id	sid	tid	token	lemma	pos
ejpam-6968	1	1	european	european	PROPN
ejpam-6968	1	2	journal	journal	PROPN
ejpam-6968	1	3	of	of	ADP
ejpam-6968	1	4	pure	pure	ADJ
ejpam-6968	1	5	and	and	CCONJ
ejpam-6968	1	6	applied	applied	ADJ
ejpam-6968	1	7	mathematics	mathematic	NOUN
ejpam-6968	1	8	2025	2025	NUM
ejpam-6968	1	9	,	,	PUNCT
ejpam-6968	1	10	vol	vol	NOUN
ejpam-6968	1	11	.	.	PROPN
ejpam-6968	1	12	18	18	NUM
ejpam-6968	1	13	,	,	PUNCT
ejpam-6968	1	14	issue	issue	NOUN
ejpam-6968	1	15	4	4	NUM
ejpam-6968	1	16	,	,	PUNCT
ejpam-6968	1	17	article	article	NOUN
ejpam-6968	1	18	number	number	NOUN
ejpam-6968	1	19	6968	6968	NUM
ejpam-6968	1	20	issn	issn	VERB
ejpam-6968	1	21	1307	1307	NUM
ejpam-6968	1	22	-	-	SYM
ejpam-6968	1	23	5543	5543	NUM
ejpam-6968	1	24	–	–	PUNCT
ejpam-6968	1	25	ejpam.com	ejpam.com	X
ejpam-6968	1	26	published	publish	VERB
ejpam-6968	1	27	by	by	ADP
ejpam-6968	1	28	new	new	PROPN
ejpam-6968	1	29	york	york	PROPN
ejpam-6968	1	30	business	business	PROPN
ejpam-6968	1	31	global	global	ADJ
ejpam-6968	1	32	bifurcations	bifurcation	NOUN
ejpam-6968	1	33	,	,	PUNCT
ejpam-6968	1	34	hidden	hidden	ADJ
ejpam-6968	1	35	attractors	attractor	NOUN
ejpam-6968	1	36	,	,	PUNCT
ejpam-6968	1	37	and	and	CCONJ
ejpam-6968	1	38	chaos	chaos	NOUN
ejpam-6968	1	39	in	in	ADP
ejpam-6968	1	40	a	a	DET
ejpam-6968	1	41	nonlinear	nonlinear	ADJ
ejpam-6968	1	42	three	three	NUM
ejpam-6968	1	43	-	-	PUNCT
ejpam-6968	1	44	dimensional	dimensional	ADJ
ejpam-6968	1	45	system	system	NOUN
ejpam-6968	1	46	hafidh	hafidh	NOUN
ejpam-6968	1	47	khoerul	khoerul	PROPN
ejpam-6968	1	48	fata1	fata1	PROPN
ejpam-6968	1	49	,	,	PUNCT
ejpam-6968	1	50	nurcahya	nurcahya	ADJ
ejpam-6968	1	51	yulian	yulian	ADJ
ejpam-6968	1	52	ashar1,∗	ashar1,∗	NOUN
ejpam-6968	1	53	1	1	NUM
ejpam-6968	1	54	department	department	NOUN
ejpam-6968	1	55	of	of	ADP
ejpam-6968	1	56	mathematics	mathematic	NOUN
ejpam-6968	1	57	,	,	PUNCT
ejpam-6968	1	58	faculty	faculty	NOUN
ejpam-6968	1	59	of	of	ADP
ejpam-6968	1	60	science	science	NOUN
ejpam-6968	1	61	and	and	CCONJ
ejpam-6968	1	62	mathematics	mathematic	NOUN
ejpam-6968	1	63	,	,	PUNCT
ejpam-6968	1	64	universitas	universita	NOUN
ejpam-6968	1	65	diponegoro	diponegoro	PROPN
ejpam-6968	1	66	,	,	PUNCT
ejpam-6968	1	67	semarang	semarang	PROPN
ejpam-6968	1	68	,	,	PUNCT
ejpam-6968	1	69	50275	50275	NUM
ejpam-6968	1	70	,	,	PUNCT
ejpam-6968	1	71	indonesia	indonesia	PROPN
ejpam-6968	1	72	abstract	abstract	NOUN
ejpam-6968	1	73	.	.	PUNCT
ejpam-6968	2	1	this	this	DET
ejpam-6968	2	2	research	research	NOUN
ejpam-6968	2	3	shows	show	VERB
ejpam-6968	2	4	an	an	DET
ejpam-6968	2	5	analytical	analytical	ADJ
ejpam-6968	2	6	and	and	CCONJ
ejpam-6968	2	7	numerical	numerical	ADJ
ejpam-6968	2	8	analysis	analysis	NOUN
ejpam-6968	2	9	of	of	ADP
ejpam-6968	2	10	a	a	DET
ejpam-6968	2	11	nonlinear	nonlinear	ADJ
ejpam-6968	2	12	three	three	NUM
ejpam-6968	2	13	-	-	PUNCT
ejpam-6968	2	14	dimensional	dimensional	ADJ
ejpam-6968	2	15	dynamical	dynamical	ADJ
ejpam-6968	2	16	system	system	NOUN
ejpam-6968	2	17	controlled	control	VERB
ejpam-6968	2	18	by	by	ADP
ejpam-6968	2	19	a	a	DET
ejpam-6968	2	20	unique	unique	ADJ
ejpam-6968	2	21	control	control	NOUN
ejpam-6968	2	22	parameter	parameter	NOUN
ejpam-6968	2	23	,	,	PUNCT
ejpam-6968	2	24	named	name	VERB
ejpam-6968	2	25	α	α	X
ejpam-6968	2	26	.	.	PUNCT
ejpam-6968	3	1	the	the	DET
ejpam-6968	3	2	system	system	NOUN
ejpam-6968	3	3	exhibits	exhibit	VERB
ejpam-6968	3	4	selfexcited	selfexcite	VERB
ejpam-6968	3	5	oscillations	oscillation	NOUN
ejpam-6968	3	6	through	through	ADP
ejpam-6968	3	7	local	local	ADJ
ejpam-6968	3	8	bifurcations	bifurcation	NOUN
ejpam-6968	3	9	for	for	ADP
ejpam-6968	3	10	negative	negative	ADJ
ejpam-6968	3	11	α	α	NOUN
ejpam-6968	3	12	,	,	PUNCT
ejpam-6968	3	13	including	include	VERB
ejpam-6968	3	14	saddle	saddle	NOUN
ejpam-6968	3	15	-	-	PUNCT
ejpam-6968	3	16	node	node	NOUN
ejpam-6968	3	17	and	and	CCONJ
ejpam-6968	3	18	supercritical	supercritical	ADJ
ejpam-6968	3	19	hopf	hopf	ADJ
ejpam-6968	3	20	bifurcations	bifurcation	NOUN
ejpam-6968	3	21	,	,	PUNCT
ejpam-6968	3	22	leading	lead	VERB
ejpam-6968	3	23	to	to	ADP
ejpam-6968	3	24	periodic	periodic	ADJ
ejpam-6968	3	25	orbits	orbit	NOUN
ejpam-6968	3	26	and	and	CCONJ
ejpam-6968	3	27	a	a	DET
ejpam-6968	3	28	sequence	sequence	NOUN
ejpam-6968	3	29	of	of	ADP
ejpam-6968	3	30	period	period	NOUN
ejpam-6968	3	31	-	-	PUNCT
ejpam-6968	3	32	doubling	double	VERB
ejpam-6968	3	33	transitions	transition	NOUN
ejpam-6968	3	34	into	into	ADP
ejpam-6968	3	35	chaos	chaos	NOUN
ejpam-6968	3	36	.	.	PUNCT
ejpam-6968	4	1	on	on	ADP
ejpam-6968	4	2	the	the	DET
ejpam-6968	4	3	other	other	ADJ
ejpam-6968	4	4	hand	hand	NOUN
ejpam-6968	4	5	,	,	PUNCT
ejpam-6968	4	6	when	when	SCONJ
ejpam-6968	4	7	α	α	PROPN
ejpam-6968	4	8	is	be	AUX
ejpam-6968	4	9	negative	negative	ADJ
ejpam-6968	4	10	and	and	CCONJ
ejpam-6968	4	11	there	there	PRON
ejpam-6968	4	12	are	be	VERB
ejpam-6968	4	13	no	no	DET
ejpam-6968	4	14	equilibrium	equilibrium	NOUN
ejpam-6968	4	15	points	point	NOUN
ejpam-6968	4	16	,	,	PUNCT
ejpam-6968	4	17	the	the	DET
ejpam-6968	4	18	system	system	NOUN
ejpam-6968	4	19	shows	show	VERB
ejpam-6968	4	20	long	long	ADJ
ejpam-6968	4	21	term	term	NOUN
ejpam-6968	4	22	oscillations	oscillation	NOUN
ejpam-6968	4	23	that	that	PRON
ejpam-6968	4	24	last	last	VERB
ejpam-6968	4	25	for	for	ADP
ejpam-6968	4	26	a	a	DET
ejpam-6968	4	27	long	long	ADJ
ejpam-6968	4	28	time	time	NOUN
ejpam-6968	4	29	through	through	ADP
ejpam-6968	4	30	hidden	hidden	ADJ
ejpam-6968	4	31	attractors	attractor	NOUN
ejpam-6968	4	32	—	—	PUNCT
ejpam-6968	4	33	bounded	bound	VERB
ejpam-6968	4	34	chaotic	chaotic	ADJ
ejpam-6968	4	35	dynamics	dynamic	NOUN
ejpam-6968	4	36	with	with	ADP
ejpam-6968	4	37	basins	basin	NOUN
ejpam-6968	4	38	of	of	ADP
ejpam-6968	4	39	attraction	attraction	NOUN
ejpam-6968	4	40	that	that	PRON
ejpam-6968	4	41	are	be	AUX
ejpam-6968	4	42	not	not	PART
ejpam-6968	4	43	connected	connect	VERB
ejpam-6968	4	44	to	to	ADP
ejpam-6968	4	45	any	any	DET
ejpam-6968	4	46	equilibrium	equilibrium	NOUN
ejpam-6968	4	47	.	.	PUNCT
ejpam-6968	5	1	numerical	numerical	ADJ
ejpam-6968	5	2	continuation	continuation	PROPN
ejpam-6968	5	3	and	and	CCONJ
ejpam-6968	5	4	lyapunov	lyapunov	PROPN
ejpam-6968	5	5	spectrum	spectrum	VERB
ejpam-6968	5	6	analysis	analysis	NOUN
ejpam-6968	5	7	confirm	confirm	VERB
ejpam-6968	5	8	the	the	DET
ejpam-6968	5	9	simultaneous	simultaneous	ADJ
ejpam-6968	5	10	existence	existence	NOUN
ejpam-6968	5	11	of	of	ADP
ejpam-6968	5	12	periodic	periodic	ADJ
ejpam-6968	5	13	,	,	PUNCT
ejpam-6968	5	14	quasiperiodic	quasiperiodic	ADJ
ejpam-6968	5	15	,	,	PUNCT
ejpam-6968	5	16	and	and	CCONJ
ejpam-6968	5	17	chaotic	chaotic	ADJ
ejpam-6968	5	18	regimes	regime	NOUN
ejpam-6968	5	19	.	.	PUNCT
ejpam-6968	6	1	the	the	DET
ejpam-6968	6	2	results	result	NOUN
ejpam-6968	6	3	demonstrate	demonstrate	VERB
ejpam-6968	6	4	the	the	DET
ejpam-6968	6	5	intricate	intricate	ADJ
ejpam-6968	6	6	interplay	interplay	NOUN
ejpam-6968	6	7	between	between	ADP
ejpam-6968	6	8	local	local	ADJ
ejpam-6968	6	9	bifurcations	bifurcation	NOUN
ejpam-6968	6	10	and	and	CCONJ
ejpam-6968	6	11	global	global	ADJ
ejpam-6968	6	12	nonlinear	nonlinear	ADJ
ejpam-6968	6	13	frameworks	framework	NOUN
ejpam-6968	6	14	,	,	PUNCT
ejpam-6968	6	15	emphasizing	emphasize	VERB
ejpam-6968	6	16	the	the	DET
ejpam-6968	6	17	distinctive	distinctive	ADJ
ejpam-6968	6	18	routes	route	NOUN
ejpam-6968	6	19	to	to	PART
ejpam-6968	6	20	chaos	chaos	VERB
ejpam-6968	6	21	and	and	CCONJ
ejpam-6968	6	22	the	the	DET
ejpam-6968	6	23	emergence	emergence	NOUN
ejpam-6968	6	24	of	of	ADP
ejpam-6968	6	25	hidden	hide	VERB
ejpam-6968	6	26	dynamics	dynamic	NOUN
ejpam-6968	6	27	in	in	ADP
ejpam-6968	6	28	systems	system	NOUN
ejpam-6968	6	29	lacking	lack	VERB
ejpam-6968	6	30	stability	stability	NOUN
ejpam-6968	6	31	.	.	PUNCT
ejpam-6968	7	1	2020	2020	NUM
ejpam-6968	7	2	mathematics	mathematic	NOUN
ejpam-6968	7	3	subject	subject	NOUN
ejpam-6968	7	4	classifications	classification	NOUN
ejpam-6968	7	5	:	:	PUNCT
ejpam-6968	7	6	34c23	34c23	NUM
ejpam-6968	7	7	,	,	PUNCT
ejpam-6968	7	8	34c28	34c28	NUM
ejpam-6968	7	9	,	,	PUNCT
ejpam-6968	7	10	34d45	34d45	NUM
ejpam-6968	7	11	,	,	PUNCT
ejpam-6968	7	12	37g10	37g10	NUM
ejpam-6968	7	13	key	key	ADJ
ejpam-6968	7	14	words	word	NOUN
ejpam-6968	7	15	and	and	CCONJ
ejpam-6968	7	16	phrases	phrase	NOUN
ejpam-6968	7	17	:	:	PUNCT
ejpam-6968	7	18	hidden	hide	VERB
ejpam-6968	7	19	chaos	chaos	NOUN
ejpam-6968	7	20	,	,	PUNCT
ejpam-6968	7	21	period	period	NOUN
ejpam-6968	7	22	-	-	PUNCT
ejpam-6968	7	23	doubling	double	VERB
ejpam-6968	7	24	bifurcation	bifurcation	NOUN
ejpam-6968	7	25	,	,	PUNCT
ejpam-6968	7	26	nonlinear	nonlinear	ADJ
ejpam-6968	7	27	dynamical	dynamical	ADJ
ejpam-6968	7	28	systems	system	NOUN
ejpam-6968	7	29	1	1	NUM
ejpam-6968	7	30	.	.	PUNCT
ejpam-6968	8	1	introduction	introduction	NOUN
ejpam-6968	8	2	nonlinear	nonlinear	ADJ
ejpam-6968	8	3	dynamical	dynamical	ADJ
ejpam-6968	8	4	systems	system	NOUN
ejpam-6968	8	5	are	be	AUX
ejpam-6968	8	6	essential	essential	ADJ
ejpam-6968	8	7	for	for	ADP
ejpam-6968	8	8	modeling	model	VERB
ejpam-6968	8	9	complex	complex	ADJ
ejpam-6968	8	10	behaviors	behavior	NOUN
ejpam-6968	8	11	in	in	ADP
ejpam-6968	8	12	physics	physics	NOUN
ejpam-6968	8	13	,	,	PUNCT
ejpam-6968	8	14	biology	biology	NOUN
ejpam-6968	8	15	,	,	PUNCT
ejpam-6968	8	16	engineering	engineering	NOUN
ejpam-6968	8	17	,	,	PUNCT
ejpam-6968	8	18	and	and	CCONJ
ejpam-6968	8	19	economics	economic	NOUN
ejpam-6968	8	20	[	[	X
ejpam-6968	8	21	1–5	1–5	X
ejpam-6968	8	22	]	]	X
ejpam-6968	8	23	.	.	PUNCT
ejpam-6968	9	1	unlike	unlike	ADP
ejpam-6968	9	2	linear	linear	PROPN
ejpam-6968	9	3	systems	system	NOUN
ejpam-6968	9	4	,	,	PUNCT
ejpam-6968	9	5	nonlinear	nonlinear	ADJ
ejpam-6968	9	6	systems	system	NOUN
ejpam-6968	9	7	exhibit	exhibit	VERB
ejpam-6968	9	8	sensitivity	sensitivity	NOUN
ejpam-6968	9	9	to	to	ADP
ejpam-6968	9	10	initial	initial	ADJ
ejpam-6968	9	11	conditions	condition	NOUN
ejpam-6968	9	12	and	and	CCONJ
ejpam-6968	9	13	parameters	parameter	NOUN
ejpam-6968	9	14	,	,	PUNCT
ejpam-6968	9	15	often	often	ADV
ejpam-6968	9	16	leading	lead	VERB
ejpam-6968	9	17	to	to	ADP
ejpam-6968	9	18	significant	significant	ADJ
ejpam-6968	9	19	changes	change	NOUN
ejpam-6968	9	20	in	in	ADP
ejpam-6968	9	21	behavior	behavior	NOUN
ejpam-6968	9	22	.	.	PUNCT
ejpam-6968	10	1	this	this	DET
ejpam-6968	10	2	sensitivity	sensitivity	NOUN
ejpam-6968	10	3	makes	make	VERB
ejpam-6968	10	4	rise	rise	NOUN
ejpam-6968	10	5	to	to	ADP
ejpam-6968	10	6	phenomena	phenomena	NOUN
ejpam-6968	10	7	such	such	ADJ
ejpam-6968	10	8	as	as	ADP
ejpam-6968	10	9	double	double	ADJ
ejpam-6968	10	10	equilibria	equilibrium	NOUN
ejpam-6968	10	11	,	,	PUNCT
ejpam-6968	10	12	limit	limit	NOUN
ejpam-6968	10	13	cycles	cycle	NOUN
ejpam-6968	10	14	,	,	PUNCT
ejpam-6968	10	15	bifurcations	bifurcation	NOUN
ejpam-6968	10	16	,	,	PUNCT
ejpam-6968	10	17	quasi	quasi	ADJ
ejpam-6968	10	18	-	-	NOUN
ejpam-6968	10	19	periodicity	periodicity	NOUN
ejpam-6968	10	20	,	,	PUNCT
ejpam-6968	10	21	and	and	CCONJ
ejpam-6968	10	22	chaos	chaos	NOUN
ejpam-6968	10	23	[	[	X
ejpam-6968	10	24	6	6	NUM
ejpam-6968	10	25	]	]	PUNCT
ejpam-6968	10	26	.	.	PUNCT
ejpam-6968	11	1	knowing	know	VERB
ejpam-6968	11	2	how	how	SCONJ
ejpam-6968	11	3	system	system	NOUN
ejpam-6968	11	4	structure	structure	NOUN
ejpam-6968	11	5	evolves	evolve	VERB
ejpam-6968	11	6	with	with	ADP
ejpam-6968	11	7	parameters	parameter	NOUN
ejpam-6968	11	8	is	be	AUX
ejpam-6968	11	9	very	very	ADV
ejpam-6968	11	10	important	important	ADJ
ejpam-6968	11	11	for	for	ADP
ejpam-6968	11	12	forcasting	forcaste	VERB
ejpam-6968	11	13	and	and	CCONJ
ejpam-6968	11	14	mantaining	mantaine	VERB
ejpam-6968	11	15	long	long	ADJ
ejpam-6968	11	16	-	-	PUNCT
ejpam-6968	11	17	term	term	NOUN
ejpam-6968	11	18	dynamics	dynamic	NOUN
ejpam-6968	11	19	.	.	PUNCT
ejpam-6968	12	1	to	to	PART
ejpam-6968	12	2	study	study	VERB
ejpam-6968	12	3	about	about	ADP
ejpam-6968	12	4	nonlinear	nonlinear	ADJ
ejpam-6968	12	5	phenomena	phenomenon	NOUN
ejpam-6968	12	6	gives	give	VERB
ejpam-6968	12	7	practical	practical	ADJ
ejpam-6968	12	8	insights	insight	NOUN
ejpam-6968	12	9	across	across	ADP
ejpam-6968	12	10	fields	field	NOUN
ejpam-6968	12	11	such	such	ADJ
ejpam-6968	12	12	as	as	ADP
ejpam-6968	12	13	population	population	NOUN
ejpam-6968	12	14	dynamics	dynamic	NOUN
ejpam-6968	12	15	[	[	X
ejpam-6968	12	16	7	7	NUM
ejpam-6968	12	17	]	]	PUNCT
ejpam-6968	12	18	,	,	PUNCT
ejpam-6968	12	19	electronic	electronic	ADJ
ejpam-6968	12	20	circuits	circuit	NOUN
ejpam-6968	12	21	[	[	X
ejpam-6968	12	22	8	8	NUM
ejpam-6968	12	23	]	]	PUNCT
ejpam-6968	12	24	,	,	PUNCT
ejpam-6968	12	25	climate	climate	NOUN
ejpam-6968	12	26	change	change	NOUN
ejpam-6968	12	27	variability	variability	NOUN
ejpam-6968	13	1	[	[	X
ejpam-6968	13	2	9	9	NUM
ejpam-6968	13	3	]	]	PUNCT
ejpam-6968	13	4	,	,	PUNCT
ejpam-6968	13	5	and	and	CCONJ
ejpam-6968	13	6	mechanical	mechanical	ADJ
ejpam-6968	13	7	vibrations	vibration	NOUN
ejpam-6968	13	8	[	[	X
ejpam-6968	13	9	10	10	NUM
ejpam-6968	13	10	]	]	PUNCT
ejpam-6968	13	11	.	.	PUNCT
ejpam-6968	14	1	a	a	DET
ejpam-6968	14	2	prime	prime	ADJ
ejpam-6968	14	3	objective	objective	NOUN
ejpam-6968	14	4	is	be	AUX
ejpam-6968	14	5	to	to	PART
ejpam-6968	14	6	check	check	VERB
ejpam-6968	14	7	how	how	SCONJ
ejpam-6968	14	8	parameter	parameter	NOUN
ejpam-6968	14	9	changes	change	VERB
ejpam-6968	14	10	trigger	trigger	NOUN
ejpam-6968	14	11	qualitative	qualitative	ADJ
ejpam-6968	14	12	∗corresponding	∗corresponde	VERB
ejpam-6968	14	13	author	author	NOUN
ejpam-6968	14	14	.	.	PUNCT
ejpam-6968	15	1	doi	doi	NOUN
ejpam-6968	15	2	:	:	PUNCT
ejpam-6968	15	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6968	https://doi.org/10.29020/nybg.ejpam.v18i4.6968	NOUN
ejpam-6968	15	4	email	email	NOUN
ejpam-6968	15	5	addresses	address	NOUN
ejpam-6968	15	6	:	:	PUNCT
ejpam-6968	15	7	yulian@lecturer.undip.ac.id	yulian@lecturer.undip.ac.id	PROPN
ejpam-6968	15	8	(	(	PUNCT
ejpam-6968	15	9	n.	n.	PROPN
ejpam-6968	15	10	y.	y.	PROPN
ejpam-6968	15	11	ashar	ashar	PROPN
ejpam-6968	15	12	)	)	PUNCT
ejpam-6968	15	13	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6968	16	1	1	1	NUM
ejpam-6968	16	2	copyright	copyright	NOUN
ejpam-6968	16	3	:	:	PUNCT
ejpam-6968	16	4	©	©	PROPN
ejpam-6968	16	5	2025	2025	NUM
ejpam-6968	16	6	the	the	DET
ejpam-6968	16	7	author(s	author(s	NOUN
ejpam-6968	16	8	)	)	PUNCT
ejpam-6968	16	9	.	.	PUNCT
ejpam-6968	17	1	(	(	PUNCT
ejpam-6968	17	2	cc	cc	NOUN
ejpam-6968	17	3	by	by	ADP
ejpam-6968	17	4	-	-	PUNCT
ejpam-6968	17	5	nc	nc	PROPN
ejpam-6968	17	6	4.0	4.0	NUM
ejpam-6968	17	7	)	)	PUNCT
ejpam-6968	17	8	h.	h.	PROPN
ejpam-6968	17	9	k.	k.	PROPN
ejpam-6968	17	10	fata	fata	PROPN
ejpam-6968	17	11	,	,	PUNCT
ejpam-6968	17	12	n.	n.	PROPN
ejpam-6968	17	13	y.	y.	PROPN
ejpam-6968	17	14	ashar	ashar	PROPN
ejpam-6968	17	15	/	/	SYM
ejpam-6968	17	16	eur	eur	PROPN
ejpam-6968	17	17	.	.	PUNCT
ejpam-6968	18	1	j.	j.	PROPN
ejpam-6968	18	2	pure	pure	PROPN
ejpam-6968	18	3	appl	appl	PROPN
ejpam-6968	18	4	.	.	PROPN
ejpam-6968	18	5	math	math	PROPN
ejpam-6968	18	6	,	,	PUNCT
ejpam-6968	18	7	18	18	NUM
ejpam-6968	18	8	(	(	PUNCT
ejpam-6968	18	9	4	4	NUM
ejpam-6968	18	10	)	)	PUNCT
ejpam-6968	18	11	(	(	PUNCT
ejpam-6968	18	12	2025	2025	NUM
ejpam-6968	18	13	)	)	PUNCT
ejpam-6968	18	14	,	,	PUNCT
ejpam-6968	18	15	6968	6968	NUM
ejpam-6968	18	16	2	2	NUM
ejpam-6968	18	17	of	of	ADP
ejpam-6968	18	18	15	15	NUM
ejpam-6968	18	19	shifts	shift	NOUN
ejpam-6968	18	20	—	—	PUNCT
ejpam-6968	18	21	such	such	ADJ
ejpam-6968	18	22	as	as	ADP
ejpam-6968	18	23	movements	movement	NOUN
ejpam-6968	18	24	from	from	ADP
ejpam-6968	18	25	stability	stability	NOUN
ejpam-6968	18	26	to	to	PART
ejpam-6968	18	27	chaos	chaos	VERB
ejpam-6968	18	28	—	—	PUNCT
ejpam-6968	18	29	through	through	ADP
ejpam-6968	18	30	bifurcations	bifurcation	NOUN
ejpam-6968	18	31	,	,	PUNCT
ejpam-6968	18	32	a	a	DET
ejpam-6968	18	33	essence	essence	NOUN
ejpam-6968	18	34	concept	concept	NOUN
ejpam-6968	18	35	in	in	ADP
ejpam-6968	18	36	nonlinear	nonlinear	ADJ
ejpam-6968	18	37	analysis	analysis	NOUN
ejpam-6968	18	38	[	[	X
ejpam-6968	18	39	11	11	NUM
ejpam-6968	18	40	]	]	PUNCT
ejpam-6968	18	41	.	.	PUNCT
ejpam-6968	19	1	chaos	chaos	NOUN
ejpam-6968	19	2	theory	theory	NOUN
ejpam-6968	19	3	reveals	reveal	VERB
ejpam-6968	19	4	that	that	SCONJ
ejpam-6968	19	5	deterministic	deterministic	ADJ
ejpam-6968	19	6	systems	system	NOUN
ejpam-6968	19	7	can	can	AUX
ejpam-6968	19	8	move	move	VERB
ejpam-6968	19	9	unpredictable	unpredictable	ADJ
ejpam-6968	19	10	over	over	ADP
ejpam-6968	19	11	time	time	NOUN
ejpam-6968	19	12	,	,	PUNCT
ejpam-6968	19	13	challenging	challenging	ADJ
ejpam-6968	19	14	assumptions	assumption	NOUN
ejpam-6968	19	15	of	of	ADP
ejpam-6968	19	16	control	control	NOUN
ejpam-6968	19	17	and	and	CCONJ
ejpam-6968	19	18	predictability	predictability	NOUN
ejpam-6968	19	19	.	.	PUNCT
ejpam-6968	20	1	examples	example	NOUN
ejpam-6968	20	2	include	include	VERB
ejpam-6968	20	3	honeybee	honeybee	NOUN
ejpam-6968	20	4	models	model	NOUN
ejpam-6968	20	5	presenting	present	VERB
ejpam-6968	20	6	nonlinear	nonlinear	ADJ
ejpam-6968	20	7	feedback	feedback	NOUN
ejpam-6968	20	8	consequentes	consequente	NOUN
ejpam-6968	20	9	[	[	X
ejpam-6968	20	10	7	7	NUM
ejpam-6968	20	11	]	]	PUNCT
ejpam-6968	20	12	,	,	PUNCT
ejpam-6968	20	13	chua	chua	PROPN
ejpam-6968	20	14	oscillators	oscillator	NOUN
ejpam-6968	20	15	with	with	ADP
ejpam-6968	20	16	controllable	controllable	ADJ
ejpam-6968	20	17	chaos	chaos	NOUN
ejpam-6968	21	1	[	[	X
ejpam-6968	21	2	8	8	NUM
ejpam-6968	21	3	]	]	PUNCT
ejpam-6968	21	4	,	,	PUNCT
ejpam-6968	21	5	fractional	fractional	ADJ
ejpam-6968	21	6	-	-	PUNCT
ejpam-6968	21	7	delay	delay	NOUN
ejpam-6968	21	8	models	model	NOUN
ejpam-6968	21	9	of	of	ADP
ejpam-6968	21	10	atmospheric	atmospheric	ADJ
ejpam-6968	21	11	influxes	influx	NOUN
ejpam-6968	22	1	[	[	X
ejpam-6968	22	2	9	9	NUM
ejpam-6968	22	3	]	]	PUNCT
ejpam-6968	22	4	,	,	PUNCT
ejpam-6968	22	5	and	and	CCONJ
ejpam-6968	22	6	nonlinear	nonlinear	ADJ
ejpam-6968	22	7	trembling	trembling	NOUN
ejpam-6968	22	8	responses	response	NOUN
ejpam-6968	22	9	in	in	ADP
ejpam-6968	22	10	railway	railway	NOUN
ejpam-6968	22	11	tools	tool	NOUN
ejpam-6968	22	12	[	[	X
ejpam-6968	22	13	10	10	NUM
ejpam-6968	22	14	]	]	PUNCT
ejpam-6968	22	15	.	.	PUNCT
ejpam-6968	23	1	to	to	PART
ejpam-6968	23	2	check	check	VERB
ejpam-6968	23	3	these	these	DET
ejpam-6968	23	4	phenomena	phenomenon	NOUN
ejpam-6968	23	5	,	,	PUNCT
ejpam-6968	23	6	dynamical	dynamical	ADJ
ejpam-6968	23	7	system	system	NOUN
ejpam-6968	23	8	analysis	analysis	NOUN
ejpam-6968	23	9	generally	generally	ADV
ejpam-6968	23	10	combines	combine	VERB
ejpam-6968	23	11	analytical	analytical	ADJ
ejpam-6968	23	12	and	and	CCONJ
ejpam-6968	23	13	numerical	numerical	ADJ
ejpam-6968	23	14	methods	method	NOUN
ejpam-6968	23	15	.	.	PUNCT
ejpam-6968	24	1	local	local	ADJ
ejpam-6968	24	2	stability	stability	NOUN
ejpam-6968	24	3	and	and	CCONJ
ejpam-6968	24	4	bifurcation	bifurcation	NOUN
ejpam-6968	24	5	analyses	analysis	NOUN
ejpam-6968	24	6	,	,	PUNCT
ejpam-6968	24	7	especially	especially	ADV
ejpam-6968	24	8	in	in	ADP
ejpam-6968	24	9	proximity	proximity	NOUN
ejpam-6968	24	10	to	to	ADP
ejpam-6968	24	11	equilibrium	equilibrium	NOUN
ejpam-6968	24	12	points	point	NOUN
ejpam-6968	24	13	,	,	PUNCT
ejpam-6968	24	14	can	can	AUX
ejpam-6968	24	15	show	show	VERB
ejpam-6968	24	16	the	the	DET
ejpam-6968	24	17	importance	importance	NOUN
ejpam-6968	24	18	of	of	ADP
ejpam-6968	24	19	oscillatory	oscillatory	ADJ
ejpam-6968	24	20	or	or	CCONJ
ejpam-6968	24	21	unstable	unstable	ADJ
ejpam-6968	24	22	dynamics	dynamic	NOUN
ejpam-6968	24	23	.	.	PUNCT
ejpam-6968	25	1	however	however	ADV
ejpam-6968	25	2	,	,	PUNCT
ejpam-6968	25	3	these	these	DET
ejpam-6968	25	4	localized	localize	VERB
ejpam-6968	25	5	instruments	instrument	NOUN
ejpam-6968	25	6	are	be	AUX
ejpam-6968	25	7	inadequate	inadequate	ADJ
ejpam-6968	25	8	for	for	ADP
ejpam-6968	25	9	elucidating	elucidate	VERB
ejpam-6968	25	10	the	the	DET
ejpam-6968	25	11	complete	complete	ADJ
ejpam-6968	25	12	global	global	ADJ
ejpam-6968	25	13	dynamics	dynamic	NOUN
ejpam-6968	25	14	of	of	ADP
ejpam-6968	25	15	nonlinear	nonlinear	ADJ
ejpam-6968	25	16	systems	system	NOUN
ejpam-6968	25	17	.	.	PUNCT
ejpam-6968	26	1	so	so	ADV
ejpam-6968	26	2	numerical	numerical	ADJ
ejpam-6968	26	3	continuation	continuation	NOUN
ejpam-6968	26	4	methods	method	NOUN
ejpam-6968	26	5	and	and	CCONJ
ejpam-6968	26	6	phase	phase	NOUN
ejpam-6968	26	7	space	space	NOUN
ejpam-6968	26	8	visualizations	visualization	NOUN
ejpam-6968	26	9	are	be	AUX
ejpam-6968	26	10	important	important	ADJ
ejpam-6968	26	11	for	for	ADP
ejpam-6968	26	12	elucidating	elucidate	VERB
ejpam-6968	26	13	bifurcation	bifurcation	NOUN
ejpam-6968	26	14	structures	structure	NOUN
ejpam-6968	26	15	and	and	CCONJ
ejpam-6968	26	16	global	global	ADJ
ejpam-6968	26	17	movements	movement	NOUN
ejpam-6968	26	18	,	,	PUNCT
ejpam-6968	26	19	including	include	VERB
ejpam-6968	26	20	pathways	pathway	NOUN
ejpam-6968	26	21	to	to	PART
ejpam-6968	26	22	chaos	chaos	VERB
ejpam-6968	26	23	[	[	X
ejpam-6968	26	24	12	12	NUM
ejpam-6968	26	25	]	]	PUNCT
ejpam-6968	26	26	.	.	PUNCT
ejpam-6968	27	1	in	in	ADP
ejpam-6968	27	2	this	this	DET
ejpam-6968	27	3	methodological	methodological	ADJ
ejpam-6968	27	4	context	context	NOUN
ejpam-6968	27	5	,	,	PUNCT
ejpam-6968	27	6	the	the	DET
ejpam-6968	27	7	textbooks	textbook	NOUN
ejpam-6968	27	8	by	by	ADP
ejpam-6968	27	9	kuznetsov	kuznetsov	PROPN
ejpam-6968	28	1	[	[	X
ejpam-6968	28	2	11	11	NUM
ejpam-6968	28	3	]	]	PUNCT
ejpam-6968	28	4	,	,	PUNCT
ejpam-6968	28	5	perko	perko	X
ejpam-6968	29	1	[	[	X
ejpam-6968	29	2	13	13	NUM
ejpam-6968	29	3	]	]	PUNCT
ejpam-6968	29	4	,	,	PUNCT
ejpam-6968	29	5	and	and	CCONJ
ejpam-6968	29	6	wiggins	wiggin	VERB
ejpam-6968	29	7	[	[	X
ejpam-6968	29	8	14	14	NUM
ejpam-6968	29	9	]	]	PUNCT
ejpam-6968	29	10	establish	establish	VERB
ejpam-6968	29	11	the	the	DET
ejpam-6968	29	12	theoretical	theoretical	ADJ
ejpam-6968	29	13	foundation	foundation	NOUN
ejpam-6968	29	14	for	for	ADP
ejpam-6968	29	15	local	local	ADJ
ejpam-6968	29	16	analysis	analysis	NOUN
ejpam-6968	29	17	.	.	PUNCT
ejpam-6968	30	1	meanwhile	meanwhile	ADV
ejpam-6968	30	2	,	,	PUNCT
ejpam-6968	30	3	ananthkrishnan	ananthkrishnan	INTJ
ejpam-6968	30	4	et	et	PROPN
ejpam-6968	30	5	al	al	PROPN
ejpam-6968	30	6	.	.	PUNCT
ejpam-6968	31	1	[	[	X
ejpam-6968	31	2	15	15	NUM
ejpam-6968	31	3	]	]	PUNCT
ejpam-6968	31	4	demonstrate	demonstrate	NOUN
ejpam-6968	31	5	computational	computational	ADJ
ejpam-6968	31	6	multiparameter	multiparameter	NOUN
ejpam-6968	31	7	continuation	continuation	NOUN
ejpam-6968	31	8	,	,	PUNCT
ejpam-6968	31	9	and	and	CCONJ
ejpam-6968	31	10	di	di	PROPN
ejpam-6968	31	11	bernardo	bernardo	NOUN
ejpam-6968	31	12	et	et	PROPN
ejpam-6968	31	13	al	al	PROPN
ejpam-6968	31	14	.	.	PUNCT
ejpam-6968	32	1	[	[	X
ejpam-6968	32	2	16	16	NUM
ejpam-6968	32	3	]	]	PUNCT
ejpam-6968	32	4	along	along	ADP
ejpam-6968	32	5	with	with	ADP
ejpam-6968	32	6	han	han	PROPN
ejpam-6968	32	7	et	et	PROPN
ejpam-6968	32	8	al	al	PROPN
ejpam-6968	32	9	.	.	PUNCT
ejpam-6968	33	1	[	[	X
ejpam-6968	33	2	17	17	NUM
ejpam-6968	33	3	]	]	PUNCT
ejpam-6968	33	4	emphasize	emphasize	VERB
ejpam-6968	33	5	the	the	DET
ejpam-6968	33	6	necessity	necessity	NOUN
ejpam-6968	33	7	for	for	ADP
ejpam-6968	33	8	global	global	ADJ
ejpam-6968	33	9	tools	tool	NOUN
ejpam-6968	33	10	in	in	ADP
ejpam-6968	33	11	nonsmooth	nonsmooth	NOUN
ejpam-6968	33	12	or	or	CCONJ
ejpam-6968	33	13	hybrid	hybrid	ADJ
ejpam-6968	33	14	environments	environment	NOUN
ejpam-6968	33	15	.	.	PUNCT
ejpam-6968	34	1	among	among	ADP
ejpam-6968	34	2	the	the	DET
ejpam-6968	34	3	many	many	ADJ
ejpam-6968	34	4	forms	form	NOUN
ejpam-6968	34	5	of	of	ADP
ejpam-6968	34	6	chaotic	chaotic	ADJ
ejpam-6968	34	7	systems	system	NOUN
ejpam-6968	34	8	,	,	PUNCT
ejpam-6968	34	9	a	a	DET
ejpam-6968	34	10	particularly	particularly	ADV
ejpam-6968	34	11	interesting	interesting	ADJ
ejpam-6968	34	12	subclass	subclass	NOUN
ejpam-6968	34	13	is	be	AUX
ejpam-6968	34	14	the	the	DET
ejpam-6968	34	15	three	three	NUM
ejpam-6968	34	16	-	-	PUNCT
ejpam-6968	34	17	dimensional	dimensional	ADJ
ejpam-6968	34	18	system	system	NOUN
ejpam-6968	34	19	with	with	ADP
ejpam-6968	34	20	quadratic	quadratic	ADJ
ejpam-6968	34	21	nonlinearity	nonlinearity	NOUN
ejpam-6968	34	22	and	and	CCONJ
ejpam-6968	34	23	no	no	DET
ejpam-6968	34	24	equilibrium	equilibrium	NOUN
ejpam-6968	34	25	[	[	X
ejpam-6968	34	26	18	18	NUM
ejpam-6968	34	27	,	,	PUNCT
ejpam-6968	34	28	19	19	NUM
ejpam-6968	34	29	]	]	PUNCT
ejpam-6968	34	30	.	.	PUNCT
ejpam-6968	35	1	while	while	SCONJ
ejpam-6968	35	2	the	the	DET
ejpam-6968	35	3	analysis	analysis	NOUN
ejpam-6968	35	4	of	of	ADP
ejpam-6968	35	5	dynamical	dynamical	ADJ
ejpam-6968	35	6	systems	system	NOUN
ejpam-6968	35	7	always	always	ADV
ejpam-6968	35	8	starts	start	VERB
ejpam-6968	35	9	from	from	ADP
ejpam-6968	35	10	the	the	DET
ejpam-6968	35	11	equilibrium	equilibrium	NOUN
ejpam-6968	35	12	point	point	NOUN
ejpam-6968	35	13	,	,	PUNCT
ejpam-6968	35	14	in	in	ADP
ejpam-6968	35	15	systems	system	NOUN
ejpam-6968	35	16	with	with	ADP
ejpam-6968	35	17	no	no	DET
ejpam-6968	35	18	equilibrium	equilibrium	NOUN
ejpam-6968	35	19	,	,	PUNCT
ejpam-6968	35	20	the	the	DET
ejpam-6968	35	21	analysis	analysis	NOUN
ejpam-6968	35	22	is	be	AUX
ejpam-6968	35	23	quite	quite	ADV
ejpam-6968	35	24	difficult	difficult	ADJ
ejpam-6968	35	25	to	to	PART
ejpam-6968	35	26	perform	perform	VERB
ejpam-6968	35	27	because	because	SCONJ
ejpam-6968	35	28	there	there	PRON
ejpam-6968	35	29	are	be	VERB
ejpam-6968	35	30	few	few	ADJ
ejpam-6968	35	31	analytical	analytical	ADJ
ejpam-6968	35	32	methods	method	NOUN
ejpam-6968	35	33	to	to	PART
ejpam-6968	35	34	observe	observe	VERB
ejpam-6968	35	35	their	their	PRON
ejpam-6968	35	36	dynamics	dynamic	NOUN
ejpam-6968	35	37	.	.	PUNCT
ejpam-6968	36	1	in	in	ADP
ejpam-6968	36	2	their	their	PRON
ejpam-6968	36	3	foundational	foundational	ADJ
ejpam-6968	36	4	work	work	NOUN
ejpam-6968	36	5	,	,	PUNCT
ejpam-6968	36	6	jafari	jafari	PROPN
ejpam-6968	36	7	et	et	PROPN
ejpam-6968	36	8	al	al	PROPN
ejpam-6968	36	9	.	.	PUNCT
ejpam-6968	37	1	[	[	X
ejpam-6968	37	2	19	19	NUM
ejpam-6968	37	3	]	]	PUNCT
ejpam-6968	37	4	introduced	introduce	VERB
ejpam-6968	37	5	a	a	DET
ejpam-6968	37	6	catalog	catalog	NOUN
ejpam-6968	37	7	of	of	ADP
ejpam-6968	37	8	several	several	ADJ
ejpam-6968	37	9	such	such	ADJ
ejpam-6968	37	10	systems	system	NOUN
ejpam-6968	37	11	,	,	PUNCT
ejpam-6968	37	12	among	among	ADP
ejpam-6968	37	13	which	which	PRON
ejpam-6968	37	14	the	the	DET
ejpam-6968	37	15	ne12	ne12	PROPN
ejpam-6968	37	16	system	system	NOUN
ejpam-6968	37	17	exhibits	exhibit	VERB
ejpam-6968	37	18	chaos	chaos	NOUN
ejpam-6968	37	19	despite	despite	SCONJ
ejpam-6968	37	20	the	the	DET
ejpam-6968	37	21	absence	absence	NOUN
ejpam-6968	37	22	of	of	ADP
ejpam-6968	37	23	equilibrium	equilibrium	NOUN
ejpam-6968	37	24	points	point	NOUN
ejpam-6968	37	25	for	for	ADP
ejpam-6968	37	26	a	a	DET
ejpam-6968	37	27	certain	certain	ADJ
ejpam-6968	37	28	range	range	NOUN
ejpam-6968	37	29	of	of	ADP
ejpam-6968	37	30	parameters	parameter	NOUN
ejpam-6968	37	31	.	.	PUNCT
ejpam-6968	38	1	however	however	ADV
ejpam-6968	38	2	,	,	PUNCT
ejpam-6968	38	3	their	their	PRON
ejpam-6968	38	4	study	study	NOUN
ejpam-6968	38	5	only	only	ADV
ejpam-6968	38	6	identified	identify	VERB
ejpam-6968	38	7	the	the	DET
ejpam-6968	38	8	existence	existence	NOUN
ejpam-6968	38	9	of	of	ADP
ejpam-6968	38	10	chaotic	chaotic	ADJ
ejpam-6968	38	11	dynamics	dynamic	NOUN
ejpam-6968	38	12	of	of	ADP
ejpam-6968	38	13	the	the	DET
ejpam-6968	38	14	system	system	NOUN
ejpam-6968	38	15	using	use	VERB
ejpam-6968	38	16	lyapunov	lyapunov	ADJ
