id	sid	tid	token	lemma	pos
ejpam-5787	1	1	european	european	PROPN
ejpam-5787	1	2	journal	journal	PROPN
ejpam-5787	1	3	of	of	ADP
ejpam-5787	1	4	pure	pure	ADJ
ejpam-5787	1	5	and	and	CCONJ
ejpam-5787	1	6	applied	applied	ADJ
ejpam-5787	1	7	mathematics	mathematic	NOUN
ejpam-5787	1	8	2025	2025	NUM
ejpam-5787	1	9	,	,	PUNCT
ejpam-5787	1	10	vol	vol	NOUN
ejpam-5787	1	11	.	.	PROPN
ejpam-5787	1	12	18	18	NUM
ejpam-5787	1	13	,	,	PUNCT
ejpam-5787	1	14	issue	issue	NOUN
ejpam-5787	1	15	1	1	NUM
ejpam-5787	1	16	,	,	PUNCT
ejpam-5787	1	17	article	article	NOUN
ejpam-5787	1	18	number	number	NOUN
ejpam-5787	1	19	5787	5787	NUM
ejpam-5787	1	20	issn	issn	PROPN
ejpam-5787	1	21	1307	1307	NUM
ejpam-5787	1	22	-	-	SYM
ejpam-5787	1	23	5543	5543	NUM
ejpam-5787	1	24	–	–	PUNCT
ejpam-5787	1	25	ejpam.com	ejpam.com	X
ejpam-5787	1	26	published	publish	VERB
ejpam-5787	1	27	by	by	ADP
ejpam-5787	1	28	new	new	PROPN
ejpam-5787	1	29	york	york	PROPN
ejpam-5787	1	30	business	business	PROPN
ejpam-5787	1	31	global	global	PROPN
ejpam-5787	1	32	the	the	DET
ejpam-5787	1	33	asymmetric	asymmetric	NOUN
ejpam-5787	1	34	periodically	periodically	ADV
ejpam-5787	1	35	forced	force	VERB
ejpam-5787	1	36	van	van	PROPN
ejpam-5787	1	37	der	der	PROPN
ejpam-5787	1	38	pol	pol	PROPN
ejpam-5787	1	39	oscillator	oscillator	NOUN
ejpam-5787	1	40	ibrahim	ibrahim	PROPN
ejpam-5787	1	41	alraddadi	alraddadi	PROPN
ejpam-5787	1	42	department	department	PROPN
ejpam-5787	1	43	of	of	ADP
ejpam-5787	1	44	mathematics	mathematic	NOUN
ejpam-5787	1	45	,	,	PUNCT
ejpam-5787	1	46	faculty	faculty	NOUN
ejpam-5787	1	47	of	of	ADP
ejpam-5787	1	48	science	science	NOUN
ejpam-5787	1	49	,	,	PUNCT
ejpam-5787	1	50	islamic	islamic	PROPN
ejpam-5787	1	51	university	university	PROPN
ejpam-5787	1	52	of	of	ADP
ejpam-5787	1	53	madinah	madinah	PROPN
ejpam-5787	1	54	,	,	PUNCT
ejpam-5787	1	55	medina	medina	PROPN
ejpam-5787	1	56	42210	42210	NUM
ejpam-5787	1	57	,	,	PUNCT
ejpam-5787	1	58	ksa	ksa	PROPN
ejpam-5787	1	59	abstract	abstract	NOUN
ejpam-5787	1	60	.	.	PUNCT
ejpam-5787	2	1	we	we	PRON
ejpam-5787	2	2	review	review	VERB
ejpam-5787	2	3	geometric	geometric	ADJ
ejpam-5787	2	4	singular	singular	ADJ
ejpam-5787	2	5	perturbation	perturbation	NOUN
ejpam-5787	2	6	theory	theory	NOUN
ejpam-5787	2	7	(	(	PUNCT
ejpam-5787	2	8	gspt	gspt	NOUN
ejpam-5787	2	9	)	)	PUNCT
ejpam-5787	2	10	which	which	PRON
ejpam-5787	2	11	has	have	AUX
ejpam-5787	2	12	been	be	AUX
ejpam-5787	2	13	used	use	VERB
ejpam-5787	2	14	to	to	PART
ejpam-5787	2	15	explain	explain	VERB
ejpam-5787	2	16	the	the	DET
ejpam-5787	2	17	behaviour	behaviour	NOUN
ejpam-5787	2	18	of	of	ADP
ejpam-5787	2	19	the	the	DET
ejpam-5787	2	20	singular	singular	ADJ
ejpam-5787	2	21	slow	slow	ADJ
ejpam-5787	2	22	-	-	PUNCT
ejpam-5787	2	23	fast	fast	ADJ
ejpam-5787	2	24	system	system	NOUN
ejpam-5787	2	25	near	near	ADP
ejpam-5787	2	26	the	the	DET
ejpam-5787	2	27	singular	singular	ADJ
ejpam-5787	2	28	limit	limit	NOUN
ejpam-5787	2	29	.	.	PUNCT
ejpam-5787	3	1	in	in	ADP
ejpam-5787	3	2	particular	particular	ADJ
ejpam-5787	3	3	,	,	PUNCT
ejpam-5787	3	4	we	we	PRON
ejpam-5787	3	5	follow	follow	VERB
ejpam-5787	3	6	the	the	DET
ejpam-5787	3	7	analysis	analysis	NOUN
ejpam-5787	3	8	of	of	ADP
ejpam-5787	3	9	guckenheimer	guckenheimer	PROPN
ejpam-5787	3	10	et	et	PROPN
ejpam-5787	3	11	al	al	PROPN
ejpam-5787	3	12	.	.	PUNCT
ejpam-5787	4	1	[	[	X
ejpam-5787	4	2	10	10	NUM
ejpam-5787	4	3	]	]	PUNCT
ejpam-5787	4	4	for	for	ADP
ejpam-5787	4	5	the	the	DET
ejpam-5787	4	6	periodically	periodically	ADV
ejpam-5787	4	7	forced	force	VERB
ejpam-5787	4	8	symmetric	symmetric	ADJ
ejpam-5787	4	9	van	van	PROPN
ejpam-5787	4	10	der	der	PROPN
ejpam-5787	4	11	pol	pol	PROPN
ejpam-5787	4	12	oscillator	oscillator	NOUN
ejpam-5787	4	13	(	(	PUNCT
ejpam-5787	4	14	β	β	NOUN
ejpam-5787	4	15	=	=	SYM
ejpam-5787	4	16	0	0	NUM
ejpam-5787	4	17	)	)	PUNCT
ejpam-5787	4	18	,	,	PUNCT
ejpam-5787	4	19	then	then	ADV
ejpam-5787	4	20	we	we	PRON
ejpam-5787	4	21	constructed	construct	VERB
ejpam-5787	4	22	the	the	DET
ejpam-5787	4	23	poincaré	poincaré	ADJ
ejpam-5787	4	24	return	return	NOUN
ejpam-5787	4	25	map	map	NOUN
ejpam-5787	4	26	for	for	ADP
ejpam-5787	4	27	studying	study	VERB
ejpam-5787	4	28	the	the	DET
ejpam-5787	4	29	bifurcation	bifurcation	NOUN
ejpam-5787	4	30	phenomena	phenomenon	NOUN
ejpam-5787	4	31	of	of	ADP
ejpam-5787	4	32	this	this	DET
ejpam-5787	4	33	model	model	NOUN
ejpam-5787	4	34	.	.	PUNCT
ejpam-5787	5	1	we	we	PRON
ejpam-5787	5	2	generalise	generalise	VERB
ejpam-5787	5	3	to	to	ADP
ejpam-5787	5	4	a	a	DET
ejpam-5787	5	5	asymmetric	asymmetric	ADJ
ejpam-5787	5	6	forced	force	VERB
ejpam-5787	5	7	van	van	PROPN
ejpam-5787	5	8	der	der	ADJ
ejpam-5787	5	9	pol	pol	PROPN
ejpam-5787	5	10	oscillator	oscillator	NOUN
ejpam-5787	5	11	for	for	ADP
ejpam-5787	5	12	β	β	X
ejpam-5787	5	13	̸=	̸=	PROPN
ejpam-5787	5	14	0	0	NUM
ejpam-5787	5	15	.	.	PUNCT
ejpam-5787	6	1	we	we	PRON
ejpam-5787	6	2	show	show	VERB
ejpam-5787	6	3	that	that	SCONJ
ejpam-5787	6	4	the	the	DET
ejpam-5787	6	5	forced	force	VERB
ejpam-5787	6	6	asymmetric	asymmetric	PROPN
ejpam-5787	6	7	van	van	PROPN
ejpam-5787	6	8	der	der	ADJ
ejpam-5787	6	9	pol	pol	PROPN
ejpam-5787	6	10	oscillator	oscillator	NOUN
ejpam-5787	6	11	can	can	AUX
ejpam-5787	6	12	become	become	VERB
ejpam-5787	6	13	frequency	frequency	NOUN
ejpam-5787	6	14	locked	lock	VERB
ejpam-5787	6	15	due	due	ADP
ejpam-5787	6	16	to	to	ADP
ejpam-5787	6	17	the	the	DET
ejpam-5787	6	18	forcing	forcing	NOUN
ejpam-5787	6	19	.	.	PUNCT
ejpam-5787	7	1	then	then	ADV
ejpam-5787	7	2	,	,	PUNCT
ejpam-5787	7	3	we	we	PRON
ejpam-5787	7	4	extend	extend	VERB
ejpam-5787	7	5	this	this	DET
ejpam-5787	7	6	analysis	analysis	NOUN
ejpam-5787	7	7	to	to	PART
ejpam-5787	7	8	show	show	VERB
ejpam-5787	7	9	how	how	SCONJ
ejpam-5787	7	10	the	the	DET
ejpam-5787	7	11	symmetry	symmetry	NOUN
ejpam-5787	7	12	breaking	break	VERB
ejpam-5787	7	13	parameter	parameter	NOUN
ejpam-5787	7	14	β	β	PROPN
ejpam-5787	7	15	in	in	ADP
ejpam-5787	7	16	a	a	DET
ejpam-5787	7	17	periodically	periodically	ADV
ejpam-5787	7	18	forced	force	VERB
ejpam-5787	7	19	van	van	PROPN
ejpam-5787	7	20	der	der	PROPN
ejpam-5787	7	21	pol	pol	PROPN
ejpam-5787	7	22	oscillator	oscillator	NOUN
ejpam-5787	7	23	influences	influence	VERB
ejpam-5787	7	24	the	the	DET
ejpam-5787	7	25	width	width	NOUN
ejpam-5787	7	26	of	of	ADP
ejpam-5787	7	27	arnold	arnold	PROPN
ejpam-5787	7	28	tongues	tongue	NOUN
ejpam-5787	7	29	(	(	PUNCT
ejpam-5787	7	30	also	also	ADV
ejpam-5787	7	31	known	know	VERB
ejpam-5787	7	32	as	as	ADP
ejpam-5787	7	33	frequency	frequency	NOUN
ejpam-5787	7	34	locking	locking	NOUN
ejpam-5787	7	35	regions	region	NOUN
ejpam-5787	7	36	)	)	PUNCT
ejpam-5787	7	37	,	,	PUNCT
ejpam-5787	7	38	and	and	CCONJ
ejpam-5787	7	39	we	we	PRON
ejpam-5787	7	40	find	find	VERB
ejpam-5787	7	41	these	these	DET
ejpam-5787	7	42	frequency	frequency	NOUN
ejpam-5787	7	43	locking	locking	NOUN
ejpam-5787	7	44	regions	region	NOUN
ejpam-5787	7	45	in	in	ADP
ejpam-5787	7	46	the	the	DET
ejpam-5787	7	47	parameter	parameter	NOUN
ejpam-5787	7	48	space	space	NOUN
ejpam-5787	7	49	(	(	PUNCT
ejpam-5787	7	50	a	a	PRON
ejpam-5787	7	51	,	,	PUNCT
ejpam-5787	7	52	ω	ω	NOUN
ejpam-5787	7	53	)	)	PUNCT
ejpam-5787	7	54	.	.	PUNCT
ejpam-5787	8	1	2020	2020	NUM
ejpam-5787	8	2	mathematics	mathematic	NOUN
ejpam-5787	8	3	subject	subject	NOUN
ejpam-5787	8	4	classifications	classification	NOUN
ejpam-5787	8	5	:	:	PUNCT
ejpam-5787	8	6	34c23	34c23	NUM
ejpam-5787	8	7	,	,	PUNCT
ejpam-5787	8	8	37c25	37c25	NUM
ejpam-5787	8	9	,	,	PUNCT
ejpam-5787	8	10	37	37	NUM
ejpam-5787	8	11	-	-	SYM
ejpam-5787	8	12	04	04	NUM
ejpam-5787	8	13	,	,	PUNCT
ejpam-5787	8	14	37c35	37c35	NUM
ejpam-5787	8	15	,	,	PUNCT
ejpam-5787	8	16	34c25	34c25	NUM
ejpam-5787	8	17	,	,	PUNCT
ejpam-5787	8	18	34c26	34c26	NUM
ejpam-5787	8	19	key	key	ADJ
ejpam-5787	8	20	words	word	NOUN
ejpam-5787	8	21	and	and	CCONJ
ejpam-5787	8	22	phrases	phrase	NOUN
ejpam-5787	8	23	:	:	PUNCT
ejpam-5787	8	24	dynamical	dynamical	ADJ
ejpam-5787	8	25	system	system	NOUN
ejpam-5787	8	26	,	,	PUNCT
ejpam-5787	8	27	periodic	periodic	ADJ
ejpam-5787	8	28	solutions	solution	NOUN
ejpam-5787	8	29	,	,	PUNCT
ejpam-5787	8	30	bifurcations	bifurcation	NOUN
ejpam-5787	8	31	slow	slow	ADJ
ejpam-5787	8	32	-	-	PUNCT
ejpam-5787	8	33	fast	fast	ADJ
ejpam-5787	8	34	nonlinear	nonlinear	ADJ
ejpam-5787	8	35	oscillator	oscillator	NOUN
ejpam-5787	8	36	models	model	NOUN
ejpam-5787	8	37	can	can	AUX
ejpam-5787	8	38	have	have	VERB
ejpam-5787	8	39	periodic	periodic	ADJ
ejpam-5787	8	40	orbits	orbit	NOUN
ejpam-5787	8	41	with	with	ADP
ejpam-5787	8	42	alternating	alternate	VERB
ejpam-5787	8	43	slow	slow	ADJ
ejpam-5787	8	44	and	and	CCONJ
ejpam-5787	8	45	fast	fast	ADJ
ejpam-5787	8	46	motion	motion	NOUN
ejpam-5787	8	47	that	that	PRON
ejpam-5787	8	48	are	be	AUX
ejpam-5787	8	49	called	call	VERB
ejpam-5787	8	50	relaxation	relaxation	NOUN
ejpam-5787	8	51	oscillations	oscillation	NOUN
ejpam-5787	8	52	[	[	X
ejpam-5787	8	53	11	11	NUM
ejpam-5787	8	54	]	]	PUNCT
ejpam-5787	8	55	.	.	PUNCT
ejpam-5787	9	1	these	these	DET
ejpam-5787	9	2	oscillations	oscillation	NOUN
ejpam-5787	9	3	occur	occur	VERB
ejpam-5787	9	4	at	at	ADP
ejpam-5787	9	5	different	different	ADJ
ejpam-5787	9	6	times	time	NOUN
ejpam-5787	9	7	in	in	ADP
ejpam-5787	9	8	slow	slow	ADJ
ejpam-5787	9	9	-	-	PUNCT
ejpam-5787	9	10	fast	fast	ADJ
ejpam-5787	9	11	dynamical	dynamical	ADJ
ejpam-5787	9	12	systems	system	NOUN
ejpam-5787	9	13	.	.	PUNCT
ejpam-5787	10	1	relaxation	relaxation	NOUN
ejpam-5787	10	2	oscillators	oscillator	NOUN
ejpam-5787	10	3	have	have	AUX
ejpam-5787	10	4	been	be	AUX
ejpam-5787	10	5	used	use	VERB
ejpam-5787	10	6	to	to	PART
ejpam-5787	10	7	understand	understand	VERB
ejpam-5787	10	8	a	a	DET
ejpam-5787	10	9	wide	wide	ADJ
ejpam-5787	10	10	range	range	NOUN
ejpam-5787	10	11	of	of	ADP
ejpam-5787	10	12	biological	biological	ADJ
ejpam-5787	10	13	problems	problem	NOUN
ejpam-5787	10	14	such	such	ADJ
ejpam-5787	10	15	as	as	ADP
ejpam-5787	10	16	heartbeat	heartbeat	NOUN
ejpam-5787	10	17	(	(	PUNCT
ejpam-5787	10	18	van	van	PROPN
ejpam-5787	10	19	der	der	PROPN
ejpam-5787	10	20	mark	mark	PROPN
ejpam-5787	10	21	and	and	CCONJ
ejpam-5787	10	22	van	van	PROPN
ejpam-5787	10	23	der	der	PROPN
ejpam-5787	10	24	pol	pol	PROPN
ejpam-5787	10	25	model	model	NOUN
ejpam-5787	10	26	[	[	X
ejpam-5787	10	27	29	29	NUM
ejpam-5787	10	28	]	]	SYM
ejpam-5787	10	29	)	)	PUNCT
ejpam-5787	10	30	,	,	PUNCT
ejpam-5787	10	31	neuronal	neuronal	ADJ
ejpam-5787	10	32	activity	activity	NOUN
ejpam-5787	10	33	(	(	PUNCT
ejpam-5787	10	34	the	the	DET
ejpam-5787	10	35	fitz	fitz	PROPN
ejpam-5787	10	36	-	-	PUNCT
ejpam-5787	10	37	hugh	hugh	PROPN
ejpam-5787	10	38	-	-	PUNCT
ejpam-5787	10	39	nagumo	nagumo	ADJ
ejpam-5787	10	40	model	model	NOUN
ejpam-5787	10	41	and	and	CCONJ
ejpam-5787	10	42	the	the	DET
ejpam-5787	10	43	morris	morris	PROPN
ejpam-5787	10	44	-	-	PUNCT
ejpam-5787	10	45	lecar	lecar	ADJ
ejpam-5787	10	46	model	model	NOUN
ejpam-5787	10	47	[	[	X
ejpam-5787	10	48	13	13	NUM
ejpam-5787	10	49	]	]	NUM
ejpam-5787	10	50	)	)	PUNCT
ejpam-5787	10	51	,	,	PUNCT
ejpam-5787	10	52	and	and	CCONJ
ejpam-5787	10	53	population	population	NOUN
ejpam-5787	10	54	cycles	cycle	NOUN
ejpam-5787	10	55	of	of	ADP
ejpam-5787	10	56	predator	predator	NOUN
ejpam-5787	10	57	-	-	PUNCT
ejpam-5787	10	58	prey	prey	NOUN
ejpam-5787	10	59	type	type	NOUN
ejpam-5787	10	60	[	[	X
ejpam-5787	10	61	23	23	NUM
ejpam-5787	10	62	]	]	PUNCT
ejpam-5787	10	63	.	.	PUNCT
ejpam-5787	11	1	since	since	SCONJ
ejpam-5787	11	2	1920	1920	NUM
ejpam-5787	11	3	,	,	PUNCT
ejpam-5787	11	4	the	the	DET
ejpam-5787	11	5	van	van	PROPN
ejpam-5787	11	6	der	der	PROPN
ejpam-5787	11	7	pol	pol	PROPN
ejpam-5787	11	8	oscillator	oscillator	NOUN
ejpam-5787	11	9	was	be	AUX
ejpam-5787	11	10	introduced	introduce	VERB
ejpam-5787	11	11	to	to	PART
ejpam-5787	11	12	illustrate	illustrate	VERB
ejpam-5787	11	13	the	the	DET
ejpam-5787	11	14	behaviour	behaviour	NOUN
ejpam-5787	11	15	observed	observe	VERB
ejpam-5787	11	16	in	in	ADP
ejpam-5787	11	17	electrical	electrical	ADJ
ejpam-5787	11	18	circuits	circuit	NOUN
ejpam-5787	11	19	by	by	ADP
ejpam-5787	11	20	balthazar	balthazar	PROPN
ejpam-5787	11	21	van	van	PROPN
ejpam-5787	11	22	der	der	PROPN
ejpam-5787	11	23	pol	pol	PROPN
ejpam-5787	11	24	and	and	CCONJ
ejpam-5787	11	25	van	van	PROPN
ejpam-5787	11	26	der	der	PROPN
ejpam-5787	11	27	mark	mark	NOUN
ejpam-5787	11	28	[	[	X
ejpam-5787	11	29	27	27	NUM
ejpam-5787	11	30	]	]	PUNCT
ejpam-5787	11	31	.	.	PUNCT
ejpam-5787	12	1	the	the	DET
ejpam-5787	12	2	van	van	PROPN
ejpam-5787	12	3	der	der	PROPN
ejpam-5787	12	4	pol	pol	PROPN
ejpam-5787	12	5	oscillator	oscillator	NOUN
ejpam-5787	12	6	is	be	AUX
ejpam-5787	12	7	a	a	DET
ejpam-5787	12	8	type	type	NOUN
ejpam-5787	12	9	of	of	ADP
ejpam-5787	12	10	a	a	DET
ejpam-5787	12	11	relaxation	relaxation	NOUN
ejpam-5787	12	12	oscillator	oscillator	NOUN
ejpam-5787	12	13	.	.	PUNCT
ejpam-5787	13	1	van	van	PROPN
ejpam-5787	13	2	der	der	PROPN
ejpam-5787	13	3	pol	pol	PROPN
ejpam-5787	13	4	and	and	CCONJ
ejpam-5787	13	5	mark	mark	PROPN
ejpam-5787	13	6	investigated	investigate	VERB
ejpam-5787	13	7	that	that	SCONJ
ejpam-5787	13	8	the	the	DET
ejpam-5787	13	9	relaxation	relaxation	NOUN
ejpam-5787	13	10	oscillation	oscillation	NOUN
ejpam-5787	13	11	of	of	ADP
ejpam-5787	13	12	the	the	DET
ejpam-5787	13	13	van	van	PROPN
ejpam-5787	13	14	der	der	PROPN
ejpam-5787	13	15	pol	pol	PROPN
ejpam-5787	13	16	oscillator	oscillator	NOUN
ejpam-5787	13	17	is	be	AUX
ejpam-5787	13	18	influenced	influence	VERB
ejpam-5787	13	19	by	by	ADP
ejpam-5787	13	20	external	external	ADJ
ejpam-5787	13	21	periodic	periodic	ADJ
ejpam-5787	13	22	forcing	forcing	NOUN
ejpam-5787	13	23	.	.	PUNCT
ejpam-5787	14	1	they	they	PRON
ejpam-5787	14	2	found	find	VERB
ejpam-5787	14	3	that	that	SCONJ
ejpam-5787	14	4	the	the	DET
ejpam-5787	14	5	period	period	NOUN
ejpam-5787	14	6	of	of	ADP
ejpam-5787	14	7	the	the	DET
ejpam-5787	14	8	relaxation	relaxation	NOUN
ejpam-5787	14	9	oscillation	oscillation	NOUN
ejpam-5787	14	10	was	be	AUX
ejpam-5787	14	11	a	a	DET
ejpam-5787	14	12	proportion	proportion	NOUN
ejpam-5787	14	13	of	of	ADP
ejpam-5787	14	14	the	the	DET
ejpam-5787	14	15	forcing	force	VERB
ejpam-5787	14	16	period	period	NOUN
ejpam-5787	14	17	over	over	ADP
ejpam-5787	14	18	wide	wide	ADJ
ejpam-5787	14	19	parameter	parameter	NOUN
ejpam-5787	14	20	regimes	regime	NOUN
ejpam-5787	14	21	,	,	PUNCT
ejpam-5787	14	22	called	call	VERB
ejpam-5787	14	23	“	"	PUNCT
ejpam-5787	14	24	frequency	frequency	NOUN
ejpam-5787	14	25	demultiplication	demultiplication	NOUN
ejpam-5787	14	26	”	"	PUNCT
ejpam-5787	15	1	[	[	X
ejpam-5787	15	2	28	28	NUM
ejpam-5787	15	3	]	]	PUNCT
ejpam-5787	15	4	.	.	PUNCT
ejpam-5787	16	1	this	this	DET
ejpam-5787	16	2	phenomenon	phenomenon	NOUN
ejpam-5787	16	3	is	be	AUX
ejpam-5787	16	4	now	now	ADV
ejpam-5787	16	5	known	know	VERB
ejpam-5787	16	6	as	as	ADP
ejpam-5787	16	7	frequency	frequency	NOUN
ejpam-5787	16	8	locking	locking	NOUN
ejpam-5787	16	9	,	,	PUNCT
ejpam-5787	16	10	phase	phase	NOUN
ejpam-5787	16	11	locking	locking	NOUN
ejpam-5787	16	12	,	,	PUNCT
ejpam-5787	16	13	entrainment	entrainment	NOUN
ejpam-5787	16	14	or	or	CCONJ
ejpam-5787	16	15	mode	mode	NOUN
ejpam-5787	16	16	locking	lock	VERB
ejpam-5787	16	17	[	[	PUNCT
ejpam-5787	16	18	16	16	NUM
ejpam-5787	16	19	]	]	PUNCT
ejpam-5787	16	20	.	.	PUNCT
ejpam-5787	17	1	there	there	PRON
ejpam-5787	17	2	has	have	AUX
ejpam-5787	17	3	been	be	AUX
ejpam-5787	17	4	a	a	DET
ejpam-5787	17	5	lot	lot	NOUN
ejpam-5787	17	6	of	of	ADP
ejpam-5787	17	7	significant	significant	ADJ
ejpam-5787	17	8	research	research	NOUN
ejpam-5787	17	9	done	do	VERB
ejpam-5787	17	10	on	on	ADP
ejpam-5787	17	11	the	the	DET
ejpam-5787	17	12	forced	force	VERB
ejpam-5787	17	13	van	van	PROPN
ejpam-5787	17	14	der	der	ADJ
ejpam-5787	17	15	pol	pol	PROPN
ejpam-5787	17	16	oscillator	oscillator	NOUN
ejpam-5787	17	17	(	(	PUNCT
ejpam-5787	17	18	see	see	VERB
ejpam-5787	17	19	e.g.[5	e.g.[5	NOUN
ejpam-5787	17	20	,	,	PUNCT
ejpam-5787	17	21	10	10	NUM
ejpam-5787	17	22	,	,	PUNCT
ejpam-5787	17	23	18	18	NUM
ejpam-5787	17	24	]	]	PUNCT
ejpam-5787	17	25	)	)	PUNCT
ejpam-5787	17	26	.	.	PUNCT
ejpam-5787	18	1	the	the	DET
ejpam-5787	18	2	van	van	PROPN
ejpam-5787	18	3	der	der	PROPN
ejpam-5787	18	4	pol	pol	PROPN
ejpam-5787	18	5	oscillator	oscillator	NOUN
ejpam-5787	18	6	is	be	AUX
ejpam-5787	18	7	applied	apply	VERB
ejpam-5787	18	8	in	in	ADP
ejpam-5787	18	9	several	several	ADJ
ejpam-5787	18	10	fields	field	NOUN
ejpam-5787	18	11	,	,	PUNCT
ejpam-5787	18	12	such	such	ADJ
ejpam-5787	18	13	doi	doi	NOUN
ejpam-5787	18	14	:	:	PUNCT
ejpam-5787	18	15	https://doi.org/10.29020/nybg.ejpam.v18i1.5787	https://doi.org/10.29020/nybg.ejpam.v18i1.5787	PRON
ejpam-5787	18	16	email	email	NOUN
ejpam-5787	18	17	address	address	NOUN
ejpam-5787	18	18	:	:	PUNCT
ejpam-5787	18	19	ialraddadi@iu.edu.sa	ialraddadi@iu.edu.sa	PROPN
ejpam-5787	18	20	(	(	PUNCT
ejpam-5787	18	21	i.	i.	NOUN
ejpam-5787	18	22	alraddadi	alraddadi	PROPN
ejpam-5787	18	23	)	)	PUNCT
ejpam-5787	18	24	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5787	18	25	1	1	NUM
ejpam-5787	18	26	copyright	copyright	NOUN
ejpam-5787	18	27	:	:	PUNCT
ejpam-5787	18	28	©	©	PROPN
ejpam-5787	18	29	2025	2025	NUM
ejpam-5787	18	30	the	the	DET
ejpam-5787	18	31	author(s	author(s	NOUN
ejpam-5787	18	32	)	)	PUNCT
ejpam-5787	18	33	.	.	PUNCT
ejpam-5787	19	1	(	(	PUNCT
ejpam-5787	19	2	cc	cc	NOUN
ejpam-5787	19	3	by	by	ADP
ejpam-5787	19	4	-	-	PUNCT
ejpam-5787	19	5	nc	nc	PROPN
ejpam-5787	19	6	4.0	4.0	NUM
ejpam-5787	19	7	)	)	PUNCT
ejpam-5787	19	8	i.	i.	NOUN
ejpam-5787	19	9	alraddadi	alraddadi	PROPN
ejpam-5787	19	10	/	/	SYM
ejpam-5787	19	11	eur	eur	PROPN
ejpam-5787	19	12	.	.	PUNCT
ejpam-5787	20	1	j.	j.	PROPN
ejpam-5787	20	2	pure	pure	PROPN
ejpam-5787	20	3	appl	appl	PROPN
ejpam-5787	20	4	.	.	PROPN
ejpam-5787	20	5	math	math	PROPN
ejpam-5787	20	6	,	,	PUNCT
ejpam-5787	20	7	18	18	NUM
ejpam-5787	20	8	(	(	PUNCT
ejpam-5787	20	9	1	1	NUM
ejpam-5787	20	10	)	)	PUNCT
ejpam-5787	20	11	(	(	PUNCT
ejpam-5787	20	12	2025	2025	NUM
ejpam-5787	20	13	)	)	PUNCT
ejpam-5787	20	14	,	,	PUNCT
ejpam-5787	20	15	5787	5787	NUM
ejpam-5787	20	16	2	2	NUM
ejpam-5787	20	17	of	of	ADP
ejpam-5787	20	18	23	23	NUM
ejpam-5787	20	19	as	as	ADP
ejpam-5787	20	20	oscillatory	oscillatory	ADJ
ejpam-5787	20	21	processes	process	NOUN
ejpam-5787	20	22	in	in	ADP
ejpam-5787	20	23	physics	physics	NOUN
ejpam-5787	20	24	,	,	PUNCT
ejpam-5787	20	25	electronics	electronic	NOUN
ejpam-5787	20	26	,	,	PUNCT
ejpam-5787	20	27	neurobiology	neurobiology	NOUN
ejpam-5787	20	28	,	,	PUNCT
ejpam-5787	20	29	and	and	CCONJ
ejpam-5787	20	30	the	the	DET
ejpam-5787	20	31	dynamics	dynamic	NOUN
ejpam-5787	20	32	of	of	ADP
ejpam-5787	20	33	glacial	glacial	ADJ
ejpam-5787	20	34	cycles	cycle	NOUN
ejpam-5787	20	35	[	[	X
ejpam-5787	20	36	3	3	NUM
ejpam-5787	20	37	,	,	PUNCT
ejpam-5787	20	38	6–8	6–8	PROPN
ejpam-5787	20	39	,	,	PUNCT
ejpam-5787	20	40	12	12	NUM
ejpam-5787	20	41	,	,	PUNCT
ejpam-5787	20	42	14	14	NUM
ejpam-5787	20	43	,	,	PUNCT
ejpam-5787	20	44	20	20	NUM
ejpam-5787	20	45	]	]	PUNCT
ejpam-5787	20	46	.	.	PUNCT
ejpam-5787	21	1	forced	force	VERB
ejpam-5787	21	2	nonlinear	nonlinear	ADJ
ejpam-5787	21	3	oscillator	oscillator	NOUN
ejpam-5787	21	4	models	model	NOUN
ejpam-5787	21	5	can	can	AUX
ejpam-5787	21	6	reproduce	reproduce	VERB
ejpam-5787	21	7	the	the	DET
ejpam-5787	21	8	oscillations	oscillation	NOUN
ejpam-5787	21	9	in	in	ADP
ejpam-5787	21	10	the	the	DET
ejpam-5787	21	11	climate	climate	NOUN
ejpam-5787	21	12	record	record	NOUN
ejpam-5787	21	13	.	.	PUNCT
ejpam-5787	22	1	examples	example	NOUN
ejpam-5787	22	2	of	of	ADP
ejpam-5787	22	3	two	two	NUM
ejpam-5787	22	4	-	-	PUNCT
ejpam-5787	22	5	dimensional	dimensional	ADJ
ejpam-5787	22	6	pleistocene	pleistocene	NOUN
ejpam-5787	22	7	ice	ice	NOUN
ejpam-5787	22	8	age	age	NOUN
ejpam-5787	22	9	models	model	NOUN
ejpam-5787	22	10	are	be	AUX
ejpam-5787	22	11	the	the	DET
ejpam-5787	22	12	forced	force	VERB
ejpam-5787	22	13	van	van	PROPN
ejpam-5787	22	14	der	der	ADJ
ejpam-5787	22	15	pol	pol	NOUN
ejpam-5787	22	16	and	and	CCONJ
ejpam-5787	22	17	the	the	DET
ejpam-5787	22	18	forced	force	VERB
ejpam-5787	22	19	van	van	PROPN
ejpam-5787	22	20	der	der	PROPN
ejpam-5787	22	21	pol	pol	NOUN
ejpam-5787	22	22	duffing	duffe	VERB
ejpam-5787	22	23	oscillators	oscillator	NOUN
ejpam-5787	22	24	[	[	X
ejpam-5787	22	25	2	2	NUM
ejpam-5787	22	26	]	]	PUNCT
ejpam-5787	22	27	.	.	PUNCT
ejpam-5787	23	1	crucifix	crucifix	PROPN
ejpam-5787	23	2	used	use	VERB
ejpam-5787	23	3	in	in	ADP
ejpam-5787	23	4	[	[	X
ejpam-5787	23	5	6	6	NUM
ejpam-5787	23	6	]	]	PUNCT
ejpam-5787	23	7	a	a	DET
ejpam-5787	23	8	forced	force	VERB
ejpam-5787	23	9	van	van	PROPN
ejpam-5787	23	10	der	der	ADJ
ejpam-5787	23	11	pol	pol	PROPN
ejpam-5787	23	12	oscillator	oscillator	PROPN
ejpam-5787	23	13	(	(	PUNCT
ejpam-5787	23	14	vdp	vdp	PROPN
ejpam-5787	23	15	)	)	PUNCT
ejpam-5787	23	16	to	to	PART
ejpam-5787	23	17	consider	consider	VERB
ejpam-5787	23	18	astronomical	astronomical	ADJ
ejpam-5787	23	19	forcing	forcing	NOUN
ejpam-5787	23	20	and	and	CCONJ
ejpam-5787	23	21	asymmetry	asymmetry	NOUN
ejpam-5787	23	22	between	between	ADP
ejpam-5787	23	23	the	the	DET
ejpam-5787	23	24	phases	phase	NOUN
ejpam-5787	23	25	of	of	ADP
ejpam-5787	23	26	ice	ice	NOUN
ejpam-5787	23	27	forming	form	VERB
ejpam-5787	23	28	and	and	CCONJ
ejpam-5787	23	29	melting	melt	VERB
ejpam-5787	23	30	during	during	ADP
ejpam-5787	23	31	the	the	DET
ejpam-5787	23	32	late	late	ADJ
ejpam-5787	23	33	pleistocene	pleistocene	NOUN
ejpam-5787	23	34	.	.	PUNCT
ejpam-5787	24	1	additionally	additionally	ADV
ejpam-5787	24	2	,	,	PUNCT
ejpam-5787	24	3	the	the	DET
ejpam-5787	24	4	van	van	PROPN
ejpam-5787	24	5	der	der	PROPN
ejpam-5787	24	6	pol	pol	PROPN
ejpam-5787	24	7	oscillator	oscillator	NOUN
ejpam-5787	24	8	has	have	AUX
ejpam-5787	24	9	been	be	AUX
ejpam-5787	24	10	modified	modify	VERB
ejpam-5787	24	11	to	to	PART
ejpam-5787	24	12	explain	explain	VERB
ejpam-5787	24	13	the	the	DET
ejpam-5787	24	14	different	different	ADJ
ejpam-5787	24	15	levels	level	NOUN
ejpam-5787	24	16	of	of	ADP
ejpam-5787	24	17	ice	ice	NOUN
ejpam-5787	24	18	volume	volume	NOUN
ejpam-5787	24	19	that	that	PRON
ejpam-5787	24	20	indicate	indicate	VERB
ejpam-5787	24	21	a	a	DET
ejpam-5787	24	22	glacial	glacial	ADJ
ejpam-5787	24	23	or	or	CCONJ
ejpam-5787	24	24	interglacial	interglacial	ADJ
ejpam-5787	24	25	case	case	NOUN
ejpam-5787	24	26	by	by	ADP
ejpam-5787	24	27	the	the	DET
ejpam-5787	24	28	signal	signal	NOUN
ejpam-5787	24	29	of	of	ADP
ejpam-5787	24	30	oscillates[7	oscillates[7	NOUN
ejpam-5787	24	31	]	]	X
ejpam-5787	24	32	.	.	PUNCT
ejpam-5787	25	1	de	de	X
ejpam-5787	25	2	saedeleer	saedeleer	PROPN
ejpam-5787	25	3	et	et	PROPN
ejpam-5787	25	4	al	al	PROPN
ejpam-5787	25	5	.	.	PUNCT
ejpam-5787	26	1	[	[	X
ejpam-5787	26	2	7	7	X
ejpam-5787	26	3	]	]	PUNCT
ejpam-5787	26	4	used	use	VERB
ejpam-5787	26	5	the	the	DET
ejpam-5787	26	6	van	van	PROPN
ejpam-5787	26	7	der	der	ADJ
ejpam-5787	26	8	pol	pol	PROPN
ejpam-5787	26	9	oscillator	oscillator	NOUN
ejpam-5787	26	10	as	as	ADP
ejpam-5787	26	11	a	a	DET
ejpam-5787	26	12	possible	possible	ADJ
ejpam-5787	26	13	low	low	ADJ
ejpam-5787	26	14	-	-	PUNCT
ejpam-5787	26	15	order	order	NOUN
ejpam-5787	26	16	model	model	NOUN
ejpam-5787	26	17	for	for	ADP
ejpam-5787	26	18	the	the	DET
ejpam-5787	26	19	first	first	ADJ
ejpam-5787	26	20	time	time	NOUN
ejpam-5787	26	21	identification	identification	NOUN
ejpam-5787	26	22	generalised	generalise	VERB
ejpam-5787	26	23	synchronisation	synchronisation	NOUN
ejpam-5787	26	24	(	(	PUNCT
ejpam-5787	26	25	see	see	VERB
ejpam-5787	26	26	more	more	ADJ
ejpam-5787	26	27	[	[	X
ejpam-5787	26	28	1	1	NUM
ejpam-5787	26	29	,	,	PUNCT
ejpam-5787	26	30	20	20	NUM
ejpam-5787	26	31	,	,	PUNCT
ejpam-5787	26	32	24	24	NUM
ejpam-5787	26	33	]	]	PUNCT
ejpam-5787	26	34	)	)	PUNCT
ejpam-5787	26	35	between	between	ADP
ejpam-5787	26	36	ice	ice	NOUN
ejpam-5787	26	37	age	age	NOUN
ejpam-5787	26	38	cycles	cycle	NOUN
ejpam-5787	26	39	and	and	CCONJ
ejpam-5787	26	40	astronomical	astronomical	ADJ
ejpam-5787	26	41	forcing	forcing	NOUN
ejpam-5787	26	42	.	.	PUNCT
ejpam-5787	27	1	the	the	DET
ejpam-5787	27	2	forced	force	VERB
ejpam-5787	27	3	vdp	vdp	PROPN
ejpam-5787	27	4	oscillator	oscillator	NOUN
ejpam-5787	27	5	is	be	AUX
ejpam-5787	27	6	used	use	VERB
ejpam-5787	27	7	by	by	ADP
ejpam-5787	27	8	ditlevsen	ditlevsen	PROPN
ejpam-5787	27	9	and	and	CCONJ
ejpam-5787	27	10	ashwin	ashwin	PROPN
ejpam-5787	27	11	as	as	ADP
ejpam-5787	27	12	a	a	DET
ejpam-5787	27	13	conceptual	conceptual	ADJ
ejpam-5787	27	14	model	model	NOUN
ejpam-5787	27	15	to	to	PART
ejpam-5787	27	16	describe	describe	VERB
ejpam-5787	27	17	the	the	DET
ejpam-5787	27	18	dynamics	dynamic	NOUN
ejpam-5787	27	19	of	of	ADP
ejpam-5787	27	20	glacial	glacial	ADJ
ejpam-5787	27	21	cycles	cycle	NOUN
ejpam-5787	27	22	and	and	CCONJ
ejpam-5787	27	23	possible	possible	ADJ
ejpam-5787	27	24	dynamical	dynamical	ADJ
ejpam-5787	27	25	causes	cause	NOUN
ejpam-5787	27	26	of	of	ADP
ejpam-5787	27	27	the	the	DET
ejpam-5787	27	28	middle	middle	PROPN
ejpam-5787	27	29	pleistocene	pleistocene	PROPN
ejpam-5787	27	30	transition	transition	NOUN
ejpam-5787	27	31	(	(	PUNCT
ejpam-5787	27	32	mpt)[8	mpt)[8	NOUN
ejpam-5787	27	33	]	]	PUNCT
ejpam-5787	27	34	.	.	PUNCT
ejpam-5787	28	1	in	in	ADP
ejpam-5787	28	2	this	this	DET
ejpam-5787	28	3	paper	paper	NOUN
ejpam-5787	28	4	,	,	PUNCT
ejpam-5787	28	5	we	we	PRON
ejpam-5787	28	6	use	use	VERB
ejpam-5787	28	7	geometric	geometric	ADJ
ejpam-5787	28	8	singular	singular	ADJ
ejpam-5787	28	9	perturbation	perturbation	NOUN
ejpam-5787	28	10	theory	theory	NOUN
ejpam-5787	28	11	(	(	PUNCT
ejpam-5787	28	12	gspt	gspt	NOUN
ejpam-5787	28	13	)	)	PUNCT
ejpam-5787	28	14	to	to	PART
ejpam-5787	28	15	explain	explain	VERB
ejpam-5787	28	16	the	the	DET
ejpam-5787	28	17	behaviour	behaviour	NOUN
ejpam-5787	28	18	of	of	ADP
ejpam-5787	28	19	the	the	DET
ejpam-5787	28	20	singular	singular	ADJ
ejpam-5787	28	21	slow	slow	ADJ
ejpam-5787	28	22	-	-	PUNCT
ejpam-5787	28	23	fast	fast	ADJ
ejpam-5787	28	24	oscillator	oscillator	NOUN
ejpam-5787	28	25	near	near	ADP
ejpam-5787	28	26	the	the	DET
ejpam-5787	28	27	singular	singular	ADJ
ejpam-5787	28	28	limit	limit	NOUN
ejpam-5787	28	29	(	(	PUNCT
ejpam-5787	28	30	see	see	VERB
ejpam-5787	28	31	more	more	ADJ
ejpam-5787	28	32	[	[	X
ejpam-5787	28	33	19	19	NUM
ejpam-5787	28	34	]	]	NUM
ejpam-5787	28	35	)	)	PUNCT
ejpam-5787	28	36	.	.	PUNCT
ejpam-5787	29	1	in	in	ADP
ejpam-5787	29	2	particular	particular	ADJ
ejpam-5787	29	3	,	,	PUNCT
ejpam-5787	29	4	we	we	PRON
ejpam-5787	29	5	followed	follow	VERB
ejpam-5787	29	6	the	the	DET
ejpam-5787	29	7	analysis	analysis	NOUN
ejpam-5787	29	8	of	of	ADP
ejpam-5787	29	9	guckenheimer	guckenheimer	PROPN
ejpam-5787	29	10	et	et	PROPN
ejpam-5787	29	11	al	al	PROPN
ejpam-5787	29	12	.	.	PUNCT
ejpam-5787	30	1	[	[	X
ejpam-5787	30	2	10	10	NUM
ejpam-5787	30	3	]	]	PUNCT
ejpam-5787	30	4	for	for	ADP
ejpam-5787	30	5	the	the	DET
ejpam-5787	30	6	periodically	periodically	ADV
ejpam-5787	30	7	forced	force	VERB
ejpam-5787	30	8	symmetric	symmetric	ADJ
ejpam-5787	30	9	van	van	PROPN
ejpam-5787	30	10	der	der	PROPN
ejpam-5787	30	11	pol	pol	PROPN
ejpam-5787	30	12	oscillator	oscillator	NOUN
ejpam-5787	30	13	(	(	PUNCT
ejpam-5787	30	14	β	β	NOUN
ejpam-5787	30	15	=	=	NOUN
ejpam-5787	30	16	0	0	NUM
ejpam-5787	30	17	)	)	PUNCT
ejpam-5787	30	18	.	.	PUNCT
ejpam-5787	31	1	section	section	NOUN
ejpam-5787	31	2	3	3	NUM
ejpam-5787	31	3	constructs	construct	VERB
ejpam-5787	31	4	the	the	DET
ejpam-5787	31	5	poincaré	poincaré	ADJ
ejpam-5787	31	6	return	return	NOUN
ejpam-5787	31	7	map	map	NOUN
ejpam-5787	31	8	for	for	ADP
ejpam-5787	31	9	studying	study	VERB
ejpam-5787	31	10	the	the	DET
ejpam-5787	31	11	bifurcation	bifurcation	NOUN
ejpam-5787	31	12	phenomena	phenomenon	NOUN
ejpam-5787	31	13	of	of	ADP
ejpam-5787	31	14	this	this	DET
ejpam-5787	31	15	model	model	NOUN
ejpam-5787	31	16	.	.	PUNCT
ejpam-5787	32	1	in	in	ADP
ejpam-5787	32	2	section	section	NOUN
ejpam-5787	32	3	4	4	NUM
ejpam-5787	32	4	,	,	PUNCT
ejpam-5787	32	5	we	we	PRON
ejpam-5787	32	6	show	show	VERB
ejpam-5787	32	7	how	how	SCONJ
ejpam-5787	32	8	the	the	DET
ejpam-5787	32	9	symmetry	symmetry	NOUN
ejpam-5787	32	10	breaking	break	VERB
ejpam-5787	32	11	parameter	parameter	NOUN
ejpam-5787	32	12	β	β	PROPN
ejpam-5787	32	13	in	in	ADP
ejpam-5787	32	14	a	a	DET
ejpam-5787	32	15	periodically	periodically	ADV
ejpam-5787	32	16	forced	force	VERB
ejpam-5787	32	17	van	van	PROPN
ejpam-5787	32	18	der	der	PROPN
ejpam-5787	32	19	pol	pol	PROPN
ejpam-5787	32	20	oscillator	oscillator	NOUN
ejpam-5787	32	21	influences	influence	VERB
ejpam-5787	32	22	the	the	DET
ejpam-5787	32	23	width	width	NOUN
ejpam-5787	32	24	of	of	ADP
ejpam-5787	32	25	arnold	arnold	PROPN
ejpam-5787	32	26	tongues	tongue	NOUN
ejpam-5787	32	27	(	(	PUNCT
ejpam-5787	32	28	also	also	ADV
ejpam-5787	32	29	known	know	VERB
ejpam-5787	32	30	as	as	ADP
ejpam-5787	32	31	frequency	frequency	NOUN
ejpam-5787	32	32	locking	locking	NOUN
ejpam-5787	32	33	regions	region	NOUN
ejpam-5787	32	34	)	)	PUNCT
ejpam-5787	32	35	.	.	PUNCT
ejpam-5787	33	1	1	1	X
ejpam-5787	33	2	.	.	X
ejpam-5787	33	3	the	the	DET
ejpam-5787	33	4	asymmetric	asymmetric	ADJ
ejpam-5787	33	5	van	van	PROPN
ejpam-5787	33	6	der	der	PROPN
ejpam-5787	33	7	pol	pol	NOUN
ejpam-5787	33	8	oscillator	oscillator	NOUN
ejpam-5787	33	9	we	we	PRON
ejpam-5787	33	10	consider	consider	VERB
ejpam-5787	33	11	the	the	DET
ejpam-5787	33	12	modified	modify	VERB
ejpam-5787	33	13	van	van	PROPN
ejpam-5787	33	14	der	der	ADJ
ejpam-5787	33	15	pol	pol	PROPN
ejpam-5787	33	16	oscillator	oscillator	NOUN
ejpam-5787	33	17	[	[	X
ejpam-5787	33	18	2	2	NUM
ejpam-5787	33	19	]	]	PUNCT
ejpam-5787	33	20	which	which	PRON
ejpam-5787	33	21	was	be	AUX
ejpam-5787	33	22	proposed	propose	VERB
ejpam-5787	33	23	as	as	ADP
ejpam-5787	33	24	a	a	DET
ejpam-5787	33	25	low	low	ADJ
ejpam-5787	33	26	-	-	PUNCT
ejpam-5787	33	27	order	order	NOUN
ejpam-5787	33	28	model	model	NOUN
ejpam-5787	33	29	of	of	ADP
ejpam-5787	33	30	the	the	DET
ejpam-5787	33	31	ice	ice	NOUN
ejpam-5787	33	32	-	-	PUNCT
ejpam-5787	33	33	age	age	NOUN
ejpam-5787	33	34	cycles	cycle	NOUN
ejpam-5787	33	35	in	in	ADP
ejpam-5787	33	36	[	[	X
ejpam-5787	33	37	6	6	NUM
ejpam-5787	33	38	,	,	PUNCT
ejpam-5787	33	39	7	7	NUM
ejpam-5787	33	40	]	]	PUNCT
ejpam-5787	33	41	.	.	PUNCT
ejpam-5787	34	1	the	the	DET
ejpam-5787	34	2	generalised	generalise	VERB
ejpam-5787	34	3	van	van	PROPN
ejpam-5787	34	4	der	der	PROPN
ejpam-5787	34	5	pol	pol	PROPN
ejpam-5787	34	6	model	model	NOUN
ejpam-5787	34	7	has	have	VERB
ejpam-5787	34	8	the	the	DET
ejpam-5787	34	9	following	follow	VERB
ejpam-5787	34	10	form	form	NOUN
ejpam-5787	34	11	[	[	X
ejpam-5787	34	12	2	2	NUM
ejpam-5787	34	13	]	]	NUM
ejpam-5787	34	14	:	:	PUNCT
ejpam-5787	34	15	τ2κ2	τ2κ2	PUNCT
ejpam-5787	34	16	d2y	d2y	PUNCT
ejpam-5787	34	17	dt2	dt2	NOUN
ejpam-5787	34	18	−	−	PROPN
ejpam-5787	34	19	ατκ(1−	ατκ(1−	PROPN
ejpam-5787	34	20	y2	y2	NOUN
ejpam-5787	34	21	)	)	PUNCT
ejpam-5787	34	22	dy	dy	NOUN
ejpam-5787	34	23	dt	dt	NOUN
ejpam-5787	35	1	+	+	CCONJ
ejpam-5787	35	2	y	y	PROPN
ejpam-5787	35	3	−	−	NOUN
ejpam-5787	35	4	γf	γf	PROPN
ejpam-5787	35	5	(	(	PUNCT
ejpam-5787	35	6	t	t	PROPN
ejpam-5787	35	7	)	)	PUNCT
ejpam-5787	35	8	+	+	NUM
ejpam-5787	35	9	β	β	X
ejpam-5787	35	10	=	=	SYM
ejpam-5787	35	11	0	0	PUNCT
ejpam-5787	35	12	(	(	PUNCT
ejpam-5787	35	13	1	1	X
ejpam-5787	35	14	)	)	PUNCT
ejpam-5787	35	15	oscillations	oscillation	NOUN
ejpam-5787	35	16	occur	occur	VERB
ejpam-5787	35	17	even	even	ADV
ejpam-5787	35	18	in	in	ADP
ejpam-5787	35	19	the	the	DET
ejpam-5787	35	20	unforced	unforced	ADJ
ejpam-5787	35	21	case	case	NOUN
ejpam-5787	35	22	γ	γ	X
ejpam-5787	35	23	=	=	SYM
ejpam-5787	35	24	0	0	NUM
ejpam-5787	35	25	.	.	PUNCT
ejpam-5787	36	1	the	the	DET
ejpam-5787	36	2	term	term	NOUN
ejpam-5787	36	3	−ατκ(1−	−ατκ(1−	PROPN
ejpam-5787	36	4	y2	y2	NOUN
ejpam-5787	36	5	)	)	PUNCT
ejpam-5787	36	6	increases	increase	VERB
ejpam-5787	36	7	the	the	DET
ejpam-5787	36	8	oscillations	oscillation	NOUN
ejpam-5787	36	9	when	when	SCONJ
ejpam-5787	36	10	y2	y2	PROPN
ejpam-5787	36	11	<	<	X
ejpam-5787	36	12	1	1	NUM
ejpam-5787	36	13	and	and	CCONJ
ejpam-5787	36	14	damps	damp	VERB
ejpam-5787	36	15	the	the	DET
ejpam-5787	36	16	oscillations	oscillation	NOUN
ejpam-5787	36	17	when	when	SCONJ
ejpam-5787	36	18	y2	y2	PROPN
ejpam-5787	36	19	>	>	X
ejpam-5787	36	20	1	1	X
ejpam-5787	36	21	.	.	PUNCT
ejpam-5787	37	1	for	for	ADP
ejpam-5787	37	2	large	large	ADJ
ejpam-5787	37	3	enough	enough	ADJ
ejpam-5787	37	4	α	α	NOUN
ejpam-5787	37	5	,	,	PUNCT
ejpam-5787	37	6	the	the	DET
ejpam-5787	37	7	van	van	PROPN
ejpam-5787	37	8	der	der	PROPN
ejpam-5787	37	9	pol	pol	PROPN
ejpam-5787	37	10	(	(	PUNCT
ejpam-5787	37	11	1	1	X
ejpam-5787	37	12	)	)	PUNCT
ejpam-5787	37	13	has	have	VERB
ejpam-5787	37	14	relaxation	relaxation	NOUN
ejpam-5787	37	15	oscillations	oscillation	NOUN
ejpam-5787	37	16	as	as	SCONJ
ejpam-5787	37	17	can	can	AUX
ejpam-5787	37	18	be	be	AUX
ejpam-5787	37	19	seen	see	VERB
ejpam-5787	37	20	in	in	ADP
ejpam-5787	37	21	the	the	DET
ejpam-5787	37	22	system	system	NOUN
ejpam-5787	37	23	of	of	ADP
ejpam-5787	37	24	equations	equation	NOUN
ejpam-5787	37	25	.	.	PUNCT
ejpam-5787	38	1	by	by	ADP
ejpam-5787	38	2	using	use	VERB
ejpam-5787	38	3	the	the	DET
ejpam-5787	38	4	liénard	liénard	ADJ
ejpam-5787	38	5	transformation	transformation	NOUN
ejpam-5787	38	6	x	x	PUNCT
ejpam-5787	38	7	=	=	PUNCT
ejpam-5787	38	8	y	y	PROPN
ejpam-5787	38	9	−	−	NOUN
ejpam-5787	38	10	y3	y3	NOUN
ejpam-5787	38	11	3	3	NUM
ejpam-5787	38	12	−	−	NOUN
ejpam-5787	38	13	ẏ/τκα	ẏ/τκα	NOUN
ejpam-5787	38	14	,	,	PUNCT
ejpam-5787	38	15	we	we	PRON
ejpam-5787	38	16	transform	transform	VERB
ejpam-5787	38	17	(	(	PUNCT
ejpam-5787	38	18	1	1	NUM
ejpam-5787	38	19	)	)	PUNCT
ejpam-5787	38	20	into	into	ADP
ejpam-5787	38	21	the	the	DET
ejpam-5787	38	22	system	system	NOUN
ejpam-5787	38	23	ẋ	ẋ	PUNCT
ejpam-5787	39	1	=	=	SYM
ejpam-5787	40	1	1	1	NUM
ejpam-5787	40	2	τκ	τκ	X
ejpam-5787	40	3	(	(	PUNCT
ejpam-5787	40	4	γk	γk	X
ejpam-5787	40	5	sin(2πωt)−	sin(2πωt)−	PROPN
ejpam-5787	40	6	β	β	X
ejpam-5787	40	7	−	−	PROPN
ejpam-5787	40	8	y	y	X
ejpam-5787	40	9	)	)	PUNCT
ejpam-5787	40	10	ẏ	ẏ	NOUN
ejpam-5787	40	11	=	=	NOUN
ejpam-5787	40	12	α	α	PROPN
ejpam-5787	40	13	τκ	τκ	X
ejpam-5787	40	14	(	(	PUNCT
ejpam-5787	40	15	y	y	NOUN
ejpam-5787	40	16	−	−	PROPN
ejpam-5787	40	17	y3	y3	NOUN
ejpam-5787	40	18	3	3	NUM
ejpam-5787	40	19	+	+	NOUN
ejpam-5787	40	20	x	x	X
ejpam-5787	40	21	)	)	PUNCT
ejpam-5787	40	22	(	(	PUNCT
ejpam-5787	40	23	2	2	X
ejpam-5787	40	24	)	)	PUNCT
ejpam-5787	40	25	which	which	PRON
ejpam-5787	40	26	is	be	AUX
ejpam-5787	40	27	a	a	DET
ejpam-5787	40	28	slow	slow	ADJ
ejpam-5787	40	29	-	-	PUNCT
ejpam-5787	40	30	fast	fast	ADJ
ejpam-5787	40	31	system	system	NOUN
ejpam-5787	40	32	if	if	SCONJ
ejpam-5787	40	33	α	α	PRON
ejpam-5787	40	34	≫	≫	PROPN
ejpam-5787	40	35	1	1	NUM
ejpam-5787	40	36	.	.	PUNCT
ejpam-5787	41	1	the	the	DET
ejpam-5787	41	2	dynamics	dynamic	NOUN
ejpam-5787	41	3	of	of	ADP
ejpam-5787	41	4	(	(	PUNCT
ejpam-5787	41	5	2	2	X
ejpam-5787	41	6	)	)	PUNCT
ejpam-5787	41	7	involves	involve	VERB
ejpam-5787	41	8	that	that	SCONJ
ejpam-5787	41	9	the	the	DET
ejpam-5787	41	10	slow	slow	ADJ
ejpam-5787	41	11	variable	variable	NOUN
ejpam-5787	41	12	x	x	PUNCT
ejpam-5787	41	13	represents	represent	VERB
ejpam-5787	41	14	the	the	DET
ejpam-5787	41	15	deviation	deviation	NOUN
ejpam-5787	41	16	of	of	ADP
ejpam-5787	41	17	ice	ice	NOUN
ejpam-5787	41	18	volume	volume	NOUN
ejpam-5787	41	19	and	and	CCONJ
ejpam-5787	41	20	the	the	DET
ejpam-5787	41	21	fast	fast	ADJ
ejpam-5787	41	22	variable	variable	NOUN
ejpam-5787	41	23	represents	represent	VERB
ejpam-5787	41	24	some	some	DET
ejpam-5787	41	25	feedback	feedback	NOUN
ejpam-5787	41	26	mechanism	mechanism	NOUN
ejpam-5787	41	27	with	with	ADP
ejpam-5787	41	28	hysteresis	hysteresis	NOUN
ejpam-5787	41	29	.	.	PUNCT
ejpam-5787	42	1	in	in	ADP
ejpam-5787	42	2	table	table	NOUN
ejpam-5787	42	3	1	1	NUM
ejpam-5787	42	4	,	,	PUNCT
ejpam-5787	42	5	the	the	DET
ejpam-5787	42	6	default	default	NOUN
ejpam-5787	42	7	parameters	parameter	NOUN
ejpam-5787	42	8	used	use	VERB
ejpam-5787	42	9	for	for	ADP
ejpam-5787	42	10	the	the	DET
ejpam-5787	42	11	i.	i.	PROPN
ejpam-5787	42	12	alraddadi	alraddadi	PROPN
ejpam-5787	42	13	/	/	SYM
ejpam-5787	42	14	eur	eur	PROPN
ejpam-5787	42	15	.	.	PUNCT
