id	sid	tid	token	lemma	pos
ejpam-5458	1	1	european	european	PROPN
ejpam-5458	1	2	journal	journal	PROPN
ejpam-5458	1	3	of	of	ADP
ejpam-5458	1	4	pure	pure	ADJ
ejpam-5458	1	5	and	and	CCONJ
ejpam-5458	1	6	applied	apply	VERB
ejpam-5458	1	7	mathematics	mathematic	NOUN
ejpam-5458	1	8	vol	vol	NOUN
ejpam-5458	1	9	.	.	PROPN
ejpam-5458	2	1	17	17	NUM
ejpam-5458	2	2	,	,	PUNCT
ejpam-5458	2	3	no	no	INTJ
ejpam-5458	2	4	.	.	NOUN
ejpam-5458	2	5	4	4	NUM
ejpam-5458	2	6	,	,	PUNCT
ejpam-5458	2	7	2024	2024	NUM
ejpam-5458	2	8	,	,	PUNCT
ejpam-5458	2	9	3708	3708	NUM
ejpam-5458	2	10	-	-	SYM
ejpam-5458	2	11	3729	3729	NUM
ejpam-5458	2	12	issn	issn	PROPN
ejpam-5458	2	13	1307	1307	NUM
ejpam-5458	2	14	-	-	SYM
ejpam-5458	2	15	5543	5543	NUM
ejpam-5458	2	16	–	–	PUNCT
ejpam-5458	2	17	ejpam.com	ejpam.com	X
ejpam-5458	2	18	published	publish	VERB
ejpam-5458	2	19	by	by	ADP
ejpam-5458	2	20	new	new	PROPN
ejpam-5458	2	21	york	york	PROPN
ejpam-5458	2	22	business	business	PROPN
ejpam-5458	2	23	global	global	ADJ
ejpam-5458	2	24	periodic	periodic	ADJ
ejpam-5458	2	25	solutions	solution	NOUN
ejpam-5458	2	26	and	and	CCONJ
ejpam-5458	2	27	bifurcations	bifurcation	NOUN
ejpam-5458	2	28	in	in	ADP
ejpam-5458	2	29	a	a	DET
ejpam-5458	2	30	long	long	ADJ
ejpam-5458	2	31	-	-	PUNCT
ejpam-5458	2	32	timescale	timescale	ADJ
ejpam-5458	2	33	oceanic	oceanic	ADJ
ejpam-5458	2	34	carbon	carbon	NOUN
ejpam-5458	2	35	cycle	cycle	NOUN
ejpam-5458	2	36	model	model	NOUN
ejpam-5458	2	37	ibrahim	ibrahim	PROPN
ejpam-5458	2	38	alraddadi	alraddadi	VERB
ejpam-5458	2	39	1	1	NUM
ejpam-5458	2	40	department	department	NOUN
ejpam-5458	2	41	of	of	ADP
ejpam-5458	2	42	mathematics	mathematic	NOUN
ejpam-5458	2	43	,	,	PUNCT
ejpam-5458	2	44	faculty	faculty	NOUN
ejpam-5458	2	45	of	of	ADP
ejpam-5458	2	46	science	science	NOUN
ejpam-5458	2	47	,	,	PUNCT
ejpam-5458	2	48	islamic	islamic	PROPN
ejpam-5458	2	49	university	university	PROPN
ejpam-5458	2	50	of	of	ADP
ejpam-5458	2	51	madinah	madinah	PROPN
ejpam-5458	2	52	,	,	PUNCT
ejpam-5458	2	53	medina	medina	PROPN
ejpam-5458	2	54	42210	42210	NUM
ejpam-5458	2	55	,	,	PUNCT
ejpam-5458	2	56	ksa	ksa	PROPN
ejpam-5458	2	57	abstract	abstract	NOUN
ejpam-5458	2	58	.	.	PUNCT
ejpam-5458	3	1	we	we	PRON
ejpam-5458	3	2	study	study	VERB
ejpam-5458	3	3	the	the	DET
ejpam-5458	3	4	dynamics	dynamic	NOUN
ejpam-5458	3	5	of	of	ADP
ejpam-5458	3	6	a	a	DET
ejpam-5458	3	7	recent	recent	ADJ
ejpam-5458	3	8	model	model	NOUN
ejpam-5458	3	9	of	of	ADP
ejpam-5458	3	10	rothman	rothman	PROPN
ejpam-5458	3	11	for	for	ADP
ejpam-5458	3	12	long	long	ADJ
ejpam-5458	3	13	timescale	timescale	ADJ
ejpam-5458	3	14	carbon	carbon	NOUN
ejpam-5458	3	15	cycle	cycle	NOUN
ejpam-5458	3	16	.	.	PUNCT
ejpam-5458	4	1	we	we	PRON
ejpam-5458	4	2	reproduce	reproduce	VERB
ejpam-5458	4	3	and	and	CCONJ
ejpam-5458	4	4	extend	extend	VERB
ejpam-5458	4	5	various	various	ADJ
ejpam-5458	4	6	results	result	NOUN
ejpam-5458	4	7	of	of	ADP
ejpam-5458	4	8	the	the	DET
ejpam-5458	4	9	rothman	rothman	PROPN
ejpam-5458	4	10	model	model	PROPN
ejpam-5458	4	11	.	.	PUNCT
ejpam-5458	5	1	we	we	PRON
ejpam-5458	5	2	present	present	VERB
ejpam-5458	5	3	numerical	numerical	ADJ
ejpam-5458	5	4	results	result	NOUN
ejpam-5458	5	5	showing	show	VERB
ejpam-5458	5	6	that	that	SCONJ
ejpam-5458	5	7	the	the	DET
ejpam-5458	5	8	model	model	NOUN
ejpam-5458	5	9	exhibits	exhibit	VERB
ejpam-5458	5	10	both	both	CCONJ
ejpam-5458	5	11	stable	stable	ADJ
ejpam-5458	5	12	and	and	CCONJ
ejpam-5458	5	13	unstable	unstable	ADJ
ejpam-5458	5	14	limit	limit	NOUN
ejpam-5458	5	15	cycles	cycle	NOUN
ejpam-5458	5	16	via	via	ADP
ejpam-5458	5	17	hopf	hopf	ADJ
ejpam-5458	5	18	bifurcations	bifurcation	NOUN
ejpam-5458	5	19	as	as	SCONJ
ejpam-5458	5	20	the	the	DET
ejpam-5458	5	21	parameters	parameter	NOUN
ejpam-5458	5	22	are	be	AUX
ejpam-5458	5	23	varied	varied	ADJ
ejpam-5458	5	24	.	.	PUNCT
ejpam-5458	6	1	we	we	PRON
ejpam-5458	6	2	numerically	numerically	ADV
ejpam-5458	6	3	find	find	VERB
ejpam-5458	6	4	normal	normal	ADJ
ejpam-5458	6	5	forms	form	NOUN
ejpam-5458	6	6	of	of	ADP
ejpam-5458	6	7	bautin	bautin	ADJ
ejpam-5458	6	8	bifurcations	bifurcation	NOUN
ejpam-5458	6	9	to	to	PART
ejpam-5458	6	10	confirm	confirm	VERB
ejpam-5458	6	11	their	their	PRON
ejpam-5458	6	12	criticality	criticality	NOUN
ejpam-5458	6	13	.	.	PUNCT
ejpam-5458	7	1	we	we	PRON
ejpam-5458	7	2	also	also	ADV
ejpam-5458	7	3	extend	extend	VERB
ejpam-5458	7	4	the	the	DET
ejpam-5458	7	5	analysis	analysis	NOUN
ejpam-5458	7	6	of	of	ADP
ejpam-5458	7	7	the	the	DET
ejpam-5458	7	8	normal	normal	ADJ
ejpam-5458	7	9	form	form	NOUN
ejpam-5458	7	10	coefficients	coefficient	NOUN
ejpam-5458	7	11	to	to	PART
ejpam-5458	7	12	identify	identify	VERB
ejpam-5458	7	13	where	where	SCONJ
ejpam-5458	7	14	the	the	DET
ejpam-5458	7	15	fold	fold	ADJ
ejpam-5458	7	16	limit	limit	NOUN
ejpam-5458	7	17	cycle	cycle	NOUN
ejpam-5458	7	18	bifurcation	bifurcation	NOUN
ejpam-5458	7	19	occurs	occur	VERB
ejpam-5458	7	20	2020	2020	NUM
ejpam-5458	7	21	mathematics	mathematic	NOUN
ejpam-5458	7	22	subject	subject	NOUN
ejpam-5458	7	23	classifications	classification	NOUN
ejpam-5458	7	24	:	:	PUNCT
ejpam-5458	7	25	34c23	34c23	NUM
ejpam-5458	7	26	,	,	PUNCT
ejpam-5458	7	27	37c25	37c25	NUM
ejpam-5458	7	28	,	,	PUNCT
ejpam-5458	7	29	37	37	NUM
ejpam-5458	7	30	-	-	SYM
ejpam-5458	7	31	04	04	NUM
ejpam-5458	7	32	,	,	PUNCT
ejpam-5458	7	33	37c35,3	37c35,3	NUM
ejpam-5458	7	34	4c25	4c25	NOUN
ejpam-5458	7	35	,	,	PUNCT
ejpam-5458	7	36	34c26	34c26	NUM
ejpam-5458	7	37	key	key	ADJ
ejpam-5458	7	38	words	word	NOUN
ejpam-5458	7	39	and	and	CCONJ
ejpam-5458	7	40	phrases	phrase	NOUN
ejpam-5458	7	41	:	:	PUNCT
ejpam-5458	7	42	dynamical	dynamical	ADJ
ejpam-5458	7	43	system	system	NOUN
ejpam-5458	7	44	,	,	PUNCT
ejpam-5458	7	45	periodic	periodic	ADJ
ejpam-5458	7	46	solutions	solution	NOUN
ejpam-5458	7	47	,	,	PUNCT
ejpam-5458	7	48	bifurcations	bifurcation	NOUN
ejpam-5458	7	49	1	1	NUM
ejpam-5458	7	50	.	.	PUNCT
ejpam-5458	8	1	introduction	introduction	NOUN
ejpam-5458	8	2	a	a	DET
ejpam-5458	8	3	modern	modern	ADJ
ejpam-5458	8	4	view	view	NOUN
ejpam-5458	8	5	of	of	ADP
ejpam-5458	8	6	climate	climate	NOUN
ejpam-5458	8	7	variability	variability	NOUN
ejpam-5458	8	8	represents	represent	VERB
ejpam-5458	8	9	a	a	DET
ejpam-5458	8	10	qualitative	qualitative	ADJ
ejpam-5458	8	11	change	change	NOUN
ejpam-5458	8	12	in	in	ADP
ejpam-5458	8	13	the	the	DET
ejpam-5458	8	14	dynamics	dynamic	NOUN
ejpam-5458	8	15	of	of	ADP
ejpam-5458	8	16	the	the	DET
ejpam-5458	8	17	earth	earth	NOUN
ejpam-5458	8	18	system	system	NOUN
ejpam-5458	8	19	as	as	SCONJ
ejpam-5458	8	20	shown	show	VERB
ejpam-5458	8	21	in	in	ADP
ejpam-5458	8	22	[	[	X
ejpam-5458	8	23	15	15	NUM
ejpam-5458	8	24	]	]	PUNCT
ejpam-5458	8	25	.	.	PUNCT
ejpam-5458	9	1	on	on	ADP
ejpam-5458	9	2	short	short	ADJ
ejpam-5458	9	3	time	time	NOUN
ejpam-5458	9	4	scales	scale	NOUN
ejpam-5458	9	5	,	,	PUNCT
ejpam-5458	9	6	the	the	DET
ejpam-5458	9	7	earth	earth	NOUN
ejpam-5458	9	8	’s	’s	PART
ejpam-5458	9	9	carbon	carbon	NOUN
ejpam-5458	9	10	cycles	cycle	NOUN
ejpam-5458	9	11	are	be	AUX
ejpam-5458	9	12	between	between	ADP
ejpam-5458	9	13	photosynthesis	photosynthesis	NOUN
ejpam-5458	9	14	,	,	PUNCT
ejpam-5458	9	15	which	which	PRON
ejpam-5458	9	16	converts	convert	VERB
ejpam-5458	9	17	carbon	carbon	NOUN
ejpam-5458	9	18	dioxide	dioxide	NOUN
ejpam-5458	9	19	(	(	PUNCT
ejpam-5458	9	20	co2	co2	NOUN
ejpam-5458	9	21	)	)	PUNCT
ejpam-5458	9	22	to	to	ADP
ejpam-5458	9	23	organic	organic	ADJ
ejpam-5458	9	24	carbon	carbon	NOUN
ejpam-5458	9	25	,	,	PUNCT
ejpam-5458	9	26	and	and	CCONJ
ejpam-5458	9	27	respiration	respiration	NOUN
ejpam-5458	9	28	,	,	PUNCT
ejpam-5458	9	29	which	which	PRON
ejpam-5458	9	30	converts	convert	VERB
ejpam-5458	9	31	organic	organic	ADJ
ejpam-5458	9	32	carbon	carbon	NOUN
ejpam-5458	9	33	back	back	ADV
ejpam-5458	9	34	to	to	ADP
ejpam-5458	9	35	co2	co2	NOUN
ejpam-5458	9	36	.	.	PUNCT
ejpam-5458	10	1	human	human	ADJ
ejpam-5458	10	2	activities	activity	NOUN
ejpam-5458	10	3	have	have	AUX
ejpam-5458	10	4	caused	cause	VERB
ejpam-5458	10	5	changes	change	NOUN
ejpam-5458	10	6	in	in	ADP
ejpam-5458	10	7	atmospheric	atmospheric	ADJ
ejpam-5458	10	8	co2	co2	NOUN
ejpam-5458	10	9	levels	level	NOUN
ejpam-5458	10	10	that	that	PRON
ejpam-5458	10	11	have	have	AUX
ejpam-5458	10	12	recently	recently	ADV
ejpam-5458	10	13	increased	increase	VERB
ejpam-5458	10	14	by	by	ADP
ejpam-5458	10	15	50	50	NUM
ejpam-5458	10	16	%	%	NOUN
ejpam-5458	10	17	compared	compare	VERB
ejpam-5458	10	18	to	to	ADP
ejpam-5458	10	19	the	the	DET
ejpam-5458	10	20	previous	previous	ADJ
ejpam-5458	10	21	years	year	NOUN
ejpam-5458	10	22	in	in	ADP
ejpam-5458	10	23	ages	age	NOUN
ejpam-5458	10	24	past	past	ADP
ejpam-5458	10	25	,	,	PUNCT
ejpam-5458	10	26	most	most	ADJ
ejpam-5458	10	27	of	of	ADP
ejpam-5458	10	28	which	which	PRON
ejpam-5458	10	29	has	have	AUX
ejpam-5458	10	30	been	be	AUX
ejpam-5458	10	31	absorbed	absorb	VERB
ejpam-5458	10	32	by	by	ADP
ejpam-5458	10	33	the	the	DET
ejpam-5458	10	34	oceans	ocean	NOUN
ejpam-5458	10	35	[	[	X
ejpam-5458	10	36	8	8	NUM
ejpam-5458	10	37	]	]	PUNCT
ejpam-5458	10	38	.	.	PUNCT
ejpam-5458	11	1	there	there	PRON
ejpam-5458	11	2	is	be	VERB
ejpam-5458	11	3	a	a	DET
ejpam-5458	11	4	lot	lot	NOUN
ejpam-5458	11	5	of	of	ADP
ejpam-5458	11	6	interest	interest	NOUN
ejpam-5458	11	7	in	in	ADP
ejpam-5458	11	8	forecasting	forecast	VERB
ejpam-5458	11	9	how	how	SCONJ
ejpam-5458	11	10	the	the	DET
ejpam-5458	11	11	climate	climate	NOUN
ejpam-5458	11	12	will	will	AUX
ejpam-5458	11	13	respond	respond	VERB
ejpam-5458	11	14	to	to	ADP
ejpam-5458	11	15	these	these	DET
ejpam-5458	11	16	changes	change	NOUN
ejpam-5458	11	17	,	,	PUNCT
ejpam-5458	11	18	as	as	SCONJ
ejpam-5458	11	19	shown	show	VERB
ejpam-5458	11	20	in	in	ADP
ejpam-5458	11	21	[	[	X
ejpam-5458	11	22	15	15	NUM
ejpam-5458	11	23	]	]	PUNCT
ejpam-5458	11	24	.	.	PUNCT
ejpam-5458	12	1	over	over	ADP
ejpam-5458	12	2	long	long	ADJ
ejpam-5458	12	3	timescales	timescale	NOUN
ejpam-5458	12	4	,	,	PUNCT
ejpam-5458	12	5	other	other	ADJ
ejpam-5458	12	6	reasons	reason	NOUN
ejpam-5458	12	7	of	of	ADP
ejpam-5458	12	8	carbon	carbon	NOUN
ejpam-5458	12	9	can	can	AUX
ejpam-5458	12	10	vary	vary	VERB
ejpam-5458	12	11	,	,	PUNCT
ejpam-5458	12	12	in	in	ADP
ejpam-5458	12	13	particular	particular	ADJ
ejpam-5458	12	14	in	in	ADP
ejpam-5458	12	15	the	the	DET
ejpam-5458	12	16	ocean	ocean	NOUN
ejpam-5458	12	17	.	.	PUNCT
ejpam-5458	13	1	significant	significant	ADJ
ejpam-5458	13	2	disruptions	disruption	NOUN
ejpam-5458	13	3	from	from	ADP
ejpam-5458	13	4	the	the	DET
ejpam-5458	13	5	global	global	ADJ
ejpam-5458	13	6	carbon	carbon	NOUN
ejpam-5458	13	7	cycle	cycle	NOUN
ejpam-5458	13	8	are	be	AUX
ejpam-5458	13	9	caused	cause	VERB
ejpam-5458	13	10	by	by	ADP
ejpam-5458	13	11	the	the	DET
ejpam-5458	13	12	changes	change	NOUN
ejpam-5458	13	13	in	in	ADP
ejpam-5458	13	14	the	the	DET
ejpam-5458	13	15	concentration	concentration	NOUN
ejpam-5458	13	16	of	of	ADP
ejpam-5458	13	17	carbon	carbon	NOUN
ejpam-5458	13	18	in	in	ADP
ejpam-5458	13	19	the	the	DET
ejpam-5458	13	20	ocean	ocean	NOUN
ejpam-5458	13	21	.	.	PUNCT
ejpam-5458	14	1	rothman	rothman	PROPN
ejpam-5458	15	1	[	[	X
ejpam-5458	15	2	12	12	NUM
ejpam-5458	15	3	]	]	PUNCT
ejpam-5458	15	4	studied	study	VERB
ejpam-5458	15	5	the	the	DET
ejpam-5458	15	6	evolution	evolution	NOUN
ejpam-5458	15	7	of	of	ADP
ejpam-5458	15	8	the	the	DET
ejpam-5458	15	9	carbonate	carbonate	NOUN
ejpam-5458	15	10	system	system	NOUN
ejpam-5458	15	11	in	in	ADP
ejpam-5458	15	12	the	the	DET
ejpam-5458	15	13	upper	upper	ADJ
ejpam-5458	15	14	ocean	ocean	NOUN
ejpam-5458	15	15	as	as	ADP
ejpam-5458	15	16	part	part	NOUN
ejpam-5458	15	17	of	of	ADP
ejpam-5458	15	18	the	the	DET
ejpam-5458	15	19	marine	marine	ADJ
ejpam-5458	15	20	carbon	carbon	NOUN
ejpam-5458	15	21	cycle	cycle	NOUN
ejpam-5458	15	22	.	.	PUNCT
ejpam-5458	16	1	these	these	DET
ejpam-5458	16	2	changes	change	NOUN
ejpam-5458	16	3	affect	affect	VERB
ejpam-5458	16	4	the	the	DET
ejpam-5458	16	5	marine	marine	ADJ
ejpam-5458	16	6	carbonate	carbonate	NOUN
ejpam-5458	16	7	system	system	NOUN
ejpam-5458	16	8	,	,	PUNCT
ejpam-5458	16	9	which	which	PRON
ejpam-5458	16	10	is	be	AUX
ejpam-5458	16	11	a	a	DET
ejpam-5458	16	12	major	major	ADJ
ejpam-5458	16	13	element	element	NOUN
ejpam-5458	16	14	of	of	ADP
ejpam-5458	16	15	fundamental	fundamental	ADJ
ejpam-5458	16	16	importance	importance	NOUN
ejpam-5458	16	17	to	to	ADP
ejpam-5458	16	18	the	the	DET
ejpam-5458	16	19	earth	earth	NOUN
ejpam-5458	16	20	’s	’s	PART
ejpam-5458	16	21	carbon	carbon	NOUN
ejpam-5458	16	22	cycle	cycle	NOUN
ejpam-5458	16	23	.	.	PUNCT
ejpam-5458	17	1	environmental	environmental	ADJ
ejpam-5458	17	2	perturbations	perturbation	NOUN
ejpam-5458	17	3	can	can	AUX
ejpam-5458	17	4	significantly	significantly	ADV
ejpam-5458	17	5	result	result	VERB
ejpam-5458	17	6	in	in	ADP
ejpam-5458	17	7	considerable	considerable	ADJ
ejpam-5458	17	8	disruptions	disruption	NOUN
ejpam-5458	17	9	in	in	ADP
ejpam-5458	17	10	the	the	DET
ejpam-5458	17	11	earth	earth	NOUN
ejpam-5458	17	12	’s	’s	PART
ejpam-5458	17	13	carbon	carbon	NOUN
ejpam-5458	17	14	cycle	cycle	NOUN
ejpam-5458	17	15	.	.	PUNCT
ejpam-5458	18	1	to	to	PART
ejpam-5458	18	2	understand	understand	VERB
ejpam-5458	18	3	these	these	DET
ejpam-5458	18	4	observations	observation	NOUN
ejpam-5458	18	5	,	,	PUNCT
ejpam-5458	18	6	rothman	rothman	PROPN
ejpam-5458	19	1	[	[	X
ejpam-5458	19	2	12	12	NUM
ejpam-5458	19	3	]	]	PUNCT
ejpam-5458	19	4	suggested	suggest	VERB
ejpam-5458	19	5	a	a	DET
ejpam-5458	19	6	mathematical	mathematical	ADJ
ejpam-5458	19	7	model	model	NOUN
ejpam-5458	19	8	to	to	PART
ejpam-5458	19	9	describe	describe	VERB
ejpam-5458	19	10	the	the	DET
ejpam-5458	19	11	characteristic	characteristic	ADJ
ejpam-5458	19	12	rate	rate	NOUN
ejpam-5458	19	13	of	of	ADP
ejpam-5458	19	14	change	change	NOUN
ejpam-5458	19	15	in	in	ADP
ejpam-5458	19	16	the	the	DET
ejpam-5458	19	17	marine	marine	ADJ
ejpam-5458	19	18	carbon	carbon	NOUN
ejpam-5458	19	19	cycle	cycle	NOUN
ejpam-5458	19	20	.	.	PUNCT
ejpam-5458	20	1	this	this	DET
ejpam-5458	20	2	model	model	NOUN
ejpam-5458	20	3	formed	form	VERB
ejpam-5458	20	4	doi	doi	PROPN
ejpam-5458	20	5	:	:	PUNCT
ejpam-5458	20	6	https://doi.org/10.29020/nybg.ejpam.v17i4.5458	https://doi.org/10.29020/nybg.ejpam.v17i4.5458	PROPN
ejpam-5458	20	7	email	email	NOUN
ejpam-5458	20	8	address	address	NOUN
ejpam-5458	20	9	:	:	PUNCT
ejpam-5458	20	10	ialraddadi@iu.edu.sa	ialraddadi@iu.edu.sa	PROPN
ejpam-5458	20	11	(	(	PUNCT
ejpam-5458	20	12	i.	i.	NOUN
ejpam-5458	20	13	alraddadi	alraddadi	PROPN
ejpam-5458	20	14	)	)	PUNCT
ejpam-5458	20	15	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5458	20	16	3708	3708	NUM
ejpam-5458	20	17	copyright	copyright	NOUN
ejpam-5458	20	18	:	:	PUNCT
ejpam-5458	20	19	©	©	PROPN
ejpam-5458	20	20	2024	2024	NUM
ejpam-5458	20	21	the	the	DET
ejpam-5458	20	22	author(s	author(s	NOUN
ejpam-5458	20	23	)	)	PUNCT
ejpam-5458	20	24	.	.	PUNCT
ejpam-5458	21	1	(	(	PUNCT
ejpam-5458	21	2	cc	cc	NOUN
ejpam-5458	21	3	by	by	ADP
ejpam-5458	21	4	-	-	PUNCT
ejpam-5458	21	5	nc	nc	PROPN
ejpam-5458	21	6	4.0	4.0	NUM
ejpam-5458	21	7	)	)	PUNCT
ejpam-5458	21	8	i.	i.	NOUN
ejpam-5458	21	9	alraddadi	alraddadi	PROPN
ejpam-5458	21	10	/	/	SYM
ejpam-5458	21	11	eur	eur	PROPN
ejpam-5458	21	12	.	.	PUNCT
ejpam-5458	22	1	j.	j.	PROPN
ejpam-5458	22	2	pure	pure	PROPN
ejpam-5458	22	3	appl	appl	PROPN
ejpam-5458	22	4	.	.	PROPN
ejpam-5458	22	5	math	math	PROPN
ejpam-5458	22	6	,	,	PUNCT
ejpam-5458	22	7	17	17	NUM
ejpam-5458	22	8	(	(	PUNCT
ejpam-5458	22	9	4	4	NUM
ejpam-5458	22	10	)	)	PUNCT
ejpam-5458	22	11	(	(	PUNCT
ejpam-5458	22	12	2024	2024	NUM
ejpam-5458	22	13	)	)	PUNCT
ejpam-5458	22	14	,	,	PUNCT
ejpam-5458	22	15	3708	3708	NUM
ejpam-5458	22	16	-	-	SYM
ejpam-5458	22	17	3729	3729	NUM
ejpam-5458	22	18	3709	3709	NUM
ejpam-5458	22	19	as	as	ADP
ejpam-5458	22	20	a	a	DET
ejpam-5458	22	21	two	two	NUM
ejpam-5458	22	22	-	-	PUNCT
ejpam-5458	22	23	equation	equation	NOUN
ejpam-5458	22	24	dynamical	dynamical	ADJ
ejpam-5458	22	25	system	system	NOUN
ejpam-5458	22	26	to	to	PART
ejpam-5458	22	27	describe	describe	VERB
ejpam-5458	22	28	the	the	DET
ejpam-5458	22	29	dynamics	dynamic	NOUN
ejpam-5458	22	30	of	of	ADP
ejpam-5458	22	31	carbon	carbon	NOUN
ejpam-5458	22	32	and	and	CCONJ
ejpam-5458	22	33	the	the	DET
ejpam-5458	22	34	response	response	NOUN
ejpam-5458	22	35	feedback	feedback	NOUN
ejpam-5458	22	36	mechanisms	mechanism	NOUN
ejpam-5458	22	37	of	of	ADP
ejpam-5458	22	38	shallow	shallow	NOUN
ejpam-5458	22	39	-	-	PUNCT
ejpam-5458	22	40	oceans	ocean	NOUN
ejpam-5458	22	41	in	in	ADP
ejpam-5458	22	42	the	the	DET
ejpam-5458	22	43	marine	marine	ADJ
ejpam-5458	22	44	carbon	carbon	NOUN
ejpam-5458	22	45	cycle	cycle	NOUN
ejpam-5458	22	46	.	.	PUNCT
ejpam-5458	23	1	rothman	rothman	PROPN
ejpam-5458	23	2	’s	’s	PART
ejpam-5458	23	3	carbon	carbon	NOUN
ejpam-5458	23	4	cycle	cycle	NOUN
ejpam-5458	23	5	model	model	NOUN
ejpam-5458	23	6	builds	build	VERB
ejpam-5458	23	7	upon	upon	SCONJ
ejpam-5458	23	8	a	a	DET
ejpam-5458	23	9	foundation	foundation	NOUN
ejpam-5458	23	10	of	of	ADP
ejpam-5458	23	11	dynamical	dynamical	ADJ
ejpam-5458	23	12	systems	system	NOUN
ejpam-5458	23	13	approaches	approach	NOUN
ejpam-5458	23	14	in	in	ADP
ejpam-5458	23	15	climate	climate	NOUN
ejpam-5458	23	16	science	science	NOUN
ejpam-5458	23	17	.	.	PUNCT
ejpam-5458	24	1	recent	recent	ADJ
ejpam-5458	24	2	work	work	NOUN
ejpam-5458	24	3	by	by	ADP
ejpam-5458	24	4	crucifix	crucifix	NOUN
ejpam-5458	25	1	[	[	X
ejpam-5458	25	2	1	1	NUM
ejpam-5458	25	3	]	]	PUNCT
ejpam-5458	25	4	on	on	ADP
ejpam-5458	25	5	oscillators	oscillator	NOUN
ejpam-5458	25	6	and	and	CCONJ
ejpam-5458	25	7	relaxation	relaxation	NOUN
ejpam-5458	25	8	phenomena	phenomenon	NOUN
ejpam-5458	25	9	in	in	ADP
ejpam-5458	25	10	pleistocene	pleistocene	NOUN
ejpam-5458	25	11	climate	climate	NOUN
ejpam-5458	25	12	theory	theory	NOUN
ejpam-5458	25	13	provides	provide	VERB
ejpam-5458	25	14	context	context	NOUN
ejpam-5458	25	15	for	for	ADP
ejpam-5458	25	16	understanding	understand	VERB
ejpam-5458	25	17	the	the	DET
ejpam-5458	25	18	significance	significance	NOUN
ejpam-5458	25	19	of	of	ADP
ejpam-5458	25	20	rothman	rothman	PROPN
ejpam-5458	25	21	’s	’s	PART
ejpam-5458	25	22	model	model	NOUN
ejpam-5458	25	23	in	in	ADP
ejpam-5458	25	24	capturing	capture	VERB
ejpam-5458	25	25	complex	complex	ADJ
ejpam-5458	25	26	carbon	carbon	NOUN
ejpam-5458	25	27	cycle	cycle	NOUN
ejpam-5458	25	28	dynamics	dynamic	NOUN
ejpam-5458	25	29	.	.	PUNCT
ejpam-5458	26	1	additionally	additionally	ADV
ejpam-5458	26	2	,	,	PUNCT
ejpam-5458	26	3	lenton	lenton	PROPN
ejpam-5458	26	4	et	et	PROPN
ejpam-5458	26	5	al	al	PROPN
ejpam-5458	26	6	.	.	PUNCT
ejpam-5458	27	1	[	[	X
ejpam-5458	27	2	5	5	NUM
ejpam-5458	27	3	]	]	PUNCT
ejpam-5458	27	4	introduced	introduce	VERB
ejpam-5458	27	5	the	the	DET
ejpam-5458	27	6	concept	concept	NOUN
ejpam-5458	27	7	of	of	ADP
ejpam-5458	27	8	tipping	tip	VERB
ejpam-5458	27	9	elements	element	NOUN
ejpam-5458	27	10	in	in	ADP
ejpam-5458	27	11	the	the	DET
ejpam-5458	27	12	earth	earth	NOUN
ejpam-5458	27	13	system	system	NOUN
ejpam-5458	27	14	,	,	PUNCT
ejpam-5458	27	15	many	many	ADJ
ejpam-5458	27	16	of	of	ADP
ejpam-5458	27	17	which	which	PRON
ejpam-5458	27	18	involve	involve	VERB
ejpam-5458	27	19	the	the	DET
ejpam-5458	27	20	carbon	carbon	NOUN
ejpam-5458	27	21	cycle	cycle	NOUN
ejpam-5458	27	22	,	,	PUNCT
ejpam-5458	27	23	underscoring	underscore	VERB
ejpam-5458	27	24	the	the	DET
ejpam-5458	27	25	importance	importance	NOUN
ejpam-5458	27	26	of	of	ADP
ejpam-5458	27	27	identifying	identify	VERB
ejpam-5458	27	28	critical	critical	ADJ
ejpam-5458	27	29	thresholds	threshold	NOUN
ejpam-5458	27	30	and	and	CCONJ
ejpam-5458	27	31	bifurcations	bifurcation	NOUN
ejpam-5458	27	32	in	in	ADP
ejpam-5458	27	33	climate	climate	NOUN
