id	sid	tid	token	lemma	pos
fumecheng-11486	1	1	11486	11486	NUM
fumecheng-11486	1	2	facta	facta	PROPN
fumecheng-11486	1	3	universitatis	universitatis	PROPN
fumecheng-11486	1	4	series	series	NOUN
fumecheng-11486	1	5	:	:	PUNCT
fumecheng-11486	1	6	mechanical	mechanical	ADJ
fumecheng-11486	1	7	engineering	engineering	NOUN
fumecheng-11486	1	8	vol	vol	NOUN
fumecheng-11486	1	9	.	.	PROPN
fumecheng-11486	1	10	21	21	NUM
fumecheng-11486	1	11	,	,	PUNCT
fumecheng-11486	1	12	no	no	DET
fumecheng-11486	1	13	2	2	NUM
fumecheng-11486	1	14	,	,	PUNCT
fumecheng-11486	1	15	2023	2023	NUM
fumecheng-11486	1	16	,	,	PUNCT
fumecheng-11486	1	17	pp	pp	ADJ
fumecheng-11486	1	18	.	.	PUNCT
fumecheng-11486	2	1	191	191	NUM
fumecheng-11486	2	2	200	200	NUM
fumecheng-11486	2	3	https://doi.org/10.22190/fume230114007h	https://doi.org/10.22190/fume230114007h	ADV
fumecheng-11486	2	4	©	©	PROPN
fumecheng-11486	2	5	2023	2023	NUM
fumecheng-11486	2	6	by	by	ADP
fumecheng-11486	2	7	university	university	PROPN
fumecheng-11486	2	8	of	of	ADP
fumecheng-11486	2	9	niš	niš	PROPN
fumecheng-11486	2	10	,	,	PUNCT
fumecheng-11486	2	11	serbia	serbia	PROPN
fumecheng-11486	2	12	|	|	ADV
fumecheng-11486	2	13	creative	creative	ADJ
fumecheng-11486	2	14	commons	common	NOUN
fumecheng-11486	2	15	license	license	NOUN
fumecheng-11486	2	16	:	:	PUNCT
fumecheng-11486	2	17	cc	cc	VERB
fumecheng-11486	2	18	by	by	ADP
fumecheng-11486	2	19	-	-	PUNCT
fumecheng-11486	2	20	nc	nc	VERB
fumecheng-11486	2	21	-	-	PUNCT
fumecheng-11486	2	22	nd	nd	ADV
fumecheng-11486	2	23	original	original	ADJ
fumecheng-11486	2	24	scientific	scientific	ADJ
fumecheng-11486	2	25	paper	paper	ADJ
fumecheng-11486	2	26	pull	pull	NOUN
fumecheng-11486	2	27	-	-	PUNCT
fumecheng-11486	2	28	down	down	ADP
fumecheng-11486	2	29	instability	instability	NOUN
fumecheng-11486	2	30	of	of	ADP
fumecheng-11486	2	31	the	the	DET
fumecheng-11486	2	32	quadratic	quadratic	ADJ
fumecheng-11486	2	33	nonlinear	nonlinear	ADJ
fumecheng-11486	2	34	oscillators	oscillator	NOUN
fumecheng-11486	2	35	ji	ji	PROPN
fumecheng-11486	2	36	-	-	PROPN
fumecheng-11486	2	37	huan	huan	PROPN
fumecheng-11486	2	38	he1,2,3	he1,2,3	PROPN
fumecheng-11486	2	39	,	,	PUNCT
fumecheng-11486	2	40	qian	qian	PROPN
fumecheng-11486	2	41	yang3	yang3	PROPN
fumecheng-11486	2	42	,	,	PUNCT
fumecheng-11486	2	43	chun	chun	PROPN
fumecheng-11486	2	44	-	-	PUNCT
fumecheng-11486	2	45	hui	hui	PROPN
fumecheng-11486	2	46	he4,5	he4,5	PROPN
fumecheng-11486	2	47	,	,	PUNCT
fumecheng-11486	2	48	abdulrahman	abdulrahman	PROPN
fumecheng-11486	2	49	ali	ali	PROPN
fumecheng-11486	2	50	alsolami5	alsolami5	PROPN
fumecheng-11486	3	1	1national	1national	ADJ
fumecheng-11486	3	2	engineering	engineering	NOUN
fumecheng-11486	3	3	laboratory	laboratory	NOUN
fumecheng-11486	3	4	for	for	ADP
fumecheng-11486	3	5	modern	modern	ADJ
fumecheng-11486	3	6	silk	silk	NOUN
fumecheng-11486	3	7	,	,	PUNCT
fumecheng-11486	3	8	college	college	NOUN
fumecheng-11486	3	9	of	of	ADP
fumecheng-11486	3	10	textile	textile	NOUN
fumecheng-11486	3	11	and	and	CCONJ
fumecheng-11486	3	12	clothing	clothing	NOUN
fumecheng-11486	3	13	engineering	engineering	NOUN
fumecheng-11486	3	14	,	,	PUNCT
fumecheng-11486	3	15	soochow	soochow	PROPN
fumecheng-11486	3	16	university	university	PROPN
fumecheng-11486	3	17	,	,	PUNCT
fumecheng-11486	3	18	suzhou	suzhou	PROPN
fumecheng-11486	3	19	,	,	PUNCT
fumecheng-11486	3	20	china	china	PROPN
fumecheng-11486	3	21	2school	2school	NUM
fumecheng-11486	3	22	of	of	ADP
fumecheng-11486	3	23	mathematics	mathematic	NOUN
fumecheng-11486	3	24	and	and	CCONJ
fumecheng-11486	3	25	information	information	NOUN
fumecheng-11486	3	26	science	science	NOUN
fumecheng-11486	3	27	,	,	PUNCT
fumecheng-11486	3	28	henan	henan	PROPN
fumecheng-11486	3	29	polytechnic	polytechnic	PROPN
fumecheng-11486	3	30	university	university	PROPN
fumecheng-11486	3	31	,	,	PUNCT
fumecheng-11486	3	32	jiaozuo	jiaozuo	PROPN
fumecheng-11486	3	33	,	,	PUNCT
fumecheng-11486	3	34	china	china	PROPN
fumecheng-11486	3	35	3school	3school	NUM
fumecheng-11486	3	36	of	of	ADP
fumecheng-11486	3	37	science	science	PROPN
fumecheng-11486	3	38	,	,	PUNCT
fumecheng-11486	3	39	xi’an	xi’an	PROPN
fumecheng-11486	3	40	university	university	PROPN
fumecheng-11486	3	41	of	of	ADP
fumecheng-11486	3	42	architecture	architecture	NOUN
fumecheng-11486	3	43	and	and	CCONJ
fumecheng-11486	3	44	technology	technology	NOUN
fumecheng-11486	3	45	,	,	PUNCT
fumecheng-11486	3	46	xi’an	xi’an	PROPN
fumecheng-11486	3	47	,	,	PUNCT
fumecheng-11486	3	48	china	china	PROPN
fumecheng-11486	3	49	4school	4school	NUM
fumecheng-11486	3	50	of	of	ADP
fumecheng-11486	3	51	mathematics	mathematics	PROPN
fumecheng-11486	3	52	,	,	PUNCT
fumecheng-11486	3	53	china	china	PROPN
fumecheng-11486	3	54	university	university	PROPN
fumecheng-11486	3	55	of	of	ADP
fumecheng-11486	3	56	mining	mining	NOUN
fumecheng-11486	3	57	and	and	CCONJ
fumecheng-11486	3	58	technology	technology	NOUN
fumecheng-11486	3	59	,	,	PUNCT
fumecheng-11486	3	60	xuzhou	xuzhou	PROPN
fumecheng-11486	3	61	,	,	PUNCT
fumecheng-11486	3	62	jiangsu	jiangsu	PROPN
fumecheng-11486	3	63	,	,	PUNCT
fumecheng-11486	3	64	china	china	PROPN
fumecheng-11486	3	65	5department	5department	NUM
fumecheng-11486	3	66	of	of	ADP
fumecheng-11486	3	67	mathematics	mathematic	NOUN
fumecheng-11486	3	68	,	,	PUNCT
fumecheng-11486	3	69	faculty	faculty	NOUN
fumecheng-11486	3	70	of	of	ADP
fumecheng-11486	3	71	science	science	NOUN
fumecheng-11486	3	72	,	,	PUNCT
fumecheng-11486	3	73	king	king	PROPN
fumecheng-11486	3	74	abdulaziz	abdulaziz	PROPN
fumecheng-11486	3	75	university	university	PROPN
fumecheng-11486	3	76	,	,	PUNCT
fumecheng-11486	3	77	jeddah	jeddah	PROPN
fumecheng-11486	3	78	,	,	PUNCT
fumecheng-11486	3	79	saudi	saudi	PROPN
fumecheng-11486	3	80	arabia	arabia	PROPN
fumecheng-11486	3	81	abstract	abstract	NOUN
fumecheng-11486	3	82	.	.	PUNCT
fumecheng-11486	4	1	a	a	DET
fumecheng-11486	4	2	nonlinear	nonlinear	ADJ
fumecheng-11486	4	3	vibration	vibration	NOUN
fumecheng-11486	4	4	system	system	NOUN
fumecheng-11486	4	5	,	,	PUNCT
fumecheng-11486	4	6	over	over	ADP
fumecheng-11486	4	7	a	a	DET
fumecheng-11486	4	8	span	span	NOUN
fumecheng-11486	4	9	of	of	ADP
fumecheng-11486	4	10	convincing	convince	VERB
fumecheng-11486	4	11	periodic	periodic	ADJ
fumecheng-11486	4	12	motion	motion	NOUN
fumecheng-11486	4	13	,	,	PUNCT
fumecheng-11486	4	14	might	might	AUX
fumecheng-11486	4	15	break	break	VERB
fumecheng-11486	4	16	out	out	ADP
fumecheng-11486	4	17	abruptly	abruptly	ADV
fumecheng-11486	4	18	a	a	DET
fumecheng-11486	4	19	catastrophic	catastrophic	ADJ
fumecheng-11486	4	20	instability	instability	NOUN
fumecheng-11486	4	21	,	,	PUNCT
fumecheng-11486	4	22	but	but	CCONJ
fumecheng-11486	4	23	the	the	DET
fumecheng-11486	4	24	lack	lack	NOUN
fumecheng-11486	4	25	of	of	ADP
fumecheng-11486	4	26	a	a	DET
fumecheng-11486	4	27	theoretical	theoretical	ADJ
fumecheng-11486	4	28	tool	tool	NOUN
fumecheng-11486	4	29	has	have	AUX
fumecheng-11486	4	30	obscured	obscure	VERB
fumecheng-11486	4	31	the	the	DET
fumecheng-11486	4	32	prediction	prediction	NOUN
fumecheng-11486	4	33	of	of	ADP
fumecheng-11486	4	34	the	the	DET
fumecheng-11486	4	35	outbreak	outbreak	NOUN
fumecheng-11486	4	36	.	.	PUNCT
fumecheng-11486	5	1	this	this	DET
fumecheng-11486	5	2	paper	paper	NOUN
fumecheng-11486	5	3	deploys	deploy	VERB
fumecheng-11486	5	4	the	the	DET
fumecheng-11486	5	5	amplitude	amplitude	NOUN
fumecheng-11486	5	6	-	-	PUNCT
fumecheng-11486	5	7	frequency	frequency	NOUN
fumecheng-11486	5	8	formulation	formulation	NOUN
fumecheng-11486	5	9	for	for	ADP
fumecheng-11486	5	10	nonlinear	nonlinear	ADJ
fumecheng-11486	5	11	oscillators	oscillator	NOUN
fumecheng-11486	5	12	to	to	PART
fumecheng-11486	5	13	reveal	reveal	VERB
fumecheng-11486	5	14	the	the	DET
fumecheng-11486	5	15	critically	critically	ADV
fumecheng-11486	5	16	important	important	ADJ
fumecheng-11486	5	17	mechanism	mechanism	NOUN
fumecheng-11486	5	18	of	of	ADP
fumecheng-11486	5	19	the	the	DET
fumecheng-11486	5	20	pseudo	pseudo	NOUN
fumecheng-11486	5	21	-	-	ADJ
fumecheng-11486	5	22	periodic	periodic	ADJ
fumecheng-11486	5	23	motion	motion	NOUN
fumecheng-11486	5	24	,	,	PUNCT
fumecheng-11486	5	25	and	and	CCONJ
fumecheng-11486	5	26	finds	find	VERB
fumecheng-11486	5	27	the	the	DET
fumecheng-11486	5	28	quadratic	quadratic	ADJ
fumecheng-11486	5	29	nonlinear	nonlinear	ADJ
fumecheng-11486	5	30	force	force	NOUN
fumecheng-11486	5	31	contributes	contribute	VERB
fumecheng-11486	5	32	to	to	ADP
fumecheng-11486	5	33	the	the	DET
fumecheng-11486	5	34	pull	pull	VERB
fumecheng-11486	5	35	-	-	PUNCT
fumecheng-11486	5	36	down	down	ADP
fumecheng-11486	5	37	phenomenon	phenomenon	NOUN
fumecheng-11486	5	38	in	in	ADP
fumecheng-11486	5	39	each	each	DET
fumecheng-11486	5	40	cycle	cycle	NOUN
fumecheng-11486	5	41	of	of	ADP
fumecheng-11486	5	42	the	the	DET
fumecheng-11486	5	43	periodic	periodic	ADJ
fumecheng-11486	5	44	motion	motion	NOUN
fumecheng-11486	5	45	,	,	PUNCT
fumecheng-11486	5	46	when	when	SCONJ
fumecheng-11486	5	47	the	the	DET
fumecheng-11486	5	48	force	force	NOUN
fumecheng-11486	5	49	reaches	reach	VERB
fumecheng-11486	5	50	a	a	DET
fumecheng-11486	5	51	threshold	threshold	NOUN
fumecheng-11486	5	52	value	value	NOUN
fumecheng-11486	5	53	,	,	PUNCT
fumecheng-11486	5	54	the	the	DET
fumecheng-11486	5	55	pull	pull	NOUN
fumecheng-11486	5	56	-	-	PUNCT
fumecheng-11486	5	57	down	down	ADP
fumecheng-11486	5	58	instability	instability	NOUN
fumecheng-11486	5	59	occurs	occur	VERB
fumecheng-11486	5	60	.	.	PUNCT
fumecheng-11486	6	1	a	a	DET
fumecheng-11486	6	2	criterion	criterion	NOUN
fumecheng-11486	6	3	for	for	ADP
fumecheng-11486	6	4	prediction	prediction	NOUN
fumecheng-11486	6	5	of	of	ADP
fumecheng-11486	6	6	the	the	DET
fumecheng-11486	6	7	pull	pull	NOUN
fumecheng-11486	6	8	-	-	PUNCT
fumecheng-11486	6	9	down	down	ADP
fumecheng-11486	6	10	instability	instability	NOUN
fumecheng-11486	6	11	is	be	AUX
fumecheng-11486	6	12	proposed	propose	VERB
fumecheng-11486	6	13	and	and	CCONJ
fumecheng-11486	6	14	verified	verify	VERB
fumecheng-11486	6	15	numerically	numerically	ADV
fumecheng-11486	6	16	.	.	PUNCT
fumecheng-11486	7	1	key	key	ADJ
fumecheng-11486	7	2	words	word	NOUN
fumecheng-11486	7	3	:	:	PUNCT
fumecheng-11486	7	4	micro	micro	ADJ
fumecheng-11486	7	5	-	-	ADJ
fumecheng-11486	7	6	electromechanical	electromechanical	ADJ
fumecheng-11486	7	7	system	system	NOUN
fumecheng-11486	7	8	,	,	PUNCT
fumecheng-11486	7	9	eardrum	eardrum	PROPN
fumecheng-11486	7	10	oscillator	oscillator	NOUN
fumecheng-11486	7	11	,	,	PUNCT
fumecheng-11486	7	12	pull	pull	NOUN
fumecheng-11486	7	13	-	-	PUNCT
fumecheng-11486	7	14	in	in	ADP
fumecheng-11486	7	15	instability	instability	NOUN
fumecheng-11486	7	16	,	,	PUNCT
fumecheng-11486	7	17	asymmetrical	asymmetrical	ADJ
fumecheng-11486	7	18	oscillation	oscillation	NOUN
fumecheng-11486	7	19	,	,	PUNCT
fumecheng-11486	7	20	vibration	vibration	NOUN
fumecheng-11486	7	21	attenuation	attenuation	NOUN
fumecheng-11486	7	22	,	,	PUNCT
fumecheng-11486	7	23	energy	energy	NOUN
fumecheng-11486	7	24	harvesting	harvesting	NOUN
fumecheng-11486	7	25	1	1	NUM
fumecheng-11486	7	26	.	.	PUNCT
fumecheng-11486	7	27	introduction	introduction	NOUN
fumecheng-11486	7	28	the	the	DET
fumecheng-11486	7	29	nonlinear	nonlinear	ADJ
fumecheng-11486	7	30	oscillators	oscillator	NOUN
fumecheng-11486	7	31	with	with	ADP
fumecheng-11486	7	32	even	even	ADJ
fumecheng-11486	7	33	nonlinearities	nonlinearitie	NOUN
fumecheng-11486	7	34	,	,	PUNCT
fumecheng-11486	7	35	especially	especially	ADV
fumecheng-11486	7	36	the	the	DET
fumecheng-11486	7	37	quadratic	quadratic	ADJ
fumecheng-11486	7	38	nonlinear	nonlinear	ADJ
fumecheng-11486	7	39	oscillators	oscillator	NOUN
fumecheng-11486	7	40	[	[	X
fumecheng-11486	7	41	1	1	NUM
fumecheng-11486	7	42	-	-	SYM
fumecheng-11486	7	43	5	5	NUM
fumecheng-11486	7	44	]	]	PUNCT
fumecheng-11486	7	45	,	,	PUNCT
fumecheng-11486	7	46	became	become	VERB
fumecheng-11486	7	47	a	a	DET
fumecheng-11486	7	48	hot	hot	ADJ
fumecheng-11486	7	49	topic	topic	NOUN
fumecheng-11486	7	50	recently	recently	ADV
fumecheng-11486	7	51	in	in	ADP
fumecheng-11486	7	52	both	both	DET
fumecheng-11486	7	53	mathematics	mathematic	NOUN
fumecheng-11486	7	54	and	and	CCONJ
fumecheng-11486	7	55	engineering	engineering	NOUN
fumecheng-11486	7	56	,	,	PUNCT
fumecheng-11486	7	57	because	because	SCONJ
fumecheng-11486	7	58	scientists	scientist	NOUN
fumecheng-11486	7	59	and	and	CCONJ
fumecheng-11486	7	60	engineers	engineer	NOUN
fumecheng-11486	7	61	can	can	AUX
fumecheng-11486	7	62	not	not	PART
fumecheng-11486	7	63	exactly	exactly	ADV
fumecheng-11486	7	64	differentiate	differentiate	VERB
fumecheng-11486	7	65	between	between	ADP
fumecheng-11486	7	66	the	the	DET
fumecheng-11486	7	67	periodic	periodic	ADJ
fumecheng-11486	7	68	motion	motion	NOUN
fumecheng-11486	7	69	and	and	CCONJ
fumecheng-11486	7	70	the	the	DET
fumecheng-11486	7	71	fake	fake	ADJ
fumecheng-11486	7	72	periodic	periodic	ADJ
fumecheng-11486	7	73	motion	motion	NOUN
fumecheng-11486	7	74	with	with	ADP
fumecheng-11486	7	75	ease	ease	NOUN
fumecheng-11486	7	76	.	.	PUNCT
fumecheng-11486	8	1	scientists	scientist	NOUN
fumecheng-11486	8	2	have	have	AUX
fumecheng-11486	8	3	now	now	ADV
fumecheng-11486	8	4	found	find	VERB
fumecheng-11486	8	5	that	that	SCONJ
fumecheng-11486	8	6	a	a	DET
fumecheng-11486	8	7	convincing	convincing	ADJ
fumecheng-11486	8	8	periodic	periodic	NOUN
fumecheng-11486	8	9	received	receive	VERB
fumecheng-11486	8	10	:	:	PUNCT
fumecheng-11486	8	11	january	january	PROPN
fumecheng-11486	8	12	14	14	NUM
fumecheng-11486	8	13	,	,	PUNCT
fumecheng-11486	8	14	2023	2023	NUM
fumecheng-11486	8	15	/	/	PUNCT
fumecheng-11486	8	16	accepted	accept	VERB
fumecheng-11486	8	17	february	february	PROPN
fumecheng-11486	8	18	08	08	NUM
fumecheng-11486	8	19	,	,	PUNCT
fumecheng-11486	8	20	2023	2023	NUM
fumecheng-11486	8	21	corresponding	correspond	VERB
fumecheng-11486	8	22	author	author	NOUN
fumecheng-11486	8	23	:	:	PUNCT
fumecheng-11486	8	24	ji	ji	PROPN
fumecheng-11486	8	25	-	-	PROPN
fumecheng-11486	8	26	huan	huan	PROPN
fumecheng-11486	8	27	he	he	PROPN
fumecheng-11486	8	28	and	and	CCONJ
fumecheng-11486	8	29	chun	chun	PROPN
fumecheng-11486	8	30	-	-	PUNCT
fumecheng-11486	8	31	hui	hui	PROPN
fumecheng-11486	8	32	he	he	PRON
fumecheng-11486	8	33	affiliation	affiliation	NOUN
fumecheng-11486	8	34	,	,	PUNCT
fumecheng-11486	8	35	national	national	ADJ
fumecheng-11486	8	36	engineering	engineering	NOUN
fumecheng-11486	8	37	laboratory	laboratory	NOUN
fumecheng-11486	8	38	for	for	ADP
fumecheng-11486	8	39	modern	modern	ADJ
fumecheng-11486	8	40	silk	silk	NOUN
fumecheng-11486	8	41	,	,	PUNCT
fumecheng-11486	8	42	college	college	NOUN
fumecheng-11486	8	43	of	of	ADP
fumecheng-11486	8	44	textile	textile	NOUN
fumecheng-11486	8	45	and	and	CCONJ
fumecheng-11486	8	46	clothing	clothing	NOUN
fumecheng-11486	8	47	engineering	engineering	NOUN
fumecheng-11486	8	48	,	,	PUNCT
fumecheng-11486	8	49	soochow	soochow	PROPN
fumecheng-11486	8	50	university	university	PROPN
fumecheng-11486	8	51	,	,	PUNCT
fumecheng-11486	8	52	suzhou	suzhou	PROPN
fumecheng-11486	8	53	,	,	PUNCT
fumecheng-11486	8	54	p.	p.	PROPN
fumecheng-11486	8	55	r.	r.	PROPN
fumecheng-11486	8	56	china	china	PROPN
fumecheng-11486	9	1	e	e	X
fumecheng-11486	9	2	-	-	PUNCT
fumecheng-11486	9	3	mails	mail	NOUN
fumecheng-11486	9	4	:	:	PUNCT
fumecheng-11486	9	5	hejihuan@suda.edu.cn	hejihuan@suda.edu.cn	NOUN
fumecheng-11486	9	6	(	(	PUNCT
fumecheng-11486	9	7	j.h	j.h	PROPN
fumecheng-11486	9	8	.	.	PUNCT
fumecheng-11486	9	9	he	he	PRON
fumecheng-11486	9	10	)	)	PUNCT
fumecheng-11486	9	11	,	,	PUNCT
fumecheng-11486	9	12	mathew_he@yahoo.com	mathew_he@yahoo.com	X
fumecheng-11486	9	13	(	(	PUNCT
fumecheng-11486	9	14	c.h	c.h	PROPN
fumecheng-11486	9	15	.	.	PUNCT
fumecheng-11486	10	1	he	he	PRON
fumecheng-11486	10	2	)	)	PUNCT
fumecheng-11486	10	3	mailto:hejihuan@suda.edu.cn	mailto:hejihuan@suda.edu.cn	VERB
fumecheng-11486	10	4	mailto:mathew_he@yahoo.com	mailto:mathew_he@yahoo.com	NOUN
fumecheng-11486	10	5	192	192	NUM
fumecheng-11486	11	1	j.h	j.h	PROPN
fumecheng-11486	11	2	.	.	PUNCT
fumecheng-11486	12	1	he	he	PRON
fumecheng-11486	12	2	,	,	PUNCT
fumecheng-11486	12	3	q.	q.	PROPN
fumecheng-11486	12	4	yang	yang	PROPN
fumecheng-11486	12	5	,	,	PUNCT
fumecheng-11486	12	6	c.h	c.h	PROPN
fumecheng-11486	12	7	.	.	PUNCT
fumecheng-11486	13	1	he	he	PRON
fumecheng-11486	13	2	,	,	PUNCT
fumecheng-11486	13	3	a.a	a.a	PROPN
fumecheng-11486	13	4	.	.	PROPN
fumecheng-11486	13	5	alsolami	alsolami	PROPN
fumecheng-11486	13	6	motion	motion	NOUN
fumecheng-11486	13	7	might	might	AUX
fumecheng-11486	13	8	be	be	AUX
fumecheng-11486	13	9	a	a	DET
fumecheng-11486	13	10	fake	fake	ADJ
fumecheng-11486	13	11	one	one	NOUN
fumecheng-11486	13	12	,	,	PUNCT
fumecheng-11486	13	13	which	which	PRON
fumecheng-11486	13	14	is	be	AUX
fumecheng-11486	13	15	called	call	VERB
fumecheng-11486	13	16	as	as	ADP
fumecheng-11486	13	17	the	the	DET
fumecheng-11486	13	18	pseudo	pseudo	NOUN
fumecheng-11486	13	19	-	-	NOUN
fumecheng-11486	13	20	periodic	periodic	ADJ
fumecheng-11486	13	21	motion	motion	NOUN
fumecheng-11486	13	22	[	[	X
fumecheng-11486	13	23	6,7	6,7	NUM
fumecheng-11486	13	24	]	]	PUNCT
fumecheng-11486	13	25	,	,	PUNCT
fumecheng-11486	13	26	after	after	ADP
fumecheng-11486	13	27	some	some	DET
fumecheng-11486	13	28	cycles	cycle	NOUN
fumecheng-11486	13	29	of	of	ADP
fumecheng-11486	13	30	seeming	seem	VERB
fumecheng-11486	13	31	periodic	periodic	ADJ
fumecheng-11486	13	32	motion	motion	NOUN
fumecheng-11486	13	33	,	,	PUNCT
fumecheng-11486	13	34	its	its	PRON
fumecheng-11486	13	35	motion	motion	NOUN
fumecheng-11486	13	36	property	property	NOUN
fumecheng-11486	13	37	will	will	AUX
fumecheng-11486	13	38	be	be	AUX
fumecheng-11486	13	39	suddenly	suddenly	ADV
fumecheng-11486	13	40	changed	change	VERB
fumecheng-11486	13	41	,	,	PUNCT
fumecheng-11486	13	42	and	and	CCONJ
fumecheng-11486	13	43	the	the	DET
fumecheng-11486	13	44	instability	instability	NOUN
fumecheng-11486	13	45	occurs	occur	VERB
fumecheng-11486	13	46	,	,	PUNCT
fumecheng-11486	13	47	and	and	CCONJ
fumecheng-11486	13	48	scientists	scientist	NOUN
fumecheng-11486	13	49	are	be	AUX
fumecheng-11486	13	50	often	often	ADV
fumecheng-11486	13	51	unable	unable	ADJ
fumecheng-11486	13	52	to	to	PART
fumecheng-11486	13	53	spot	spot	VERB
fumecheng-11486	13	54	the	the	DET
fumecheng-11486	13	55	pseudo	pseudo	NOUN
fumecheng-11486	13	56	-	-	ADJ
fumecheng-11486	13	57	periodic	periodic	ADJ
fumecheng-11486	13	58	motion	motion	NOUN
fumecheng-11486	13	59	.	.	PUNCT
fumecheng-11486	14	1	though	though	SCONJ
fumecheng-11486	14	2	mathematicians	mathematician	NOUN
fumecheng-11486	14	3	can	can	AUX
fumecheng-11486	14	4	reveal	reveal	VERB
fumecheng-11486	14	5	easily	easily	ADV
fumecheng-11486	14	6	the	the	DET
fumecheng-11486	14	7	bifurcation	bifurcation	NOUN
fumecheng-11486	14	8	property	property	NOUN
fumecheng-11486	14	9	of	of	ADP
fumecheng-11486	14	10	such	such	DET
fumecheng-11486	14	11	a	a	DET
fumecheng-11486	14	12	nonlinear	nonlinear	ADJ
fumecheng-11486	14	13	oscillator	oscillator	NOUN
fumecheng-11486	14	14	[	[	X
fumecheng-11486	14	15	8	8	NUM
fumecheng-11486	14	16	]	]	PUNCT
fumecheng-11486	14	17	,	,	PUNCT
fumecheng-11486	14	18	the	the	DET
fumecheng-11486	14	19	pseudo	pseudo	NOUN
fumecheng-11486	14	20	-	-	ADJ
fumecheng-11486	14	21	periodic	periodic	ADJ
fumecheng-11486	14	22	motion	motion	NOUN
fumecheng-11486	14	23	of	of	ADP
fumecheng-11486	14	24	the	the	DET
fumecheng-11486	14	25	quadratic	quadratic	ADJ
fumecheng-11486	14	26	nonlinear	nonlinear	ADJ
fumecheng-11486	14	27	oscillator	oscillator	NOUN
fumecheng-11486	14	28	has	have	AUX
fumecheng-11486	14	29	never	never	ADV
fumecheng-11486	14	30	been	be	AUX
fumecheng-11486	14	31	reported	report	VERB
fumecheng-11486	14	32	,	,	PUNCT
fumecheng-11486	14	33	and	and	CCONJ
fumecheng-11486	14	34	the	the	DET
fumecheng-11486	14	35	critically	critically	ADV
fumecheng-11486	14	36	important	important	ADJ
fumecheng-11486	14	37	mechanism	mechanism	NOUN
fumecheng-11486	14	38	of	of	ADP
fumecheng-11486	14	39	the	the	DET
fumecheng-11486	14	40	pseudo	pseudo	NOUN
fumecheng-11486	14	41	-	-	ADJ
fumecheng-11486	14	42	periodic	periodic	ADJ
fumecheng-11486	14	43	motion	motion	NOUN
fumecheng-11486	14	44	needs	need	VERB
fumecheng-11486	14	45	to	to	PART
fumecheng-11486	14	46	be	be	AUX
fumecheng-11486	14	47	revealed	reveal	VERB
fumecheng-11486	14	48	,	,	PUNCT
fumecheng-11486	14	49	so	so	SCONJ
fumecheng-11486	14	50	that	that	SCONJ