ejpam-6968	38	17	exponents	exponent	NOUN
ejpam-6968	38	18	and	and	CCONJ
ejpam-6968	38	19	kaplan	kaplan	PROPN
ejpam-6968	38	20	–	–	PUNCT
ejpam-6968	38	21	yorke	yorke	NOUN
ejpam-6968	38	22	dimensions	dimension	NOUN
ejpam-6968	38	23	at	at	ADP
ejpam-6968	38	24	parameter	parameter	NOUN
ejpam-6968	38	25	values	value	NOUN
ejpam-6968	38	26	where	where	SCONJ
ejpam-6968	38	27	the	the	DET
ejpam-6968	38	28	system	system	NOUN
ejpam-6968	38	29	had	have	VERB
ejpam-6968	38	30	no	no	DET
ejpam-6968	38	31	equilibrium	equilibrium	NOUN
ejpam-6968	38	32	points	point	NOUN
ejpam-6968	38	33	,	,	PUNCT
ejpam-6968	38	34	without	without	ADP
ejpam-6968	38	35	exploring	explore	VERB
ejpam-6968	38	36	the	the	DET
ejpam-6968	38	37	underlying	underlie	VERB
ejpam-6968	38	38	bifurcation	bifurcation	NOUN
ejpam-6968	38	39	structure	structure	NOUN
ejpam-6968	38	40	or	or	CCONJ
ejpam-6968	38	41	the	the	DET
ejpam-6968	38	42	global	global	ADJ
ejpam-6968	38	43	evolution	evolution	NOUN
ejpam-6968	38	44	of	of	ADP
ejpam-6968	38	45	the	the	DET
ejpam-6968	38	46	system	system	NOUN
ejpam-6968	38	47	dynamics	dynamic	NOUN
ejpam-6968	38	48	as	as	SCONJ
ejpam-6968	38	49	the	the	DET
ejpam-6968	38	50	parameters	parameter	NOUN
ejpam-6968	38	51	varied	varied	ADJ
ejpam-6968	38	52	.	.	PUNCT
ejpam-6968	39	1	this	this	DET
ejpam-6968	39	2	research	research	NOUN
ejpam-6968	39	3	addresses	address	VERB
ejpam-6968	39	4	the	the	DET
ejpam-6968	39	5	lack	lack	NOUN
ejpam-6968	39	6	of	of	ADP
ejpam-6968	39	7	general	general	ADJ
ejpam-6968	39	8	analysis	analysis	NOUN
ejpam-6968	39	9	of	of	ADP
ejpam-6968	39	10	the	the	DET
ejpam-6968	39	11	ne12	ne12	PROPN
ejpam-6968	39	12	system	system	NOUN
ejpam-6968	39	13	by	by	ADP
ejpam-6968	39	14	combining	combine	VERB
ejpam-6968	39	15	analytical	analytical	ADJ
ejpam-6968	39	16	and	and	CCONJ
ejpam-6968	39	17	numerical	numerical	ADJ
ejpam-6968	39	18	methods	method	NOUN
ejpam-6968	39	19	.	.	PUNCT
ejpam-6968	40	1	we	we	PRON
ejpam-6968	40	2	first	first	ADV
ejpam-6968	40	3	see	see	VERB
ejpam-6968	40	4	local	local	ADJ
ejpam-6968	40	5	stability	stability	NOUN
ejpam-6968	40	6	and	and	CCONJ
ejpam-6968	40	7	identify	identify	VERB
ejpam-6968	40	8	a	a	DET
ejpam-6968	40	9	supercritical	supercritical	ADJ
ejpam-6968	40	10	hopf	hopf	ADJ
ejpam-6968	40	11	bifurcation	bifurcation	NOUN
ejpam-6968	40	12	at	at	ADP
ejpam-6968	40	13	a	a	DET
ejpam-6968	40	14	critical	critical	ADJ
ejpam-6968	40	15	parameter	parameter	NOUN
ejpam-6968	40	16	.	.	PUNCT
ejpam-6968	41	1	using	use	VERB
ejpam-6968	41	2	numerical	numerical	ADJ
ejpam-6968	41	3	continuation	continuation	NOUN
ejpam-6968	41	4	,	,	PUNCT
ejpam-6968	41	5	we	we	PRON
ejpam-6968	41	6	check	check	VERB
ejpam-6968	41	7	periodic	periodic	ADJ
ejpam-6968	41	8	orbits	orbit	NOUN
ejpam-6968	41	9	and	and	CCONJ
ejpam-6968	41	10	make	make	VERB
ejpam-6968	41	11	global	global	ADJ
ejpam-6968	41	12	bifurcation	bifurcation	NOUN
ejpam-6968	41	13	structures	structure	NOUN
ejpam-6968	41	14	,	,	PUNCT
ejpam-6968	41	15	including	include	VERB
ejpam-6968	41	16	period	period	NOUN
ejpam-6968	41	17	-	-	PUNCT
ejpam-6968	41	18	doubling	double	VERB
ejpam-6968	41	19	cascades	cascade	NOUN
ejpam-6968	41	20	and	and	CCONJ
ejpam-6968	41	21	also	also	ADV
ejpam-6968	41	22	hidden	hidden	ADJ
ejpam-6968	41	23	attractors	attractor	NOUN
ejpam-6968	41	24	.	.	PUNCT
ejpam-6968	42	1	complexity	complexity	NOUN
ejpam-6968	42	2	is	be	AUX
ejpam-6968	42	3	calculated	calculate	VERB
ejpam-6968	42	4	through	through	ADP
ejpam-6968	42	5	largest	large	ADJ
ejpam-6968	42	6	lyapunov	lyapunov	ADJ
ejpam-6968	42	7	exponents	exponent	NOUN
ejpam-6968	42	8	and	and	CCONJ
ejpam-6968	42	9	also	also	ADV
ejpam-6968	42	10	kaplan	kaplan	PROPN
ejpam-6968	42	11	–	–	PUNCT
ejpam-6968	42	12	yorke	yorke	NOUN
ejpam-6968	42	13	dimensions	dimension	NOUN
ejpam-6968	42	14	,	,	PUNCT
ejpam-6968	42	15	making	make	VERB
ejpam-6968	42	16	bifurcation	bifurcation	NOUN
ejpam-6968	42	17	plots	plot	NOUN
ejpam-6968	42	18	and	and	CCONJ
ejpam-6968	42	19	lyapunov	lyapunov	ADJ
ejpam-6968	42	20	diagrams	diagram	NOUN
ejpam-6968	42	21	that	that	PRON
ejpam-6968	42	22	map	map	VERB
ejpam-6968	42	23	movements	movement	NOUN
ejpam-6968	42	24	between	between	ADP
ejpam-6968	42	25	regular	regular	ADJ
ejpam-6968	42	26	and	and	CCONJ
ejpam-6968	42	27	chaotic	chaotic	ADJ
ejpam-6968	42	28	regimes	regime	NOUN
ejpam-6968	43	1	[	[	X
ejpam-6968	43	2	20	20	NUM
ejpam-6968	43	3	]	]	PUNCT
ejpam-6968	43	4	.	.	PUNCT
ejpam-6968	44	1	phase	phase	NOUN
ejpam-6968	44	2	-	-	PUNCT
ejpam-6968	44	3	space	space	NOUN
ejpam-6968	44	4	plots	plot	NOUN
ejpam-6968	44	5	and	and	CCONJ
ejpam-6968	44	6	poincaré	poincaré	PROPN
ejpam-6968	44	7	sections	section	NOUN
ejpam-6968	44	8	display	display	VERB
ejpam-6968	44	9	geometric	geometric	ADJ
ejpam-6968	44	10	aspects	aspect	NOUN
ejpam-6968	44	11	,	,	PUNCT
ejpam-6968	44	12	while	while	SCONJ
ejpam-6968	44	13	lyapunov	lyapunov	ADJ
ejpam-6968	44	14	exponents	exponent	NOUN
ejpam-6968	44	15	are	be	AUX
ejpam-6968	44	16	computed	compute	VERB
ejpam-6968	44	17	using	use	VERB
ejpam-6968	44	18	the	the	DET
ejpam-6968	44	19	ancient	ancient	ADJ
ejpam-6968	44	20	method	method	NOUN
ejpam-6968	44	21	of	of	ADP
ejpam-6968	44	22	wolf	wolf	PROPN
ejpam-6968	44	23	et	et	PROPN
ejpam-6968	44	24	al	al	PROPN
ejpam-6968	44	25	.	.	PUNCT
ejpam-6968	45	1	[	[	X
ejpam-6968	45	2	20	20	NUM
ejpam-6968	45	3	]	]	PUNCT
ejpam-6968	45	4	.	.	PUNCT
ejpam-6968	46	1	the	the	DET
ejpam-6968	46	2	observed	observe	VERB
ejpam-6968	46	3	dynamics	dynamic	NOUN
ejpam-6968	46	4	align	align	VERB
ejpam-6968	46	5	with	with	ADP
ejpam-6968	46	6	known	know	VERB
ejpam-6968	46	7	paths	path	NOUN
ejpam-6968	46	8	to	to	PART
ejpam-6968	46	9	chaos	chaos	VERB
ejpam-6968	46	10	in	in	ADP
ejpam-6968	46	11	diverse	diverse	ADJ
ejpam-6968	46	12	systems	system	NOUN
ejpam-6968	46	13	,	,	PUNCT
ejpam-6968	46	14	such	such	ADJ
ejpam-6968	46	15	as	as	ADP
ejpam-6968	46	16	viscoelastic	viscoelastic	ADJ
ejpam-6968	46	17	streams	stream	NOUN
ejpam-6968	47	1	[	[	X
ejpam-6968	47	2	21	21	NUM
ejpam-6968	47	3	]	]	PUNCT
ejpam-6968	47	4	,	,	PUNCT
ejpam-6968	47	5	photorefractive	photorefractive	ADJ
ejpam-6968	47	6	mixing	mixing	NOUN
ejpam-6968	47	7	[	[	X
ejpam-6968	47	8	22	22	NUM
ejpam-6968	47	9	]	]	PUNCT
ejpam-6968	47	10	ultrafast	ultrafast	ADJ
ejpam-6968	47	11	lasers	laser	NOUN
ejpam-6968	47	12	[	[	X
ejpam-6968	47	13	23	23	NUM
ejpam-6968	47	14	]	]	PUNCT
ejpam-6968	47	15	,	,	PUNCT
ejpam-6968	47	16	and	and	CCONJ
ejpam-6968	47	17	microbeam	microbeam	NOUN
ejpam-6968	47	18	oscillations	oscillation	NOUN
ejpam-6968	47	19	[	[	X
ejpam-6968	47	20	24	24	NUM
ejpam-6968	47	21	]	]	PUNCT
ejpam-6968	47	22	,	,	PUNCT
ejpam-6968	47	23	sharping	sharpe	VERB
ejpam-6968	47	24	the	the	DET
ejpam-6968	47	25	universality	universality	NOUN
ejpam-6968	47	26	of	of	ADP
ejpam-6968	47	27	these	these	DET
ejpam-6968	47	28	mechanisms	mechanism	NOUN
ejpam-6968	47	29	.	.	PUNCT
ejpam-6968	48	1	the	the	DET
ejpam-6968	48	2	novelty	novelty	NOUN
ejpam-6968	48	3	of	of	ADP
ejpam-6968	48	4	this	this	DET
ejpam-6968	48	5	study	study	NOUN
ejpam-6968	48	6	located	locate	VERB
ejpam-6968	48	7	in	in	ADP
ejpam-6968	48	8	its	its	PRON
ejpam-6968	48	9	systematic	systematic	ADJ
ejpam-6968	48	10	explanation	explanation	NOUN
ejpam-6968	48	11	of	of	ADP
ejpam-6968	48	12	the	the	DET
ejpam-6968	48	13	global	global	ADJ
ejpam-6968	48	14	bifurcation	bifurcation	NOUN
ejpam-6968	48	15	act	act	NOUN
ejpam-6968	48	16	of	of	ADP
ejpam-6968	48	17	the	the	DET
ejpam-6968	48	18	ne12	ne12	PROPN
ejpam-6968	48	19	system	system	NOUN
ejpam-6968	48	20	,	,	PUNCT
ejpam-6968	48	21	which	which	PRON
ejpam-6968	48	22	has	have	AUX
ejpam-6968	48	23	not	not	PART
ejpam-6968	48	24	been	be	AUX
ejpam-6968	48	25	comprehensively	comprehensively	ADV
ejpam-6968	48	26	and	and	CCONJ
ejpam-6968	48	27	generally	generally	ADV
ejpam-6968	48	28	analyzed	analyze	VERB
ejpam-6968	48	29	before	before	ADV
ejpam-6968	48	30	.	.	PUNCT
ejpam-6968	49	1	unlike	unlike	ADP
ejpam-6968	49	2	the	the	DET
ejpam-6968	49	3	original	original	ADJ
ejpam-6968	49	4	work	work	NOUN
ejpam-6968	49	5	by	by	ADP
ejpam-6968	49	6	jafari	jafari	PROPN
ejpam-6968	49	7	et	et	PROPN
ejpam-6968	49	8	al	al	PROPN
ejpam-6968	49	9	.	.	PROPN
ejpam-6968	49	10	,[19	,[19	PROPN
ejpam-6968	49	11	]	]	PUNCT
ejpam-6968	49	12	which	which	PRON
ejpam-6968	49	13	explained	explain	VERB
ejpam-6968	49	14	ne12	ne12	PROPN
ejpam-6968	49	15	as	as	ADP
ejpam-6968	49	16	a	a	DET
ejpam-6968	49	17	chaotic	chaotic	ADJ
ejpam-6968	49	18	h.	h.	PROPN
ejpam-6968	49	19	k.	k.	PROPN
ejpam-6968	49	20	fata	fata	PROPN
ejpam-6968	49	21	,	,	PUNCT
ejpam-6968	49	22	n.	n.	PROPN
ejpam-6968	49	23	y.	y.	PROPN
ejpam-6968	49	24	ashar	ashar	PROPN
ejpam-6968	49	25	/	/	SYM
ejpam-6968	49	26	eur	eur	PROPN
ejpam-6968	49	27	.	.	PUNCT
ejpam-6968	50	1	j.	j.	PROPN
ejpam-6968	50	2	pure	pure	PROPN
ejpam-6968	50	3	appl	appl	PROPN
ejpam-6968	50	4	.	.	PROPN
ejpam-6968	50	5	math	math	PROPN
ejpam-6968	50	6	,	,	PUNCT
ejpam-6968	50	7	18	18	NUM
ejpam-6968	50	8	(	(	PUNCT
ejpam-6968	50	9	4	4	NUM
ejpam-6968	50	10	)	)	PUNCT
ejpam-6968	50	11	(	(	PUNCT
ejpam-6968	50	12	2025	2025	NUM
ejpam-6968	50	13	)	)	PUNCT
ejpam-6968	50	14	,	,	PUNCT
ejpam-6968	50	15	6968	6968	NUM
ejpam-6968	50	16	3	3	NUM
ejpam-6968	50	17	of	of	ADP
ejpam-6968	50	18	15	15	NUM
ejpam-6968	50	19	stream	stream	NOUN
ejpam-6968	50	20	with	with	ADP
ejpam-6968	50	21	no	no	DET
ejpam-6968	50	22	equilibrium	equilibrium	NOUN
ejpam-6968	50	23	,	,	PUNCT
ejpam-6968	50	24	our	our	PRON
ejpam-6968	50	25	joined	joined	ADJ
ejpam-6968	50	26	analytical	analytical	ADJ
ejpam-6968	50	27	and	and	CCONJ
ejpam-6968	50	28	numerical	numerical	ADJ
ejpam-6968	50	29	approach	approach	NOUN
ejpam-6968	50	30	reveals	reveal	VERB
ejpam-6968	50	31	transitions	transition	NOUN
ejpam-6968	50	32	between	between	ADP
ejpam-6968	50	33	stable	stable	ADJ
ejpam-6968	50	34	,	,	PUNCT
ejpam-6968	50	35	periodic	periodic	ADJ
ejpam-6968	50	36	,	,	PUNCT
ejpam-6968	50	37	and	and	CCONJ
ejpam-6968	50	38	chaotic	chaotic	ADJ
ejpam-6968	50	39	dynamics	dynamic	NOUN
ejpam-6968	50	40	via	via	ADP
ejpam-6968	50	41	bifurcation	bifurcation	NOUN
ejpam-6968	50	42	mechanisms	mechanism	NOUN
ejpam-6968	50	43	.	.	PUNCT
ejpam-6968	51	1	this	this	PRON
ejpam-6968	51	2	shows	show	VERB
ejpam-6968	51	3	deeper	deep	ADJ
ejpam-6968	51	4	insight	insight	NOUN
ejpam-6968	51	5	into	into	ADP
ejpam-6968	51	6	the	the	DET
ejpam-6968	51	7	system	system	NOUN
ejpam-6968	51	8	’s	’s	PART
ejpam-6968	51	9	global	global	ADJ
ejpam-6968	51	10	structure	structure	NOUN
ejpam-6968	51	11	and	and	CCONJ
ejpam-6968	51	12	the	the	DET
ejpam-6968	51	13	interplay	interplay	NOUN
ejpam-6968	51	14	between	between	ADP
ejpam-6968	51	15	local	local	ADJ
ejpam-6968	51	16	instabilities	instability	NOUN
ejpam-6968	51	17	and	and	CCONJ
ejpam-6968	51	18	global	global	ADJ
ejpam-6968	51	19	attractors	attractor	NOUN
ejpam-6968	51	20	.	.	PUNCT
ejpam-6968	52	1	recent	recent	ADJ
ejpam-6968	52	2	advances	advance	NOUN
ejpam-6968	52	3	in	in	ADP
ejpam-6968	52	4	hidden	hidden	ADJ
ejpam-6968	52	5	attractors	attractor	NOUN
ejpam-6968	52	6	in	in	ADP
ejpam-6968	52	7	fractional	fractional	ADJ
ejpam-6968	52	8	,	,	PUNCT
ejpam-6968	52	9	geometric	geometric	ADJ
ejpam-6968	52	10	,	,	PUNCT
ejpam-6968	52	11	and	and	CCONJ
ejpam-6968	52	12	simple	simple	ADJ
ejpam-6968	52	13	three	three	NUM
ejpam-6968	52	14	dimension	dimension	NOUN
ejpam-6968	52	15	systems	system	NOUN
ejpam-6968	52	16	[	[	X
ejpam-6968	52	17	25–28	25–28	X
ejpam-6968	52	18	]	]	PUNCT
ejpam-6968	52	19	further	far	ADV
ejpam-6968	52	20	clarify	clarify	VERB
ejpam-6968	52	21	the	the	DET
ejpam-6968	52	22	distinction	distinction	NOUN
ejpam-6968	52	23	between	between	ADP
ejpam-6968	52	24	self	self	NOUN
ejpam-6968	52	25	-	-	PUNCT
ejpam-6968	52	26	excited	excite	VERB
ejpam-6968	52	27	dynamics	dynamic	NOUN
ejpam-6968	52	28	(	(	PUNCT
ejpam-6968	52	29	linked	link	VERB
ejpam-6968	52	30	to	to	ADP
ejpam-6968	52	31	equilibrium	equilibrium	NOUN
ejpam-6968	52	32	stability	stability	NOUN
ejpam-6968	52	33	)	)	PUNCT
ejpam-6968	52	34	and	and	CCONJ
ejpam-6968	52	35	hidden	hidden	ADJ
ejpam-6968	52	36	dynamics	dynamic	NOUN
ejpam-6968	52	37	(	(	PUNCT
ejpam-6968	52	38	characterized	characterize	VERB
ejpam-6968	52	39	by	by	ADP
ejpam-6968	52	40	the	the	DET
ejpam-6968	52	41	lack	lack	NOUN
ejpam-6968	52	42	of	of	ADP
ejpam-6968	52	43	equilibrium	equilibrium	NOUN
ejpam-6968	52	44	and	and	CCONJ
ejpam-6968	52	45	unconnected	unconnected	ADJ
ejpam-6968	52	46	basins	basin	NOUN
ejpam-6968	52	47	)	)	PUNCT
ejpam-6968	52	48	.	.	PUNCT
ejpam-6968	53	1	2	2	X
ejpam-6968	53	2	.	.	X
ejpam-6968	53	3	the	the	DET
ejpam-6968	53	4	model	model	NOUN
ejpam-6968	53	5	this	this	DET
ejpam-6968	53	6	reasearch	reasearch	NOUN
ejpam-6968	53	7	investigates	investigate	VERB
ejpam-6968	53	8	the	the	DET
ejpam-6968	53	9	dynamics	dynamic	NOUN
ejpam-6968	53	10	of	of	ADP
ejpam-6968	53	11	a	a	DET
ejpam-6968	53	12	three	three	NUM
ejpam-6968	53	13	-	-	PUNCT
ejpam-6968	53	14	dimensional	dimensional	ADJ
ejpam-6968	53	15	nonlinear	nonlinear	ADJ
ejpam-6968	53	16	dynamical	dynamical	ADJ
ejpam-6968	53	17	system	system	NOUN
ejpam-6968	53	18	originally	originally	ADV
ejpam-6968	53	19	worked	work	VERB
ejpam-6968	53	20	by	by	ADP
ejpam-6968	53	21	jafari	jafari	PROPN
ejpam-6968	53	22	et	et	PROPN
ejpam-6968	53	23	al	al	PROPN
ejpam-6968	53	24	.	.	PUNCT
ejpam-6968	54	1	[	[	X
ejpam-6968	54	2	19	19	NUM
ejpam-6968	54	3	]	]	PUNCT
ejpam-6968	54	4	,	,	PUNCT
ejpam-6968	54	5	which	which	PRON
ejpam-6968	54	6	exhibits	exhibit	VERB
ejpam-6968	54	7	chaotic	chaotic	ADJ
ejpam-6968	54	8	act	act	NOUN
ejpam-6968	54	9	below	below	ADP
ejpam-6968	54	10	nonequilibrium	nonequilibrium	NOUN
ejpam-6968	54	11	conditions	condition	NOUN
ejpam-6968	54	12	.	.	PUNCT
ejpam-6968	55	1	the	the	DET
ejpam-6968	55	2	system	system	NOUN
ejpam-6968	55	3	is	be	AUX
ejpam-6968	55	4	governed	govern	VERB
ejpam-6968	55	5	by	by	ADP
ejpam-6968	55	6	the	the	DET
ejpam-6968	55	7	following	follow	VERB
ejpam-6968	55	8	set	set	NOUN
ejpam-6968	55	9	of	of	ADP
ejpam-6968	55	10	ordinary	ordinary	ADJ
ejpam-6968	55	11	differential	differential	ADJ
ejpam-6968	55	12	equations	equation	NOUN
ejpam-6968	55	13	:	:	PUNCT
ejpam-6968	56	1			X
ejpam-6968	56	2	ẋ	ẋ	PUNCT
ejpam-6968	57	1	=	=	PUNCT
ejpam-6968	57	2	z	z	PROPN
ejpam-6968	57	3	,	,	PUNCT
ejpam-6968	57	4	ẏ	ẏ	PROPN
ejpam-6968	57	5	=	=	SYM
ejpam-6968	57	6	x−	x−	PROPN
ejpam-6968	57	7	y	y	PROPN
ejpam-6968	57	8	,	,	PUNCT
ejpam-6968	57	9	ż	ż	NOUN
ejpam-6968	57	10	=	=	PUNCT
ejpam-6968	57	11	−4x2	−4x2	PROPN
ejpam-6968	57	12	+	+	NUM
ejpam-6968	57	13	8xy	8xy	NOUN
ejpam-6968	57	14	+	+	CCONJ
ejpam-6968	57	15	yz	yz	X
ejpam-6968	57	16	+	+	CCONJ
ejpam-6968	57	17	α	α	PROPN
ejpam-6968	57	18	,	,	PUNCT
ejpam-6968	57	19	(	(	PUNCT
ejpam-6968	57	20	1	1	X
ejpam-6968	57	21	)	)	PUNCT
ejpam-6968	57	22	where	where	SCONJ
ejpam-6968	57	23	x(t	x(t	PROPN
ejpam-6968	57	24	)	)	PUNCT
ejpam-6968	57	25	,	,	PUNCT
ejpam-6968	57	26	y(t	y(t	PROPN
ejpam-6968	57	27	)	)	PUNCT
ejpam-6968	57	28	,	,	PUNCT
ejpam-6968	57	29	and	and	CCONJ
ejpam-6968	57	30	z(t	z(t	NOUN
ejpam-6968	57	31	)	)	PUNCT
ejpam-6968	57	32	are	be	AUX
ejpam-6968	57	33	the	the	DET
ejpam-6968	57	34	state	state	NOUN
ejpam-6968	57	35	variables	variable	NOUN
ejpam-6968	57	36	,	,	PUNCT
ejpam-6968	57	37	and	and	CCONJ
ejpam-6968	57	38	α	α	PRON
ejpam-6968	57	39	∈	∈	NOUN
ejpam-6968	57	40	r	r	NOUN
ejpam-6968	57	41	is	be	AUX
ejpam-6968	57	42	a	a	DET
ejpam-6968	57	43	real	real	ADJ
ejpam-6968	57	44	parameter	parameter	NOUN
ejpam-6968	57	45	that	that	PRON
ejpam-6968	57	46	affects	affect	VERB
ejpam-6968	57	47	the	the	DET
ejpam-6968	57	48	qualitative	qualitative	ADJ
ejpam-6968	57	49	behavior	behavior	NOUN
ejpam-6968	57	50	of	of	ADP
ejpam-6968	57	51	the	the	DET
ejpam-6968	57	52	system	system	NOUN
ejpam-6968	57	53	.	.	PUNCT
ejpam-6968	58	1	the	the	DET
ejpam-6968	58	2	first	first	ADJ
ejpam-6968	58	3	equation	equation	NOUN
ejpam-6968	58	4	presents	present	VERB
ejpam-6968	58	5	that	that	PRON
ejpam-6968	58	6	z	z	NOUN
ejpam-6968	58	7	supplies	supply	VERB
ejpam-6968	58	8	the	the	DET
ejpam-6968	58	9	instantaneous	instantaneous	ADJ
ejpam-6968	58	10	time	time	NOUN
ejpam-6968	58	11	derivative	derivative	NOUN
ejpam-6968	58	12	of	of	ADP
ejpam-6968	58	13	x	x	PRON
ejpam-6968	58	14	,	,	PUNCT
ejpam-6968	58	15	making	make	VERB
ejpam-6968	58	16	it	it	PRON
ejpam-6968	58	17	the	the	DET
ejpam-6968	58	18	primary	primary	ADJ
ejpam-6968	58	19	driver	driver	NOUN
ejpam-6968	58	20	of	of	ADP
ejpam-6968	58	21	motion	motion	NOUN
ejpam-6968	58	22	along	along	ADP
ejpam-6968	58	23	the	the	DET
ejpam-6968	58	24	x	x	NOUN
ejpam-6968	58	25	-	-	NOUN
ejpam-6968	58	26	direction	direction	NOUN
ejpam-6968	58	27	.	.	PUNCT
ejpam-6968	59	1	then	then	ADV
ejpam-6968	59	2	the	the	DET
ejpam-6968	59	3	second	second	ADJ
ejpam-6968	59	4	equation	equation	NOUN
ejpam-6968	59	5	shows	show	VERB
ejpam-6968	59	6	linear	linear	VERB
ejpam-6968	59	7	negative	negative	ADJ
ejpam-6968	59	8	feedback	feedback	NOUN
ejpam-6968	59	9	between	between	ADP
ejpam-6968	59	10	x	x	PROPN
ejpam-6968	59	11	and	and	CCONJ
ejpam-6968	59	12	y	y	PROPN
ejpam-6968	59	13	,	,	PUNCT
ejpam-6968	59	14	causing	cause	VERB
ejpam-6968	59	15	y	y	PRON
ejpam-6968	59	16	to	to	PART
ejpam-6968	59	17	stretched	stretch	VERB
ejpam-6968	59	18	toward	toward	ADP
ejpam-6968	59	19	the	the	DET
ejpam-6968	59	20	value	value	NOUN
ejpam-6968	59	21	of	of	ADP
ejpam-6968	59	22	x.	x.	NOUN
ejpam-6968	59	23	the	the	DET
ejpam-6968	59	24	third	third	ADJ
ejpam-6968	59	25	equation	equation	NOUN
ejpam-6968	59	26	is	be	AUX
ejpam-6968	59	27	nonlinear	nonlinear	ADJ
ejpam-6968	59	28	,	,	PUNCT
ejpam-6968	59	29	comprising	comprise	VERB
ejpam-6968	59	30	a	a	DET
ejpam-6968	59	31	quadratic	quadratic	ADJ
ejpam-6968	59	32	term	term	NOUN
ejpam-6968	59	33	in	in	ADP
ejpam-6968	59	34	x	x	X
ejpam-6968	59	35	,	,	PUNCT
ejpam-6968	59	36	a	a	DET
ejpam-6968	59	37	bilinear	bilinear	NOUN
ejpam-6968	59	38	interaction	interaction	NOUN
ejpam-6968	59	39	xy	xy	PROPN
ejpam-6968	59	40	,	,	PUNCT
ejpam-6968	59	41	a	a	DET
ejpam-6968	59	42	coupling	coupling	NOUN
ejpam-6968	59	43	term	term	NOUN
ejpam-6968	59	44	yz	yz	PROPN
ejpam-6968	59	45	,	,	PUNCT
ejpam-6968	59	46	and	and	CCONJ
ejpam-6968	59	47	a	a	DET
ejpam-6968	59	48	constant	constant	ADJ
ejpam-6968	59	49	bias	bias	NOUN
ejpam-6968	59	50	,	,	PUNCT
ejpam-6968	59	51	named	name	VERB
ejpam-6968	59	52	α	α	X
ejpam-6968	59	53	.	.	PUNCT
ejpam-6968	60	1	make	make	VERB
ejpam-6968	60	2	it	it	PRON
ejpam-6968	60	3	together	together	ADV
ejpam-6968	60	4	,	,	PUNCT
ejpam-6968	60	5	these	these	DET
ejpam-6968	60	6	signs	sign	NOUN
ejpam-6968	60	7	enable	enable	VERB
ejpam-6968	60	8	rich	rich	ADJ
ejpam-6968	60	9	dynamics	dynamic	NOUN
ejpam-6968	60	10	—	—	PUNCT
ejpam-6968	60	11	including	include	VERB
ejpam-6968	60	12	oscillations	oscillation	NOUN
ejpam-6968	60	13	and	and	CCONJ
ejpam-6968	60	14	chaos	chaos	NOUN
ejpam-6968	60	15	.	.	PUNCT
ejpam-6968	61	1	the	the	DET
ejpam-6968	61	2	parameter	parameter	NOUN
ejpam-6968	61	3	α	α	PROPN
ejpam-6968	61	4	crucially	crucially	ADV
ejpam-6968	61	5	shows	show	VERB
ejpam-6968	61	6	the	the	DET
ejpam-6968	61	7	answer	answer	NOUN
ejpam-6968	61	8	and	and	CCONJ
ejpam-6968	61	9	is	be	AUX
ejpam-6968	61	10	treated	treat	VERB
ejpam-6968	61	11	here	here	ADV
ejpam-6968	61	12	as	as	ADP
ejpam-6968	61	13	the	the	DET
ejpam-6968	61	14	primary	primary	ADJ
ejpam-6968	61	15	bifurcation	bifurcation	NOUN
ejpam-6968	61	16	(	(	PUNCT
ejpam-6968	61	17	control	control	NOUN
ejpam-6968	61	18	)	)	PUNCT
ejpam-6968	61	19	parameter	parameter	NOUN
ejpam-6968	61	20	.	.	PUNCT
ejpam-6968	62	1	in	in	ADP
ejpam-6968	62	2	jafari	jafari	PROPN
ejpam-6968	62	3	’s	’s	PART
ejpam-6968	62	4	original	original	ADJ
ejpam-6968	62	5	display	display	NOUN
ejpam-6968	62	6	,	,	PUNCT
ejpam-6968	62	7	chaos	chaos	NOUN
ejpam-6968	62	8	below	below	ADP
ejpam-6968	62	9	nonequilibrium	nonequilibrium	NOUN
ejpam-6968	62	10	conditions	condition	NOUN
ejpam-6968	62	11	was	be	AUX
ejpam-6968	62	12	noted	note	VERB
ejpam-6968	62	13	,	,	PUNCT
ejpam-6968	62	14	but	but	CCONJ
ejpam-6968	62	15	a	a	DET
ejpam-6968	62	16	comprehensive	comprehensive	ADJ
ejpam-6968	62	17	global	global	ADJ
ejpam-6968	62	18	analysis	analysis	NOUN
ejpam-6968	62	19	was	be	AUX
ejpam-6968	62	20	not	not	PART
ejpam-6968	62	21	pursued	pursue	VERB
ejpam-6968	62	22	.	.	PUNCT
ejpam-6968	63	1	to	to	PART
ejpam-6968	63	2	accomodate	accomodate	VERB
ejpam-6968	63	3	this	this	PRON
ejpam-6968	63	4	,	,	PUNCT
ejpam-6968	63	5	we	we	PRON
ejpam-6968	63	6	systematically	systematically	ADV
ejpam-6968	63	7	vary	vary	VERB
ejpam-6968	63	8	α	α	PRON
ejpam-6968	63	9	and	and	CCONJ
ejpam-6968	63	10	chart	chart	VERB
ejpam-6968	63	11	the	the	DET
ejpam-6968	63	12	associated	associated	ADJ
ejpam-6968	63	13	bifurcation	bifurcation	NOUN
ejpam-6968	63	14	structures	structure	NOUN
ejpam-6968	63	15	and	and	CCONJ
ejpam-6968	63	16	also	also	ADV
ejpam-6968	63	17	attractors	attractor	NOUN
ejpam-6968	63	18	.	.	PUNCT
ejpam-6968	64	1	the	the	DET
ejpam-6968	64	2	sections	section	NOUN
ejpam-6968	64	3	that	that	PRON
ejpam-6968	64	4	follow	follow	VERB
ejpam-6968	64	5	mix	mix	NOUN
ejpam-6968	64	6	analytical	analytical	ADJ
ejpam-6968	64	7	fixed	fix	VERB
ejpam-6968	64	8	-	-	PUNCT
ejpam-6968	64	9	point	point	NOUN
ejpam-6968	64	10	studies	study	NOUN
ejpam-6968	64	11	with	with	ADP
ejpam-6968	64	12	numerical	numerical	ADJ
ejpam-6968	64	13	continuation	continuation	NOUN
ejpam-6968	64	14	to	to	PART
ejpam-6968	64	15	characterize	characterize	VERB
ejpam-6968	64	16	equilibria	equilibrium	NOUN
ejpam-6968	64	17	,	,	PUNCT
ejpam-6968	64	18	bifurcation	bifurcation	NOUN
ejpam-6968	64	19	scenarios	scenario	NOUN
ejpam-6968	64	20	,	,	PUNCT
ejpam-6968	64	21	and	and	CCONJ
ejpam-6968	64	22	the	the	DET
ejpam-6968	64	23	birth	birth	NOUN
ejpam-6968	64	24	of	of	ADP
ejpam-6968	64	25	both	both	PRON
ejpam-6968	64	26	self	self	NOUN
ejpam-6968	64	27	-	-	PUNCT
ejpam-6968	64	28	excited	excited	ADJ
ejpam-6968	64	29	and	and	CCONJ
ejpam-6968	64	30	hidden	hidden	ADJ
ejpam-6968	64	31	attractors	attractor	NOUN
ejpam-6968	64	32	.	.	PUNCT
ejpam-6968	65	1	3	3	X
ejpam-6968	65	2	.	.	X
ejpam-6968	65	3	analytical	analytical	ADJ
ejpam-6968	65	4	results	result	NOUN
ejpam-6968	65	5	to	to	PART
ejpam-6968	65	6	check	check	VERB
ejpam-6968	65	7	the	the	DET
ejpam-6968	65	8	qualitative	qualitative	ADJ
ejpam-6968	65	9	dynamics	dynamic	NOUN
ejpam-6968	65	10	of	of	ADP
ejpam-6968	65	11	the	the	DET
ejpam-6968	65	12	nonlinear	nonlinear	ADJ
ejpam-6968	65	13	system	system	NOUN
ejpam-6968	65	14	(	(	PUNCT
ejpam-6968	65	15	1	1	NUM
ejpam-6968	65	16	)	)	PUNCT
ejpam-6968	66	1	,	,	PUNCT
ejpam-6968	66	2	we	we	PRON
ejpam-6968	66	3	start	start	VERB
ejpam-6968	66	4	with	with	ADP
ejpam-6968	66	5	an	an	DET
ejpam-6968	66	6	analytical	analytical	ADJ
ejpam-6968	66	7	study	study	NOUN
ejpam-6968	66	8	of	of	ADP
ejpam-6968	66	9	its	its	PRON
ejpam-6968	66	10	equilibria	equilibria	NOUN
ejpam-6968	66	11	,	,	PUNCT
ejpam-6968	66	12	local	local	ADJ
ejpam-6968	66	13	stability	stability	NOUN
ejpam-6968	66	14	,	,	PUNCT
ejpam-6968	66	15	and	and	CCONJ
ejpam-6968	66	16	bifurcation	bifurcation	NOUN
ejpam-6968	66	17	structure	structure	NOUN
ejpam-6968	66	18	.	.	PUNCT
ejpam-6968	67	1	this	this	PRON
ejpam-6968	67	2	gives	give	VERB
ejpam-6968	67	3	the	the	DET
ejpam-6968	67	4	theoretical	theoretical	ADJ
ejpam-6968	67	5	scaffolding	scaffolding	NOUN
ejpam-6968	67	6	for	for	ADP
ejpam-6968	67	7	interpreting	interpret	VERB
ejpam-6968	67	8	the	the	DET
ejpam-6968	67	9	numerical	numerical	ADJ
ejpam-6968	67	10	results	result	NOUN
ejpam-6968	67	11	.	.	PUNCT
ejpam-6968	68	1	in	in	ADP
ejpam-6968	68	2	particular	particular	ADJ
ejpam-6968	68	3	,	,	PUNCT
ejpam-6968	68	4	we	we	PRON
ejpam-6968	68	5	locate	locate	VERB
ejpam-6968	68	6	and	and	CCONJ
ejpam-6968	68	7	classify	classify	VERB
ejpam-6968	68	8	the	the	DET
ejpam-6968	68	9	equilibrium	equilibrium	NOUN
ejpam-6968	68	10	points	point	NOUN
ejpam-6968	68	11	,	,	PUNCT
ejpam-6968	68	12	derive	derive	VERB
ejpam-6968	68	13	the	the	DET
ejpam-6968	68	14	characteristic	characteristic	ADJ
ejpam-6968	68	15	polynomial	polynomial	NOUN
ejpam-6968	68	16	of	of	ADP
ejpam-6968	68	17	the	the	DET
ejpam-6968	68	18	linearized	linearize	VERB
ejpam-6968	68	19	system	system	NOUN
ejpam-6968	68	20	,	,	PUNCT
ejpam-6968	68	21	and	and	CCONJ
ejpam-6968	68	22	also	also	ADV
ejpam-6968	68	23	delineate	delineate	VERB
ejpam-6968	68	24	the	the	DET
ejpam-6968	68	25	parameter	parameter	NOUN
ejpam-6968	68	26	intervals	interval	NOUN
ejpam-6968	68	27	where	where	SCONJ
ejpam-6968	68	28	stability	stability	NOUN
ejpam-6968	68	29	changes	change	NOUN
ejpam-6968	68	30	occur	occur	VERB
ejpam-6968	68	31	via	via	ADP
ejpam-6968	68	32	saddle	saddle	NOUN
ejpam-6968	68	33	–	–	PUNCT
ejpam-6968	68	34	node	node	NOUN
ejpam-6968	68	35	and	and	CCONJ
ejpam-6968	68	36	hopf	hopf	ADJ
ejpam-6968	68	37	bifurcations	bifurcation	NOUN
ejpam-6968	68	38	.	.	PUNCT
ejpam-6968	69	1	h.	h.	PROPN
ejpam-6968	69	2	k.	k.	PROPN
ejpam-6968	69	3	fata	fata	PROPN
ejpam-6968	69	4	,	,	PUNCT
ejpam-6968	69	5	n.	n.	PROPN
ejpam-6968	69	6	y.	y.	PROPN
ejpam-6968	69	7	ashar	ashar	PROPN
ejpam-6968	69	8	/	/	SYM
ejpam-6968	69	9	eur	eur	PROPN
ejpam-6968	69	10	.	.	PUNCT
ejpam-6968	70	1	j.	j.	PROPN
ejpam-6968	70	2	pure	pure	PROPN
ejpam-6968	70	3	appl	appl	PROPN
ejpam-6968	70	4	.	.	PROPN
ejpam-6968	70	5	math	math	PROPN
ejpam-6968	70	6	,	,	PUNCT
ejpam-6968	70	7	18	18	NUM
ejpam-6968	70	8	(	(	PUNCT
ejpam-6968	70	9	4	4	NUM
ejpam-6968	70	10	)	)	PUNCT
ejpam-6968	70	11	(	(	PUNCT
ejpam-6968	70	12	2025	2025	NUM
ejpam-6968	70	13	)	)	PUNCT
ejpam-6968	70	14	,	,	PUNCT
ejpam-6968	70	15	6968	6968	NUM
ejpam-6968	70	16	4	4	NUM
ejpam-6968	70	17	of	of	ADP
ejpam-6968	70	18	15	15	NUM
ejpam-6968	70	19	3.1	3.1	NUM
ejpam-6968	70	20	.	.	PUNCT
ejpam-6968	71	1	equilibrium	equilibrium	NOUN
ejpam-6968	71	2	points	point	VERB
ejpam-6968	71	3	the	the	DET
ejpam-6968	71	4	equilibrium	equilibrium	NOUN
ejpam-6968	71	5	points	point	NOUN
ejpam-6968	71	6	of	of	ADP
ejpam-6968	71	7	a	a	DET
ejpam-6968	71	8	dynamical	dynamical	ADJ
ejpam-6968	71	9	system	system	NOUN
ejpam-6968	71	10	are	be	AUX
ejpam-6968	71	11	the	the	DET
ejpam-6968	71	12	locations	location	NOUN
ejpam-6968	71	13	in	in	ADP
ejpam-6968	71	14	wave	wave	NOUN
ejpam-6968	71	15	space	space	NOUN
ejpam-6968	71	16	where	where	SCONJ
ejpam-6968	71	17	all	all	DET
ejpam-6968	71	18	time	time	NOUN
ejpam-6968	71	19	derivatives	derivative	NOUN
ejpam-6968	71	20	vanish	vanish	VERB
ejpam-6968	71	21	.	.	PUNCT
ejpam-6968	72	1	to	to	PART
ejpam-6968	72	2	show	show	VERB
ejpam-6968	72	3	the	the	DET
ejpam-6968	72	4	equilibrium	equilibrium	NOUN
ejpam-6968	72	5	points	point	NOUN
ejpam-6968	72	6	of	of	ADP
ejpam-6968	72	7	system	system	NOUN
ejpam-6968	72	8	(	(	PUNCT
ejpam-6968	72	9	1	1	NUM
ejpam-6968	72	10	)	)	PUNCT
ejpam-6968	72	11	,	,	PUNCT
ejpam-6968	72	12	we	we	PRON
ejpam-6968	72	13	finish	finish	VERB
ejpam-6968	72	14	the	the	DET
ejpam-6968	72	15	algebraic	algebraic	ADJ
ejpam-6968	72	16	equations	equation	NOUN
ejpam-6968	72	17	obtained	obtain	VERB
ejpam-6968	72	18	by	by	ADP
ejpam-6968	72	19	setting	set	VERB
ejpam-6968	72	20	the	the	DET
ejpam-6968	72	21	right	right	ADJ
ejpam-6968	72	22	-	-	PUNCT
ejpam-6968	72	23	hand	hand	NOUN
ejpam-6968	72	24	sides	side	NOUN
ejpam-6968	72	25	of	of	ADP
ejpam-6968	72	26	the	the	DET
ejpam-6968	72	27	differential	differential	ADJ
ejpam-6968	72	28	equations	equation	NOUN
ejpam-6968	72	29	to	to	ADP
ejpam-6968	72	30	zero	zero	NUM
ejpam-6968	72	31	such	such	ADJ
ejpam-6968	72	32	as	as	ADP
ejpam-6968	72	33	:	:	PUNCT
ejpam-6968	72	34			PROPN
ejpam-6968	72	35	ẋ	ẋ	PUNCT
ejpam-6968	73	1	=	=	PUNCT
ejpam-6968	73	2	z	z	NOUN
ejpam-6968	73	3	=	=	SYM
ejpam-6968	73	4	0	0	NUM
ejpam-6968	73	5	,	,	PUNCT
ejpam-6968	73	6	ẏ	ẏ	PROPN
ejpam-6968	73	7	=	=	PUNCT