ejpam-5787	43	1	j.	j.	PROPN
ejpam-5787	43	2	pure	pure	PROPN
ejpam-5787	43	3	appl	appl	PROPN
ejpam-5787	43	4	.	.	PROPN
ejpam-5787	43	5	math	math	PROPN
ejpam-5787	43	6	,	,	PUNCT
ejpam-5787	43	7	18	18	NUM
ejpam-5787	43	8	(	(	PUNCT
ejpam-5787	43	9	1	1	NUM
ejpam-5787	43	10	)	)	PUNCT
ejpam-5787	43	11	(	(	PUNCT
ejpam-5787	43	12	2025	2025	NUM
ejpam-5787	43	13	)	)	PUNCT
ejpam-5787	43	14	,	,	PUNCT
ejpam-5787	43	15	5787	5787	NUM
ejpam-5787	43	16	3	3	NUM
ejpam-5787	43	17	of	of	ADP
ejpam-5787	43	18	23	23	NUM
ejpam-5787	43	19	(	(	PUNCT
ejpam-5787	43	20	a	a	NOUN
ejpam-5787	43	21	)	)	PUNCT
ejpam-5787	43	22	(	(	PUNCT
ejpam-5787	43	23	b	b	X
ejpam-5787	43	24	)	)	PUNCT
ejpam-5787	43	25	figure	figure	NOUN
ejpam-5787	43	26	1	1	NUM
ejpam-5787	43	27	:	:	PUNCT
ejpam-5787	43	28	phase	phase	NOUN
ejpam-5787	43	29	portrait	portrait	NOUN
ejpam-5787	43	30	(	(	PUNCT
ejpam-5787	43	31	a	a	NOUN
ejpam-5787	43	32	)	)	PUNCT
ejpam-5787	43	33	and	and	CCONJ
ejpam-5787	43	34	time	time	NOUN
ejpam-5787	43	35	series	series	PROPN
ejpam-5787	43	36	(	(	PUNCT
ejpam-5787	43	37	b	b	NOUN
ejpam-5787	43	38	)	)	PUNCT
ejpam-5787	43	39	showing	show	VERB
ejpam-5787	43	40	periodically	periodically	ADV
ejpam-5787	43	41	forced	force	VERB
ejpam-5787	43	42	van	van	PROPN
ejpam-5787	43	43	der	der	ADJ
ejpam-5787	43	44	pol	pol	PROPN
ejpam-5787	43	45	oscillator	oscillator	NOUN
ejpam-5787	43	46	(	(	PUNCT
ejpam-5787	43	47	3	3	NUM
ejpam-5787	43	48	)	)	PUNCT
ejpam-5787	43	49	which	which	PRON
ejpam-5787	43	50	has	have	VERB
ejpam-5787	43	51	relaxation	relaxation	NOUN
ejpam-5787	43	52	oscillations	oscillation	NOUN
ejpam-5787	43	53	with	with	ADP
ejpam-5787	43	54	slow	slow	ADJ
ejpam-5787	43	55	variable	variable	NOUN
ejpam-5787	43	56	x	x	PUNCT
ejpam-5787	43	57	and	and	CCONJ
ejpam-5787	43	58	fast	fast	ADJ
ejpam-5787	43	59	variable	variable	ADJ
ejpam-5787	43	60	y.	y.	NOUN
ejpam-5787	43	61	the	the	DET
ejpam-5787	43	62	parameters	parameter	NOUN
ejpam-5787	43	63	values	value	NOUN
ejpam-5787	43	64	are	be	AUX
ejpam-5787	43	65	given	give	VERB
ejpam-5787	43	66	in	in	ADP
ejpam-5787	43	67	table	table	NOUN
ejpam-5787	43	68	1	1	NUM
ejpam-5787	43	69	.	.	PUNCT
ejpam-5787	44	1	the	the	DET
ejpam-5787	44	2	green	green	ADJ
ejpam-5787	44	3	line	line	NOUN
ejpam-5787	44	4	is	be	AUX
ejpam-5787	44	5	the	the	DET
ejpam-5787	44	6	y−nullcline	y−nullcline	NOUN
ejpam-5787	44	7	,	,	PUNCT
ejpam-5787	44	8	and	and	CCONJ
ejpam-5787	44	9	the	the	DET
ejpam-5787	44	10	blue	blue	ADJ
ejpam-5787	44	11	line	line	NOUN
ejpam-5787	44	12	is	be	AUX
ejpam-5787	44	13	the	the	DET
ejpam-5787	44	14	x−nullcline	x−nullcline	PROPN
ejpam-5787	44	15	.	.	PUNCT
ejpam-5787	45	1	in	in	ADP
ejpam-5787	45	2	(	(	PUNCT
ejpam-5787	45	3	a	a	X
ejpam-5787	45	4	)	)	PUNCT
ejpam-5787	45	5	,	,	PUNCT
ejpam-5787	45	6	there	there	PRON
ejpam-5787	45	7	is	be	VERB
ejpam-5787	45	8	an	an	DET
ejpam-5787	45	9	unstable	unstable	ADJ
ejpam-5787	45	10	equilibrium	equilibrium	NOUN
ejpam-5787	45	11	point	point	NOUN
ejpam-5787	45	12	which	which	PRON
ejpam-5787	45	13	is	be	AUX
ejpam-5787	45	14	surrounded	surround	VERB
ejpam-5787	45	15	by	by	ADP
ejpam-5787	45	16	stable	stable	ADJ
ejpam-5787	45	17	limit	limit	NOUN
ejpam-5787	45	18	cycle	cycle	NOUN
ejpam-5787	45	19	.	.	PUNCT
ejpam-5787	46	1	the	the	DET
ejpam-5787	46	2	arrows	arrow	NOUN
ejpam-5787	46	3	show	show	VERB
ejpam-5787	46	4	the	the	DET
ejpam-5787	46	5	direction	direction	NOUN
ejpam-5787	46	6	of	of	ADP
ejpam-5787	46	7	the	the	DET
ejpam-5787	46	8	vector	vector	NOUN
ejpam-5787	46	9	field	field	NOUN
ejpam-5787	46	10	of	of	ADP
ejpam-5787	46	11	(	(	PUNCT
ejpam-5787	46	12	3	3	NUM
ejpam-5787	46	13	)	)	PUNCT
ejpam-5787	46	14	.	.	PUNCT
ejpam-5787	47	1	forced	force	VERB
ejpam-5787	47	2	van	van	PROPN
ejpam-5787	47	3	der	der	ADJ
ejpam-5787	47	4	pol	pol	PROPN
ejpam-5787	47	5	oscillator	oscillator	NOUN
ejpam-5787	47	6	(	(	PUNCT
ejpam-5787	47	7	2	2	NUM
ejpam-5787	47	8	)	)	PUNCT
ejpam-5787	47	9	are	be	AUX
ejpam-5787	47	10	taken	take	VERB
ejpam-5787	47	11	from	from	ADP
ejpam-5787	47	12	[	[	X
ejpam-5787	47	13	2	2	NUM
ejpam-5787	47	14	]	]	PUNCT
ejpam-5787	47	15	,	,	PUNCT
ejpam-5787	47	16	ω	ω	PROPN
ejpam-5787	47	17	is	be	AUX
ejpam-5787	47	18	the	the	DET
ejpam-5787	47	19	frequency	frequency	NOUN
ejpam-5787	47	20	(	(	PUNCT
ejpam-5787	47	21	obliquity	obliquity	NOUN
ejpam-5787	47	22	forcing	forcing	NOUN
ejpam-5787	47	23	is	be	AUX
ejpam-5787	47	24	ω	ω	NUM
ejpam-5787	47	25	≈	≈	PROPN
ejpam-5787	47	26	1	1	NUM
ejpam-5787	47	27	41	41	NUM
ejpam-5787	47	28	)	)	PUNCT
ejpam-5787	47	29	and	and	CCONJ
ejpam-5787	47	30	k	k	PROPN
ejpam-5787	47	31	represents	represent	VERB
ejpam-5787	47	32	the	the	DET
ejpam-5787	47	33	amplitude	amplitude	NOUN
ejpam-5787	47	34	of	of	ADP
ejpam-5787	47	35	the	the	DET
ejpam-5787	47	36	forcing	forcing	NOUN
ejpam-5787	47	37	.	.	PUNCT
ejpam-5787	48	1	2	2	X
ejpam-5787	48	2	.	.	X
ejpam-5787	48	3	applications	application	NOUN
ejpam-5787	48	4	to	to	ADP
ejpam-5787	48	5	the	the	DET
ejpam-5787	48	6	symmetric	symmetric	ADJ
ejpam-5787	48	7	forced	force	VERB
ejpam-5787	48	8	van	van	PROPN
ejpam-5787	48	9	der	der	ADJ
ejpam-5787	48	10	pol	pol	NOUN
ejpam-5787	48	11	equation	equation	NOUN
ejpam-5787	48	12	2.1	2.1	NUM
ejpam-5787	48	13	.	.	PUNCT
ejpam-5787	49	1	the	the	DET
ejpam-5787	49	2	periodically	periodically	ADV
ejpam-5787	49	3	forced	force	VERB
ejpam-5787	49	4	van	van	PROPN
ejpam-5787	49	5	der	der	ADJ
ejpam-5787	49	6	pol	pol	PROPN
ejpam-5787	49	7	oscillator	oscillator	NOUN
ejpam-5787	49	8	note	note	VERB
ejpam-5787	49	9	that	that	SCONJ
ejpam-5787	49	10	the	the	DET
ejpam-5787	49	11	van	van	PROPN
ejpam-5787	49	12	der	der	ADJ
ejpam-5787	49	13	pol	pol	PROPN
ejpam-5787	49	14	oscillator	oscillator	NOUN
ejpam-5787	49	15	for	for	ADP
ejpam-5787	49	16	small	small	ADJ
ejpam-5787	49	17	ε	ε	PROPN
ejpam-5787	49	18	has	have	VERB
ejpam-5787	49	19	a	a	DET
ejpam-5787	49	20	periodic	periodic	ADJ
ejpam-5787	49	21	orbit	orbit	NOUN
ejpam-5787	49	22	with	with	ADP
ejpam-5787	49	23	attracting	attract	VERB
ejpam-5787	49	24	and	and	CCONJ
ejpam-5787	49	25	slow	slow	ADJ
ejpam-5787	49	26	and	and	CCONJ
ejpam-5787	49	27	fast	fast	ADJ
ejpam-5787	49	28	motions	motion	NOUN
ejpam-5787	49	29	.	.	PUNCT
ejpam-5787	50	1	geometric	geometric	ADJ
ejpam-5787	50	2	singular	singular	ADJ
ejpam-5787	50	3	perturbation	perturbation	NOUN
ejpam-5787	50	4	theory	theory	NOUN
ejpam-5787	50	5	was	be	AUX
ejpam-5787	50	6	used	use	VERB
ejpam-5787	50	7	in	in	ADP
ejpam-5787	50	8	[	[	X
ejpam-5787	50	9	10	10	NUM
ejpam-5787	50	10	]	]	PUNCT
ejpam-5787	50	11	to	to	PART
ejpam-5787	50	12	understand	understand	VERB
ejpam-5787	50	13	the	the	DET
ejpam-5787	50	14	full	full	ADJ
ejpam-5787	50	15	system	system	NOUN
ejpam-5787	50	16	.	.	PUNCT
ejpam-5787	51	1	the	the	DET
ejpam-5787	51	2	following	follow	VERB
ejpam-5787	51	3	discussion	discussion	NOUN
ejpam-5787	51	4	is	be	AUX
ejpam-5787	51	5	based	base	VERB
ejpam-5787	51	6	on	on	ADP
ejpam-5787	51	7	[	[	X
ejpam-5787	51	8	10	10	NUM
ejpam-5787	51	9	,	,	PUNCT
ejpam-5787	51	10	11	11	NUM
ejpam-5787	51	11	,	,	PUNCT
ejpam-5787	51	12	30	30	NUM
ejpam-5787	51	13	,	,	PUNCT
ejpam-5787	51	14	31	31	NUM
ejpam-5787	51	15	]	]	PUNCT
ejpam-5787	51	16	.	.	PUNCT
ejpam-5787	52	1	here	here	ADV
ejpam-5787	52	2	,	,	PUNCT
ejpam-5787	52	3	we	we	PRON
ejpam-5787	52	4	consider	consider	VERB
ejpam-5787	52	5	the	the	DET
ejpam-5787	52	6	symmetric	symmetric	ADJ
ejpam-5787	52	7	van	van	PROPN
ejpam-5787	52	8	der	der	PROPN
ejpam-5787	52	9	pol	pol	PROPN
ejpam-5787	52	10	oscillator	oscillator	NOUN
ejpam-5787	52	11	(	(	PUNCT
ejpam-5787	52	12	2	2	NUM
ejpam-5787	52	13	)	)	PUNCT
ejpam-5787	52	14	where	where	SCONJ
ejpam-5787	52	15	(	(	PUNCT
ejpam-5787	52	16	β	β	X
ejpam-5787	52	17	=	=	NOUN
ejpam-5787	52	18	0	0	NUM
ejpam-5787	52	19	)	)	PUNCT
ejpam-5787	52	20	with	with	ADP
ejpam-5787	52	21	periodic	periodic	ADJ
ejpam-5787	52	22	forcing	forcing	ADJ
ejpam-5787	52	23	[	[	X
ejpam-5787	52	24	2	2	NUM
ejpam-5787	52	25	]	]	PUNCT
ejpam-5787	52	26	:	:	PUNCT
ejpam-5787	52	27	ẋ	ẋ	PROPN
ejpam-5787	53	1	=	=	SYM
ejpam-5787	53	2	1	1	NUM
ejpam-5787	53	3	τκ	τκ	X
ejpam-5787	53	4	(	(	PUNCT
ejpam-5787	53	5	γk	γk	X
ejpam-5787	53	6	sin(2πωt)−	sin(2πωt)−	PROPN
ejpam-5787	53	7	β	β	X
ejpam-5787	53	8	−	−	PROPN
ejpam-5787	53	9	y	y	X
ejpam-5787	53	10	)	)	PUNCT
ejpam-5787	53	11	ẏ	ẏ	NOUN
ejpam-5787	53	12	=	=	NOUN
ejpam-5787	54	1	α	α	PROPN
ejpam-5787	54	2	τκ	τκ	X
ejpam-5787	54	3	(	(	PUNCT
ejpam-5787	54	4	y	y	NOUN
ejpam-5787	54	5	−	−	PROPN
ejpam-5787	54	6	y3	y3	NOUN
ejpam-5787	54	7	3	3	NUM
ejpam-5787	54	8	+	+	NOUN
ejpam-5787	54	9	x	x	X
ejpam-5787	54	10	)	)	PUNCT
ejpam-5787	54	11	(	(	PUNCT
ejpam-5787	54	12	3	3	X
ejpam-5787	54	13	)	)	PUNCT
ejpam-5787	54	14	is	be	AUX
ejpam-5787	54	15	a	a	DET
ejpam-5787	54	16	non	non	ADJ
ejpam-5787	54	17	-	-	ADJ
ejpam-5787	54	18	autonomous	autonomous	ADJ
ejpam-5787	54	19	system	system	NOUN
ejpam-5787	54	20	as	as	SCONJ
ejpam-5787	54	21	shown	show	VERB
ejpam-5787	54	22	in	in	ADP
ejpam-5787	54	23	figure	figure	NOUN
ejpam-5787	54	24	1	1	NUM
ejpam-5787	54	25	.	.	PUNCT
ejpam-5787	55	1	we	we	PRON
ejpam-5787	55	2	set	set	VERB
ejpam-5787	55	3	τκ	τκ	NOUN
ejpam-5787	55	4	=	=	SYM
ejpam-5787	55	5	1	1	NUM
ejpam-5787	55	6	through	through	ADP
ejpam-5787	55	7	a	a	DET
ejpam-5787	55	8	suitable	suitable	ADJ
ejpam-5787	55	9	rescaling	rescaling	NOUN
ejpam-5787	55	10	of	of	ADP
ejpam-5787	55	11	time	time	NOUN
ejpam-5787	55	12	.	.	PUNCT
ejpam-5787	56	1	we	we	PRON
ejpam-5787	56	2	define	define	VERB
ejpam-5787	56	3	a	a	DET
ejpam-5787	56	4	new	new	ADJ
ejpam-5787	56	5	parameter	parameter	NOUN
ejpam-5787	56	6	ε	ε	PROPN
ejpam-5787	56	7	=	=	SYM
ejpam-5787	56	8	1	1	NUM
ejpam-5787	56	9	α	α	NOUN
ejpam-5787	56	10	,	,	PUNCT
ejpam-5787	56	11	a	a	DET
ejpam-5787	56	12	=	=	SYM
ejpam-5787	56	13	γ	γ	X
ejpam-5787	56	14	,	,	PUNCT
ejpam-5787	56	15	k1	k1	NOUN
ejpam-5787	56	16	=	=	SYM
ejpam-5787	56	17	1	1	NUM
ejpam-5787	56	18	and	and	CCONJ
ejpam-5787	56	19	θ	θ	PROPN
ejpam-5787	56	20	=	=	SYM
ejpam-5787	56	21	ωt	ωt	PROPN
ejpam-5787	56	22	of	of	ADP
ejpam-5787	56	23	the	the	DET
ejpam-5787	56	24	form	form	NOUN
ejpam-5787	56	25	ẋ	ẋ	PUNCT
ejpam-5787	57	1	=	=	PUNCT
ejpam-5787	57	2	a	a	DET
ejpam-5787	57	3	sin(2πθ)−	sin(2πθ)−	NOUN
ejpam-5787	57	4	y	y	PROPN
ejpam-5787	57	5	−	−	NOUN
ejpam-5787	57	6	β	β	X
ejpam-5787	57	7	εẏ	εẏ	PUNCT
ejpam-5787	57	8	=	=	PUNCT
ejpam-5787	58	1	y	y	PROPN
ejpam-5787	58	2	−	−	NOUN
ejpam-5787	58	3	y3	y3	NOUN
ejpam-5787	58	4	3	3	NUM
ejpam-5787	59	1	+	+	CCONJ
ejpam-5787	59	2	x	x	SYM
ejpam-5787	59	3	θ̇	θ̇	PROPN
ejpam-5787	59	4	=	=	SYM
ejpam-5787	59	5	ω	ω	PROPN
ejpam-5787	59	6	(	(	PUNCT
ejpam-5787	59	7	4	4	NUM
ejpam-5787	59	8	)	)	PUNCT
ejpam-5787	59	9	where	where	SCONJ
ejpam-5787	59	10	ẋ	ẋ	PROPN
ejpam-5787	59	11	≡	≡	PROPN
ejpam-5787	59	12	dx	dx	PROPN
ejpam-5787	60	1	dt	dt	X
ejpam-5787	60	2	,	,	PUNCT
ejpam-5787	60	3	ẏ	ẏ	PROPN
ejpam-5787	60	4	≡	≡	PROPN
ejpam-5787	60	5	dy	dy	X
ejpam-5787	60	6	dt	dt	PROPN
ejpam-5787	60	7	and	and	CCONJ
ejpam-5787	60	8	θ̇	θ̇	PRON
ejpam-5787	60	9	≡	≡	PROPN
ejpam-5787	60	10	dθ	dθ	PROPN
ejpam-5787	60	11	dt	dt	PROPN
ejpam-5787	60	12	.	.	PUNCT
ejpam-5787	61	1	when	when	SCONJ
ejpam-5787	61	2	0	0	NUM
ejpam-5787	61	3	<	<	X
ejpam-5787	61	4	ε	ε	PROPN
ejpam-5787	61	5	≪	≪	PUNCT
ejpam-5787	61	6	1	1	NUM
ejpam-5787	61	7	,	,	PUNCT
ejpam-5787	61	8	the	the	DET
ejpam-5787	61	9	system	system	NOUN
ejpam-5787	61	10	has	have	VERB
ejpam-5787	61	11	a	a	DET
ejpam-5787	61	12	relaxation	relaxation	NOUN
ejpam-5787	61	13	oscillation	oscillation	NOUN
ejpam-5787	61	14	as	as	SCONJ
ejpam-5787	61	15	shown	show	VERB
ejpam-5787	61	16	in	in	ADP
ejpam-5787	61	17	figure	figure	NOUN
ejpam-5787	61	18	1	1	NUM
ejpam-5787	61	19	.	.	PUNCT
ejpam-5787	62	1	the	the	DET
ejpam-5787	62	2	slow	slow	ADJ
ejpam-5787	62	3	variable	variable	NOUN
ejpam-5787	62	4	is	be	AUX
ejpam-5787	62	5	x	x	PUNCT
ejpam-5787	62	6	and	and	CCONJ
ejpam-5787	62	7	the	the	DET
ejpam-5787	62	8	fast	fast	ADJ
ejpam-5787	62	9	variable	variable	NOUN
ejpam-5787	62	10	is	be	AUX
ejpam-5787	62	11	y.	y.	NOUN
ejpam-5787	62	12	we	we	PRON
ejpam-5787	62	13	transform	transform	VERB
ejpam-5787	62	14	the	the	DET
ejpam-5787	62	15	slow	slow	ADJ
ejpam-5787	62	16	time	time	NOUN
ejpam-5787	62	17	scale	scale	NOUN
ejpam-5787	62	18	t	t	PROPN
ejpam-5787	62	19	to	to	PART
ejpam-5787	62	20	fast	fast	ADJ
ejpam-5787	62	21	time	time	NOUN
ejpam-5787	62	22	scale	scale	NOUN
ejpam-5787	62	23	t	t	NOUN
ejpam-5787	62	24	by	by	ADP
ejpam-5787	62	25	rescaling	rescale	VERB
ejpam-5787	62	26	the	the	DET
ejpam-5787	62	27	time	time	NOUN
ejpam-5787	62	28	t	t	NOUN
ejpam-5787	62	29	=	=	SYM
ejpam-5787	62	30	εt	εt	PROPN
ejpam-5787	62	31	i.	i.	PROPN
ejpam-5787	62	32	alraddadi	alraddadi	PROPN
ejpam-5787	62	33	/	/	SYM
ejpam-5787	62	34	eur	eur	PROPN
ejpam-5787	62	35	.	.	PUNCT
ejpam-5787	63	1	j.	j.	PROPN
ejpam-5787	63	2	pure	pure	PROPN
ejpam-5787	63	3	appl	appl	PROPN
ejpam-5787	63	4	.	.	PROPN
ejpam-5787	63	5	math	math	PROPN
ejpam-5787	63	6	,	,	PUNCT
ejpam-5787	63	7	18	18	NUM
ejpam-5787	63	8	(	(	PUNCT
ejpam-5787	63	9	1	1	NUM
ejpam-5787	63	10	)	)	PUNCT
ejpam-5787	63	11	(	(	PUNCT
ejpam-5787	63	12	2025	2025	NUM
ejpam-5787	63	13	)	)	PUNCT
ejpam-5787	63	14	,	,	PUNCT
ejpam-5787	63	15	5787	5787	NUM
ejpam-5787	63	16	4	4	NUM
ejpam-5787	63	17	of	of	ADP
ejpam-5787	63	18	23	23	NUM
ejpam-5787	63	19	dx	dx	NOUN
ejpam-5787	63	20	dt	dt	NOUN
ejpam-5787	64	1	=	=	SYM
ejpam-5787	64	2	ε(a	ε(a	PROPN
ejpam-5787	64	3	sin(2πθ)−	sin(2πθ)−	VERB
ejpam-5787	64	4	y	y	NOUN
ejpam-5787	64	5	−	−	PROPN
ejpam-5787	64	6	β	β	NOUN
ejpam-5787	64	7	)	)	PUNCT
ejpam-5787	64	8	dy	dy	NOUN
ejpam-5787	65	1	dt	dt	NOUN
ejpam-5787	65	2	=	=	SYM
ejpam-5787	65	3	y	y	PROPN
ejpam-5787	65	4	−	−	PROPN
ejpam-5787	65	5	y3	y3	NOUN
ejpam-5787	65	6	3	3	NUM
ejpam-5787	65	7	+	+	CCONJ
ejpam-5787	65	8	x	x	SYM
ejpam-5787	65	9	dθ	dθ	NOUN
ejpam-5787	65	10	dt	dt	X
ejpam-5787	65	11	=	=	SYM
ejpam-5787	65	12	εω	εω	X
ejpam-5787	65	13	.	.	X
ejpam-5787	65	14	(	(	PUNCT
ejpam-5787	65	15	5	5	X
ejpam-5787	65	16	)	)	PUNCT
ejpam-5787	65	17	we	we	PRON
ejpam-5787	65	18	now	now	ADV
ejpam-5787	65	19	study	study	VERB
ejpam-5787	65	20	the	the	DET
ejpam-5787	65	21	two	two	NUM
ejpam-5787	65	22	systems	system	NOUN
ejpam-5787	65	23	in	in	ADP
ejpam-5787	65	24	the	the	DET
ejpam-5787	65	25	singular	singular	NOUN
ejpam-5787	65	26	limit	limit	NOUN
ejpam-5787	65	27	ε	ε	PROPN
ejpam-5787	65	28	=	=	SYM
ejpam-5787	65	29	0	0	PUNCT
ejpam-5787	65	30	as	as	SCONJ
ejpam-5787	65	31	follows	follow	VERB
ejpam-5787	65	32	namely	namely	ADV
ejpam-5787	65	33	the	the	DET
ejpam-5787	65	34	slow	slow	ADJ
ejpam-5787	65	35	subsystem	subsystem	NOUN
ejpam-5787	65	36	:	:	PUNCT
ejpam-5787	65	37	ẋ	ẋ	PROPN
ejpam-5787	66	1	=	=	PUNCT
ejpam-5787	67	1	a	a	DET
ejpam-5787	67	2	sin(2πθ)−	sin(2πθ)−	NOUN
ejpam-5787	67	3	y	y	NOUN
ejpam-5787	67	4	−	−	NOUN
ejpam-5787	67	5	β	β	NOUN
ejpam-5787	67	6	0	0	X
ejpam-5787	68	1	=	=	SYM
ejpam-5787	68	2	y	y	PROPN
ejpam-5787	68	3	−	−	NOUN
ejpam-5787	68	4	y3	y3	NOUN
ejpam-5787	68	5	3	3	NUM
ejpam-5787	68	6	+	+	CCONJ
ejpam-5787	68	7	x	x	SYM
ejpam-5787	68	8	θ̇	θ̇	PROPN
ejpam-5787	68	9	=	=	SYM
ejpam-5787	68	10	ω	ω	PROPN
ejpam-5787	68	11	(	(	PUNCT
ejpam-5787	68	12	6	6	NUM
ejpam-5787	68	13	)	)	PUNCT
ejpam-5787	68	14	and	and	CCONJ
ejpam-5787	68	15	the	the	DET
ejpam-5787	68	16	fast	fast	ADJ
ejpam-5787	68	17	subsystem	subsystem	NOUN
ejpam-5787	68	18	:	:	PUNCT
ejpam-5787	68	19	dx	dx	PROPN
ejpam-5787	68	20	dt	dt	X
ejpam-5787	69	1	=	=	SYM
ejpam-5787	69	2	0	0	NUM
ejpam-5787	69	3	dy	dy	NOUN
ejpam-5787	69	4	dt	dt	NOUN
ejpam-5787	69	5	=	=	PUNCT
ejpam-5787	69	6	(	(	PUNCT
ejpam-5787	69	7	y	y	PROPN
ejpam-5787	69	8	−	−	PROPN
ejpam-5787	69	9	y3	y3	NOUN
ejpam-5787	69	10	3	3	NUM
ejpam-5787	69	11	+	+	CCONJ
ejpam-5787	69	12	x−	x−	PROPN
ejpam-5787	69	13	β	β	X
ejpam-5787	69	14	)	)	PUNCT
ejpam-5787	69	15	dθ	dθ	NOUN
ejpam-5787	69	16	dt	dt	NOUN
ejpam-5787	70	1	=	=	SYM
ejpam-5787	70	2	0	0	NUM
ejpam-5787	70	3	(	(	PUNCT
ejpam-5787	70	4	7	7	NUM
ejpam-5787	70	5	)	)	PUNCT
ejpam-5787	70	6	2.2	2.2	NUM
ejpam-5787	70	7	.	.	PUNCT
ejpam-5787	71	1	the	the	DET
ejpam-5787	71	2	slow	slow	ADJ
ejpam-5787	71	3	system	system	NOUN
ejpam-5787	71	4	the	the	DET
ejpam-5787	71	5	flow	flow	NOUN
ejpam-5787	71	6	of	of	ADP
ejpam-5787	71	7	(	(	PUNCT
ejpam-5787	71	8	6	6	NUM
ejpam-5787	71	9	)	)	PUNCT
ejpam-5787	71	10	is	be	AUX
ejpam-5787	71	11	called	call	VERB
ejpam-5787	71	12	the	the	DET
ejpam-5787	71	13	slow	slow	ADJ
ejpam-5787	71	14	flow	flow	NOUN
ejpam-5787	71	15	on	on	ADP
ejpam-5787	71	16	the	the	DET
ejpam-5787	71	17	critical	critical	ADJ
ejpam-5787	71	18	/	/	SYM
ejpam-5787	71	19	slow	slow	ADJ
ejpam-5787	71	20	manifold	manifold	NOUN
ejpam-5787	71	21	.	.	PUNCT
ejpam-5787	72	1	the	the	DET
ejpam-5787	72	2	critical	critical	ADJ
ejpam-5787	72	3	manifold	manifold	NOUN
ejpam-5787	72	4	is	be	AUX
ejpam-5787	72	5	in	in	ADP
ejpam-5787	72	6	this	this	DET
ejpam-5787	72	7	case	case	NOUN
ejpam-5787	72	8	given	give	VERB
ejpam-5787	72	9	by	by	ADP
ejpam-5787	72	10	s	s	PRON
ejpam-5787	72	11	:	:	PUNCT
ejpam-5787	73	1	=	=	SYM
ejpam-5787	73	2	{	{	PUNCT
ejpam-5787	73	3	(	(	PUNCT
ejpam-5787	73	4	x	x	NOUN
ejpam-5787	73	5	,	,	PUNCT
ejpam-5787	73	6	y	y	PROPN
ejpam-5787	73	7	,	,	PUNCT
ejpam-5787	73	8	θ	θ	NOUN
ejpam-5787	73	9	)	)	PUNCT
ejpam-5787	73	10	∈	∈	NOUN
ejpam-5787	73	11	r3|	r3|	VERB
ejpam-5787	74	1	y	y	PROPN
ejpam-5787	74	2	−	−	PUNCT
ejpam-5787	74	3	y3	y3	NOUN
ejpam-5787	74	4	3	3	NUM
ejpam-5787	74	5	+	+	NOUN
ejpam-5787	74	6	x	x	SYM
ejpam-5787	74	7	=	=	SYM
ejpam-5787	74	8	0	0	NUM
ejpam-5787	74	9	}	}	PUNCT
ejpam-5787	74	10	(	(	PUNCT
ejpam-5787	74	11	8)	8)	NUM
ejpam-5787	74	12	it	it	PRON
ejpam-5787	74	13	is	be	AUX
ejpam-5787	74	14	apparent	apparent	ADJ
ejpam-5787	74	15	that	that	SCONJ
ejpam-5787	74	16	x	x	X
ejpam-5787	74	17	=	=	PRON
ejpam-5787	74	18	y3	y3	NOUN
ejpam-5787	74	19	3	3	NUM
ejpam-5787	74	20	−	−	NOUN
ejpam-5787	74	21	y	y	PROPN
ejpam-5787	74	22	defines	define	VERB
ejpam-5787	74	23	the	the	DET
ejpam-5787	74	24	critical	critical	ADJ
ejpam-5787	74	25	manifold	manifold	NOUN
ejpam-5787	74	26	which	which	PRON
ejpam-5787	74	27	is	be	AUX
ejpam-5787	74	28	the	the	DET
ejpam-5787	74	29	set	set	NOUN
ejpam-5787	74	30	of	of	ADP
ejpam-5787	74	31	equilibrium	equilibrium	NOUN
ejpam-5787	74	32	points	point	NOUN
ejpam-5787	74	33	for	for	ADP
ejpam-5787	74	34	the	the	DET
ejpam-5787	74	35	fast	fast	ADJ
ejpam-5787	74	36	subsystem	subsystem	NOUN
ejpam-5787	74	37	(	(	PUNCT
ejpam-5787	74	38	7	7	NUM
ejpam-5787	74	39	)	)	PUNCT
ejpam-5787	74	40	.	.	PUNCT
ejpam-5787	75	1	note	note	VERB
ejpam-5787	75	2	that	that	SCONJ
ejpam-5787	75	3	(	(	PUNCT
ejpam-5787	75	4	4	4	X
ejpam-5787	75	5	)	)	PUNCT
ejpam-5787	75	6	has	have	VERB
ejpam-5787	75	7	a	a	DET
ejpam-5787	75	8	repelling	repelling	NOUN
ejpam-5787	75	9	sheet	sheet	NOUN
ejpam-5787	75	10	sr	sr	NOUN
ejpam-5787	75	11	=	=	PROPN
ejpam-5787	75	12	s∩{−1	s∩{−1	PROPN
ejpam-5787	75	13	<	<	X
ejpam-5787	75	14	y	y	X
ejpam-5787	75	15	<	<	X
ejpam-5787	75	16	1	1	NUM
ejpam-5787	75	17	}	}	PUNCT
ejpam-5787	75	18	and	and	CCONJ
ejpam-5787	75	19	two	two	NUM
ejpam-5787	75	20	attracting	attract	VERB
ejpam-5787	75	21	sheets	sheet	NOUN
ejpam-5787	75	22	sa	sa	NOUN
ejpam-5787	75	23	=	=	SYM
ejpam-5787	75	24	s	s	NOUN
ejpam-5787	75	25	∩	∩	NOUN
ejpam-5787	75	26	{	{	PUNCT
ejpam-5787	75	27	y	y	NOUN
ejpam-5787	75	28	<	<	X
ejpam-5787	75	29	−1	−1	NOUN
ejpam-5787	75	30	}	}	PUNCT
ejpam-5787	75	31	,	,	PUNCT
ejpam-5787	75	32	sa	sa	ADP
ejpam-5787	75	33	=	=	SYM
ejpam-5787	75	34	s	s	PART
ejpam-5787	75	35	∩	∩	NOUN
ejpam-5787	75	36	{	{	PUNCT
ejpam-5787	75	37	y	y	X
ejpam-5787	75	38	>	>	X
ejpam-5787	75	39	1	1	NUM
ejpam-5787	75	40	}	}	PUNCT
ejpam-5787	75	41	,	,	PUNCT
ejpam-5787	75	42	and	and	CCONJ
ejpam-5787	75	43	trajectories	trajectory	NOUN
ejpam-5787	75	44	of	of	ADP
ejpam-5787	75	45	the	the	DET
ejpam-5787	75	46	daes	daes	PROPN
ejpam-5787	75	47	on	on	ADP
ejpam-5787	75	48	the	the	DET
ejpam-5787	75	49	critical	critical	ADJ
ejpam-5787	75	50	manifold	manifold	NOUN
ejpam-5787	75	51	are	be	AUX
ejpam-5787	75	52	the	the	DET
ejpam-5787	75	53	slow	slow	ADJ
ejpam-5787	75	54	trajectories	trajectory	NOUN
ejpam-5787	75	55	that	that	PRON
ejpam-5787	75	56	are	be	AUX
ejpam-5787	75	57	wholly	wholly	ADV
ejpam-5787	75	58	defined	define	VERB
ejpam-5787	75	59	up	up	ADP
ejpam-5787	75	60	to	to	ADP
ejpam-5787	75	61	the	the	DET
ejpam-5787	75	62	time	time	NOUN
ejpam-5787	75	63	when	when	SCONJ
ejpam-5787	75	64	a	a	DET
ejpam-5787	75	65	trajectory	trajectory	NOUN
ejpam-5787	75	66	hits	hit	VERB
ejpam-5787	75	67	a	a	DET
ejpam-5787	75	68	fold	fold	NOUN
ejpam-5787	75	69	on	on	ADP
ejpam-5787	75	70	the	the	DET
ejpam-5787	75	71	critical	critical	ADJ
ejpam-5787	75	72	manifold	manifold	NOUN
ejpam-5787	75	73	.	.	PUNCT
ejpam-5787	76	1	there	there	PRON
ejpam-5787	76	2	are	be	VERB
ejpam-5787	76	3	fold	fold	ADJ
ejpam-5787	76	4	points	point	NOUN
ejpam-5787	76	5	on	on	ADP
ejpam-5787	76	6	the	the	DET
ejpam-5787	76	7	two	two	NUM
ejpam-5787	76	8	lines	line	NOUN
ejpam-5787	76	9	:	:	PUNCT
ejpam-5787	76	10	l−	l−	NOUN
ejpam-5787	76	11	=	=	PUNCT
ejpam-5787	76	12	{	{	PUNCT
ejpam-5787	76	13	(	(	PUNCT
ejpam-5787	76	14	−	−	PROPN
ejpam-5787	76	15	1	1	NUM
ejpam-5787	76	16	,	,	PUNCT
ejpam-5787	76	17	2/3	2/3	NUM
ejpam-5787	76	18	,	,	PUNCT
ejpam-5787	76	19	θ	θ	NOUN
ejpam-5787	76	20	)	)	PUNCT
ejpam-5787	76	21	:	:	PUNCT
ejpam-5787	76	22	θ	θ	PROPN
ejpam-5787	76	23	∈	∈	PROPN
ejpam-5787	76	24	(	(	PUNCT
ejpam-5787	76	25	0	0	NUM
ejpam-5787	76	26	,	,	PUNCT
ejpam-5787	76	27	2πn	2πn	ADJ
ejpam-5787	76	28	)	)	PUNCT
ejpam-5787	76	29	}	}	PUNCT
ejpam-5787	76	30	and	and	CCONJ
ejpam-5787	76	31	l+	l+	NOUN
ejpam-5787	76	32	=	=	SYM
ejpam-5787	76	33	{	{	PUNCT
ejpam-5787	76	34	(	(	PUNCT
ejpam-5787	76	35	1,−2/3	1,−2/3	NUM
ejpam-5787	76	36	,	,	PUNCT
ejpam-5787	76	37	θ	θ	PROPN
ejpam-5787	76	38	)	)	PUNCT
ejpam-5787	76	39	:	:	PUNCT
ejpam-5787	76	40	θ	θ	PROPN
ejpam-5787	76	41	∈	∈	PROPN
ejpam-5787	76	42	(	(	PUNCT
ejpam-5787	76	43	0	0	NUM
ejpam-5787	76	44	,	,	PUNCT
ejpam-5787	76	45	2πn	2πn	ADJ
ejpam-5787	76	46	)	)	PUNCT
ejpam-5787	76	47	}	}	PUNCT
ejpam-5787	76	48	,	,	PUNCT
ejpam-5787	76	49	where	where	SCONJ
ejpam-5787	76	50	n	n	PRON
ejpam-5787	76	51	is	be	AUX
ejpam-5787	76	52	positive	positive	ADJ
ejpam-5787	76	53	integer	integer	NOUN
ejpam-5787	76	54	z+	z+	PRON
ejpam-5787	76	55	.	.	PROPN
ejpam-5787	76	56	2.3	2.3	NUM
ejpam-5787	76	57	.	.	PUNCT
ejpam-5787	77	1	the	the	DET
ejpam-5787	77	2	layer	layer	NOUN
ejpam-5787	77	3	problem	problem	VERB
ejpam-5787	77	4	the	the	DET
ejpam-5787	77	5	family	family	NOUN
ejpam-5787	77	6	of	of	ADP
ejpam-5787	77	7	differential	differential	ADJ
ejpam-5787	77	8	equations	equation	NOUN
ejpam-5787	77	9	(	(	PUNCT
ejpam-5787	77	10	7	7	X
ejpam-5787	77	11	)	)	PUNCT
ejpam-5787	77	12	is	be	AUX
ejpam-5787	77	13	called	call	VERB
ejpam-5787	77	14	the	the	DET
ejpam-5787	77	15	layer	layer	NOUN
ejpam-5787	77	16	problem	problem	NOUN
ejpam-5787	77	17	.	.	PUNCT
ejpam-5787	78	1	the	the	DET
ejpam-5787	78	2	solutions	solution	NOUN
ejpam-5787	78	3	of	of	ADP
ejpam-5787	78	4	differential	differential	ADJ
ejpam-5787	78	5	equations	equation	NOUN
ejpam-5787	78	6	dx	dx	PROPN
ejpam-5787	78	7	dt	dt	NOUN
ejpam-5787	79	1	=	=	SYM
ejpam-5787	79	2	0	0	NUM
ejpam-5787	79	3	and	and	CCONJ
ejpam-5787	79	4	dθ	dθ	PROPN
ejpam-5787	79	5	dt	dt	PROPN
ejpam-5787	79	6	=	=	SYM
ejpam-5787	79	7	0	0	PROPN
ejpam-5787	79	8	can	can	AUX
ejpam-5787	79	9	solved	solve	VERB
ejpam-5787	79	10	analytically	analytically	ADV
ejpam-5787	79	11	to	to	PART
ejpam-5787	79	12	give	give	VERB
ejpam-5787	79	13	:	:	PUNCT
ejpam-5787	79	14	x(t	x(t	PROPN
ejpam-5787	79	15	)	)	PUNCT
ejpam-5787	80	1	=	=	SYM
ejpam-5787	80	2	c1	c1	PROPN
ejpam-5787	80	3	,	,	PUNCT
ejpam-5787	80	4	θ(t	θ(t	PROPN
ejpam-5787	80	5	)	)	PUNCT
ejpam-5787	81	1	=	=	SYM
ejpam-5787	81	2	c2	c2	PROPN
ejpam-5787	81	3	∀c1,2	∀c1,2	PROPN
ejpam-5787	81	4	∈	∈	PROPN
ejpam-5787	81	5	r	r	NOUN
ejpam-5787	81	6	(	(	PUNCT
ejpam-5787	81	7	9	9	NUM
ejpam-5787	81	8	)	)	PUNCT
ejpam-5787	81	9	i.	i.	NOUN
ejpam-5787	81	10	alraddadi	alraddadi	PROPN
ejpam-5787	81	11	/	/	SYM
ejpam-5787	81	12	eur	eur	PROPN
ejpam-5787	81	13	.	.	PUNCT
ejpam-5787	82	1	j.	j.	PROPN
ejpam-5787	82	2	pure	pure	PROPN
ejpam-5787	82	3	appl	appl	PROPN
ejpam-5787	82	4	.	.	PROPN
ejpam-5787	82	5	math	math	PROPN
ejpam-5787	82	6	,	,	PUNCT
ejpam-5787	82	7	18	18	NUM
ejpam-5787	82	8	(	(	PUNCT
ejpam-5787	82	9	1	1	NUM
ejpam-5787	82	10	)	)	PUNCT
ejpam-5787	82	11	(	(	PUNCT
ejpam-5787	82	12	2025	2025	NUM
ejpam-5787	82	13	)	)	PUNCT
ejpam-5787	82	14	,	,	PUNCT
ejpam-5787	82	15	5787	5787	NUM
ejpam-5787	82	16	5	5	NUM
ejpam-5787	82	17	of	of	ADP
ejpam-5787	82	18	23	23	NUM
ejpam-5787	82	19	figure	figure	NOUN
ejpam-5787	82	20	2	2	NUM
ejpam-5787	82	21	:	:	PUNCT
ejpam-5787	82	22	three	three	NUM
ejpam-5787	82	23	-	-	PUNCT
ejpam-5787	82	24	dimensional	dimensional	ADJ
ejpam-5787	82	25	view	view	NOUN
ejpam-5787	82	26	of	of	ADP
ejpam-5787	82	27	the	the	DET
ejpam-5787	82	28	periodically	periodically	ADV
ejpam-5787	82	29	forced	force	VERB
ejpam-5787	82	30	van	van	PROPN
ejpam-5787	82	31	der	der	ADJ
ejpam-5787	82	32	pol	pol	NOUN
ejpam-5787	82	33	equation	equation	NOUN
ejpam-5787	82	34	for	for	ADP
ejpam-5787	82	35	β	β	X
ejpam-5787	82	36	=	=	SYM
ejpam-5787	82	37	0	0	NUM
ejpam-5787	82	38	.	.	PUNCT
ejpam-5787	83	1	the	the	DET
ejpam-5787	83	2	surface	surface	NOUN
ejpam-5787	83	3	represents	represent	VERB
ejpam-5787	83	4	a	a	DET
ejpam-5787	83	5	two	two	NUM
ejpam-5787	83	6	-	-	PUNCT
ejpam-5787	83	7	dimensional	dimensional	ADJ
ejpam-5787	83	8	critical	critical	ADJ
ejpam-5787	83	9	manifold	manifold	ADJ
ejpam-5787	83	10	s.	s.	PROPN
ejpam-5787	83	11	a	a	DET
ejpam-5787	83	12	typical	typical	ADJ
ejpam-5787	83	13	trajectory	trajectory	NOUN
ejpam-5787	83	14	(	(	PUNCT
ejpam-5787	83	15	blue	blue	NOUN
ejpam-5787	83	16	)	)	PUNCT
ejpam-5787	83	17	of	of	ADP
ejpam-5787	83	18	(	(	PUNCT
ejpam-5787	83	19	4	4	X
ejpam-5787	83	20	)	)	PUNCT
ejpam-5787	83	21	remains	remain	VERB
ejpam-5787	83	22	close	close	ADJ
ejpam-5787	83	23	to	to	ADP
ejpam-5787	83	24	the	the	DET
ejpam-5787	83	25	stable	stable	ADJ
ejpam-5787	83	26	branch	branch	NOUN
ejpam-5787	83	27	(	(	PUNCT
ejpam-5787	83	28	y	y	PROPN
ejpam-5787	83	29	≤	≤	PROPN
ejpam-5787	83	30	−1	−1	NOUN
ejpam-5787	83	31	)	)	PUNCT
ejpam-5787	83	32	of	of	ADP
ejpam-5787	83	33	s	s	PRON
ejpam-5787	83	34	before	before	ADP
ejpam-5787	83	35	jumping	jump	VERB
ejpam-5787	83	36	to	to	ADP
ejpam-5787	83	37	other	other	ADJ
ejpam-5787	83	38	stable	stable	ADJ
ejpam-5787	83	39	branch	branch	NOUN
ejpam-5787	83	40	(	(	PUNCT
ejpam-5787	83	41	y	y	PROPN
ejpam-5787	83	42	≥	≥	NUM
ejpam-5787	83	43	1	1	NUM
ejpam-5787	83	44	)	)	PUNCT
ejpam-5787	83	45	at	at	ADP
ejpam-5787	83	46	the	the	DET
ejpam-5787	83	47	lines	line	NOUN
ejpam-5787	83	48	of	of	ADP
ejpam-5787	83	49	fold	fold	ADJ
ejpam-5787	83	50	points	point	NOUN
ejpam-5787	83	51	l±.	l±.	PUNCT
ejpam-5787	83	52	the	the	DET
ejpam-5787	83	53	trajectories	trajectory	NOUN
ejpam-5787	83	54	of	of	ADP
ejpam-5787	83	55	the	the	DET
ejpam-5787	83	56	fast	fast	ADJ
ejpam-5787	83	57	subsystem	subsystem	NOUN
ejpam-5787	83	58	(	(	PUNCT
ejpam-5787	83	59	layer	layer	NOUN
ejpam-5787	83	60	)	)	PUNCT
ejpam-5787	83	61	problem	problem	NOUN
ejpam-5787	83	62	(	(	PUNCT
ejpam-5787	83	63	7	7	X
ejpam-5787	83	64	)	)	PUNCT
ejpam-5787	83	65	are	be	AUX
ejpam-5787	83	66	computed	compute	VERB
ejpam-5787	83	67	to	to	ADP
ejpam-5787	83	68	dy	dy	X
ejpam-5787	83	69	dt	dt	NOUN
ejpam-5787	83	70	=	=	SYM
ejpam-5787	83	71	g(y	g(y	PROPN
ejpam-5787	83	72	)	)	PUNCT
ejpam-5787	83	73	,	,	PUNCT
ejpam-5787	83	74	where	where	SCONJ
ejpam-5787	83	75	g(y	g(y	NOUN
ejpam-5787	83	76	)	)	PUNCT
ejpam-5787	84	1	=	=	SYM
ejpam-5787	84	2	y	y	PROPN
ejpam-5787	84	3	−	−	NOUN
ejpam-5787	84	4	y3	y3	NOUN
ejpam-5787	84	5	3	3	NUM
ejpam-5787	84	6	+	+	NOUN
ejpam-5787	84	7	x	x	SYM
ejpam-5787	84	8	(	(	PUNCT
ejpam-5787	84	9	10	10	NUM
ejpam-5787	84	10	)	)	PUNCT
ejpam-5787	84	11	with	with	ADP
ejpam-5787	84	12	x	x	SYM
ejpam-5787	84	13	acting	act	VERB
ejpam-5787	84	14	as	as	ADP
ejpam-5787	84	15	a	a	DET
ejpam-5787	84	16	parameter	parameter	NOUN
ejpam-5787	84	17	(	(	PUNCT
ejpam-5787	84	18	see	see	VERB
ejpam-5787	84	19	figure	figure	NOUN
ejpam-5787	84	20	3	3	NUM
ejpam-5787	84	21	)	)	PUNCT
ejpam-5787	84	22	.	.	PUNCT
ejpam-5787	85	1	it	it	PRON
ejpam-5787	85	2	is	be	AUX
ejpam-5787	85	3	simple	simple	ADJ
ejpam-5787	85	4	to	to	PART
ejpam-5787	85	5	find	find	VERB
ejpam-5787	85	6	the	the	DET
ejpam-5787	85	7	equilibrium	equilibrium	NOUN
ejpam-5787	85	8	points	point	NOUN
ejpam-5787	85	9	of	of	ADP
ejpam-5787	85	10	g(y	g(y	NOUN
ejpam-5787	85	11	)	)	PUNCT
ejpam-5787	85	12	since	since	SCONJ
ejpam-5787	85	13	it	it	PRON
ejpam-5787	85	14	is	be	AUX
ejpam-5787	85	15	dependent	dependent	ADJ
ejpam-5787	85	16	on	on	ADP
ejpam-5787	85	17	the	the	DET
ejpam-5787	85	18	variable	variable	ADJ
ejpam-5787	85	19	y.	y.	NOUN
ejpam-5787	85	20	the	the	DET
ejpam-5787	85	21	equilibria	equilibrium	NOUN
ejpam-5787	85	22	of	of	ADP
ejpam-5787	85	23	the	the	DET
ejpam-5787	85	24	equation	equation	NOUN
ejpam-5787	85	25	is	be	AUX
ejpam-5787	85	26	given	give	VERB
ejpam-5787	85	27	by	by	ADP
ejpam-5787	85	28	the	the	DET
ejpam-5787	85	29	solutions	solution	NOUN
ejpam-5787	85	30	of	of	ADP
ejpam-5787	85	31	the	the	DET
ejpam-5787	85	32	equation	equation	NOUN
ejpam-5787	85	33	g(y	g(y	NOUN
ejpam-5787	85	34	)	)	PUNCT
ejpam-5787	85	35	=	=	SYM
ejpam-5787	85	36	0	0	NUM
ejpam-5787	85	37	⇐	⇐	ADJ
ejpam-5787	85	38	⇒	⇒	NOUN
ejpam-5787	85	39	x	x	PUNCT
ejpam-5787	86	1	=	=	SYM
ejpam-5787	86	2	y3	y3	NOUN
ejpam-5787	86	3	3	3	NUM
ejpam-5787	86	4	−	−	NOUN
ejpam-5787	86	5	y.	y.	NOUN
ejpam-5787	86	6	at	at	ADP
ejpam-5787	86	7	the	the	DET
ejpam-5787	86	8	bifurcation	bifurcation	NOUN
ejpam-5787	86	9	points	point	NOUN
ejpam-5787	86	10	,	,	PUNCT
ejpam-5787	86	11	the	the	DET
ejpam-5787	86	12	derivative	derivative	NOUN
ejpam-5787	86	13	of	of	ADP
ejpam-5787	86	14	g(y	g(y	PROPN
ejpam-5787	86	15	)	)	PUNCT
ejpam-5787	86	16	with	with	ADP
ejpam-5787	86	17	respect	respect	NOUN
ejpam-5787	86	18	to	to	ADP
ejpam-5787	86	19	y	y	PROPN
ejpam-5787	86	20	is	be	AUX
ejpam-5787	86	21	∂	∂	NUM
ejpam-5787	86	22	∂y	∂y	X
ejpam-5787	86	23	g(y	g(y	PROPN
ejpam-5787	86	24	)	)	PUNCT
ejpam-5787	86	25	=	=	PUNCT
ejpam-5787	86	26	0	0	NUM
ejpam-5787	86	27	⇐	⇐	ADJ
ejpam-5787	86	28	⇒	⇒	NOUN
ejpam-5787	86	29	(	(	PUNCT
ejpam-5787	86	30	1−	1−	NUM
ejpam-5787	86	31	y2	y2	NOUN
ejpam-5787	86	32	)	)	PUNCT
ejpam-5787	86	33	=	=	PUNCT
ejpam-5787	87	1	0	0	X
ejpam-5787	87	2	.	.	PUNCT
ejpam-5787	88	1	hence	hence	ADV
ejpam-5787	88	2	,	,	PUNCT
ejpam-5787	88	3	the	the	DET
ejpam-5787	88	4	bifurcation	bifurcation	NOUN
ejpam-5787	88	5	points	point	NOUN
ejpam-5787	88	6	(	(	PUNCT
ejpam-5787	88	7	called	call	VERB
ejpam-5787	88	8	singular	singular	ADJ
ejpam-5787	88	9	points	point	NOUN
ejpam-5787	88	10	)	)	PUNCT
ejpam-5787	88	11	are	be	AUX
ejpam-5787	88	12	(	(	PUNCT
ejpam-5787	88	13	x	x	NOUN
ejpam-5787	88	14	,	,	PUNCT
ejpam-5787	88	15	y	y	NOUN
ejpam-5787	88	16	)	)	PUNCT
ejpam-5787	88	17	=	=	SYM
ejpam-5787	88	18	(	(	PUNCT
ejpam-5787	88	19	±2	±2	NOUN
ejpam-5787	88	20	3	3	NUM
ejpam-5787	88	21	,	,	PUNCT
ejpam-5787	88	22	∓1	∓1	NUM
ejpam-5787	88	23	)	)	PUNCT
ejpam-5787	88	24	.	.	PUNCT
ejpam-5787	89	1	2.4	2.4	NUM
ejpam-5787	89	2	.	.	PUNCT
ejpam-5787	90	1	the	the	DET
ejpam-5787	90	2	desingularised	desingularised	ADJ
ejpam-5787	90	3	reduced	reduce	VERB
ejpam-5787	90	4	system	system	NOUN
ejpam-5787	90	5	for	for	ADP
ejpam-5787	90	6	ε	ε	PROPN
ejpam-5787	90	7	=	=	SYM
ejpam-5787	90	8	0	0	PROPN
ejpam-5787	90	9	,	,	PUNCT
ejpam-5787	90	10	the	the	DET
ejpam-5787	90	11	system	system	NOUN
ejpam-5787	90	12	(	(	PUNCT
ejpam-5787	90	13	6	6	NUM
ejpam-5787	90	14	)	)	PUNCT
ejpam-5787	90	15	can	can	AUX
ejpam-5787	90	16	be	be	AUX
ejpam-5787	90	17	reduced	reduce	VERB
ejpam-5787	90	18	to	to	ADP
ejpam-5787	90	19	the	the	DET
ejpam-5787	90	20	system	system	NOUN
ejpam-5787	90	21	of	of	ADP
ejpam-5787	90	22	odes	ode	NOUN
ejpam-5787	90	23	on	on	ADP
ejpam-5787	90	24	normally	normally	ADV
ejpam-5787	90	25	hyperbolic	hyperbolic	ADJ
ejpam-5787	90	26	critical	critical	ADJ
ejpam-5787	90	27	manifolds	manifold	NOUN
ejpam-5787	90	28	.	.	PUNCT
ejpam-5787	91	1	the	the	DET
ejpam-5787	91	2	trajectories	trajectory	NOUN
ejpam-5787	91	3	of	of	ADP
ejpam-5787	91	4	the	the	DET
ejpam-5787	91	5	reduced	reduce	VERB
ejpam-5787	91	6	system	system	NOUN
ejpam-5787	91	7	are	be	AUX
ejpam-5787	91	8	good	good	ADJ
ejpam-5787	91	9	approximations	approximation	NOUN
ejpam-5787	91	10	to	to	ADP
ejpam-5787	91	11	the	the	DET
ejpam-5787	91	12	solutions	solution	NOUN
ejpam-5787	91	13	of	of	ADP
ejpam-5787	91	14	the	the	DET
ejpam-5787	91	15	full	full	ADJ
ejpam-5787	91	16	system	system	NOUN
ejpam-5787	91	17	(	(	PUNCT
ejpam-5787	91	18	4	4	NUM
ejpam-5787	91	19	)	)	PUNCT
ejpam-5787	91	20	near	near	ADP
ejpam-5787	91	21	these	these	DET
ejpam-5787	91	22	manifolds	manifold	NOUN
ejpam-5787	91	23	.	.	PUNCT
ejpam-5787	92	1	the	the	DET
ejpam-5787	92	2	projection	projection	NOUN
ejpam-5787	92	3	of	of	ADP
ejpam-5787	92	4	the	the	DET
ejpam-5787	92	5	system	system	NOUN
ejpam-5787	92	6	can	can	AUX
ejpam-5787	92	7	be	be	AUX
ejpam-5787	92	8	defined	define	VERB
ejpam-5787	92	9	as	as	ADP
ejpam-5787	92	10	x	x	X
ejpam-5787	92	11	=	=	SYM
ejpam-5787	92	12	φ(y	φ(y	PROPN
ejpam-5787	92	13	,	,	PUNCT
ejpam-5787	92	14	θ	θ	NOUN
ejpam-5787	92	15	)	)	PUNCT
ejpam-5787	92	16	on	on	ADP
ejpam-5787	92	17	the	the	DET
ejpam-5787	92	18	critical	critical	ADJ
ejpam-5787	92	19	manifold	manifold	NOUN
ejpam-5787	92	20	and	and	CCONJ
ejpam-5787	92	21	the	the	DET
ejpam-5787	92	22	slow	slow	ADJ
ejpam-5787	92	23	flow	flow	NOUN
ejpam-5787	92	24	represented	represent	VERB
ejpam-5787	92	25	in	in	ADP
ejpam-5787	92	26	the	the	DET
ejpam-5787	92	27	terms	term	NOUN
ejpam-5787	92	28	(	(	PUNCT
ejpam-5787	92	29	y	y	PROPN
ejpam-5787	92	30	,	,	PUNCT
ejpam-5787	92	31	θ	θ	PROPN
ejpam-5787	92	32	)	)	PUNCT
ejpam-5787	92	33	.	.	PUNCT
ejpam-5787	93	1	since	since	SCONJ
ejpam-5787	93	2	the	the	DET
ejpam-5787	93	3	critical	critical	ADJ
ejpam-5787	93	4	manifold	manifold	NOUN
ejpam-5787	93	5	s	s	NOUN
ejpam-5787	93	6	is	be	AUX
ejpam-5787	93	7	a	a	DET
ejpam-5787	93	8	curve	curve	NOUN
ejpam-5787	93	9	with	with	ADP
ejpam-5787	93	10	the	the	DET
ejpam-5787	93	11	function	function	NOUN
ejpam-5787	93	12	x	x	PUNCT
ejpam-5787	93	13	=	=	SYM
ejpam-5787	93	14	φ(y	φ(y	PROPN
ejpam-5787	93	15	,	,	PUNCT
ejpam-5787	93	16	θ	θ	NOUN
ejpam-5787	93	17	)	)	PUNCT
ejpam-5787	93	18	=	=	SYM
ejpam-5787	93	19	y3	y3	NOUN
ejpam-5787	93	20	3	3	NUM
ejpam-5787	93	21	−	−	NOUN
ejpam-5787	93	22	y	y	PROPN
ejpam-5787	93	23	one	one	NOUN
ejpam-5787	93	24	can	can	AUX
ejpam-5787	93	25	see	see	VERB
ejpam-5787	93	26	that	that	SCONJ
ejpam-5787	93	27	this	this	DET
ejpam-5787	93	28	curve	curve	NOUN
ejpam-5787	93	29	has	have	AUX
ejpam-5787	93	30	fold	fold	VERB
ejpam-5787	93	31	points	point	NOUN
ejpam-5787	93	32	when	when	SCONJ
ejpam-5787	93	33	y	y	PROPN
ejpam-5787	93	34	=	=	PUNCT
ejpam-5787	93	35	±1	±1	VERB
ejpam-5787	93	36	.	.	PUNCT
ejpam-5787	94	1	by	by	ADP
ejpam-5787	94	2	differentiating	differentiate	VERB
ejpam-5787	94	3	the	the	DET
ejpam-5787	94	4	critical	critical	ADJ
ejpam-5787	94	5	manifold	manifold	NOUN
ejpam-5787	94	6	to	to	PART
ejpam-5787	94	7	obtain	obtain	VERB
ejpam-5787	94	8	ẋ	ẋ	PROPN
ejpam-5787	94	9	=	=	PRON
ejpam-5787	94	10	(	(	PUNCT
ejpam-5787	94	11	y2	y2	INTJ
ejpam-5787	94	12	−	−	PROPN
ejpam-5787	94	13	1)ẏ	1)ẏ	NUM
ejpam-5787	94	14	,	,	PUNCT
ejpam-5787	94	15	the	the	DET
ejpam-5787	94	16	implicit	implicit	ADJ
ejpam-5787	94	17	function	function	NOUN
ejpam-5787	94	18	theorem	theorem	NOUN
ejpam-5787	94	19	means	mean	VERB
ejpam-5787	94	20	that	that	SCONJ
ejpam-5787	94	21	g(φ(y	g(φ(y	VERB
ejpam-5787	94	22	,	,	PUNCT
ejpam-5787	94	23	θ	θ	NOUN
ejpam-5787	94	24	)	)	PUNCT
ejpam-5787	94	25	,	,	PUNCT
ejpam-5787	94	26	y	y	PROPN
ejpam-5787	94	27	,	,	PUNCT
ejpam-5787	94	28	θ	θ	PROPN
ejpam-5787	94	29	)	)	PUNCT
ejpam-5787	94	30	=	=	SYM
ejpam-5787	95	1	0	0	X
ejpam-5787	95	2	.	.	PUNCT
ejpam-5787	96	1	this	this	PRON
ejpam-5787	96	2	implies	imply	VERB
ejpam-5787	96	3	that	that	SCONJ
ejpam-5787	96	4	a	a	DET
ejpam-5787	96	5	chain	chain	NOUN
ejpam-5787	96	6	rule	rule	NOUN
ejpam-5787	96	7	gives	give	VERB
ejpam-5787	96	8	the	the	DET
ejpam-5787	96	9	relationship	relationship	NOUN
ejpam-5787	96	10	i.	i.	PROPN
ejpam-5787	96	11	alraddadi	alraddadi	PROPN
ejpam-5787	96	12	/	/	SYM
ejpam-5787	96	13	eur	eur	PROPN
ejpam-5787	96	14	.	.	PUNCT