fumecheng-11486	14	51	its	its	PRON
fumecheng-11486	14	52	instability	instability	NOUN
fumecheng-11486	14	53	can	can	AUX
fumecheng-11486	14	54	be	be	AUX
fumecheng-11486	14	55	completely	completely	ADV
fumecheng-11486	14	56	avoided	avoid	VERB
fumecheng-11486	14	57	.	.	PUNCT
fumecheng-11486	15	1	we	we	PRON
fumecheng-11486	15	2	consider	consider	VERB
fumecheng-11486	15	3	an	an	DET
fumecheng-11486	15	4	important	important	ADJ
fumecheng-11486	15	5	nonlinear	nonlinear	ADJ
fumecheng-11486	15	6	oscillator	oscillator	NOUN
fumecheng-11486	15	7	which	which	PRON
fumecheng-11486	15	8	involves	involve	VERB
fumecheng-11486	15	9	even	even	ADV
fumecheng-11486	15	10	nonlinearities	nonlinearitie	NOUN
fumecheng-11486	15	11	,	,	PUNCT
fumecheng-11486	15	12	the	the	DET
fumecheng-11486	15	13	toda	toda	PROPN
fumecheng-11486	15	14	oscillator	oscillator	NOUN
fumecheng-11486	15	15	[	[	X
fumecheng-11486	15	16	9,10,11	9,10,11	NUM
fumecheng-11486	15	17	]	]	PUNCT
fumecheng-11486	15	18	,	,	PUNCT
fumecheng-11486	15	19	which	which	PRON
fumecheng-11486	15	20	plays	play	VERB
fumecheng-11486	15	21	an	an	DET
fumecheng-11486	15	22	important	important	ADJ
fumecheng-11486	15	23	role	role	NOUN
fumecheng-11486	15	24	in	in	ADP
fumecheng-11486	15	25	physics	physics	NOUN
fumecheng-11486	15	26	:	:	PUNCT
fumecheng-11486	15	27	2	2	NUM
fumecheng-11486	15	28	2	2	NUM
fumecheng-11486	15	29	(	(	PUNCT
fumecheng-11486	15	30	1	1	NUM
fumecheng-11486	15	31	)	)	PUNCT
fumecheng-11486	15	32	0	0	NUM
fumecheng-11486	16	1	+	+	NUM
fumecheng-11486	17	1	−	−	NOUN
fumecheng-11486	18	1	=	=	PRON
fumecheng-11486	18	2	ud	ud	NOUN
fumecheng-11486	18	3	u	u	NOUN
fumecheng-11486	18	4	k	k	PROPN
fumecheng-11486	18	5	e	e	X
fumecheng-11486	18	6	dt	dt	X
fumecheng-11486	18	7	(	(	PUNCT
fumecheng-11486	18	8	1	1	NUM
fumecheng-11486	18	9	)	)	PUNCT
fumecheng-11486	18	10	where	where	SCONJ
fumecheng-11486	18	11	k	k	PROPN
fumecheng-11486	18	12	is	be	AUX
fumecheng-11486	18	13	constant	constant	ADJ
fumecheng-11486	18	14	.	.	PUNCT
fumecheng-11486	19	1	eq	eq	X
fumecheng-11486	19	2	.	.	PUNCT
fumecheng-11486	20	1	(	(	PUNCT
fumecheng-11486	20	2	1	1	X
fumecheng-11486	20	3	)	)	PUNCT
fumecheng-11486	20	4	can	can	AUX
fumecheng-11486	20	5	be	be	AUX
fumecheng-11486	20	6	written	write	VERB
fumecheng-11486	20	7	equivalently	equivalently	ADV
fumecheng-11486	20	8	in	in	ADP
fumecheng-11486	20	9	the	the	DET
fumecheng-11486	20	10	following	follow	VERB
fumecheng-11486	20	11	form	form	NOUN
fumecheng-11486	20	12	2	2	NUM
fumecheng-11486	20	13	2	2	NUM
fumecheng-11486	20	14	3	3	NUM
fumecheng-11486	20	15	4	4	NUM
fumecheng-11486	20	16	2	2	NUM
fumecheng-11486	20	17	0	0	NUM
fumecheng-11486	20	18	2	2	NUM
fumecheng-11486	20	19	6	6	NUM
fumecheng-11486	20	20	24	24	NUM
fumecheng-11486	20	21	+	+	CCONJ
fumecheng-11486	21	1	+	+	PUNCT
fumecheng-11486	21	2	+	+	PUNCT
fumecheng-11486	21	3	+	+	PUNCT
fumecheng-11486	21	4	+	+	NOUN
fumecheng-11486	21	5	=	=	SYM
fumecheng-11486	21	6	d	d	SYM
fumecheng-11486	21	7	u	u	X
fumecheng-11486	22	1	k	k	PROPN
fumecheng-11486	22	2	k	k	PROPN
fumecheng-11486	22	3	k	k	PROPN
fumecheng-11486	22	4	u	u	X
fumecheng-11486	22	5	u	u	VERB
fumecheng-11486	22	6	u	u	X
fumecheng-11486	22	7	u	u	X
fumecheng-11486	22	8	dt	dt	X
fumecheng-11486	22	9	(	(	PUNCT
fumecheng-11486	22	10	2	2	NUM
fumecheng-11486	22	11	)	)	PUNCT
fumecheng-11486	22	12	the	the	DET
fumecheng-11486	22	13	toda	toda	PROPN
fumecheng-11486	22	14	oscillator	oscillator	PROPN
fumecheng-11486	22	15	behaves	behave	VERB
fumecheng-11486	22	16	periodically	periodically	ADV
fumecheng-11486	22	17	when	when	SCONJ
fumecheng-11486	22	18	k	k	PROPN
fumecheng-11486	22	19	is	be	AUX
fumecheng-11486	22	20	small	small	ADJ
fumecheng-11486	22	21	,	,	PUNCT
fumecheng-11486	22	22	however	however	ADV
fumecheng-11486	22	23	the	the	DET
fumecheng-11486	22	24	amplitude	amplitude	NOUN
fumecheng-11486	22	25	might	might	AUX
fumecheng-11486	22	26	lead	lead	VERB
fumecheng-11486	22	27	to	to	ADP
fumecheng-11486	22	28	either	either	DET
fumecheng-11486	22	29	infinity	infinity	NOUN
fumecheng-11486	22	30	or	or	CCONJ
fumecheng-11486	22	31	zero	zero	NUM
fumecheng-11486	22	32	when	when	SCONJ
fumecheng-11486	22	33	the	the	DET
fumecheng-11486	22	34	absolute	absolute	ADJ
fumecheng-11486	22	35	value	value	NOUN
fumecheng-11486	22	36	of	of	ADP
fumecheng-11486	22	37	k	k	PROPN
fumecheng-11486	22	38	reaches	reach	VERB
fumecheng-11486	22	39	a	a	DET
fumecheng-11486	22	40	threshold	threshold	NOUN
fumecheng-11486	22	41	value	value	NOUN
fumecheng-11486	22	42	.	.	PUNCT
fumecheng-11486	23	1	as	as	ADP
fumecheng-11486	23	2	another	another	DET
fumecheng-11486	23	3	example	example	NOUN
fumecheng-11486	23	4	,	,	PUNCT
fumecheng-11486	23	5	we	we	PRON
fumecheng-11486	23	6	consider	consider	VERB
fumecheng-11486	23	7	a	a	DET
fumecheng-11486	23	8	microelectromechanical	microelectromechanical	ADJ
fumecheng-11486	23	9	system	system	NOUN
fumecheng-11486	23	10	,	,	PUNCT
fumecheng-11486	23	11	which	which	PRON
fumecheng-11486	23	12	can	can	AUX
fumecheng-11486	23	13	be	be	AUX
fumecheng-11486	23	14	modelled	model	VERB
fumecheng-11486	23	15	by	by	ADP
fumecheng-11486	23	16	the	the	DET
fumecheng-11486	23	17	following	follow	VERB
fumecheng-11486	23	18	differential	differential	ADJ
fumecheng-11486	23	19	equation	equation	NOUN
fumecheng-11486	23	20	[	[	X
fumecheng-11486	23	21	12	12	NUM
fumecheng-11486	23	22	]	]	X
fumecheng-11486	23	23	:	:	PUNCT
fumecheng-11486	23	24	2	2	NUM
fumecheng-11486	23	25	2	2	NUM
fumecheng-11486	23	26	0	0	NUM
fumecheng-11486	23	27	1	1	NUM
fumecheng-11486	23	28	+	+	CCONJ
fumecheng-11486	23	29	−	−	PROPN
fumecheng-11486	23	30	=	=	SYM
fumecheng-11486	23	31	−	−	PROPN
fumecheng-11486	24	1	d	d	X
fumecheng-11486	24	2	u	u	X
fumecheng-11486	24	3	k	k	PROPN
fumecheng-11486	24	4	u	u	X
fumecheng-11486	24	5	udt	udt	X
fumecheng-11486	24	6	(	(	PUNCT
fumecheng-11486	24	7	3	3	NUM
fumecheng-11486	24	8	)	)	PUNCT
fumecheng-11486	24	9	where	where	SCONJ
fumecheng-11486	24	10	u	u	NOUN
fumecheng-11486	24	11	is	be	AUX
fumecheng-11486	24	12	dimensionless	dimensionless	ADJ
fumecheng-11486	24	13	displacement	displacement	NOUN
fumecheng-11486	24	14	and	and	CCONJ
fumecheng-11486	24	15	k	k	PROPN
fumecheng-11486	24	16	is	be	AUX
fumecheng-11486	24	17	a	a	DET
fumecheng-11486	24	18	voltage	voltage	NOUN
fumecheng-11486	24	19	-	-	PUNCT
fumecheng-11486	24	20	related	relate	VERB
fumecheng-11486	24	21	parameter	parameter	NOUN
fumecheng-11486	24	22	.	.	PUNCT
fumecheng-11486	25	1	eq	eq	ADJ
fumecheng-11486	25	2	.	.	PUNCT
fumecheng-11486	26	1	(	(	PUNCT
fumecheng-11486	26	2	3	3	X
fumecheng-11486	26	3	)	)	PUNCT
fumecheng-11486	26	4	can	can	AUX
fumecheng-11486	26	5	be	be	AUX
fumecheng-11486	26	6	written	write	VERB
fumecheng-11486	26	7	as	as	ADP
fumecheng-11486	26	8	2	2	NUM
fumecheng-11486	26	9	2	2	NUM
fumecheng-11486	26	10	3	3	NUM
fumecheng-11486	26	11	4	4	NUM
fumecheng-11486	26	12	2	2	NUM
fumecheng-11486	26	13	(	(	PUNCT
fumecheng-11486	26	14	1	1	NUM
fumecheng-11486	26	15	)	)	PUNCT
fumecheng-11486	26	16	0	0	NUM
fumecheng-11486	27	1	+	+	CCONJ
fumecheng-11486	27	2	−	−	PROPN
fumecheng-11486	28	1	+	+	CCONJ
fumecheng-11486	28	2	+	+	PUNCT
fumecheng-11486	28	3	+	+	PUNCT
fumecheng-11486	28	4	+	+	NOUN
fumecheng-11486	28	5	=	=	SYM
fumecheng-11486	28	6	d	d	X
fumecheng-11486	28	7	u	u	X
fumecheng-11486	28	8	u	u	X
fumecheng-11486	28	9	k	k	PROPN
fumecheng-11486	28	10	u	u	X
fumecheng-11486	28	11	u	u	X
fumecheng-11486	28	12	u	u	X
fumecheng-11486	28	13	dt	dt	X
fumecheng-11486	28	14	(	(	PUNCT
fumecheng-11486	28	15	4	4	NUM
fumecheng-11486	28	16	)	)	PUNCT
fumecheng-11486	28	17	the	the	DET
fumecheng-11486	28	18	even	even	ADJ
fumecheng-11486	28	19	nonlinearities	nonlinearitie	NOUN
fumecheng-11486	28	20	in	in	ADP
fumecheng-11486	28	21	eq	eq	ADP
fumecheng-11486	28	22	.	.	PUNCT
fumecheng-11486	29	1	(	(	PUNCT
fumecheng-11486	29	2	4	4	X
fumecheng-11486	29	3	)	)	PUNCT
fumecheng-11486	29	4	are	be	AUX
fumecheng-11486	29	5	the	the	DET
fumecheng-11486	29	6	main	main	ADJ
fumecheng-11486	29	7	contributor	contributor	NOUN
fumecheng-11486	29	8	to	to	ADP
fumecheng-11486	29	9	the	the	DET
fumecheng-11486	29	10	pull	pull	VERB
fumecheng-11486	29	11	-	-	PUNCT
fumecheng-11486	29	12	in	in	ADP
fumecheng-11486	29	13	instability	instability	NOUN
fumecheng-11486	29	14	,	,	PUNCT
fumecheng-11486	29	15	which	which	PRON
fumecheng-11486	29	16	should	should	AUX
fumecheng-11486	29	17	be	be	AUX
fumecheng-11486	29	18	avoided	avoid	VERB
fumecheng-11486	29	19	in	in	ADP
fumecheng-11486	29	20	the	the	DET
fumecheng-11486	29	21	practical	practical	ADJ
fumecheng-11486	29	22	applications	application	NOUN
fumecheng-11486	29	23	.	.	PUNCT
fumecheng-11486	30	1	the	the	DET
fumecheng-11486	30	2	pull	pull	NOUN
fumecheng-11486	30	3	-	-	PUNCT
fumecheng-11486	30	4	in	in	ADP
fumecheng-11486	30	5	instability	instability	NOUN
fumecheng-11486	30	6	has	have	AUX
fumecheng-11486	30	7	been	be	AUX
fumecheng-11486	30	8	widely	widely	ADV
fumecheng-11486	30	9	studied	study	VERB
fumecheng-11486	30	10	in	in	ADP
fumecheng-11486	30	11	the	the	DET
fumecheng-11486	30	12	micro	micro	ADJ
fumecheng-11486	30	13	electromechanical	electromechanical	ADJ
fumecheng-11486	30	14	systems	system	NOUN
fumecheng-11486	30	15	(	(	PUNCT
fumecheng-11486	30	16	mems	mem	NOUN
fumecheng-11486	30	17	)	)	PUNCT
fumecheng-11486	31	1	[	[	X
fumecheng-11486	31	2	13	13	NUM
fumecheng-11486	31	3	-	-	SYM
fumecheng-11486	31	4	17	17	NUM
fumecheng-11486	31	5	]	]	PUNCT
fumecheng-11486	31	6	,	,	PUNCT
fumecheng-11486	31	7	when	when	SCONJ
fumecheng-11486	31	8	the	the	DET
fumecheng-11486	31	9	voltage	voltage	NOUN
fumecheng-11486	31	10	is	be	AUX
fumecheng-11486	31	11	larger	large	ADJ
fumecheng-11486	31	12	than	than	ADP
fumecheng-11486	31	13	its	its	PRON
fumecheng-11486	31	14	threshold	threshold	NOUN
fumecheng-11486	31	15	value	value	NOUN
fumecheng-11486	31	16	,	,	PUNCT
fumecheng-11486	31	17	the	the	DET
fumecheng-11486	31	18	pull	pull	NOUN
fumecheng-11486	31	19	-	-	PUNCT
fumecheng-11486	31	20	in	in	ADP
fumecheng-11486	31	21	instability	instability	NOUN
fumecheng-11486	31	22	occurs	occur	VERB
fumecheng-11486	31	23	,	,	PUNCT
fumecheng-11486	31	24	otherwise	otherwise	ADV
fumecheng-11486	31	25	the	the	DET
fumecheng-11486	31	26	systems	system	NOUN
fumecheng-11486	31	27	move	move	VERB
fumecheng-11486	31	28	periodically	periodically	ADV
fumecheng-11486	31	29	.	.	PUNCT
fumecheng-11486	32	1	in	in	ADP
fumecheng-11486	32	2	this	this	DET
fumecheng-11486	32	3	paper	paper	NOUN
fumecheng-11486	32	4	we	we	PRON
fumecheng-11486	32	5	focus	focus	VERB
fumecheng-11486	32	6	on	on	ADP
fumecheng-11486	32	7	a	a	DET
fumecheng-11486	32	8	similar	similar	ADJ
fumecheng-11486	32	9	phenomenon	phenomenon	NOUN
fumecheng-11486	32	10	in	in	ADP
fumecheng-11486	32	11	quadratic	quadratic	ADJ
fumecheng-11486	32	12	nonlinear	nonlinear	ADJ
fumecheng-11486	32	13	oscillators	oscillator	NOUN
fumecheng-11486	32	14	[	[	X
fumecheng-11486	32	15	18,19	18,19	NUM
fumecheng-11486	32	16	]	]	PUNCT
fumecheng-11486	32	17	,	,	PUNCT
fumecheng-11486	32	18	and	and	CCONJ
fumecheng-11486	32	19	we	we	PRON
fumecheng-11486	32	20	call	call	VERB
fumecheng-11486	32	21	it	it	PRON
fumecheng-11486	32	22	as	as	ADP
fumecheng-11486	32	23	the	the	DET
fumecheng-11486	32	24	pull	pull	NOUN
fumecheng-11486	32	25	-	-	PUNCT
fumecheng-11486	32	26	down	down	ADP
fumecheng-11486	32	27	instability	instability	NOUN
fumecheng-11486	32	28	.	.	PUNCT
fumecheng-11486	33	1	2	2	X
fumecheng-11486	33	2	.	.	X
fumecheng-11486	33	3	the	the	DET
fumecheng-11486	33	4	quadratic	quadratic	ADJ
fumecheng-11486	33	5	nonlinear	nonlinear	ADJ
fumecheng-11486	33	6	oscillator	oscillator	NOUN
fumecheng-11486	33	7	we	we	PRON
fumecheng-11486	33	8	consider	consider	VERB
fumecheng-11486	33	9	the	the	DET
fumecheng-11486	33	10	following	follow	VERB
fumecheng-11486	33	11	quadratic	quadratic	ADJ
fumecheng-11486	33	12	nonlinear	nonlinear	ADJ
fumecheng-11486	33	13	oscillator	oscillator	NOUN
fumecheng-11486	33	14	2	2	NUM
fumecheng-11486	33	15	2	2	NUM
fumecheng-11486	33	16	2	2	NUM
fumecheng-11486	33	17	0	0	NUM
fumecheng-11486	33	18	+	+	NUM
fumecheng-11486	33	19	+	+	NUM
fumecheng-11486	33	20	=	=	SYM
fumecheng-11486	33	21	d	d	X
fumecheng-11486	33	22	u	u	X
fumecheng-11486	33	23	u	u	X
fumecheng-11486	33	24	u	u	NOUN
fumecheng-11486	33	25	dt	dt	NOUN
fumecheng-11486	33	26			PROPN
fumecheng-11486	33	27	(	(	PUNCT
fumecheng-11486	33	28	5	5	NUM
fumecheng-11486	33	29	)	)	PUNCT
fumecheng-11486	33	30	with	with	ADP
fumecheng-11486	33	31	the	the	DET
fumecheng-11486	33	32	following	follow	VERB
fumecheng-11486	33	33	initial	initial	ADJ
fumecheng-11486	33	34	conditions	condition	NOUN
fumecheng-11486	33	35	pull	pull	VERB
fumecheng-11486	33	36	-	-	PUNCT
fumecheng-11486	33	37	down	down	ADP
fumecheng-11486	33	38	instability	instability	NOUN
fumecheng-11486	33	39	of	of	ADP
fumecheng-11486	33	40	the	the	DET
fumecheng-11486	33	41	quadratic	quadratic	ADJ
fumecheng-11486	33	42	nonlinear	nonlinear	ADJ
fumecheng-11486	33	43	oscillators	oscillator	NOUN
fumecheng-11486	33	44	193	193	NUM
fumecheng-11486	33	45	(	(	PUNCT
fumecheng-11486	33	46	0	0	NUM
fumecheng-11486	33	47	)	)	PUNCT
fumecheng-11486	33	48	,	,	PUNCT
fumecheng-11486	33	49	(	(	PUNCT
fumecheng-11486	33	50	0	0	NUM
fumecheng-11486	33	51	)	)	PUNCT
fumecheng-11486	33	52	0=	0=	NOUN
fumecheng-11486	34	1	=	=	NOUN
fumecheng-11486	34	2	u	u	X
fumecheng-11486	34	3	a	a	DET
fumecheng-11486	34	4	u	u	NOUN
fumecheng-11486	34	5	(	(	PUNCT
fumecheng-11486	34	6	6	6	NUM
fumecheng-11486	34	7	)	)	PUNCT
fumecheng-11486	34	8	where	where	SCONJ
fumecheng-11486	34	9	u	u	NOUN
fumecheng-11486	34	10	is	be	AUX
fumecheng-11486	34	11	the	the	DET
fumecheng-11486	34	12	displacement	displacement	NOUN
fumecheng-11486	34	13	,	,	PUNCT
fumecheng-11486	34	14	β	β	X
fumecheng-11486	34	15	is	be	AUX
fumecheng-11486	34	16	a	a	DET
fumecheng-11486	34	17	positive	positive	ADJ
fumecheng-11486	34	18	constant	constant	ADJ
fumecheng-11486	34	19	,	,	PUNCT
fumecheng-11486	34	20	a	a	PRON
fumecheng-11486	34	21	is	be	AUX
fumecheng-11486	34	22	the	the	DET
fumecheng-11486	34	23	initial	initial	ADJ
fumecheng-11486	34	24	amplitude	amplitude	NOUN
fumecheng-11486	34	25	.	.	PUNCT
fumecheng-11486	35	1	eq	eq	ADP
fumecheng-11486	35	2	.	.	PUNCT
fumecheng-11486	36	1	(	(	PUNCT
fumecheng-11486	36	2	5	5	X
fumecheng-11486	36	3	)	)	PUNCT
fumecheng-11486	36	4	is	be	AUX
fumecheng-11486	36	5	called	call	VERB
fumecheng-11486	36	6	as	as	ADP
fumecheng-11486	36	7	the	the	DET
fumecheng-11486	36	8	eardrum	eardrum	NOUN
fumecheng-11486	36	9	oscillator	oscillator	NOUN
fumecheng-11486	36	10	[	[	X
fumecheng-11486	36	11	19	19	NUM
fumecheng-11486	36	12	]	]	PUNCT
fumecheng-11486	36	13	.	.	PUNCT
fumecheng-11486	37	1	for	for	ADP
fumecheng-11486	37	2	small	small	ADJ
fumecheng-11486	37	3	values	value	NOUN
fumecheng-11486	37	4	of	of	ADP
fumecheng-11486	37	5	β	β	X
fumecheng-11486	37	6	,	,	PUNCT
fumecheng-11486	37	7	a	a	DET
fumecheng-11486	37	8	periodic	periodic	ADJ
fumecheng-11486	37	9	motion	motion	NOUN
fumecheng-11486	37	10	is	be	AUX
fumecheng-11486	37	11	predicted	predict	VERB
fumecheng-11486	37	12	;	;	PUNCT
fumecheng-11486	37	13	however	however	ADV
fumecheng-11486	37	14	,	,	PUNCT
fumecheng-11486	37	15	when	when	SCONJ
fumecheng-11486	37	16	it	it	PRON
fumecheng-11486	37	17	increases	increase	VERB
fumecheng-11486	37	18	to	to	ADP
fumecheng-11486	37	19	a	a	DET
fumecheng-11486	37	20	threshold	threshold	NOUN
fumecheng-11486	37	21	value	value	NOUN
fumecheng-11486	37	22	,	,	PUNCT
fumecheng-11486	37	23	the	the	DET
fumecheng-11486	37	24	kinetic	kinetic	ADJ
fumecheng-11486	37	25	energy	energy	NOUN
fumecheng-11486	37	26	will	will	AUX
fumecheng-11486	37	27	be	be	AUX
fumecheng-11486	37	28	gradually	gradually	ADV
fumecheng-11486	37	29	consumed	consume	VERB
fumecheng-11486	37	30	,	,	PUNCT
fumecheng-11486	37	31	and	and	CCONJ
fumecheng-11486	37	32	finally	finally	ADV
fumecheng-11486	37	33	the	the	DET
fumecheng-11486	37	34	periodic	periodic	ADJ
fumecheng-11486	37	35	motion	motion	NOUN
fumecheng-11486	37	36	is	be	AUX
fumecheng-11486	37	37	forbidden	forbid	VERB
fumecheng-11486	37	38	,	,	PUNCT
fumecheng-11486	37	39	this	this	DET
fumecheng-11486	37	40	phenomenon	phenomenon	NOUN
fumecheng-11486	37	41	is	be	AUX
fumecheng-11486	37	42	called	call	VERB
fumecheng-11486	37	43	as	as	ADP
fumecheng-11486	37	44	the	the	DET
fumecheng-11486	37	45	pull	pull	NOUN
fumecheng-11486	37	46	-	-	PUNCT
fumecheng-11486	37	47	down	down	ADP
fumecheng-11486	37	48	instability	instability	NOUN
fumecheng-11486	37	49	.	.	PUNCT
fumecheng-11486	38	1	fig	fig	NOUN
fumecheng-11486	38	2	.	.	PUNCT
fumecheng-11486	39	1	1	1	NUM
fumecheng-11486	39	2	shows	show	VERB
fumecheng-11486	39	3	the	the	DET
fumecheng-11486	39	4	dynamical	dynamical	ADJ
fumecheng-11486	39	5	properties	property	NOUN
fumecheng-11486	39	6	of	of	ADP
fumecheng-11486	39	7	eq	eq	PROPN
fumecheng-11486	39	8	.	.	PUNCT
fumecheng-11486	40	1	(	(	PUNCT
fumecheng-11486	40	2	5	5	NUM
fumecheng-11486	40	3	)	)	PUNCT
fumecheng-11486	40	4	when	when	SCONJ
fumecheng-11486	40	5	a=0.1	a=0.1	ADJ
fumecheng-11486	40	6	.	.	PUNCT
fumecheng-11486	41	1	when	when	SCONJ
fumecheng-11486	41	2	β<<1	β<<1	PROPN
fumecheng-11486	41	3	,	,	PUNCT
fumecheng-11486	41	4	a	a	DET
fumecheng-11486	41	5	periodic	periodic	ADJ
fumecheng-11486	41	6	solution	solution	NOUN
fumecheng-11486	41	7	is	be	AUX
fumecheng-11486	41	8	predicted	predict	VERB
fumecheng-11486	41	9	as	as	SCONJ
fumecheng-11486	41	10	shown	show	VERB
fumecheng-11486	41	11	in	in	ADP
fumecheng-11486	41	12	fig	fig	NOUN
fumecheng-11486	41	13	.	.	PUNCT
fumecheng-11486	42	1	1(b	1(b	NUM
fumecheng-11486	42	2	)	)	PUNCT
fumecheng-11486	42	3	.	.	PUNCT
fumecheng-11486	43	1	when	when	SCONJ
fumecheng-11486	43	2	β	β	X
fumecheng-11486	43	3	is	be	AUX
fumecheng-11486	43	4	larger	large	ADJ
fumecheng-11486	43	5	than	than	ADP
fumecheng-11486	43	6	a	a	DET
fumecheng-11486	43	7	threshold	threshold	NOUN
fumecheng-11486	43	8	value	value	NOUN
fumecheng-11486	43	9	,	,	PUNCT
fumecheng-11486	43	10	the	the	DET
fumecheng-11486	43	11	pull	pull	NOUN
fumecheng-11486	43	12	-	-	PUNCT
fumecheng-11486	43	13	down	down	ADP
fumecheng-11486	43	14	instability	instability	NOUN
fumecheng-11486	43	15	occurs	occur	VERB
fumecheng-11486	43	16	as	as	SCONJ
fumecheng-11486	43	17	shown	show	VERB
fumecheng-11486	43	18	in	in	ADP
fumecheng-11486	43	19	fig	fig	NOUN
fumecheng-11486	43	20	.	.	PUNCT
fumecheng-11486	44	1	1(d	1(d	NUM
fumecheng-11486	44	2	)	)	PUNCT
fumecheng-11486	44	3	.	.	PUNCT
fumecheng-11486	45	1	for	for	ADP
fumecheng-11486	45	2	β	β	PRON
fumecheng-11486	45	3	near	near	ADP
fumecheng-11486	45	4	to	to	ADP
fumecheng-11486	45	5	the	the	DET
fumecheng-11486	45	6	threshold	threshold	NOUN
fumecheng-11486	45	7	value	value	NOUN
fumecheng-11486	45	8	,	,	PUNCT
fumecheng-11486	45	9	the	the	DET
fumecheng-11486	45	10	system	system	NOUN
fumecheng-11486	45	11	will	will	AUX
fumecheng-11486	45	12	have	have	VERB
fumecheng-11486	45	13	a	a	DET
fumecheng-11486	45	14	periodic	periodic	ADJ
fumecheng-11486	45	15	motion	motion	NOUN
fumecheng-11486	45	16	first	first	ADV
fumecheng-11486	45	17	,	,	PUNCT
fumecheng-11486	45	18	and	and	CCONJ
fumecheng-11486	45	19	after	after	ADP
fumecheng-11486	45	20	some	some	DET
fumecheng-11486	45	21	cycles	cycle	NOUN
fumecheng-11486	45	22	,	,	PUNCT
fumecheng-11486	45	23	the	the	DET
fumecheng-11486	45	24	pull	pull	NOUN
fumecheng-11486	45	25	-	-	PUNCT
fumecheng-11486	45	26	down	down	ADP
fumecheng-11486	45	27	instability	instability	NOUN
fumecheng-11486	45	28	happens	happen	VERB
fumecheng-11486	45	29	suddenly	suddenly	ADV
fumecheng-11486	45	30	.	.	PUNCT
fumecheng-11486	46	1	this	this	DET
fumecheng-11486	46	2	phenomenon	phenomenon	NOUN
fumecheng-11486	46	3	is	be	AUX
fumecheng-11486	46	4	called	call	VERB
fumecheng-11486	46	5	as	as	ADP
fumecheng-11486	46	6	the	the	DET
fumecheng-11486	46	7	pseudo	pseudo	NOUN
fumecheng-11486	46	8	-	-	NOUN
fumecheng-11486	46	9	periodic	periodic	ADJ
fumecheng-11486	46	10	motion	motion	NOUN
fumecheng-11486	46	11	[	[	X
fumecheng-11486	46	12	6,7	6,7	NUM
fumecheng-11486	46	13	]	]	PUNCT
fumecheng-11486	46	14	as	as	SCONJ
fumecheng-11486	46	15	shown	show	VERB
fumecheng-11486	46	16	in	in	ADP
fumecheng-11486	46	17	fig	fig	NOUN
fumecheng-11486	46	18	.	.	PUNCT
fumecheng-11486	47	1	1(c	1(c	NUM
fumecheng-11486	47	2	)	)	PUNCT
fumecheng-11486	47	3	.	.	PUNCT
fumecheng-11486	48	1	(	(	PUNCT
fumecheng-11486	48	2	a	a	X
fumecheng-11486	48	3	)	)	PUNCT
fumecheng-11486	48	4	(	(	PUNCT
fumecheng-11486	48	5	b	b	X
fumecheng-11486	48	6	)	)	PUNCT