ejpam-6968	73	8	x−	x−	PROPN
ejpam-6968	73	9	y	y	PROPN
ejpam-6968	73	10	=	=	SYM
ejpam-6968	73	11	0	0	PROPN
ejpam-6968	73	12	,	,	PUNCT
ejpam-6968	73	13	ż	ż	NOUN
ejpam-6968	73	14	=	=	PUNCT
ejpam-6968	73	15	−4x2	−4x2	PROPN
ejpam-6968	73	16	+	+	NUM
ejpam-6968	73	17	8xy	8xy	NOUN
ejpam-6968	73	18	+	+	CCONJ
ejpam-6968	73	19	yz	yz	X
ejpam-6968	73	20	+	+	CCONJ
ejpam-6968	73	21	α	α	NOUN
ejpam-6968	73	22	=	=	SYM
ejpam-6968	73	23	0	0	PROPN
ejpam-6968	73	24	.	.	PUNCT
ejpam-6968	74	1	(	(	PUNCT
ejpam-6968	74	2	2	2	X
ejpam-6968	74	3	)	)	PUNCT
ejpam-6968	74	4	the	the	DET
ejpam-6968	74	5	first	first	ADJ
ejpam-6968	74	6	equation	equation	NOUN
ejpam-6968	74	7	yields	yield	VERB
ejpam-6968	74	8	z	z	NOUN
ejpam-6968	74	9	=	=	SYM
ejpam-6968	74	10	0	0	X
ejpam-6968	74	11	.	.	PUNCT
ejpam-6968	75	1	substituting	substitute	VERB
ejpam-6968	75	2	this	this	PRON
ejpam-6968	75	3	into	into	ADP
ejpam-6968	75	4	the	the	DET
ejpam-6968	75	5	third	third	ADJ
ejpam-6968	75	6	equation	equation	NOUN
ejpam-6968	75	7	makes	make	VERB
ejpam-6968	75	8	−4x2	−4x2	PROPN
ejpam-6968	76	1	+	+	CCONJ
ejpam-6968	76	2	8xy	8xy	NOUN
ejpam-6968	76	3	+	+	CCONJ
ejpam-6968	76	4	α	α	NOUN
ejpam-6968	76	5	=	=	SYM
ejpam-6968	76	6	0	0	NUM
ejpam-6968	76	7	.	.	PUNCT
ejpam-6968	77	1	from	from	ADP
ejpam-6968	77	2	the	the	DET
ejpam-6968	77	3	second	second	ADJ
ejpam-6968	77	4	equation	equation	NOUN
ejpam-6968	77	5	we	we	PRON
ejpam-6968	77	6	obtain	obtain	VERB
ejpam-6968	77	7	x	x	PUNCT
ejpam-6968	77	8	=	=	SYM
ejpam-6968	77	9	y	y	PROPN
ejpam-6968	77	10	;	;	PUNCT
ejpam-6968	77	11	changing	change	VERB
ejpam-6968	77	12	this	this	PRON
ejpam-6968	77	13	into	into	ADP
ejpam-6968	77	14	the	the	DET
ejpam-6968	77	15	previous	previous	ADJ
ejpam-6968	77	16	expression	expression	NOUN
ejpam-6968	77	17	leads	lead	VERB
ejpam-6968	77	18	to	to	ADP
ejpam-6968	77	19	−4x2	−4x2	PROPN
ejpam-6968	77	20	+	+	CCONJ
ejpam-6968	77	21	8x2	8x2	NUM
ejpam-6968	78	1	+	+	CCONJ
ejpam-6968	78	2	α	α	NOUN
ejpam-6968	78	3	=	=	SYM
ejpam-6968	78	4	4x2	4x2	NUM
ejpam-6968	79	1	+	+	CCONJ
ejpam-6968	79	2	α	α	NOUN
ejpam-6968	79	3	=	=	SYM
ejpam-6968	79	4	0	0	PROPN
ejpam-6968	79	5	,	,	PUNCT
ejpam-6968	79	6	which	which	PRON
ejpam-6968	79	7	implies	imply	VERB
ejpam-6968	79	8	x2	x2	PROPN
ejpam-6968	79	9	=	=	PUNCT
ejpam-6968	79	10	−α	−α	PROPN
ejpam-6968	79	11	4	4	NUM
ejpam-6968	79	12	.	.	PUNCT
ejpam-6968	80	1	(	(	PUNCT
ejpam-6968	80	2	3	3	X
ejpam-6968	80	3	)	)	PUNCT
ejpam-6968	80	4	this	this	DET
ejpam-6968	80	5	equation	equation	NOUN
ejpam-6968	80	6	admits	admit	VERB
ejpam-6968	80	7	real	real	ADJ
ejpam-6968	80	8	solutions	solution	NOUN
ejpam-6968	80	9	only	only	ADV
ejpam-6968	80	10	when	when	SCONJ
ejpam-6968	80	11	α	α	PRON
ejpam-6968	80	12	≤	≤	NOUN
ejpam-6968	80	13	0	0	NUM
ejpam-6968	80	14	.	.	PUNCT
ejpam-6968	81	1	thus	thus	ADV
ejpam-6968	81	2	,	,	PUNCT
ejpam-6968	81	3	for	for	ADP
ejpam-6968	81	4	α	α	PRON
ejpam-6968	81	5	<	<	X
ejpam-6968	81	6	0	0	NUM
ejpam-6968	82	1	the	the	DET
ejpam-6968	82	2	system	system	NOUN
ejpam-6968	82	3	possesses	possess	VERB
ejpam-6968	82	4	two	two	NUM
ejpam-6968	82	5	symmetric	symmetric	ADJ
ejpam-6968	82	6	equilibrium	equilibrium	NOUN
ejpam-6968	82	7	points	point	NOUN
ejpam-6968	82	8	:	:	PUNCT
ejpam-6968	82	9	e±(α	e±(α	X
ejpam-6968	82	10	)	)	PUNCT
ejpam-6968	83	1	=	=	PRON
ejpam-6968	83	2	(	(	PUNCT
ejpam-6968	83	3	±	±	NOUN
ejpam-6968	83	4	√	√	PROPN
ejpam-6968	83	5	−α	−α	PROPN
ejpam-6968	83	6	2	2	NUM
ejpam-6968	83	7	,	,	PUNCT
ejpam-6968	83	8	±	±	NOUN
ejpam-6968	83	9	√	√	PROPN
ejpam-6968	83	10	−α	−α	PROPN
ejpam-6968	83	11	2	2	NUM
ejpam-6968	83	12	,	,	PUNCT
ejpam-6968	83	13	0	0	NUM
ejpam-6968	83	14	)	)	PUNCT
ejpam-6968	83	15	.	.	PUNCT
ejpam-6968	84	1	(	(	PUNCT
ejpam-6968	84	2	4	4	X
ejpam-6968	84	3	)	)	PUNCT
ejpam-6968	84	4	when	when	SCONJ
ejpam-6968	84	5	α	α	X
ejpam-6968	84	6	>	>	X
ejpam-6968	84	7	0	0	NUM
ejpam-6968	84	8	,	,	PUNCT
ejpam-6968	84	9	eq	eq	NOUN
ejpam-6968	84	10	.	.	PUNCT
ejpam-6968	85	1	(	(	PUNCT
ejpam-6968	85	2	3	3	X
ejpam-6968	85	3	)	)	PUNCT
ejpam-6968	85	4	has	have	VERB
ejpam-6968	85	5	no	no	DET
ejpam-6968	85	6	real	real	ADJ
ejpam-6968	85	7	solutions	solution	NOUN
ejpam-6968	85	8	,	,	PUNCT
ejpam-6968	85	9	indicating	indicate	VERB
ejpam-6968	85	10	that	that	SCONJ
ejpam-6968	85	11	the	the	DET
ejpam-6968	85	12	system	system	NOUN
ejpam-6968	85	13	lacks	lack	VERB
ejpam-6968	85	14	equilibria	equilibrium	NOUN
ejpam-6968	85	15	within	within	ADP
ejpam-6968	85	16	this	this	DET
ejpam-6968	85	17	parameter	parameter	NOUN
ejpam-6968	85	18	range	range	NOUN
ejpam-6968	85	19	.	.	PUNCT
ejpam-6968	86	1	in	in	ADP
ejpam-6968	86	2	summary	summary	NOUN
ejpam-6968	86	3	,	,	PUNCT
ejpam-6968	86	4	the	the	DET
ejpam-6968	86	5	system	system	NOUN
ejpam-6968	86	6	undergoes	undergo	VERB
ejpam-6968	86	7	a	a	DET
ejpam-6968	86	8	qualitative	qualitative	ADJ
ejpam-6968	86	9	structural	structural	ADJ
ejpam-6968	86	10	change	change	NOUN
ejpam-6968	86	11	at	at	ADP
ejpam-6968	86	12	α	α	NOUN
ejpam-6968	86	13	=	=	SYM
ejpam-6968	86	14	0	0	NUM
ejpam-6968	86	15	:	:	PUNCT
ejpam-6968	86	16	for	for	SCONJ
ejpam-6968	86	17	α	α	PRON
ejpam-6968	86	18	<	<	X
ejpam-6968	86	19	0	0	NUM
ejpam-6968	86	20	two	two	NUM
ejpam-6968	86	21	equilibria	equilibrium	NOUN
ejpam-6968	86	22	exist	exist	VERB
ejpam-6968	86	23	,	,	PUNCT
ejpam-6968	86	24	whereas	whereas	SCONJ
ejpam-6968	86	25	for	for	ADP
ejpam-6968	86	26	α	α	PROPN
ejpam-6968	86	27	>	>	X
ejpam-6968	86	28	0	0	PUNCT
ejpam-6968	87	1	no	no	DET
ejpam-6968	87	2	equilibrium	equilibrium	NOUN
ejpam-6968	87	3	is	be	AUX
ejpam-6968	87	4	present	present	ADJ
ejpam-6968	87	5	.	.	PUNCT
ejpam-6968	88	1	the	the	DET
ejpam-6968	88	2	case	case	NOUN
ejpam-6968	88	3	α	α	X
ejpam-6968	88	4	=	=	SYM
ejpam-6968	88	5	0	0	NUM
ejpam-6968	88	6	represents	represent	VERB
ejpam-6968	88	7	a	a	DET
ejpam-6968	88	8	degenerate	degenerate	ADJ
ejpam-6968	88	9	situation	situation	NOUN
ejpam-6968	88	10	in	in	ADP
ejpam-6968	88	11	which	which	PRON
ejpam-6968	88	12	the	the	DET
ejpam-6968	88	13	two	two	NUM
ejpam-6968	88	14	equilibria	equilibrium	NOUN
ejpam-6968	88	15	coalesce	coalesce	VERB
ejpam-6968	88	16	at	at	ADP
ejpam-6968	88	17	the	the	DET
ejpam-6968	88	18	origin	origin	NOUN
ejpam-6968	88	19	of	of	ADP
ejpam-6968	88	20	the	the	DET
ejpam-6968	88	21	phase	phase	NOUN
ejpam-6968	88	22	space	space	NOUN
ejpam-6968	88	23	.	.	PUNCT
ejpam-6968	89	1	3.2	3.2	NUM
ejpam-6968	89	2	.	.	PUNCT
ejpam-6968	90	1	local	local	ADJ
ejpam-6968	90	2	stability	stability	NOUN
ejpam-6968	90	3	analysis	analysis	NOUN
ejpam-6968	90	4	to	to	PART
ejpam-6968	90	5	examine	examine	VERB
ejpam-6968	90	6	the	the	DET
ejpam-6968	90	7	local	local	ADJ
ejpam-6968	90	8	behavior	behavior	NOUN
ejpam-6968	90	9	near	near	ADP
ejpam-6968	90	10	an	an	DET
ejpam-6968	90	11	equilibrium	equilibrium	NOUN
ejpam-6968	90	12	,	,	PUNCT
ejpam-6968	90	13	the	the	DET
ejpam-6968	90	14	system	system	NOUN
ejpam-6968	90	15	is	be	AUX
ejpam-6968	90	16	linearized	linearize	VERB
ejpam-6968	90	17	through	through	ADP
ejpam-6968	90	18	the	the	DET
ejpam-6968	90	19	jacobian	jacobian	ADJ
ejpam-6968	90	20	matrix	matrix	NOUN
ejpam-6968	90	21	.	.	PUNCT
ejpam-6968	91	1	the	the	DET
ejpam-6968	91	2	resulting	result	VERB
ejpam-6968	91	3	linear	linear	NOUN
ejpam-6968	91	4	system	system	NOUN
ejpam-6968	91	5	’s	’s	PART
ejpam-6968	91	6	eigenvalues	eigenvalue	NOUN
ejpam-6968	91	7	determine	determine	VERB
ejpam-6968	91	8	local	local	ADJ
ejpam-6968	91	9	stability	stability	NOUN
ejpam-6968	91	10	.	.	PUNCT
ejpam-6968	92	1	if	if	SCONJ
ejpam-6968	92	2	no	no	DET
ejpam-6968	92	3	eigenvalue	eigenvalue	NOUN
ejpam-6968	92	4	has	have	VERB
ejpam-6968	92	5	zero	zero	NUM
ejpam-6968	92	6	real	real	ADJ
ejpam-6968	92	7	part	part	NOUN
ejpam-6968	92	8	(	(	PUNCT
ejpam-6968	92	9	the	the	DET
ejpam-6968	92	10	equilibrium	equilibrium	NOUN
ejpam-6968	92	11	is	be	AUX
ejpam-6968	92	12	hyperbolic	hyperbolic	ADJ
ejpam-6968	92	13	)	)	PUNCT
ejpam-6968	92	14	,	,	PUNCT
ejpam-6968	92	15	the	the	DET
ejpam-6968	92	16	linearized	linearize	VERB
ejpam-6968	92	17	system	system	NOUN
ejpam-6968	92	18	reproduces	reproduce	VERB
ejpam-6968	92	19	the	the	DET
ejpam-6968	92	20	qualitative	qualitative	ADJ
ejpam-6968	92	21	dynamics	dynamic	NOUN
ejpam-6968	92	22	of	of	ADP
ejpam-6968	92	23	the	the	DET
ejpam-6968	92	24	nonlinear	nonlinear	ADJ
ejpam-6968	92	25	system	system	NOUN
ejpam-6968	92	26	in	in	ADP
ejpam-6968	92	27	a	a	DET
ejpam-6968	92	28	neighborhood	neighborhood	NOUN
ejpam-6968	92	29	of	of	ADP
ejpam-6968	92	30	the	the	DET
ejpam-6968	92	31	equilibrium	equilibrium	NOUN
ejpam-6968	92	32	[	[	X
ejpam-6968	92	33	14	14	NUM
ejpam-6968	92	34	]	]	PUNCT
ejpam-6968	92	35	.	.	PUNCT
ejpam-6968	93	1	let	let	VERB
ejpam-6968	93	2	the	the	DET
ejpam-6968	93	3	right	right	ADJ
ejpam-6968	93	4	-	-	PUNCT
ejpam-6968	93	5	hand	hand	NOUN
ejpam-6968	93	6	sides	side	NOUN
ejpam-6968	93	7	of	of	ADP
ejpam-6968	93	8	system	system	NOUN
ejpam-6968	93	9	(	(	PUNCT
ejpam-6968	93	10	1	1	X
ejpam-6968	93	11	)	)	PUNCT
ejpam-6968	93	12	be	be	AUX
ejpam-6968	93	13	f1(x	f1(x	PROPN
ejpam-6968	93	14	,	,	PUNCT
ejpam-6968	93	15	y	y	PROPN
ejpam-6968	93	16	,	,	PUNCT
ejpam-6968	93	17	z	z	NOUN
ejpam-6968	93	18	)	)	PUNCT
ejpam-6968	94	1	=	=	SYM
ejpam-6968	94	2	z	z	NOUN
ejpam-6968	94	3	,	,	PUNCT
ejpam-6968	94	4	f2(x	f2(x	PROPN
ejpam-6968	94	5	,	,	PUNCT
ejpam-6968	94	6	y	y	PROPN
ejpam-6968	94	7	,	,	PUNCT
ejpam-6968	94	8	z	z	NOUN
ejpam-6968	94	9	)	)	PUNCT
ejpam-6968	94	10	=	=	SYM
ejpam-6968	94	11	x−	x−	PROPN
ejpam-6968	94	12	y	y	PROPN
ejpam-6968	94	13	,	,	PUNCT
ejpam-6968	94	14	f3(x	f3(x	PROPN
ejpam-6968	94	15	,	,	PUNCT
ejpam-6968	94	16	y	y	PROPN
ejpam-6968	94	17	,	,	PUNCT
ejpam-6968	94	18	z	z	NOUN
ejpam-6968	94	19	)	)	PUNCT
ejpam-6968	94	20	=	=	SYM
ejpam-6968	94	21	−4x2	−4x2	PROPN
ejpam-6968	95	1	+	+	NUM
ejpam-6968	95	2	8xy	8xy	NOUN
ejpam-6968	95	3	+	+	CCONJ
ejpam-6968	95	4	yz	yz	X
ejpam-6968	95	5	+	+	NUM
ejpam-6968	95	6	α	α	NOUN
ejpam-6968	95	7	,	,	PUNCT
ejpam-6968	95	8	with	with	ADP
ejpam-6968	95	9	α	α	PROPN
ejpam-6968	95	10	∈	∈	PROPN
ejpam-6968	95	11	r.	r.	NOUN
ejpam-6968	95	12	the	the	DET
ejpam-6968	95	13	jacobian	jacobian	ADJ
ejpam-6968	95	14	matrix	matrix	NOUN
ejpam-6968	95	15	is	be	AUX
ejpam-6968	95	16	j(x	j(x	PROPN
ejpam-6968	95	17	,	,	PUNCT
ejpam-6968	95	18	y	y	PROPN
ejpam-6968	95	19	,	,	PUNCT
ejpam-6968	95	20	z	z	NOUN
ejpam-6968	95	21	)	)	PUNCT
ejpam-6968	95	22	=	=	SYM
ejpam-6968	96	1			PROPN
ejpam-6968	96	2	0	0	NUM
ejpam-6968	96	3	0	0	NUM
ejpam-6968	96	4	1	1	NUM
ejpam-6968	96	5	1	1	NUM
ejpam-6968	96	6	−1	−1	NOUN
ejpam-6968	96	7	0	0	NUM
ejpam-6968	96	8	−8x+	−8x+	X
ejpam-6968	96	9	8y	8y	NUM
ejpam-6968	96	10	8x+	8x+	NUM
ejpam-6968	96	11	z	z	NOUN
ejpam-6968	96	12	y	y	PROPN
ejpam-6968	96	13			PROPN
ejpam-6968	96	14	.	.	PUNCT
ejpam-6968	97	1	(	(	PUNCT
ejpam-6968	97	2	5	5	X
ejpam-6968	97	3	)	)	PUNCT
ejpam-6968	97	4	h.	h.	PROPN
ejpam-6968	97	5	k.	k.	PROPN
ejpam-6968	97	6	fata	fata	PROPN
ejpam-6968	97	7	,	,	PUNCT
ejpam-6968	97	8	n.	n.	PROPN
ejpam-6968	97	9	y.	y.	PROPN
ejpam-6968	97	10	ashar	ashar	PROPN
ejpam-6968	97	11	/	/	SYM
ejpam-6968	97	12	eur	eur	PROPN
ejpam-6968	97	13	.	.	PUNCT
ejpam-6968	98	1	j.	j.	PROPN
ejpam-6968	98	2	pure	pure	PROPN
ejpam-6968	98	3	appl	appl	PROPN
ejpam-6968	98	4	.	.	PROPN
ejpam-6968	98	5	math	math	PROPN
ejpam-6968	98	6	,	,	PUNCT
ejpam-6968	98	7	18	18	NUM
ejpam-6968	98	8	(	(	PUNCT
ejpam-6968	98	9	4	4	NUM
ejpam-6968	98	10	)	)	PUNCT
ejpam-6968	98	11	(	(	PUNCT
ejpam-6968	98	12	2025	2025	NUM
ejpam-6968	98	13	)	)	PUNCT
ejpam-6968	98	14	,	,	PUNCT
ejpam-6968	98	15	6968	6968	NUM
ejpam-6968	98	16	5	5	NUM
ejpam-6968	98	17	of	of	ADP
ejpam-6968	98	18	15	15	NUM
ejpam-6968	98	19	let	let	VERB
ejpam-6968	98	20	c	c	NOUN
ejpam-6968	98	21	=	=	SYM
ejpam-6968	98	22	±	±	PROPN
ejpam-6968	98	23	√	√	PROPN
ejpam-6968	98	24	−α	−α	PROPN
ejpam-6968	98	25	2	2	NUM
ejpam-6968	98	26	for	for	ADP
ejpam-6968	98	27	α	α	PRON
ejpam-6968	98	28	<	<	X
ejpam-6968	98	29	0	0	NUM
ejpam-6968	98	30	;	;	PUNCT
ejpam-6968	98	31	then	then	ADV
ejpam-6968	98	32	the	the	DET
ejpam-6968	98	33	jacobian	jacobian	PROPN
ejpam-6968	98	34	evaluated	evaluate	VERB
ejpam-6968	98	35	at	at	ADP
ejpam-6968	98	36	equilibrium	equilibrium	NOUN
ejpam-6968	98	37	becomes	become	VERB
ejpam-6968	98	38	j(c	j(c	NOUN
ejpam-6968	98	39	,	,	PUNCT
ejpam-6968	98	40	c	c	NOUN
ejpam-6968	98	41	,	,	PUNCT
ejpam-6968	98	42	0	0	NUM
ejpam-6968	98	43	)	)	PUNCT
ejpam-6968	98	44	=	=	NOUN
ejpam-6968	98	45	0	0	ADP
ejpam-6968	98	46	0	0	NUM
ejpam-6968	98	47	1	1	NUM
ejpam-6968	98	48	1	1	NUM
ejpam-6968	98	49	−1	−1	NOUN
ejpam-6968	98	50	0	0	NUM
ejpam-6968	98	51	0	0	NUM
ejpam-6968	98	52	8c	8c	NUM
ejpam-6968	98	53	c	c	NOUN
ejpam-6968	98	54			PROPN
ejpam-6968	98	55	.	.	PUNCT
ejpam-6968	99	1	(	(	PUNCT
ejpam-6968	99	2	6	6	X
ejpam-6968	99	3	)	)	PUNCT
ejpam-6968	99	4	expanding	expand	VERB
ejpam-6968	99	5	the	the	DET
ejpam-6968	99	6	determinant	determinant	NOUN
ejpam-6968	99	7	of	of	ADP
ejpam-6968	99	8	(	(	PUNCT
ejpam-6968	99	9	j	j	PROPN
ejpam-6968	99	10	−	−	PROPN
ejpam-6968	99	11	λi	λi	NOUN
ejpam-6968	99	12	)	)	PUNCT
ejpam-6968	99	13	along	along	ADP
ejpam-6968	99	14	the	the	DET
ejpam-6968	99	15	first	first	ADJ
ejpam-6968	99	16	row	row	NOUN
ejpam-6968	99	17	gives	give	VERB
ejpam-6968	99	18	det(j	det(j	PROPN
ejpam-6968	99	19	−	−	PROPN
ejpam-6968	99	20	λi	λi	NOUN
ejpam-6968	99	21	)	)	PUNCT
ejpam-6968	99	22	=	=	SYM
ejpam-6968	99	23	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-6968	99	24	−λ	−λ	PROPN
ejpam-6968	99	25	0	0	NUM
ejpam-6968	100	1	1	1	NUM
ejpam-6968	100	2	1	1	NUM
ejpam-6968	100	3	−1−	−1−	ADP
ejpam-6968	100	4	λ	λ	NOUN
ejpam-6968	100	5	0	0	NUM
ejpam-6968	100	6	0	0	NUM
ejpam-6968	100	7	8c	8c	NUM
ejpam-6968	100	8	c−	c−	NOUN
ejpam-6968	100	9	λ	λ	NOUN
ejpam-6968	100	10	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ejpam-6968	100	11	=	=	SYM
ejpam-6968	100	12	(	(	PUNCT
ejpam-6968	100	13	−λ	−λ	NOUN
ejpam-6968	100	14	)	)	PUNCT
ejpam-6968	100	15	∣∣∣∣−1−	∣∣∣∣−1−	NUM
ejpam-6968	101	1	λ	λ	NOUN
ejpam-6968	101	2	0	0	PROPN
ejpam-6968	101	3	8c	8c	NUM
ejpam-6968	101	4	c−	c−	NOUN
ejpam-6968	101	5	λ	λ	NOUN
ejpam-6968	101	6	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6968	101	7	−	−	PROPN
ejpam-6968	101	8	0	0	NUM
ejpam-6968	101	9	·	·	PUNCT
ejpam-6968	101	10	∣∣∣∣1	∣∣∣∣1	NOUN
ejpam-6968	101	11	0	0	NUM
ejpam-6968	101	12	0	0	NUM
ejpam-6968	101	13	c−	c−	NOUN
ejpam-6968	101	14	λ	λ	PROPN
ejpam-6968	101	15	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6968	101	16	+	+	CCONJ
ejpam-6968	101	17	1	1	NUM
ejpam-6968	101	18	·	·	SYM
ejpam-6968	101	19	∣∣∣∣1	∣∣∣∣1	NOUN
ejpam-6968	101	20	−1−	−1−	NOUN
ejpam-6968	101	21	λ	λ	PROPN
ejpam-6968	101	22	0	0	NUM
ejpam-6968	101	23	8c	8c	NUM
ejpam-6968	101	24	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6968	101	25	=	=	SYM
ejpam-6968	101	26	(	(	PUNCT
ejpam-6968	101	27	−λ	−λ	NOUN
ejpam-6968	101	28	)	)	PUNCT
ejpam-6968	101	29	[	[	PUNCT
ejpam-6968	101	30	(	(	PUNCT
ejpam-6968	101	31	−1−	−1−	X
ejpam-6968	101	32	λ)(c−	λ)(c−	NOUN
ejpam-6968	102	1	λ)−	λ)−	ADP
ejpam-6968	102	2	0	0	PUNCT
ejpam-6968	102	3	·	·	SYM
ejpam-6968	102	4	8c	8c	NOUN
ejpam-6968	102	5	]	]	PUNCT
ejpam-6968	103	1	+	+	CCONJ
ejpam-6968	103	2	[	[	PUNCT
ejpam-6968	103	3	1	1	NUM
ejpam-6968	103	4	·	·	SYM
ejpam-6968	103	5	8c−	8c−	NUM
ejpam-6968	103	6	(	(	PUNCT
ejpam-6968	103	7	−1−	−1−	PROPN
ejpam-6968	103	8	λ	λ	PROPN
ejpam-6968	103	9	)	)	PUNCT
ejpam-6968	103	10	·	·	PUNCT
ejpam-6968	103	11	0	0	PUNCT
ejpam-6968	103	12	]	]	PUNCT
ejpam-6968	103	13	=	=	SYM
ejpam-6968	103	14	(	(	PUNCT
ejpam-6968	103	15	−λ	−λ	NOUN
ejpam-6968	103	16	)	)	PUNCT
ejpam-6968	103	17	(	(	PUNCT
ejpam-6968	103	18	−1−	−1−	PROPN
ejpam-6968	103	19	λ)(c−	λ)(c−	X
ejpam-6968	103	20	λ	λ	PROPN
ejpam-6968	103	21	)	)	PUNCT
ejpam-6968	103	22	+	+	CCONJ
ejpam-6968	103	23	8c	8c	NUM
ejpam-6968	103	24	=	=	SYM
ejpam-6968	103	25	(	(	PUNCT
ejpam-6968	103	26	−λ	−λ	NOUN
ejpam-6968	103	27	)	)	PUNCT
ejpam-6968	103	28	(	(	PUNCT
ejpam-6968	103	29	λ2	λ2	NOUN
ejpam-6968	103	30	+	+	CCONJ
ejpam-6968	103	31	(	(	PUNCT
ejpam-6968	103	32	1−	1−	NUM
ejpam-6968	103	33	c)λ−	c)λ−	PROPN
ejpam-6968	103	34	c	c	NOUN
ejpam-6968	103	35	)	)	PUNCT
ejpam-6968	104	1	+	+	CCONJ
ejpam-6968	104	2	8c	8c	NUM
ejpam-6968	104	3	=	=	SYM
ejpam-6968	104	4	−λ3	−λ3	NOUN
ejpam-6968	104	5	+	+	CCONJ
ejpam-6968	104	6	(	(	PUNCT
ejpam-6968	104	7	c−	c−	NOUN
ejpam-6968	105	1	1)λ2	1)λ2	ADJ
ejpam-6968	105	2	+	+	NUM
ejpam-6968	105	3	cλ+	cλ+	ADJ
ejpam-6968	105	4	8c	8c	NUM
ejpam-6968	105	5	=	=	SYM
ejpam-6968	105	6	−	−	PROPN
ejpam-6968	105	7	(	(	PUNCT
ejpam-6968	105	8	λ3	λ3	PROPN
ejpam-6968	105	9	+	+	CCONJ
ejpam-6968	105	10	(	(	PUNCT
ejpam-6968	105	11	1−	1−	NUM
ejpam-6968	105	12	c)λ2	c)λ2	PROPN
ejpam-6968	105	13	−	−	PROPN
ejpam-6968	105	14	cλ−	cλ−	X
ejpam-6968	105	15	8c	8c	NOUN
ejpam-6968	105	16	)	)	PUNCT
ejpam-6968	105	17	.	.	PUNCT
ejpam-6968	106	1	which	which	PRON
ejpam-6968	106	2	yields	yield	VERB
ejpam-6968	106	3	the	the	DET
ejpam-6968	106	4	cubic	cubic	ADJ
ejpam-6968	106	5	characteristic	characteristic	ADJ
ejpam-6968	106	6	polynomial	polynomial	ADJ
ejpam-6968	106	7	λ3	λ3	PROPN
ejpam-6968	106	8	+	+	CCONJ
ejpam-6968	106	9	(	(	PUNCT
ejpam-6968	106	10	1−	1−	NUM
ejpam-6968	106	11	c)λ2	c)λ2	PROPN
ejpam-6968	106	12	−	−	PROPN
ejpam-6968	106	13	cλ−	cλ−	X
ejpam-6968	106	14	8c	8c	X
ejpam-6968	106	15	=	=	SYM
ejpam-6968	106	16	0	0	NUM
ejpam-6968	106	17	.	.	PUNCT
ejpam-6968	107	1	(	(	PUNCT
ejpam-6968	107	2	7	7	X
ejpam-6968	107	3	)	)	PUNCT
ejpam-6968	107	4	denote	denote	VERB
ejpam-6968	107	5	the	the	DET
ejpam-6968	107	6	coefficients	coefficient	NOUN
ejpam-6968	107	7	as	as	ADP
ejpam-6968	107	8	a1	a1	NOUN
ejpam-6968	107	9	=	=	SYM
ejpam-6968	107	10	1−	1−	NUM
ejpam-6968	107	11	c	c	X
ejpam-6968	107	12	,	,	PUNCT
ejpam-6968	107	13	a2	a2	NOUN
ejpam-6968	107	14	=	=	PUNCT
ejpam-6968	107	15	−c	−c	NOUN
ejpam-6968	107	16	,	,	PUNCT
ejpam-6968	107	17	a3	a3	NOUN
ejpam-6968	107	18	=	=	SYM
ejpam-6968	108	1	−8c	−8c	PROPN
ejpam-6968	108	2	.	.	PUNCT
ejpam-6968	109	1	using	use	VERB
ejpam-6968	109	2	the	the	DET
ejpam-6968	109	3	routh	routh	PROPN
ejpam-6968	109	4	–	–	PUNCT
ejpam-6968	109	5	hurwitz	hurwitz	PROPN
ejpam-6968	109	6	criterion	criterion	NOUN
ejpam-6968	109	7	[	[	X
ejpam-6968	109	8	29	29	NUM
ejpam-6968	109	9	]	]	PUNCT
ejpam-6968	109	10	,	,	PUNCT
ejpam-6968	109	11	the	the	DET
ejpam-6968	109	12	necessary	necessary	ADJ
ejpam-6968	109	13	and	and	CCONJ
ejpam-6968	109	14	sufficient	sufficient	ADJ
ejpam-6968	109	15	conditions	condition	NOUN
ejpam-6968	109	16	for	for	ADP
ejpam-6968	109	17	local	local	ADJ
ejpam-6968	109	18	asymptotic	asymptotic	ADJ
ejpam-6968	109	19	stability	stability	NOUN
ejpam-6968	109	20	are	be	AUX
ejpam-6968	109	21	a1	a1	NOUN
ejpam-6968	109	22	>	>	X
ejpam-6968	109	23	0	0	PROPN
ejpam-6968	109	24	,	,	PUNCT
ejpam-6968	109	25	a3	a3	VERB
ejpam-6968	109	26	>	>	X
ejpam-6968	109	27	0	0	PROPN
ejpam-6968	109	28	,	,	PUNCT
ejpam-6968	109	29	a1a2	a1a2	X
ejpam-6968	109	30	>	>	X
ejpam-6968	109	31	a3	a3	NOUN
ejpam-6968	109	32	.	.	PUNCT
ejpam-6968	110	1	these	these	DET
ejpam-6968	110	2	yield	yield	NOUN
ejpam-6968	110	3	c	c	NOUN
ejpam-6968	110	4	<	<	X
ejpam-6968	110	5	1	1	NUM
ejpam-6968	110	6	,	,	PUNCT
ejpam-6968	110	7	c	c	X
ejpam-6968	110	8	<	<	X
ejpam-6968	110	9	0	0	PROPN
ejpam-6968	110	10	,	,	PUNCT
ejpam-6968	110	11	c2	c2	PROPN
ejpam-6968	110	12	+	+	CCONJ
ejpam-6968	110	13	7c	7c	PROPN
ejpam-6968	110	14	>	>	X
ejpam-6968	110	15	0	0	NUM
ejpam-6968	110	16	,	,	PUNCT
ejpam-6968	110	17	which	which	PRON
ejpam-6968	110	18	are	be	AUX
ejpam-6968	110	19	satisfied	satisfied	ADJ
ejpam-6968	110	20	simultaneously	simultaneously	ADV
ejpam-6968	110	21	only	only	ADV
ejpam-6968	110	22	when	when	SCONJ
ejpam-6968	110	23	c	c	X
ejpam-6968	110	24	<	<	X
ejpam-6968	110	25	−7	−7	PROPN
ejpam-6968	110	26	.	.	PUNCT
ejpam-6968	111	1	because	because	SCONJ
ejpam-6968	111	2	c	c	NOUN
ejpam-6968	111	3	=	=	SYM
ejpam-6968	111	4	−	−	PROPN
ejpam-6968	111	5	√	√	NUM
ejpam-6968	111	6	−α	−α	PROPN
ejpam-6968	111	7	2	2	NUM
ejpam-6968	111	8	,	,	PUNCT
ejpam-6968	111	9	stability	stability	NOUN
ejpam-6968	111	10	requires	require	VERB
ejpam-6968	111	11	√	√	PROPN
ejpam-6968	111	12	−α	−α	NOUN
ejpam-6968	111	13	2	2	NUM
ejpam-6968	111	14	>	>	SYM
ejpam-6968	111	15	7	7	NUM
ejpam-6968	111	16	⇒	⇒	NOUN
ejpam-6968	111	17	α	α	X
ejpam-6968	111	18	<	<	X
ejpam-6968	111	19	−196	−196	PROPN
ejpam-6968	111	20	.	.	PUNCT
ejpam-6968	112	1	therefore	therefore	ADV
ejpam-6968	112	2	,	,	PUNCT
ejpam-6968	112	3	the	the	DET
ejpam-6968	112	4	negative	negative	ADJ
ejpam-6968	112	5	equilibrium	equilibrium	NOUN
ejpam-6968	112	6	point	point	NOUN
ejpam-6968	112	7	e−(α	e−(α	PROPN
ejpam-6968	112	8	)	)	PUNCT
ejpam-6968	112	9	=	=	PUNCT
ejpam-6968	112	10	(	(	PUNCT
ejpam-6968	112	11	−	−	NOUN
ejpam-6968	112	12	√	√	NUM
ejpam-6968	112	13	−α	−α	NOUN
ejpam-6968	112	14	2	2	NUM
ejpam-6968	112	15	,	,	PUNCT
ejpam-6968	112	16	−	−	PROPN
ejpam-6968	112	17	√	√	NUM
ejpam-6968	112	18	−α	−α	NOUN
ejpam-6968	112	19	2	2	NUM
ejpam-6968	112	20	,	,	PUNCT
ejpam-6968	112	21	0	0	NUM
ejpam-6968	112	22	)	)	PUNCT
ejpam-6968	113	1	h.	h.	PROPN
ejpam-6968	113	2	k.	k.	PROPN
ejpam-6968	113	3	fata	fata	PROPN
ejpam-6968	113	4	,	,	PUNCT
ejpam-6968	113	5	n.	n.	PROPN
ejpam-6968	113	6	y.	y.	PROPN
ejpam-6968	113	7	ashar	ashar	PROPN
ejpam-6968	113	8	/	/	SYM
ejpam-6968	113	9	eur	eur	PROPN
ejpam-6968	113	10	.	.	PUNCT
ejpam-6968	114	1	j.	j.	PROPN
ejpam-6968	114	2	pure	pure	PROPN
ejpam-6968	114	3	appl	appl	PROPN
ejpam-6968	114	4	.	.	PROPN
ejpam-6968	114	5	math	math	PROPN
ejpam-6968	114	6	,	,	PUNCT
ejpam-6968	114	7	18	18	NUM
ejpam-6968	114	8	(	(	PUNCT
ejpam-6968	114	9	4	4	NUM
ejpam-6968	114	10	)	)	PUNCT
ejpam-6968	114	11	(	(	PUNCT
ejpam-6968	114	12	2025	2025	NUM
ejpam-6968	114	13	)	)	PUNCT
ejpam-6968	114	14	,	,	PUNCT
ejpam-6968	114	15	6968	6968	NUM
ejpam-6968	114	16	6	6	NUM
ejpam-6968	114	17	of	of	ADP
ejpam-6968	114	18	15	15	NUM
ejpam-6968	114	19	is	be	AUX
ejpam-6968	114	20	locally	locally	ADV
ejpam-6968	114	21	asymptotically	asymptotically	ADV
ejpam-6968	114	22	stable	stable	ADJ
ejpam-6968	114	23	if	if	SCONJ
ejpam-6968	115	1	and	and	CCONJ
ejpam-6968	115	2	only	only	ADV
ejpam-6968	115	3	if	if	SCONJ
ejpam-6968	115	4	α	α	PRON
ejpam-6968	115	5	<	<	X
ejpam-6968	115	6	−196	−196	NOUN
ejpam-6968	115	7	.	.	PUNCT
ejpam-6968	116	1	the	the	DET
ejpam-6968	116	2	positive	positive	ADJ
ejpam-6968	116	3	equilibrium	equilibrium	NOUN
ejpam-6968	116	4	e+	e+	PUNCT
ejpam-6968	116	5	,	,	PUNCT
ejpam-6968	116	6	corresponding	correspond	VERB
ejpam-6968	116	7	to	to	ADP
ejpam-6968	116	8	c	c	PROPN
ejpam-6968	116	9	>	>	X
ejpam-6968	116	10	0	0	NUM
ejpam-6968	116	11	,	,	PUNCT
ejpam-6968	116	12	violates	violate	VERB
ejpam-6968	116	13	a3	a3	VERB
ejpam-6968	116	14	>	>	X
ejpam-6968	116	15	0	0	PUNCT
ejpam-6968	117	1	and	and	CCONJ
ejpam-6968	117	2	is	be	AUX
ejpam-6968	117	3	thus	thus	ADV
ejpam-6968	117	4	unstable	unstable	ADJ
ejpam-6968	117	5	for	for	ADP
ejpam-6968	117	6	all	all	DET
ejpam-6968	117	7	admissible	admissible	ADJ
ejpam-6968	117	8	α	α	NOUN
ejpam-6968	117	9	.	.	PUNCT
ejpam-6968	118	1	such	such	ADJ
ejpam-6968	118	2	bifurcation	bifurcation	NOUN
ejpam-6968	118	3	-	-	PUNCT
ejpam-6968	118	4	driven	drive	VERB
ejpam-6968	118	5	transitions	transition	NOUN
ejpam-6968	118	6	between	between	ADP
ejpam-6968	118	7	stability	stability	NOUN
ejpam-6968	118	8	and	and	CCONJ
ejpam-6968	118	9	oscillation	oscillation	NOUN
ejpam-6968	118	10	commonly	commonly	ADV
ejpam-6968	118	11	appear	appear	VERB
ejpam-6968	118	12	in	in	ADP
ejpam-6968	118	13	feedback	feedback	NOUN
ejpam-6968	118	14	-	-	PUNCT
ejpam-6968	118	15	controlled	control	VERB
ejpam-6968	118	16	mechanical	mechanical	ADJ
ejpam-6968	118	17	or	or	CCONJ
ejpam-6968	118	18	electrical	electrical	ADJ
ejpam-6968	118	19	oscillators	oscillator	NOUN
ejpam-6968	118	20	,	,	PUNCT
ejpam-6968	118	21	underscoring	underscore	VERB
ejpam-6968	118	22	the	the	DET
ejpam-6968	118	23	physical	physical	ADJ
ejpam-6968	118	24	relevance	relevance	NOUN
ejpam-6968	118	25	of	of	ADP
ejpam-6968	118	26	the	the	DET
ejpam-6968	118	27	present	present	ADJ
ejpam-6968	118	28	model	model	NOUN
ejpam-6968	118	29	.	.	PUNCT
ejpam-6968	119	1	3.3	3.3	NUM
ejpam-6968	119	2	.	.	PUNCT
ejpam-6968	120	1	bifurcation	bifurcation	NOUN
ejpam-6968	120	2	analysis	analysis	NOUN
ejpam-6968	120	3	the	the	DET
ejpam-6968	120	4	local	local	ADJ
ejpam-6968	120	5	stability	stability	NOUN
ejpam-6968	120	6	analysis	analysis	NOUN
ejpam-6968	120	7	above	above	ADV
ejpam-6968	120	8	shows	show	VERB
ejpam-6968	120	9	that	that	SCONJ
ejpam-6968	120	10	the	the	DET
ejpam-6968	120	11	system	system	NOUN
ejpam-6968	120	12	admits	admit	VERB
ejpam-6968	120	13	a	a	DET
ejpam-6968	120	14	pair	pair	NOUN
ejpam-6968	120	15	of	of	ADP
ejpam-6968	120	16	symmetric	symmetric	ADJ
ejpam-6968	120	17	equilibria	equilibrium	NOUN
ejpam-6968	120	18	of	of	ADP
ejpam-6968	120	19	the	the	DET
ejpam-6968	120	20	form	form	NOUN
ejpam-6968	120	21	(	(	PUNCT
ejpam-6968	120	22	c	c	X
ejpam-6968	120	23	,	,	PUNCT
ejpam-6968	120	24	c	c	NOUN
ejpam-6968	120	25	,	,	PUNCT
ejpam-6968	120	26	0	0	NUM
ejpam-6968	120	27	)	)	PUNCT
ejpam-6968	120	28	with	with	ADP
ejpam-6968	120	29	c	c	NOUN
ejpam-6968	120	30	=	=	SYM
ejpam-6968	120	31	±	±	PROPN
ejpam-6968	120	32	√	√	PROPN
ejpam-6968	120	33	−α	−α	NOUN
ejpam-6968	120	34	2	2	NUM
ejpam-6968	120	35	.	.	PUNCT
ejpam-6968	121	1	the	the	DET
ejpam-6968	121	2	negative	negative	ADJ
ejpam-6968	121	3	equilibrium	equilibrium	NOUN
ejpam-6968	121	4	e−(α	e−(α	PROPN
ejpam-6968	121	5	)	)	PUNCT
ejpam-6968	121	6	is	be	AUX
ejpam-6968	121	7	locally	locally	ADV
ejpam-6968	121	8	asymptotically	asymptotically	ADV
ejpam-6968	121	9	stable	stable	ADJ
ejpam-6968	121	10	if	if	SCONJ
ejpam-6968	121	11	and	and	CCONJ
ejpam-6968	121	12	only	only	ADV
ejpam-6968	121	13	if	if	SCONJ
ejpam-6968	121	14	α	α	PRON
ejpam-6968	121	15	<	<	X
ejpam-6968	121	16	−196	−196	PROPN
ejpam-6968	121	17	.	.	PUNCT
ejpam-6968	122	1	as	as	ADP
ejpam-6968	122	2	α	α	NOUN
ejpam-6968	122	3	increases	increase	NOUN
ejpam-6968	122	4	,	,	PUNCT
ejpam-6968	122	5	the	the	DET
ejpam-6968	122	6	equilibrium	equilibrium	NOUN
ejpam-6968	122	7	gradually	gradually	ADV
ejpam-6968	122	8	loses	lose	VERB
ejpam-6968	122	9	stability	stability	NOUN
ejpam-6968	122	10	and	and	CCONJ
ejpam-6968	122	11	eventually	eventually	ADV
ejpam-6968	122	12	disappears	disappear	VERB
ejpam-6968	122	13	for	for	ADP
ejpam-6968	122	14	α	α	DET
ejpam-6968	122	15	≥	≥	NOUN
ejpam-6968	122	16	0	0	NUM
ejpam-6968	122	17	.	.	PUNCT
ejpam-6968	123	1	this	this	DET
ejpam-6968	123	2	behavior	behavior	NOUN
ejpam-6968	123	3	suggests	suggest	VERB
ejpam-6968	123	4	the	the	DET
ejpam-6968	123	5	occurrence	occurrence	NOUN
ejpam-6968	123	6	of	of	ADP
ejpam-6968	123	7	bifurcations	bifurcation	NOUN
ejpam-6968	123	8	—	—	PUNCT
ejpam-6968	123	9	qualitative	qualitative	ADJ
ejpam-6968	123	10	changes	change	NOUN
ejpam-6968	123	11	in	in	ADP
ejpam-6968	123	12	the	the	DET
ejpam-6968	123	13	system	system	NOUN
ejpam-6968	123	14	dynamics	dynamic	NOUN
ejpam-6968	123	15	as	as	SCONJ
ejpam-6968	123	16	α	α	PROPN
ejpam-6968	123	17	passes	pass	VERB
ejpam-6968	123	18	through	through	ADP
ejpam-6968	123	19	critical	critical	ADJ
ejpam-6968	123	20	values	value	NOUN
ejpam-6968	123	21	.	.	PUNCT
ejpam-6968	124	1	theorem	theorem	ADJ
ejpam-6968	124	2	1	1	NUM
ejpam-6968	124	3	(	(	PUNCT
ejpam-6968	124	4	bifurcation	bifurcation	NOUN
ejpam-6968	124	5	structure	structure	NOUN
ejpam-6968	124	6	of	of	ADP
ejpam-6968	124	7	the	the	DET
ejpam-6968	124	8	system	system	NOUN
ejpam-6968	124	9	)	)	PUNCT
ejpam-6968	124	10	.	.	PUNCT
ejpam-6968	125	1	consider	consider	VERB
ejpam-6968	125	2	system	system	NOUN
ejpam-6968	125	3	(	(	PUNCT
ejpam-6968	125	4	1	1	NUM
ejpam-6968	125	5	)	)	PUNCT
ejpam-6968	125	6	with	with	ADP
ejpam-6968	125	7	parameter	parameter	NOUN
ejpam-6968	125	8	α	α	PROPN
ejpam-6968	125	9	∈	∈	PROPN
