinear	nonlinear	ADJ
ajrhss-3200	25	8	oscillator	oscillator	NOUN
ajrhss-3200	25	9	.	.	PUNCT
ajrhss-3200	26	1	causes	cause	NOUN
ajrhss-3200	26	2	of	of	ADP
ajrhss-3200	26	3	nonlinear	nonlinear	ADJ
ajrhss-3200	26	4	vibrations	vibration	NOUN
ajrhss-3200	26	5	.	.	PUNCT
ajrhss-3200	27	1	•	•	NUM
ajrhss-3200	27	2	nonlinear	nonlinear	ADJ
ajrhss-3200	27	3	vibrations	vibration	NOUN
ajrhss-3200	27	4	occur	occur	VERB
ajrhss-3200	27	5	in	in	ADP
ajrhss-3200	27	6	the	the	DET
ajrhss-3200	27	7	following	following	ADJ
ajrhss-3200	27	8	cases	case	NOUN
ajrhss-3200	27	9	:	:	PUNCT
ajrhss-3200	27	10	•	•	NUM
ajrhss-3200	27	11	nonlinearity	nonlinearity	NOUN
ajrhss-3200	27	12	of	of	ADP
ajrhss-3200	27	13	the	the	DET
ajrhss-3200	27	14	material	material	NOUN
ajrhss-3200	27	15	•	•	ADP
ajrhss-3200	27	16	large	large	ADJ
ajrhss-3200	27	17	deformations	deformation	NOUN
ajrhss-3200	27	18	•	•	VERB
ajrhss-3200	27	19	geometric	geometric	ADJ
ajrhss-3200	27	20	nonlinearity	nonlinearity	NOUN
ajrhss-3200	27	21	of	of	ADP
ajrhss-3200	27	22	contact	contact	NOUN
ajrhss-3200	27	23	forces	force	NOUN
ajrhss-3200	27	24	•	•	VERB
ajrhss-3200	27	25	various	various	ADJ
ajrhss-3200	27	26	elastic	elastic	ADJ
ajrhss-3200	27	27	modes	mode	NOUN
ajrhss-3200	27	28	of	of	ADP
ajrhss-3200	27	29	structures	structure	NOUN
ajrhss-3200	27	30	•	•	PRON
ajrhss-3200	27	31	aerodynamic	aerodynamic	ADJ
ajrhss-3200	27	32	effects	effect	NOUN
ajrhss-3200	27	33	(	(	PUNCT
ajrhss-3200	27	34	flutter	flutter	NOUN
ajrhss-3200	27	35	,	,	PUNCT
ajrhss-3200	27	36	buffeting	buffeting	NOUN
ajrhss-3200	27	37	)	)	PUNCT
ajrhss-3200	27	38	•	•	NUM
ajrhss-3200	27	39	backlash	backlash	NOUN
ajrhss-3200	27	40	in	in	ADP
ajrhss-3200	27	41	mechanical	mechanical	ADJ
ajrhss-3200	27	42	connections	connection	NOUN
ajrhss-3200	27	43	as	as	ADP
ajrhss-3200	27	44	a	a	DET
ajrhss-3200	27	45	result	result	NOUN
ajrhss-3200	27	46	of	of	ADP
ajrhss-3200	27	47	these	these	DET
ajrhss-3200	27	48	reasons	reason	NOUN
ajrhss-3200	27	49	,	,	PUNCT
ajrhss-3200	27	50	the	the	DET
ajrhss-3200	27	51	vibration	vibration	NOUN
ajrhss-3200	27	52	equations	equation	NOUN
ajrhss-3200	27	53	become	become	VERB
ajrhss-3200	27	54	more	more	ADV
ajrhss-3200	27	55	complicated	complicated	ADJ
ajrhss-3200	27	56	,	,	PUNCT
ajrhss-3200	27	57	and	and	CCONJ
ajrhss-3200	27	58	their	their	PRON