fumecheng-11486	48	7	(	(	PUNCT
fumecheng-11486	48	8	c	c	X
fumecheng-11486	48	9	)	)	PUNCT
fumecheng-11486	48	10	(	(	PUNCT
fumecheng-11486	48	11	d	d	X
fumecheng-11486	48	12	)	)	PUNCT
fumecheng-11486	48	13	fig	fig	NOUN
fumecheng-11486	48	14	.	.	PUNCT
fumecheng-11486	49	1	1	1	NUM
fumecheng-11486	49	2	periodic	periodic	ADJ
fumecheng-11486	49	3	motion	motion	NOUN
fumecheng-11486	49	4	and	and	CCONJ
fumecheng-11486	49	5	pull	pull	NOUN
fumecheng-11486	49	6	-	-	PUNCT
fumecheng-11486	49	7	down	down	ADP
fumecheng-11486	49	8	instability	instability	NOUN
fumecheng-11486	49	9	of	of	ADP
fumecheng-11486	49	10	the	the	DET
fumecheng-11486	49	11	quadratic	quadratic	ADJ
fumecheng-11486	49	12	nonlinear	nonlinear	ADJ
fumecheng-11486	49	13	oscillator	oscillator	NOUN
fumecheng-11486	49	14	when	when	SCONJ
fumecheng-11486	49	15	a=0.1	a=0.1	ADJ
fumecheng-11486	49	16	.	.	PUNCT
fumecheng-11486	50	1	(	(	PUNCT
fumecheng-11486	50	2	a	a	X
fumecheng-11486	50	3	)	)	PUNCT
fumecheng-11486	50	4	phase	phase	NOUN
fumecheng-11486	50	5	diagram	diagram	NOUN
fumecheng-11486	50	6	;	;	PUNCT
fumecheng-11486	50	7	(	(	PUNCT
fumecheng-11486	50	8	b	b	X
fumecheng-11486	50	9	)	)	PUNCT
fumecheng-11486	50	10	periodic	periodic	ADJ
fumecheng-11486	50	11	motion	motion	NOUN
fumecheng-11486	50	12	;	;	PUNCT
fumecheng-11486	50	13	(	(	PUNCT
fumecheng-11486	50	14	c	c	X
fumecheng-11486	50	15	)	)	PUNCT
fumecheng-11486	50	16	pseudo	pseudo	NOUN
fumecheng-11486	50	17	-	-	ADJ
fumecheng-11486	50	18	periodic	periodic	ADJ
fumecheng-11486	50	19	motion	motion	NOUN
fumecheng-11486	50	20	;	;	PUNCT
fumecheng-11486	50	21	and	and	CCONJ
fumecheng-11486	50	22	(	(	PUNCT
fumecheng-11486	50	23	d	d	NOUN
fumecheng-11486	50	24	)	)	PUNCT
fumecheng-11486	50	25	pull	pull	NOUN
fumecheng-11486	50	26	-	-	PUNCT
fumecheng-11486	50	27	down	down	NOUN
fumecheng-11486	50	28	instability	instability	NOUN
fumecheng-11486	50	29	a	a	DET
fumecheng-11486	50	30	periodic	periodic	ADJ
fumecheng-11486	50	31	motion	motion	NOUN
fumecheng-11486	50	32	can	can	AUX
fumecheng-11486	50	33	be	be	AUX
fumecheng-11486	50	34	generally	generally	ADV
fumecheng-11486	50	35	expressed	express	VERB
fumecheng-11486	50	36	by	by	ADP
fumecheng-11486	50	37	a	a	DET
fumecheng-11486	50	38	sinusoidal	sinusoidal	NOUN
fumecheng-11486	50	39	function	function	NOUN
fumecheng-11486	50	40	u(t	u(t	NOUN
fumecheng-11486	50	41	)	)	PUNCT
fumecheng-11486	50	42	=	=	SYM
fumecheng-11486	50	43	bsin(ωt+θ	bsin(ωt+θ	PROPN
fumecheng-11486	50	44	)	)	PUNCT
fumecheng-11486	50	45	,	,	PUNCT
fumecheng-11486	50	46	where	where	SCONJ
fumecheng-11486	50	47	b	b	NOUN
fumecheng-11486	50	48	and	and	CCONJ
fumecheng-11486	50	49	θ	θ	PROPN
fumecheng-11486	50	50	are	be	AUX
fumecheng-11486	50	51	determined	determine	VERB
fumecheng-11486	50	52	by	by	ADP
fumecheng-11486	50	53	the	the	DET
fumecheng-11486	50	54	initial	initial	ADJ
fumecheng-11486	50	55	conditions	condition	NOUN
fumecheng-11486	50	56	.	.	PUNCT
fumecheng-11486	51	1	the	the	DET
fumecheng-11486	51	2	displacement	displacement	NOUN
fumecheng-11486	51	3	of	of	ADP
fumecheng-11486	51	4	the	the	DET
fumecheng-11486	51	5	harmonic	harmonic	ADJ
fumecheng-11486	51	6	motion	motion	NOUN
fumecheng-11486	51	7	varies	vary	VERB
fumecheng-11486	51	8	from	from	ADP
fumecheng-11486	51	9	b	b	NOUN
fumecheng-11486	51	10	to	to	ADP
fumecheng-11486	51	11	negative	negative	PROPN
fumecheng-11486	51	12	b	b	NOUN
fumecheng-11486	51	13	periodically	periodically	ADV
fumecheng-11486	51	14	.	.	PUNCT
fumecheng-11486	52	1	194	194	NUM
fumecheng-11486	52	2	j.h	j.h	PROPN
fumecheng-11486	52	3	.	.	PUNCT
fumecheng-11486	53	1	he	he	PRON
fumecheng-11486	53	2	,	,	PUNCT
fumecheng-11486	53	3	q.	q.	PROPN
fumecheng-11486	53	4	yang	yang	PROPN
fumecheng-11486	53	5	,	,	PUNCT
fumecheng-11486	53	6	c.h	c.h	PROPN
fumecheng-11486	53	7	.	.	PUNCT
fumecheng-11486	54	1	he	he	PRON
fumecheng-11486	54	2	,	,	PUNCT
fumecheng-11486	54	3	a.a	a.a	PROPN
fumecheng-11486	54	4	.	.	PROPN
fumecheng-11486	54	5	alsolami	alsolami	PROPN
fumecheng-11486	54	6	in	in	ADP
fumecheng-11486	54	7	fig	fig	NOUN
fumecheng-11486	54	8	.	.	PUNCT
fumecheng-11486	55	1	1	1	NUM
fumecheng-11486	55	2	,	,	PUNCT
fumecheng-11486	55	3	we	we	PRON
fumecheng-11486	55	4	find	find	VERB
fumecheng-11486	55	5	that	that	SCONJ
fumecheng-11486	55	6	during	during	ADP
fumecheng-11486	55	7	the	the	DET
fumecheng-11486	55	8	periodic	periodic	ADJ
fumecheng-11486	55	9	motion	motion	NOUN
fumecheng-11486	55	10	(	(	PUNCT
fumecheng-11486	55	11	fig	fig	NOUN
fumecheng-11486	55	12	.	.	PUNCT
fumecheng-11486	56	1	1(b	1(b	NUM
fumecheng-11486	56	2	)	)	PUNCT
fumecheng-11486	56	3	)	)	PUNCT
fumecheng-11486	57	1	and	and	CCONJ
fumecheng-11486	57	2	the	the	DET
fumecheng-11486	57	3	pseudo	pseudo	NOUN
fumecheng-11486	57	4	-	-	ADJ
fumecheng-11486	57	5	periodic	periodic	ADJ
fumecheng-11486	57	6	motion	motion	NOUN
fumecheng-11486	57	7	(	(	PUNCT
fumecheng-11486	57	8	fig	fig	NOUN
fumecheng-11486	57	9	.	.	PUNCT
fumecheng-11486	57	10	1(c	1(c	NUM
fumecheng-11486	57	11	)	)	PUNCT
fumecheng-11486	57	12	)	)	PUNCT
fumecheng-11486	57	13	,	,	PUNCT
fumecheng-11486	57	14	the	the	DET
fumecheng-11486	57	15	quadratic	quadratic	ADJ
fumecheng-11486	57	16	force	force	NOUN
fumecheng-11486	57	17	pulls	pull	VERB
fumecheng-11486	57	18	down	down	ADP
fumecheng-11486	57	19	the	the	DET
fumecheng-11486	57	20	system	system	NOUN
fumecheng-11486	57	21	in	in	ADP
fumecheng-11486	57	22	each	each	DET
fumecheng-11486	57	23	cycle	cycle	NOUN
fumecheng-11486	57	24	.	.	PUNCT
fumecheng-11486	58	1	the	the	DET
fumecheng-11486	58	2	amplitude	amplitude	NOUN
fumecheng-11486	58	3	changes	change	VERB
fumecheng-11486	58	4	from	from	ADP
fumecheng-11486	58	5	0.1	0.1	NUM
fumecheng-11486	58	6	to	to	ADP
fumecheng-11486	58	7	negative	negative	ADJ
fumecheng-11486	58	8	0.11	0.11	NUM
fumecheng-11486	58	9	in	in	ADP
fumecheng-11486	58	10	fig	fig	NOUN
fumecheng-11486	58	11	.	.	PUNCT
fumecheng-11486	59	1	1(b	1(b	NUM
fumecheng-11486	59	2	)	)	PUNCT
fumecheng-11486	59	3	and	and	CCONJ
fumecheng-11486	59	4	negative	negative	ADJ
fumecheng-11486	59	5	0.2	0.2	NUM
fumecheng-11486	59	6	in	in	ADP
fumecheng-11486	59	7	fig	fig	NOUN
fumecheng-11486	59	8	.	.	PUNCT
fumecheng-11486	60	1	1(c	1(c	NUM
fumecheng-11486	60	2	)	)	PUNCT
fumecheng-11486	60	3	,	,	PUNCT
fumecheng-11486	60	4	respectively	respectively	ADV
fumecheng-11486	60	5	.	.	PUNCT
fumecheng-11486	61	1	this	this	DET
fumecheng-11486	61	2	unsymmetrical	unsymmetrical	ADJ
fumecheng-11486	61	3	oscillation	oscillation	NOUN
fumecheng-11486	61	4	phenomenon	phenomenon	NOUN
fumecheng-11486	61	5	is	be	AUX
fumecheng-11486	61	6	interesting	interesting	ADJ
fumecheng-11486	61	7	and	and	CCONJ
fumecheng-11486	61	8	amazing	amazing	ADJ
fumecheng-11486	61	9	because	because	SCONJ
fumecheng-11486	61	10	it	it	PRON
fumecheng-11486	61	11	can	can	AUX
fumecheng-11486	61	12	not	not	PART
fumecheng-11486	61	13	be	be	AUX
fumecheng-11486	61	14	seen	see	VERB
fumecheng-11486	61	15	in	in	ADP
fumecheng-11486	61	16	any	any	DET
fumecheng-11486	61	17	a	a	DET
fumecheng-11486	61	18	conservative	conservative	ADJ
fumecheng-11486	61	19	nonlinear	nonlinear	ADJ
fumecheng-11486	61	20	oscillator	oscillator	NOUN
fumecheng-11486	61	21	[	[	X
fumecheng-11486	61	22	20	20	NUM
fumecheng-11486	61	23	-	-	SYM
fumecheng-11486	61	24	22	22	NUM
fumecheng-11486	61	25	]	]	PUNCT
fumecheng-11486	61	26	,	,	PUNCT
fumecheng-11486	61	27	and	and	CCONJ
fumecheng-11486	61	28	it	it	PRON
fumecheng-11486	61	29	can	can	AUX
fumecheng-11486	61	30	be	be	AUX
fumecheng-11486	61	31	concluded	conclude	VERB
fumecheng-11486	61	32	that	that	SCONJ
fumecheng-11486	61	33	the	the	DET
fumecheng-11486	61	34	quadratic	quadratic	ADJ
fumecheng-11486	61	35	nonlinear	nonlinear	ADJ
fumecheng-11486	61	36	oscillator	oscillator	NOUN
fumecheng-11486	61	37	can	can	AUX
fumecheng-11486	61	38	not	not	PART
fumecheng-11486	61	39	be	be	AUX
fumecheng-11486	61	40	always	always	ADV
fumecheng-11486	61	41	used	use	VERB
fumecheng-11486	61	42	for	for	ADP
fumecheng-11486	61	43	vibration	vibration	NOUN
fumecheng-11486	61	44	attenuation	attenuation	NOUN
fumecheng-11486	61	45	and	and	CCONJ
fumecheng-11486	61	46	an	an	DET
fumecheng-11486	61	47	energy	energy	NOUN
fumecheng-11486	61	48	harvesting	harvesting	NOUN
fumecheng-11486	61	49	system	system	NOUN
fumecheng-11486	61	50	[	[	X
fumecheng-11486	61	51	23,24	23,24	ADP
fumecheng-11486	61	52	]	]	PUNCT
fumecheng-11486	61	53	.	.	PUNCT
fumecheng-11486	62	1	the	the	DET
fumecheng-11486	62	2	unsymmetrical	unsymmetrical	ADJ
fumecheng-11486	62	3	amplitude	amplitude	NOUN
fumecheng-11486	62	4	in	in	ADP
fumecheng-11486	62	5	each	each	DET
fumecheng-11486	62	6	cycle	cycle	NOUN
fumecheng-11486	62	7	certainly	certainly	ADV
fumecheng-11486	62	8	frustrates	frustrate	VERB
fumecheng-11486	62	9	scientists	scientist	NOUN
fumecheng-11486	62	10	and	and	CCONJ
fumecheng-11486	62	11	engineers	engineer	NOUN
fumecheng-11486	62	12	,	,	PUNCT
fumecheng-11486	62	13	because	because	SCONJ
fumecheng-11486	62	14	even	even	ADV
fumecheng-11486	62	15	the	the	DET
fumecheng-11486	62	16	van	van	PROPN
fumecheng-11486	62	17	der	der	ADJ
fumecheng-11486	62	18	pol	pol	PROPN
fumecheng-11486	62	19	oscillator	oscillator	NOUN
fumecheng-11486	62	20	[	[	X
fumecheng-11486	62	21	25	25	NUM
fumecheng-11486	62	22	]	]	PUNCT
fumecheng-11486	62	23	leads	lead	VERB
fumecheng-11486	62	24	to	to	ADP
fumecheng-11486	62	25	a	a	DET
fumecheng-11486	62	26	sinusoidal	sinusoidal	ADJ
fumecheng-11486	62	27	motion	motion	NOUN
fumecheng-11486	62	28	when	when	SCONJ
fumecheng-11486	62	29	time	time	NOUN
fumecheng-11486	62	30	tends	tend	VERB
fumecheng-11486	62	31	to	to	PART
fumecheng-11486	62	32	infinity	infinity	VERB
fumecheng-11486	62	33	.	.	PUNCT
fumecheng-11486	63	1	when	when	SCONJ
fumecheng-11486	63	2	β	β	X
fumecheng-11486	63	3	increases	increase	VERB
fumecheng-11486	63	4	to	to	ADP
fumecheng-11486	63	5	a	a	DET
fumecheng-11486	63	6	threshold	threshold	NOUN
fumecheng-11486	63	7	value	value	NOUN
fumecheng-11486	63	8	,	,	PUNCT
fumecheng-11486	63	9	the	the	DET
fumecheng-11486	63	10	pull	pull	NOUN
fumecheng-11486	63	11	-	-	PUNCT
fumecheng-11486	63	12	down	down	ADP
fumecheng-11486	63	13	instability	instability	NOUN
fumecheng-11486	63	14	occurs	occur	VERB
fumecheng-11486	63	15	,	,	PUNCT
fumecheng-11486	63	16	and	and	CCONJ
fumecheng-11486	63	17	a	a	DET
fumecheng-11486	63	18	lack	lack	NOUN
fumecheng-11486	63	19	of	of	ADP
fumecheng-11486	63	20	a	a	DET
fumecheng-11486	63	21	theoretical	theoretical	ADJ
fumecheng-11486	63	22	model	model	NOUN
fumecheng-11486	63	23	to	to	PART
fumecheng-11486	63	24	predict	predict	VERB
fumecheng-11486	63	25	the	the	DET
fumecheng-11486	63	26	time	time	NOUN
fumecheng-11486	63	27	and	and	CCONJ
fumecheng-11486	63	28	the	the	DET
fumecheng-11486	63	29	condition	condition	NOUN
fumecheng-11486	63	30	of	of	ADP
fumecheng-11486	63	31	the	the	DET
fumecheng-11486	63	32	pull	pull	NOUN
fumecheng-11486	63	33	-	-	PUNCT
fumecheng-11486	63	34	down	down	ADP
fumecheng-11486	63	35	outbreak	outbreak	NOUN
fumecheng-11486	63	36	has	have	AUX
fumecheng-11486	63	37	greatly	greatly	ADV
fumecheng-11486	63	38	reduced	reduce	VERB
fumecheng-11486	63	39	the	the	DET
fumecheng-11486	63	40	operation	operation	NOUN
fumecheng-11486	63	41	reliability	reliability	NOUN
fumecheng-11486	63	42	,	,	PUNCT
fumecheng-11486	63	43	and	and	CCONJ
fumecheng-11486	63	44	hindered	hinder	VERB
fumecheng-11486	63	45	its	its	PRON
fumecheng-11486	63	46	applications	application	NOUN
fumecheng-11486	63	47	.	.	PUNCT
fumecheng-11486	64	1	3	3	X
fumecheng-11486	64	2	.	.	X
fumecheng-11486	64	3	periodic	periodic	ADJ
fumecheng-11486	64	4	motion	motion	NOUN
fumecheng-11486	64	5	with	with	ADP
fumecheng-11486	64	6	asymmetric	asymmetric	ADJ
fumecheng-11486	64	7	amplitudes	amplitude	NOUN
fumecheng-11486	64	8	this	this	DET
fumecheng-11486	64	9	section	section	NOUN
fumecheng-11486	64	10	introduces	introduce	VERB
fumecheng-11486	64	11	the	the	DET
fumecheng-11486	64	12	frequency	frequency	NOUN
fumecheng-11486	64	13	formulation	formulation	NOUN
fumecheng-11486	64	14	for	for	ADP
fumecheng-11486	64	15	nonlinear	nonlinear	ADJ
fumecheng-11486	64	16	oscillators	oscillator	NOUN
fumecheng-11486	64	17	[	[	X
fumecheng-11486	64	18	26	26	NUM
fumecheng-11486	64	19	]	]	PUNCT
fumecheng-11486	64	20	and	and	CCONJ
fumecheng-11486	64	21	extends	extend	VERB
fumecheng-11486	64	22	to	to	ADP
fumecheng-11486	64	23	the	the	DET
fumecheng-11486	64	24	nonlinear	nonlinear	ADJ
fumecheng-11486	64	25	oscillators	oscillator	NOUN
fumecheng-11486	64	26	with	with	ADP
fumecheng-11486	64	27	even	even	ADJ
fumecheng-11486	64	28	nonlinearities	nonlinearitie	NOUN
fumecheng-11486	64	29	.	.	PUNCT
fumecheng-11486	65	1	considering	consider	VERB
fumecheng-11486	65	2	a	a	DET
fumecheng-11486	65	3	nonlinear	nonlinear	ADJ
fumecheng-11486	65	4	equation	equation	NOUN
fumecheng-11486	65	5	in	in	ADP
fumecheng-11486	65	6	the	the	DET
fumecheng-11486	65	7	form	form	NOUN
fumecheng-11486	65	8	2	2	NUM
fumecheng-11486	65	9	2	2	NUM
fumecheng-11486	65	10	(	(	PUNCT
fumecheng-11486	65	11	)	)	PUNCT
fumecheng-11486	65	12	0	0	PUNCT
fumecheng-11486	66	1	+	+	NUM
fumecheng-11486	66	2	=	=	SYM
fumecheng-11486	66	3	d	d	X
fumecheng-11486	66	4	u	u	SYM
fumecheng-11486	66	5	u	u	X
fumecheng-11486	66	6	dt	dt	X
fumecheng-11486	66	7			NOUN
fumecheng-11486	66	8	,	,	PUNCT
fumecheng-11486	66	9	(	(	PUNCT
fumecheng-11486	66	10	0	0	NUM
fumecheng-11486	66	11	)	)	PUNCT
fumecheng-11486	66	12	,	,	PUNCT
fumecheng-11486	66	13	(	(	PUNCT
fumecheng-11486	66	14	0	0	NUM
fumecheng-11486	66	15	)	)	PUNCT
fumecheng-11486	66	16	0=	0=	NOUN
fumecheng-11486	67	1	=	=	NOUN
fumecheng-11486	67	2	x	x	X
fumecheng-11486	67	3	a	a	X
fumecheng-11486	67	4	x	x	X
fumecheng-11486	67	5	(	(	PUNCT
fumecheng-11486	67	6	7	7	NUM
fumecheng-11486	67	7	)	)	PUNCT
fumecheng-11486	67	8	where	where	SCONJ
fumecheng-11486	67	9	λ	λ	PROPN
fumecheng-11486	67	10	is	be	AUX
fumecheng-11486	67	11	a	a	DET
fumecheng-11486	67	12	nonlinear	nonlinear	ADJ
fumecheng-11486	67	13	function	function	NOUN
fumecheng-11486	67	14	of	of	ADP
fumecheng-11486	67	15	u	u	NOUN
fumecheng-11486	67	16	,	,	PUNCT
fumecheng-11486	67	17	generally	generally	ADV
fumecheng-11486	67	18	it	it	PRON
fumecheng-11486	67	19	can	can	AUX
fumecheng-11486	67	20	be	be	AUX
fumecheng-11486	67	21	expressed	express	VERB
fumecheng-11486	67	22	as	as	ADP
fumecheng-11486	67	23	3	3	NUM
fumecheng-11486	67	24	2	2	NUM
fumecheng-11486	67	25	1	1	NUM
fumecheng-11486	67	26	1	1	NUM
fumecheng-11486	67	27	3	3	NUM
fumecheng-11486	67	28	2	2	NUM
fumecheng-11486	67	29	1	1	NUM
fumecheng-11486	67	30	(	(	PUNCT
fumecheng-11486	67	31	)	)	PUNCT
fumecheng-11486	68	1	+	+	PUNCT
fumecheng-11486	69	1	+	+	PUNCT
fumecheng-11486	69	2	=	=	X
fumecheng-11486	69	3	+	+	X
fumecheng-11486	69	4	+	+	PUNCT
fumecheng-11486	69	5	+	+	CCONJ
fumecheng-11486	69	6	n	n	PRON
fumecheng-11486	69	7	nu	nu	INTJ
fumecheng-11486	69	8	a	a	DET
fumecheng-11486	69	9	u	u	NOUN
fumecheng-11486	69	10	a	a	DET
fumecheng-11486	69	11	u	u	NOUN
fumecheng-11486	69	12	a	a	DET
fumecheng-11486	69	13	u	u	PROPN
fumecheng-11486	69	14	(	(	PUNCT
fumecheng-11486	69	15	8)	8)	NUM
fumecheng-11486	69	16	for	for	ADP
fumecheng-11486	69	17	a	a	DET
fumecheng-11486	69	18	nonlinear	nonlinear	ADJ
fumecheng-11486	69	19	oscillator	oscillator	NOUN
fumecheng-11486	69	20	,	,	PUNCT
fumecheng-11486	69	21	it	it	PRON
fumecheng-11486	69	22	requires	require	VERB
fumecheng-11486	69	23	(	(	PUNCT
fumecheng-11486	69	24	)	)	PUNCT
fumecheng-11486	69	25	0	0	NUM
fumecheng-11486	69	26	u	u	NOUN
fumecheng-11486	69	27	u	u	NOUN
fumecheng-11486	69	28			X
fumecheng-11486	69	29	(	(	PUNCT
fumecheng-11486	69	30	9	9	NUM
fumecheng-11486	69	31	)	)	PUNCT
fumecheng-11486	69	32	the	the	DET
fumecheng-11486	69	33	frequency	frequency	NOUN
fumecheng-11486	69	34	formulation	formulation	NOUN
fumecheng-11486	69	35	is	be	AUX
fumecheng-11486	69	36	[	[	X
fumecheng-11486	69	37	26	26	NUM
fumecheng-11486	69	38	]	]	SYM
fumecheng-11486	69	39	3	3	NUM
fumecheng-11486	69	40	2	2	NUM
fumecheng-11486	69	41	2	2	NUM
fumecheng-11486	69	42	(	(	PUNCT
fumecheng-11486	69	43	)	)	PUNCT
fumecheng-11486	69	44	=	=	PUNCT
fumecheng-11486	70	1	=	=	PUNCT
fumecheng-11486	70	2	u	u	X
fumecheng-11486	70	3	a	a	DET
fumecheng-11486	70	4	u	u	X
fumecheng-11486	70	5	u	u	NOUN
fumecheng-11486	70	6			ADJ
fumecheng-11486	70	7			X
fumecheng-11486	70	8	(	(	PUNCT
fumecheng-11486	70	9	10	10	NUM
fumecheng-11486	70	10	)	)	PUNCT
fumecheng-11486	70	11	the	the	DET
fumecheng-11486	70	12	frequency	frequency	NOUN
fumecheng-11486	70	13	formulation	formulation	NOUN
fumecheng-11486	70	14	is	be	AUX
fumecheng-11486	70	15	simple	simple	ADJ
fumecheng-11486	70	16	but	but	CCONJ
fumecheng-11486	70	17	it	it	PRON
fumecheng-11486	70	18	gives	give	VERB
fumecheng-11486	70	19	a	a	DET
fumecheng-11486	70	20	relatively	relatively	ADV
fumecheng-11486	70	21	high	high	ADJ
fumecheng-11486	70	22	accuracy	accuracy	NOUN
fumecheng-11486	70	23	of	of	ADP
fumecheng-11486	70	24	the	the	DET
fumecheng-11486	70	25	frequency	frequency	NOUN
fumecheng-11486	70	26	-	-	PUNCT
fumecheng-11486	70	27	amplitude	amplitude	NOUN
fumecheng-11486	70	28	relationship	relationship	NOUN
fumecheng-11486	70	29	,	,	PUNCT
fumecheng-11486	70	30	and	and	CCONJ
fumecheng-11486	70	31	it	it	PRON
fumecheng-11486	70	32	becomes	become	VERB
fumecheng-11486	70	33	a	a	DET
fumecheng-11486	70	34	universal	universal	ADJ
fumecheng-11486	70	35	tool	tool	NOUN
fumecheng-11486	70	36	to	to	ADP
fumecheng-11486	70	37	various	various	ADJ
fumecheng-11486	70	38	vibration	vibration	NOUN
fumecheng-11486	70	39	systems	system	NOUN
fumecheng-11486	70	40	[	[	X
fumecheng-11486	70	41	27	27	NUM
fumecheng-11486	70	42	-	-	SYM
fumecheng-11486	70	43	29	29	NUM
fumecheng-11486	70	44	]	]	PUNCT
fumecheng-11486	70	45	.	.	PUNCT
fumecheng-11486	71	1	for	for	ADP
fumecheng-11486	71	2	λ(u)=a1u+a3u3	λ(u)=a1u+a3u3	ADV
fumecheng-11486	71	3	,	,	PUNCT
fumecheng-11486	71	4	eq	eq	ADJ
fumecheng-11486	71	5	.	.	PUNCT
fumecheng-11486	71	6	(	(	PUNCT
fumecheng-11486	71	7	7	7	X
fumecheng-11486	71	8	)	)	PUNCT
fumecheng-11486	71	9	is	be	AUX
fumecheng-11486	71	10	the	the	DET
fumecheng-11486	71	11	duffing	duffing	NOUN
fumecheng-11486	71	12	equation	equation	NOUN
fumecheng-11486	71	13	,	,	PUNCT
fumecheng-11486	71	14	and	and	CCONJ
fumecheng-11486	71	15	eq	eq	NOUN
fumecheng-11486	71	16	.	.	PUNCT
fumecheng-11486	72	1	(	(	PUNCT
fumecheng-11486	72	2	10	10	NUM
fumecheng-11486	72	3	)	)	PUNCT
fumecheng-11486	72	4	leads	lead	VERB
fumecheng-11486	72	5	to	to	ADP
fumecheng-11486	72	6	the	the	DET
fumecheng-11486	72	7	following	follow	VERB
fumecheng-11486	72	8	result	result	NOUN
fumecheng-11486	72	9	2	2	NUM
fumecheng-11486	72	10	2	2	NUM
fumecheng-11486	72	11	1	1	NUM
fumecheng-11486	72	12	3	3	NUM
fumecheng-11486	72	13	3	3	NUM
fumecheng-11486	72	14	=	=	SYM
fumecheng-11486	72	15	4	4	NUM
fumecheng-11486	72	16	+	+	NOUN
fumecheng-11486	72	17	a	a	DET
fumecheng-11486	72	18	a	a	DET
fumecheng-11486	72	19	a	a	ADV
fumecheng-11486	72	20	(	(	PUNCT
fumecheng-11486	72	21	11	11	NUM
fumecheng-11486	72	22	)	)	PUNCT
fumecheng-11486	72	23	eq	eq	NOUN
fumecheng-11486	72	24	.	.	PUNCT
fumecheng-11486	73	1	(	(	PUNCT
fumecheng-11486	73	2	11	11	NUM
fumecheng-11486	73	3	)	)	PUNCT
fumecheng-11486	73	4	is	be	AUX
fumecheng-11486	73	5	same	same	ADJ
fumecheng-11486	73	6	as	as	ADP
fumecheng-11486	73	7	that	that	PRON
fumecheng-11486	73	8	obtained	obtain	VERB
fumecheng-11486	73	9	by	by	ADP
fumecheng-11486	73	10	the	the	DET
fumecheng-11486	73	11	homotopy	homotopy	NOUN
fumecheng-11486	73	12	perturbation	perturbation	NOUN
fumecheng-11486	73	13	method	method	NOUN
fumecheng-11486	73	14	[	[	X
fumecheng-11486	73	15	30	30	NUM
fumecheng-11486	73	16	]	]	PUNCT
fumecheng-11486	73	17	.	.	PUNCT
fumecheng-11486	74	1	using	use	VERB
fumecheng-11486	74	2	the	the	DET
fumecheng-11486	74	3	frequency	frequency	NOUN
fumecheng-11486	74	4	formulation	formulation	NOUN
fumecheng-11486	74	5	of	of	ADP
fumecheng-11486	74	6	eq	eq	PROPN
fumecheng-11486	74	7	.	.	PUNCT
fumecheng-11486	75	1	(	(	PUNCT
fumecheng-11486	75	2	10	10	NUM
fumecheng-11486	75	3	)	)	PUNCT
fumecheng-11486	75	4	,	,	PUNCT
fumecheng-11486	75	5	for	for	ADP
fumecheng-11486	75	6	eqs	eqs	PROPN
fumecheng-11486	75	7	.	.	PUNCT
fumecheng-11486	76	1	(	(	PUNCT
fumecheng-11486	76	2	5	5	NUM
fumecheng-11486	76	3	)	)	PUNCT
fumecheng-11486	76	4	and	and	CCONJ
fumecheng-11486	76	5	(	(	PUNCT
fumecheng-11486	76	6	6	6	NUM
fumecheng-11486	76	7	)	)	PUNCT
fumecheng-11486	76	8	,	,	PUNCT
fumecheng-11486	76	9	we	we	PRON
fumecheng-11486	76	10	have	have	VERB