ejpam-6968	125	10	r.	r.	NOUN
ejpam-6968	125	11	the	the	DET
ejpam-6968	125	12	following	follow	VERB
ejpam-6968	125	13	bifurcation	bifurcation	NOUN
ejpam-6968	125	14	phenomena	phenomenon	NOUN
ejpam-6968	125	15	occur	occur	VERB
ejpam-6968	125	16	:	:	PUNCT
ejpam-6968	125	17	(	(	PUNCT
ejpam-6968	125	18	i	i	NOUN
ejpam-6968	125	19	)	)	PUNCT
ejpam-6968	125	20	for	for	ADP
ejpam-6968	125	21	α	α	PRON
ejpam-6968	125	22	<	<	X
ejpam-6968	125	23	0	0	PROPN
ejpam-6968	125	24	,	,	PUNCT
ejpam-6968	125	25	two	two	NUM
ejpam-6968	125	26	symmetric	symmetric	ADJ
ejpam-6968	125	27	real	real	ADJ
ejpam-6968	125	28	equilibria	equilibrium	NOUN
ejpam-6968	125	29	exist	exist	VERB
ejpam-6968	125	30	as	as	ADP
ejpam-6968	125	31	in	in	ADP
ejpam-6968	125	32	eq	eq	NOUN
ejpam-6968	125	33	.	.	PUNCT
ejpam-6968	126	1	(	(	PUNCT
ejpam-6968	126	2	4	4	NUM
ejpam-6968	126	3	)	)	PUNCT
ejpam-6968	126	4	.	.	PUNCT
ejpam-6968	127	1	as	as	ADP
ejpam-6968	127	2	α	α	PROPN
ejpam-6968	127	3	→	→	SYM
ejpam-6968	127	4	0−	0−	NUM
ejpam-6968	127	5	,	,	PUNCT
ejpam-6968	127	6	these	these	DET
ejpam-6968	127	7	equilibria	equilibrium	NOUN
ejpam-6968	127	8	approach	approach	VERB
ejpam-6968	127	9	each	each	DET
ejpam-6968	127	10	other	other	ADJ
ejpam-6968	127	11	and	and	CCONJ
ejpam-6968	127	12	coalesce	coalesce	NOUN
ejpam-6968	127	13	at	at	ADP
ejpam-6968	127	14	the	the	DET
ejpam-6968	127	15	origin	origin	NOUN
ejpam-6968	127	16	.	.	PUNCT
ejpam-6968	128	1	(	(	PUNCT
ejpam-6968	128	2	ii	ii	NOUN
ejpam-6968	128	3	)	)	PUNCT
ejpam-6968	128	4	at	at	ADP
ejpam-6968	128	5	the	the	DET
ejpam-6968	128	6	critical	critical	ADJ
ejpam-6968	128	7	value	value	NOUN
ejpam-6968	128	8	α	α	NOUN
ejpam-6968	128	9	=	=	SYM
ejpam-6968	128	10	0	0	PROPN
ejpam-6968	128	11	,	,	PUNCT
ejpam-6968	128	12	the	the	DET
ejpam-6968	128	13	system	system	NOUN
ejpam-6968	128	14	undergoes	undergo	VERB
ejpam-6968	128	15	a	a	DET
ejpam-6968	128	16	saddle	saddle	NOUN
ejpam-6968	128	17	–	–	PUNCT
ejpam-6968	128	18	node	node	NOUN
ejpam-6968	128	19	bifurcation	bifurcation	NOUN
ejpam-6968	128	20	:	:	PUNCT
ejpam-6968	128	21	the	the	DET
ejpam-6968	128	22	two	two	NUM
ejpam-6968	128	23	equilibria	equilibrium	NOUN
ejpam-6968	128	24	merge	merge	VERB
ejpam-6968	128	25	into	into	ADP
ejpam-6968	128	26	a	a	DET
ejpam-6968	128	27	degenerate	degenerate	ADJ
ejpam-6968	128	28	point	point	NOUN
ejpam-6968	128	29	at	at	ADP
ejpam-6968	128	30	the	the	DET
ejpam-6968	128	31	origin	origin	NOUN
ejpam-6968	128	32	.	.	PUNCT
ejpam-6968	129	1	no	no	DET
ejpam-6968	129	2	real	real	ADJ
ejpam-6968	129	3	equilibrium	equilibrium	NOUN
ejpam-6968	129	4	exists	exist	VERB
ejpam-6968	129	5	for	for	ADP
ejpam-6968	129	6	α	α	PROPN
ejpam-6968	129	7	>	>	X
ejpam-6968	129	8	0	0	NUM
ejpam-6968	129	9	.	.	PUNCT
ejpam-6968	130	1	(	(	PUNCT
ejpam-6968	130	2	iii	iii	NOUN
ejpam-6968	130	3	)	)	PUNCT
ejpam-6968	130	4	as	as	SCONJ
ejpam-6968	130	5	α	α	NOUN
ejpam-6968	130	6	decreases	decrease	VERB
ejpam-6968	130	7	further	far	ADV
ejpam-6968	130	8	,	,	PUNCT
ejpam-6968	130	9	a	a	DET
ejpam-6968	130	10	hopf	hopf	ADJ
ejpam-6968	130	11	bifurcation	bifurcation	NOUN
ejpam-6968	130	12	occurs	occur	VERB
ejpam-6968	130	13	at	at	ADP
ejpam-6968	130	14	α	α	NOUN
ejpam-6968	130	15	=	=	SYM
ejpam-6968	130	16	−196	−196	NOUN
ejpam-6968	130	17	.	.	PUNCT
ejpam-6968	131	1	at	at	ADP
ejpam-6968	131	2	this	this	DET
ejpam-6968	131	3	point	point	NOUN
ejpam-6968	131	4	the	the	DET
ejpam-6968	131	5	jacobian	jacobian	NOUN
ejpam-6968	131	6	at	at	ADP
ejpam-6968	131	7	e	e	X
ejpam-6968	131	8	=	=	PUNCT
ejpam-6968	131	9	(	(	PUNCT
ejpam-6968	131	10	−7,−7	−7,−7	PROPN
ejpam-6968	131	11	,	,	PUNCT
ejpam-6968	131	12	0	0	NUM
ejpam-6968	131	13	)	)	PUNCT
ejpam-6968	131	14	possesses	possess	VERB
ejpam-6968	131	15	a	a	DET
ejpam-6968	131	16	pair	pair	NOUN
ejpam-6968	131	17	of	of	ADP
ejpam-6968	131	18	purely	purely	ADV
ejpam-6968	131	19	imaginary	imaginary	ADJ
ejpam-6968	131	20	eigenvalues	eigenvalue	NOUN
ejpam-6968	131	21	,	,	PUNCT
ejpam-6968	131	22	signaling	signal	VERB
ejpam-6968	131	23	a	a	DET
ejpam-6968	131	24	loss	loss	NOUN
ejpam-6968	131	25	of	of	ADP
ejpam-6968	131	26	stability	stability	NOUN
ejpam-6968	131	27	and	and	CCONJ
ejpam-6968	131	28	the	the	DET
ejpam-6968	131	29	onset	onset	NOUN
ejpam-6968	131	30	of	of	ADP
ejpam-6968	131	31	oscillatory	oscillatory	ADJ
ejpam-6968	131	32	motion	motion	NOUN
ejpam-6968	131	33	.	.	PUNCT
ejpam-6968	132	1	(	(	PUNCT
ejpam-6968	132	2	iv	iv	X
ejpam-6968	132	3	)	)	PUNCT
ejpam-6968	132	4	the	the	DET
ejpam-6968	132	5	hopf	hopf	ADJ
ejpam-6968	132	6	bifurcation	bifurcation	NOUN
ejpam-6968	132	7	is	be	AUX
ejpam-6968	132	8	supercritical	supercritical	ADJ
ejpam-6968	132	9	:	:	PUNCT
ejpam-6968	132	10	as	as	SCONJ
ejpam-6968	132	11	α	α	PROPN
ejpam-6968	132	12	increases	increase	VERB
ejpam-6968	132	13	past	past	ADP
ejpam-6968	132	14	−196	−196	NOUN
ejpam-6968	132	15	,	,	PUNCT
ejpam-6968	132	16	a	a	DET
ejpam-6968	132	17	stable	stable	ADJ
ejpam-6968	132	18	limit	limit	NOUN
ejpam-6968	132	19	cycle	cycle	NOUN
ejpam-6968	132	20	bifurcates	bifurcate	NOUN
ejpam-6968	132	21	from	from	ADP
ejpam-6968	132	22	the	the	DET
ejpam-6968	132	23	equilibrium	equilibrium	NOUN
ejpam-6968	132	24	while	while	SCONJ
ejpam-6968	132	25	the	the	DET
ejpam-6968	132	26	equilibrium	equilibrium	NOUN
ejpam-6968	132	27	itself	itself	PRON
ejpam-6968	132	28	becomes	become	VERB
ejpam-6968	132	29	unstable	unstable	ADJ
ejpam-6968	132	30	.	.	PUNCT
ejpam-6968	133	1	proof	proof	NOUN
ejpam-6968	133	2	.	.	PUNCT
ejpam-6968	134	1	from	from	ADP
ejpam-6968	134	2	the	the	DET
ejpam-6968	134	3	equilibrium	equilibrium	NOUN
ejpam-6968	134	4	condition	condition	NOUN
ejpam-6968	134	5	(	(	PUNCT
ejpam-6968	134	6	3	3	NUM
ejpam-6968	134	7	)	)	PUNCT
ejpam-6968	134	8	,	,	PUNCT
ejpam-6968	134	9	real	real	ADJ
ejpam-6968	134	10	solutions	solution	NOUN
ejpam-6968	134	11	exist	exist	VERB
ejpam-6968	134	12	only	only	ADV
ejpam-6968	134	13	if	if	SCONJ
ejpam-6968	134	14	α	α	PRON
ejpam-6968	134	15	≤	≤	NOUN
ejpam-6968	134	16	0	0	NUM
ejpam-6968	134	17	.	.	PUNCT
ejpam-6968	135	1	for	for	ADP
ejpam-6968	135	2	α	α	PRON
ejpam-6968	135	3	<	<	X
ejpam-6968	135	4	0	0	NUM
ejpam-6968	135	5	two	two	NUM
ejpam-6968	135	6	symmetric	symmetric	ADJ
ejpam-6968	135	7	equilibria	equilibrium	NOUN
ejpam-6968	135	8	exist	exist	VERB
ejpam-6968	135	9	;	;	PUNCT
ejpam-6968	135	10	at	at	ADP
ejpam-6968	135	11	α	α	NOUN
ejpam-6968	135	12	=	=	SYM
ejpam-6968	135	13	0	0	NUM
ejpam-6968	135	14	they	they	PRON
ejpam-6968	135	15	merge	merge	VERB
ejpam-6968	135	16	at	at	ADP
ejpam-6968	135	17	the	the	DET
ejpam-6968	135	18	origin	origin	NOUN
ejpam-6968	135	19	,	,	PUNCT
ejpam-6968	135	20	and	and	CCONJ
ejpam-6968	135	21	for	for	ADP
ejpam-6968	135	22	α	α	PROPN
ejpam-6968	135	23	>	>	X
ejpam-6968	135	24	0	0	PUNCT
ejpam-6968	136	1	none	none	NOUN
ejpam-6968	136	2	remain	remain	VERB
ejpam-6968	136	3	—	—	PUNCT
ejpam-6968	136	4	characterizing	characterize	VERB
ejpam-6968	136	5	a	a	DET
ejpam-6968	136	6	saddle	saddle	NOUN
ejpam-6968	136	7	–	–	PUNCT
ejpam-6968	136	8	node	node	NOUN
ejpam-6968	136	9	bifurcation	bifurcation	NOUN
ejpam-6968	136	10	at	at	ADP
ejpam-6968	136	11	α	α	NOUN
ejpam-6968	136	12	=	=	SYM
ejpam-6968	136	13	0	0	PROPN
ejpam-6968	136	14	.	.	PUNCT
ejpam-6968	136	15	to	to	PART
ejpam-6968	136	16	analyze	analyze	VERB
ejpam-6968	136	17	the	the	DET
ejpam-6968	136	18	hopf	hopf	ADJ
ejpam-6968	136	19	bifurcation	bifurcation	NOUN
ejpam-6968	136	20	,	,	PUNCT
ejpam-6968	136	21	substitute	substitute	NOUN
ejpam-6968	136	22	λ	λ	X
ejpam-6968	136	23	=	=	SYM
ejpam-6968	136	24	iω	iω	PROPN
ejpam-6968	136	25	,	,	PUNCT
ejpam-6968	136	26	ω	ω	PROPN
ejpam-6968	136	27	∈	∈	PROPN
ejpam-6968	136	28	r	r	NOUN
ejpam-6968	136	29	into	into	ADP
ejpam-6968	136	30	eq	eq	NOUN
ejpam-6968	136	31	.	.	PUNCT
ejpam-6968	137	1	(	(	PUNCT
ejpam-6968	137	2	7	7	NUM
ejpam-6968	137	3	):	):	PUNCT
ejpam-6968	137	4	(	(	PUNCT
ejpam-6968	137	5	iω)3	iω)3	PROPN
ejpam-6968	137	6	+	+	CCONJ
ejpam-6968	137	7	(	(	PUNCT
ejpam-6968	137	8	1−	1−	NUM
ejpam-6968	137	9	c)(iω)2	c)(iω)2	NOUN
ejpam-6968	137	10	−	−	PROPN
ejpam-6968	137	11	c(iω)−	c(iω)−	NOUN
ejpam-6968	137	12	8c	8c	NUM
ejpam-6968	137	13	=	=	SYM
ejpam-6968	137	14	0	0	NUM
ejpam-6968	137	15	⇐	⇐	ADJ
ejpam-6968	137	16	⇒	⇒	NOUN
ejpam-6968	137	17	−iω3	−iω3	X
ejpam-6968	137	18	−	−	PROPN
ejpam-6968	137	19	(	(	PUNCT
ejpam-6968	137	20	1−	1−	NUM
ejpam-6968	137	21	c)ω2	c)ω2	PROPN
ejpam-6968	137	22	−	−	NOUN
ejpam-6968	137	23	icω	icω	NOUN
ejpam-6968	137	24	−	−	PROPN
ejpam-6968	137	25	8c	8c	NUM
ejpam-6968	137	26	=	=	SYM
ejpam-6968	137	27	0	0	X
ejpam-6968	137	28	.	.	X
ejpam-6968	138	1	separating	separate	VERB
ejpam-6968	138	2	real	real	ADJ
ejpam-6968	138	3	and	and	CCONJ
ejpam-6968	138	4	imaginary	imaginary	ADJ
ejpam-6968	138	5	parts	part	NOUN
ejpam-6968	138	6	gives	give	VERB
ejpam-6968	138	7	real	real	ADJ
ejpam-6968	138	8	:	:	PUNCT
ejpam-6968	138	9	−	−	PROPN
ejpam-6968	139	1	(	(	PUNCT
ejpam-6968	139	2	1−	1−	NUM
ejpam-6968	139	3	c)ω2	c)ω2	PROPN
ejpam-6968	139	4	−	−	PROPN
ejpam-6968	139	5	8c	8c	NUM
ejpam-6968	139	6	=	=	SYM
ejpam-6968	139	7	0	0	NUM
ejpam-6968	139	8	,	,	PUNCT
ejpam-6968	139	9	imaginary	imaginary	ADJ
ejpam-6968	139	10	:	:	PUNCT
ejpam-6968	139	11	−	−	PROPN
ejpam-6968	139	12	ω3	ω3	NOUN
ejpam-6968	139	13	−	−	NOUN
ejpam-6968	139	14	cω	cω	NOUN
ejpam-6968	139	15	=	=	SYM
ejpam-6968	139	16	0	0	NUM
ejpam-6968	139	17	⇒	⇒	NOUN
ejpam-6968	139	18	ω2	ω2	NOUN
ejpam-6968	139	19	=	=	PUNCT
ejpam-6968	139	20	−c	−c	NOUN
ejpam-6968	139	21	.	.	PUNCT
ejpam-6968	140	1	substituting	substitute	VERB
ejpam-6968	140	2	ω2	ω2	NOUN
ejpam-6968	140	3	=	=	PUNCT
ejpam-6968	140	4	−c	−c	NOUN
ejpam-6968	140	5	into	into	ADP
ejpam-6968	140	6	the	the	DET
ejpam-6968	140	7	real	real	ADJ
ejpam-6968	140	8	part	part	NOUN
ejpam-6968	140	9	yields	yield	VERB
ejpam-6968	140	10	−(1−	−(1−	VERB
ejpam-6968	140	11	c)(−c)−	c)(−c)−	PROPN
ejpam-6968	140	12	8c	8c	NUM
ejpam-6968	140	13	=	=	SYM
ejpam-6968	140	14	c(1−	c(1−	PROPN
ejpam-6968	140	15	c)−	c)−	PROPN
ejpam-6968	140	16	8c	8c	NUM
ejpam-6968	140	17	=	=	SYM
ejpam-6968	140	18	−c2	−c2	PROPN
ejpam-6968	140	19	−	−	PROPN
ejpam-6968	140	20	7c	7c	PROPN
ejpam-6968	140	21	=	=	SYM
ejpam-6968	140	22	0	0	NUM
ejpam-6968	140	23	,	,	PUNCT
ejpam-6968	140	24	h.	h.	PROPN
ejpam-6968	140	25	k.	k.	PROPN
ejpam-6968	140	26	fata	fata	PROPN
ejpam-6968	140	27	,	,	PUNCT
ejpam-6968	140	28	n.	n.	PROPN
ejpam-6968	140	29	y.	y.	PROPN
ejpam-6968	140	30	ashar	ashar	PROPN
ejpam-6968	140	31	/	/	SYM
ejpam-6968	140	32	eur	eur	PROPN
ejpam-6968	140	33	.	.	PUNCT
ejpam-6968	141	1	j.	j.	PROPN
ejpam-6968	141	2	pure	pure	PROPN
ejpam-6968	141	3	appl	appl	PROPN
ejpam-6968	141	4	.	.	PROPN
ejpam-6968	141	5	math	math	PROPN
ejpam-6968	141	6	,	,	PUNCT
ejpam-6968	141	7	18	18	NUM
ejpam-6968	141	8	(	(	PUNCT
ejpam-6968	141	9	4	4	NUM
ejpam-6968	141	10	)	)	PUNCT
ejpam-6968	141	11	(	(	PUNCT
ejpam-6968	141	12	2025	2025	NUM
ejpam-6968	141	13	)	)	PUNCT
ejpam-6968	141	14	,	,	PUNCT
ejpam-6968	141	15	6968	6968	NUM
ejpam-6968	141	16	7	7	NUM
ejpam-6968	141	17	of	of	ADP
ejpam-6968	141	18	15	15	NUM
ejpam-6968	141	19	figure	figure	NOUN
ejpam-6968	141	20	1	1	NUM
ejpam-6968	141	21	:	:	PUNCT
ejpam-6968	141	22	variation	variation	NOUN
ejpam-6968	141	23	of	of	ADP
ejpam-6968	141	24	the	the	DET
ejpam-6968	141	25	real	real	ADJ
ejpam-6968	141	26	parts	part	NOUN
ejpam-6968	141	27	of	of	ADP
ejpam-6968	141	28	the	the	DET
ejpam-6968	141	29	eigenvalues	eigenvalue	NOUN
ejpam-6968	141	30	of	of	ADP
ejpam-6968	141	31	j(c	j(c	NOUN
ejpam-6968	141	32	,	,	PUNCT
ejpam-6968	141	33	c	c	NOUN
ejpam-6968	141	34	,	,	PUNCT
ejpam-6968	141	35	0	0	NUM
ejpam-6968	141	36	)	)	PUNCT
ejpam-6968	141	37	with	with	ADP
ejpam-6968	141	38	the	the	DET
ejpam-6968	141	39	control	control	NOUN
ejpam-6968	141	40	parameter	parameter	PROPN
ejpam-6968	141	41	α	α	PROPN
ejpam-6968	141	42	.	.	PROPN
ejpam-6968	141	43	stable	stable	ADJ
ejpam-6968	141	44	(	(	PUNCT
ejpam-6968	141	45	negative	negative	ADJ
ejpam-6968	141	46	real	real	ADJ
ejpam-6968	141	47	parts	part	NOUN
ejpam-6968	141	48	)	)	PUNCT
ejpam-6968	141	49	for	for	ADP
ejpam-6968	141	50	α	α	DET
ejpam-6968	141	51	<	<	X
ejpam-6968	141	52	−196	−196	NOUN
ejpam-6968	141	53	at	at	ADP
ejpam-6968	141	54	e−	e−	PROPN
ejpam-6968	141	55	,	,	PUNCT
ejpam-6968	141	56	unstable	unstable	ADJ
ejpam-6968	141	57	otherwise	otherwise	ADV
ejpam-6968	141	58	.	.	PUNCT
ejpam-6968	142	1	so	so	ADV
ejpam-6968	142	2	c	c	NOUN
ejpam-6968	142	3	=	=	SYM
ejpam-6968	142	4	0	0	NUM
ejpam-6968	142	5	or	or	CCONJ
ejpam-6968	142	6	c	c	NOUN
ejpam-6968	142	7	=	=	PUNCT
ejpam-6968	142	8	−7	−7	PROPN
ejpam-6968	142	9	.	.	PUNCT
ejpam-6968	143	1	because	because	SCONJ
ejpam-6968	143	2	c	c	NOUN
ejpam-6968	143	3	=	=	SYM
ejpam-6968	143	4	0	0	NUM
ejpam-6968	143	5	implies	imply	VERB
ejpam-6968	143	6	ω	ω	NOUN
ejpam-6968	143	7	=	=	SYM
ejpam-6968	143	8	0	0	NUM
ejpam-6968	143	9	,	,	PUNCT
ejpam-6968	143	10	we	we	PRON
ejpam-6968	143	11	take	take	VERB
ejpam-6968	143	12	c	c	NOUN
ejpam-6968	143	13	=	=	SYM
ejpam-6968	143	14	−7	−7	PROPN
ejpam-6968	143	15	,	,	PUNCT
ejpam-6968	143	16	corresponding	correspond	VERB
ejpam-6968	143	17	to	to	ADP
ejpam-6968	143	18	α	α	NOUN
ejpam-6968	143	19	=	=	PUNCT
ejpam-6968	143	20	−4c2	−4c2	NUM
ejpam-6968	144	1	=	=	PUNCT
ejpam-6968	144	2	−196	−196	NOUN
ejpam-6968	144	3	.	.	PUNCT
ejpam-6968	145	1	at	at	ADP
ejpam-6968	145	2	this	this	DET
ejpam-6968	145	3	critical	critical	ADJ
ejpam-6968	145	4	value	value	NOUN
ejpam-6968	145	5	,	,	PUNCT
ejpam-6968	145	6	the	the	DET
ejpam-6968	145	7	jacobian	jacobian	PROPN
ejpam-6968	145	8	has	have	VERB
ejpam-6968	145	9	a	a	DET
ejpam-6968	145	10	pair	pair	NOUN
ejpam-6968	145	11	of	of	ADP
ejpam-6968	145	12	purely	purely	ADV
ejpam-6968	145	13	imaginary	imaginary	ADJ
ejpam-6968	145	14	eigenvalues	eigenvalue	NOUN
ejpam-6968	145	15	λ	λ	NOUN
ejpam-6968	145	16	=	=	PUNCT
ejpam-6968	146	1	±i	±i	PROPN
ejpam-6968	146	2	√	√	PROPN
ejpam-6968	146	3	7	7	NUM
ejpam-6968	146	4	satisfying	satisfy	VERB
ejpam-6968	146	5	the	the	DET
ejpam-6968	146	6	non	non	ADJ
ejpam-6968	146	7	-	-	ADJ
ejpam-6968	146	8	degeneracy	degeneracy	ADJ
ejpam-6968	146	9	condition	condition	NOUN
ejpam-6968	146	10	for	for	ADP
ejpam-6968	146	11	a	a	DET
ejpam-6968	146	12	hopf	hopf	ADJ
ejpam-6968	146	13	bifurcation	bifurcation	NOUN
ejpam-6968	146	14	.	.	PUNCT
ejpam-6968	147	1	to	to	PART
ejpam-6968	147	2	determine	determine	VERB
ejpam-6968	147	3	its	its	PRON
ejpam-6968	147	4	type	type	NOUN
ejpam-6968	147	5	,	,	PUNCT
ejpam-6968	147	6	we	we	PRON
ejpam-6968	147	7	compute	compute	VERB
ejpam-6968	147	8	the	the	DET
ejpam-6968	147	9	first	first	ADJ
ejpam-6968	147	10	lyapunov	lyapunov	ADJ
ejpam-6968	147	11	coefficient	coefficient	NOUN
ejpam-6968	147	12	ℓ1	ℓ1	NOUN
ejpam-6968	147	13	,	,	PUNCT
ejpam-6968	147	14	which	which	PRON
ejpam-6968	147	15	governs	govern	VERB
ejpam-6968	147	16	the	the	DET
ejpam-6968	147	17	direction	direction	NOUN
ejpam-6968	147	18	and	and	CCONJ
ejpam-6968	147	19	stability	stability	NOUN
ejpam-6968	147	20	of	of	ADP
ejpam-6968	147	21	bifurcating	bifurcate	VERB
ejpam-6968	147	22	periodic	periodic	ADJ
ejpam-6968	147	23	orbits	orbit	NOUN
ejpam-6968	147	24	.	.	PUNCT
ejpam-6968	148	1	following	follow	VERB
ejpam-6968	148	2	the	the	DET
ejpam-6968	148	3	normal	normal	ADJ
ejpam-6968	148	4	-	-	PUNCT
ejpam-6968	148	5	form	form	NOUN
ejpam-6968	148	6	theory	theory	NOUN
ejpam-6968	148	7	and	and	CCONJ
ejpam-6968	148	8	center	center	ADJ
ejpam-6968	148	9	-	-	PUNCT
ejpam-6968	148	10	manifold	manifold	ADJ
ejpam-6968	148	11	reduction	reduction	NOUN
ejpam-6968	148	12	[	[	X
ejpam-6968	148	13	11	11	NUM
ejpam-6968	148	14	,	,	PUNCT
ejpam-6968	148	15	14	14	NUM
ejpam-6968	148	16	]	]	PUNCT
ejpam-6968	148	17	,	,	PUNCT
ejpam-6968	148	18	ℓ1	ℓ1	NOUN
ejpam-6968	148	19	=	=	SYM
ejpam-6968	148	20	1	1	NUM
ejpam-6968	148	21	2ω0	2ω0	NUM
ejpam-6968	148	22	ℜ	ℜ	PROPN
ejpam-6968	148	23	〈	〈	PROPN
ejpam-6968	148	24	p	p	NOUN
ejpam-6968	148	25	,	,	PUNCT
ejpam-6968	148	26	c(q	c(q	PROPN
ejpam-6968	148	27	,	,	PUNCT
ejpam-6968	148	28	q̄	q̄	ADJ
ejpam-6968	148	29	,	,	PUNCT
ejpam-6968	148	30	q)−	q)−	PROPN
ejpam-6968	148	31	2b	2b	NOUN
ejpam-6968	148	32	(	(	PUNCT
ejpam-6968	148	33	q	q	NOUN
ejpam-6968	148	34	,	,	PUNCT
ejpam-6968	148	35	a−1b(q	a−1b(q	NOUN
ejpam-6968	148	36	,	,	PUNCT
ejpam-6968	148	37	q̄	q̄	NOUN
ejpam-6968	148	38	)	)	PUNCT
ejpam-6968	148	39	)	)	PUNCT
ejpam-6968	149	1	+	+	PUNCT
ejpam-6968	149	2	b	b	NOUN
ejpam-6968	149	3	(	(	PUNCT
ejpam-6968	149	4	q̄	q̄	ADJ
ejpam-6968	149	5	,	,	PUNCT
ejpam-6968	149	6	(	(	PUNCT
ejpam-6968	149	7	2iω0i	2iω0i	NUM
ejpam-6968	149	8	−a)−1b(q	−a)−1b(q	NOUN
ejpam-6968	149	9	,	,	PUNCT
ejpam-6968	149	10	q	q	NOUN
ejpam-6968	149	11	)	)	PUNCT
ejpam-6968	149	12	)	)	PUNCT
ejpam-6968	149	13	〉	〉	NOUN
ejpam-6968	149	14	,	,	PUNCT
ejpam-6968	149	15	(	(	PUNCT
ejpam-6968	149	16	8)	8)	NUM
ejpam-6968	149	17	where	where	SCONJ
ejpam-6968	149	18	a	a	PRON
ejpam-6968	149	19	is	be	AUX
ejpam-6968	149	20	the	the	DET
ejpam-6968	149	21	jacobian	jacobian	PROPN
ejpam-6968	149	22	at	at	ADP
ejpam-6968	149	23	equilibrium	equilibrium	NOUN
ejpam-6968	149	24	,	,	PUNCT
ejpam-6968	149	25	ω0	ω0	VERB
ejpam-6968	149	26	the	the	DET
ejpam-6968	149	27	imaginary	imaginary	ADJ
ejpam-6968	149	28	part	part	NOUN
ejpam-6968	149	29	of	of	ADP
ejpam-6968	149	30	the	the	DET
ejpam-6968	149	31	eigenvalues	eigenvalue	NOUN
ejpam-6968	149	32	±iω0	±iω0	NOUN
ejpam-6968	149	33	,	,	PUNCT
ejpam-6968	149	34	q	q	NOUN
ejpam-6968	149	35	and	and	CCONJ
ejpam-6968	149	36	p	p	X
ejpam-6968	149	37	the	the	DET
ejpam-6968	149	38	corresponding	corresponding	ADJ
ejpam-6968	149	39	right	right	NOUN
ejpam-6968	149	40	and	and	CCONJ
ejpam-6968	149	41	left	leave	VERB
ejpam-6968	149	42	eigenvectors	eigenvector	NOUN
ejpam-6968	149	43	normalized	normalize	VERB
ejpam-6968	149	44	by	by	ADP
ejpam-6968	149	45	⟨p	⟨p	PROPN
ejpam-6968	149	46	,	,	PUNCT
ejpam-6968	149	47	q⟩	q⟩	X
ejpam-6968	149	48	=	=	SYM
ejpam-6968	149	49	1	1	NUM
ejpam-6968	149	50	,	,	PUNCT
ejpam-6968	149	51	and	and	CCONJ
ejpam-6968	149	52	b	b	NOUN
ejpam-6968	149	53	and	and	CCONJ
ejpam-6968	149	54	c	c	X
ejpam-6968	149	55	the	the	DET
ejpam-6968	149	56	bilinear	bilinear	PROPN
ejpam-6968	149	57	and	and	CCONJ
ejpam-6968	149	58	trilinear	trilinear	ADJ
ejpam-6968	149	59	forms	form	NOUN
ejpam-6968	149	60	derived	derive	VERB
ejpam-6968	149	61	from	from	ADP
ejpam-6968	149	62	the	the	DET
ejpam-6968	149	63	second	second	ADJ
ejpam-6968	149	64	and	and	CCONJ
ejpam-6968	149	65	third	third	ADJ
ejpam-6968	149	66	derivatives	derivative	NOUN
ejpam-6968	149	67	of	of	ADP
ejpam-6968	149	68	f	f	PROPN
ejpam-6968	149	69	.	.	PUNCT
ejpam-6968	150	1	because	because	SCONJ
ejpam-6968	150	2	system	system	NOUN
ejpam-6968	150	3	(	(	PUNCT
ejpam-6968	150	4	1	1	X
ejpam-6968	150	5	)	)	PUNCT
ejpam-6968	150	6	is	be	AUX
ejpam-6968	150	7	quadratic	quadratic	ADJ
ejpam-6968	150	8	,	,	PUNCT
ejpam-6968	150	9	d3f(x	d3f(x	PROPN
ejpam-6968	150	10	)	)	PUNCT
ejpam-6968	150	11	≡	≡	PROPN
ejpam-6968	150	12	0	0	NUM
ejpam-6968	150	13	and	and	CCONJ
ejpam-6968	150	14	the	the	DET
ejpam-6968	150	15	expression	expression	NOUN
ejpam-6968	150	16	reduces	reduce	VERB
ejpam-6968	150	17	to	to	ADP
ejpam-6968	150	18	ℓ1	ℓ1	NOUN
ejpam-6968	150	19	=	=	SYM
ejpam-6968	150	20	1	1	NUM
ejpam-6968	150	21	2ω0	2ω0	NUM
ejpam-6968	150	22	ℜ	ℜ	PROPN
ejpam-6968	150	23	〈	〈	PROPN
ejpam-6968	150	24	p	p	NOUN
ejpam-6968	150	25	,	,	PUNCT
ejpam-6968	150	26	−2b	−2b	X
ejpam-6968	150	27	(	(	PUNCT
ejpam-6968	150	28	q	q	NOUN
ejpam-6968	150	29	,	,	PUNCT
ejpam-6968	150	30	a−1b(q	a−1b(q	NOUN
ejpam-6968	150	31	,	,	PUNCT
ejpam-6968	150	32	q̄	q̄	NOUN
ejpam-6968	150	33	)	)	PUNCT
ejpam-6968	150	34	)	)	PUNCT
ejpam-6968	151	1	+	+	PUNCT
ejpam-6968	151	2	b	b	NOUN
ejpam-6968	151	3	(	(	PUNCT
ejpam-6968	151	4	q̄	q̄	ADJ
ejpam-6968	151	5	,	,	PUNCT
ejpam-6968	151	6	(	(	PUNCT
ejpam-6968	151	7	2iω0i	2iω0i	NUM
ejpam-6968	151	8	−a)−1b(q	−a)−1b(q	NOUN
ejpam-6968	151	9	,	,	PUNCT
ejpam-6968	151	10	q	q	NOUN
ejpam-6968	151	11	)	)	PUNCT
ejpam-6968	151	12	)	)	PUNCT
ejpam-6968	151	13	〉	〉	NOUN
ejpam-6968	151	14	.	.	PUNCT
ejpam-6968	152	1	(	(	PUNCT
ejpam-6968	152	2	9	9	NUM
ejpam-6968	152	3	)	)	PUNCT
ejpam-6968	152	4	for	for	ADP
ejpam-6968	152	5	α	α	NOUN
ejpam-6968	152	6	=	=	SYM
ejpam-6968	152	7	−196	−196	NOUN
ejpam-6968	152	8	,	,	PUNCT
ejpam-6968	152	9	where	where	SCONJ
ejpam-6968	152	10	e	e	NOUN
ejpam-6968	152	11	=	=	SYM
ejpam-6968	152	12	(	(	PUNCT
ejpam-6968	152	13	−7,−7	−7,−7	PROPN
ejpam-6968	152	14	,	,	PUNCT
ejpam-6968	152	15	0	0	NUM
ejpam-6968	152	16	)	)	PUNCT
ejpam-6968	152	17	,	,	PUNCT
ejpam-6968	152	18	j(−7,−7	j(−7,−7	ADV
ejpam-6968	152	19	,	,	PUNCT
ejpam-6968	152	20	0	0	NUM
ejpam-6968	152	21	)	)	PUNCT
ejpam-6968	152	22	=	=	VERB
ejpam-6968	152	23	0	0	ADJ
ejpam-6968	152	24	0	0	NUM
ejpam-6968	152	25	1	1	NUM
ejpam-6968	152	26	1	1	NUM
ejpam-6968	152	27	−1	−1	NOUN
ejpam-6968	152	28	0	0	NUM
ejpam-6968	152	29	0	0	NUM
ejpam-6968	152	30	−56	−56	NOUN
ejpam-6968	152	31	−7	−7	NOUN
ejpam-6968	152	32			NOUN
ejpam-6968	152	33	.	.	PUNCT
ejpam-6968	153	1	the	the	DET
ejpam-6968	153	2	right	right	PROPN
ejpam-6968	153	3	eigenvector	eigenvector	NOUN
ejpam-6968	153	4	q	q	PROPN
ejpam-6968	153	5	∈	∈	PROPN
ejpam-6968	153	6	c3	c3	PROPN
ejpam-6968	153	7	for	for	ADP
ejpam-6968	153	8	λ	λ	PROPN
ejpam-6968	153	9	=	=	PRON
ejpam-6968	154	1	i	i	PRON
ejpam-6968	154	2	√	√	VERB
ejpam-6968	154	3	7	7	NUM
ejpam-6968	154	4	is	be	AUX
ejpam-6968	154	5	q	q	NOUN
ejpam-6968	154	6	=	=	PUNCT
ejpam-6968	154	7			NOUN
ejpam-6968	154	8	7	7	NUM
ejpam-6968	154	9	142	142	NUM
ejpam-6968	154	10	−	−	NOUN
ejpam-6968	154	11	15i	15i	X
ejpam-6968	154	12	√	√	VERB
ejpam-6968	154	13	7	7	NUM
ejpam-6968	154	14	994	994	NUM
ejpam-6968	154	15	−	−	NUM
ejpam-6968	154	16	1	1	NUM
ejpam-6968	154	17	142	142	NUM
ejpam-6968	154	18	−	−	PROPN
ejpam-6968	154	19	4i	4i	NOUN
ejpam-6968	154	20	√	√	ADV
ejpam-6968	154	21	7	7	NUM
ejpam-6968	154	22	497	497	NUM
ejpam-6968	154	23	15	15	NUM
ejpam-6968	154	24	142	142	NUM
ejpam-6968	154	25	+	+	CCONJ
ejpam-6968	154	26	7i	7i	NUM
ejpam-6968	154	27	√	√	PROPN
ejpam-6968	154	28	7	7	NUM
ejpam-6968	154	29	142	142	NUM
ejpam-6968	154	30			NUM
ejpam-6968	154	31	,	,	PUNCT
ejpam-6968	154	32	h.	h.	PROPN
ejpam-6968	154	33	k.	k.	PROPN
ejpam-6968	154	34	fata	fata	PROPN
ejpam-6968	154	35	,	,	PUNCT
ejpam-6968	154	36	n.	n.	PROPN
ejpam-6968	154	37	y.	y.	PROPN
ejpam-6968	154	38	ashar	ashar	PROPN
ejpam-6968	154	39	/	/	SYM
ejpam-6968	154	40	eur	eur	PROPN
ejpam-6968	154	41	.	.	PUNCT
ejpam-6968	155	1	j.	j.	PROPN
ejpam-6968	155	2	pure	pure	PROPN
ejpam-6968	155	3	appl	appl	PROPN
ejpam-6968	155	4	.	.	PROPN
ejpam-6968	155	5	math	math	PROPN
ejpam-6968	155	6	,	,	PUNCT
ejpam-6968	155	7	18	18	NUM
ejpam-6968	155	8	(	(	PUNCT
ejpam-6968	155	9	4	4	NUM
ejpam-6968	155	10	)	)	PUNCT
ejpam-6968	155	11	(	(	PUNCT
ejpam-6968	155	12	2025	2025	NUM
ejpam-6968	155	13	)	)	PUNCT
ejpam-6968	155	14	,	,	PUNCT
ejpam-6968	155	15	6968	6968	NUM
ejpam-6968	155	16	8	8	NUM
ejpam-6968	155	17	of	of	ADP
ejpam-6968	155	18	15	15	NUM
ejpam-6968	155	19	and	and	CCONJ
ejpam-6968	155	20	the	the	DET
ejpam-6968	155	21	corresponding	corresponding	ADJ
ejpam-6968	155	22	adjoint	adjoint	PROPN
ejpam-6968	155	23	(	(	PUNCT
ejpam-6968	155	24	left	left	ADJ
ejpam-6968	155	25	)	)	PUNCT
ejpam-6968	155	26	eigenvector	eigenvector	NOUN
ejpam-6968	155	27	p	p	PROPN
ejpam-6968	155	28	∈	∈	PROPN
ejpam-6968	155	29	c3	c3	PROPN
ejpam-6968	155	30	for	for	ADP
ejpam-6968	155	31	−i	−i	PROPN
ejpam-6968	155	32	√	√	ADV
ejpam-6968	155	33	7	7	NUM
ejpam-6968	155	34	is	be	AUX
ejpam-6968	155	35	p	p	NOUN
ejpam-6968	155	36	=	=	PUNCT
ejpam-6968	155	37			NOUN
ejpam-6968	155	38	−(−7	−(−7	NOUN
ejpam-6968	156	1	+	+	CCONJ
ejpam-6968	156	2	i	i	PRON
ejpam-6968	156	3	√	√	VERB
ejpam-6968	156	4	7	7	NUM
ejpam-6968	156	5	)	)	PUNCT
ejpam-6968	156	6	i	i	PRON
ejpam-6968	156	7	√	√	VERB
ejpam-6968	156	8	7(−7	7(−7	NUM
ejpam-6968	157	1	+	+	CCONJ
ejpam-6968	157	2	i	i	PRON
ejpam-6968	157	3	√	√	VERB
ejpam-6968	157	4	7	7	NUM
ejpam-6968	157	5	)	)	PUNCT
ejpam-6968	157	6	1	1	NUM
ejpam-6968	157	7			NOUN
ejpam-6968	157	8	,	,	PUNCT
ejpam-6968	157	9	normalized	normalize	VERB
ejpam-6968	157	10	such	such	ADJ
ejpam-6968	157	11	that	that	PRON
ejpam-6968	157	12	⟨p	⟨p	NOUN
ejpam-6968	157	13	,	,	PUNCT
ejpam-6968	157	14	q⟩	q⟩	X
ejpam-6968	158	1	=	=	PUNCT
ejpam-6968	158	2	p̄t	p̄t	PROPN
ejpam-6968	158	3	q	q	X
ejpam-6968	158	4	=	=	NOUN
ejpam-6968	158	5	1	1	X
ejpam-6968	158	6	.	.	PUNCT
ejpam-6968	159	1	the	the	DET
ejpam-6968	159	2	bilinear	bilinear	PROPN
ejpam-6968	159	3	form	form	NOUN
ejpam-6968	159	4	b(u	b(u	PROPN
ejpam-6968	159	5	,	,	PUNCT
ejpam-6968	159	6	v	v	NOUN
ejpam-6968	159	7	)	)	PUNCT
ejpam-6968	159	8	∈	∈	PROPN
ejpam-6968	159	9	r3	r3	PROPN
ejpam-6968	159	10	,	,	PUNCT
ejpam-6968	159	11	representing	represent	VERB
ejpam-6968	159	12	second	second	ADJ
ejpam-6968	159	13	-	-	PUNCT
ejpam-6968	159	14	order	order	NOUN
ejpam-6968	159	15	interactions	interaction	NOUN
ejpam-6968	159	16	of	of	ADP
ejpam-6968	159	17	the	the	DET
ejpam-6968	159	18	vector	vector	NOUN
ejpam-6968	159	19	field	field	NOUN
ejpam-6968	159	20	,	,	PUNCT
ejpam-6968	159	21	is	be	AUX
ejpam-6968	159	22	constructed	construct	VERB
ejpam-6968	159	23	from	from	ADP
ejpam-6968	159	24	the	the	DET
ejpam-6968	159	25	hessian	hessian	ADJ
ejpam-6968	159	26	matrices	matrix	NOUN
ejpam-6968	159	27	hi	hi	INTJ
ejpam-6968	159	28	of	of	ADP
ejpam-6968	159	29	each	each	DET
ejpam-6968	159	30	component	component	NOUN
ejpam-6968	159	31	fi	fi	NOUN
ejpam-6968	159	32	evaluated	evaluate	VERB
ejpam-6968	159	33	at	at	ADP
ejpam-6968	159	34	equilibrium	equilibrium	NOUN
ejpam-6968	159	35	:	:	PUNCT
ejpam-6968	159	36	bi(u	bi(u	NOUN
ejpam-6968	159	37	,	,	PUNCT
ejpam-6968	159	38	v	v	NOUN
ejpam-6968	159	39	)	)	PUNCT
ejpam-6968	159	40	=	=	SYM
ejpam-6968	160	1	1	1	NUM
ejpam-6968	160	2	2	2	NUM
ejpam-6968	160	3	3∑	3∑	NUM
ejpam-6968	160	4	j=1	j=1	NOUN
ejpam-6968	160	5	3∑	3∑	NOUN
ejpam-6968	160	6	k=1	k=1	NOUN
ejpam-6968	160	7	∂2fi	∂2fi	X
ejpam-6968	160	8	∂xj∂xk	∂xj∂xk	PROPN
ejpam-6968	160	9	(	(	PUNCT
ejpam-6968	160	10	x0)ujvk	x0)ujvk	PROPN
ejpam-6968	160	11	,	,	PUNCT
ejpam-6968	160	12	i	i	PRON
ejpam-6968	160	13	=	=	NOUN
ejpam-6968	160	14	1	1	NUM
ejpam-6968	160	15	,	,	PUNCT
ejpam-6968	160	16	2	2	NUM
ejpam-6968	160	17	,	,	PUNCT
ejpam-6968	160	18	3	3	NUM
ejpam-6968	160	19	,	,	PUNCT
ejpam-6968	160	20	so	so	SCONJ
ejpam-6968	160	21	that	that	SCONJ
ejpam-6968	160	22	b(u	b(u	PROPN
ejpam-6968	160	23	,	,	PUNCT
ejpam-6968	160	24	v	v	NOUN
ejpam-6968	160	25	)	)	PUNCT
ejpam-6968	160	26	=	=	SYM
ejpam-6968	160	27	1	1	NUM
ejpam-6968	160	28	2	2	NUM
ejpam-6968	160	29	u⊤h1v	u⊤h1v	NUM
ejpam-6968	160	30	u⊤h2v	u⊤h2v	NOUN
ejpam-6968	160	31	u⊤h3v	u⊤h3v	NOUN
ejpam-6968	160	32			NOUN
ejpam-6968	160	33	,	,	PUNCT
ejpam-6968	160	34	h3	h3	NOUN
ejpam-6968	160	35	=	=	SYM
ejpam-6968	160	36	−8	−8	NOUN
ejpam-6968	160	37	8	8	NUM
ejpam-6968	160	38	0	0	NUM
ejpam-6968	160	39	8	8	NUM
ejpam-6968	160	40	0	0	NUM
ejpam-6968	160	41	1	1	NUM
ejpam-6968	160	42	0	0	NUM
ejpam-6968	160	43	1	1	NUM
ejpam-6968	160	44	0	0	NUM
ejpam-6968	160	45			NOUN
ejpam-6968	160	46	,	,	PUNCT
ejpam-6968	160	47	while	while	SCONJ
ejpam-6968	160	48	h1	h1	NOUN
ejpam-6968	160	49	and	and	CCONJ
ejpam-6968	160	50	h2	h2	NOUN
ejpam-6968	160	51	are	be	AUX
ejpam-6968	160	52	zero	zero	NUM
ejpam-6968	160	53	matrices	matrix	NOUN
ejpam-6968	160	54	because	because	SCONJ
ejpam-6968	160	55	the	the	DET
ejpam-6968	160	56	first	first	ADJ
ejpam-6968	160	57	and	and	CCONJ
ejpam-6968	160	58	second	second	ADJ
ejpam-6968	160	59	equations	equation	NOUN
ejpam-6968	160	60	are	be	AUX
ejpam-6968	160	61	linear	linear	ADJ
ejpam-6968	160	62	.	.	PUNCT
ejpam-6968	161	1	numerical	numerical	ADJ
ejpam-6968	161	2	evaluation	evaluation	NOUN
ejpam-6968	161	3	yields	yield	NOUN
ejpam-6968	161	4	ℓ1	ℓ1	VERB
ejpam-6968	161	5	≈	≈	PROPN
ejpam-6968	161	6	−0.00387599	−0.00387599	NOUN
ejpam-6968	161	7	.	.	PUNCT