ejpam-5458	27	34	models	model	NOUN
ejpam-5458	27	35	.	.	PUNCT
ejpam-5458	28	1	the	the	DET
ejpam-5458	28	2	theory	theory	NOUN
ejpam-5458	28	3	of	of	ADP
ejpam-5458	28	4	dynamical	dynamical	ADJ
ejpam-5458	28	5	systems	system	NOUN
ejpam-5458	28	6	provides	provide	VERB
ejpam-5458	28	7	many	many	ADJ
ejpam-5458	28	8	useful	useful	ADJ
ejpam-5458	28	9	techniques	technique	NOUN
ejpam-5458	28	10	to	to	PART
ejpam-5458	28	11	analyse	analyse	VERB
ejpam-5458	28	12	the	the	DET
ejpam-5458	28	13	observed	observe	VERB
ejpam-5458	28	14	behaviour	behaviour	NOUN
ejpam-5458	28	15	of	of	ADP
ejpam-5458	28	16	the	the	DET
ejpam-5458	28	17	model	model	NOUN
ejpam-5458	28	18	,	,	PUNCT
ejpam-5458	28	19	such	such	ADJ
ejpam-5458	28	20	as	as	ADP
ejpam-5458	28	21	bifurcation	bifurcation	NOUN
ejpam-5458	28	22	phenomena	phenomenon	NOUN
ejpam-5458	28	23	.	.	PUNCT
ejpam-5458	29	1	this	this	DET
ejpam-5458	29	2	approach	approach	NOUN
ejpam-5458	29	3	can	can	AUX
ejpam-5458	29	4	help	help	VERB
ejpam-5458	29	5	us	we	PRON
ejpam-5458	29	6	to	to	PART
ejpam-5458	29	7	understand	understand	VERB
ejpam-5458	29	8	the	the	DET
ejpam-5458	29	9	important	important	ADJ
ejpam-5458	29	10	features	feature	NOUN
ejpam-5458	29	11	of	of	ADP
ejpam-5458	29	12	the	the	DET
ejpam-5458	29	13	marine	marine	ADJ
ejpam-5458	29	14	carbonate	carbonate	NOUN
ejpam-5458	29	15	system	system	NOUN
ejpam-5458	29	16	.	.	PUNCT
ejpam-5458	30	1	in	in	ADP
ejpam-5458	30	2	this	this	DET
ejpam-5458	30	3	article	article	NOUN
ejpam-5458	30	4	presents	present	VERB
ejpam-5458	30	5	a	a	DET
ejpam-5458	30	6	study	study	NOUN
ejpam-5458	30	7	of	of	ADP
ejpam-5458	30	8	oscillations	oscillation	NOUN
ejpam-5458	30	9	in	in	ADP
ejpam-5458	30	10	a	a	DET
ejpam-5458	30	11	long	long	ADJ
ejpam-5458	30	12	-	-	PUNCT
ejpam-5458	30	13	timescale	timescale	NOUN
ejpam-5458	30	14	carbon	carbon	NOUN
ejpam-5458	30	15	cycle	cycle	NOUN
ejpam-5458	30	16	model	model	NOUN
ejpam-5458	30	17	(	(	PUNCT
ejpam-5458	30	18	7	7	X
ejpam-5458	30	19	)	)	PUNCT
ejpam-5458	30	20	introduced	introduce	VERB
ejpam-5458	30	21	by	by	ADP
ejpam-5458	30	22	rothman	rothman	PROPN
ejpam-5458	30	23	[	[	X
ejpam-5458	30	24	12	12	NUM
ejpam-5458	30	25	]	]	PUNCT
ejpam-5458	30	26	.	.	PUNCT
ejpam-5458	31	1	we	we	PRON
ejpam-5458	31	2	briefly	briefly	ADV
ejpam-5458	31	3	introduce	introduce	VERB
ejpam-5458	31	4	the	the	DET
ejpam-5458	31	5	carbon	carbon	NOUN
ejpam-5458	31	6	cycle	cycle	NOUN
ejpam-5458	31	7	model	model	NOUN
ejpam-5458	31	8	,	,	PUNCT
ejpam-5458	31	9	analyse	analyse	VERB
ejpam-5458	31	10	the	the	DET
ejpam-5458	31	11	stability	stability	NOUN
ejpam-5458	31	12	of	of	ADP
ejpam-5458	31	13	the	the	DET
ejpam-5458	31	14	equilibrium	equilibrium	NOUN
ejpam-5458	31	15	point	point	NOUN
ejpam-5458	31	16	and	and	CCONJ
ejpam-5458	31	17	show	show	VERB
ejpam-5458	31	18	the	the	DET
ejpam-5458	31	19	region	region	NOUN
ejpam-5458	31	20	of	of	ADP
ejpam-5458	31	21	stability	stability	NOUN
ejpam-5458	31	22	in	in	ADP
ejpam-5458	31	23	parameter	parameter	NOUN
ejpam-5458	31	24	space	space	NOUN
ejpam-5458	31	25	.	.	PUNCT
ejpam-5458	32	1	we	we	PRON
ejpam-5458	32	2	present	present	VERB
ejpam-5458	32	3	numerical	numerical	ADJ
ejpam-5458	32	4	results	result	NOUN
ejpam-5458	32	5	showing	show	VERB
ejpam-5458	32	6	that	that	SCONJ
ejpam-5458	32	7	the	the	DET
ejpam-5458	32	8	model	model	NOUN
ejpam-5458	32	9	exhibits	exhibit	VERB
ejpam-5458	32	10	both	both	CCONJ
ejpam-5458	32	11	stable	stable	ADJ
ejpam-5458	32	12	and	and	CCONJ
ejpam-5458	32	13	unstable	unstable	ADJ
ejpam-5458	32	14	limit	limit	NOUN
ejpam-5458	32	15	cycles	cycle	NOUN
ejpam-5458	32	16	via	via	ADP
ejpam-5458	32	17	hopf	hopf	ADJ
ejpam-5458	32	18	bifurcations	bifurcation	NOUN
ejpam-5458	32	19	as	as	SCONJ
ejpam-5458	32	20	the	the	DET
ejpam-5458	32	21	parameters	parameter	NOUN
ejpam-5458	32	22	are	be	AUX
ejpam-5458	32	23	varied	varied	ADJ
ejpam-5458	32	24	.	.	PUNCT
ejpam-5458	33	1	we	we	PRON
ejpam-5458	33	2	study	study	VERB
ejpam-5458	33	3	the	the	DET
ejpam-5458	33	4	normal	normal	ADJ
ejpam-5458	33	5	form	form	NOUN
ejpam-5458	33	6	of	of	ADP
ejpam-5458	33	7	hopf	hopf	ADJ
ejpam-5458	33	8	and	and	CCONJ
ejpam-5458	33	9	bautin	bautin	ADJ
ejpam-5458	33	10	bifurcations	bifurcation	NOUN
ejpam-5458	33	11	for	for	ADP
ejpam-5458	33	12	rothman	rothman	PROPN
ejpam-5458	33	13	’s	’s	PART
ejpam-5458	33	14	carbon	carbon	NOUN
ejpam-5458	33	15	cycle	cycle	NOUN
ejpam-5458	33	16	model	model	NOUN
ejpam-5458	33	17	(	(	PUNCT
ejpam-5458	33	18	7	7	NUM
ejpam-5458	33	19	)	)	PUNCT
ejpam-5458	33	20	.	.	PUNCT
ejpam-5458	34	1	we	we	PRON
ejpam-5458	34	2	review	review	VERB
ejpam-5458	34	3	the	the	DET
ejpam-5458	34	4	technique	technique	NOUN
ejpam-5458	34	5	for	for	ADP
ejpam-5458	34	6	computing	compute	VERB
ejpam-5458	34	7	lyapunov	lyapunov	ADJ
ejpam-5458	34	8	coefficients	coefficient	NOUN
ejpam-5458	34	9	.	.	PUNCT
ejpam-5458	35	1	we	we	PRON
ejpam-5458	35	2	use	use	VERB
ejpam-5458	35	3	maple	maple	NOUN
ejpam-5458	35	4	to	to	PART
ejpam-5458	35	5	compute	compute	VERB
ejpam-5458	35	6	the	the	DET
ejpam-5458	35	7	first	first	ADJ
ejpam-5458	35	8	and	and	CCONJ
ejpam-5458	35	9	second	second	ADJ
ejpam-5458	35	10	lyapunov	lyapunov	ADJ
ejpam-5458	35	11	coefficients	coefficient	VERB
ejpam-5458	35	12	l1	l1	PROPN
ejpam-5458	35	13	and	and	CCONJ
ejpam-5458	35	14	l2	l2	NOUN
ejpam-5458	35	15	in	in	ADP
ejpam-5458	35	16	the	the	DET
ejpam-5458	35	17	normal	normal	ADJ
ejpam-5458	35	18	form	form	NOUN
ejpam-5458	35	19	at	at	ADP
ejpam-5458	35	20	a	a	DET
ejpam-5458	35	21	bifurcation	bifurcation	NOUN
ejpam-5458	35	22	point	point	NOUN
ejpam-5458	35	23	where	where	SCONJ
ejpam-5458	35	24	l0	l0	NOUN
ejpam-5458	35	25	=	=	NOUN
ejpam-5458	35	26	0	0	X
ejpam-5458	35	27	.	.	PUNCT
ejpam-5458	36	1	we	we	PRON
ejpam-5458	36	2	also	also	ADV
ejpam-5458	36	3	extend	extend	VERB
ejpam-5458	36	4	the	the	DET
ejpam-5458	36	5	analysis	analysis	NOUN
ejpam-5458	36	6	of	of	ADP
ejpam-5458	36	7	the	the	DET
ejpam-5458	36	8	normal	normal	ADJ
ejpam-5458	36	9	form	form	NOUN
ejpam-5458	36	10	coefficients	coefficient	NOUN
ejpam-5458	36	11	to	to	PART
ejpam-5458	36	12	identify	identify	VERB
ejpam-5458	36	13	where	where	SCONJ
ejpam-5458	36	14	the	the	DET
ejpam-5458	36	15	fold	fold	ADJ
ejpam-5458	36	16	limit	limit	NOUN
ejpam-5458	36	17	cycle	cycle	NOUN
ejpam-5458	36	18	bifurcation	bifurcation	NOUN
ejpam-5458	36	19	occurs	occur	VERB
ejpam-5458	36	20	.	.	PUNCT
ejpam-5458	37	1	2	2	X
ejpam-5458	37	2	.	.	X
ejpam-5458	37	3	rothman	rothman	PROPN
ejpam-5458	37	4	’s	’s	PART
ejpam-5458	37	5	carbon	carbon	NOUN
ejpam-5458	37	6	cycle	cycle	NOUN
ejpam-5458	37	7	model	model	NOUN
ejpam-5458	37	8	a	a	DET
ejpam-5458	37	9	model	model	NOUN
ejpam-5458	37	10	of	of	ADP
ejpam-5458	37	11	the	the	DET
ejpam-5458	37	12	marine	marine	ADJ
ejpam-5458	37	13	carbon	carbon	NOUN
ejpam-5458	37	14	cycle	cycle	NOUN
ejpam-5458	37	15	illustrates	illustrate	VERB
ejpam-5458	37	16	the	the	DET
ejpam-5458	37	17	interactions	interaction	NOUN
ejpam-5458	37	18	of	of	ADP
ejpam-5458	37	19	shallow	shallow	ADJ
ejpam-5458	37	20	-	-	PUNCT
ejpam-5458	37	21	ocean	ocean	NOUN
ejpam-5458	37	22	respiration	respiration	NOUN
ejpam-5458	37	23	with	with	ADP
ejpam-5458	37	24	fluxes	flux	NOUN
ejpam-5458	37	25	of	of	ADP
ejpam-5458	37	26	carbon	carbon	NOUN
ejpam-5458	37	27	into	into	ADP
ejpam-5458	37	28	and	and	CCONJ
ejpam-5458	37	29	out	out	ADP
ejpam-5458	37	30	of	of	ADP
ejpam-5458	37	31	the	the	DET
ejpam-5458	37	32	shallow	shallow	ADJ
ejpam-5458	37	33	ocean	ocean	NOUN
ejpam-5458	37	34	.	.	PUNCT
ejpam-5458	38	1	we	we	PRON
ejpam-5458	38	2	consider	consider	VERB
ejpam-5458	38	3	the	the	DET
ejpam-5458	38	4	upper	upper	ADJ
ejpam-5458	38	5	ocean	ocean	NOUN
ejpam-5458	38	6	to	to	PART
ejpam-5458	38	7	be	be	AUX
ejpam-5458	38	8	a	a	DET
ejpam-5458	38	9	well	well	ADV
ejpam-5458	38	10	-	-	PUNCT
ejpam-5458	38	11	mixed	mix	VERB
ejpam-5458	38	12	open	open	ADJ
ejpam-5458	38	13	system	system	NOUN
ejpam-5458	38	14	.	.	PUNCT
ejpam-5458	39	1	the	the	DET
ejpam-5458	39	2	main	main	ADJ
ejpam-5458	39	3	carbonate	carbonate	NOUN
ejpam-5458	39	4	input	input	NOUN
ejpam-5458	39	5	is	be	AUX
ejpam-5458	39	6	dissolved	dissolve	VERB
ejpam-5458	39	7	calcium	calcium	NOUN
ejpam-5458	39	8	carbonate	carbonate	NOUN
ejpam-5458	39	9	(	(	PUNCT
ejpam-5458	39	10	caco3	caco3	NOUN
ejpam-5458	39	11	)	)	PUNCT
ejpam-5458	39	12	which	which	PRON
ejpam-5458	39	13	is	be	AUX
ejpam-5458	39	14	transported	transport	VERB
ejpam-5458	39	15	to	to	ADP
ejpam-5458	39	16	the	the	DET
ejpam-5458	39	17	shallow	shallow	ADJ
ejpam-5458	39	18	ocean	ocean	NOUN
ejpam-5458	39	19	by	by	ADP
ejpam-5458	39	20	rivers	river	NOUN
ejpam-5458	39	21	and	and	CCONJ
ejpam-5458	39	22	the	the	DET
ejpam-5458	39	23	output	output	NOUN
ejpam-5458	39	24	from	from	ADP
ejpam-5458	39	25	the	the	DET
ejpam-5458	39	26	shallow	shallow	ADJ
ejpam-5458	39	27	ocean	ocean	NOUN
ejpam-5458	39	28	to	to	ADP
ejpam-5458	39	29	the	the	DET
ejpam-5458	39	30	sediments	sediment	NOUN
ejpam-5458	39	31	.	.	PUNCT
ejpam-5458	40	1	rothman	rothman	PROPN
ejpam-5458	40	2	’s	’s	PART
ejpam-5458	40	3	carbon	carbon	NOUN
ejpam-5458	40	4	cycle	cycle	NOUN
ejpam-5458	40	5	model	model	NOUN
ejpam-5458	40	6	builds	build	VERB
ejpam-5458	40	7	upon	upon	SCONJ
ejpam-5458	40	8	his	his	PRON
ejpam-5458	40	9	previous	previous	ADJ
ejpam-5458	40	10	studies	study	NOUN
ejpam-5458	40	11	on	on	ADP
ejpam-5458	40	12	carbon	carbon	NOUN
ejpam-5458	40	13	cycle	cycle	NOUN
ejpam-5458	40	14	dynamics	dynamic	NOUN
ejpam-5458	40	15	[	[	X
ejpam-5458	40	16	10	10	NUM
ejpam-5458	40	17	,	,	PUNCT
ejpam-5458	40	18	11	11	NUM
ejpam-5458	40	19	,	,	PUNCT
ejpam-5458	40	20	13	13	NUM
ejpam-5458	40	21	]	]	PUNCT
ejpam-5458	40	22	.	.	PUNCT
ejpam-5458	41	1	the	the	DET
ejpam-5458	41	2	system	system	NOUN
ejpam-5458	41	3	can	can	AUX
ejpam-5458	41	4	be	be	AUX
ejpam-5458	41	5	written	write	VERB
ejpam-5458	41	6	in	in	ADP
ejpam-5458	41	7	the	the	DET
ejpam-5458	41	8	following	following	ADJ
ejpam-5458	41	9	mathematical	mathematical	ADJ
ejpam-5458	41	10	form	form	NOUN
ejpam-5458	41	11	[	[	X
ejpam-5458	41	12	12	12	NUM
ejpam-5458	41	13	]	]	X
ejpam-5458	41	14	:	:	PUNCT
ejpam-5458	42	1	ȧ	ȧ	PROPN
ejpam-5458	42	2	=	=	PROPN
ejpam-5458	42	3	2[jin	2[jin	NUM
ejpam-5458	42	4	−b(a	−b(a	NOUN
ejpam-5458	42	5	,	,	PUNCT
ejpam-5458	42	6	w	w	NOUN
ejpam-5458	42	7	)	)	PUNCT
ejpam-5458	42	8	]	]	PUNCT
ejpam-5458	42	9	,	,	PUNCT
ejpam-5458	42	10	ẇ	ẇ	PROPN
ejpam-5458	42	11	=	=	SYM
ejpam-5458	42	12	(	(	PUNCT
ejpam-5458	42	13	1	1	NUM
ejpam-5458	42	14	+	+	CCONJ
ejpam-5458	42	15	ν)jin	ν)jin	PROPN
ejpam-5458	42	16	−b(a	−b(a	PROPN
ejpam-5458	42	17	,	,	PUNCT
ejpam-5458	42	18	w	w	NOUN
ejpam-5458	42	19	)	)	PUNCT
ejpam-5458	42	20	+	+	ADJ
ejpam-5458	42	21	r(a	r(a	ADJ
ejpam-5458	42	22	,	,	PUNCT
ejpam-5458	42	23	w)−	w)−	PROPN
ejpam-5458	42	24	(	(	PUNCT
ejpam-5458	42	25	w	w	NOUN
ejpam-5458	42	26	−	−	NOUN
ejpam-5458	43	1	w0)/τw	w0)/τw	PROPN
ejpam-5458	43	2	(	(	PUNCT
ejpam-5458	43	3	1	1	NUM
ejpam-5458	43	4	)	)	PUNCT
ejpam-5458	43	5	where	where	SCONJ
ejpam-5458	43	6	a	a	PRON
ejpam-5458	43	7	is	be	AUX
ejpam-5458	43	8	total	total	ADJ
ejpam-5458	43	9	alkalinity	alkalinity	NOUN
ejpam-5458	43	10	,	,	PUNCT
ejpam-5458	43	11	w	w	NOUN
ejpam-5458	43	12	is	be	AUX
ejpam-5458	43	13	total	total	ADJ
ejpam-5458	43	14	dissolved	dissolve	VERB
ejpam-5458	43	15	inorganic	inorganic	ADJ
ejpam-5458	43	16	carbon	carbon	NOUN
ejpam-5458	43	17	,	,	PUNCT
ejpam-5458	43	18	and	and	CCONJ
ejpam-5458	43	19	other	other	ADJ
ejpam-5458	43	20	terms	term	NOUN
ejpam-5458	43	21	represent	represent	VERB
ejpam-5458	43	22	various	various	ADJ
ejpam-5458	43	23	fluxes	flux	NOUN
ejpam-5458	43	24	and	and	CCONJ
ejpam-5458	43	25	parameters	parameter	NOUN
ejpam-5458	43	26	.	.	PUNCT
ejpam-5458	44	1	key	key	ADJ
ejpam-5458	44	2	advancements	advancement	NOUN
ejpam-5458	44	3	in	in	ADP
ejpam-5458	44	4	this	this	DET
ejpam-5458	44	5	model	model	NOUN
ejpam-5458	44	6	(	(	PUNCT
ejpam-5458	44	7	1	1	X
ejpam-5458	44	8	)	)	PUNCT
ejpam-5458	44	9	include	include	VERB
ejpam-5458	44	10	the	the	DET
ejpam-5458	44	11	explicit	explicit	ADJ
ejpam-5458	44	12	representation	representation	NOUN
ejpam-5458	44	13	of	of	ADP
ejpam-5458	44	14	ocean	ocean	NOUN
ejpam-5458	44	15	carbonate	carbonate	NOUN
ejpam-5458	44	16	chemistry	chemistry	NOUN
ejpam-5458	44	17	,	,	PUNCT
ejpam-5458	44	18	allowing	allow	VERB
ejpam-5458	44	19	for	for	ADP
ejpam-5458	44	20	a	a	DET
ejpam-5458	44	21	more	more	ADV
ejpam-5458	44	22	detailed	detailed	ADJ
ejpam-5458	44	23	analysis	analysis	NOUN
ejpam-5458	44	24	of	of	ADP
ejpam-5458	44	25	marine	marine	ADJ
ejpam-5458	44	26	carbon	carbon	NOUN
ejpam-5458	44	27	dynamics	dynamic	NOUN
ejpam-5458	44	28	.	.	PUNCT
ejpam-5458	45	1	the	the	DET
ejpam-5458	45	2	incorporation	incorporation	NOUN
ejpam-5458	45	3	of	of	ADP
ejpam-5458	45	4	nonlinear	nonlinear	ADJ
ejpam-5458	45	5	feedbacks	feedback	NOUN
ejpam-5458	45	6	captures	capture	VERB
ejpam-5458	45	7	complex	complex	ADJ
ejpam-5458	45	8	interactions	interaction	NOUN
ejpam-5458	45	9	within	within	ADP
ejpam-5458	45	10	the	the	DET
ejpam-5458	45	11	carbonate	carbonate	NOUN
ejpam-5458	45	12	system	system	NOUN
ejpam-5458	45	13	,	,	PUNCT
ejpam-5458	45	14	enabling	enable	VERB
ejpam-5458	45	15	the	the	DET
ejpam-5458	45	16	model	model	NOUN
ejpam-5458	45	17	to	to	PART
ejpam-5458	45	18	produce	produce	VERB
ejpam-5458	45	19	rich	rich	ADJ
ejpam-5458	45	20	dynamical	dynamical	ADJ
ejpam-5458	45	21	behavior	behavior	NOUN
ejpam-5458	45	22	.	.	PUNCT
ejpam-5458	46	1	while	while	SCONJ
ejpam-5458	46	2	rothman	rothman	PROPN
ejpam-5458	46	3	’s	’s	PART
ejpam-5458	46	4	earlier	early	ADJ
ejpam-5458	46	5	works	work	NOUN
ejpam-5458	46	6	[	[	X
ejpam-5458	46	7	10	10	NUM
ejpam-5458	46	8	,	,	PUNCT
ejpam-5458	46	9	13	13	NUM
ejpam-5458	46	10	]	]	PUNCT
ejpam-5458	46	11	primarily	primarily	ADV
ejpam-5458	46	12	addressed	address	VERB
ejpam-5458	46	13	either	either	CCONJ
ejpam-5458	46	14	long	long	ADJ
ejpam-5458	46	15	-	-	PUNCT
ejpam-5458	46	16	term	term	NOUN
ejpam-5458	46	17	(	(	PUNCT
ejpam-5458	46	18	million	million	NUM
ejpam-5458	46	19	-	-	PUNCT
ejpam-5458	46	20	year	year	NOUN
ejpam-5458	46	21	)	)	PUNCT
ejpam-5458	46	22	carbon	carbon	NOUN
ejpam-5458	46	23	cycle	cycle	NOUN
ejpam-5458	46	24	stability	stability	NOUN
ejpam-5458	46	25	or	or	CCONJ
ejpam-5458	46	26	conceptual	conceptual	ADJ
ejpam-5458	46	27	frameworks	framework	NOUN
ejpam-5458	46	28	,	,	PUNCT
ejpam-5458	46	29	and	and	CCONJ
ejpam-5458	46	30	other	other	ADJ
ejpam-5458	46	31	models	model	NOUN
ejpam-5458	46	32	in	in	ADP
ejpam-5458	46	33	the	the	DET
ejpam-5458	46	34	field	field	NOUN
ejpam-5458	46	35	often	often	ADV
ejpam-5458	46	36	focused	focus	VERB
ejpam-5458	46	37	on	on	ADP
ejpam-5458	46	38	short	short	ADJ
ejpam-5458	46	39	-	-	PUNCT
ejpam-5458	46	40	term	term	NOUN
ejpam-5458	46	41	(	(	PUNCT
ejpam-5458	46	42	annual	annual	ADJ
ejpam-5458	46	43	to	to	ADP
ejpam-5458	46	44	decadal	decadal	NOUN
ejpam-5458	46	45	)	)	PUNCT
ejpam-5458	46	46	fluctuations	fluctuation	NOUN
ejpam-5458	46	47	,	,	PUNCT
ejpam-5458	46	48	this	this	DET
ejpam-5458	46	49	model	model	NOUN
ejpam-5458	46	50	uniquely	uniquely	ADV
ejpam-5458	46	51	bridges	bridge	VERB
ejpam-5458	46	52	the	the	DET
ejpam-5458	46	53	gap	gap	NOUN
ejpam-5458	46	54	i.	i.	PROPN
ejpam-5458	46	55	alraddadi	alraddadi	PROPN
ejpam-5458	46	56	/	/	SYM
ejpam-5458	46	57	eur	eur	PROPN
ejpam-5458	46	58	.	.	PUNCT
ejpam-5458	47	1	j.	j.	PROPN
ejpam-5458	47	2	pure	pure	PROPN
ejpam-5458	47	3	appl	appl	PROPN
ejpam-5458	47	4	.	.	PROPN
ejpam-5458	47	5	math	math	PROPN
ejpam-5458	47	6	,	,	PUNCT
ejpam-5458	47	7	17	17	NUM
ejpam-5458	47	8	(	(	PUNCT
ejpam-5458	47	9	4	4	NUM
ejpam-5458	47	10	)	)	PUNCT
ejpam-5458	47	11	(	(	PUNCT
ejpam-5458	47	12	2024	2024	NUM
ejpam-5458	47	13	)	)	PUNCT
ejpam-5458	47	14	,	,	PUNCT
ejpam-5458	47	15	3708	3708	NUM
ejpam-5458	47	16	-	-	SYM
ejpam-5458	47	17	3729	3729	NUM
ejpam-5458	47	18	3710	3710	NUM
ejpam-5458	47	19	by	by	ADP
ejpam-5458	47	20	exploring	explore	VERB
ejpam-5458	47	21	carbon	carbon	NOUN
ejpam-5458	47	22	cycle	cycle	NOUN
ejpam-5458	47	23	variations	variation	NOUN
ejpam-5458	47	24	on	on	ADP
ejpam-5458	47	25	intermediate	intermediate	ADJ
ejpam-5458	47	26	timescales	timescale	NOUN
ejpam-5458	47	27	,	,	PUNCT
ejpam-5458	47	28	ranging	range	VERB
ejpam-5458	47	29	from	from	ADP
ejpam-5458	47	30	thousands	thousand	NOUN
ejpam-5458	47	31	to	to	ADP
ejpam-5458	47	32	hundreds	hundred	NOUN
ejpam-5458	47	33	of	of	ADP
ejpam-5458	47	34	thousands	thousand	NOUN
ejpam-5458	47	35	of	of	ADP
ejpam-5458	47	36	years	year	NOUN
ejpam-5458	47	37	.	.	PUNCT
ejpam-5458	48	1	notably	notably	ADV
ejpam-5458	48	2	,	,	PUNCT
ejpam-5458	48	3	the	the	DET
ejpam-5458	48	4	model	model	NOUN
ejpam-5458	48	5	demonstrates	demonstrate	VERB
ejpam-5458	48	6	the	the	DET
ejpam-5458	48	7	potential	potential	NOUN
ejpam-5458	48	8	for	for	ADP
ejpam-5458	48	9	selfsustained	selfsustaine	VERB
ejpam-5458	48	10	oscillations	oscillation	NOUN
ejpam-5458	48	11	,	,	PUNCT
ejpam-5458	48	12	providing	provide	VERB
ejpam-5458	48	13	a	a	DET
ejpam-5458	48	14	mechanism	mechanism	NOUN
ejpam-5458	48	15	for	for	ADP
ejpam-5458	48	16	intrinsic	intrinsic	ADJ
ejpam-5458	48	17	carbon	carbon	NOUN
ejpam-5458	48	18	cycle	cycle	NOUN
ejpam-5458	48	19	variability	variability	NOUN
ejpam-5458	48	20	that	that	PRON
ejpam-5458	48	21	does	do	AUX
ejpam-5458	48	22	not	not	PART
ejpam-5458	48	23	depend	depend	VERB
ejpam-5458	48	24	on	on	ADP
ejpam-5458	48	25	external	external	ADJ
ejpam-5458	48	26	forcing	forcing	NOUN
ejpam-5458	48	27	.	.	PUNCT
ejpam-5458	49	1	while	while	SCONJ
ejpam-5458	49	2	saltzman	saltzman	PROPN
ejpam-5458	49	3	and	and	CCONJ
ejpam-5458	49	4	maasch	maasch	PROPN
ejpam-5458	49	5	’s	’s	PART
ejpam-5458	49	6	low	low	ADJ
ejpam-5458	49	7	-	-	PUNCT
ejpam-5458	49	8	order	order	NOUN
ejpam-5458	49	9	models	model	NOUN
ejpam-5458	49	10	[	[	X
ejpam-5458	49	11	7	7	X
ejpam-5458	49	12	]	]	ADJ
ejpam-5458	49	13	focus	focus	NOUN
ejpam-5458	49	14	on	on	ADP
ejpam-5458	49	15	glacial	glacial	ADJ
ejpam-5458	49	16	-	-	PUNCT
ejpam-5458	49	17	interglacial	interglacial	ADJ
ejpam-5458	49	18	cycles	cycle	NOUN
ejpam-5458	49	19	,	,	PUNCT
ejpam-5458	49	20	rothman	rothman	PROPN
ejpam-5458	49	21	’s	’s	PART
ejpam-5458	49	22	approach	approach	NOUN
ejpam-5458	49	23	specifically	specifically	ADV
ejpam-5458	49	24	addresses	address	VERB
ejpam-5458	49	25	the	the	DET
ejpam-5458	49	26	dynamics	dynamic	NOUN
ejpam-5458	49	27	of	of	ADP
ejpam-5458	49	28	the	the	DET
ejpam-5458	49	29	upper	upper	ADJ
ejpam-5458	49	30	ocean	ocean	NOUN
ejpam-5458	49	31	carbonate	carbonate	NOUN
ejpam-5458	49	32	system	system	NOUN
ejpam-5458	49	33	on	on	ADP
ejpam-5458	49	34	intermediate	intermediate	ADJ
ejpam-5458	49	35	timescales	timescale	NOUN
ejpam-5458	49	36	,	,	PUNCT
ejpam-5458	49	37	providing	provide	VERB
ejpam-5458	49	38	a	a	DET
ejpam-5458	49	39	more	more	ADV
ejpam-5458	49	40	detailed	detailed	ADJ
ejpam-5458	49	41	treatment	treatment	NOUN
ejpam-5458	49	42	of	of	ADP
ejpam-5458	49	43	carbonate	carbonate	NOUN
ejpam-5458	49	44	chemistry	chemistry	NOUN
ejpam-5458	49	45	feedbacks	feedback	NOUN
ejpam-5458	49	46	.	.	PUNCT
ejpam-5458	50	1	paillard	paillard	NOUN
ejpam-5458	50	2	and	and	CCONJ
ejpam-5458	50	3	parrenin	parrenin	NOUN
ejpam-5458	50	4	’s	’s	PART
ejpam-5458	50	5	conceptual	conceptual	ADJ
ejpam-5458	50	6	model	model	NOUN
ejpam-5458	51	1	[	[	X
ejpam-5458	51	2	9	9	NUM
ejpam-5458	51	3	]	]	PUNCT
ejpam-5458	51	4	relies	rely	VERB
ejpam-5458	51	5	heavily	heavily	ADV
ejpam-5458	51	6	on	on	ADP
ejpam-5458	51	7	threshold	threshold	NOUN
ejpam-5458	51	8	mechanisms	mechanism	NOUN
ejpam-5458	51	9	;	;	PUNCT
ejpam-5458	51	10	in	in	ADP
ejpam-5458	51	11	contrast	contrast	NOUN
ejpam-5458	51	12	,	,	PUNCT
ejpam-5458	51	13	rothman	rothman	PROPN
ejpam-5458	51	14	’s	’s	PART
ejpam-5458	51	15	model	model	NOUN