fumecheng-11486	76	11	pull	pull	VERB
fumecheng-11486	76	12	-	-	PUNCT
fumecheng-11486	76	13	down	down	ADP
fumecheng-11486	76	14	instability	instability	NOUN
fumecheng-11486	76	15	of	of	ADP
fumecheng-11486	76	16	the	the	DET
fumecheng-11486	76	17	quadratic	quadratic	ADJ
fumecheng-11486	76	18	nonlinear	nonlinear	ADJ
fumecheng-11486	76	19	oscillators	oscillator	NOUN
fumecheng-11486	76	20	195	195	NUM
fumecheng-11486	76	21	3	3	NUM
fumecheng-11486	76	22	=	=	SYM
fumecheng-11486	76	23	1	1	NUM
fumecheng-11486	76	24	2	2	NUM
fumecheng-11486	76	25	+	+	CCONJ
fumecheng-11486	76	26	a	a	ADV
fumecheng-11486	77	1			NOUN
fumecheng-11486	77	2	(	(	PUNCT
fumecheng-11486	77	3	12	12	NUM
fumecheng-11486	77	4	)	)	PUNCT
fumecheng-11486	77	5	table	table	NOUN
fumecheng-11486	77	6	1	1	NUM
fumecheng-11486	77	7	shows	show	NOUN
fumecheng-11486	77	8	eq	eq	NOUN
fumecheng-11486	77	9	.	.	PUNCT
fumecheng-11486	78	1	(	(	PUNCT
fumecheng-11486	78	2	12	12	NUM
fumecheng-11486	78	3	)	)	PUNCT
fumecheng-11486	78	4	has	have	VERB
fumecheng-11486	78	5	good	good	ADJ
fumecheng-11486	78	6	accuracy	accuracy	NOUN
fumecheng-11486	78	7	of	of	ADP
fumecheng-11486	78	8	the	the	DET
fumecheng-11486	78	9	approximate	approximate	ADJ
fumecheng-11486	78	10	period	period	NOUN
fumecheng-11486	78	11	,	,	PUNCT
fumecheng-11486	78	12	t=2π	t=2π	PROPN
fumecheng-11486	78	13	/	/	SYM
fumecheng-11486	78	14	ω	ω	PROPN
fumecheng-11486	78	15	,	,	PUNCT
fumecheng-11486	78	16	for	for	ADP
fumecheng-11486	78	17	βa<<1	βa<<1	PROPN
fumecheng-11486	78	18	,	,	PUNCT
fumecheng-11486	78	19	and	and	CCONJ
fumecheng-11486	78	20	its	its	PRON
fumecheng-11486	78	21	accuracy	accuracy	NOUN
fumecheng-11486	78	22	deteriorates	deteriorate	VERB
fumecheng-11486	78	23	greatly	greatly	ADV
fumecheng-11486	78	24	when	when	SCONJ
fumecheng-11486	78	25	the	the	DET
fumecheng-11486	78	26	value	value	NOUN
fumecheng-11486	78	27	of	of	ADP
fumecheng-11486	78	28	βa	βa	PUNCT
fumecheng-11486	78	29	becomes	become	VERB
fumecheng-11486	78	30	large	large	ADJ
fumecheng-11486	78	31	.	.	PUNCT
fumecheng-11486	79	1	the	the	DET
fumecheng-11486	79	2	errors	error	NOUN
fumecheng-11486	79	3	arise	arise	VERB
fumecheng-11486	79	4	in	in	ADP
fumecheng-11486	79	5	the	the	DET
fumecheng-11486	79	6	quadratic	quadratic	ADJ
fumecheng-11486	79	7	force	force	NOUN
fumecheng-11486	79	8	,	,	PUNCT
fumecheng-11486	79	9	f	f	X
fumecheng-11486	79	10	=	=	X
fumecheng-11486	79	11	βu2	βu2	VERB
fumecheng-11486	79	12	.	.	PUNCT
fumecheng-11486	80	1	when	when	SCONJ
fumecheng-11486	80	2	the	the	DET
fumecheng-11486	80	3	quadratic	quadratic	ADJ
fumecheng-11486	80	4	force	force	NOUN
fumecheng-11486	80	5	is	be	AUX
fumecheng-11486	80	6	small	small	ADJ
fumecheng-11486	80	7	,	,	PUNCT
fumecheng-11486	80	8	eq	eq	ADJ
fumecheng-11486	80	9	.	.	PUNCT
fumecheng-11486	81	1	(	(	PUNCT
fumecheng-11486	81	2	5	5	X
fumecheng-11486	81	3	)	)	PUNCT
fumecheng-11486	81	4	can	can	AUX
fumecheng-11486	81	5	be	be	AUX
fumecheng-11486	81	6	solved	solve	VERB
fumecheng-11486	81	7	by	by	ADP
fumecheng-11486	81	8	the	the	DET
fumecheng-11486	81	9	perturbation	perturbation	NOUN
fumecheng-11486	81	10	method	method	NOUN
fumecheng-11486	81	11	[	[	X
fumecheng-11486	81	12	19	19	NUM
fumecheng-11486	81	13	]	]	PUNCT
fumecheng-11486	81	14	,	,	PUNCT
fumecheng-11486	81	15	but	but	CCONJ
fumecheng-11486	81	16	in	in	ADP
fumecheng-11486	81	17	practical	practical	ADJ
fumecheng-11486	81	18	applications	application	NOUN
fumecheng-11486	81	19	,	,	PUNCT
fumecheng-11486	81	20	we	we	PRON
fumecheng-11486	81	21	do	do	AUX
fumecheng-11486	81	22	not	not	PART
fumecheng-11486	81	23	know	know	VERB
fumecheng-11486	81	24	the	the	DET
fumecheng-11486	81	25	criterion	criterion	NOUN
fumecheng-11486	81	26	for	for	ADP
fumecheng-11486	81	27	the	the	DET
fumecheng-11486	81	28	small	small	ADJ
fumecheng-11486	81	29	value	value	NOUN
fumecheng-11486	81	30	.	.	PUNCT
fumecheng-11486	82	1	table	table	NOUN
fumecheng-11486	82	2	1	1	NUM
fumecheng-11486	82	3	comparison	comparison	NOUN
fumecheng-11486	82	4	the	the	DET
fumecheng-11486	82	5	approximate	approximate	ADJ
fumecheng-11486	82	6	periods	period	NOUN
fumecheng-11486	82	7	with	with	ADP
fumecheng-11486	82	8	the	the	DET
fumecheng-11486	82	9	exact	exact	ADJ
fumecheng-11486	82	10	one	one	PRON
fumecheng-11486	82	11	a	a	DET
fumecheng-11486	82	12	β	β	X
fumecheng-11486	82	13	exact	exact	ADJ
fumecheng-11486	82	14	period	period	NOUN
fumecheng-11486	82	15	approximate	approximate	ADJ
fumecheng-11486	82	16	period	period	NOUN
fumecheng-11486	82	17	eq.(12	eq.(12	NOUN
fumecheng-11486	82	18	)	)	PUNCT
fumecheng-11486	82	19	error	error	NOUN
fumecheng-11486	82	20	approximate	approximate	ADJ
fumecheng-11486	82	21	period	period	NOUN
fumecheng-11486	82	22	eq.(20	eq.(20	PROPN
fumecheng-11486	82	23	)	)	PUNCT
fumecheng-11486	82	24	error	error	NOUN
fumecheng-11486	82	25	(	(	PUNCT
fumecheng-11486	82	26	%	%	NOUN
fumecheng-11486	82	27	)	)	PUNCT
fumecheng-11486	82	28	0.1	0.1	NUM
fumecheng-11486	82	29	1	1	NUM
fumecheng-11486	82	30	6.266	6.266	NUM
fumecheng-11486	82	31	6.0276	6.0276	NUM
fumecheng-11486	82	32	3.8	3.8	NUM
fumecheng-11486	82	33	%	%	NOUN
fumecheng-11486	82	34	6.300	6.300	NUM
fumecheng-11486	82	35	0.55	0.55	NUM
fumecheng-11486	82	36	%	%	NOUN
fumecheng-11486	82	37	0.3	0.3	NUM
fumecheng-11486	82	38	1	1	NUM
fumecheng-11486	82	39	6.627	6.627	NUM
fumecheng-11486	82	40	5.5979	5.5979	NUM
fumecheng-11486	82	41	15.5	15.5	NUM
fumecheng-11486	82	42	%	%	NOUN
fumecheng-11486	82	43	6.450	6.450	NUM
fumecheng-11486	82	44	2.66	2.66	NUM
fumecheng-11486	82	45	%	%	NOUN
fumecheng-11486	82	46	0.5	0.5	NUM
fumecheng-11486	82	47	0.3	0.3	NUM
fumecheng-11486	82	48	6.308	6.308	NUM
fumecheng-11486	82	49	5.9109	5.9109	NUM
fumecheng-11486	82	50	6.2	6.2	NUM
fumecheng-11486	82	51	%	%	NOUN
fumecheng-11486	82	52	6.323	6.323	NUM
fumecheng-11486	82	53	0.24	0.24	NUM
fumecheng-11486	82	54	%	%	NOUN
fumecheng-11486	82	55	0.7	0.7	NUM
fumecheng-11486	82	56	0.3	0.3	NUM
fumecheng-11486	82	57	6.399	6.399	NUM
fumecheng-11486	82	58	5.7795	5.7795	NUM
fumecheng-11486	82	59	9.6	9.6	NUM
fumecheng-11486	82	60	%	%	NOUN
fumecheng-11486	82	61	6.363	6.363	NUM
fumecheng-11486	82	62	0.56	0.56	NUM
fumecheng-11486	82	63	%	%	NOUN
fumecheng-11486	82	64	eq	eq	NOUN
fumecheng-11486	82	65	.	.	PUNCT
fumecheng-11486	83	1	(	(	PUNCT
fumecheng-11486	83	2	10	10	NUM
fumecheng-11486	83	3	)	)	PUNCT
fumecheng-11486	83	4	is	be	AUX
fumecheng-11486	83	5	valid	valid	ADJ
fumecheng-11486	83	6	for	for	ADP
fumecheng-11486	83	7	nonlinear	nonlinear	ADJ
fumecheng-11486	83	8	oscillators	oscillator	NOUN
fumecheng-11486	83	9	with	with	ADP
fumecheng-11486	83	10	only	only	ADJ
fumecheng-11486	83	11	odd	odd	ADJ
fumecheng-11486	83	12	nonlinear	nonlinear	ADJ
fumecheng-11486	83	13	terms	term	NOUN
fumecheng-11486	83	14	,	,	PUNCT
fumecheng-11486	83	15	our	our	PRON
fumecheng-11486	83	16	problem	problem	NOUN
fumecheng-11486	83	17	has	have	VERB
fumecheng-11486	83	18	a	a	DET
fumecheng-11486	83	19	quadratic	quadratic	ADJ
fumecheng-11486	83	20	nonlinear	nonlinear	ADJ
fumecheng-11486	83	21	term	term	NOUN
fumecheng-11486	83	22	,	,	PUNCT
fumecheng-11486	83	23	so	so	CCONJ
fumecheng-11486	83	24	the	the	DET
fumecheng-11486	83	25	frequency	frequency	NOUN
fumecheng-11486	83	26	formulation	formulation	NOUN
fumecheng-11486	83	27	has	have	VERB
fumecheng-11486	83	28	to	to	PART
fumecheng-11486	83	29	be	be	AUX
fumecheng-11486	83	30	modified	modify	VERB
fumecheng-11486	83	31	.	.	PUNCT
fumecheng-11486	84	1	we	we	PRON
fumecheng-11486	84	2	re	re	VERB
fumecheng-11486	84	3	-	-	VERB
fumecheng-11486	84	4	write	write	VERB
fumecheng-11486	84	5	eq	eq	X
fumecheng-11486	84	6	.	.	PUNCT
fumecheng-11486	85	1	(	(	PUNCT
fumecheng-11486	85	2	5	5	NUM
fumecheng-11486	85	3	)	)	PUNCT
fumecheng-11486	85	4	in	in	ADP
fumecheng-11486	85	5	the	the	DET
fumecheng-11486	85	6	form	form	NOUN
fumecheng-11486	85	7	2	2	NUM
fumecheng-11486	85	8	2	2	NUM
fumecheng-11486	85	9	(	(	PUNCT
fumecheng-11486	85	10	1	1	NUM
fumecheng-11486	85	11	)	)	PUNCT
fumecheng-11486	85	12	0	0	NUM
fumecheng-11486	85	13	,	,	PUNCT
fumecheng-11486	85	14	0	0	NUM
fumecheng-11486	86	1	+	+	NUM
fumecheng-11486	86	2	−	−	PROPN
fumecheng-11486	86	3	=	=	SYM
fumecheng-11486	86	4			PROPN
fumecheng-11486	87	1	d	d	X
fumecheng-11486	88	1	u	u	PRON
fumecheng-11486	89	1	u	u	VERB
fumecheng-11486	89	2	u	u	X
fumecheng-11486	89	3	u	u	NOUN
fumecheng-11486	89	4	dt	dt	PROPN
fumecheng-11486	89	5			PROPN
fumecheng-11486	89	6	(	(	PUNCT
fumecheng-11486	89	7	13	13	NUM
fumecheng-11486	89	8	)	)	SYM
fumecheng-11486	89	9	2	2	NUM
fumecheng-11486	89	10	2	2	NUM
fumecheng-11486	89	11	(	(	PUNCT
fumecheng-11486	89	12	1	1	NUM
fumecheng-11486	89	13	)	)	PUNCT
fumecheng-11486	89	14	0	0	NUM
fumecheng-11486	89	15	,	,	PUNCT
fumecheng-11486	89	16	0	0	NUM
fumecheng-11486	90	1	+	+	NUM
fumecheng-11486	90	2	+	+	SYM
fumecheng-11486	90	3	=	=	NOUN
fumecheng-11486	90	4			X
fumecheng-11486	91	1	d	d	X
fumecheng-11486	91	2	u	u	PRON
fumecheng-11486	91	3	u	u	X
fumecheng-11486	91	4	u	u	X
fumecheng-11486	91	5	u	u	NOUN
fumecheng-11486	91	6	dt	dt	PROPN
fumecheng-11486	91	7			PROPN
fumecheng-11486	91	8	(	(	PUNCT
fumecheng-11486	91	9	14	14	NUM
fumecheng-11486	91	10	)	)	PUNCT
fumecheng-11486	91	11	eqs	eqs	PROPN
fumecheng-11486	91	12	.	.	PUNCT
fumecheng-11486	92	1	(	(	PUNCT
fumecheng-11486	92	2	13	13	NUM
fumecheng-11486	92	3	)	)	PUNCT
fumecheng-11486	92	4	and	and	CCONJ
fumecheng-11486	92	5	(	(	PUNCT
fumecheng-11486	92	6	14	14	NUM
fumecheng-11486	92	7	)	)	PUNCT
fumecheng-11486	92	8	give	give	NOUN
fumecheng-11486	92	9	,	,	PUNCT
fumecheng-11486	92	10	respectively	respectively	ADV
fumecheng-11486	92	11	,	,	PUNCT
fumecheng-11486	92	12	the	the	DET
fumecheng-11486	92	13	following	follow	VERB
fumecheng-11486	92	14	frequency	frequency	NOUN
fumecheng-11486	92	15	formulations	formulation	NOUN
fumecheng-11486	92	16	:	:	PUNCT
fumecheng-11486	92	17	2	2	NUM
fumecheng-11486	92	18	1	1	NUM
fumecheng-11486	92	19	3	3	NUM
fumecheng-11486	92	20	=	=	SYM
fumecheng-11486	92	21	1	1	NUM
fumecheng-11486	92	22	2	2	NUM
fumecheng-11486	92	23	−	−	NOUN
fumecheng-11486	92	24	a	a	ADV
fumecheng-11486	92	25			PROPN
fumecheng-11486	92	26	(	(	PUNCT
fumecheng-11486	92	27	15	15	NUM
fumecheng-11486	92	28	)	)	SYM
fumecheng-11486	93	1	2	2	NUM
fumecheng-11486	93	2	2	2	NUM
fumecheng-11486	93	3	3	3	NUM
fumecheng-11486	93	4	=	=	SYM
fumecheng-11486	93	5	1	1	NUM
fumecheng-11486	93	6	2	2	NUM
fumecheng-11486	93	7	+	+	CCONJ
fumecheng-11486	93	8	a	a	ADV
fumecheng-11486	94	1			NOUN
fumecheng-11486	94	2	(	(	PUNCT
fumecheng-11486	94	3	16	16	NUM
fumecheng-11486	94	4	)	)	PUNCT
fumecheng-11486	94	5	the	the	DET
fumecheng-11486	94	6	solution	solution	NOUN
fumecheng-11486	94	7	can	can	AUX
fumecheng-11486	94	8	be	be	AUX
fumecheng-11486	94	9	approximately	approximately	ADV
fumecheng-11486	94	10	expressed	express	VERB
fumecheng-11486	94	11	as	as	ADP
fumecheng-11486	94	12	2	2	NUM
fumecheng-11486	94	13	1	1	NUM
fumecheng-11486	94	14	cos	co	NOUN
fumecheng-11486	94	15	,	,	PUNCT
fumecheng-11486	94	16	0	0	NUM
fumecheng-11486	94	17	(	(	PUNCT
fumecheng-11486	94	18	)	)	PUNCT
fumecheng-11486	94	19	(	(	PUNCT
fumecheng-11486	94	20	)	)	PUNCT
fumecheng-11486	94	21	cos	cos	PROPN
fumecheng-11486	94	22	,	,	PUNCT
fumecheng-11486	94	23	0	0	NUM
fumecheng-11486	95	1	a	a	DET
fumecheng-11486	95	2	t	t	X
fumecheng-11486	95	3	u	u	X
fumecheng-11486	95	4	u	u	X
fumecheng-11486	95	5	t	t	PROPN
fumecheng-11486	95	6	a	a	PRON
fumecheng-11486	95	7	a	a	DET
fumecheng-11486	95	8	t	t	NOUN
fumecheng-11486	95	9	u	u	NOUN
fumecheng-11486	95	10			X
fumecheng-11486	95	11			X
fumecheng-11486	95	12			X
fumecheng-11486	95	13	=	=	PUNCT
fumecheng-11486	95	14			NOUN
fumecheng-11486	95	15	+	+	CCONJ
fumecheng-11486	95	16			NOUN
fumecheng-11486	95	17			PROPN
fumecheng-11486	95	18	(	(	PUNCT
fumecheng-11486	95	19	17	17	NUM
fumecheng-11486	95	20	)	)	PUNCT
fumecheng-11486	95	21	where	where	SCONJ
fumecheng-11486	95	22	δa	δa	PROPN
fumecheng-11486	95	23	in	in	ADP
fumecheng-11486	95	24	the	the	DET
fumecheng-11486	95	25	increment	increment	NOUN
fumecheng-11486	95	26	of	of	ADP
fumecheng-11486	95	27	the	the	DET
fumecheng-11486	95	28	amplitude	amplitude	NOUN
fumecheng-11486	95	29	when	when	SCONJ
fumecheng-11486	95	30	u<0	u<0	NOUN
fumecheng-11486	95	31	.	.	PUNCT
fumecheng-11486	96	1	the	the	DET
fumecheng-11486	96	2	periods	period	NOUN
fumecheng-11486	96	3	of	of	ADP
fumecheng-11486	96	4	eqs	eqs	PROPN
fumecheng-11486	96	5	.	.	PUNCT
fumecheng-11486	97	1	(	(	PUNCT
fumecheng-11486	97	2	13	13	NUM
fumecheng-11486	97	3	)	)	PUNCT
fumecheng-11486	97	4	and	and	CCONJ
fumecheng-11486	97	5	(	(	PUNCT
fumecheng-11486	97	6	14	14	NUM
fumecheng-11486	97	7	)	)	PUNCT
fumecheng-11486	97	8	are	be	AUX
fumecheng-11486	97	9	,	,	PUNCT
fumecheng-11486	97	10	respectively	respectively	ADV
fumecheng-11486	97	11	,	,	PUNCT
fumecheng-11486	97	12	given	give	VERB
fumecheng-11486	97	13	as	as	ADP
fumecheng-11486	97	14	1	1	NUM
fumecheng-11486	97	15	1	1	NUM
fumecheng-11486	97	16	2	2	NUM
fumecheng-11486	97	17	2	2	NUM
fumecheng-11486	97	18	=	=	SYM
fumecheng-11486	97	19	3	3	NUM
fumecheng-11486	97	20	1	1	NUM
fumecheng-11486	97	21	2	2	NUM
fumecheng-11486	97	22	=	=	SYM
fumecheng-11486	97	23	−	−	PROPN
fumecheng-11486	97	24	t	t	NOUN
fumecheng-11486	98	1	a	a	DET
fumecheng-11486	98	2			PROPN
fumecheng-11486	98	3			PROPN
fumecheng-11486	98	4			PROPN
fumecheng-11486	98	5			PROPN
fumecheng-11486	98	6	(	(	PUNCT
fumecheng-11486	98	7	18	18	NUM
fumecheng-11486	98	8	)	)	PUNCT
fumecheng-11486	98	9	196	196	NUM
fumecheng-11486	98	10	j.h	j.h	PROPN
fumecheng-11486	98	11	.	.	PUNCT
fumecheng-11486	99	1	he	he	PRON
fumecheng-11486	99	2	,	,	PUNCT
fumecheng-11486	99	3	q.	q.	PROPN
fumecheng-11486	99	4	yang	yang	PROPN
fumecheng-11486	99	5	,	,	PUNCT
fumecheng-11486	99	6	c.h	c.h	PROPN
fumecheng-11486	99	7	.	.	PUNCT
fumecheng-11486	100	1	he	he	PRON
fumecheng-11486	100	2	,	,	PUNCT
fumecheng-11486	100	3	a.a	a.a	PROPN
fumecheng-11486	100	4	.	.	PROPN
fumecheng-11486	100	5	alsolami	alsolami	PROPN
fumecheng-11486	100	6	2	2	NUM
fumecheng-11486	100	7	2	2	NUM
fumecheng-11486	100	8	2	2	NUM
fumecheng-11486	100	9	2	2	NUM
fumecheng-11486	100	10	=	=	SYM
fumecheng-11486	100	11	3	3	NUM
fumecheng-11486	100	12	1	1	NUM
fumecheng-11486	100	13	+	+	NUM
fumecheng-11486	100	14	2	2	NUM
fumecheng-11486	100	15	=	=	SYM
fumecheng-11486	100	16	t	t	X
fumecheng-11486	100	17	a	a	DET
fumecheng-11486	100	18			PROPN
fumecheng-11486	100	19			PROPN
fumecheng-11486	100	20			PROPN
fumecheng-11486	100	21			PROPN
fumecheng-11486	100	22	(	(	PUNCT
fumecheng-11486	100	23	19	19	NUM
fumecheng-11486	100	24	)	)	PUNCT
fumecheng-11486	100	25	so	so	SCONJ
fumecheng-11486	100	26	the	the	DET
fumecheng-11486	100	27	period	period	NOUN
fumecheng-11486	100	28	of	of	ADP
fumecheng-11486	100	29	eq	eq	NOUN
fumecheng-11486	100	30	.	.	PUNCT
fumecheng-11486	101	1	(	(	PUNCT
fumecheng-11486	101	2	5	5	X
fumecheng-11486	101	3	)	)	PUNCT
fumecheng-11486	101	4	can	can	AUX
fumecheng-11486	101	5	be	be	AUX
fumecheng-11486	101	6	calculated	calculate	VERB
fumecheng-11486	101	7	as	as	ADP
fumecheng-11486	101	8	1	1	NUM
fumecheng-11486	101	9	2	2	NUM
fumecheng-11486	101	10	=	=	SYM
fumecheng-11486	101	11	2	2	NUM
fumecheng-11486	101	12	3	3	NUM
fumecheng-11486	101	13	3	3	NUM
fumecheng-11486	101	14	1	1	NUM
fumecheng-11486	101	15	1	1	NUM
fumecheng-11486	101	16	+	+	NUM
fumecheng-11486	101	17	2	2	NUM
fumecheng-11486	101	18	2	2	NUM
fumecheng-11486	101	19	+	+	CCONJ
fumecheng-11486	101	20	=	=	SYM
fumecheng-11486	102	1	+	+	CCONJ
fumecheng-11486	103	1	−	−	PROPN
fumecheng-11486	103	2	t	t	NOUN
fumecheng-11486	103	3	t	t	PROPN
fumecheng-11486	103	4	t	t	PROPN
fumecheng-11486	103	5	a	a	DET
fumecheng-11486	103	6	a	a	DET
fumecheng-11486	103	7			PROPN
fumecheng-11486	103	8			PROPN
fumecheng-11486	103	9			PROPN
fumecheng-11486	103	10			PROPN
fumecheng-11486	103	11	(	(	PUNCT
fumecheng-11486	103	12	20	20	NUM
fumecheng-11486	103	13	)	)	PUNCT
fumecheng-11486	103	14	eq	eq	NOUN
fumecheng-11486	103	15	.	.	PUNCT
fumecheng-11486	104	1	(	(	PUNCT
fumecheng-11486	104	2	20	20	NUM
fumecheng-11486	104	3	)	)	PUNCT
fumecheng-11486	104	4	shows	show	VERB
fumecheng-11486	104	5	much	much	ADV
fumecheng-11486	104	6	better	well	ADJ
fumecheng-11486	104	7	accuracy	accuracy	NOUN
fumecheng-11486	104	8	for	for	ADP
fumecheng-11486	104	9	βa<0.5	βa<0.5	PROPN
fumecheng-11486	104	10	,	,	PUNCT
fumecheng-11486	104	11	see	see	VERB
fumecheng-11486	104	12	table	table	NOUN
fumecheng-11486	104	13	1	1	NUM
fumecheng-11486	104	14	.	.	PUNCT
fumecheng-11486	104	15	when	when	SCONJ
fumecheng-11486	104	16	βa=1.1547	βa=1.1547	PROPN
fumecheng-11486	104	17	,	,	PUNCT
fumecheng-11486	104	18	the	the	DET
fumecheng-11486	104	19	period	period	NOUN
fumecheng-11486	104	20	by	by	ADP
fumecheng-11486	104	21	eq	eq	PROPN
fumecheng-11486	104	22	.	.	PUNCT
fumecheng-11486	104	23	(	(	PUNCT
fumecheng-11486	104	24	20	20	NUM
fumecheng-11486	104	25	)	)	PUNCT
fumecheng-11486	104	26	becomes	become	VERB
fumecheng-11486	104	27	infinite	infinite	ADJ
fumecheng-11486	104	28	large	large	ADJ
fumecheng-11486	104	29	.	.	PUNCT
fumecheng-11486	105	1	4	4	X
fumecheng-11486	105	2	.	.	X
fumecheng-11486	105	3	pull	pull	NOUN
fumecheng-11486	105	4	-	-	PUNCT
fumecheng-11486	105	5	down	down	ADP
fumecheng-11486	105	6	instability	instability	NOUN
fumecheng-11486	105	7	when	when	SCONJ
fumecheng-11486	105	8	βa	βa	PRON
fumecheng-11486	105	9	tends	tend	VERB
fumecheng-11486	105	10	to	to	ADP
fumecheng-11486	105	11	the	the	DET
fumecheng-11486	105	12	threshold	threshold	NOUN
fumecheng-11486	105	13	value	value	NOUN
fumecheng-11486	105	14	,	,	PUNCT
fumecheng-11486	105	15	the	the	DET
fumecheng-11486	105	16	pull	pull	NOUN
fumecheng-11486	105	17	-	-	PUNCT
fumecheng-11486	105	18	down	down	ADP
fumecheng-11486	105	19	instability	instability	NOUN
fumecheng-11486	105	20	occurs	occur	VERB
fumecheng-11486	105	21	.	.	PUNCT
fumecheng-11486	106	1	the	the	DET
fumecheng-11486	106	2	motion	motion	NOUN
fumecheng-11486	106	3	of	of	ADP
fumecheng-11486	106	4	eq	eq	PROPN
fumecheng-11486	106	5	.	.	PUNCT
fumecheng-11486	107	1	(	(	PUNCT
fumecheng-11486	107	2	5	5	X
fumecheng-11486	107	3	)	)	PUNCT
fumecheng-11486	107	4	can	can	AUX
fumecheng-11486	107	5	be	be	AUX
fumecheng-11486	107	6	decomposed	decompose	VERB
fumecheng-11486	107	7	into	into	ADP
fumecheng-11486	107	8	two	two	NUM
fumecheng-11486	107	9	parts	part	NOUN
fumecheng-11486	107	10	as	as	SCONJ
fumecheng-11486	107	11	given	give	VERB
fumecheng-11486	107	12	in	in	ADP
fumecheng-11486	107	13	eqs	eqs	PROPN
fumecheng-11486	107	14	.	.	PUNCT
fumecheng-11486	108	1	(	(	PUNCT
fumecheng-11486	108	2	13	13	NUM
fumecheng-11486	108	3	)	)	PUNCT
fumecheng-11486	108	4	and	and	CCONJ
fumecheng-11486	108	5	(	(	PUNCT
fumecheng-11486	108	6	14	14	NUM
fumecheng-11486	108	7	)	)	PUNCT
fumecheng-11486	108	8	.	.	PUNCT
fumecheng-11486	109	1	it	it	PRON
fumecheng-11486	109	2	is	be	AUX
fumecheng-11486	109	3	obvious	obvious	ADJ
fumecheng-11486	109	4	that	that	SCONJ
fumecheng-11486	109	5	eq	eq	ADP
fumecheng-11486	109	6	.	.	PUNCT
fumecheng-11486	110	1	(	(	PUNCT
fumecheng-11486	110	2	13	13	NUM
fumecheng-11486	110	3	)	)	PUNCT
fumecheng-11486	110	4	has	have	VERB
fumecheng-11486	110	5	a	a	DET
fumecheng-11486	110	6	tendance	tendance	NOUN
fumecheng-11486	110	7	of	of	ADP
fumecheng-11486	110	8	a	a	DET
fumecheng-11486	110	9	pull	pull	NOUN
fumecheng-11486	110	10	-	-	PUNCT
fumecheng-11486	110	11	down	down	ADP
fumecheng-11486	110	12	motion	motion	NOUN
fumecheng-11486	110	13	,	,	PUNCT
fumecheng-11486	110	14	and	and	CCONJ
fumecheng-11486	110	15	eq	eq	NOUN
fumecheng-11486	110	16	.	.	PUNCT
fumecheng-11486	111	1	(	(	PUNCT
fumecheng-11486	111	2	14	14	NUM
fumecheng-11486	111	3	)	)	PUNCT
fumecheng-11486	111	4	gives	give	VERB
fumecheng-11486	111	5	an	an	DET
fumecheng-11486	111	6	opposite	opposite	ADJ
fumecheng-11486	111	7	motion	motion	NOUN
fumecheng-11486	111	8	.	.	PUNCT
fumecheng-11486	112	1	we	we	PRON
fumecheng-11486	112	2	consider	consider	VERB
fumecheng-11486	112	3	an	an	DET
fumecheng-11486	112	4	extreme	extreme	ADJ
fumecheng-11486	112	5	case	case	NOUN
fumecheng-11486	112	6	when	when	SCONJ
fumecheng-11486	112	7	u1=-2a	u1=-2a	NOUN
fumecheng-11486	112	8	for	for	ADP
fumecheng-11486	112	9	eq	eq	PROPN
fumecheng-11486	112	10	.	.	PUNCT
fumecheng-11486	113	1	(	(	PUNCT
fumecheng-11486	113	2	13	13	NUM
fumecheng-11486	113	3	)	)	PUNCT
fumecheng-11486	113	4	,	,	PUNCT
fumecheng-11486	113	5	and	and	CCONJ
fumecheng-11486	113	6	u2	u2	NOUN
fumecheng-11486	113	7	=	=	PROPN
fumecheng-11486	113	8	a	a	NOUN
fumecheng-11486	113	9	for	for	ADP