ajrhss-3200	27	59	solutions	solution	NOUN
ajrhss-3200	27	60	also	also	ADV
ajrhss-3200	27	61	differ	differ	VERB
ajrhss-3200	27	62	from	from	ADP
ajrhss-3200	27	63	those	those	PRON
ajrhss-3200	27	64	in	in	ADP
ajrhss-3200	27	65	linear	linear	PROPN
ajrhss-3200	27	66	systems	system	NOUN
ajrhss-3200	27	67	.	.	PUNCT
ajrhss-3200	28	1	the	the	DET
ajrhss-3200	28	2	interaction	interaction	NOUN
ajrhss-3200	28	3	of	of	ADP
ajrhss-3200	28	4	dissipation	dissipation	NOUN
ajrhss-3200	28	5	and	and	CCONJ
ajrhss-3200	28	6	nonlinearity	nonlinearity	NOUN
ajrhss-3200	28	7	.	.	PUNCT
ajrhss-3200	29	1	the	the	DET
ajrhss-3200	29	2	presence	presence	NOUN
ajrhss-3200	29	3	of	of	ADP
ajrhss-3200	29	4	dissipation	dissipation	NOUN
ajrhss-3200	29	5	has	have	VERB
ajrhss-3200	29	6	a	a	DET
ajrhss-3200	29	7	strong	strong	ADJ
ajrhss-3200	29	8	effect	effect	NOUN
ajrhss-3200	29	9	on	on	ADP
ajrhss-3200	29	10	the	the	DET
ajrhss-3200	29	11	vibration	vibration	NOUN
ajrhss-3200	29	12	amplitude	amplitude	NOUN
ajrhss-3200	29	13	of	of	ADP
ajrhss-3200	29	14	the	the	DET
ajrhss-3200	29	15	system	system	NOUN
ajrhss-3200	29	16	.	.	PUNCT
ajrhss-3200	30	1	in	in	ADP
ajrhss-3200	30	2	linear	linear	PROPN
ajrhss-3200	30	3	systems	system	NOUN
ajrhss-3200	30	4	,	,	PUNCT
ajrhss-3200	30	5	energy	energy	NOUN
ajrhss-3200	30	6	loss	loss	NOUN
ajrhss-3200	30	7	dampens	dampen	VERB
ajrhss-3200	30	8	the	the	DET
ajrhss-3200	30	9	vibration	vibration	NOUN
ajrhss-3200	30	10	,	,	PUNCT
ajrhss-3200	30	11	while	while	SCONJ
ajrhss-3200	30	12	in	in	ADP
ajrhss-3200	30	13	nonlinear	nonlinear	ADJ
ajrhss-3200	30	14	systems	system	NOUN
ajrhss-3200	30	15	:	:	PUNCT
ajrhss-3200	31	1	1	1	X
ajrhss-3200	31	2	.	.	X
ajrhss-3200	31	3	the	the	DET
ajrhss-3200	31	4	appearance	appearance	NOUN
ajrhss-3200	31	5	of	of	ADP
ajrhss-3200	31	6	a	a	DET
ajrhss-3200	31	7	limit	limit	NOUN
ajrhss-3200	31	8	cycle	cycle	NOUN
ajrhss-3200	31	9	2	2	NUM
ajrhss-3200	31	10	.	.	PUNCT
ajrhss-3200	31	11	autooscillation	autooscillation	NOUN
ajrhss-3200	31	12	(	(	PUNCT
ajrhss-3200	31	13	spontaneous	spontaneous	ADJ
ajrhss-3200	31	14	oscillation	oscillation	NOUN
ajrhss-3200	31	15	)	)	PUNCT
ajrhss-3200	32	1	3	3	NUM
ajrhss-3200	32	2	.	.	PUNCT
ajrhss-3200	32	3	complex	complex	ADJ
ajrhss-3200	32	4	resonant	resonant	ADJ
ajrhss-3200	32	5	responses	response	NOUN
ajrhss-3200	32	6	4	4	NUM