ejpam-5458	51	16	demonstrates	demonstrate	VERB
ejpam-5458	51	17	how	how	SCONJ
ejpam-5458	51	18	continuous	continuous	ADJ
ejpam-5458	51	19	nonlinear	nonlinear	ADJ
ejpam-5458	51	20	feedbacks	feedback	NOUN
ejpam-5458	51	21	can	can	AUX
ejpam-5458	51	22	lead	lead	VERB
ejpam-5458	51	23	to	to	ADP
ejpam-5458	51	24	complex	complex	ADJ
ejpam-5458	51	25	dynamics	dynamic	NOUN
ejpam-5458	51	26	,	,	PUNCT
ejpam-5458	51	27	including	include	VERB
ejpam-5458	51	28	limit	limit	NOUN
ejpam-5458	51	29	cycles	cycle	NOUN
ejpam-5458	51	30	.	.	PUNCT
ejpam-5458	52	1	this	this	DET
ejpam-5458	52	2	model	model	NOUN
ejpam-5458	52	3	’s	’s	PART
ejpam-5458	52	4	significance	significance	NOUN
ejpam-5458	52	5	lies	lie	VERB
ejpam-5458	52	6	in	in	ADP
ejpam-5458	52	7	its	its	PRON
ejpam-5458	52	8	ability	ability	NOUN
ejpam-5458	52	9	to	to	PART
ejpam-5458	52	10	bridge	bridge	VERB
ejpam-5458	52	11	short	short	ADJ
ejpam-5458	52	12	-	-	PUNCT
ejpam-5458	52	13	term	term	NOUN
ejpam-5458	52	14	variability	variability	NOUN
ejpam-5458	52	15	and	and	CCONJ
ejpam-5458	52	16	longterm	longterm	ADJ
ejpam-5458	52	17	trends	trend	NOUN
ejpam-5458	52	18	in	in	ADP
ejpam-5458	52	19	the	the	DET
ejpam-5458	52	20	carbon	carbon	NOUN
ejpam-5458	52	21	cycle	cycle	NOUN
ejpam-5458	52	22	,	,	PUNCT
ejpam-5458	52	23	offering	offer	VERB
ejpam-5458	52	24	new	new	ADJ
ejpam-5458	52	25	insights	insight	NOUN
ejpam-5458	52	26	into	into	ADP
ejpam-5458	52	27	intrinsic	intrinsic	ADJ
ejpam-5458	52	28	carbon	carbon	NOUN
ejpam-5458	52	29	cycle	cycle	NOUN
ejpam-5458	52	30	variability	variability	NOUN
ejpam-5458	52	31	and	and	CCONJ
ejpam-5458	52	32	potential	potential	ADJ
ejpam-5458	52	33	explanations	explanation	NOUN
ejpam-5458	52	34	for	for	ADP
ejpam-5458	52	35	observed	observed	ADJ
ejpam-5458	52	36	historical	historical	ADJ
ejpam-5458	52	37	variations	variation	NOUN
ejpam-5458	52	38	.	.	PUNCT
ejpam-5458	53	1	the	the	DET
ejpam-5458	53	2	model	model	NOUN
ejpam-5458	53	3	(	(	PUNCT
ejpam-5458	53	4	1	1	X
ejpam-5458	53	5	)	)	PUNCT
ejpam-5458	53	6	expresses	express	VERB
ejpam-5458	53	7	the	the	DET
ejpam-5458	53	8	concentrations	concentration	NOUN
ejpam-5458	53	9	of	of	ADP
ejpam-5458	53	10	total	total	ADJ
ejpam-5458	53	11	alkalinity	alkalinity	NOUN
ejpam-5458	53	12	(	(	PUNCT
ejpam-5458	53	13	a	a	NOUN
ejpam-5458	53	14	)	)	PUNCT
ejpam-5458	53	15	and	and	CCONJ
ejpam-5458	53	16	total	total	ADJ
ejpam-5458	53	17	dissolved	dissolve	VERB
ejpam-5458	53	18	inorganic	inorganic	ADJ
ejpam-5458	53	19	carbon	carbon	NOUN
ejpam-5458	53	20	(	(	PUNCT
ejpam-5458	53	21	dic	dic	ADJ
ejpam-5458	53	22	)	)	PUNCT
ejpam-5458	53	23	w	w	NOUN
ejpam-5458	53	24	in	in	ADP
ejpam-5458	53	25	units	unit	NOUN
ejpam-5458	53	26	of	of	ADP
ejpam-5458	53	27	µmot.kg−1	µmot.kg−1	PROPN
ejpam-5458	53	28	.	.	PUNCT
ejpam-5458	54	1	figure	figure	NOUN
ejpam-5458	54	2	1	1	NUM
ejpam-5458	54	3	illustrates	illustrate	VERB
ejpam-5458	54	4	a	a	DET
ejpam-5458	54	5	schematic	schematic	ADJ
ejpam-5458	54	6	diagram	diagram	NOUN
ejpam-5458	54	7	of	of	ADP
ejpam-5458	54	8	(	(	PUNCT
ejpam-5458	54	9	1	1	NUM
ejpam-5458	54	10	)	)	PUNCT
ejpam-5458	54	11	,	,	PUNCT
ejpam-5458	54	12	jin	jin	PROPN
ejpam-5458	54	13	is	be	AUX
ejpam-5458	54	14	the	the	DET
ejpam-5458	54	15	rate	rate	NOUN
ejpam-5458	54	16	equivalent	equivalent	ADJ
ejpam-5458	54	17	to	to	ADP
ejpam-5458	54	18	the	the	DET
ejpam-5458	54	19	change	change	NOUN
ejpam-5458	54	20	of	of	ADP
ejpam-5458	54	21	dissolved	dissolved	ADJ
ejpam-5458	54	22	caco3	caco3	NOUN
ejpam-5458	54	23	concentration	concentration	NOUN
ejpam-5458	54	24	added	add	VERB
ejpam-5458	54	25	by	by	ADP
ejpam-5458	54	26	the	the	DET
ejpam-5458	54	27	rivers	river	NOUN
ejpam-5458	54	28	in	in	ADP
ejpam-5458	54	29	oceans	ocean	NOUN
ejpam-5458	54	30	.	.	PUNCT
ejpam-5458	55	1	the	the	DET
ejpam-5458	55	2	flux	flux	PROPN
ejpam-5458	55	3	b(a	b(a	PROPN
ejpam-5458	55	4	,	,	PUNCT
ejpam-5458	55	5	w	w	NOUN
ejpam-5458	55	6	)	)	PUNCT
ejpam-5458	55	7	indicates	indicate	VERB
ejpam-5458	55	8	the	the	DET
ejpam-5458	55	9	rate	rate	NOUN
ejpam-5458	55	10	at	at	ADP
ejpam-5458	55	11	which	which	PRON
ejpam-5458	55	12	caco3	caco3	NOUN
ejpam-5458	55	13	exits	exit	VERB
ejpam-5458	55	14	from	from	ADP
ejpam-5458	55	15	the	the	DET
ejpam-5458	55	16	system	system	NOUN
ejpam-5458	55	17	to	to	PART
ejpam-5458	55	18	be	be	AUX
ejpam-5458	55	19	buried	bury	VERB
ejpam-5458	55	20	in	in	ADP
ejpam-5458	55	21	sediments	sediment	NOUN
ejpam-5458	55	22	in	in	ADP
ejpam-5458	55	23	the	the	DET
ejpam-5458	55	24	deep	deep	ADJ
ejpam-5458	55	25	ocean	ocean	NOUN
ejpam-5458	55	26	.	.	PUNCT
ejpam-5458	56	1	the	the	DET
ejpam-5458	56	2	flux	flux	NOUN
ejpam-5458	56	3	r(a	r(a	PROPN
ejpam-5458	56	4	,	,	PUNCT
ejpam-5458	56	5	w	w	NOUN
ejpam-5458	56	6	)	)	PUNCT
ejpam-5458	56	7	shows	show	VERB
ejpam-5458	56	8	the	the	DET
ejpam-5458	56	9	rate	rate	NOUN
ejpam-5458	56	10	of	of	ADP
ejpam-5458	56	11	the	the	DET
ejpam-5458	56	12	upper	upper	ADJ
ejpam-5458	56	13	ocean	ocean	NOUN
ejpam-5458	56	14	production	production	NOUN
ejpam-5458	56	15	of	of	ADP
ejpam-5458	56	16	co2	co2	NOUN
ejpam-5458	56	17	by	by	ADP
ejpam-5458	56	18	the	the	DET
ejpam-5458	56	19	respiration	respiration	NOUN
ejpam-5458	56	20	process	process	NOUN
ejpam-5458	56	21	.	.	PUNCT
ejpam-5458	57	1	the	the	DET
ejpam-5458	57	2	dimensionless	dimensionless	ADJ
ejpam-5458	57	3	term	term	NOUN
ejpam-5458	57	4	ν	ν	NOUN
ejpam-5458	57	5	corresponds	correspond	NOUN
ejpam-5458	57	6	to	to	ADP
ejpam-5458	57	7	the	the	DET
ejpam-5458	57	8	strength	strength	NOUN
ejpam-5458	57	9	of	of	ADP
ejpam-5458	57	10	an	an	DET
ejpam-5458	57	11	external	external	ADJ
ejpam-5458	57	12	source	source	NOUN
ejpam-5458	57	13	of	of	ADP
ejpam-5458	57	14	co2	co2	NOUN
ejpam-5458	57	15	(	(	PUNCT
ejpam-5458	57	16	e.g.	e.g.	ADV
ejpam-5458	57	17	volcanic	volcanic	ADJ
ejpam-5458	57	18	emissions	emission	NOUN
ejpam-5458	57	19	)	)	PUNCT
ejpam-5458	57	20	.	.	PUNCT
ejpam-5458	58	1	the	the	DET
ejpam-5458	58	2	functional	functional	ADJ
ejpam-5458	58	3	specification	specification	NOUN
ejpam-5458	58	4	of	of	ADP
ejpam-5458	58	5	feedback	feedback	NOUN
ejpam-5458	58	6	(	(	PUNCT
ejpam-5458	58	7	b	b	NOUN
ejpam-5458	58	8	and	and	CCONJ
ejpam-5458	58	9	r	r	NOUN
ejpam-5458	58	10	)	)	PUNCT
ejpam-5458	58	11	is	be	AUX
ejpam-5458	58	12	expressed	express	VERB
ejpam-5458	58	13	below	below	ADP
ejpam-5458	58	14	b(a	b(a	NOUN
ejpam-5458	58	15	,	,	PUNCT
ejpam-5458	58	16	w	w	NOUN
ejpam-5458	58	17	)	)	PUNCT
ejpam-5458	58	18	=	=	SYM
ejpam-5458	59	1	b[c(a	b[c(a	NOUN
ejpam-5458	59	2	,	,	PUNCT
ejpam-5458	59	3	w	w	NOUN
ejpam-5458	59	4	)	)	PUNCT
ejpam-5458	59	5	]	]	PUNCT
ejpam-5458	60	1	=	=	SYM
ejpam-5458	60	2	b	b	PROPN
ejpam-5458	60	3	∗	∗	NOUN
ejpam-5458	60	4	jins(c	jins(c	PROPN
ejpam-5458	60	5	,	,	PUNCT
ejpam-5458	60	6	cp	cp	NOUN
ejpam-5458	60	7	)	)	PUNCT
ejpam-5458	60	8	,	,	PUNCT
ejpam-5458	60	9	s(c	s(c	PROPN
ejpam-5458	60	10	,	,	PUNCT
ejpam-5458	60	11	cp	cp	NOUN
ejpam-5458	60	12	)	)	PUNCT
ejpam-5458	60	13	=	=	SYM
ejpam-5458	60	14	cγ	cγ	PROPN
ejpam-5458	60	15	cγ	cγ	PROPN
ejpam-5458	60	16	+	+	X
ejpam-5458	60	17	cγp	cγp	NOUN
ejpam-5458	60	18	(	(	PUNCT
ejpam-5458	60	19	2	2	NUM
ejpam-5458	60	20	)	)	PUNCT
ejpam-5458	60	21	where	where	SCONJ
ejpam-5458	60	22	s	s	NOUN
ejpam-5458	60	23	is	be	AUX
ejpam-5458	60	24	a	a	DET
ejpam-5458	60	25	sigmodial	sigmodial	ADJ
ejpam-5458	60	26	function	function	NOUN
ejpam-5458	60	27	,	,	PUNCT
ejpam-5458	60	28	and	and	CCONJ
ejpam-5458	60	29	bjin	bjin	NOUN
ejpam-5458	60	30	denotes	denote	VERB
ejpam-5458	60	31	the	the	DET
ejpam-5458	60	32	maximum	maximum	ADJ
ejpam-5458	60	33	rate	rate	NOUN
ejpam-5458	60	34	of	of	ADP
ejpam-5458	60	35	carbonate	carbonate	NOUN
ejpam-5458	60	36	burial	burial	PROPN
ejpam-5458	60	37	b.	b.	PROPN
ejpam-5458	60	38	for	for	ADP
ejpam-5458	60	39	s	s	NOUN
ejpam-5458	60	40	=	=	SYM
ejpam-5458	60	41	0.5	0.5	NUM
ejpam-5458	60	42	,	,	PUNCT
ejpam-5458	60	43	cp	cp	PROPN
ejpam-5458	60	44	represents	represent	VERB
ejpam-5458	60	45	the	the	DET
ejpam-5458	60	46	transitional	transitional	ADJ
ejpam-5458	60	47	carbonate	carbonate	NOUN
ejpam-5458	60	48	ion	ion	NOUN
ejpam-5458	60	49	concentration	concentration	NOUN
ejpam-5458	60	50	.	.	PUNCT
ejpam-5458	61	1	the	the	DET
ejpam-5458	61	2	exponent	exponent	NOUN
ejpam-5458	61	3	γ	γ	PROPN
ejpam-5458	61	4	is	be	AUX
ejpam-5458	61	5	the	the	DET
ejpam-5458	61	6	sigmoid	sigmoid	NOUN
ejpam-5458	61	7	sharpness	sharpness	NOUN
ejpam-5458	61	8	of	of	ADP
ejpam-5458	61	9	the	the	DET
ejpam-5458	61	10	transition	transition	NOUN
ejpam-5458	61	11	r(a	r(a	PROPN
ejpam-5458	61	12	,	,	PUNCT
ejpam-5458	61	13	w	w	NOUN
ejpam-5458	61	14	)	)	PUNCT
ejpam-5458	61	15	=	=	SYM
ejpam-5458	61	16	r[c(a	r[c(a	PROPN
ejpam-5458	61	17	,	,	PUNCT
ejpam-5458	61	18	w	w	NOUN
ejpam-5458	61	19	)	)	PUNCT
ejpam-5458	61	20	]	]	PUNCT
ejpam-5458	62	1	=	=	PUNCT
ejpam-5458	62	2	θjins̄(c	θjins̄(c	NOUN
ejpam-5458	62	3	,	,	PUNCT
ejpam-5458	62	4	cx	cx	NOUN
ejpam-5458	62	5	)	)	PUNCT
ejpam-5458	62	6	,	,	PUNCT
ejpam-5458	62	7	(	(	PUNCT
ejpam-5458	62	8	3	3	X
ejpam-5458	62	9	)	)	PUNCT
ejpam-5458	62	10	where	where	SCONJ
ejpam-5458	62	11	s̄	s̄	NOUN
ejpam-5458	62	12	=	=	SYM
ejpam-5458	62	13	1−	1−	NUM
ejpam-5458	62	14	s	s	NOUN
ejpam-5458	62	15	,	,	PUNCT
ejpam-5458	62	16	θjin	θjin	NOUN
ejpam-5458	62	17	is	be	AUX
ejpam-5458	62	18	the	the	DET
ejpam-5458	62	19	maximum	maximum	ADJ
ejpam-5458	62	20	value	value	NOUN
ejpam-5458	62	21	of	of	ADP
ejpam-5458	62	22	carbonate	carbonate	NOUN
ejpam-5458	62	23	respiration	respiration	NOUN
ejpam-5458	62	24	r	r	NOUN
ejpam-5458	62	25	,	,	PUNCT
ejpam-5458	62	26	and	and	CCONJ
ejpam-5458	62	27	cx	cx	PROPN
ejpam-5458	62	28	represents	represent	VERB
ejpam-5458	62	29	the	the	DET
ejpam-5458	62	30	crossover	crossover	NOUN
ejpam-5458	62	31	concentration	concentration	NOUN
ejpam-5458	62	32	at	at	ADP
ejpam-5458	62	33	the	the	DET
ejpam-5458	62	34	midway	midway	NOUN
ejpam-5458	62	35	point	point	NOUN
ejpam-5458	62	36	that	that	PRON
ejpam-5458	62	37	exists	exist	VERB
ejpam-5458	62	38	when	when	SCONJ
ejpam-5458	62	39	r	r	NOUN
ejpam-5458	62	40	transits	transit	NOUN
ejpam-5458	62	41	from	from	ADP
ejpam-5458	62	42	a	a	DET
ejpam-5458	62	43	high	high	ADJ
ejpam-5458	62	44	state	state	NOUN
ejpam-5458	62	45	to	to	ADP
ejpam-5458	62	46	a	a	DET
ejpam-5458	62	47	low	low	ADJ
ejpam-5458	62	48	state	state	NOUN
ejpam-5458	62	49	.	.	PUNCT
ejpam-5458	63	1	the	the	DET
ejpam-5458	63	2	differential	differential	ADJ
ejpam-5458	63	3	equation	equation	NOUN
ejpam-5458	63	4	in	in	ADP
ejpam-5458	63	5	(	(	PUNCT
ejpam-5458	63	6	4	4	NUM
ejpam-5458	63	7	)	)	PUNCT
ejpam-5458	63	8	below	below	ADV
ejpam-5458	63	9	describes	describe	VERB
ejpam-5458	63	10	the	the	DET
ejpam-5458	63	11	rate	rate	NOUN
ejpam-5458	63	12	of	of	ADP
ejpam-5458	63	13	change	change	NOUN
ejpam-5458	63	14	of	of	ADP
ejpam-5458	63	15	c	c	NOUN
ejpam-5458	63	16	which	which	PRON
ejpam-5458	63	17	depends	depend	VERB
ejpam-5458	63	18	on	on	ADP
ejpam-5458	63	19	a	a	PRON
ejpam-5458	63	20	and	and	CCONJ
ejpam-5458	63	21	w	w	PROPN
ejpam-5458	63	22	dc	dc	PROPN
ejpam-5458	63	23	dt	dt	X
ejpam-5458	63	24	=	=	SYM
ejpam-5458	63	25	da	da	PROPN
ejpam-5458	63	26	dt	dt	X
ejpam-5458	63	27	∂c	∂c	PROPN
ejpam-5458	64	1	∂a	∂a	PROPN
ejpam-5458	65	1	+	+	NUM
ejpam-5458	65	2	dw	dw	NOUN
ejpam-5458	65	3	dt	dt	PROPN
ejpam-5458	65	4	∂c	∂c	PROPN
ejpam-5458	65	5	∂w	∂w	PROPN
ejpam-5458	65	6	(	(	PUNCT
ejpam-5458	65	7	4	4	NUM
ejpam-5458	65	8	)	)	PUNCT
ejpam-5458	65	9	to	to	PART
ejpam-5458	65	10	approximate	approximate	VERB
ejpam-5458	65	11	the	the	DET
ejpam-5458	65	12	magnitude	magnitude	NOUN
ejpam-5458	65	13	of	of	ADP
ejpam-5458	65	14	the	the	DET
ejpam-5458	65	15	partial	partial	ADJ
ejpam-5458	65	16	derivatives	derivative	NOUN
ejpam-5458	65	17	∂c	∂c	PUNCT
ejpam-5458	66	1	∂a	∂a	NOUN
ejpam-5458	66	2	and	and	CCONJ
ejpam-5458	66	3	∂c	∂c	PROPN
ejpam-5458	67	1	∂w	∂w	PROPN
ejpam-5458	67	2	,	,	PUNCT
ejpam-5458	67	3	we	we	PRON
ejpam-5458	67	4	use	use	VERB
ejpam-5458	67	5	the	the	DET
ejpam-5458	67	6	”	"	PUNCT
ejpam-5458	67	7	buffer	buffer	NOUN
ejpam-5458	67	8	function	function	NOUN
ejpam-5458	67	9	”	"	PUNCT
ejpam-5458	67	10	f(c	f(c	PROPN
ejpam-5458	67	11	)	)	PUNCT
ejpam-5458	68	1	[	[	X
ejpam-5458	68	2	12](see	12](see	NUM
ejpam-5458	68	3	figure	figure	NOUN
ejpam-5458	68	4	2	2	NUM
ejpam-5458	68	5	):	):	PUNCT
ejpam-5458	68	6	∂c	∂c	PUNCT
ejpam-5458	69	1	∂a	∂a	PROPN
ejpam-5458	70	1	≈	≈	PROPN
ejpam-5458	70	2	−	−	PROPN
ejpam-5458	71	1	∂c	∂c	PROPN
ejpam-5458	71	2	∂w	∂w	PROPN
ejpam-5458	71	3	≡	≡	PROPN
ejpam-5458	71	4	f(c	f(c	PROPN
ejpam-5458	71	5	)	)	PUNCT
ejpam-5458	71	6	,	,	PUNCT
ejpam-5458	71	7	f(c	f(c	PROPN
ejpam-5458	71	8	)	)	PUNCT
ejpam-5458	72	1	=	=	SYM
ejpam-5458	72	2	f0	f0	ADJ
ejpam-5458	72	3	cβ	cβ	NOUN
ejpam-5458	72	4	cβ	cβ	PROPN
ejpam-5458	72	5	+	+	CCONJ
ejpam-5458	72	6	cβf	cβf	PROPN
ejpam-5458	72	7	(	(	PUNCT
ejpam-5458	72	8	5	5	NUM
ejpam-5458	72	9	)	)	PUNCT
ejpam-5458	72	10	where	where	SCONJ
ejpam-5458	72	11	f0	f0	PROPN
ejpam-5458	72	12	,	,	PUNCT
ejpam-5458	72	13	β	β	X
ejpam-5458	72	14	and	and	CCONJ
ejpam-5458	72	15	cβf	cβf	NOUN
ejpam-5458	72	16	are	be	AUX
ejpam-5458	72	17	specific	specific	ADJ
ejpam-5458	72	18	values	value	NOUN
ejpam-5458	72	19	for	for	ADP
ejpam-5458	72	20	the	the	DET
ejpam-5458	72	21	equilibrium	equilibrium	NOUN
ejpam-5458	72	22	of	of	ADP
ejpam-5458	72	23	the	the	DET
ejpam-5458	72	24	carbonate	carbonate	NOUN
ejpam-5458	72	25	system	system	NOUN
ejpam-5458	72	26	which	which	PRON
ejpam-5458	72	27	reduces	reduce	VERB
ejpam-5458	72	28	equation	equation	NOUN
ejpam-5458	72	29	(	(	PUNCT
ejpam-5458	72	30	5	5	NUM
ejpam-5458	72	31	)	)	PUNCT
ejpam-5458	72	32	to	to	ADP
ejpam-5458	72	33	the	the	DET
ejpam-5458	72	34	expression	expression	NOUN
ejpam-5458	72	35	in	in	ADP
ejpam-5458	72	36	(	(	PUNCT
ejpam-5458	72	37	6	6	NUM
ejpam-5458	72	38	):	):	PUNCT
ejpam-5458	72	39	ċ	ċ	PROPN
ejpam-5458	72	40	=	=	SYM
ejpam-5458	72	41	f(c)(ȧ−	f(c)(ȧ−	PROPN
ejpam-5458	72	42	ẇ	ẇ	PROPN
ejpam-5458	72	43	)	)	PUNCT
ejpam-5458	72	44	(	(	PUNCT
ejpam-5458	72	45	6	6	NUM
ejpam-5458	72	46	)	)	PUNCT
ejpam-5458	72	47	i.	i.	NOUN
ejpam-5458	72	48	alraddadi	alraddadi	PROPN
ejpam-5458	72	49	/	/	SYM
ejpam-5458	72	50	eur	eur	PROPN
ejpam-5458	72	51	.	.	PUNCT
ejpam-5458	73	1	j.	j.	PROPN
ejpam-5458	73	2	pure	pure	PROPN
ejpam-5458	73	3	appl	appl	PROPN
ejpam-5458	73	4	.	.	PROPN
ejpam-5458	73	5	math	math	PROPN
ejpam-5458	73	6	,	,	PUNCT
ejpam-5458	73	7	17	17	NUM
ejpam-5458	73	8	(	(	PUNCT
ejpam-5458	73	9	4	4	NUM
ejpam-5458	73	10	)	)	PUNCT
ejpam-5458	73	11	(	(	PUNCT
ejpam-5458	73	12	2024	2024	NUM
ejpam-5458	73	13	)	)	PUNCT
ejpam-5458	73	14	,	,	PUNCT
ejpam-5458	73	15	3708	3708	NUM
ejpam-5458	73	16	-	-	SYM
ejpam-5458	73	17	3729	3729	NUM
ejpam-5458	73	18	3711	3711	NUM
ejpam-5458	73	19	figure	figure	VERB
ejpam-5458	73	20	1	1	NUM
ejpam-5458	73	21	:	:	PUNCT
ejpam-5458	73	22	schematic	schematic	ADJ
ejpam-5458	73	23	diagram	diagram	NOUN
ejpam-5458	73	24	of	of	ADP
ejpam-5458	73	25	the	the	DET
ejpam-5458	73	26	evolution	evolution	NOUN
ejpam-5458	73	27	of	of	ADP
ejpam-5458	73	28	the	the	DET
ejpam-5458	73	29	model	model	NOUN
ejpam-5458	73	30	(	(	PUNCT
ejpam-5458	73	31	1	1	NUM
ejpam-5458	73	32	)	)	PUNCT
ejpam-5458	73	33	as	as	SCONJ
ejpam-5458	73	34	shown	show	VERB
ejpam-5458	73	35	in	in	ADP
ejpam-5458	73	36	[	[	X
ejpam-5458	73	37	12	12	NUM
ejpam-5458	73	38	]	]	PUNCT
ejpam-5458	73	39	.	.	PUNCT
ejpam-5458	74	1	the	the	DET
ejpam-5458	74	2	left	left	ADJ
ejpam-5458	74	3	and	and	CCONJ
ejpam-5458	74	4	right	right	ADJ
ejpam-5458	74	5	panels	panel	NOUN
ejpam-5458	74	6	show	show	VERB
ejpam-5458	74	7	how	how	SCONJ
ejpam-5458	74	8	total	total	ADJ
ejpam-5458	74	9	alkalinity	alkalinity	NOUN
ejpam-5458	74	10	a	a	PRON
ejpam-5458	74	11	and	and	CCONJ
ejpam-5458	74	12	total	total	ADJ
ejpam-5458	74	13	dissolved	dissolve	VERB
ejpam-5458	74	14	inorganic	inorganic	ADJ
ejpam-5458	74	15	carbon	carbon	NOUN
ejpam-5458	74	16	(	(	PUNCT
ejpam-5458	74	17	dic	dic	NOUN
ejpam-5458	74	18	)	)	PUNCT
ejpam-5458	74	19	w	w	NOUN
ejpam-5458	74	20	changed	change	VERB
ejpam-5458	74	21	over	over	ADP
ejpam-5458	74	22	the	the	DET
ejpam-5458	74	23	chemical	chemical	ADJ
ejpam-5458	74	24	state	state	NOUN
ejpam-5458	74	25	of	of	ADP
ejpam-5458	74	26	the	the	DET
ejpam-5458	74	27	upper	upper	ADJ
ejpam-5458	74	28	ocean	ocean	NOUN
ejpam-5458	74	29	.	.	PUNCT
ejpam-5458	75	1	this	this	DET
ejpam-5458	75	2	diagram	diagram	NOUN
ejpam-5458	75	3	has	have	VERB
ejpam-5458	75	4	three	three	NUM
ejpam-5458	75	5	blue	blue	ADJ
ejpam-5458	75	6	lines	line	NOUN
ejpam-5458	75	7	:	:	PUNCT
ejpam-5458	75	8	the	the	DET
ejpam-5458	75	9	wavy	wavy	ADJ
ejpam-5458	75	10	line	line	NOUN
ejpam-5458	75	11	shows	show	VERB
ejpam-5458	75	12	the	the	DET
ejpam-5458	75	13	air	air	NOUN
ejpam-5458	75	14	and	and	CCONJ
ejpam-5458	75	15	water	water	NOUN
ejpam-5458	75	16	interface	interface	NOUN
ejpam-5458	75	17	,	,	PUNCT
ejpam-5458	75	18	and	and	CCONJ
ejpam-5458	75	19	a	a	DET
ejpam-5458	75	20	thick	thick	ADJ
ejpam-5458	75	21	line	line	NOUN
ejpam-5458	75	22	separates	separate	VERB
ejpam-5458	75	23	the	the	DET
ejpam-5458	75	24	shallow	shallow	ADJ
ejpam-5458	75	25	sea	sea	NOUN
ejpam-5458	75	26	from	from	ADP
ejpam-5458	75	27	the	the	DET
ejpam-5458	75	28	deep	deep	ADJ
ejpam-5458	75	29	sea	sea	NOUN
ejpam-5458	75	30	.	.	PUNCT
ejpam-5458	76	1	the	the	DET
ejpam-5458	76	2	dashed	dash	VERB
ejpam-5458	76	3	line	line	NOUN
ejpam-5458	76	4	represents	represent	VERB
ejpam-5458	76	5	the	the	DET
ejpam-5458	76	6	sediment	sediment	NOUN
ejpam-5458	76	7	–	–	PUNCT
ejpam-5458	76	8	seawater	seawater	NOUN
ejpam-5458	76	9	interface	interface	NOUN
ejpam-5458	76	10	.	.	PUNCT
ejpam-5458	77	1	concentration	concentration	NOUN
ejpam-5458	77	2	fluxes	flux	NOUN
ejpam-5458	77	3	are	be	AUX
ejpam-5458	77	4	shown	show	VERB
ejpam-5458	77	5	by	by	ADP
ejpam-5458	77	6	arrows	arrow	NOUN
ejpam-5458	77	7	that	that	PRON
ejpam-5458	77	8	only	only	ADV
ejpam-5458	77	9	move	move	VERB
ejpam-5458	77	10	in	in	ADP
ejpam-5458	77	11	one	one	NUM
ejpam-5458	77	12	direction	direction	NOUN
ejpam-5458	77	13	.	.	PUNCT
ejpam-5458	78	1	the	the	DET
ejpam-5458	78	2	dashed	dash	VERB
ejpam-5458	78	3	line	line	NOUN
ejpam-5458	78	4	between	between	ADP
ejpam-5458	78	5	the	the	DET
ejpam-5458	78	6	sediment	sediment	NOUN
ejpam-5458	78	7	and	and	CCONJ
ejpam-5458	78	8	seawater	seawater	NOUN
ejpam-5458	78	9	indicates	indicate	VERB
ejpam-5458	78	10	no	no	DET
ejpam-5458	78	11	dynamic	dynamic	ADJ
ejpam-5458	78	12	difference	difference	NOUN
ejpam-5458	78	13	between	between	ADP
ejpam-5458	78	14	the	the	DET
ejpam-5458	78	15	deep	deep	ADJ
ejpam-5458	78	16	sea	sea	NOUN
ejpam-5458	78	17	and	and	CCONJ
ejpam-5458	78	18	sediment	sediment	NOUN
ejpam-5458	78	19	.	.	PUNCT
ejpam-5458	79	1	this	this	DET
ejpam-5458	79	2	feedback	feedback	NOUN
ejpam-5458	79	3	b(a	b(a	NOUN
ejpam-5458	79	4	,	,	PUNCT
ejpam-5458	79	5	w	w	NOUN
ejpam-5458	79	6	)	)	PUNCT
ejpam-5458	79	7	and	and	CCONJ
ejpam-5458	79	8	r(a	r(a	PROPN
ejpam-5458	79	9	,	,	PUNCT
ejpam-5458	79	10	w	w	NOUN
ejpam-5458	79	11	)	)	PUNCT
ejpam-5458	79	12	determines	determine	VERB
ejpam-5458	79	13	the	the	DET
ejpam-5458	79	14	extent	extent	NOUN
ejpam-5458	79	15	of	of	ADP
ejpam-5458	79	16	a	a	DET
ejpam-5458	79	17	and	and	CCONJ
ejpam-5458	79	18	w	w	NOUN
ejpam-5458	79	19	accumulation	accumulation	NOUN
ejpam-5458	79	20	before	before	ADP
ejpam-5458	79	21	leaving	leave	VERB
ejpam-5458	79	22	the	the	DET
ejpam-5458	79	23	system	system	NOUN
ejpam-5458	79	24	.	.	PUNCT
ejpam-5458	80	1	where	where	SCONJ
ejpam-5458	80	2	c	c	NOUN
ejpam-5458	80	3	is	be	AUX
ejpam-5458	80	4	the	the	DET
ejpam-5458	80	5	concentrations	concentration	NOUN
ejpam-5458	80	6	of	of	ADP
ejpam-5458	80	7	co2−	co2−	NOUN
ejpam-5458	80	8	3	3	NUM
ejpam-5458	80	9	.	.	PUNCT
ejpam-5458	81	1	by	by	ADP
ejpam-5458	81	2	substituting	substitute	VERB
ejpam-5458	81	3	(	(	PUNCT
ejpam-5458	81	4	2	2	NUM