fumecheng-11486	113	10	eq	eq	NOUN
fumecheng-11486	113	11	.	.	PUNCT
fumecheng-11486	114	1	(	(	PUNCT
fumecheng-11486	114	2	14	14	NUM
fumecheng-11486	114	3	)	)	PUNCT
fumecheng-11486	114	4	,	,	PUNCT
fumecheng-11486	114	5	the	the	DET
fumecheng-11486	114	6	combined	combined	ADJ
fumecheng-11486	114	7	displacement	displacement	NOUN
fumecheng-11486	114	8	is	be	AUX
fumecheng-11486	114	9	u1+u2=-2a+a=-a	u1+u2=-2a+a=-a	ADJ
fumecheng-11486	114	10	,	,	PUNCT
fumecheng-11486	114	11	so	so	SCONJ
fumecheng-11486	114	12	eq	eq	ADP
fumecheng-11486	114	13	.	.	PUNCT
fumecheng-11486	115	1	(	(	PUNCT
fumecheng-11486	115	2	5	5	X
fumecheng-11486	115	3	)	)	PUNCT
fumecheng-11486	115	4	is	be	AUX
fumecheng-11486	115	5	still	still	ADV
fumecheng-11486	115	6	periodic	periodic	ADJ
fumecheng-11486	115	7	.	.	PUNCT
fumecheng-11486	116	1	however	however	ADV
fumecheng-11486	116	2	if	if	SCONJ
fumecheng-11486	116	3	u1<-2a	u1<-2a	ADJ
fumecheng-11486	116	4	,	,	PUNCT
fumecheng-11486	116	5	we	we	PRON
fumecheng-11486	116	6	have	have	VERB
fumecheng-11486	116	7	|u1+u2|>a	|u1+u2|>a	NUM
fumecheng-11486	116	8	,	,	PUNCT
fumecheng-11486	116	9	under	under	ADP
fumecheng-11486	116	10	such	such	ADJ
fumecheng-11486	116	11	case	case	NOUN
fumecheng-11486	116	12	,	,	PUNCT
fumecheng-11486	116	13	the	the	DET
fumecheng-11486	116	14	motion	motion	NOUN
fumecheng-11486	116	15	is	be	AUX
fumecheng-11486	116	16	pulled	pull	VERB
fumecheng-11486	116	17	down	down	ADP
fumecheng-11486	116	18	,	,	PUNCT
fumecheng-11486	116	19	and	and	CCONJ
fumecheng-11486	116	20	its	its	PRON
fumecheng-11486	116	21	periodic	periodic	ADJ
fumecheng-11486	116	22	motion	motion	NOUN
fumecheng-11486	116	23	is	be	AUX
fumecheng-11486	116	24	forbidden	forbid	VERB
fumecheng-11486	116	25	.	.	PUNCT
fumecheng-11486	117	1	we	we	PRON
fumecheng-11486	117	2	consider	consider	VERB
fumecheng-11486	117	3	the	the	DET
fumecheng-11486	117	4	extreme	extreme	ADJ
fumecheng-11486	117	5	condition	condition	NOUN
fumecheng-11486	117	6	of	of	ADP
fumecheng-11486	117	7	u1=-2a	u1=-2a	NOUN
fumecheng-11486	117	8	,	,	PUNCT
fumecheng-11486	117	9	eq	eq	NOUN
fumecheng-11486	117	10	.	.	PUNCT
fumecheng-11486	118	1	(	(	PUNCT
fumecheng-11486	118	2	13	13	NUM
fumecheng-11486	118	3	)	)	PUNCT
fumecheng-11486	118	4	can	can	AUX
fumecheng-11486	118	5	be	be	AUX
fumecheng-11486	118	6	written	write	VERB
fumecheng-11486	118	7	approximately	approximately	ADV
fumecheng-11486	118	8	as	as	ADP
fumecheng-11486	118	9	2	2	NUM
fumecheng-11486	118	10	2	2	NUM
fumecheng-11486	118	11	(	(	PUNCT
fumecheng-11486	118	12	1	1	NUM
fumecheng-11486	118	13	2	2	NUM
fumecheng-11486	118	14	)	)	PUNCT
fumecheng-11486	118	15	0	0	NUM
fumecheng-11486	119	1	+	+	NUM
fumecheng-11486	119	2	−	−	NOUN
fumecheng-11486	119	3	=	=	SYM
fumecheng-11486	119	4	d	d	PUNCT
fumecheng-11486	119	5	u	u	NOUN
fumecheng-11486	119	6	a	a	DET
fumecheng-11486	119	7	u	u	NOUN
fumecheng-11486	119	8	dt	dt	PROPN
fumecheng-11486	119	9			PROPN
fumecheng-11486	119	10	(	(	PUNCT
fumecheng-11486	119	11	21	21	NUM
fumecheng-11486	119	12	)	)	PUNCT
fumecheng-11486	119	13	this	this	PRON
fumecheng-11486	119	14	predicts	predict	VERB
fumecheng-11486	119	15	2	2	NUM
fumecheng-11486	119	16	1	1	NUM
fumecheng-11486	119	17	=	=	SYM
fumecheng-11486	119	18	1	1	NUM
fumecheng-11486	119	19	2−	2−	NUM
fumecheng-11486	119	20	a	a	ADV
fumecheng-11486	120	1			PROPN
fumecheng-11486	120	2	(	(	PUNCT
fumecheng-11486	120	3	22	22	NUM
fumecheng-11486	120	4	)	)	PUNCT
fumecheng-11486	120	5	the	the	DET
fumecheng-11486	120	6	pull	pull	NOUN
fumecheng-11486	120	7	-	-	PUNCT
fumecheng-11486	120	8	down	down	ADP
fumecheng-11486	120	9	instability	instability	NOUN
fumecheng-11486	120	10	occurs	occur	VERB
fumecheng-11486	120	11	when	when	SCONJ
fumecheng-11486	120	12	2	2	NUM
fumecheng-11486	120	13	1	1	NUM
fumecheng-11486	120	14	0	0	NUM
fumecheng-11486	120	15			PROPN
fumecheng-11486	120	16	,	,	PUNCT
fumecheng-11486	120	17	that	that	ADV
fumecheng-11486	120	18	is	is	ADV
fumecheng-11486	120	19	0.5a	0.5a	ADJ
fumecheng-11486	120	20	(	(	PUNCT
fumecheng-11486	120	21	23	23	NUM
fumecheng-11486	120	22	)	)	PUNCT
fumecheng-11486	120	23	so	so	ADV
fumecheng-11486	120	24	βa=0.5	βa=0.5	NOUN
fumecheng-11486	120	25	is	be	AUX
fumecheng-11486	120	26	the	the	DET
fumecheng-11486	120	27	threshold	threshold	NOUN
fumecheng-11486	120	28	value	value	NOUN
fumecheng-11486	120	29	.	.	PUNCT
fumecheng-11486	121	1	we	we	PRON
fumecheng-11486	121	2	give	give	VERB
fumecheng-11486	121	3	another	another	DET
fumecheng-11486	121	4	approach	approach	NOUN
fumecheng-11486	121	5	to	to	ADP
fumecheng-11486	121	6	determination	determination	NOUN
fumecheng-11486	121	7	of	of	ADP
fumecheng-11486	121	8	the	the	DET
fumecheng-11486	121	9	threshold	threshold	NOUN
fumecheng-11486	121	10	value	value	NOUN
fumecheng-11486	121	11	.	.	PUNCT
fumecheng-11486	122	1	eq	eq	X
fumecheng-11486	122	2	.	.	PUNCT
fumecheng-11486	123	1	(	(	PUNCT
fumecheng-11486	123	2	5	5	X
fumecheng-11486	123	3	)	)	PUNCT
fumecheng-11486	123	4	can	can	AUX
fumecheng-11486	123	5	be	be	AUX
fumecheng-11486	123	6	written	write	VERB
fumecheng-11486	123	7	in	in	ADP
fumecheng-11486	123	8	the	the	DET
fumecheng-11486	123	9	form	form	NOUN
fumecheng-11486	123	10	2	2	NUM
fumecheng-11486	123	11	2	2	NUM
fumecheng-11486	123	12	31	31	NUM
fumecheng-11486	123	13	1	1	NUM
fumecheng-11486	123	14	1	1	NUM
fumecheng-11486	123	15	(	(	PUNCT
fumecheng-11486	123	16	)	)	PUNCT
fumecheng-11486	123	17	2	2	NUM
fumecheng-11486	123	18	2	2	NUM
fumecheng-11486	123	19	3	3	NUM
fumecheng-11486	123	20	+	+	CCONJ
fumecheng-11486	123	21	+	+	CCONJ
fumecheng-11486	123	22	=	=	SYM
fumecheng-11486	123	23	du	du	PROPN
fumecheng-11486	123	24	u	u	PROPN
fumecheng-11486	123	25	u	u	NOUN
fumecheng-11486	123	26	h	h	NOUN
fumecheng-11486	123	27	dt	dt	NOUN
fumecheng-11486	123	28			PROPN
fumecheng-11486	123	29	(	(	PUNCT
fumecheng-11486	123	30	24	24	NUM
fumecheng-11486	123	31	)	)	PUNCT
fumecheng-11486	123	32	where	where	SCONJ
fumecheng-11486	123	33	h	h	NOUN
fumecheng-11486	123	34	is	be	AUX
fumecheng-11486	123	35	the	the	DET
fumecheng-11486	123	36	hamilton	hamilton	PROPN
fumecheng-11486	123	37	constant	constant	PROPN
fumecheng-11486	123	38	.	.	PUNCT
fumecheng-11486	124	1	by	by	ADP
fumecheng-11486	124	2	the	the	DET
fumecheng-11486	124	3	initial	initial	ADJ
fumecheng-11486	124	4	conditions	condition	NOUN
fumecheng-11486	124	5	given	give	VERB
fumecheng-11486	124	6	in	in	ADP
fumecheng-11486	124	7	eq	eq	ADP
fumecheng-11486	124	8	.	.	PUNCT
fumecheng-11486	125	1	(	(	PUNCT
fumecheng-11486	125	2	6	6	NUM
fumecheng-11486	125	3	)	)	PUNCT
fumecheng-11486	125	4	,	,	PUNCT
fumecheng-11486	125	5	eq	eq	NOUN
fumecheng-11486	125	6	.	.	PUNCT
fumecheng-11486	126	1	(	(	PUNCT
fumecheng-11486	126	2	24	24	NUM
fumecheng-11486	126	3	)	)	PUNCT
fumecheng-11486	126	4	becomes	become	VERB
fumecheng-11486	126	5	2	2	NUM
fumecheng-11486	126	6	2	2	NUM
fumecheng-11486	126	7	2	2	NUM
fumecheng-11486	126	8	3	3	NUM
fumecheng-11486	126	9	31	31	NUM
fumecheng-11486	126	10	1	1	NUM
fumecheng-11486	126	11	1	1	NUM
fumecheng-11486	126	12	(	(	PUNCT
fumecheng-11486	126	13	)	)	PUNCT
fumecheng-11486	126	14	(	(	PUNCT
fumecheng-11486	126	15	)	)	PUNCT
fumecheng-11486	126	16	(	(	PUNCT
fumecheng-11486	126	17	)	)	PUNCT
fumecheng-11486	127	1	2	2	NUM
fumecheng-11486	127	2	2	2	NUM
fumecheng-11486	127	3	3	3	NUM
fumecheng-11486	127	4	=	=	SYM
fumecheng-11486	127	5	−	−	PROPN
fumecheng-11486	127	6	+	+	CCONJ
fumecheng-11486	127	7	−	−	PROPN
fumecheng-11486	127	8	du	du	PROPN
fumecheng-11486	127	9	a	a	DET
fumecheng-11486	127	10	u	u	NOUN
fumecheng-11486	127	11	a	a	DET
fumecheng-11486	127	12	u	u	NOUN
fumecheng-11486	127	13	dt	dt	PROPN
fumecheng-11486	127	14			PROPN
fumecheng-11486	127	15	(	(	PUNCT
fumecheng-11486	127	16	25	25	NUM
fumecheng-11486	127	17	)	)	PUNCT
fumecheng-11486	128	1	when	when	SCONJ
fumecheng-11486	128	2	u	u	PROPN
fumecheng-11486	128	3	=	=	PROPN
fumecheng-11486	128	4	-2a	-2a	PROPN
fumecheng-11486	128	5	,	,	PUNCT
fumecheng-11486	128	6	the	the	DET
fumecheng-11486	128	7	kinetic	kinetic	ADJ
fumecheng-11486	128	8	energy	energy	NOUN
fumecheng-11486	128	9	tends	tend	VERB
fumecheng-11486	128	10	to	to	ADP
fumecheng-11486	128	11	zero	zero	NUM
fumecheng-11486	128	12	,	,	PUNCT
fumecheng-11486	128	13	so	so	ADV
fumecheng-11486	128	14	the	the	DET
fumecheng-11486	128	15	pull	pull	NOUN
fumecheng-11486	128	16	-	-	PUNCT
fumecheng-11486	128	17	down	down	ADP
fumecheng-11486	128	18	instability	instability	NOUN
fumecheng-11486	128	19	occurs	occur	VERB
fumecheng-11486	128	20	when	when	SCONJ
fumecheng-11486	128	21	2	2	NUM
fumecheng-11486	128	22	2	2	NUM
fumecheng-11486	128	23	2	2	NUM
fumecheng-11486	128	24	3	3	NUM
fumecheng-11486	128	25	31	31	NUM
fumecheng-11486	128	26	1	1	NUM
fumecheng-11486	128	27	1	1	NUM
fumecheng-11486	128	28	(	(	PUNCT
fumecheng-11486	128	29	)	)	PUNCT
fumecheng-11486	128	30	(	(	PUNCT
fumecheng-11486	128	31	2	2	X
fumecheng-11486	128	32	)	)	PUNCT
fumecheng-11486	128	33	(	(	PUNCT
fumecheng-11486	128	34	(	(	PUNCT
fumecheng-11486	128	35	2	2	NUM
fumecheng-11486	128	36	)	)	PUNCT
fumecheng-11486	128	37	)	)	PUNCT
fumecheng-11486	129	1	(	(	PUNCT
fumecheng-11486	129	2	(	(	PUNCT
fumecheng-11486	129	3	2	2	NUM
fumecheng-11486	129	4	)	)	PUNCT
fumecheng-11486	129	5	)	)	PUNCT
fumecheng-11486	129	6	0	0	NUM
fumecheng-11486	130	1	2	2	NUM
fumecheng-11486	130	2	2	2	NUM
fumecheng-11486	130	3	3	3	NUM
fumecheng-11486	130	4	=	=	SYM
fumecheng-11486	130	5	−	−	PROPN
fumecheng-11486	130	6	=	=	PUNCT
fumecheng-11486	130	7	−	−	PROPN
fumecheng-11486	130	8	−	−	PROPN
fumecheng-11486	131	1	+	+	CCONJ
fumecheng-11486	131	2	−	−	PROPN
fumecheng-11486	131	3	−	−	PROPN
fumecheng-11486	131	4			PROPN
fumecheng-11486	131	5	du	du	PROPN
fumecheng-11486	131	6	u	u	PROPN
fumecheng-11486	131	7	a	a	DET
fumecheng-11486	131	8	a	a	DET
fumecheng-11486	131	9	a	a	DET
fumecheng-11486	131	10	a	a	DET
fumecheng-11486	131	11	a	a	DET
fumecheng-11486	131	12	dt	dt	NOUN
fumecheng-11486	131	13			PROPN
fumecheng-11486	131	14	(	(	PUNCT
fumecheng-11486	131	15	26	26	NUM
fumecheng-11486	131	16	)	)	PUNCT
fumecheng-11486	131	17	pull	pull	NOUN
fumecheng-11486	131	18	-	-	PUNCT
fumecheng-11486	131	19	down	down	ADP
fumecheng-11486	131	20	instability	instability	NOUN
fumecheng-11486	131	21	of	of	ADP
fumecheng-11486	131	22	the	the	DET
fumecheng-11486	131	23	quadratic	quadratic	ADJ
fumecheng-11486	131	24	nonlinear	nonlinear	ADJ
fumecheng-11486	131	25	oscillators	oscillator	NOUN
fumecheng-11486	131	26	197	197	NUM
fumecheng-11486	131	27	eq	eq	NOUN
fumecheng-11486	131	28	.	.	PUNCT
fumecheng-11486	132	1	(	(	PUNCT
fumecheng-11486	132	2	26	26	NUM
fumecheng-11486	132	3	)	)	PUNCT
fumecheng-11486	132	4	results	result	NOUN
fumecheng-11486	132	5	in	in	ADP
fumecheng-11486	132	6	βa>0.5	βa>0.5	PUNCT
fumecheng-11486	132	7	as	as	SCONJ
fumecheng-11486	132	8	shown	show	VERB
fumecheng-11486	132	9	in	in	ADP
fumecheng-11486	132	10	eq	eq	ADP
fumecheng-11486	132	11	.	.	PUNCT
fumecheng-11486	133	1	(	(	PUNCT
fumecheng-11486	133	2	23	23	NUM
fumecheng-11486	133	3	)	)	PUNCT
fumecheng-11486	133	4	.	.	PUNCT
fumecheng-11486	134	1	when	when	SCONJ
fumecheng-11486	134	2	βa<0.5	βa<0.5	NOUN
fumecheng-11486	134	3	,	,	PUNCT
fumecheng-11486	134	4	a	a	DET
fumecheng-11486	134	5	periodic	periodic	ADJ
fumecheng-11486	134	6	motion	motion	NOUN
fumecheng-11486	134	7	or	or	CCONJ
fumecheng-11486	134	8	a	a	DET
fumecheng-11486	134	9	pseudo	pseudo	NOUN
fumecheng-11486	134	10	-	-	ADJ
fumecheng-11486	134	11	periodic	periodic	ADJ
fumecheng-11486	134	12	motion	motion	NOUN
fumecheng-11486	134	13	is	be	AUX
fumecheng-11486	134	14	predicted	predict	VERB
fumecheng-11486	134	15	.	.	PUNCT
fumecheng-11486	135	1	when	when	SCONJ
fumecheng-11486	135	2	βa>0.5	βa>0.5	NOUN
fumecheng-11486	135	3	,	,	PUNCT
fumecheng-11486	135	4	the	the	DET
fumecheng-11486	135	5	pull	pull	NOUN
fumecheng-11486	135	6	-	-	PUNCT
fumecheng-11486	135	7	down	down	ADP
fumecheng-11486	135	8	instability	instability	NOUN
fumecheng-11486	135	9	occurs	occur	VERB
fumecheng-11486	135	10	.	.	PUNCT
fumecheng-11486	136	1	to	to	PART
fumecheng-11486	136	2	verify	verify	VERB
fumecheng-11486	136	3	this	this	DET
fumecheng-11486	136	4	criterion	criterion	NOUN
fumecheng-11486	136	5	,	,	PUNCT
fumecheng-11486	136	6	we	we	PRON
fumecheng-11486	136	7	consider	consider	VERB
fumecheng-11486	136	8	various	various	ADJ
fumecheng-11486	136	9	values	value	NOUN
fumecheng-11486	136	10	of	of	ADP
fumecheng-11486	136	11	a	a	PRON
fumecheng-11486	136	12	and	and	CCONJ
fumecheng-11486	136	13	β	β	NOUN
fumecheng-11486	136	14	,	,	PUNCT
fumecheng-11486	136	15	and	and	CCONJ
fumecheng-11486	136	16	the	the	DET
fumecheng-11486	136	17	results	result	NOUN
fumecheng-11486	136	18	are	be	AUX
fumecheng-11486	136	19	illustrated	illustrate	VERB
fumecheng-11486	136	20	in	in	ADP
fumecheng-11486	136	21	figs	fig	NOUN
fumecheng-11486	136	22	.	.	PUNCT
fumecheng-11486	137	1	2	2	NUM
fumecheng-11486	137	2	-	-	SYM
fumecheng-11486	137	3	4	4	NUM
fumecheng-11486	137	4	.	.	PUNCT
fumecheng-11486	138	1	when	when	SCONJ
fumecheng-11486	138	2	the	the	DET
fumecheng-11486	138	3	value	value	NOUN
fumecheng-11486	138	4	of	of	ADP
fumecheng-11486	138	5	βa	βa	PRON
fumecheng-11486	138	6	is	be	AUX
fumecheng-11486	138	7	less	less	ADJ
fumecheng-11486	138	8	than	than	ADP
fumecheng-11486	138	9	the	the	DET
fumecheng-11486	138	10	threshold	threshold	NOUN
fumecheng-11486	138	11	value	value	NOUN
fumecheng-11486	138	12	,	,	PUNCT
fumecheng-11486	138	13	0.5	0.5	NUM
fumecheng-11486	138	14	,	,	PUNCT
fumecheng-11486	138	15	but	but	CCONJ
fumecheng-11486	138	16	it	it	PRON
fumecheng-11486	138	17	is	be	AUX
fumecheng-11486	138	18	near	near	ADJ
fumecheng-11486	138	19	to	to	ADP
fumecheng-11486	138	20	the	the	DET
fumecheng-11486	138	21	value	value	NOUN
fumecheng-11486	138	22	,	,	PUNCT
fumecheng-11486	138	23	the	the	DET
fumecheng-11486	138	24	pseudo	pseudo	NOUN
fumecheng-11486	138	25	-	-	ADJ
fumecheng-11486	138	26	periodic	periodic	ADJ
fumecheng-11486	138	27	motion	motion	NOUN
fumecheng-11486	138	28	is	be	AUX
fumecheng-11486	138	29	observed	observe	VERB
fumecheng-11486	138	30	,	,	PUNCT
fumecheng-11486	138	31	for	for	ADP
fumecheng-11486	138	32	example	example	NOUN
fumecheng-11486	138	33	,	,	PUNCT
fumecheng-11486	138	34	βa=0.495	βa=0.495	PROPN
fumecheng-11486	138	35	in	in	ADP
fumecheng-11486	138	36	fig	fig	NOUN
fumecheng-11486	138	37	.	.	PUNCT
fumecheng-11486	139	1	2(c	2(c	NUM
fumecheng-11486	139	2	)	)	PUNCT
fumecheng-11486	140	1	;	;	PUNCT
fumecheng-11486	140	2	while	while	SCONJ
fumecheng-11486	140	3	it	it	PRON
fumecheng-11486	140	4	is	be	AUX
fumecheng-11486	140	5	far	far	ADV
fumecheng-11486	140	6	from	from	ADP
fumecheng-11486	140	7	the	the	DET
fumecheng-11486	140	8	value	value	NOUN
fumecheng-11486	140	9	,	,	PUNCT
fumecheng-11486	140	10	for	for	ADP
fumecheng-11486	140	11	example	example	NOUN
fumecheng-11486	140	12	,	,	PUNCT
fumecheng-11486	140	13	βa=0.3	βa=0.3	X
fumecheng-11486	140	14	in	in	ADP
fumecheng-11486	140	15	fig	fig	NOUN
fumecheng-11486	140	16	.	.	PUNCT
fumecheng-11486	141	1	2(c	2(c	NUM
fumecheng-11486	141	2	)	)	PUNCT
fumecheng-11486	141	3	,	,	PUNCT
fumecheng-11486	141	4	a	a	DET
fumecheng-11486	141	5	periodic	periodic	ADJ
fumecheng-11486	141	6	motion	motion	NOUN
fumecheng-11486	141	7	is	be	AUX
fumecheng-11486	141	8	seen	see	VERB
fumecheng-11486	141	9	.	.	PUNCT
fumecheng-11486	142	1	so	so	ADV
fumecheng-11486	142	2	far	far	ADV
fumecheng-11486	142	3	,	,	PUNCT
fumecheng-11486	142	4	we	we	PRON
fumecheng-11486	142	5	have	have	VERB
fumecheng-11486	142	6	no	no	DET
fumecheng-11486	142	7	criterion	criterion	NOUN
fumecheng-11486	142	8	for	for	ADP
fumecheng-11486	142	9	exactly	exactly	ADV
fumecheng-11486	142	10	predicting	predict	VERB
fumecheng-11486	142	11	the	the	DET
fumecheng-11486	142	12	value	value	NOUN
fumecheng-11486	142	13	of	of	ADP
fumecheng-11486	142	14	βa	βa	INTJ
fumecheng-11486	142	15	for	for	ADP
fumecheng-11486	142	16	a	a	DET
fumecheng-11486	142	17	pseudo	pseudo	NOUN
fumecheng-11486	142	18	-	-	ADJ
fumecheng-11486	142	19	periodic	periodic	ADJ
fumecheng-11486	142	20	motion	motion	NOUN
fumecheng-11486	142	21	,	,	PUNCT
fumecheng-11486	142	22	where	where	SCONJ
fumecheng-11486	142	23	an	an	DET
fumecheng-11486	142	24	unsymmetrical	unsymmetrical	ADJ
fumecheng-11486	142	25	oscillation	oscillation	NOUN
fumecheng-11486	142	26	deteriorates	deteriorate	VERB
fumecheng-11486	142	27	gradually	gradually	ADV
fumecheng-11486	142	28	in	in	ADP
fumecheng-11486	142	29	each	each	DET
fumecheng-11486	142	30	cycle	cycle	NOUN
fumecheng-11486	142	31	,	,	PUNCT
fumecheng-11486	142	32	and	and	CCONJ
fumecheng-11486	142	33	when	when	SCONJ
fumecheng-11486	142	34	u	u	PRON
fumecheng-11486	142	35	reaches	reach	VERB
fumecheng-11486	142	36	negative	negative	ADJ
fumecheng-11486	142	37	2a	2a	NUM
fumecheng-11486	142	38	,	,	PUNCT
fumecheng-11486	142	39	the	the	DET
fumecheng-11486	142	40	convincing	convincing	ADJ
fumecheng-11486	142	41	periodic	periodic	ADJ
fumecheng-11486	142	42	motion	motion	NOUN
fumecheng-11486	142	43	stops	stop	VERB
fumecheng-11486	142	44	suddenly	suddenly	ADV
fumecheng-11486	142	45	.	.	PUNCT
fumecheng-11486	143	1	(	(	PUNCT
fumecheng-11486	143	2	a	a	X
fumecheng-11486	143	3	)	)	PUNCT
fumecheng-11486	143	4	(	(	PUNCT
fumecheng-11486	143	5	b	b	X
fumecheng-11486	143	6	)	)	PUNCT
fumecheng-11486	143	7	(	(	PUNCT
fumecheng-11486	143	8	b	b	NOUN
fumecheng-11486	143	9	)	)	PUNCT
fumecheng-11486	143	10	(	(	PUNCT
fumecheng-11486	143	11	d	d	NOUN
fumecheng-11486	143	12	)	)	PUNCT
fumecheng-11486	143	13	fig	fig	NOUN
fumecheng-11486	143	14	.	.	PUNCT
fumecheng-11486	144	1	2	2	NUM
fumecheng-11486	144	2	the	the	DET
fumecheng-11486	144	3	criterion	criterion	NOUN
fumecheng-11486	144	4	of	of	ADP
fumecheng-11486	144	5	the	the	DET
fumecheng-11486	144	6	pull	pull	NOUN
fumecheng-11486	144	7	-	-	PUNCT
fumecheng-11486	144	8	down	down	ADP
fumecheng-11486	144	9	instability	instability	NOUN
fumecheng-11486	144	10	when	when	SCONJ
fumecheng-11486	144	11	a=0.3	a=0.3	ADJ
fumecheng-11486	144	12	.	.	PUNCT
fumecheng-11486	145	1	(	(	PUNCT
fumecheng-11486	145	2	a	a	X
fumecheng-11486	145	3	)	)	PUNCT
fumecheng-11486	145	4	phase	phase	NOUN
fumecheng-11486	145	5	diagram	diagram	NOUN
fumecheng-11486	145	6	;	;	PUNCT
fumecheng-11486	145	7	(	(	PUNCT
fumecheng-11486	145	8	b	b	X
fumecheng-11486	145	9	)	)	PUNCT
fumecheng-11486	145	10	periodic	periodic	ADJ
fumecheng-11486	145	11	motion	motion	NOUN
fumecheng-11486	145	12	βa=0.3	βa=0.3	ADP
fumecheng-11486	145	13	;	;	PUNCT
fumecheng-11486	145	14	(	(	PUNCT
fumecheng-11486	145	15	c	c	X
fumecheng-11486	145	16	)	)	PUNCT
fumecheng-11486	145	17	pseudo	pseudo	NOUN
fumecheng-11486	145	18	-	-	ADJ
fumecheng-11486	145	19	periodic	periodic	ADJ
fumecheng-11486	145	20	motion	motion	NOUN
fumecheng-11486	145	21	βa=0.495	βa=0.495	PROPN
fumecheng-11486	145	22	and	and	CCONJ
fumecheng-11486	145	23	(	(	PUNCT
fumecheng-11486	145	24	d	d	NOUN
fumecheng-11486	145	25	)	)	PUNCT
fumecheng-11486	145	26	pull	pull	NOUN
fumecheng-11486	145	27	-	-	PUNCT
fumecheng-11486	145	28	down	down	NOUN
fumecheng-11486	145	29	instability	instability	NOUN
fumecheng-11486	145	30	βa=0.51	βa=0.51	NOUN
fumecheng-11486	145	31	198	198	NUM
fumecheng-11486	145	32	j.h	j.h	PROPN
fumecheng-11486	145	33	.	.	PUNCT
fumecheng-11486	146	1	he	he	PRON
fumecheng-11486	146	2	,	,	PUNCT
fumecheng-11486	146	3	q.	q.	PROPN
fumecheng-11486	146	4	yang	yang	PROPN
fumecheng-11486	146	5	,	,	PUNCT
fumecheng-11486	146	6	c.h	c.h	PROPN
fumecheng-11486	146	7	.	.	PUNCT
fumecheng-11486	147	1	he	he	PRON
fumecheng-11486	147	2	,	,	PUNCT
fumecheng-11486	147	3	a.a	a.a	PROPN
fumecheng-11486	147	4	.	.	PROPN
fumecheng-11486	147	5	alsolami	alsolami	PROPN
fumecheng-11486	147	6	(	(	PUNCT
fumecheng-11486	147	7	a	a	NOUN
fumecheng-11486	147	8	)	)	PUNCT
fumecheng-11486	147	9	(	(	PUNCT
fumecheng-11486	147	10	b	b	X
fumecheng-11486	147	11	)	)	PUNCT
fumecheng-11486	147	12	(	(	PUNCT
fumecheng-11486	147	13	b	b	NOUN
fumecheng-11486	147	14	)	)	PUNCT
fumecheng-11486	147	15	(	(	PUNCT
fumecheng-11486	147	16	d	d	X
fumecheng-11486	147	17	)	)	PUNCT
fumecheng-11486	147	18	fig	fig	NOUN
fumecheng-11486	147	19	.	.	PUNCT
fumecheng-11486	148	1	3	3	NUM
fumecheng-11486	148	2	the	the	DET
fumecheng-11486	148	3	criterion	criterion	NOUN
fumecheng-11486	148	4	of	of	ADP
fumecheng-11486	148	5	the	the	DET
fumecheng-11486	148	6	pull	pull	NOUN
fumecheng-11486	148	7	-	-	PUNCT
fumecheng-11486	148	8	down	down	NOUN
fumecheng-11486	148	9	instability	instability	NOUN
fumecheng-11486	148	10	when	when	SCONJ
fumecheng-11486	148	11	a=0.5	a=0.5	NUM