ajrhss-3200	32	7	.	.	PUNCT
ajrhss-3200	32	8	hysteresis	hysteresis	NOUN
ajrhss-3200	32	9	phenomena	phenomenon	NOUN
ajrhss-3200	32	10	observed	observe	VERB
ajrhss-3200	32	11	.	.	PUNCT
ajrhss-3200	33	1	for	for	ADP
ajrhss-3200	33	2	example	example	NOUN
ajrhss-3200	33	3	,	,	PUNCT
ajrhss-3200	33	4	in	in	ADP
ajrhss-3200	33	5	the	the	DET
ajrhss-3200	33	6	van	van	PROPN
ajrhss-3200	33	7	der	der	PROPN
ajrhss-3200	33	8	pol	pol	PROPN
ajrhss-3200	33	9	oscillator	oscillator	NOUN
ajrhss-3200	33	10	:	:	PUNCT
ajrhss-3200	33	11	\ddot{x}-\mu(1	\ddot{x}-\mu(1	NOUN
ajrhss-3200	33	12	-	-	PUNCT
ajrhss-3200	33	13	x^2)\dot{x	x^2)\dot{x	NOUN
ajrhss-3200	33	14	}	}	PUNCT
ajrhss-3200	33	15	+	+	NUM
ajrhss-3200	33	16	x	x	SYM
ajrhss-3200	33	17	=	=	SYM
ajrhss-3200	33	18	0	0	NOUN
ajrhss-3200	33	19	this	this	DET
ajrhss-3200	33	20	equation	equation	NOUN
ajrhss-3200	33	21	describes	describe	VERB
ajrhss-3200	33	22	a	a	DET
ajrhss-3200	33	23	system	system	NOUN
ajrhss-3200	33	24	with	with	ADP
ajrhss-3200	33	25	dissipative	dissipative	NOUN
ajrhss-3200	33	26	but	but	CCONJ
ajrhss-3200	33	27	nonlinear	nonlinear	ADJ
ajrhss-3200	33	28	autooscillations	autooscillation	NOUN
ajrhss-3200	33	29	.	.	PUNCT
ajrhss-3200	34	1	spatial	spatial	ADJ
ajrhss-3200	34	2	portraits	portrait	NOUN
ajrhss-3200	34	3	and	and	CCONJ
ajrhss-3200	34	4	stability	stability	NOUN
ajrhss-3200	34	5	.	.	PUNCT
ajrhss-3200	35	1	spatial	spatial	ADJ
ajrhss-3200	35	2	portraits	portrait	NOUN
ajrhss-3200	35	3	are	be	AUX
ajrhss-3200	35	4	important	important	ADJ
ajrhss-3200	35	5	in	in	ADP
ajrhss-3200	35	6	the	the	DET
ajrhss-3200	35	7	analysis	analysis	NOUN
ajrhss-3200	35	8	of	of	ADP
ajrhss-3200	35	9	nonlinear	nonlinear	ADJ
ajrhss-3200	35	10	systems	system	NOUN
ajrhss-3200	35	11	.	.	PUNCT
ajrhss-3200	36	1	the	the	DET
ajrhss-3200	36	2	spatial	spatial	ADJ
ajrhss-3200	36	3	portrait	portrait	NOUN
ajrhss-3200	36	4	exhibits	exhibit	VERB
ajrhss-3200	36	5	the	the	DET
ajrhss-3200	36	6	following	follow	VERB
ajrhss-3200	36	7	:	:	PUNCT
ajrhss-3200	36	8	stable	stable	ADJ
ajrhss-3200	36	9	focus	focus	NOUN
ajrhss-3200	36	10	unstable	unstable	ADJ
ajrhss-3200	36	11	focus	focus	NOUN
ajrhss-3200	36	12	limit	limit	NOUN
ajrhss-3200	36	13	cycles	cycle	NOUN
ajrhss-3200	36	14	multicycle	multicycle	NOUN
ajrhss-3200	36	15	regimes	regime	NOUN
ajrhss-3200	36	16	linear	linear	ADJ