ejpam-5458	81	5	)	)	PUNCT
ejpam-5458	81	6	and	and	CCONJ
ejpam-5458	81	7	(	(	PUNCT
ejpam-5458	81	8	3	3	X
ejpam-5458	81	9	)	)	PUNCT
ejpam-5458	81	10	into	into	ADP
ejpam-5458	81	11	model	model	NOUN
ejpam-5458	81	12	(	(	PUNCT
ejpam-5458	81	13	1	1	NUM
ejpam-5458	81	14	)	)	PUNCT
ejpam-5458	81	15	,	,	PUNCT
ejpam-5458	81	16	we	we	PRON
ejpam-5458	81	17	obtain	obtain	VERB
ejpam-5458	81	18	ċ	ċ	NOUN
ejpam-5458	81	19	as	as	ADP
ejpam-5458	81	20	a	a	DET
ejpam-5458	81	21	function	function	NOUN
ejpam-5458	81	22	of	of	ADP
ejpam-5458	81	23	c	c	PROPN
ejpam-5458	81	24	and	and	CCONJ
ejpam-5458	81	25	w	w	NOUN
ejpam-5458	81	26	:	:	PUNCT
ejpam-5458	81	27	ċ/f(c	ċ/f(c	PROPN
ejpam-5458	81	28	)	)	PUNCT
ejpam-5458	81	29	=	=	PUNCT
ejpam-5458	82	1	µ[1−	µ[1−	NUM
ejpam-5458	82	2	bs(c	bs(c	NOUN
ejpam-5458	82	3	,	,	PUNCT
ejpam-5458	82	4	cp)−	cp)−	ADJ
ejpam-5458	82	5	θs̄(c	θs̄(c	NOUN
ejpam-5458	82	6	,	,	PUNCT
ejpam-5458	82	7	cx)−	cx)−	NOUN
ejpam-5458	82	8	ν	ν	X
ejpam-5458	82	9	]	]	X
ejpam-5458	83	1	+	+	CCONJ
ejpam-5458	83	2	w	w	PROPN
ejpam-5458	83	3	−	−	PROPN
ejpam-5458	83	4	w0	w0	PROPN
ejpam-5458	83	5	ẇ	ẇ	PROPN
ejpam-5458	83	6	=	=	SYM
ejpam-5458	83	7	µ[1−	µ[1−	PROPN
ejpam-5458	83	8	bs(c	bs(c	NOUN
ejpam-5458	83	9	,	,	PUNCT
ejpam-5458	83	10	cp	cp	X
ejpam-5458	83	11	)	)	PUNCT
ejpam-5458	83	12	+	+	CCONJ
ejpam-5458	84	1	θs̄(c	θs̄(c	PROPN
ejpam-5458	84	2	,	,	PUNCT
ejpam-5458	84	3	cx	cx	NOUN
ejpam-5458	84	4	)	)	PUNCT
ejpam-5458	85	1	+	+	CCONJ
ejpam-5458	86	1	ν]−	ν]−	PROPN
ejpam-5458	86	2	w	w	ADJ
ejpam-5458	86	3	+	+	PROPN
ejpam-5458	86	4	w0	w0	PROPN
ejpam-5458	86	5	(	(	PUNCT
ejpam-5458	86	6	7	7	NUM
ejpam-5458	86	7	)	)	PUNCT
ejpam-5458	86	8	is	be	AUX
ejpam-5458	86	9	called	call	VERB
ejpam-5458	86	10	rothman	rothman	PROPN
ejpam-5458	86	11	’s	’s	PART
ejpam-5458	86	12	carbon	carbon	NOUN
ejpam-5458	86	13	cycle	cycle	NOUN
ejpam-5458	86	14	model	model	NOUN
ejpam-5458	86	15	[	[	X
ejpam-5458	86	16	12	12	NUM
ejpam-5458	86	17	]	]	PUNCT
ejpam-5458	86	18	with	with	ADP
ejpam-5458	86	19	respect	respect	NOUN
ejpam-5458	86	20	to	to	ADP
ejpam-5458	86	21	the	the	DET
ejpam-5458	86	22	new	new	ADJ
ejpam-5458	86	23	timescale	timescale	NOUN
ejpam-5458	86	24	dt	dt	X
ejpam-5458	86	25	=	=	SYM
ejpam-5458	86	26	dt	dt	PROPN
ejpam-5458	86	27	/	/	SYM
ejpam-5458	86	28	τw	τw	NOUN
ejpam-5458	86	29	.	.	PUNCT
ejpam-5458	87	1	the	the	DET
ejpam-5458	87	2	value	value	NOUN
ejpam-5458	87	3	of	of	ADP
ejpam-5458	87	4	parameters	parameter	NOUN
ejpam-5458	87	5	µ	µ	NUM
ejpam-5458	87	6	,	,	PUNCT
ejpam-5458	87	7	b	b	PROPN
ejpam-5458	87	8	,	,	PUNCT
ejpam-5458	87	9	θ	θ	PROPN
ejpam-5458	87	10	,	,	PUNCT
ejpam-5458	87	11	cp	cp	PROPN
ejpam-5458	87	12	,	,	PUNCT
ejpam-5458	87	13	cx	cx	PROPN
ejpam-5458	87	14	,	,	PUNCT
ejpam-5458	87	15	cf	cf	NOUN
ejpam-5458	87	16	,	,	PUNCT
ejpam-5458	87	17	w0	w0	PROPN
ejpam-5458	87	18	,	,	PUNCT
ejpam-5458	87	19	γ	γ	PROPN
ejpam-5458	87	20	and	and	CCONJ
ejpam-5458	87	21	β	β	X
ejpam-5458	87	22	are	be	AUX
ejpam-5458	87	23	listed	list	VERB
ejpam-5458	87	24	in	in	ADP
ejpam-5458	87	25	table	table	NOUN
ejpam-5458	87	26	1	1	NUM
ejpam-5458	87	27	.	.	PUNCT
ejpam-5458	88	1	these	these	DET
ejpam-5458	88	2	parameters	parameter	NOUN
ejpam-5458	88	3	correspond	correspond	VERB
ejpam-5458	88	4	to	to	ADP
ejpam-5458	88	5	the	the	DET
ejpam-5458	88	6	properties	property	NOUN
ejpam-5458	88	7	of	of	ADP
ejpam-5458	88	8	the	the	DET
ejpam-5458	88	9	modern	modern	ADJ
ejpam-5458	88	10	ocean	ocean	NOUN
ejpam-5458	88	11	.	.	PUNCT
ejpam-5458	89	1	we	we	PRON
ejpam-5458	89	2	change	change	VERB
ejpam-5458	89	3	the	the	DET
ejpam-5458	89	4	value	value	NOUN
ejpam-5458	89	5	of	of	ADP
ejpam-5458	89	6	cx	cx	PROPN
ejpam-5458	89	7	,	,	PUNCT
ejpam-5458	89	8	b	b	PROPN
ejpam-5458	89	9	,	,	PUNCT
ejpam-5458	89	10	µ	µ	NOUN
ejpam-5458	89	11	,	,	PUNCT
ejpam-5458	89	12	cp	cp	NOUN
ejpam-5458	89	13	,	,	PUNCT
ejpam-5458	89	14	θ	θ	PROPN
ejpam-5458	89	15	and	and	CCONJ
ejpam-5458	89	16	ν	ν	NOUN
ejpam-5458	89	17	to	to	PART
ejpam-5458	89	18	show	show	VERB
ejpam-5458	89	19	the	the	DET
ejpam-5458	89	20	stability	stability	NOUN
ejpam-5458	89	21	region	region	NOUN
ejpam-5458	89	22	of	of	ADP
ejpam-5458	89	23	(	(	PUNCT
ejpam-5458	89	24	7	7	NUM
ejpam-5458	89	25	)	)	PUNCT
ejpam-5458	89	26	in	in	ADP
ejpam-5458	89	27	the	the	DET
ejpam-5458	89	28	parameter	parameter	NOUN
ejpam-5458	89	29	space	space	NOUN
ejpam-5458	89	30	.	.	PUNCT
ejpam-5458	90	1	3	3	X
ejpam-5458	90	2	.	.	X
ejpam-5458	90	3	steady	steady	ADJ
ejpam-5458	90	4	state	state	NOUN
ejpam-5458	90	5	and	and	CCONJ
ejpam-5458	90	6	stability	stability	NOUN
ejpam-5458	90	7	analysis	analysis	NOUN
ejpam-5458	90	8	in	in	ADP
ejpam-5458	90	9	this	this	DET
ejpam-5458	90	10	section	section	NOUN
ejpam-5458	90	11	,	,	PUNCT
ejpam-5458	90	12	we	we	PRON
ejpam-5458	90	13	analyse	analyse	VERB
ejpam-5458	90	14	the	the	DET
ejpam-5458	90	15	behaviour	behaviour	NOUN
ejpam-5458	90	16	of	of	ADP
ejpam-5458	90	17	rothman	rothman	PROPN
ejpam-5458	90	18	’s	’s	PART
ejpam-5458	90	19	carbon	carbon	NOUN
ejpam-5458	90	20	cycle	cycle	NOUN
ejpam-5458	90	21	model	model	NOUN
ejpam-5458	90	22	(	(	PUNCT
ejpam-5458	90	23	7	7	NUM
ejpam-5458	90	24	)	)	PUNCT
ejpam-5458	90	25	and	and	CCONJ
ejpam-5458	90	26	in	in	ADP
ejpam-5458	90	27	particular	particular	ADJ
ejpam-5458	90	28	,	,	PUNCT
ejpam-5458	90	29	the	the	DET
ejpam-5458	90	30	stability	stability	NOUN
ejpam-5458	90	31	of	of	ADP
ejpam-5458	90	32	the	the	DET
ejpam-5458	90	33	equilibrium	equilibrium	NOUN
ejpam-5458	90	34	point	point	NOUN
ejpam-5458	90	35	.	.	PUNCT
ejpam-5458	91	1	the	the	DET
ejpam-5458	91	2	nullclines	nullcline	NOUN
ejpam-5458	91	3	(	(	PUNCT
ejpam-5458	91	4	ċ	ċ	NOUN
ejpam-5458	91	5	=	=	SYM
ejpam-5458	91	6	ẇ	ẇ	PROPN
ejpam-5458	91	7	=	=	SYM
ejpam-5458	91	8	0	0	NUM
ejpam-5458	91	9	)	)	PUNCT
ejpam-5458	91	10	of	of	ADP
ejpam-5458	91	11	(	(	PUNCT
ejpam-5458	91	12	7	7	X
ejpam-5458	91	13	)	)	PUNCT
ejpam-5458	91	14	are	be	AUX
ejpam-5458	91	15	given	give	VERB
ejpam-5458	91	16	by	by	ADP
ejpam-5458	91	17	w0	w0	PROPN
ejpam-5458	91	18	=	=	PUNCT
ejpam-5458	91	19	µ[1−	µ[1−	NUM
ejpam-5458	91	20	bs(c	bs(c	NOUN
ejpam-5458	91	21	,	,	PUNCT
ejpam-5458	91	22	cp)−	cp)−	ADJ
ejpam-5458	91	23	θs̄(c	θs̄(c	NOUN
ejpam-5458	91	24	,	,	PUNCT
ejpam-5458	91	25	cx)−	cx)−	NOUN
ejpam-5458	91	26	ν	ν	X
ejpam-5458	91	27	]	]	X
ejpam-5458	91	28	+	+	CCONJ
ejpam-5458	91	29	w	w	NOUN
ejpam-5458	91	30	or	or	CCONJ
ejpam-5458	91	31	f(c	f(c	PROPN
ejpam-5458	91	32	)	)	PUNCT
ejpam-5458	92	1	=	=	NOUN
ejpam-5458	92	2	0	0	NUM
ejpam-5458	92	3	w	w	NOUN
ejpam-5458	92	4	=	=	SYM
ejpam-5458	92	5	µ[1−	µ[1−	NUM
ejpam-5458	92	6	bs(c	bs(c	NOUN
ejpam-5458	92	7	,	,	PUNCT
ejpam-5458	92	8	cp	cp	X
ejpam-5458	92	9	)	)	PUNCT
ejpam-5458	92	10	+	+	CCONJ
ejpam-5458	93	1	θs̄(c	θs̄(c	PROPN
ejpam-5458	93	2	,	,	PUNCT
ejpam-5458	93	3	cx	cx	NOUN
ejpam-5458	93	4	)	)	PUNCT
ejpam-5458	94	1	+	+	CCONJ
ejpam-5458	94	2	ν	ν	X
ejpam-5458	94	3	]	]	X
ejpam-5458	94	4	+	+	NUM
ejpam-5458	94	5	w0	w0	PROPN
ejpam-5458	94	6	(	(	PUNCT
ejpam-5458	94	7	8)	8)	NUM
ejpam-5458	94	8	i.	i.	NOUN
ejpam-5458	94	9	alraddadi	alraddadi	PROPN
ejpam-5458	94	10	/	/	SYM
ejpam-5458	94	11	eur	eur	PROPN
ejpam-5458	94	12	.	.	PUNCT
ejpam-5458	95	1	j.	j.	PROPN
ejpam-5458	95	2	pure	pure	PROPN
ejpam-5458	95	3	appl	appl	PROPN
ejpam-5458	95	4	.	.	PROPN
ejpam-5458	95	5	math	math	PROPN
ejpam-5458	95	6	,	,	PUNCT
ejpam-5458	95	7	17	17	NUM
ejpam-5458	95	8	(	(	PUNCT
ejpam-5458	95	9	4	4	NUM
ejpam-5458	95	10	)	)	PUNCT
ejpam-5458	95	11	(	(	PUNCT
ejpam-5458	95	12	2024	2024	NUM
ejpam-5458	95	13	)	)	PUNCT
ejpam-5458	95	14	,	,	PUNCT
ejpam-5458	95	15	3708	3708	NUM
ejpam-5458	95	16	-	-	SYM
ejpam-5458	95	17	3729	3729	NUM
ejpam-5458	95	18	3712	3712	NUM
ejpam-5458	95	19	figure	figure	NOUN
ejpam-5458	95	20	2	2	NUM
ejpam-5458	95	21	:	:	PUNCT
ejpam-5458	95	22	the	the	DET
ejpam-5458	95	23	buffer	buffer	NOUN
ejpam-5458	95	24	function	function	NOUN
ejpam-5458	95	25	f(c	f(c	PROPN
ejpam-5458	95	26	)	)	PUNCT
ejpam-5458	95	27	characterises	characterise	VERB
ejpam-5458	95	28	the	the	DET
ejpam-5458	95	29	equilibrium	equilibrium	NOUN
ejpam-5458	95	30	chemistry	chemistry	NOUN
ejpam-5458	95	31	of	of	ADP
ejpam-5458	95	32	the	the	DET
ejpam-5458	95	33	carbonate	carbonate	NOUN
ejpam-5458	95	34	system	system	NOUN
ejpam-5458	95	35	.	.	PUNCT
ejpam-5458	96	1	the	the	DET
ejpam-5458	96	2	smooth	smooth	ADJ
ejpam-5458	96	3	curve	curve	NOUN
ejpam-5458	96	4	is	be	AUX
ejpam-5458	96	5	approximated	approximate	VERB
ejpam-5458	96	6	by	by	ADP
ejpam-5458	96	7	(	(	PUNCT
ejpam-5458	96	8	5	5	NUM
ejpam-5458	96	9	)	)	PUNCT
ejpam-5458	96	10	.	.	PUNCT
ejpam-5458	97	1	the	the	DET
ejpam-5458	97	2	parameters	parameter	NOUN
ejpam-5458	97	3	f0	f0	PROPN
ejpam-5458	97	4	=	=	PUNCT
ejpam-5458	97	5	0.694	0.694	NUM
ejpam-5458	97	6	,	,	PUNCT
ejpam-5458	97	7	β	β	X
ejpam-5458	97	8	=	=	SYM
ejpam-5458	97	9	1.7	1.7	NUM
ejpam-5458	97	10	and	and	CCONJ
ejpam-5458	97	11	cf	cf	NOUN
ejpam-5458	97	12	=	=	SYM
ejpam-5458	97	13	43.9	43.9	NUM
ejpam-5458	97	14	are	be	AUX
ejpam-5458	97	15	specific	specific	ADJ
ejpam-5458	97	16	values	value	NOUN
ejpam-5458	97	17	for	for	ADP
ejpam-5458	97	18	the	the	DET
ejpam-5458	97	19	equilibrium	equilibrium	NOUN
ejpam-5458	97	20	of	of	ADP
ejpam-5458	97	21	the	the	DET
ejpam-5458	97	22	carbonate	carbonate	NOUN
ejpam-5458	97	23	system	system	NOUN
ejpam-5458	97	24	.	.	PUNCT
ejpam-5458	98	1	where	where	SCONJ
ejpam-5458	98	2	s̄(c	s̄(c	NOUN
ejpam-5458	98	3	,	,	PUNCT
ejpam-5458	98	4	cx	cx	NOUN
ejpam-5458	98	5	)	)	PUNCT
ejpam-5458	98	6	=	=	SYM
ejpam-5458	98	7	1	1	NUM
ejpam-5458	98	8	−	−	ADP
ejpam-5458	98	9	s(c	s(c	PROPN
ejpam-5458	98	10	,	,	PUNCT
ejpam-5458	98	11	cx	cx	PROPN
ejpam-5458	98	12	)	)	PUNCT
ejpam-5458	98	13	.	.	PUNCT
ejpam-5458	99	1	to	to	PART
ejpam-5458	99	2	find	find	VERB
ejpam-5458	99	3	the	the	DET
ejpam-5458	99	4	equilibrium	equilibrium	NOUN
ejpam-5458	99	5	point	point	NOUN
ejpam-5458	99	6	(	(	PUNCT
ejpam-5458	99	7	c∗	c∗	PROPN
ejpam-5458	99	8	,	,	PUNCT
ejpam-5458	99	9	w∗	w∗	NOUN
ejpam-5458	99	10	)	)	PUNCT
ejpam-5458	99	11	of	of	ADP
ejpam-5458	99	12	(	(	PUNCT
ejpam-5458	99	13	7	7	NUM
ejpam-5458	99	14	)	)	PUNCT
ejpam-5458	99	15	,	,	PUNCT
ejpam-5458	99	16	we	we	PRON
ejpam-5458	99	17	substitute	substitute	VERB
ejpam-5458	99	18	w	w	VERB
ejpam-5458	99	19	into	into	ADP
ejpam-5458	99	20	(	(	PUNCT
ejpam-5458	99	21	ċ	ċ	NOUN
ejpam-5458	99	22	=	=	SYM
ejpam-5458	99	23	0	0	NUM
ejpam-5458	99	24	):	):	PUNCT
ejpam-5458	99	25	µ[2−	µ[2−	PROPN
ejpam-5458	99	26	2bs(c	2bs(c	NUM
ejpam-5458	99	27	,	,	PUNCT
ejpam-5458	99	28	cp	cp	NOUN
ejpam-5458	99	29	)	)	PUNCT
ejpam-5458	99	30	]	]	PUNCT
ejpam-5458	100	1	=	=	SYM
ejpam-5458	100	2	0	0	NUM
ejpam-5458	100	3	bs(c	bs(c	NOUN
ejpam-5458	100	4	,	,	PUNCT
ejpam-5458	100	5	cp	cp	X
ejpam-5458	100	6	)	)	PUNCT
ejpam-5458	100	7	=	=	SYM
ejpam-5458	100	8	1	1	NUM
ejpam-5458	100	9	b	b	X
ejpam-5458	100	10	cγ	cγ	X
ejpam-5458	100	11	cγ	cγ	NOUN
ejpam-5458	100	12	+	+	X
ejpam-5458	100	13	cγp	cγp	PROPN
ejpam-5458	100	14	=	=	SYM
ejpam-5458	100	15	1	1	NUM
ejpam-5458	100	16	c∗	c∗	NOUN
ejpam-5458	100	17	=	=	SYM
ejpam-5458	100	18	(	(	PUNCT
ejpam-5458	100	19	b−	b−	NOUN
ejpam-5458	100	20	1	1	NUM
ejpam-5458	100	21	)	)	PUNCT
ejpam-5458	100	22	−1	−1	NOUN
ejpam-5458	100	23	γ	γ	PROPN
ejpam-5458	100	24	cγp	cγp	NOUN
ejpam-5458	100	25	(	(	PUNCT
ejpam-5458	100	26	9	9	NUM
ejpam-5458	100	27	)	)	PUNCT
ejpam-5458	100	28	from	from	ADP
ejpam-5458	100	29	(	(	PUNCT
ejpam-5458	100	30	3	3	NUM
ejpam-5458	100	31	)	)	PUNCT
ejpam-5458	100	32	,	,	PUNCT
ejpam-5458	100	33	w∗	w∗	NOUN
ejpam-5458	100	34	=	=	SYM
ejpam-5458	100	35	µ[θ(1−	µ[θ(1−	PROPN
ejpam-5458	100	36	s(c	s(c	PROPN
ejpam-5458	100	37	,	,	PUNCT
ejpam-5458	100	38	cx	cx	NOUN
ejpam-5458	100	39	)	)	PUNCT
ejpam-5458	100	40	)	)	PUNCT
ejpam-5458	101	1	+	+	CCONJ
ejpam-5458	101	2	ν	ν	X
ejpam-5458	101	3	]	]	X
ejpam-5458	101	4	+	+	NUM
ejpam-5458	101	5	w0	w0	PROPN
ejpam-5458	101	6	w∗	w∗	NOUN
ejpam-5458	101	7	=	=	PROPN
ejpam-5458	101	8	w0	w0	PROPN
ejpam-5458	101	9	+	+	CCONJ
ejpam-5458	101	10	µ[θ(1−	µ[θ(1−	PROPN
ejpam-5458	101	11	cγ	cγ	PROPN
ejpam-5458	101	12	cγ	cγ	NOUN
ejpam-5458	101	13	+	+	CCONJ
ejpam-5458	101	14	cγx	cγx	NOUN
ejpam-5458	101	15	)	)	PUNCT
ejpam-5458	102	1	+	+	PUNCT
ejpam-5458	102	2	ν	ν	X
ejpam-5458	102	3	]	]	X
ejpam-5458	102	4	w∗	w∗	NOUN
ejpam-5458	102	5	=	=	SYM
ejpam-5458	102	6	w0	w0	PROPN
ejpam-5458	102	7	+	+	CCONJ
ejpam-5458	103	1	µ[θ	µ[θ	ADV
ejpam-5458	103	2	−	−	NOUN
ejpam-5458	103	3	θcγp	θcγp	NOUN
ejpam-5458	103	4	cγp	cγp	NOUN
ejpam-5458	103	5	+	+	CCONJ
ejpam-5458	103	6	(	(	PUNCT
ejpam-5458	103	7	b−	b−	PROPN
ejpam-5458	103	8	1)cγx	1)cγx	PROPN
ejpam-5458	104	1	+	+	CCONJ
ejpam-5458	104	2	ν	ν	X
ejpam-5458	104	3	]	]	X
ejpam-5458	104	4	(	(	PUNCT
ejpam-5458	104	5	10	10	NUM
ejpam-5458	104	6	)	)	PUNCT
ejpam-5458	104	7	now	now	ADV
ejpam-5458	104	8	,	,	PUNCT
ejpam-5458	104	9	we	we	PRON
ejpam-5458	104	10	introduce	introduce	VERB
ejpam-5458	104	11	new	new	ADJ
ejpam-5458	104	12	variables	variable	NOUN
ejpam-5458	104	13	v	v	ADP
ejpam-5458	104	14	and	and	CCONJ
ejpam-5458	104	15	u	u	NOUN
ejpam-5458	104	16	for	for	ADP
ejpam-5458	104	17	shifting	shift	VERB
ejpam-5458	104	18	an	an	DET
ejpam-5458	104	19	equilibrium	equilibrium	NOUN
ejpam-5458	104	20	point	point	NOUN
ejpam-5458	104	21	(	(	PUNCT
ejpam-5458	104	22	c∗	c∗	PROPN
ejpam-5458	104	23	,	,	PUNCT
ejpam-5458	104	24	w∗	w∗	NOUN
ejpam-5458	104	25	)	)	PUNCT
ejpam-5458	104	26	to	to	ADP
ejpam-5458	104	27	the	the	DET
ejpam-5458	104	28	origin	origin	NOUN
ejpam-5458	104	29	(	(	PUNCT
ejpam-5458	104	30	0	0	NUM
ejpam-5458	104	31	,	,	PUNCT
ejpam-5458	104	32	0	0	NUM
ejpam-5458	104	33	):	):	PUNCT
ejpam-5458	104	34	v	v	NOUN
ejpam-5458	104	35	=	=	SYM
ejpam-5458	104	36	c−	c−	ADJ
ejpam-5458	104	37	c∗	c∗	PROPN
ejpam-5458	104	38	u	u	NOUN
ejpam-5458	104	39	=	=	PROPN
ejpam-5458	104	40	w	w	PROPN
ejpam-5458	104	41	−	−	PROPN
ejpam-5458	104	42	w∗	w∗	NOUN
ejpam-5458	104	43	is	be	AUX
ejpam-5458	104	44	an	an	DET
ejpam-5458	104	45	equilibrium	equilibrium	NOUN
ejpam-5458	104	46	point	point	NOUN
ejpam-5458	104	47	for	for	ADP
ejpam-5458	104	48	a	a	DET
ejpam-5458	104	49	two	two	NUM
ejpam-5458	104	50	-	-	PUNCT
ejpam-5458	104	51	dimensional	dimensional	ADJ
ejpam-5458	104	52	dynamical	dynamical	ADJ
ejpam-5458	104	53	system	system	NOUN
ejpam-5458	104	54	:	:	PUNCT
ejpam-5458	104	55	v̇	v̇	NOUN
ejpam-5458	104	56	=	=	SYM
ejpam-5458	104	57	f(v	f(v	NOUN
ejpam-5458	104	58	,	,	PUNCT
ejpam-5458	104	59	u	u	NOUN
ejpam-5458	104	60	)	)	PUNCT
ejpam-5458	104	61	u̇	u̇	NOUN
ejpam-5458	105	1	=	=	SYM
ejpam-5458	105	2	g(v	g(v	PROPN
ejpam-5458	105	3	,	,	PUNCT
ejpam-5458	105	4	u	u	NOUN
ejpam-5458	105	5	)	)	PUNCT
ejpam-5458	105	6	(	(	PUNCT
ejpam-5458	105	7	11	11	NUM
ejpam-5458	105	8	)	)	PUNCT
ejpam-5458	105	9	where	where	SCONJ
ejpam-5458	105	10	g	g	PROPN
ejpam-5458	105	11	and	and	CCONJ
ejpam-5458	105	12	f	f	PROPN
ejpam-5458	105	13	are	be	AUX
ejpam-5458	105	14	nonlinear	nonlinear	ADJ
ejpam-5458	105	15	,	,	PUNCT
ejpam-5458	105	16	corresponding	correspond	VERB
ejpam-5458	105	17	to	to	ADP
ejpam-5458	105	18	the	the	DET
ejpam-5458	105	19	linear	linear	ADJ
ejpam-5458	105	20	form	form	NOUN
ejpam-5458	105	21	[	[	PUNCT
ejpam-5458	105	22	v̇	v̇	NOUN
ejpam-5458	105	23	u̇	u̇	NOUN
ejpam-5458	105	24	]	]	X
ejpam-5458	106	1	=	=	PUNCT
ejpam-5458	106	2	[	[	PUNCT
ejpam-5458	106	3	fv	fv	X
ejpam-5458	106	4	fu	fu	NOUN
ejpam-5458	106	5	gv	gv	AUX
ejpam-5458	106	6	gu	gu	NOUN
ejpam-5458	106	7	]	]	PUNCT
ejpam-5458	107	1	[	[	PUNCT
ejpam-5458	107	2	v	v	NUM
ejpam-5458	107	3	u	u	NOUN
ejpam-5458	107	4	]	]	X
ejpam-5458	107	5	(	(	PUNCT
ejpam-5458	107	6	12	12	NUM
ejpam-5458	107	7	)	)	PUNCT
ejpam-5458	107	8	where	where	SCONJ
ejpam-5458	107	9	j(v	j(v	PROPN
ejpam-5458	107	10	,	,	PUNCT
ejpam-5458	107	11	u	u	NOUN
ejpam-5458	107	12	)	)	PUNCT
ejpam-5458	107	13	=	=	PUNCT
ejpam-5458	108	1	[	[	PUNCT
ejpam-5458	108	2	fv	fv	X
ejpam-5458	108	3	fu	fu	NOUN
ejpam-5458	108	4	gv	gv	ADP
ejpam-5458	108	5	gu	gu	X
ejpam-5458	108	6	]	]	PUNCT
ejpam-5458	108	7	i.	i.	PROPN
ejpam-5458	108	8	alraddadi	alraddadi	PROPN
ejpam-5458	108	9	/	/	SYM
ejpam-5458	108	10	eur	eur	PROPN
ejpam-5458	108	11	.	.	PUNCT
ejpam-5458	109	1	j.	j.	PROPN
ejpam-5458	109	2	pure	pure	PROPN
ejpam-5458	109	3	appl	appl	PROPN
ejpam-5458	109	4	.	.	PROPN
ejpam-5458	109	5	math	math	PROPN
ejpam-5458	109	6	,	,	PUNCT
ejpam-5458	109	7	17	17	NUM
ejpam-5458	109	8	(	(	PUNCT
ejpam-5458	109	9	4	4	NUM
ejpam-5458	109	10	)	)	PUNCT
ejpam-5458	109	11	(	(	PUNCT
ejpam-5458	109	12	2024	2024	NUM
ejpam-5458	109	13	)	)	PUNCT
ejpam-5458	109	14	,	,	PUNCT
ejpam-5458	109	15	3708	3708	NUM
ejpam-5458	109	16	-	-	SYM
ejpam-5458	109	17	3729	3729	NUM
ejpam-5458	109	18	3713	3713	NUM
ejpam-5458	109	19	figure	figure	NOUN
ejpam-5458	109	20	3	3	NUM
ejpam-5458	109	21	:	:	PUNCT
ejpam-5458	109	22	the	the	DET
ejpam-5458	109	23	phase	phase	NOUN
ejpam-5458	109	24	portrait	portrait	NOUN
ejpam-5458	109	25	(	(	PUNCT
ejpam-5458	109	26	a	a	NOUN
ejpam-5458	109	27	)	)	PUNCT
ejpam-5458	109	28	and	and	CCONJ
ejpam-5458	109	29	time	time	NOUN
ejpam-5458	109	30	series	series	NOUN
ejpam-5458	109	31	(	(	PUNCT
ejpam-5458	109	32	b	b	NOUN
ejpam-5458	109	33	-	-	PUNCT
ejpam-5458	109	34	c	c	NOUN
ejpam-5458	109	35	)	)	PUNCT
ejpam-5458	109	36	show	show	VERB
ejpam-5458	109	37	a	a	DET
ejpam-5458	109	38	stable	stable	ADJ
ejpam-5458	109	39	limit	limit	NOUN
ejpam-5458	109	40	cycle	cycle	NOUN
ejpam-5458	109	41	of	of	ADP
ejpam-5458	109	42	rothman	rothman	PROPN
ejpam-5458	109	43	’s	’s	PART
ejpam-5458	109	44	carbon	carbon	NOUN
ejpam-5458	109	45	cycle	cycle	NOUN
ejpam-5458	109	46	model	model	NOUN
ejpam-5458	109	47	(	(	PUNCT
ejpam-5458	109	48	7	7	NUM
ejpam-5458	109	49	)	)	PUNCT
ejpam-5458	109	50	for	for	ADP
ejpam-5458	109	51	cx	cx	NOUN
ejpam-5458	109	52	=	=	SYM
ejpam-5458	109	53	70	70	NUM
ejpam-5458	109	54	.	.	PUNCT
ejpam-5458	110	1	the	the	DET
ejpam-5458	110	2	initial	initial	ADJ
ejpam-5458	110	3	condition	condition	NOUN
ejpam-5458	110	4	and	and	CCONJ
ejpam-5458	110	5	other	other	ADJ
ejpam-5458	110	6	parameters	parameter	NOUN
ejpam-5458	110	7	are	be	AUX
ejpam-5458	110	8	given	give	VERB
ejpam-5458	110	9	values	value	NOUN
ejpam-5458	110	10	in	in	ADP
ejpam-5458	110	11	table	table	NOUN
ejpam-5458	110	12	1	1	NUM
ejpam-5458	110	13	.	.	PUNCT
ejpam-5458	111	1	the	the	DET
ejpam-5458	111	2	black	black	ADJ
ejpam-5458	111	3	circle	circle	NOUN
ejpam-5458	111	4	represents	represent	VERB
ejpam-5458	111	5	an	an	DET
ejpam-5458	111	6	unstable	unstable	ADJ
ejpam-5458	111	7	equilibrium	equilibrium	NOUN
ejpam-5458	111	8	point	point	NOUN
ejpam-5458	111	9	(	(	PUNCT
ejpam-5458	111	10	c∗	c∗	PROPN
ejpam-5458	111	11	,	,	PUNCT
ejpam-5458	111	12	w∗	w∗	PROPN
ejpam-5458	111	13	)	)	PUNCT
ejpam-5458	111	14	.	.	PUNCT
ejpam-5458	112	1	the	the	DET
ejpam-5458	112	2	nullclines	nullcline	NOUN
ejpam-5458	112	3	represent	represent	VERB
ejpam-5458	112	4	the	the	DET
ejpam-5458	112	5	red	red	ADJ
ejpam-5458	112	6	line	line	NOUN
ejpam-5458	112	7	ẇ	ẇ	PROPN
ejpam-5458	112	8	=	=	SYM
ejpam-5458	112	9	0	0	NUM
ejpam-5458	112	10	and	and	CCONJ
ejpam-5458	112	11	black	black	ADJ
ejpam-5458	112	12	line	line	NOUN
ejpam-5458	112	13	ċ	ċ	NOUN
ejpam-5458	113	1	=	=	SYM
ejpam-5458	113	2	0	0	PROPN
ejpam-5458	113	3	.	.	PUNCT
ejpam-5458	113	4	is	be	AUX
ejpam-5458	113	5	the	the	DET
ejpam-5458	113	6	jacobian	jacobian	ADJ
ejpam-5458	113	7	matrix	matrix	NOUN
ejpam-5458	113	8	of	of	ADP
ejpam-5458	113	9	(	(	PUNCT
ejpam-5458	113	10	11	11	NUM
ejpam-5458	113	11	)	)	PUNCT
ejpam-5458	113	12	at	at	ADP
ejpam-5458	113	13	the	the	DET
ejpam-5458	113	14	equilibrium	equilibrium	NOUN
ejpam-5458	113	15	point	point	NOUN
ejpam-5458	113	16	(	(	PUNCT
ejpam-5458	113	17	v	v	NOUN
ejpam-5458	113	18	,	,	PUNCT
ejpam-5458	113	19	u	u	NOUN
ejpam-5458	113	20	)	)	PUNCT
ejpam-5458	113	21	.	.	PUNCT
ejpam-5458	114	1	the	the	DET
ejpam-5458	114	2	trace	trace	NOUN
ejpam-5458	114	3	τ(v	τ(v	PROPN
ejpam-5458	114	4	,	,	PUNCT