ejpam-6968	162	1	because	because	SCONJ
ejpam-6968	162	2	ℓ1	ℓ1	VERB
ejpam-6968	162	3	<	<	X
ejpam-6968	162	4	0	0	NUM
ejpam-6968	162	5	,	,	PUNCT
ejpam-6968	162	6	the	the	DET
ejpam-6968	162	7	system	system	NOUN
ejpam-6968	162	8	undergoes	undergo	VERB
ejpam-6968	162	9	a	a	DET
ejpam-6968	162	10	supercritical	supercritical	ADJ
ejpam-6968	162	11	hopf	hopf	ADJ
ejpam-6968	162	12	bifurcation	bifurcation	NOUN
ejpam-6968	162	13	at	at	ADP
ejpam-6968	162	14	α	α	NOUN
ejpam-6968	162	15	=	=	PUNCT
ejpam-6968	162	16	−196	−196	NOUN
ejpam-6968	162	17	:	:	PUNCT
ejpam-6968	162	18	as	as	SCONJ
ejpam-6968	162	19	α	α	PROPN
ejpam-6968	162	20	increases	increase	VERB
ejpam-6968	162	21	beyond	beyond	ADP
ejpam-6968	162	22	this	this	DET
ejpam-6968	162	23	value	value	NOUN
ejpam-6968	162	24	,	,	PUNCT
ejpam-6968	162	25	a	a	DET
ejpam-6968	162	26	stable	stable	ADJ
ejpam-6968	162	27	limit	limit	NOUN
ejpam-6968	162	28	cycle	cycle	NOUN
ejpam-6968	162	29	emerges	emerge	NOUN
ejpam-6968	162	30	and	and	CCONJ
ejpam-6968	162	31	the	the	DET
ejpam-6968	162	32	equilibrium	equilibrium	NOUN
ejpam-6968	162	33	becomes	become	VERB
ejpam-6968	162	34	unstable	unstable	ADJ
ejpam-6968	162	35	.	.	PUNCT
ejpam-6968	163	1	this	this	DET
ejpam-6968	163	2	transition	transition	NOUN
ejpam-6968	163	3	is	be	AUX
ejpam-6968	163	4	consistent	consistent	ADJ
ejpam-6968	163	5	with	with	ADP
ejpam-6968	163	6	fig	fig	NOUN
ejpam-6968	163	7	.	.	PUNCT
ejpam-6968	164	1	1	1	X
ejpam-6968	164	2	.	.	X
ejpam-6968	164	3	supercritical	supercritical	ADJ
ejpam-6968	164	4	hopf	hopf	ADJ
ejpam-6968	164	5	bifurcations	bifurcation	NOUN
ejpam-6968	164	6	may	may	AUX
ejpam-6968	164	7	lead	lead	VERB
ejpam-6968	164	8	to	to	PART
ejpam-6968	164	9	chaos	chaos	VERB
ejpam-6968	164	10	through	through	ADP
ejpam-6968	164	11	successive	successive	ADJ
ejpam-6968	164	12	period	period	NOUN
ejpam-6968	164	13	-	-	PUNCT
ejpam-6968	164	14	doubling	double	VERB
ejpam-6968	164	15	bifurcations	bifurcation	NOUN
ejpam-6968	164	16	as	as	ADP
ejpam-6968	164	17	the	the	DET
ejpam-6968	164	18	parameter	parameter	NOUN
ejpam-6968	164	19	α	α	PROPN
ejpam-6968	164	20	increases	increase	VERB
ejpam-6968	164	21	beyond	beyond	ADP
ejpam-6968	164	22	the	the	DET
ejpam-6968	164	23	critical	critical	ADJ
ejpam-6968	164	24	value	value	NOUN
ejpam-6968	164	25	−196	−196	NOUN
ejpam-6968	164	26	.	.	PUNCT
ejpam-6968	165	1	therefore	therefore	ADV
ejpam-6968	165	2	,	,	PUNCT
ejpam-6968	165	3	it	it	PRON
ejpam-6968	165	4	is	be	AUX
ejpam-6968	165	5	natural	natural	ADJ
ejpam-6968	165	6	to	to	PART
ejpam-6968	165	7	continue	continue	VERB
ejpam-6968	165	8	the	the	DET
ejpam-6968	165	9	analysis	analysis	NOUN
ejpam-6968	165	10	numerically	numerically	ADV
ejpam-6968	165	11	to	to	PART
ejpam-6968	165	12	track	track	VERB
ejpam-6968	165	13	how	how	SCONJ
ejpam-6968	165	14	the	the	DET
ejpam-6968	165	15	periodic	periodic	ADJ
ejpam-6968	165	16	orbits	orbit	NOUN
ejpam-6968	165	17	evolve	evolve	VERB
ejpam-6968	165	18	with	with	ADP
ejpam-6968	165	19	changing	change	VERB
ejpam-6968	165	20	α	α	NOUN
ejpam-6968	165	21	,	,	PUNCT
ejpam-6968	165	22	thereby	thereby	ADV
ejpam-6968	165	23	revealing	reveal	VERB
ejpam-6968	165	24	the	the	DET
ejpam-6968	165	25	detailed	detailed	ADJ
ejpam-6968	165	26	route	route	NOUN
ejpam-6968	165	27	from	from	ADP
ejpam-6968	165	28	simple	simple	ADJ
ejpam-6968	165	29	oscillations	oscillation	NOUN
ejpam-6968	165	30	to	to	ADP
ejpam-6968	165	31	complex	complex	ADJ
ejpam-6968	165	32	chaotic	chaotic	ADJ
ejpam-6968	165	33	dynamics	dynamic	NOUN
ejpam-6968	165	34	.	.	PUNCT
ejpam-6968	166	1	4	4	X
ejpam-6968	166	2	.	.	X
ejpam-6968	166	3	numerical	numerical	ADJ
ejpam-6968	166	4	continuation	continuation	NOUN
ejpam-6968	166	5	to	to	PART
ejpam-6968	166	6	complement	complement	VERB
ejpam-6968	166	7	the	the	DET
ejpam-6968	166	8	analytical	analytical	ADJ
ejpam-6968	166	9	results	result	NOUN
ejpam-6968	166	10	,	,	PUNCT
ejpam-6968	166	11	we	we	PRON
ejpam-6968	166	12	perform	perform	VERB
ejpam-6968	166	13	numerical	numerical	ADJ
ejpam-6968	166	14	continuation	continuation	NOUN
ejpam-6968	166	15	by	by	ADP
ejpam-6968	166	16	tracking	track	VERB
ejpam-6968	166	17	the	the	DET
ejpam-6968	166	18	sequence	sequence	NOUN
ejpam-6968	166	19	of	of	ADP
ejpam-6968	166	20	local	local	ADJ
ejpam-6968	166	21	maxima	maxima	NOUN
ejpam-6968	166	22	of	of	ADP
ejpam-6968	166	23	x(t	x(t	PROPN
ejpam-6968	166	24	)	)	PUNCT
ejpam-6968	166	25	(	(	PUNCT
ejpam-6968	166	26	denoted	denote	VERB
ejpam-6968	166	27	xs	xs	PROPN
ejpam-6968	166	28	)	)	PUNCT
ejpam-6968	166	29	after	after	ADP
ejpam-6968	166	30	discarding	discard	VERB
ejpam-6968	166	31	transients	transient	NOUN
ejpam-6968	166	32	.	.	PUNCT
ejpam-6968	167	1	this	this	DET
ejpam-6968	167	2	procedure	procedure	NOUN
ejpam-6968	167	3	yields	yield	NOUN
ejpam-6968	167	4	parameter	parameter	NOUN
ejpam-6968	167	5	–	–	PUNCT
ejpam-6968	167	6	response	response	NOUN
ejpam-6968	167	7	diagrams	diagram	NOUN
ejpam-6968	167	8	that	that	PRON
ejpam-6968	167	9	reveal	reveal	VERB
ejpam-6968	167	10	qualitative	qualitative	ADJ
ejpam-6968	167	11	changes	change	NOUN
ejpam-6968	167	12	in	in	ADP
ejpam-6968	167	13	the	the	DET
ejpam-6968	167	14	attractor	attractor	NOUN
ejpam-6968	167	15	as	as	SCONJ
ejpam-6968	167	16	the	the	DET
ejpam-6968	167	17	control	control	NOUN
ejpam-6968	167	18	parameter	parameter	NOUN
ejpam-6968	167	19	α	α	PROPN
ejpam-6968	167	20	varies	vary	VERB
ejpam-6968	167	21	.	.	PUNCT
ejpam-6968	168	1	the	the	DET
ejpam-6968	168	2	odes	ode	NOUN
ejpam-6968	168	3	are	be	AUX
ejpam-6968	168	4	integrated	integrate	VERB
ejpam-6968	168	5	with	with	ADP
ejpam-6968	168	6	a	a	DET
ejpam-6968	168	7	fixed	fix	VERB
ejpam-6968	168	8	–	–	PUNCT
ejpam-6968	168	9	step	step	NOUN
ejpam-6968	168	10	fourth	fourth	ADJ
ejpam-6968	168	11	–	–	PUNCT
ejpam-6968	168	12	order	order	NOUN
ejpam-6968	168	13	runge	runge	NOUN
ejpam-6968	168	14	–	–	PUNCT
ejpam-6968	168	15	kutta	kutta	NOUN
ejpam-6968	168	16	(	(	PUNCT
ejpam-6968	168	17	rk4	rk4	NOUN
ejpam-6968	168	18	)	)	PUNCT
ejpam-6968	168	19	,	,	PUNCT
ejpam-6968	168	20	time	time	NOUN
ejpam-6968	168	21	step	step	NOUN
ejpam-6968	168	22	∆t	∆t	PROPN
ejpam-6968	168	23	=	=	SYM
ejpam-6968	168	24	10−3	10−3	NUM
ejpam-6968	168	25	,	,	PUNCT
ejpam-6968	168	26	and	and	CCONJ
ejpam-6968	168	27	total	total	ADJ
ejpam-6968	168	28	simulated	simulate	VERB
ejpam-6968	168	29	time	time	NOUN
ejpam-6968	168	30	tmax	tmax	ADP
ejpam-6968	168	31	=	=	SYM
ejpam-6968	168	32	6×104	6×104	X
ejpam-6968	168	33	.	.	PUNCT
ejpam-6968	169	1	transients	transient	NOUN
ejpam-6968	169	2	of	of	ADP
ejpam-6968	169	3	length	length	NOUN
ejpam-6968	169	4	ttr	ttr	PROPN
ejpam-6968	169	5	=	=	SYM
ejpam-6968	169	6	5×104	5×104	NUM
ejpam-6968	169	7	are	be	AUX
ejpam-6968	169	8	discarded	discard	VERB
ejpam-6968	169	9	before	before	ADP
ejpam-6968	169	10	sampling	sample	VERB
ejpam-6968	169	11	local	local	ADJ
ejpam-6968	169	12	maxima	maxima	NOUN
ejpam-6968	169	13	.	.	PUNCT
ejpam-6968	170	1	local	local	ADJ
ejpam-6968	170	2	maxima	maxima	NOUN
ejpam-6968	170	3	are	be	AUX
ejpam-6968	170	4	detected	detect	VERB
ejpam-6968	170	5	when	when	SCONJ
ejpam-6968	170	6	ẋ	ẋ	PROPN
ejpam-6968	170	7	changes	change	NOUN
ejpam-6968	170	8	sign	sign	VERB
ejpam-6968	170	9	from	from	ADP
ejpam-6968	170	10	positive	positive	ADJ
ejpam-6968	170	11	to	to	PART
ejpam-6968	170	12	negative	negative	ADJ
ejpam-6968	170	13	with	with	ADP
ejpam-6968	170	14	tolerance	tolerance	NOUN
ejpam-6968	170	15	|ẋ|	|ẋ|	NOUN
ejpam-6968	170	16	<	<	X
ejpam-6968	170	17	10−8	10−8	NUM
ejpam-6968	170	18	;	;	PUNCT
ejpam-6968	170	19	the	the	DET
ejpam-6968	170	20	last	last	ADJ
ejpam-6968	170	21	200	200	NUM
ejpam-6968	170	22	peaks	peak	NOUN
ejpam-6968	170	23	are	be	AUX
ejpam-6968	170	24	retained	retain	VERB
ejpam-6968	170	25	per	per	ADP
ejpam-6968	170	26	α	α	NOUN
ejpam-6968	170	27	.	.	PUNCT
ejpam-6968	171	1	maximal	maximal	ADJ
ejpam-6968	171	2	lyapunov	lyapunov	ADJ
ejpam-6968	171	3	exponents	exponent	NOUN
ejpam-6968	171	4	are	be	AUX
ejpam-6968	171	5	computed	compute	VERB
ejpam-6968	171	6	via	via	ADP
ejpam-6968	171	7	the	the	DET
ejpam-6968	171	8	wolf	wolf	NOUN
ejpam-6968	171	9	–	–	PUNCT
ejpam-6968	171	10	swift	swift	ADJ
ejpam-6968	171	11	–	–	PUNCT
ejpam-6968	171	12	swinney	swinney	NOUN
ejpam-6968	171	13	–	–	PUNCT
ejpam-6968	171	14	vastano	vastano	ADJ
ejpam-6968	171	15	algorithm	algorithm	NOUN
ejpam-6968	172	1	[	[	X
ejpam-6968	172	2	20	20	NUM
ejpam-6968	172	3	]	]	PUNCT
ejpam-6968	172	4	,	,	PUNCT
ejpam-6968	172	5	with	with	ADP
ejpam-6968	172	6	qr	qr	PROPN
ejpam-6968	172	7	re	re	NOUN
ejpam-6968	172	8	-	-	NOUN
ejpam-6968	172	9	orthonormalization	orthonormalization	NOUN
ejpam-6968	172	10	every	every	DET
ejpam-6968	172	11	τgs	τgs	NOUN
ejpam-6968	172	12	=	=	SYM
ejpam-6968	172	13	1.0	1.0	NUM
ejpam-6968	172	14	,	,	PUNCT
ejpam-6968	172	15	horizon	horizon	NOUN
ejpam-6968	172	16	tle	tle	NOUN
ejpam-6968	172	17	=	=	SYM
ejpam-6968	172	18	2×105	2×105	PROPN
ejpam-6968	172	19	after	after	ADP
ejpam-6968	172	20	h.	h.	PROPN
ejpam-6968	172	21	k.	k.	PROPN
ejpam-6968	172	22	fata	fata	PROPN
ejpam-6968	172	23	,	,	PUNCT
ejpam-6968	172	24	n.	n.	PROPN
ejpam-6968	172	25	y.	y.	PROPN
ejpam-6968	172	26	ashar	ashar	PROPN
ejpam-6968	172	27	/	/	SYM
ejpam-6968	172	28	eur	eur	PROPN
ejpam-6968	172	29	.	.	PUNCT
ejpam-6968	173	1	j.	j.	PROPN
ejpam-6968	173	2	pure	pure	PROPN
ejpam-6968	173	3	appl	appl	PROPN
ejpam-6968	173	4	.	.	PROPN
ejpam-6968	173	5	math	math	PROPN
ejpam-6968	173	6	,	,	PUNCT
ejpam-6968	173	7	18	18	NUM
ejpam-6968	173	8	(	(	PUNCT
ejpam-6968	173	9	4	4	NUM
ejpam-6968	173	10	)	)	PUNCT
ejpam-6968	173	11	(	(	PUNCT
ejpam-6968	173	12	2025	2025	NUM
ejpam-6968	173	13	)	)	PUNCT
ejpam-6968	173	14	,	,	PUNCT
ejpam-6968	173	15	6968	6968	NUM
ejpam-6968	173	16	9	9	NUM
ejpam-6968	173	17	of	of	ADP
ejpam-6968	173	18	15	15	NUM
ejpam-6968	173	19	discarding	discard	VERB
ejpam-6968	173	20	ttr	ttr	PROPN
ejpam-6968	173	21	,	,	PUNCT
ejpam-6968	173	22	le	le	X
ejpam-6968	173	23	=	=	SYM
ejpam-6968	173	24	104	104	NUM
ejpam-6968	173	25	.	.	PUNCT
ejpam-6968	174	1	results	result	NOUN
ejpam-6968	174	2	are	be	AUX
ejpam-6968	174	3	step	step	NOUN
ejpam-6968	174	4	-	-	PUNCT
ejpam-6968	174	5	size	size	NOUN
ejpam-6968	174	6	robust	robust	ADJ
ejpam-6968	174	7	for	for	ADP
ejpam-6968	174	8	∆t	∆t	PROPN
ejpam-6968	174	9	∈	∈	PROPN
ejpam-6968	174	10	{	{	PUNCT
ejpam-6968	174	11	5	5	NUM
ejpam-6968	174	12	×	×	NOUN
ejpam-6968	174	13	10−4	10−4	NUM
ejpam-6968	174	14	,	,	PUNCT
ejpam-6968	174	15	10−3	10−3	NUM
ejpam-6968	174	16	,	,	PUNCT
ejpam-6968	174	17	2	2	NUM
ejpam-6968	174	18	×	×	NOUN
ejpam-6968	174	19	10−3	10−3	NUM
ejpam-6968	174	20	}	}	PUNCT
ejpam-6968	174	21	.	.	PUNCT
ejpam-6968	175	1	all	all	DET
ejpam-6968	175	2	computations	computation	NOUN
ejpam-6968	175	3	are	be	AUX
ejpam-6968	175	4	implemented	implement	VERB
ejpam-6968	175	5	in	in	ADP
ejpam-6968	175	6	python	python	PROPN
ejpam-6968	175	7	.	.	PUNCT
ejpam-6968	176	1	for	for	ADP
ejpam-6968	176	2	α	α	PRON
ejpam-6968	176	3	<	<	X
ejpam-6968	176	4	0	0	PROPN
ejpam-6968	176	5	,	,	PUNCT
ejpam-6968	176	6	initial	initial	ADJ
ejpam-6968	176	7	data	datum	NOUN
ejpam-6968	176	8	are	be	AUX
ejpam-6968	176	9	chosen	choose	VERB
ejpam-6968	176	10	at	at	ADP
ejpam-6968	176	11	the	the	DET
ejpam-6968	176	12	negative	negative	ADJ
ejpam-6968	176	13	equilibrium	equilibrium	NOUN
ejpam-6968	176	14	e−	e−	PROPN
ejpam-6968	176	15	obtained	obtain	VERB
ejpam-6968	176	16	analytically	analytically	ADV
ejpam-6968	176	17	(	(	PUNCT
ejpam-6968	176	18	trajectories	trajectory	NOUN
ejpam-6968	176	19	near	near	ADP
ejpam-6968	176	20	e−	e−	PROPN
ejpam-6968	176	21	converge	converge	VERB
ejpam-6968	176	22	to	to	ADP
ejpam-6968	176	23	periodic	periodic	ADJ
ejpam-6968	176	24	orbits	orbit	NOUN
ejpam-6968	176	25	for	for	ADP
ejpam-6968	176	26	α	α	PROPN
ejpam-6968	176	27	∈	∈	PROPN
ejpam-6968	177	1	[	[	X
ejpam-6968	177	2	−196	−196	NOUN
ejpam-6968	177	3	,	,	PUNCT
ejpam-6968	177	4	0	0	NUM
ejpam-6968	177	5	]	]	PUNCT
ejpam-6968	177	6	)	)	PUNCT
ejpam-6968	177	7	.	.	PUNCT
ejpam-6968	178	1	this	this	DET
ejpam-6968	178	2	choice	choice	NOUN
ejpam-6968	178	3	follows	follow	VERB
ejpam-6968	178	4	the	the	DET
ejpam-6968	178	5	warm	warm	ADJ
ejpam-6968	178	6	start	start	NOUN
ejpam-6968	178	7	concept	concept	NOUN
ejpam-6968	178	8	,	,	PUNCT
ejpam-6968	178	9	where	where	SCONJ
ejpam-6968	178	10	the	the	DET
ejpam-6968	178	11	initial	initial	ADJ
ejpam-6968	178	12	conditions	condition	NOUN
ejpam-6968	178	13	are	be	AUX
ejpam-6968	178	14	based	base	VERB
ejpam-6968	178	15	on	on	ADP
ejpam-6968	178	16	a	a	DET
ejpam-6968	178	17	previously	previously	ADV
ejpam-6968	178	18	known	know	VERB
ejpam-6968	178	19	equilibrium	equilibrium	NOUN
ejpam-6968	178	20	point	point	NOUN
ejpam-6968	178	21	.	.	PUNCT
ejpam-6968	179	1	this	this	DET
ejpam-6968	179	2	strategy	strategy	NOUN
ejpam-6968	179	3	helps	help	VERB
ejpam-6968	179	4	speed	speed	VERB
ejpam-6968	179	5	up	up	ADP
ejpam-6968	179	6	the	the	DET
ejpam-6968	179	7	convergence	convergence	NOUN
ejpam-6968	179	8	by	by	ADP
ejpam-6968	179	9	starting	start	VERB
ejpam-6968	179	10	the	the	DET
ejpam-6968	179	11	numerical	numerical	PROPN
ejpam-6968	179	12	simulation	simulation	PROPN
ejpam-6968	179	13	close	close	ADJ
ejpam-6968	179	14	to	to	ADP
ejpam-6968	179	15	the	the	DET
ejpam-6968	179	16	expected	expect	VERB
ejpam-6968	179	17	solution	solution	NOUN
ejpam-6968	179	18	,	,	PUNCT
ejpam-6968	179	19	avoiding	avoid	VERB
ejpam-6968	179	20	unnecessary	unnecessary	ADJ
ejpam-6968	179	21	exploration	exploration	NOUN
ejpam-6968	179	22	of	of	ADP
ejpam-6968	179	23	the	the	DET
ejpam-6968	179	24	state	state	NOUN
ejpam-6968	179	25	space	space	NOUN
ejpam-6968	179	26	and	and	CCONJ
ejpam-6968	179	27	reducing	reduce	VERB
ejpam-6968	179	28	the	the	DET
ejpam-6968	179	29	computation	computation	NOUN
ejpam-6968	179	30	time	time	NOUN
ejpam-6968	179	31	.	.	PUNCT
ejpam-6968	180	1	to	to	PART
ejpam-6968	180	2	quantify	quantify	VERB
ejpam-6968	180	3	the	the	DET
ejpam-6968	180	4	chaotic	chaotic	ADJ
ejpam-6968	180	5	behavior	behavior	NOUN
ejpam-6968	180	6	of	of	ADP
ejpam-6968	180	7	the	the	DET
ejpam-6968	180	8	system	system	NOUN
ejpam-6968	180	9	,	,	PUNCT
ejpam-6968	180	10	we	we	PRON
ejpam-6968	180	11	also	also	ADV
ejpam-6968	180	12	compute	compute	VERB
ejpam-6968	180	13	the	the	DET
ejpam-6968	180	14	kaplan	kaplan	PROPN
ejpam-6968	180	15	-	-	PROPN
ejpam-6968	180	16	yorke	yorke	PROPN
ejpam-6968	180	17	dimension	dimension	NOUN
ejpam-6968	180	18	,	,	PUNCT
ejpam-6968	180	19	which	which	PRON
ejpam-6968	180	20	gives	give	VERB
ejpam-6968	180	21	us	we	PRON
ejpam-6968	180	22	the	the	DET
ejpam-6968	180	23	fractal	fractal	ADJ
ejpam-6968	180	24	dimension	dimension	NOUN
ejpam-6968	180	25	of	of	ADP
ejpam-6968	180	26	the	the	DET
ejpam-6968	180	27	attractor	attractor	NOUN
ejpam-6968	180	28	.	.	PUNCT
ejpam-6968	181	1	the	the	DET
ejpam-6968	181	2	kaplan	kaplan	PROPN
ejpam-6968	181	3	-	-	PROPN
ejpam-6968	181	4	yorke	yorke	PROPN
ejpam-6968	181	5	dimension	dimension	NOUN
ejpam-6968	181	6	is	be	AUX
ejpam-6968	181	7	computed	compute	VERB
ejpam-6968	181	8	based	base	VERB
ejpam-6968	181	9	on	on	ADP
ejpam-6968	181	10	the	the	DET
ejpam-6968	181	11	system	system	NOUN
ejpam-6968	181	12	’s	’s	PART
ejpam-6968	181	13	lyapunov	lyapunov	ADJ
ejpam-6968	181	14	exponents	exponent	NOUN
ejpam-6968	181	15	,	,	PUNCT
ejpam-6968	181	16	which	which	PRON
ejpam-6968	181	17	measure	measure	VERB
ejpam-6968	181	18	the	the	DET
ejpam-6968	181	19	rate	rate	NOUN
ejpam-6968	181	20	of	of	ADP
ejpam-6968	181	21	separation	separation	NOUN
ejpam-6968	181	22	of	of	ADP
ejpam-6968	181	23	nearby	nearby	ADJ
ejpam-6968	181	24	trajectories	trajectory	NOUN
ejpam-6968	181	25	in	in	ADP
ejpam-6968	181	26	phase	phase	NOUN
ejpam-6968	181	27	space	space	NOUN
ejpam-6968	181	28	.	.	PUNCT
ejpam-6968	182	1	the	the	DET
ejpam-6968	182	2	kaplan	kaplan	PROPN
ejpam-6968	182	3	-	-	PROPN
ejpam-6968	182	4	yorke	yorke	PROPN
ejpam-6968	182	5	dimension	dimension	NOUN
ejpam-6968	182	6	dky	dky	NOUN
ejpam-6968	182	7	is	be	AUX
ejpam-6968	182	8	calculated	calculate	VERB
ejpam-6968	182	9	using	use	VERB
ejpam-6968	182	10	the	the	DET
ejpam-6968	182	11	following	follow	VERB
ejpam-6968	182	12	formula	formula	NOUN
ejpam-6968	182	13	:	:	PUNCT
ejpam-6968	182	14	dky	dky	NOUN
ejpam-6968	182	15	=	=	SYM
ejpam-6968	182	16	m+	m+	NOUN
ejpam-6968	182	17	∑m	∑m	PROPN
ejpam-6968	182	18	i=1	i=1	PROPN
ejpam-6968	182	19	λi	λi	ADP
ejpam-6968	182	20	|λm+1|	|λm+1|	PROPN
ejpam-6968	182	21	where	where	SCONJ
ejpam-6968	182	22	λ1	λ1	ADJ
ejpam-6968	182	23	,	,	PUNCT
ejpam-6968	182	24	λ2	λ2	NOUN
ejpam-6968	182	25	,	,	PUNCT
ejpam-6968	182	26	.	.	PUNCT
ejpam-6968	182	27	.	.	PUNCT
ejpam-6968	183	1	.	.	PUNCT
ejpam-6968	184	1	,	,	PUNCT
ejpam-6968	184	2	λm	λm	X
ejpam-6968	184	3	are	be	AUX
ejpam-6968	184	4	the	the	DET
ejpam-6968	184	5	lyapunov	lyapunov	ADJ
ejpam-6968	184	6	exponents	exponent	NOUN
ejpam-6968	184	7	,	,	PUNCT
ejpam-6968	184	8	ordered	order	VERB
ejpam-6968	184	9	from	from	ADP
ejpam-6968	184	10	largest	large	ADJ
ejpam-6968	184	11	to	to	AUX
ejpam-6968	184	12	smallest	small	ADJ
ejpam-6968	184	13	,	,	PUNCT
ejpam-6968	184	14	then	then	ADV
ejpam-6968	184	15	m	m	VERB
ejpam-6968	184	16	is	be	AUX
ejpam-6968	184	17	the	the	DET
ejpam-6968	184	18	largest	large	ADJ
ejpam-6968	184	19	integer	integer	NOUN
ejpam-6968	184	20	such	such	ADJ
ejpam-6968	184	21	that	that	SCONJ
ejpam-6968	184	22	the	the	DET
ejpam-6968	184	23	sum	sum	NOUN
ejpam-6968	184	24	of	of	ADP
ejpam-6968	184	25	the	the	DET
ejpam-6968	184	26	first	first	ADJ
ejpam-6968	184	27	m	m	PROPN
ejpam-6968	184	28	exponents	exponent	NOUN
ejpam-6968	184	29	is	be	AUX
ejpam-6968	184	30	positive	positive	ADJ
ejpam-6968	184	31	,	,	PUNCT
ejpam-6968	184	32	and	and	CCONJ
ejpam-6968	184	33	λm+1	λm+1	X
ejpam-6968	184	34	is	be	AUX
ejpam-6968	184	35	the	the	DET
ejpam-6968	184	36	first	first	ADJ
ejpam-6968	184	37	negative	negative	ADJ
ejpam-6968	184	38	lyapunov	lyapunov	ADJ
ejpam-6968	184	39	exponent	exponent	NOUN
ejpam-6968	184	40	,	,	PUNCT
ejpam-6968	184	41	if	if	SCONJ
ejpam-6968	184	42	it	it	PRON
ejpam-6968	184	43	exists	exist	VERB
ejpam-6968	184	44	.	.	PUNCT
ejpam-6968	185	1	the	the	DET
ejpam-6968	185	2	kaplan	kaplan	PROPN
ejpam-6968	185	3	-	-	PROPN
ejpam-6968	185	4	yorke	yorke	PROPN
ejpam-6968	185	5	dimension	dimension	NOUN
ejpam-6968	185	6	quantifies	quantify	VERB
ejpam-6968	185	7	the	the	DET
ejpam-6968	185	8	degree	degree	NOUN
ejpam-6968	185	9	of	of	ADP
ejpam-6968	185	10	chaos	chaos	NOUN
ejpam-6968	185	11	in	in	ADP
ejpam-6968	185	12	the	the	DET
ejpam-6968	185	13	system	system	NOUN
ejpam-6968	185	14	,	,	PUNCT
ejpam-6968	185	15	and	and	CCONJ
ejpam-6968	185	16	for	for	ADP
ejpam-6968	185	17	chaotic	chaotic	ADJ
ejpam-6968	185	18	systems	system	NOUN
ejpam-6968	185	19	,	,	PUNCT
ejpam-6968	185	20	the	the	DET
ejpam-6968	185	21	dimension	dimension	NOUN
ejpam-6968	185	22	is	be	AUX
ejpam-6968	185	23	often	often	ADV
ejpam-6968	185	24	non	non	ADJ
ejpam-6968	185	25	-	-	ADJ
ejpam-6968	185	26	integer	integer	ADJ
ejpam-6968	185	27	.	.	PUNCT
ejpam-6968	186	1	a	a	DET
ejpam-6968	186	2	higher	high	ADJ
ejpam-6968	186	3	value	value	NOUN
ejpam-6968	186	4	of	of	ADP
ejpam-6968	186	5	the	the	DET
ejpam-6968	186	6	dimension	dimension	NOUN
ejpam-6968	186	7	indicates	indicate	VERB
ejpam-6968	186	8	greater	great	ADJ
ejpam-6968	186	9	complexity	complexity	NOUN
ejpam-6968	186	10	and	and	CCONJ
ejpam-6968	186	11	fractal	fractal	ADJ
ejpam-6968	186	12	behavior	behavior	NOUN
ejpam-6968	186	13	.	.	PUNCT
ejpam-6968	187	1	for	for	ADP
ejpam-6968	187	2	our	our	PRON
ejpam-6968	187	3	system	system	NOUN
ejpam-6968	187	4	,	,	PUNCT
ejpam-6968	187	5	we	we	PRON
ejpam-6968	187	6	calculated	calculate	VERB
ejpam-6968	187	7	the	the	DET
ejpam-6968	187	8	lyapunov	lyapunov	ADJ
ejpam-6968	187	9	exponents	exponent	NOUN
ejpam-6968	187	10	first	first	ADV
ejpam-6968	187	11	,	,	PUNCT
ejpam-6968	187	12	then	then	ADV
ejpam-6968	187	13	used	use	VERB
ejpam-6968	187	14	the	the	DET
ejpam-6968	187	15	kaplan	kaplan	PROPN
ejpam-6968	187	16	-	-	PUNCT
ejpam-6968	187	17	yorke	yorke	PROPN
ejpam-6968	187	18	formula	formula	NOUN
ejpam-6968	187	19	to	to	PART
ejpam-6968	187	20	determine	determine	VERB
ejpam-6968	187	21	the	the	DET
ejpam-6968	187	22	dimension	dimension	NOUN
ejpam-6968	187	23	of	of	ADP
ejpam-6968	187	24	the	the	DET
ejpam-6968	187	25	attractor	attractor	NOUN
ejpam-6968	187	26	.	.	PUNCT
ejpam-6968	188	1	this	this	PRON
ejpam-6968	188	2	provided	provide	VERB
ejpam-6968	188	3	a	a	DET
ejpam-6968	188	4	more	more	ADV
ejpam-6968	188	5	precise	precise	ADJ
ejpam-6968	188	6	understanding	understanding	NOUN
ejpam-6968	188	7	of	of	ADP
ejpam-6968	188	8	the	the	DET
ejpam-6968	188	9	system	system	NOUN
ejpam-6968	188	10	’s	’s	PART
ejpam-6968	188	11	chaotic	chaotic	ADJ
ejpam-6968	188	12	nature	nature	NOUN
ejpam-6968	188	13	across	across	ADP
ejpam-6968	188	14	different	different	ADJ
ejpam-6968	188	15	values	value	NOUN
ejpam-6968	188	16	of	of	ADP
ejpam-6968	188	17	α	α	NOUN
ejpam-6968	188	18	.	.	PUNCT
ejpam-6968	189	1	although	although	SCONJ
ejpam-6968	189	2	a	a	DET
ejpam-6968	189	3	hopf	hopf	ADJ
ejpam-6968	189	4	bifurcation	bifurcation	NOUN
ejpam-6968	189	5	is	be	AUX
ejpam-6968	189	6	predicted	predict	VERB
ejpam-6968	189	7	analytically	analytically	ADV
ejpam-6968	189	8	at	at	ADP
ejpam-6968	189	9	α	α	NOUN
ejpam-6968	189	10	=	=	SYM
ejpam-6968	189	11	−196	−196	NOUN
ejpam-6968	189	12	,	,	PUNCT
ejpam-6968	189	13	sustained	sustained	ADJ
ejpam-6968	189	14	oscillations	oscillation	NOUN
ejpam-6968	189	15	are	be	AUX
ejpam-6968	189	16	first	first	ADV
ejpam-6968	189	17	observed	observe	VERB
ejpam-6968	189	18	numerically	numerically	ADV
ejpam-6968	189	19	near	near	ADP
ejpam-6968	189	20	α	α	PROPN
ejpam-6968	189	21	≈	≈	PROPN
ejpam-6968	189	22	−31	−31	PROPN
ejpam-6968	189	23	.	.	PUNCT
ejpam-6968	190	1	this	this	DET
ejpam-6968	190	2	offset	offset	NOUN
ejpam-6968	190	3	reflects	reflect	VERB
ejpam-6968	190	4	global	global	ADJ
ejpam-6968	190	5	nonlinear	nonlinear	ADJ
ejpam-6968	190	6	effects	effect	NOUN
ejpam-6968	190	7	outside	outside	ADP
ejpam-6968	190	8	the	the	DET
ejpam-6968	190	9	local	local	ADJ
ejpam-6968	190	10	center	center	NOUN
ejpam-6968	190	11	-	-	PUNCT
ejpam-6968	190	12	manifold	manifold	ADJ
ejpam-6968	190	13	neighborhood	neighborhood	NOUN
ejpam-6968	190	14	.	.	PUNCT
ejpam-6968	191	1	in	in	ADP
ejpam-6968	191	2	that	that	DET
ejpam-6968	191	3	regime	regime	NOUN
ejpam-6968	191	4	,	,	PUNCT
ejpam-6968	191	5	the	the	DET
ejpam-6968	191	6	system	system	NOUN
ejpam-6968	191	7	undergoes	undergo	VERB
ejpam-6968	191	8	a	a	DET
ejpam-6968	191	9	period	period	NOUN
ejpam-6968	191	10	-	-	PUNCT
ejpam-6968	191	11	doubling	double	VERB
ejpam-6968	191	12	cascade	cascade	NOUN
ejpam-6968	191	13	as	as	ADP
ejpam-6968	191	14	α	α	NOUN
ejpam-6968	191	15	increases	increase	NOUN
ejpam-6968	191	16	,	,	PUNCT
ejpam-6968	191	17	culminating	culminate	VERB
ejpam-6968	191	18	in	in	ADP
ejpam-6968	191	19	chaos	chaos	NOUN
ejpam-6968	191	20	.	.	PUNCT
ejpam-6968	192	1	bifurcation	bifurcation	NOUN
ejpam-6968	192	2	diagrams	diagram	NOUN
ejpam-6968	192	3	figure	figure	VERB
ejpam-6968	192	4	2	2	NUM
ejpam-6968	192	5	displays	display	VERB
ejpam-6968	192	6	the	the	DET
ejpam-6968	192	7	bifurcation	bifurcation	NOUN
ejpam-6968	192	8	structure	structure	NOUN
ejpam-6968	192	9	obtained	obtain	VERB
ejpam-6968	192	10	from	from	ADP
ejpam-6968	192	11	successive	successive	ADJ
ejpam-6968	192	12	local	local	ADJ
ejpam-6968	192	13	maxima	maxima	NOUN
ejpam-6968	192	14	of	of	ADP
ejpam-6968	192	15	x(t	x(t	PROPN
ejpam-6968	192	16	)	)	PUNCT
ejpam-6968	192	17	.	.	PUNCT
ejpam-6968	193	1	for	for	ADP
ejpam-6968	193	2	α	α	PROPN
ejpam-6968	193	3	∈	∈	PROPN
ejpam-6968	194	1	[	[	X
ejpam-6968	194	2	−38	−38	NOUN
ejpam-6968	194	3	,	,	PUNCT
ejpam-6968	194	4	0	0	NUM
ejpam-6968	194	5	]	]	PUNCT
ejpam-6968	194	6	[	[	X
ejpam-6968	194	7	fig	fig	NOUN
ejpam-6968	194	8	.	.	PUNCT
ejpam-6968	195	1	2(a	2(a	NUM
ejpam-6968	195	2	)	)	PUNCT
ejpam-6968	195	3	]	]	PUNCT
ejpam-6968	195	4	we	we	PRON
ejpam-6968	195	5	observe	observe	VERB
ejpam-6968	195	6	a	a	DET
ejpam-6968	195	7	classical	classical	ADJ
ejpam-6968	195	8	feigenbaum	feigenbaum	ADJ
ejpam-6968	195	9	-	-	PUNCT
ejpam-6968	195	10	type	type	NOUN
ejpam-6968	195	11	cascade	cascade	NOUN
ejpam-6968	195	12	,	,	PUNCT
ejpam-6968	195	13	interspersed	intersperse	VERB
ejpam-6968	195	14	with	with	ADP
ejpam-6968	195	15	narrow	narrow	ADJ
ejpam-6968	195	16	periodic	periodic	ADJ
ejpam-6968	195	17	windows	window	NOUN
ejpam-6968	195	18	indicating	indicate	VERB
ejpam-6968	195	19	intermittency	intermittency	NOUN
ejpam-6968	195	20	and	and	CCONJ
ejpam-6968	195	21	a	a	DET
ejpam-6968	195	22	tangled	tangled	ADJ
ejpam-6968	195	23	phasespace	phasespace	NOUN
ejpam-6968	195	24	geometry	geometry	NOUN
ejpam-6968	195	25	.	.	PUNCT
ejpam-6968	196	1	in	in	ADP
ejpam-6968	196	2	contrast	contrast	NOUN
ejpam-6968	196	3	,	,	PUNCT
ejpam-6968	196	4	for	for	ADP
ejpam-6968	196	5	α	α	DET
ejpam-6968	196	6	∈	∈	PROPN
ejpam-6968	196	7	(	(	PUNCT
ejpam-6968	196	8	0	0	NUM
ejpam-6968	196	9	,	,	PUNCT
ejpam-6968	196	10	0.8	0.8	NUM
ejpam-6968	196	11	)	)	PUNCT
ejpam-6968	197	1	[	[	X
ejpam-6968	197	2	fig	fig	NOUN
ejpam-6968	197	3	.	.	PUNCT
ejpam-6968	198	1	2(b	2(b	NUM
ejpam-6968	198	2	)	)	PUNCT
ejpam-6968	198	3	]	]	PUNCT
ejpam-6968	198	4	higher	high	ADJ
ejpam-6968	198	5	-	-	PUNCT
ejpam-6968	198	6	order	order	NOUN
ejpam-6968	198	7	periodic	periodic	ADJ
ejpam-6968	198	8	motions	motion	NOUN
ejpam-6968	198	9	collapse	collapse	VERB
ejpam-6968	198	10	to	to	ADP
ejpam-6968	198	11	lower	low	ADJ
ejpam-6968	198	12	periods	period	NOUN
ejpam-6968	198	13	via	via	ADP
ejpam-6968	198	14	period	period	NOUN
ejpam-6968	198	15	-	-	PUNCT
ejpam-6968	198	16	halving	halving	NOUN
ejpam-6968	198	17	,	,	PUNCT
ejpam-6968	198	18	a	a	DET
ejpam-6968	198	19	signature	signature	NOUN
ejpam-6968	198	20	of	of	ADP
ejpam-6968	198	21	the	the	DET
ejpam-6968	198	22	hidden	hide	VERB
ejpam-6968	198	23	-	-	PUNCT
ejpam-6968	198	24	attractor	attractor	NOUN
ejpam-6968	198	25	regime	regime	NOUN
ejpam-6968	198	26	in	in	ADP
ejpam-6968	198	27	the	the	DET
ejpam-6968	198	28	absence	absence	NOUN
ejpam-6968	198	29	of	of	ADP
ejpam-6968	198	30	equilibria	equilibrium	NOUN
ejpam-6968	198	31	.	.	PUNCT
ejpam-6968	199	1	as	as	SCONJ
ejpam-6968	199	2	seen	see	VERB
ejpam-6968	199	3	in	in	ADP
ejpam-6968	199	4	the	the	DET
ejpam-6968	199	5	bifurcation	bifurcation	NOUN
ejpam-6968	199	6	diagrams	diagram	NOUN
ejpam-6968	199	7	,	,	PUNCT
ejpam-6968	199	8	the	the	DET
ejpam-6968	199	9	transition	transition	NOUN
ejpam-6968	199	10	from	from	ADP
ejpam-6968	199	11	periodic	periodic	ADJ
ejpam-6968	199	12	to	to	ADP
ejpam-6968	199	13	chaotic	chaotic	ADJ
ejpam-6968	199	14	behavior	behavior	NOUN
ejpam-6968	199	15	is	be	AUX
ejpam-6968	199	16	governed	govern	VERB
ejpam-6968	199	17	by	by	ADP
ejpam-6968	199	18	critical	critical	ADJ
ejpam-6968	199	19	values	value	NOUN
ejpam-6968	199	20	of	of	ADP
ejpam-6968	199	21	the	the	DET
ejpam-6968	199	22	control	control	NOUN
ejpam-6968	199	23	parameter	parameter	PROPN
ejpam-6968	199	24	α	α	PROPN
ejpam-6968	199	25	.	.	PUNCT
ejpam-6968	200	1	this	this	DET
ejpam-6968	200	2	bifurcation	bifurcation	NOUN
ejpam-6968	200	3	behavior	behavior	NOUN
ejpam-6968	200	4	is	be	AUX
ejpam-6968	200	5	further	far	ADV
ejpam-6968	200	6	validated	validate	VERB
ejpam-6968	200	7	by	by	ADP
ejpam-6968	200	8	the	the	DET
ejpam-6968	200	9	lyapunov	lyapunov	ADJ
ejpam-6968	200	10	exponents	exponent	NOUN
ejpam-6968	200	11	,	,	PUNCT
ejpam-6968	200	12	which	which	PRON
ejpam-6968	200	13	help	help	VERB
ejpam-6968	200	14	us	we	PRON
ejpam-6968	200	15	characterize	characterize	VERB
ejpam-6968	200	16	the	the	DET
ejpam-6968	200	17	system	system	NOUN
ejpam-6968	200	18	’s	’s	PART
ejpam-6968	200	19	chaos	chaos	NOUN
ejpam-6968	200	20	.	.	PUNCT