ajrhss-3200	36	17	convergence	convergence	NOUN
ajrhss-3200	36	18	strange	strange	ADJ
ajrhss-3200	36	19	attractors	attractor	NOUN
ajrhss-3200	36	20	(	(	PUNCT
ajrhss-3200	36	21	in	in	ADP
ajrhss-3200	36	22	some	some	DET
ajrhss-3200	36	23	systems	system	NOUN
ajrhss-3200	36	24	)	)	PUNCT
ajrhss-3200	36	25	the	the	DET
ajrhss-3200	36	26	lyapunov	lyapunov	ADJ
ajrhss-3200	36	27	function	function	NOUN
ajrhss-3200	36	28	method	method	NOUN
ajrhss-3200	36	29	allows	allow	VERB
ajrhss-3200	36	30	us	we	PRON
ajrhss-3200	36	31	to	to	PART
ajrhss-3200	36	32	evaluate	evaluate	VERB
ajrhss-3200	36	33	the	the	DET
ajrhss-3200	36	34	stability	stability	NOUN
ajrhss-3200	36	35	of	of	ADP
ajrhss-3200	36	36	a	a	DET
ajrhss-3200	36	37	dissipative	dissipative	ADJ
ajrhss-3200	36	38	system	system	NOUN
ajrhss-3200	36	39	.	.	PUNCT
ajrhss-3200	37	1	if	if	SCONJ
ajrhss-3200	37	2	for	for	ADP
ajrhss-3200	37	3	some	some	DET
ajrhss-3200	37	4	function	function	NOUN
ajrhss-3200	37	5	:	:	PUNCT
ajrhss-3200	37	6	\dot{v	\dot{v	ADP
ajrhss-3200	37	7	}	}	PUNCT
ajrhss-3200	37	8	<	<	X
ajrhss-3200	37	9	0	0	PUNCT
ajrhss-3200	37	10	then	then	ADV
ajrhss-3200	37	11	the	the	DET
ajrhss-3200	37	12	system	system	NOUN
ajrhss-3200	37	13	is	be	AUX
ajrhss-3200	37	14	asymptotically	asymptotically	ADV
ajrhss-3200	37	15	stable	stable	ADJ
ajrhss-3200	37	16	.	.	PUNCT
ajrhss-3200	38	1	resonance	resonance	NOUN
ajrhss-3200	38	2	phenomena	phenomenon	NOUN
ajrhss-3200	38	3	.	.	PUNCT
ajrhss-3200	39	1	resonance	resonance	NOUN
ajrhss-3200	39	2	manifests	manifest	VERB
ajrhss-3200	39	3	itself	itself	PRON
ajrhss-3200	39	4	in	in	ADP
ajrhss-3200	39	5	nonlinear	nonlinear	ADJ
ajrhss-3200	39	6	systems	system	NOUN
ajrhss-3200	39	7	as	as	SCONJ
ajrhss-3200	39	8	follows	follow	VERB
ajrhss-3200	39	9	:	:	PUNCT
ajrhss-3200	40	1	superharmonic	superharmonic	ADJ
ajrhss-3200	40	2	resonance	resonance	NOUN
ajrhss-3200	40	3	(	(	PUNCT
ajrhss-3200	40	4	in	in	ADP
ajrhss-3200	40	5	frequency	frequency	NOUN
ajrhss-3200	40	6	dividers	divider	NOUN
ajrhss-3200	40	7	)	)	PUNCT
ajrhss-3200	40	8	american	american	ADJ
ajrhss-3200	40	9	journal	journal	PROPN
ajrhss-3200	40	10	of	of	ADP
ajrhss-3200	40	11	research	research	NOUN
ajrhss-3200	40	12	in	in	ADP
ajrhss-3200	40	13	humanities	humanity	NOUN
ajrhss-3200	40	14	and	and	CCONJ
ajrhss-3200	40	15	social	social	ADJ