ejpam-5787	97	1	j.	j.	PROPN
ejpam-5787	97	2	pure	pure	PROPN
ejpam-5787	97	3	appl	appl	PROPN
ejpam-5787	97	4	.	.	PROPN
ejpam-5787	97	5	math	math	PROPN
ejpam-5787	97	6	,	,	PUNCT
ejpam-5787	97	7	18	18	NUM
ejpam-5787	97	8	(	(	PUNCT
ejpam-5787	97	9	1	1	NUM
ejpam-5787	97	10	)	)	PUNCT
ejpam-5787	97	11	(	(	PUNCT
ejpam-5787	97	12	2025	2025	NUM
ejpam-5787	97	13	)	)	PUNCT
ejpam-5787	97	14	,	,	PUNCT
ejpam-5787	97	15	5787	5787	NUM
ejpam-5787	97	16	6	6	NUM
ejpam-5787	97	17	of	of	ADP
ejpam-5787	97	18	23	23	NUM
ejpam-5787	97	19	-1.25	-1.25	NUM
ejpam-5787	97	20	-1	-1	NOUN
ejpam-5787	97	21	-0.75	-0.75	NUM
ejpam-5787	97	22	-0.5	-0.5	PROPN
ejpam-5787	97	23	-0.25	-0.25	NUM
ejpam-5787	97	24	0	0	NUM
ejpam-5787	97	25	0.25	0.25	NUM
ejpam-5787	97	26	0.5	0.5	NUM
ejpam-5787	97	27	0.75	0.75	NUM
ejpam-5787	97	28	1	1	NUM
ejpam-5787	97	29	1.25	1.25	NUM
ejpam-5787	97	30	x	x	SYM
ejpam-5787	97	31	-3	-3	PUNCT
ejpam-5787	97	32	-2	-2	INTJ
ejpam-5787	97	33	-1	-1	SYM
ejpam-5787	97	34	0	0	NUM
ejpam-5787	97	35	1	1	NUM
ejpam-5787	97	36	2	2	NUM
ejpam-5787	97	37	3	3	NUM
ejpam-5787	97	38	y	y	PROPN
ejpam-5787	97	39	figure	figure	NOUN
ejpam-5787	97	40	3	3	NUM
ejpam-5787	97	41	:	:	PUNCT
ejpam-5787	97	42	phase	phase	NOUN
ejpam-5787	97	43	portrait	portrait	NOUN
ejpam-5787	97	44	showing	show	VERB
ejpam-5787	97	45	the	the	DET
ejpam-5787	97	46	solutions	solution	NOUN
ejpam-5787	97	47	of	of	ADP
ejpam-5787	97	48	the	the	DET
ejpam-5787	97	49	fast	fast	ADJ
ejpam-5787	97	50	system	system	NOUN
ejpam-5787	97	51	(	(	PUNCT
ejpam-5787	97	52	7	7	NUM
ejpam-5787	97	53	)	)	PUNCT
ejpam-5787	97	54	(	(	PUNCT
ejpam-5787	97	55	sold	sell	VERB
ejpam-5787	97	56	line	line	NOUN
ejpam-5787	97	57	and	and	CCONJ
ejpam-5787	97	58	dashed	dash	VERB
ejpam-5787	97	59	line	line	NOUN
ejpam-5787	97	60	)	)	PUNCT
ejpam-5787	97	61	and	and	CCONJ
ejpam-5787	97	62	the	the	DET
ejpam-5787	97	63	fast	fast	ADJ
ejpam-5787	97	64	flow	flow	NOUN
ejpam-5787	97	65	subsystem	subsystem	NOUN
ejpam-5787	97	66	indicated	indicate	VERB
ejpam-5787	97	67	by	by	ADP
ejpam-5787	97	68	the	the	DET
ejpam-5787	97	69	arrows	arrow	NOUN
ejpam-5787	97	70	.	.	PUNCT
ejpam-5787	98	1	the	the	DET
ejpam-5787	98	2	blue	blue	ADJ
ejpam-5787	98	3	line	line	NOUN
ejpam-5787	98	4	and	and	CCONJ
ejpam-5787	98	5	dashed	dash	VERB
ejpam-5787	98	6	red	red	ADJ
ejpam-5787	98	7	line	line	NOUN
ejpam-5787	98	8	are	be	AUX
ejpam-5787	98	9	the	the	DET
ejpam-5787	98	10	critical	critical	ADJ
ejpam-5787	98	11	manifold	manifold	NOUN
ejpam-5787	98	12	s	s	PROPN
ejpam-5787	98	13	of	of	ADP
ejpam-5787	98	14	vdp	vdp	PROPN
ejpam-5787	98	15	.	.	PROPN
ejpam-5787	99	1	for	for	ADP
ejpam-5787	99	2	−1	−1	NOUN
ejpam-5787	99	3	<	<	X
ejpam-5787	99	4	y	y	X
ejpam-5787	99	5	<	<	X
ejpam-5787	99	6	1	1	NUM
ejpam-5787	99	7	,	,	PUNCT
ejpam-5787	99	8	there	there	PRON
ejpam-5787	99	9	is	be	VERB
ejpam-5787	99	10	an	an	DET
ejpam-5787	99	11	unstable	unstable	ADJ
ejpam-5787	99	12	submanifold	submanifold	NOUN
ejpam-5787	99	13	(	(	PUNCT
ejpam-5787	99	14	f	f	PROPN
ejpam-5787	99	15	′(y	′(y	PROPN
ejpam-5787	99	16	)	)	PUNCT
ejpam-5787	99	17	>	>	X
ejpam-5787	99	18	0	0	NUM
ejpam-5787	99	19	)	)	PUNCT
ejpam-5787	99	20	of	of	ADP
ejpam-5787	99	21	s	s	PRON
ejpam-5787	99	22	while	while	SCONJ
ejpam-5787	99	23	the	the	DET
ejpam-5787	99	24	stable	stable	ADJ
ejpam-5787	99	25	submanifolds	submanifold	NOUN
ejpam-5787	99	26	(	(	PUNCT
ejpam-5787	99	27	f	f	PROPN
ejpam-5787	99	28	′(y	′(y	PROPN
ejpam-5787	99	29	)	)	PUNCT
ejpam-5787	99	30	<	<	X
ejpam-5787	99	31	0	0	NUM
ejpam-5787	99	32	)	)	PUNCT
ejpam-5787	99	33	of	of	ADP
ejpam-5787	99	34	s	s	PRON
ejpam-5787	99	35	are	be	AUX
ejpam-5787	99	36	two	two	NUM
ejpam-5787	99	37	disjoint	disjoint	ADJ
ejpam-5787	99	38	branches	branch	NOUN
ejpam-5787	99	39	where	where	SCONJ
ejpam-5787	99	40	y	y	PROPN
ejpam-5787	99	41	<	<	X
ejpam-5787	99	42	1	1	NUM
ejpam-5787	99	43	and	and	CCONJ
ejpam-5787	99	44	y	y	PROPN
ejpam-5787	99	45	>	>	X
ejpam-5787	100	1	1	1	X
ejpam-5787	100	2	.	.	PUNCT
ejpam-5787	101	1	if	if	SCONJ
ejpam-5787	101	2	|x|	|x|	PROPN
ejpam-5787	101	3	<	<	X
ejpam-5787	101	4	2	2	NUM
ejpam-5787	101	5	3	3	NUM
ejpam-5787	101	6	,	,	PUNCT
ejpam-5787	101	7	then	then	ADV
ejpam-5787	101	8	a	a	DET
ejpam-5787	101	9	system	system	NOUN
ejpam-5787	101	10	(	(	PUNCT
ejpam-5787	101	11	7	7	X
ejpam-5787	101	12	)	)	PUNCT
ejpam-5787	101	13	has	have	VERB
ejpam-5787	101	14	a	a	DET
ejpam-5787	101	15	single	single	ADJ
ejpam-5787	101	16	stable	stable	ADJ
ejpam-5787	101	17	equilibrium	equilibrium	NOUN
ejpam-5787	101	18	point	point	NOUN
ejpam-5787	101	19	at	at	ADP
ejpam-5787	101	20	the	the	DET
ejpam-5787	101	21	origin	origin	NOUN
ejpam-5787	101	22	point	point	NOUN
ejpam-5787	101	23	(	(	PUNCT
ejpam-5787	101	24	0	0	NUM
ejpam-5787	101	25	,	,	PUNCT
ejpam-5787	101	26	0	0	NUM
ejpam-5787	101	27	)	)	PUNCT
ejpam-5787	101	28	.	.	PUNCT
ejpam-5787	102	1	in	in	ADP
ejpam-5787	102	2	this	this	DET
ejpam-5787	102	3	figure	figure	NOUN
ejpam-5787	102	4	,	,	PUNCT
ejpam-5787	102	5	there	there	PRON
ejpam-5787	102	6	are	be	VERB
ejpam-5787	102	7	two	two	NUM
ejpam-5787	102	8	stable	stable	ADJ
ejpam-5787	102	9	equilibrium	equilibrium	NOUN
ejpam-5787	102	10	points	point	NOUN
ejpam-5787	102	11	(	(	PUNCT
ejpam-5787	102	12	black	black	ADJ
ejpam-5787	102	13	circle	circle	NOUN
ejpam-5787	102	14	)	)	PUNCT
ejpam-5787	102	15	(	(	PUNCT
ejpam-5787	102	16	±2	±2	NOUN
ejpam-5787	102	17	3	3	NUM
ejpam-5787	102	18	,	,	PUNCT
ejpam-5787	102	19	∓1	∓1	NUM
ejpam-5787	102	20	)	)	PUNCT
ejpam-5787	102	21	and	and	CCONJ
ejpam-5787	102	22	one	one	NUM
ejpam-5787	102	23	unstable	unstable	ADJ
ejpam-5787	102	24	equilibrium	equilibrium	NOUN
ejpam-5787	102	25	point	point	NOUN
ejpam-5787	102	26	(	(	PUNCT
ejpam-5787	102	27	blue	blue	ADJ
ejpam-5787	102	28	circle	circle	NOUN
ejpam-5787	102	29	)	)	PUNCT
ejpam-5787	102	30	(	(	PUNCT
ejpam-5787	102	31	0	0	NUM
ejpam-5787	102	32	,	,	PUNCT
ejpam-5787	102	33	0	0	NUM
ejpam-5787	102	34	)	)	PUNCT
ejpam-5787	102	35	for	for	ADP
ejpam-5787	102	36	|x|	|x|	PROPN
ejpam-5787	102	37	>	>	SYM
ejpam-5787	102	38	2	2	NUM
ejpam-5787	102	39	3	3	NUM
ejpam-5787	102	40	.	.	PUNCT
ejpam-5787	103	1	note	note	VERB
ejpam-5787	103	2	this	this	DET
ejpam-5787	103	3	phase	phase	NOUN
ejpam-5787	103	4	portrait	portrait	NOUN
ejpam-5787	103	5	is	be	AUX
ejpam-5787	103	6	independent	independent	ADJ
ejpam-5787	103	7	of	of	ADP
ejpam-5787	103	8	the	the	DET
ejpam-5787	103	9	slow	slow	ADJ
ejpam-5787	103	10	evolution	evolution	NOUN
ejpam-5787	103	11	of	of	ADP
ejpam-5787	103	12	θ	θ	PROPN
ejpam-5787	103	13	.	.	PUNCT
ejpam-5787	104	1	∂g	∂g	PROPN
ejpam-5787	104	2	∂y	∂y	PRON
ejpam-5787	105	1	ẏ	ẏ	NOUN
ejpam-5787	105	2	+	+	CCONJ
ejpam-5787	105	3	∂g	∂g	PROPN
ejpam-5787	105	4	∂x	∂x	NOUN
ejpam-5787	105	5	ẋ+	ẋ+	PROPN
ejpam-5787	105	6	∂g	∂g	PUNCT
ejpam-5787	106	1	∂θ	∂θ	PROPN
ejpam-5787	106	2	θ̇	θ̇	NOUN
ejpam-5787	106	3	=	=	NOUN
ejpam-5787	106	4	0	0	PUNCT
ejpam-5787	106	5	since	since	SCONJ
ejpam-5787	106	6	gy	gy	PROPN
ejpam-5787	106	7	is	be	AUX
ejpam-5787	106	8	non	non	ADJ
ejpam-5787	106	9	zero	zero	NUM
ejpam-5787	106	10	,	,	PUNCT
ejpam-5787	106	11	this	this	DET
ejpam-5787	106	12	equation	equation	NOUN
ejpam-5787	106	13	can	can	AUX
ejpam-5787	106	14	be	be	AUX
ejpam-5787	106	15	solved	solve	VERB
ejpam-5787	106	16	for	for	ADP
ejpam-5787	106	17	ẏ.	ẏ.	PROPN
ejpam-5787	106	18	gyẏ	gyẏ	PROPN
ejpam-5787	106	19	=	=	SYM
ejpam-5787	106	20	−(gxf(x	−(gxf(x	PROPN
ejpam-5787	106	21	,	,	PUNCT
ejpam-5787	106	22	y	y	PROPN
ejpam-5787	106	23	,	,	PUNCT
ejpam-5787	106	24	θ	θ	NOUN
ejpam-5787	106	25	)	)	PUNCT
ejpam-5787	106	26	+	+	CCONJ
ejpam-5787	106	27	gθω	gθω	NOUN
ejpam-5787	106	28	)	)	PUNCT
ejpam-5787	106	29	,	,	PUNCT
ejpam-5787	106	30	where	where	SCONJ
ejpam-5787	106	31	gy	gy	AUX
ejpam-5787	106	32	=	=	SYM
ejpam-5787	106	33	1−	1−	NUM
ejpam-5787	106	34	y2	y2	NOUN
ejpam-5787	106	35	,	,	PUNCT
ejpam-5787	106	36	gx	gx	PROPN
ejpam-5787	106	37	=	=	PROPN
ejpam-5787	106	38	1	1	NUM
ejpam-5787	106	39	,	,	PUNCT
ejpam-5787	106	40	gθ	gθ	PROPN
ejpam-5787	106	41	=	=	SYM
ejpam-5787	106	42	0	0	PROPN
ejpam-5787	106	43	and	and	CCONJ
ejpam-5787	106	44	f(x	f(x	PROPN
ejpam-5787	106	45	,	,	PUNCT
ejpam-5787	106	46	y	y	PROPN
ejpam-5787	106	47	,	,	PUNCT
ejpam-5787	106	48	θ	θ	PROPN
ejpam-5787	106	49	)	)	PUNCT
ejpam-5787	106	50	=	=	NOUN
ejpam-5787	106	51	a	a	DET
ejpam-5787	106	52	sin(2πθ)−	sin(2πθ)−	NOUN
ejpam-5787	106	53	y	y	NOUN
ejpam-5787	106	54	−	−	NOUN
ejpam-5787	106	55	β	β	X
ejpam-5787	106	56	.	.	PUNCT
ejpam-5787	107	1	then	then	ADV
ejpam-5787	107	2	,	,	PUNCT
ejpam-5787	107	3	(	(	PUNCT
ejpam-5787	107	4	1−	1−	NUM
ejpam-5787	107	5	y2)ẏ	y2)ẏ	NOUN
ejpam-5787	107	6	=	=	SYM
ejpam-5787	107	7	−(a	−(a	X
ejpam-5787	107	8	sin(2πθ)−	sin(2πθ)−	VERB
ejpam-5787	107	9	y	y	NOUN
ejpam-5787	107	10	−	−	PROPN
ejpam-5787	107	11	β	β	NOUN
ejpam-5787	107	12	)	)	PUNCT
ejpam-5787	107	13	(	(	PUNCT
ejpam-5787	107	14	11	11	NUM
ejpam-5787	107	15	)	)	PUNCT
ejpam-5787	107	16	we	we	PRON
ejpam-5787	107	17	rescale	rescale	VERB
ejpam-5787	107	18	the	the	DET
ejpam-5787	107	19	time	time	NOUN
ejpam-5787	107	20	by	by	ADP
ejpam-5787	107	21	t	t	PROPN
ejpam-5787	107	22	=	=	SYM
ejpam-5787	107	23	(	(	PUNCT
ejpam-5787	107	24	y2	y2	INTJ
ejpam-5787	107	25	−	−	PROPN
ejpam-5787	107	26	1)s	1)s	PROPN
ejpam-5787	107	27	and	and	CCONJ
ejpam-5787	107	28	substitute	substitute	NOUN
ejpam-5787	107	29	into	into	ADP
ejpam-5787	107	30	the	the	DET
ejpam-5787	107	31	rhs	rhs	PROPN
ejpam-5787	107	32	of	of	ADP
ejpam-5787	107	33	(	(	PUNCT
ejpam-5787	107	34	4	4	NUM
ejpam-5787	107	35	)	)	PUNCT
ejpam-5787	107	36	to	to	PART
ejpam-5787	107	37	obtain	obtain	VERB
ejpam-5787	107	38	the	the	DET
ejpam-5787	107	39	reduced	reduce	VERB
ejpam-5787	107	40	system	system	NOUN
ejpam-5787	107	41	as	as	SCONJ
ejpam-5787	107	42	follows	follow	VERB
ejpam-5787	107	43	:	:	PUNCT
ejpam-5787	107	44	dθ	dθ	PROPN
ejpam-5787	107	45	ds	ds	PROPN
ejpam-5787	107	46	=	=	SYM
ejpam-5787	107	47	−ωgy	−ωgy	PROPN
ejpam-5787	107	48	,	,	PUNCT
ejpam-5787	107	49	dy	dy	NOUN
ejpam-5787	107	50	ds	ds	PROPN
ejpam-5787	107	51	=	=	SYM
ejpam-5787	107	52	gxf(x	gxf(x	PROPN
ejpam-5787	107	53	,	,	PUNCT
ejpam-5787	107	54	y	y	PROPN
ejpam-5787	107	55	,	,	PUNCT
ejpam-5787	107	56	θ	θ	NOUN
ejpam-5787	107	57	)	)	PUNCT
ejpam-5787	107	58	+	+	CCONJ
ejpam-5787	107	59	gθω	gθω	NOUN
ejpam-5787	107	60	.	.	PUNCT
ejpam-5787	108	1	we	we	PRON
ejpam-5787	108	2	rewrite	rewrite	VERB
ejpam-5787	108	3	the	the	DET
ejpam-5787	108	4	system	system	NOUN
ejpam-5787	108	5	as	as	ADP
ejpam-5787	108	6	dθ	dθ	NOUN
ejpam-5787	108	7	ds	ds	PROPN
ejpam-5787	108	8	=	=	PUNCT
ejpam-5787	108	9	ω(y2	ω(y2	NOUN
ejpam-5787	108	10	−	−	NOUN
ejpam-5787	108	11	1	1	NUM
ejpam-5787	108	12	)	)	PUNCT
ejpam-5787	108	13	,	,	PUNCT
ejpam-5787	108	14	dy	dy	NOUN
ejpam-5787	108	15	ds	ds	NOUN
ejpam-5787	108	16	=	=	PUNCT
ejpam-5787	108	17	a	a	DET
ejpam-5787	108	18	sin(2πθ)−	sin(2πθ)−	NOUN
ejpam-5787	109	1	y	y	NOUN
ejpam-5787	109	2	−	−	NOUN
ejpam-5787	109	3	β	β	X
ejpam-5787	109	4	.	.	PUNCT
ejpam-5787	110	1	(	(	PUNCT
ejpam-5787	110	2	12	12	NUM
ejpam-5787	110	3	)	)	PUNCT
ejpam-5787	110	4	which	which	PRON
ejpam-5787	110	5	is	be	AUX
ejpam-5787	110	6	called	call	VERB
ejpam-5787	110	7	the	the	DET
ejpam-5787	110	8	desingularised	desingularised	ADJ
ejpam-5787	110	9	reduced	reduce	VERB
ejpam-5787	110	10	system	system	NOUN
ejpam-5787	110	11	of	of	ADP
ejpam-5787	110	12	forced	force	VERB
ejpam-5787	110	13	van	van	PROPN
ejpam-5787	110	14	der	der	ADJ
ejpam-5787	110	15	pol	pol	NOUN
ejpam-5787	110	16	equation	equation	NOUN
ejpam-5787	110	17	(	(	PUNCT
ejpam-5787	110	18	4	4	NUM
ejpam-5787	110	19	)	)	PUNCT
ejpam-5787	110	20	.	.	PUNCT
ejpam-5787	111	1	the	the	DET
ejpam-5787	111	2	desingularised	desingularise	VERB
ejpam-5787	111	3	reduced	reduce	VERB
ejpam-5787	111	4	system	system	NOUN
ejpam-5787	111	5	is	be	AUX
ejpam-5787	111	6	a	a	DET
ejpam-5787	111	7	time	time	NOUN
ejpam-5787	111	8	-	-	PUNCT
ejpam-5787	111	9	reparameterised	reparameterise	VERB
ejpam-5787	111	10	slow	slow	ADJ
ejpam-5787	111	11	flow	flow	NOUN
ejpam-5787	111	12	.	.	PUNCT
ejpam-5787	112	1	the	the	DET
ejpam-5787	112	2	time	time	NOUN
ejpam-5787	112	3	t	t	PROPN
ejpam-5787	112	4	and	and	CCONJ
ejpam-5787	112	5	the	the	DET
ejpam-5787	112	6	time	time	NOUN
ejpam-5787	112	7	s	s	PART
ejpam-5787	112	8	both	both	PRON
ejpam-5787	112	9	move	move	VERB
ejpam-5787	112	10	in	in	ADP
ejpam-5787	112	11	the	the	DET
ejpam-5787	112	12	same	same	ADJ
ejpam-5787	112	13	direction	direction	NOUN
ejpam-5787	112	14	on	on	ADP
ejpam-5787	112	15	the	the	DET
ejpam-5787	112	16	stable	stable	ADJ
ejpam-5787	112	17	branch	branch	NOUN
ejpam-5787	112	18	of	of	ADP
ejpam-5787	112	19	the	the	DET
ejpam-5787	112	20	critical	critical	ADJ
ejpam-5787	112	21	manifold	manifold	NOUN
ejpam-5787	112	22	,	,	PUNCT
ejpam-5787	112	23	but	but	CCONJ
ejpam-5787	112	24	they	they	PRON
ejpam-5787	112	25	move	move	VERB
ejpam-5787	112	26	in	in	ADP
ejpam-5787	112	27	opposite	opposite	ADJ
ejpam-5787	112	28	directions	direction	NOUN
ejpam-5787	112	29	on	on	ADP
ejpam-5787	112	30	the	the	DET
ejpam-5787	112	31	unstable	unstable	ADJ
ejpam-5787	112	32	branch	branch	NOUN
ejpam-5787	112	33	of	of	ADP
ejpam-5787	112	34	the	the	DET
ejpam-5787	112	35	critical	critical	ADJ
ejpam-5787	112	36	manifold	manifold	NOUN
ejpam-5787	112	37	.	.	PUNCT
ejpam-5787	113	1	in	in	ADP
ejpam-5787	113	2	this	this	DET
ejpam-5787	113	3	i.	i.	NOUN
ejpam-5787	113	4	alraddadi	alraddadi	PROPN
ejpam-5787	113	5	/	/	SYM
ejpam-5787	113	6	eur	eur	PROPN
ejpam-5787	113	7	.	.	PUNCT
ejpam-5787	114	1	j.	j.	PROPN
ejpam-5787	114	2	pure	pure	PROPN
ejpam-5787	114	3	appl	appl	PROPN
ejpam-5787	114	4	.	.	PROPN
ejpam-5787	114	5	math	math	PROPN
ejpam-5787	114	6	,	,	PUNCT
ejpam-5787	114	7	18	18	NUM
ejpam-5787	114	8	(	(	PUNCT
ejpam-5787	114	9	1	1	NUM
ejpam-5787	114	10	)	)	PUNCT
ejpam-5787	114	11	(	(	PUNCT
ejpam-5787	114	12	2025	2025	NUM
ejpam-5787	114	13	)	)	PUNCT
ejpam-5787	114	14	,	,	PUNCT
ejpam-5787	114	15	5787	5787	NUM
ejpam-5787	114	16	7	7	NUM
ejpam-5787	114	17	of	of	ADP
ejpam-5787	114	18	23	23	NUM
ejpam-5787	114	19	section	section	NOUN
ejpam-5787	114	20	we	we	PRON
ejpam-5787	114	21	focus	focus	VERB
ejpam-5787	114	22	on	on	ADP
ejpam-5787	114	23	the	the	DET
ejpam-5787	114	24	symmetric	symmetric	PROPN
ejpam-5787	114	25	vdp	vdp	PROPN
ejpam-5787	114	26	(	(	PUNCT
ejpam-5787	114	27	4	4	NUM
ejpam-5787	114	28	)	)	PUNCT
ejpam-5787	114	29	when	when	SCONJ
ejpam-5787	114	30	β	β	X
ejpam-5787	114	31	=	=	SYM
ejpam-5787	114	32	0	0	NUM
ejpam-5787	114	33	,	,	PUNCT
ejpam-5787	114	34	following	follow	VERB
ejpam-5787	114	35	the	the	DET
ejpam-5787	114	36	analysis	analysis	NOUN
ejpam-5787	114	37	in	in	ADP
ejpam-5787	114	38	[	[	X
ejpam-5787	114	39	10	10	NUM
ejpam-5787	114	40	]	]	PUNCT
ejpam-5787	114	41	.	.	PUNCT
ejpam-5787	115	1	the	the	DET
ejpam-5787	115	2	equilibria	equilibrium	NOUN
ejpam-5787	115	3	of	of	ADP
ejpam-5787	115	4	(	(	PUNCT
ejpam-5787	115	5	12	12	NUM
ejpam-5787	115	6	)	)	PUNCT
ejpam-5787	115	7	are	be	AUX
ejpam-5787	115	8	folded	fold	VERB
ejpam-5787	115	9	singularities	singularity	NOUN
ejpam-5787	115	10	which	which	PRON
ejpam-5787	115	11	lie	lie	VERB
ejpam-5787	115	12	on	on	ADP
ejpam-5787	115	13	the	the	DET
ejpam-5787	115	14	fold	fold	ADJ
ejpam-5787	115	15	lines	line	NOUN
ejpam-5787	115	16	l±.	l±.	ADJ
ejpam-5787	115	17	trajectories	trajectory	NOUN
ejpam-5787	115	18	of	of	ADP
ejpam-5787	115	19	(	(	PUNCT
ejpam-5787	115	20	12	12	NUM
ejpam-5787	115	21	)	)	PUNCT
ejpam-5787	115	22	are	be	AUX
ejpam-5787	115	23	located	locate	VERB
ejpam-5787	115	24	on	on	ADP
ejpam-5787	115	25	the	the	DET
ejpam-5787	115	26	slow	slow	ADJ
ejpam-5787	115	27	flow	flow	NOUN
ejpam-5787	115	28	along	along	ADP
ejpam-5787	115	29	stable	stable	ADJ
ejpam-5787	115	30	sheets	sheet	NOUN
ejpam-5787	115	31	of	of	ADP
ejpam-5787	115	32	the	the	DET
ejpam-5787	115	33	critical	critical	ADJ
ejpam-5787	115	34	manifold	manifold	NOUN
ejpam-5787	115	35	until	until	SCONJ
ejpam-5787	115	36	it	it	PRON
ejpam-5787	115	37	reaches	reach	VERB
ejpam-5787	115	38	the	the	DET
ejpam-5787	115	39	boundary	boundary	NOUN
ejpam-5787	115	40	of	of	ADP
ejpam-5787	115	41	this	this	DET
ejpam-5787	115	42	stable	stable	ADJ
ejpam-5787	115	43	sheet	sheet	NOUN
ejpam-5787	115	44	on	on	ADP
ejpam-5787	115	45	(	(	PUNCT
ejpam-5787	115	46	θ,±1	θ,±1	PROPN
ejpam-5787	115	47	)	)	PUNCT
ejpam-5787	115	48	.	.	PUNCT
ejpam-5787	116	1	these	these	DET
ejpam-5787	116	2	points	point	NOUN
ejpam-5787	116	3	(	(	PUNCT
ejpam-5787	116	4	y	y	NOUN
ejpam-5787	116	5	=	=	PUNCT
ejpam-5787	116	6	±1	±1	PROPN
ejpam-5787	116	7	)	)	PUNCT
ejpam-5787	116	8	are	be	AUX
ejpam-5787	116	9	the	the	DET
ejpam-5787	116	10	boundaries	boundary	NOUN
ejpam-5787	116	11	of	of	ADP
ejpam-5787	116	12	two	two	NUM
ejpam-5787	116	13	stable	stable	ADJ
ejpam-5787	116	14	sheets	sheet	NOUN
ejpam-5787	116	15	.	.	PUNCT
ejpam-5787	117	1	then	then	ADV
ejpam-5787	117	2	,	,	PUNCT
ejpam-5787	117	3	the	the	DET
ejpam-5787	117	4	trajectories	trajectory	NOUN
ejpam-5787	117	5	jump	jump	VERB
ejpam-5787	117	6	from	from	ADP
ejpam-5787	117	7	the	the	DET
ejpam-5787	117	8	fold	fold	ADJ
ejpam-5787	117	9	line	line	NOUN
ejpam-5787	117	10	to	to	ADP
ejpam-5787	117	11	another	another	DET
ejpam-5787	117	12	stable	stable	ADJ
ejpam-5787	117	13	sheet	sheet	NOUN
ejpam-5787	117	14	and	and	CCONJ
ejpam-5787	117	15	they	they	PRON
ejpam-5787	117	16	are	be	AUX
ejpam-5787	117	17	crossing	cross	VERB
ejpam-5787	117	18	with	with	ADP
ejpam-5787	117	19	y	y	PROPN
ejpam-5787	117	20	>	>	X
ejpam-5787	117	21	1	1	NUM
ejpam-5787	117	22	or	or	CCONJ
ejpam-5787	117	23	y	y	NOUN
ejpam-5787	117	24	<	<	X
ejpam-5787	117	25	−1	−1	NOUN
ejpam-5787	117	26	.	.	PUNCT
ejpam-5787	118	1	the	the	DET
ejpam-5787	118	2	equilibrium	equilibrium	NOUN
ejpam-5787	118	3	points	point	NOUN
ejpam-5787	118	4	(	(	PUNCT
ejpam-5787	118	5	called	call	VERB
ejpam-5787	118	6	folded	fold	VERB
ejpam-5787	118	7	singularities	singularity	NOUN
ejpam-5787	118	8	)	)	PUNCT
ejpam-5787	118	9	of	of	ADP
ejpam-5787	118	10	(	(	PUNCT
ejpam-5787	118	11	12	12	NUM
ejpam-5787	118	12	)	)	PUNCT
ejpam-5787	118	13	are	be	AUX
ejpam-5787	118	14	θ∗	θ∗	NOUN
ejpam-5787	118	15	=	=	PUNCT
ejpam-5787	118	16	sin−1(±1	sin−1(±1	NUM
ejpam-5787	118	17	a	a	PRON
ejpam-5787	118	18	)	)	PUNCT
ejpam-5787	118	19	2π	2π	NOUN
ejpam-5787	118	20	and	and	CCONJ
ejpam-5787	118	21	y∗	y∗	PROPN
ejpam-5787	118	22	=	=	PUNCT
ejpam-5787	118	23	±1	±1	VERB
ejpam-5787	118	24	.	.	PUNCT
ejpam-5787	119	1	there	there	PRON
ejpam-5787	119	2	is	be	VERB
ejpam-5787	119	3	no	no	DET
ejpam-5787	119	4	solution	solution	NOUN
ejpam-5787	119	5	for	for	ADP
ejpam-5787	119	6	a	a	DET
ejpam-5787	119	7	<	<	X
ejpam-5787	119	8	1	1	NUM
ejpam-5787	119	9	as	as	SCONJ
ejpam-5787	119	10	shown	show	VERB
ejpam-5787	119	11	in	in	ADP
ejpam-5787	119	12	figure	figure	NOUN
ejpam-5787	119	13	5(a	5(a	NUM
ejpam-5787	119	14	)	)	PUNCT
ejpam-5787	119	15	.	.	PUNCT
ejpam-5787	120	1	we	we	PRON
ejpam-5787	120	2	get	get	VERB
ejpam-5787	120	3	two	two	NUM
ejpam-5787	120	4	folded	fold	VERB
ejpam-5787	120	5	singularities	singularity	NOUN
ejpam-5787	120	6	on	on	ADP
ejpam-5787	120	7	the	the	DET
ejpam-5787	120	8	line	line	NOUN
ejpam-5787	120	9	l±1	l±1	PUNCT
ejpam-5787	121	1	at	at	ADP
ejpam-5787	121	2	(	(	PUNCT
ejpam-5787	121	3	y	y	PROPN
ejpam-5787	121	4	,	,	PUNCT
ejpam-5787	121	5	θ	θ	NOUN
ejpam-5787	121	6	)	)	PUNCT
ejpam-5787	121	7	=	=	NOUN
ejpam-5787	121	8	(	(	PUNCT
ejpam-5787	121	9	±1	±1	VERB
ejpam-5787	121	10	,	,	PUNCT
ejpam-5787	121	11	1/4	1/4	NUM
ejpam-5787	121	12	)	)	PUNCT
ejpam-5787	121	13	for	for	ADP
ejpam-5787	121	14	a	a	DET
ejpam-5787	121	15	=	=	SYM
ejpam-5787	121	16	1	1	NUM
ejpam-5787	121	17	,	,	PUNCT
ejpam-5787	121	18	and	and	CCONJ
ejpam-5787	121	19	we	we	PRON
ejpam-5787	121	20	have	have	VERB
ejpam-5787	121	21	four	four	NUM
ejpam-5787	121	22	folded	fold	VERB
ejpam-5787	121	23	singularities	singularity	NOUN
ejpam-5787	121	24	for	for	ADP
ejpam-5787	121	25	a	a	DET
ejpam-5787	121	26	>	>	SYM
ejpam-5787	121	27	1	1	NUM
ejpam-5787	121	28	on	on	ADP
ejpam-5787	121	29	the	the	DET
ejpam-5787	121	30	line	line	NOUN
ejpam-5787	121	31	l±1	l±1	NOUN
ejpam-5787	121	32	as	as	SCONJ
ejpam-5787	121	33	shown	show	VERB
ejpam-5787	121	34	below	below	ADP
ejpam-5787	121	35	p1,2(θ	p1,2(θ	ADJ
ejpam-5787	121	36	∗	∗	NOUN
ejpam-5787	121	37	1,2	1,2	NUM
ejpam-5787	121	38	,	,	PUNCT
ejpam-5787	121	39	y	y	PROPN
ejpam-5787	121	40	∗	∗	NOUN
ejpam-5787	121	41	)	)	PUNCT
ejpam-5787	121	42	=	=	SYM
ejpam-5787	121	43	(	(	PUNCT
ejpam-5787	121	44	sin−1	sin−1	PROPN
ejpam-5787	121	45	(	(	PUNCT
ejpam-5787	121	46	1a	1a	NOUN
ejpam-5787	121	47	)	)	PUNCT
ejpam-5787	121	48	2π	2π	NOUN
ejpam-5787	121	49	,	,	PUNCT
ejpam-5787	121	50	1	1	NUM
ejpam-5787	121	51	)	)	PUNCT
ejpam-5787	121	52	and	and	CCONJ
ejpam-5787	121	53	(	(	PUNCT
ejpam-5787	121	54	sin−1(−1	sin−1(−1	PROPN
ejpam-5787	121	55	a	a	PRON
ejpam-5787	121	56	)	)	PUNCT
ejpam-5787	121	57	2π	2π	NOUN
ejpam-5787	121	58	,	,	PUNCT
ejpam-5787	121	59	−1	−1	NOUN
ejpam-5787	121	60	)	)	PUNCT
ejpam-5787	121	61	,	,	PUNCT
ejpam-5787	121	62	where	where	SCONJ
ejpam-5787	121	63	θ∗1,2	θ∗1,2	PROPN
ejpam-5787	121	64	<	<	X
ejpam-5787	121	65	1/4	1/4	NUM
ejpam-5787	121	66	p3,4(θ	p3,4(θ	PROPN
ejpam-5787	121	67	∗	∗	NOUN
ejpam-5787	121	68	3,4	3,4	NUM
ejpam-5787	121	69	,	,	PUNCT
ejpam-5787	121	70	y	y	PROPN
ejpam-5787	121	71	∗	∗	NOUN
ejpam-5787	121	72	)	)	PUNCT
ejpam-5787	121	73	=	=	SYM
ejpam-5787	121	74	(	(	PUNCT
ejpam-5787	121	75	sin−1	sin−1	PROPN
ejpam-5787	121	76	(	(	PUNCT
ejpam-5787	121	77	1a	1a	NOUN
ejpam-5787	121	78	)	)	PUNCT
ejpam-5787	121	79	2π	2π	NOUN
ejpam-5787	121	80	,	,	PUNCT
ejpam-5787	121	81	1	1	NUM
ejpam-5787	121	82	)	)	PUNCT
ejpam-5787	121	83	and	and	CCONJ
ejpam-5787	121	84	(	(	PUNCT
ejpam-5787	121	85	sin−1(−1	sin−1(−1	PROPN
ejpam-5787	121	86	a	a	PRON
ejpam-5787	121	87	)	)	PUNCT
ejpam-5787	121	88	2π	2π	NOUN
ejpam-5787	121	89	,	,	PUNCT
ejpam-5787	121	90	−1	−1	NOUN
ejpam-5787	121	91	)	)	PUNCT
ejpam-5787	121	92	,	,	PUNCT
ejpam-5787	121	93	where	where	SCONJ
ejpam-5787	121	94	θ∗3,4	θ∗3,4	ADJ
ejpam-5787	121	95	>	>	X
ejpam-5787	121	96	1/4	1/4	NUM
ejpam-5787	121	97	to	to	PART
ejpam-5787	121	98	analyse	analyse	VERB
ejpam-5787	121	99	the	the	DET
ejpam-5787	121	100	stability	stability	NOUN
ejpam-5787	121	101	of	of	ADP
ejpam-5787	121	102	the	the	DET
ejpam-5787	121	103	equilibrium	equilibrium	NOUN
ejpam-5787	121	104	points	point	NOUN
ejpam-5787	121	105	,	,	PUNCT
ejpam-5787	121	106	we	we	PRON
ejpam-5787	121	107	calculate	calculate	VERB
ejpam-5787	121	108	the	the	DET
ejpam-5787	121	109	jacobian	jacobian	ADJ
ejpam-5787	121	110	matrix	matrix	NOUN
ejpam-5787	121	111	of	of	ADP
ejpam-5787	121	112	(	(	PUNCT
ejpam-5787	121	113	12	12	NUM
ejpam-5787	121	114	)	)	PUNCT
ejpam-5787	121	115	at	at	ADP
ejpam-5787	121	116	(	(	PUNCT
ejpam-5787	121	117	θ∗	θ∗	NOUN
ejpam-5787	121	118	,	,	PUNCT
ejpam-5787	121	119	y∗	y∗	PROPN
ejpam-5787	121	120	):	):	PUNCT
ejpam-5787	121	121	j(θ∗	j(θ∗	ADJ
ejpam-5787	121	122	,	,	PUNCT
ejpam-5787	121	123	y∗	y∗	PROPN
ejpam-5787	121	124	)	)	PUNCT
ejpam-5787	122	1	=	=	PUNCT
ejpam-5787	123	1	[	[	PUNCT
ejpam-5787	123	2	0	0	NUM
ejpam-5787	123	3	2ωy	2ωy	NOUN
ejpam-5787	123	4	2πa	2πa	NOUN
ejpam-5787	123	5	cos(2πθ	cos(2πθ	SYM
ejpam-5787	123	6	)	)	PUNCT
ejpam-5787	123	7	−1	−1	NOUN
ejpam-5787	123	8	]	]	PUNCT
ejpam-5787	123	9	and	and	CCONJ
ejpam-5787	123	10	the	the	DET
ejpam-5787	123	11	eigenvalues	eigenvalues	PROPN
ejpam-5787	123	12	of	of	ADP
ejpam-5787	123	13	(	(	PUNCT
ejpam-5787	123	14	j	j	PROPN
ejpam-5787	123	15	−	−	PROPN
ejpam-5787	123	16	λi	λi	NOUN
ejpam-5787	123	17	)	)	PUNCT
ejpam-5787	123	18	at	at	ADP
ejpam-5787	123	19	(	(	PUNCT
ejpam-5787	123	20	θ	θ	PROPN
ejpam-5787	123	21	,	,	PUNCT
ejpam-5787	123	22	y	y	NOUN
ejpam-5787	123	23	)	)	PUNCT
ejpam-5787	123	24	where	where	SCONJ
ejpam-5787	123	25	i	i	PRON
ejpam-5787	123	26	is	be	AUX
ejpam-5787	123	27	the	the	DET
ejpam-5787	123	28	identity	identity	NOUN
ejpam-5787	123	29	matrix	matrix	NOUN
ejpam-5787	123	30	:	:	PUNCT
ejpam-5787	123	31	λ1,2	λ1,2	PROPN
ejpam-5787	123	32	=	=	PUNCT
ejpam-5787	123	33	−1±	−1±	NOUN
ejpam-5787	123	34	√	√	ADV
ejpam-5787	123	35	1	1	NUM
ejpam-5787	123	36	+	+	NUM
ejpam-5787	123	37	16ωπa	16ωπa	NOUN
ejpam-5787	123	38	cos(2πθ	cos(2πθ	SYM
ejpam-5787	123	39	)	)	PUNCT
ejpam-5787	123	40	2	2	NUM
ejpam-5787	123	41	the	the	DET
ejpam-5787	123	42	classification	classification	NOUN
ejpam-5787	123	43	of	of	ADP
ejpam-5787	123	44	equilibria	equilibrium	NOUN
ejpam-5787	123	45	according	accord	VERB
ejpam-5787	123	46	to	to	ADP
ejpam-5787	123	47	λ1,2	λ1,2	PROPN
ejpam-5787	123	48	:	:	PUNCT
ejpam-5787	123	49	a	a	DET
ejpam-5787	123	50	=	=	SYM
ejpam-5787	123	51	1	1	NUM
ejpam-5787	123	52	and	and	CCONJ
ejpam-5787	123	53	θ	θ	PROPN
ejpam-5787	123	54	=	=	SYM
ejpam-5787	123	55	1/4	1/4	NUM
ejpam-5787	123	56	,	,	PUNCT
ejpam-5787	123	57	j	j	PROPN
ejpam-5787	123	58	has	have	VERB
ejpam-5787	123	59	λ1	λ1	PROPN
ejpam-5787	123	60	=	=	SYM
ejpam-5787	123	61	0	0	NUM
ejpam-5787	123	62	and	and	CCONJ
ejpam-5787	123	63	λ2	λ2	NOUN
ejpam-5787	123	64	=	=	SYM
ejpam-5787	123	65	−1	−1	NOUN
ejpam-5787	123	66	of	of	ADP
ejpam-5787	123	67	which	which	PRON
ejpam-5787	123	68	the	the	DET
ejpam-5787	123	69	equilibrium	equilibrium	NOUN
ejpam-5787	123	70	points	point	NOUN
ejpam-5787	123	71	are	be	AUX
ejpam-5787	123	72	folded	fold	VERB
ejpam-5787	123	73	saddle	saddle	NOUN
ejpam-5787	123	74	-	-	PUNCT
ejpam-5787	123	75	nodes	node	NOUN
ejpam-5787	123	76	on	on	ADP
ejpam-5787	123	77	the	the	DET
ejpam-5787	123	78	line	line	NOUN
ejpam-5787	123	79	l1	l1	PROPN
ejpam-5787	123	80	or	or	CCONJ
ejpam-5787	123	81	l−1	l−1	PROPN
ejpam-5787	123	82	.	.	PUNCT
ejpam-5787	124	1	for	for	ADP
ejpam-5787	124	2	a	a	PRON
ejpam-5787	124	3	>	>	SYM
ejpam-5787	124	4	1	1	NUM
ejpam-5787	124	5	,	,	PUNCT
ejpam-5787	124	6	two	two	NUM
ejpam-5787	124	7	equilibrium	equilibrium	NOUN
ejpam-5787	124	8	points	point	NOUN
ejpam-5787	124	9	p1,4	p1,4	ADV
ejpam-5787	124	10	are	be	AUX
ejpam-5787	124	11	folded	fold	VERB
ejpam-5787	124	12	saddles	saddle	NOUN
ejpam-5787	124	13	(	(	PUNCT
ejpam-5787	124	14	see	see	VERB
ejpam-5787	124	15	figure	figure	NOUN
ejpam-5787	124	16	4	4	NUM
ejpam-5787	124	17	)	)	PUNCT
ejpam-5787	124	18	.	.	PUNCT
ejpam-5787	125	1	when	when	SCONJ
ejpam-5787	125	2	1	1	NUM
ejpam-5787	125	3	<	<	X
ejpam-5787	125	4	a	a	DET
ejpam-5787	125	5	<	<	X
ejpam-5787	125	6	√	√	PROPN
ejpam-5787	125	7	1	1	NUM
ejpam-5787	125	8	+	+	CCONJ
ejpam-5787	125	9	(	(	PUNCT
ejpam-5787	125	10	1	1	NUM
ejpam-5787	125	11	16πω	16πω	NOUN
ejpam-5787	125	12	)	)	PUNCT
ejpam-5787	125	13	2	2	NUM
ejpam-5787	125	14	,	,	PUNCT
ejpam-5787	125	15	two	two	NUM
ejpam-5787	125	16	other	other	ADJ
ejpam-5787	125	17	equilibrium	equilibrium	NOUN
ejpam-5787	125	18	points	point	NOUN
ejpam-5787	125	19	p2,3	p2,3	NOUN
ejpam-5787	125	20	are	be	AUX
ejpam-5787	125	21	stable	stable	ADJ
ejpam-5787	125	22	node	node	NOUN
ejpam-5787	125	23	(	(	PUNCT
ejpam-5787	125	24	see	see	VERB
ejpam-5787	125	25	figure	figure	NOUN
ejpam-5787	125	26	5(b	5(b	NUM
ejpam-5787	125	27	)	)	PUNCT
ejpam-5787	125	28	)	)	PUNCT
ejpam-5787	125	29	.	.	PUNCT
ejpam-5787	126	1	for	for	ADP
ejpam-5787	126	2	a	a	DET
ejpam-5787	126	3	=	=	NOUN
ejpam-5787	126	4	√	√	NUM
ejpam-5787	126	5	1	1	NUM
ejpam-5787	126	6	+	+	CCONJ
ejpam-5787	126	7	(	(	PUNCT
ejpam-5787	126	8	1	1	NUM
ejpam-5787	126	9	16πω	16πω	NOUN
ejpam-5787	126	10	)	)	PUNCT
ejpam-5787	126	11	2	2	NUM
ejpam-5787	126	12	,	,	PUNCT
ejpam-5787	126	13	these	these	DET
ejpam-5787	126	14	equilibrium	equilibrium	NOUN
ejpam-5787	126	15	points	point	NOUN
ejpam-5787	126	16	p2,3	p2,3	PROPN
ejpam-5787	126	17	are	be	AUX
ejpam-5787	126	18	folded	fold	VERB
ejpam-5787	126	19	nodes	node	NOUN
ejpam-5787	126	20	,	,	PUNCT
ejpam-5787	126	21	and	and	CCONJ
ejpam-5787	126	22	for	for	ADP
ejpam-5787	126	23	a	a	DET
ejpam-5787	126	24	>	>	SYM
ejpam-5787	126	25	√	√	NUM
ejpam-5787	126	26	1	1	NUM
ejpam-5787	126	27	+	+	CCONJ
ejpam-5787	126	28	(	(	PUNCT
ejpam-5787	126	29	1	1	NUM
ejpam-5787	126	30	16πω	16πω	NOUN
ejpam-5787	126	31	)	)	PUNCT
ejpam-5787	126	32	2	2	NUM
ejpam-5787	126	33	p2,3	p2,3	NOUN
ejpam-5787	126	34	are	be	AUX
ejpam-5787	126	35	folded	fold	VERB
ejpam-5787	126	36	foci	focus	NOUN
ejpam-5787	126	37	.	.	PUNCT
ejpam-5787	127	1	also	also	ADV
ejpam-5787	127	2	,	,	PUNCT
ejpam-5787	127	3	we	we	PRON
ejpam-5787	127	4	compute	compute	VERB
ejpam-5787	127	5	stable	stable	ADJ
ejpam-5787	127	6	and	and	CCONJ
ejpam-5787	127	7	unstable	unstable	ADJ
ejpam-5787	127	8	manifolds	manifold	NOUN
ejpam-5787	127	9	ws	ws	NOUN
ejpam-5787	127	10	and	and	CCONJ
ejpam-5787	127	11	wu	wu	PROPN
ejpam-5787	127	12	of	of	ADP
ejpam-5787	127	13	the	the	DET
ejpam-5787	127	14	folded	fold	VERB
ejpam-5787	127	15	saddle	saddle	NOUN
ejpam-5787	127	16	(	(	PUNCT
ejpam-5787	127	17	θs,±1	θs,±1	NOUN
ejpam-5787	127	18	)	)	PUNCT
ejpam-5787	127	19	in	in	ADP
ejpam-5787	127	20	the	the	DET
ejpam-5787	127	21	desingularised	desingularise	VERB
ejpam-5787	127	22	slow	slow	ADJ
ejpam-5787	127	23	flow	flow	NOUN
ejpam-5787	127	24	system	system	NOUN
ejpam-5787	127	25	(	(	PUNCT
ejpam-5787	127	26	12	12	NUM
ejpam-5787	127	27	)	)	PUNCT
ejpam-5787	127	28	for	for	ADP
ejpam-5787	127	29	β	β	X
ejpam-5787	127	30	=	=	SYM
ejpam-5787	127	31	1.2	1.2	NUM
ejpam-5787	127	32	as	as	SCONJ
ejpam-5787	127	33	shown	show	VERB
ejpam-5787	127	34	in	in	ADP
ejpam-5787	127	35	figure	figure	NOUN
ejpam-5787	127	36	6	6	NUM
ejpam-5787	127	37	.	.	PUNCT
ejpam-5787	128	1	a	a	DET
ejpam-5787	128	2	trajectory	trajectory	NOUN
ejpam-5787	128	3	wu	wu	PROPN
ejpam-5787	128	4	denotes	denote	VERB
ejpam-5787	128	5	the	the	DET
ejpam-5787	128	6	first	first	ADJ
ejpam-5787	128	7	intersection	intersection	NOUN
ejpam-5787	128	8	with	with	ADP
ejpam-5787	128	9	y	y	PROPN
ejpam-5787	128	10	=	=	PUNCT
ejpam-5787	128	11	±1	±1	VERB
ejpam-5787	128	12	.	.	PUNCT
ejpam-5787	129	1	in	in	ADP
ejpam-5787	129	2	the	the	DET
ejpam-5787	129	3	backward	backward	ADJ
ejpam-5787	129	4	time	time	NOUN
ejpam-5787	129	5	on	on	ADP
ejpam-5787	129	6	the	the	DET
ejpam-5787	129	7	stable	stable	ADJ
ejpam-5787	129	8	manifold	manifold	ADJ
ejpam-5787	129	9	branch	branch	NOUN
ejpam-5787	129	10	,	,	PUNCT
ejpam-5787	129	11	a	a	DET
ejpam-5787	129	12	trajectory	trajectory	NOUN
ejpam-5787	129	13	ws	ws	NOUN
ejpam-5787	129	14	denotes	denote	VERB
ejpam-5787	129	15	the	the	DET
ejpam-5787	129	16	first	first	ADJ
ejpam-5787	129	17	intersection	intersection	NOUN
ejpam-5787	129	18	with	with	ADP
ejpam-5787	129	19	y	y	PROPN
ejpam-5787	129	20	=	=	PUNCT
ejpam-5787	129	21	±2	±2	NOUN
ejpam-5787	129	22	.	.	PUNCT
ejpam-5787	130	1	in	in	ADP
ejpam-5787	130	2	this	this	DET
ejpam-5787	130	3	following	follow	VERB
ejpam-5787	130	4	analysis	analysis	NOUN
ejpam-5787	130	5	,	,	PUNCT
ejpam-5787	130	6	we	we	PRON
ejpam-5787	130	7	compute	compute	VERB
ejpam-5787	130	8	a	a	DET
ejpam-5787	130	9	poincaré	poincaré	ADJ
ejpam-5787	130	10	map	map	NOUN
ejpam-5787	130	11	for	for	ADP
ejpam-5787	130	12	(	(	PUNCT
ejpam-5787	130	13	4	4	NUM
ejpam-5787	130	14	)	)	PUNCT
ejpam-5787	130	15	that	that	PRON
ejpam-5787	130	16	has	have	VERB
ejpam-5787	130	17	a	a	DET
ejpam-5787	130	18	return	return	NOUN
ejpam-5787	130	19	mechanism	mechanism	NOUN
ejpam-5787	130	20	via	via	ADP
ejpam-5787	130	21	a	a	DET
ejpam-5787	130	22	folded	fold	VERB
ejpam-5787	130	23	critical	critical	ADJ
ejpam-5787	130	24	manifold	manifold	NOUN
ejpam-5787	130	25	.	.	PUNCT
ejpam-5787	131	1	i.	i.	PROPN
ejpam-5787	131	2	alraddadi	alraddadi	PROPN
ejpam-5787	131	3	/	/	SYM
ejpam-5787	131	4	eur	eur	PROPN
ejpam-5787	131	5	.	.	PUNCT
ejpam-5787	132	1	j.	j.	PROPN
ejpam-5787	132	2	pure	pure	PROPN
ejpam-5787	132	3	appl	appl	PROPN
ejpam-5787	132	4	.	.	PROPN
ejpam-5787	132	5	math	math	PROPN
ejpam-5787	132	6	,	,	PUNCT
ejpam-5787	132	7	18	18	NUM
ejpam-5787	132	8	(	(	PUNCT
ejpam-5787	132	9	1	1	NUM
ejpam-5787	132	10	)	)	PUNCT
ejpam-5787	132	11	(	(	PUNCT
ejpam-5787	132	12	2025	2025	NUM
ejpam-5787	132	13	)	)	PUNCT
ejpam-5787	132	14	,	,	PUNCT
ejpam-5787	132	15	5787	5787	NUM
ejpam-5787	132	16	8	8	NUM
ejpam-5787	132	17	of	of	ADP
ejpam-5787	132	18	23	23	NUM
ejpam-5787	132	19	(	(	PUNCT
ejpam-5787	132	20	a	a	NOUN
ejpam-5787	132	21	)	)	PUNCT
ejpam-5787	132	22	(	(	PUNCT
ejpam-5787	132	23	b	b	X
ejpam-5787	132	24	)	)	PUNCT
ejpam-5787	132	25	figure	figure	NOUN
ejpam-5787	132	26	4	4	NUM
ejpam-5787	132	27	:	:	PUNCT
ejpam-5787	132	28	trajectories	trajectory	NOUN
ejpam-5787	132	29	of	of	ADP
ejpam-5787	132	30	the	the	DET
ejpam-5787	132	31	desingularised	desingularise	VERB
ejpam-5787	132	32	slow	slow	ADJ
ejpam-5787	132	33	flow	flow	NOUN
ejpam-5787	132	34	(	(	PUNCT
ejpam-5787	132	35	12	12	NUM
ejpam-5787	132	36	)	)	PUNCT
ejpam-5787	132	37	for	for	ADP
ejpam-5787	132	38	β	β	X
ejpam-5787	132	39	=	=	SYM
ejpam-5787	132	40	0	0	NUM
ejpam-5787	132	41	.	.	PUNCT
ejpam-5787	133	1	(	(	PUNCT
ejpam-5787	133	2	a	a	X
ejpam-5787	133	3	)	)	PUNCT
ejpam-5787	133	4	the	the	DET
ejpam-5787	133	5	parameter	parameter	NOUN
ejpam-5787	133	6	values	value	NOUN
ejpam-5787	133	7	are	be	AUX
ejpam-5787	133	8	a	a	DET
ejpam-5787	133	9	=	=	SYM
ejpam-5787	133	10	2.3	2.3	NUM
ejpam-5787	133	11	and	and	CCONJ
ejpam-5787	133	12	ω	ω	NUM
ejpam-5787	133	13	=	=	SYM
ejpam-5787	133	14	1	1	NUM
ejpam-5787	133	15	,	,	PUNCT
ejpam-5787	133	16	(	(	PUNCT
ejpam-5787	133	17	b	b	X
ejpam-5787	133	18	)	)	PUNCT
ejpam-5787	133	19	a	a	DET
ejpam-5787	133	20	=	=	SYM
ejpam-5787	133	21	20	20	NUM
ejpam-5787	133	22	and	and	CCONJ
ejpam-5787	133	23	ω	ω	NUM
ejpam-5787	133	24	=	=	SYM
ejpam-5787	133	25	5	5	NUM
ejpam-5787	133	26	.	.	PUNCT
ejpam-5787	134	1	there	there	PRON
ejpam-5787	134	2	are	be	VERB
ejpam-5787	134	3	four	four	NUM
ejpam-5787	134	4	folded	fold	VERB
ejpam-5787	134	5	singularities	singularity	NOUN
ejpam-5787	134	6	obtained	obtain	VERB
ejpam-5787	134	7	in	in	ADP
ejpam-5787	134	8	both	both	DET
ejpam-5787	134	9	cases	case	NOUN
ejpam-5787	134	10	.	.	PUNCT
ejpam-5787	135	1	the	the	DET
ejpam-5787	135	2	two	two	NUM
ejpam-5787	135	3	folded	fold	VERB
ejpam-5787	135	4	saddles	saddle	NOUN
ejpam-5787	135	5	equilibria	equilibrium	NOUN
ejpam-5787	135	6	(	(	PUNCT
ejpam-5787	135	7	θs,±1	θs,±1	NOUN
ejpam-5787	135	8	)	)	PUNCT
ejpam-5787	135	9	are	be	AUX
ejpam-5787	135	10	indicated	indicate	VERB
ejpam-5787	135	11	by	by	ADP
ejpam-5787	135	12	the	the	DET
ejpam-5787	135	13	cross	cross	NOUN
ejpam-5787	135	14	and	and	CCONJ
ejpam-5787	135	15	the	the	DET
ejpam-5787	135	16	two	two	NUM
ejpam-5787	135	17	folded	fold	VERB
ejpam-5787	135	18	foci	focus	NOUN
ejpam-5787	135	19	equilibria	equilibrium	NOUN
ejpam-5787	135	20	(	(	PUNCT
ejpam-5787	135	21	θn,±1	θn,±1	ADJ
ejpam-5787	135	22	)	)	PUNCT
ejpam-5787	135	23	are	be	AUX
ejpam-5787	135	24	indicated	indicate	VERB
ejpam-5787	135	25	by	by	ADP
ejpam-5787	135	26	the	the	DET
ejpam-5787	135	27	circle	circle	NOUN
ejpam-5787	135	28	.	.	PUNCT
ejpam-5787	136	1	the	the	DET
ejpam-5787	136	2	stable	stable	ADJ
ejpam-5787	136	3	ws	ws	NOUN
ejpam-5787	136	4	(	(	PUNCT
ejpam-5787	136	5	green	green	ADJ
ejpam-5787	136	6	)	)	PUNCT
ejpam-5787	136	7	and	and	CCONJ
ejpam-5787	136	8	unstable	unstable	ADJ
ejpam-5787	136	9	wu	wu	PROPN
ejpam-5787	136	10	(	(	PUNCT
ejpam-5787	136	11	blue	blue	ADJ
ejpam-5787	136	12	)	)	PUNCT
ejpam-5787	136	13	manifolds	manifold	NOUN
ejpam-5787	136	14	of	of	ADP
ejpam-5787	136	15	the	the	DET
ejpam-5787	136	16	folded	fold	VERB
ejpam-5787	136	17	saddles	saddle	NOUN
ejpam-5787	136	18	are	be	AUX
ejpam-5787	136	19	on	on	ADP
ejpam-5787	136	20	the	the	DET
ejpam-5787	136	21	fold	fold	ADJ
ejpam-5787	136	22	lines	line	NOUN
ejpam-5787	136	23	y	y	PROPN
ejpam-5787	136	24	=	=	PUNCT
ejpam-5787	136	25	±1	±1	PROPN
ejpam-5787	136	26	.	.	PUNCT
ejpam-5787	137	1	(	(	PUNCT
ejpam-5787	137	2	a	a	X
ejpam-5787	137	3	)	)	PUNCT
ejpam-5787	137	4	(	(	PUNCT
ejpam-5787	137	5	b	b	X
ejpam-5787	137	6	)	)	PUNCT
ejpam-5787	137	7	figure	figure	NOUN
ejpam-5787	137	8	5	5	NUM
ejpam-5787	137	9	:	:	PUNCT
ejpam-5787	137	10	trajectories	trajectory	NOUN
ejpam-5787	137	11	of	of	ADP
ejpam-5787	137	12	the	the	DET
ejpam-5787	137	13	desingularised	desingularise	VERB
ejpam-5787	137	14	slow	slow	ADJ
ejpam-5787	137	15	flow	flow	NOUN
ejpam-5787	137	16	(	(	PUNCT
ejpam-5787	137	17	12	12	NUM
ejpam-5787	137	18	)	)	PUNCT
ejpam-5787	137	19	for	for	ADP
ejpam-5787	137	20	β	β	X
ejpam-5787	137	21	=	=	SYM
ejpam-5787	137	22	0	0	NUM
ejpam-5787	137	23	and	and	CCONJ
ejpam-5787	137	24	ω	ω	NUM
ejpam-5787	137	25	=	=	SYM
ejpam-5787	137	26	0.54559	0.54559	NUM
ejpam-5787	137	27	.	.	PUNCT
ejpam-5787	138	1	(	(	PUNCT
ejpam-5787	138	2	a	a	X