ejpam-5458	114	5	u	u	NOUN
ejpam-5458	114	6	)	)	PUNCT
ejpam-5458	114	7	and	and	CCONJ
ejpam-5458	114	8	the	the	DET
ejpam-5458	114	9	determinant	determinant	PROPN
ejpam-5458	114	10	∆(v	∆(v	PROPN
ejpam-5458	114	11	,	,	PUNCT
ejpam-5458	114	12	u	u	NOUN
ejpam-5458	114	13	)	)	PUNCT
ejpam-5458	114	14	of	of	ADP
ejpam-5458	114	15	j	j	PROPN
ejpam-5458	114	16	are	be	AUX
ejpam-5458	114	17	τ	τ	PROPN
ejpam-5458	114	18	=	=	SYM
ejpam-5458	114	19	trj	trj	X
ejpam-5458	114	20	=	=	SYM
ejpam-5458	114	21	fv	fv	PROPN
ejpam-5458	114	22	+	+	CCONJ
ejpam-5458	114	23	gu	gu	NOUN
ejpam-5458	114	24	∆	∆	PROPN
ejpam-5458	114	25	=	=	PUNCT
ejpam-5458	114	26	detj	detj	NOUN
ejpam-5458	114	27	=	=	PUNCT
ejpam-5458	114	28	fvgu	fvgu	NOUN
ejpam-5458	114	29	−	−	PROPN
ejpam-5458	114	30	gvgu	gvgu	NOUN
ejpam-5458	114	31	to	to	PART
ejpam-5458	114	32	analyse	analyse	VERB
ejpam-5458	114	33	the	the	DET
ejpam-5458	114	34	stability	stability	NOUN
ejpam-5458	114	35	of	of	ADP
ejpam-5458	114	36	the	the	DET
ejpam-5458	114	37	equilibrium	equilibrium	NOUN
ejpam-5458	114	38	point	point	NOUN
ejpam-5458	114	39	,	,	PUNCT
ejpam-5458	114	40	we	we	PRON
ejpam-5458	114	41	find	find	VERB
ejpam-5458	114	42	the	the	DET
ejpam-5458	114	43	eigenvalues	eigenvalue	NOUN
ejpam-5458	114	44	of	of	ADP
ejpam-5458	114	45	(	(	PUNCT
ejpam-5458	114	46	j	j	PROPN
ejpam-5458	114	47	−	−	PROPN
ejpam-5458	114	48	λi	λi	NOUN
ejpam-5458	114	49	)	)	PUNCT
ejpam-5458	114	50	at	at	ADP
ejpam-5458	114	51	(	(	PUNCT
ejpam-5458	114	52	u	u	NOUN
ejpam-5458	114	53	,	,	PUNCT
ejpam-5458	114	54	v	v	NOUN
ejpam-5458	114	55	)	)	PUNCT
ejpam-5458	114	56	where	where	SCONJ
ejpam-5458	114	57	i	i	PRON
ejpam-5458	114	58	is	be	AUX
ejpam-5458	114	59	the	the	DET
ejpam-5458	114	60	identity	identity	NOUN
ejpam-5458	114	61	matrix	matrix	NOUN
ejpam-5458	114	62	:	:	PUNCT
ejpam-5458	114	63	λ1,2	λ1,2	PROPN
ejpam-5458	114	64	=	=	SYM
ejpam-5458	114	65	τ	τ	X
ejpam-5458	114	66	±	±	NUM
ejpam-5458	114	67	√	√	NOUN
ejpam-5458	114	68	τ2	τ2	PROPN
ejpam-5458	114	69	−	−	PROPN
ejpam-5458	114	70	4∆	4∆	NUM
ejpam-5458	114	71	2	2	NUM
ejpam-5458	114	72	according	accord	VERB
ejpam-5458	114	73	to	to	ADP
ejpam-5458	114	74	τ	τ	PROPN
ejpam-5458	114	75	and	and	CCONJ
ejpam-5458	114	76	∆	∆	PROPN
ejpam-5458	114	77	of	of	ADP
ejpam-5458	114	78	j	j	PROPN
ejpam-5458	114	79	,	,	PUNCT
ejpam-5458	114	80	the	the	DET
ejpam-5458	114	81	stable	stable	ADJ
ejpam-5458	114	82	equilibrium	equilibrium	NOUN
ejpam-5458	114	83	point	point	NOUN
ejpam-5458	114	84	is	be	AUX
ejpam-5458	114	85	(	(	PUNCT
ejpam-5458	114	86	τ	τ	X
ejpam-5458	114	87	<	<	X
ejpam-5458	114	88	0	0	NUM
ejpam-5458	114	89	)	)	PUNCT
ejpam-5458	114	90	and	and	CCONJ
ejpam-5458	114	91	unstable	unstable	ADJ
ejpam-5458	114	92	equilibrium	equilibrium	NOUN
ejpam-5458	114	93	point	point	NOUN
ejpam-5458	114	94	is	be	AUX
ejpam-5458	114	95	(	(	PUNCT
ejpam-5458	114	96	τ	τ	X
ejpam-5458	114	97	>	>	X
ejpam-5458	114	98	0	0	NUM
ejpam-5458	114	99	)	)	PUNCT
ejpam-5458	114	100	.	.	PUNCT
ejpam-5458	115	1	now	now	ADV
ejpam-5458	115	2	,	,	PUNCT
ejpam-5458	115	3	we	we	PRON
ejpam-5458	115	4	return	return	VERB
ejpam-5458	115	5	to	to	ADP
ejpam-5458	115	6	the	the	DET
ejpam-5458	115	7	rothman	rothman	PROPN
ejpam-5458	115	8	carbon	carbon	PROPN
ejpam-5458	115	9	cycle	cycle	NOUN
ejpam-5458	115	10	model	model	NOUN
ejpam-5458	115	11	(	(	PUNCT
ejpam-5458	115	12	7	7	NUM
ejpam-5458	115	13	)	)	PUNCT
ejpam-5458	115	14	,	,	PUNCT
ejpam-5458	115	15	τ	τ	PROPN
ejpam-5458	115	16	=	=	PUNCT
ejpam-5458	115	17	−1±	−1±	NOUN
ejpam-5458	115	18	∆	∆	X
ejpam-5458	115	19	2	2	NUM
ejpam-5458	115	20	(	(	PUNCT
ejpam-5458	115	21	1−	1−	NUM
ejpam-5458	115	22	θbcγpc	θbcγpc	NOUN
ejpam-5458	115	23	γ	γ	X
ejpam-5458	115	24	x	x	PROPN
ejpam-5458	115	25	cγp	cγp	PROPN
ejpam-5458	115	26	+	+	X
ejpam-5458	116	1	[	[	X
ejpam-5458	116	2	(	(	PUNCT
ejpam-5458	116	3	b−	b−	PROPN
ejpam-5458	116	4	1)cγx]2	1)cγx]2	NUM
ejpam-5458	116	5	)	)	PUNCT
ejpam-5458	116	6	(	(	PUNCT
ejpam-5458	116	7	13	13	X
ejpam-5458	116	8	)	)	PUNCT
ejpam-5458	116	9	i.	i.	NOUN
ejpam-5458	116	10	alraddadi	alraddadi	PROPN
ejpam-5458	116	11	/	/	SYM
ejpam-5458	116	12	eur	eur	PROPN
ejpam-5458	116	13	.	.	PUNCT
ejpam-5458	117	1	j.	j.	PROPN
ejpam-5458	117	2	pure	pure	PROPN
ejpam-5458	117	3	appl	appl	PROPN
ejpam-5458	117	4	.	.	PROPN
ejpam-5458	117	5	math	math	PROPN
ejpam-5458	117	6	,	,	PUNCT
ejpam-5458	117	7	17	17	NUM
ejpam-5458	117	8	(	(	PUNCT
ejpam-5458	117	9	4	4	NUM
ejpam-5458	117	10	)	)	PUNCT
ejpam-5458	117	11	(	(	PUNCT
ejpam-5458	117	12	2024	2024	NUM
ejpam-5458	117	13	)	)	PUNCT
ejpam-5458	117	14	,	,	PUNCT
ejpam-5458	117	15	3708	3708	NUM
ejpam-5458	117	16	-	-	SYM
ejpam-5458	117	17	3729	3729	NUM
ejpam-5458	117	18	3714	3714	NUM
ejpam-5458	117	19	figure	figure	NOUN
ejpam-5458	117	20	4	4	NUM
ejpam-5458	117	21	:	:	PUNCT
ejpam-5458	117	22	this	this	DET
ejpam-5458	117	23	figure	figure	NOUN
ejpam-5458	117	24	shows	show	VERB
ejpam-5458	117	25	the	the	DET
ejpam-5458	117	26	stability	stability	NOUN
ejpam-5458	117	27	region	region	NOUN
ejpam-5458	117	28	of	of	ADP
ejpam-5458	117	29	the	the	DET
ejpam-5458	117	30	equilibrium	equilibrium	NOUN
ejpam-5458	117	31	point	point	NOUN
ejpam-5458	117	32	(	(	PUNCT
ejpam-5458	117	33	c∗	c∗	PROPN
ejpam-5458	117	34	,	,	PUNCT
ejpam-5458	117	35	w∗	w∗	NOUN
ejpam-5458	117	36	)	)	PUNCT
ejpam-5458	117	37	for	for	ADP
ejpam-5458	117	38	rothman	rothman	PROPN
ejpam-5458	117	39	’s	’s	PART
ejpam-5458	117	40	carbon	carbon	NOUN
ejpam-5458	117	41	cycle	cycle	NOUN
ejpam-5458	117	42	model	model	NOUN
ejpam-5458	117	43	(	(	PUNCT
ejpam-5458	117	44	7	7	NUM
ejpam-5458	117	45	)	)	PUNCT
ejpam-5458	117	46	in	in	ADP
ejpam-5458	117	47	parameter	parameter	NOUN
ejpam-5458	117	48	space	space	NOUN
ejpam-5458	117	49	of	of	ADP
ejpam-5458	117	50	cp	cp	PROPN
ejpam-5458	117	51	and	and	CCONJ
ejpam-5458	117	52	b.	b.	PROPN
ejpam-5458	117	53	other	other	ADJ
ejpam-5458	117	54	parameters	parameter	NOUN
ejpam-5458	117	55	are	be	AUX
ejpam-5458	117	56	given	give	VERB
ejpam-5458	117	57	in	in	ADP
ejpam-5458	117	58	table	table	NOUN
ejpam-5458	117	59	1	1	NUM
ejpam-5458	117	60	.	.	PUNCT
ejpam-5458	118	1	the	the	DET
ejpam-5458	118	2	stability	stability	NOUN
ejpam-5458	118	3	region	region	NOUN
ejpam-5458	118	4	is	be	AUX
ejpam-5458	118	5	divided	divide	VERB
ejpam-5458	118	6	into	into	ADP
ejpam-5458	118	7	four	four	NUM
ejpam-5458	118	8	regions	region	NOUN
ejpam-5458	118	9	.	.	PUNCT
ejpam-5458	119	1	the	the	DET
ejpam-5458	119	2	yellow	yellow	ADJ
ejpam-5458	119	3	and	and	CCONJ
ejpam-5458	119	4	green	green	ADJ
ejpam-5458	119	5	regions	region	NOUN
ejpam-5458	119	6	represent	represent	VERB
ejpam-5458	119	7	the	the	DET
ejpam-5458	119	8	stable	stable	ADJ
ejpam-5458	119	9	and	and	CCONJ
ejpam-5458	119	10	unstable	unstable	ADJ
ejpam-5458	119	11	node	node	NOUN
ejpam-5458	119	12	respectively	respectively	ADV
ejpam-5458	119	13	,	,	PUNCT
ejpam-5458	119	14	where	where	SCONJ
ejpam-5458	119	15	(	(	PUNCT
ejpam-5458	119	16	c∗	c∗	PROPN
ejpam-5458	119	17	,	,	PUNCT
ejpam-5458	119	18	w∗	w∗	PROPN
ejpam-5458	119	19	)	)	PUNCT
ejpam-5458	119	20	has	have	VERB
ejpam-5458	119	21	real	real	ADJ
ejpam-5458	119	22	eigenvalues	eigenvalue	NOUN
ejpam-5458	119	23	.	.	PUNCT
ejpam-5458	120	1	the	the	DET
ejpam-5458	120	2	blue	blue	ADJ
ejpam-5458	120	3	and	and	CCONJ
ejpam-5458	120	4	red	red	ADJ
ejpam-5458	120	5	regions	region	NOUN
ejpam-5458	120	6	represent	represent	VERB
ejpam-5458	120	7	a	a	DET
ejpam-5458	120	8	stable	stable	ADJ
ejpam-5458	120	9	spiral	spiral	NOUN
ejpam-5458	120	10	and	and	CCONJ
ejpam-5458	120	11	an	an	DET
ejpam-5458	120	12	unstable	unstable	ADJ
ejpam-5458	120	13	spiral	spiral	NOUN
ejpam-5458	120	14	where	where	SCONJ
ejpam-5458	120	15	(	(	PUNCT
ejpam-5458	120	16	c∗	c∗	PROPN
ejpam-5458	120	17	,	,	PUNCT
ejpam-5458	120	18	w∗	w∗	NOUN
ejpam-5458	120	19	)	)	PUNCT
ejpam-5458	120	20	has	have	VERB
ejpam-5458	120	21	complex	complex	ADJ
ejpam-5458	120	22	eigenvalues	eigenvalue	NOUN
ejpam-5458	120	23	.	.	PUNCT
ejpam-5458	121	1	note	note	VERB
ejpam-5458	121	2	hopf	hopf	ADJ
ejpam-5458	121	3	bifurcations	bifurcation	NOUN
ejpam-5458	121	4	occur	occur	VERB
ejpam-5458	121	5	on	on	ADP
ejpam-5458	121	6	the	the	DET
ejpam-5458	121	7	boundary	boundary	NOUN
ejpam-5458	121	8	between	between	ADP
ejpam-5458	121	9	the	the	DET
ejpam-5458	121	10	blue	blue	ADJ
ejpam-5458	121	11	and	and	CCONJ
ejpam-5458	121	12	red	red	ADJ
ejpam-5458	121	13	regions	region	NOUN
ejpam-5458	121	14	where	where	SCONJ
ejpam-5458	121	15	(	(	PUNCT
ejpam-5458	121	16	c∗	c∗	PROPN
ejpam-5458	121	17	,	,	PUNCT
ejpam-5458	121	18	w∗	w∗	PROPN
ejpam-5458	121	19	)	)	PUNCT
ejpam-5458	121	20	has	have	VERB
ejpam-5458	121	21	purely	purely	ADV
ejpam-5458	121	22	imaginary	imaginary	ADJ
ejpam-5458	121	23	eigenvalues	eigenvalue	NOUN
ejpam-5458	121	24	.	.	PUNCT
ejpam-5458	122	1	where	where	SCONJ
ejpam-5458	122	2	,	,	PUNCT
ejpam-5458	122	3	∆	∆	PROPN
ejpam-5458	122	4	=	=	PUNCT
ejpam-5458	122	5	2µγf0(b−	2µγf0(b−	NUM
ejpam-5458	122	6	1	1	NUM
ejpam-5458	122	7	)	)	PUNCT
ejpam-5458	122	8	1	1	NUM
ejpam-5458	122	9	γ	γ	X
ejpam-5458	122	10	+1	+1	PROPN
ejpam-5458	122	11	cβ−1	cβ−1	VERB
ejpam-5458	122	12	p	p	PRON
ejpam-5458	122	13	b(b−	b(b−	NOUN
ejpam-5458	122	14	1)β	1)β	PROPN
ejpam-5458	122	15	/	/	SYM
ejpam-5458	122	16	γcβf	γcβf	NOUN
ejpam-5458	122	17	+	+	CCONJ
ejpam-5458	122	18	bcβp	bcβp	NOUN
ejpam-5458	122	19	(	(	PUNCT
ejpam-5458	122	20	14	14	NUM
ejpam-5458	122	21	)	)	PUNCT
ejpam-5458	122	22	since	since	SCONJ
ejpam-5458	122	23	b	b	PROPN
ejpam-5458	122	24	>	>	SYM
ejpam-5458	122	25	1	1	NUM
ejpam-5458	122	26	and	and	CCONJ
ejpam-5458	122	27	all	all	DET
ejpam-5458	122	28	parameters	parameter	NOUN
ejpam-5458	122	29	are	be	AUX
ejpam-5458	122	30	positive	positive	ADJ
ejpam-5458	122	31	,	,	PUNCT
ejpam-5458	122	32	the	the	DET
ejpam-5458	122	33	sign	sign	NOUN
ejpam-5458	122	34	of	of	ADP
ejpam-5458	122	35	τ	τ	PROPN
ejpam-5458	122	36	depends	depend	VERB
ejpam-5458	122	37	on	on	ADP
ejpam-5458	122	38	θ	θ	PROPN
ejpam-5458	122	39	and	and	CCONJ
ejpam-5458	122	40	µ	µ	X
ejpam-5458	122	41	(	(	PUNCT
ejpam-5458	122	42	i.e.	i.e.	X
ejpam-5458	122	43	τ	τ	X
ejpam-5458	122	44	>	>	X
ejpam-5458	122	45	0	0	PUNCT
ejpam-5458	122	46	when	when	SCONJ
ejpam-5458	122	47	µ	µ	X
ejpam-5458	122	48	≫	≫	PROPN
ejpam-5458	122	49	0	0	NUM
ejpam-5458	122	50	and	and	CCONJ
ejpam-5458	122	51	τ	τ	X
ejpam-5458	122	52	<	<	X
ejpam-5458	122	53	0	0	PUNCT
ejpam-5458	122	54	when	when	SCONJ
ejpam-5458	122	55	θ	θ	PROPN
ejpam-5458	122	56	>	>	X
ejpam-5458	122	57	0	0	NUM
ejpam-5458	122	58	)	)	PUNCT
ejpam-5458	122	59	.	.	PUNCT
ejpam-5458	123	1	λ1,2	λ1,2	NUM
ejpam-5458	123	2	are	be	AUX
ejpam-5458	123	3	pure	pure	ADJ
ejpam-5458	123	4	imaginary	imaginary	ADJ
ejpam-5458	123	5	when	when	SCONJ
ejpam-5458	123	6	τ	τ	PROPN
ejpam-5458	123	7	=	=	SYM
ejpam-5458	123	8	0	0	PUNCT
ejpam-5458	123	9	(	(	PUNCT
ejpam-5458	123	10	let	let	VERB
ejpam-5458	123	11	µ	µ	X
ejpam-5458	123	12	=	=	PUNCT
ejpam-5458	123	13	µc	µc	ADP
ejpam-5458	123	14	where	where	SCONJ
ejpam-5458	123	15	τ	τ	X
ejpam-5458	123	16	=	=	NOUN
ejpam-5458	123	17	0	0	NUM
ejpam-5458	123	18	)	)	PUNCT
ejpam-5458	123	19	.	.	PUNCT
ejpam-5458	124	1	the	the	DET
ejpam-5458	124	2	stability	stability	NOUN
ejpam-5458	124	3	of	of	ADP
ejpam-5458	124	4	this	this	DET
ejpam-5458	124	5	equilibrium	equilibrium	NOUN
ejpam-5458	124	6	point	point	NOUN
ejpam-5458	124	7	(	(	PUNCT
ejpam-5458	124	8	c∗	c∗	PROPN
ejpam-5458	124	9	,	,	PUNCT
ejpam-5458	124	10	w∗	w∗	PROPN
ejpam-5458	124	11	)	)	PUNCT
ejpam-5458	124	12	is	be	AUX
ejpam-5458	124	13	determined	determine	VERB
ejpam-5458	124	14	by	by	ADP
ejpam-5458	124	15	the	the	DET
ejpam-5458	124	16	sign	sign	NOUN
ejpam-5458	124	17	of	of	ADP
ejpam-5458	124	18	the	the	DET
ejpam-5458	124	19	eigenvalues	eigenvalues	PROPN
ejpam-5458	124	20	λ1,2	λ1,2	PROPN
ejpam-5458	124	21	of	of	ADP
ejpam-5458	124	22	the	the	DET
ejpam-5458	124	23	jacobian	jacobian	ADJ
ejpam-5458	124	24	matrix	matrix	NOUN
ejpam-5458	124	25	.	.	PUNCT
ejpam-5458	125	1	we	we	PRON
ejpam-5458	125	2	use	use	VERB
ejpam-5458	125	3	(	(	PUNCT
ejpam-5458	125	4	13	13	NUM
ejpam-5458	125	5	)	)	PUNCT
ejpam-5458	125	6	and	and	CCONJ
ejpam-5458	125	7	(	(	PUNCT
ejpam-5458	125	8	14	14	NUM
ejpam-5458	125	9	)	)	PUNCT
ejpam-5458	125	10	to	to	PART
ejpam-5458	125	11	find	find	VERB
ejpam-5458	125	12	numerically	numerically	ADV
ejpam-5458	125	13	(	(	PUNCT
ejpam-5458	125	14	using	use	VERB
ejpam-5458	125	15	matlab	matlab	PROPN
ejpam-5458	125	16	)	)	PUNCT
ejpam-5458	125	17	λ1,2	λ1,2	NOUN
ejpam-5458	125	18	.	.	PUNCT
ejpam-5458	126	1	in	in	ADP
ejpam-5458	126	2	figure	figure	NOUN
ejpam-5458	126	3	5	5	NUM
ejpam-5458	126	4	,	,	PUNCT
ejpam-5458	126	5	we	we	PRON
ejpam-5458	126	6	examine	examine	VERB
ejpam-5458	126	7	the	the	DET
ejpam-5458	126	8	stability	stability	NOUN
ejpam-5458	126	9	of	of	ADP
ejpam-5458	126	10	(	(	PUNCT
ejpam-5458	126	11	c∗	c∗	PROPN
ejpam-5458	126	12	,	,	PUNCT
ejpam-5458	126	13	w∗	w∗	NOUN
ejpam-5458	126	14	)	)	PUNCT
ejpam-5458	126	15	over	over	ADP
ejpam-5458	126	16	a	a	DET
ejpam-5458	126	17	range	range	NOUN
ejpam-5458	126	18	of	of	ADP
ejpam-5458	126	19	values	value	NOUN
ejpam-5458	126	20	of	of	ADP
ejpam-5458	126	21	parameters	parameter	NOUN
ejpam-5458	126	22	b	b	PROPN
ejpam-5458	126	23	(	(	PUNCT
ejpam-5458	126	24	a	a	DET
ejpam-5458	126	25	-	-	PUNCT
ejpam-5458	126	26	b	b	NOUN
ejpam-5458	126	27	)	)	PUNCT
ejpam-5458	126	28	and	and	CCONJ
ejpam-5458	126	29	cp	cp	INTJ
ejpam-5458	126	30	(	(	PUNCT
ejpam-5458	126	31	c	c	NOUN
ejpam-5458	126	32	-	-	PUNCT
ejpam-5458	126	33	d	d	NOUN
ejpam-5458	126	34	)	)	PUNCT
ejpam-5458	126	35	,	,	PUNCT
ejpam-5458	126	36	respectively	respectively	ADV
ejpam-5458	126	37	.	.	PUNCT
ejpam-5458	127	1	other	other	ADJ
ejpam-5458	127	2	parameter	parameter	NOUN
ejpam-5458	127	3	values	value	NOUN
ejpam-5458	127	4	of	of	ADP
ejpam-5458	127	5	(	(	PUNCT
ejpam-5458	127	6	7	7	X
ejpam-5458	127	7	)	)	PUNCT
ejpam-5458	127	8	are	be	AUX
ejpam-5458	127	9	given	give	VERB
ejpam-5458	127	10	in	in	ADP
ejpam-5458	127	11	table	table	NOUN
ejpam-5458	127	12	1	1	NUM
ejpam-5458	127	13	.	.	PUNCT
ejpam-5458	128	1	the	the	DET
ejpam-5458	128	2	colored	colored	ADJ
ejpam-5458	128	3	branch	branch	NOUN
ejpam-5458	128	4	shows	show	VERB
ejpam-5458	128	5	the	the	DET
ejpam-5458	128	6	location	location	NOUN
ejpam-5458	128	7	and	and	CCONJ
ejpam-5458	128	8	the	the	DET
ejpam-5458	128	9	stability	stability	NOUN
ejpam-5458	128	10	of	of	ADP
ejpam-5458	128	11	(	(	PUNCT
ejpam-5458	128	12	c∗	c∗	PROPN
ejpam-5458	128	13	,	,	PUNCT
ejpam-5458	128	14	w∗	w∗	NOUN
ejpam-5458	128	15	)	)	PUNCT
ejpam-5458	128	16	when	when	SCONJ
ejpam-5458	128	17	one	one	NUM
ejpam-5458	128	18	parameter	parameter	NOUN
ejpam-5458	128	19	is	be	AUX
ejpam-5458	128	20	varied	varied	ADJ
ejpam-5458	128	21	.	.	PUNCT
ejpam-5458	129	1	green	green	ADJ
ejpam-5458	129	2	/	/	SYM
ejpam-5458	129	3	yellow	yellow	ADJ
ejpam-5458	129	4	branches	branch	NOUN
ejpam-5458	129	5	indicate	indicate	VERB
ejpam-5458	129	6	that	that	SCONJ
ejpam-5458	129	7	a	a	DET
ejpam-5458	129	8	stable	stable	ADJ
ejpam-5458	129	9	/	/	SYM
ejpam-5458	129	10	unstable	unstable	ADJ
ejpam-5458	129	11	node	node	NOUN
ejpam-5458	129	12	equilibrium	equilibrium	NOUN
ejpam-5458	129	13	point	point	NOUN
ejpam-5458	129	14	has	have	VERB
ejpam-5458	129	15	positive	positive	ADJ
ejpam-5458	129	16	/negative	/negative	ADJ
ejpam-5458	129	17	real	real	ADJ
ejpam-5458	129	18	eigenvalues	eigenvalue	NOUN
ejpam-5458	129	19	,	,	PUNCT
ejpam-5458	129	20	respectively	respectively	ADV
ejpam-5458	129	21	.	.	PUNCT
ejpam-5458	130	1	red	red	ADJ
ejpam-5458	130	2	/	/	SYM
ejpam-5458	130	3	blue	blue	ADJ
ejpam-5458	130	4	branches	branch	NOUN
ejpam-5458	130	5	indicate	indicate	VERB
ejpam-5458	130	6	that	that	SCONJ
ejpam-5458	130	7	a	a	DET
ejpam-5458	130	8	stable	stable	ADJ
ejpam-5458	130	9	/	/	SYM
ejpam-5458	130	10	unstable	unstable	ADJ
ejpam-5458	130	11	spiral	spiral	ADJ
ejpam-5458	130	12	equilibrium	equilibrium	NOUN
ejpam-5458	130	13	point	point	NOUN
ejpam-5458	130	14	has	have	VERB
ejpam-5458	130	15	negative	negative	ADJ
ejpam-5458	130	16	/	/	SYM
ejpam-5458	130	17	positive	positive	ADJ
ejpam-5458	130	18	real	real	ADJ
ejpam-5458	130	19	parts	part	NOUN
ejpam-5458	130	20	of	of	ADP
ejpam-5458	130	21	complex	complex	ADJ
ejpam-5458	130	22	eigenvalues	eigenvalue	NOUN
ejpam-5458	130	23	,	,	PUNCT
ejpam-5458	130	24	respectively	respectively	ADV
ejpam-5458	130	25	.	.	PUNCT
ejpam-5458	131	1	as	as	SCONJ
ejpam-5458	131	2	discussed	discuss	VERB
ejpam-5458	131	3	in	in	ADP
ejpam-5458	131	4	[	[	X
ejpam-5458	131	5	12	12	NUM
ejpam-5458	131	6	]	]	PUNCT
ejpam-5458	131	7	,	,	PUNCT
ejpam-5458	131	8	rothman	rothman	PROPN
ejpam-5458	131	9	identifies	identify	VERB
ejpam-5458	131	10	supercritical	supercritical	ADJ
ejpam-5458	131	11	and	and	CCONJ
ejpam-5458	131	12	subcritical	subcritical	ADJ
ejpam-5458	131	13	hopf	hopf	ADJ
ejpam-5458	131	14	bifurcation	bifurcation	NOUN
ejpam-5458	131	15	branches	branch	NOUN
ejpam-5458	131	16	and	and	CCONJ
ejpam-5458	131	17	the	the	DET
ejpam-5458	131	18	stable	stable	ADJ
ejpam-5458	131	19	equilibrium	equilibrium	NOUN
ejpam-5458	131	20	point	point	NOUN
ejpam-5458	131	21	are	be	AUX
ejpam-5458	131	22	in	in	ADP
ejpam-5458	131	23	the	the	DET
ejpam-5458	131	24	parameter	parameter	NOUN
ejpam-5458	131	25	space	space	NOUN
ejpam-5458	131	26	.	.	PUNCT
ejpam-5458	132	1	here	here	ADV
ejpam-5458	132	2	,	,	PUNCT
ejpam-5458	132	3	we	we	PRON
ejpam-5458	132	4	review	review	VERB
ejpam-5458	132	5	some	some	DET
ejpam-5458	132	6	results	result	NOUN
ejpam-5458	132	7	from	from	ADP
ejpam-5458	132	8	[	[	X
ejpam-5458	132	9	12	12	NUM
ejpam-5458	132	10	]	]	PUNCT
ejpam-5458	132	11	to	to	PART
ejpam-5458	132	12	extend	extend	VERB
ejpam-5458	132	13	in	in	ADP
ejpam-5458	132	14	the	the	DET
ejpam-5458	132	15	analysis	analysis	NOUN
ejpam-5458	132	16	of	of	ADP
ejpam-5458	132	17	the	the	DET
ejpam-5458	132	18	equilibrium	equilibrium	NOUN
ejpam-5458	132	19	point	point	NOUN
ejpam-5458	132	20	in	in	ADP
ejpam-5458	132	21	the	the	DET
ejpam-5458	132	22	parameter	parameter	NOUN
ejpam-5458	132	23	spaces	space	NOUN
ejpam-5458	132	24	as	as	SCONJ
ejpam-5458	132	25	shown	show	VERB
ejpam-5458	132	26	in	in	ADP
ejpam-5458	132	27	figure	figure	NOUN
ejpam-5458	132	28	6	6	NUM
ejpam-5458	132	29	.	.	PUNCT
ejpam-5458	133	1	the	the	DET
ejpam-5458	133	2	stability	stability	NOUN
ejpam-5458	133	3	of	of	ADP
ejpam-5458	133	4	(	(	PUNCT
ejpam-5458	133	5	c∗	c∗	PROPN
ejpam-5458	133	6	,	,	PUNCT
ejpam-5458	133	7	w∗	w∗	PROPN
ejpam-5458	133	8	)	)	PUNCT
ejpam-5458	133	9	is	be	AUX
ejpam-5458	133	10	indicated	indicate	VERB
ejpam-5458	133	11	by	by	ADP
ejpam-5458	133	12	the	the	DET
ejpam-5458	133	13	yellow	yellow	ADJ
ejpam-5458	133	14	region	region	NOUN
ejpam-5458	133	15	(	(	PUNCT
ejpam-5458	133	16	stable	stable	ADJ
ejpam-5458	133	17	node	node	NOUN
ejpam-5458	133	18	)	)	PUNCT
ejpam-5458	133	19	,	,	PUNCT
ejpam-5458	133	20	the	the	DET
ejpam-5458	133	21	green	green	ADJ
ejpam-5458	133	22	region	region	NOUN
ejpam-5458	133	23	(	(	PUNCT
ejpam-5458	133	24	unstable	unstable	ADJ
ejpam-5458	133	25	node	node	NOUN
ejpam-5458	133	26	)	)	PUNCT
ejpam-5458	133	27	,	,	PUNCT
ejpam-5458	133	28	the	the	DET
ejpam-5458	133	29	blue	blue	ADJ
ejpam-5458	133	30	region	region	NOUN
ejpam-5458	133	31	(	(	PUNCT
ejpam-5458	133	32	stable	stable	ADJ
ejpam-5458	133	33	spiral	spiral	NOUN
ejpam-5458	133	34	)	)	PUNCT
ejpam-5458	133	35	and	and	CCONJ
ejpam-5458	133	36	the	the	DET
ejpam-5458	133	37	red	red	ADJ
ejpam-5458	133	38	region	region	NOUN
ejpam-5458	133	39	(	(	PUNCT
ejpam-5458	133	40	unstable	unstable	ADJ
ejpam-5458	133	41	node	node	NOUN
ejpam-5458	133	42	)	)	PUNCT
ejpam-5458	133	43	.	.	PUNCT
ejpam-5458	134	1	a	a	DET
ejpam-5458	134	2	hopf	hopf	ADJ
ejpam-5458	134	3	bifurcation	bifurcation	NOUN
ejpam-5458	134	4	occurs	occur	VERB
ejpam-5458	134	5	in	in	ADP
ejpam-5458	134	6	the	the	DET