ajrhss-3200	40	16	sciences	science	NOUN
ajrhss-3200	40	17	volume	volume	NOUN
ajrhss-3200	40	18	43	43	NUM
ajrhss-3200	40	19	december	december	PROPN
ajrhss-3200	40	20	2025	2025	NUM
ajrhss-3200	40	21	p	p	NOUN
ajrhss-3200	40	22	a	a	DET
ajrhss-3200	40	23	g	g	NOUN
ajrhss-3200	40	24	e	e	NOUN
ajrhss-3200	40	25	|	|	ADV
ajrhss-3200	40	26	6	6	NUM
ajrhss-3200	40	27	www.americanjournal.org	www.americanjournal.org	NOUN
ajrhss-3200	40	28	subharmonic	subharmonic	ADJ
ajrhss-3200	40	29	resonance	resonance	NOUN
ajrhss-3200	40	30	(	(	PUNCT
ajrhss-3200	40	31	in	in	ADP
ajrhss-3200	40	32	multipliers	multiplier	NOUN
ajrhss-3200	40	33	)	)	PUNCT
ajrhss-3200	40	34	combination	combination	NOUN
ajrhss-3200	40	35	resonance	resonance	NOUN
ajrhss-3200	40	36	the	the	DET
ajrhss-3200	40	37	frequency	frequency	NOUN
ajrhss-3200	40	38	-	-	PUNCT
ajrhss-3200	40	39	amplitude	amplitude	NOUN
ajrhss-3200	40	40	characteristic	characteristic	NOUN
ajrhss-3200	40	41	of	of	ADP
ajrhss-3200	40	42	nonlinear	nonlinear	ADJ
ajrhss-3200	40	43	systems	system	NOUN
ajrhss-3200	40	44	is	be	AUX
ajrhss-3200	40	45	usually	usually	ADV
ajrhss-3200	40	46	curvilinear	curvilinear	ADJ
ajrhss-3200	40	47	and	and	CCONJ
ajrhss-3200	40	48	has	have	VERB
ajrhss-3200	40	49	hysteresis	hysteresis	NOUN
ajrhss-3200	40	50	.	.	PUNCT
ajrhss-3200	41	1	for	for	ADP
ajrhss-3200	41	2	example	example	NOUN
ajrhss-3200	41	3	,	,	PUNCT
ajrhss-3200	41	4	in	in	ADP
ajrhss-3200	41	5	the	the	DET
ajrhss-3200	41	6	duffing	duffing	NOUN
ajrhss-3200	41	7	oscillator	oscillator	NOUN
ajrhss-3200	41	8	,	,	PUNCT
ajrhss-3200	41	9	the	the	DET
ajrhss-3200	41	10	phenomenon	phenomenon	NOUN
ajrhss-3200	41	11	of	of	ADP
ajrhss-3200	41	12	amplitude	amplitude	NOUN
ajrhss-3200	41	13	jumps	jump	VERB
ajrhss-3200	41	14	is	be	AUX
ajrhss-3200	41	15	observed	observe	VERB
ajrhss-3200	41	16	as	as	ADP
ajrhss-3200	41	17	a	a	DET
ajrhss-3200	41	18	result	result	NOUN
ajrhss-3200	41	19	of	of	ADP
ajrhss-3200	41	20	the	the	DET
ajrhss-3200	41	21	nonlinearity	nonlinearity	NOUN
ajrhss-3200	41	22	of	of	ADP
ajrhss-3200	41	23	the	the	DET
ajrhss-3200	41	24	stiffness	stiffness	NOUN
ajrhss-3200	41	25	.	.	PUNCT
ajrhss-3200	42	1	this	this	DET
ajrhss-3200	42	2	article	article	NOUN
ajrhss-3200	42	3	provides	provide	VERB
ajrhss-3200	42	4	a	a	DET
ajrhss-3200	42	5	comprehensive	comprehensive	ADJ