ejpam-5787	138	3	)	)	PUNCT
ejpam-5787	138	4	shows	show	VERB
ejpam-5787	138	5	no	no	DET
ejpam-5787	138	6	folded	folded	ADJ
ejpam-5787	138	7	equilibria	equilibrium	NOUN
ejpam-5787	138	8	for	for	ADP
ejpam-5787	138	9	a	a	DET
ejpam-5787	138	10	=	=	SYM
ejpam-5787	138	11	0.9	0.9	NUM
ejpam-5787	138	12	.	.	PUNCT
ejpam-5787	139	1	(	(	PUNCT
ejpam-5787	139	2	b	b	X
ejpam-5787	139	3	)	)	PUNCT
ejpam-5787	139	4	four	four	NUM
ejpam-5787	139	5	folded	fold	VERB
ejpam-5787	139	6	singularities	singularity	NOUN
ejpam-5787	139	7	obtained	obtain	VERB
ejpam-5787	139	8	for	for	ADP
ejpam-5787	139	9	a	a	DET
ejpam-5787	139	10	=	=	SYM
ejpam-5787	139	11	1.00041	1.00041	NUM
ejpam-5787	139	12	.	.	PUNCT
ejpam-5787	140	1	the	the	DET
ejpam-5787	140	2	two	two	NUM
ejpam-5787	140	3	folded	fold	VERB
ejpam-5787	140	4	saddles	saddle	NOUN
ejpam-5787	140	5	equilibria	equilibrium	NOUN
ejpam-5787	140	6	(	(	PUNCT
ejpam-5787	140	7	θs,±1	θs,±1	NOUN
ejpam-5787	140	8	)	)	PUNCT
ejpam-5787	140	9	indicated	indicate	VERB
ejpam-5787	140	10	by	by	ADP
ejpam-5787	140	11	the	the	DET
ejpam-5787	140	12	cross	cross	NOUN
ejpam-5787	140	13	and	and	CCONJ
ejpam-5787	140	14	the	the	DET
ejpam-5787	140	15	two	two	NUM
ejpam-5787	140	16	folded	fold	VERB
ejpam-5787	140	17	nodes	node	NOUN
ejpam-5787	140	18	equilibria	equilibrium	NOUN
ejpam-5787	140	19	(	(	PUNCT
ejpam-5787	140	20	θn,±1	θn,±1	ADJ
ejpam-5787	140	21	)	)	PUNCT
ejpam-5787	140	22	indicated	indicate	VERB
ejpam-5787	140	23	by	by	ADP
ejpam-5787	140	24	the	the	DET
ejpam-5787	140	25	circle	circle	NOUN
ejpam-5787	140	26	.	.	PUNCT
ejpam-5787	141	1	the	the	DET
ejpam-5787	141	2	stable	stable	ADJ
ejpam-5787	141	3	ws	ws	NOUN
ejpam-5787	141	4	(	(	PUNCT
ejpam-5787	141	5	green	green	ADJ
ejpam-5787	141	6	)	)	PUNCT
ejpam-5787	141	7	and	and	CCONJ
ejpam-5787	141	8	unstable	unstable	ADJ
ejpam-5787	141	9	wu	wu	PROPN
ejpam-5787	141	10	(	(	PUNCT
ejpam-5787	141	11	blue	blue	ADJ
ejpam-5787	141	12	)	)	PUNCT
ejpam-5787	141	13	manifolds	manifold	NOUN
ejpam-5787	141	14	of	of	ADP
ejpam-5787	141	15	the	the	DET
ejpam-5787	141	16	folded	fold	VERB
ejpam-5787	141	17	saddles	saddle	NOUN
ejpam-5787	141	18	are	be	AUX
ejpam-5787	141	19	on	on	ADP
ejpam-5787	141	20	the	the	DET
ejpam-5787	141	21	fold	fold	ADJ
ejpam-5787	141	22	lines	line	NOUN
ejpam-5787	141	23	y	y	PROPN
ejpam-5787	141	24	=	=	PUNCT
ejpam-5787	141	25	±1	±1	VERB
ejpam-5787	141	26	.	.	PUNCT
ejpam-5787	142	1	this	this	DET
ejpam-5787	142	2	case	case	NOUN
ejpam-5787	142	3	shows	show	VERB
ejpam-5787	142	4	the	the	DET
ejpam-5787	142	5	connection	connection	NOUN
ejpam-5787	142	6	between	between	ADP
ejpam-5787	142	7	the	the	DET
ejpam-5787	142	8	folded	folded	ADJ
ejpam-5787	142	9	saddle	saddle	NOUN
ejpam-5787	142	10	and	and	CCONJ
ejpam-5787	142	11	the	the	DET
ejpam-5787	142	12	folded	fold	VERB
ejpam-5787	142	13	node	node	NOUN
ejpam-5787	142	14	.	.	PUNCT
ejpam-5787	143	1	i.	i.	PROPN
ejpam-5787	143	2	alraddadi	alraddadi	PROPN
ejpam-5787	143	3	/	/	SYM
ejpam-5787	143	4	eur	eur	PROPN
ejpam-5787	143	5	.	.	PUNCT
ejpam-5787	144	1	j.	j.	PROPN
ejpam-5787	144	2	pure	pure	PROPN
ejpam-5787	144	3	appl	appl	PROPN
ejpam-5787	144	4	.	.	PROPN
ejpam-5787	144	5	math	math	PROPN
ejpam-5787	144	6	,	,	PUNCT
ejpam-5787	144	7	18	18	NUM
ejpam-5787	144	8	(	(	PUNCT
ejpam-5787	144	9	1	1	NUM
ejpam-5787	144	10	)	)	PUNCT
ejpam-5787	144	11	(	(	PUNCT
ejpam-5787	144	12	2025	2025	NUM
ejpam-5787	144	13	)	)	PUNCT
ejpam-5787	144	14	,	,	PUNCT
ejpam-5787	144	15	5787	5787	NUM
ejpam-5787	144	16	9	9	NUM
ejpam-5787	144	17	of	of	ADP
ejpam-5787	144	18	23	23	NUM
ejpam-5787	144	19	(	(	PUNCT
ejpam-5787	144	20	a	a	NOUN
ejpam-5787	144	21	)	)	PUNCT
ejpam-5787	144	22	(	(	PUNCT
ejpam-5787	144	23	b	b	X
ejpam-5787	144	24	)	)	PUNCT
ejpam-5787	144	25	(	(	PUNCT
ejpam-5787	144	26	c	c	X
ejpam-5787	144	27	)	)	PUNCT
ejpam-5787	144	28	figure	figure	NOUN
ejpam-5787	144	29	6	6	NUM
ejpam-5787	144	30	:	:	PUNCT
ejpam-5787	144	31	trajectories	trajectory	NOUN
ejpam-5787	144	32	of	of	ADP
ejpam-5787	144	33	the	the	DET
ejpam-5787	144	34	desingularised	desingularise	VERB
ejpam-5787	144	35	slow	slow	ADJ
ejpam-5787	144	36	flow	flow	NOUN
ejpam-5787	144	37	(	(	PUNCT
ejpam-5787	144	38	12	12	NUM
ejpam-5787	144	39	)	)	PUNCT
ejpam-5787	144	40	for	for	ADP
ejpam-5787	144	41	β	β	X
ejpam-5787	144	42	=	=	SYM
ejpam-5787	144	43	1.2	1.2	NUM
ejpam-5787	144	44	.	.	PUNCT
ejpam-5787	145	1	(	(	PUNCT
ejpam-5787	145	2	a	a	DET
ejpam-5787	145	3	-	-	PUNCT
ejpam-5787	145	4	b	b	NOUN
ejpam-5787	145	5	)	)	PUNCT
ejpam-5787	145	6	show	show	VERB
ejpam-5787	145	7	the	the	DET
ejpam-5787	145	8	four	four	NUM
ejpam-5787	145	9	folded	fold	VERB
ejpam-5787	145	10	saddle	saddle	NOUN
ejpam-5787	145	11	equilibria	equilibrium	NOUN
ejpam-5787	145	12	on	on	ADP
ejpam-5787	145	13	the	the	DET
ejpam-5787	145	14	fold	fold	ADJ
ejpam-5787	145	15	lines	line	NOUN
ejpam-5787	145	16	y	y	PROPN
ejpam-5787	145	17	=	=	PUNCT
ejpam-5787	145	18	±1	±1	VERB
ejpam-5787	145	19	.	.	PUNCT
ejpam-5787	146	1	the	the	DET
ejpam-5787	146	2	two	two	NUM
ejpam-5787	146	3	folded	fold	VERB
ejpam-5787	146	4	saddles	saddle	NOUN
ejpam-5787	146	5	equilibria	equilibrium	NOUN
ejpam-5787	146	6	(	(	PUNCT
ejpam-5787	146	7	θs,±1	θs,±1	NOUN
ejpam-5787	146	8	)	)	PUNCT
ejpam-5787	146	9	are	be	AUX
ejpam-5787	146	10	indicated	indicate	VERB
ejpam-5787	146	11	by	by	ADP
ejpam-5787	146	12	the	the	DET
ejpam-5787	146	13	cross	cross	NOUN
ejpam-5787	146	14	and	and	CCONJ
ejpam-5787	146	15	the	the	DET
ejpam-5787	146	16	two	two	NUM
ejpam-5787	146	17	folded	fold	VERB
ejpam-5787	146	18	foci	focus	NOUN
ejpam-5787	146	19	equilibria	equilibrium	NOUN
ejpam-5787	146	20	(	(	PUNCT
ejpam-5787	146	21	θn,±1	θn,±1	ADJ
ejpam-5787	146	22	)	)	PUNCT
ejpam-5787	146	23	are	be	AUX
ejpam-5787	146	24	indicated	indicate	VERB
ejpam-5787	146	25	by	by	ADP
ejpam-5787	146	26	the	the	DET
ejpam-5787	146	27	circle	circle	NOUN
ejpam-5787	146	28	.	.	PUNCT
ejpam-5787	147	1	in	in	ADP
ejpam-5787	147	2	(	(	PUNCT
ejpam-5787	147	3	c	c	NOUN
ejpam-5787	147	4	)	)	PUNCT
ejpam-5787	147	5	,	,	PUNCT
ejpam-5787	147	6	there	there	PRON
ejpam-5787	147	7	are	be	VERB
ejpam-5787	147	8	only	only	ADV
ejpam-5787	147	9	two	two	NUM
ejpam-5787	147	10	folded	fold	VERB
ejpam-5787	147	11	equilibria	equilibrium	NOUN
ejpam-5787	147	12	on	on	ADP
ejpam-5787	147	13	the	the	DET
ejpam-5787	147	14	fold	fold	ADJ
ejpam-5787	147	15	line	line	NOUN
ejpam-5787	147	16	y	y	PROPN
ejpam-5787	147	17	=	=	SYM
ejpam-5787	147	18	−1	−1	NOUN
ejpam-5787	147	19	.	.	PUNCT
ejpam-5787	148	1	these	these	DET
ejpam-5787	148	2	folded	fold	VERB
ejpam-5787	148	3	equilibria	equilibrium	NOUN
ejpam-5787	148	4	are	be	AUX
ejpam-5787	148	5	folded	fold	VERB
ejpam-5787	148	6	saddles	saddle	NOUN
ejpam-5787	148	7	and	and	CCONJ
ejpam-5787	148	8	folded	fold	VERB
ejpam-5787	148	9	foci	focus	NOUN
ejpam-5787	148	10	.	.	PUNCT
ejpam-5787	149	1	the	the	DET
ejpam-5787	149	2	stable	stable	ADJ
ejpam-5787	149	3	ws	ws	NOUN
ejpam-5787	149	4	(	(	PUNCT
ejpam-5787	149	5	green	green	ADJ
ejpam-5787	149	6	)	)	PUNCT
ejpam-5787	149	7	and	and	CCONJ
ejpam-5787	149	8	unstable	unstable	ADJ
ejpam-5787	149	9	wu	wu	PROPN
ejpam-5787	149	10	(	(	PUNCT
ejpam-5787	149	11	blue	blue	ADJ
ejpam-5787	149	12	)	)	PUNCT
ejpam-5787	149	13	are	be	AUX
ejpam-5787	149	14	manifolds	manifold	NOUN
ejpam-5787	149	15	of	of	ADP
ejpam-5787	149	16	the	the	DET
ejpam-5787	149	17	folded	fold	VERB
ejpam-5787	149	18	saddles	saddle	NOUN
ejpam-5787	149	19	on	on	ADP
ejpam-5787	149	20	the	the	DET
ejpam-5787	149	21	fold	fold	ADJ
ejpam-5787	149	22	lines	line	NOUN
ejpam-5787	149	23	y	y	PROPN
ejpam-5787	149	24	=	=	PUNCT
ejpam-5787	149	25	±1	±1	VERB
ejpam-5787	149	26	.	.	PUNCT
ejpam-5787	150	1	3	3	X
ejpam-5787	150	2	.	.	X
ejpam-5787	150	3	return	return	NOUN
ejpam-5787	150	4	map	map	NOUN
ejpam-5787	150	5	for	for	ADP
ejpam-5787	150	6	the	the	DET
ejpam-5787	150	7	periodically	periodically	ADV
ejpam-5787	150	8	forced	force	VERB
ejpam-5787	150	9	singular	singular	PROPN
ejpam-5787	150	10	vdp	vdp	PROPN
ejpam-5787	150	11	oscillator	oscillator	NOUN
ejpam-5787	150	12	the	the	DET
ejpam-5787	150	13	dynamics	dynamic	NOUN
ejpam-5787	150	14	of	of	ADP
ejpam-5787	150	15	return	return	NOUN
ejpam-5787	150	16	map	map	NOUN
ejpam-5787	150	17	in	in	ADP
ejpam-5787	150	18	slow	slow	ADV
ejpam-5787	150	19	-	-	PUNCT
ejpam-5787	150	20	fast	fast	ADJ
ejpam-5787	150	21	systems	system	NOUN
ejpam-5787	150	22	were	be	AUX
ejpam-5787	150	23	studied	study	VERB
ejpam-5787	150	24	by	by	ADP
ejpam-5787	150	25	szmolyan	szmolyan	NOUN
ejpam-5787	150	26	and	and	CCONJ
ejpam-5787	150	27	wechselberger	wechselberger	NOUN
ejpam-5787	150	28	[	[	X
ejpam-5787	150	29	26	26	NUM
ejpam-5787	150	30	]	]	PUNCT
ejpam-5787	150	31	,	,	PUNCT
ejpam-5787	150	32	and	and	CCONJ
ejpam-5787	150	33	guckenheimer[9–11	guckenheimer[9–11	NOUN
ejpam-5787	150	34	]	]	PUNCT
ejpam-5787	150	35	.	.	PUNCT
ejpam-5787	151	1	in	in	ADP
ejpam-5787	151	2	this	this	DET
ejpam-5787	151	3	section	section	NOUN
ejpam-5787	151	4	we	we	PRON
ejpam-5787	151	5	study	study	VERB
ejpam-5787	151	6	the	the	DET
ejpam-5787	151	7	bifurcation	bifurcation	NOUN
ejpam-5787	151	8	analysis	analysis	NOUN
ejpam-5787	151	9	of	of	ADP
ejpam-5787	151	10	periodic	periodic	ADJ
ejpam-5787	151	11	orbits	orbit	NOUN
ejpam-5787	151	12	of	of	ADP
ejpam-5787	151	13	(	(	PUNCT
ejpam-5787	151	14	12	12	NUM
ejpam-5787	151	15	)	)	PUNCT
ejpam-5787	151	16	via	via	ADP
ejpam-5787	151	17	a	a	DET
ejpam-5787	151	18	poincaré	poincaré	ADJ
ejpam-5787	151	19	return	return	NOUN
ejpam-5787	151	20	map	map	NOUN
ejpam-5787	151	21	.	.	PUNCT
ejpam-5787	152	1	these	these	DET
ejpam-5787	152	2	bifurcations	bifurcation	NOUN
ejpam-5787	152	3	correspond	correspond	VERB
ejpam-5787	152	4	to	to	ADP
ejpam-5787	152	5	the	the	DET
ejpam-5787	152	6	bifurcation	bifurcation	NOUN
ejpam-5787	152	7	of	of	ADP
ejpam-5787	152	8	periodic	periodic	ADJ
ejpam-5787	152	9	orbits	orbit	NOUN
ejpam-5787	152	10	in	in	ADP
ejpam-5787	152	11	the	the	DET
ejpam-5787	152	12	periodically	periodically	ADV
ejpam-5787	152	13	forced	force	VERB
ejpam-5787	152	14	singular	singular	NOUN
ejpam-5787	152	15	(	(	PUNCT
ejpam-5787	152	16	vdp	vdp	PROPN
ejpam-5787	152	17	)	)	PUNCT
ejpam-5787	152	18	oscillator	oscillator	NOUN
ejpam-5787	152	19	(	(	PUNCT
ejpam-5787	152	20	4	4	NUM
ejpam-5787	152	21	)	)	PUNCT
ejpam-5787	152	22	.	.	PUNCT
ejpam-5787	153	1	we	we	PRON
ejpam-5787	153	2	follow	follow	VERB
ejpam-5787	153	3	the	the	DET
ejpam-5787	153	4	construction	construction	NOUN
ejpam-5787	153	5	of	of	ADP
ejpam-5787	153	6	the	the	DET
ejpam-5787	153	7	return	return	NOUN
ejpam-5787	153	8	map	map	NOUN
ejpam-5787	153	9	of	of	ADP
ejpam-5787	153	10	the	the	DET
ejpam-5787	153	11	desingularised	desingularise	VERB
ejpam-5787	153	12	slow	slow	ADJ
ejpam-5787	153	13	flow	flow	NOUN
ejpam-5787	153	14	system	system	NOUN
ejpam-5787	153	15	as	as	SCONJ
ejpam-5787	153	16	found	find	VERB
ejpam-5787	153	17	in	in	ADP
ejpam-5787	153	18	[	[	X
ejpam-5787	153	19	10	10	NUM
ejpam-5787	153	20	]	]	PUNCT
ejpam-5787	153	21	,	,	PUNCT
ejpam-5787	153	22	together	together	ADV
ejpam-5787	153	23	with	with	ADP
ejpam-5787	153	24	our	our	PRON
ejpam-5787	153	25	analysis	analysis	NOUN
ejpam-5787	153	26	of	of	ADP
ejpam-5787	153	27	(	(	PUNCT
ejpam-5787	153	28	12	12	NUM
ejpam-5787	153	29	)	)	PUNCT
ejpam-5787	153	30	in	in	ADP
ejpam-5787	153	31	subsection	subsection	NOUN
ejpam-5787	153	32	(	(	PUNCT
ejpam-5787	153	33	2.4	2.4	NUM
ejpam-5787	153	34	)	)	PUNCT
ejpam-5787	153	35	.	.	PUNCT
ejpam-5787	154	1	we	we	PRON
ejpam-5787	154	2	defined	define	VERB
ejpam-5787	154	3	the	the	DET
ejpam-5787	154	4	first	first	ADJ
ejpam-5787	154	5	return	return	NOUN
ejpam-5787	154	6	map	map	NOUN
ejpam-5787	154	7	from	from	ADP
ejpam-5787	154	8	y	y	PROPN
ejpam-5787	154	9	=	=	SYM
ejpam-5787	154	10	2	2	NUM
ejpam-5787	154	11	(	(	PUNCT
ejpam-5787	154	12	s2(θ	s2(θ	ADJ
ejpam-5787	154	13	,	,	PUNCT
ejpam-5787	154	14	2	2	NUM
ejpam-5787	154	15	)	)	PUNCT
ejpam-5787	154	16	)	)	PUNCT
ejpam-5787	154	17	to	to	ADP
ejpam-5787	154	18	itself	itself	PRON
ejpam-5787	154	19	for	for	ADP
ejpam-5787	154	20	the	the	DET
ejpam-5787	154	21	desingularised	desingularise	VERB
ejpam-5787	154	22	slow	slow	ADJ
ejpam-5787	154	23	flow	flow	NOUN
ejpam-5787	154	24	system	system	NOUN
ejpam-5787	154	25	(	(	PUNCT
ejpam-5787	154	26	12	12	NUM
ejpam-5787	154	27	):	):	PUNCT
ejpam-5787	154	28	f	f	PROPN
ejpam-5787	154	29	:	:	PUNCT
ejpam-5787	154	30	s2	s2	PROPN
ejpam-5787	154	31	→	→	SYM
ejpam-5787	154	32	s2	s2	PROPN
ejpam-5787	154	33	i.	i.	NOUN
ejpam-5787	154	34	alraddadi	alraddadi	PROPN
ejpam-5787	154	35	/	/	SYM
ejpam-5787	154	36	eur	eur	PROPN
ejpam-5787	154	37	.	.	PUNCT
ejpam-5787	155	1	j.	j.	PROPN
ejpam-5787	155	2	pure	pure	PROPN
ejpam-5787	155	3	appl	appl	PROPN
ejpam-5787	155	4	.	.	PROPN
ejpam-5787	155	5	math	math	PROPN
ejpam-5787	155	6	,	,	PUNCT
ejpam-5787	155	7	18	18	NUM
ejpam-5787	155	8	(	(	PUNCT
ejpam-5787	155	9	1	1	NUM
ejpam-5787	155	10	)	)	PUNCT
ejpam-5787	155	11	(	(	PUNCT
ejpam-5787	155	12	2025	2025	NUM
ejpam-5787	155	13	)	)	PUNCT
ejpam-5787	155	14	,	,	PUNCT
ejpam-5787	155	15	5787	5787	NUM
ejpam-5787	155	16	10	10	NUM
ejpam-5787	155	17	of	of	ADP
ejpam-5787	155	18	23	23	NUM
ejpam-5787	155	19	by	by	ADP
ejpam-5787	155	20	the	the	DET
ejpam-5787	155	21	flow	flow	NOUN
ejpam-5787	155	22	of	of	ADP
ejpam-5787	155	23	(	(	PUNCT
ejpam-5787	155	24	12	12	NUM
ejpam-5787	155	25	)	)	PUNCT
ejpam-5787	155	26	,	,	PUNCT
ejpam-5787	155	27	s2(θ	s2(θ	PROPN
ejpam-5787	155	28	,	,	PUNCT
ejpam-5787	155	29	2	2	NUM
ejpam-5787	155	30	)	)	PUNCT
ejpam-5787	155	31	as	as	ADP
ejpam-5787	155	32	the	the	DET
ejpam-5787	155	33	poincaré	poincaré	ADJ
ejpam-5787	155	34	section	section	NOUN
ejpam-5787	155	35	where	where	SCONJ
ejpam-5787	155	36	the	the	DET
ejpam-5787	155	37	first	first	ADJ
ejpam-5787	155	38	intersection	intersection	NOUN
ejpam-5787	155	39	of	of	ADP
ejpam-5787	155	40	the	the	DET
ejpam-5787	155	41	trajectory	trajectory	NOUN
ejpam-5787	155	42	starting	start	VERB
ejpam-5787	155	43	at	at	ADP
ejpam-5787	155	44	s2(θ	s2(θ	PROPN
ejpam-5787	155	45	,	,	PUNCT
ejpam-5787	155	46	2	2	NUM
ejpam-5787	155	47	)	)	PUNCT
ejpam-5787	155	48	with	with	ADP
ejpam-5787	155	49	θ	θ	PROPN
ejpam-5787	155	50	being	be	AUX
ejpam-5787	155	51	mod	mod	ADJ
ejpam-5787	155	52	1	1	NUM
ejpam-5787	155	53	.	.	PUNCT
ejpam-5787	156	1	the	the	DET
ejpam-5787	156	2	map	map	NOUN
ejpam-5787	156	3	f	f	PROPN
ejpam-5787	156	4	can	can	AUX
ejpam-5787	156	5	be	be	AUX
ejpam-5787	156	6	decomposed	decompose	VERB
ejpam-5787	156	7	into	into	ADP
ejpam-5787	156	8	four	four	NUM
ejpam-5787	156	9	maps	map	NOUN
ejpam-5787	156	10	(	(	PUNCT
ejpam-5787	156	11	discontinuous	discontinuous	ADJ
ejpam-5787	156	12	):	):	PUNCT
ejpam-5787	156	13	f	f	X
ejpam-5787	156	14	=	=	SYM
ejpam-5787	156	15	j−	j−	PROPN
ejpam-5787	156	16	◦	◦	NOUN
ejpam-5787	156	17	p−	p−	NOUN
ejpam-5787	156	18	◦	◦	NOUN
ejpam-5787	156	19	j+	j+	NUM
ejpam-5787	156	20	◦	◦	NOUN
ejpam-5787	156	21	p+	p+	NOUN
ejpam-5787	156	22	(	(	PUNCT
ejpam-5787	156	23	13	13	NUM
ejpam-5787	156	24	)	)	PUNCT
ejpam-5787	156	25	where	where	SCONJ
ejpam-5787	156	26	p+	p+	ADV
ejpam-5787	156	27	:	:	PUNCT
ejpam-5787	156	28	s2	s2	PROPN
ejpam-5787	156	29	→	→	SYM
ejpam-5787	156	30	s1	s1	PROPN
ejpam-5787	156	31	,	,	PUNCT
ejpam-5787	156	32	j+	j+	NUM
ejpam-5787	156	33	:	:	PUNCT
ejpam-5787	156	34	s1	s1	PROPN
ejpam-5787	156	35	→	→	SYM
ejpam-5787	156	36	s−2	s−2	PROPN
ejpam-5787	156	37	,	,	PUNCT
ejpam-5787	156	38	p−	p−	INTJ
ejpam-5787	156	39	:	:	PUNCT
ejpam-5787	156	40	s−2	s−2	PROPN
ejpam-5787	156	41	→	→	SYM
ejpam-5787	156	42	s−1	s−1	PROPN
ejpam-5787	156	43	,	,	PUNCT
ejpam-5787	156	44	j−	j−	VERB
ejpam-5787	156	45	:	:	PUNCT
ejpam-5787	156	46	s−1	s−1	PROPN
ejpam-5787	156	47	→	→	SYM
ejpam-5787	156	48	s2	s2	PROPN
ejpam-5787	156	49	,	,	PUNCT
ejpam-5787	156	50	note	note	VERB
ejpam-5787	156	51	that	that	SCONJ
ejpam-5787	156	52	s±1	s±1	NOUN
ejpam-5787	156	53	=	=	SYM
ejpam-5787	156	54	l±.	l±.	ADJ
ejpam-5787	156	55	two	two	NUM
ejpam-5787	156	56	maps	map	NOUN
ejpam-5787	156	57	p±(θ	p±(θ	PROPN
ejpam-5787	156	58	,	,	PUNCT
ejpam-5787	156	59	y	y	NOUN
ejpam-5787	156	60	)	)	PUNCT
ejpam-5787	156	61	are	be	AUX
ejpam-5787	156	62	well	well	ADV
ejpam-5787	156	63	defined	define	VERB
ejpam-5787	156	64	on	on	ADP
ejpam-5787	156	65	the	the	DET
ejpam-5787	156	66	stable	stable	ADJ
ejpam-5787	156	67	slow	slow	ADJ
ejpam-5787	156	68	manifold	manifold	ADJ
ejpam-5787	156	69	s±2	s±2	NOUN
ejpam-5787	156	70	(	(	PUNCT
ejpam-5787	156	71	from	from	ADP
ejpam-5787	156	72	y	y	NOUN
ejpam-5787	156	73	=	=	PUNCT
ejpam-5787	156	74	±2	±2	NOUN
ejpam-5787	156	75	to	to	ADP
ejpam-5787	156	76	the	the	DET
ejpam-5787	156	77	fold	fold	ADJ
ejpam-5787	156	78	lines	line	NOUN
ejpam-5787	156	79	y	y	PROPN
ejpam-5787	156	80	=	=	PUNCT
ejpam-5787	156	81	±1	±1	PROPN
ejpam-5787	156	82	)	)	PUNCT
ejpam-5787	156	83	and	and	CCONJ
ejpam-5787	156	84	j±(θ	j±(θ	PROPN
ejpam-5787	156	85	,	,	PUNCT
ejpam-5787	156	86	y	y	PROPN
ejpam-5787	156	87	)	)	PUNCT
ejpam-5787	156	88	represent	represent	VERB
ejpam-5787	156	89	the	the	DET
ejpam-5787	156	90	transition	transition	NOUN
ejpam-5787	156	91	map	map	NOUN
ejpam-5787	156	92	from	from	ADP
ejpam-5787	156	93	fold	fold	ADJ
ejpam-5787	156	94	lines	line	NOUN
ejpam-5787	156	95	l±	l±	VERB
ejpam-5787	156	96	to	to	ADP
ejpam-5787	156	97	s∓2	s∓2	PROPN
ejpam-5787	156	98	.	.	PUNCT
ejpam-5787	157	1	in	in	ADP
ejpam-5787	157	2	figure	figure	NOUN
ejpam-5787	157	3	2	2	NUM
ejpam-5787	157	4	,	,	PUNCT
ejpam-5787	157	5	we	we	PRON
ejpam-5787	157	6	note	note	VERB
ejpam-5787	157	7	that	that	SCONJ
ejpam-5787	157	8	trajectories	trajectory	NOUN
ejpam-5787	157	9	of	of	ADP
ejpam-5787	157	10	the	the	DET
ejpam-5787	157	11	periodically	periodically	ADV
ejpam-5787	157	12	forced	force	VERB
ejpam-5787	157	13	singular	singular	NOUN
ejpam-5787	157	14	(	(	PUNCT
ejpam-5787	157	15	vdp	vdp	PROPN
ejpam-5787	157	16	)	)	PUNCT
ejpam-5787	157	17	oscillator	oscillator	NOUN
ejpam-5787	157	18	(	(	PUNCT
ejpam-5787	157	19	4	4	NUM
ejpam-5787	157	20	)	)	PUNCT
ejpam-5787	157	21	continue	continue	VERB
ejpam-5787	157	22	on	on	ADP
ejpam-5787	157	23	the	the	DET
ejpam-5787	157	24	stable	stable	ADJ
ejpam-5787	157	25	branch	branch	NOUN
ejpam-5787	157	26	of	of	ADP
ejpam-5787	157	27	the	the	DET
ejpam-5787	157	28	critical	critical	ADJ
ejpam-5787	157	29	manifold	manifold	NOUN
ejpam-5787	157	30	s	s	NUM
ejpam-5787	157	31	until	until	SCONJ
ejpam-5787	157	32	it	it	PRON
ejpam-5787	157	33	reaches	reach	VERB
ejpam-5787	157	34	a	a	DET
ejpam-5787	157	35	fold	fold	ADJ
ejpam-5787	157	36	line	line	NOUN
ejpam-5787	157	37	l±1	l±1	NOUN
ejpam-5787	157	38	,	,	PUNCT
ejpam-5787	157	39	then	then	ADV
ejpam-5787	157	40	jump	jump	VERB
ejpam-5787	157	41	to	to	ADP
ejpam-5787	157	42	another	another	DET
ejpam-5787	157	43	stable	stable	ADJ
ejpam-5787	157	44	branch	branch	NOUN
ejpam-5787	157	45	of	of	ADP
ejpam-5787	157	46	s	s	PRON
ejpam-5787	157	47	.	.	PUNCT
ejpam-5787	158	1	this	this	DET
ejpam-5787	158	2	jumping	jump	VERB
ejpam-5787	158	3	behaviour	behaviour	NOUN
ejpam-5787	158	4	is	be	AUX
ejpam-5787	158	5	well	well	ADV
ejpam-5787	158	6	defined	define	VERB
ejpam-5787	158	7	by	by	ADP
ejpam-5787	158	8	the	the	DET
ejpam-5787	158	9	maps	map	NOUN
ejpam-5787	158	10	:	:	PUNCT
ejpam-5787	158	11	j+(θ	j+(θ	NOUN
ejpam-5787	158	12	,	,	PUNCT
ejpam-5787	158	13	1	1	X
ejpam-5787	158	14	)	)	PUNCT
ejpam-5787	158	15	=	=	SYM
ejpam-5787	158	16	(	(	PUNCT
ejpam-5787	158	17	θ,−2	θ,−2	VERB
ejpam-5787	158	18	)	)	PUNCT
ejpam-5787	158	19	and	and	CCONJ
ejpam-5787	158	20	j−(θ,−1	j−(θ,−1	NOUN
ejpam-5787	158	21	)	)	PUNCT
ejpam-5787	159	1	=	=	SYM
ejpam-5787	159	2	(	(	PUNCT
ejpam-5787	159	3	θ	θ	PROPN
ejpam-5787	159	4	,	,	PUNCT
ejpam-5787	159	5	2	2	NUM
ejpam-5787	159	6	)	)	PUNCT
ejpam-5787	159	7	.	.	PUNCT
ejpam-5787	160	1	in	in	ADP
ejpam-5787	160	2	the	the	DET
ejpam-5787	160	3	singular	singular	ADJ
ejpam-5787	160	4	case	case	NOUN
ejpam-5787	160	5	where	where	SCONJ
ejpam-5787	160	6	ε	ε	PROPN
ejpam-5787	160	7	→	→	SYM
ejpam-5787	160	8	0	0	NUM
ejpam-5787	160	9	,	,	PUNCT
ejpam-5787	160	10	there	there	PRON
ejpam-5787	160	11	are	be	VERB
ejpam-5787	160	12	regions	region	NOUN
ejpam-5787	160	13	where	where	SCONJ
ejpam-5787	160	14	no	no	DET
ejpam-5787	160	15	trajectories	trajectory	NOUN
ejpam-5787	160	16	arrive	arrive	VERB
ejpam-5787	160	17	at	at	ADP
ejpam-5787	160	18	the	the	DET
ejpam-5787	160	19	fold	fold	ADJ
ejpam-5787	160	20	line	line	NOUN
ejpam-5787	160	21	l±1	l±1	NOUN
ejpam-5787	160	22	,	,	PUNCT
ejpam-5787	160	23	while	while	SCONJ
ejpam-5787	160	24	for	for	ADP
ejpam-5787	160	25	sufficiently	sufficiently	ADV
ejpam-5787	160	26	small	small	ADJ
ejpam-5787	160	27	ε	ε	PROPN
ejpam-5787	160	28	,	,	PUNCT
ejpam-5787	160	29	some	some	DET
ejpam-5787	160	30	trajectories	trajectory	NOUN
ejpam-5787	160	31	of	of	ADP
ejpam-5787	160	32	the	the	DET
ejpam-5787	160	33	nonsingular	nonsingular	ADJ
ejpam-5787	160	34	system	system	NOUN
ejpam-5787	160	35	(	(	PUNCT
ejpam-5787	160	36	4	4	X
ejpam-5787	160	37	)	)	PUNCT
ejpam-5787	160	38	cross	cross	VERB
ejpam-5787	160	39	the	the	DET
ejpam-5787	160	40	fold	fold	ADJ
ejpam-5787	160	41	lines	line	NOUN
ejpam-5787	160	42	near	near	ADP
ejpam-5787	160	43	the	the	DET
ejpam-5787	160	44	folded	fold	VERB
ejpam-5787	160	45	saddle	saddle	NOUN
ejpam-5787	160	46	equilibria	equilibrium	NOUN
ejpam-5787	160	47	and	and	CCONJ
ejpam-5787	160	48	continue	continue	VERB
ejpam-5787	160	49	on	on	ADP
ejpam-5787	160	50	the	the	DET
ejpam-5787	160	51	unstable	unstable	ADJ
ejpam-5787	160	52	branch	branch	NOUN
ejpam-5787	160	53	of	of	ADP
ejpam-5787	160	54	the	the	DET
ejpam-5787	160	55	critical	critical	ADJ
ejpam-5787	160	56	manifold	manifold	ADJ
ejpam-5787	160	57	s.	s.	PROPN
ejpam-5787	160	58	these	these	DET
ejpam-5787	160	59	trajectories	trajectory	NOUN
ejpam-5787	160	60	are	be	AUX
ejpam-5787	160	61	called	call	VERB
ejpam-5787	160	62	canards	canard	NOUN
ejpam-5787	160	63	[	[	X
ejpam-5787	160	64	15	15	NUM
ejpam-5787	160	65	]	]	PUNCT
ejpam-5787	160	66	,	,	PUNCT
ejpam-5787	160	67	and	and	CCONJ
ejpam-5787	160	68	can	can	AUX
ejpam-5787	160	69	appear	appear	VERB
ejpam-5787	160	70	in	in	ADP
ejpam-5787	160	71	attractors	attractor	NOUN
ejpam-5787	160	72	near	near	ADP
ejpam-5787	160	73	the	the	DET
ejpam-5787	160	74	folded	fold	VERB
ejpam-5787	160	75	singularity	singularity	NOUN
ejpam-5787	160	76	.	.	PUNCT
ejpam-5787	161	1	the	the	DET
ejpam-5787	161	2	properties	property	NOUN
ejpam-5787	161	3	of	of	ADP
ejpam-5787	161	4	canard	canard	NOUN
ejpam-5787	161	5	trajectories	trajectory	NOUN
ejpam-5787	161	6	in	in	ADP
ejpam-5787	161	7	forced	force	VERB
ejpam-5787	161	8	van	van	PROPN
ejpam-5787	161	9	der	der	PROPN
ejpam-5787	161	10	pol	pol	PROPN
ejpam-5787	161	11	systems	system	NOUN
ejpam-5787	161	12	were	be	AUX
ejpam-5787	161	13	studied	study	VERB
ejpam-5787	161	14	by	by	ADP
ejpam-5787	161	15	guckenheimer	guckenheimer	PROPN
ejpam-5787	161	16	,	,	PUNCT
ejpam-5787	161	17	hoffman	hoffman	NOUN
ejpam-5787	161	18	and	and	CCONJ
ejpam-5787	161	19	weckesser	weckesser	VERB
ejpam-5787	161	20	and	and	CCONJ
ejpam-5787	161	21	later	later	ADV
ejpam-5787	161	22	by	by	ADP
ejpam-5787	161	23	szmolyan	szmolyan	NOUN
ejpam-5787	161	24	and	and	CCONJ
ejpam-5787	161	25	wechselberger	wechselberger	NOUN
ejpam-5787	161	26	[	[	X
ejpam-5787	161	27	4	4	NUM
ejpam-5787	161	28	,	,	PUNCT
ejpam-5787	161	29	25	25	NUM
ejpam-5787	161	30	,	,	PUNCT
ejpam-5787	161	31	26	26	NUM
ejpam-5787	161	32	,	,	PUNCT
ejpam-5787	161	33	31	31	NUM
ejpam-5787	161	34	]	]	PUNCT
ejpam-5787	161	35	.	.	PUNCT
ejpam-5787	162	1	moreover	moreover	ADV
ejpam-5787	162	2	,	,	PUNCT
ejpam-5787	162	3	guckenheimer	guckenheimer	PROPN
ejpam-5787	162	4	et	et	PROPN
ejpam-5787	162	5	al	al	PROPN
ejpam-5787	162	6	.	.	PROPN
ejpam-5787	162	7	observed	observe	VERB
ejpam-5787	162	8	that	that	SCONJ
ejpam-5787	162	9	there	there	PRON
ejpam-5787	162	10	can	can	AUX
ejpam-5787	162	11	be	be	AUX
ejpam-5787	162	12	can	can	AUX
ejpam-5787	162	13	be	be	AUX
ejpam-5787	162	14	chaotic	chaotic	ADJ
ejpam-5787	162	15	attractors	attractor	NOUN
ejpam-5787	162	16	for	for	ADP
ejpam-5787	162	17	return	return	NOUN
ejpam-5787	162	18	map	map	NOUN
ejpam-5787	162	19	f	f	X
ejpam-5787	162	20	(	(	PUNCT
ejpam-5787	162	21	13	13	NUM
ejpam-5787	162	22	)	)	PUNCT
ejpam-5787	162	23	by	by	ADP
ejpam-5787	162	24	analysing	analyse	VERB
ejpam-5787	162	25	the	the	DET
ejpam-5787	162	26	behaviour	behaviour	NOUN
ejpam-5787	162	27	associated	associate	VERB
ejpam-5787	162	28	with	with	ADP
ejpam-5787	162	29	canard	canard	NOUN
ejpam-5787	162	30	trajectories	trajectory	NOUN
ejpam-5787	162	31	[	[	X
ejpam-5787	162	32	10	10	NUM
ejpam-5787	162	33	]	]	PUNCT
ejpam-5787	162	34	.	.	PUNCT
ejpam-5787	163	1	they	they	PRON
ejpam-5787	163	2	examined	examine	VERB
ejpam-5787	163	3	various	various	ADJ
ejpam-5787	163	4	aspects	aspect	NOUN
ejpam-5787	163	5	of	of	ADP
ejpam-5787	163	6	the	the	DET
ejpam-5787	163	7	dynamics	dynamic	NOUN
ejpam-5787	163	8	of	of	ADP
ejpam-5787	163	9	the	the	DET
ejpam-5787	163	10	return	return	NOUN
ejpam-5787	163	11	map	map	NOUN
ejpam-5787	163	12	.	.	PUNCT
ejpam-5787	164	1	3.1	3.1	NUM
ejpam-5787	164	2	.	.	PUNCT
ejpam-5787	164	3	numerical	numerical	ADJ
ejpam-5787	164	4	approximation	approximation	NOUN
ejpam-5787	164	5	of	of	ADP
ejpam-5787	164	6	the	the	DET
ejpam-5787	164	7	first	first	ADJ
ejpam-5787	164	8	return	return	NOUN
ejpam-5787	164	9	map	map	NOUN
ejpam-5787	164	10	the	the	DET
ejpam-5787	164	11	first	first	ADJ
ejpam-5787	164	12	return	return	NOUN
ejpam-5787	164	13	map	map	NOUN
ejpam-5787	164	14	f	f	X
ejpam-5787	164	15	(	(	PUNCT
ejpam-5787	164	16	13	13	NUM
ejpam-5787	164	17	)	)	PUNCT
ejpam-5787	164	18	is	be	AUX
ejpam-5787	164	19	computed	compute	VERB
ejpam-5787	164	20	by	by	ADP
ejpam-5787	164	21	using	use	VERB
ejpam-5787	164	22	a	a	DET
ejpam-5787	164	23	matlab	matlab	PROPN
ejpam-5787	164	24	numerical	numerical	PROPN
ejpam-5787	164	25	approximation	approximation	NOUN
ejpam-5787	164	26	scheme	scheme	NOUN
ejpam-5787	165	1	[	[	X
ejpam-5787	165	2	17	17	NUM
ejpam-5787	165	3	]	]	PUNCT
ejpam-5787	165	4	.	.	PUNCT
ejpam-5787	166	1	following	follow	VERB
ejpam-5787	166	2	the	the	DET
ejpam-5787	166	3	computation	computation	NOUN
ejpam-5787	166	4	technique	technique	NOUN
ejpam-5787	166	5	of	of	ADP
ejpam-5787	166	6	the	the	DET
ejpam-5787	166	7	first	first	ADJ
ejpam-5787	166	8	return	return	NOUN
ejpam-5787	166	9	map	map	NOUN
ejpam-5787	166	10	,	,	PUNCT
ejpam-5787	166	11	we	we	PRON
ejpam-5787	166	12	compute	compute	VERB
ejpam-5787	166	13	p+	p+	ADV
ejpam-5787	166	14	and	and	CCONJ
ejpam-5787	166	15	p−	p−	NOUN
ejpam-5787	166	16	separately	separately	ADV
ejpam-5787	166	17	,	,	PUNCT
ejpam-5787	166	18	while	while	SCONJ
ejpam-5787	166	19	j+	j+	NUM
ejpam-5787	166	20	and	and	CCONJ
ejpam-5787	166	21	j−	j−	PROPN
ejpam-5787	166	22	are	be	AUX
ejpam-5787	166	23	explicit	explicit	ADJ
ejpam-5787	166	24	as	as	SCONJ
ejpam-5787	166	25	known	know	VERB
ejpam-5787	166	26	in	in	ADP
ejpam-5787	166	27	(	(	PUNCT
ejpam-5787	166	28	13	13	NUM
ejpam-5787	166	29	)	)	PUNCT
ejpam-5787	166	30	.	.	PUNCT
ejpam-5787	167	1	these	these	DET
ejpam-5787	167	2	maps	map	NOUN
ejpam-5787	167	3	p+	p+	VERB
ejpam-5787	167	4	and	and	CCONJ
ejpam-5787	167	5	p−	p−	NOUN
ejpam-5787	167	6	are	be	AUX
ejpam-5787	167	7	approximated	approximate	VERB
ejpam-5787	167	8	by	by	ADP
ejpam-5787	167	9	solving	solve	VERB
ejpam-5787	167	10	system	system	NOUN
ejpam-5787	167	11	(	(	PUNCT
ejpam-5787	167	12	12	12	NUM
ejpam-5787	167	13	):	):	PUNCT
ejpam-5787	167	14	starting	start	VERB
ejpam-5787	167	15	at	at	ADP
ejpam-5787	167	16	y	y	PROPN
ejpam-5787	167	17	=	=	PUNCT
ejpam-5787	167	18	±2	±2	NOUN
ejpam-5787	167	19	and	and	CCONJ
ejpam-5787	167	20	finishing	finish	VERB
ejpam-5787	167	21	at	at	ADP
ejpam-5787	167	22	an	an	DET
ejpam-5787	167	23	event	event	NOUN
ejpam-5787	167	24	where	where	SCONJ
ejpam-5787	167	25	y	y	PROPN
ejpam-5787	167	26	=	=	PUNCT
ejpam-5787	167	27	±1	±1	VERB
ejpam-5787	167	28	.	.	PUNCT
ejpam-5787	168	1	we	we	PRON
ejpam-5787	168	2	use	use	VERB
ejpam-5787	168	3	the	the	DET
ejpam-5787	168	4	matlab	matlab	PROPN
ejpam-5787	168	5	numerical	numerical	PROPN
ejpam-5787	168	6	ode45	ode45	PROPN
ejpam-5787	168	7	solver	solver	VERB
ejpam-5787	168	8	with	with	ADP
ejpam-5787	168	9	an	an	DET
ejpam-5787	168	10	associated	associated	ADJ
ejpam-5787	168	11	termination	termination	NOUN
ejpam-5787	168	12	event	event	NOUN
ejpam-5787	168	13	that	that	PRON
ejpam-5787	168	14	stops	stop	VERB
ejpam-5787	168	15	the	the	DET
ejpam-5787	168	16	integration	integration	NOUN
ejpam-5787	168	17	of	of	ADP
ejpam-5787	168	18	(	(	PUNCT
ejpam-5787	168	19	12	12	NUM
ejpam-5787	168	20	)	)	PUNCT
ejpam-5787	168	21	where	where	SCONJ
ejpam-5787	168	22	the	the	DET
ejpam-5787	168	23	flow	flow	NOUN
ejpam-5787	168	24	intersects	intersect	VERB
ejpam-5787	168	25	y	y	NOUN
ejpam-5787	168	26	=	=	PUNCT
ejpam-5787	168	27	−1	−1	NOUN
ejpam-5787	168	28	or	or	CCONJ
ejpam-5787	168	29	y	y	NOUN
ejpam-5787	168	30	=	=	SYM
ejpam-5787	168	31	1	1	X
ejpam-5787	168	32	.	.	PUNCT
ejpam-5787	169	1	the	the	DET
ejpam-5787	169	2	map	map	NOUN
ejpam-5787	169	3	f	f	X
ejpam-5787	169	4	(	(	PUNCT
ejpam-5787	169	5	13	13	NUM
ejpam-5787	169	6	)	)	PUNCT
ejpam-5787	169	7	depends	depend	VERB
ejpam-5787	169	8	on	on	ADP
ejpam-5787	169	9	three	three	NUM
ejpam-5787	169	10	parameter	parameter	NOUN
ejpam-5787	169	11	values	value	NOUN
ejpam-5787	169	12	a	a	DET
ejpam-5787	169	13	,	,	PUNCT
ejpam-5787	169	14	ω	ω	PROPN
ejpam-5787	169	15	and	and	CCONJ
ejpam-5787	169	16	β	β	X
ejpam-5787	169	17	because	because	SCONJ
ejpam-5787	169	18	they	they	PRON
ejpam-5787	169	19	are	be	AUX
ejpam-5787	169	20	found	find	VERB
ejpam-5787	169	21	by	by	ADP
ejpam-5787	169	22	solving	solve	VERB
ejpam-5787	169	23	(	(	PUNCT
ejpam-5787	169	24	12	12	NUM
ejpam-5787	169	25	)	)	PUNCT
ejpam-5787	169	26	.	.	PUNCT
ejpam-5787	170	1	for	for	ADP
ejpam-5787	170	2	some	some	DET
ejpam-5787	170	3	parameter	parameter	NOUN
ejpam-5787	170	4	value	value	NOUN
ejpam-5787	170	5	a	a	PRON
ejpam-5787	170	6	(	(	PUNCT
ejpam-5787	170	7	given	give	VERB
ejpam-5787	170	8	that	that	SCONJ
ejpam-5787	170	9	|a|	|a|	NOUN
ejpam-5787	170	10	is	be	AUX
ejpam-5787	170	11	big	big	ADJ
ejpam-5787	170	12	enough	enough	ADV
ejpam-5787	170	13	)	)	PUNCT
ejpam-5787	170	14	,	,	PUNCT
ejpam-5787	170	15	the	the	DET
ejpam-5787	170	16	map	map	NOUN
ejpam-5787	170	17	p−(θ	p−(θ	PROPN
ejpam-5787	170	18	,	,	PUNCT
ejpam-5787	170	19	y	y	NOUN
ejpam-5787	170	20	)	)	PUNCT
ejpam-5787	170	21	or	or	CCONJ
ejpam-5787	170	22	p+(θ	p+(θ	NOUN
ejpam-5787	170	23	,	,	PUNCT
ejpam-5787	170	24	y	y	NOUN
ejpam-5787	170	25	)	)	PUNCT
ejpam-5787	170	26	may	may	AUX
ejpam-5787	170	27	not	not	PART
ejpam-5787	170	28	be	be	AUX
ejpam-5787	170	29	defined	define	VERB
ejpam-5787	170	30	because	because	SCONJ
ejpam-5787	170	31	it	it	PRON
ejpam-5787	170	32	evolves	evolve	VERB
ejpam-5787	170	33	towards	towards	ADP
ejpam-5787	170	34	a	a	DET
ejpam-5787	170	35	periodic	periodic	ADJ
ejpam-5787	170	36	orbit	orbit	NOUN
ejpam-5787	170	37	on	on	ADP
ejpam-5787	170	38	the	the	DET
ejpam-5787	170	39	stable	stable	ADJ
ejpam-5787	170	40	branch	branch	NOUN
ejpam-5787	170	41	of	of	ADP
ejpam-5787	170	42	the	the	DET
ejpam-5787	170	43	critical	critical	ADJ
ejpam-5787	170	44	manifold	manifold	NOUN
ejpam-5787	170	45	and	and	CCONJ
ejpam-5787	170	46	it	it	PRON
ejpam-5787	170	47	can	can	AUX
ejpam-5787	170	48	never	never	ADV
ejpam-5787	170	49	reach	reach	VERB
ejpam-5787	170	50	the	the	DET
ejpam-5787	170	51	fold	fold	NOUN
ejpam-5787	170	52	again	again	ADV
ejpam-5787	170	53	.	.	PUNCT
ejpam-5787	171	1	the	the	DET
ejpam-5787	171	2	matlab	matlab	PROPN
ejpam-5787	171	3	code	code	NOUN
ejpam-5787	171	4	catches	catch	VERB
ejpam-5787	171	5	this	this	DET
ejpam-5787	171	6	case	case	NOUN
ejpam-5787	171	7	as	as	ADP
ejpam-5787	171	8	special	special	ADJ
ejpam-5787	171	9	by	by	ADP
ejpam-5787	171	10	using	use	VERB
ejpam-5787	171	11	a	a	DET
ejpam-5787	171	12	break	break	NOUN
ejpam-5787	171	13	.	.	PUNCT
ejpam-5787	172	1	i.	i.	PROPN
ejpam-5787	172	2	alraddadi	alraddadi	PROPN
ejpam-5787	172	3	/	/	SYM
ejpam-5787	172	4	eur	eur	PROPN
ejpam-5787	172	5	.	.	PUNCT
ejpam-5787	173	1	j.	j.	PROPN
ejpam-5787	173	2	pure	pure	PROPN
ejpam-5787	173	3	appl	appl	PROPN
ejpam-5787	173	4	.	.	PROPN
ejpam-5787	173	5	math	math	PROPN
ejpam-5787	173	6	,	,	PUNCT
ejpam-5787	173	7	18	18	NUM
ejpam-5787	173	8	(	(	PUNCT
ejpam-5787	173	9	1	1	NUM
ejpam-5787	173	10	)	)	PUNCT
ejpam-5787	173	11	(	(	PUNCT
ejpam-5787	173	12	2025	2025	NUM
ejpam-5787	173	13	)	)	PUNCT
ejpam-5787	173	14	,	,	PUNCT
ejpam-5787	173	15	5787	5787	NUM
ejpam-5787	173	16	11	11	NUM
ejpam-5787	173	17	of	of	ADP
ejpam-5787	173	18	23	23	NUM
ejpam-5787	173	19	3.2	3.2	NUM
ejpam-5787	173	20	.	.	PUNCT
ejpam-5787	174	1	dynamics	dynamic	NOUN
ejpam-5787	174	2	and	and	CCONJ
ejpam-5787	174	3	bifurcations	bifurcation	NOUN
ejpam-5787	174	4	of	of	ADP
ejpam-5787	174	5	the	the	DET
ejpam-5787	174	6	first	first	ADJ
ejpam-5787	174	7	return	return	NOUN
ejpam-5787	174	8	map	map	VERB
ejpam-5787	174	9	the	the	DET
ejpam-5787	174	10	return	return	NOUN
ejpam-5787	174	11	map	map	NOUN
ejpam-5787	174	12	discussed	discuss	VERB
ejpam-5787	174	13	above	above	ADV
ejpam-5787	174	14	can	can	AUX
ejpam-5787	174	15	be	be	AUX
ejpam-5787	174	16	iterated	iterate	VERB
ejpam-5787	174	17	to	to	PART
ejpam-5787	174	18	understand	understand	VERB
ejpam-5787	174	19	the	the	DET
ejpam-5787	174	20	dynamics	dynamic	NOUN
ejpam-5787	174	21	of	of	ADP
ejpam-5787	174	22	trajectories	trajectory	NOUN
ejpam-5787	174	23	in	in	ADP
ejpam-5787	174	24	this	this	DET
ejpam-5787	174	25	singular	singular	ADJ
ejpam-5787	174	26	system	system	NOUN
ejpam-5787	174	27	(	(	PUNCT
ejpam-5787	174	28	4	4	NUM
ejpam-5787	174	29	)	)	PUNCT
ejpam-5787	174	30	in	in	ADP
ejpam-5787	174	31	the	the	DET
ejpam-5787	174	32	limit	limit	NOUN
ejpam-5787	174	33	ε	ε	PROPN
ejpam-5787	174	34	→	→	SYM
ejpam-5787	174	35	0	0	NUM
ejpam-5787	174	36	.	.	PUNCT
ejpam-5787	175	1	these	these	DET
ejpam-5787	175	2	trajectories	trajectory	NOUN
ejpam-5787	175	3	are	be	AUX
ejpam-5787	175	4	governed	govern	VERB
ejpam-5787	175	5	by	by	ADP
ejpam-5787	175	6	θn+1	θn+1	PROPN
ejpam-5787	175	7	=	=	SYM
ejpam-5787	175	8	f	f	PROPN
ejpam-5787	175	9	(	(	PUNCT
ejpam-5787	175	10	θn	θn	NOUN
ejpam-5787	175	11	)	)	PUNCT
ejpam-5787	175	12	for	for	ADP
ejpam-5787	175	13	a	a	DET
ejpam-5787	175	14	given	give	VERB
ejpam-5787	175	15	initial	initial	ADJ
ejpam-5787	175	16	condition	condition	NOUN
ejpam-5787	175	17	on	on	ADP
ejpam-5787	175	18	s2	s2	PROPN
ejpam-5787	175	19	.	.	PUNCT
ejpam-5787	176	1	the	the	DET
ejpam-5787	176	2	intersection	intersection	NOUN
ejpam-5787	176	3	point	point	NOUN
ejpam-5787	176	4	of	of	ADP
ejpam-5787	176	5	the	the	DET
ejpam-5787	176	6	flow	flow	NOUN
ejpam-5787	176	7	(	(	PUNCT
ejpam-5787	176	8	12	12	NUM
ejpam-5787	176	9	)	)	PUNCT
ejpam-5787	176	10	with	with	ADP
ejpam-5787	176	11	poincaré	poincaré	ADJ
ejpam-5787	176	12	section	section	NOUN
ejpam-5787	176	13	s2	s2	PROPN
ejpam-5787	176	14	is	be	AUX
ejpam-5787	176	15	a	a	DET
ejpam-5787	176	16	fixed	fix	VERB
ejpam-5787	176	17	point	point	NOUN
ejpam-5787	176	18	for	for	ADP
ejpam-5787	176	19	the	the	DET
ejpam-5787	176	20	return	return	NOUN
ejpam-5787	176	21	map	map	NOUN
ejpam-5787	176	22	f	f	X
ejpam-5787	176	23	(	(	PUNCT
ejpam-5787	176	24	13	13	NUM
ejpam-5787	176	25	)	)	PUNCT
ejpam-5787	176	26	.	.	PUNCT
ejpam-5787	177	1	in	in	ADP
ejpam-5787	177	2	particular	particular	ADJ
ejpam-5787	177	3	,	,	PUNCT
ejpam-5787	177	4	there	there	PRON
ejpam-5787	177	5	will	will	AUX
ejpam-5787	177	6	be	be	AUX
ejpam-5787	177	7	fixed	fix	VERB
ejpam-5787	177	8	points	point	NOUN
ejpam-5787	177	9	of	of	ADP
ejpam-5787	177	10	the	the	DET
ejpam-5787	177	11	poincaré	poincaré	ADJ
ejpam-5787	177	12	return	return	NOUN
ejpam-5787	177	13	map	map	NOUN
ejpam-5787	177	14	where	where	SCONJ
ejpam-5787	177	15	f	f	PROPN
ejpam-5787	177	16	(	(	PUNCT
ejpam-5787	177	17	θ	θ	NOUN
ejpam-5787	177	18	)	)	PUNCT
ejpam-5787	177	19	=	=	SYM
ejpam-5787	177	20	θ	θ	X
ejpam-5787	177	21	.	.	PUNCT
ejpam-5787	178	1	as	as	ADP
ejpam-5787	178	2	in	in	ADP
ejpam-5787	178	3	figure	figure	NOUN
ejpam-5787	178	4	8	8	NUM
ejpam-5787	178	5	,	,	PUNCT
ejpam-5787	178	6	fixed	fix	VERB
ejpam-5787	178	7	points	point	NOUN
ejpam-5787	178	8	of	of	ADP
ejpam-5787	178	9	the	the	DET
ejpam-5787	178	10	poincaré	poincaré	ADJ
ejpam-5787	178	11	return	return	NOUN
ejpam-5787	178	12	map	map	NOUN
ejpam-5787	178	13	occur	occur	VERB
ejpam-5787	178	14	where	where	SCONJ