ejpam-5458	134	7	boundary	boundary	NOUN
ejpam-5458	134	8	between	between	ADP
ejpam-5458	134	9	the	the	DET
ejpam-5458	134	10	red	red	ADJ
ejpam-5458	134	11	and	and	CCONJ
ejpam-5458	134	12	blue	blue	ADJ
ejpam-5458	134	13	regions	region	NOUN
ejpam-5458	134	14	where	where	SCONJ
ejpam-5458	134	15	the	the	DET
ejpam-5458	134	16	eigenvalues	eigenvalue	NOUN
ejpam-5458	134	17	have	have	VERB
ejpam-5458	134	18	pure	pure	ADJ
ejpam-5458	134	19	imaginary	imaginary	ADJ
ejpam-5458	134	20	values	value	NOUN
ejpam-5458	134	21	as	as	SCONJ
ejpam-5458	134	22	shown	show	VERB
ejpam-5458	134	23	in	in	ADP
ejpam-5458	134	24	[	[	X
ejpam-5458	134	25	12	12	NUM
ejpam-5458	134	26	,	,	PUNCT
ejpam-5458	134	27	fig.3	fig.3	PROPN
ejpam-5458	134	28	]	]	PUNCT
ejpam-5458	134	29	.	.	PUNCT
ejpam-5458	135	1	i.	i.	PROPN
ejpam-5458	135	2	alraddadi	alraddadi	PROPN
ejpam-5458	135	3	/	/	SYM
ejpam-5458	135	4	eur	eur	PROPN
ejpam-5458	135	5	.	.	PUNCT
ejpam-5458	136	1	j.	j.	PROPN
ejpam-5458	136	2	pure	pure	PROPN
ejpam-5458	136	3	appl	appl	PROPN
ejpam-5458	136	4	.	.	PROPN
ejpam-5458	136	5	math	math	PROPN
ejpam-5458	136	6	,	,	PUNCT
ejpam-5458	136	7	17	17	NUM
ejpam-5458	136	8	(	(	PUNCT
ejpam-5458	136	9	4	4	NUM
ejpam-5458	136	10	)	)	PUNCT
ejpam-5458	136	11	(	(	PUNCT
ejpam-5458	136	12	2024	2024	NUM
ejpam-5458	136	13	)	)	PUNCT
ejpam-5458	136	14	,	,	PUNCT
ejpam-5458	136	15	3708	3708	NUM
ejpam-5458	136	16	-	-	SYM
ejpam-5458	136	17	3729	3729	NUM
ejpam-5458	136	18	3715	3715	NUM
ejpam-5458	136	19	figure	figure	NOUN
ejpam-5458	136	20	5	5	NUM
ejpam-5458	136	21	:	:	PUNCT
ejpam-5458	136	22	the	the	DET
ejpam-5458	136	23	location	location	NOUN
ejpam-5458	136	24	and	and	CCONJ
ejpam-5458	136	25	stability	stability	NOUN
ejpam-5458	136	26	of	of	ADP
ejpam-5458	136	27	the	the	DET
ejpam-5458	136	28	equilibrium	equilibrium	NOUN
ejpam-5458	136	29	point	point	NOUN
ejpam-5458	136	30	are	be	AUX
ejpam-5458	136	31	shown	show	VERB
ejpam-5458	136	32	for	for	ADP
ejpam-5458	136	33	rothman	rothman	PROPN
ejpam-5458	136	34	’s	’s	PART
ejpam-5458	136	35	carbon	carbon	NOUN
ejpam-5458	136	36	cycle	cycle	NOUN
ejpam-5458	136	37	model	model	NOUN
ejpam-5458	136	38	(	(	PUNCT
ejpam-5458	136	39	7	7	NUM
ejpam-5458	136	40	)	)	PUNCT
ejpam-5458	136	41	with	with	ADP
ejpam-5458	136	42	parameters	parameter	NOUN
ejpam-5458	136	43	as	as	SCONJ
ejpam-5458	136	44	given	give	VERB
ejpam-5458	136	45	in	in	ADP
ejpam-5458	136	46	table	table	NOUN
ejpam-5458	136	47	1	1	NUM
ejpam-5458	136	48	.	.	PUNCT
ejpam-5458	137	1	panels	panel	NOUN
ejpam-5458	137	2	(	(	PUNCT
ejpam-5458	137	3	a	a	X
ejpam-5458	137	4	)	)	PUNCT
ejpam-5458	137	5	and	and	CCONJ
ejpam-5458	137	6	(	(	PUNCT
ejpam-5458	137	7	b	b	X
ejpam-5458	137	8	)	)	PUNCT
ejpam-5458	137	9	show	show	VERB
ejpam-5458	137	10	the	the	DET
ejpam-5458	137	11	location	location	NOUN
ejpam-5458	137	12	and	and	CCONJ
ejpam-5458	137	13	the	the	DET
ejpam-5458	137	14	stability	stability	NOUN
ejpam-5458	137	15	of	of	ADP
ejpam-5458	137	16	the	the	DET
ejpam-5458	137	17	equilibrium	equilibrium	NOUN
ejpam-5458	137	18	point	point	NOUN
ejpam-5458	137	19	(	(	PUNCT
ejpam-5458	137	20	c∗	c∗	PROPN
ejpam-5458	137	21	,	,	PUNCT
ejpam-5458	137	22	w∗	w∗	NOUN
ejpam-5458	137	23	)	)	PUNCT
ejpam-5458	137	24	for	for	ADP
ejpam-5458	137	25	varying	vary	VERB
ejpam-5458	137	26	the	the	DET
ejpam-5458	137	27	parameter	parameter	PROPN
ejpam-5458	137	28	b.	b.	PROPN
ejpam-5458	137	29	similarly	similarly	ADV
ejpam-5458	137	30	,	,	PUNCT
ejpam-5458	137	31	panels	panel	NOUN
ejpam-5458	137	32	(	(	PUNCT
ejpam-5458	137	33	c	c	NOUN
ejpam-5458	137	34	)	)	PUNCT
ejpam-5458	137	35	and	and	CCONJ
ejpam-5458	137	36	(	(	PUNCT
ejpam-5458	137	37	d	d	X
ejpam-5458	137	38	)	)	PUNCT
ejpam-5458	137	39	show	show	VERB
ejpam-5458	137	40	the	the	DET
ejpam-5458	137	41	location	location	NOUN
ejpam-5458	137	42	and	and	CCONJ
ejpam-5458	137	43	stability	stability	NOUN
ejpam-5458	137	44	,	,	PUNCT
ejpam-5458	137	45	but	but	CCONJ
ejpam-5458	137	46	for	for	ADP
ejpam-5458	137	47	the	the	DET
ejpam-5458	137	48	parameter	parameter	NOUN
ejpam-5458	137	49	cp	cp	INTJ
ejpam-5458	137	50	instead	instead	ADV
ejpam-5458	137	51	.	.	PUNCT
ejpam-5458	138	1	in	in	ADP
ejpam-5458	138	2	all	all	DET
ejpam-5458	138	3	cases	case	NOUN
ejpam-5458	138	4	,	,	PUNCT
ejpam-5458	138	5	other	other	ADJ
ejpam-5458	138	6	parameter	parameter	NOUN
ejpam-5458	138	7	values	value	NOUN
ejpam-5458	138	8	are	be	AUX
ejpam-5458	138	9	given	give	VERB
ejpam-5458	138	10	in	in	ADP
ejpam-5458	138	11	table	table	NOUN
ejpam-5458	138	12	1	1	NUM
ejpam-5458	138	13	.	.	PUNCT
ejpam-5458	139	1	the	the	DET
ejpam-5458	139	2	stability	stability	NOUN
ejpam-5458	139	3	of	of	ADP
ejpam-5458	139	4	the	the	DET
ejpam-5458	139	5	equilibrium	equilibrium	NOUN
ejpam-5458	139	6	point	point	NOUN
ejpam-5458	139	7	(	(	PUNCT
ejpam-5458	139	8	c∗	c∗	PROPN
ejpam-5458	139	9	,	,	PUNCT
ejpam-5458	139	10	w∗	w∗	PROPN
ejpam-5458	139	11	)	)	PUNCT
ejpam-5458	139	12	is	be	AUX
ejpam-5458	139	13	determined	determine	VERB
ejpam-5458	139	14	by	by	ADP
ejpam-5458	139	15	the	the	DET
ejpam-5458	139	16	sign	sign	NOUN
ejpam-5458	139	17	of	of	ADP
ejpam-5458	139	18	the	the	DET
ejpam-5458	139	19	eigenvalues	eigenvalue	NOUN
ejpam-5458	139	20	λ1,2	λ1,2	PROPN
ejpam-5458	139	21	.	.	PUNCT
ejpam-5458	140	1	the	the	DET
ejpam-5458	140	2	location	location	NOUN
ejpam-5458	140	3	and	and	CCONJ
ejpam-5458	140	4	the	the	DET
ejpam-5458	140	5	stability	stability	NOUN
ejpam-5458	140	6	of	of	ADP
ejpam-5458	140	7	(	(	PUNCT
ejpam-5458	140	8	c∗	c∗	PROPN
ejpam-5458	140	9	,	,	PUNCT
ejpam-5458	140	10	w∗	w∗	PROPN
ejpam-5458	140	11	)	)	PUNCT
ejpam-5458	140	12	is	be	AUX
ejpam-5458	140	13	indicated	indicate	VERB
ejpam-5458	140	14	by	by	ADP
ejpam-5458	140	15	blue	blue	ADJ
ejpam-5458	140	16	(	(	PUNCT
ejpam-5458	140	17	stable	stable	ADJ
ejpam-5458	140	18	spiral	spiral	NOUN
ejpam-5458	140	19	)	)	PUNCT
ejpam-5458	140	20	and	and	CCONJ
ejpam-5458	140	21	red	red	ADJ
ejpam-5458	140	22	(	(	PUNCT
ejpam-5458	140	23	unstable	unstable	ADJ
ejpam-5458	140	24	spiral	spiral	NOUN
ejpam-5458	140	25	)	)	PUNCT
ejpam-5458	140	26	.	.	PUNCT
ejpam-5458	141	1	the	the	DET
ejpam-5458	141	2	analysis	analysis	NOUN
ejpam-5458	141	3	and	and	CCONJ
ejpam-5458	141	4	explanation	explanation	NOUN
ejpam-5458	141	5	of	of	ADP
ejpam-5458	141	6	rothman	rothman	PROPN
ejpam-5458	141	7	’s	’s	PART
ejpam-5458	141	8	carbon	carbon	NOUN
ejpam-5458	141	9	cycle	cycle	NOUN
ejpam-5458	141	10	model	model	NOUN
ejpam-5458	141	11	is	be	AUX
ejpam-5458	141	12	discussed	discuss	VERB
ejpam-5458	141	13	in	in	ADP
ejpam-5458	141	14	more	more	ADJ
ejpam-5458	141	15	detail	detail	NOUN
ejpam-5458	141	16	in	in	ADP
ejpam-5458	141	17	[	[	X
ejpam-5458	141	18	12	12	NUM
ejpam-5458	141	19	]	]	PUNCT
ejpam-5458	141	20	.	.	PUNCT
ejpam-5458	142	1	the	the	DET
ejpam-5458	142	2	model	model	NOUN
ejpam-5458	142	3	(	(	PUNCT
ejpam-5458	142	4	7	7	X
ejpam-5458	142	5	)	)	PUNCT
ejpam-5458	142	6	exhibits	exhibit	VERB
ejpam-5458	142	7	both	both	CCONJ
ejpam-5458	142	8	stable	stable	ADJ
ejpam-5458	142	9	and	and	CCONJ
ejpam-5458	142	10	unstable	unstable	ADJ
ejpam-5458	142	11	limit	limit	NOUN
ejpam-5458	142	12	cycles	cycle	NOUN
ejpam-5458	142	13	via	via	ADP
ejpam-5458	142	14	hopf	hopf	ADJ
ejpam-5458	142	15	bifurcations	bifurcation	NOUN
ejpam-5458	142	16	as	as	SCONJ
ejpam-5458	142	17	the	the	DET
ejpam-5458	142	18	parameter	parameter	NOUN
ejpam-5458	142	19	cx	cx	PROPN
ejpam-5458	142	20	is	be	AUX
ejpam-5458	142	21	varied	varied	ADJ
ejpam-5458	142	22	.	.	PUNCT
ejpam-5458	143	1	there	there	PRON
ejpam-5458	143	2	is	be	VERB
ejpam-5458	143	3	only	only	ADV
ejpam-5458	143	4	one	one	NUM
ejpam-5458	143	5	stable	stable	ADJ
ejpam-5458	143	6	equilibrium	equilibrium	NOUN
ejpam-5458	143	7	point	point	NOUN
ejpam-5458	143	8	(	(	PUNCT
ejpam-5458	143	9	c∗	c∗	PROPN
ejpam-5458	143	10	,	,	PUNCT
ejpam-5458	143	11	w∗	w∗	NOUN
ejpam-5458	143	12	)	)	PUNCT
ejpam-5458	143	13	of	of	ADP
ejpam-5458	143	14	(	(	PUNCT
ejpam-5458	143	15	7	7	NUM
ejpam-5458	143	16	)	)	PUNCT
ejpam-5458	143	17	for	for	ADP
ejpam-5458	143	18	cx	cx	NOUN
ejpam-5458	143	19	<	<	X
ejpam-5458	143	20	55.89	55.89	NUM
ejpam-5458	143	21	(	(	PUNCT
ejpam-5458	143	22	see	see	VERB
ejpam-5458	143	23	figure	figure	NOUN
ejpam-5458	143	24	7	7	NUM
ejpam-5458	143	25	)	)	PUNCT
ejpam-5458	143	26	.	.	PUNCT
ejpam-5458	144	1	an	an	DET
ejpam-5458	144	2	unstable	unstable	ADJ
ejpam-5458	144	3	limit	limit	NOUN
ejpam-5458	144	4	cycle	cycle	NOUN
ejpam-5458	144	5	appears	appear	VERB
ejpam-5458	144	6	between	between	ADP
ejpam-5458	144	7	the	the	DET
ejpam-5458	144	8	stable	stable	ADJ
ejpam-5458	144	9	equilibrium	equilibrium	NOUN
ejpam-5458	144	10	point	point	NOUN
ejpam-5458	144	11	and	and	CCONJ
ejpam-5458	144	12	the	the	DET
ejpam-5458	144	13	stable	stable	ADJ
ejpam-5458	144	14	limit	limit	NOUN
ejpam-5458	144	15	cycle	cycle	NOUN
ejpam-5458	144	16	when	when	SCONJ
ejpam-5458	144	17	55.89	55.89	NUM
ejpam-5458	144	18	<	<	X
ejpam-5458	144	19	cx	cx	X
ejpam-5458	144	20	<	<	X
ejpam-5458	144	21	62.61	62.61	NUM
ejpam-5458	144	22	(	(	PUNCT
ejpam-5458	144	23	see	see	VERB
ejpam-5458	144	24	figure	figure	NOUN
ejpam-5458	144	25	8)	8)	NUM
ejpam-5458	144	26	.	.	PUNCT
ejpam-5458	145	1	there	there	PRON
ejpam-5458	145	2	is	be	VERB
ejpam-5458	145	3	a	a	DET
ejpam-5458	145	4	stable	stable	ADJ
ejpam-5458	145	5	limit	limit	NOUN
ejpam-5458	145	6	cycle	cycle	NOUN
ejpam-5458	145	7	and	and	CCONJ
ejpam-5458	145	8	an	an	DET
ejpam-5458	145	9	unstable	unstable	ADJ
ejpam-5458	145	10	equilibrium	equilibrium	NOUN
ejpam-5458	145	11	point	point	NOUN
ejpam-5458	145	12	when	when	SCONJ
ejpam-5458	145	13	cx	cx	PROPN
ejpam-5458	145	14	>	>	X
ejpam-5458	145	15	62.61	62.61	NUM
ejpam-5458	145	16	(	(	PUNCT
ejpam-5458	145	17	see	see	VERB
ejpam-5458	145	18	figure	figure	NOUN
ejpam-5458	145	19	3	3	NUM
ejpam-5458	145	20	)	)	PUNCT
ejpam-5458	145	21	.	.	PUNCT
ejpam-5458	146	1	4	4	X
ejpam-5458	146	2	.	.	X
ejpam-5458	146	3	bifurcations	bifurcation	NOUN
ejpam-5458	146	4	of	of	ADP
ejpam-5458	146	5	rothman	rothman	PROPN
ejpam-5458	146	6	’s	’s	PART
ejpam-5458	146	7	carbon	carbon	NOUN
ejpam-5458	146	8	cycle	cycle	NOUN
ejpam-5458	146	9	model	model	NOUN
ejpam-5458	146	10	this	this	DET
ejpam-5458	146	11	section	section	NOUN
ejpam-5458	146	12	illustrates	illustrate	VERB
ejpam-5458	146	13	the	the	DET
ejpam-5458	146	14	normal	normal	ADJ
ejpam-5458	146	15	form	form	NOUN
ejpam-5458	146	16	of	of	ADP
ejpam-5458	146	17	hopf	hopf	ADJ
ejpam-5458	146	18	and	and	CCONJ
ejpam-5458	146	19	bautin	bautin	ADJ
ejpam-5458	146	20	bifurcations	bifurcation	NOUN
ejpam-5458	146	21	,	,	PUNCT
ejpam-5458	146	22	which	which	PRON
ejpam-5458	146	23	include	include	VERB
ejpam-5458	146	24	the	the	DET
ejpam-5458	146	25	saddle	saddle	NOUN
ejpam-5458	146	26	-	-	PUNCT
ejpam-5458	146	27	node	node	NOUN
ejpam-5458	146	28	bifurcation	bifurcation	NOUN
ejpam-5458	146	29	of	of	ADP
ejpam-5458	146	30	limit	limit	NOUN
ejpam-5458	146	31	cycles	cycle	NOUN
ejpam-5458	146	32	.	.	PUNCT
ejpam-5458	147	1	section	section	NOUN
ejpam-5458	147	2	4.1	4.1	NUM
ejpam-5458	147	3	illustrates	illustrate	VERB
ejpam-5458	147	4	the	the	DET
ejpam-5458	147	5	conditions	condition	NOUN
ejpam-5458	147	6	and	and	CCONJ
ejpam-5458	147	7	highlights	highlight	NOUN
ejpam-5458	147	8	the	the	DET
ejpam-5458	147	9	lyapunov	lyapunov	ADJ
ejpam-5458	147	10	coefficients	coefficient	NOUN
ejpam-5458	147	11	that	that	PRON
ejpam-5458	147	12	appear	appear	VERB
ejpam-5458	147	13	in	in	ADP
ejpam-5458	147	14	this	this	DET
ejpam-5458	147	15	normal	normal	ADJ
ejpam-5458	147	16	form	form	NOUN
ejpam-5458	147	17	.	.	PUNCT
ejpam-5458	148	1	in	in	ADP
ejpam-5458	148	2	addition	addition	NOUN
ejpam-5458	148	3	,	,	PUNCT
ejpam-5458	148	4	we	we	PRON
ejpam-5458	148	5	review	review	VERB
ejpam-5458	148	6	the	the	DET
ejpam-5458	148	7	technique	technique	NOUN
ejpam-5458	148	8	for	for	ADP
ejpam-5458	148	9	computing	compute	VERB
ejpam-5458	148	10	lyapunov	lyapunov	ADJ
ejpam-5458	148	11	coefficients	coefficient	NOUN
ejpam-5458	148	12	.	.	PUNCT
ejpam-5458	149	1	we	we	PRON
ejpam-5458	149	2	use	use	VERB
ejpam-5458	149	3	theorem	theorem	NOUN
ejpam-5458	149	4	1	1	NUM
ejpam-5458	149	5	in	in	ADP
ejpam-5458	149	6	section	section	NOUN
ejpam-5458	149	7	4.1	4.1	NUM
ejpam-5458	149	8	and	and	CCONJ
ejpam-5458	149	9	theorem	theorem	VERB
ejpam-5458	149	10	2	2	NUM
ejpam-5458	149	11	in	in	ADP
ejpam-5458	149	12	section	section	NOUN
ejpam-5458	149	13	4.2	4.2	NUM
ejpam-5458	149	14	to	to	PART
ejpam-5458	149	15	identify	identify	VERB
ejpam-5458	149	16	the	the	DET
ejpam-5458	149	17	topological	topological	ADJ
ejpam-5458	149	18	normal	normal	ADJ
ejpam-5458	149	19	form	form	NOUN
ejpam-5458	149	20	for	for	ADP
ejpam-5458	149	21	hopf	hopf	ADJ
ejpam-5458	149	22	and	and	CCONJ
ejpam-5458	149	23	i.	i.	PROPN
ejpam-5458	149	24	alraddadi	alraddadi	PROPN
ejpam-5458	149	25	/	/	SYM
ejpam-5458	149	26	eur	eur	PROPN
ejpam-5458	149	27	.	.	PUNCT
ejpam-5458	150	1	j.	j.	PROPN
ejpam-5458	150	2	pure	pure	PROPN
ejpam-5458	150	3	appl	appl	PROPN
ejpam-5458	150	4	.	.	PROPN
ejpam-5458	150	5	math	math	PROPN
ejpam-5458	150	6	,	,	PUNCT
ejpam-5458	150	7	17	17	NUM
ejpam-5458	150	8	(	(	PUNCT
ejpam-5458	150	9	4	4	NUM
ejpam-5458	150	10	)	)	PUNCT
ejpam-5458	150	11	(	(	PUNCT
ejpam-5458	150	12	2024	2024	NUM
ejpam-5458	150	13	)	)	PUNCT
ejpam-5458	150	14	,	,	PUNCT
ejpam-5458	150	15	3708	3708	NUM
ejpam-5458	150	16	-	-	SYM
ejpam-5458	150	17	3729	3729	NUM
ejpam-5458	150	18	3716	3716	NUM
ejpam-5458	150	19	figure	figure	NOUN
ejpam-5458	150	20	6	6	NUM
ejpam-5458	150	21	:	:	PUNCT
ejpam-5458	150	22	the	the	DET
ejpam-5458	150	23	stability	stability	NOUN
ejpam-5458	150	24	region	region	NOUN
ejpam-5458	150	25	of	of	ADP
ejpam-5458	150	26	the	the	DET
ejpam-5458	150	27	equilibrium	equilibrium	NOUN
ejpam-5458	150	28	point	point	NOUN
ejpam-5458	150	29	(	(	PUNCT
ejpam-5458	150	30	c∗	c∗	PROPN
ejpam-5458	150	31	,	,	PUNCT
ejpam-5458	150	32	w∗	w∗	PROPN
ejpam-5458	150	33	)	)	PUNCT
ejpam-5458	150	34	is	be	AUX
ejpam-5458	150	35	shown	show	VERB
ejpam-5458	150	36	for	for	ADP
ejpam-5458	150	37	rothman	rothman	PROPN
ejpam-5458	150	38	’s	’s	PART
ejpam-5458	150	39	carbon	carbon	NOUN
ejpam-5458	150	40	cycle	cycle	NOUN
ejpam-5458	150	41	model	model	NOUN
ejpam-5458	150	42	(	(	PUNCT
ejpam-5458	150	43	7	7	NUM
ejpam-5458	150	44	)	)	PUNCT
ejpam-5458	150	45	.	.	PUNCT
ejpam-5458	151	1	in	in	ADP
ejpam-5458	151	2	the	the	DET
ejpam-5458	151	3	parameter	parameter	NOUN
ejpam-5458	151	4	space	space	NOUN
ejpam-5458	151	5	(	(	PUNCT
ejpam-5458	151	6	a	a	NOUN
ejpam-5458	151	7	-	-	PUNCT
ejpam-5458	151	8	d	d	NOUN
ejpam-5458	151	9	)	)	PUNCT
ejpam-5458	151	10	,	,	PUNCT
ejpam-5458	151	11	two	two	NUM
ejpam-5458	151	12	parameters	parameter	NOUN
ejpam-5458	151	13	are	be	AUX
ejpam-5458	151	14	varying	vary	VERB
ejpam-5458	151	15	and	and	CCONJ
ejpam-5458	151	16	other	other	ADJ
ejpam-5458	151	17	parameters	parameter	NOUN
ejpam-5458	151	18	are	be	AUX
ejpam-5458	151	19	given	give	VERB
ejpam-5458	151	20	in	in	ADP
ejpam-5458	151	21	table	table	NOUN
ejpam-5458	151	22	1	1	NUM
ejpam-5458	151	23	.	.	PUNCT
ejpam-5458	152	1	(	(	PUNCT
ejpam-5458	152	2	a	a	DET
ejpam-5458	152	3	-	-	PUNCT
ejpam-5458	152	4	c	c	NOUN
ejpam-5458	152	5	)	)	PUNCT
ejpam-5458	152	6	show	show	VERB
ejpam-5458	152	7	the	the	DET
ejpam-5458	152	8	stability	stability	NOUN
ejpam-5458	152	9	diagram	diagram	NOUN
ejpam-5458	152	10	for	for	ADP
ejpam-5458	152	11	the	the	DET
ejpam-5458	152	12	parameter	parameter	NOUN
ejpam-5458	152	13	spaces	space	NOUN
ejpam-5458	152	14	of	of	ADP
ejpam-5458	152	15	µ	µ	NOUN
ejpam-5458	152	16	against	against	ADP
ejpam-5458	152	17	b	b	NOUN
ejpam-5458	152	18	,	,	PUNCT
ejpam-5458	152	19	cx	cx	PROPN
ejpam-5458	152	20	and	and	CCONJ
ejpam-5458	152	21	θ	θ	PROPN
ejpam-5458	152	22	,	,	PUNCT
ejpam-5458	152	23	(	(	PUNCT
ejpam-5458	152	24	d	d	X
ejpam-5458	152	25	)	)	PUNCT
ejpam-5458	152	26	shows	show	VERB
ejpam-5458	152	27	the	the	DET
ejpam-5458	152	28	parameter	parameter	NOUN
ejpam-5458	152	29	space	space	NOUN
ejpam-5458	152	30	of	of	ADP
ejpam-5458	152	31	θ	θ	PROPN
ejpam-5458	152	32	and	and	CCONJ
ejpam-5458	152	33	cx	cx	PROPN
ejpam-5458	152	34	.	.	PUNCT
ejpam-5458	153	1	the	the	DET
ejpam-5458	153	2	stability	stability	NOUN
ejpam-5458	153	3	region	region	NOUN
ejpam-5458	153	4	is	be	AUX
ejpam-5458	153	5	divided	divide	VERB
ejpam-5458	153	6	into	into	ADP
ejpam-5458	153	7	four	four	NUM
ejpam-5458	153	8	regions	region	NOUN
ejpam-5458	153	9	:	:	PUNCT
ejpam-5458	153	10	yellow	yellow	ADJ
ejpam-5458	153	11	(	(	PUNCT
ejpam-5458	153	12	stable	stable	ADJ
ejpam-5458	153	13	node	node	NOUN
ejpam-5458	153	14	)	)	PUNCT
ejpam-5458	153	15	and	and	CCONJ
ejpam-5458	153	16	green	green	ADJ
ejpam-5458	153	17	(	(	PUNCT
ejpam-5458	153	18	unstable	unstable	ADJ
ejpam-5458	153	19	node	node	NOUN
ejpam-5458	153	20	)	)	PUNCT
ejpam-5458	153	21	regions	region	NOUN
ejpam-5458	153	22	,	,	PUNCT
ejpam-5458	153	23	which	which	PRON
ejpam-5458	153	24	indicate	indicate	VERB
ejpam-5458	153	25	where	where	SCONJ
ejpam-5458	153	26	(	(	PUNCT
ejpam-5458	153	27	c∗	c∗	ADJ
ejpam-5458	153	28	,	,	PUNCT
ejpam-5458	153	29	w∗	w∗	PROPN
ejpam-5458	153	30	)	)	PUNCT
ejpam-5458	153	31	has	have	VERB
ejpam-5458	153	32	real	real	ADJ
ejpam-5458	153	33	eigenvalues	eigenvalue	NOUN
ejpam-5458	153	34	.	.	PUNCT
ejpam-5458	154	1	stable	stable	ADJ
ejpam-5458	154	2	and	and	CCONJ
ejpam-5458	154	3	unstable	unstable	ADJ
ejpam-5458	154	4	spiral	spiral	ADJ
ejpam-5458	154	5	equilibrium	equilibrium	NOUN
ejpam-5458	154	6	points	point	NOUN
ejpam-5458	154	7	are	be	AUX
ejpam-5458	154	8	indicated	indicate	VERB
ejpam-5458	154	9	by	by	ADP
ejpam-5458	154	10	blue	blue	ADJ
ejpam-5458	154	11	and	and	CCONJ
ejpam-5458	154	12	red	red	ADJ
ejpam-5458	154	13	regions	region	NOUN
ejpam-5458	154	14	where	where	SCONJ
ejpam-5458	154	15	(	(	PUNCT
ejpam-5458	154	16	c∗	c∗	PROPN
ejpam-5458	154	17	,	,	PUNCT
ejpam-5458	154	18	w∗	w∗	NOUN
ejpam-5458	154	19	)	)	PUNCT
ejpam-5458	154	20	has	have	VERB
ejpam-5458	154	21	complex	complex	ADJ
ejpam-5458	154	22	eigenvalues	eigenvalue	NOUN
ejpam-5458	154	23	.	.	PUNCT
ejpam-5458	155	1	note	note	VERB
ejpam-5458	155	2	hopf	hopf	ADJ
ejpam-5458	155	3	bifurcations	bifurcation	NOUN
ejpam-5458	155	4	occur	occur	VERB
ejpam-5458	155	5	at	at	ADP
ejpam-5458	155	6	the	the	DET
ejpam-5458	155	7	boundary	boundary	NOUN
ejpam-5458	155	8	between	between	ADP
ejpam-5458	155	9	blue	blue	ADJ
ejpam-5458	155	10	and	and	CCONJ
ejpam-5458	155	11	red	red	ADJ
ejpam-5458	155	12	regions	region	NOUN
ejpam-5458	155	13	where	where	SCONJ
ejpam-5458	155	14	(	(	PUNCT
ejpam-5458	155	15	c∗	c∗	PROPN
ejpam-5458	155	16	,	,	PUNCT
ejpam-5458	155	17	w∗	w∗	PROPN
ejpam-5458	155	18	)	)	PUNCT
ejpam-5458	155	19	has	have	VERB
ejpam-5458	155	20	purely	purely	ADV
ejpam-5458	155	21	imaginary	imaginary	ADJ
ejpam-5458	155	22	eigenvalues	eigenvalue	NOUN
ejpam-5458	155	23	.	.	PUNCT
ejpam-5458	156	1	bautin	bautin	ADJ
ejpam-5458	156	2	bifurcations	bifurcation	NOUN
ejpam-5458	156	3	.	.	PUNCT
ejpam-5458	157	1	section	section	NOUN
ejpam-5458	157	2	5	5	NUM
ejpam-5458	157	3	derives	derive	VERB
ejpam-5458	157	4	the	the	DET
ejpam-5458	157	5	normal	normal	ADJ
ejpam-5458	157	6	form	form	NOUN
ejpam-5458	157	7	of	of	ADP
ejpam-5458	157	8	hopf	hopf	ADJ
ejpam-5458	157	9	and	and	CCONJ
ejpam-5458	157	10	bautin	bautin	ADJ
ejpam-5458	157	11	bifurcations	bifurcation	NOUN
ejpam-5458	157	12	for	for	ADP
ejpam-5458	157	13	rothman	rothman	PROPN
ejpam-5458	157	14	’s	’s	PART
ejpam-5458	157	15	carbon	carbon	NOUN
ejpam-5458	157	16	cycle	cycle	NOUN
ejpam-5458	157	17	model	model	NOUN
ejpam-5458	157	18	(	(	PUNCT
ejpam-5458	157	19	7	7	NUM
ejpam-5458	157	20	)	)	PUNCT
ejpam-5458	157	21	.	.	PUNCT
ejpam-5458	158	1	in	in	ADP
ejpam-5458	158	2	this	this	DET
ejpam-5458	158	3	section	section	NOUN
ejpam-5458	158	4	,	,	PUNCT
ejpam-5458	158	5	we	we	PRON
ejpam-5458	158	6	identify	identify	VERB