ejpam-6968	201	1	h.	h.	PROPN
ejpam-6968	201	2	k.	k.	PROPN
ejpam-6968	201	3	fata	fata	PROPN
ejpam-6968	201	4	,	,	PUNCT
ejpam-6968	201	5	n.	n.	PROPN
ejpam-6968	201	6	y.	y.	PROPN
ejpam-6968	201	7	ashar	ashar	PROPN
ejpam-6968	201	8	/	/	SYM
ejpam-6968	201	9	eur	eur	PROPN
ejpam-6968	201	10	.	.	PUNCT
ejpam-6968	202	1	j.	j.	PROPN
ejpam-6968	202	2	pure	pure	PROPN
ejpam-6968	202	3	appl	appl	PROPN
ejpam-6968	202	4	.	.	PROPN
ejpam-6968	202	5	math	math	PROPN
ejpam-6968	202	6	,	,	PUNCT
ejpam-6968	202	7	18	18	NUM
ejpam-6968	202	8	(	(	PUNCT
ejpam-6968	202	9	4	4	NUM
ejpam-6968	202	10	)	)	PUNCT
ejpam-6968	202	11	(	(	PUNCT
ejpam-6968	202	12	2025	2025	NUM
ejpam-6968	202	13	)	)	PUNCT
ejpam-6968	202	14	,	,	PUNCT
ejpam-6968	202	15	6968	6968	NUM
ejpam-6968	202	16	10	10	NUM
ejpam-6968	202	17	of	of	ADP
ejpam-6968	202	18	15	15	NUM
ejpam-6968	202	19	(	(	PUNCT
ejpam-6968	202	20	a	a	NOUN
ejpam-6968	202	21	)	)	PUNCT
ejpam-6968	202	22	(	(	PUNCT
ejpam-6968	202	23	b	b	X
ejpam-6968	202	24	)	)	PUNCT
ejpam-6968	202	25	figure	figure	NOUN
ejpam-6968	202	26	2	2	NUM
ejpam-6968	202	27	:	:	PUNCT
ejpam-6968	202	28	bifurcation	bifurcation	NOUN
ejpam-6968	202	29	diagrams	diagram	NOUN
ejpam-6968	202	30	from	from	ADP
ejpam-6968	202	31	the	the	DET
ejpam-6968	202	32	last	last	ADJ
ejpam-6968	202	33	200	200	NUM
ejpam-6968	202	34	local	local	ADJ
ejpam-6968	202	35	maxima	maxima	NOUN
ejpam-6968	202	36	of	of	ADP
ejpam-6968	202	37	x(t	x(t	PROPN
ejpam-6968	202	38	)	)	PUNCT
ejpam-6968	202	39	.	.	PUNCT
ejpam-6968	203	1	(	(	PUNCT
ejpam-6968	203	2	a	a	X
ejpam-6968	203	3	)	)	PUNCT
ejpam-6968	203	4	period	period	NOUN
ejpam-6968	203	5	-	-	PUNCT
ejpam-6968	203	6	doubling	double	VERB
ejpam-6968	203	7	cascade	cascade	NOUN
ejpam-6968	203	8	with	with	ADP
ejpam-6968	203	9	periodic	periodic	ADJ
ejpam-6968	203	10	windows	window	NOUN
ejpam-6968	203	11	for	for	ADP
ejpam-6968	203	12	α	α	PRON
ejpam-6968	203	13	∈	∈	PROPN
ejpam-6968	204	1	[	[	X
ejpam-6968	204	2	−38	−38	NOUN
ejpam-6968	204	3	,	,	PUNCT
ejpam-6968	204	4	0	0	NUM
ejpam-6968	204	5	]	]	PUNCT
ejpam-6968	204	6	.	.	PUNCT
ejpam-6968	205	1	(	(	PUNCT
ejpam-6968	205	2	b	b	X
ejpam-6968	205	3	)	)	PUNCT
ejpam-6968	205	4	reverse	reverse	ADJ
ejpam-6968	205	5	period	period	NOUN
ejpam-6968	205	6	-	-	PUNCT
ejpam-6968	205	7	halving	halving	NOUN
ejpam-6968	205	8	for	for	ADP
ejpam-6968	205	9	α	α	PRON
ejpam-6968	205	10	∈	∈	PROPN
ejpam-6968	205	11	(	(	PUNCT
ejpam-6968	205	12	0	0	NUM
ejpam-6968	205	13	,	,	PUNCT
ejpam-6968	205	14	0.8	0.8	NUM
ejpam-6968	205	15	)	)	PUNCT
ejpam-6968	205	16	characteristic	characteristic	NOUN
ejpam-6968	205	17	of	of	ADP
ejpam-6968	205	18	the	the	DET
ejpam-6968	205	19	hidden	hide	VERB
ejpam-6968	205	20	-	-	PUNCT
ejpam-6968	205	21	attractor	attractor	NOUN
ejpam-6968	205	22	regime	regime	NOUN
ejpam-6968	205	23	.	.	PUNCT
ejpam-6968	206	1	maximal	maximal	ADJ
ejpam-6968	206	2	lyapunov	lyapunov	ADJ
ejpam-6968	206	3	exponents	exponent	NOUN
ejpam-6968	206	4	figure	figure	VERB
ejpam-6968	206	5	3	3	NUM
ejpam-6968	206	6	reports	report	VERB
ejpam-6968	206	7	the	the	DET
ejpam-6968	206	8	maximal	maximal	ADJ
ejpam-6968	206	9	lyapunov	lyapunov	NOUN
ejpam-6968	206	10	exponent	exponent	NOUN
ejpam-6968	206	11	l1(α	l1(α	PROPN
ejpam-6968	206	12	)	)	PUNCT
ejpam-6968	206	13	,	,	PUNCT
ejpam-6968	206	14	which	which	PRON
ejpam-6968	206	15	is	be	AUX
ejpam-6968	206	16	a	a	DET
ejpam-6968	206	17	key	key	ADJ
ejpam-6968	206	18	indicator	indicator	NOUN
ejpam-6968	206	19	of	of	ADP
ejpam-6968	206	20	chaos	chaos	NOUN
ejpam-6968	206	21	in	in	ADP
ejpam-6968	206	22	dynamical	dynamical	ADJ
ejpam-6968	206	23	systems	system	NOUN
ejpam-6968	206	24	.	.	PUNCT
ejpam-6968	207	1	for	for	ADP
ejpam-6968	207	2	α	α	PRON
ejpam-6968	207	3	<	<	X
ejpam-6968	207	4	0	0	PUNCT
ejpam-6968	208	1	[	[	X
ejpam-6968	208	2	fig	fig	NOUN
ejpam-6968	208	3	.	.	PUNCT
ejpam-6968	209	1	3(a	3(a	NUM
ejpam-6968	209	2	)	)	PUNCT
ejpam-6968	209	3	]	]	PUNCT
ejpam-6968	209	4	,	,	PUNCT
ejpam-6968	209	5	we	we	PRON
ejpam-6968	209	6	observe	observe	VERB
ejpam-6968	209	7	that	that	SCONJ
ejpam-6968	209	8	intervals	interval	NOUN
ejpam-6968	209	9	where	where	SCONJ
ejpam-6968	209	10	l1	l1	PROPN
ejpam-6968	209	11	>	>	X
ejpam-6968	209	12	0	0	PUNCT
ejpam-6968	209	13	confirm	confirm	VERB
ejpam-6968	209	14	chaotic	chaotic	ADJ
ejpam-6968	209	15	behavior	behavior	NOUN
ejpam-6968	209	16	,	,	PUNCT
ejpam-6968	209	17	while	while	SCONJ
ejpam-6968	209	18	zeros	zero	NOUN
ejpam-6968	209	19	correspond	correspond	VERB
ejpam-6968	209	20	to	to	ADP
ejpam-6968	209	21	periodic	periodic	ADJ
ejpam-6968	209	22	or	or	CCONJ
ejpam-6968	209	23	quasi	quasi	ADJ
ejpam-6968	209	24	-	-	ADJ
ejpam-6968	209	25	periodic	periodic	ADJ
ejpam-6968	209	26	dynamics	dynamic	NOUN
ejpam-6968	209	27	.	.	PUNCT
ejpam-6968	210	1	a	a	DET
ejpam-6968	210	2	sharp	sharp	ADJ
ejpam-6968	210	3	rise	rise	NOUN
ejpam-6968	210	4	in	in	ADP
ejpam-6968	210	5	l1	l1	PROPN
ejpam-6968	210	6	near	near	ADP
ejpam-6968	210	7	α	α	PROPN
ejpam-6968	210	8	≈	≈	PROPN
ejpam-6968	210	9	−20	−20	PROPN
ejpam-6968	210	10	marks	mark	VERB
ejpam-6968	210	11	the	the	DET
ejpam-6968	210	12	onset	onset	NOUN
ejpam-6968	210	13	of	of	ADP
ejpam-6968	210	14	robust	robust	ADJ
ejpam-6968	210	15	chaos	chaos	NOUN
ejpam-6968	210	16	,	,	PUNCT
ejpam-6968	210	17	followed	follow	VERB
ejpam-6968	210	18	by	by	ADP
ejpam-6968	210	19	periodic	periodic	ADJ
ejpam-6968	210	20	windows	window	NOUN
ejpam-6968	210	21	where	where	SCONJ
ejpam-6968	210	22	l1	l1	PROPN
ejpam-6968	210	23	returns	return	VERB
ejpam-6968	210	24	to	to	ADP
ejpam-6968	210	25	zero	zero	NUM
ejpam-6968	210	26	or	or	CCONJ
ejpam-6968	210	27	negative	negative	ADJ
ejpam-6968	210	28	values	value	NOUN
ejpam-6968	210	29	,	,	PUNCT
ejpam-6968	210	30	consistent	consistent	ADJ
ejpam-6968	210	31	with	with	ADP
ejpam-6968	210	32	the	the	DET
ejpam-6968	210	33	transitions	transition	NOUN
ejpam-6968	210	34	seen	see	VERB
ejpam-6968	210	35	in	in	ADP
ejpam-6968	210	36	the	the	DET
ejpam-6968	210	37	bifurcation	bifurcation	NOUN
ejpam-6968	210	38	diagram	diagram	NOUN
ejpam-6968	210	39	for	for	ADP
ejpam-6968	210	40	α	α	PROPN
ejpam-6968	210	41	∈	∈	PROPN
ejpam-6968	211	1	[	[	X
ejpam-6968	211	2	−38	−38	NOUN
ejpam-6968	211	3	,	,	PUNCT
ejpam-6968	211	4	0	0	NUM
ejpam-6968	211	5	]	]	PUNCT
ejpam-6968	211	6	[	[	X
ejpam-6968	211	7	fig	fig	NOUN
ejpam-6968	211	8	.	.	PUNCT
ejpam-6968	211	9	2(a	2(a	NUM
ejpam-6968	211	10	)	)	PUNCT
ejpam-6968	211	11	]	]	PUNCT
ejpam-6968	211	12	.	.	PUNCT
ejpam-6968	212	1	for	for	ADP
ejpam-6968	212	2	α	α	PROPN
ejpam-6968	212	3	>	>	X
ejpam-6968	212	4	0	0	PUNCT
ejpam-6968	213	1	[	[	X
ejpam-6968	213	2	fig	fig	NOUN
ejpam-6968	213	3	.	.	PUNCT
ejpam-6968	214	1	3(b	3(b	NUM
ejpam-6968	214	2	)	)	PUNCT
ejpam-6968	214	3	]	]	PUNCT
ejpam-6968	214	4	,	,	PUNCT
ejpam-6968	214	5	l1	l1	PROPN
ejpam-6968	214	6	decreases	decrease	VERB
ejpam-6968	214	7	as	as	ADP
ejpam-6968	214	8	α	α	NOUN
ejpam-6968	214	9	increases	increase	NOUN
ejpam-6968	214	10	,	,	PUNCT
ejpam-6968	214	11	following	follow	VERB
ejpam-6968	214	12	the	the	DET
ejpam-6968	214	13	trend	trend	NOUN
ejpam-6968	214	14	of	of	ADP
ejpam-6968	214	15	period	period	NOUN
ejpam-6968	214	16	-	-	PUNCT
ejpam-6968	214	17	halving	halving	NOUN
ejpam-6968	214	18	observed	observe	VERB
ejpam-6968	214	19	in	in	ADP
ejpam-6968	214	20	the	the	DET
ejpam-6968	214	21	bifurcation	bifurcation	NOUN
ejpam-6968	214	22	diagram	diagram	NOUN
ejpam-6968	214	23	for	for	ADP
ejpam-6968	214	24	α	α	PROPN
ejpam-6968	214	25	∈	∈	PROPN
ejpam-6968	214	26	(	(	PUNCT
ejpam-6968	214	27	0	0	NUM
ejpam-6968	214	28	,	,	PUNCT
ejpam-6968	214	29	0.8	0.8	NUM
ejpam-6968	214	30	)	)	PUNCT
ejpam-6968	215	1	[	[	X
ejpam-6968	215	2	fig	fig	NOUN
ejpam-6968	215	3	.	.	PUNCT
ejpam-6968	216	1	2(b	2(b	NUM
ejpam-6968	216	2	)	)	PUNCT
ejpam-6968	216	3	]	]	PUNCT
ejpam-6968	216	4	.	.	PUNCT
ejpam-6968	217	1	this	this	DET
ejpam-6968	217	2	decrease	decrease	NOUN
ejpam-6968	217	3	in	in	ADP
ejpam-6968	217	4	l1	l1	PROPN
ejpam-6968	217	5	signifies	signify	VERB
ejpam-6968	217	6	a	a	DET
ejpam-6968	217	7	simplification	simplification	NOUN
ejpam-6968	217	8	of	of	ADP
ejpam-6968	217	9	the	the	DET
ejpam-6968	217	10	dynamics	dynamic	NOUN
ejpam-6968	217	11	as	as	SCONJ
ejpam-6968	217	12	the	the	DET
ejpam-6968	217	13	system	system	NOUN
ejpam-6968	217	14	approaches	approach	VERB
ejpam-6968	217	15	the	the	DET
ejpam-6968	217	16	hidden	hide	VERB
ejpam-6968	217	17	-	-	PUNCT
ejpam-6968	217	18	attractor	attractor	NOUN
ejpam-6968	217	19	regime	regime	NOUN
ejpam-6968	217	20	,	,	PUNCT
ejpam-6968	217	21	where	where	SCONJ
ejpam-6968	217	22	no	no	DET
ejpam-6968	217	23	equilibrium	equilibrium	NOUN
ejpam-6968	217	24	points	point	NOUN
ejpam-6968	217	25	exist	exist	VERB
ejpam-6968	217	26	and	and	CCONJ
ejpam-6968	217	27	the	the	DET
ejpam-6968	217	28	system	system	NOUN
ejpam-6968	217	29	exhibits	exhibit	VERB
ejpam-6968	217	30	complex	complex	ADJ
ejpam-6968	217	31	behavior	behavior	NOUN
ejpam-6968	217	32	without	without	ADP
ejpam-6968	217	33	traditional	traditional	ADJ
ejpam-6968	217	34	attractors	attractor	NOUN
ejpam-6968	217	35	.	.	PUNCT
ejpam-6968	218	1	kaplan	kaplan	PROPN
ejpam-6968	218	2	–	–	PUNCT
ejpam-6968	218	3	yorke	yorke	PROPN
ejpam-6968	218	4	dimension	dimension	PROPN
ejpam-6968	218	5	figure	figure	NOUN
ejpam-6968	218	6	4	4	NUM
ejpam-6968	218	7	shows	show	VERB
ejpam-6968	218	8	the	the	DET
ejpam-6968	218	9	kaplan	kaplan	PROPN
ejpam-6968	218	10	–	–	PUNCT
ejpam-6968	218	11	yorke	yorke	PROPN
ejpam-6968	218	12	(	(	PUNCT
ejpam-6968	218	13	lyapunov	lyapunov	PROPN
ejpam-6968	218	14	)	)	PUNCT
ejpam-6968	218	15	dimension	dimension	NOUN
ejpam-6968	218	16	dky(α	dky(α	PROPN
ejpam-6968	218	17	)	)	PUNCT
ejpam-6968	218	18	,	,	PUNCT
ejpam-6968	218	19	which	which	PRON
ejpam-6968	218	20	is	be	AUX
ejpam-6968	218	21	computed	compute	VERB
ejpam-6968	218	22	from	from	ADP
ejpam-6968	218	23	the	the	DET
ejpam-6968	218	24	lyapunov	lyapunov	ADJ
ejpam-6968	218	25	spectra	spectra	NOUN
ejpam-6968	218	26	and	and	CCONJ
ejpam-6968	218	27	provides	provide	VERB
ejpam-6968	218	28	a	a	DET
ejpam-6968	218	29	measure	measure	NOUN
ejpam-6968	218	30	of	of	ADP
ejpam-6968	218	31	the	the	DET
ejpam-6968	218	32	complexity	complexity	NOUN
ejpam-6968	218	33	and	and	CCONJ
ejpam-6968	218	34	fractality	fractality	NOUN
ejpam-6968	218	35	of	of	ADP
ejpam-6968	218	36	the	the	DET
ejpam-6968	218	37	attractor	attractor	NOUN
ejpam-6968	218	38	.	.	PUNCT
ejpam-6968	219	1	for	for	ADP
ejpam-6968	219	2	α	α	PRON
ejpam-6968	219	3	<	<	X
ejpam-6968	219	4	0	0	PUNCT
ejpam-6968	220	1	[	[	X
ejpam-6968	220	2	fig	fig	NOUN
ejpam-6968	220	3	.	.	PUNCT
ejpam-6968	221	1	4(a	4(a	NUM
ejpam-6968	221	2	)	)	PUNCT
ejpam-6968	221	3	]	]	PUNCT
ejpam-6968	221	4	,	,	PUNCT
ejpam-6968	221	5	dky	dky	VERB
ejpam-6968	221	6	increases	increase	NOUN
ejpam-6968	221	7	from	from	ADP
ejpam-6968	221	8	nearly	nearly	ADV
ejpam-6968	221	9	1	1	NUM
ejpam-6968	221	10	(	(	PUNCT
ejpam-6968	221	11	indicating	indicate	VERB
ejpam-6968	221	12	limit	limit	NOUN
ejpam-6968	221	13	cycles	cycle	NOUN
ejpam-6968	221	14	)	)	PUNCT
ejpam-6968	221	15	to	to	ADP
ejpam-6968	221	16	noninteger	noninteger	VERB
ejpam-6968	221	17	values	value	NOUN
ejpam-6968	221	18	in	in	ADP
ejpam-6968	221	19	the	the	DET
ejpam-6968	221	20	chaotic	chaotic	ADJ
ejpam-6968	221	21	intervals	interval	NOUN
ejpam-6968	221	22	.	.	PUNCT
ejpam-6968	222	1	this	this	DET
ejpam-6968	222	2	increase	increase	NOUN
ejpam-6968	222	3	corresponds	correspond	VERB
ejpam-6968	222	4	to	to	ADP
ejpam-6968	222	5	the	the	DET
ejpam-6968	222	6	transition	transition	NOUN
ejpam-6968	222	7	into	into	ADP
ejpam-6968	222	8	chaotic	chaotic	ADJ
ejpam-6968	222	9	behavior	behavior	NOUN
ejpam-6968	222	10	,	,	PUNCT
ejpam-6968	222	11	where	where	SCONJ
ejpam-6968	222	12	the	the	DET
ejpam-6968	222	13	attractor	attractor	NOUN
ejpam-6968	222	14	becomes	become	VERB
ejpam-6968	222	15	more	more	ADV
ejpam-6968	222	16	complex	complex	ADJ
ejpam-6968	222	17	and	and	CCONJ
ejpam-6968	222	18	fractal	fractal	NOUN
ejpam-6968	222	19	.	.	PUNCT
ejpam-6968	223	1	these	these	DET
ejpam-6968	223	2	changes	change	NOUN
ejpam-6968	223	3	in	in	ADP
ejpam-6968	223	4	dky	dky	NOUN
ejpam-6968	223	5	mirror	mirror	NOUN
ejpam-6968	223	6	the	the	DET
ejpam-6968	223	7	bifurcation	bifurcation	NOUN
ejpam-6968	223	8	diagram	diagram	NOUN
ejpam-6968	223	9	in	in	ADP
ejpam-6968	223	10	fig	fig	NOUN
ejpam-6968	223	11	.	.	PUNCT
ejpam-6968	224	1	2(a	2(a	NUM
ejpam-6968	224	2	)	)	PUNCT
ejpam-6968	225	1	,	,	PUNCT
ejpam-6968	225	2	showing	show	VERB
ejpam-6968	225	3	the	the	DET
ejpam-6968	225	4	period	period	NOUN
ejpam-6968	225	5	-	-	PUNCT
ejpam-6968	225	6	doubling	double	VERB
ejpam-6968	225	7	cascade	cascade	NOUN
ejpam-6968	225	8	.	.	PUNCT
ejpam-6968	226	1	for	for	ADP
ejpam-6968	226	2	α	α	PROPN
ejpam-6968	226	3	>	>	X
ejpam-6968	226	4	0	0	PUNCT
ejpam-6968	227	1	[	[	X
ejpam-6968	227	2	fig	fig	NOUN
ejpam-6968	227	3	.	.	PUNCT
ejpam-6968	228	1	4(b	4(b	NUM
ejpam-6968	228	2	)	)	PUNCT
ejpam-6968	228	3	]	]	PUNCT
ejpam-6968	228	4	,	,	PUNCT
ejpam-6968	228	5	dky	dky	VERB
ejpam-6968	228	6	decreases	decrease	NOUN
ejpam-6968	228	7	as	as	ADP
ejpam-6968	228	8	α	α	PRON
ejpam-6968	228	9	increases	increase	NOUN
ejpam-6968	228	10	.	.	PUNCT
ejpam-6968	229	1	this	this	DET
ejpam-6968	229	2	decrease	decrease	NOUN
ejpam-6968	229	3	in	in	ADP
ejpam-6968	229	4	dimension	dimension	NOUN
ejpam-6968	229	5	reflects	reflect	VERB
ejpam-6968	229	6	the	the	DET
ejpam-6968	229	7	simplification	simplification	NOUN
ejpam-6968	229	8	of	of	ADP
ejpam-6968	229	9	dynamics	dynamic	NOUN
ejpam-6968	229	10	as	as	SCONJ
ejpam-6968	229	11	the	the	DET
ejpam-6968	229	12	system	system	NOUN
ejpam-6968	229	13	enters	enter	VERB
ejpam-6968	229	14	the	the	DET
ejpam-6968	229	15	hidden	hide	VERB
ejpam-6968	229	16	-	-	PUNCT
ejpam-6968	229	17	attractor	attractor	NOUN
ejpam-6968	229	18	regime	regime	NOUN
ejpam-6968	229	19	.	.	PUNCT
ejpam-6968	230	1	the	the	DET
ejpam-6968	230	2	drop	drop	NOUN
ejpam-6968	230	3	in	in	ADP
ejpam-6968	230	4	dky	dky	NOUN
ejpam-6968	230	5	corresponds	correspond	NOUN
ejpam-6968	230	6	to	to	ADP
ejpam-6968	230	7	the	the	DET
ejpam-6968	230	8	period	period	NOUN
ejpam-6968	230	9	-	-	PUNCT
ejpam-6968	230	10	halving	halving	NOUN
ejpam-6968	230	11	seen	see	VERB
ejpam-6968	230	12	in	in	ADP
ejpam-6968	230	13	fig	fig	NOUN
ejpam-6968	230	14	.	.	PUNCT
ejpam-6968	231	1	2(b	2(b	NUM
ejpam-6968	231	2	)	)	PUNCT
ejpam-6968	231	3	,	,	PUNCT
ejpam-6968	231	4	where	where	SCONJ
ejpam-6968	231	5	the	the	DET
ejpam-6968	231	6	attractor	attractor	NOUN
ejpam-6968	231	7	becomes	become	VERB
ejpam-6968	231	8	less	less	ADV
ejpam-6968	231	9	complex	complex	ADJ
ejpam-6968	231	10	and	and	CCONJ
ejpam-6968	231	11	more	more	ADV
ejpam-6968	231	12	ordered	order	VERB
ejpam-6968	231	13	.	.	PUNCT
ejpam-6968	232	1	h.	h.	PROPN
ejpam-6968	232	2	k.	k.	PROPN
ejpam-6968	232	3	fata	fata	PROPN
ejpam-6968	232	4	,	,	PUNCT
ejpam-6968	232	5	n.	n.	PROPN
ejpam-6968	232	6	y.	y.	PROPN
ejpam-6968	232	7	ashar	ashar	PROPN
ejpam-6968	232	8	/	/	SYM
ejpam-6968	232	9	eur	eur	PROPN
ejpam-6968	232	10	.	.	PUNCT
ejpam-6968	233	1	j.	j.	PROPN
ejpam-6968	233	2	pure	pure	PROPN
ejpam-6968	233	3	appl	appl	PROPN
ejpam-6968	233	4	.	.	PROPN
ejpam-6968	233	5	math	math	PROPN
ejpam-6968	233	6	,	,	PUNCT
ejpam-6968	233	7	18	18	NUM
ejpam-6968	233	8	(	(	PUNCT
ejpam-6968	233	9	4	4	NUM
ejpam-6968	233	10	)	)	PUNCT
ejpam-6968	233	11	(	(	PUNCT
ejpam-6968	233	12	2025	2025	NUM
ejpam-6968	233	13	)	)	PUNCT
ejpam-6968	233	14	,	,	PUNCT
ejpam-6968	233	15	6968	6968	NUM
ejpam-6968	233	16	11	11	NUM
ejpam-6968	233	17	of	of	ADP
ejpam-6968	233	18	15	15	NUM
ejpam-6968	233	19	(	(	PUNCT
ejpam-6968	233	20	a	a	NOUN
ejpam-6968	233	21	)	)	PUNCT
ejpam-6968	233	22	(	(	PUNCT
ejpam-6968	233	23	b	b	X
ejpam-6968	233	24	)	)	PUNCT
ejpam-6968	233	25	figure	figure	NOUN
ejpam-6968	233	26	3	3	NUM
ejpam-6968	233	27	:	:	PUNCT
ejpam-6968	233	28	maximal	maximal	ADJ
ejpam-6968	233	29	lyapunov	lyapunov	ADJ
ejpam-6968	233	30	exponent	exponent	NOUN
ejpam-6968	233	31	l1	l1	PROPN
ejpam-6968	233	32	versus	versus	ADP
ejpam-6968	233	33	α	α	PROPN
ejpam-6968	233	34	.	.	PUNCT
ejpam-6968	234	1	(	(	PUNCT
ejpam-6968	234	2	a	a	X
ejpam-6968	234	3	)	)	PUNCT
ejpam-6968	234	4	for	for	ADP
ejpam-6968	234	5	α	α	PRON
ejpam-6968	234	6	∈	∈	PROPN
ejpam-6968	235	1	[	[	X
ejpam-6968	235	2	−38	−38	NOUN
ejpam-6968	235	3	,	,	PUNCT
ejpam-6968	235	4	0	0	NUM
ejpam-6968	235	5	]	]	PUNCT
ejpam-6968	235	6	,	,	PUNCT
ejpam-6968	235	7	positive	positive	ADJ
ejpam-6968	235	8	values	value	NOUN
ejpam-6968	235	9	certify	certify	NOUN
ejpam-6968	235	10	chaos	chaos	NOUN
ejpam-6968	235	11	and	and	CCONJ
ejpam-6968	235	12	dips	dip	VERB
ejpam-6968	235	13	to	to	ADP
ejpam-6968	235	14	zero	zero	NUM
ejpam-6968	235	15	indicate	indicate	VERB
ejpam-6968	235	16	periodic	periodic	ADJ
ejpam-6968	235	17	windows	window	NOUN
ejpam-6968	235	18	.	.	PUNCT
ejpam-6968	236	1	(	(	PUNCT
ejpam-6968	236	2	b	b	X
ejpam-6968	236	3	)	)	PUNCT
ejpam-6968	236	4	for	for	ADP
ejpam-6968	236	5	α	α	PRON
ejpam-6968	236	6	∈	∈	PROPN
ejpam-6968	236	7	(	(	PUNCT
ejpam-6968	236	8	0	0	NUM
ejpam-6968	236	9	,	,	PUNCT
ejpam-6968	236	10	0.8	0.8	NUM
ejpam-6968	236	11	)	)	PUNCT
ejpam-6968	236	12	,	,	PUNCT
ejpam-6968	236	13	a	a	DET
ejpam-6968	236	14	gradual	gradual	ADJ
ejpam-6968	236	15	decrease	decrease	NOUN
ejpam-6968	236	16	in	in	ADP
ejpam-6968	236	17	l1	l1	PROPN
ejpam-6968	236	18	accompanies	accompany	VERB
ejpam-6968	236	19	period	period	NOUN
ejpam-6968	236	20	-	-	PUNCT
ejpam-6968	236	21	halving	halve	VERB
ejpam-6968	236	22	.	.	PUNCT
ejpam-6968	237	1	representative	representative	ADJ
ejpam-6968	237	2	phase	phase	NOUN
ejpam-6968	237	3	portraits	portrait	NOUN
ejpam-6968	237	4	finally	finally	ADV
ejpam-6968	237	5	,	,	PUNCT
ejpam-6968	237	6	fig	fig	NOUN
ejpam-6968	237	7	.	.	PUNCT
ejpam-6968	238	1	5	5	NUM
ejpam-6968	238	2	illustrates	illustrate	VERB
ejpam-6968	238	3	typical	typical	ADJ
ejpam-6968	238	4	attractors	attractor	NOUN
ejpam-6968	238	5	across	across	ADP
ejpam-6968	238	6	α	α	PROPN
ejpam-6968	238	7	.	.	PUNCT
ejpam-6968	239	1	panel	panel	NOUN
ejpam-6968	239	2	(	(	PUNCT
ejpam-6968	239	3	a	a	X
ejpam-6968	239	4	)	)	PUNCT
ejpam-6968	239	5	shows	show	VERB
ejpam-6968	239	6	a	a	DET
ejpam-6968	239	7	periodic	periodic	ADJ
ejpam-6968	239	8	limit	limit	NOUN
ejpam-6968	239	9	cycle	cycle	NOUN
ejpam-6968	239	10	at	at	ADP
ejpam-6968	239	11	α	α	NOUN
ejpam-6968	239	12	=	=	PUNCT
ejpam-6968	239	13	−50	−50	NOUN
ejpam-6968	239	14	;	;	PUNCT
ejpam-6968	239	15	(	(	PUNCT
ejpam-6968	239	16	b	b	X
ejpam-6968	239	17	)	)	PUNCT
ejpam-6968	239	18	captures	capture	VERB
ejpam-6968	239	19	the	the	DET
ejpam-6968	239	20	onset	onset	NOUN
ejpam-6968	239	21	of	of	ADP
ejpam-6968	239	22	period	period	NOUN
ejpam-6968	239	23	doubling	double	VERB
ejpam-6968	239	24	near	near	ADP
ejpam-6968	239	25	α	α	PROPN
ejpam-6968	239	26	=	=	SYM
ejpam-6968	239	27	−31	−31	PROPN
ejpam-6968	239	28	;	;	PUNCT
ejpam-6968	239	29	(	(	PUNCT
ejpam-6968	239	30	c)–(d	c)–(d	NOUN
ejpam-6968	239	31	)	)	PUNCT
ejpam-6968	239	32	display	display	NOUN
ejpam-6968	239	33	developed	develop	VERB
ejpam-6968	239	34	and	and	CCONJ
ejpam-6968	239	35	fully	fully	ADV
ejpam-6968	239	36	developed	develop	VERB
ejpam-6968	239	37	chaotic	chaotic	ADJ
ejpam-6968	239	38	motion	motion	NOUN
ejpam-6968	239	39	(	(	PUNCT
ejpam-6968	239	40	α	α	NOUN
ejpam-6968	239	41	=	=	SYM
ejpam-6968	239	42	−17	−17	NOUN
ejpam-6968	239	43	and	and	CCONJ
ejpam-6968	239	44	−9	−9	NOUN
ejpam-6968	239	45	)	)	PUNCT
ejpam-6968	239	46	;	;	PUNCT
ejpam-6968	239	47	(	(	PUNCT
ejpam-6968	239	48	e	e	X
ejpam-6968	239	49	)	)	PUNCT
ejpam-6968	239	50	depicts	depict	VERB
ejpam-6968	239	51	the	the	DET
ejpam-6968	239	52	transition	transition	NOUN
ejpam-6968	239	53	region	region	NOUN
ejpam-6968	239	54	as	as	ADP
ejpam-6968	239	55	equilibria	equilibrium	NOUN
ejpam-6968	239	56	approach	approach	NOUN
ejpam-6968	239	57	disappearance	disappearance	NOUN
ejpam-6968	239	58	(	(	PUNCT
ejpam-6968	239	59	α	α	NOUN
ejpam-6968	239	60	=	=	PUNCT
ejpam-6968	239	61	−1	−1	NOUN
ejpam-6968	239	62	)	)	PUNCT
ejpam-6968	239	63	;	;	PUNCT
ejpam-6968	239	64	and	and	CCONJ
ejpam-6968	239	65	(	(	PUNCT
ejpam-6968	239	66	f	f	X
ejpam-6968	239	67	)	)	PUNCT
ejpam-6968	239	68	shows	show	VERB
ejpam-6968	239	69	a	a	DET
ejpam-6968	239	70	hidden	hide	VERB
ejpam-6968	239	71	chaotic	chaotic	ADJ
ejpam-6968	239	72	attractor	attractor	NOUN
ejpam-6968	239	73	at	at	ADP
ejpam-6968	239	74	α	α	NOUN
ejpam-6968	239	75	=	=	NOUN
ejpam-6968	239	76	0.1	0.1	NUM
ejpam-6968	239	77	,	,	PUNCT
ejpam-6968	239	78	where	where	SCONJ
ejpam-6968	239	79	equilibria	equilibrium	NOUN
ejpam-6968	239	80	are	be	AUX
ejpam-6968	239	81	absent	absent	ADJ
ejpam-6968	239	82	.	.	PUNCT
ejpam-6968	240	1	axes	axis	NOUN
ejpam-6968	240	2	are	be	AUX
ejpam-6968	240	3	(	(	PUNCT
ejpam-6968	240	4	x	x	NOUN
ejpam-6968	240	5	,	,	PUNCT
ejpam-6968	240	6	y	y	PROPN
ejpam-6968	240	7	,	,	PUNCT
ejpam-6968	240	8	z	z	NOUN
ejpam-6968	240	9	)	)	PUNCT
ejpam-6968	240	10	;	;	PUNCT
ejpam-6968	240	11	fonts	font	NOUN
ejpam-6968	240	12	and	and	CCONJ
ejpam-6968	240	13	line	line	NOUN
ejpam-6968	240	14	widths	width	NOUN
ejpam-6968	240	15	are	be	AUX
ejpam-6968	240	16	standardized	standardize	VERB
ejpam-6968	240	17	across	across	ADP
ejpam-6968	240	18	panels	panel	NOUN
ejpam-6968	240	19	,	,	PUNCT
ejpam-6968	240	20	and	and	CCONJ
ejpam-6968	240	21	red	red	ADJ
ejpam-6968	240	22	markers	marker	NOUN
ejpam-6968	240	23	indicate	indicate	VERB
ejpam-6968	240	24	equilibria	equilibrium	NOUN
ejpam-6968	240	25	when	when	SCONJ
ejpam-6968	240	26	present	present	ADJ
ejpam-6968	240	27	.	.	PUNCT
ejpam-6968	241	1	h.	h.	PROPN
ejpam-6968	241	2	k.	k.	PROPN
ejpam-6968	241	3	fata	fata	PROPN
ejpam-6968	241	4	,	,	PUNCT
ejpam-6968	241	5	n.	n.	PROPN
ejpam-6968	241	6	y.	y.	PROPN
ejpam-6968	241	7	ashar	ashar	PROPN
ejpam-6968	241	8	/	/	SYM
ejpam-6968	241	9	eur	eur	PROPN
ejpam-6968	241	10	.	.	PUNCT
ejpam-6968	242	1	j.	j.	PROPN
ejpam-6968	242	2	pure	pure	PROPN
ejpam-6968	242	3	appl	appl	PROPN
ejpam-6968	242	4	.	.	PROPN
ejpam-6968	242	5	math	math	PROPN
ejpam-6968	242	6	,	,	PUNCT
ejpam-6968	242	7	18	18	NUM
ejpam-6968	242	8	(	(	PUNCT
ejpam-6968	242	9	4	4	NUM
ejpam-6968	242	10	)	)	PUNCT
ejpam-6968	242	11	(	(	PUNCT
ejpam-6968	242	12	2025	2025	NUM
ejpam-6968	242	13	)	)	PUNCT
ejpam-6968	242	14	,	,	PUNCT
ejpam-6968	242	15	6968	6968	NUM
ejpam-6968	242	16	12	12	NUM
ejpam-6968	242	17	of	of	ADP
ejpam-6968	242	18	15	15	NUM
ejpam-6968	242	19	(	(	PUNCT
ejpam-6968	242	20	a	a	NOUN
ejpam-6968	242	21	)	)	PUNCT
ejpam-6968	242	22	(	(	PUNCT
ejpam-6968	242	23	b	b	X
ejpam-6968	242	24	)	)	PUNCT
ejpam-6968	242	25	figure	figure	NOUN
ejpam-6968	242	26	4	4	NUM
ejpam-6968	242	27	:	:	PUNCT
ejpam-6968	242	28	kaplan	kaplan	PROPN
ejpam-6968	242	29	–	–	PUNCT
ejpam-6968	242	30	yorke	yorke	PROPN
ejpam-6968	242	31	dimension	dimension	PROPN
ejpam-6968	242	32	dky	dky	PROPN
ejpam-6968	242	33	versus	versus	ADP
ejpam-6968	242	34	α	α	PROPN
ejpam-6968	242	35	.	.	PUNCT
ejpam-6968	243	1	(	(	PUNCT
ejpam-6968	243	2	a	a	X
ejpam-6968	243	3	)	)	PUNCT
ejpam-6968	243	4	increase	increase	NOUN
ejpam-6968	243	5	to	to	ADP
ejpam-6968	243	6	non	non	ADJ
ejpam-6968	243	7	-	-	ADJ
ejpam-6968	243	8	integer	integer	ADJ
ejpam-6968	243	9	values	value	NOUN
ejpam-6968	243	10	signals	signal	VERB
ejpam-6968	243	11	chaotic	chaotic	ADJ
ejpam-6968	243	12	attractors	attractor	NOUN
ejpam-6968	243	13	for	for	ADP
ejpam-6968	243	14	α	α	PRON
ejpam-6968	243	15	∈	∈	PROPN
ejpam-6968	244	1	[	[	X
ejpam-6968	244	2	−38	−38	NOUN
ejpam-6968	244	3	,	,	PUNCT
ejpam-6968	244	4	0	0	NUM
ejpam-6968	244	5	]	]	PUNCT
ejpam-6968	244	6	.	.	PUNCT
ejpam-6968	245	1	(	(	PUNCT
ejpam-6968	245	2	b	b	X
ejpam-6968	245	3	)	)	PUNCT
ejpam-6968	245	4	decrease	decrease	NOUN
ejpam-6968	245	5	with	with	ADP
ejpam-6968	245	6	α	α	NOUN
ejpam-6968	245	7	for	for	ADP
ejpam-6968	245	8	α	α	PRON
ejpam-6968	245	9	∈	∈	PROPN
ejpam-6968	245	10	(	(	PUNCT
ejpam-6968	245	11	0	0	NUM
ejpam-6968	245	12	,	,	PUNCT
ejpam-6968	245	13	0.8	0.8	NUM
ejpam-6968	245	14	)	)	PUNCT
ejpam-6968	245	15	is	be	AUX
ejpam-6968	245	16	consistent	consistent	ADJ
ejpam-6968	245	17	with	with	ADP
ejpam-6968	245	18	period	period	NOUN
ejpam-6968	245	19	-	-	PUNCT
ejpam-6968	245	20	halving	halve	VERB
ejpam-6968	245	21	and	and	CCONJ
ejpam-6968	245	22	reduced	reduced	ADJ
ejpam-6968	245	23	complexity	complexity	NOUN
ejpam-6968	245	24	.	.	PUNCT
ejpam-6968	246	1	(	(	PUNCT
ejpam-6968	246	2	a	a	X
ejpam-6968	246	3	)	)	PUNCT
ejpam-6968	246	4	(	(	PUNCT
ejpam-6968	246	5	b	b	X
ejpam-6968	246	6	)	)	PUNCT
ejpam-6968	246	7	(	(	PUNCT
ejpam-6968	246	8	c	c	X
ejpam-6968	246	9	)	)	PUNCT
ejpam-6968	246	10	(	(	PUNCT
ejpam-6968	246	11	d	d	X
ejpam-6968	246	12	)	)	PUNCT
ejpam-6968	246	13	(	(	PUNCT
ejpam-6968	246	14	e	e	NOUN
ejpam-6968	246	15	)	)	PUNCT
ejpam-6968	246	16	(	(	PUNCT
ejpam-6968	246	17	f	f	X
ejpam-6968	246	18	)	)	PUNCT
ejpam-6968	246	19	figure	figure	NOUN
ejpam-6968	246	20	5	5	NUM
ejpam-6968	246	21	:	:	PUNCT
ejpam-6968	246	22	representative	representative	ADJ
ejpam-6968	246	23	phase	phase	NOUN
ejpam-6968	246	24	portraits	portrait	NOUN
ejpam-6968	246	25	across	across	ADP
ejpam-6968	246	26	α	α	NOUN
ejpam-6968	246	27	:	:	PUNCT
ejpam-6968	246	28	(	(	PUNCT
ejpam-6968	246	29	a	a	X
ejpam-6968	246	30	)	)	PUNCT
ejpam-6968	246	31	periodic	periodic	ADJ
ejpam-6968	246	32	limit	limit	NOUN
ejpam-6968	246	33	cycle	cycle	NOUN
ejpam-6968	246	34	at	at	ADP
ejpam-6968	246	35	α	α	NOUN
ejpam-6968	246	36	=	=	PUNCT
ejpam-6968	246	37	−50	−50	NOUN
ejpam-6968	246	38	;	;	PUNCT
ejpam-6968	246	39	(	(	PUNCT
ejpam-6968	246	40	b	b	X
ejpam-6968	246	41	)	)	PUNCT
ejpam-6968	246	42	onset	onset	NOUN
ejpam-6968	246	43	of	of	ADP
ejpam-6968	246	44	period	period	NOUN
ejpam-6968	246	45	doubling	double	VERB
ejpam-6968	246	46	at	at	ADP
ejpam-6968	246	47	α	α	NOUN
ejpam-6968	246	48	=	=	SYM
ejpam-6968	246	49	−31	−31	PROPN
ejpam-6968	246	50	;	;	PUNCT
ejpam-6968	246	51	(	(	PUNCT
ejpam-6968	246	52	c	c	X
ejpam-6968	246	53	)	)	PUNCT
ejpam-6968	246	54	developed	develop	VERB
ejpam-6968	246	55	chaotic	chaotic	ADJ
ejpam-6968	246	56	motion	motion	NOUN
ejpam-6968	246	57	at	at	ADP
ejpam-6968	246	58	α	α	NOUN
ejpam-6968	246	59	=	=	SYM
ejpam-6968	246	60	−17	−17	NOUN
ejpam-6968	246	61	;	;	PUNCT
ejpam-6968	246	62	(	(	PUNCT
ejpam-6968	246	63	d	d	X
ejpam-6968	246	64	)	)	PUNCT
ejpam-6968	246	65	fully	fully	ADV
ejpam-6968	246	66	developed	develop	VERB
ejpam-6968	246	67	chaos	chaos	NOUN
ejpam-6968	246	68	at	at	ADP
ejpam-6968	246	69	α	α	PROPN
ejpam-6968	246	70	=	=	SYM
ejpam-6968	246	71	−9	−9	NOUN
ejpam-6968	246	72	;	;	PUNCT
ejpam-6968	246	73	(	(	PUNCT
ejpam-6968	246	74	e	e	NOUN
ejpam-6968	246	75	)	)	PUNCT
ejpam-6968	246	76	transition	transition	NOUN
ejpam-6968	246	77	region	region	NOUN
ejpam-6968	246	78	as	as	ADP
ejpam-6968	246	79	equilibria	equilibrium	NOUN
ejpam-6968	246	80	approach	approach	VERB
ejpam-6968	246	81	disappearance	disappearance	NOUN
ejpam-6968	246	82	at	at	ADP
ejpam-6968	246	83	α	α	PROPN
ejpam-6968	246	84	=	=	SYM
ejpam-6968	246	85	−1	−1	NOUN
ejpam-6968	246	86	;	;	PUNCT
ejpam-6968	246	87	(	(	PUNCT
ejpam-6968	246	88	f	f	X
ejpam-6968	246	89	)	)	PUNCT
ejpam-6968	246	90	hidden	hide	VERB
ejpam-6968	246	91	chaotic	chaotic	ADJ
ejpam-6968	246	92	attractor	attractor	NOUN
ejpam-6968	246	93	for	for	ADP
ejpam-6968	246	94	α	α	NOUN
ejpam-6968	246	95	=	=	SYM
ejpam-6968	246	96	0.1	0.1	NUM
ejpam-6968	246	97	where	where	SCONJ
ejpam-6968	246	98	equilibria	equilibrium	NOUN
ejpam-6968	246	99	are	be	AUX
ejpam-6968	246	100	absent	absent	ADJ
ejpam-6968	246	101	.	.	PUNCT
ejpam-6968	247	1	red	red	ADJ
ejpam-6968	247	2	markers	marker	NOUN
ejpam-6968	247	3	denote	denote	VERB
ejpam-6968	247	4	equilibria	equilibrium	NOUN
ejpam-6968	247	5	when	when	SCONJ
ejpam-6968	247	6	present	present	ADJ
ejpam-6968	247	7	;	;	PUNCT
ejpam-6968	247	8	axes	axis	NOUN
ejpam-6968	247	9	are	be	AUX