ejpam-5787	178	15	the	the	DET
ejpam-5787	178	16	graph	graph	NOUN
ejpam-5787	178	17	of	of	ADP
ejpam-5787	178	18	f	f	PROPN
ejpam-5787	178	19	(	(	PUNCT
ejpam-5787	178	20	θ	θ	NOUN
ejpam-5787	178	21	)	)	PUNCT
ejpam-5787	178	22	and	and	CCONJ
ejpam-5787	178	23	the	the	DET
ejpam-5787	178	24	diagonal	diagonal	ADJ
ejpam-5787	178	25	line	line	NOUN
ejpam-5787	178	26	intersect	intersect	ADJ
ejpam-5787	178	27	point	point	NOUN
ejpam-5787	178	28	f	f	PROPN
ejpam-5787	178	29	(	(	PUNCT
ejpam-5787	178	30	θ	θ	NOUN
ejpam-5787	178	31	)	)	PUNCT
ejpam-5787	178	32	=	=	SYM
ejpam-5787	178	33	θ	θ	X
ejpam-5787	178	34	.	.	PUNCT
ejpam-5787	179	1	this	this	DET
ejpam-5787	179	2	figure	figure	NOUN
ejpam-5787	179	3	shows	show	VERB
ejpam-5787	179	4	an	an	DET
ejpam-5787	179	5	example	example	NOUN
ejpam-5787	179	6	of	of	ADP
ejpam-5787	179	7	the	the	DET
ejpam-5787	179	8	stability	stability	NOUN
ejpam-5787	179	9	of	of	ADP
ejpam-5787	179	10	the	the	DET
ejpam-5787	179	11	fixed	fix	VERB
ejpam-5787	179	12	point	point	NOUN
ejpam-5787	179	13	which	which	PRON
ejpam-5787	179	14	is	be	AUX
ejpam-5787	179	15	indicated	indicate	VERB
ejpam-5787	179	16	by	by	ADP
ejpam-5787	179	17	the	the	DET
ejpam-5787	179	18	cobwebs	cobwebs	NOUN
ejpam-5787	179	19	converging	converge	VERB
ejpam-5787	179	20	to	to	ADP
ejpam-5787	179	21	the	the	DET
ejpam-5787	179	22	stable	stable	ADJ
ejpam-5787	179	23	fixed	fix	VERB
ejpam-5787	179	24	point	point	NOUN
ejpam-5787	179	25	.	.	PUNCT
ejpam-5787	180	1	more	more	ADV
ejpam-5787	180	2	generally	generally	ADV
ejpam-5787	180	3	,	,	PUNCT
ejpam-5787	180	4	a	a	DET
ejpam-5787	180	5	periodic	periodic	ADJ
ejpam-5787	180	6	orbit	orbit	NOUN
ejpam-5787	180	7	of	of	ADP
ejpam-5787	180	8	the	the	DET
ejpam-5787	180	9	original	original	ADJ
ejpam-5787	180	10	ode	ode	NOUN
ejpam-5787	180	11	gives	give	VERB
ejpam-5787	180	12	a	a	DET
ejpam-5787	180	13	periodic	periodic	ADJ
ejpam-5787	180	14	orbit	orbit	NOUN
ejpam-5787	180	15	of	of	ADP
ejpam-5787	180	16	the	the	DET
ejpam-5787	180	17	poincaré	poincaré	ADJ
ejpam-5787	180	18	return	return	NOUN
ejpam-5787	180	19	map	map	NOUN
ejpam-5787	180	20	.	.	PUNCT
ejpam-5787	181	1	in	in	ADP
ejpam-5787	181	2	other	other	ADJ
ejpam-5787	181	3	words	word	NOUN
ejpam-5787	181	4	,	,	PUNCT
ejpam-5787	181	5	periodic	periodic	ADJ
ejpam-5787	181	6	orbits	orbit	NOUN
ejpam-5787	181	7	of	of	ADP
ejpam-5787	181	8	the	the	DET
ejpam-5787	181	9	map	map	NOUN
ejpam-5787	181	10	f	f	PROPN
ejpam-5787	181	11	correspond	correspond	VERB
ejpam-5787	181	12	to	to	ADP
ejpam-5787	181	13	periodic	periodic	ADJ
ejpam-5787	181	14	orbits	orbit	NOUN
ejpam-5787	181	15	of	of	ADP
ejpam-5787	181	16	(	(	PUNCT
ejpam-5787	181	17	4	4	NUM
ejpam-5787	181	18	)	)	PUNCT
ejpam-5787	181	19	.	.	PUNCT
ejpam-5787	182	1	recall	recall	VERB
ejpam-5787	182	2	that	that	SCONJ
ejpam-5787	182	3	θ	θ	PROPN
ejpam-5787	182	4	will	will	AUX
ejpam-5787	182	5	be	be	AUX
ejpam-5787	182	6	a	a	DET
ejpam-5787	182	7	periodic	periodic	ADJ
ejpam-5787	182	8	point	point	NOUN
ejpam-5787	182	9	for	for	ADP
ejpam-5787	182	10	f	f	PROPN
ejpam-5787	182	11	of	of	ADP
ejpam-5787	182	12	period	period	NOUN
ejpam-5787	183	1	n	n	CCONJ
ejpam-5787	183	2	if	if	SCONJ
ejpam-5787	183	3	fn(θ	fn(θ	NOUN
ejpam-5787	183	4	)	)	PUNCT
ejpam-5787	184	1	=	=	SYM
ejpam-5787	184	2	θ	θ	X
ejpam-5787	184	3	.	.	PUNCT
ejpam-5787	184	4	moreover	moreover	ADV
ejpam-5787	184	5	,	,	PUNCT
ejpam-5787	184	6	stable	stable	ADJ
ejpam-5787	184	7	fixed	fix	VERB
ejpam-5787	184	8	point	point	NOUN
ejpam-5787	184	9	or	or	CCONJ
ejpam-5787	184	10	stable	stable	ADJ
ejpam-5787	184	11	periodic	periodic	ADJ
ejpam-5787	184	12	orbits	orbit	NOUN
ejpam-5787	184	13	for	for	ADP
ejpam-5787	184	14	the	the	DET
ejpam-5787	184	15	return	return	NOUN
ejpam-5787	184	16	map	map	NOUN
ejpam-5787	184	17	that	that	PRON
ejpam-5787	184	18	correspond	correspond	VERB
ejpam-5787	184	19	to	to	ADP
ejpam-5787	184	20	a	a	DET
ejpam-5787	184	21	stable	stable	ADJ
ejpam-5787	184	22	periodic	periodic	ADJ
ejpam-5787	184	23	orbit	orbit	NOUN
ejpam-5787	184	24	of	of	ADP
ejpam-5787	184	25	the	the	DET
ejpam-5787	184	26	flow	flow	NOUN
ejpam-5787	184	27	.	.	PUNCT
ejpam-5787	185	1	figure	figure	NOUN
ejpam-5787	185	2	10	10	NUM
ejpam-5787	185	3	shows	show	VERB
ejpam-5787	185	4	two	two	NUM
ejpam-5787	185	5	examples	example	NOUN
ejpam-5787	185	6	of	of	ADP
ejpam-5787	185	7	the	the	DET
ejpam-5787	185	8	first	first	ADJ
ejpam-5787	185	9	return	return	NOUN
ejpam-5787	185	10	map	map	NOUN
ejpam-5787	185	11	(	(	PUNCT
ejpam-5787	185	12	13	13	NUM
ejpam-5787	185	13	)	)	PUNCT
ejpam-5787	185	14	for	for	ADP
ejpam-5787	185	15	β	β	X
ejpam-5787	185	16	=	=	SYM
ejpam-5787	185	17	0	0	NUM
ejpam-5787	185	18	and	and	CCONJ
ejpam-5787	185	19	ω	ω	NUM
ejpam-5787	185	20	=	=	SYM
ejpam-5787	185	21	0.54559	0.54559	NUM
ejpam-5787	185	22	.	.	PUNCT
ejpam-5787	186	1	for	for	ADP
ejpam-5787	186	2	a	a	DET
ejpam-5787	186	3	<	<	X
ejpam-5787	186	4	1	1	NUM
ejpam-5787	186	5	,	,	PUNCT
ejpam-5787	186	6	the	the	DET
ejpam-5787	186	7	return	return	NOUN
ejpam-5787	186	8	map	map	NOUN
ejpam-5787	186	9	(	(	PUNCT
ejpam-5787	186	10	13	13	NUM
ejpam-5787	186	11	)	)	PUNCT
ejpam-5787	186	12	becomes	become	VERB
ejpam-5787	186	13	an	an	DET
ejpam-5787	186	14	invertible	invertible	ADJ
ejpam-5787	186	15	circle	circle	NOUN
ejpam-5787	186	16	map	map	NOUN
ejpam-5787	186	17	(	(	PUNCT
ejpam-5787	186	18	figure	figure	NOUN
ejpam-5787	186	19	10(a	10(a	NUM
ejpam-5787	186	20	)	)	PUNCT
ejpam-5787	186	21	)	)	PUNCT
ejpam-5787	186	22	.	.	PUNCT
ejpam-5787	187	1	for	for	ADP
ejpam-5787	187	2	a	a	DET
ejpam-5787	187	3	>	>	X
ejpam-5787	187	4	1	1	NUM
ejpam-5787	187	5	,	,	PUNCT
ejpam-5787	187	6	the	the	DET
ejpam-5787	187	7	return	return	NOUN
ejpam-5787	187	8	map	map	NOUN
ejpam-5787	187	9	(	(	PUNCT
ejpam-5787	187	10	13	13	NUM
ejpam-5787	187	11	)	)	PUNCT
ejpam-5787	187	12	become	become	VERB
ejpam-5787	187	13	noninvertible	noninvertible	ADJ
ejpam-5787	187	14	(	(	PUNCT
ejpam-5787	187	15	figure	figure	NOUN
ejpam-5787	187	16	10(b	10(b	NUM
ejpam-5787	187	17	)	)	PUNCT
ejpam-5787	187	18	)	)	PUNCT
ejpam-5787	187	19	.	.	PUNCT
ejpam-5787	188	1	the	the	DET
ejpam-5787	188	2	flow	flow	NOUN
ejpam-5787	188	3	of	of	ADP
ejpam-5787	188	4	(	(	PUNCT
ejpam-5787	188	5	13	13	NUM
ejpam-5787	188	6	)	)	PUNCT
ejpam-5787	188	7	starts	start	VERB
ejpam-5787	188	8	at	at	ADP
ejpam-5787	188	9	s2	s2	PROPN
ejpam-5787	188	10	for	for	ADP
ejpam-5787	188	11	various	various	ADJ
ejpam-5787	188	12	initial	initial	ADJ
ejpam-5787	188	13	conditions	condition	NOUN
ejpam-5787	188	14	θ	θ	PROPN
ejpam-5787	188	15	.	.	PROPN
ejpam-5787	189	1	for	for	ADP
ejpam-5787	189	2	a	a	DET
ejpam-5787	189	3	<	<	X
ejpam-5787	189	4	1	1	NUM
ejpam-5787	189	5	,	,	PUNCT
ejpam-5787	189	6	the	the	DET
ejpam-5787	189	7	graph	graph	NOUN
ejpam-5787	189	8	of	of	ADP
ejpam-5787	189	9	the	the	DET
ejpam-5787	189	10	first	first	ADJ
ejpam-5787	189	11	return	return	NOUN
ejpam-5787	189	12	map	map	NOUN
ejpam-5787	189	13	(	(	PUNCT
ejpam-5787	189	14	13	13	NUM
ejpam-5787	189	15	)	)	PUNCT
ejpam-5787	189	16	is	be	AUX
ejpam-5787	189	17	the	the	DET
ejpam-5787	189	18	smooth	smooth	ADJ
ejpam-5787	189	19	curve	curve	NOUN
ejpam-5787	189	20	that	that	PRON
ejpam-5787	189	21	appears	appear	VERB
ejpam-5787	189	22	in	in	ADP
ejpam-5787	189	23	(	(	PUNCT
ejpam-5787	189	24	figure	figure	NOUN
ejpam-5787	189	25	10(a	10(a	NUM
ejpam-5787	189	26	)	)	PUNCT
ejpam-5787	189	27	)	)	PUNCT
ejpam-5787	189	28	.	.	PUNCT
ejpam-5787	190	1	whereas	whereas	SCONJ
ejpam-5787	190	2	for	for	ADP
ejpam-5787	190	3	a	a	DET
ejpam-5787	190	4	>	>	SYM
ejpam-5787	190	5	1	1	NUM
ejpam-5787	190	6	,	,	PUNCT
ejpam-5787	190	7	there	there	PRON
ejpam-5787	190	8	is	be	VERB
ejpam-5787	190	9	a	a	DET
ejpam-5787	190	10	gap	gap	NOUN
ejpam-5787	190	11	region	region	NOUN
ejpam-5787	190	12	in	in	ADP
ejpam-5787	190	13	the	the	DET
ejpam-5787	190	14	graph	graph	NOUN
ejpam-5787	190	15	of	of	ADP
ejpam-5787	190	16	f	f	PROPN
ejpam-5787	190	17	because	because	SCONJ
ejpam-5787	190	18	of	of	ADP
ejpam-5787	190	19	the	the	DET
ejpam-5787	190	20	presence	presence	NOUN
ejpam-5787	190	21	of	of	ADP
ejpam-5787	190	22	folded	fold	VERB
ejpam-5787	190	23	equilibria	equilibrium	NOUN
ejpam-5787	190	24	in	in	ADP
ejpam-5787	190	25	s±1	s±1	NOUN
ejpam-5787	190	26	as	as	SCONJ
ejpam-5787	190	27	shwon	shwon	VERB
ejpam-5787	190	28	in	in	ADP
ejpam-5787	190	29	figure	figure	NOUN
ejpam-5787	190	30	9	9	NUM
ejpam-5787	190	31	.	.	PUNCT
ejpam-5787	191	1	in	in	ADP
ejpam-5787	191	2	this	this	DET
ejpam-5787	191	3	case	case	NOUN
ejpam-5787	191	4	the	the	DET
ejpam-5787	191	5	trajectories	trajectory	NOUN
ejpam-5787	191	6	can	can	AUX
ejpam-5787	191	7	not	not	PART
ejpam-5787	191	8	leave	leave	VERB
ejpam-5787	191	9	the	the	DET
ejpam-5787	191	10	folded	fold	VERB
ejpam-5787	191	11	equilibria	equilibrium	NOUN
ejpam-5787	191	12	region	region	NOUN
ejpam-5787	191	13	between	between	ADP
ejpam-5787	191	14	the	the	DET
ejpam-5787	191	15	folded	folded	ADJ
ejpam-5787	191	16	saddle	saddle	NOUN
ejpam-5787	191	17	and	and	CCONJ
ejpam-5787	191	18	unstable	unstable	ADJ
ejpam-5787	191	19	manifold	manifold	NOUN
ejpam-5787	191	20	of	of	ADP
ejpam-5787	191	21	the	the	DET
ejpam-5787	191	22	folded	fold	VERB
ejpam-5787	191	23	saddle	saddle	NOUN
ejpam-5787	191	24	(	(	PUNCT
ejpam-5787	191	25	see	see	VERB
ejpam-5787	191	26	figure	figure	NOUN
ejpam-5787	191	27	7	7	NUM
ejpam-5787	191	28	)	)	PUNCT
ejpam-5787	191	29	.	.	PUNCT
ejpam-5787	192	1	this	this	PRON
ejpam-5787	192	2	creates	create	VERB
ejpam-5787	192	3	a	a	DET
ejpam-5787	192	4	discontinuity	discontinuity	NOUN
ejpam-5787	192	5	in	in	ADP
ejpam-5787	192	6	the	the	DET
ejpam-5787	192	7	graph	graph	NOUN
ejpam-5787	192	8	of	of	ADP
ejpam-5787	192	9	the	the	DET
ejpam-5787	192	10	first	first	ADJ
ejpam-5787	192	11	return	return	NOUN
ejpam-5787	192	12	map	map	NOUN
ejpam-5787	192	13	(	(	PUNCT
ejpam-5787	192	14	13	13	NUM
ejpam-5787	192	15	)	)	PUNCT
ejpam-5787	192	16	(	(	PUNCT
ejpam-5787	192	17	figure	figure	NOUN
ejpam-5787	192	18	10(b	10(b	NUM
ejpam-5787	192	19	)	)	PUNCT
ejpam-5787	192	20	)	)	PUNCT
ejpam-5787	192	21	.	.	PUNCT
ejpam-5787	193	1	i.	i.	PROPN
ejpam-5787	193	2	alraddadi	alraddadi	PROPN
ejpam-5787	193	3	/	/	SYM
ejpam-5787	193	4	eur	eur	PROPN
ejpam-5787	193	5	.	.	PUNCT
ejpam-5787	194	1	j.	j.	PROPN
ejpam-5787	194	2	pure	pure	PROPN
ejpam-5787	194	3	appl	appl	PROPN
ejpam-5787	194	4	.	.	PROPN
ejpam-5787	194	5	math	math	PROPN
ejpam-5787	194	6	,	,	PUNCT
ejpam-5787	194	7	18	18	NUM
ejpam-5787	194	8	(	(	PUNCT
ejpam-5787	194	9	1	1	NUM
ejpam-5787	194	10	)	)	PUNCT
ejpam-5787	194	11	(	(	PUNCT
ejpam-5787	194	12	2025	2025	NUM
ejpam-5787	194	13	)	)	PUNCT
ejpam-5787	194	14	,	,	PUNCT
ejpam-5787	194	15	5787	5787	NUM
ejpam-5787	194	16	12	12	NUM
ejpam-5787	194	17	of	of	ADP
ejpam-5787	194	18	23	23	NUM
ejpam-5787	194	19	(	(	PUNCT
ejpam-5787	194	20	a	a	NOUN
ejpam-5787	194	21	)	)	PUNCT
ejpam-5787	194	22	(	(	PUNCT
ejpam-5787	194	23	b	b	X
ejpam-5787	194	24	)	)	PUNCT
ejpam-5787	194	25	figure	figure	NOUN
ejpam-5787	194	26	7	7	NUM
ejpam-5787	194	27	:	:	PUNCT
ejpam-5787	194	28	schematic	schematic	ADJ
ejpam-5787	194	29	diagram	diagram	NOUN
ejpam-5787	194	30	shows	show	VERB
ejpam-5787	194	31	vector	vector	NOUN
ejpam-5787	194	32	field	field	NOUN
ejpam-5787	194	33	of	of	ADP
ejpam-5787	194	34	the	the	DET
ejpam-5787	194	35	desingularised	desingularise	VERB
ejpam-5787	194	36	system	system	NOUN
ejpam-5787	194	37	(	(	PUNCT
ejpam-5787	194	38	12	12	NUM
ejpam-5787	194	39	)	)	PUNCT
ejpam-5787	194	40	on	on	ADP
ejpam-5787	194	41	the	the	DET
ejpam-5787	194	42	upper	upper	ADJ
ejpam-5787	194	43	stable	stable	ADJ
ejpam-5787	194	44	part	part	NOUN
ejpam-5787	194	45	of	of	ADP
ejpam-5787	194	46	manifold	manifold	NOUN
ejpam-5787	194	47	for	for	ADP
ejpam-5787	194	48	any	any	DET
ejpam-5787	194	49	trajectory	trajectory	NOUN
ejpam-5787	194	50	starts	start	VERB
ejpam-5787	194	51	at	at	ADP
ejpam-5787	194	52	y	y	PROPN
ejpam-5787	194	53	=	=	SYM
ejpam-5787	194	54	2	2	X
ejpam-5787	194	55	.	.	PUNCT
ejpam-5787	194	56	(	(	PUNCT
ejpam-5787	194	57	a	a	X
ejpam-5787	194	58	)	)	PUNCT
ejpam-5787	194	59	for	for	ADP
ejpam-5787	194	60	a	a	DET
ejpam-5787	194	61	<	<	X
ejpam-5787	194	62	1	1	NUM
ejpam-5787	194	63	,	,	PUNCT
ejpam-5787	194	64	there	there	PRON
ejpam-5787	194	65	is	be	VERB
ejpam-5787	194	66	no	no	DET
ejpam-5787	194	67	folded	folded	ADJ
ejpam-5787	194	68	equilibria	equilibrium	NOUN
ejpam-5787	194	69	,	,	PUNCT
ejpam-5787	194	70	trajectory	trajectory	NOUN
ejpam-5787	194	71	can	can	AUX
ejpam-5787	194	72	reach	reach	VERB
ejpam-5787	194	73	everywhere	everywhere	ADV
ejpam-5787	194	74	on	on	ADP
ejpam-5787	194	75	the	the	DET
ejpam-5787	194	76	line	line	NOUN
ejpam-5787	194	77	y	y	PROPN
ejpam-5787	194	78	=	=	SYM
ejpam-5787	194	79	1	1	X
ejpam-5787	194	80	.	.	PUNCT
ejpam-5787	195	1	in	in	ADP
ejpam-5787	195	2	this	this	DET
ejpam-5787	195	3	case	case	NOUN
ejpam-5787	195	4	the	the	DET
ejpam-5787	195	5	map	map	NOUN
ejpam-5787	195	6	from	from	ADP
ejpam-5787	195	7	y	y	PROPN
ejpam-5787	195	8	=	=	SYM
ejpam-5787	195	9	2	2	NUM
ejpam-5787	195	10	to	to	ADP
ejpam-5787	195	11	y	y	PROPN
ejpam-5787	195	12	=	=	SYM
ejpam-5787	195	13	1	1	NUM
ejpam-5787	195	14	is	be	AUX
ejpam-5787	195	15	a	a	DET
ejpam-5787	195	16	homeomorphism	homeomorphism	NOUN
ejpam-5787	195	17	.	.	PUNCT
ejpam-5787	196	1	(	(	PUNCT
ejpam-5787	196	2	b	b	X
ejpam-5787	196	3	)	)	PUNCT
ejpam-5787	196	4	for	for	ADP
ejpam-5787	196	5	a	a	DET
ejpam-5787	196	6	>	>	SYM
ejpam-5787	196	7	1	1	NUM
ejpam-5787	196	8	,	,	PUNCT
ejpam-5787	196	9	a	a	PRON
ejpam-5787	196	10	is	be	AUX
ejpam-5787	196	11	folded	fold	VERB
ejpam-5787	196	12	saddle	saddle	ADJ
ejpam-5787	196	13	equilibria	equilibrium	NOUN
ejpam-5787	196	14	and	and	CCONJ
ejpam-5787	196	15	b	b	NOUN
ejpam-5787	196	16	is	be	AUX
ejpam-5787	196	17	folded	fold	VERB
ejpam-5787	196	18	sink	sink	NOUN
ejpam-5787	196	19	,	,	PUNCT
ejpam-5787	196	20	and	and	CCONJ
ejpam-5787	196	21	c	c	X
ejpam-5787	196	22	where	where	SCONJ
ejpam-5787	196	23	is	be	AUX
ejpam-5787	196	24	the	the	DET
ejpam-5787	196	25	unstable	unstable	ADJ
ejpam-5787	196	26	manifold	manifold	NOUN
ejpam-5787	196	27	of	of	ADP
ejpam-5787	196	28	the	the	DET
ejpam-5787	196	29	folded	fold	VERB
ejpam-5787	196	30	saddle	saddle	NOUN
ejpam-5787	196	31	hits	hit	VERB
ejpam-5787	196	32	the	the	DET
ejpam-5787	196	33	fold	fold	NOUN
ejpam-5787	196	34	.	.	PUNCT
ejpam-5787	197	1	note	note	NOUN
ejpam-5787	197	2	that	that	SCONJ
ejpam-5787	197	3	trajectories	trajectory	NOUN
ejpam-5787	197	4	reach	reach	VERB
ejpam-5787	197	5	everywhere	everywhere	ADV
ejpam-5787	197	6	on	on	ADP
ejpam-5787	197	7	the	the	DET
ejpam-5787	197	8	line	line	NOUN
ejpam-5787	197	9	y	y	PROPN
ejpam-5787	197	10	=	=	NOUN
ejpam-5787	197	11	1	1	NUM
ejpam-5787	197	12	except	except	SCONJ
ejpam-5787	197	13	the	the	DET
ejpam-5787	197	14	region	region	NOUN
ejpam-5787	197	15	between	between	ADP
ejpam-5787	197	16	a	a	PRON
ejpam-5787	197	17	and	and	CCONJ
ejpam-5787	197	18	c	c	NOUN
ejpam-5787	197	19	,	,	PUNCT
ejpam-5787	197	20	this	this	PRON
ejpam-5787	197	21	creating	create	VERB
ejpam-5787	197	22	a	a	DET
ejpam-5787	197	23	gap	gap	NOUN
ejpam-5787	197	24	.	.	PUNCT
ejpam-5787	198	1	the	the	DET
ejpam-5787	198	2	reason	reason	NOUN
ejpam-5787	198	3	for	for	ADP
ejpam-5787	198	4	this	this	DET
ejpam-5787	198	5	gap	gap	NOUN
ejpam-5787	198	6	is	be	AUX
ejpam-5787	198	7	due	due	ADJ
ejpam-5787	198	8	to	to	ADP
ejpam-5787	198	9	the	the	DET
ejpam-5787	198	10	folded	fold	VERB
ejpam-5787	198	11	equilibria	equilibrium	NOUN
ejpam-5787	198	12	region	region	NOUN
ejpam-5787	198	13	where	where	SCONJ
ejpam-5787	198	14	no	no	DET
ejpam-5787	198	15	trajectory	trajectory	NOUN
ejpam-5787	198	16	exits	exit	VERB
ejpam-5787	198	17	.	.	PUNCT
ejpam-5787	199	1	this	this	DET
ejpam-5787	199	2	region	region	NOUN
ejpam-5787	199	3	is	be	AUX
ejpam-5787	199	4	located	locate	VERB
ejpam-5787	199	5	between	between	ADP
ejpam-5787	199	6	folded	fold	VERB
ejpam-5787	199	7	saddle	saddle	NOUN
ejpam-5787	199	8	equilibria	equilibrium	NOUN
ejpam-5787	199	9	(	(	PUNCT
ejpam-5787	199	10	a	a	X
ejpam-5787	199	11	)	)	PUNCT
ejpam-5787	199	12	and	and	CCONJ
ejpam-5787	199	13	the	the	DET
ejpam-5787	199	14	unstable	unstable	ADJ
ejpam-5787	199	15	manifold	manifold	NOUN
ejpam-5787	199	16	of	of	ADP
ejpam-5787	199	17	the	the	DET
ejpam-5787	199	18	folded	fold	VERB
ejpam-5787	199	19	saddle	saddle	NOUN
ejpam-5787	199	20	equilibria	equilibrium	NOUN
ejpam-5787	199	21	(	(	PUNCT
ejpam-5787	199	22	c	c	NOUN
ejpam-5787	199	23	)	)	PUNCT
ejpam-5787	199	24	.	.	PUNCT
ejpam-5787	200	1	figure	figure	NOUN
ejpam-5787	200	2	11	11	NUM
ejpam-5787	200	3	shows	show	VERB
ejpam-5787	200	4	a	a	DET
ejpam-5787	200	5	saddle	saddle	NOUN
ejpam-5787	200	6	-	-	PUNCT
ejpam-5787	200	7	node	node	NOUN
ejpam-5787	200	8	bifurcation	bifurcation	NOUN
ejpam-5787	200	9	of	of	ADP
ejpam-5787	200	10	the	the	DET
ejpam-5787	200	11	first	first	ADJ
ejpam-5787	200	12	return	return	NOUN
ejpam-5787	200	13	map	map	NOUN
ejpam-5787	200	14	(	(	PUNCT
ejpam-5787	200	15	13	13	NUM
ejpam-5787	200	16	)	)	PUNCT
ejpam-5787	200	17	for	for	ADP
ejpam-5787	200	18	a	a	DET
ejpam-5787	200	19	=	=	SYM
ejpam-5787	200	20	1.02	1.02	NUM
ejpam-5787	200	21	and	and	CCONJ
ejpam-5787	200	22	three	three	NUM
ejpam-5787	200	23	different	different	ADJ
ejpam-5787	200	24	value	value	NOUN
ejpam-5787	200	25	of	of	ADP
ejpam-5787	200	26	ω	ω	PROPN
ejpam-5787	200	27	=	=	SYM
ejpam-5787	200	28	0.18	0.18	NUM
ejpam-5787	200	29	,	,	PUNCT
ejpam-5787	200	30	0.19	0.19	NUM
ejpam-5787	200	31	,	,	PUNCT
ejpam-5787	200	32	0.20	0.20	NUM
ejpam-5787	200	33	.	.	PUNCT
ejpam-5787	201	1	we	we	PRON
ejpam-5787	201	2	see	see	VERB
ejpam-5787	201	3	a	a	DET
ejpam-5787	201	4	saddle	saddle	NOUN
ejpam-5787	201	5	-	-	PUNCT
ejpam-5787	201	6	node	node	NOUN
ejpam-5787	201	7	bifurcation	bifurcation	NOUN
ejpam-5787	201	8	of	of	ADP
ejpam-5787	201	9	the	the	DET
ejpam-5787	201	10	first	first	ADJ
ejpam-5787	201	11	return	return	NOUN
ejpam-5787	201	12	map	map	NOUN
ejpam-5787	201	13	that	that	PRON
ejpam-5787	201	14	is	be	AUX
ejpam-5787	201	15	passing	pass	VERB
ejpam-5787	201	16	through	through	ADP
ejpam-5787	201	17	a	a	DET
ejpam-5787	201	18	saddle	saddle	NOUN
ejpam-5787	201	19	point	point	NOUN
ejpam-5787	201	20	in	in	ADP
ejpam-5787	201	21	(	(	PUNCT
ejpam-5787	201	22	b	b	NOUN
ejpam-5787	201	23	)	)	PUNCT
ejpam-5787	201	24	.	.	PUNCT
ejpam-5787	202	1	the	the	DET
ejpam-5787	202	2	saddle	saddle	NOUN
ejpam-5787	202	3	-	-	PUNCT
ejpam-5787	202	4	node	node	NOUN
ejpam-5787	202	5	bifurcation	bifurcation	NOUN
ejpam-5787	202	6	of	of	ADP
ejpam-5787	202	7	the	the	DET
ejpam-5787	202	8	periodic	periodic	ADJ
ejpam-5787	202	9	orbit	orbit	NOUN
ejpam-5787	202	10	occurs	occur	VERB
ejpam-5787	202	11	on	on	ADP
ejpam-5787	202	12	the	the	DET
ejpam-5787	202	13	boundary	boundary	NOUN
ejpam-5787	202	14	of	of	ADP
ejpam-5787	202	15	the	the	DET
ejpam-5787	202	16	frequency	frequency	NOUN
ejpam-5787	202	17	locking	locking	NOUN
ejpam-5787	202	18	region	region	NOUN
ejpam-5787	202	19	as	as	SCONJ
ejpam-5787	202	20	discussed	discuss	VERB
ejpam-5787	202	21	in	in	ADP
ejpam-5787	202	22	more	more	ADJ
ejpam-5787	202	23	details	detail	NOUN
ejpam-5787	202	24	(	(	PUNCT
ejpam-5787	202	25	see	see	VERB
ejpam-5787	202	26	section	section	NOUN
ejpam-5787	202	27	3.3	3.3	NUM
ejpam-5787	202	28	)	)	PUNCT
ejpam-5787	202	29	.	.	PUNCT
ejpam-5787	203	1	also	also	ADV
ejpam-5787	203	2	,	,	PUNCT
ejpam-5787	203	3	the	the	DET
ejpam-5787	203	4	saddle	saddle	NOUN
ejpam-5787	203	5	-	-	PUNCT
ejpam-5787	203	6	node	node	NOUN
ejpam-5787	203	7	bifurcation	bifurcation	NOUN
ejpam-5787	203	8	of	of	ADP
ejpam-5787	203	9	the	the	DET
ejpam-5787	203	10	first	first	ADJ
ejpam-5787	203	11	return	return	NOUN
ejpam-5787	203	12	map	map	NOUN
ejpam-5787	203	13	(	(	PUNCT
ejpam-5787	203	14	13	13	NUM
ejpam-5787	203	15	)	)	PUNCT
ejpam-5787	203	16	occurs	occur	VERB
ejpam-5787	203	17	as	as	SCONJ
ejpam-5787	203	18	β	β	X
ejpam-5787	203	19	varies	vary	VERB
ejpam-5787	203	20	(	(	PUNCT
ejpam-5787	203	21	see	see	VERB
ejpam-5787	203	22	figure	figure	NOUN
ejpam-5787	203	23	13	13	NUM
ejpam-5787	203	24	)	)	PUNCT
ejpam-5787	203	25	.	.	PUNCT
ejpam-5787	204	1	i.	i.	PROPN
ejpam-5787	204	2	alraddadi	alraddadi	PROPN
ejpam-5787	204	3	/	/	SYM
ejpam-5787	204	4	eur	eur	PROPN
ejpam-5787	204	5	.	.	PUNCT
ejpam-5787	205	1	j.	j.	PROPN
ejpam-5787	205	2	pure	pure	PROPN
ejpam-5787	205	3	appl	appl	PROPN
ejpam-5787	205	4	.	.	PROPN
ejpam-5787	205	5	math	math	PROPN
ejpam-5787	205	6	,	,	PUNCT
ejpam-5787	205	7	18	18	NUM
ejpam-5787	205	8	(	(	PUNCT
ejpam-5787	205	9	1	1	NUM
ejpam-5787	205	10	)	)	PUNCT
ejpam-5787	205	11	(	(	PUNCT
ejpam-5787	205	12	2025	2025	NUM
ejpam-5787	205	13	)	)	PUNCT
ejpam-5787	205	14	,	,	PUNCT
ejpam-5787	205	15	5787	5787	NUM
ejpam-5787	205	16	13	13	NUM
ejpam-5787	205	17	of	of	ADP
ejpam-5787	205	18	23	23	NUM
ejpam-5787	205	19	(	(	PUNCT
ejpam-5787	205	20	a	a	NOUN
ejpam-5787	205	21	)	)	PUNCT
ejpam-5787	205	22	(	(	PUNCT
ejpam-5787	205	23	b	b	X
ejpam-5787	205	24	)	)	PUNCT
ejpam-5787	205	25	figure	figure	NOUN
ejpam-5787	205	26	8	8	NUM
ejpam-5787	205	27	:	:	PUNCT
ejpam-5787	205	28	(	(	PUNCT
ejpam-5787	205	29	a	a	X
ejpam-5787	205	30	)	)	PUNCT
ejpam-5787	205	31	the	the	DET
ejpam-5787	205	32	first	first	ADJ
ejpam-5787	205	33	return	return	NOUN
ejpam-5787	205	34	map	map	NOUN
ejpam-5787	205	35	f	f	X
ejpam-5787	205	36	(	(	PUNCT
ejpam-5787	205	37	13	13	NUM
ejpam-5787	205	38	)	)	PUNCT
ejpam-5787	205	39	for	for	ADP
ejpam-5787	205	40	a	a	DET
ejpam-5787	205	41	=	=	SYM
ejpam-5787	205	42	1.1	1.1	NUM
ejpam-5787	205	43	,	,	PUNCT
ejpam-5787	205	44	ω	ω	NOUN
ejpam-5787	205	45	=	=	SYM
ejpam-5787	205	46	0.35	0.35	NUM
ejpam-5787	205	47	and	and	CCONJ
ejpam-5787	205	48	β	β	X
ejpam-5787	205	49	=	=	NOUN
ejpam-5787	205	50	0	0	X
ejpam-5787	205	51	.	.	PUNCT
ejpam-5787	206	1	the	the	DET
ejpam-5787	206	2	red	red	ADJ
ejpam-5787	206	3	points	point	NOUN
ejpam-5787	206	4	are	be	AUX
ejpam-5787	206	5	the	the	DET
ejpam-5787	206	6	graph	graph	NOUN
ejpam-5787	206	7	of	of	ADP
ejpam-5787	206	8	the	the	DET
ejpam-5787	206	9	first	first	ADJ
ejpam-5787	206	10	return	return	NOUN
ejpam-5787	206	11	map	map	NOUN
ejpam-5787	206	12	and	and	CCONJ
ejpam-5787	206	13	the	the	DET
ejpam-5787	206	14	black	black	ADJ
ejpam-5787	206	15	line	line	NOUN
ejpam-5787	206	16	is	be	AUX
ejpam-5787	206	17	the	the	DET
ejpam-5787	206	18	diagonal	diagonal	ADJ
ejpam-5787	206	19	line	line	NOUN
ejpam-5787	206	20	.	.	PUNCT
ejpam-5787	207	1	the	the	DET
ejpam-5787	207	2	two	two	NUM
ejpam-5787	207	3	fixed	fix	VERB
ejpam-5787	207	4	points	point	NOUN
ejpam-5787	207	5	of	of	ADP
ejpam-5787	207	6	(	(	PUNCT
ejpam-5787	207	7	13	13	NUM
ejpam-5787	207	8	)	)	PUNCT
ejpam-5787	207	9	are	be	AUX
ejpam-5787	207	10	indicated	indicate	VERB
ejpam-5787	207	11	by	by	ADP
ejpam-5787	207	12	the	the	DET
ejpam-5787	207	13	intersection	intersection	NOUN
ejpam-5787	207	14	points	point	NOUN
ejpam-5787	207	15	of	of	ADP
ejpam-5787	207	16	f	f	PROPN
ejpam-5787	207	17	(	(	PUNCT
ejpam-5787	207	18	θ	θ	NOUN
ejpam-5787	207	19	)	)	PUNCT
ejpam-5787	207	20	(	(	PUNCT
ejpam-5787	207	21	red	red	PROPN
ejpam-5787	207	22	)	)	PUNCT
ejpam-5787	207	23	with	with	ADP
ejpam-5787	207	24	the	the	DET
ejpam-5787	207	25	diagonal	diagonal	ADJ
ejpam-5787	207	26	θ	θ	PROPN
ejpam-5787	207	27	(	(	PUNCT
ejpam-5787	207	28	black	black	NOUN
ejpam-5787	207	29	)	)	PUNCT
ejpam-5787	207	30	.	.	PUNCT
ejpam-5787	208	1	the	the	DET
ejpam-5787	208	2	stability	stability	NOUN
ejpam-5787	208	3	of	of	ADP
ejpam-5787	208	4	these	these	DET
ejpam-5787	208	5	fixed	fix	VERB
ejpam-5787	208	6	points	point	NOUN
ejpam-5787	208	7	depends	depend	VERB
ejpam-5787	208	8	on	on	ADP
ejpam-5787	208	9	the	the	DET
ejpam-5787	208	10	slope	slope	NOUN
ejpam-5787	208	11	of	of	ADP
ejpam-5787	208	12	the	the	DET
ejpam-5787	208	13	function	function	NOUN
ejpam-5787	208	14	f	f	PROPN
ejpam-5787	208	15	(	(	PUNCT
ejpam-5787	208	16	θ	θ	PROPN
ejpam-5787	208	17	)	)	PUNCT
ejpam-5787	208	18	.	.	PUNCT
ejpam-5787	209	1	(	(	PUNCT
ejpam-5787	209	2	b	b	X
ejpam-5787	209	3	)	)	PUNCT
ejpam-5787	209	4	a	a	DET
ejpam-5787	209	5	cobweb	cobweb	ADJ
ejpam-5787	209	6	diagram	diagram	NOUN
ejpam-5787	209	7	shows	show	VERB
ejpam-5787	209	8	a	a	DET
ejpam-5787	209	9	blue	blue	ADJ
ejpam-5787	209	10	trajectory	trajectory	NOUN
ejpam-5787	209	11	attracted	attract	VERB
ejpam-5787	209	12	to	to	ADP
ejpam-5787	209	13	a	a	DET
ejpam-5787	209	14	stable	stable	ADJ
ejpam-5787	209	15	fixed	fix	VERB
ejpam-5787	209	16	point	point	NOUN
ejpam-5787	209	17	of	of	ADP
ejpam-5787	209	18	f	f	PROPN
ejpam-5787	209	19	(	(	PUNCT
ejpam-5787	209	20	13	13	NUM
ejpam-5787	209	21	)	)	PUNCT
ejpam-5787	209	22	.	.	PUNCT
ejpam-5787	210	1	(	(	PUNCT
ejpam-5787	210	2	a	a	X
ejpam-5787	210	3	)	)	PUNCT
ejpam-5787	210	4	(	(	PUNCT
ejpam-5787	210	5	b	b	X
ejpam-5787	210	6	)	)	PUNCT
ejpam-5787	210	7	figure	figure	NOUN
ejpam-5787	210	8	9	9	NUM
ejpam-5787	210	9	:	:	PUNCT
ejpam-5787	210	10	the	the	DET
ejpam-5787	210	11	first	first	ADJ
ejpam-5787	210	12	return	return	NOUN
ejpam-5787	210	13	map	map	NOUN
ejpam-5787	210	14	f	f	X
ejpam-5787	210	15	(	(	PUNCT
ejpam-5787	210	16	13	13	NUM
ejpam-5787	210	17	)	)	PUNCT
ejpam-5787	210	18	for	for	ADP
ejpam-5787	210	19	β	β	X
ejpam-5787	210	20	=	=	SYM
ejpam-5787	210	21	0	0	NUM
ejpam-5787	210	22	.	.	PUNCT
ejpam-5787	211	1	(	(	PUNCT
ejpam-5787	211	2	a	a	X
ejpam-5787	211	3	)	)	PUNCT
ejpam-5787	211	4	corresponds	correspond	NOUN
ejpam-5787	211	5	to	to	ADP
ejpam-5787	211	6	the	the	DET
ejpam-5787	211	7	parameter	parameter	NOUN
ejpam-5787	211	8	choice	choice	NOUN
ejpam-5787	211	9	a	a	DET
ejpam-5787	211	10	=	=	SYM
ejpam-5787	211	11	2.3	2.3	NUM
ejpam-5787	211	12	,	,	PUNCT
ejpam-5787	211	13	ω	ω	NOUN
ejpam-5787	211	14	=	=	SYM
ejpam-5787	211	15	1	1	NUM
ejpam-5787	211	16	in	in	ADP
ejpam-5787	211	17	the	the	DET
ejpam-5787	211	18	desingularised	desingularise	VERB
ejpam-5787	211	19	system	system	NOUN
ejpam-5787	211	20	(	(	PUNCT
ejpam-5787	211	21	12	12	NUM
ejpam-5787	211	22	)	)	PUNCT
ejpam-5787	211	23	in	in	ADP
ejpam-5787	211	24	figure	figure	NOUN
ejpam-5787	211	25	4(a	4(a	NUM
ejpam-5787	211	26	)	)	PUNCT
ejpam-5787	211	27	,	,	PUNCT
ejpam-5787	211	28	and	and	CCONJ
ejpam-5787	211	29	(	(	PUNCT
ejpam-5787	211	30	b	b	NOUN
ejpam-5787	211	31	)	)	PUNCT
ejpam-5787	212	1	to	to	ADP
ejpam-5787	212	2	a	a	DET
ejpam-5787	212	3	=	=	SYM
ejpam-5787	212	4	20	20	NUM
ejpam-5787	212	5	,	,	PUNCT
ejpam-5787	212	6	ω	ω	NOUN
ejpam-5787	212	7	=	=	SYM
ejpam-5787	212	8	5	5	NUM
ejpam-5787	212	9	in	in	ADP
ejpam-5787	212	10	figure	figure	NOUN
ejpam-5787	212	11	4(b	4(b	NUM
ejpam-5787	212	12	)	)	PUNCT
ejpam-5787	212	13	.	.	PUNCT
ejpam-5787	213	1	note	note	VERB
ejpam-5787	213	2	the	the	DET
ejpam-5787	213	3	presence	presence	NOUN
ejpam-5787	213	4	of	of	ADP
ejpam-5787	213	5	fixed	fix	VERB
ejpam-5787	213	6	points	point	NOUN
ejpam-5787	213	7	and	and	CCONJ
ejpam-5787	213	8	discontinuities	discontinuity	NOUN
ejpam-5787	213	9	.	.	PUNCT
ejpam-5787	214	1	i.	i.	PROPN
ejpam-5787	214	2	alraddadi	alraddadi	PROPN
ejpam-5787	214	3	/	/	SYM
ejpam-5787	214	4	eur	eur	PROPN
ejpam-5787	214	5	.	.	PUNCT
ejpam-5787	215	1	j.	j.	PROPN
ejpam-5787	215	2	pure	pure	PROPN
ejpam-5787	215	3	appl	appl	PROPN
ejpam-5787	215	4	.	.	PROPN
ejpam-5787	215	5	math	math	PROPN
ejpam-5787	215	6	,	,	PUNCT
ejpam-5787	215	7	18	18	NUM
ejpam-5787	215	8	(	(	PUNCT
ejpam-5787	215	9	1	1	NUM
ejpam-5787	215	10	)	)	PUNCT
ejpam-5787	215	11	(	(	PUNCT
ejpam-5787	215	12	2025	2025	NUM
ejpam-5787	215	13	)	)	PUNCT
ejpam-5787	215	14	,	,	PUNCT
ejpam-5787	215	15	5787	5787	NUM
ejpam-5787	215	16	14	14	NUM
ejpam-5787	215	17	of	of	ADP
ejpam-5787	215	18	23	23	NUM
ejpam-5787	215	19	(	(	PUNCT
ejpam-5787	215	20	a	a	NOUN
ejpam-5787	215	21	)	)	PUNCT
ejpam-5787	215	22	(	(	PUNCT
ejpam-5787	215	23	b	b	X
ejpam-5787	215	24	)	)	PUNCT
ejpam-5787	215	25	figure	figure	NOUN
ejpam-5787	215	26	10	10	NUM
ejpam-5787	215	27	:	:	PUNCT
ejpam-5787	215	28	the	the	DET
ejpam-5787	215	29	first	first	ADJ
ejpam-5787	215	30	return	return	NOUN
ejpam-5787	215	31	map	map	NOUN
ejpam-5787	215	32	f	f	X
ejpam-5787	215	33	(	(	PUNCT
ejpam-5787	215	34	13	13	NUM
ejpam-5787	215	35	)	)	PUNCT
ejpam-5787	215	36	for	for	ADP
ejpam-5787	215	37	β	β	X
ejpam-5787	215	38	=	=	SYM
ejpam-5787	215	39	0	0	NUM
ejpam-5787	215	40	and	and	CCONJ
ejpam-5787	215	41	ω	ω	NUM
ejpam-5787	215	42	=	=	SYM
ejpam-5787	215	43	0.54559	0.54559	NUM
ejpam-5787	215	44	.	.	PUNCT
ejpam-5787	216	1	(	(	PUNCT
ejpam-5787	216	2	a	a	X
ejpam-5787	216	3	)	)	PUNCT
ejpam-5787	216	4	corresponds	correspond	VERB
ejpam-5787	216	5	to	to	ADP
ejpam-5787	216	6	a	a	DET
ejpam-5787	216	7	=	=	SYM
ejpam-5787	216	8	0.9	0.9	NUM
ejpam-5787	216	9	,	,	PUNCT
ejpam-5787	216	10	the	the	DET
ejpam-5787	216	11	parameter	parameter	NOUN
ejpam-5787	216	12	choice	choice	NOUN
ejpam-5787	216	13	in	in	ADP
ejpam-5787	216	14	the	the	DET
ejpam-5787	216	15	desingularised	desingularise	VERB
ejpam-5787	216	16	system	system	NOUN
ejpam-5787	216	17	(	(	PUNCT
ejpam-5787	216	18	12	12	NUM
ejpam-5787	216	19	)	)	PUNCT
ejpam-5787	216	20	in	in	ADP
ejpam-5787	216	21	figure	figure	NOUN
ejpam-5787	216	22	5(a	5(a	NUM
ejpam-5787	216	23	)	)	PUNCT
ejpam-5787	216	24	,	,	PUNCT
ejpam-5787	216	25	and	and	CCONJ
ejpam-5787	216	26	(	(	PUNCT
ejpam-5787	216	27	b	b	NOUN
ejpam-5787	216	28	)	)	PUNCT
ejpam-5787	216	29	to	to	ADP
ejpam-5787	216	30	a	a	DET
ejpam-5787	216	31	=	=	SYM
ejpam-5787	216	32	1.00041	1.00041	NUM
ejpam-5787	216	33	,	,	PUNCT
ejpam-5787	216	34	the	the	DET
ejpam-5787	216	35	parameter	parameter	NOUN
ejpam-5787	216	36	choice	choice	NOUN
ejpam-5787	216	37	in	in	ADP
ejpam-5787	216	38	figure	figure	NOUN
ejpam-5787	216	39	5(b	5(b	NUM
ejpam-5787	216	40	)	)	PUNCT
ejpam-5787	216	41	.	.	PUNCT
ejpam-5787	217	1	the	the	DET
ejpam-5787	217	2	first	first	ADJ
ejpam-5787	217	3	return	return	NOUN
ejpam-5787	217	4	map	map	NOUN
ejpam-5787	217	5	(	(	PUNCT
ejpam-5787	217	6	13	13	NUM
ejpam-5787	217	7	)	)	PUNCT
ejpam-5787	217	8	is	be	AUX
ejpam-5787	217	9	an	an	DET
ejpam-5787	217	10	invertible	invertible	ADJ
ejpam-5787	217	11	circle	circle	NOUN
ejpam-5787	217	12	map	map	NOUN
ejpam-5787	217	13	in	in	ADP
ejpam-5787	217	14	(	(	PUNCT
ejpam-5787	217	15	a	a	NOUN
ejpam-5787	217	16	)	)	PUNCT
ejpam-5787	217	17	.	.	PUNCT
ejpam-5787	218	1	(	(	PUNCT
ejpam-5787	218	2	b	b	X
ejpam-5787	218	3	)	)	PUNCT
ejpam-5787	218	4	the	the	DET
ejpam-5787	218	5	first	first	ADJ
ejpam-5787	218	6	return	return	NOUN
ejpam-5787	218	7	map	map	NOUN
ejpam-5787	218	8	(	(	PUNCT
ejpam-5787	218	9	13	13	NUM
ejpam-5787	218	10	)	)	PUNCT
ejpam-5787	218	11	becomes	become	VERB
ejpam-5787	218	12	noninvertible	noninvertible	NOUN
ejpam-5787	218	13	.	.	PUNCT
ejpam-5787	219	1	note	note	VERB
ejpam-5787	219	2	the	the	DET
ejpam-5787	219	3	gap	gap	NOUN
ejpam-5787	219	4	appearing	appear	VERB
ejpam-5787	219	5	in	in	ADP
ejpam-5787	219	6	(	(	PUNCT
ejpam-5787	219	7	b	b	NOUN
ejpam-5787	219	8	)	)	PUNCT
ejpam-5787	219	9	.	.	PUNCT
ejpam-5787	220	1	the	the	DET
ejpam-5787	220	2	reason	reason	NOUN
ejpam-5787	220	3	for	for	ADP
ejpam-5787	220	4	this	this	DET
ejpam-5787	220	5	gap	gap	NOUN
ejpam-5787	220	6	is	be	AUX
ejpam-5787	220	7	due	due	ADJ
ejpam-5787	220	8	to	to	ADP
ejpam-5787	220	9	the	the	DET
ejpam-5787	220	10	folded	fold	VERB
ejpam-5787	220	11	equilibria	equilibrium	NOUN
ejpam-5787	220	12	region	region	NOUN
ejpam-5787	220	13	where	where	SCONJ
ejpam-5787	220	14	no	no	DET
ejpam-5787	220	15	trajectory	trajectory	NOUN
ejpam-5787	220	16	exits	exit	VERB
ejpam-5787	220	17	.	.	PUNCT
ejpam-5787	221	1	this	this	DET
ejpam-5787	221	2	region	region	NOUN
ejpam-5787	221	3	is	be	AUX
ejpam-5787	221	4	located	locate	VERB
ejpam-5787	221	5	between	between	ADP
ejpam-5787	221	6	the	the	DET
ejpam-5787	221	7	folded	fold	VERB
ejpam-5787	221	8	saddle	saddle	NOUN
ejpam-5787	221	9	and	and	CCONJ
ejpam-5787	221	10	the	the	DET
ejpam-5787	221	11	unstable	unstable	ADJ
ejpam-5787	221	12	manifold	manifold	NOUN
ejpam-5787	221	13	of	of	ADP
ejpam-5787	221	14	the	the	DET
ejpam-5787	221	15	folded	fold	VERB
ejpam-5787	221	16	saddle	saddle	NOUN
ejpam-5787	221	17	.	.	PUNCT
ejpam-5787	222	1	(	(	PUNCT
ejpam-5787	222	2	a	a	X
ejpam-5787	222	3	)	)	PUNCT
ejpam-5787	222	4	(	(	PUNCT
ejpam-5787	222	5	b	b	X
ejpam-5787	222	6	)	)	PUNCT
ejpam-5787	222	7	(	(	PUNCT
ejpam-5787	222	8	c	c	X
ejpam-5787	222	9	)	)	PUNCT
ejpam-5787	222	10	figure	figure	NOUN
ejpam-5787	222	11	11	11	NUM
ejpam-5787	222	12	:	:	PUNCT
ejpam-5787	222	13	the	the	DET
ejpam-5787	222	14	first	first	ADJ
ejpam-5787	222	15	return	return	NOUN
ejpam-5787	222	16	map	map	NOUN
ejpam-5787	222	17	f	f	X
ejpam-5787	222	18	(	(	PUNCT
ejpam-5787	222	19	13	13	NUM
ejpam-5787	222	20	)	)	PUNCT
ejpam-5787	222	21	for	for	ADP
ejpam-5787	222	22	ω	ω	NUM
ejpam-5787	222	23	=	=	SYM
ejpam-5787	222	24	0.35	0.35	NUM
ejpam-5787	222	25	with	with	ADP
ejpam-5787	222	26	different	different	ADJ
ejpam-5787	222	27	values	value	NOUN
ejpam-5787	222	28	of	of	ADP
ejpam-5787	222	29	a	a	DET
ejpam-5787	222	30	(	(	PUNCT
ejpam-5787	222	31	a	a	DET
ejpam-5787	222	32	-	-	PUNCT
ejpam-5787	222	33	c	c	NOUN
ejpam-5787	222	34	)	)	PUNCT
ejpam-5787	222	35	where	where	SCONJ
ejpam-5787	222	36	a	a	DET
ejpam-5787	222	37	=	=	SYM
ejpam-5787	222	38	1.05	1.05	NUM
ejpam-5787	222	39	,	,	PUNCT
ejpam-5787	222	40	a	a	DET
ejpam-5787	222	41	=	=	SYM
ejpam-5787	222	42	1.08	1.08	NUM
ejpam-5787	222	43	and	and	CCONJ
ejpam-5787	222	44	a	a	DET
ejpam-5787	222	45	=	=	NOUN
ejpam-5787	222	46	1.1	1.1	NUM
ejpam-5787	222	47	respectively	respectively	ADV
ejpam-5787	222	48	.	.	PUNCT
ejpam-5787	223	1	there	there	PRON
ejpam-5787	223	2	is	be	VERB
ejpam-5787	223	3	a	a	DET
ejpam-5787	223	4	saddle	saddle	NOUN
ejpam-5787	223	5	-	-	PUNCT
ejpam-5787	223	6	node	node	NOUN
ejpam-5787	223	7	bifurcation	bifurcation	NOUN
ejpam-5787	223	8	of	of	ADP
ejpam-5787	223	9	the	the	DET
ejpam-5787	223	10	first	first	ADJ
ejpam-5787	223	11	return	return	NOUN
ejpam-5787	223	12	map	map	NOUN
ejpam-5787	223	13	at	at	ADP
ejpam-5787	223	14	a	a	DET
ejpam-5787	223	15	=	=	NOUN
ejpam-5787	223	16	1.08	1.08	NUM
ejpam-5787	223	17	where	where	SCONJ
ejpam-5787	223	18	the	the	DET
ejpam-5787	223	19	red	red	ADJ
ejpam-5787	223	20	curve	curve	NOUN
ejpam-5787	223	21	of	of	ADP
ejpam-5787	223	22	f	f	PROPN
ejpam-5787	223	23	becomes	become	VERB
ejpam-5787	223	24	tangent	tangent	NOUN
ejpam-5787	223	25	to	to	ADP
ejpam-5787	223	26	the	the	DET
ejpam-5787	223	27	diagonal	diagonal	ADJ
ejpam-5787	223	28	line	line	NOUN
ejpam-5787	223	29	(	(	PUNCT
ejpam-5787	223	30	black	black	NOUN
ejpam-5787	223	31	)	)	PUNCT
ejpam-5787	223	32	.	.	PUNCT
ejpam-5787	224	1	3.3	3.3	NUM
ejpam-5787	224	2	.	.	PUNCT
ejpam-5787	224	3	frequency	frequency	NOUN
ejpam-5787	224	4	locking	locking	NOUN
ejpam-5787	224	5	in	in	ADP
ejpam-5787	224	6	the	the	DET
ejpam-5787	224	7	iteration	iteration	NOUN
ejpam-5787	224	8	of	of	ADP
ejpam-5787	224	9	the	the	DET
ejpam-5787	224	10	return	return	NOUN
ejpam-5787	224	11	map	map	NOUN
ejpam-5787	224	12	frequency	frequency	NOUN
ejpam-5787	224	13	locking	locking	NOUN
ejpam-5787	224	14	can	can	AUX
ejpam-5787	224	15	occur	occur	VERB
ejpam-5787	224	16	for	for	ADP
ejpam-5787	224	17	iterations	iteration	NOUN
ejpam-5787	224	18	of	of	ADP
ejpam-5787	224	19	the	the	DET
ejpam-5787	224	20	poincaré	poincaré	ADJ
ejpam-5787	224	21	map	map	NOUN
ejpam-5787	224	22	and	and	CCONJ
ejpam-5787	224	23	there	there	PRON
ejpam-5787	224	24	are	be	VERB
ejpam-5787	224	25	transitions	transition	NOUN
ejpam-5787	224	26	between	between	ADP
ejpam-5787	224	27	periodic	periodic	NOUN
ejpam-5787	224	28	(	(	PUNCT
ejpam-5787	224	29	also	also	ADV
ejpam-5787	224	30	called	call	VERB
ejpam-5787	224	31	phase	phase	NOUN
ejpam-5787	224	32	locking	locking	NOUN
ejpam-5787	224	33	)	)	PUNCT
ejpam-5787	224	34	and	and	CCONJ
ejpam-5787	224	35	quasiperiodic	quasiperiodic	ADJ
ejpam-5787	224	36	motion	motion	NOUN
ejpam-5787	224	37	[	[	X
ejpam-5787	224	38	22	22	NUM
ejpam-5787	224	39	]	]	PUNCT
ejpam-5787	224	40	.	.	PUNCT
ejpam-5787	225	1	both	both	DET
ejpam-5787	225	2	types	type	NOUN
ejpam-5787	225	3	of	of	ADP
ejpam-5787	225	4	behaviour	behaviour	NOUN
ejpam-5787	225	5	can	can	AUX
ejpam-5787	225	6	be	be	AUX
ejpam-5787	225	7	distinguished	distinguish	VERB
ejpam-5787	225	8	by	by	ADP
ejpam-5787	225	9	computing	compute	VERB
ejpam-5787	225	10	the	the	DET
ejpam-5787	225	11	rotation	rotation	NOUN
ejpam-5787	225	12	number	number	NOUN
ejpam-5787	225	13	n	n	CCONJ
ejpam-5787	225	14	[	[	X
ejpam-5787	225	15	20	20	NUM
ejpam-5787	225	16	]	]	PUNCT
ejpam-5787	225	17	.	.	PUNCT
ejpam-5787	226	1	if	if	SCONJ