ajrhss-3200	42	6	analysis	analysis	NOUN
ajrhss-3200	42	7	of	of	ADP
ajrhss-3200	42	8	nonlinear	nonlinear	ADJ
ajrhss-3200	42	9	oscillations	oscillation	NOUN
ajrhss-3200	42	10	of	of	ADP
ajrhss-3200	42	11	dissipative	dissipative	ADJ
ajrhss-3200	42	12	mechanical	mechanical	ADJ
ajrhss-3200	42	13	systems	system	NOUN
ajrhss-3200	42	14	with	with	ADP
ajrhss-3200	42	15	a	a	DET
ajrhss-3200	42	16	limited	limited	ADJ
ajrhss-3200	42	17	number	number	NOUN
ajrhss-3200	42	18	of	of	ADP
ajrhss-3200	42	19	degrees	degree	NOUN
ajrhss-3200	42	20	of	of	ADP
ajrhss-3200	42	21	freedom	freedom	NOUN
ajrhss-3200	42	22	.	.	PUNCT
ajrhss-3200	43	1	the	the	DET
ajrhss-3200	43	2	role	role	NOUN
ajrhss-3200	43	3	of	of	ADP
ajrhss-3200	43	4	dissipation	dissipation	NOUN
ajrhss-3200	43	5	,	,	PUNCT
ajrhss-3200	43	6	various	various	ADJ
ajrhss-3200	43	7	sources	source	NOUN
ajrhss-3200	43	8	of	of	ADP
ajrhss-3200	43	9	nonlinearity	nonlinearity	NOUN
ajrhss-3200	43	10	,	,	PUNCT
ajrhss-3200	43	11	resonance	resonance	NOUN
ajrhss-3200	43	12	phenomena	phenomenon	NOUN
ajrhss-3200	43	13	,	,	PUNCT
ajrhss-3200	43	14	spatial	spatial	ADJ
ajrhss-3200	43	15	portraits	portrait	NOUN
ajrhss-3200	43	16	,	,	PUNCT
ajrhss-3200	43	17	limit	limit	NOUN
ajrhss-3200	43	18	cycles	cycle	NOUN
ajrhss-3200	43	19	,	,	PUNCT
ajrhss-3200	43	20	and	and	CCONJ
ajrhss-3200	43	21	stability	stability	NOUN
ajrhss-3200	43	22	issues	issue	NOUN
ajrhss-3200	43	23	are	be	AUX
ajrhss-3200	43	24	considered	consider	VERB
ajrhss-3200	43	25	.	.	PUNCT
ajrhss-3200	44	1	nonlinear	nonlinear	ADJ
ajrhss-3200	44	2	dissipative	dissipative	ADJ
ajrhss-3200	44	3	systems	system	NOUN
ajrhss-3200	44	4	have	have	VERB
ajrhss-3200	44	5	a	a	DET
ajrhss-3200	44	6	much	much	ADV
ajrhss-3200	44	7	richer	rich	ADJ
ajrhss-3200	44	8	dynamic	dynamic	ADJ
ajrhss-3200	44	9	behavior	behavior	NOUN
ajrhss-3200	44	10	than	than	ADP
ajrhss-3200	44	11	linear	linear	PROPN
ajrhss-3200	44	12	systems	system	NOUN
ajrhss-3200	44	13	,	,	PUNCT
ajrhss-3200	44	14	and	and	CCONJ
ajrhss-3200	44	15	their	their	PRON
ajrhss-3200	44	16	analysis	analysis	NOUN
ajrhss-3200	44	17	is	be	AUX
ajrhss-3200	44	18	one	one	NUM
ajrhss-3200	44	19	of	of	ADP
ajrhss-3200	44	20	the	the	DET
ajrhss-3200	44	21	main	main	ADJ
ajrhss-3200	44	22	directions	direction	NOUN
ajrhss-3200	44	23	of	of	ADP
ajrhss-3200	44	24	modern	modern	ADJ