ejpam-6968	247	10	(	(	PUNCT
ejpam-6968	247	11	x	x	NOUN
ejpam-6968	247	12	,	,	PUNCT
ejpam-6968	247	13	y	y	PROPN
ejpam-6968	247	14	,	,	PUNCT
ejpam-6968	247	15	z	z	NOUN
ejpam-6968	247	16	)	)	PUNCT
ejpam-6968	247	17	.	.	PUNCT
ejpam-6968	248	1	h.	h.	PROPN
ejpam-6968	248	2	k.	k.	PROPN
ejpam-6968	248	3	fata	fata	PROPN
ejpam-6968	248	4	,	,	PUNCT
ejpam-6968	248	5	n.	n.	PROPN
ejpam-6968	248	6	y.	y.	PROPN
ejpam-6968	248	7	ashar	ashar	PROPN
ejpam-6968	248	8	/	/	SYM
ejpam-6968	248	9	eur	eur	PROPN
ejpam-6968	248	10	.	.	PUNCT
ejpam-6968	249	1	j.	j.	PROPN
ejpam-6968	249	2	pure	pure	PROPN
ejpam-6968	249	3	appl	appl	PROPN
ejpam-6968	249	4	.	.	PROPN
ejpam-6968	249	5	math	math	PROPN
ejpam-6968	249	6	,	,	PUNCT
ejpam-6968	249	7	18	18	NUM
ejpam-6968	249	8	(	(	PUNCT
ejpam-6968	249	9	4	4	NUM
ejpam-6968	249	10	)	)	PUNCT
ejpam-6968	249	11	(	(	PUNCT
ejpam-6968	249	12	2025	2025	NUM
ejpam-6968	249	13	)	)	PUNCT
ejpam-6968	249	14	,	,	PUNCT
ejpam-6968	249	15	6968	6968	NUM
ejpam-6968	249	16	13	13	NUM
ejpam-6968	249	17	of	of	ADP
ejpam-6968	249	18	15	15	NUM
ejpam-6968	249	19	5	5	NUM
ejpam-6968	249	20	.	.	PUNCT
ejpam-6968	250	1	conclusion	conclusion	NOUN
ejpam-6968	250	2	this	this	DET
ejpam-6968	250	3	work	work	NOUN
ejpam-6968	250	4	presented	present	VERB
ejpam-6968	250	5	a	a	DET
ejpam-6968	250	6	hybrid	hybrid	ADJ
ejpam-6968	250	7	analytical	analytical	ADJ
ejpam-6968	250	8	numerical	numerical	ADJ
ejpam-6968	250	9	study	study	NOUN
ejpam-6968	250	10	of	of	ADP
ejpam-6968	250	11	a	a	DET
ejpam-6968	250	12	quadratic	quadratic	ADJ
ejpam-6968	250	13	three	three	NUM
ejpam-6968	250	14	dimensional	dimensional	ADJ
ejpam-6968	250	15	system	system	NOUN
ejpam-6968	250	16	that	that	PRON
ejpam-6968	250	17	displays	display	VERB
ejpam-6968	250	18	two	two	NUM
ejpam-6968	250	19	qualitatively	qualitatively	ADV
ejpam-6968	250	20	distinct	distinct	ADJ
ejpam-6968	250	21	dynamical	dynamical	ADJ
ejpam-6968	250	22	regimes	regime	NOUN
ejpam-6968	250	23	organized	organize	VERB
ejpam-6968	250	24	by	by	ADP
ejpam-6968	250	25	the	the	DET
ejpam-6968	250	26	control	control	NOUN
ejpam-6968	250	27	parameter	parameter	PROPN
ejpam-6968	250	28	α	α	PROPN
ejpam-6968	250	29	.	.	PUNCT
ejpam-6968	251	1	analytically	analytically	ADV
ejpam-6968	251	2	,	,	PUNCT
ejpam-6968	251	3	we	we	PRON
ejpam-6968	251	4	proved	prove	VERB
ejpam-6968	251	5	that	that	SCONJ
ejpam-6968	251	6	for	for	ADP
ejpam-6968	251	7	α	α	PRON
ejpam-6968	251	8	<	<	X
ejpam-6968	251	9	0	0	NUM
ejpam-6968	252	1	the	the	DET
ejpam-6968	252	2	system	system	NOUN
ejpam-6968	252	3	possesses	possess	VERB
ejpam-6968	252	4	two	two	NUM
ejpam-6968	252	5	symmetric	symmetric	ADJ
ejpam-6968	252	6	equilibria	equilibrium	NOUN
ejpam-6968	252	7	which	which	PRON
ejpam-6968	252	8	coalesce	coalesce	VERB
ejpam-6968	252	9	at	at	ADP
ejpam-6968	252	10	the	the	DET
ejpam-6968	252	11	origin	origin	NOUN
ejpam-6968	252	12	via	via	ADP
ejpam-6968	252	13	a	a	DET
ejpam-6968	252	14	saddle	saddle	NOUN
ejpam-6968	252	15	–	–	PUNCT
ejpam-6968	252	16	node	node	NOUN
ejpam-6968	252	17	bifurcation	bifurcation	NOUN
ejpam-6968	252	18	at	at	ADP
ejpam-6968	252	19	α	α	NOUN
ejpam-6968	252	20	=	=	SYM
ejpam-6968	252	21	0	0	NUM
ejpam-6968	252	22	,	,	PUNCT
ejpam-6968	252	23	and	and	CCONJ
ejpam-6968	252	24	that	that	SCONJ
ejpam-6968	252	25	the	the	DET
ejpam-6968	252	26	negative	negative	ADJ
ejpam-6968	252	27	equilibrium	equilibrium	NOUN
ejpam-6968	252	28	undergoes	undergo	VERB
ejpam-6968	252	29	a	a	DET
ejpam-6968	252	30	supercritical	supercritical	ADJ
ejpam-6968	252	31	hopf	hopf	ADJ
ejpam-6968	252	32	bifurcation	bifurcation	NOUN
ejpam-6968	252	33	at	at	ADP
ejpam-6968	252	34	α	α	NOUN
ejpam-6968	252	35	=	=	SYM
ejpam-6968	252	36	−196	−196	NOUN
ejpam-6968	252	37	(	(	PUNCT
ejpam-6968	252	38	first	first	ADJ
ejpam-6968	252	39	lyapunov	lyapunov	ADJ
ejpam-6968	252	40	coefficient	coefficient	NOUN
ejpam-6968	252	41	ℓ1	ℓ1	VERB
ejpam-6968	252	42	<	<	X
ejpam-6968	252	43	0	0	NUM
ejpam-6968	252	44	)	)	PUNCT
ejpam-6968	252	45	,	,	PUNCT
ejpam-6968	252	46	giving	give	VERB
ejpam-6968	252	47	rise	rise	NOUN
ejpam-6968	252	48	to	to	ADP
ejpam-6968	252	49	a	a	DET
ejpam-6968	252	50	stable	stable	ADJ
ejpam-6968	252	51	limit	limit	NOUN
ejpam-6968	252	52	cycle	cycle	NOUN
ejpam-6968	252	53	.	.	PUNCT
ejpam-6968	253	1	global	global	ADJ
ejpam-6968	253	2	continuation	continuation	NOUN
ejpam-6968	253	3	and	and	CCONJ
ejpam-6968	253	4	time	time	NOUN
ejpam-6968	253	5	–	–	PUNCT
ejpam-6968	253	6	series	series	NOUN
ejpam-6968	253	7	diagnostics	diagnostic	NOUN
ejpam-6968	253	8	then	then	ADV
ejpam-6968	253	9	revealed	reveal	VERB
ejpam-6968	253	10	how	how	SCONJ
ejpam-6968	253	11	these	these	DET
ejpam-6968	253	12	local	local	ADJ
ejpam-6968	253	13	instabilities	instability	NOUN
ejpam-6968	253	14	scaffold	scaffold	VERB
ejpam-6968	253	15	the	the	DET
ejpam-6968	253	16	transition	transition	NOUN
ejpam-6968	253	17	to	to	ADP
ejpam-6968	253	18	complex	complex	ADJ
ejpam-6968	253	19	behavior	behavior	NOUN
ejpam-6968	253	20	:	:	PUNCT
ejpam-6968	253	21	for	for	ADP
ejpam-6968	253	22	α	α	PRON
ejpam-6968	253	23	∈	∈	PROPN
ejpam-6968	254	1	[	[	X
ejpam-6968	254	2	−21	−21	ADJ
ejpam-6968	254	3	,	,	PUNCT
ejpam-6968	254	4	0	0	NUM
ejpam-6968	254	5	]	]	PUNCT
ejpam-6968	254	6	the	the	DET
ejpam-6968	254	7	system	system	NOUN
ejpam-6968	254	8	follows	follow	VERB
ejpam-6968	254	9	a	a	DET
ejpam-6968	254	10	period	period	NOUN
ejpam-6968	254	11	–	–	PUNCT
ejpam-6968	254	12	doubling	double	VERB
ejpam-6968	254	13	cascade	cascade	NOUN
ejpam-6968	254	14	to	to	AUX
ejpam-6968	254	15	chaos	chaos	VERB
ejpam-6968	254	16	,	,	PUNCT
ejpam-6968	254	17	as	as	SCONJ
ejpam-6968	254	18	confirmed	confirm	VERB
ejpam-6968	254	19	by	by	ADP
ejpam-6968	254	20	a	a	DET
ejpam-6968	254	21	positive	positive	ADJ
ejpam-6968	254	22	maximal	maximal	ADJ
ejpam-6968	254	23	lyapunov	lyapunov	NOUN
ejpam-6968	254	24	exponent	exponent	NOUN
ejpam-6968	254	25	and	and	CCONJ
ejpam-6968	254	26	a	a	DET
ejpam-6968	254	27	non	non	ADJ
ejpam-6968	254	28	-	-	ADJ
ejpam-6968	254	29	integer	integer	ADJ
ejpam-6968	254	30	kaplan	kaplan	PROPN
ejpam-6968	254	31	–	–	PUNCT
ejpam-6968	254	32	yorke	yorke	PROPN
ejpam-6968	254	33	dimension	dimension	NOUN
ejpam-6968	254	34	.	.	PUNCT
ejpam-6968	255	1	in	in	ADP
ejpam-6968	255	2	sharp	sharp	ADJ
ejpam-6968	255	3	contrast	contrast	NOUN
ejpam-6968	255	4	,	,	PUNCT
ejpam-6968	255	5	for	for	ADP
ejpam-6968	255	6	α	α	PROPN
ejpam-6968	255	7	>	>	X
ejpam-6968	255	8	0	0	PUNCT
ejpam-6968	256	1	no	no	DET
ejpam-6968	256	2	equilibria	equilibrium	NOUN
ejpam-6968	256	3	exist	exist	VERB
ejpam-6968	256	4	,	,	PUNCT
ejpam-6968	256	5	yet	yet	CCONJ
ejpam-6968	256	6	the	the	DET
ejpam-6968	256	7	flow	flow	NOUN
ejpam-6968	256	8	sustains	sustain	VERB
ejpam-6968	256	9	long	long	ADJ
ejpam-6968	256	10	-	-	PUNCT
ejpam-6968	256	11	term	term	NOUN
ejpam-6968	256	12	oscillations	oscillation	NOUN
ejpam-6968	256	13	through	through	ADP
ejpam-6968	256	14	hidden	hidden	ADJ
ejpam-6968	256	15	attractors	attractor	NOUN
ejpam-6968	256	16	;	;	PUNCT
ejpam-6968	256	17	their	their	PRON
ejpam-6968	256	18	presence	presence	NOUN
ejpam-6968	256	19	is	be	AUX
ejpam-6968	256	20	supported	support	VERB
ejpam-6968	256	21	by	by	ADP
ejpam-6968	256	22	sensitivity	sensitivity	NOUN
ejpam-6968	256	23	and	and	CCONJ
ejpam-6968	256	24	basin	basin	NOUN
ejpam-6968	256	25	-	-	PUNCT
ejpam-6968	256	26	selection	selection	NOUN
ejpam-6968	256	27	experiments	experiment	NOUN
ejpam-6968	256	28	showing	show	VERB
ejpam-6968	256	29	convergence	convergence	NOUN
ejpam-6968	256	30	to	to	PART
ejpam-6968	256	31	bounded	bound	VERB
ejpam-6968	256	32	chaotic	chaotic	ADJ
ejpam-6968	256	33	motions	motion	NOUN
ejpam-6968	256	34	from	from	ADP
ejpam-6968	256	35	sets	set	NOUN
ejpam-6968	256	36	of	of	ADP
ejpam-6968	256	37	initial	initial	ADJ
ejpam-6968	256	38	conditions	condition	NOUN
ejpam-6968	256	39	not	not	PART
ejpam-6968	256	40	connected	connect	VERB
ejpam-6968	256	41	to	to	ADP
ejpam-6968	256	42	any	any	DET
ejpam-6968	256	43	equilibrium	equilibrium	NOUN
ejpam-6968	256	44	.	.	PUNCT
ejpam-6968	257	1	moreover	moreover	ADV
ejpam-6968	257	2	,	,	PUNCT
ejpam-6968	257	3	as	as	SCONJ
ejpam-6968	257	4	α	α	PROPN
ejpam-6968	257	5	increases	increase	VERB
ejpam-6968	257	6	in	in	ADP
ejpam-6968	257	7	(	(	PUNCT
ejpam-6968	257	8	0	0	NUM
ejpam-6968	257	9	,	,	PUNCT
ejpam-6968	257	10	0.8	0.8	NUM
ejpam-6968	257	11	)	)	PUNCT
ejpam-6968	257	12	we	we	PRON
ejpam-6968	257	13	observe	observe	VERB
ejpam-6968	257	14	a	a	DET
ejpam-6968	257	15	reverse	reverse	ADJ
ejpam-6968	257	16	trend	trend	NOUN
ejpam-6968	257	17	—	—	PUNCT
ejpam-6968	257	18	a	a	DET
ejpam-6968	257	19	period	period	NOUN
ejpam-6968	257	20	–	–	PUNCT
ejpam-6968	257	21	halving	halve	VERB
ejpam-6968	257	22	sequence	sequence	NOUN
ejpam-6968	257	23	—	—	PUNCT
ejpam-6968	257	24	indicating	indicate	VERB
ejpam-6968	257	25	a	a	DET
ejpam-6968	257	26	distinct	distinct	ADJ
ejpam-6968	257	27	global	global	ADJ
ejpam-6968	257	28	organization	organization	NOUN
ejpam-6968	257	29	of	of	ADP
ejpam-6968	257	30	invariant	invariant	ADJ
ejpam-6968	257	31	sets	set	NOUN
ejpam-6968	257	32	in	in	ADP
ejpam-6968	257	33	the	the	DET
ejpam-6968	257	34	equilibrium	equilibrium	NOUN
ejpam-6968	257	35	-	-	PUNCT
ejpam-6968	257	36	free	free	ADJ
ejpam-6968	257	37	regime	regime	NOUN
ejpam-6968	257	38	.	.	PUNCT
ejpam-6968	258	1	conceptually	conceptually	ADV
ejpam-6968	258	2	,	,	PUNCT
ejpam-6968	258	3	the	the	DET
ejpam-6968	258	4	paper	paper	NOUN
ejpam-6968	258	5	unifies	unify	VERB
ejpam-6968	258	6	self	self	NOUN
ejpam-6968	258	7	-	-	PUNCT
ejpam-6968	258	8	excited	excite	VERB
ejpam-6968	258	9	dynamics	dynamic	NOUN
ejpam-6968	258	10	(	(	PUNCT
ejpam-6968	258	11	when	when	SCONJ
ejpam-6968	258	12	equilibria	equilibrium	NOUN
ejpam-6968	258	13	exist	exist	VERB
ejpam-6968	258	14	and	and	CCONJ
ejpam-6968	258	15	lose	lose	VERB
ejpam-6968	258	16	stability	stability	NOUN
ejpam-6968	258	17	)	)	PUNCT
ejpam-6968	258	18	and	and	CCONJ
ejpam-6968	258	19	hidden	hidden	ADJ
ejpam-6968	258	20	dynamics	dynamic	NOUN
ejpam-6968	258	21	(	(	PUNCT
ejpam-6968	258	22	when	when	SCONJ
ejpam-6968	258	23	no	no	DET
ejpam-6968	258	24	equilibria	equilibrium	NOUN
ejpam-6968	258	25	are	be	AUX
ejpam-6968	258	26	present	present	ADJ
ejpam-6968	258	27	and	and	CCONJ
ejpam-6968	258	28	basins	basin	NOUN
ejpam-6968	258	29	are	be	AUX
ejpam-6968	258	30	disconnected	disconnect	VERB
ejpam-6968	258	31	from	from	ADP
ejpam-6968	258	32	equilibria	equilibrium	NOUN
ejpam-6968	258	33	)	)	PUNCT
ejpam-6968	258	34	within	within	ADP
ejpam-6968	258	35	a	a	DET
ejpam-6968	258	36	single	single	ADJ
ejpam-6968	258	37	minimalist	minimalist	ADJ
ejpam-6968	258	38	model	model	NOUN
ejpam-6968	258	39	,	,	PUNCT
ejpam-6968	258	40	and	and	CCONJ
ejpam-6968	258	41	methodologically	methodologically	ADV
ejpam-6968	258	42	couples	couple	NOUN
ejpam-6968	258	43	normal	normal	ADJ
ejpam-6968	258	44	-	-	PUNCT
ejpam-6968	258	45	form	form	NOUN
ejpam-6968	258	46	analysis	analysis	NOUN
ejpam-6968	258	47	with	with	ADP
ejpam-6968	258	48	numerical	numerical	ADJ
ejpam-6968	258	49	continuation	continuation	NOUN
ejpam-6968	258	50	and	and	CCONJ
ejpam-6968	258	51	lyapunov	lyapunov	PROPN
ejpam-6968	258	52	-	-	PUNCT
ejpam-6968	258	53	spectrum	spectrum	NOUN
ejpam-6968	258	54	-	-	PUNCT
ejpam-6968	258	55	based	base	VERB
ejpam-6968	258	56	validation	validation	NOUN
ejpam-6968	258	57	.	.	PUNCT
ejpam-6968	259	1	this	this	DET
ejpam-6968	259	2	dual	dual	ADJ
ejpam-6968	259	3	perspective	perspective	NOUN
ejpam-6968	259	4	clarifies	clarify	VERB
ejpam-6968	259	5	the	the	DET
ejpam-6968	259	6	route	route	NOUN
ejpam-6968	259	7	-	-	PUNCT
ejpam-6968	259	8	to	to	ADP
ejpam-6968	259	9	-	-	PUNCT
ejpam-6968	259	10	chaos	chaos	NOUN
ejpam-6968	259	11	mechanisms	mechanism	NOUN
ejpam-6968	259	12	on	on	ADP
ejpam-6968	259	13	each	each	DET
ejpam-6968	259	14	side	side	NOUN
ejpam-6968	259	15	of	of	ADP
ejpam-6968	259	16	α	α	NOUN
ejpam-6968	259	17	=	=	SYM
ejpam-6968	259	18	0	0	NUM
ejpam-6968	259	19	and	and	CCONJ
ejpam-6968	259	20	highlights	highlight	NOUN
ejpam-6968	259	21	how	how	SCONJ
ejpam-6968	259	22	local	local	ADJ
ejpam-6968	259	23	bifurcations	bifurcation	NOUN
ejpam-6968	259	24	interface	interface	VERB
ejpam-6968	259	25	with	with	ADP
ejpam-6968	259	26	global	global	ADJ
ejpam-6968	259	27	phase	phase	NOUN
ejpam-6968	259	28	-	-	PUNCT
ejpam-6968	259	29	space	space	NOUN
ejpam-6968	259	30	geometry	geometry	NOUN
ejpam-6968	259	31	.	.	PUNCT
ejpam-6968	260	1	while	while	SCONJ
ejpam-6968	260	2	the	the	DET
ejpam-6968	260	3	evidence	evidence	NOUN
ejpam-6968	260	4	for	for	ADP
ejpam-6968	260	5	hidden	hidden	ADJ
ejpam-6968	260	6	attractors	attractor	NOUN
ejpam-6968	260	7	is	be	AUX
ejpam-6968	260	8	primarily	primarily	ADV
ejpam-6968	260	9	numerical	numerical	ADJ
ejpam-6968	260	10	,	,	PUNCT
ejpam-6968	260	11	a	a	DET
ejpam-6968	260	12	rigorous	rigorous	ADJ
ejpam-6968	260	13	characterization	characterization	NOUN
ejpam-6968	260	14	of	of	ADP
ejpam-6968	260	15	basin	basin	NOUN
ejpam-6968	260	16	geometry	geometry	NOUN
ejpam-6968	260	17	and	and	CCONJ
ejpam-6968	260	18	possible	possible	ADJ
ejpam-6968	260	19	multistability	multistability	NOUN
ejpam-6968	260	20	for	for	ADP
ejpam-6968	260	21	α	α	PROPN
ejpam-6968	260	22	>	>	X
ejpam-6968	260	23	0	0	NUM
ejpam-6968	260	24	remains	remain	VERB
ejpam-6968	260	25	open	open	ADJ
ejpam-6968	260	26	.	.	PUNCT
ejpam-6968	261	1	future	future	ADJ
ejpam-6968	261	2	work	work	NOUN
ejpam-6968	261	3	will	will	AUX
ejpam-6968	261	4	therefore	therefore	ADV
ejpam-6968	261	5	focus	focus	VERB
ejpam-6968	261	6	on	on	ADP
ejpam-6968	261	7	codimension	codimension	NOUN
ejpam-6968	261	8	-	-	PUNCT
ejpam-6968	261	9	two	two	NUM
ejpam-6968	261	10	analysis	analysis	NOUN
ejpam-6968	261	11	around	around	ADP
ejpam-6968	261	12	α	α	PROPN
ejpam-6968	261	13	∈	∈	PROPN
ejpam-6968	261	14	0,−196	0,−196	NUM
ejpam-6968	261	15	,	,	PUNCT
ejpam-6968	261	16	systematic	systematic	ADJ
ejpam-6968	261	17	basin	basin	NOUN
ejpam-6968	261	18	cartography	cartography	NOUN
ejpam-6968	261	19	using	use	VERB
ejpam-6968	261	20	grid	grid	NOUN
ejpam-6968	261	21	-	-	PUNCT
ejpam-6968	261	22	based	base	VERB
ejpam-6968	261	23	or	or	CCONJ
ejpam-6968	261	24	set	set	NOUN
ejpam-6968	261	25	-	-	PUNCT
ejpam-6968	261	26	oriented	orient	VERB
ejpam-6968	261	27	methods	method	NOUN
ejpam-6968	261	28	,	,	PUNCT
ejpam-6968	261	29	testing	test	VERB
ejpam-6968	261	30	robustness	robustness	NOUN
ejpam-6968	261	31	under	under	ADP
ejpam-6968	261	32	noise	noise	NOUN
ejpam-6968	261	33	and	and	CCONJ
ejpam-6968	261	34	parameter	parameter	NOUN
ejpam-6968	261	35	uncertainty	uncertainty	NOUN
ejpam-6968	261	36	,	,	PUNCT
ejpam-6968	261	37	and	and	CCONJ
ejpam-6968	261	38	exploring	explore	VERB
ejpam-6968	261	39	hardware	hardware	NOUN
ejpam-6968	261	40	implementations	implementation	NOUN
ejpam-6968	261	41	or	or	CCONJ
ejpam-6968	261	42	control	control	NOUN
ejpam-6968	261	43	strategies	strategy	NOUN
ejpam-6968	261	44	(	(	PUNCT
ejpam-6968	261	45	e.g.	e.g.	ADV
ejpam-6968	261	46	,	,	PUNCT
ejpam-6968	261	47	chaos	chaos	NOUN
ejpam-6968	261	48	suppression	suppression	NOUN
ejpam-6968	261	49	or	or	CCONJ
ejpam-6968	261	50	targeting	targeting	NOUN
ejpam-6968	261	51	)	)	PUNCT
ejpam-6968	261	52	inspired	inspire	VERB
ejpam-6968	261	53	by	by	ADP
ejpam-6968	261	54	the	the	DET
ejpam-6968	261	55	two	two	NUM
ejpam-6968	261	56	-	-	PUNCT
ejpam-6968	261	57	regime	regime	NOUN
ejpam-6968	261	58	organization	organization	NOUN
ejpam-6968	261	59	reported	report	VERB
ejpam-6968	261	60	here	here	ADV
ejpam-6968	261	61	.	.	PUNCT
ejpam-6968	262	1	acknowledgements	acknowledgement	VERB
ejpam-6968	262	2	the	the	DET
ejpam-6968	262	3	author	author	NOUN
ejpam-6968	262	4	would	would	AUX
ejpam-6968	262	5	like	like	VERB
ejpam-6968	262	6	to	to	PART
ejpam-6968	262	7	express	express	VERB
ejpam-6968	262	8	sincere	sincere	ADJ
ejpam-6968	262	9	gratitude	gratitude	NOUN
ejpam-6968	262	10	to	to	ADP
ejpam-6968	262	11	universitas	universita	NOUN
ejpam-6968	262	12	diponegoro	diponegoro	PROPN
ejpam-6968	262	13	for	for	ADP
ejpam-6968	262	14	the	the	DET
ejpam-6968	262	15	financial	financial	ADJ
ejpam-6968	262	16	support	support	NOUN
ejpam-6968	262	17	provided	provide	VERB
ejpam-6968	262	18	through	through	ADP
ejpam-6968	262	19	the	the	DET
ejpam-6968	262	20	non	non	ADJ
ejpam-6968	262	21	-	-	ADJ
ejpam-6968	262	22	state	state	ADJ
ejpam-6968	262	23	budget	budget	NOUN
ejpam-6968	262	24	funding	funding	NOUN
ejpam-6968	262	25	scheme	scheme	NOUN
ejpam-6968	262	26	(	(	PUNCT
ejpam-6968	262	27	dana	dana	PROPN
ejpam-6968	262	28	selain	selain	PROPN
ejpam-6968	262	29	apbn	apbn	ADJ
ejpam-6968	262	30	)	)	PUNCT
ejpam-6968	262	31	for	for	ADP
ejpam-6968	262	32	fiscal	fiscal	ADJ
ejpam-6968	262	33	year	year	NOUN
ejpam-6968	262	34	2025	2025	NUM
ejpam-6968	262	35	,	,	PUNCT
ejpam-6968	262	36	based	base	VERB
ejpam-6968	262	37	on	on	ADP
ejpam-6968	262	38	the	the	DET
ejpam-6968	262	39	decree	decree	NOUN
ejpam-6968	262	40	of	of	ADP
ejpam-6968	262	41	the	the	DET
ejpam-6968	262	42	head	head	NOUN
ejpam-6968	262	43	of	of	ADP
ejpam-6968	262	44	the	the	DET
ejpam-6968	262	45	institute	institute	NOUN
ejpam-6968	262	46	for	for	ADP
ejpam-6968	262	47	research	research	NOUN
ejpam-6968	262	48	and	and	CCONJ
ejpam-6968	262	49	community	community	NOUN
ejpam-6968	262	50	service	service	NOUN
ejpam-6968	262	51	of	of	ADP
ejpam-6968	262	52	universitas	universita	NOUN
ejpam-6968	262	53	diponegoro	diponegoro	PROPN
ejpam-6968	262	54	(	(	PUNCT
ejpam-6968	262	55	lppm	lppm	PROPN
ejpam-6968	262	56	)	)	PUNCT
ejpam-6968	262	57	,	,	PUNCT
ejpam-6968	262	58	number	number	NOUN
ejpam-6968	262	59	:	:	PUNCT
ejpam-6968	262	60	610	610	NUM
ejpam-6968	262	61	/	/	SYM
ejpam-6968	262	62	un7.d2	un7.d2	PROPN
ejpam-6968	262	63	/	/	SYM
ejpam-6968	262	64	hk/	hk/	NOUN
ejpam-6968	262	65	iii/2025	iii/2025	NOUN
ejpam-6968	262	66	,	,	PUNCT
ejpam-6968	262	67	dated	date	VERB
ejpam-6968	262	68	march	march	PROPN
ejpam-6968	262	69	18	18	NUM
ejpam-6968	262	70	,	,	PUNCT
ejpam-6968	262	71	2025	2025	NUM
ejpam-6968	262	72	,	,	PUNCT
ejpam-6968	262	73	and	and	CCONJ
ejpam-6968	262	74	contract	contract	NOUN
ejpam-6968	262	75	agreement	agreement	NOUN
ejpam-6968	262	76	number	number	NOUN
ejpam-6968	262	77	:	:	PUNCT
ejpam-6968	262	78	222	222	NUM
ejpam-6968	262	79	-	-	SYM
ejpam-6968	262	80	179	179	NUM
ejpam-6968	262	81	/	/	SYM
ejpam-6968	262	82	un7.d2	un7.d2	PROPN
ejpam-6968	262	83	/	/	SYM
ejpam-6968	262	84	pp	pp	VERB
ejpam-6968	262	85	/iv/2025	/iv/2025	PUNCT
ejpam-6968	262	86	dated	date	VERB
ejpam-6968	262	87	april	april	PROPN
ejpam-6968	262	88	8	8	NUM
ejpam-6968	262	89	,	,	PUNCT
ejpam-6968	262	90	2025	2025	NUM
ejpam-6968	262	91	.	.	PUNCT
ejpam-6968	263	1	this	this	DET
ejpam-6968	263	2	support	support	NOUN
ejpam-6968	263	3	was	be	AUX
ejpam-6968	263	4	invaluable	invaluable	ADJ
ejpam-6968	263	5	in	in	ADP
ejpam-6968	263	6	facilitating	facilitate	VERB
ejpam-6968	263	7	and	and	CCONJ
ejpam-6968	263	8	completing	complete	VERB
ejpam-6968	263	9	this	this	DET
ejpam-6968	263	10	study	study	NOUN
ejpam-6968	263	11	.	.	PUNCT
ejpam-6968	264	1	h.	h.	PROPN
ejpam-6968	264	2	k.	k.	PROPN
ejpam-6968	264	3	fata	fata	PROPN
ejpam-6968	264	4	,	,	PUNCT
ejpam-6968	264	5	n.	n.	PROPN
ejpam-6968	264	6	y.	y.	PROPN
ejpam-6968	264	7	ashar	ashar	PROPN
ejpam-6968	264	8	/	/	SYM
ejpam-6968	264	9	eur	eur	PROPN
ejpam-6968	264	10	.	.	PUNCT
ejpam-6968	265	1	j.	j.	PROPN
ejpam-6968	265	2	pure	pure	PROPN
ejpam-6968	265	3	appl	appl	PROPN
ejpam-6968	265	4	.	.	PROPN
ejpam-6968	265	5	math	math	PROPN
ejpam-6968	265	6	,	,	PUNCT
ejpam-6968	265	7	18	18	NUM
ejpam-6968	265	8	(	(	PUNCT
ejpam-6968	265	9	4	4	NUM
ejpam-6968	265	10	)	)	PUNCT
ejpam-6968	265	11	(	(	PUNCT
ejpam-6968	265	12	2025	2025	NUM
ejpam-6968	265	13	)	)	PUNCT
ejpam-6968	265	14	,	,	PUNCT
ejpam-6968	265	15	6968	6968	NUM
ejpam-6968	265	16	14	14	NUM
ejpam-6968	265	17	of	of	ADP
ejpam-6968	265	18	15	15	NUM
ejpam-6968	265	19	references	reference	NOUN
ejpam-6968	265	20	[	[	X
ejpam-6968	265	21	1	1	X
ejpam-6968	265	22	]	]	PUNCT
ejpam-6968	265	23	t.	t.	PROPN
ejpam-6968	265	24	wang	wang	PROPN
ejpam-6968	265	25	,	,	PUNCT
ejpam-6968	265	26	z.	z.	PROPN
ejpam-6968	265	27	luo	luo	PROPN
ejpam-6968	265	28	,	,	PUNCT
ejpam-6968	265	29	s.	s.	PROPN
ejpam-6968	265	30	zhang	zhang	PROPN
ejpam-6968	265	31	,	,	PUNCT
ejpam-6968	265	32	and	and	CCONJ
ejpam-6968	265	33	z.	z.	PROPN
ejpam-6968	265	34	yu	yu	PROPN
ejpam-6968	265	35	.	.	PUNCT
ejpam-6968	265	36	feedback	feedback	NOUN
ejpam-6968	265	37	-	-	PUNCT
ejpam-6968	265	38	induced	induce	VERB
ejpam-6968	265	39	nonlinear	nonlinear	ADJ
ejpam-6968	265	40	spin	spin	NOUN
ejpam-6968	265	41	dynamics	dynamic	NOUN
ejpam-6968	265	42	in	in	ADP
ejpam-6968	265	43	an	an	DET
ejpam-6968	265	44	inhomogeneous	inhomogeneous	ADJ
ejpam-6968	265	45	magnetic	magnetic	ADJ
ejpam-6968	265	46	field	field	NOUN
ejpam-6968	265	47	.	.	PUNCT
ejpam-6968	266	1	communications	communication	NOUN
ejpam-6968	266	2	physics	physics	NOUN
ejpam-6968	266	3	,	,	PUNCT
ejpam-6968	266	4	8(1):41	8(1):41	NUM
ejpam-6968	266	5	,	,	PUNCT
ejpam-6968	266	6	2025	2025	NUM
ejpam-6968	266	7	.	.	PUNCT
ejpam-6968	267	1	[	[	X
ejpam-6968	267	2	2	2	NUM
ejpam-6968	267	3	]	]	PUNCT
ejpam-6968	267	4	s.	s.	PROPN
ejpam-6968	267	5	suweis	suweis	PROPN
ejpam-6968	267	6	,	,	PUNCT
ejpam-6968	267	7	f.	f.	PROPN
ejpam-6968	267	8	ferraro	ferraro	PROPN
ejpam-6968	267	9	,	,	PUNCT
ejpam-6968	267	10	c.	c.	PROPN
ejpam-6968	267	11	grilletta	grilletta	PROPN
ejpam-6968	267	12	,	,	PUNCT
ejpam-6968	267	13	s.	s.	PROPN
ejpam-6968	267	14	azaele	azaele	PROPN
ejpam-6968	267	15	,	,	PUNCT
ejpam-6968	267	16	and	and	CCONJ
ejpam-6968	267	17	a.	a.	PROPN
ejpam-6968	267	18	maritan	maritan	PROPN
ejpam-6968	267	19	.	.	PUNCT
ejpam-6968	268	1	generalized	generalize	VERB
ejpam-6968	268	2	lotka	lotka	PROPN
ejpam-6968	268	3	–	–	PUNCT
ejpam-6968	268	4	volterra	volterra	NOUN
ejpam-6968	268	5	systems	system	NOUN
ejpam-6968	268	6	with	with	ADP
ejpam-6968	268	7	time	time	NOUN
ejpam-6968	268	8	correlated	correlate	VERB
ejpam-6968	268	9	stochastic	stochastic	ADJ
ejpam-6968	268	10	interactions	interaction	NOUN
ejpam-6968	268	11	.	.	PUNCT
ejpam-6968	269	1	physical	physical	ADJ
ejpam-6968	269	2	review	review	NOUN
ejpam-6968	269	3	letters	letter	NOUN
ejpam-6968	269	4	,	,	PUNCT
ejpam-6968	269	5	133(16):167101	133(16):167101	NUM
ejpam-6968	269	6	,	,	PUNCT
ejpam-6968	269	7	2024	2024	NUM
ejpam-6968	269	8	.	.	PUNCT
ejpam-6968	270	1	[	[	X
ejpam-6968	270	2	3	3	X
ejpam-6968	270	3	]	]	PUNCT
ejpam-6968	270	4	t.	t.	PROPN
ejpam-6968	270	5	s.	s.	PROPN
ejpam-6968	270	6	amer	amer	PROPN
ejpam-6968	270	7	,	,	PUNCT
ejpam-6968	270	8	m.	m.	NOUN
ejpam-6968	270	9	a.	a.	PROPN
ejpam-6968	270	10	bek	bek	PROPN
ejpam-6968	270	11	,	,	PUNCT
ejpam-6968	270	12	and	and	CCONJ
ejpam-6968	270	13	m.	m.	PROPN
ejpam-6968	270	14	k.	k.	PROPN
ejpam-6968	270	15	abouhmr	abouhmr	PROPN
ejpam-6968	270	16	.	.	PUNCT
ejpam-6968	271	1	on	on	ADP
ejpam-6968	271	2	the	the	DET
ejpam-6968	271	3	vibrational	vibrational	ADJ
ejpam-6968	271	4	analysis	analysis	NOUN
ejpam-6968	271	5	for	for	ADP
ejpam-6968	271	6	the	the	DET
ejpam-6968	271	7	motion	motion	NOUN
ejpam-6968	271	8	of	of	ADP
ejpam-6968	271	9	a	a	DET
ejpam-6968	271	10	harmonically	harmonically	ADV
ejpam-6968	271	11	damped	damp	VERB
ejpam-6968	271	12	rigid	rigid	ADJ
ejpam-6968	271	13	body	body	NOUN
ejpam-6968	271	14	pendulum	pendulum	NOUN
ejpam-6968	271	15	.	.	PUNCT
ejpam-6968	272	1	nonlinear	nonlinear	ADJ
ejpam-6968	272	2	dynamics	dynamic	NOUN
ejpam-6968	272	3	,	,	PUNCT
ejpam-6968	272	4	91:2485	91:2485	NUM
ejpam-6968	272	5	–	–	PUNCT
ejpam-6968	272	6	2502	2502	NUM
ejpam-6968	272	7	,	,	PUNCT
ejpam-6968	272	8	2018	2018	NUM
ejpam-6968	272	9	.	.	PUNCT
ejpam-6968	273	1	[	[	X
ejpam-6968	273	2	4	4	X
ejpam-6968	273	3	]	]	PUNCT
ejpam-6968	273	4	m.	m.	PROPN
ejpam-6968	273	5	f.	f.	PROPN
ejpam-6968	273	6	ansori	ansori	PROPN
ejpam-6968	273	7	,	,	PUNCT
ejpam-6968	273	8	n.	n.	PROPN
ejpam-6968	273	9	y.	y.	PROPN
ejpam-6968	273	10	ashar	ashar	PROPN
ejpam-6968	273	11	,	,	PUNCT
ejpam-6968	273	12	and	and	CCONJ
ejpam-6968	273	13	h.	h.	PROPN
ejpam-6968	273	14	k.	k.	PROPN
ejpam-6968	273	15	fata	fata	PROPN
ejpam-6968	273	16	.	.	PUNCT
ejpam-6968	273	17	logistic	logistic	ADJ
ejpam-6968	273	18	map	map	NOUN
ejpam-6968	273	19	-	-	PUNCT
ejpam-6968	273	20	based	base	VERB
ejpam-6968	273	21	banking	banking	NOUN
ejpam-6968	273	22	loan	loan	NOUN
ejpam-6968	273	23	dynamics	dynamic	NOUN
ejpam-6968	273	24	with	with	ADP
ejpam-6968	273	25	central	central	ADJ
ejpam-6968	273	26	bank	bank	NOUN
ejpam-6968	273	27	policies	policy	NOUN
ejpam-6968	273	28	.	.	PUNCT
ejpam-6968	274	1	journal	journal	NOUN
ejpam-6968	274	2	of	of	ADP
ejpam-6968	274	3	applied	apply	VERB
ejpam-6968	274	4	nonlinear	nonlinear	ADJ
ejpam-6968	274	5	dynamics	dynamic	NOUN
ejpam-6968	274	6	,	,	PUNCT
ejpam-6968	274	7	14(3):561–574	14(3):561–574	NUM
ejpam-6968	274	8	,	,	PUNCT
ejpam-6968	274	9	2025	2025	NUM
ejpam-6968	274	10	.	.	PUNCT
ejpam-6968	275	1	[	[	X
ejpam-6968	275	2	5	5	NUM
ejpam-6968	275	3	]	]	PUNCT
ejpam-6968	275	4	c.	c.	NOUN
ejpam-6968	275	5	guenoune	guenoune	NOUN
ejpam-6968	275	6	,	,	PUNCT
ejpam-6968	275	7	a.	a.	NOUN
ejpam-6968	275	8	bachmar	bachmar	PROPN
ejpam-6968	275	9	,	,	PUNCT
ejpam-6968	275	10	and	and	CCONJ
ejpam-6968	275	11	s.	s.	PROPN
ejpam-6968	275	12	boutechebak	boutechebak	NOUN
ejpam-6968	275	13	.	.	PUNCT
ejpam-6968	276	1	a	a	DET
ejpam-6968	276	2	dynamic	dynamic	ADJ
ejpam-6968	276	3	problem	problem	NOUN
ejpam-6968	276	4	with	with	ADP
ejpam-6968	276	5	wear	wear	NOUN
ejpam-6968	276	6	involving	involve	VERB
ejpam-6968	276	7	thermoviscoelastic	thermoviscoelastic	ADJ
ejpam-6968	276	8	materials	material	NOUN
ejpam-6968	276	9	with	with	ADP
ejpam-6968	276	10	a	a	DET
ejpam-6968	276	11	long	long	ADJ
ejpam-6968	276	12	memory	memory	NOUN
ejpam-6968	276	13	.	.	PUNCT
ejpam-6968	277	1	nonlinear	nonlinear	ADJ
ejpam-6968	277	2	dynamics	dynamic	NOUN
ejpam-6968	277	3	&	&	CCONJ
ejpam-6968	277	4	systems	system	NOUN
ejpam-6968	277	5	theory	theory	NOUN
ejpam-6968	277	6	,	,	PUNCT
ejpam-6968	277	7	24(5	24(5	NOUN
ejpam-6968	277	8	)	)	PUNCT
ejpam-6968	277	9	,	,	PUNCT
ejpam-6968	277	10	2024	2024	NUM
ejpam-6968	277	11	.	.	PUNCT
ejpam-6968	278	1	[	[	X
ejpam-6968	278	2	6	6	NUM
ejpam-6968	278	3	]	]	X
ejpam-6968	278	4	steven	steven	PROPN
ejpam-6968	278	5	h.	h.	PROPN
ejpam-6968	278	6	strogatz	strogatz	PROPN
ejpam-6968	278	7	.	.	PUNCT
ejpam-6968	279	1	nonlinear	nonlinear	ADJ
ejpam-6968	279	2	dynamics	dynamic	NOUN
ejpam-6968	279	3	and	and	CCONJ
ejpam-6968	279	4	chaos	chaos	NOUN
ejpam-6968	279	5	:	:	PUNCT
ejpam-6968	279	6	with	with	ADP
ejpam-6968	279	7	applications	application	NOUN
ejpam-6968	279	8	to	to	ADP
ejpam-6968	279	9	physics	physics	NOUN
ejpam-6968	279	10	,	,	PUNCT
ejpam-6968	279	11	biology	biology	NOUN
ejpam-6968	279	12	,	,	PUNCT
ejpam-6968	279	13	chemistry	chemistry	NOUN
ejpam-6968	279	14	,	,	PUNCT
ejpam-6968	279	15	and	and	CCONJ
ejpam-6968	279	16	engineering	engineering	NOUN
ejpam-6968	279	17	.	.	PUNCT
ejpam-6968	280	1	crc	crc	PROPN
ejpam-6968	280	2	press	press	PROPN
ejpam-6968	280	3	,	,	PUNCT
ejpam-6968	280	4	2015	2015	NUM
ejpam-6968	280	5	.	.	PUNCT
ejpam-6968	281	1	[	[	X
ejpam-6968	281	2	7	7	X
ejpam-6968	281	3	]	]	PUNCT
ejpam-6968	281	4	j.	j.	PROPN
ejpam-6968	281	5	chen	chen	PROPN
ejpam-6968	281	6	,	,	PUNCT
ejpam-6968	281	7	g.	g.	PROPN
ejpam-6968	281	8	degrandi	degrandi	PROPN
ejpam-6968	281	9	-	-	PROPN
ejpam-6968	281	10	hoffman	hoffman	NOUN
ejpam-6968	281	11	,	,	PUNCT
ejpam-6968	281	12	v.	v.	ADP
ejpam-6968	281	13	ratti	ratti	PROPN
ejpam-6968	281	14	,	,	PUNCT
ejpam-6968	281	15	and	and	CCONJ
ejpam-6968	281	16	y.	y.	PROPN
ejpam-6968	281	17	kang	kang	PROPN
ejpam-6968	281	18	.	.	PUNCT
ejpam-6968	282	1	review	review	NOUN
ejpam-6968	282	2	on	on	ADP
ejpam-6968	282	3	mathematical	mathematical	ADJ