ejpam-5787	226	2	we	we	PRON
ejpam-5787	226	3	find	find	VERB
ejpam-5787	226	4	that	that	SCONJ
ejpam-5787	226	5	the	the	DET
ejpam-5787	226	6	rotation	rotation	NOUN
ejpam-5787	226	7	number	number	NOUN
ejpam-5787	226	8	n	n	PROPN
ejpam-5787	226	9	of	of	ADP
ejpam-5787	226	10	the	the	DET
ejpam-5787	226	11	poincaré	poincaré	ADJ
ejpam-5787	226	12	return	return	NOUN
ejpam-5787	226	13	map	map	NOUN
ejpam-5787	226	14	is	be	AUX
ejpam-5787	226	15	rational	rational	ADJ
ejpam-5787	226	16	,	,	PUNCT
ejpam-5787	226	17	i.e.	i.e.	X
ejpam-5787	226	18	n	n	X
ejpam-5787	226	19	=	=	SYM
ejpam-5787	226	20	p	p	NOUN
ejpam-5787	226	21	/	/	SYM
ejpam-5787	226	22	q	q	NOUN
ejpam-5787	226	23	with	with	ADP
ejpam-5787	226	24	p	p	NOUN
ejpam-5787	226	25	and	and	CCONJ
ejpam-5787	226	26	q	q	NOUN
ejpam-5787	226	27	integers	integer	NOUN
ejpam-5787	226	28	,	,	PUNCT
ejpam-5787	226	29	then	then	ADV
ejpam-5787	226	30	we	we	PRON
ejpam-5787	226	31	say	say	VERB
ejpam-5787	226	32	the	the	DET
ejpam-5787	226	33	motion	motion	NOUN
ejpam-5787	226	34	is	be	AUX
ejpam-5787	226	35	phase	phase	NOUN
ejpam-5787	226	36	-	-	PUNCT
ejpam-5787	226	37	locked	lock	VERB
ejpam-5787	226	38	.	.	PUNCT
ejpam-5787	227	1	otherwise	otherwise	ADV
ejpam-5787	227	2	,	,	PUNCT
ejpam-5787	227	3	we	we	PRON
ejpam-5787	227	4	say	say	VERB
ejpam-5787	227	5	the	the	DET
ejpam-5787	227	6	motion	motion	NOUN
ejpam-5787	227	7	is	be	AUX
ejpam-5787	227	8	i.	i.	PROPN
ejpam-5787	227	9	alraddadi	alraddadi	PROPN
ejpam-5787	227	10	/	/	SYM
ejpam-5787	227	11	eur	eur	PROPN
ejpam-5787	227	12	.	.	PUNCT
ejpam-5787	228	1	j.	j.	PROPN
ejpam-5787	228	2	pure	pure	PROPN
ejpam-5787	228	3	appl	appl	PROPN
ejpam-5787	228	4	.	.	PROPN
ejpam-5787	228	5	math	math	PROPN
ejpam-5787	228	6	,	,	PUNCT
ejpam-5787	228	7	18	18	NUM
ejpam-5787	228	8	(	(	PUNCT
ejpam-5787	228	9	1	1	NUM
ejpam-5787	228	10	)	)	PUNCT
ejpam-5787	228	11	(	(	PUNCT
ejpam-5787	228	12	2025	2025	NUM
ejpam-5787	228	13	)	)	PUNCT
ejpam-5787	228	14	,	,	PUNCT
ejpam-5787	228	15	5787	5787	NUM
ejpam-5787	228	16	15	15	NUM
ejpam-5787	228	17	of	of	ADP
ejpam-5787	228	18	23	23	NUM
ejpam-5787	228	19	quasiperiodic	quasiperiodic	ADJ
ejpam-5787	228	20	.	.	PUNCT
ejpam-5787	229	1	frequency	frequency	NOUN
ejpam-5787	229	2	locking	locking	NOUN
ejpam-5787	229	3	regions	region	NOUN
ejpam-5787	229	4	(	(	PUNCT
ejpam-5787	229	5	also	also	ADV
ejpam-5787	229	6	called	call	VERB
ejpam-5787	229	7	arnold	arnold	PROPN
ejpam-5787	229	8	tongues	tongue	NOUN
ejpam-5787	229	9	)	)	PUNCT
ejpam-5787	229	10	identify	identify	VERB
ejpam-5787	229	11	a	a	DET
ejpam-5787	229	12	periodic	periodic	ADJ
ejpam-5787	229	13	solution	solution	NOUN
ejpam-5787	229	14	which	which	PRON
ejpam-5787	229	15	generically	generically	ADV
ejpam-5787	229	16	persists	persist	VERB
ejpam-5787	229	17	as	as	ADP
ejpam-5787	229	18	the	the	DET
ejpam-5787	229	19	amplitude	amplitude	NOUN
ejpam-5787	229	20	a	a	PRON
ejpam-5787	229	21	and	and	CCONJ
ejpam-5787	229	22	the	the	DET
ejpam-5787	229	23	frequency	frequency	NOUN
ejpam-5787	229	24	ω	ω	NOUN
ejpam-5787	229	25	of	of	ADP
ejpam-5787	229	26	the	the	DET
ejpam-5787	229	27	forcing	forcing	NOUN
ejpam-5787	229	28	are	be	AUX
ejpam-5787	229	29	varied	varied	ADJ
ejpam-5787	229	30	[	[	X
ejpam-5787	229	31	22	22	NUM
ejpam-5787	229	32	]	]	PUNCT
ejpam-5787	229	33	.	.	PUNCT
ejpam-5787	230	1	boundaries	boundary	NOUN
ejpam-5787	230	2	of	of	ADP
ejpam-5787	230	3	arnold	arnold	PROPN
ejpam-5787	230	4	tongues	tongues	PROPN
ejpam-5787	230	5	correspond	correspond	VERB
ejpam-5787	230	6	to	to	ADP
ejpam-5787	230	7	saddle	saddle	NOUN
ejpam-5787	230	8	-	-	PUNCT
ejpam-5787	230	9	node	node	NOUN
ejpam-5787	230	10	bifurcations	bifurcation	NOUN
ejpam-5787	230	11	of	of	ADP
ejpam-5787	230	12	these	these	DET
ejpam-5787	230	13	n	n	PRON
ejpam-5787	230	14	-periodic	-periodic	ADJ
ejpam-5787	230	15	orbits[21	orbits[21	NOUN
ejpam-5787	230	16	]	]	PUNCT
ejpam-5787	230	17	.	.	PUNCT
ejpam-5787	231	1	in	in	ADP
ejpam-5787	231	2	this	this	DET
ejpam-5787	231	3	subsection	subsection	NOUN
ejpam-5787	231	4	,	,	PUNCT
ejpam-5787	231	5	we	we	PRON
ejpam-5787	231	6	show	show	VERB
ejpam-5787	231	7	the	the	DET
ejpam-5787	231	8	frequency	frequency	NOUN
ejpam-5787	231	9	locking	locking	NOUN
ejpam-5787	231	10	regions	region	NOUN
ejpam-5787	231	11	(	(	PUNCT
ejpam-5787	231	12	or	or	CCONJ
ejpam-5787	231	13	arnold	arnold	PROPN
ejpam-5787	231	14	tongues	tongue	NOUN
ejpam-5787	231	15	)	)	PUNCT
ejpam-5787	231	16	in	in	ADP
ejpam-5787	231	17	the	the	DET
ejpam-5787	231	18	parameter	parameter	NOUN
ejpam-5787	231	19	space	space	NOUN
ejpam-5787	231	20	(	(	PUNCT
ejpam-5787	231	21	a	a	DET
ejpam-5787	231	22	,	,	PUNCT
ejpam-5787	231	23	ω	ω	NOUN
ejpam-5787	231	24	)	)	PUNCT
ejpam-5787	231	25	.	.	PUNCT
ejpam-5787	232	1	subsequently	subsequently	ADV
ejpam-5787	232	2	,	,	PUNCT
ejpam-5787	232	3	we	we	PRON
ejpam-5787	232	4	show	show	VERB
ejpam-5787	232	5	that	that	SCONJ
ejpam-5787	232	6	a	a	DET
ejpam-5787	232	7	periodic	periodic	ADJ
ejpam-5787	232	8	solution	solution	NOUN
ejpam-5787	232	9	persists	persist	VERB
ejpam-5787	232	10	for	for	ADP
ejpam-5787	232	11	varying	vary	VERB
ejpam-5787	232	12	a	a	PRON
ejpam-5787	232	13	and	and	CCONJ
ejpam-5787	232	14	ω	ω	NOUN
ejpam-5787	232	15	and	and	CCONJ
ejpam-5787	232	16	that	that	SCONJ
ejpam-5787	232	17	this	this	DET
ejpam-5787	232	18	solution	solution	NOUN
ejpam-5787	232	19	is	be	AUX
ejpam-5787	232	20	frequency	frequency	NOUN
ejpam-5787	232	21	locked	lock	VERB
ejpam-5787	232	22	(	(	PUNCT
ejpam-5787	232	23	forming	form	VERB
ejpam-5787	232	24	arnold	arnold	PROPN
ejpam-5787	232	25	tongue	tongue	PROPN
ejpam-5787	232	26	)	)	PUNCT
ejpam-5787	232	27	.	.	PUNCT
ejpam-5787	233	1	as	as	SCONJ
ejpam-5787	233	2	shown	show	VERB
ejpam-5787	233	3	in	in	ADP
ejpam-5787	233	4	figure	figure	NOUN
ejpam-5787	233	5	11	11	NUM
ejpam-5787	233	6	,	,	PUNCT
ejpam-5787	233	7	the	the	DET
ejpam-5787	233	8	saddle	saddle	NOUN
ejpam-5787	233	9	-	-	PUNCT
ejpam-5787	233	10	node	node	NOUN
ejpam-5787	233	11	bifurcation	bifurcation	NOUN
ejpam-5787	233	12	of	of	ADP
ejpam-5787	233	13	the	the	DET
ejpam-5787	233	14	first	first	ADJ
ejpam-5787	233	15	return	return	NOUN
ejpam-5787	233	16	map	map	NOUN
ejpam-5787	233	17	occurs	occur	VERB
ejpam-5787	233	18	on	on	ADP
ejpam-5787	233	19	the	the	DET
ejpam-5787	233	20	boundary	boundary	NOUN
ejpam-5787	233	21	of	of	ADP
ejpam-5787	233	22	frequency	frequency	NOUN
ejpam-5787	233	23	locking	locking	NOUN
ejpam-5787	233	24	in	in	ADP
ejpam-5787	233	25	a	a	DET
ejpam-5787	233	26	parameter	parameter	NOUN
ejpam-5787	233	27	space	space	NOUN
ejpam-5787	233	28	(	(	PUNCT
ejpam-5787	233	29	a	a	DET
ejpam-5787	233	30	,	,	PUNCT
ejpam-5787	233	31	ω	ω	NOUN
ejpam-5787	233	32	)	)	PUNCT
ejpam-5787	233	33	of	of	ADP
ejpam-5787	233	34	the	the	DET
ejpam-5787	233	35	system	system	NOUN
ejpam-5787	233	36	for	for	ADP
ejpam-5787	233	37	relatively	relatively	ADV
ejpam-5787	233	38	weak	weak	ADJ
ejpam-5787	233	39	forcing	forcing	NOUN
ejpam-5787	233	40	.	.	PUNCT
ejpam-5787	234	1	in	in	ADP
ejpam-5787	234	2	parameter	parameter	NOUN
ejpam-5787	234	3	space	space	NOUN
ejpam-5787	234	4	(	(	PUNCT
ejpam-5787	234	5	a	a	DET
ejpam-5787	234	6	,	,	PUNCT
ejpam-5787	234	7	ω	ω	NOUN
ejpam-5787	234	8	)	)	PUNCT
ejpam-5787	234	9	,	,	PUNCT
ejpam-5787	234	10	frequency	frequency	NOUN
ejpam-5787	234	11	locking	locking	NOUN
ejpam-5787	234	12	regions	region	NOUN
ejpam-5787	234	13	exist	exist	VERB
ejpam-5787	234	14	where	where	SCONJ
ejpam-5787	234	15	the	the	DET
ejpam-5787	234	16	period	period	NOUN
ejpam-5787	234	17	n	n	PRON
ejpam-5787	234	18	of	of	ADP
ejpam-5787	234	19	the	the	DET
ejpam-5787	234	20	oscillator	oscillator	NOUN
ejpam-5787	234	21	remains	remain	VERB
ejpam-5787	234	22	constant	constant	ADJ
ejpam-5787	234	23	under	under	ADP
ejpam-5787	234	24	perturbation	perturbation	NOUN
ejpam-5787	234	25	.	.	PUNCT
ejpam-5787	235	1	we	we	PRON
ejpam-5787	235	2	identify	identify	VERB
ejpam-5787	235	3	the	the	DET
ejpam-5787	235	4	frequency	frequency	NOUN
ejpam-5787	235	5	locking	locking	NOUN
ejpam-5787	235	6	by	by	ADP
ejpam-5787	235	7	estimating	estimate	VERB
ejpam-5787	235	8	the	the	DET
ejpam-5787	235	9	iterations	iteration	NOUN
ejpam-5787	235	10	of	of	ADP
ejpam-5787	235	11	the	the	DET
ejpam-5787	235	12	poincaré	poincaré	ADJ
ejpam-5787	235	13	return	return	NOUN
ejpam-5787	235	14	map	map	NOUN
ejpam-5787	236	1	f	f	PROPN
ejpam-5787	236	2	and	and	CCONJ
ejpam-5787	236	3	we	we	PRON
ejpam-5787	236	4	numerically	numerically	ADV
ejpam-5787	236	5	solved	solve	VERB
ejpam-5787	236	6	the	the	DET
ejpam-5787	236	7	desingularised	desingularised	ADJ
ejpam-5787	236	8	system	system	NOUN
ejpam-5787	236	9	(	(	PUNCT
ejpam-5787	236	10	4	4	NUM
ejpam-5787	236	11	)	)	PUNCT
ejpam-5787	236	12	to	to	PART
ejpam-5787	236	13	construct	construct	VERB
ejpam-5787	236	14	the	the	DET
ejpam-5787	236	15	return	return	NOUN
ejpam-5787	236	16	map	map	NOUN
ejpam-5787	236	17	f	f	PROPN
ejpam-5787	236	18	.	.	PUNCT
ejpam-5787	237	1	from	from	ADP
ejpam-5787	237	2	our	our	PRON
ejpam-5787	237	3	computation	computation	NOUN
ejpam-5787	237	4	,	,	PUNCT
ejpam-5787	237	5	shown	show	VERB
ejpam-5787	237	6	in	in	ADP
ejpam-5787	237	7	figure	figure	NOUN
ejpam-5787	237	8	12	12	NUM
ejpam-5787	237	9	,	,	PUNCT
ejpam-5787	237	10	we	we	PRON
ejpam-5787	237	11	show	show	VERB
ejpam-5787	237	12	the	the	DET
ejpam-5787	237	13	iterations	iteration	NOUN
ejpam-5787	237	14	of	of	ADP
ejpam-5787	237	15	the	the	DET
ejpam-5787	237	16	poincaré	poincaré	ADJ
ejpam-5787	237	17	return	return	NOUN
ejpam-5787	237	18	map	map	NOUN
ejpam-5787	237	19	for	for	ADP
ejpam-5787	237	20	a	a	DET
ejpam-5787	237	21	typical	typical	ADJ
ejpam-5787	237	22	point	point	NOUN
ejpam-5787	237	23	after	after	ADP
ejpam-5787	237	24	ignoring	ignore	VERB
ejpam-5787	237	25	a	a	DET
ejpam-5787	237	26	transient	transient	NOUN
ejpam-5787	237	27	of	of	ADP
ejpam-5787	237	28	100	100	NUM
ejpam-5787	237	29	iterations	iteration	NOUN
ejpam-5787	237	30	so	so	SCONJ
ejpam-5787	237	31	as	as	SCONJ
ejpam-5787	237	32	to	to	PART
ejpam-5787	237	33	identify	identify	VERB
ejpam-5787	237	34	the	the	DET
ejpam-5787	237	35	period	period	NOUN
ejpam-5787	237	36	n	n	ADP
ejpam-5787	237	37	of	of	ADP
ejpam-5787	237	38	the	the	DET
ejpam-5787	237	39	oscillator	oscillator	NOUN
ejpam-5787	237	40	to	to	PART
ejpam-5787	237	41	get	get	VERB
ejpam-5787	237	42	an	an	DET
ejpam-5787	237	43	attractor	attractor	NOUN
ejpam-5787	237	44	point	point	NOUN
ejpam-5787	237	45	of	of	ADP
ejpam-5787	237	46	the	the	DET
ejpam-5787	237	47	system	system	NOUN
ejpam-5787	237	48	.	.	PUNCT
ejpam-5787	238	1	we	we	PRON
ejpam-5787	238	2	describe	describe	VERB
ejpam-5787	238	3	our	our	PRON
ejpam-5787	238	4	method	method	NOUN
ejpam-5787	238	5	as	as	ADP
ejpam-5787	238	6	the	the	DET
ejpam-5787	238	7	following	following	NOUN
ejpam-5787	238	8	:	:	PUNCT
ejpam-5787	238	9	(	(	PUNCT
ejpam-5787	238	10	i	i	NOUN
ejpam-5787	238	11	)	)	PUNCT
ejpam-5787	238	12	for	for	ADP
ejpam-5787	238	13	different	different	ADJ
ejpam-5787	238	14	values	value	NOUN
ejpam-5787	238	15	of	of	ADP
ejpam-5787	238	16	a	a	PRON
ejpam-5787	238	17	and	and	CCONJ
ejpam-5787	238	18	ω	ω	NUM
ejpam-5787	238	19	,	,	PUNCT
ejpam-5787	238	20	we	we	PRON
ejpam-5787	238	21	numerically	numerically	ADV
ejpam-5787	238	22	solved	solve	VERB
ejpam-5787	238	23	the	the	DET
ejpam-5787	238	24	desingularised	desingularised	ADJ
ejpam-5787	238	25	system	system	NOUN
ejpam-5787	238	26	(	(	PUNCT
ejpam-5787	238	27	4	4	NUM
ejpam-5787	238	28	)	)	PUNCT
ejpam-5787	238	29	to	to	PART
ejpam-5787	238	30	construct	construct	VERB
ejpam-5787	238	31	the	the	DET
ejpam-5787	238	32	poincaré	poincaré	ADJ
ejpam-5787	238	33	return	return	NOUN
ejpam-5787	238	34	map	map	NOUN
ejpam-5787	239	1	f	f	X
ejpam-5787	239	2	.	.	PUNCT
ejpam-5787	240	1	(	(	PUNCT
ejpam-5787	240	2	ii	ii	NOUN
ejpam-5787	240	3	)	)	PUNCT
ejpam-5787	240	4	pick	pick	VERB
ejpam-5787	240	5	a	a	DET
ejpam-5787	240	6	random	random	ADJ
ejpam-5787	240	7	initial	initial	ADJ
ejpam-5787	240	8	condition	condition	NOUN
ejpam-5787	240	9	θ∗.	θ∗.	PROPN
ejpam-5787	240	10	(	(	PUNCT
ejpam-5787	240	11	iii	iii	NOUN
ejpam-5787	240	12	)	)	PUNCT
ejpam-5787	240	13	we	we	PRON
ejpam-5787	240	14	set	set	VERB
ejpam-5787	240	15	θ0	θ0	NOUN
ejpam-5787	240	16	=	=	SYM
ejpam-5787	240	17	fnt(θ∗	fnt(θ∗	X
ejpam-5787	240	18	)	)	PUNCT
ejpam-5787	240	19	mod	mod	NOUN
ejpam-5787	240	20	1	1	NUM
ejpam-5787	240	21	,	,	PUNCT
ejpam-5787	240	22	where	where	SCONJ
ejpam-5787	240	23	nt	not	PART
ejpam-5787	240	24	iterates	iterate	VERB
ejpam-5787	240	25	500	500	NUM
ejpam-5787	240	26	times	time	NOUN
ejpam-5787	240	27	for	for	ADP
ejpam-5787	240	28	the	the	DET
ejpam-5787	240	29	poincaré	poincaré	ADJ
ejpam-5787	240	30	return	return	NOUN
ejpam-5787	240	31	map	map	NOUN
ejpam-5787	240	32	f	f	X
ejpam-5787	240	33	(	(	PUNCT
ejpam-5787	240	34	13	13	NUM
ejpam-5787	240	35	)	)	PUNCT
ejpam-5787	240	36	.	.	PUNCT
ejpam-5787	241	1	(	(	PUNCT
ejpam-5787	241	2	iv	iv	X
ejpam-5787	241	3	)	)	PUNCT
ejpam-5787	241	4	we	we	PRON
ejpam-5787	241	5	use	use	VERB
ejpam-5787	241	6	the	the	DET
ejpam-5787	241	7	iterations	iteration	NOUN
ejpam-5787	241	8	of	of	ADP
ejpam-5787	241	9	the	the	DET
ejpam-5787	241	10	poincaré	poincaré	ADJ
ejpam-5787	241	11	return	return	NOUN
ejpam-5787	241	12	map	map	NOUN
ejpam-5787	241	13	for	for	ADP
ejpam-5787	241	14	a	a	DET
ejpam-5787	241	15	typical	typical	ADJ
ejpam-5787	241	16	point	point	NOUN
ejpam-5787	241	17	after	after	ADP
ejpam-5787	241	18	ignoring	ignore	VERB
ejpam-5787	241	19	a	a	DET
ejpam-5787	241	20	transient	transient	NOUN
ejpam-5787	241	21	of	of	ADP
ejpam-5787	241	22	100	100	NUM
ejpam-5787	241	23	iterations	iteration	NOUN
ejpam-5787	241	24	so	so	SCONJ
ejpam-5787	241	25	as	as	SCONJ
ejpam-5787	241	26	to	to	PART
ejpam-5787	241	27	identify	identify	VERB
ejpam-5787	241	28	a	a	DET
ejpam-5787	241	29	trajectory	trajectory	NOUN
ejpam-5787	241	30	attractor	attractor	NOUN
ejpam-5787	241	31	of	of	ADP
ejpam-5787	241	32	the	the	DET
ejpam-5787	241	33	system	system	NOUN
ejpam-5787	241	34	.	.	PUNCT
ejpam-5787	242	1	(	(	PUNCT
ejpam-5787	242	2	v	v	X
ejpam-5787	242	3	)	)	PUNCT
ejpam-5787	242	4	we	we	PRON
ejpam-5787	242	5	try	try	VERB
ejpam-5787	242	6	to	to	PART
ejpam-5787	242	7	find	find	VERB
ejpam-5787	242	8	the	the	DET
ejpam-5787	242	9	average	average	ADJ
ejpam-5787	242	10	period	period	NOUN
ejpam-5787	242	11	of	of	ADP
ejpam-5787	242	12	θi	θi	NOUN
ejpam-5787	242	13	where	where	SCONJ
ejpam-5787	242	14	i	i	PRON
ejpam-5787	242	15	≤	≤	ADV
ejpam-5787	242	16	nmax	nmax	ADV
ejpam-5787	242	17	by	by	ADP
ejpam-5787	242	18	searching	search	VERB
ejpam-5787	242	19	for	for	ADP
ejpam-5787	242	20	smallest	small	ADJ
ejpam-5787	242	21	i	i	PRON
ejpam-5787	242	22	∈	∈	PROPN
ejpam-5787	242	23	{	{	PUNCT
ejpam-5787	242	24	1	1	NUM
ejpam-5787	242	25	,	,	PUNCT
ejpam-5787	242	26	.	.	PUNCT
ejpam-5787	242	27	.	.	PUNCT
ejpam-5787	243	1	.	.	PUNCT
ejpam-5787	244	1	,	,	PUNCT
ejpam-5787	244	2	nmax	nmax	ADV
ejpam-5787	244	3	}	}	PUNCT
ejpam-5787	244	4	such	such	ADJ
ejpam-5787	244	5	that	that	SCONJ
ejpam-5787	244	6	|(f	|(f	PROPN
ejpam-5787	244	7	i(θ0	i(θ0	PROPN
ejpam-5787	244	8	)	)	PUNCT
ejpam-5787	244	9	mod	mod	PROPN
ejpam-5787	245	1	1)−	1)−	PROPN
ejpam-5787	245	2	θ0|	θ0|	PROPN
ejpam-5787	245	3	<	<	X
ejpam-5787	245	4	ϵ	ϵ	X
ejpam-5787	245	5	(	(	PUNCT
ejpam-5787	245	6	a	a	X
ejpam-5787	245	7	)	)	PUNCT
ejpam-5787	245	8	if	if	SCONJ
ejpam-5787	245	9	this	this	PRON
ejpam-5787	245	10	is	be	AUX
ejpam-5787	245	11	satisfied	satisfied	ADJ
ejpam-5787	245	12	,	,	PUNCT
ejpam-5787	245	13	then	then	ADV
ejpam-5787	245	14	we	we	PRON
ejpam-5787	245	15	set	set	VERB
ejpam-5787	245	16	n	n	NOUN
ejpam-5787	245	17	=	=	SYM
ejpam-5787	245	18	f	f	PROPN
ejpam-5787	245	19	i(θ0)−	i(θ0)−	PROPN
ejpam-5787	245	20	θ0	θ0	PROPN
ejpam-5787	245	21	.	.	PUNCT
ejpam-5787	246	1	(	(	PUNCT
ejpam-5787	246	2	b	b	X
ejpam-5787	246	3	)	)	PUNCT
ejpam-5787	246	4	if	if	SCONJ
ejpam-5787	246	5	it	it	PRON
ejpam-5787	246	6	is	be	AUX
ejpam-5787	246	7	not	not	PART
ejpam-5787	246	8	satisfied	satisfied	ADJ
ejpam-5787	246	9	,	,	PUNCT
ejpam-5787	246	10	then	then	ADV
ejpam-5787	246	11	we	we	PRON
ejpam-5787	246	12	set	set	VERB
ejpam-5787	246	13	n	n	NOUN
ejpam-5787	246	14	=	=	SYM
ejpam-5787	246	15	0	0	NUM
ejpam-5787	246	16	.	.	NOUN
ejpam-5787	246	17	4	4	X
ejpam-5787	246	18	.	.	X
ejpam-5787	246	19	symmetry	symmetry	NOUN
ejpam-5787	246	20	breaking	break	VERB
ejpam-5787	246	21	in	in	ADP
ejpam-5787	246	22	sections	section	NOUN
ejpam-5787	246	23	2	2	NUM
ejpam-5787	246	24	and	and	CCONJ
ejpam-5787	246	25	3	3	NUM
ejpam-5787	246	26	we	we	PRON
ejpam-5787	246	27	reviewed	review	VERB
ejpam-5787	246	28	the	the	DET
ejpam-5787	246	29	results	result	NOUN
ejpam-5787	246	30	of	of	ADP
ejpam-5787	246	31	[	[	X
ejpam-5787	246	32	10	10	NUM
ejpam-5787	246	33	]	]	PUNCT
ejpam-5787	246	34	,	,	PUNCT
ejpam-5787	246	35	the	the	DET
ejpam-5787	246	36	symmetric	symmetric	ADJ
ejpam-5787	246	37	forced	force	VERB
ejpam-5787	246	38	van	van	PROPN
ejpam-5787	246	39	der	der	ADJ
ejpam-5787	246	40	pol	pol	PROPN
ejpam-5787	246	41	oscillator	oscillator	NOUN
ejpam-5787	246	42	(	(	PUNCT
ejpam-5787	246	43	4	4	NUM
ejpam-5787	246	44	)	)	PUNCT
ejpam-5787	246	45	for	for	ADP
ejpam-5787	246	46	β	β	X
ejpam-5787	246	47	=	=	SYM
ejpam-5787	246	48	0	0	X
ejpam-5787	246	49	.	.	PUNCT
ejpam-5787	247	1	here	here	ADV
ejpam-5787	247	2	we	we	PRON
ejpam-5787	247	3	generalise	generalise	VERB
ejpam-5787	247	4	to	to	ADP
ejpam-5787	247	5	a	a	DET
ejpam-5787	247	6	asymmetric	asymmetric	ADJ
ejpam-5787	247	7	forced	force	VERB
ejpam-5787	247	8	van	van	PROPN
ejpam-5787	247	9	der	der	ADJ
ejpam-5787	247	10	pol	pol	PROPN
ejpam-5787	247	11	oscillator	oscillator	NOUN
ejpam-5787	247	12	for	for	ADP
ejpam-5787	247	13	β	β	X
ejpam-5787	247	14	̸=	̸=	PROPN
ejpam-5787	247	15	0	0	NUM
ejpam-5787	247	16	.	.	PUNCT
ejpam-5787	248	1	in	in	ADP
ejpam-5787	248	2	this	this	DET
ejpam-5787	248	3	section	section	NOUN
ejpam-5787	248	4	,	,	PUNCT
ejpam-5787	248	5	we	we	PRON
ejpam-5787	248	6	show	show	VERB
ejpam-5787	248	7	that	that	SCONJ
ejpam-5787	248	8	the	the	DET
ejpam-5787	248	9	forced	force	VERB
ejpam-5787	248	10	asymmetric	asymmetric	PROPN
ejpam-5787	248	11	van	van	PROPN
ejpam-5787	248	12	der	der	ADJ
ejpam-5787	248	13	pol	pol	PROPN
ejpam-5787	248	14	oscillator	oscillator	NOUN
ejpam-5787	248	15	can	can	AUX
ejpam-5787	248	16	become	become	VERB
ejpam-5787	248	17	frequency	frequency	NOUN
ejpam-5787	248	18	locked	lock	VERB
ejpam-5787	248	19	due	due	ADP
ejpam-5787	248	20	to	to	ADP
ejpam-5787	248	21	the	the	DET
ejpam-5787	248	22	forcing	forcing	NOUN
ejpam-5787	248	23	.	.	PUNCT
ejpam-5787	249	1	we	we	PRON
ejpam-5787	249	2	also	also	ADV
ejpam-5787	249	3	show	show	VERB
ejpam-5787	249	4	how	how	SCONJ
ejpam-5787	249	5	the	the	DET
ejpam-5787	249	6	symmetry	symmetry	NOUN
ejpam-5787	249	7	breaking	break	VERB
ejpam-5787	249	8	parameter	parameter	NOUN
ejpam-5787	249	9	β	β	PROPN
ejpam-5787	249	10	in	in	ADP
ejpam-5787	249	11	a	a	DET
ejpam-5787	249	12	periodically	periodically	ADV
ejpam-5787	249	13	forced	force	VERB
ejpam-5787	249	14	van	van	PROPN
ejpam-5787	249	15	der	der	PROPN
ejpam-5787	249	16	pol	pol	PROPN
ejpam-5787	249	17	oscillator	oscillator	NOUN
ejpam-5787	249	18	influences	influence	VERB
ejpam-5787	249	19	the	the	DET
ejpam-5787	249	20	width	width	NOUN
ejpam-5787	249	21	of	of	ADP
ejpam-5787	249	22	arnold	arnold	PROPN
ejpam-5787	249	23	i.	i.	PROPN
ejpam-5787	249	24	alraddadi	alraddadi	PROPN
ejpam-5787	249	25	/	/	SYM
ejpam-5787	249	26	eur	eur	PROPN
ejpam-5787	249	27	.	.	PUNCT
ejpam-5787	250	1	j.	j.	PROPN
ejpam-5787	250	2	pure	pure	PROPN
ejpam-5787	250	3	appl	appl	PROPN
ejpam-5787	250	4	.	.	PROPN
ejpam-5787	250	5	math	math	PROPN
ejpam-5787	250	6	,	,	PUNCT
ejpam-5787	250	7	18	18	NUM
ejpam-5787	250	8	(	(	PUNCT
ejpam-5787	250	9	1	1	NUM
ejpam-5787	250	10	)	)	PUNCT
ejpam-5787	250	11	(	(	PUNCT
ejpam-5787	250	12	2025	2025	NUM
ejpam-5787	250	13	)	)	PUNCT
ejpam-5787	250	14	,	,	PUNCT
ejpam-5787	250	15	5787	5787	NUM
ejpam-5787	250	16	16	16	NUM
ejpam-5787	250	17	of	of	ADP
ejpam-5787	250	18	23	23	NUM
ejpam-5787	250	19	figure	figure	NOUN
ejpam-5787	250	20	12	12	NUM
ejpam-5787	250	21	:	:	PUNCT
ejpam-5787	250	22	(	(	PUNCT
ejpam-5787	250	23	a	a	PRON
ejpam-5787	250	24	,	,	PUNCT
ejpam-5787	250	25	ω	ω	NOUN
ejpam-5787	250	26	)	)	PUNCT
ejpam-5787	250	27	parameter	parameter	NOUN
ejpam-5787	250	28	plane	plane	NOUN
ejpam-5787	250	29	showing	show	VERB
ejpam-5787	250	30	regions	region	NOUN
ejpam-5787	250	31	of	of	ADP
ejpam-5787	250	32	the	the	DET
ejpam-5787	250	33	existence	existence	NOUN
ejpam-5787	250	34	of	of	ADP
ejpam-5787	250	35	a	a	DET
ejpam-5787	250	36	stable	stable	ADJ
ejpam-5787	250	37	period	period	NOUN
ejpam-5787	250	38	of	of	ADP
ejpam-5787	250	39	n	n	DET
ejpam-5787	250	40	orbits	orbit	NOUN
ejpam-5787	250	41	for	for	ADP
ejpam-5787	250	42	the	the	DET
ejpam-5787	250	43	return	return	NOUN
ejpam-5787	250	44	map	map	NOUN
ejpam-5787	250	45	f	f	PROPN
ejpam-5787	250	46	in	in	ADP
ejpam-5787	250	47	(	(	PUNCT
ejpam-5787	250	48	13	13	NUM
ejpam-5787	250	49	)	)	PUNCT
ejpam-5787	250	50	for	for	ADP
ejpam-5787	250	51	the	the	DET
ejpam-5787	250	52	symmetric	symmetric	ADJ
ejpam-5787	250	53	van	van	PROPN
ejpam-5787	250	54	der	der	PROPN
ejpam-5787	250	55	pol	pol	PROPN
ejpam-5787	250	56	oscillator	oscillator	NOUN
ejpam-5787	250	57	.	.	PUNCT
ejpam-5787	251	1	the	the	DET
ejpam-5787	251	2	colorbar	colorbar	NOUN
ejpam-5787	251	3	indicates	indicate	VERB
ejpam-5787	251	4	the	the	DET
ejpam-5787	251	5	rotation	rotation	NOUN
ejpam-5787	251	6	numbers	number	NOUN
ejpam-5787	251	7	n	n	ADP
ejpam-5787	251	8	of	of	ADP
ejpam-5787	251	9	the	the	DET
ejpam-5787	251	10	return	return	NOUN
ejpam-5787	251	11	map	map	NOUN
ejpam-5787	251	12	.	.	PUNCT
ejpam-5787	252	1	observe	observe	VERB
ejpam-5787	252	2	in	in	ADP
ejpam-5787	252	3	this	this	DET
ejpam-5787	252	4	case	case	NOUN
ejpam-5787	252	5	β	β	X
ejpam-5787	252	6	=	=	SYM
ejpam-5787	252	7	0	0	NUM
ejpam-5787	252	8	,	,	PUNCT
ejpam-5787	252	9	(	(	PUNCT
ejpam-5787	252	10	from	from	ADP
ejpam-5787	252	11	down	down	ADP
ejpam-5787	252	12	to	to	ADP
ejpam-5787	252	13	up	up	ADP
ejpam-5787	252	14	)	)	PUNCT
ejpam-5787	252	15	there	there	PRON
ejpam-5787	252	16	are	be	VERB
ejpam-5787	252	17	phase	phase	NOUN
ejpam-5787	252	18	-	-	PUNCT
ejpam-5787	252	19	locking	lock	VERB
ejpam-5787	252	20	regions	region	NOUN
ejpam-5787	252	21	in	in	ADP
ejpam-5787	252	22	n	n	PRON
ejpam-5787	252	23	-periodic	-periodic	ADJ
ejpam-5787	252	24	orbits	orbit	NOUN
ejpam-5787	252	25	of	of	ADP
ejpam-5787	252	26	(	(	PUNCT
ejpam-5787	252	27	13	13	NUM
ejpam-5787	252	28	)	)	PUNCT
ejpam-5787	252	29	(	(	PUNCT
ejpam-5787	252	30	in	in	ADP
ejpam-5787	252	31	different	different	ADJ
ejpam-5787	252	32	colours	colour	NOUN
ejpam-5787	252	33	)	)	PUNCT
ejpam-5787	252	34	.	.	PUNCT
ejpam-5787	253	1	these	these	DET
ejpam-5787	253	2	regions	region	NOUN
ejpam-5787	253	3	correspond	correspond	VERB
ejpam-5787	253	4	well	well	ADV
ejpam-5787	253	5	with	with	ADP
ejpam-5787	253	6	standard	standard	ADJ
ejpam-5787	253	7	arnold	arnold	PROPN
ejpam-5787	253	8	tongues	tongues	PROPN
ejpam-5787	253	9	type	type	NOUN
ejpam-5787	253	10	pictures	picture	NOUN
ejpam-5787	253	11	(	(	PUNCT
ejpam-5787	253	12	frequency	frequency	NOUN
ejpam-5787	253	13	-	-	PUNCT
ejpam-5787	253	14	locking	locking	NOUN
ejpam-5787	253	15	):	):	PUNCT
ejpam-5787	253	16	the	the	DET
ejpam-5787	253	17	frequency	frequency	NOUN
ejpam-5787	253	18	ratio	ratio	NOUN
ejpam-5787	253	19	is	be	AUX
ejpam-5787	253	20	ω	ω	NUM
ejpam-5787	253	21	and	and	CCONJ
ejpam-5787	253	22	the	the	DET
ejpam-5787	253	23	forcing	force	VERB
ejpam-5787	253	24	amplitude	amplitude	NOUN
ejpam-5787	253	25	is	be	AUX
ejpam-5787	253	26	a.	a.	NOUN
ejpam-5787	253	27	the	the	DET
ejpam-5787	253	28	large	large	ADJ
ejpam-5787	253	29	regions	region	NOUN
ejpam-5787	253	30	correspond	correspond	VERB
ejpam-5787	253	31	to	to	ADP
ejpam-5787	253	32	arnold	arnold	PROPN
ejpam-5787	253	33	tongues	tongue	NOUN
ejpam-5787	253	34	for	for	ADP
ejpam-5787	253	35	frequency	frequency	NOUN
ejpam-5787	253	36	-	-	PUNCT
ejpam-5787	253	37	locking	lock	VERB
ejpam-5787	253	38	1:1	1:1	NUM
ejpam-5787	253	39	(	(	PUNCT
ejpam-5787	253	40	black	black	NOUN
ejpam-5787	253	41	)	)	PUNCT
ejpam-5787	253	42	,	,	PUNCT
ejpam-5787	253	43	3:1(light	3:1(light	NUM
ejpam-5787	253	44	blue	blue	NOUN
ejpam-5787	253	45	)	)	PUNCT
ejpam-5787	253	46	,	,	PUNCT
ejpam-5787	253	47	5:1(pink	5:1(pink	NUM
ejpam-5787	253	48	)	)	PUNCT
ejpam-5787	253	49	,	,	PUNCT
ejpam-5787	253	50	7:1(dark	7:1(dark	PROPN
ejpam-5787	253	51	blue	blue	NOUN
ejpam-5787	253	52	)	)	PUNCT
ejpam-5787	253	53	.	.	PUNCT
ejpam-5787	254	1	note	note	VERB
ejpam-5787	254	2	that	that	SCONJ
ejpam-5787	254	3	there	there	PRON
ejpam-5787	254	4	are	be	VERB
ejpam-5787	254	5	bistability	bistability	NOUN
ejpam-5787	254	6	regions	region	NOUN
ejpam-5787	254	7	between	between	ADP
ejpam-5787	254	8	these	these	DET
ejpam-5787	254	9	tongues	tongue	NOUN
ejpam-5787	254	10	depending	depend	VERB
ejpam-5787	254	11	on	on	ADP
ejpam-5787	254	12	the	the	DET
ejpam-5787	254	13	initial	initial	ADJ
ejpam-5787	254	14	conditions	condition	NOUN
ejpam-5787	254	15	.	.	PUNCT
ejpam-5787	255	1	the	the	DET
ejpam-5787	255	2	boundary	boundary	NOUN
ejpam-5787	255	3	of	of	ADP
ejpam-5787	255	4	the	the	DET
ejpam-5787	255	5	arnold	arnold	PROPN
ejpam-5787	255	6	tongues	tongue	NOUN
ejpam-5787	255	7	is	be	AUX
ejpam-5787	255	8	typically	typically	ADV
ejpam-5787	255	9	the	the	DET
ejpam-5787	255	10	saddle	saddle	NOUN
ejpam-5787	255	11	-	-	PUNCT
ejpam-5787	255	12	node	node	NOUN
ejpam-5787	255	13	bifurcation	bifurcation	NOUN
ejpam-5787	255	14	of	of	ADP
ejpam-5787	255	15	a	a	DET
ejpam-5787	255	16	periodic	periodic	ADJ
ejpam-5787	255	17	point	point	NOUN
ejpam-5787	255	18	of	of	ADP
ejpam-5787	255	19	map	map	NOUN
ejpam-5787	255	20	f	f	X
ejpam-5787	255	21	(	(	PUNCT
ejpam-5787	255	22	13	13	NUM
ejpam-5787	255	23	)	)	PUNCT
ejpam-5787	255	24	(	(	PUNCT
ejpam-5787	255	25	compare	compare	VERB
ejpam-5787	255	26	to	to	ADP
ejpam-5787	255	27	[	[	X
ejpam-5787	255	28	10	10	NUM
ejpam-5787	255	29	,	,	PUNCT
ejpam-5787	255	30	figure	figure	NOUN
ejpam-5787	255	31	7.1	7.1	NUM
ejpam-5787	255	32	]	]	PUNCT
ejpam-5787	255	33	)	)	PUNCT
ejpam-5787	255	34	.	.	PUNCT
ejpam-5787	256	1	tongues	tongue	NOUN
ejpam-5787	256	2	(	(	PUNCT
ejpam-5787	256	3	also	also	ADV
ejpam-5787	256	4	known	know	VERB
ejpam-5787	256	5	as	as	ADP
ejpam-5787	256	6	frequency	frequency	NOUN
ejpam-5787	256	7	locking	locking	NOUN
ejpam-5787	256	8	regions	region	NOUN
ejpam-5787	256	9	)	)	PUNCT
ejpam-5787	256	10	,	,	PUNCT
ejpam-5787	256	11	and	and	CCONJ
ejpam-5787	256	12	we	we	PRON
ejpam-5787	256	13	find	find	VERB
ejpam-5787	256	14	these	these	DET
ejpam-5787	256	15	frequency	frequency	NOUN
ejpam-5787	256	16	locking	locking	NOUN
ejpam-5787	256	17	regions	region	NOUN
ejpam-5787	256	18	in	in	ADP
ejpam-5787	256	19	the	the	DET
ejpam-5787	256	20	parameter	parameter	NOUN
ejpam-5787	256	21	space	space	NOUN
ejpam-5787	256	22	(	(	PUNCT
ejpam-5787	256	23	a	a	DET
ejpam-5787	256	24	,	,	PUNCT
ejpam-5787	256	25	ω	ω	NOUN
ejpam-5787	256	26	)	)	PUNCT
ejpam-5787	256	27	.	.	PUNCT
ejpam-5787	257	1	(	(	PUNCT
ejpam-5787	257	2	a	a	X
ejpam-5787	257	3	)	)	PUNCT
ejpam-5787	257	4	(	(	PUNCT
ejpam-5787	257	5	b	b	X
ejpam-5787	257	6	)	)	PUNCT
ejpam-5787	257	7	(	(	PUNCT
ejpam-5787	257	8	c	c	X
ejpam-5787	257	9	)	)	PUNCT
ejpam-5787	257	10	figure	figure	NOUN
ejpam-5787	257	11	13	13	NUM
ejpam-5787	257	12	:	:	PUNCT
ejpam-5787	257	13	the	the	DET
ejpam-5787	257	14	first	first	ADJ
ejpam-5787	257	15	return	return	NOUN
ejpam-5787	257	16	map	map	NOUN
ejpam-5787	257	17	f	f	X
ejpam-5787	257	18	(	(	PUNCT
ejpam-5787	257	19	13	13	NUM
ejpam-5787	257	20	)	)	PUNCT
ejpam-5787	257	21	when	when	SCONJ
ejpam-5787	257	22	a	a	DET
ejpam-5787	257	23	=	=	SYM
ejpam-5787	257	24	1.02	1.02	NUM
ejpam-5787	257	25	and	and	CCONJ
ejpam-5787	257	26	ω	ω	NUM
ejpam-5787	257	27	=	=	NOUN
ejpam-5787	257	28	1.19	1.19	NUM
ejpam-5787	257	29	with	with	ADP
ejpam-5787	257	30	different	different	ADJ
ejpam-5787	257	31	values	value	NOUN
ejpam-5787	257	32	of	of	ADP
ejpam-5787	257	33	β	β	PROPN
ejpam-5787	257	34	.	.	PUNCT
ejpam-5787	258	1	(	(	PUNCT
ejpam-5787	258	2	a	a	DET
ejpam-5787	258	3	-	-	PUNCT
ejpam-5787	258	4	c	c	NOUN
ejpam-5787	258	5	)	)	PUNCT
ejpam-5787	258	6	show	show	VERB
ejpam-5787	258	7	β	β	X
ejpam-5787	258	8	=	=	PUNCT
ejpam-5787	258	9	0.8	0.8	NUM
ejpam-5787	258	10	,	,	PUNCT
ejpam-5787	258	11	0.81	0.81	NUM
ejpam-5787	258	12	and	and	CCONJ
ejpam-5787	258	13	0.82	0.82	NUM
ejpam-5787	258	14	respectively	respectively	ADV
ejpam-5787	258	15	,	,	PUNCT
ejpam-5787	258	16	a	a	DET
ejpam-5787	258	17	saddle	saddle	NOUN
ejpam-5787	258	18	-	-	PUNCT
ejpam-5787	258	19	node	node	NOUN
ejpam-5787	258	20	bifurcation	bifurcation	NOUN
ejpam-5787	258	21	of	of	ADP
ejpam-5787	258	22	the	the	DET
ejpam-5787	258	23	first	first	ADJ
ejpam-5787	258	24	return	return	NOUN
ejpam-5787	258	25	map	map	NOUN
ejpam-5787	258	26	f	f	X
ejpam-5787	258	27	(	(	PUNCT
ejpam-5787	258	28	13	13	NUM
ejpam-5787	258	29	)	)	PUNCT
ejpam-5787	258	30	.	.	PUNCT
ejpam-5787	259	1	figure	figure	NOUN
ejpam-5787	259	2	14	14	NUM
ejpam-5787	259	3	illustrates	illustrate	VERB
ejpam-5787	259	4	the	the	DET
ejpam-5787	259	5	frequency	frequency	NOUN
ejpam-5787	259	6	-	-	PUNCT
ejpam-5787	259	7	locking	lock	VERB
ejpam-5787	259	8	regions	region	NOUN
ejpam-5787	259	9	of	of	ADP
ejpam-5787	259	10	the	the	DET
ejpam-5787	259	11	iteration	iteration	NOUN
ejpam-5787	259	12	of	of	ADP
ejpam-5787	259	13	f	f	PROPN
ejpam-5787	259	14	(	(	PUNCT
ejpam-5787	259	15	13	13	NUM
ejpam-5787	259	16	)	)	PUNCT
ejpam-5787	259	17	in	in	ADP
ejpam-5787	259	18	the	the	DET
ejpam-5787	259	19	i.	i.	PROPN
ejpam-5787	259	20	alraddadi	alraddadi	PROPN
ejpam-5787	259	21	/	/	SYM
ejpam-5787	259	22	eur	eur	PROPN
ejpam-5787	259	23	.	.	PUNCT
ejpam-5787	260	1	j.	j.	PROPN
ejpam-5787	260	2	pure	pure	PROPN
ejpam-5787	260	3	appl	appl	PROPN
ejpam-5787	260	4	.	.	PROPN
ejpam-5787	260	5	math	math	PROPN
ejpam-5787	260	6	,	,	PUNCT
ejpam-5787	260	7	18	18	NUM
ejpam-5787	260	8	(	(	PUNCT
ejpam-5787	260	9	1	1	NUM
ejpam-5787	260	10	)	)	PUNCT
ejpam-5787	260	11	(	(	PUNCT
ejpam-5787	260	12	2025	2025	NUM
ejpam-5787	260	13	)	)	PUNCT
ejpam-5787	260	14	,	,	PUNCT
ejpam-5787	260	15	5787	5787	NUM
ejpam-5787	260	16	17	17	NUM
ejpam-5787	260	17	of	of	ADP
ejpam-5787	260	18	23	23	NUM
ejpam-5787	260	19	two	two	NUM
ejpam-5787	260	20	-	-	PUNCT
ejpam-5787	260	21	parameter	parameter	NOUN
ejpam-5787	260	22	plane	plane	NOUN
ejpam-5787	260	23	(	(	PUNCT
ejpam-5787	260	24	a	a	DET
ejpam-5787	260	25	,	,	PUNCT
ejpam-5787	260	26	ω	ω	NOUN
ejpam-5787	260	27	)	)	PUNCT
ejpam-5787	260	28	for	for	ADP
ejpam-5787	260	29	different	different	ADJ
ejpam-5787	260	30	values	value	NOUN
ejpam-5787	260	31	of	of	ADP
ejpam-5787	260	32	β	β	X
ejpam-5787	260	33	=	=	PUNCT
ejpam-5787	260	34	0.25	0.25	NUM
ejpam-5787	260	35	,	,	PUNCT
ejpam-5787	260	36	0.5	0.5	NUM
ejpam-5787	260	37	,	,	PUNCT
ejpam-5787	260	38	0.8	0.8	NUM
ejpam-5787	260	39	,	,	PUNCT
ejpam-5787	260	40	1	1	NUM
ejpam-5787	260	41	.	.	PUNCT
ejpam-5787	261	1	the	the	DET
ejpam-5787	261	2	arnold	arnold	PROPN
ejpam-5787	261	3	tongue	tongue	NOUN
ejpam-5787	261	4	regions	region	NOUN
ejpam-5787	261	5	appear	appear	VERB
ejpam-5787	261	6	in	in	ADP
ejpam-5787	261	7	this	this	DET
ejpam-5787	261	8	case	case	NOUN
ejpam-5787	261	9	β	β	X
ejpam-5787	261	10	̸=	̸=	PROPN
ejpam-5787	261	11	0	0	NUM
ejpam-5787	261	12	.	.	PUNCT
ejpam-5787	262	1	note	note	VERB
ejpam-5787	262	2	that	that	SCONJ
ejpam-5787	262	3	the	the	DET
ejpam-5787	262	4	width	width	NOUN
ejpam-5787	262	5	of	of	ADP
ejpam-5787	262	6	arnold	arnold	PROPN
ejpam-5787	262	7	tongues	tongue	NOUN
ejpam-5787	262	8	depends	depend	VERB
ejpam-5787	262	9	on	on	ADP
ejpam-5787	262	10	the	the	DET
ejpam-5787	262	11	parameter	parameter	NOUN
ejpam-5787	262	12	β	β	NOUN
ejpam-5787	262	13	.	.	PUNCT
ejpam-5787	263	1	there	there	PRON
ejpam-5787	263	2	are	be	VERB
ejpam-5787	263	3	large	large	ADJ
ejpam-5787	263	4	arnold	arnold	PROPN
ejpam-5787	263	5	tongue	tongue	NOUN
ejpam-5787	263	6	regions	region	NOUN
ejpam-5787	263	7	of	of	ADP
ejpam-5787	263	8	period	period	NOUN
ejpam-5787	263	9	1	1	NUM
ejpam-5787	263	10	,	,	PUNCT
ejpam-5787	263	11	3	3	NUM
ejpam-5787	263	12	,	,	PUNCT
ejpam-5787	263	13	5	5	NUM
ejpam-5787	263	14	,	,	PUNCT
ejpam-5787	263	15	8	8	NUM
ejpam-5787	263	16	for	for	ADP
ejpam-5787	263	17	small	small	ADJ
ejpam-5787	263	18	β	β	X
ejpam-5787	263	19	=	=	SYM
ejpam-5787	263	20	0.5	0.5	NUM
ejpam-5787	263	21	(	(	PUNCT
ejpam-5787	263	22	figure	figure	NOUN
ejpam-5787	263	23	14(a	14(a	NUM
ejpam-5787	263	24	)	)	PUNCT
ejpam-5787	263	25	)	)	PUNCT
ejpam-5787	263	26	.	.	PUNCT
ejpam-5787	264	1	increasing	increase	VERB
ejpam-5787	264	2	β	β	PRON
ejpam-5787	264	3	to	to	ADP
ejpam-5787	264	4	1	1	NUM
ejpam-5787	264	5	,	,	PUNCT
ejpam-5787	264	6	leads	lead	VERB
ejpam-5787	264	7	to	to	ADP
ejpam-5787	264	8	slightly	slightly	ADV
ejpam-5787	264	9	smaller	small	ADJ
ejpam-5787	264	10	arnold	arnold	PROPN
ejpam-5787	264	11	tongue	tongue	NOUN
ejpam-5787	264	12	regions	region	NOUN
ejpam-5787	264	13	of	of	ADP
ejpam-5787	264	14	periods	period	NOUN
ejpam-5787	264	15	between	between	ADP
ejpam-5787	264	16	1	1	NUM
ejpam-5787	264	17	and	and	CCONJ
ejpam-5787	264	18	25	25	NUM
ejpam-5787	264	19	as	as	SCONJ
ejpam-5787	264	20	shown	show	VERB
ejpam-5787	264	21	in	in	ADP
ejpam-5787	264	22	figure	figure	NOUN
ejpam-5787	264	23	14(b	14(b	NUM
ejpam-5787	264	24	-	-	SYM
ejpam-5787	264	25	d	d	NOUN
ejpam-5787	264	26	)	)	PUNCT
ejpam-5787	264	27	.	.	PUNCT
ejpam-5787	265	1	moreover	moreover	ADV
ejpam-5787	265	2	,	,	PUNCT
ejpam-5787	265	3	(	(	PUNCT
ejpam-5787	265	4	figure	figure	NOUN
ejpam-5787	265	5	14(d	14(d	NUM
ejpam-5787	265	6	)	)	PUNCT
ejpam-5787	265	7	)	)	PUNCT
ejpam-5787	265	8	shows	show	VERB
ejpam-5787	265	9	the	the	DET
ejpam-5787	265	10	bistability	bistability	NOUN
ejpam-5787	265	11	regions	region	NOUN
ejpam-5787	265	12	,	,	PUNCT
ejpam-5787	265	13	but	but	CCONJ
ejpam-5787	265	14	these	these	DET
ejpam-5787	265	15	regions	region	NOUN
ejpam-5787	265	16	are	be	AUX
ejpam-5787	265	17	very	very	ADV
ejpam-5787	265	18	narrow	narrow	ADJ
ejpam-5787	265	19	as	as	SCONJ
ejpam-5787	265	20	compared	compare	VERB
ejpam-5787	265	21	with	with	ADP
ejpam-5787	265	22	β	β	X
ejpam-5787	265	23	=	=	SYM
ejpam-5787	265	24	0	0	PUNCT
ejpam-5787	265	25	in	in	ADP
ejpam-5787	265	26	figure	figure	NOUN
ejpam-5787	265	27	12	12	NUM
ejpam-5787	265	28	.	.	PUNCT
ejpam-5787	266	1	there	there	PRON
ejpam-5787	266	2	is	be	VERB
ejpam-5787	266	3	a	a	DET
ejpam-5787	266	4	reason	reason	NOUN
ejpam-5787	266	5	for	for	ADP
ejpam-5787	266	6	the	the	DET
ejpam-5787	266	7	white	white	ADJ
ejpam-5787	266	8	wedge	wedge	NOUN
ejpam-5787	266	9	,	,	PUNCT
ejpam-5787	266	10	where	where	SCONJ
ejpam-5787	266	11	no	no	DET
ejpam-5787	266	12	rotation	rotation	NOUN
ejpam-5787	266	13	numbers	number	NOUN
ejpam-5787	266	14	are	be	AUX
ejpam-5787	266	15	shown	show	VERB
ejpam-5787	266	16	.	.	PUNCT
ejpam-5787	267	1	in	in	ADP
ejpam-5787	267	2	other	other	ADJ
ejpam-5787	267	3	words	word	NOUN
ejpam-5787	267	4	,	,	PUNCT
ejpam-5787	267	5	trajectories	trajectory	NOUN
ejpam-5787	267	6	start	start	VERB
ejpam-5787	267	7	to	to	PART
ejpam-5787	267	8	get	get	VERB
ejpam-5787	267	9	non	non	PRON
ejpam-5787	267	10	returning	return	VERB
ejpam-5787	267	11	points	point	NOUN
ejpam-5787	267	12	in	in	ADP
ejpam-5787	267	13	the	the	DET
ejpam-5787	267	14	white	white	ADJ
ejpam-5787	267	15	wedge	wedge	NOUN
ejpam-5787	267	16	.	.	PUNCT
ejpam-5787	268	1	(	(	PUNCT
ejpam-5787	268	2	a	a	X
ejpam-5787	268	3	)	)	PUNCT
ejpam-5787	268	4	(	(	PUNCT
ejpam-5787	268	5	b	b	X
ejpam-5787	268	6	)	)	PUNCT
ejpam-5787	268	7	(	(	PUNCT
ejpam-5787	268	8	c	c	X
ejpam-5787	268	9	)	)	PUNCT
ejpam-5787	268	10	(	(	PUNCT
ejpam-5787	268	11	d	d	X
ejpam-5787	268	12	)	)	PUNCT
ejpam-5787	268	13	figure	figure	NOUN
ejpam-5787	268	14	14	14	NUM
ejpam-5787	268	15	:	:	PUNCT
ejpam-5787	268	16	the	the	DET
ejpam-5787	268	17	(	(	PUNCT
ejpam-5787	268	18	a	a	PRON
ejpam-5787	268	19	,	,	PUNCT
ejpam-5787	268	20	ω	ω	NOUN
ejpam-5787	268	21	)	)	PUNCT
ejpam-5787	268	22	parameter	parameter	NOUN
ejpam-5787	268	23	plane	plane	NOUN
ejpam-5787	268	24	showing	show	VERB
ejpam-5787	268	25	regions	region	NOUN
ejpam-5787	268	26	of	of	ADP
ejpam-5787	268	27	the	the	DET
ejpam-5787	268	28	stable	stable	ADJ
ejpam-5787	268	29	periodic	periodic	ADJ
ejpam-5787	268	30	orbit	orbit	NOUN
ejpam-5787	268	31	of	of	ADP