fumecheng-11486	148	12	.	.	PUNCT
fumecheng-11486	149	1	(	(	PUNCT
fumecheng-11486	149	2	a	a	DET
fumecheng-11486	149	3	)	)	PUNCT
fumecheng-11486	149	4	phase	phase	NOUN
fumecheng-11486	149	5	diagram	diagram	NOUN
fumecheng-11486	149	6	;	;	PUNCT
fumecheng-11486	149	7	(	(	PUNCT
fumecheng-11486	149	8	b	b	X
fumecheng-11486	149	9	)	)	PUNCT
fumecheng-11486	149	10	periodic	periodic	ADJ
fumecheng-11486	149	11	motion	motion	NOUN
fumecheng-11486	149	12	βa=0.15	βa=0.15	PROPN
fumecheng-11486	149	13	;	;	PUNCT
fumecheng-11486	149	14	(	(	PUNCT
fumecheng-11486	149	15	c	c	X
fumecheng-11486	149	16	)	)	PUNCT
fumecheng-11486	149	17	pseudo	pseudo	NOUN
fumecheng-11486	149	18	-	-	ADJ
fumecheng-11486	149	19	periodic	periodic	ADJ
fumecheng-11486	149	20	motion	motion	NOUN
fumecheng-11486	149	21	βa=0.495	βa=0.495	PROPN
fumecheng-11486	149	22	and	and	CCONJ
fumecheng-11486	149	23	(	(	PUNCT
fumecheng-11486	149	24	d	d	NOUN
fumecheng-11486	149	25	)	)	PUNCT
fumecheng-11486	149	26	pull	pull	NOUN
fumecheng-11486	149	27	-	-	PUNCT
fumecheng-11486	149	28	down	down	NOUN
fumecheng-11486	149	29	instability	instability	NOUN
fumecheng-11486	149	30	βa=0.55	βa=0.55	NOUN
fumecheng-11486	149	31	in	in	ADP
fumecheng-11486	149	32	figs	fig	NOUN
fumecheng-11486	149	33	.	.	PUNCT
fumecheng-11486	150	1	2	2	NUM
fumecheng-11486	150	2	-	-	SYM
fumecheng-11486	150	3	4	4	NUM
fumecheng-11486	150	4	,	,	PUNCT
fumecheng-11486	150	5	we	we	PRON
fumecheng-11486	150	6	can	can	AUX
fumecheng-11486	150	7	see	see	VERB
fumecheng-11486	150	8	that	that	SCONJ
fumecheng-11486	150	9	when	when	SCONJ
fumecheng-11486	150	10	βa	βa	PRON
fumecheng-11486	150	11	is	be	AUX
fumecheng-11486	150	12	small	small	ADJ
fumecheng-11486	150	13	,	,	PUNCT
fumecheng-11486	150	14	a	a	DET
fumecheng-11486	150	15	periodic	periodic	ADJ
fumecheng-11486	150	16	motion	motion	NOUN
fumecheng-11486	150	17	is	be	AUX
fumecheng-11486	150	18	predicted	predict	VERB
fumecheng-11486	150	19	.	.	PUNCT
fumecheng-11486	151	1	with	with	ADP
fumecheng-11486	151	2	gradually	gradually	ADV
fumecheng-11486	151	3	increasing	increase	VERB
fumecheng-11486	151	4	βa	βa	NUM
fumecheng-11486	151	5	,	,	PUNCT
fumecheng-11486	151	6	a	a	DET
fumecheng-11486	151	7	pseudo	pseudo	NOUN
fumecheng-11486	151	8	-	-	ADJ
fumecheng-11486	151	9	periodic	periodic	ADJ
fumecheng-11486	151	10	motion	motion	NOUN
fumecheng-11486	151	11	might	might	AUX
fumecheng-11486	151	12	occur	occur	VERB
fumecheng-11486	151	13	.	.	PUNCT
fumecheng-11486	152	1	finally	finally	ADV
fumecheng-11486	152	2	,	,	PUNCT
fumecheng-11486	152	3	when	when	SCONJ
fumecheng-11486	152	4	βa	βa	PRON
fumecheng-11486	152	5	is	be	AUX
fumecheng-11486	152	6	larger	large	ADJ
fumecheng-11486	152	7	than	than	ADP
fumecheng-11486	152	8	0.5	0.5	NUM
fumecheng-11486	152	9	,	,	PUNCT
fumecheng-11486	152	10	the	the	DET
fumecheng-11486	152	11	pull	pull	NOUN
fumecheng-11486	152	12	-	-	PUNCT
fumecheng-11486	152	13	in	in	ADP
fumecheng-11486	152	14	instability	instability	NOUN
fumecheng-11486	152	15	is	be	AUX
fumecheng-11486	152	16	observed	observe	VERB
fumecheng-11486	152	17	.	.	PUNCT
fumecheng-11486	153	1	5	5	X
fumecheng-11486	153	2	.	.	X
fumecheng-11486	153	3	conclusion	conclusion	NOUN
fumecheng-11486	153	4	this	this	DET
fumecheng-11486	153	5	paper	paper	NOUN
fumecheng-11486	153	6	proposes	propose	VERB
fumecheng-11486	153	7	an	an	DET
fumecheng-11486	153	8	extremely	extremely	ADV
fumecheng-11486	153	9	important	important	ADJ
fumecheng-11486	153	10	concept	concept	NOUN
fumecheng-11486	153	11	of	of	ADP
fumecheng-11486	153	12	the	the	DET
fumecheng-11486	153	13	pull	pull	NOUN
fumecheng-11486	153	14	-	-	PUNCT
fumecheng-11486	153	15	down	down	ADP
fumecheng-11486	153	16	breakout	breakout	NOUN
fumecheng-11486	153	17	for	for	ADP
fumecheng-11486	153	18	nonlinear	nonlinear	ADJ
fumecheng-11486	153	19	oscillators	oscillator	NOUN
fumecheng-11486	153	20	with	with	ADP
fumecheng-11486	153	21	even	even	ADJ
fumecheng-11486	153	22	nonlinearities	nonlinearitie	NOUN
fumecheng-11486	153	23	,	,	PUNCT
fumecheng-11486	153	24	and	and	CCONJ
fumecheng-11486	153	25	it	it	PRON
fumecheng-11486	153	26	will	will	AUX
fumecheng-11486	153	27	become	become	VERB
fumecheng-11486	153	28	a	a	DET
fumecheng-11486	153	29	powerful	powerful	ADJ
fumecheng-11486	153	30	research	research	NOUN
fumecheng-11486	153	31	tool	tool	NOUN
fumecheng-11486	153	32	in	in	ADP
fumecheng-11486	153	33	nonlinear	nonlinear	ADJ
fumecheng-11486	153	34	vibration	vibration	NOUN
fumecheng-11486	153	35	theory	theory	NOUN
fumecheng-11486	153	36	.	.	PUNCT
fumecheng-11486	154	1	a	a	DET
fumecheng-11486	154	2	sophisticated	sophisticated	ADJ
fumecheng-11486	154	3	modification	modification	NOUN
fumecheng-11486	154	4	of	of	ADP
fumecheng-11486	154	5	the	the	DET
fumecheng-11486	154	6	frequency	frequency	NOUN
fumecheng-11486	154	7	formulation	formulation	NOUN
fumecheng-11486	154	8	is	be	AUX
fumecheng-11486	154	9	suggested	suggest	VERB
fumecheng-11486	154	10	,	,	PUNCT
fumecheng-11486	154	11	and	and	CCONJ
fumecheng-11486	154	12	a	a	DET
fumecheng-11486	154	13	criterion	criterion	NOUN
fumecheng-11486	154	14	is	be	AUX
fumecheng-11486	154	15	built	build	VERB
fumecheng-11486	154	16	for	for	ADP
fumecheng-11486	154	17	judging	judge	VERB
fumecheng-11486	154	18	the	the	DET
fumecheng-11486	154	19	pull	pull	VERB
fumecheng-11486	154	20	-	-	PUNCT
fumecheng-11486	154	21	down	down	ADP
fumecheng-11486	154	22	instability	instability	NOUN
fumecheng-11486	154	23	,	,	PUNCT
fumecheng-11486	154	24	the	the	DET
fumecheng-11486	154	25	unsymmetrical	unsymmetrical	ADJ
fumecheng-11486	154	26	amplitude	amplitude	NOUN
fumecheng-11486	154	27	motion	motion	NOUN
fumecheng-11486	154	28	,	,	PUNCT
fumecheng-11486	154	29	and	and	CCONJ
fumecheng-11486	154	30	the	the	DET
fumecheng-11486	154	31	pseudo	pseudo	NOUN
fumecheng-11486	154	32	-	-	ADJ
fumecheng-11486	154	33	periodic	periodic	ADJ
fumecheng-11486	154	34	motion	motion	NOUN
fumecheng-11486	154	35	.	.	PUNCT
fumecheng-11486	155	1	the	the	DET
fumecheng-11486	155	2	amplitude	amplitude	NOUN
fumecheng-11486	155	3	increment	increment	NOUN
fumecheng-11486	155	4	,	,	PUNCT
fumecheng-11486	155	5	δa	δa	PROPN
fumecheng-11486	155	6	,	,	PUNCT
fumecheng-11486	155	7	in	in	ADP
fumecheng-11486	155	8	eq	eq	ADP
fumecheng-11486	155	9	.	.	PUNCT
fumecheng-11486	155	10	(	(	PUNCT
fumecheng-11486	155	11	17	17	NUM
fumecheng-11486	155	12	)	)	PUNCT
fumecheng-11486	155	13	will	will	AUX
fumecheng-11486	155	14	be	be	AUX
fumecheng-11486	155	15	discussed	discuss	VERB
fumecheng-11486	155	16	in	in	ADP
fumecheng-11486	155	17	a	a	DET
fumecheng-11486	155	18	forthcoming	forthcoming	ADJ
fumecheng-11486	155	19	paper	paper	NOUN
fumecheng-11486	155	20	,	,	PUNCT
fumecheng-11486	155	21	and	and	CCONJ
fumecheng-11486	155	22	when	when	SCONJ
fumecheng-11486	155	23	the	the	DET
fumecheng-11486	155	24	absolute	absolute	ADJ
fumecheng-11486	155	25	value	value	NOUN
fumecheng-11486	155	26	of	of	ADP
fumecheng-11486	155	27	δa	δa	NOUN
fumecheng-11486	155	28	is	be	AUX
fumecheng-11486	155	29	larger	large	ADJ
fumecheng-11486	155	30	than	than	ADP
fumecheng-11486	155	31	a	a	PRON
fumecheng-11486	155	32	,	,	PUNCT
fumecheng-11486	155	33	the	the	DET
fumecheng-11486	155	34	pull	pull	NOUN
fumecheng-11486	155	35	-	-	PUNCT
fumecheng-11486	155	36	down	down	ADP
fumecheng-11486	155	37	instability	instability	NOUN
fumecheng-11486	155	38	occurs	occur	VERB
fumecheng-11486	155	39	abruptly	abruptly	ADV
fumecheng-11486	155	40	.	.	PUNCT
fumecheng-11486	156	1	hence	hence	ADV
fumecheng-11486	156	2	,	,	PUNCT
fumecheng-11486	156	3	the	the	DET
fumecheng-11486	156	4	amplitude	amplitude	NOUN
fumecheng-11486	156	5	change	change	NOUN
fumecheng-11486	156	6	is	be	AUX
fumecheng-11486	156	7	the	the	DET
fumecheng-11486	156	8	best	good	ADJ
fumecheng-11486	156	9	parameter	parameter	NOUN
fumecheng-11486	156	10	to	to	PART
fumecheng-11486	156	11	predict	predict	VERB
fumecheng-11486	156	12	the	the	DET
fumecheng-11486	156	13	pseudo	pseudo	NOUN
fumecheng-11486	156	14	-	-	ADJ
fumecheng-11486	156	15	periodic	periodic	ADJ
fumecheng-11486	156	16	motion	motion	NOUN
fumecheng-11486	156	17	and	and	CCONJ
fumecheng-11486	156	18	the	the	DET
fumecheng-11486	156	19	time	time	NOUN
fumecheng-11486	156	20	when	when	SCONJ
fumecheng-11486	156	21	the	the	DET
fumecheng-11486	156	22	pull	pull	NOUN
fumecheng-11486	156	23	-	-	PUNCT
fumecheng-11486	156	24	down	down	ADP
fumecheng-11486	156	25	instability	instability	NOUN
fumecheng-11486	156	26	occurs	occur	VERB
fumecheng-11486	156	27	.	.	PUNCT
fumecheng-11486	157	1	pull	pull	VERB
fumecheng-11486	157	2	-	-	PUNCT
fumecheng-11486	157	3	down	down	ADP
fumecheng-11486	157	4	instability	instability	NOUN
fumecheng-11486	157	5	of	of	ADP
fumecheng-11486	157	6	the	the	DET
fumecheng-11486	157	7	quadratic	quadratic	ADJ
fumecheng-11486	157	8	nonlinear	nonlinear	ADJ
fumecheng-11486	157	9	oscillators	oscillator	NOUN
fumecheng-11486	157	10	199	199	NUM
fumecheng-11486	157	11	(	(	PUNCT
fumecheng-11486	157	12	a	a	NOUN
fumecheng-11486	157	13	)	)	PUNCT
fumecheng-11486	157	14	(	(	PUNCT
fumecheng-11486	157	15	b	b	X
fumecheng-11486	157	16	)	)	PUNCT
fumecheng-11486	157	17	(	(	PUNCT
fumecheng-11486	157	18	c	c	X
fumecheng-11486	157	19	)	)	PUNCT
fumecheng-11486	157	20	(	(	PUNCT
fumecheng-11486	157	21	d	d	X
fumecheng-11486	157	22	)	)	PUNCT
fumecheng-11486	157	23	fig	fig	NOUN
fumecheng-11486	157	24	.	.	PUNCT
fumecheng-11486	158	1	4	4	NUM
fumecheng-11486	158	2	the	the	DET
fumecheng-11486	158	3	criterion	criterion	NOUN
fumecheng-11486	158	4	of	of	ADP
fumecheng-11486	158	5	the	the	DET
fumecheng-11486	158	6	pull	pull	NOUN
fumecheng-11486	158	7	-	-	PUNCT
fumecheng-11486	158	8	down	down	ADP
fumecheng-11486	158	9	instability	instability	NOUN
fumecheng-11486	158	10	when	when	SCONJ
fumecheng-11486	158	11	a=0.7	a=0.7	ADV
fumecheng-11486	158	12	:	:	PUNCT
fumecheng-11486	158	13	(	(	PUNCT
fumecheng-11486	158	14	a	a	X
fumecheng-11486	158	15	)	)	PUNCT
fumecheng-11486	158	16	phase	phase	NOUN
fumecheng-11486	158	17	diagram	diagram	NOUN
fumecheng-11486	158	18	;	;	PUNCT
fumecheng-11486	158	19	(	(	PUNCT
fumecheng-11486	158	20	b	b	X
fumecheng-11486	158	21	)	)	PUNCT
fumecheng-11486	158	22	periodic	periodic	ADJ
fumecheng-11486	158	23	motion	motion	NOUN
fumecheng-11486	158	24	βa=0.21	βa=0.21	NOUN
fumecheng-11486	158	25	;	;	PUNCT
fumecheng-11486	158	26	(	(	PUNCT
fumecheng-11486	158	27	c	c	X
fumecheng-11486	158	28	)	)	PUNCT
fumecheng-11486	158	29	pseudo	pseudo	NOUN
fumecheng-11486	158	30	-	-	ADJ
fumecheng-11486	158	31	periodic	periodic	ADJ
fumecheng-11486	158	32	motion	motion	NOUN
fumecheng-11486	158	33	βa=0.49	βa=0.49	NOUN
fumecheng-11486	158	34	and	and	CCONJ
fumecheng-11486	158	35	(	(	PUNCT
fumecheng-11486	158	36	d	d	NOUN
fumecheng-11486	158	37	)	)	PUNCT
fumecheng-11486	158	38	pull	pull	NOUN
fumecheng-11486	158	39	-	-	PUNCT
fumecheng-11486	158	40	down	down	ADP
fumecheng-11486	158	41	instability	instability	NOUN
fumecheng-11486	158	42	βa=0.56	βa=0.56	ADJ
fumecheng-11486	158	43	references	reference	NOUN
fumecheng-11486	158	44	1	1	NUM
fumecheng-11486	158	45	.	.	PUNCT
fumecheng-11486	158	46	beléndez	beléndez	PROPN
fumecheng-11486	158	47	,	,	PUNCT
fumecheng-11486	158	48	a.	a.	NOUN
fumecheng-11486	158	49	,	,	PUNCT
fumecheng-11486	158	50	pascual	pascual	NOUN
fumecheng-11486	158	51	,	,	PUNCT
fumecheng-11486	158	52	c.	c.	NOUN
fumecheng-11486	158	53	,	,	PUNCT
fumecheng-11486	158	54	beléndez	beléndez	NOUN
fumecheng-11486	158	55	,	,	PUNCT
fumecheng-11486	158	56	t.	t.	PROPN
fumecheng-11486	158	57	,	,	PUNCT
fumecheng-11486	158	58	hernández	hernández	PROPN
fumecheng-11486	158	59	,	,	PUNCT
fumecheng-11486	158	60	a.	a.	NOUN
fumecheng-11486	158	61	,	,	PUNCT
fumecheng-11486	158	62	2009	2009	NUM
fumecheng-11486	158	63	,	,	PUNCT
fumecheng-11486	158	64	solution	solution	NOUN
fumecheng-11486	158	65	for	for	ADP
fumecheng-11486	158	66	an	an	DET
fumecheng-11486	158	67	anti	anti	ADJ
fumecheng-11486	158	68	-	-	ADJ
fumecheng-11486	158	69	symmetric	symmetric	ADJ
fumecheng-11486	158	70	quadratic	quadratic	ADJ
fumecheng-11486	158	71	nonlinear	nonlinear	ADJ
fumecheng-11486	158	72	oscillator	oscillator	NOUN
fumecheng-11486	158	73	by	by	ADP
fumecheng-11486	158	74	a	a	DET
fumecheng-11486	158	75	modified	modify	VERB
fumecheng-11486	158	76	he	he	PRON
fumecheng-11486	158	77	’s	’s	NOUN
fumecheng-11486	158	78	homotopy	homotopy	PROPN
fumecheng-11486	158	79	perturbation	perturbation	NOUN
fumecheng-11486	158	80	method	method	NOUN
fumecheng-11486	158	81	,	,	PUNCT
fumecheng-11486	158	82	nonlinear	nonlinear	ADJ
fumecheng-11486	158	83	analysis	analysis	NOUN
fumecheng-11486	158	84	:	:	PUNCT
fumecheng-11486	158	85	real	real	ADJ
fumecheng-11486	158	86	world	world	NOUN
fumecheng-11486	158	87	applications	application	NOUN
fumecheng-11486	158	88	,	,	PUNCT
fumecheng-11486	158	89	10(1	10(1	NUM
fumecheng-11486	158	90	)	)	PUNCT
fumecheng-11486	158	91	,	,	PUNCT
fumecheng-11486	158	92	pp	pp	PROPN
fumecheng-11486	158	93	.	.	PUNCT
fumecheng-11486	159	1	416	416	NUM
fumecheng-11486	159	2	-	-	SYM
fumecheng-11486	159	3	427	427	NUM
fumecheng-11486	159	4	.	.	NOUN
fumecheng-11486	160	1	2	2	NUM
fumecheng-11486	160	2	.	.	X
fumecheng-11486	160	3	yeasmin	yeasmin	PROPN
fumecheng-11486	160	4	,	,	PUNCT
fumecheng-11486	160	5	i.a	i.a	PROPN
fumecheng-11486	160	6	.	.	PROPN
fumecheng-11486	160	7	,	,	PUNCT
fumecheng-11486	160	8	rahman	rahman	PROPN
fumecheng-11486	160	9	,	,	PUNCT
fumecheng-11486	160	10	m.	m.	NOUN
fumecheng-11486	160	11	,	,	PUNCT
fumecheng-11486	160	12	alam	alam	PROPN
fumecheng-11486	160	13	,	,	PUNCT
fumecheng-11486	160	14	m.	m.	NOUN
fumecheng-11486	160	15	,	,	PUNCT
fumecheng-11486	160	16	2021	2021	NUM
fumecheng-11486	160	17	,	,	PUNCT
fumecheng-11486	160	18	the	the	DET
fumecheng-11486	160	19	modified	modify	VERB
fumecheng-11486	160	20	lindstedt	lindstedt	PROPN
fumecheng-11486	160	21	–	–	PUNCT
fumecheng-11486	160	22	poincare	poincare	PROPN
fumecheng-11486	160	23	method	method	NOUN
fumecheng-11486	160	24	for	for	ADP
fumecheng-11486	160	25	solving	solve	VERB
fumecheng-11486	160	26	quadratic	quadratic	ADJ
fumecheng-11486	160	27	nonlinear	nonlinear	ADJ
fumecheng-11486	160	28	oscillators	oscillator	NOUN
fumecheng-11486	160	29	,	,	PUNCT
fumecheng-11486	160	30	journal	journal	NOUN
fumecheng-11486	160	31	of	of	ADP
fumecheng-11486	160	32	low	low	ADJ
fumecheng-11486	160	33	frequency	frequency	NOUN
fumecheng-11486	160	34	noise	noise	NOUN
fumecheng-11486	160	35	,	,	PUNCT
fumecheng-11486	160	36	vibration	vibration	NOUN
fumecheng-11486	160	37	and	and	CCONJ
fumecheng-11486	160	38	active	active	ADJ
fumecheng-11486	160	39	control	control	NOUN
fumecheng-11486	160	40	,	,	PUNCT
fumecheng-11486	160	41	40(3	40(3	NUM
fumecheng-11486	160	42	)	)	PUNCT
fumecheng-11486	160	43	,	,	PUNCT
fumecheng-11486	160	44	pp	pp	ADJ
fumecheng-11486	160	45	.	.	PUNCT
fumecheng-11486	161	1	1351	1351	NUM
fumecheng-11486	161	2	-	-	SYM
fumecheng-11486	161	3	1368	1368	NUM
fumecheng-11486	161	4	.	.	PUNCT
fumecheng-11486	162	1	3	3	X
fumecheng-11486	162	2	.	.	X
fumecheng-11486	162	3	yeasmin	yeasmin	PROPN
fumecheng-11486	162	4	,	,	PUNCT
fumecheng-11486	162	5	i.a	i.a	PROPN
fumecheng-11486	162	6	.	.	PROPN
fumecheng-11486	162	7	,	,	PUNCT
fumecheng-11486	162	8	sharif	sharif	PROPN
fumecheng-11486	162	9	,	,	PUNCT
fumecheng-11486	162	10	n.	n.	PROPN
fumecheng-11486	162	11	,	,	PUNCT
fumecheng-11486	162	12	rahman	rahman	PROPN
fumecheng-11486	162	13	,	,	PUNCT
fumecheng-11486	162	14	m.s	m.s	PROPN
fumecheng-11486	162	15	.	.	PROPN
fumecheng-11486	162	16	,	,	PUNCT
fumecheng-11486	162	17	alam	alam	PROPN
fumecheng-11486	162	18	,	,	PUNCT
fumecheng-11486	162	19	m.s	m.s	PROPN
fumecheng-11486	162	20	.	.	PROPN
fumecheng-11486	162	21	,	,	PUNCT
fumecheng-11486	162	22	2022	2022	NUM
fumecheng-11486	162	23	,	,	PUNCT
fumecheng-11486	162	24	analytical	analytical	ADJ
fumecheng-11486	162	25	technique	technique	NOUN
fumecheng-11486	162	26	for	for	ADP
fumecheng-11486	162	27	solving	solve	VERB
fumecheng-11486	162	28	the	the	DET
fumecheng-11486	162	29	quadratic	quadratic	ADJ
fumecheng-11486	162	30	nonlinear	nonlinear	ADJ
fumecheng-11486	162	31	oscillator	oscillator	NOUN
fumecheng-11486	162	32	,	,	PUNCT
fumecheng-11486	162	33	results	result	NOUN
fumecheng-11486	162	34	in	in	ADP
fumecheng-11486	162	35	physics	physics	NOUN
fumecheng-11486	162	36	,	,	PUNCT
fumecheng-11486	162	37	18(2020	18(2020	NUM
fumecheng-11486	162	38	)	)	PUNCT
fumecheng-11486	162	39	,	,	PUNCT
fumecheng-11486	162	40	103303	103303	NUM
fumecheng-11486	162	41	.	.	PUNCT
fumecheng-11486	163	1	4	4	NUM
fumecheng-11486	163	2	.	.	X
fumecheng-11486	164	1	zhu	zhu	PROPN
fumecheng-11486	164	2	,	,	PUNCT
fumecheng-11486	164	3	j.w	j.w	PROPN
fumecheng-11486	164	4	.	.	PROPN
fumecheng-11486	164	5	,	,	PUNCT
fumecheng-11486	164	6	2014	2014	NUM
fumecheng-11486	164	7	,	,	PUNCT
fumecheng-11486	164	8	a	a	DET
fumecheng-11486	164	9	new	new	ADJ
fumecheng-11486	164	10	exact	exact	ADJ
fumecheng-11486	164	11	solution	solution	NOUN
fumecheng-11486	164	12	of	of	ADP
fumecheng-11486	164	13	a	a	DET
fumecheng-11486	164	14	damped	damped	ADJ
fumecheng-11486	164	15	quadratic	quadratic	ADJ
fumecheng-11486	164	16	non	non	ADJ
fumecheng-11486	164	17	-	-	ADJ
fumecheng-11486	164	18	linear	linear	ADJ
fumecheng-11486	164	19	oscillator	oscillator	NOUN
fumecheng-11486	164	20	,	,	PUNCT
fumecheng-11486	164	21	applied	apply	VERB
fumecheng-11486	164	22	mathematical	mathematical	ADJ
fumecheng-11486	164	23	modelling	modelling	NOUN
fumecheng-11486	164	24	,	,	PUNCT
fumecheng-11486	164	25	38(24	38(24	NUM
fumecheng-11486	164	26	)	)	PUNCT
fumecheng-11486	164	27	,	,	PUNCT
fumecheng-11486	164	28	pp	pp	ADJ
fumecheng-11486	164	29	.	.	PUNCT
fumecheng-11486	165	1	5986	5986	NUM
fumecheng-11486	165	2	-	-	SYM
fumecheng-11486	165	3	5993	5993	NUM
fumecheng-11486	165	4	.	.	PUNCT
fumecheng-11486	166	1	5	5	NUM
fumecheng-11486	166	2	.	.	X
fumecheng-11486	166	3	scott	scott	PROPN
fumecheng-11486	166	4	,	,	PUNCT
fumecheng-11486	166	5	a.p	a.p	PROPN
fumecheng-11486	166	6	.	.	PROPN
fumecheng-11486	166	7	,	,	PUNCT
fumecheng-11486	166	8	radom	radom	NOUN
fumecheng-11486	166	9	,	,	PUNCT
fumecheng-11486	166	10	l.	l.	PROPN
fumecheng-11486	166	11	,	,	PUNCT
fumecheng-11486	166	12	1996	1996	NUM
fumecheng-11486	166	13	,	,	PUNCT
fumecheng-11486	166	14	harmonic	harmonic	ADJ
fumecheng-11486	166	15	vibrational	vibrational	ADJ
fumecheng-11486	166	16	frequencies	frequency	NOUN
fumecheng-11486	166	17	:	:	PUNCT
fumecheng-11486	166	18	an	an	DET
fumecheng-11486	166	19	evaluation	evaluation	NOUN
fumecheng-11486	166	20	of	of	ADP
fumecheng-11486	166	21	hartree	hartree	ADJ
fumecheng-11486	166	22	-	-	PUNCT
fumecheng-11486	166	23	fock	fock	ADJ
fumecheng-11486	166	24	,	,	PUNCT
fumecheng-11486	166	25	moller	moller	NOUN
fumecheng-11486	166	26	-	-	PUNCT
fumecheng-11486	166	27	plesset	plesset	VERB
fumecheng-11486	166	28	,	,	PUNCT
fumecheng-11486	166	29	quadratic	quadratic	ADJ
fumecheng-11486	166	30	configuration	configuration	NOUN
fumecheng-11486	166	31	interaction	interaction	NOUN
fumecheng-11486	166	32	,	,	PUNCT
fumecheng-11486	166	33	density	density	NOUN
fumecheng-11486	166	34	functional	functional	ADJ
fumecheng-11486	166	35	theory	theory	NOUN
fumecheng-11486	166	36	,	,	PUNCT
fumecheng-11486	166	37	and	and	CCONJ
fumecheng-11486	166	38	semiempirical	semiempirical	ADJ
fumecheng-11486	166	39	scale	scale	NOUN
fumecheng-11486	166	40	factors	factor	NOUN
fumecheng-11486	166	41	,	,	PUNCT
fumecheng-11486	166	42	journal	journal	NOUN
fumecheng-11486	166	43	of	of	ADP
fumecheng-11486	166	44	physical	physical	ADJ
fumecheng-11486	166	45	chemistry	chemistry	NOUN
fumecheng-11486	166	46	,	,	PUNCT
fumecheng-11486	166	47	100(41	100(41	NUM
fumecheng-11486	166	48	)	)	PUNCT
fumecheng-11486	166	49	,	,	PUNCT
fumecheng-11486	166	50	pp	pp	PROPN
fumecheng-11486	166	51	.	.	PUNCT
fumecheng-11486	167	1	16502	16502	NUM
fumecheng-11486	167	2	-	-	SYM
fumecheng-11486	167	3	16513	16513	NUM
fumecheng-11486	167	4	.	.	PUNCT
fumecheng-11486	168	1	6	6	NUM
fumecheng-11486	168	2	.	.	X
fumecheng-11486	168	3	yang	yang	PROPN
fumecheng-11486	168	4	,	,	PUNCT
fumecheng-11486	168	5	q.	q.	PROPN
fumecheng-11486	168	6	,	,	PUNCT
fumecheng-11486	168	7	2023	2023	NUM
fumecheng-11486	168	8	,	,	PUNCT
fumecheng-11486	168	9	a	a	DET
fumecheng-11486	168	10	mathematical	mathematical	ADJ
fumecheng-11486	168	11	control	control	NOUN
fumecheng-11486	168	12	for	for	ADP
fumecheng-11486	168	13	the	the	DET
fumecheng-11486	168	14	pseudo	pseudo	NOUN
fumecheng-11486	168	15	-	-	ADJ