ajrhss-3200	44	25	theoretical	theoretical	ADJ
ajrhss-3200	44	26	and	and	CCONJ
ajrhss-3200	44	27	applied	applied	ADJ
ajrhss-3200	44	28	mechanics	mechanic	NOUN
ajrhss-3200	44	29	.	.	PUNCT
ajrhss-3200	45	1	systems	system	NOUN
ajrhss-3200	45	2	of	of	ADP
ajrhss-3200	45	3	this	this	DET
ajrhss-3200	45	4	type	type	NOUN
ajrhss-3200	45	5	are	be	AUX
ajrhss-3200	45	6	found	find	VERB
ajrhss-3200	45	7	in	in	ADP
ajrhss-3200	45	8	many	many	ADJ
ajrhss-3200	45	9	technical	technical	ADJ
ajrhss-3200	45	10	devices	device	NOUN
ajrhss-3200	45	11	,	,	PUNCT
ajrhss-3200	45	12	and	and	CCONJ
ajrhss-3200	45	13	their	their	PRON
ajrhss-3200	45	14	correct	correct	ADJ
ajrhss-3200	45	15	modeling	modeling	NOUN
ajrhss-3200	45	16	and	and	CCONJ
ajrhss-3200	45	17	control	control	NOUN
ajrhss-3200	45	18	are	be	AUX
ajrhss-3200	45	19	of	of	ADP
ajrhss-3200	45	20	great	great	ADJ
ajrhss-3200	45	21	practical	practical	ADJ
ajrhss-3200	45	22	importance	importance	NOUN
ajrhss-3200	45	23	.	.	PUNCT
ajrhss-3200	46	1	references	reference	NOUN
ajrhss-3200	46	2	1	1	NUM
ajrhss-3200	46	3	.	.	PUNCT
ajrhss-3200	47	1	nayfeh	nayfeh	PROPN
ajrhss-3200	47	2	a.h	a.h	PROPN
ajrhss-3200	47	3	.	.	PROPN
ajrhss-3200	47	4	,	,	PUNCT
ajrhss-3200	47	5	mook	mook	PROPN
ajrhss-3200	47	6	d.t	d.t	PROPN
ajrhss-3200	47	7	.	.	PROPN
ajrhss-3200	47	8	nonlinear	nonlinear	ADJ
ajrhss-3200	47	9	oscillations	oscillation	NOUN
ajrhss-3200	47	10	.	.	PUNCT
ajrhss-3200	48	1	wiley	wiley	NOUN
ajrhss-3200	48	2	-	-	PUNCT
ajrhss-3200	48	3	interscience	interscience	NOUN
ajrhss-3200	48	4	.	.	PUNCT
ajrhss-3200	49	1	2	2	X
ajrhss-3200	49	2	.	.	X
ajrhss-3200	49	3	verhulst	verhulst	PROPN
ajrhss-3200	49	4	f.	f.	PROPN
ajrhss-3200	49	5	nonlinear	nonlinear	PROPN
ajrhss-3200	49	6	differential	differential	PROPN
ajrhss-3200	49	7	equations	equation	NOUN
ajrhss-3200	49	8	and	and	CCONJ
ajrhss-3200	49	9	dynamical	dynamical	ADJ
ajrhss-3200	49	10	systems	system	NOUN
ajrhss-3200	49	11	.	.	PUNCT
ajrhss-3200	50	1	springer	springer	NOUN
ajrhss-3200	50	2	.	.	PUNCT
ajrhss-3200	51	1	3	3	X
ajrhss-3200	51	2	.	.	X
ajrhss-3200	51	3	stoker	stoker	PROPN
ajrhss-3200	51	4	j.j	j.j	PROPN
ajrhss-3200	51	5	.	.	PROPN
ajrhss-3200	51	6	nonlinear	nonlinear	ADJ
ajrhss-3200	51	7	vibrations	vibration	NOUN
ajrhss-3200	51	8	in	in	ADP
ajrhss-3200	51	9	mechanical	mechanical	ADJ