ejpam-5787	268	32	the	the	DET
ejpam-5787	268	33	return	return	NOUN
ejpam-5787	268	34	map	map	NOUN
ejpam-5787	269	1	f	f	X
ejpam-5787	269	2	(	(	PUNCT
ejpam-5787	269	3	13	13	NUM
ejpam-5787	269	4	)	)	PUNCT
ejpam-5787	269	5	as	as	ADP
ejpam-5787	269	6	β	β	X
ejpam-5787	269	7	̸=	̸=	PROPN
ejpam-5787	269	8	0	0	NUM
ejpam-5787	269	9	.	.	PUNCT
ejpam-5787	270	1	the	the	DET
ejpam-5787	270	2	colorbar	colorbar	NOUN
ejpam-5787	270	3	indicates	indicate	VERB
ejpam-5787	270	4	the	the	DET
ejpam-5787	270	5	rotation	rotation	NOUN
ejpam-5787	270	6	period	period	NOUN
ejpam-5787	270	7	n	n	ADP
ejpam-5787	270	8	of	of	ADP
ejpam-5787	270	9	(	(	PUNCT
ejpam-5787	270	10	13	13	NUM
ejpam-5787	270	11	)	)	PUNCT
ejpam-5787	270	12	for	for	ADP
ejpam-5787	270	13	β	β	X
ejpam-5787	270	14	=	=	SYM
ejpam-5787	270	15	0.5	0.5	NUM
ejpam-5787	270	16	,	,	PUNCT
ejpam-5787	270	17	0.8	0.8	NUM
ejpam-5787	270	18	,	,	PUNCT
ejpam-5787	270	19	1	1	NUM
ejpam-5787	270	20	and	and	CCONJ
ejpam-5787	270	21	1.2	1.2	NUM
ejpam-5787	270	22	.	.	PUNCT
ejpam-5787	271	1	the	the	DET
ejpam-5787	271	2	arnold	arnold	PROPN
ejpam-5787	271	3	tongues	tongue	NOUN
ejpam-5787	271	4	regions	region	NOUN
ejpam-5787	271	5	appear	appear	VERB
ejpam-5787	271	6	for	for	ADP
ejpam-5787	271	7	β	β	X
ejpam-5787	271	8	̸=	̸=	PROPN
ejpam-5787	271	9	0	0	NUM
ejpam-5787	271	10	.	.	PUNCT
ejpam-5787	272	1	(	(	PUNCT
ejpam-5787	272	2	a	a	X
ejpam-5787	272	3	)	)	PUNCT
ejpam-5787	272	4	the	the	DET
ejpam-5787	272	5	large	large	ADJ
ejpam-5787	272	6	regions	region	NOUN
ejpam-5787	272	7	correspond	correspond	VERB
ejpam-5787	272	8	to	to	ADP
ejpam-5787	272	9	arnold	arnold	PROPN
ejpam-5787	272	10	tongues	tongue	NOUN
ejpam-5787	272	11	for	for	ADP
ejpam-5787	272	12	frequency	frequency	NOUN
ejpam-5787	272	13	-	-	PUNCT
ejpam-5787	272	14	locking	lock	VERB
ejpam-5787	272	15	1:1	1:1	NUM
ejpam-5787	272	16	(	(	PUNCT
ejpam-5787	272	17	brown	brown	PROPN
ejpam-5787	272	18	)	)	PUNCT
ejpam-5787	272	19	,	,	PUNCT
ejpam-5787	272	20	3:1	3:1	NUM
ejpam-5787	272	21	(	(	PUNCT
ejpam-5787	272	22	purple	purple	NOUN
ejpam-5787	272	23	)	)	PUNCT
ejpam-5787	272	24	,	,	PUNCT
ejpam-5787	272	25	5:1	5:1	NUM
ejpam-5787	272	26	(	(	PUNCT
ejpam-5787	272	27	light	light	ADJ
ejpam-5787	272	28	blue	blue	NOUN
ejpam-5787	272	29	)	)	PUNCT
ejpam-5787	272	30	and	and	CCONJ
ejpam-5787	272	31	8:1	8:1	NUM
ejpam-5787	272	32	(	(	PUNCT
ejpam-5787	272	33	brown	brown	NOUN
ejpam-5787	272	34	)	)	PUNCT
ejpam-5787	272	35	.	.	PUNCT
ejpam-5787	273	1	as	as	ADP
ejpam-5787	273	2	β	β	NOUN
ejpam-5787	273	3	increases	increase	NOUN
ejpam-5787	273	4	,	,	PUNCT
ejpam-5787	273	5	(	(	PUNCT
ejpam-5787	273	6	b	b	X
ejpam-5787	273	7	-	-	PUNCT
ejpam-5787	273	8	d	d	NOUN
ejpam-5787	273	9	)	)	PUNCT
ejpam-5787	273	10	there	there	PRON
ejpam-5787	273	11	are	be	VERB
ejpam-5787	273	12	smaller	small	ADJ
ejpam-5787	273	13	arnold	arnold	PROPN
ejpam-5787	273	14	tongues	tongue	NOUN
ejpam-5787	273	15	regions	region	NOUN
ejpam-5787	273	16	for	for	ADP
ejpam-5787	273	17	frequency	frequency	NOUN
ejpam-5787	273	18	-	-	PUNCT
ejpam-5787	273	19	locking	locking	NOUN
ejpam-5787	273	20	between	between	ADP
ejpam-5787	273	21	periods	period	NOUN
ejpam-5787	273	22	1	1	NUM
ejpam-5787	273	23	and	and	CCONJ
ejpam-5787	273	24	15	15	NUM
ejpam-5787	273	25	as	as	ADP
ejpam-5787	273	26	a	a	DET
ejpam-5787	273	27	region	region	NOUN
ejpam-5787	273	28	where	where	SCONJ
ejpam-5787	273	29	the	the	DET
ejpam-5787	273	30	return	return	NOUN
ejpam-5787	273	31	is	be	AUX
ejpam-5787	273	32	no	no	ADV
ejpam-5787	273	33	longer	long	ADV
ejpam-5787	273	34	defined	define	VERB
ejpam-5787	273	35	appears	appear	VERB
ejpam-5787	273	36	for	for	ADP
ejpam-5787	273	37	small	small	ADJ
ejpam-5787	273	38	a.	a.	NOUN
ejpam-5787	273	39	(	(	PUNCT
ejpam-5787	273	40	d	d	X
ejpam-5787	273	41	)	)	PUNCT
ejpam-5787	273	42	there	there	PRON
ejpam-5787	273	43	are	be	VERB
ejpam-5787	273	44	bistability	bistability	NOUN
ejpam-5787	273	45	regions	region	NOUN
ejpam-5787	273	46	but	but	CCONJ
ejpam-5787	273	47	these	these	DET
ejpam-5787	273	48	regions	region	NOUN
ejpam-5787	273	49	are	be	AUX
ejpam-5787	273	50	very	very	ADV
ejpam-5787	273	51	narrow	narrow	ADJ
ejpam-5787	273	52	as	as	SCONJ
ejpam-5787	273	53	compared	compare	VERB
ejpam-5787	273	54	with	with	ADP
ejpam-5787	273	55	β	β	X
ejpam-5787	273	56	=	=	SYM
ejpam-5787	273	57	0	0	PUNCT
ejpam-5787	273	58	in	in	ADP
ejpam-5787	273	59	figure	figure	NOUN
ejpam-5787	273	60	12	12	NUM
ejpam-5787	273	61	.	.	PUNCT
ejpam-5787	274	1	figure	figure	NOUN
ejpam-5787	274	2	15	15	NUM
ejpam-5787	274	3	shows	show	VERB
ejpam-5787	274	4	the	the	DET
ejpam-5787	274	5	graph	graph	NOUN
ejpam-5787	274	6	of	of	ADP
ejpam-5787	274	7	the	the	DET
ejpam-5787	274	8	first	first	ADJ
ejpam-5787	274	9	return	return	NOUN
ejpam-5787	274	10	map	map	NOUN
ejpam-5787	274	11	(	(	PUNCT
ejpam-5787	274	12	13	13	NUM
ejpam-5787	274	13	)	)	PUNCT
ejpam-5787	274	14	for	for	ADP
ejpam-5787	274	15	β	β	X
ejpam-5787	274	16	=	=	SYM
ejpam-5787	274	17	1	1	NUM
ejpam-5787	274	18	and	and	CCONJ
ejpam-5787	274	19	a	a	PRON
ejpam-5787	274	20	with	with	ADP
ejpam-5787	274	21	different	different	ADJ
ejpam-5787	274	22	i.	i.	NOUN
ejpam-5787	274	23	alraddadi	alraddadi	PROPN
ejpam-5787	274	24	/	/	SYM
ejpam-5787	274	25	eur	eur	PROPN
ejpam-5787	274	26	.	.	PUNCT
ejpam-5787	275	1	j.	j.	PROPN
ejpam-5787	275	2	pure	pure	PROPN
ejpam-5787	275	3	appl	appl	PROPN
ejpam-5787	275	4	.	.	PROPN
ejpam-5787	275	5	math	math	PROPN
ejpam-5787	275	6	,	,	PUNCT
ejpam-5787	275	7	18	18	NUM
ejpam-5787	275	8	(	(	PUNCT
ejpam-5787	275	9	1	1	NUM
ejpam-5787	275	10	)	)	PUNCT
ejpam-5787	275	11	(	(	PUNCT
ejpam-5787	275	12	2025	2025	NUM
ejpam-5787	275	13	)	)	PUNCT
ejpam-5787	275	14	,	,	PUNCT
ejpam-5787	275	15	5787	5787	NUM
ejpam-5787	275	16	18	18	NUM
ejpam-5787	275	17	of	of	ADP
ejpam-5787	275	18	23	23	NUM
ejpam-5787	275	19	values	value	NOUN
ejpam-5787	275	20	of	of	ADP
ejpam-5787	275	21	ω	ω	PROPN
ejpam-5787	275	22	.	.	PUNCT
ejpam-5787	276	1	the	the	DET
ejpam-5787	276	2	saddle	saddle	NOUN
ejpam-5787	276	3	-	-	PUNCT
ejpam-5787	276	4	node	node	NOUN
ejpam-5787	276	5	bifurcation	bifurcation	NOUN
ejpam-5787	276	6	of	of	ADP
ejpam-5787	276	7	the	the	DET
ejpam-5787	276	8	first	first	ADJ
ejpam-5787	276	9	return	return	NOUN
ejpam-5787	276	10	map	map	NOUN
ejpam-5787	276	11	(	(	PUNCT
ejpam-5787	276	12	13	13	NUM
ejpam-5787	276	13	)	)	PUNCT
ejpam-5787	276	14	occurs	occur	VERB
ejpam-5787	276	15	as	as	ADP
ejpam-5787	276	16	ω	ω	NUM
ejpam-5787	276	17	varies	varie	NOUN
ejpam-5787	276	18	.	.	PUNCT
ejpam-5787	277	1	in	in	ADP
ejpam-5787	277	2	figure	figure	NOUN
ejpam-5787	277	3	14(c	14(c	NUM
ejpam-5787	277	4	)	)	PUNCT
ejpam-5787	277	5	,	,	PUNCT
ejpam-5787	277	6	this	this	DET
ejpam-5787	277	7	case	case	NOUN
ejpam-5787	277	8	corresponds	correspond	VERB
ejpam-5787	277	9	to	to	ADP
ejpam-5787	277	10	the	the	DET
ejpam-5787	277	11	attractor	attractor	NOUN
ejpam-5787	277	12	point	point	NOUN
ejpam-5787	277	13	of	of	ADP
ejpam-5787	277	14	periodic	periodic	ADJ
ejpam-5787	277	15	orbits	orbit	NOUN
ejpam-5787	277	16	moving	move	VERB
ejpam-5787	277	17	forward	forward	ADV
ejpam-5787	277	18	from	from	ADP
ejpam-5787	277	19	inside	inside	ADP
ejpam-5787	277	20	a	a	DET
ejpam-5787	277	21	frequency	frequency	NOUN
ejpam-5787	277	22	locking	locking	NOUN
ejpam-5787	277	23	region	region	NOUN
ejpam-5787	277	24	to	to	ADP
ejpam-5787	277	25	the	the	DET
ejpam-5787	277	26	outside	outside	NOUN
ejpam-5787	277	27	of	of	ADP
ejpam-5787	277	28	the	the	DET
ejpam-5787	277	29	frequency	frequency	NOUN
ejpam-5787	277	30	locking	locking	NOUN
ejpam-5787	277	31	region	region	NOUN
ejpam-5787	277	32	.	.	PUNCT
ejpam-5787	278	1	as	as	SCONJ
ejpam-5787	278	2	ω	ω	X
ejpam-5787	278	3	increases	increase	NOUN
ejpam-5787	278	4	in	in	ADP
ejpam-5787	278	5	figure	figure	NOUN
ejpam-5787	278	6	16(a	16(a	NUM
ejpam-5787	278	7	)	)	PUNCT
ejpam-5787	278	8	,	,	PUNCT
ejpam-5787	278	9	we	we	PRON
ejpam-5787	278	10	note	note	VERB
ejpam-5787	278	11	this	this	DET
ejpam-5787	278	12	discontinuity	discontinuity	NOUN
ejpam-5787	278	13	in	in	ADP
ejpam-5787	278	14	the	the	DET
ejpam-5787	278	15	first	first	ADJ
ejpam-5787	278	16	return	return	NOUN
ejpam-5787	278	17	map	map	NOUN
ejpam-5787	278	18	f	f	X
ejpam-5787	278	19	(	(	PUNCT
ejpam-5787	278	20	13	13	NUM
ejpam-5787	278	21	)	)	PUNCT
ejpam-5787	278	22	hits	hit	VERB
ejpam-5787	278	23	the	the	DET
ejpam-5787	278	24	periodic	periodic	ADJ
ejpam-5787	278	25	orbit	orbit	NOUN
ejpam-5787	278	26	.	.	PUNCT
ejpam-5787	279	1	in	in	ADP
ejpam-5787	279	2	figure	figure	NOUN
ejpam-5787	279	3	17	17	NUM
ejpam-5787	279	4	,	,	PUNCT
ejpam-5787	279	5	the	the	DET
ejpam-5787	279	6	black	black	ADJ
ejpam-5787	279	7	circle	circle	NOUN
ejpam-5787	279	8	corresponds	correspond	VERB
ejpam-5787	279	9	to	to	ADP
ejpam-5787	279	10	the	the	DET
ejpam-5787	279	11	value	value	NOUN
ejpam-5787	279	12	of	of	ADP
ejpam-5787	279	13	(	(	PUNCT
ejpam-5787	279	14	a	a	DET
ejpam-5787	279	15	,	,	PUNCT
ejpam-5787	279	16	ω	ω	PROPN
ejpam-5787	279	17	,	,	PUNCT
ejpam-5787	279	18	β	β	NOUN
ejpam-5787	279	19	)	)	PUNCT
ejpam-5787	279	20	in	in	ADP
ejpam-5787	279	21	figure	figure	NOUN
ejpam-5787	279	22	16	16	NUM
ejpam-5787	279	23	.	.	PUNCT
ejpam-5787	280	1	(	(	PUNCT
ejpam-5787	280	2	a	a	X
ejpam-5787	280	3	)	)	PUNCT
ejpam-5787	280	4	(	(	PUNCT
ejpam-5787	280	5	b	b	X
ejpam-5787	280	6	)	)	PUNCT
ejpam-5787	280	7	(	(	PUNCT
ejpam-5787	280	8	c	c	X
ejpam-5787	280	9	)	)	PUNCT
ejpam-5787	280	10	figure	figure	NOUN
ejpam-5787	280	11	15	15	NUM
ejpam-5787	280	12	:	:	PUNCT
ejpam-5787	280	13	the	the	DET
ejpam-5787	280	14	graph	graph	NOUN
ejpam-5787	280	15	of	of	ADP
ejpam-5787	280	16	the	the	DET
ejpam-5787	280	17	first	first	ADJ
ejpam-5787	280	18	return	return	NOUN
ejpam-5787	280	19	map	map	NOUN
ejpam-5787	280	20	f	f	X
ejpam-5787	280	21	(	(	PUNCT
ejpam-5787	280	22	13	13	NUM
ejpam-5787	280	23	)	)	PUNCT
ejpam-5787	280	24	for	for	ADP
ejpam-5787	280	25	β	β	X
ejpam-5787	280	26	=	=	SYM
ejpam-5787	280	27	1	1	NUM
ejpam-5787	280	28	and	and	CCONJ
ejpam-5787	280	29	a	a	DET
ejpam-5787	280	30	=	=	NOUN
ejpam-5787	280	31	1.65	1.65	NUM
ejpam-5787	280	32	with	with	ADP
ejpam-5787	280	33	different	different	ADJ
ejpam-5787	280	34	values	value	NOUN
ejpam-5787	280	35	of	of	ADP
ejpam-5787	280	36	ω	ω	PROPN
ejpam-5787	280	37	.	.	PUNCT
ejpam-5787	281	1	(	(	PUNCT
ejpam-5787	281	2	a	a	X
ejpam-5787	281	3	-	-	PUNCT
ejpam-5787	281	4	c	c	NOUN
ejpam-5787	281	5	)	)	PUNCT
ejpam-5787	281	6	shows	show	VERB
ejpam-5787	281	7	a	a	DET
ejpam-5787	281	8	saddle	saddle	NOUN
ejpam-5787	281	9	-	-	PUNCT
ejpam-5787	281	10	node	node	NOUN
ejpam-5787	281	11	bifurcation	bifurcation	NOUN
ejpam-5787	281	12	of	of	ADP
ejpam-5787	281	13	the	the	DET
ejpam-5787	281	14	first	first	ADJ
ejpam-5787	281	15	return	return	NOUN
ejpam-5787	281	16	map	map	NOUN
ejpam-5787	281	17	for	for	ADP
ejpam-5787	281	18	β	β	X
ejpam-5787	281	19	=	=	SYM
ejpam-5787	281	20	1	1	NUM
ejpam-5787	281	21	as	as	ADP
ejpam-5787	281	22	ω	ω	PROPN
ejpam-5787	281	23	presents	present	NOUN
ejpam-5787	281	24	throughout	throughout	ADP
ejpam-5787	281	25	ω	ω	PROPN
ejpam-5787	281	26	=	=	SYM
ejpam-5787	281	27	1.81	1.81	NUM
ejpam-5787	281	28	.	.	PUNCT
ejpam-5787	282	1	i.	i.	PROPN
ejpam-5787	282	2	alraddadi	alraddadi	PROPN
ejpam-5787	282	3	/	/	SYM
ejpam-5787	282	4	eur	eur	PROPN
ejpam-5787	282	5	.	.	PUNCT
ejpam-5787	283	1	j.	j.	PROPN
ejpam-5787	283	2	pure	pure	PROPN
ejpam-5787	283	3	appl	appl	PROPN
ejpam-5787	283	4	.	.	PROPN
ejpam-5787	283	5	math	math	PROPN
ejpam-5787	283	6	,	,	PUNCT
ejpam-5787	283	7	18	18	NUM
ejpam-5787	283	8	(	(	PUNCT
ejpam-5787	283	9	1	1	NUM
ejpam-5787	283	10	)	)	PUNCT
ejpam-5787	283	11	(	(	PUNCT
ejpam-5787	283	12	2025	2025	NUM
ejpam-5787	283	13	)	)	PUNCT
ejpam-5787	283	14	,	,	PUNCT
ejpam-5787	283	15	5787	5787	NUM
ejpam-5787	283	16	19	19	NUM
ejpam-5787	283	17	of	of	ADP
ejpam-5787	283	18	23	23	NUM
ejpam-5787	283	19	(	(	PUNCT
ejpam-5787	283	20	a	a	NOUN
ejpam-5787	283	21	)	)	PUNCT
ejpam-5787	283	22	(	(	PUNCT
ejpam-5787	283	23	b	b	X
ejpam-5787	283	24	)	)	PUNCT
ejpam-5787	283	25	figure	figure	NOUN
ejpam-5787	283	26	16	16	NUM
ejpam-5787	283	27	:	:	PUNCT
ejpam-5787	283	28	(	(	PUNCT
ejpam-5787	283	29	a	a	X
ejpam-5787	283	30	)	)	PUNCT
ejpam-5787	283	31	the	the	DET
ejpam-5787	283	32	graph	graph	NOUN
ejpam-5787	283	33	of	of	ADP
ejpam-5787	283	34	the	the	DET
ejpam-5787	283	35	first	first	ADJ
ejpam-5787	283	36	return	return	NOUN
ejpam-5787	283	37	map	map	NOUN
ejpam-5787	283	38	f	f	X
ejpam-5787	283	39	(	(	PUNCT
ejpam-5787	283	40	13	13	NUM
ejpam-5787	283	41	)	)	PUNCT
ejpam-5787	283	42	for	for	ADP
ejpam-5787	283	43	β	β	X
ejpam-5787	283	44	=	=	SYM
ejpam-5787	283	45	1	1	NUM
ejpam-5787	283	46	and	and	CCONJ
ejpam-5787	283	47	a	a	DET
ejpam-5787	283	48	=	=	SYM
ejpam-5787	283	49	1.65	1.65	NUM
ejpam-5787	283	50	and	and	CCONJ
ejpam-5787	283	51	ω	ω	NUM
ejpam-5787	283	52	=	=	PROPN
ejpam-5787	283	53	1.92	1.92	NUM
ejpam-5787	283	54	.	.	PUNCT
ejpam-5787	284	1	(	(	PUNCT
ejpam-5787	284	2	b	b	X
ejpam-5787	284	3	)	)	PUNCT
ejpam-5787	284	4	the	the	DET
ejpam-5787	284	5	flow	flow	NOUN
ejpam-5787	284	6	of	of	ADP
ejpam-5787	284	7	(	(	PUNCT
ejpam-5787	284	8	13	13	NUM
ejpam-5787	284	9	)	)	PUNCT
ejpam-5787	284	10	on	on	ADP
ejpam-5787	284	11	the	the	DET
ejpam-5787	284	12	desingularised	desingularise	VERB
ejpam-5787	284	13	slow	slow	ADJ
ejpam-5787	284	14	flow	flow	NOUN
ejpam-5787	284	15	system	system	NOUN
ejpam-5787	284	16	(	(	PUNCT
ejpam-5787	284	17	12	12	NUM
ejpam-5787	284	18	)	)	PUNCT
ejpam-5787	284	19	for	for	ADP
ejpam-5787	284	20	two	two	NUM
ejpam-5787	284	21	different	different	ADJ
ejpam-5787	284	22	initial	initial	ADJ
ejpam-5787	284	23	values	value	NOUN
ejpam-5787	284	24	of	of	ADP
ejpam-5787	284	25	θ	θ	PROPN
ejpam-5787	284	26	.	.	PUNCT
ejpam-5787	285	1	the	the	DET
ejpam-5787	285	2	value	value	NOUN
ejpam-5787	285	3	of	of	ADP
ejpam-5787	285	4	θ	θ	PROPN
ejpam-5787	285	5	is	be	AUX
ejpam-5787	285	6	0.271	0.271	NUM
ejpam-5787	285	7	(	(	PUNCT
ejpam-5787	285	8	blue	blue	ADJ
ejpam-5787	285	9	)	)	PUNCT
ejpam-5787	285	10	and	and	CCONJ
ejpam-5787	285	11	0.273	0.273	NUM
ejpam-5787	285	12	(	(	PUNCT
ejpam-5787	285	13	red	red	ADJ
ejpam-5787	285	14	)	)	PUNCT
ejpam-5787	285	15	.	.	PUNCT
ejpam-5787	286	1	for	for	ADP
ejpam-5787	286	2	(	(	PUNCT
ejpam-5787	286	3	a	a	NOUN
ejpam-5787	286	4	)	)	PUNCT
ejpam-5787	286	5	θ	θ	NOUN
ejpam-5787	286	6	=	=	PUNCT
ejpam-5787	286	7	0.271	0.271	NUM
ejpam-5787	286	8	is	be	AUX
ejpam-5787	286	9	on	on	ADP
ejpam-5787	286	10	the	the	DET
ejpam-5787	286	11	left	left	ADJ
ejpam-5787	286	12	curve	curve	NOUN
ejpam-5787	286	13	of	of	ADP
ejpam-5787	286	14	the	the	DET
ejpam-5787	286	15	diagonal	diagonal	ADJ
ejpam-5787	286	16	line	line	NOUN
ejpam-5787	286	17	,	,	PUNCT
ejpam-5787	286	18	and	and	CCONJ
ejpam-5787	286	19	θ	θ	X
ejpam-5787	286	20	=	=	PUNCT
ejpam-5787	286	21	0.273	0.273	NUM
ejpam-5787	286	22	is	be	AUX
ejpam-5787	286	23	on	on	ADP
ejpam-5787	286	24	the	the	DET
ejpam-5787	286	25	right	right	ADJ
ejpam-5787	286	26	curve	curve	NOUN
ejpam-5787	286	27	.	.	PUNCT
ejpam-5787	287	1	for	for	ADP
ejpam-5787	287	2	(	(	PUNCT
ejpam-5787	287	3	b	b	NOUN
ejpam-5787	287	4	)	)	PUNCT
ejpam-5787	287	5	the	the	DET
ejpam-5787	287	6	blue	blue	ADJ
ejpam-5787	287	7	and	and	CCONJ
ejpam-5787	287	8	red	red	ADJ
ejpam-5787	287	9	trajectories	trajectory	NOUN
ejpam-5787	287	10	start	start	VERB
ejpam-5787	287	11	close	close	ADV
ejpam-5787	287	12	together	together	ADV
ejpam-5787	287	13	,	,	PUNCT
ejpam-5787	287	14	hit	hit	VERB
ejpam-5787	287	15	the	the	DET
ejpam-5787	287	16	upper	upper	ADJ
ejpam-5787	287	17	fold	fold	ADJ
ejpam-5787	287	18	line	line	NOUN
ejpam-5787	287	19	,	,	PUNCT
ejpam-5787	287	20	and	and	CCONJ
ejpam-5787	287	21	then	then	ADV
ejpam-5787	287	22	jump	jump	VERB
ejpam-5787	287	23	to	to	ADP
ejpam-5787	287	24	another	another	DET
ejpam-5787	287	25	branch	branch	NOUN
ejpam-5787	287	26	.	.	PUNCT
ejpam-5787	288	1	the	the	DET
ejpam-5787	288	2	red	red	PROPN
ejpam-5787	288	3	trajectory	trajectory	NOUN
ejpam-5787	288	4	goes	go	VERB
ejpam-5787	288	5	to	to	ADP
ejpam-5787	288	6	the	the	DET
ejpam-5787	288	7	left	left	NOUN
ejpam-5787	288	8	of	of	ADP
ejpam-5787	288	9	the	the	DET
ejpam-5787	288	10	folded	fold	VERB
ejpam-5787	288	11	saddle	saddle	NOUN
ejpam-5787	288	12	in	in	ADP
ejpam-5787	288	13	the	the	DET
ejpam-5787	288	14	lower	low	ADJ
ejpam-5787	288	15	folded	fold	VERB
ejpam-5787	288	16	line	line	NOUN
ejpam-5787	288	17	.	.	PUNCT
ejpam-5787	289	1	while	while	SCONJ
ejpam-5787	289	2	the	the	DET
ejpam-5787	289	3	blue	blue	ADJ
ejpam-5787	289	4	trajectory	trajectory	NOUN
ejpam-5787	289	5	comes	come	VERB
ejpam-5787	289	6	close	close	ADV
ejpam-5787	289	7	to	to	ADP
ejpam-5787	289	8	the	the	DET
ejpam-5787	289	9	folded	fold	VERB
ejpam-5787	289	10	saddle	saddle	NOUN
ejpam-5787	289	11	.	.	PUNCT
ejpam-5787	290	1	vertical	vertical	ADJ
ejpam-5787	290	2	lines	line	NOUN
ejpam-5787	290	3	indicate	indicate	VERB
ejpam-5787	290	4	the	the	DET
ejpam-5787	290	5	endpoint	endpoint	NOUN
ejpam-5787	290	6	of	of	ADP
ejpam-5787	290	7	the	the	DET
ejpam-5787	290	8	red	red	ADJ
ejpam-5787	290	9	and	and	CCONJ
ejpam-5787	290	10	blue	blue	ADJ
ejpam-5787	290	11	trajectories	trajectory	NOUN
ejpam-5787	290	12	.	.	PUNCT
ejpam-5787	291	1	(	(	PUNCT
ejpam-5787	291	2	b	b	X
ejpam-5787	291	3	)	)	PUNCT
ejpam-5787	291	4	corresponds	correspond	VERB
ejpam-5787	291	5	to	to	ADP
ejpam-5787	291	6	the	the	DET
ejpam-5787	291	7	black	black	ADJ
ejpam-5787	291	8	circle	circle	NOUN
ejpam-5787	291	9	in	in	ADP
ejpam-5787	291	10	figure	figure	NOUN
ejpam-5787	291	11	17	17	NUM
ejpam-5787	291	12	.	.	PUNCT
ejpam-5787	292	1	(	(	PUNCT
ejpam-5787	292	2	b	b	X
ejpam-5787	292	3	)	)	PUNCT
ejpam-5787	292	4	for	for	ADP
ejpam-5787	292	5	periodic	periodic	ADJ
ejpam-5787	292	6	orbits	orbit	NOUN
ejpam-5787	292	7	at	at	ADP
ejpam-5787	292	8	discontinuity	discontinuity	NOUN
ejpam-5787	292	9	where	where	SCONJ
ejpam-5787	292	10	ε	ε	PROPN
ejpam-5787	292	11	→	→	SYM
ejpam-5787	292	12	0	0	PROPN
ejpam-5787	292	13	.	.	PUNCT
ejpam-5787	293	1	while	while	SCONJ
ejpam-5787	293	2	periodic	periodic	ADJ
ejpam-5787	293	3	orbits	orbit	NOUN
ejpam-5787	293	4	at	at	ADP
ejpam-5787	293	5	the	the	DET
ejpam-5787	293	6	discontinuity	discontinuity	NOUN
ejpam-5787	293	7	for	for	ADP
ejpam-5787	293	8	sufficiently	sufficiently	ADV
ejpam-5787	293	9	small	small	ADJ
ejpam-5787	293	10	ε	ε	PROPN
ejpam-5787	293	11	>	>	X
ejpam-5787	293	12	0	0	PROPN
ejpam-5787	293	13	,	,	PUNCT
ejpam-5787	293	14	some	some	DET
ejpam-5787	293	15	layer	layer	NOUN
ejpam-5787	293	16	trajectories	trajectory	NOUN
ejpam-5787	293	17	of	of	ADP
ejpam-5787	293	18	the	the	DET
ejpam-5787	293	19	nonsingular	nonsingular	ADJ
ejpam-5787	293	20	system	system	NOUN
ejpam-5787	293	21	(	(	PUNCT
ejpam-5787	293	22	4	4	X
ejpam-5787	293	23	)	)	PUNCT
ejpam-5787	293	24	cross	cross	VERB
ejpam-5787	293	25	the	the	DET
ejpam-5787	293	26	fold	fold	ADJ
ejpam-5787	293	27	lines	line	NOUN
ejpam-5787	293	28	near	near	ADP
ejpam-5787	293	29	the	the	DET
ejpam-5787	293	30	folded	fold	VERB
ejpam-5787	293	31	saddle	saddle	NOUN
ejpam-5787	293	32	equilibria	equilibrium	NOUN
ejpam-5787	293	33	and	and	CCONJ
ejpam-5787	293	34	continue	continue	VERB
ejpam-5787	293	35	the	the	DET
ejpam-5787	293	36	unstable	unstable	ADJ
ejpam-5787	293	37	branch	branch	NOUN
ejpam-5787	293	38	of	of	ADP
ejpam-5787	293	39	the	the	DET
ejpam-5787	293	40	critical	critical	ADJ
ejpam-5787	293	41	manifold	manifold	NOUN
ejpam-5787	293	42	s	s	PART
ejpam-5787	293	43	then	then	ADV
ejpam-5787	293	44	move	move	VERB
ejpam-5787	293	45	to	to	ADP
ejpam-5787	293	46	another	another	DET
ejpam-5787	293	47	stable	stable	ADJ
ejpam-5787	293	48	branch	branch	NOUN
ejpam-5787	293	49	of	of	ADP
ejpam-5787	293	50	the	the	DET
ejpam-5787	293	51	critical	critical	ADJ
ejpam-5787	293	52	manifold	manifold	ADJ
ejpam-5787	293	53	s.	s.	PROPN
ejpam-5787	293	54	periodic	periodic	ADJ
ejpam-5787	293	55	orbits	orbit	NOUN
ejpam-5787	293	56	without	without	ADP
ejpam-5787	293	57	discontinuity	discontinuity	NOUN
ejpam-5787	293	58	where	where	SCONJ
ejpam-5787	293	59	ε	ε	PROPN
ejpam-5787	293	60	̸=	̸=	PROPN
ejpam-5787	293	61	0	0	NUM
ejpam-5787	293	62	,	,	PUNCT
ejpam-5787	293	63	there	there	PRON
ejpam-5787	293	64	is	be	VERB
ejpam-5787	293	65	a	a	DET
ejpam-5787	293	66	region	region	NOUN
ejpam-5787	293	67	of	of	ADP
ejpam-5787	293	68	canard	canard	NOUN
ejpam-5787	293	69	trajectory	trajectory	NOUN
ejpam-5787	293	70	where	where	SCONJ
ejpam-5787	293	71	no	no	DET
ejpam-5787	293	72	trajectories	trajectory	NOUN
ejpam-5787	293	73	jump	jump	VERB
ejpam-5787	293	74	at	at	ADP
ejpam-5787	293	75	the	the	DET
ejpam-5787	293	76	fold	fold	ADJ
ejpam-5787	293	77	line	line	NOUN
ejpam-5787	293	78	.	.	PUNCT
ejpam-5787	294	1	i.	i.	PROPN
ejpam-5787	294	2	alraddadi	alraddadi	PROPN
ejpam-5787	294	3	/	/	SYM
ejpam-5787	294	4	eur	eur	PROPN
ejpam-5787	294	5	.	.	PUNCT
ejpam-5787	295	1	j.	j.	PROPN
ejpam-5787	295	2	pure	pure	PROPN
ejpam-5787	295	3	appl	appl	PROPN
ejpam-5787	295	4	.	.	PROPN
ejpam-5787	295	5	math	math	PROPN
ejpam-5787	295	6	,	,	PUNCT
ejpam-5787	295	7	18	18	NUM
ejpam-5787	295	8	(	(	PUNCT
ejpam-5787	295	9	1	1	NUM
ejpam-5787	295	10	)	)	PUNCT
ejpam-5787	295	11	(	(	PUNCT
ejpam-5787	295	12	2025	2025	NUM
ejpam-5787	295	13	)	)	PUNCT
ejpam-5787	295	14	,	,	PUNCT
ejpam-5787	295	15	5787	5787	NUM
ejpam-5787	295	16	20	20	NUM
ejpam-5787	295	17	of	of	ADP
ejpam-5787	295	18	23	23	NUM
ejpam-5787	295	19	parameter	parameter	NOUN
ejpam-5787	295	20	value	value	NOUN
ejpam-5787	295	21	description	description	NOUN
ejpam-5787	295	22	α	α	NOUN
ejpam-5787	295	23	11.11	11.11	NUM
ejpam-5787	295	24	fast	fast	ADJ
ejpam-5787	295	25	/	/	SYM
ejpam-5787	295	26	slow	slow	ADJ
ejpam-5787	295	27	timescale	timescale	NOUN
ejpam-5787	295	28	separation	separation	NOUN
ejpam-5787	295	29	β	β	PROPN
ejpam-5787	295	30	0.25	0.25	NUM
ejpam-5787	295	31	symmetry	symmetry	NOUN
ejpam-5787	295	32	breaking	break	VERB
ejpam-5787	295	33	γ	γ	X
ejpam-5787	295	34	0.75	0.75	NUM
ejpam-5787	295	35	effective	effective	ADJ
ejpam-5787	295	36	forcing	force	VERB
ejpam-5787	295	37	amplitude	amplitude	NOUN
ejpam-5787	295	38	κ	κ	ADP
ejpam-5787	295	39	35.09	35.09	NUM
ejpam-5787	295	40	unforced	unforced	ADJ
ejpam-5787	295	41	oscillation	oscillation	NOUN
ejpam-5787	295	42	timescale	timescale	NOUN
ejpam-5787	295	43	has	have	VERB
ejpam-5787	295	44	period	period	NOUN
ejpam-5787	295	45	100	100	NUM
ejpam-5787	295	46	kyr	kyr	PROPN
ejpam-5787	295	47	for	for	ADP
ejpam-5787	295	48	time	time	NOUN
ejpam-5787	295	49	scaling	scale	VERB
ejpam-5787	295	50	τ	τ	X
ejpam-5787	295	51	=	=	SYM
ejpam-5787	295	52	1	1	NUM
ejpam-5787	295	53	τ	τ	SYM
ejpam-5787	295	54	1	1	NUM
ejpam-5787	295	55	time	time	NOUN
ejpam-5787	295	56	scaling	scale	VERB
ejpam-5787	295	57	table	table	NOUN
ejpam-5787	295	58	1	1	NUM
ejpam-5787	295	59	:	:	PUNCT
ejpam-5787	295	60	shows	show	VERB
ejpam-5787	295	61	the	the	DET
ejpam-5787	295	62	default	default	NOUN
ejpam-5787	295	63	parameters	parameter	NOUN
ejpam-5787	295	64	for	for	ADP
ejpam-5787	295	65	the	the	DET
ejpam-5787	295	66	forced	force	VERB
ejpam-5787	295	67	van	van	PROPN
ejpam-5787	295	68	der	der	ADJ
ejpam-5787	295	69	pol	pol	PROPN
ejpam-5787	295	70	oscillators	oscillator	NOUN
ejpam-5787	295	71	(	(	PUNCT
ejpam-5787	295	72	2	2	NUM
ejpam-5787	295	73	)	)	PUNCT
ejpam-5787	295	74	(	(	PUNCT
ejpam-5787	295	75	taken	take	VERB
ejpam-5787	295	76	from	from	ADP
ejpam-5787	295	77	[	[	X
ejpam-5787	295	78	2	2	NUM
ejpam-5787	295	79	]	]	PUNCT
ejpam-5787	295	80	)	)	PUNCT
ejpam-5787	295	81	.	.	PUNCT
ejpam-5787	296	1	(	(	PUNCT
ejpam-5787	296	2	a	a	X
ejpam-5787	296	3	)	)	PUNCT
ejpam-5787	296	4	(	(	PUNCT
ejpam-5787	296	5	b	b	X
ejpam-5787	296	6	)	)	PUNCT
ejpam-5787	296	7	figure	figure	NOUN
ejpam-5787	296	8	17	17	NUM
ejpam-5787	296	9	:	:	PUNCT
ejpam-5787	296	10	the	the	DET
ejpam-5787	296	11	(	(	PUNCT
ejpam-5787	296	12	a	a	PRON
ejpam-5787	296	13	,	,	PUNCT
ejpam-5787	296	14	ω	ω	NOUN
ejpam-5787	296	15	)	)	PUNCT
ejpam-5787	296	16	parameter	parameter	NOUN
ejpam-5787	296	17	plane	plane	NOUN
ejpam-5787	296	18	showing	show	VERB
ejpam-5787	296	19	regions	region	NOUN
ejpam-5787	296	20	of	of	ADP
ejpam-5787	296	21	the	the	DET
ejpam-5787	296	22	stable	stable	ADJ
ejpam-5787	296	23	periodic	periodic	ADJ
ejpam-5787	296	24	orbit	orbit	NOUN
ejpam-5787	296	25	of	of	ADP
ejpam-5787	296	26	the	the	DET
ejpam-5787	296	27	return	return	NOUN
ejpam-5787	296	28	map	map	NOUN
ejpam-5787	297	1	f	f	X
ejpam-5787	297	2	(	(	PUNCT
ejpam-5787	297	3	13	13	NUM
ejpam-5787	297	4	)	)	PUNCT
ejpam-5787	297	5	for	for	ADP
ejpam-5787	297	6	β	β	X
ejpam-5787	297	7	=	=	SYM
ejpam-5787	297	8	1	1	NUM
ejpam-5787	297	9	as	as	SCONJ
ejpam-5787	297	10	shown	show	VERB
ejpam-5787	297	11	in	in	ADP
ejpam-5787	297	12	figure	figure	NOUN
ejpam-5787	297	13	14(c	14(c	NUM
ejpam-5787	297	14	)	)	PUNCT
ejpam-5787	297	15	.	.	PUNCT
ejpam-5787	298	1	(	(	PUNCT
ejpam-5787	298	2	b	b	X
ejpam-5787	298	3	)	)	PUNCT
ejpam-5787	298	4	shows	show	VERB
ejpam-5787	298	5	a	a	DET
ejpam-5787	298	6	small	small	ADJ
ejpam-5787	298	7	range	range	NOUN
ejpam-5787	298	8	region	region	NOUN
ejpam-5787	298	9	for	for	ADP
ejpam-5787	298	10	a	a	PRON
ejpam-5787	298	11	and	and	CCONJ
ejpam-5787	298	12	ω	ω	NOUN
ejpam-5787	298	13	.	.	PUNCT
ejpam-5787	299	1	note	note	VERB
ejpam-5787	299	2	the	the	DET
ejpam-5787	299	3	white	white	ADJ
ejpam-5787	299	4	region	region	NOUN
ejpam-5787	299	5	is	be	AUX
ejpam-5787	299	6	not	not	PART
ejpam-5787	299	7	identified	identify	VERB
ejpam-5787	299	8	as	as	ADP
ejpam-5787	299	9	a	a	DET
ejpam-5787	299	10	low	low	ADJ
ejpam-5787	299	11	period	period	NOUN
ejpam-5787	299	12	periodic	periodic	ADJ
ejpam-5787	299	13	orbit	orbit	NOUN
ejpam-5787	299	14	of	of	ADP
ejpam-5787	299	15	the	the	DET
ejpam-5787	299	16	system	system	NOUN
ejpam-5787	299	17	as	as	SCONJ
ejpam-5787	299	18	shown	show	VERB
ejpam-5787	299	19	between	between	ADP
ejpam-5787	299	20	frequency	frequency	NOUN
ejpam-5787	299	21	-	-	PUNCT
ejpam-5787	299	22	locking	lock	VERB
ejpam-5787	299	23	regions	region	NOUN
ejpam-5787	299	24	4:1	4:1	NUM
ejpam-5787	299	25	(	(	PUNCT
ejpam-5787	299	26	yellow	yellow	ADJ
ejpam-5787	299	27	)	)	PUNCT
ejpam-5787	299	28	and	and	CCONJ
ejpam-5787	299	29	5:1	5:1	NUM
ejpam-5787	299	30	(	(	PUNCT
ejpam-5787	299	31	pink	pink	ADJ
ejpam-5787	299	32	)	)	PUNCT
ejpam-5787	299	33	.	.	PUNCT
ejpam-5787	300	1	the	the	DET
ejpam-5787	300	2	black	black	ADJ
ejpam-5787	300	3	circle	circle	NOUN
ejpam-5787	300	4	represents	represent	VERB
ejpam-5787	300	5	a	a	DET
ejpam-5787	300	6	=	=	SYM
ejpam-5787	300	7	1.65	1.65	NUM
ejpam-5787	300	8	and	and	CCONJ
ejpam-5787	300	9	ω	ω	NUM
ejpam-5787	300	10	=	=	NOUN
ejpam-5787	300	11	1.92	1.92	NUM
ejpam-5787	300	12	as	as	SCONJ
ejpam-5787	300	13	shown	show	VERB
ejpam-5787	300	14	in	in	ADP
ejpam-5787	300	15	figure	figure	NOUN
ejpam-5787	300	16	16	16	NUM
ejpam-5787	300	17	.	.	PUNCT
ejpam-5787	301	1	5	5	X
ejpam-5787	301	2	.	.	X
ejpam-5787	301	3	conclusion	conclusion	NOUN
ejpam-5787	301	4	we	we	PRON
ejpam-5787	301	5	use	use	VERB
ejpam-5787	301	6	geometric	geometric	ADJ
ejpam-5787	301	7	singular	singular	ADJ
ejpam-5787	301	8	perturbation	perturbation	NOUN
ejpam-5787	301	9	theory	theory	NOUN
ejpam-5787	301	10	(	(	PUNCT
ejpam-5787	301	11	gspt	gspt	NOUN
ejpam-5787	301	12	)	)	PUNCT
ejpam-5787	301	13	to	to	PART
ejpam-5787	301	14	explain	explain	VERB
ejpam-5787	301	15	the	the	DET
ejpam-5787	301	16	behaviour	behaviour	NOUN
ejpam-5787	301	17	of	of	ADP
ejpam-5787	301	18	the	the	DET
ejpam-5787	301	19	singular	singular	ADJ
ejpam-5787	301	20	slow	slow	ADJ
ejpam-5787	301	21	-	-	PUNCT
ejpam-5787	301	22	fast	fast	ADJ
ejpam-5787	301	23	system	system	NOUN
ejpam-5787	301	24	near	near	ADP
ejpam-5787	301	25	the	the	DET
ejpam-5787	301	26	singular	singular	ADJ
ejpam-5787	301	27	limit	limit	NOUN
ejpam-5787	301	28	.	.	PUNCT
ejpam-5787	302	1	in	in	ADP
ejpam-5787	302	2	particular	particular	ADJ
ejpam-5787	302	3	,	,	PUNCT
ejpam-5787	302	4	we	we	PRON
ejpam-5787	302	5	followed	follow	VERB
ejpam-5787	302	6	the	the	DET
ejpam-5787	302	7	analysis	analysis	NOUN
ejpam-5787	302	8	of	of	ADP
ejpam-5787	302	9	guckenheimer	guckenheimer	PROPN
ejpam-5787	302	10	et	et	PROPN
ejpam-5787	302	11	al	al	PROPN
ejpam-5787	302	12	.	.	PUNCT
ejpam-5787	303	1	[	[	X
ejpam-5787	303	2	10	10	NUM
ejpam-5787	303	3	]	]	PUNCT
ejpam-5787	303	4	for	for	ADP
ejpam-5787	303	5	the	the	DET
ejpam-5787	303	6	periodically	periodically	ADV
ejpam-5787	303	7	forced	force	VERB
ejpam-5787	303	8	symmetric	symmetric	ADJ
ejpam-5787	303	9	van	van	PROPN
ejpam-5787	303	10	der	der	PROPN
ejpam-5787	303	11	pol	pol	PROPN
ejpam-5787	303	12	oscillator	oscillator	NOUN
ejpam-5787	303	13	(	(	PUNCT
ejpam-5787	303	14	β	β	NOUN
ejpam-5787	303	15	=	=	SYM
ejpam-5787	303	16	0	0	NUM
ejpam-5787	303	17	)	)	PUNCT
ejpam-5787	303	18	,	,	PUNCT
ejpam-5787	303	19	then	then	ADV
ejpam-5787	303	20	we	we	PRON
ejpam-5787	303	21	construct	construct	VERB
ejpam-5787	303	22	a	a	DET
ejpam-5787	303	23	poincaré	poincaré	ADJ
ejpam-5787	303	24	return	return	NOUN
ejpam-5787	303	25	map	map	NOUN
ejpam-5787	303	26	to	to	PART
ejpam-5787	303	27	study	study	VERB
ejpam-5787	303	28	the	the	DET
ejpam-5787	303	29	bifurcation	bifurcation	NOUN
ejpam-5787	303	30	phenomena	phenomenon	NOUN
ejpam-5787	303	31	of	of	ADP
ejpam-5787	303	32	this	this	DET
ejpam-5787	303	33	model	model	NOUN
ejpam-5787	303	34	.	.	PUNCT
ejpam-5787	304	1	subsequently	subsequently	ADV
ejpam-5787	304	2	,	,	PUNCT
ejpam-5787	304	3	we	we	PRON
ejpam-5787	304	4	show	show	VERB
ejpam-5787	304	5	that	that	SCONJ
ejpam-5787	304	6	a	a	DET
ejpam-5787	304	7	periodic	periodic	ADJ
ejpam-5787	304	8	solution	solution	NOUN
ejpam-5787	304	9	persists	persist	VERB
ejpam-5787	304	10	for	for	ADP
ejpam-5787	304	11	varying	vary	VERB
ejpam-5787	304	12	a	a	PRON
ejpam-5787	304	13	and	and	CCONJ
ejpam-5787	304	14	ω	ω	NOUN
ejpam-5787	304	15	and	and	CCONJ
ejpam-5787	304	16	that	that	SCONJ
ejpam-5787	304	17	this	this	DET
ejpam-5787	304	18	solution	solution	NOUN
ejpam-5787	304	19	is	be	AUX
ejpam-5787	304	20	frequency	frequency	NOUN
ejpam-5787	304	21	locked	lock	VERB
ejpam-5787	304	22	(	(	PUNCT
ejpam-5787	304	23	forming	form	VERB
ejpam-5787	304	24	arnold	arnold	PROPN
ejpam-5787	304	25	tongues	tongue	NOUN
ejpam-5787	304	26	)	)	PUNCT
ejpam-5787	304	27	.	.	PUNCT
ejpam-5787	305	1	as	as	SCONJ
ejpam-5787	305	2	shown	show	VERB
ejpam-5787	305	3	in	in	ADP
ejpam-5787	305	4	figure	figure	NOUN
ejpam-5787	305	5	11	11	NUM
ejpam-5787	305	6	,	,	PUNCT
ejpam-5787	305	7	we	we	PRON
ejpam-5787	305	8	show	show	VERB
ejpam-5787	305	9	that	that	SCONJ
ejpam-5787	305	10	the	the	DET
ejpam-5787	305	11	saddle	saddle	NOUN
ejpam-5787	305	12	-	-	PUNCT
ejpam-5787	305	13	node	node	NOUN
ejpam-5787	305	14	bifurcation	bifurcation	NOUN
ejpam-5787	305	15	of	of	ADP
ejpam-5787	305	16	the	the	DET
ejpam-5787	305	17	first	first	ADJ
ejpam-5787	305	18	return	return	NOUN
ejpam-5787	305	19	map	map	NOUN
ejpam-5787	305	20	occurs	occur	VERB
ejpam-5787	305	21	on	on	ADP
ejpam-5787	305	22	the	the	DET
ejpam-5787	305	23	boundary	boundary	NOUN
ejpam-5787	305	24	of	of	ADP
ejpam-5787	305	25	frequency	frequency	NOUN
ejpam-5787	305	26	locking	locking	NOUN
ejpam-5787	305	27	in	in	ADP
ejpam-5787	305	28	a	a	DET
ejpam-5787	305	29	parameter	parameter	NOUN
ejpam-5787	305	30	space	space	NOUN
ejpam-5787	305	31	(	(	PUNCT
ejpam-5787	305	32	a	a	DET
ejpam-5787	305	33	,	,	PUNCT
ejpam-5787	305	34	ω	ω	NOUN
ejpam-5787	305	35	)	)	PUNCT
ejpam-5787	305	36	of	of	ADP
ejpam-5787	305	37	the	the	DET
ejpam-5787	305	38	system	system	NOUN
ejpam-5787	305	39	for	for	ADP
ejpam-5787	305	40	relatively	relatively	ADV
ejpam-5787	305	41	weak	weak	ADJ
ejpam-5787	305	42	forcing	forcing	NOUN
ejpam-5787	305	43	.	.	PUNCT
ejpam-5787	306	1	in	in	ADP
ejpam-5787	306	2	parameter	parameter	NOUN
ejpam-5787	306	3	space	space	NOUN
ejpam-5787	306	4	(	(	PUNCT
ejpam-5787	306	5	a	a	DET
ejpam-5787	306	6	,	,	PUNCT
ejpam-5787	306	7	ω	ω	NOUN
ejpam-5787	306	8	)	)	PUNCT
ejpam-5787	306	9	,	,	PUNCT
ejpam-5787	306	10	frequency	frequency	NOUN
ejpam-5787	306	11	locking	locking	NOUN
ejpam-5787	306	12	regions	region	NOUN
ejpam-5787	306	13	exist	exist	VERB
ejpam-5787	306	14	where	where	SCONJ
ejpam-5787	306	15	the	the	DET
ejpam-5787	306	16	period	period	NOUN
ejpam-5787	306	17	n	n	PRON
ejpam-5787	306	18	of	of	ADP
ejpam-5787	306	19	the	the	DET
ejpam-5787	306	20	oscillator	oscillator	NOUN
ejpam-5787	306	21	remains	remain	VERB
ejpam-5787	306	22	constant	constant	ADJ
ejpam-5787	306	23	under	under	ADP
ejpam-5787	306	24	perturbation	perturbation	NOUN
ejpam-5787	306	25	.	.	PUNCT
ejpam-5787	307	1	in	in	ADP
ejpam-5787	307	2	this	this	DET
ejpam-5787	307	3	thesis	thesis	NOUN
ejpam-5787	307	4	,	,	PUNCT
ejpam-5787	307	5	we	we	PRON
ejpam-5787	307	6	identify	identify	VERB
ejpam-5787	307	7	the	the	DET
ejpam-5787	307	8	frequency	frequency	NOUN
ejpam-5787	307	9	locking	locking	NOUN
ejpam-5787	307	10	by	by	ADP
ejpam-5787	307	11	estimating	estimate	VERB
ejpam-5787	307	12	the	the	DET
ejpam-5787	307	13	iterations	iteration	NOUN
ejpam-5787	307	14	of	of	ADP
ejpam-5787	307	15	the	the	DET
ejpam-5787	307	16	return	return	NOUN
ejpam-5787	307	17	map	map	NOUN
ejpam-5787	308	1	f	f	PROPN
ejpam-5787	308	2	and	and	CCONJ
ejpam-5787	308	3	we	we	PRON
ejpam-5787	308	4	numerically	numerically	ADV
ejpam-5787	308	5	solve	solve	VERB
ejpam-5787	308	6	the	the	DET
ejpam-5787	308	7	desingularised	desingularise	VERB
ejpam-5787	308	8	system	system	NOUN
ejpam-5787	308	9	(	(	PUNCT
ejpam-5787	308	10	12	12	NUM
ejpam-5787	308	11	)	)	PUNCT
ejpam-5787	308	12	to	to	PART
ejpam-5787	308	13	construct	construct	VERB
ejpam-5787	308	14	the	the	DET
ejpam-5787	308	15	return	return	NOUN
ejpam-5787	308	16	map	map	NOUN
ejpam-5787	308	17	f	f	PROPN
ejpam-5787	308	18	.	.	PUNCT
ejpam-5787	309	1	from	from	ADP
ejpam-5787	309	2	our	our	PRON
ejpam-5787	309	3	computations	computation	NOUN
ejpam-5787	309	4	such	such	ADJ
ejpam-5787	309	5	as	as	SCONJ
ejpam-5787	309	6	shown	show	VERB
ejpam-5787	309	7	in	in	ADP
ejpam-5787	309	8	figure	figure	NOUN
ejpam-5787	309	9	12	12	NUM
ejpam-5787	309	10	,	,	PUNCT
ejpam-5787	309	11	we	we	PRON
ejpam-5787	309	12	can	can	AUX
ejpam-5787	309	13	identify	identify	VERB
ejpam-5787	309	14	the	the	DET
ejpam-5787	309	15	rotation	rotation	NOUN
ejpam-5787	309	16	numbers	number	NOUN
ejpam-5787	309	17	of	of	ADP
ejpam-5787	309	18	attractors	attractor	NOUN
ejpam-5787	309	19	of	of	ADP
ejpam-5787	309	20	the	the	DET
ejpam-5787	309	21	system	system	NOUN
ejpam-5787	309	22	.	.	PUNCT
ejpam-5787	310	1	for	for	ADP
ejpam-5787	310	2	β	β	X
ejpam-5787	310	3	̸=	̸=	PROPN
ejpam-5787	310	4	0	0	NUM
ejpam-5787	310	5	,	,	PUNCT
ejpam-5787	310	6	we	we	PRON
ejpam-5787	310	7	i.	i.	AUX
ejpam-5787	310	8	alraddadi	alraddadi	PROPN
ejpam-5787	310	9	/	/	SYM
ejpam-5787	310	10	eur	eur	PROPN
ejpam-5787	310	11	.	.	PUNCT
ejpam-5787	311	1	j.	j.	PROPN
ejpam-5787	311	2	pure	pure	PROPN
ejpam-5787	311	3	appl	appl	PROPN
ejpam-5787	311	4	.	.	PROPN
ejpam-5787	311	5	math	math	PROPN
ejpam-5787	311	6	,	,	PUNCT
ejpam-5787	311	7	18	18	NUM
ejpam-5787	311	8	(	(	PUNCT
ejpam-5787	311	9	1	1	NUM
ejpam-5787	311	10	)	)	PUNCT
ejpam-5787	311	11	(	(	PUNCT
ejpam-5787	311	12	2025	2025	NUM
ejpam-5787	311	13	)	)	PUNCT
ejpam-5787	311	14	,	,	PUNCT
ejpam-5787	311	15	5787	5787	NUM
ejpam-5787	311	16	21	21	NUM
ejpam-5787	311	17	of	of	ADP
ejpam-5787	311	18	23	23	NUM
ejpam-5787	311	19	show	show	VERB
ejpam-5787	311	20	that	that	SCONJ
ejpam-5787	311	21	the	the	DET
ejpam-5787	311	22	forced	force	VERB
ejpam-5787	311	23	asymmetric	asymmetric	PROPN
ejpam-5787	311	24	van	van	PROPN
ejpam-5787	311	25	der	der	ADJ
ejpam-5787	311	26	pol	pol	PROPN
ejpam-5787	311	27	oscillator	oscillator	NOUN
ejpam-5787	311	28	can	can	AUX
ejpam-5787	311	29	become	become	VERB
ejpam-5787	311	30	frequency	frequency	NOUN
ejpam-5787	311	31	locked	lock	VERB
ejpam-5787	311	32	due	due	ADP
ejpam-5787	311	33	to	to	ADP
ejpam-5787	311	34	the	the	DET
ejpam-5787	311	35	forcing	forcing	NOUN
ejpam-5787	311	36	.	.	PUNCT
ejpam-5787	312	1	we	we	PRON
ejpam-5787	312	2	also	also	ADV
ejpam-5787	312	3	show	show	VERB
ejpam-5787	312	4	how	how	SCONJ
ejpam-5787	312	5	the	the	DET
ejpam-5787	312	6	symmetry	symmetry	NOUN
ejpam-5787	312	7	breaking	break	VERB
ejpam-5787	312	8	parameter	parameter	NOUN
ejpam-5787	312	9	β	β	PROPN
ejpam-5787	312	10	in	in	ADP
ejpam-5787	312	11	a	a	DET
ejpam-5787	312	12	periodically	periodically	ADV
ejpam-5787	312	13	forced	force	VERB
ejpam-5787	312	14	van	van	PROPN
ejpam-5787	312	15	der	der	PROPN