ejpam-5458	158	7	the	the	DET
ejpam-5458	158	8	bautin	bautin	ADJ
ejpam-5458	158	9	bifurcation	bifurcation	NOUN
ejpam-5458	158	10	and	and	CCONJ
ejpam-5458	158	11	classify	classify	VERB
ejpam-5458	158	12	its	its	PRON
ejpam-5458	158	13	criticality	criticality	NOUN
ejpam-5458	158	14	by	by	ADP
ejpam-5458	158	15	finding	find	VERB
ejpam-5458	158	16	appropriate	appropriate	ADJ
ejpam-5458	158	17	coefficients	coefficient	NOUN
ejpam-5458	158	18	in	in	ADP
ejpam-5458	158	19	the	the	DET
ejpam-5458	158	20	normal	normal	ADJ
ejpam-5458	158	21	form	form	NOUN
ejpam-5458	158	22	.	.	PUNCT
ejpam-5458	159	1	in	in	ADP
ejpam-5458	159	2	addition	addition	NOUN
ejpam-5458	159	3	,	,	PUNCT
ejpam-5458	159	4	we	we	PRON
ejpam-5458	159	5	use	use	VERB
ejpam-5458	159	6	the	the	DET
ejpam-5458	159	7	normal	normal	ADJ
ejpam-5458	159	8	form	form	NOUN
ejpam-5458	159	9	coefficients	coefficient	NOUN
ejpam-5458	159	10	to	to	PART
ejpam-5458	159	11	identify	identify	VERB
ejpam-5458	159	12	the	the	DET
ejpam-5458	159	13	saddle	saddle	NOUN
ejpam-5458	159	14	-	-	PUNCT
ejpam-5458	159	15	node	node	NOUN
ejpam-5458	159	16	bifurcation	bifurcation	NOUN
ejpam-5458	159	17	of	of	ADP
ejpam-5458	159	18	limit	limit	NOUN
ejpam-5458	159	19	cycles	cycle	NOUN
ejpam-5458	159	20	when	when	SCONJ
ejpam-5458	159	21	it	it	PRON
ejpam-5458	159	22	occurs	occur	VERB
ejpam-5458	159	23	.	.	PUNCT
ejpam-5458	160	1	4.1	4.1	NUM
ejpam-5458	160	2	.	.	PUNCT
ejpam-5458	160	3	computation	computation	NOUN
ejpam-5458	160	4	of	of	ADP
ejpam-5458	160	5	the	the	DET
ejpam-5458	160	6	critical	critical	ADJ
ejpam-5458	160	7	normal	normal	ADJ
ejpam-5458	160	8	form	form	NOUN
ejpam-5458	160	9	coefficients	coefficient	VERB
ejpam-5458	160	10	the	the	DET
ejpam-5458	160	11	coefficients	coefficient	NOUN
ejpam-5458	160	12	of	of	ADP
ejpam-5458	160	13	the	the	DET
ejpam-5458	160	14	normal	normal	ADJ
ejpam-5458	160	15	form	form	NOUN
ejpam-5458	160	16	at	at	ADP
ejpam-5458	160	17	the	the	DET
ejpam-5458	160	18	bifurcation	bifurcation	NOUN
ejpam-5458	160	19	point	point	NOUN
ejpam-5458	160	20	can	can	AUX
ejpam-5458	160	21	be	be	AUX
ejpam-5458	160	22	calculated	calculate	VERB
ejpam-5458	160	23	in	in	ADP
ejpam-5458	160	24	several	several	ADJ
ejpam-5458	160	25	ways	way	NOUN
ejpam-5458	160	26	.	.	PUNCT
ejpam-5458	161	1	we	we	PRON
ejpam-5458	161	2	follow	follow	VERB
ejpam-5458	161	3	a	a	DET
ejpam-5458	161	4	method	method	NOUN
ejpam-5458	161	5	that	that	PRON
ejpam-5458	161	6	is	be	AUX
ejpam-5458	161	7	used	use	VERB
ejpam-5458	161	8	in	in	ADP
ejpam-5458	161	9	[	[	X
ejpam-5458	161	10	4	4	NUM
ejpam-5458	161	11	]	]	PUNCT
ejpam-5458	161	12	and	and	CCONJ
ejpam-5458	161	13	then	then	ADV
ejpam-5458	161	14	we	we	PRON
ejpam-5458	161	15	apply	apply	VERB
ejpam-5458	161	16	it	it	PRON
ejpam-5458	161	17	to	to	ADP
ejpam-5458	161	18	an	an	DET
ejpam-5458	161	19	example	example	NOUN
ejpam-5458	161	20	of	of	ADP
ejpam-5458	161	21	odes	ode	NOUN
ejpam-5458	161	22	dependent	dependent	ADJ
ejpam-5458	161	23	on	on	ADP
ejpam-5458	161	24	one	one	NUM
ejpam-5458	161	25	parameter	parameter	NOUN
ejpam-5458	161	26	.	.	PUNCT
ejpam-5458	162	1	we	we	PRON
ejpam-5458	162	2	consider	consider	VERB
ejpam-5458	162	3	the	the	DET
ejpam-5458	162	4	autonomous	autonomous	ADJ
ejpam-5458	162	5	system	system	NOUN
ejpam-5458	162	6	ẋ	ẋ	PUNCT
ejpam-5458	163	1	=	=	SYM
ejpam-5458	163	2	f(x	f(x	PROPN
ejpam-5458	163	3	,	,	PUNCT
ejpam-5458	163	4	α	α	NOUN
ejpam-5458	163	5	)	)	PUNCT
ejpam-5458	163	6	(	(	PUNCT
ejpam-5458	163	7	15	15	NUM
ejpam-5458	163	8	)	)	PUNCT
ejpam-5458	163	9	i.	i.	NOUN
ejpam-5458	163	10	alraddadi	alraddadi	PROPN
ejpam-5458	163	11	/	/	SYM
ejpam-5458	163	12	eur	eur	PROPN
ejpam-5458	163	13	.	.	PUNCT
ejpam-5458	164	1	j.	j.	PROPN
ejpam-5458	164	2	pure	pure	PROPN
ejpam-5458	164	3	appl	appl	PROPN
ejpam-5458	164	4	.	.	PROPN
ejpam-5458	164	5	math	math	PROPN
ejpam-5458	164	6	,	,	PUNCT
ejpam-5458	164	7	17	17	NUM
ejpam-5458	164	8	(	(	PUNCT
ejpam-5458	164	9	4	4	NUM
ejpam-5458	164	10	)	)	PUNCT
ejpam-5458	164	11	(	(	PUNCT
ejpam-5458	164	12	2024	2024	NUM
ejpam-5458	164	13	)	)	PUNCT
ejpam-5458	164	14	,	,	PUNCT
ejpam-5458	164	15	3708	3708	NUM
ejpam-5458	164	16	-	-	SYM
ejpam-5458	164	17	3729	3729	NUM
ejpam-5458	164	18	3717	3717	NUM
ejpam-5458	164	19	figure	figure	NOUN
ejpam-5458	164	20	7	7	NUM
ejpam-5458	164	21	:	:	PUNCT
ejpam-5458	164	22	the	the	DET
ejpam-5458	164	23	phase	phase	NOUN
ejpam-5458	164	24	portraits	portrait	NOUN
ejpam-5458	164	25	show	show	VERB
ejpam-5458	164	26	solutions	solution	NOUN
ejpam-5458	164	27	of	of	ADP
ejpam-5458	164	28	rothman	rothman	PROPN
ejpam-5458	164	29	’s	’s	PART
ejpam-5458	164	30	carbon	carbon	NOUN
ejpam-5458	164	31	cycle	cycle	NOUN
ejpam-5458	164	32	model	model	NOUN
ejpam-5458	164	33	(	(	PUNCT
ejpam-5458	164	34	7	7	NUM
ejpam-5458	164	35	)	)	PUNCT
ejpam-5458	164	36	for	for	ADP
ejpam-5458	164	37	ν	ν	NOUN
ejpam-5458	164	38	=	=	SYM
ejpam-5458	164	39	0.4	0.4	NUM
ejpam-5458	164	40	.	.	PUNCT
ejpam-5458	165	1	the	the	DET
ejpam-5458	165	2	parameter	parameter	NOUN
ejpam-5458	165	3	cx	cx	PROPN
ejpam-5458	165	4	=	=	NOUN
ejpam-5458	165	5	55.88	55.88	NUM
ejpam-5458	165	6	(	(	PUNCT
ejpam-5458	165	7	a	a	NOUN
ejpam-5458	165	8	)	)	PUNCT
ejpam-5458	165	9	,	,	PUNCT
ejpam-5458	165	10	cx	cx	PROPN
ejpam-5458	166	1	=	=	SYM
ejpam-5458	166	2	60	60	NUM
ejpam-5458	166	3	(	(	PUNCT
ejpam-5458	166	4	b	b	NOUN
ejpam-5458	166	5	)	)	PUNCT
ejpam-5458	166	6	and	and	CCONJ
ejpam-5458	166	7	cx	cx	NOUN
ejpam-5458	166	8	=	=	SYM
ejpam-5458	167	1	62.62	62.62	NUM
ejpam-5458	167	2	(	(	PUNCT
ejpam-5458	167	3	c	c	NOUN
ejpam-5458	167	4	)	)	PUNCT
ejpam-5458	167	5	,	,	PUNCT
ejpam-5458	167	6	and	and	CCONJ
ejpam-5458	167	7	other	other	ADJ
ejpam-5458	167	8	parameters	parameter	NOUN
ejpam-5458	167	9	are	be	AUX
ejpam-5458	167	10	given	give	VERB
ejpam-5458	167	11	in	in	ADP
ejpam-5458	167	12	table	table	NOUN
ejpam-5458	167	13	1	1	NUM
ejpam-5458	167	14	.	.	PUNCT
ejpam-5458	168	1	(	(	PUNCT
ejpam-5458	168	2	b	b	X
ejpam-5458	168	3	-	-	PUNCT
ejpam-5458	168	4	c	c	NOUN
ejpam-5458	168	5	)	)	PUNCT
ejpam-5458	168	6	show	show	VERB
ejpam-5458	168	7	solutions	solution	NOUN
ejpam-5458	168	8	of	of	ADP
ejpam-5458	168	9	(	(	PUNCT
ejpam-5458	168	10	7	7	NUM
ejpam-5458	168	11	)	)	PUNCT
ejpam-5458	168	12	with	with	ADP
ejpam-5458	168	13	different	different	ADJ
ejpam-5458	168	14	initial	initial	ADJ
ejpam-5458	168	15	conditions	condition	NOUN
ejpam-5458	168	16	.	.	PUNCT
ejpam-5458	169	1	the	the	DET
ejpam-5458	169	2	model	model	NOUN
ejpam-5458	169	3	(	(	PUNCT
ejpam-5458	169	4	7	7	X
ejpam-5458	169	5	)	)	PUNCT
ejpam-5458	169	6	exhibits	exhibit	VERB
ejpam-5458	169	7	both	both	CCONJ
ejpam-5458	169	8	stable	stable	ADJ
ejpam-5458	169	9	and	and	CCONJ
ejpam-5458	169	10	unstable	unstable	ADJ
ejpam-5458	169	11	limit	limit	NOUN
ejpam-5458	169	12	cycles	cycle	NOUN
ejpam-5458	169	13	via	via	ADP
ejpam-5458	169	14	hopf	hopf	ADJ
ejpam-5458	169	15	bifurcations	bifurcation	NOUN
ejpam-5458	169	16	as	as	SCONJ
ejpam-5458	169	17	the	the	DET
ejpam-5458	169	18	parameter	parameter	NOUN
ejpam-5458	169	19	cx	cx	PROPN
ejpam-5458	169	20	is	be	AUX
ejpam-5458	169	21	varied	varied	ADJ
ejpam-5458	169	22	.	.	PUNCT
ejpam-5458	170	1	in	in	ADP
ejpam-5458	170	2	(	(	PUNCT
ejpam-5458	170	3	a	a	DET
ejpam-5458	170	4	-	-	PUNCT
ejpam-5458	170	5	b	b	NOUN
ejpam-5458	170	6	)	)	PUNCT
ejpam-5458	170	7	,	,	PUNCT
ejpam-5458	170	8	there	there	PRON
ejpam-5458	170	9	is	be	VERB
ejpam-5458	170	10	a	a	DET
ejpam-5458	170	11	stable	stable	ADJ
ejpam-5458	170	12	equilibrium	equilibrium	NOUN
ejpam-5458	170	13	point	point	NOUN
ejpam-5458	170	14	(	(	PUNCT
ejpam-5458	170	15	black	black	ADJ
ejpam-5458	170	16	point	point	NOUN
ejpam-5458	170	17	)	)	PUNCT
ejpam-5458	170	18	(	(	PUNCT
ejpam-5458	170	19	c∗	c∗	PROPN
ejpam-5458	170	20	,	,	PUNCT
ejpam-5458	170	21	w∗	w∗	PROPN
ejpam-5458	170	22	)	)	PUNCT
ejpam-5458	170	23	.	.	PUNCT
ejpam-5458	171	1	(	(	PUNCT
ejpam-5458	171	2	b	b	X
ejpam-5458	171	3	)	)	PUNCT
ejpam-5458	171	4	an	an	DET
ejpam-5458	171	5	unstable	unstable	ADJ
ejpam-5458	171	6	limit	limit	NOUN
ejpam-5458	171	7	cycle	cycle	NOUN
ejpam-5458	171	8	appears	appear	VERB
ejpam-5458	171	9	between	between	ADP
ejpam-5458	171	10	the	the	DET
ejpam-5458	171	11	stable	stable	ADJ
ejpam-5458	171	12	equilibrium	equilibrium	NOUN
ejpam-5458	171	13	point	point	NOUN
ejpam-5458	171	14	and	and	CCONJ
ejpam-5458	171	15	the	the	DET
ejpam-5458	171	16	stable	stable	ADJ
ejpam-5458	171	17	limit	limit	NOUN
ejpam-5458	171	18	cycle	cycle	NOUN
ejpam-5458	171	19	.	.	PUNCT
ejpam-5458	172	1	in	in	ADP
ejpam-5458	172	2	(	(	PUNCT
ejpam-5458	172	3	c	c	NOUN
ejpam-5458	172	4	)	)	PUNCT
ejpam-5458	172	5	,	,	PUNCT
ejpam-5458	172	6	there	there	PRON
ejpam-5458	172	7	is	be	VERB
ejpam-5458	172	8	a	a	DET
ejpam-5458	172	9	stable	stable	ADJ
ejpam-5458	172	10	limit	limit	NOUN
ejpam-5458	172	11	cycle	cycle	NOUN
ejpam-5458	172	12	and	and	CCONJ
ejpam-5458	172	13	an	an	DET
ejpam-5458	172	14	unstable	unstable	ADJ
ejpam-5458	172	15	equilibrium	equilibrium	NOUN
ejpam-5458	172	16	point	point	NOUN
ejpam-5458	172	17	(	(	PUNCT
ejpam-5458	172	18	black	black	ADJ
ejpam-5458	172	19	circle	circle	NOUN
ejpam-5458	172	20	)	)	PUNCT
ejpam-5458	172	21	when	when	SCONJ
ejpam-5458	172	22	cx	cx	PROPN
ejpam-5458	172	23	=	=	PROPN
ejpam-5458	172	24	62.62	62.62	NUM
ejpam-5458	172	25	.	.	PUNCT
ejpam-5458	173	1	with	with	ADP
ejpam-5458	173	2	smooth	smooth	ADJ
ejpam-5458	173	3	right	right	ADJ
ejpam-5458	173	4	hand	hand	NOUN
ejpam-5458	173	5	side	side	NOUN
ejpam-5458	173	6	f	f	PROPN
ejpam-5458	173	7	and	and	CCONJ
ejpam-5458	173	8	the	the	DET
ejpam-5458	173	9	vector	vector	NOUN
ejpam-5458	173	10	of	of	ADP
ejpam-5458	173	11	state	state	NOUN
ejpam-5458	173	12	variables	variable	NOUN
ejpam-5458	173	13	x	x	PUNCT
ejpam-5458	173	14	∈	∈	PROPN
ejpam-5458	173	15	rn	rn	PROPN
ejpam-5458	173	16	and	and	CCONJ
ejpam-5458	173	17	parameters	parameter	NOUN
ejpam-5458	173	18	α	α	PROPN
ejpam-5458	173	19	∈	∈	PROPN
ejpam-5458	173	20	rm	rm	PROPN
ejpam-5458	173	21	,	,	PUNCT
ejpam-5458	173	22	having	have	VERB
ejpam-5458	173	23	at	at	ADP
ejpam-5458	173	24	(	(	PUNCT
ejpam-5458	173	25	x	x	NOUN
ejpam-5458	173	26	,	,	PUNCT
ejpam-5458	173	27	α	α	NOUN
ejpam-5458	173	28	)	)	PUNCT
ejpam-5458	173	29	=	=	SYM
ejpam-5458	173	30	(	(	PUNCT
ejpam-5458	173	31	0	0	NUM
ejpam-5458	173	32	,	,	PUNCT
ejpam-5458	173	33	0	0	NUM
ejpam-5458	173	34	)	)	PUNCT
ejpam-5458	173	35	an	an	DET
ejpam-5458	173	36	equilibrium	equilibrium	NOUN
ejpam-5458	173	37	point	point	NOUN
ejpam-5458	173	38	with	with	ADP
ejpam-5458	173	39	eigenvalues	eigenvalue	VERB
ejpam-5458	173	40	λ1,2	λ1,2	ADJ
ejpam-5458	173	41	=	=	SYM
ejpam-5458	173	42	±iω0	±iω0	NOUN
ejpam-5458	173	43	,	,	PUNCT
ejpam-5458	173	44	ω0	ω0	ADV
ejpam-5458	173	45	>	>	X
ejpam-5458	173	46	0	0	X
ejpam-5458	173	47	.	.	PUNCT
ejpam-5458	173	48	consider	consider	VERB
ejpam-5458	173	49	the	the	DET
ejpam-5458	173	50	system	system	NOUN
ejpam-5458	173	51	(	(	PUNCT
ejpam-5458	173	52	15	15	NUM
ejpam-5458	173	53	)	)	PUNCT
ejpam-5458	173	54	can	can	AUX
ejpam-5458	173	55	be	be	AUX
ejpam-5458	173	56	written	write	VERB
ejpam-5458	173	57	as	as	ADP
ejpam-5458	173	58	ẋ	ẋ	PROPN
ejpam-5458	173	59	=	=	SYM
ejpam-5458	174	1	a(α)x+	a(α)x+	X
ejpam-5458	174	2	f	f	X
ejpam-5458	174	3	(	(	PUNCT
ejpam-5458	174	4	x	x	NOUN
ejpam-5458	174	5	,	,	PUNCT
ejpam-5458	174	6	α	α	NOUN
ejpam-5458	174	7	)	)	PUNCT
ejpam-5458	174	8	(	(	PUNCT
ejpam-5458	174	9	16	16	NUM
ejpam-5458	174	10	)	)	PUNCT
ejpam-5458	174	11	where	where	SCONJ
ejpam-5458	174	12	a(α	a(α	NOUN
ejpam-5458	174	13	)	)	PUNCT
ejpam-5458	174	14	is	be	AUX
ejpam-5458	174	15	the	the	DET
ejpam-5458	174	16	jacobian	jacobian	ADJ
ejpam-5458	174	17	matrix	matrix	NOUN
ejpam-5458	174	18	of	of	ADP
ejpam-5458	174	19	(	(	PUNCT
ejpam-5458	174	20	15	15	NUM
ejpam-5458	174	21	)	)	PUNCT
ejpam-5458	174	22	and	and	CCONJ
ejpam-5458	174	23	f	f	PROPN
ejpam-5458	174	24	is	be	AUX
ejpam-5458	174	25	a	a	DET
ejpam-5458	174	26	smooth	smooth	ADJ
ejpam-5458	174	27	vector	vector	NOUN
ejpam-5458	174	28	field	field	NOUN
ejpam-5458	174	29	with	with	ADP
ejpam-5458	174	30	zero	zero	NUM
ejpam-5458	174	31	jacobian	jacobian	ADJ
ejpam-5458	174	32	,	,	PUNCT
ejpam-5458	174	33	so	so	SCONJ
ejpam-5458	174	34	the	the	DET
ejpam-5458	174	35	taylor	taylor	PROPN
ejpam-5458	174	36	expansion	expansion	NOUN
ejpam-5458	174	37	in	in	ADP
ejpam-5458	174	38	x	x	PROPN
ejpam-5458	174	39	starts	start	VERB
ejpam-5458	174	40	with	with	ADP
ejpam-5458	174	41	the	the	DET
ejpam-5458	174	42	quadratic	quadratic	ADJ
ejpam-5458	174	43	term	term	NOUN
ejpam-5458	174	44	as	as	SCONJ
ejpam-5458	174	45	follows	follow	VERB
ejpam-5458	174	46	:	:	PUNCT
ejpam-5458	174	47	f	f	PROPN
ejpam-5458	174	48	(	(	PUNCT
ejpam-5458	174	49	x	x	X
ejpam-5458	174	50	,	,	PUNCT
ejpam-5458	174	51	0	0	NUM
ejpam-5458	174	52	)	)	PUNCT
ejpam-5458	174	53	=	=	SYM
ejpam-5458	174	54	1	1	NUM
ejpam-5458	174	55	2	2	NUM
ejpam-5458	174	56	!	!	PUNCT
ejpam-5458	175	1	b(x	b(x	VERB
ejpam-5458	175	2	,	,	PUNCT
ejpam-5458	175	3	x	x	X
ejpam-5458	175	4	)	)	PUNCT
ejpam-5458	176	1	+	+	CCONJ
ejpam-5458	176	2	1	1	NUM
ejpam-5458	176	3	3	3	NUM
ejpam-5458	176	4	!	!	PUNCT
ejpam-5458	177	1	c(x	c(x	NOUN
ejpam-5458	177	2	,	,	PUNCT
ejpam-5458	177	3	x	x	NOUN
ejpam-5458	177	4	,	,	PUNCT
ejpam-5458	177	5	x	x	X
ejpam-5458	177	6	)	)	PUNCT
ejpam-5458	177	7	+	+	CCONJ
ejpam-5458	177	8	1	1	NUM
ejpam-5458	177	9	4	4	NUM
ejpam-5458	177	10	!	!	PUNCT
ejpam-5458	178	1	d(x	d(x	NOUN
ejpam-5458	178	2	,	,	PUNCT
ejpam-5458	178	3	x	x	X
ejpam-5458	178	4	,	,	PUNCT
ejpam-5458	178	5	x	x	X
ejpam-5458	178	6	,	,	PUNCT
ejpam-5458	178	7	x	x	X
ejpam-5458	178	8	)	)	PUNCT
ejpam-5458	179	1	+	+	ADJ
ejpam-5458	179	2	o(||x||)5	o(||x||)5	NOUN
ejpam-5458	179	3	(	(	PUNCT
ejpam-5458	179	4	17	17	NUM
ejpam-5458	179	5	)	)	PUNCT
ejpam-5458	179	6	i.	i.	NOUN
ejpam-5458	179	7	alraddadi	alraddadi	PROPN
ejpam-5458	179	8	/	/	SYM
ejpam-5458	179	9	eur	eur	PROPN
ejpam-5458	179	10	.	.	PUNCT
ejpam-5458	180	1	j.	j.	PROPN
ejpam-5458	180	2	pure	pure	PROPN
ejpam-5458	180	3	appl	appl	PROPN
ejpam-5458	180	4	.	.	PROPN
ejpam-5458	180	5	math	math	PROPN
ejpam-5458	180	6	,	,	PUNCT
ejpam-5458	180	7	17	17	NUM
ejpam-5458	180	8	(	(	PUNCT
ejpam-5458	180	9	4	4	NUM
ejpam-5458	180	10	)	)	PUNCT
ejpam-5458	180	11	(	(	PUNCT
ejpam-5458	180	12	2024	2024	NUM
ejpam-5458	180	13	)	)	PUNCT
ejpam-5458	180	14	,	,	PUNCT
ejpam-5458	180	15	3708	3708	NUM
ejpam-5458	180	16	-	-	SYM
ejpam-5458	180	17	3729	3729	NUM
ejpam-5458	180	18	3718	3718	NUM
ejpam-5458	180	19	figure	figure	NOUN
ejpam-5458	180	20	8	8	NUM
ejpam-5458	180	21	:	:	PUNCT
ejpam-5458	180	22	the	the	DET
ejpam-5458	180	23	phase	phase	NOUN
ejpam-5458	180	24	portrait	portrait	NOUN
ejpam-5458	180	25	(	(	PUNCT
ejpam-5458	180	26	a	a	NOUN
ejpam-5458	180	27	)	)	PUNCT
ejpam-5458	180	28	and	and	CCONJ
ejpam-5458	180	29	time	time	NOUN
ejpam-5458	180	30	series	series	NOUN
ejpam-5458	180	31	(	(	PUNCT
ejpam-5458	180	32	b	b	X
ejpam-5458	180	33	-	-	PUNCT
ejpam-5458	180	34	c	c	NOUN
ejpam-5458	180	35	)	)	PUNCT
ejpam-5458	180	36	are	be	AUX
ejpam-5458	180	37	shown	show	VERB
ejpam-5458	180	38	for	for	ADP
ejpam-5458	180	39	rothman	rothman	PROPN
ejpam-5458	180	40	’s	’s	PART
ejpam-5458	180	41	carbon	carbon	NOUN
ejpam-5458	180	42	cycle	cycle	NOUN
ejpam-5458	180	43	model	model	NOUN
ejpam-5458	180	44	(	(	PUNCT
ejpam-5458	180	45	7	7	NUM
ejpam-5458	180	46	)	)	PUNCT
ejpam-5458	180	47	when	when	SCONJ
ejpam-5458	180	48	cx	cx	PROPN
ejpam-5458	180	49	=	=	PROPN
ejpam-5458	180	50	55.88	55.88	NUM
ejpam-5458	180	51	.	.	PUNCT
ejpam-5458	181	1	the	the	DET
ejpam-5458	181	2	initial	initial	ADJ
ejpam-5458	181	3	conditions	condition	NOUN
ejpam-5458	181	4	and	and	CCONJ
ejpam-5458	181	5	parameters	parameter	NOUN
ejpam-5458	181	6	are	be	AUX
ejpam-5458	181	7	given	give	VERB
ejpam-5458	181	8	in	in	ADP
ejpam-5458	181	9	table	table	NOUN
ejpam-5458	181	10	1	1	NUM
ejpam-5458	181	11	.	.	PUNCT
ejpam-5458	182	1	the	the	DET
ejpam-5458	182	2	black	black	ADJ
ejpam-5458	182	3	point	point	NOUN
ejpam-5458	182	4	represents	represent	VERB
ejpam-5458	182	5	the	the	DET
ejpam-5458	182	6	stable	stable	ADJ
ejpam-5458	182	7	equilibrium	equilibrium	NOUN
ejpam-5458	182	8	point	point	NOUN
ejpam-5458	182	9	(	(	PUNCT
ejpam-5458	182	10	c∗	c∗	PROPN
ejpam-5458	182	11	,	,	PUNCT
ejpam-5458	182	12	w∗	w∗	NOUN
ejpam-5458	182	13	)	)	PUNCT
ejpam-5458	182	14	and	and	CCONJ
ejpam-5458	182	15	the	the	DET
ejpam-5458	182	16	nullclines	nullcline	NOUN
ejpam-5458	182	17	are	be	AUX
ejpam-5458	182	18	shown	show	VERB
ejpam-5458	182	19	by	by	ADP
ejpam-5458	182	20	the	the	DET
ejpam-5458	182	21	red	red	ADJ
ejpam-5458	182	22	line	line	NOUN
ejpam-5458	182	23	ẇ	ẇ	PROPN
ejpam-5458	182	24	=	=	SYM
ejpam-5458	182	25	0	0	NUM
ejpam-5458	182	26	and	and	CCONJ
ejpam-5458	182	27	black	black	ADJ
ejpam-5458	182	28	line	line	NOUN
ejpam-5458	182	29	ċ	ċ	NOUN
ejpam-5458	183	1	=	=	SYM
ejpam-5458	183	2	0	0	PROPN
ejpam-5458	183	3	.	.	PUNCT
ejpam-5458	184	1	where	where	SCONJ
ejpam-5458	184	2	b	b	NOUN
ejpam-5458	184	3	,	,	PUNCT
ejpam-5458	184	4	c	c	PROPN
ejpam-5458	184	5	and	and	CCONJ
ejpam-5458	184	6	d	d	PROPN
ejpam-5458	184	7	are	be	AUX
ejpam-5458	184	8	multilinear	multilinear	NOUN
ejpam-5458	184	9	symmetric	symmetric	ADJ
ejpam-5458	184	10	functions	function	NOUN
ejpam-5458	184	11	[	[	X
ejpam-5458	184	12	4	4	NUM
ejpam-5458	184	13	]	]	X
ejpam-5458	184	14	:	:	PUNCT
ejpam-5458	184	15	b(x	b(x	NOUN
ejpam-5458	184	16	,	,	PUNCT
ejpam-5458	184	17	y	y	NOUN
ejpam-5458	184	18	)	)	PUNCT
ejpam-5458	185	1	=	=	PUNCT
ejpam-5458	185	2	n∑	n∑	PROPN
ejpam-5458	185	3	j	j	PROPN
ejpam-5458	185	4	,	,	PUNCT
ejpam-5458	185	5	k=1	k=1	PROPN
ejpam-5458	185	6	∂2fi(ξ	∂2fi(ξ	PROPN
ejpam-5458	185	7	)	)	PUNCT
ejpam-5458	185	8	∂ξj∂ξk	∂ξj∂ξk	PROPN
ejpam-5458	185	9	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5458	185	10	ξ=0	ξ=0	PROPN
ejpam-5458	185	11	xjyk	xjyk	PROPN
ejpam-5458	185	12	,	,	PUNCT
ejpam-5458	185	13	i	i	PRON
ejpam-5458	185	14	=	=	NOUN
ejpam-5458	185	15	1	1	NUM
ejpam-5458	185	16	,	,	PUNCT
ejpam-5458	185	17	.	.	PUNCT
ejpam-5458	185	18	.	.	PUNCT
ejpam-5458	186	1	.	.	PUNCT
ejpam-5458	187	1	,	,	PUNCT
ejpam-5458	187	2	n	n	X
ejpam-5458	187	3	(	(	PUNCT
ejpam-5458	187	4	18	18	NUM
ejpam-5458	187	5	)	)	PUNCT
ejpam-5458	187	6	c(x	c(x	NOUN
ejpam-5458	187	7	,	,	PUNCT
ejpam-5458	187	8	y	y	PROPN
ejpam-5458	187	9	,	,	PUNCT
ejpam-5458	187	10	z	z	NOUN
ejpam-5458	187	11	)	)	PUNCT
ejpam-5458	187	12	=	=	SYM
ejpam-5458	187	13	n∑	n∑	PROPN
ejpam-5458	187	14	j	j	PROPN
ejpam-5458	187	15	,	,	PUNCT
ejpam-5458	187	16	k	k	PROPN
ejpam-5458	187	17	,	,	PUNCT
ejpam-5458	187	18	l=1	l=1	NOUN
ejpam-5458	187	19	∂3fi(ξ	∂3fi(ξ	NOUN
ejpam-5458	187	20	)	)	PUNCT
ejpam-5458	187	21	∂ξj∂ξk∂l	∂ξj∂ξk∂l	PROPN
ejpam-5458	187	22	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5458	187	23	ξ=0	ξ=0	PROPN
ejpam-5458	187	24	xjykzl	xjykzl	NOUN
ejpam-5458	187	25	,	,	PUNCT
ejpam-5458	187	26	i	i	PRON
ejpam-5458	187	27	=	=	NOUN
ejpam-5458	187	28	1	1	NUM
ejpam-5458	187	29	,	,	PUNCT
ejpam-5458	187	30	.	.	PUNCT
ejpam-5458	187	31	.	.	PUNCT
ejpam-5458	188	1	.	.	PUNCT
ejpam-5458	189	1	,	,	PUNCT
ejpam-5458	189	2	n	n	X
ejpam-5458	189	3	(	(	PUNCT
ejpam-5458	189	4	19	19	NUM
ejpam-5458	189	5	)	)	PUNCT
ejpam-5458	189	6	c(x	c(x	NOUN
ejpam-5458	189	7	,	,	PUNCT
ejpam-5458	189	8	y	y	PROPN
ejpam-5458	189	9	,	,	PUNCT
ejpam-5458	189	10	z	z	PROPN
ejpam-5458	189	11	,	,	PUNCT
ejpam-5458	189	12	u	u	NOUN
ejpam-5458	189	13	)	)	PUNCT
ejpam-5458	189	14	=	=	SYM
ejpam-5458	189	15	n∑	n∑	PROPN
ejpam-5458	189	16	j	j	PROPN
ejpam-5458	189	17	,	,	PUNCT
ejpam-5458	189	18	k	k	PROPN
ejpam-5458	189	19	,	,	PUNCT
ejpam-5458	189	20	l	l	NOUN
ejpam-5458	189	21	,	,	PUNCT
ejpam-5458	189	22	r=1	r=1	ADJ
ejpam-5458	189	23	∂4fi(ξ	∂4fi(ξ	X
ejpam-5458	189	24	)	)	PUNCT
ejpam-5458	189	25	∂ξj∂ξk∂ξl∂ξr	∂ξj∂ξk∂ξl∂ξr	PROPN
ejpam-5458	189	26	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5458	189	27	ξ=0	ξ=0	PROPN