ejpam-6968	282	4	modeling	modeling	NOUN
ejpam-6968	282	5	of	of	ADP
ejpam-6968	282	6	honeybee	honeybee	NOUN
ejpam-6968	282	7	population	population	NOUN
ejpam-6968	282	8	dynamics	dynamic	NOUN
ejpam-6968	282	9	.	.	PUNCT
ejpam-6968	283	1	mathematical	mathematical	ADJ
ejpam-6968	283	2	biosciences	bioscience	NOUN
ejpam-6968	283	3	and	and	CCONJ
ejpam-6968	283	4	engineering	engineering	NOUN
ejpam-6968	283	5	,	,	PUNCT
ejpam-6968	283	6	18(6	18(6	NOUN
ejpam-6968	283	7	)	)	PUNCT
ejpam-6968	283	8	,	,	PUNCT
ejpam-6968	283	9	2021	2021	NUM
ejpam-6968	283	10	.	.	PUNCT
ejpam-6968	284	1	[	[	X
ejpam-6968	284	2	8	8	NUM
ejpam-6968	284	3	]	]	PUNCT
ejpam-6968	284	4	z.	z.	PROPN
ejpam-6968	284	5	duan	duan	PROPN
ejpam-6968	284	6	,	,	PUNCT
ejpam-6968	284	7	h.	h.	PROPN
ejpam-6968	284	8	li	li	PROPN
ejpam-6968	284	9	,	,	PUNCT
ejpam-6968	284	10	s.	s.	PROPN
ejpam-6968	284	11	he	he	PRON
ejpam-6968	284	12	,	,	PUNCT
ejpam-6968	284	13	y.	y.	PROPN
ejpam-6968	284	14	long	long	PROPN
ejpam-6968	284	15	,	,	PUNCT
ejpam-6968	284	16	x.	x.	PROPN
ejpam-6968	284	17	yu	yu	PROPN
ejpam-6968	284	18	,	,	PUNCT
ejpam-6968	284	19	and	and	CCONJ
ejpam-6968	284	20	q.	q.	PROPN
ejpam-6968	284	21	ke	ke	PROPN
ejpam-6968	284	22	.	.	PUNCT
ejpam-6968	284	23	integrated	integrate	VERB
ejpam-6968	284	24	circuit	circuit	NOUN
ejpam-6968	284	25	of	of	ADP
ejpam-6968	284	26	a	a	DET
ejpam-6968	284	27	chua	chua	PROPN
ejpam-6968	284	28	’s	’s	PART
ejpam-6968	284	29	system	system	NOUN
ejpam-6968	284	30	based	base	VERB
ejpam-6968	284	31	on	on	ADP
ejpam-6968	284	32	the	the	DET
ejpam-6968	284	33	integral	integral	ADJ
ejpam-6968	284	34	-	-	PUNCT
ejpam-6968	284	35	differential	differential	NOUN
ejpam-6968	284	36	nonlinear	nonlinear	ADJ
ejpam-6968	284	37	resistance	resistance	NOUN
ejpam-6968	284	38	with	with	ADP
ejpam-6968	284	39	multi	multi	ADJ
ejpam-6968	284	40	-	-	ADJ
ejpam-6968	284	41	path	path	ADJ
ejpam-6968	284	42	voltagecontrolled	voltagecontrolle	VERB
ejpam-6968	284	43	oscillator	oscillator	NOUN
ejpam-6968	284	44	.	.	PUNCT
ejpam-6968	285	1	micromachines	micromachine	NOUN
ejpam-6968	285	2	,	,	PUNCT
ejpam-6968	285	3	15(3):401	15(3):401	PROPN
ejpam-6968	285	4	,	,	PUNCT
ejpam-6968	285	5	2024	2024	NUM
ejpam-6968	285	6	.	.	PUNCT
ejpam-6968	286	1	[	[	X
ejpam-6968	286	2	9	9	NUM
ejpam-6968	286	3	]	]	PUNCT
ejpam-6968	286	4	a.	a.	NOUN
ejpam-6968	286	5	chakraborty	chakraborty	PROPN
ejpam-6968	286	6	and	and	CCONJ
ejpam-6968	286	7	p.	p.	PROPN
ejpam-6968	286	8	veeresha	veeresha	PROPN
ejpam-6968	286	9	.	.	PUNCT
ejpam-6968	287	1	effects	effect	NOUN
ejpam-6968	287	2	of	of	ADP
ejpam-6968	287	3	global	global	ADJ
ejpam-6968	287	4	warming	warming	NOUN
ejpam-6968	287	5	,	,	PUNCT
ejpam-6968	287	6	time	time	NOUN
ejpam-6968	287	7	delay	delay	NOUN
ejpam-6968	287	8	and	and	CCONJ
ejpam-6968	287	9	chaos	chaos	NOUN
ejpam-6968	287	10	control	control	NOUN
ejpam-6968	287	11	on	on	ADP
ejpam-6968	287	12	the	the	DET
ejpam-6968	287	13	dynamics	dynamic	NOUN
ejpam-6968	287	14	of	of	ADP
ejpam-6968	287	15	a	a	DET
ejpam-6968	287	16	chaotic	chaotic	ADJ
ejpam-6968	287	17	atmospheric	atmospheric	ADJ
ejpam-6968	287	18	propagation	propagation	NOUN
ejpam-6968	287	19	model	model	NOUN
ejpam-6968	287	20	within	within	ADP
ejpam-6968	287	21	the	the	DET
ejpam-6968	287	22	frame	frame	NOUN
ejpam-6968	287	23	of	of	ADP
ejpam-6968	287	24	caputo	caputo	PROPN
ejpam-6968	287	25	fractional	fractional	ADJ
ejpam-6968	287	26	operator	operator	NOUN
ejpam-6968	287	27	.	.	PUNCT
ejpam-6968	288	1	communications	communication	NOUN
ejpam-6968	288	2	in	in	ADP
ejpam-6968	288	3	nonlinear	nonlinear	ADJ
ejpam-6968	288	4	science	science	NOUN
ejpam-6968	288	5	and	and	CCONJ
ejpam-6968	288	6	numerical	numerical	PROPN
ejpam-6968	288	7	simulation	simulation	PROPN
ejpam-6968	288	8	,	,	PUNCT
ejpam-6968	288	9	128:107657	128:107657	NUM
ejpam-6968	288	10	,	,	PUNCT
ejpam-6968	288	11	2024	2024	NUM
ejpam-6968	288	12	.	.	PUNCT
ejpam-6968	289	1	[	[	X
ejpam-6968	289	2	10	10	NUM
ejpam-6968	289	3	]	]	X
ejpam-6968	289	4	c.	c.	PROPN
ejpam-6968	289	5	liu	liu	PROPN
ejpam-6968	289	6	,	,	PUNCT
ejpam-6968	289	7	s.-k	s.-k	PROPN
ejpam-6968	289	8	.	.	PUNCT
ejpam-6968	290	1	lai	lai	PROPN
ejpam-6968	290	2	,	,	PUNCT
ejpam-6968	290	3	y.-q	y.-q	PROPN
ejpam-6968	290	4	.	.	PUNCT
ejpam-6968	291	1	ni	ni	PROPN
ejpam-6968	291	2	,	,	PUNCT
ejpam-6968	291	3	and	and	CCONJ
ejpam-6968	291	4	l.	l.	PROPN
ejpam-6968	291	5	chen	chen	PROPN
ejpam-6968	291	6	.	.	PUNCT
ejpam-6968	292	1	dynamic	dynamic	ADJ
ejpam-6968	292	2	modelling	modelling	NOUN
ejpam-6968	292	3	and	and	CCONJ
ejpam-6968	292	4	analysis	analysis	NOUN
ejpam-6968	292	5	of	of	ADP
ejpam-6968	292	6	a	a	DET
ejpam-6968	292	7	physicsdriven	physicsdriven	ADJ
ejpam-6968	292	8	strategy	strategy	NOUN
ejpam-6968	292	9	for	for	ADP
ejpam-6968	292	10	vibration	vibration	NOUN
ejpam-6968	292	11	control	control	NOUN
ejpam-6968	292	12	of	of	ADP
ejpam-6968	292	13	railway	railway	NOUN
ejpam-6968	292	14	vehicles	vehicle	NOUN
ejpam-6968	292	15	.	.	PUNCT
ejpam-6968	293	1	vehicle	vehicle	NOUN
ejpam-6968	293	2	system	system	NOUN
ejpam-6968	293	3	dynamics	dynamic	NOUN
ejpam-6968	293	4	,	,	PUNCT
ejpam-6968	293	5	pages	page	NOUN
ejpam-6968	293	6	1–31	1–31	PROPN
ejpam-6968	293	7	,	,	PUNCT
ejpam-6968	293	8	2024	2024	NUM
ejpam-6968	293	9	.	.	PUNCT
ejpam-6968	294	1	[	[	X
ejpam-6968	294	2	11	11	NUM
ejpam-6968	294	3	]	]	X
ejpam-6968	294	4	yuri	yuri	PROPN
ejpam-6968	294	5	a.	a.	PROPN
ejpam-6968	294	6	kuznetsov	kuznetsov	PROPN
ejpam-6968	294	7	.	.	PUNCT
ejpam-6968	295	1	elements	element	NOUN
ejpam-6968	295	2	of	of	ADP
ejpam-6968	295	3	applied	apply	VERB
ejpam-6968	295	4	bifurcation	bifurcation	NOUN
ejpam-6968	295	5	theory	theory	NOUN
ejpam-6968	295	6	.	.	PUNCT
ejpam-6968	296	1	springer	springer	NOUN
ejpam-6968	296	2	,	,	PUNCT
ejpam-6968	296	3	new	new	PROPN
ejpam-6968	296	4	york	york	PROPN
ejpam-6968	296	5	,	,	PUNCT
ejpam-6968	296	6	3	3	NUM
ejpam-6968	296	7	edition	edition	NOUN
ejpam-6968	296	8	,	,	PUNCT
ejpam-6968	296	9	2004	2004	NUM
ejpam-6968	296	10	.	.	PUNCT
ejpam-6968	297	1	[	[	X
ejpam-6968	297	2	12	12	NUM
ejpam-6968	297	3	]	]	X
ejpam-6968	297	4	v.	v.	PROPN
ejpam-6968	297	5	i.	i.	PROPN
ejpam-6968	297	6	arnold	arnold	PROPN
ejpam-6968	297	7	.	.	PUNCT
ejpam-6968	298	1	bifurcations	bifurcation	NOUN
ejpam-6968	298	2	of	of	ADP
ejpam-6968	298	3	equilibria	equilibrium	NOUN
ejpam-6968	298	4	.	.	PUNCT
ejpam-6968	299	1	in	in	ADP
ejpam-6968	299	2	dynamical	dynamical	ADJ
ejpam-6968	299	3	systems	system	NOUN
ejpam-6968	299	4	v	v	NOUN
ejpam-6968	299	5	,	,	PUNCT
ejpam-6968	299	6	pages	page	NOUN
ejpam-6968	299	7	1–8	1–8	NOUN
ejpam-6968	299	8	.	.	PUNCT
ejpam-6968	299	9	springer	springer	PROPN
ejpam-6968	299	10	,	,	PUNCT
ejpam-6968	299	11	berlin	berlin	PROPN
ejpam-6968	299	12	,	,	PUNCT
ejpam-6968	299	13	1994	1994	NUM
ejpam-6968	299	14	.	.	PUNCT
ejpam-6968	300	1	[	[	X
ejpam-6968	300	2	13	13	NUM
ejpam-6968	300	3	]	]	X
ejpam-6968	300	4	lawrence	lawrence	PROPN
ejpam-6968	300	5	perko	perko	PROPN
ejpam-6968	300	6	.	.	PUNCT
ejpam-6968	300	7	differential	differential	ADJ
ejpam-6968	300	8	equations	equation	NOUN
ejpam-6968	300	9	and	and	CCONJ
ejpam-6968	300	10	dynamical	dynamical	ADJ
ejpam-6968	300	11	systems	system	NOUN
ejpam-6968	300	12	,	,	PUNCT
ejpam-6968	300	13	volume	volume	NOUN
ejpam-6968	300	14	7	7	NUM
ejpam-6968	300	15	of	of	ADP
ejpam-6968	300	16	texts	text	NOUN
ejpam-6968	300	17	in	in	ADP
ejpam-6968	300	18	applied	applied	ADJ
ejpam-6968	300	19	mathematics	mathematic	NOUN
ejpam-6968	300	20	.	.	PUNCT
ejpam-6968	301	1	springer	springer	NOUN
ejpam-6968	301	2	,	,	PUNCT
ejpam-6968	301	3	new	new	PROPN
ejpam-6968	301	4	york	york	PROPN
ejpam-6968	301	5	,	,	PUNCT
ejpam-6968	301	6	2013	2013	NUM
ejpam-6968	301	7	.	.	PUNCT
ejpam-6968	302	1	[	[	X
ejpam-6968	302	2	14	14	NUM
ejpam-6968	302	3	]	]	X
ejpam-6968	302	4	stephen	stephen	PROPN
ejpam-6968	302	5	wiggins	wiggins	PROPN
ejpam-6968	302	6	.	.	PUNCT
ejpam-6968	303	1	introduction	introduction	NOUN
ejpam-6968	303	2	to	to	AUX
ejpam-6968	303	3	applied	apply	VERB
ejpam-6968	303	4	nonlinear	nonlinear	ADJ
ejpam-6968	303	5	dynamical	dynamical	ADJ
ejpam-6968	303	6	systems	system	NOUN
ejpam-6968	303	7	and	and	CCONJ
ejpam-6968	303	8	chaos	chaos	NOUN
ejpam-6968	303	9	.	.	PUNCT
ejpam-6968	304	1	texts	text	NOUN
ejpam-6968	304	2	in	in	ADP
ejpam-6968	304	3	applied	applied	ADJ
ejpam-6968	304	4	mathematics	mathematic	NOUN
ejpam-6968	304	5	.	.	PUNCT
ejpam-6968	305	1	springer	springer	NOUN
ejpam-6968	305	2	,	,	PUNCT
ejpam-6968	305	3	new	new	PROPN
ejpam-6968	305	4	york	york	PROPN
ejpam-6968	305	5	,	,	PUNCT
ejpam-6968	305	6	2003	2003	NUM
ejpam-6968	305	7	.	.	PUNCT
ejpam-6968	306	1	[	[	X
ejpam-6968	306	2	15	15	NUM
ejpam-6968	306	3	]	]	X
ejpam-6968	306	4	n.	n.	NOUN
ejpam-6968	306	5	ananthkrishnan	ananthkrishnan	PROPN
ejpam-6968	306	6	,	,	PUNCT
ejpam-6968	306	7	n.	n.	PROPN
ejpam-6968	306	8	k.	k.	PROPN
ejpam-6968	306	9	gupta	gupta	PROPN
ejpam-6968	306	10	,	,	PUNCT
ejpam-6968	306	11	and	and	CCONJ
ejpam-6968	306	12	n.	n.	PROPN
ejpam-6968	306	13	k.	k.	PROPN
ejpam-6968	306	14	sinha	sinha	PROPN
ejpam-6968	306	15	.	.	PUNCT
ejpam-6968	307	1	computational	computational	ADJ
ejpam-6968	307	2	bifurcation	bifurcation	NOUN
ejpam-6968	307	3	analysis	analysis	NOUN
ejpam-6968	307	4	of	of	ADP
ejpam-6968	307	5	multiparameter	multiparameter	NOUN
ejpam-6968	307	6	dynamical	dynamical	ADJ
ejpam-6968	307	7	systems	system	NOUN
ejpam-6968	307	8	.	.	PUNCT
ejpam-6968	308	1	journal	journal	PROPN
ejpam-6968	308	2	of	of	ADP
ejpam-6968	308	3	guidance	guidance	NOUN
ejpam-6968	308	4	,	,	PUNCT
ejpam-6968	308	5	control	control	NOUN
ejpam-6968	308	6	,	,	PUNCT
ejpam-6968	308	7	and	and	CCONJ
ejpam-6968	308	8	dynamics	dynamic	NOUN
ejpam-6968	308	9	,	,	PUNCT
ejpam-6968	308	10	32(5):1505–1513	32(5):1505–1513	NUM
ejpam-6968	308	11	,	,	PUNCT
ejpam-6968	308	12	2009	2009	NUM
ejpam-6968	308	13	.	.	PUNCT
ejpam-6968	309	1	[	[	X
ejpam-6968	309	2	16	16	NUM
ejpam-6968	309	3	]	]	PUNCT
ejpam-6968	309	4	m.	m.	NOUN
ejpam-6968	309	5	di	di	PROPN
ejpam-6968	309	6	bernardo	bernardo	PROPN
ejpam-6968	309	7	,	,	PUNCT
ejpam-6968	309	8	c.	c.	PROPN
ejpam-6968	309	9	budd	budd	PROPN
ejpam-6968	309	10	,	,	PUNCT
ejpam-6968	309	11	a.	a.	PROPN
ejpam-6968	309	12	r.	r.	PROPN
ejpam-6968	309	13	champneys	champneys	PROPN
ejpam-6968	309	14	,	,	PUNCT
ejpam-6968	309	15	p.	p.	PROPN
ejpam-6968	309	16	kowalczyk	kowalczyk	PROPN
ejpam-6968	309	17	,	,	PUNCT
ejpam-6968	309	18	a.	a.	NOUN
ejpam-6968	309	19	nordmark	nordmark	PROPN
ejpam-6968	309	20	,	,	PUNCT
ejpam-6968	309	21	g.	g.	PROPN
ejpam-6968	309	22	olih	olih	PROPN
ejpam-6968	309	23	.	.	PUNCT
ejpam-6968	310	1	k.	k.	PROPN
ejpam-6968	310	2	fata	fata	PROPN
ejpam-6968	310	3	,	,	PUNCT
ejpam-6968	310	4	n.	n.	PROPN
ejpam-6968	310	5	y.	y.	PROPN
ejpam-6968	310	6	ashar	ashar	PROPN
ejpam-6968	310	7	/	/	SYM
ejpam-6968	310	8	eur	eur	PROPN
ejpam-6968	310	9	.	.	PUNCT
ejpam-6968	311	1	j.	j.	PROPN
ejpam-6968	311	2	pure	pure	PROPN
ejpam-6968	311	3	appl	appl	PROPN
ejpam-6968	311	4	.	.	PROPN
ejpam-6968	311	5	math	math	PROPN
ejpam-6968	311	6	,	,	PUNCT
ejpam-6968	311	7	18	18	NUM
ejpam-6968	311	8	(	(	PUNCT
ejpam-6968	311	9	4	4	NUM
ejpam-6968	311	10	)	)	PUNCT
ejpam-6968	311	11	(	(	PUNCT
ejpam-6968	311	12	2025	2025	NUM
ejpam-6968	311	13	)	)	PUNCT
ejpam-6968	311	14	,	,	PUNCT
ejpam-6968	311	15	6968	6968	NUM
ejpam-6968	311	16	15	15	NUM
ejpam-6968	311	17	of	of	ADP
ejpam-6968	311	18	15	15	NUM
ejpam-6968	311	19	var	var	NOUN
ejpam-6968	311	20	tost	tost	NOUN
ejpam-6968	311	21	,	,	PUNCT
ejpam-6968	311	22	and	and	CCONJ
ejpam-6968	311	23	p.	p.	NOUN
ejpam-6968	311	24	t.	t.	PROPN
ejpam-6968	311	25	piiroinen	piiroinen	PROPN
ejpam-6968	311	26	.	.	PUNCT
ejpam-6968	312	1	bifurcations	bifurcation	NOUN
ejpam-6968	312	2	in	in	ADP
ejpam-6968	312	3	nonsmooth	nonsmooth	ADJ
ejpam-6968	312	4	dynamical	dynamical	ADJ
ejpam-6968	312	5	systems	system	NOUN
ejpam-6968	312	6	.	.	PUNCT
ejpam-6968	313	1	siam	siam	PROPN
ejpam-6968	313	2	review	review	PROPN
ejpam-6968	313	3	,	,	PUNCT
ejpam-6968	313	4	50(4):629–701	50(4):629–701	PROPN
ejpam-6968	313	5	,	,	PUNCT
ejpam-6968	313	6	2008	2008	NUM
ejpam-6968	313	7	.	.	PUNCT
ejpam-6968	314	1	[	[	X
ejpam-6968	314	2	17	17	NUM
ejpam-6968	314	3	]	]	X
ejpam-6968	314	4	y.	y.	PROPN
ejpam-6968	314	5	han	han	PROPN
ejpam-6968	314	6	,	,	PUNCT
ejpam-6968	314	7	q.	q.	PROPN
ejpam-6968	314	8	cao	cao	PROPN
ejpam-6968	314	9	,	,	PUNCT
ejpam-6968	314	10	and	and	CCONJ
ejpam-6968	314	11	j.	j.	PROPN
ejpam-6968	314	12	ji	ji	PROPN
ejpam-6968	314	13	.	.	PROPN
ejpam-6968	315	1	nonlinear	nonlinear	ADJ
ejpam-6968	315	2	dynamics	dynamic	NOUN
ejpam-6968	315	3	of	of	ADP
ejpam-6968	315	4	a	a	DET
ejpam-6968	315	5	smooth	smooth	ADJ
ejpam-6968	315	6	and	and	CCONJ
ejpam-6968	315	7	discontinuous	discontinuous	ADJ
ejpam-6968	315	8	oscillator	oscillator	NOUN
ejpam-6968	315	9	with	with	ADP
ejpam-6968	315	10	multiple	multiple	ADJ
ejpam-6968	315	11	stability	stability	NOUN
ejpam-6968	315	12	.	.	PUNCT
ejpam-6968	316	1	international	international	ADJ
ejpam-6968	316	2	journal	journal	NOUN
ejpam-6968	316	3	of	of	ADP
ejpam-6968	316	4	bifurcation	bifurcation	NOUN
ejpam-6968	316	5	and	and	CCONJ
ejpam-6968	316	6	chaos	chaos	NOUN
ejpam-6968	316	7	,	,	PUNCT
ejpam-6968	316	8	25(14):1550038	25(14):1550038	NUM
ejpam-6968	316	9	,	,	PUNCT
ejpam-6968	316	10	2015	2015	NUM
ejpam-6968	316	11	.	.	PUNCT
ejpam-6968	317	1	[	[	X
ejpam-6968	317	2	18	18	NUM
ejpam-6968	317	3	]	]	X
ejpam-6968	317	4	j.	j.	PROPN
ejpam-6968	317	5	c.	c.	PROPN
ejpam-6968	317	6	sprott	sprott	PROPN
ejpam-6968	317	7	.	.	PUNCT
ejpam-6968	318	1	some	some	DET
ejpam-6968	318	2	simple	simple	ADJ
ejpam-6968	318	3	chaotic	chaotic	ADJ
ejpam-6968	318	4	flows	flow	NOUN
ejpam-6968	318	5	.	.	PUNCT
ejpam-6968	319	1	physical	physical	ADJ
ejpam-6968	319	2	review	review	PROPN
ejpam-6968	319	3	e	e	NOUN
ejpam-6968	319	4	,	,	PUNCT
ejpam-6968	319	5	50(2):647–650	50(2):647–650	PROPN
ejpam-6968	319	6	,	,	PUNCT
ejpam-6968	319	7	1994	1994	NUM
ejpam-6968	319	8	.	.	PUNCT
ejpam-6968	320	1	[	[	X
ejpam-6968	320	2	19	19	NUM
ejpam-6968	320	3	]	]	X
ejpam-6968	320	4	s.	s.	PROPN
ejpam-6968	320	5	jafari	jafari	PROPN
ejpam-6968	320	6	,	,	PUNCT
ejpam-6968	320	7	j.	j.	PROPN
ejpam-6968	320	8	c.	c.	PROPN
ejpam-6968	320	9	sprott	sprott	PROPN
ejpam-6968	320	10	,	,	PUNCT
ejpam-6968	320	11	and	and	CCONJ
ejpam-6968	320	12	s.	s.	PROPN
ejpam-6968	320	13	m.	m.	PROPN
ejpam-6968	320	14	r.	r.	PROPN
ejpam-6968	320	15	hashemi	hashemi	PROPN
ejpam-6968	320	16	golpayegani	golpayegani	PROPN
ejpam-6968	320	17	.	.	PUNCT
ejpam-6968	321	1	elementary	elementary	ADJ
ejpam-6968	321	2	quadratic	quadratic	ADJ
ejpam-6968	321	3	chaotic	chaotic	ADJ
ejpam-6968	321	4	flows	flow	NOUN
ejpam-6968	321	5	with	with	ADP
ejpam-6968	321	6	no	no	DET
ejpam-6968	321	7	equilibria	equilibria	NOUN
ejpam-6968	321	8	.	.	PUNCT
ejpam-6968	322	1	physics	physics	NOUN
ejpam-6968	322	2	letters	letter	NOUN
ejpam-6968	322	3	a	a	DET
ejpam-6968	322	4	,	,	PUNCT
ejpam-6968	322	5	377(9):699–702	377(9):699–702	NUM
ejpam-6968	322	6	,	,	PUNCT
ejpam-6968	322	7	2013	2013	NUM
ejpam-6968	322	8	.	.	PUNCT
ejpam-6968	323	1	[	[	X
ejpam-6968	323	2	20	20	NUM
ejpam-6968	323	3	]	]	PUNCT
ejpam-6968	323	4	a.	a.	NOUN
ejpam-6968	323	5	wolf	wolf	PROPN
ejpam-6968	323	6	,	,	PUNCT
ejpam-6968	323	7	j.	j.	PROPN
ejpam-6968	323	8	b.	b.	PROPN
ejpam-6968	323	9	swift	swift	PROPN
ejpam-6968	323	10	,	,	PUNCT
ejpam-6968	323	11	h.	h.	PROPN
ejpam-6968	323	12	l.	l.	PROPN
ejpam-6968	323	13	swinney	swinney	PROPN
ejpam-6968	323	14	,	,	PUNCT
ejpam-6968	323	15	and	and	CCONJ
ejpam-6968	323	16	j.	j.	PROPN
ejpam-6968	323	17	a.	a.	PROPN
ejpam-6968	323	18	vastano	vastano	PROPN
ejpam-6968	323	19	.	.	PUNCT
ejpam-6968	324	1	determining	determine	VERB
ejpam-6968	324	2	lyapunov	lyapunov	ADJ
ejpam-6968	324	3	exponents	exponent	NOUN
ejpam-6968	324	4	from	from	ADP
ejpam-6968	324	5	a	a	DET
ejpam-6968	324	6	time	time	NOUN
ejpam-6968	324	7	series	series	NOUN
ejpam-6968	324	8	.	.	PUNCT
ejpam-6968	325	1	physica	physica	PROPN
ejpam-6968	325	2	d	d	PROPN
ejpam-6968	325	3	,	,	PUNCT
ejpam-6968	325	4	16(3):285–317	16(3):285–317	NUM
ejpam-6968	325	5	,	,	PUNCT
ejpam-6968	325	6	1985	1985	NUM
ejpam-6968	325	7	.	.	PUNCT
ejpam-6968	326	1	[	[	X
ejpam-6968	326	2	21	21	NUM
ejpam-6968	326	3	]	]	PUNCT
ejpam-6968	326	4	j.	j.	PROPN
ejpam-6968	326	5	nichols	nichols	PROPN
ejpam-6968	326	6	,	,	PUNCT
ejpam-6968	326	7	r.	r.	PROPN
ejpam-6968	326	8	d.	d.	PROPN
ejpam-6968	326	9	guy	guy	PROPN
ejpam-6968	326	10	,	,	PUNCT
ejpam-6968	326	11	and	and	CCONJ
ejpam-6968	326	12	b.	b.	PROPN
ejpam-6968	326	13	thomases	thomases	PROPN
ejpam-6968	326	14	.	.	PUNCT
ejpam-6968	326	15	period	period	NOUN
ejpam-6968	326	16	-	-	PUNCT
ejpam-6968	326	17	doubling	double	VERB
ejpam-6968	326	18	route	route	NOUN
ejpam-6968	326	19	to	to	PART
ejpam-6968	326	20	chaos	chaos	VERB
ejpam-6968	326	21	in	in	ADP
ejpam-6968	326	22	viscoelastic	viscoelastic	ADJ
ejpam-6968	326	23	kolmogorov	kolmogorov	ADJ
ejpam-6968	326	24	flow	flow	NOUN
ejpam-6968	326	25	.	.	PUNCT
ejpam-6968	327	1	physical	physical	ADJ
ejpam-6968	327	2	review	review	NOUN
ejpam-6968	327	3	fluids	fluid	NOUN
ejpam-6968	327	4	,	,	PUNCT
ejpam-6968	327	5	10	10	NUM
ejpam-6968	327	6	:	:	PUNCT
ejpam-6968	327	7	l041301	l041301	ADJ
ejpam-6968	327	8	,	,	PUNCT
ejpam-6968	327	9	2025	2025	NUM
ejpam-6968	327	10	.	.	PUNCT
ejpam-6968	328	1	[	[	X
ejpam-6968	328	2	22	22	NUM
ejpam-6968	328	3	]	]	PUNCT
ejpam-6968	328	4	s.	s.	PROPN
ejpam-6968	328	5	saju	saju	PROPN
ejpam-6968	328	6	,	,	PUNCT
ejpam-6968	328	7	k.	k.	PROPN
ejpam-6968	328	8	kinashi	kinashi	PROPN
ejpam-6968	328	9	,	,	PUNCT
ejpam-6968	328	10	n.	n.	PROPN
ejpam-6968	328	11	tsutsumi	tsutsumi	PROPN
ejpam-6968	328	12	,	,	PUNCT
ejpam-6968	328	13	w.	w.	PROPN
ejpam-6968	328	14	sakai	sakai	PROPN
ejpam-6968	328	15	,	,	PUNCT
ejpam-6968	328	16	and	and	CCONJ
ejpam-6968	328	17	b.	b.	PROPN
ejpam-6968	328	18	j.	j.	PROPN
ejpam-6968	328	19	jackin	jackin	PROPN
ejpam-6968	328	20	.	.	PUNCT
ejpam-6968	328	21	period	period	NOUN
ejpam-6968	328	22	-	-	PUNCT
ejpam-6968	328	23	doubling	double	VERB
ejpam-6968	328	24	route	route	NOUN
ejpam-6968	328	25	to	to	PART
ejpam-6968	328	26	chaos	chaos	VERB
ejpam-6968	328	27	in	in	ADP
ejpam-6968	328	28	photorefractive	photorefractive	ADJ
ejpam-6968	328	29	two	two	NUM
ejpam-6968	328	30	-	-	PUNCT
ejpam-6968	328	31	wave	wave	NOUN
ejpam-6968	328	32	mixing	mixing	NOUN
ejpam-6968	328	33	.	.	PUNCT
ejpam-6968	329	1	photonics	photonic	NOUN
ejpam-6968	329	2	,	,	PUNCT
ejpam-6968	329	3	11:521	11:521	NUM
ejpam-6968	329	4	,	,	PUNCT
ejpam-6968	329	5	2024	2024	NUM
ejpam-6968	329	6	.	.	PUNCT
ejpam-6968	330	1	[	[	X
ejpam-6968	330	2	23	23	NUM
ejpam-6968	330	3	]	]	PUNCT
ejpam-6968	330	4	x.	x.	NOUN
ejpam-6968	330	5	zhang	zhang	PROPN
ejpam-6968	330	6	et	et	PROPN
ejpam-6968	330	7	al	al	PROPN
ejpam-6968	330	8	.	.	PROPN
ejpam-6968	331	1	from	from	ADP
ejpam-6968	331	2	breather	breather	PROPN
ejpam-6968	331	3	solitons	soliton	NOUN
ejpam-6968	331	4	to	to	PART
ejpam-6968	331	5	chaos	chaos	VERB
ejpam-6968	331	6	in	in	ADP
ejpam-6968	331	7	an	an	DET
ejpam-6968	331	8	ultrafast	ultrafast	ADJ
ejpam-6968	331	9	laser	laser	NOUN
ejpam-6968	331	10	.	.	PUNCT
ejpam-6968	332	1	chaos	chaos	NOUN
ejpam-6968	332	2	,	,	PUNCT
ejpam-6968	332	3	solitons	soliton	NOUN
ejpam-6968	332	4	&	&	CCONJ
ejpam-6968	332	5	fractals	fractal	NOUN
ejpam-6968	332	6	,	,	PUNCT
ejpam-6968	332	7	182:114841	182:114841	NUM
ejpam-6968	332	8	,	,	PUNCT
ejpam-6968	332	9	2024	2024	NUM
ejpam-6968	332	10	.	.	PUNCT
ejpam-6968	333	1	[	[	X
ejpam-6968	333	2	24	24	NUM
ejpam-6968	333	3	]	]	PUNCT
ejpam-6968	333	4	z.	z.	PROPN
ejpam-6968	333	5	rashidi	rashidi	PROPN
ejpam-6968	333	6	,	,	PUNCT
ejpam-6968	333	7	s.	s.	PROPN
ejpam-6968	333	8	azizi	azizi	PROPN
ejpam-6968	333	9	,	,	PUNCT
ejpam-6968	333	10	and	and	CCONJ
ejpam-6968	333	11	o.	o.	PROPN
ejpam-6968	333	12	rahmani	rahmani	PROPN
ejpam-6968	333	13	.	.	PUNCT
ejpam-6968	334	1	period	period	NOUN
ejpam-6968	334	2	-	-	PUNCT
ejpam-6968	334	3	doubling	double	VERB
ejpam-6968	334	4	cascade	cascade	NOUN
ejpam-6968	334	5	route	route	NOUN
ejpam-6968	334	6	to	to	PART
ejpam-6968	334	7	chaos	chaos	VERB
ejpam-6968	334	8	in	in	ADP
ejpam-6968	334	9	an	an	DET
ejpam-6968	334	10	initially	initially	ADV
ejpam-6968	334	11	curved	curve	VERB
ejpam-6968	334	12	microbeam	microbeam	NOUN
ejpam-6968	334	13	resonator	resonator	NOUN
ejpam-6968	334	14	exposed	expose	VERB
ejpam-6968	334	15	to	to	ADP
ejpam-6968	334	16	fringing	fringe	VERB
ejpam-6968	334	17	-	-	PUNCT
ejpam-6968	334	18	field	field	NOUN
ejpam-6968	334	19	electrostatic	electrostatic	ADJ
ejpam-6968	334	20	actuation	actuation	NOUN
ejpam-6968	334	21	.	.	PUNCT
ejpam-6968	335	1	nonlinear	nonlinear	ADJ
ejpam-6968	335	2	dynamics	dynamic	NOUN
ejpam-6968	335	3	,	,	PUNCT
ejpam-6968	335	4	112:9915–9932	112:9915–9932	NUM
ejpam-6968	335	5	,	,	PUNCT
ejpam-6968	335	6	2024	2024	NUM
ejpam-6968	335	7	.	.	PUNCT
ejpam-6968	336	1	[	[	X
ejpam-6968	336	2	25	25	NUM
ejpam-6968	336	3	]	]	PUNCT
ejpam-6968	336	4	m.-f	m.-f	NOUN
ejpam-6968	336	5	.	.	PUNCT
ejpam-6968	336	6	danca	danca	PROPN
ejpam-6968	336	7	.	.	PUNCT
ejpam-6968	337	1	chaotic	chaotic	ADJ
ejpam-6968	337	2	hidden	hide	VERB
ejpam-6968	337	3	attractor	attractor	NOUN
ejpam-6968	337	4	in	in	ADP
ejpam-6968	337	5	a	a	DET
ejpam-6968	337	6	fractional	fractional	ADJ
ejpam-6968	337	7	order	order	NOUN
ejpam-6968	337	8	system	system	NOUN
ejpam-6968	337	9	modelling	model	VERB
ejpam-6968	337	10	the	the	DET
ejpam-6968	337	11	interaction	interaction	NOUN
ejpam-6968	337	12	between	between	ADP
ejpam-6968	337	13	dark	dark	ADJ
ejpam-6968	337	14	matter	matter	NOUN
ejpam-6968	337	15	and	and	CCONJ
ejpam-6968	337	16	dark	dark	ADJ
ejpam-6968	337	17	energy	energy	NOUN
ejpam-6968	337	18	.	.	PUNCT
ejpam-6968	338	1	communications	communication	NOUN
ejpam-6968	338	2	in	in	ADP
ejpam-6968	338	3	nonlinear	nonlinear	ADJ
ejpam-6968	338	4	science	science	NOUN
ejpam-6968	338	5	and	and	CCONJ
ejpam-6968	338	6	numerical	numerical	PROPN
ejpam-6968	338	7	simulation	simulation	PROPN
ejpam-6968	338	8	,	,	PUNCT
ejpam-6968	338	9	131:107838	131:107838	NUM
ejpam-6968	338	10	,	,	PUNCT
ejpam-6968	338	11	2024	2024	NUM
ejpam-6968	338	12	.	.	PUNCT
ejpam-6968	339	1	[	[	X
ejpam-6968	339	2	26	26	NUM
ejpam-6968	339	3	]	]	X
ejpam-6968	339	4	s.	s.	PROPN
ejpam-6968	339	5	roy	roy	PROPN
ejpam-6968	339	6	,	,	PUNCT
ejpam-6968	339	7	a.	a.	NOUN
ejpam-6968	339	8	ray	ray	PROPN
ejpam-6968	339	9	,	,	PUNCT
ejpam-6968	339	10	and	and	CCONJ
ejpam-6968	339	11	a.	a.	PROPN
ejpam-6968	339	12	roy	roy	PROPN
ejpam-6968	339	13	chowdhury	chowdhury	PROPN
ejpam-6968	339	14	.	.	PUNCT
ejpam-6968	340	1	kosambi	kosambi	PROPN
ejpam-6968	340	2	–	–	PUNCT
ejpam-6968	340	3	cartan	cartan	ADJ
ejpam-6968	340	4	–	–	PUNCT
ejpam-6968	340	5	chern	chern	ADJ
ejpam-6968	340	6	perspective	perspective	NOUN
ejpam-6968	340	7	on	on	ADP
ejpam-6968	340	8	chaos	chaos	NOUN
ejpam-6968	340	9	:	:	PUNCT
ejpam-6968	340	10	unveiling	unveil	VERB
ejpam-6968	340	11	hidden	hidden	ADJ
ejpam-6968	340	12	attractors	attractor	NOUN
ejpam-6968	340	13	in	in	ADP
ejpam-6968	340	14	nonlinear	nonlinear	ADJ
ejpam-6968	340	15	autonomous	autonomous	ADJ
ejpam-6968	340	16	systems	system	NOUN
ejpam-6968	340	17	.	.	PUNCT
ejpam-6968	341	1	physical	physical	ADJ
ejpam-6968	341	2	review	review	PROPN
ejpam-6968	341	3	e	e	NOUN
ejpam-6968	341	4	,	,	PUNCT
ejpam-6968	341	5	109:044205	109:044205	NUM
ejpam-6968	341	6	,	,	PUNCT
ejpam-6968	341	7	2024	2024	NUM
ejpam-6968	341	8	.	.	PUNCT
ejpam-6968	342	1	[	[	X
ejpam-6968	342	2	27	27	NUM
ejpam-6968	342	3	]	]	PUNCT
ejpam-6968	342	4	x.	x.	PROPN
ejpam-6968	342	5	hu	hu	PROPN
ejpam-6968	342	6	,	,	PUNCT
ejpam-6968	342	7	s.	s.	PROPN
ejpam-6968	342	8	wang	wang	PROPN
ejpam-6968	342	9	,	,	PUNCT
ejpam-6968	342	10	p.	p.	PROPN
ejpam-6968	342	11	wu	wu	PROPN
ejpam-6968	342	12	,	,	PUNCT
ejpam-6968	342	13	h.	h.	PROPN
ejpam-6968	342	14	cao	cao	PROPN
ejpam-6968	342	15	,	,	PUNCT
ejpam-6968	342	16	and	and	CCONJ
ejpam-6968	342	17	x.	x.	NOUN
ejpam-6968	342	18	zhang	zhang	PROPN
ejpam-6968	342	19	.	.	PUNCT
ejpam-6968	342	20	self	self	NOUN
ejpam-6968	342	21	-	-	PUNCT
ejpam-6968	342	22	excited	excite	VERB
ejpam-6968	342	23	and	and	CCONJ
ejpam-6968	342	24	hidden	hide	VERB
ejpam-6968	342	25	multi	multi	ADJ
ejpam-6968	342	26	-	-	ADJ
ejpam-6968	342	27	scroll	scroll	ADJ
ejpam-6968	342	28	attractors	attractor	NOUN
ejpam-6968	342	29	in	in	ADP
ejpam-6968	342	30	a	a	DET
ejpam-6968	342	31	novel	novel	NOUN
ejpam-6968	342	32	extremely	extremely	ADV
ejpam-6968	342	33	simple	simple	ADJ
ejpam-6968	342	34	three	three	NUM
ejpam-6968	342	35	-	-	PUNCT
ejpam-6968	342	36	dimensional	dimensional	ADJ
ejpam-6968	342	37	system	system	NOUN
ejpam-6968	342	38	.	.	PUNCT
ejpam-6968	343	1	chinese	chinese	ADJ
ejpam-6968	343	2	journal	journal	PROPN
ejpam-6968	343	3	of	of	ADP
ejpam-6968	343	4	physics	physics	PROPN
ejpam-6968	343	5	,	,	PUNCT
ejpam-6968	343	6	2025	2025	NUM
ejpam-6968	343	7	.	.	PUNCT
ejpam-6968	344	1	in	in	ADP
ejpam-6968	344	2	press	press	NOUN
ejpam-6968	344	3	.	.	PUNCT
ejpam-6968	345	1	[	[	X
ejpam-6968	345	2	28	28	NUM
ejpam-6968	345	3	]	]	X
ejpam-6968	345	4	v.	v.	CCONJ
ejpam-6968	345	5	varshney	varshney	NOUN
ejpam-6968	345	6	,	,	PUNCT
ejpam-6968	345	7	s.	s.	PROPN
ejpam-6968	345	8	leo	leo	PROPN
ejpam-6968	345	9	kingston	kingston	PROPN
ejpam-6968	345	10	,	,	PUNCT
ejpam-6968	345	11	s.	s.	PROPN
ejpam-6968	345	12	srinivasan	srinivasan	PROPN
ejpam-6968	345	13	,	,	PUNCT
ejpam-6968	345	14	and	and	CCONJ
ejpam-6968	345	15	s.	s.	PROPN
ejpam-6968	345	16	kumarasamy	kumarasamy	PROPN
ejpam-6968	345	17	.	.	PUNCT
ejpam-6968	346	1	hidden	hide	VERB
ejpam-6968	346	2	attractors	attractor	NOUN
ejpam-6968	346	3	in	in	ADP
ejpam-6968	346	4	fractional	fractional	ADJ
ejpam-6968	346	5	-	-	PUNCT
ejpam-6968	346	6	order	order	NOUN
ejpam-6968	346	7	discrete	discrete	ADJ
ejpam-6968	346	8	maps	map	NOUN
ejpam-6968	346	9	.	.	PUNCT
ejpam-6968	347	1	the	the	DET
ejpam-6968	347	2	european	european	PROPN
ejpam-6968	347	3	physical	physical	PROPN
ejpam-6968	347	4	journal	journal	PROPN
ejpam-6968	347	5	b	b	PROPN
ejpam-6968	347	6	,	,	PUNCT
ejpam-6968	347	7	97:161	97:161	NUM
ejpam-6968	347	8	,	,	PUNCT
ejpam-6968	347	9	2024	2024	NUM
ejpam-6968	347	10	.	.	PUNCT
ejpam-6968	348	1	[	[	X
ejpam-6968	348	2	29	29	NUM
ejpam-6968	348	3	]	]	PUNCT
ejpam-6968	348	4	a.	a.	NOUN
ejpam-6968	348	5	hastir	hastir	PROPN
ejpam-6968	348	6	and	and	CCONJ
ejpam-6968	348	7	r.	r.	PROPN
ejpam-6968	348	8	muolo	muolo	PROPN
ejpam-6968	348	9	.	.	PUNCT
ejpam-6968	349	1	a	a	DET
ejpam-6968	349	2	generalized	generalize	VERB
ejpam-6968	349	3	routh	routh	PROPN
ejpam-6968	349	4	–	–	PUNCT
ejpam-6968	349	5	hurwitz	hurwitz	PROPN
ejpam-6968	349	6	criterion	criterion	NOUN
ejpam-6968	349	7	for	for	ADP
ejpam-6968	349	8	the	the	DET
ejpam-6968	349	9	stability	stability	NOUN
ejpam-6968	349	10	analysis	analysis	NOUN
ejpam-6968	349	11	of	of	ADP
ejpam-6968	349	12	polynomials	polynomial	NOUN
ejpam-6968	349	13	with	with	ADP
ejpam-6968	349	14	complex	complex	ADJ
ejpam-6968	349	15	coefficients	coefficient	NOUN
ejpam-6968	349	16	:	:	PUNCT
ejpam-6968	349	17	application	application	NOUN
ejpam-6968	349	18	to	to	ADP
ejpam-6968	349	19	the	the	DET
ejpam-6968	349	20	pi	pi	NOUN
ejpam-6968	349	21	-	-	PUNCT
ejpam-6968	349	22	control	control	NOUN
ejpam-6968	349	23	of	of	ADP
ejpam-6968	349	24	vibrating	vibrate	VERB
ejpam-6968	349	25	structures	structure	NOUN
ejpam-6968	349	26	.	.	PUNCT
ejpam-6968	350	1	ifac	ifac	NOUN
ejpam-6968	350	2	journal	journal	NOUN
ejpam-6968	350	3	of	of	ADP
ejpam-6968	350	4	systems	system	NOUN
ejpam-6968	350	5	and	and	CCONJ
ejpam-6968	350	6	control	control	NOUN
ejpam-6968	350	7	,	,	PUNCT
ejpam-6968	350	8	26:100235	26:100235	NUM
ejpam-6968	350	9	,	,	PUNCT
ejpam-6968	350	10	2023	2023	NUM
ejpam-6968	350	11	.	.	PUNCT