ejpam-5787	312	16	pol	pol	PROPN
ejpam-5787	312	17	oscillator	oscillator	NOUN
ejpam-5787	312	18	influences	influence	VERB
ejpam-5787	312	19	the	the	DET
ejpam-5787	312	20	width	width	NOUN
ejpam-5787	312	21	of	of	ADP
ejpam-5787	312	22	arnold	arnold	PROPN
ejpam-5787	312	23	tongues	tongue	NOUN
ejpam-5787	312	24	(	(	PUNCT
ejpam-5787	312	25	also	also	ADV
ejpam-5787	312	26	known	know	VERB
ejpam-5787	312	27	as	as	ADP
ejpam-5787	312	28	frequency	frequency	NOUN
ejpam-5787	312	29	locking	locking	NOUN
ejpam-5787	312	30	regions	region	NOUN
ejpam-5787	312	31	)	)	PUNCT
ejpam-5787	312	32	,	,	PUNCT
ejpam-5787	312	33	and	and	CCONJ
ejpam-5787	312	34	we	we	PRON
ejpam-5787	312	35	showed	show	VERB
ejpam-5787	312	36	the	the	DET
ejpam-5787	312	37	frequency	frequency	NOUN
ejpam-5787	312	38	locking	locking	NOUN
ejpam-5787	312	39	regions	region	NOUN
ejpam-5787	312	40	(	(	PUNCT
ejpam-5787	312	41	or	or	CCONJ
ejpam-5787	312	42	arnold	arnold	PROPN
ejpam-5787	312	43	tongues	tongue	NOUN
ejpam-5787	312	44	)	)	PUNCT
ejpam-5787	312	45	in	in	ADP
ejpam-5787	312	46	the	the	DET
ejpam-5787	312	47	parameter	parameter	NOUN
ejpam-5787	312	48	space	space	NOUN
ejpam-5787	312	49	(	(	PUNCT
ejpam-5787	312	50	a	a	PRON
ejpam-5787	312	51	,	,	PUNCT
ejpam-5787	312	52	ω	ω	NOUN
ejpam-5787	312	53	)	)	PUNCT
ejpam-5787	312	54	.	.	PUNCT
ejpam-5787	313	1	data	datum	NOUN
ejpam-5787	313	2	availability	availability	NOUN
ejpam-5787	313	3	statement	statement	NOUN
ejpam-5787	313	4	:	:	PUNCT
ejpam-5787	313	5	all	all	DET
ejpam-5787	313	6	data	datum	NOUN
ejpam-5787	313	7	generated	generate	VERB
ejpam-5787	313	8	or	or	CCONJ
ejpam-5787	313	9	analysed	analyse	VERB
ejpam-5787	313	10	during	during	ADP
ejpam-5787	313	11	the	the	DET
ejpam-5787	313	12	research	research	NOUN
ejpam-5787	313	13	investigation	investigation	NOUN
ejpam-5787	313	14	have	have	AUX
ejpam-5787	313	15	been	be	AUX
ejpam-5787	313	16	included	include	VERB
ejpam-5787	313	17	in	in	ADP
ejpam-5787	313	18	the	the	DET
ejpam-5787	313	19	paper	paper	NOUN
ejpam-5787	313	20	.	.	PUNCT
ejpam-5787	314	1	references	reference	NOUN
ejpam-5787	314	2	[	[	X
ejpam-5787	314	3	1	1	NUM
ejpam-5787	314	4	]	]	X
ejpam-5787	314	5	henry	henry	PROPN
ejpam-5787	314	6	di	di	PROPN
ejpam-5787	314	7	abarbanel	abarbanel	PROPN
ejpam-5787	314	8	,	,	PUNCT
ejpam-5787	314	9	nikolai	nikolai	PROPN
ejpam-5787	314	10	f	f	PROPN
ejpam-5787	314	11	rulkov	rulkov	PROPN
ejpam-5787	314	12	,	,	PUNCT
ejpam-5787	314	13	and	and	CCONJ
ejpam-5787	314	14	mikhail	mikhail	PROPN
ejpam-5787	314	15	m	m	PROPN
ejpam-5787	314	16	sushchik	sushchik	ADJ
ejpam-5787	314	17	.	.	PUNCT
ejpam-5787	315	1	generalized	generalized	ADJ
ejpam-5787	315	2	synchronization	synchronization	NOUN
ejpam-5787	315	3	of	of	ADP
ejpam-5787	315	4	chaos	chaos	NOUN
ejpam-5787	315	5	:	:	PUNCT
ejpam-5787	315	6	the	the	DET
ejpam-5787	315	7	auxiliary	auxiliary	ADJ
ejpam-5787	315	8	system	system	NOUN
ejpam-5787	315	9	approach	approach	NOUN
ejpam-5787	315	10	.	.	PUNCT
ejpam-5787	316	1	physical	physical	ADJ
ejpam-5787	316	2	review	review	PROPN
ejpam-5787	316	3	e	e	NOUN
ejpam-5787	316	4	,	,	PUNCT
ejpam-5787	316	5	53(5):4528	53(5):4528	NUM
ejpam-5787	316	6	,	,	PUNCT
ejpam-5787	316	7	1996	1996	NUM
ejpam-5787	316	8	.	.	PUNCT
ejpam-5787	317	1	[	[	X
ejpam-5787	317	2	2	2	NUM
ejpam-5787	317	3	]	]	X
ejpam-5787	317	4	peter	peter	PROPN
ejpam-5787	317	5	ashwin	ashwin	PROPN
ejpam-5787	317	6	,	,	PUNCT
ejpam-5787	317	7	charles	charles	PROPN
ejpam-5787	317	8	david	david	PROPN
ejpam-5787	317	9	camp	camp	PROPN
ejpam-5787	317	10	,	,	PUNCT
ejpam-5787	317	11	and	and	CCONJ
ejpam-5787	317	12	anna	anna	PROPN
ejpam-5787	317	13	s	s	PROPN
ejpam-5787	317	14	von	von	PROPN
ejpam-5787	317	15	der	der	PROPN
ejpam-5787	317	16	heydt	heydt	PROPN
ejpam-5787	317	17	.	.	PUNCT
ejpam-5787	318	1	chaotic	chaotic	ADJ
ejpam-5787	318	2	and	and	CCONJ
ejpam-5787	318	3	nonchaotic	nonchaotic	ADJ
ejpam-5787	318	4	response	response	NOUN
ejpam-5787	318	5	to	to	ADP
ejpam-5787	318	6	quasiperiodic	quasiperiodic	ADJ
ejpam-5787	318	7	forcing	forcing	NOUN
ejpam-5787	318	8	:	:	PUNCT
ejpam-5787	318	9	limits	limit	NOUN
ejpam-5787	318	10	to	to	ADP
ejpam-5787	318	11	predictability	predictability	NOUN
ejpam-5787	318	12	of	of	ADP
ejpam-5787	318	13	ice	ice	NOUN
ejpam-5787	318	14	ages	age	NOUN
ejpam-5787	318	15	paced	pace	VERB
ejpam-5787	318	16	by	by	ADP
ejpam-5787	318	17	milankovitch	milankovitch	NOUN
ejpam-5787	318	18	forcing	force	VERB
ejpam-5787	318	19	.	.	PUNCT
ejpam-5787	319	1	dynamics	dynamic	NOUN
ejpam-5787	319	2	and	and	CCONJ
ejpam-5787	319	3	statistics	statistic	NOUN
ejpam-5787	319	4	of	of	ADP
ejpam-5787	319	5	the	the	DET
ejpam-5787	319	6	climate	climate	NOUN
ejpam-5787	319	7	system	system	NOUN
ejpam-5787	319	8	,	,	PUNCT
ejpam-5787	319	9	3(1	3(1	NUM
ejpam-5787	319	10	)	)	PUNCT
ejpam-5787	319	11	,	,	PUNCT
ejpam-5787	319	12	2018	2018	NUM
ejpam-5787	319	13	.	.	PUNCT
ejpam-5787	320	1	[	[	X
ejpam-5787	320	2	3	3	NUM
ejpam-5787	320	3	]	]	X
ejpam-5787	320	4	alexander	alexander	NOUN
ejpam-5787	320	5	balanov	balanov	PROPN
ejpam-5787	320	6	,	,	PUNCT
ejpam-5787	320	7	natalia	natalia	PROPN
ejpam-5787	320	8	janson	janson	PROPN
ejpam-5787	320	9	,	,	PUNCT
ejpam-5787	320	10	dmitry	dmitry	PROPN
ejpam-5787	320	11	postnov	postnov	NOUN
ejpam-5787	320	12	,	,	PUNCT
ejpam-5787	320	13	and	and	CCONJ
ejpam-5787	320	14	olga	olga	PROPN
ejpam-5787	320	15	sosnovtseva	sosnovtseva	PROPN
ejpam-5787	320	16	.	.	PUNCT
ejpam-5787	321	1	from	from	ADP
ejpam-5787	321	2	simple	simple	ADJ
ejpam-5787	321	3	to	to	ADP
ejpam-5787	321	4	complex	complex	ADJ
ejpam-5787	321	5	.	.	PUNCT
ejpam-5787	321	6	springer	springer	NOUN
ejpam-5787	321	7	.	.	PUNCT
ejpam-5787	322	1	[	[	X
ejpam-5787	322	2	4	4	X
ejpam-5787	322	3	]	]	PUNCT
ejpam-5787	322	4	katherine	katherine	PROPN
ejpam-5787	322	5	bold	bold	PROPN
ejpam-5787	322	6	,	,	PUNCT
ejpam-5787	322	7	chantal	chantal	PROPN
ejpam-5787	322	8	edwards	edwards	PROPN
ejpam-5787	322	9	,	,	PUNCT
ejpam-5787	322	10	john	john	PROPN
ejpam-5787	322	11	guckenheimer	guckenheimer	PROPN
ejpam-5787	322	12	,	,	PUNCT
ejpam-5787	322	13	sabyasachi	sabyasachi	ADJ
ejpam-5787	322	14	guharay	guharay	NOUN
ejpam-5787	322	15	,	,	PUNCT
ejpam-5787	322	16	kathleen	kathleen	PROPN
ejpam-5787	322	17	hoffman	hoffman	PROPN
ejpam-5787	322	18	,	,	PUNCT
ejpam-5787	322	19	judith	judith	PROPN
ejpam-5787	322	20	hubbard	hubbard	PROPN
ejpam-5787	322	21	,	,	PUNCT
ejpam-5787	322	22	ricardo	ricardo	PROPN
ejpam-5787	322	23	oliva	oliva	PROPN
ejpam-5787	322	24	,	,	PUNCT
ejpam-5787	322	25	and	and	CCONJ
ejpam-5787	322	26	warren	warren	PROPN
ejpam-5787	322	27	weckesser	weckesser	PROPN
ejpam-5787	322	28	.	.	PUNCT
ejpam-5787	323	1	the	the	DET
ejpam-5787	323	2	forced	force	VERB
ejpam-5787	323	3	van	van	PROPN
ejpam-5787	323	4	der	der	PROPN
ejpam-5787	323	5	pol	pol	PROPN
ejpam-5787	323	6	equation	equation	PROPN
ejpam-5787	323	7	ii	ii	PROPN
ejpam-5787	323	8	:	:	PUNCT
ejpam-5787	323	9	canards	canard	NOUN
ejpam-5787	323	10	in	in	ADP
ejpam-5787	323	11	the	the	DET
ejpam-5787	323	12	reduced	reduce	VERB
ejpam-5787	323	13	system	system	NOUN
ejpam-5787	323	14	.	.	PUNCT
ejpam-5787	324	1	siam	siam	PROPN
ejpam-5787	324	2	journal	journal	PROPN
ejpam-5787	324	3	on	on	ADP
ejpam-5787	324	4	applied	apply	VERB
ejpam-5787	324	5	dynamical	dynamical	ADJ
ejpam-5787	324	6	systems	system	NOUN
ejpam-5787	324	7	,	,	PUNCT
ejpam-5787	324	8	2(4):570–608	2(4):570–608	NUM
ejpam-5787	324	9	,	,	PUNCT
ejpam-5787	324	10	2003	2003	NUM
ejpam-5787	324	11	.	.	PUNCT
ejpam-5787	325	1	[	[	X
ejpam-5787	325	2	5	5	X
ejpam-5787	325	3	]	]	X
ejpam-5787	325	4	mary	mary	PROPN
ejpam-5787	325	5	l.	l.	PROPN
ejpam-5787	325	6	cartwright	cartwright	PROPN
ejpam-5787	325	7	and	and	CCONJ
ejpam-5787	325	8	je	je	PROPN
ejpam-5787	325	9	littlewood	littlewood	PROPN
ejpam-5787	325	10	.	.	PUNCT
ejpam-5787	326	1	on	on	ADP
ejpam-5787	326	2	non	non	ADJ
ejpam-5787	326	3	-	-	ADJ
ejpam-5787	326	4	linear	linear	ADJ
ejpam-5787	326	5	differential	differential	ADJ
ejpam-5787	326	6	equations	equation	NOUN
ejpam-5787	326	7	of	of	ADP
ejpam-5787	326	8	the	the	DET
ejpam-5787	326	9	second	second	ADJ
ejpam-5787	326	10	order	order	NOUN
ejpam-5787	326	11	.	.	PUNCT
ejpam-5787	327	1	j.	j.	PROPN
ejpam-5787	327	2	london	london	PROPN
ejpam-5787	327	3	math	math	PROPN
ejpam-5787	327	4	.	.	PUNCT
ejpam-5787	328	1	soc	soc	PROPN
ejpam-5787	328	2	,	,	PUNCT
ejpam-5787	328	3	20	20	NUM
ejpam-5787	328	4	,	,	PUNCT
ejpam-5787	328	5	1945	1945	NUM
ejpam-5787	328	6	.	.	PUNCT
ejpam-5787	329	1	[	[	X
ejpam-5787	329	2	6	6	NUM
ejpam-5787	329	3	]	]	PUNCT
ejpam-5787	329	4	michel	michel	PROPN
ejpam-5787	329	5	crucifix	crucifix	PROPN
ejpam-5787	329	6	.	.	PUNCT
ejpam-5787	330	1	oscillators	oscillator	NOUN
ejpam-5787	330	2	and	and	CCONJ
ejpam-5787	330	3	relaxation	relaxation	NOUN
ejpam-5787	330	4	phenomena	phenomenon	NOUN
ejpam-5787	330	5	in	in	ADP
ejpam-5787	330	6	pleistocene	pleistocene	PROPN
ejpam-5787	330	7	climate	climate	NOUN
ejpam-5787	330	8	theory	theory	NOUN
ejpam-5787	330	9	.	.	PUNCT
ejpam-5787	331	1	trans	trans	PROPN
ejpam-5787	331	2	.	.	PUNCT
ejpam-5787	331	3	r.	r.	PROPN
ejpam-5787	331	4	soc	soc	PROPN
ejpam-5787	331	5	.	.	PUNCT
ejpam-5787	332	1	a	a	DET
ejpam-5787	332	2	,	,	PUNCT
ejpam-5787	332	3	370:1140–1165	370:1140–1165	NUM
ejpam-5787	332	4	,	,	PUNCT
ejpam-5787	332	5	2012	2012	NUM
ejpam-5787	332	6	.	.	PUNCT
ejpam-5787	333	1	[	[	X
ejpam-5787	333	2	7	7	X
ejpam-5787	333	3	]	]	X
ejpam-5787	333	4	bernard	bernard	PROPN
ejpam-5787	333	5	de	de	PROPN
ejpam-5787	333	6	saedeleer	saedeleer	PROPN
ejpam-5787	333	7	,	,	PUNCT
ejpam-5787	333	8	michel	michel	PROPN
ejpam-5787	333	9	crucifix	crucifix	PROPN
ejpam-5787	333	10	,	,	PUNCT
ejpam-5787	333	11	and	and	CCONJ
ejpam-5787	333	12	sebastian	sebastian	ADJ
ejpam-5787	333	13	wieczorek	wieczorek	PROPN
ejpam-5787	333	14	.	.	PUNCT
ejpam-5787	333	15	is	be	AUX
ejpam-5787	333	16	the	the	DET
ejpam-5787	333	17	astronomical	astronomical	ADJ
ejpam-5787	333	18	forcing	force	VERB
ejpam-5787	333	19	a	a	DET
ejpam-5787	333	20	reliable	reliable	ADJ
ejpam-5787	333	21	and	and	CCONJ
ejpam-5787	333	22	unique	unique	ADJ
ejpam-5787	333	23	pacemaker	pacemaker	NOUN
ejpam-5787	333	24	for	for	ADP
ejpam-5787	333	25	climate	climate	NOUN
ejpam-5787	333	26	?	?	PUNCT
ejpam-5787	334	1	a	a	DET
ejpam-5787	334	2	conceptual	conceptual	ADJ
ejpam-5787	334	3	model	model	NOUN
ejpam-5787	334	4	study	study	NOUN
ejpam-5787	334	5	.	.	PUNCT
ejpam-5787	335	1	climate	climate	NOUN
ejpam-5787	335	2	dynamics	dynamic	NOUN
ejpam-5787	335	3	,	,	PUNCT
ejpam-5787	335	4	2013	2013	NUM
ejpam-5787	335	5	.	.	PUNCT
ejpam-5787	336	1	[	[	X
ejpam-5787	336	2	8	8	NUM
ejpam-5787	336	3	]	]	X
ejpam-5787	336	4	peter	peter	PROPN
ejpam-5787	336	5	ditlevsen	ditlevsen	PROPN
ejpam-5787	336	6	and	and	CCONJ
ejpam-5787	336	7	peter	peter	PROPN
ejpam-5787	336	8	ashwin	ashwin	PROPN
ejpam-5787	336	9	.	.	PUNCT
ejpam-5787	337	1	complex	complex	ADJ
ejpam-5787	337	2	climate	climate	NOUN
ejpam-5787	337	3	response	response	NOUN
ejpam-5787	337	4	to	to	ADP
ejpam-5787	337	5	astronomical	astronomical	ADJ
ejpam-5787	337	6	forcing	forcing	NOUN
ejpam-5787	337	7	:	:	PUNCT
ejpam-5787	337	8	the	the	DET
ejpam-5787	337	9	middle	middle	ADJ
ejpam-5787	337	10	-	-	PUNCT
ejpam-5787	337	11	pleistocene	pleistocene	NOUN
ejpam-5787	337	12	transition	transition	NOUN
ejpam-5787	337	13	in	in	ADP
ejpam-5787	337	14	glacial	glacial	ADJ
ejpam-5787	337	15	cycles	cycle	NOUN
ejpam-5787	337	16	and	and	CCONJ
ejpam-5787	337	17	changes	change	NOUN
ejpam-5787	337	18	in	in	ADP
ejpam-5787	337	19	frequency	frequency	NOUN
ejpam-5787	337	20	locking	locking	NOUN
ejpam-5787	337	21	.	.	PUNCT
ejpam-5787	338	1	pages	page	NOUN
ejpam-5787	338	2	1–13	1–13	PROPN
ejpam-5787	338	3	,	,	PUNCT
ejpam-5787	338	4	2018	2018	NUM
ejpam-5787	338	5	.	.	PUNCT
ejpam-5787	339	1	[	[	X
ejpam-5787	339	2	9	9	NUM
ejpam-5787	339	3	]	]	X
ejpam-5787	339	4	john	john	PROPN
ejpam-5787	339	5	guckenheimer	guckenheimer	PROPN
ejpam-5787	339	6	.	.	PUNCT
ejpam-5787	340	1	return	return	NOUN
ejpam-5787	340	2	maps	map	NOUN
ejpam-5787	340	3	of	of	ADP
ejpam-5787	340	4	folded	fold	VERB
ejpam-5787	340	5	nodes	node	NOUN
ejpam-5787	340	6	and	and	CCONJ
ejpam-5787	340	7	folded	fold	VERB
ejpam-5787	340	8	saddle	saddle	NOUN
ejpam-5787	340	9	-	-	PUNCT
ejpam-5787	340	10	nodes	node	NOUN
ejpam-5787	340	11	.	.	PUNCT
ejpam-5787	341	1	chaos	chaos	NOUN
ejpam-5787	341	2	:	:	PUNCT
ejpam-5787	341	3	an	an	DET
ejpam-5787	341	4	interdisciplinary	interdisciplinary	ADJ
ejpam-5787	341	5	journal	journal	NOUN
ejpam-5787	341	6	of	of	ADP
ejpam-5787	341	7	nonlinear	nonlinear	ADJ
ejpam-5787	341	8	science	science	NOUN
ejpam-5787	341	9	,	,	PUNCT
ejpam-5787	341	10	18(1):015108	18(1):015108	NUM
ejpam-5787	341	11	,	,	PUNCT
ejpam-5787	341	12	2008	2008	NUM
ejpam-5787	341	13	.	.	PUNCT
ejpam-5787	342	1	[	[	X
ejpam-5787	342	2	10	10	NUM
ejpam-5787	342	3	]	]	X
ejpam-5787	342	4	john	john	PROPN
ejpam-5787	342	5	guckenheimer	guckenheimer	PROPN
ejpam-5787	342	6	,	,	PUNCT
ejpam-5787	342	7	kathleen	kathleen	PROPN
ejpam-5787	342	8	hoffman	hoffman	PROPN
ejpam-5787	342	9	,	,	PUNCT
ejpam-5787	342	10	and	and	CCONJ
ejpam-5787	342	11	warren	warren	PROPN
ejpam-5787	342	12	weckesser	weckesser	PROPN
ejpam-5787	342	13	.	.	PUNCT
ejpam-5787	343	1	the	the	DET
ejpam-5787	343	2	forced	force	VERB
ejpam-5787	343	3	van	van	PROPN
ejpam-5787	343	4	der	der	ADJ
ejpam-5787	343	5	pol	pol	NOUN
ejpam-5787	343	6	equation	equation	NOUN
ejpam-5787	343	7	i	i	PRON
ejpam-5787	343	8	:	:	PUNCT
ejpam-5787	343	9	the	the	DET
ejpam-5787	343	10	slow	slow	ADJ
ejpam-5787	343	11	flow	flow	NOUN
ejpam-5787	343	12	and	and	CCONJ
ejpam-5787	343	13	its	its	PRON
ejpam-5787	343	14	bifurcations	bifurcation	NOUN
ejpam-5787	343	15	.	.	PUNCT
ejpam-5787	344	1	siam	siam	PROPN
ejpam-5787	344	2	j.	j.	PROPN
ejpam-5787	344	3	applied	apply	VERB
ejpam-5787	344	4	dynamical	dynamical	ADJ
ejpam-5787	344	5	systems	system	NOUN
ejpam-5787	344	6	,	,	PUNCT
ejpam-5787	344	7	2(1):1–35	2(1):1–35	NUM
ejpam-5787	344	8	,	,	PUNCT
ejpam-5787	344	9	2003	2003	NUM
ejpam-5787	344	10	.	.	PUNCT
ejpam-5787	345	1	[	[	X
ejpam-5787	345	2	11	11	NUM
ejpam-5787	345	3	]	]	X
ejpam-5787	345	4	john	john	PROPN
ejpam-5787	345	5	guckenheimer	guckenheimer	PROPN
ejpam-5787	345	6	,	,	PUNCT
ejpam-5787	345	7	kathleen	kathleen	PROPN
ejpam-5787	345	8	hoffman	hoffman	PROPN
ejpam-5787	345	9	,	,	PUNCT
ejpam-5787	345	10	and	and	CCONJ
ejpam-5787	345	11	warren	warren	PROPN
ejpam-5787	345	12	weckesser	weckesser	PROPN
ejpam-5787	345	13	.	.	PUNCT
ejpam-5787	346	1	bifurcations	bifurcation	NOUN
ejpam-5787	346	2	of	of	ADP
ejpam-5787	346	3	relaxation	relaxation	NOUN
ejpam-5787	346	4	oscillations	oscillation	NOUN
ejpam-5787	346	5	near	near	ADP
ejpam-5787	346	6	folded	fold	VERB
ejpam-5787	346	7	saddles	saddle	NOUN
ejpam-5787	346	8	.	.	PUNCT
ejpam-5787	347	1	i.	i.	PROPN
ejpam-5787	347	2	j.	j.	PROPN
ejpam-5787	347	3	bifurcation	bifurcation	PROPN
ejpam-5787	347	4	and	and	CCONJ
ejpam-5787	347	5	chaos	chaos	NOUN
ejpam-5787	347	6	,	,	PUNCT
ejpam-5787	347	7	15(11):3411	15(11):3411	NUM
ejpam-5787	347	8	–	–	PUNCT
ejpam-5787	347	9	3421	3421	NUM
ejpam-5787	347	10	,	,	PUNCT
ejpam-5787	347	11	2005	2005	NUM
ejpam-5787	347	12	.	.	PUNCT
ejpam-5787	348	1	i.	i.	PROPN
ejpam-5787	348	2	alraddadi	alraddadi	PROPN
ejpam-5787	348	3	/	/	SYM
ejpam-5787	348	4	eur	eur	PROPN
ejpam-5787	348	5	.	.	PUNCT
ejpam-5787	349	1	j.	j.	PROPN
ejpam-5787	349	2	pure	pure	PROPN
ejpam-5787	349	3	appl	appl	PROPN
ejpam-5787	349	4	.	.	PROPN
ejpam-5787	349	5	math	math	PROPN
ejpam-5787	349	6	,	,	PUNCT
ejpam-5787	349	7	18	18	NUM
ejpam-5787	349	8	(	(	PUNCT
ejpam-5787	349	9	1	1	NUM
ejpam-5787	349	10	)	)	PUNCT
ejpam-5787	349	11	(	(	PUNCT
ejpam-5787	349	12	2025	2025	NUM
ejpam-5787	349	13	)	)	PUNCT
ejpam-5787	349	14	,	,	PUNCT
ejpam-5787	349	15	5787	5787	NUM
ejpam-5787	349	16	22	22	NUM
ejpam-5787	349	17	of	of	ADP
ejpam-5787	349	18	23	23	NUM
ejpam-5787	350	1	[	[	X
ejpam-5787	350	2	12	12	NUM
ejpam-5787	350	3	]	]	X
ejpam-5787	350	4	chihiro	chihiro	PROPN
ejpam-5787	350	5	hayashi	hayashi	PROPN
ejpam-5787	350	6	.	.	PUNCT
ejpam-5787	351	1	nonlinear	nonlinear	ADJ
ejpam-5787	351	2	oscillations	oscillation	NOUN
ejpam-5787	351	3	in	in	ADP
ejpam-5787	351	4	physical	physical	ADJ
ejpam-5787	351	5	systems	system	NOUN
ejpam-5787	351	6	.	.	PUNCT
ejpam-5787	352	1	princeton	princeton	PROPN
ejpam-5787	352	2	university	university	PROPN
ejpam-5787	352	3	press	press	NOUN
ejpam-5787	352	4	,	,	PUNCT
ejpam-5787	352	5	2014	2014	NUM
ejpam-5787	352	6	.	.	PUNCT
ejpam-5787	353	1	[	[	X
ejpam-5787	353	2	13	13	NUM
ejpam-5787	353	3	]	]	X
ejpam-5787	353	4	sze	sze	PROPN
ejpam-5787	353	5	-	-	PUNCT
ejpam-5787	353	6	bi	bi	PROPN
ejpam-5787	353	7	hsu	hsu	PROPN
ejpam-5787	353	8	and	and	CCONJ
ejpam-5787	353	9	junping	junpe	VERB
ejpam-5787	353	10	shi	shi	PROPN
ejpam-5787	353	11	.	.	PUNCT
ejpam-5787	354	1	relaxation	relaxation	NOUN
ejpam-5787	354	2	oscillation	oscillation	NOUN
ejpam-5787	354	3	profile	profile	NOUN
ejpam-5787	354	4	of	of	ADP
ejpam-5787	354	5	limit	limit	NOUN
ejpam-5787	354	6	cycle	cycle	NOUN
ejpam-5787	354	7	in	in	ADP
ejpam-5787	354	8	predatorprey	predatorprey	NOUN
ejpam-5787	354	9	system	system	NOUN
ejpam-5787	354	10	.	.	PUNCT
ejpam-5787	355	1	discrete	discrete	VERB
ejpam-5787	355	2	&	&	CCONJ
ejpam-5787	355	3	continuous	continuous	ADJ
ejpam-5787	355	4	dynamical	dynamical	ADJ
ejpam-5787	355	5	systems	system	NOUN
ejpam-5787	355	6	-	-	PUNCT
ejpam-5787	355	7	b	b	NOUN
ejpam-5787	355	8	,	,	PUNCT
ejpam-5787	355	9	11(4):893	11(4):893	NUM
ejpam-5787	355	10	,	,	PUNCT
ejpam-5787	355	11	2009	2009	NUM
ejpam-5787	355	12	.	.	PUNCT
ejpam-5787	356	1	[	[	X
ejpam-5787	356	2	14	14	NUM
ejpam-5787	356	3	]	]	X
ejpam-5787	356	4	eugene	eugene	PROPN
ejpam-5787	356	5	m.	m.	PROPN
ejpam-5787	356	6	izhikevich	izhikevich	PROPN
ejpam-5787	356	7	.	.	PUNCT
ejpam-5787	357	1	dynamical	dynamical	ADJ
ejpam-5787	357	2	systems	system	NOUN
ejpam-5787	357	3	in	in	ADP
ejpam-5787	357	4	neuroscience	neuroscience	NOUN
ejpam-5787	357	5	:	:	PUNCT
ejpam-5787	357	6	the	the	DET
ejpam-5787	357	7	geometry	geometry	NOUN
ejpam-5787	357	8	of	of	ADP
ejpam-5787	357	9	excitability	excitability	NOUN
ejpam-5787	357	10	and	and	CCONJ
ejpam-5787	357	11	bursting	bursting	NOUN
ejpam-5787	357	12	.	.	PUNCT
ejpam-5787	358	1	the	the	DET
ejpam-5787	358	2	mit	mit	PROPN
ejpam-5787	358	3	press	press	NOUN
ejpam-5787	358	4	,	,	PUNCT
ejpam-5787	358	5	07	07	NUM
ejpam-5787	358	6	2006	2006	NUM
ejpam-5787	358	7	.	.	PUNCT
ejpam-5787	359	1	[	[	X
ejpam-5787	359	2	15	15	NUM
ejpam-5787	359	3	]	]	X
ejpam-5787	359	4	christian	christian	PROPN
ejpam-5787	359	5	kuehn	kuehn	PROPN
ejpam-5787	359	6	.	.	PUNCT
ejpam-5787	360	1	multiple	multiple	ADJ
ejpam-5787	360	2	time	time	NOUN
ejpam-5787	360	3	scale	scale	NOUN
ejpam-5787	360	4	dynamics	dynamic	NOUN
ejpam-5787	360	5	,	,	PUNCT
ejpam-5787	360	6	volume	volume	NOUN
ejpam-5787	360	7	191	191	NUM
ejpam-5787	360	8	.	.	PUNCT
ejpam-5787	360	9	springer	springer	NOUN
ejpam-5787	360	10	,	,	PUNCT
ejpam-5787	360	11	2015	2015	NUM
ejpam-5787	360	12	.	.	PUNCT
ejpam-5787	361	1	[	[	X
ejpam-5787	361	2	16	16	NUM
ejpam-5787	361	3	]	]	X
ejpam-5787	361	4	yuri	yuri	PROPN
ejpam-5787	361	5	a.	a.	PROPN
ejpam-5787	361	6	kuznetsov	kuznetsov	PROPN
ejpam-5787	361	7	.	.	PUNCT
ejpam-5787	362	1	elements	element	NOUN
ejpam-5787	362	2	of	of	ADP
ejpam-5787	362	3	applied	apply	VERB
ejpam-5787	362	4	bifurcation	bifurcation	NOUN
ejpam-5787	362	5	theory	theory	NOUN
ejpam-5787	362	6	,	,	PUNCT
ejpam-5787	362	7	second	second	ADJ
ejpam-5787	362	8	edition	edition	NOUN
ejpam-5787	362	9	.	.	PUNCT
ejpam-5787	363	1	library	library	PROPN
ejpam-5787	363	2	,	,	PUNCT
ejpam-5787	363	3	page	page	NOUN
ejpam-5787	363	4	591	591	NUM
ejpam-5787	363	5	,	,	PUNCT
ejpam-5787	363	6	1998	1998	NUM
ejpam-5787	363	7	.	.	PUNCT
ejpam-5787	364	1	[	[	X
ejpam-5787	364	2	17	17	NUM
ejpam-5787	364	3	]	]	X
ejpam-5787	364	4	stephen	stephen	PROPN
ejpam-5787	364	5	lynch	lynch	PROPN
ejpam-5787	364	6	.	.	PUNCT
ejpam-5787	365	1	dynamical	dynamical	ADJ
ejpam-5787	365	2	systems	system	NOUN
ejpam-5787	365	3	with	with	ADP
ejpam-5787	365	4	applications	application	NOUN
ejpam-5787	365	5	using	use	VERB
ejpam-5787	365	6	matlab	matlab	PROPN
ejpam-5787	365	7	®	®	PROPN
ejpam-5787	365	8	.	.	PUNCT
ejpam-5787	366	1	springer	springer	PROPN
ejpam-5787	366	2	international	international	ADJ
ejpam-5787	366	3	publishing	publishing	NOUN
ejpam-5787	366	4	,	,	PUNCT
ejpam-5787	366	5	2014	2014	NUM
ejpam-5787	366	6	.	.	PUNCT
ejpam-5787	367	1	[	[	X
ejpam-5787	367	2	18	18	NUM
ejpam-5787	367	3	]	]	X
ejpam-5787	367	4	r	r	NOUN
ejpam-5787	367	5	mettin	mettin	NOUN
ejpam-5787	367	6	,	,	PUNCT
ejpam-5787	367	7	u	u	NOUN
ejpam-5787	367	8	parlitz	parlitz	NOUN
ejpam-5787	367	9	,	,	PUNCT
ejpam-5787	367	10	and	and	CCONJ
ejpam-5787	367	11	w	w	NOUN
ejpam-5787	367	12	lauterborn	lauterborn	VERB
ejpam-5787	367	13	.	.	PUNCT
ejpam-5787	368	1	bifurcation	bifurcation	NOUN
ejpam-5787	368	2	structure	structure	NOUN
ejpam-5787	368	3	of	of	ADP
ejpam-5787	368	4	the	the	DET
ejpam-5787	368	5	driven	drive	VERB
ejpam-5787	368	6	van	van	PROPN
ejpam-5787	368	7	der	der	PROPN
ejpam-5787	368	8	pol	pol	PROPN
ejpam-5787	368	9	oscillator	oscillator	NOUN
ejpam-5787	368	10	.	.	PUNCT
ejpam-5787	369	1	international	international	ADJ
ejpam-5787	369	2	journal	journal	NOUN
ejpam-5787	369	3	of	of	ADP
ejpam-5787	369	4	bifurcation	bifurcation	NOUN
ejpam-5787	369	5	and	and	CCONJ
ejpam-5787	369	6	chaos	chaos	NOUN
ejpam-5787	369	7	,	,	PUNCT
ejpam-5787	369	8	3(06):1529–1555	3(06):1529–1555	NUM
ejpam-5787	369	9	,	,	PUNCT
ejpam-5787	369	10	1993	1993	NUM
ejpam-5787	369	11	.	.	PUNCT
ejpam-5787	370	1	[	[	X
ejpam-5787	370	2	19	19	NUM
ejpam-5787	370	3	]	]	X
ejpam-5787	370	4	karl	karl	PROPN
ejpam-5787	370	5	h	h	PROPN
ejpam-5787	370	6	m	m	PROPN
ejpam-5787	370	7	nyman	nyman	PROPN
ejpam-5787	370	8	,	,	PUNCT
ejpam-5787	370	9	peter	peter	PROPN
ejpam-5787	370	10	ashwin	ashwin	PROPN
ejpam-5787	370	11	,	,	PUNCT
ejpam-5787	370	12	and	and	CCONJ
ejpam-5787	370	13	peter	peter	PROPN
ejpam-5787	370	14	d	d	PROPN
ejpam-5787	370	15	ditlevsen	ditlevsen	PROPN
ejpam-5787	370	16	.	.	PUNCT
ejpam-5787	371	1	bifurcation	bifurcation	NOUN
ejpam-5787	371	2	of	of	ADP
ejpam-5787	371	3	critical	critical	ADJ
ejpam-5787	371	4	sets	set	NOUN
ejpam-5787	371	5	and	and	CCONJ
ejpam-5787	371	6	relaxation	relaxation	NOUN
ejpam-5787	371	7	oscillations	oscillation	NOUN
ejpam-5787	371	8	in	in	ADP
ejpam-5787	371	9	singular	singular	ADJ
ejpam-5787	371	10	fast	fast	ADJ
ejpam-5787	371	11	-	-	PUNCT
ejpam-5787	371	12	slow	slow	NOUN
ejpam-5787	371	13	systems	system	NOUN
ejpam-5787	371	14	.	.	PUNCT
ejpam-5787	372	1	nonlinearity	nonlinearity	NOUN
ejpam-5787	372	2	,	,	PUNCT
ejpam-5787	372	3	33(6):2853	33(6):2853	NUM
ejpam-5787	372	4	–	–	PUNCT
ejpam-5787	372	5	2904	2904	NUM
ejpam-5787	372	6	,	,	PUNCT
ejpam-5787	372	7	apr	apr	NOUN
ejpam-5787	372	8	2020	2020	NUM
ejpam-5787	372	9	.	.	PUNCT
ejpam-5787	373	1	[	[	X
ejpam-5787	373	2	20	20	NUM
ejpam-5787	373	3	]	]	X
ejpam-5787	373	4	arkady	arkady	PROPN
ejpam-5787	373	5	pikovsky	pikovsky	PROPN
ejpam-5787	373	6	,	,	PUNCT
ejpam-5787	373	7	jurgen	jurgen	PROPN
ejpam-5787	373	8	kurths	kurths	PROPN
ejpam-5787	373	9	,	,	PUNCT
ejpam-5787	373	10	michael	michael	PROPN
ejpam-5787	373	11	rosenblum	rosenblum	PROPN
ejpam-5787	373	12	,	,	PUNCT
ejpam-5787	373	13	and	and	CCONJ
ejpam-5787	373	14	jürgen	jürgen	PROPN
ejpam-5787	373	15	kurths	kurth	NOUN
ejpam-5787	373	16	.	.	PUNCT
ejpam-5787	374	1	synchronization	synchronization	NOUN
ejpam-5787	374	2	:	:	PUNCT
ejpam-5787	374	3	a	a	DET
ejpam-5787	374	4	universal	universal	ADJ
ejpam-5787	374	5	concept	concept	NOUN
ejpam-5787	374	6	in	in	ADP
ejpam-5787	374	7	nonlinear	nonlinear	ADJ
ejpam-5787	374	8	sciences	science	NOUN
ejpam-5787	374	9	,	,	PUNCT
ejpam-5787	374	10	volume	volume	NOUN
ejpam-5787	374	11	12	12	NUM
ejpam-5787	374	12	.	.	PUNCT
ejpam-5787	375	1	cambridge	cambridge	PROPN
ejpam-5787	375	2	university	university	PROPN
ejpam-5787	375	3	press	press	NOUN
ejpam-5787	375	4	,	,	PUNCT
ejpam-5787	375	5	2003	2003	NUM
ejpam-5787	375	6	.	.	PUNCT
ejpam-5787	376	1	[	[	X
ejpam-5787	376	2	21	21	NUM
ejpam-5787	376	3	]	]	X
ejpam-5787	376	4	arkady	arkady	PROPN
ejpam-5787	376	5	pikovsky	pikovsky	PROPN
ejpam-5787	376	6	,	,	PUNCT
ejpam-5787	376	7	michael	michael	PROPN
ejpam-5787	376	8	rosenblum	rosenblum	PROPN
ejpam-5787	376	9	,	,	PUNCT
ejpam-5787	376	10	and	and	CCONJ
ejpam-5787	376	11	jürgen	jürgen	PROPN
ejpam-5787	376	12	kurths	kurth	NOUN
ejpam-5787	376	13	.	.	PUNCT
ejpam-5787	377	1	synchronization	synchronization	NOUN
ejpam-5787	377	2	:	:	PUNCT
ejpam-5787	377	3	a	a	DET
ejpam-5787	377	4	universal	universal	ADJ
ejpam-5787	377	5	concept	concept	NOUN
ejpam-5787	377	6	in	in	ADP
ejpam-5787	377	7	nonlinear	nonlinear	ADJ
ejpam-5787	377	8	sciences	sciences	PROPN
ejpam-5787	377	9	.	.	PUNCT
ejpam-5787	378	1	cambridge	cambridge	PROPN
ejpam-5787	378	2	nonlinear	nonlinear	PROPN
ejpam-5787	378	3	science	science	PROPN
ejpam-5787	378	4	series	series	PROPN
ejpam-5787	378	5	12	12	NUM
ejpam-5787	378	6	,	,	PUNCT
ejpam-5787	378	7	2003	2003	NUM
ejpam-5787	378	8	.	.	PUNCT
ejpam-5787	379	1	[	[	X
ejpam-5787	379	2	22	22	NUM
ejpam-5787	379	3	]	]	X
ejpam-5787	379	4	arkady	arkady	PROPN
ejpam-5787	379	5	s	s	PART
ejpam-5787	379	6	pikovsky	pikovsky	ADJ
ejpam-5787	379	7	,	,	PUNCT
ejpam-5787	379	8	ulrike	ulrike	NOUN
ejpam-5787	379	9	feudel	feudel	NOUN
ejpam-5787	379	10	,	,	PUNCT
ejpam-5787	379	11	and	and	CCONJ
ejpam-5787	379	12	sergey	sergey	PROPN
ejpam-5787	379	13	p	p	PROPN
ejpam-5787	379	14	kuznetsov	kuznetsov	PROPN
ejpam-5787	379	15	.	.	PUNCT
ejpam-5787	380	1	strange	strange	ADJ
ejpam-5787	380	2	nonchaotic	nonchaotic	ADJ
ejpam-5787	380	3	attractors	attractor	NOUN
ejpam-5787	380	4	:	:	PUNCT
ejpam-5787	380	5	dynamics	dynamic	NOUN
ejpam-5787	380	6	between	between	ADP
ejpam-5787	380	7	order	order	NOUN
ejpam-5787	380	8	and	and	CCONJ
ejpam-5787	380	9	chaos	chaos	NOUN
ejpam-5787	380	10	in	in	ADP
ejpam-5787	380	11	quasiperiodically	quasiperiodically	ADV
ejpam-5787	380	12	forced	force	VERB
ejpam-5787	380	13	systems	system	NOUN
ejpam-5787	380	14	,	,	PUNCT
ejpam-5787	380	15	volume	volume	NOUN
ejpam-5787	380	16	56	56	NUM
ejpam-5787	380	17	.	.	PUNCT
ejpam-5787	381	1	world	world	NOUN
ejpam-5787	381	2	scientific	scientific	PROPN
ejpam-5787	381	3	,	,	PUNCT
ejpam-5787	381	4	2006	2006	NUM
ejpam-5787	381	5	.	.	PUNCT
ejpam-5787	382	1	[	[	X
ejpam-5787	382	2	23	23	NUM
ejpam-5787	382	3	]	]	X
ejpam-5787	382	4	c.	c.	NOUN
ejpam-5787	382	5	rocsoreanu	rocsoreanu	PROPN
ejpam-5787	382	6	,	,	PUNCT
ejpam-5787	382	7	a.	a.	NOUN
ejpam-5787	382	8	georgescu	georgescu	NOUN
ejpam-5787	382	9	,	,	PUNCT
ejpam-5787	382	10	and	and	CCONJ
ejpam-5787	382	11	n.	n.	NOUN
ejpam-5787	382	12	giurgiteanu	giurgiteanu	PROPN
ejpam-5787	382	13	.	.	PUNCT
ejpam-5787	383	1	the	the	DET
ejpam-5787	383	2	fitzhugh	fitzhugh	PROPN
ejpam-5787	383	3	-	-	PUNCT
ejpam-5787	383	4	nagumo	nagumo	ADJ
ejpam-5787	383	5	model	model	NOUN
ejpam-5787	383	6	:	:	PUNCT
ejpam-5787	383	7	bifurcation	bifurcation	NOUN
ejpam-5787	383	8	and	and	CCONJ
ejpam-5787	383	9	dynamics	dynamic	NOUN
ejpam-5787	383	10	.	.	PUNCT
ejpam-5787	384	1	mathematical	mathematical	ADJ
ejpam-5787	384	2	modelling	modelling	NOUN
ejpam-5787	384	3	:	:	PUNCT
ejpam-5787	384	4	theory	theory	NOUN
ejpam-5787	384	5	and	and	CCONJ
ejpam-5787	384	6	applications	application	NOUN
ejpam-5787	384	7	.	.	PUNCT
ejpam-5787	385	1	springer	springer	PROPN
ejpam-5787	385	2	netherlands	netherlands	PROPN
ejpam-5787	385	3	,	,	PUNCT
ejpam-5787	385	4	2012	2012	NUM
ejpam-5787	385	5	.	.	PUNCT
ejpam-5787	386	1	[	[	X
ejpam-5787	386	2	24	24	NUM
ejpam-5787	386	3	]	]	X
ejpam-5787	386	4	nikolai	nikolai	PROPN
ejpam-5787	386	5	f	f	PROPN
ejpam-5787	386	6	rulkov	rulkov	PROPN
ejpam-5787	386	7	,	,	PUNCT
ejpam-5787	386	8	mikhail	mikhail	PROPN
ejpam-5787	386	9	m	m	NOUN
ejpam-5787	386	10	sushchik	sushchik	NOUN
ejpam-5787	386	11	,	,	PUNCT
ejpam-5787	386	12	lev	lev	NOUN
ejpam-5787	386	13	s	s	PART
ejpam-5787	386	14	tsimring	tsimring	NOUN
ejpam-5787	386	15	,	,	PUNCT
ejpam-5787	386	16	and	and	CCONJ
ejpam-5787	386	17	henry	henry	PROPN
ejpam-5787	386	18	di	di	PROPN
ejpam-5787	386	19	abarbanel	abarbanel	PROPN
ejpam-5787	386	20	.	.	PUNCT
ejpam-5787	387	1	generalized	generalized	ADJ
ejpam-5787	387	2	synchronization	synchronization	NOUN
ejpam-5787	387	3	of	of	ADP
ejpam-5787	387	4	chaos	chaos	NOUN
ejpam-5787	387	5	in	in	ADP
ejpam-5787	387	6	directionally	directionally	ADV
ejpam-5787	387	7	coupled	couple	VERB
ejpam-5787	387	8	chaotic	chaotic	ADJ
ejpam-5787	387	9	systems	system	NOUN
ejpam-5787	387	10	.	.	PUNCT
ejpam-5787	388	1	physical	physical	ADJ
ejpam-5787	388	2	review	review	PROPN
ejpam-5787	388	3	e	e	PROPN
ejpam-5787	388	4	,	,	PUNCT
ejpam-5787	388	5	51(2):980	51(2):980	PROPN
ejpam-5787	388	6	,	,	PUNCT
ejpam-5787	388	7	1995	1995	NUM
ejpam-5787	388	8	.	.	PUNCT
ejpam-5787	389	1	[	[	X
ejpam-5787	389	2	25	25	NUM
ejpam-5787	389	3	]	]	X
ejpam-5787	389	4	peter	peter	PROPN
ejpam-5787	389	5	szmolyan	szmolyan	PROPN
ejpam-5787	389	6	and	and	CCONJ
ejpam-5787	389	7	martin	martin	PROPN
ejpam-5787	389	8	wechselberger	wechselberger	NOUN
ejpam-5787	389	9	.	.	PUNCT
ejpam-5787	390	1	canards	canard	NOUN
ejpam-5787	390	2	in	in	ADP
ejpam-5787	390	3	r3	r3	PROPN
ejpam-5787	390	4	.	.	PUNCT
ejpam-5787	391	1	journal	journal	PROPN
ejpam-5787	391	2	of	of	ADP
ejpam-5787	391	3	differential	differential	ADJ
ejpam-5787	391	4	equations	equation	NOUN
ejpam-5787	391	5	,	,	PUNCT
ejpam-5787	391	6	177(2):419–453	177(2):419–453	NUM
ejpam-5787	391	7	,	,	PUNCT
ejpam-5787	391	8	2001	2001	NUM
ejpam-5787	391	9	.	.	PUNCT
ejpam-5787	392	1	[	[	X
ejpam-5787	392	2	26	26	NUM
ejpam-5787	392	3	]	]	X
ejpam-5787	392	4	peter	peter	PROPN
ejpam-5787	392	5	szmolyan	szmolyan	PROPN
ejpam-5787	392	6	and	and	CCONJ
ejpam-5787	392	7	martin	martin	PROPN
ejpam-5787	392	8	wechselberger	wechselberger	NOUN
ejpam-5787	392	9	.	.	PUNCT
ejpam-5787	393	1	relaxation	relaxation	NOUN
ejpam-5787	393	2	oscillations	oscillation	NOUN
ejpam-5787	393	3	in	in	ADP
ejpam-5787	393	4	r3	r3	PROPN
ejpam-5787	393	5	.	.	PUNCT
ejpam-5787	394	1	journal	journal	PROPN
ejpam-5787	394	2	of	of	ADP
ejpam-5787	394	3	differential	differential	ADJ
ejpam-5787	394	4	equations	equation	NOUN
ejpam-5787	394	5	,	,	PUNCT
ejpam-5787	394	6	200(1):69–104	200(1):69–104	NOUN
ejpam-5787	394	7	,	,	PUNCT
ejpam-5787	394	8	2004	2004	NUM
ejpam-5787	394	9	.	.	PUNCT
ejpam-5787	395	1	[	[	X
ejpam-5787	395	2	27	27	NUM
ejpam-5787	395	3	]	]	X
ejpam-5787	395	4	balth	balth	NOUN
ejpam-5787	395	5	van	van	PROPN
ejpam-5787	395	6	der	der	PROPN
ejpam-5787	395	7	pol	pol	PROPN
ejpam-5787	395	8	.	.	PUNCT
ejpam-5787	396	1	on	on	ADP
ejpam-5787	396	2	“	"	PUNCT
ejpam-5787	396	3	relaxation	relaxation	NOUN
ejpam-5787	396	4	-	-	PUNCT
ejpam-5787	396	5	oscillations	oscillation	NOUN
ejpam-5787	396	6	”	"	PUNCT
ejpam-5787	396	7	.	.	PUNCT
ejpam-5787	397	1	the	the	DET
ejpam-5787	397	2	london	london	PROPN
ejpam-5787	397	3	,	,	PUNCT
ejpam-5787	397	4	edinburgh	edinburgh	PROPN
ejpam-5787	397	5	,	,	PUNCT
ejpam-5787	397	6	and	and	CCONJ
ejpam-5787	397	7	dublin	dublin	PROPN
ejpam-5787	397	8	philosophical	philosophical	PROPN
ejpam-5787	397	9	magazine	magazine	NOUN
ejpam-5787	397	10	and	and	CCONJ
ejpam-5787	397	11	journal	journal	NOUN
ejpam-5787	397	12	of	of	ADP
ejpam-5787	397	13	science	science	NOUN
ejpam-5787	397	14	,	,	PUNCT
ejpam-5787	397	15	2(11):978–992	2(11):978–992	NUM
ejpam-5787	397	16	,	,	PUNCT
ejpam-5787	397	17	1926	1926	NUM
ejpam-5787	397	18	.	.	PUNCT
ejpam-5787	398	1	[	[	X
ejpam-5787	398	2	28	28	NUM
ejpam-5787	398	3	]	]	X
ejpam-5787	398	4	balth	balth	NOUN
ejpam-5787	398	5	van	van	PROPN
ejpam-5787	398	6	der	der	PROPN
ejpam-5787	398	7	pol	pol	PROPN
ejpam-5787	398	8	and	and	CCONJ
ejpam-5787	398	9	jan	jan	PROPN
ejpam-5787	398	10	van	van	PROPN
ejpam-5787	398	11	der	der	PROPN
ejpam-5787	398	12	mark	mark	PROPN
ejpam-5787	398	13	.	.	PUNCT
ejpam-5787	399	1	frequency	frequency	NOUN
ejpam-5787	399	2	demultiplication	demultiplication	NOUN
ejpam-5787	399	3	.	.	PUNCT
ejpam-5787	400	1	nature	nature	NOUN
ejpam-5787	400	2	,	,	PUNCT
ejpam-5787	400	3	120(3019):363–364	120(3019):363–364	NUM
ejpam-5787	400	4	,	,	PUNCT
ejpam-5787	400	5	1927	1927	NUM
ejpam-5787	400	6	.	.	PUNCT
ejpam-5787	401	1	[	[	X
ejpam-5787	401	2	29	29	NUM
ejpam-5787	401	3	]	]	X
ejpam-5787	401	4	balth	balth	NOUN
ejpam-5787	401	5	van	van	PROPN
ejpam-5787	401	6	der	der	PROPN
ejpam-5787	401	7	pol	pol	PROPN
ejpam-5787	401	8	and	and	CCONJ
ejpam-5787	401	9	jan	jan	PROPN
ejpam-5787	401	10	van	van	PROPN
ejpam-5787	401	11	der	der	PROPN
ejpam-5787	401	12	mark	mark	NOUN
ejpam-5787	401	13	.	.	PUNCT
ejpam-5787	402	1	lxxii	lxxii	PROPN
ejpam-5787	402	2	.	.	PUNCT
ejpam-5787	403	1	the	the	DET
ejpam-5787	403	2	heartbeat	heartbeat	NOUN
ejpam-5787	403	3	considered	consider	VERB
ejpam-5787	403	4	as	as	ADP
ejpam-5787	403	5	a	a	DET
ejpam-5787	403	6	relaxation	relaxation	NOUN
ejpam-5787	403	7	oscillation	oscillation	NOUN
ejpam-5787	403	8	,	,	PUNCT
ejpam-5787	403	9	and	and	CCONJ
ejpam-5787	403	10	an	an	DET
ejpam-5787	403	11	electrical	electrical	ADJ
ejpam-5787	403	12	model	model	NOUN
ejpam-5787	403	13	of	of	ADP
ejpam-5787	403	14	the	the	DET
ejpam-5787	403	15	heart	heart	NOUN
ejpam-5787	403	16	.	.	PUNCT
ejpam-5787	404	1	the	the	DET
ejpam-5787	404	2	london	london	PROPN
ejpam-5787	404	3	,	,	PUNCT
ejpam-5787	404	4	edinburgh	edinburgh	PROPN
ejpam-5787	404	5	,	,	PUNCT
ejpam-5787	404	6	and	and	CCONJ
ejpam-5787	404	7	dublin	dublin	PROPN
ejpam-5787	404	8	philosophical	philosophical	PROPN
ejpam-5787	404	9	magazine	magazine	NOUN
ejpam-5787	404	10	and	and	CCONJ
ejpam-5787	404	11	journal	journal	NOUN
ejpam-5787	404	12	of	of	ADP
ejpam-5787	404	13	science	science	NOUN
ejpam-5787	404	14	,	,	PUNCT
ejpam-5787	404	15	6(38):763–775	6(38):763–775	NOUN
ejpam-5787	404	16	,	,	PUNCT
ejpam-5787	404	17	1928	1928	NUM
ejpam-5787	404	18	.	.	PUNCT
ejpam-5787	405	1	[	[	X
ejpam-5787	405	2	30	30	NUM
ejpam-5787	405	3	]	]	PUNCT
ejpam-5787	405	4	ferdinand	ferdinand	NOUN
ejpam-5787	405	5	verhulst	verhulst	PROPN
ejpam-5787	405	6	and	and	CCONJ
ejpam-5787	405	7	taoufik	taoufik	ADJ
ejpam-5787	405	8	bakri	bakri	NOUN
ejpam-5787	405	9	.	.	PUNCT
ejpam-5787	406	1	the	the	DET
ejpam-5787	406	2	dynamics	dynamic	NOUN
ejpam-5787	406	3	of	of	ADP
ejpam-5787	406	4	slow	slow	ADJ
ejpam-5787	406	5	manifolds	manifold	NOUN
ejpam-5787	406	6	.	.	PUNCT
ejpam-5787	407	1	journal	journal	PROPN
ejpam-5787	407	2	of	of	ADP
ejpam-5787	407	3	i.	i.	PROPN
ejpam-5787	407	4	alraddadi	alraddadi	PROPN
ejpam-5787	407	5	/	/	SYM
ejpam-5787	407	6	eur	eur	PROPN
ejpam-5787	407	7	.	.	PUNCT
ejpam-5787	408	1	j.	j.	PROPN
ejpam-5787	408	2	pure	pure	PROPN
ejpam-5787	408	3	appl	appl	PROPN
ejpam-5787	408	4	.	.	PROPN
ejpam-5787	408	5	math	math	PROPN
ejpam-5787	408	6	,	,	PUNCT
ejpam-5787	408	7	18	18	NUM
ejpam-5787	408	8	(	(	PUNCT
ejpam-5787	408	9	1	1	NUM
ejpam-5787	408	10	)	)	PUNCT
ejpam-5787	408	11	(	(	PUNCT
ejpam-5787	408	12	2025	2025	NUM
ejpam-5787	408	13	)	)	PUNCT
ejpam-5787	408	14	,	,	PUNCT
ejpam-5787	408	15	5787	5787	NUM
ejpam-5787	408	16	23	23	NUM
ejpam-5787	408	17	of	of	ADP
ejpam-5787	408	18	23	23	NUM
ejpam-5787	408	19	the	the	DET
ejpam-5787	408	20	indonesian	indonesian	ADJ
ejpam-5787	408	21	mathematical	mathematical	ADJ
ejpam-5787	408	22	society	society	NOUN
ejpam-5787	408	23	,	,	PUNCT
ejpam-5787	408	24	13:1–16	13:1–16	NUM
ejpam-5787	408	25	,	,	PUNCT
ejpam-5787	408	26	2007	2007	NUM
ejpam-5787	408	27	.	.	PUNCT
ejpam-5787	409	1	[	[	X
ejpam-5787	409	2	31	31	NUM
ejpam-5787	409	3	]	]	PUNCT
ejpam-5787	409	4	martin	martin	PROPN
ejpam-5787	409	5	wechselberger	wechselberger	NOUN
ejpam-5787	409	6	.	.	PUNCT
ejpam-5787	410	1	à	à	PROPN
ejpam-5787	410	2	propos	propos	PROPN
ejpam-5787	410	3	de	de	PROPN
ejpam-5787	410	4	canards	canard	NOUN
ejpam-5787	410	5	(	(	PUNCT
ejpam-5787	410	6	apropos	apropos	NOUN
ejpam-5787	410	7	canards	canard	NOUN
ejpam-5787	410	8	)	)	PUNCT
ejpam-5787	410	9	.	.	PUNCT
ejpam-5787	411	1	transactions	transaction	NOUN
ejpam-5787	411	2	of	of	ADP
ejpam-5787	411	3	the	the	DET
ejpam-5787	411	4	american	american	PROPN
ejpam-5787	411	5	mathematical	mathematical	PROPN
ejpam-5787	411	6	society	society	NOUN
ejpam-5787	411	7	,	,	PUNCT
ejpam-5787	411	8	364(6):3289–3309	364(6):3289–3309	PROPN
ejpam-5787	411	9	,	,	PUNCT
ejpam-5787	411	10	2012	2012	NUM
ejpam-5787	411	11	.	.	PUNCT