fumecheng-11486	168	16	pull	pull	NOUN
fumecheng-11486	168	17	-	-	PUNCT
fumecheng-11486	168	18	in	in	ADP
fumecheng-11486	168	19	stability	stability	NOUN
fumecheng-11486	168	20	arising	arise	VERB
fumecheng-11486	168	21	in	in	ADP
fumecheng-11486	168	22	a	a	DET
fumecheng-11486	168	23	micro	micro	ADJ
fumecheng-11486	168	24	-	-	ADJ
fumecheng-11486	168	25	electromechanical	electromechanical	ADJ
fumecheng-11486	168	26	system	system	NOUN
fumecheng-11486	168	27	,	,	PUNCT
fumecheng-11486	168	28	journal	journal	NOUN
fumecheng-11486	168	29	of	of	ADP
fumecheng-11486	168	30	low	low	ADJ
fumecheng-11486	168	31	frequency	frequency	NOUN
fumecheng-11486	168	32	noise	noise	NOUN
fumecheng-11486	168	33	,	,	PUNCT
fumecheng-11486	168	34	vibration	vibration	NOUN
fumecheng-11486	168	35	and	and	CCONJ
fumecheng-11486	168	36	active	active	ADJ
fumecheng-11486	168	37	control	control	NOUN
fumecheng-11486	168	38	,	,	PUNCT
fumecheng-11486	168	39	doi	doi	NOUN
fumecheng-11486	168	40	:	:	PUNCT
fumecheng-11486	168	41	10.1177/14613484221133603	10.1177/14613484221133603	NUM
fumecheng-11486	168	42	7	7	NUM
fumecheng-11486	168	43	.	.	PUNCT
fumecheng-11486	169	1	he	he	PRON
fumecheng-11486	169	2	,	,	PUNCT
fumecheng-11486	169	3	j.h	j.h	PROPN
fumecheng-11486	169	4	.	.	PROPN
fumecheng-11486	169	5	,	,	PUNCT
fumecheng-11486	169	6	yang	yang	PROPN
fumecheng-11486	169	7	,	,	PUNCT
fumecheng-11486	169	8	q.	q.	PROPN
fumecheng-11486	169	9	,	,	PUNCT
fumecheng-11486	169	10	he	he	PRON
fumecheng-11486	169	11	,	,	PUNCT
fumecheng-11486	169	12	c.h	c.h	PROPN
fumecheng-11486	169	13	.	.	PROPN
fumecheng-11486	169	14	,	,	PUNCT
fumecheng-11486	169	15	li	li	PROPN
fumecheng-11486	169	16	,	,	PUNCT
fumecheng-11486	169	17	h.b	h.b	PROPN
fumecheng-11486	169	18	.	.	PROPN
fumecheng-11486	169	19	,	,	PUNCT
fumecheng-11486	169	20	buhe	buhe	PROPN
fumecheng-11486	169	21	,	,	PUNCT
fumecheng-11486	169	22	e.	e.	PROPN
fumecheng-11486	169	23	,	,	PUNCT
fumecheng-11486	169	24	2022	2022	NUM
fumecheng-11486	169	25	,	,	PUNCT
fumecheng-11486	169	26	pull	pull	NOUN
fumecheng-11486	169	27	-	-	PUNCT
fumecheng-11486	169	28	in	in	ADP
fumecheng-11486	169	29	stability	stability	NOUN
fumecheng-11486	169	30	of	of	ADP
fumecheng-11486	169	31	a	a	DET
fumecheng-11486	169	32	fractal	fractal	ADJ
fumecheng-11486	169	33	system	system	NOUN
fumecheng-11486	169	34	and	and	CCONJ
fumecheng-11486	169	35	its	its	PRON
fumecheng-11486	169	36	pull	pull	VERB
fumecheng-11486	169	37	-	-	PUNCT
fumecheng-11486	169	38	in	in	ADP
fumecheng-11486	169	39	plateau	plateau	NOUN
fumecheng-11486	169	40	,	,	PUNCT
fumecheng-11486	169	41	fractals	fractal	NOUN
fumecheng-11486	169	42	,	,	PUNCT
fumecheng-11486	169	43	30(9	30(9	NOUN
fumecheng-11486	169	44	)	)	PUNCT
fumecheng-11486	169	45	,	,	PUNCT
fumecheng-11486	169	46	2250185	2250185	NUM
fumecheng-11486	169	47	.	.	PUNCT
fumecheng-11486	170	1	200	200	NUM
fumecheng-11486	170	2	j.h	j.h	PROPN
fumecheng-11486	170	3	.	.	PUNCT
fumecheng-11486	171	1	he	he	PRON
fumecheng-11486	171	2	,	,	PUNCT
fumecheng-11486	171	3	q.	q.	PROPN
fumecheng-11486	171	4	yang	yang	PROPN
fumecheng-11486	171	5	,	,	PUNCT
fumecheng-11486	171	6	c.h	c.h	PROPN
fumecheng-11486	171	7	.	.	PUNCT
fumecheng-11486	172	1	he	he	PRON
fumecheng-11486	172	2	,	,	PUNCT
fumecheng-11486	172	3	a.a	a.a	PROPN
fumecheng-11486	172	4	.	.	PROPN
fumecheng-11486	172	5	alsolami	alsolami	PROPN
fumecheng-11486	172	6	8	8	NUM
fumecheng-11486	172	7	.	.	PUNCT
fumecheng-11486	172	8	luo	luo	PROPN
fumecheng-11486	172	9	,	,	PUNCT
fumecheng-11486	172	10	a.c.j	a.c.j	NOUN
fumecheng-11486	172	11	.	.	PROPN
fumecheng-11486	172	12	,	,	PUNCT
fumecheng-11486	172	13	yu	yu	PROPN
fumecheng-11486	172	14	,	,	PUNCT
fumecheng-11486	172	15	b.	b.	PROPN
fumecheng-11486	172	16	,	,	PUNCT
fumecheng-11486	172	17	2014	2014	NUM
fumecheng-11486	172	18	,	,	PUNCT
fumecheng-11486	172	19	bifurcation	bifurcation	NOUN
fumecheng-11486	172	20	trees	tree	NOUN
fumecheng-11486	172	21	of	of	ADP
fumecheng-11486	172	22	periodic	periodic	ADJ
fumecheng-11486	172	23	motions	motion	NOUN
fumecheng-11486	172	24	to	to	PART
fumecheng-11486	172	25	chaos	chaos	VERB
fumecheng-11486	172	26	in	in	ADP
fumecheng-11486	172	27	a	a	DET
fumecheng-11486	172	28	parametric	parametric	ADJ
fumecheng-11486	172	29	,	,	PUNCT
fumecheng-11486	172	30	quadratic	quadratic	ADJ
fumecheng-11486	172	31	nonlinear	nonlinear	ADJ
fumecheng-11486	172	32	oscillator	oscillator	NOUN
fumecheng-11486	172	33	,	,	PUNCT
fumecheng-11486	172	34	international	international	ADJ
fumecheng-11486	172	35	journal	journal	NOUN
fumecheng-11486	172	36	of	of	ADP
fumecheng-11486	172	37	dynamics	dynamic	NOUN
fumecheng-11486	172	38	and	and	CCONJ
fumecheng-11486	172	39	control	control	NOUN
fumecheng-11486	172	40	,	,	PUNCT
fumecheng-11486	172	41	24(5	24(5	NUM
fumecheng-11486	172	42	)	)	PUNCT
fumecheng-11486	172	43	,	,	PUNCT
fumecheng-11486	172	44	1450075	1450075	NUM
fumecheng-11486	172	45	.	.	PUNCT
fumecheng-11486	173	1	9	9	X
fumecheng-11486	173	2	.	.	X
fumecheng-11486	173	3	elias	elias	PROPN
fumecheng-11486	173	4	-	-	PUNCT
fumecheng-11486	173	5	zuniga	zuniga	PROPN
fumecheng-11486	173	6	,	,	PUNCT
fumecheng-11486	173	7	a.	a.	NOUN
fumecheng-11486	173	8	,	,	PUNCT
fumecheng-11486	173	9	palacios	palacio	NOUN
fumecheng-11486	173	10	-	-	PUNCT
fumecheng-11486	173	11	pineda	pineda	PROPN
fumecheng-11486	173	12	,	,	PUNCT
fumecheng-11486	173	13	l.m	l.m	PROPN
fumecheng-11486	173	14	.	.	PROPN
fumecheng-11486	173	15	,	,	PUNCT
fumecheng-11486	173	16	jimenez	jimenez	PROPN
fumecheng-11486	173	17	-	-	PUNCT
fumecheng-11486	173	18	cedeno	cedeno	PROPN
fumecheng-11486	173	19	,	,	PUNCT
fumecheng-11486	173	20	i.h	i.h	PROPN
fumecheng-11486	173	21	.	.	PROPN
fumecheng-11486	173	22	,	,	PUNCT
fumecheng-11486	173	23	et	et	PROPN
fumecheng-11486	173	24	al	al	PROPN
fumecheng-11486	173	25	.	.	PROPN
fumecheng-11486	173	26	,	,	PUNCT
fumecheng-11486	173	27	2021	2021	NUM
fumecheng-11486	173	28	,	,	PUNCT
fumecheng-11486	173	29	equivalent	equivalent	ADJ
fumecheng-11486	173	30	power	power	NOUN
fumecheng-11486	173	31	-	-	PUNCT
fumecheng-11486	173	32	form	form	NOUN
fumecheng-11486	173	33	representation	representation	NOUN
fumecheng-11486	173	34	of	of	ADP
fumecheng-11486	173	35	the	the	DET
fumecheng-11486	173	36	fractal	fractal	ADJ
fumecheng-11486	173	37	toda	toda	PROPN
fumecheng-11486	173	38	oscillator	oscillator	PROPN
fumecheng-11486	173	39	,	,	PUNCT
fumecheng-11486	173	40	fractals	fractal	NOUN
fumecheng-11486	173	41	,	,	PUNCT
fumecheng-11486	173	42	29(2	29(2	NUM
fumecheng-11486	173	43	)	)	PUNCT
fumecheng-11486	173	44	,	,	PUNCT
fumecheng-11486	173	45	2150034	2150034	NUM
fumecheng-11486	173	46	.	.	PUNCT
fumecheng-11486	174	1	10	10	NUM
fumecheng-11486	174	2	.	.	PUNCT
fumecheng-11486	174	3	kurz	kurz	PROPN
fumecheng-11486	174	4	,	,	PUNCT
fumecheng-11486	174	5	t.	t.	PROPN
fumecheng-11486	174	6	,	,	PUNCT
fumecheng-11486	174	7	lauterborn	lauterborn	VERB
fumecheng-11486	174	8	,	,	PUNCT
fumecheng-11486	174	9	w.	w.	NOUN
fumecheng-11486	174	10	,	,	PUNCT
fumecheng-11486	174	11	1988	1988	NUM
fumecheng-11486	174	12	,	,	PUNCT
fumecheng-11486	174	13	bifurcation	bifurcation	NOUN
fumecheng-11486	174	14	structure	structure	NOUN
fumecheng-11486	174	15	of	of	ADP
fumecheng-11486	174	16	the	the	DET
fumecheng-11486	174	17	toda	toda	PROPN
fumecheng-11486	174	18	oscillator	oscillator	PROPN
fumecheng-11486	174	19	,	,	PUNCT
fumecheng-11486	174	20	physical	physical	ADJ
fumecheng-11486	174	21	review	review	NOUN
fumecheng-11486	174	22	a	a	DET
fumecheng-11486	174	23	,	,	PUNCT
fumecheng-11486	174	24	37(3	37(3	NUM
fumecheng-11486	174	25	)	)	PUNCT
fumecheng-11486	174	26	,	,	PUNCT
fumecheng-11486	174	27	pp	pp	ADP
fumecheng-11486	174	28	.	.	PUNCT
fumecheng-11486	175	1	1029	1029	NUM
fumecheng-11486	175	2	-	-	SYM
fumecheng-11486	175	3	1031	1031	NUM
fumecheng-11486	175	4	.	.	PUNCT
fumecheng-11486	176	1	11	11	NUM
fumecheng-11486	176	2	.	.	PUNCT
fumecheng-11486	177	1	feng	feng	PROPN
fumecheng-11486	177	2	,	,	PUNCT
fumecheng-11486	177	3	g.q	g.q	PROPN
fumecheng-11486	177	4	.	.	PROPN
fumecheng-11486	177	5	,	,	PUNCT
fumecheng-11486	177	6	niu	niu	PROPN
fumecheng-11486	177	7	,	,	PUNCT
fumecheng-11486	177	8	j.y	j.y	PROPN
fumecheng-11486	177	9	.	.	PROPN
fumecheng-11486	177	10	,	,	PUNCT
fumecheng-11486	177	11	2023	2023	NUM
fumecheng-11486	177	12	,	,	PUNCT
fumecheng-11486	177	13	an	an	DET
fumecheng-11486	177	14	analytical	analytical	ADJ
fumecheng-11486	177	15	solution	solution	NOUN
fumecheng-11486	177	16	of	of	ADP
fumecheng-11486	177	17	the	the	DET
fumecheng-11486	177	18	fractal	fractal	ADJ
fumecheng-11486	177	19	toda	toda	PROPN
fumecheng-11486	177	20	oscillator	oscillator	PROPN
fumecheng-11486	177	21	,	,	PUNCT
fumecheng-11486	177	22	results	result	NOUN
fumecheng-11486	177	23	in	in	ADP
fumecheng-11486	177	24	physics	physics	NOUN
fumecheng-11486	177	25	,	,	PUNCT
fumecheng-11486	177	26	44	44	NUM
fumecheng-11486	177	27	,	,	PUNCT
fumecheng-11486	177	28	106208	106208	NUM
fumecheng-11486	177	29	.	.	PUNCT
fumecheng-11486	178	1	12	12	NUM
fumecheng-11486	178	2	.	.	PUNCT
fumecheng-11486	179	1	feng	feng	PROPN
fumecheng-11486	179	2	,	,	PUNCT
fumecheng-11486	179	3	g.q	g.q	PROPN
fumecheng-11486	179	4	.	.	PROPN
fumecheng-11486	179	5	,	,	PUNCT
fumecheng-11486	179	6	niu	niu	PROPN
fumecheng-11486	179	7	,	,	PUNCT
fumecheng-11486	179	8	j.y	j.y	PROPN
fumecheng-11486	179	9	.	.	PROPN
fumecheng-11486	179	10	,	,	PUNCT
fumecheng-11486	179	11	2023	2023	NUM
fumecheng-11486	179	12	,	,	PUNCT
fumecheng-11486	179	13	the	the	DET
fumecheng-11486	179	14	analysis	analysis	NOUN
fumecheng-11486	179	15	for	for	ADP
fumecheng-11486	179	16	the	the	DET
fumecheng-11486	179	17	dynamic	dynamic	ADJ
fumecheng-11486	179	18	pull	pull	NOUN
fumecheng-11486	179	19	-	-	PUNCT
fumecheng-11486	179	20	in	in	NOUN
fumecheng-11486	179	21	of	of	ADP
fumecheng-11486	179	22	a	a	DET
fumecheng-11486	179	23	micro	micro	ADJ
fumecheng-11486	179	24	-	-	ADJ
fumecheng-11486	179	25	electromechanical	electromechanical	ADJ
fumecheng-11486	179	26	system	system	NOUN
fumecheng-11486	179	27	,	,	PUNCT
fumecheng-11486	179	28	journal	journal	NOUN
fumecheng-11486	179	29	of	of	ADP
fumecheng-11486	179	30	low	low	ADJ
fumecheng-11486	179	31	frequency	frequency	NOUN
fumecheng-11486	179	32	noise	noise	NOUN
fumecheng-11486	179	33	,	,	PUNCT
fumecheng-11486	179	34	vibration	vibration	NOUN
fumecheng-11486	179	35	and	and	CCONJ
fumecheng-11486	179	36	active	active	ADJ
fumecheng-11486	179	37	control	control	NOUN
fumecheng-11486	179	38	,	,	PUNCT
fumecheng-11486	179	39	doi	doi	NOUN
fumecheng-11486	179	40	:	:	PUNCT
fumecheng-11486	179	41	10.1177/14613484221145588	10.1177/14613484221145588	NUM
fumecheng-11486	179	42	13	13	NUM
fumecheng-11486	179	43	.	.	PUNCT
fumecheng-11486	180	1	liu	liu	PROPN
fumecheng-11486	180	2	,	,	PUNCT
fumecheng-11486	180	3	x.s	x.s	PROPN
fumecheng-11486	180	4	.	.	PROPN
fumecheng-11486	180	5	,	,	PUNCT
fumecheng-11486	180	6	zhang	zhang	PROPN
fumecheng-11486	180	7	,	,	PUNCT
fumecheng-11486	180	8	l.j	l.j	PROPN
fumecheng-11486	180	9	.	.	PROPN
fumecheng-11486	180	10	,	,	PUNCT
fumecheng-11486	180	11	zhang	zhang	PROPN
fumecheng-11486	180	12	,	,	PUNCT
fumecheng-11486	180	13	m.j	m.j	PROPN
fumecheng-11486	180	14	.	.	PROPN
fumecheng-11486	180	15	,	,	PUNCT
fumecheng-11486	180	16	2022	2022	NUM
fumecheng-11486	180	17	,	,	PUNCT
fumecheng-11486	180	18	studies	study	NOUN
fumecheng-11486	180	19	on	on	ADP
fumecheng-11486	180	20	pull	pull	NOUN
fumecheng-11486	180	21	-	-	PUNCT
fumecheng-11486	180	22	in	in	ADP
fumecheng-11486	180	23	instability	instability	NOUN
fumecheng-11486	180	24	of	of	ADP
fumecheng-11486	180	25	an	an	DET
fumecheng-11486	180	26	electrostatic	electrostatic	ADJ
fumecheng-11486	180	27	mems	mem	NOUN
fumecheng-11486	180	28	actuator	actuator	NOUN
fumecheng-11486	180	29	:	:	PUNCT
fumecheng-11486	180	30	dynamical	dynamical	ADJ
fumecheng-11486	180	31	system	system	NOUN
fumecheng-11486	180	32	approach	approach	NOUN
fumecheng-11486	180	33	,	,	PUNCT
fumecheng-11486	180	34	j.	j.	PROPN
fumecheng-11486	180	35	appl	appl	PROPN
fumecheng-11486	180	36	.	.	PROPN
fumecheng-11486	181	1	anal	anal	PROPN
fumecheng-11486	181	2	.	.	PROPN
fumecheng-11486	181	3	,	,	PUNCT
fumecheng-11486	181	4	12(2	12(2	NUM
fumecheng-11486	181	5	)	)	PUNCT
fumecheng-11486	181	6	,	,	PUNCT
fumecheng-11486	181	7	pp	pp	PROPN
fumecheng-11486	181	8	.	.	PUNCT
fumecheng-11486	182	1	850	850	NUM
fumecheng-11486	182	2	-	-	SYM
fumecheng-11486	182	3	861	861	NUM
fumecheng-11486	182	4	.	.	PUNCT
fumecheng-11486	183	1	14	14	NUM
fumecheng-11486	183	2	.	.	PUNCT
fumecheng-11486	183	3	sedighi	sedighi	PROPN
fumecheng-11486	183	4	,	,	PUNCT
fumecheng-11486	183	5	h.m	h.m	PROPN
fumecheng-11486	183	6	.	.	PROPN
fumecheng-11486	183	7	,	,	PUNCT
fumecheng-11486	183	8	keivani	keivani	PROPN
fumecheng-11486	183	9	,	,	PUNCT
fumecheng-11486	183	10	m.	m.	NOUN
fumecheng-11486	183	11	,	,	PUNCT
fumecheng-11486	183	12	abadyan	abadyan	PROPN
fumecheng-11486	183	13	,	,	PUNCT
fumecheng-11486	183	14	m.	m.	NOUN
fumecheng-11486	183	15	,	,	PUNCT
fumecheng-11486	183	16	2015	2015	NUM
fumecheng-11486	183	17	,	,	PUNCT
fumecheng-11486	183	18	modified	modify	VERB
fumecheng-11486	183	19	continuum	continuum	ADJ
fumecheng-11486	183	20	model	model	NOUN
fumecheng-11486	183	21	for	for	ADP
fumecheng-11486	183	22	stability	stability	NOUN
fumecheng-11486	183	23	analysis	analysis	NOUN
fumecheng-11486	183	24	of	of	ADP
fumecheng-11486	183	25	asymmetric	asymmetric	ADJ
fumecheng-11486	183	26	fgm	fgm	PROPN
fumecheng-11486	183	27	double	double	ADJ
fumecheng-11486	183	28	-	-	PUNCT
fumecheng-11486	183	29	sided	sided	ADJ
fumecheng-11486	183	30	nems	nem	NOUN
fumecheng-11486	183	31	:	:	PUNCT
fumecheng-11486	183	32	corrections	correction	NOUN
fumecheng-11486	183	33	due	due	ADJ
fumecheng-11486	183	34	to	to	ADP
fumecheng-11486	183	35	finite	finite	VERB
fumecheng-11486	183	36	conductivity	conductivity	NOUN
fumecheng-11486	183	37	,	,	PUNCT
fumecheng-11486	183	38	surface	surface	NOUN
fumecheng-11486	183	39	energy	energy	NOUN
fumecheng-11486	183	40	and	and	CCONJ
fumecheng-11486	183	41	nonlocal	nonlocal	ADJ
fumecheng-11486	183	42	effect	effect	NOUN
fumecheng-11486	183	43	,	,	PUNCT
fumecheng-11486	183	44	compos	compos	PROPN
fumecheng-11486	183	45	.	.	PUNCT
fumecheng-11486	184	1	b.	b.	PROPN
fumecheng-11486	184	2	eng	eng	PROPN
fumecheng-11486	184	3	.	.	PROPN
fumecheng-11486	184	4	,	,	PUNCT
fumecheng-11486	184	5	83	83	NUM
fumecheng-11486	184	6	,	,	PUNCT
fumecheng-11486	184	7	pp	pp	ADJ
fumecheng-11486	184	8	.	.	PUNCT
fumecheng-11486	185	1	117	117	NUM
fumecheng-11486	185	2	-	-	SYM
fumecheng-11486	185	3	133	133	NUM
fumecheng-11486	185	4	.	.	PUNCT
fumecheng-11486	186	1	15	15	NUM
fumecheng-11486	186	2	.	.	X
fumecheng-11486	186	3	skrzypacz	skrzypacz	NOUN
fumecheng-11486	186	4	,	,	PUNCT
fumecheng-11486	186	5	p.	p.	NOUN
fumecheng-11486	186	6	,	,	PUNCT
fumecheng-11486	186	7	kadyrov	kadyrov	PROPN
fumecheng-11486	186	8	,	,	PUNCT
fumecheng-11486	186	9	s.	s.	PROPN
fumecheng-11486	186	10	,	,	PUNCT
fumecheng-11486	186	11	nurakhmetov	nurakhmetov	ADJ
fumecheng-11486	186	12	,	,	PUNCT
fumecheng-11486	186	13	d.	d.	PROPN
fumecheng-11486	186	14	,	,	PUNCT
fumecheng-11486	186	15	wei	wei	PROPN
fumecheng-11486	186	16	,	,	PUNCT
fumecheng-11486	186	17	d.m	d.m	PROPN
fumecheng-11486	186	18	.	.	PROPN
fumecheng-11486	186	19	,	,	PUNCT
fumecheng-11486	186	20	2019	2019	NUM
fumecheng-11486	186	21	,	,	PUNCT
fumecheng-11486	186	22	analysis	analysis	NOUN
fumecheng-11486	186	23	of	of	ADP
fumecheng-11486	186	24	dynamic	dynamic	ADJ
fumecheng-11486	186	25	pull	pull	NOUN
fumecheng-11486	186	26	-	-	PUNCT
fumecheng-11486	186	27	in	in	ADP
fumecheng-11486	186	28	voltage	voltage	NOUN
fumecheng-11486	186	29	of	of	ADP
fumecheng-11486	186	30	a	a	DET
fumecheng-11486	186	31	graphene	graphene	NOUN
fumecheng-11486	186	32	mems	mem	NOUN
fumecheng-11486	186	33	model	model	NOUN
fumecheng-11486	186	34	,	,	PUNCT
fumecheng-11486	186	35	nonlinear	nonlinear	ADJ
fumecheng-11486	186	36	anal	anal	ADJ
fumecheng-11486	186	37	real	real	ADJ
fumecheng-11486	186	38	world	world	NOUN
fumecheng-11486	186	39	appl	appl	PROPN
fumecheng-11486	186	40	.	.	PROPN
fumecheng-11486	186	41	,	,	PUNCT
fumecheng-11486	186	42	45	45	NUM
fumecheng-11486	186	43	,	,	PUNCT
fumecheng-11486	186	44	pp	pp	ADJ
fumecheng-11486	186	45	.	.	PUNCT
fumecheng-11486	187	1	581	581	NUM
fumecheng-11486	187	2	-	-	SYM
fumecheng-11486	187	3	589	589	NUM
fumecheng-11486	187	4	.	.	PUNCT
fumecheng-11486	188	1	16	16	NUM
fumecheng-11486	188	2	.	.	PUNCT
fumecheng-11486	188	3	skrzypacz	skrzypacz	NOUN
fumecheng-11486	188	4	,	,	PUNCT
fumecheng-11486	188	5	p.	p.	PROPN
fumecheng-11486	188	6	,	,	PUNCT
fumecheng-11486	188	7	wei	wei	PROPN
fumecheng-11486	188	8	,	,	PUNCT
fumecheng-11486	188	9	d.m	d.m	PROPN
fumecheng-11486	188	10	.	.	PROPN
fumecheng-11486	188	11	,	,	PUNCT
fumecheng-11486	188	12	nurakhmetov	nurakhmetov	ADJ
fumecheng-11486	188	13	,	,	PUNCT
fumecheng-11486	188	14	d.	d.	PROPN
fumecheng-11486	188	15	,	,	PUNCT
fumecheng-11486	188	16	kostsov	kostsov	PROPN
fumecheng-11486	188	17	,	,	PUNCT
fumecheng-11486	188	18	e.g.	e.g.	ADV
fumecheng-11486	188	19	,	,	PUNCT
fumecheng-11486	188	20	et	et	PROPN
fumecheng-11486	188	21	al	al	PROPN
fumecheng-11486	188	22	.	.	PROPN
fumecheng-11486	188	23	,	,	PUNCT
fumecheng-11486	188	24	2021	2021	NUM
fumecheng-11486	188	25	,	,	PUNCT
fumecheng-11486	188	26	analysis	analysis	NOUN
fumecheng-11486	188	27	of	of	ADP
fumecheng-11486	188	28	dynamic	dynamic	ADJ
fumecheng-11486	188	29	pull	pull	NOUN
fumecheng-11486	188	30	-	-	PUNCT
fumecheng-11486	188	31	in	in	NOUN
fumecheng-11486	188	32	voltage	voltage	NOUN
fumecheng-11486	188	33	and	and	CCONJ
fumecheng-11486	188	34	response	response	NOUN
fumecheng-11486	188	35	time	time	NOUN
fumecheng-11486	188	36	for	for	ADP
fumecheng-11486	188	37	a	a	DET
fumecheng-11486	188	38	micro	micro	ADJ
fumecheng-11486	188	39	-	-	ADJ
fumecheng-11486	188	40	electro	electro	ADJ
fumecheng-11486	188	41	-	-	PUNCT
fumecheng-11486	188	42	mechanical	mechanical	ADJ
fumecheng-11486	188	43	oscillator	oscillator	NOUN
fumecheng-11486	188	44	made	make	VERB
fumecheng-11486	188	45	of	of	ADP
fumecheng-11486	188	46	power	power	NOUN
fumecheng-11486	188	47	-	-	PUNCT
fumecheng-11486	188	48	law	law	NOUN
fumecheng-11486	188	49	materials	material	NOUN
fumecheng-11486	188	50	,	,	PUNCT
fumecheng-11486	188	51	nonlinear	nonlinear	ADJ
fumecheng-11486	188	52	dyn	dyn	NOUN
fumecheng-11486	188	53	.	.	PUNCT
fumecheng-11486	188	54	,	,	PUNCT
fumecheng-11486	188	55	105(1	105(1	NUM
fumecheng-11486	188	56	)	)	PUNCT
fumecheng-11486	188	57	,	,	PUNCT
fumecheng-11486	188	58	pp	pp	ADP
fumecheng-11486	188	59	.	.	PUNCT
fumecheng-11486	189	1	227	227	NUM
fumecheng-11486	189	2	-	-	SYM
fumecheng-11486	189	3	240	240	NUM
fumecheng-11486	189	4	.	.	PUNCT
fumecheng-11486	190	1	17	17	NUM
fumecheng-11486	190	2	.	.	PUNCT
fumecheng-11486	191	1	aliasghary	aliasghary	PROPN
fumecheng-11486	191	2	,	,	PUNCT
fumecheng-11486	191	3	m.	m.	NOUN
fumecheng-11486	191	4	,	,	PUNCT
fumecheng-11486	191	5	mobki	mobki	PROPN
fumecheng-11486	191	6	,	,	PUNCT
fumecheng-11486	191	7	h.	h.	PROPN
fumecheng-11486	191	8	,	,	PUNCT
fumecheng-11486	191	9	ouakad	ouakad	VERB
fumecheng-11486	191	10	,	,	PUNCT
fumecheng-11486	191	11	h.m	h.m	PROPN
fumecheng-11486	191	12	.	.	PROPN
fumecheng-11486	191	13	,	,	PUNCT
fumecheng-11486	191	14	2022	2022	NUM
fumecheng-11486	191	15	,	,	PUNCT
fumecheng-11486	191	16	pull	pull	NOUN
fumecheng-11486	191	17	-	-	PUNCT
fumecheng-11486	191	18	in	in	ADP
fumecheng-11486	191	19	phenomenon	phenomenon	NOUN
fumecheng-11486	191	20	in	in	ADP
fumecheng-11486	191	21	the	the	DET
fumecheng-11486	191	22	electrostatically	electrostatically	ADV
fumecheng-11486	191	23	micro	micro	NOUN
fumecheng-11486	191	24	-	-	NOUN
fumecheng-11486	191	25	switch	switch	NOUN
fumecheng-11486	191	26	suspended	suspend	VERB
fumecheng-11486	191	27	between	between	ADP
fumecheng-11486	191	28	two	two	NUM
fumecheng-11486	191	29	conductive	conductive	ADJ
fumecheng-11486	191	30	plates	plate	NOUN
fumecheng-11486	191	31	using	use	VERB
fumecheng-11486	191	32	the	the	DET
fumecheng-11486	191	33	artificial	artificial	ADJ
fumecheng-11486	191	34	neural	neural	ADJ
fumecheng-11486	191	35	network	network	NOUN
fumecheng-11486	191	36	,	,	PUNCT
fumecheng-11486	191	37	journal	journal	NOUN
fumecheng-11486	191	38	of	of	ADP
fumecheng-11486	191	39	applied	applied	ADJ
fumecheng-11486	191	40	and	and	CCONJ
fumecheng-11486	191	41	computational	computational	ADJ
fumecheng-11486	191	42	mechanics	mechanic	NOUN