ajrhss-3200	51	10	and	and	CCONJ
ajrhss-3200	51	11	electrical	electrical	ADJ
ajrhss-3200	51	12	systems	system	NOUN
ajrhss-3200	51	13	.	.	PUNCT
ajrhss-3200	52	1	wiley	wiley	PROPN
ajrhss-3200	52	2	.	.	PUNCT
ajrhss-3200	53	1	4	4	X
ajrhss-3200	53	2	.	.	X
ajrhss-3200	53	3	khalil	khalil	PROPN
ajrhss-3200	53	4	h.	h.	PROPN
ajrhss-3200	53	5	nonlinear	nonlinear	PROPN
ajrhss-3200	53	6	systems	systems	PROPN
ajrhss-3200	53	7	.	.	PUNCT
ajrhss-3200	54	1	prentice	prentice	PROPN
ajrhss-3200	54	2	hall	hall	PROPN
ajrhss-3200	54	3	.	.	PUNCT
ajrhss-3200	55	1	5	5	NUM
ajrhss-3200	55	2	.	.	NUM
ajrhss-3200	55	3	bogoliubov	bogoliubov	PROPN
ajrhss-3200	55	4	n.	n.	PROPN
ajrhss-3200	55	5	,	,	PUNCT
ajrhss-3200	55	6	mitropolsky	mitropolsky	PROPN
ajrhss-3200	55	7	y.	y.	PROPN
ajrhss-3200	55	8	asymptotic	asymptotic	ADJ
ajrhss-3200	55	9	methods	method	NOUN
ajrhss-3200	55	10	in	in	ADP
ajrhss-3200	55	11	the	the	DET
ajrhss-3200	55	12	theory	theory	NOUN
ajrhss-3200	55	13	of	of	ADP
ajrhss-3200	55	14	nonlinear	nonlinear	ADJ
ajrhss-3200	55	15	oscillations	oscillation	NOUN
ajrhss-3200	55	16	.	.	PUNCT
ajrhss-3200	56	1	6	6	X
ajrhss-3200	56	2	.	.	X
ajrhss-3200	56	3	kovacic	kovacic	PROPN
ajrhss-3200	56	4	i.	i.	PROPN
ajrhss-3200	56	5	,	,	PUNCT
ajrhss-3200	56	6	brennan	brennan	PROPN
ajrhss-3200	56	7	m.	m.	NOUN
ajrhss-3200	56	8	the	the	DET
ajrhss-3200	56	9	duffing	duffing	NOUN
ajrhss-3200	56	10	equation	equation	NOUN
ajrhss-3200	56	11	:	:	PUNCT
ajrhss-3200	56	12	nonlinear	nonlinear	ADJ
ajrhss-3200	56	13	oscillators	oscillator	NOUN
ajrhss-3200	56	14	and	and	CCONJ
ajrhss-3200	56	15	their	their	PRON
ajrhss-3200	56	16	behaviour	behaviour	NOUN
ajrhss-3200	56	17	.	.	PUNCT
ajrhss-3200	57	1	7	7	X
ajrhss-3200	57	2	.	.	X
ajrhss-3200	57	3	van	van	PROPN
ajrhss-3200	57	4	der	der	PROPN
ajrhss-3200	57	5	pol	pol	PROPN
ajrhss-3200	57	6	b.	b.	PROPN
ajrhss-3200	57	7	on	on	ADP
ajrhss-3200	57	8	relaxation	relaxation	NOUN
ajrhss-3200	57	9	oscillations	oscillation	NOUN
ajrhss-3200	57	10	.	.	PUNCT
ajrhss-3200	58	1	8	8	X
ajrhss-3200	58	2	.	.	X
ajrhss-3200	58	3	nayfeh	nayfeh	PROPN
ajrhss-3200	58	4	a.h	a.h	PROPN
ajrhss-3200	58	5	.	.	PROPN
ajrhss-3200	58	6	introduction	introduction	NOUN
ajrhss-3200	58	7	to	to	ADP
ajrhss-3200	58	8	perturbation	perturbation	NOUN
ajrhss-3200	58	9	techniques	technique	NOUN
ajrhss-3200	58	10	.	.	PUNCT