fumecheng-11486	191	43	,	,	PUNCT
fumecheng-11486	191	44	8(4	8(4	NUM
fumecheng-11486	191	45	)	)	PUNCT
fumecheng-11486	191	46	,	,	PUNCT
fumecheng-11486	191	47	pp	pp	ADP
fumecheng-11486	191	48	.	.	PUNCT
fumecheng-11486	192	1	1222	1222	NUM
fumecheng-11486	192	2	-	-	SYM
fumecheng-11486	192	3	1235	1235	NUM
fumecheng-11486	192	4	.	.	PUNCT
fumecheng-11486	193	1	18	18	NUM
fumecheng-11486	193	2	.	.	X
fumecheng-11486	193	3	molla	molla	PROPN
fumecheng-11486	193	4	,	,	PUNCT
fumecheng-11486	193	5	m.h.u	m.h.u	NOUN
fumecheng-11486	193	6	.	.	PROPN
fumecheng-11486	193	7	,	,	PUNCT
fumecheng-11486	193	8	razzak	razzak	PROPN
fumecheng-11486	193	9	,	,	PUNCT
fumecheng-11486	193	10	m.a	m.a	PROPN
fumecheng-11486	193	11	.	.	PROPN
fumecheng-11486	193	12	,	,	PUNCT
fumecheng-11486	193	13	alam	alam	PROPN
fumecheng-11486	193	14	,	,	PUNCT
fumecheng-11486	193	15	m.s	m.s	PROPN
fumecheng-11486	193	16	.	.	PROPN
fumecheng-11486	193	17	,	,	PUNCT
fumecheng-11486	193	18	2017	2017	NUM
fumecheng-11486	193	19	,	,	PUNCT
fumecheng-11486	193	20	an	an	DET
fumecheng-11486	193	21	analytical	analytical	ADJ
fumecheng-11486	193	22	technique	technique	NOUN
fumecheng-11486	193	23	for	for	ADP
fumecheng-11486	193	24	solving	solve	VERB
fumecheng-11486	193	25	quadratic	quadratic	ADJ
fumecheng-11486	193	26	nonlinear	nonlinear	ADJ
fumecheng-11486	193	27	oscillator	oscillator	NOUN
fumecheng-11486	193	28	,	,	PUNCT
fumecheng-11486	193	29	multidiscipline	multidiscipline	VERB
fumecheng-11486	193	30	modeling	modeling	NOUN
fumecheng-11486	193	31	in	in	ADP
fumecheng-11486	193	32	materials	material	NOUN
fumecheng-11486	193	33	and	and	CCONJ
fumecheng-11486	193	34	structures	structure	NOUN
fumecheng-11486	193	35	,	,	PUNCT
fumecheng-11486	193	36	13(3	13(3	NUM
fumecheng-11486	193	37	)	)	PUNCT
fumecheng-11486	193	38	,	,	PUNCT
fumecheng-11486	193	39	pp	pp	ADP
fumecheng-11486	193	40	.	.	PUNCT
fumecheng-11486	194	1	424	424	NUM
fumecheng-11486	194	2	-	-	SYM
fumecheng-11486	194	3	433	433	NUM
fumecheng-11486	194	4	.	.	PUNCT
fumecheng-11486	195	1	19	19	NUM
fumecheng-11486	195	2	.	.	PUNCT
fumecheng-11486	196	1	mickens	mickens	PROPN
fumecheng-11486	196	2	,	,	PUNCT
fumecheng-11486	196	3	r.e	r.e	PROPN
fumecheng-11486	196	4	.	.	PROPN
fumecheng-11486	196	5	,	,	PUNCT
fumecheng-11486	196	6	1981	1981	NUM
fumecheng-11486	196	7	,	,	PUNCT
fumecheng-11486	196	8	an	an	DET
fumecheng-11486	196	9	introduction	introduction	NOUN
fumecheng-11486	196	10	to	to	ADP
fumecheng-11486	196	11	nonlinear	nonlinear	ADJ
fumecheng-11486	196	12	oscillations	oscillation	NOUN
fumecheng-11486	196	13	,	,	PUNCT
fumecheng-11486	196	14	cambridge	cambridge	PROPN
fumecheng-11486	196	15	university	university	PROPN
fumecheng-11486	196	16	press	press	PROPN
fumecheng-11486	196	17	,	,	PUNCT
fumecheng-11486	196	18	cambridge	cambridge	PROPN
fumecheng-11486	196	19	,	,	PUNCT
fumecheng-11486	196	20	england	england	PROPN
fumecheng-11486	196	21	.	.	PUNCT
fumecheng-11486	197	1	20	20	NUM
fumecheng-11486	197	2	.	.	PUNCT
fumecheng-11486	198	1	ma	ma	PROPN
fumecheng-11486	198	2	,	,	PUNCT
fumecheng-11486	198	3	h.j	h.j	PROPN
fumecheng-11486	198	4	.	.	PROPN
fumecheng-11486	198	5	,	,	PUNCT
fumecheng-11486	198	6	2022	2022	NUM
fumecheng-11486	198	7	,	,	PUNCT
fumecheng-11486	198	8	simplified	simplified	ADJ
fumecheng-11486	198	9	hamiltonian	hamiltonian	ADJ
fumecheng-11486	198	10	-	-	PUNCT
fumecheng-11486	198	11	based	base	VERB
fumecheng-11486	198	12	frequency	frequency	NOUN
fumecheng-11486	198	13	-	-	PUNCT
fumecheng-11486	198	14	amplitude	amplitude	NOUN
fumecheng-11486	198	15	formulation	formulation	NOUN
fumecheng-11486	198	16	for	for	ADP
fumecheng-11486	198	17	nonlinear	nonlinear	ADJ
fumecheng-11486	198	18	vibration	vibration	NOUN
fumecheng-11486	198	19	systems	system	NOUN
fumecheng-11486	198	20	,	,	PUNCT
fumecheng-11486	198	21	facta	facta	PROPN
fumecheng-11486	198	22	universitatis	universitatis	PROPN
fumecheng-11486	198	23	-	-	PUNCT
fumecheng-11486	198	24	series	series	NOUN
fumecheng-11486	198	25	mechanical	mechanical	ADJ
fumecheng-11486	198	26	engineering	engineering	NOUN
fumecheng-11486	198	27	,	,	PUNCT
fumecheng-11486	198	28	20(2	20(2	NUM
fumecheng-11486	198	29	)	)	PUNCT
fumecheng-11486	198	30	,	,	PUNCT
fumecheng-11486	198	31	pp	pp	PROPN
fumecheng-11486	198	32	.	.	PUNCT
fumecheng-11486	199	1	445	445	NUM
fumecheng-11486	199	2	-	-	SYM
fumecheng-11486	199	3	455	455	NUM
fumecheng-11486	199	4	.	.	PUNCT
fumecheng-11486	200	1	21	21	NUM
fumecheng-11486	200	2	.	.	PUNCT
fumecheng-11486	200	3	mirzabeigy	mirzabeigy	PROPN
fumecheng-11486	200	4	,	,	PUNCT
fumecheng-11486	200	5	a.	a.	NOUN
fumecheng-11486	200	6	,	,	PUNCT
fumecheng-11486	200	7	2022	2022	NUM
fumecheng-11486	200	8	,	,	PUNCT
fumecheng-11486	200	9	a	a	DET
fumecheng-11486	200	10	simple	simple	ADJ
fumecheng-11486	200	11	approach	approach	NOUN
fumecheng-11486	200	12	for	for	ADP
fumecheng-11486	200	13	dealing	deal	VERB
fumecheng-11486	200	14	with	with	ADP
fumecheng-11486	200	15	autonomous	autonomous	ADJ
fumecheng-11486	200	16	conservative	conservative	ADJ
fumecheng-11486	200	17	oscillator	oscillator	NOUN
fumecheng-11486	200	18	under	under	ADP
fumecheng-11486	200	19	initial	initial	ADJ
fumecheng-11486	200	20	velocity	velocity	NOUN
fumecheng-11486	200	21	,	,	PUNCT
fumecheng-11486	200	22	journal	journal	NOUN
fumecheng-11486	200	23	of	of	ADP
fumecheng-11486	200	24	applied	applied	ADJ
fumecheng-11486	200	25	and	and	CCONJ
fumecheng-11486	200	26	computational	computational	ADJ
fumecheng-11486	200	27	mechanics	mechanic	NOUN
fumecheng-11486	200	28	,	,	PUNCT
fumecheng-11486	200	29	8(3	8(3	NUM
fumecheng-11486	200	30	)	)	PUNCT
fumecheng-11486	200	31	,	,	PUNCT
fumecheng-11486	200	32	pp	pp	ADP
fumecheng-11486	200	33	.	.	PUNCT
fumecheng-11486	201	1	918	918	NUM
fumecheng-11486	201	2	-	-	SYM
fumecheng-11486	201	3	924	924	NUM
fumecheng-11486	201	4	.	.	NOUN
fumecheng-11486	202	1	22	22	NUM
fumecheng-11486	202	2	.	.	PUNCT
fumecheng-11486	203	1	el	el	PROPN
fumecheng-11486	203	2	-	-	PUNCT
fumecheng-11486	203	3	dib	dib	PROPN
fumecheng-11486	203	4	,	,	PUNCT
fumecheng-11486	203	5	y.o	y.o	PROPN
fumecheng-11486	203	6	.	.	PROPN
fumecheng-11486	203	7	,	,	PUNCT
fumecheng-11486	203	8	2023	2023	NUM
fumecheng-11486	203	9	,	,	PUNCT
fumecheng-11486	203	10	properties	property	NOUN
fumecheng-11486	203	11	of	of	ADP
fumecheng-11486	203	12	complex	complex	ADJ
fumecheng-11486	203	13	damping	damp	VERB
fumecheng-11486	203	14	helmholtz	helmholtz	NOUN
fumecheng-11486	203	15	-	-	PUNCT
fumecheng-11486	203	16	duffing	duffing	NOUN
fumecheng-11486	203	17	oscillator	oscillator	NOUN
fumecheng-11486	203	18	arising	arise	VERB
fumecheng-11486	203	19	in	in	ADP
fumecheng-11486	203	20	fluid	fluid	ADJ
fumecheng-11486	203	21	mechanics	mechanic	NOUN
fumecheng-11486	203	22	,	,	PUNCT
fumecheng-11486	203	23	journal	journal	NOUN
fumecheng-11486	203	24	of	of	ADP
fumecheng-11486	203	25	low	low	ADJ
fumecheng-11486	203	26	frequency	frequency	NOUN
fumecheng-11486	203	27	noise	noise	NOUN
fumecheng-11486	203	28	,	,	PUNCT
fumecheng-11486	203	29	vibration	vibration	NOUN
fumecheng-11486	203	30	and	and	CCONJ
fumecheng-11486	203	31	active	active	ADJ
fumecheng-11486	203	32	control	control	NOUN
fumecheng-11486	203	33	,	,	PUNCT
fumecheng-11486	203	34	doi	doi	NOUN
fumecheng-11486	203	35	:	:	PUNCT
fumecheng-11486	203	36	10.1177/14613484221138560	10.1177/14613484221138560	NUM
fumecheng-11486	203	37	23	23	NUM
fumecheng-11486	203	38	.	.	PUNCT
fumecheng-11486	204	1	mann	mann	PROPN
fumecheng-11486	204	2	,	,	PUNCT
fumecheng-11486	204	3	b.p	b.p	PROPN
fumecheng-11486	204	4	.	.	PROPN
fumecheng-11486	204	5	,	,	PUNCT
fumecheng-11486	204	6	sims	sim	NOUN
fumecheng-11486	204	7	,	,	PUNCT
fumecheng-11486	204	8	n.d	n.d	PROPN
fumecheng-11486	204	9	.	.	PROPN
fumecheng-11486	204	10	,	,	PUNCT
fumecheng-11486	204	11	2009	2009	NUM
fumecheng-11486	204	12	,	,	PUNCT
fumecheng-11486	204	13	energy	energy	NOUN
fumecheng-11486	204	14	harvesting	harvesting	NOUN
fumecheng-11486	204	15	from	from	ADP
fumecheng-11486	204	16	the	the	DET
fumecheng-11486	204	17	nonlinear	nonlinear	ADJ
fumecheng-11486	204	18	oscillations	oscillation	NOUN
fumecheng-11486	204	19	of	of	ADP
fumecheng-11486	204	20	magnetic	magnetic	ADJ
fumecheng-11486	204	21	levitation	levitation	NOUN
fumecheng-11486	204	22	,	,	PUNCT
fumecheng-11486	204	23	journal	journal	NOUN
fumecheng-11486	204	24	of	of	ADP
fumecheng-11486	204	25	sound	sound	NOUN
fumecheng-11486	204	26	and	and	CCONJ
fumecheng-11486	204	27	vibration	vibration	NOUN
fumecheng-11486	204	28	,	,	PUNCT
fumecheng-11486	204	29	319(1	319(1	NUM
fumecheng-11486	204	30	-	-	SYM
fumecheng-11486	204	31	2	2	NUM
fumecheng-11486	204	32	)	)	PUNCT
fumecheng-11486	204	33	,	,	PUNCT
fumecheng-11486	204	34	pp	pp	ADP
fumecheng-11486	204	35	.	.	PUNCT
fumecheng-11486	205	1	515	515	NUM
fumecheng-11486	205	2	-	-	SYM
fumecheng-11486	205	3	530	530	NUM
fumecheng-11486	205	4	.	.	X
fumecheng-11486	206	1	24	24	NUM
fumecheng-11486	206	2	.	.	PUNCT
fumecheng-11486	206	3	beeby	beeby	PROPN
fumecheng-11486	206	4	,	,	PUNCT
fumecheng-11486	206	5	s.p	s.p	PROPN
fumecheng-11486	206	6	.	.	PROPN
fumecheng-11486	206	7	,	,	PUNCT
fumecheng-11486	206	8	tudor	tudor	PROPN
fumecheng-11486	206	9	,	,	PUNCT
fumecheng-11486	206	10	m.j	m.j	PROPN
fumecheng-11486	206	11	.	.	PROPN
fumecheng-11486	206	12	,	,	PUNCT
fumecheng-11486	206	13	white	white	PROPN
fumecheng-11486	206	14	,	,	PUNCT
fumecheng-11486	206	15	n.m	n.m	PROPN
fumecheng-11486	206	16	.	.	PROPN
fumecheng-11486	206	17	,	,	PUNCT
fumecheng-11486	206	18	2006	2006	NUM
fumecheng-11486	206	19	,	,	PUNCT
fumecheng-11486	206	20	energy	energy	NOUN
fumecheng-11486	206	21	harvesting	harvesting	NOUN
fumecheng-11486	206	22	vibration	vibration	NOUN
fumecheng-11486	206	23	sources	source	NOUN
fumecheng-11486	206	24	for	for	ADP
fumecheng-11486	206	25	microsystems	microsystem	NOUN
fumecheng-11486	206	26	applications	application	NOUN
fumecheng-11486	206	27	,	,	PUNCT
fumecheng-11486	206	28	measurement	measurement	NOUN
fumecheng-11486	206	29	science	science	NOUN
fumecheng-11486	206	30	and	and	CCONJ
fumecheng-11486	206	31	technology	technology	NOUN
fumecheng-11486	206	32	,	,	PUNCT
fumecheng-11486	206	33	17(12	17(12	NUM
fumecheng-11486	206	34	)	)	PUNCT
fumecheng-11486	206	35	,	,	PUNCT
fumecheng-11486	206	36	pp	pp	ADP
fumecheng-11486	206	37	.	.	PUNCT
fumecheng-11486	207	1	r175	r175	PROPN
fumecheng-11486	207	2	-	-	PUNCT
fumecheng-11486	207	3	r195	r195	PROPN
fumecheng-11486	207	4	.	.	PROPN
fumecheng-11486	207	5	25	25	NUM
fumecheng-11486	207	6	.	.	PUNCT
fumecheng-11486	208	1	ginoux	ginoux	VERB
fumecheng-11486	208	2	,	,	PUNCT
fumecheng-11486	208	3	j.m	j.m	PROPN
fumecheng-11486	208	4	.	.	PROPN
fumecheng-11486	208	5	,	,	PUNCT
fumecheng-11486	208	6	llibre	llibre	PROPN
fumecheng-11486	208	7	,	,	PUNCT
fumecheng-11486	208	8	j.	j.	PROPN
fumecheng-11486	208	9	,	,	PUNCT
fumecheng-11486	208	10	2023	2023	NUM
fumecheng-11486	208	11	,	,	PUNCT
fumecheng-11486	208	12	a	a	DET
fumecheng-11486	208	13	family	family	NOUN
fumecheng-11486	208	14	of	of	ADP
fumecheng-11486	208	15	periodic	periodic	ADJ
fumecheng-11486	208	16	orbits	orbit	NOUN
fumecheng-11486	208	17	for	for	ADP
fumecheng-11486	208	18	the	the	DET
fumecheng-11486	208	19	extended	extended	ADJ
fumecheng-11486	208	20	hamiltonian	hamiltonian	ADJ
fumecheng-11486	208	21	system	system	NOUN
fumecheng-11486	208	22	of	of	ADP
fumecheng-11486	208	23	the	the	DET
fumecheng-11486	208	24	van	van	PROPN
fumecheng-11486	208	25	der	der	PROPN
fumecheng-11486	208	26	pol	pol	PROPN
fumecheng-11486	208	27	oscillator	oscillator	PROPN
fumecheng-11486	208	28	,	,	PUNCT
fumecheng-11486	208	29	journal	journal	NOUN
fumecheng-11486	208	30	of	of	ADP
fumecheng-11486	208	31	geometry	geometry	NOUN
fumecheng-11486	208	32	and	and	CCONJ
fumecheng-11486	208	33	physics,183	physics,183	PROPN
fumecheng-11486	208	34	,	,	PUNCT
fumecheng-11486	208	35	104705	104705	NUM
fumecheng-11486	208	36	.	.	PUNCT
fumecheng-11486	209	1	26	26	NUM
fumecheng-11486	209	2	.	.	PUNCT
fumecheng-11486	210	1	he	he	PRON
fumecheng-11486	210	2	,	,	PUNCT
fumecheng-11486	210	3	j.h	j.h	PROPN
fumecheng-11486	210	4	.	.	PROPN
fumecheng-11486	210	5	,	,	PUNCT
fumecheng-11486	210	6	2019	2019	NUM
fumecheng-11486	210	7	,	,	PUNCT
fumecheng-11486	210	8	the	the	DET
fumecheng-11486	210	9	simplest	simple	ADJ
fumecheng-11486	210	10	approach	approach	NOUN
fumecheng-11486	210	11	to	to	ADP
fumecheng-11486	210	12	nonlinear	nonlinear	ADJ
fumecheng-11486	210	13	oscillators	oscillator	NOUN
fumecheng-11486	210	14	,	,	PUNCT
fumecheng-11486	210	15	results	result	VERB
fumecheng-11486	210	16	phys	phy	NOUN
fumecheng-11486	210	17	,	,	PUNCT
fumecheng-11486	210	18	15	15	NUM
fumecheng-11486	210	19	,	,	PUNCT
fumecheng-11486	210	20	102546	102546	NUM
fumecheng-11486	210	21	.	.	PUNCT
fumecheng-11486	211	1	27	27	NUM
fumecheng-11486	211	2	.	.	X
fumecheng-11486	212	1	tian	tian	ADJ
fumecheng-11486	212	2	,	,	PUNCT
fumecheng-11486	212	3	y.	y.	NOUN
fumecheng-11486	212	4	,	,	PUNCT
fumecheng-11486	212	5	2022	2022	NUM
fumecheng-11486	212	6	,	,	PUNCT
fumecheng-11486	212	7	frequency	frequency	NOUN
fumecheng-11486	212	8	formula	formula	NOUN
fumecheng-11486	212	9	for	for	ADP
fumecheng-11486	212	10	a	a	DET
fumecheng-11486	212	11	class	class	NOUN
fumecheng-11486	212	12	of	of	ADP
fumecheng-11486	212	13	fractal	fractal	ADJ
fumecheng-11486	212	14	vibration	vibration	NOUN
fumecheng-11486	212	15	system	system	NOUN
fumecheng-11486	212	16	,	,	PUNCT
fumecheng-11486	212	17	reports	report	NOUN
fumecheng-11486	212	18	in	in	ADP
fumecheng-11486	212	19	mechanical	mechanical	ADJ
fumecheng-11486	212	20	engineering	engineering	NOUN
fumecheng-11486	212	21	,	,	PUNCT
fumecheng-11486	212	22	3(1	3(1	NUM
fumecheng-11486	212	23	)	)	PUNCT
fumecheng-11486	212	24	,	,	PUNCT
fumecheng-11486	212	25	pp	pp	ADP
fumecheng-11486	212	26	.	.	PUNCT
fumecheng-11486	213	1	55	55	NUM
fumecheng-11486	213	2	-	-	SYM
fumecheng-11486	213	3	61	61	NUM
fumecheng-11486	213	4	.	.	PUNCT
fumecheng-11486	214	1	28	28	NUM
fumecheng-11486	214	2	.	.	PUNCT
fumecheng-11486	215	1	feng	feng	PROPN
fumecheng-11486	215	2	,	,	PUNCT
fumecheng-11486	215	3	g.q	g.q	PROPN
fumecheng-11486	215	4	.	.	PROPN
fumecheng-11486	215	5	,	,	PUNCT
fumecheng-11486	215	6	2021	2021	NUM
fumecheng-11486	215	7	,	,	PUNCT
fumecheng-11486	215	8	he	he	PRON
fumecheng-11486	215	9	's	's	PART
fumecheng-11486	215	10	frequency	frequency	NOUN
fumecheng-11486	215	11	formula	formula	NOUN
fumecheng-11486	215	12	to	to	ADP
fumecheng-11486	215	13	fractal	fractal	ADJ
fumecheng-11486	215	14	undamped	undampe	VERB
fumecheng-11486	215	15	duffing	duffing	NOUN
fumecheng-11486	215	16	equation	equation	NOUN
fumecheng-11486	215	17	,	,	PUNCT
fumecheng-11486	215	18	journal	journal	NOUN
fumecheng-11486	215	19	of	of	ADP
fumecheng-11486	215	20	low	low	ADJ
fumecheng-11486	215	21	frequency	frequency	NOUN
fumecheng-11486	215	22	noise	noise	NOUN
fumecheng-11486	215	23	,	,	PUNCT
fumecheng-11486	215	24	vibration	vibration	NOUN
fumecheng-11486	215	25	and	and	CCONJ
fumecheng-11486	215	26	active	active	ADJ
fumecheng-11486	215	27	control	control	NOUN
fumecheng-11486	215	28	,	,	PUNCT
fumecheng-11486	215	29	40(4	40(4	NUM
fumecheng-11486	215	30	)	)	PUNCT
fumecheng-11486	215	31	,	,	PUNCT
fumecheng-11486	215	32	pp	pp	ADP
fumecheng-11486	215	33	.	.	PUNCT
fumecheng-11486	215	34	1671	1671	NUM
fumecheng-11486	215	35	-	-	SYM
fumecheng-11486	215	36	1676	1676	NUM
fumecheng-11486	215	37	.	.	PUNCT
fumecheng-11486	216	1	29	29	NUM
fumecheng-11486	216	2	.	.	PUNCT
fumecheng-11486	217	1	elías	elías	PROPN
fumecheng-11486	217	2	-	-	PUNCT
fumecheng-11486	217	3	zúñiga	zúñiga	PROPN
fumecheng-11486	217	4	,	,	PUNCT
fumecheng-11486	217	5	a.	a.	NOUN
fumecheng-11486	217	6	,	,	PUNCT
fumecheng-11486	217	7	palacios	palacio	NOUN
fumecheng-11486	217	8	-	-	PUNCT
fumecheng-11486	217	9	pineda	pineda	PROPN
fumecheng-11486	217	10	,	,	PUNCT
fumecheng-11486	217	11	l.	l.	PROPN
fumecheng-11486	217	12	m.	m.	PROPN
fumecheng-11486	217	13	,	,	PUNCT
fumecheng-11486	217	14	olvera	olvera	PROPN
fumecheng-11486	217	15	-	-	PUNCT
fumecheng-11486	217	16	trejo	trejo	PROPN
fumecheng-11486	217	17	,	,	PUNCT
fumecheng-11486	217	18	d.	d.	PROPN
fumecheng-11486	217	19	,	,	PUNCT
fumecheng-11486	217	20	martínez	martínez	PROPN
fumecheng-11486	217	21	-	-	PUNCT
fumecheng-11486	217	22	romero	romero	PROPN
fumecheng-11486	217	23	,	,	PUNCT
fumecheng-11486	217	24	o.	o.	NOUN
fumecheng-11486	217	25	,	,	PUNCT
fumecheng-11486	217	26	2022	2022	NUM
fumecheng-11486	217	27	,	,	PUNCT
fumecheng-11486	217	28	recent	recent	ADJ
fumecheng-11486	217	29	strategy	strategy	NOUN
fumecheng-11486	217	30	to	to	PART
fumecheng-11486	217	31	study	study	VERB
fumecheng-11486	217	32	fractal	fractal	ADJ
fumecheng-11486	217	33	-	-	PUNCT
fumecheng-11486	217	34	order	order	NOUN
fumecheng-11486	217	35	viscoelastic	viscoelastic	ADJ
fumecheng-11486	217	36	polymer	polymer	NOUN
fumecheng-11486	217	37	materials	material	NOUN
fumecheng-11486	217	38	using	use	VERB
fumecheng-11486	217	39	an	an	DET
fumecheng-11486	217	40	ancient	ancient	ADJ
fumecheng-11486	217	41	chinese	chinese	ADJ
fumecheng-11486	217	42	algorithm	algorithm	NOUN
fumecheng-11486	217	43	and	and	CCONJ
fumecheng-11486	217	44	he	he	PRON
fumecheng-11486	217	45	’s	’	VERB
fumecheng-11486	217	46	formulation	formulation	NOUN
fumecheng-11486	217	47	,	,	PUNCT
fumecheng-11486	217	48	journal	journal	NOUN
fumecheng-11486	217	49	of	of	ADP
fumecheng-11486	217	50	low	low	ADJ
fumecheng-11486	217	51	frequency	frequency	NOUN
fumecheng-11486	217	52	noise	noise	NOUN
fumecheng-11486	217	53	,	,	PUNCT
fumecheng-11486	217	54	vibration	vibration	NOUN
fumecheng-11486	217	55	and	and	CCONJ
fumecheng-11486	217	56	active	active	ADJ
fumecheng-11486	217	57	control	control	NOUN
fumecheng-11486	217	58	,	,	PUNCT
fumecheng-11486	217	59	41(3	41(3	NUM
fumecheng-11486	217	60	)	)	PUNCT
fumecheng-11486	217	61	,	,	PUNCT
fumecheng-11486	218	1	pp	pp	PROPN
fumecheng-11486	218	2	.	.	PUNCT
fumecheng-11486	219	1	842	842	NUM
fumecheng-11486	219	2	-	-	SYM
fumecheng-11486	219	3	851	851	NUM
fumecheng-11486	219	4	.	.	PUNCT
fumecheng-11486	220	1	30	30	NUM
fumecheng-11486	220	2	.	.	PUNCT
fumecheng-11486	221	1	belendez	belendez	PROPN
fumecheng-11486	221	2	,	,	PUNCT
fumecheng-11486	221	3	a.	a.	PROPN
fumecheng-11486	221	4	,	,	PUNCT
fumecheng-11486	221	5	hernandez	hernandez	PROPN
fumecheng-11486	221	6	,	,	PUNCT
fumecheng-11486	221	7	a.	a.	NOUN
fumecheng-11486	221	8	,	,	PUNCT
fumecheng-11486	221	9	belendez	belendez	NOUN
fumecheng-11486	221	10	,	,	PUNCT
fumecheng-11486	221	11	t.	t.	PROPN
fumecheng-11486	221	12	,	,	PUNCT
fumecheng-11486	221	13	fernandez	fernandez	PROPN
fumecheng-11486	221	14	,	,	PUNCT
fumecheng-11486	221	15	e.	e.	PROPN
fumecheng-11486	221	16	,	,	PUNCT
fumecheng-11486	221	17	et	et	PROPN
fumecheng-11486	221	18	al	al	PROPN
fumecheng-11486	221	19	.	.	PROPN
fumecheng-11486	221	20	,	,	PUNCT
fumecheng-11486	221	21	2007	2007	NUM
fumecheng-11486	221	22	,	,	PUNCT
fumecheng-11486	221	23	application	application	NOUN
fumecheng-11486	221	24	of	of	ADP
fumecheng-11486	221	25	he	he	PRON
fumecheng-11486	221	26	's	's	PART
fumecheng-11486	221	27	homotopy	homotopy	NOUN
fumecheng-11486	221	28	perturbation	perturbation	NOUN
fumecheng-11486	221	29	method	method	NOUN
fumecheng-11486	221	30	to	to	ADP
fumecheng-11486	221	31	the	the	DET
fumecheng-11486	221	32	duffing	duffing	NOUN
fumecheng-11486	221	33	-	-	PUNCT
fumecheng-11486	221	34	harmonic	harmonic	ADJ
fumecheng-11486	221	35	oscillator	oscillator	NOUN
fumecheng-11486	221	36	,	,	PUNCT
fumecheng-11486	221	37	international	international	ADJ
fumecheng-11486	221	38	journal	journal	NOUN
fumecheng-11486	221	39	of	of	ADP
fumecheng-11486	221	40	nonlinear	nonlinear	PROPN
fumecheng-11486	221	41	sciences	sciences	PROPN
fumecheng-11486	221	42	and	and	CCONJ
fumecheng-11486	221	43	numerical	numerical	PROPN
fumecheng-11486	221	44	simulation	simulation	PROPN
fumecheng-11486	221	45	,	,	PUNCT
fumecheng-11486	221	46	8(1	8(1	NOUN
fumecheng-11486	221	47	)	)	PUNCT
fumecheng-11486	221	48	,	,	PUNCT
fumecheng-11486	221	49	pp	pp	PROPN
fumecheng-11486	221	50	.	.	PUNCT
fumecheng-11486	222	1	79	79	NUM
fumecheng-11486	222	2	-	-	SYM
fumecheng-11486	222	3	88	88	NUM
fumecheng-11486	222	4	.	.	PUNCT
fumecheng-11486	223	1	https://www.webofscience.com/wos/author/record/33361634	https://www.webofscience.com/wos/author/record/33361634	PROPN
fumecheng-11486	224	1	https://www.webofscience.com/wos/author/record/14768325	https://www.webofscience.com/wos/author/record/14768325	PROPN