ejpam-5458	189	28	xjykzlur	xjykzlur	PROPN
ejpam-5458	189	29	,	,	PUNCT
ejpam-5458	189	30	i	i	PRON
ejpam-5458	189	31	=	=	NOUN
ejpam-5458	189	32	1	1	NUM
ejpam-5458	189	33	,	,	PUNCT
ejpam-5458	189	34	.	.	PUNCT
ejpam-5458	189	35	.	.	PUNCT
ejpam-5458	190	1	.	.	PUNCT
ejpam-5458	191	1	,	,	PUNCT
ejpam-5458	191	2	n	n	X
ejpam-5458	191	3	(	(	PUNCT
ejpam-5458	191	4	20	20	NUM
ejpam-5458	191	5	)	)	PUNCT
ejpam-5458	191	6	the	the	DET
ejpam-5458	191	7	jacobian	jacobian	ADJ
ejpam-5458	191	8	matrix	matrix	NOUN
ejpam-5458	191	9	a	a	PRON
ejpam-5458	191	10	of	of	ADP
ejpam-5458	191	11	(	(	PUNCT
ejpam-5458	191	12	15	15	NUM
ejpam-5458	191	13	)	)	PUNCT
ejpam-5458	191	14	at	at	ADP
ejpam-5458	191	15	the	the	DET
ejpam-5458	191	16	equilibrium	equilibrium	NOUN
ejpam-5458	191	17	point	point	NOUN
ejpam-5458	191	18	(	(	PUNCT
ejpam-5458	191	19	x	x	NOUN
ejpam-5458	191	20	,	,	PUNCT
ejpam-5458	191	21	α	α	NOUN
ejpam-5458	191	22	)	)	PUNCT
ejpam-5458	191	23	=	=	SYM
ejpam-5458	191	24	(	(	PUNCT
ejpam-5458	191	25	0	0	NUM
ejpam-5458	191	26	,	,	PUNCT
ejpam-5458	191	27	0	0	NUM
ejpam-5458	191	28	)	)	PUNCT
ejpam-5458	191	29	has	have	VERB
ejpam-5458	191	30	pure	pure	ADJ
ejpam-5458	191	31	imaginary	imaginary	ADJ
ejpam-5458	191	32	eigenvalues	eigenvalue	NOUN
ejpam-5458	191	33	λ1,2	λ1,2	ADJ
ejpam-5458	191	34	=	=	PUNCT
ejpam-5458	191	35	±iω0	±iω0	NOUN
ejpam-5458	191	36	(	(	PUNCT
ejpam-5458	191	37	the	the	DET
ejpam-5458	191	38	hopf	hopf	ADJ
ejpam-5458	191	39	bifurcation	bifurcation	NOUN
ejpam-5458	191	40	condition	condition	NOUN
ejpam-5458	191	41	is	be	AUX
ejpam-5458	191	42	satisfied	satisfied	ADJ
ejpam-5458	191	43	)	)	PUNCT
ejpam-5458	191	44	.	.	PUNCT
ejpam-5458	192	1	i.	i.	PROPN
ejpam-5458	192	2	alraddadi	alraddadi	PROPN
ejpam-5458	192	3	/	/	SYM
ejpam-5458	192	4	eur	eur	PROPN
ejpam-5458	192	5	.	.	PUNCT
ejpam-5458	193	1	j.	j.	PROPN
ejpam-5458	193	2	pure	pure	PROPN
ejpam-5458	193	3	appl	appl	PROPN
ejpam-5458	193	4	.	.	PROPN
ejpam-5458	193	5	math	math	PROPN
ejpam-5458	193	6	,	,	PUNCT
ejpam-5458	193	7	17	17	NUM
ejpam-5458	193	8	(	(	PUNCT
ejpam-5458	193	9	4	4	NUM
ejpam-5458	193	10	)	)	PUNCT
ejpam-5458	193	11	(	(	PUNCT
ejpam-5458	193	12	2024	2024	NUM
ejpam-5458	193	13	)	)	PUNCT
ejpam-5458	193	14	,	,	PUNCT
ejpam-5458	193	15	3708	3708	NUM
ejpam-5458	193	16	-	-	SYM
ejpam-5458	193	17	3729	3729	NUM
ejpam-5458	193	18	3719	3719	NUM
ejpam-5458	193	19	parameter	parameter	NOUN
ejpam-5458	193	20	value	value	NOUN
ejpam-5458	193	21	description	description	NOUN
ejpam-5458	193	22	µ	µ	X
ejpam-5458	193	23	250	250	NUM
ejpam-5458	193	24	characteristic	characteristic	ADJ
ejpam-5458	193	25	concentration	concentration	NOUN
ejpam-5458	193	26	jinτw	jinτw	NOUN
ejpam-5458	193	27	b	b	PROPN
ejpam-5458	193	28	4	4	NUM
ejpam-5458	193	29	maximum	maximum	ADJ
ejpam-5458	193	30	caco3	caco3	NOUN
ejpam-5458	193	31	burial	burial	NOUN
ejpam-5458	193	32	rate	rate	NOUN
ejpam-5458	193	33	θ	θ	PROPN
ejpam-5458	193	34	5	5	NUM
ejpam-5458	193	35	maximum	maximum	ADJ
ejpam-5458	193	36	respiration	respiration	NOUN
ejpam-5458	193	37	feedback	feedback	NOUN
ejpam-5458	193	38	rate	rate	NOUN
ejpam-5458	193	39	cx	cx	PROPN
ejpam-5458	193	40	70	70	NUM
ejpam-5458	193	41	respiration	respiration	NOUN
ejpam-5458	193	42	cp	cp	NUM
ejpam-5458	194	1	110	110	NUM
ejpam-5458	194	2	burial	burial	NOUN
ejpam-5458	194	3	ν	ν	NOUN
ejpam-5458	194	4	0	0	NUM
ejpam-5458	194	5	injection	injection	NOUN
ejpam-5458	194	6	rate	rate	NOUN
ejpam-5458	194	7	w0	w0	PROPN
ejpam-5458	194	8	2000	2000	NUM
ejpam-5458	194	9	reference	reference	NOUN
ejpam-5458	194	10	dic	dic	PROPN
ejpam-5458	194	11	concentration	concentration	NOUN
ejpam-5458	194	12	γ	γ	PROPN
ejpam-5458	194	13	4	4	NUM
ejpam-5458	194	14	sigmoid	sigmoid	NOUN
ejpam-5458	194	15	sharpness	sharpness	NOUN
ejpam-5458	194	16	index	index	NOUN
ejpam-5458	194	17	f0	f0	VERB
ejpam-5458	194	18	0.694	0.694	NUM
ejpam-5458	194	19	maximum	maximum	ADJ
ejpam-5458	194	20	buffer	buffer	NOUN
ejpam-5458	194	21	factor	factor	NOUN
ejpam-5458	194	22	cf	cf	NOUN
ejpam-5458	194	23	43.9	43.9	NUM
ejpam-5458	194	24	buffering	buffering	NOUN
ejpam-5458	194	25	β	β	ADP
ejpam-5458	194	26	1.7	1.7	NUM
ejpam-5458	194	27	sigmoid	sigmoid	NOUN
ejpam-5458	194	28	sharpness	sharpness	NOUN
ejpam-5458	194	29	index	index	NOUN
ejpam-5458	194	30	table	table	NOUN
ejpam-5458	194	31	1	1	NUM
ejpam-5458	194	32	:	:	PUNCT
ejpam-5458	194	33	this	this	DET
ejpam-5458	194	34	table	table	NOUN
ejpam-5458	194	35	shows	show	VERB
ejpam-5458	194	36	the	the	DET
ejpam-5458	194	37	default	default	NOUN
ejpam-5458	194	38	parameters	parameter	NOUN
ejpam-5458	194	39	for	for	ADP
ejpam-5458	194	40	rothman	rothman	PROPN
ejpam-5458	194	41	’s	’s	PART
ejpam-5458	194	42	carbon	carbon	NOUN
ejpam-5458	194	43	cycle	cycle	NOUN
ejpam-5458	194	44	model	model	NOUN
ejpam-5458	194	45	(	(	PUNCT
ejpam-5458	194	46	7	7	NUM
ejpam-5458	194	47	)	)	PUNCT
ejpam-5458	194	48	[	[	X
ejpam-5458	194	49	12	12	NUM
ejpam-5458	194	50	,	,	PUNCT
ejpam-5458	194	51	si	si	X
ejpam-5458	194	52	appendix	appendix	NOUN
ejpam-5458	194	53	,	,	PUNCT
ejpam-5458	194	54	table	table	NOUN
ejpam-5458	194	55	s1	s1	NOUN
ejpam-5458	194	56	]	]	PUNCT
ejpam-5458	194	57	.	.	PUNCT
ejpam-5458	195	1	let	let	VERB
ejpam-5458	195	2	q(α	q(α	PROPN
ejpam-5458	195	3	)	)	PUNCT
ejpam-5458	195	4	∈	∈	PROPN
ejpam-5458	195	5	c2	c2	PROPN
ejpam-5458	195	6	be	be	VERB
ejpam-5458	195	7	an	an	DET
ejpam-5458	195	8	eigenvector	eigenvector	NOUN
ejpam-5458	195	9	of	of	ADP
ejpam-5458	195	10	a	a	DET
ejpam-5458	195	11	corresponding	corresponding	NOUN
ejpam-5458	195	12	to	to	ADP
ejpam-5458	195	13	λ(α	λ(α	NUM
ejpam-5458	195	14	)	)	PUNCT
ejpam-5458	195	15	,	,	PUNCT
ejpam-5458	195	16	and	and	CCONJ
ejpam-5458	195	17	p(α	p(α	PROPN
ejpam-5458	195	18	)	)	PUNCT
ejpam-5458	195	19	∈	∈	PROPN
ejpam-5458	195	20	c2	c2	PROPN
ejpam-5458	195	21	be	be	VERB
ejpam-5458	195	22	an	an	DET
ejpam-5458	195	23	eigenvector	eigenvector	NOUN
ejpam-5458	195	24	of	of	ADP
ejpam-5458	195	25	the	the	DET
ejpam-5458	195	26	transpose	transpose	NOUN
ejpam-5458	195	27	at	at	ADP
ejpam-5458	195	28	corresponding	correspond	VERB
ejpam-5458	195	29	to	to	ADP
ejpam-5458	195	30	λ(α	λ(α	NUM
ejpam-5458	195	31	)	)	PUNCT
ejpam-5458	195	32	.	.	PUNCT
ejpam-5458	196	1	it	it	PRON
ejpam-5458	196	2	follows	follow	VERB
ejpam-5458	196	3	that	that	SCONJ
ejpam-5458	196	4	:	:	PUNCT
ejpam-5458	196	5	a(α)q(α	a(α)q(α	X
ejpam-5458	196	6	)	)	PUNCT
ejpam-5458	196	7	=	=	SYM
ejpam-5458	196	8	λ(α)q(α	λ(α)q(α	NOUN
ejpam-5458	196	9	)	)	PUNCT
ejpam-5458	196	10	,	,	PUNCT
ejpam-5458	196	11	at	at	ADP
ejpam-5458	196	12	(	(	PUNCT
ejpam-5458	196	13	α)p(α	α)p(α	NUM
ejpam-5458	196	14	)	)	PUNCT
ejpam-5458	196	15	=	=	SYM
ejpam-5458	196	16	λ(α)q(α	λ(α)q(α	NOUN
ejpam-5458	196	17	)	)	PUNCT
ejpam-5458	196	18	⟨p	⟨p	NOUN
ejpam-5458	196	19	,	,	PUNCT
ejpam-5458	196	20	q⟩	q⟩	X
ejpam-5458	197	1	=	=	PUNCT
ejpam-5458	197	2	2∑	2∑	NUM
ejpam-5458	197	3	i=1	i=1	X
ejpam-5458	197	4	p̄iqi	p̄iqi	NOUN
ejpam-5458	197	5	=	=	SYM
ejpam-5458	197	6	1	1	NUM
ejpam-5458	197	7	we	we	PRON
ejpam-5458	197	8	introduce	introduce	VERB
ejpam-5458	197	9	the	the	DET
ejpam-5458	197	10	complex	complex	ADJ
ejpam-5458	197	11	variable	variable	NOUN
ejpam-5458	197	12	z	z	NOUN
ejpam-5458	197	13	=	=	SYM
ejpam-5458	197	14	(	(	PUNCT
ejpam-5458	197	15	p	p	X
ejpam-5458	197	16	,	,	PUNCT
ejpam-5458	197	17	x	x	NOUN
ejpam-5458	197	18	)	)	PUNCT
ejpam-5458	197	19	,	,	PUNCT
ejpam-5458	197	20	where	where	SCONJ
ejpam-5458	197	21	x	x	ADP
ejpam-5458	197	22	=	=	SYM
ejpam-5458	197	23	zq	zq	PROPN
ejpam-5458	197	24	+	+	PROPN
ejpam-5458	197	25	z̄q̄	z̄q̄	PROPN
ejpam-5458	197	26	system	system	NOUN
ejpam-5458	197	27	(	(	PUNCT
ejpam-5458	197	28	15	15	NUM
ejpam-5458	197	29	)	)	PUNCT
ejpam-5458	197	30	can	can	AUX
ejpam-5458	197	31	be	be	AUX
ejpam-5458	197	32	written	write	VERB
ejpam-5458	197	33	as	as	ADP
ejpam-5458	197	34	the	the	DET
ejpam-5458	197	35	formula	formula	NOUN
ejpam-5458	197	36	[	[	X
ejpam-5458	197	37	4	4	NUM
ejpam-5458	197	38	,	,	PUNCT
ejpam-5458	197	39	lemma	lemma	X
ejpam-5458	197	40	3.3	3.3	NUM
ejpam-5458	197	41	,	,	PUNCT
ejpam-5458	197	42	p.66	p.66	X
ejpam-5458	197	43	]	]	NOUN
ejpam-5458	197	44	:	:	PUNCT
ejpam-5458	197	45	ż	ż	NOUN
ejpam-5458	197	46	=	=	PUNCT
ejpam-5458	197	47	λ(α)z	λ(α)z	PROPN
ejpam-5458	197	48	+	+	PUNCT
ejpam-5458	197	49	g(z	g(z	PROPN
ejpam-5458	197	50	,	,	PUNCT
ejpam-5458	197	51	z	z	PROPN
ejpam-5458	197	52	,	,	PUNCT
ejpam-5458	197	53	α	α	NOUN
ejpam-5458	197	54	)	)	PUNCT
ejpam-5458	197	55	,	,	PUNCT
ejpam-5458	197	56	(	(	PUNCT
ejpam-5458	197	57	21	21	NUM
ejpam-5458	197	58	)	)	PUNCT
ejpam-5458	198	1	where	where	SCONJ
ejpam-5458	198	2	g(z	g(z	ADJ
ejpam-5458	198	3	,	,	PUNCT
ejpam-5458	198	4	z̄	z̄	NOUN
ejpam-5458	198	5	,	,	PUNCT
ejpam-5458	198	6	α	α	NOUN
ejpam-5458	198	7	)	)	PUNCT
ejpam-5458	198	8	=	=	SYM
ejpam-5458	198	9	⟨p	⟨p	PROPN
ejpam-5458	198	10	,	,	PUNCT
ejpam-5458	198	11	f	f	PROPN
ejpam-5458	198	12	(	(	PUNCT
ejpam-5458	198	13	zq	zq	PROPN
ejpam-5458	198	14	+	+	PROPN
ejpam-5458	198	15	z̄q̄	z̄q̄	PROPN
ejpam-5458	198	16	,	,	PUNCT
ejpam-5458	198	17	α)⟩	α)⟩	PROPN
ejpam-5458	198	18	is	be	AUX
ejpam-5458	198	19	a	a	DET
ejpam-5458	198	20	smooth	smooth	ADJ
ejpam-5458	198	21	function	function	NOUN
ejpam-5458	198	22	and	and	CCONJ
ejpam-5458	198	23	can	can	AUX
ejpam-5458	198	24	be	be	AUX
ejpam-5458	198	25	written	write	VERB
ejpam-5458	198	26	as	as	ADP
ejpam-5458	198	27	a	a	DET
ejpam-5458	198	28	formal	formal	ADJ
ejpam-5458	198	29	taylor	taylor	PROPN
ejpam-5458	198	30	series	series	NOUN
ejpam-5458	198	31	in	in	ADP
ejpam-5458	198	32	two	two	NUM
ejpam-5458	198	33	complex	complex	ADJ
ejpam-5458	198	34	variables	variable	NOUN
ejpam-5458	198	35	(	(	PUNCT
ejpam-5458	198	36	z	z	NOUN
ejpam-5458	198	37	and	and	CCONJ
ejpam-5458	198	38	z̄	z̄	NOUN
ejpam-5458	198	39	):	):	PUNCT
ejpam-5458	198	40	g(z	g(z	ADJ
ejpam-5458	198	41	,	,	PUNCT
ejpam-5458	198	42	z̄	z̄	NOUN
ejpam-5458	198	43	,	,	PUNCT
ejpam-5458	198	44	α	α	NOUN
ejpam-5458	198	45	)	)	PUNCT
ejpam-5458	198	46	=	=	PUNCT
ejpam-5458	198	47	∑	∑	PUNCT
ejpam-5458	198	48	k+l≥2	k+l≥2	PROPN
ejpam-5458	198	49	1	1	NUM
ejpam-5458	198	50	k!l	k!l	PROPN
ejpam-5458	198	51	!	!	PUNCT
ejpam-5458	199	1	gkl(α)z	gkl(α)z	PROPN
ejpam-5458	199	2	kz̄l	kz̄l	PROPN
ejpam-5458	199	3	,	,	PUNCT
ejpam-5458	199	4	k	k	NOUN
ejpam-5458	199	5	,	,	PUNCT
ejpam-5458	199	6	l	l	NOUN
ejpam-5458	199	7	=	=	SYM
ejpam-5458	199	8	0	0	NUM
ejpam-5458	199	9	,	,	PUNCT
ejpam-5458	199	10	1	1	NUM
ejpam-5458	199	11	,	,	PUNCT
ejpam-5458	199	12	...	...	PUNCT
ejpam-5458	199	13	(	(	PUNCT
ejpam-5458	199	14	22	22	NUM
ejpam-5458	199	15	)	)	PUNCT
ejpam-5458	199	16	where	where	SCONJ
ejpam-5458	199	17	gkl(α	gkl(α	NOUN
ejpam-5458	199	18	)	)	PUNCT
ejpam-5458	200	1	=	=	NOUN
ejpam-5458	200	2	∂k+l	∂k+l	X
ejpam-5458	200	3	∂zk∂z̄l	∂zk∂z̄l	PROPN
ejpam-5458	200	4	⟨p	⟨p	PROPN
ejpam-5458	200	5	,	,	PUNCT
ejpam-5458	200	6	f	f	PROPN
ejpam-5458	200	7	(	(	PUNCT
ejpam-5458	200	8	zq+	zq+	PROPN
ejpam-5458	200	9	z̄q̄	z̄q̄	PROPN
ejpam-5458	200	10	,	,	PUNCT
ejpam-5458	200	11	α)⟩	α)⟩	PROPN
ejpam-5458	200	12	∣∣	∣∣	NUM
ejpam-5458	200	13	z=0	z=0	PROPN
ejpam-5458	200	14	.	.	PUNCT
ejpam-5458	201	1	to	to	PART
ejpam-5458	201	2	simplify	simplify	VERB
ejpam-5458	201	3	(	(	PUNCT
ejpam-5458	201	4	15	15	NUM
ejpam-5458	201	5	)	)	PUNCT
ejpam-5458	201	6	,	,	PUNCT
ejpam-5458	201	7	we	we	PRON
ejpam-5458	201	8	remove	remove	VERB
ejpam-5458	201	9	all	all	DET
ejpam-5458	201	10	the	the	DET
ejpam-5458	201	11	quadratic	quadratic	ADJ
ejpam-5458	201	12	terms	term	NOUN
ejpam-5458	201	13	by	by	ADP
ejpam-5458	201	14	coordinate	coordinate	NOUN
ejpam-5458	201	15	changes	change	NOUN
ejpam-5458	201	16	as	as	SCONJ
ejpam-5458	201	17	shown	show	VERB
ejpam-5458	201	18	by	by	ADP
ejpam-5458	201	19	the	the	DET
ejpam-5458	201	20	following	follow	VERB
ejpam-5458	201	21	[	[	X
ejpam-5458	201	22	[	[	X
ejpam-5458	201	23	4],lemma(3.6	4],lemma(3.6	NUM
ejpam-5458	201	24	)	)	PUNCT
ejpam-5458	201	25	p.96	p.96	ADP
ejpam-5458	201	26	]	]	X
ejpam-5458	201	27	:	:	PUNCT
ejpam-5458	202	1	ż	ż	NOUN
ejpam-5458	202	2	=	=	PUNCT
ejpam-5458	202	3	λz	λz	PROPN
ejpam-5458	202	4	+	+	NUM
ejpam-5458	202	5	g30	g30	PROPN
ejpam-5458	202	6	6	6	NUM
ejpam-5458	202	7	z3	z3	PROPN
ejpam-5458	202	8	+	+	CCONJ
ejpam-5458	202	9	g21	g21	PROPN
ejpam-5458	202	10	2	2	NUM
ejpam-5458	202	11	z2z̄	z2z̄	NUM
ejpam-5458	202	12	+	+	CCONJ
ejpam-5458	202	13	g12	g12	PROPN
ejpam-5458	202	14	2	2	PROPN
ejpam-5458	202	15	zz̄2	zz̄2	PROPN
ejpam-5458	202	16	+	+	CCONJ
ejpam-5458	202	17	g03	g03	VERB
ejpam-5458	202	18	6	6	NUM
ejpam-5458	202	19	z̄3	z̄3	NUM
ejpam-5458	202	20	+	+	ADV
ejpam-5458	202	21	o(|z|)4	o(|z|)4	ADJ
ejpam-5458	202	22	(	(	PUNCT
ejpam-5458	202	23	23	23	NUM
ejpam-5458	202	24	)	)	PUNCT
ejpam-5458	202	25	where	where	SCONJ
ejpam-5458	202	26	λ	λ	PROPN
ejpam-5458	202	27	=	=	SYM
ejpam-5458	202	28	µ(α	µ(α	PROPN
ejpam-5458	202	29	)	)	PUNCT
ejpam-5458	202	30	±	±	NOUN
ejpam-5458	202	31	iω(α	iω(α	PROPN
ejpam-5458	202	32	)	)	PUNCT
ejpam-5458	202	33	,	,	PUNCT
ejpam-5458	202	34	µ(0	µ(0	NOUN
ejpam-5458	202	35	)	)	PUNCT
ejpam-5458	202	36	=	=	SYM
ejpam-5458	202	37	0	0	NUM
ejpam-5458	202	38	,	,	PUNCT
ejpam-5458	202	39	ω(0	ω(0	PROPN
ejpam-5458	202	40	)	)	PUNCT
ejpam-5458	202	41	=	=	PUNCT
ejpam-5458	202	42	ω0	ω0	CCONJ
ejpam-5458	202	43	>	>	PUNCT
ejpam-5458	202	44	0	0	PUNCT
ejpam-5458	203	1	and	and	CCONJ
ejpam-5458	203	2	gij	gij	NOUN
ejpam-5458	203	3	=	=	SYM
ejpam-5458	203	4	gij(α	gij(α	NOUN
ejpam-5458	203	5	)	)	PUNCT
ejpam-5458	203	6	,	,	PUNCT
ejpam-5458	203	7	can	can	AUX
ejpam-5458	203	8	be	be	AUX
ejpam-5458	203	9	transformed	transform	VERB
ejpam-5458	203	10	by	by	ADP
ejpam-5458	203	11	an	an	DET
ejpam-5458	203	12	invertible	invertible	ADJ
ejpam-5458	203	13	parameter	parameter	NOUN
ejpam-5458	203	14	-	-	PUNCT
ejpam-5458	203	15	dependent	dependent	ADJ
ejpam-5458	203	16	change	change	NOUN
ejpam-5458	203	17	of	of	ADP
ejpam-5458	203	18	complex	complex	ADJ
ejpam-5458	203	19	coordinates	coordinate	NOUN
ejpam-5458	203	20	,	,	PUNCT
ejpam-5458	203	21	i.	i.	PROPN
ejpam-5458	203	22	alraddadi	alraddadi	PROPN
ejpam-5458	203	23	/	/	SYM
ejpam-5458	203	24	eur	eur	PROPN
ejpam-5458	203	25	.	.	PUNCT
ejpam-5458	204	1	j.	j.	PROPN
ejpam-5458	204	2	pure	pure	PROPN
ejpam-5458	204	3	appl	appl	PROPN
ejpam-5458	204	4	.	.	PROPN
ejpam-5458	204	5	math	math	PROPN
ejpam-5458	204	6	,	,	PUNCT
ejpam-5458	204	7	17	17	NUM
ejpam-5458	204	8	(	(	PUNCT
ejpam-5458	204	9	4	4	NUM
ejpam-5458	204	10	)	)	PUNCT
ejpam-5458	204	11	(	(	PUNCT
ejpam-5458	204	12	2024	2024	NUM
ejpam-5458	204	13	)	)	PUNCT
ejpam-5458	204	14	,	,	PUNCT
ejpam-5458	204	15	3708	3708	NUM
ejpam-5458	204	16	-	-	SYM
ejpam-5458	204	17	3729	3729	NUM
ejpam-5458	204	18	3720	3720	NUM
ejpam-5458	204	19	z	z	NOUN
ejpam-5458	204	20	=	=	SYM
ejpam-5458	204	21	w	w	PROPN
ejpam-5458	204	22	+	+	CCONJ
ejpam-5458	204	23	h20	h20	PROPN
ejpam-5458	204	24	2	2	NUM
ejpam-5458	204	25	w2	w2	NOUN
ejpam-5458	204	26	+	+	CCONJ
ejpam-5458	204	27	h11ww̄	h11ww̄	PROPN
ejpam-5458	204	28	+	+	CCONJ
ejpam-5458	204	29	h02	h02	PROPN
ejpam-5458	204	30	2	2	NUM
ejpam-5458	204	31	w̄2	w̄2	NOUN
ejpam-5458	204	32	+	+	CCONJ
ejpam-5458	204	33	h03	h03	NOUN
ejpam-5458	204	34	6	6	NUM
ejpam-5458	204	35	w3	w3	NOUN
ejpam-5458	204	36	+	+	CCONJ
ejpam-5458	204	37	h12	h12	NOUN
ejpam-5458	205	1	2	2	NUM
ejpam-5458	205	2	ww̄2	ww̄2	PROPN
ejpam-5458	205	3	+	+	NUM
ejpam-5458	205	4	h03	h03	NOUN
ejpam-5458	205	5	6	6	NUM
ejpam-5458	205	6	w̄3	w̄3	NOUN
ejpam-5458	205	7	h20	h20	PROPN
ejpam-5458	205	8	=	=	SYM
ejpam-5458	205	9	g20	g20	PROPN
ejpam-5458	205	10	λ	λ	PROPN
ejpam-5458	205	11	,	,	PUNCT
ejpam-5458	205	12	h11	h11	NOUN
ejpam-5458	205	13	=	=	SYM
ejpam-5458	205	14	g11	g11	PROPN
ejpam-5458	205	15	λ	λ	PROPN
ejpam-5458	205	16	,	,	PUNCT
ejpam-5458	205	17	h02	h02	NOUN
ejpam-5458	205	18	=	=	PUNCT
ejpam-5458	205	19	g02	g02	NOUN
ejpam-5458	205	20	2λ̄−	2λ̄−	NUM
ejpam-5458	205	21	λ	λ	PROPN
ejpam-5458	205	22	,	,	PUNCT
ejpam-5458	205	23	h03	h03	NOUN
ejpam-5458	205	24	=	=	PUNCT
ejpam-5458	205	25	g03	g03	NOUN
ejpam-5458	205	26	2λ̄−	2λ̄−	NUM
ejpam-5458	205	27	λ	λ	PROPN
ejpam-5458	205	28	h12	h12	NOUN
ejpam-5458	205	29	=	=	PROPN
ejpam-5458	205	30	g12	g12	PROPN
ejpam-5458	205	31	2λ̄	2λ̄	NUM
ejpam-5458	205	32	(	(	PUNCT
ejpam-5458	205	33	24	24	NUM
ejpam-5458	205	34	)	)	PUNCT
ejpam-5458	205	35	for	for	ADP
ejpam-5458	205	36	all	all	DET
ejpam-5458	205	37	sufficiently	sufficiently	ADV
ejpam-5458	205	38	small	small	ADJ
ejpam-5458	205	39	|α|	|α|	PROPN
ejpam-5458	205	40	,	,	PUNCT
ejpam-5458	205	41	for	for	ADP
ejpam-5458	205	42	an	an	DET
ejpam-5458	205	43	equation	equation	NOUN
ejpam-5458	205	44	with	with	ADP
ejpam-5458	205	45	only	only	ADV
ejpam-5458	205	46	one	one	NUM
ejpam-5458	205	47	cubic	cubic	ADJ
ejpam-5458	205	48	term	term	NOUN
ejpam-5458	205	49	:	:	PUNCT
ejpam-5458	205	50	ẇ	ẇ	PROPN
ejpam-5458	205	51	=	=	SYM
ejpam-5458	205	52	λw	λw	X
ejpam-5458	205	53	+	+	CCONJ
ejpam-5458	205	54	c1w	c1w	NOUN
ejpam-5458	205	55	2w̄	2w̄	NUM
ejpam-5458	205	56	+	+	ADJ
ejpam-5458	205	57	o(|w|)4	o(|w|)4	NOUN
ejpam-5458	205	58	(	(	PUNCT
ejpam-5458	205	59	25	25	NUM
ejpam-5458	205	60	)	)	PUNCT
ejpam-5458	205	61	where	where	SCONJ
ejpam-5458	205	62	c1	c1	PROPN
ejpam-5458	205	63	=	=	PROPN
ejpam-5458	205	64	g20g11(2λ+λ̄	g20g11(2λ+λ̄	PROPN
ejpam-5458	205	65	)	)	PUNCT
ejpam-5458	205	66	2|λ|2	2|λ|2	NOUN
ejpam-5458	206	1	+	+	NUM
ejpam-5458	206	2	|g11|2	|g11|2	NOUN
ejpam-5458	206	3	λ	λ	X
ejpam-5458	206	4	+	+	CCONJ
ejpam-5458	206	5	|g02|2	|g02|2	NUM
ejpam-5458	206	6	2(2λ−λ̄	2(2λ−λ̄	NUM
ejpam-5458	206	7	)	)	PUNCT
ejpam-5458	207	1	+	+	CCONJ
ejpam-5458	207	2	g21	g21	PROPN
ejpam-5458	207	3	2	2	NUM
ejpam-5458	207	4	.	.	PUNCT
ejpam-5458	208	1	from	from	ADP
ejpam-5458	208	2	[	[	X
ejpam-5458	208	3	4	4	NUM
ejpam-5458	208	4	,	,	PUNCT
ejpam-5458	208	5	lemma	lemma	PROPN
ejpam-5458	208	6	3.7	3.7	NUM
ejpam-5458	208	7	,	,	PUNCT
ejpam-5458	208	8	p	p	NOUN
ejpam-5458	208	9	98	98	NUM
ejpam-5458	208	10	]	]	PUNCT
ejpam-5458	208	11	,	,	PUNCT
ejpam-5458	208	12	suppose	suppose	VERB
ejpam-5458	208	13	µ(0	µ(0	NUM
ejpam-5458	208	14	)	)	PUNCT
ejpam-5458	208	15	̸=	̸=	PROPN
ejpam-5458	208	16	0	0	NUM
ejpam-5458	208	17	and	and	CCONJ
ejpam-5458	208	18	re(c1(0	re(c1(0	PROPN
ejpam-5458	208	19	)	)	PUNCT
ejpam-5458	208	20	)	)	PUNCT
ejpam-5458	209	1	̸=	̸=	PROPN
ejpam-5458	209	2	0	0	NUM
ejpam-5458	209	3	.	.	PUNCT
ejpam-5458	210	1	then	then	ADV
ejpam-5458	210	2	,	,	PUNCT
ejpam-5458	210	3	the	the	DET
ejpam-5458	210	4	equation	equation	NOUN
ejpam-5458	210	5	can	can	AUX
ejpam-5458	210	6	be	be	AUX
ejpam-5458	210	7	transformed	transform	VERB
ejpam-5458	210	8	by	by	ADP
ejpam-5458	210	9	a	a	DET
ejpam-5458	210	10	parameter	parameter	NOUN
ejpam-5458	210	11	-	-	PUNCT
ejpam-5458	210	12	dependent	dependent	ADJ
ejpam-5458	210	13	linear	linear	ADJ
ejpam-5458	210	14	coordinate	coordinate	NOUN
ejpam-5458	210	15	transformation	transformation	NOUN
ejpam-5458	210	16	,	,	PUNCT
ejpam-5458	210	17	a	a	DET
ejpam-5458	210	18	time	time	NOUN
ejpam-5458	210	19	rescaling	rescaling	NOUN
ejpam-5458	210	20	,	,	PUNCT
ejpam-5458	210	21	and	and	CCONJ
ejpam-5458	210	22	a	a	DET
ejpam-5458	210	23	nonlinear	nonlinear	ADJ
ejpam-5458	210	24	time	time	NOUN
ejpam-5458	210	25	reparametrization	reparametrization	NOUN
ejpam-5458	210	26	into	into	ADP
ejpam-5458	210	27	an	an	DET
ejpam-5458	210	28	equation	equation	NOUN
ejpam-5458	210	29	of	of	ADP
ejpam-5458	210	30	the	the	DET
ejpam-5458	210	31	form	form	NOUN
ejpam-5458	210	32	du	du	PROPN
ejpam-5458	210	33	dθ	dθ	PROPN
ejpam-5458	210	34	=	=	PROPN
ejpam-5458	210	35	(	(	PUNCT
ejpam-5458	210	36	β	β	X
ejpam-5458	210	37	+	+	CCONJ
ejpam-5458	210	38	i)u+	i)u+	NUM
ejpam-5458	210	39	l1(β	l1(β	PROPN
ejpam-5458	210	40	)	)	PUNCT
ejpam-5458	210	41	|l1(β)|	|l1(β)|	PUNCT
ejpam-5458	211	1	u|u|2	u|u|2	PROPN
ejpam-5458	211	2	+	+	NOUN
ejpam-5458	211	3	o(|u|4	o(|u|4	NOUN
ejpam-5458	211	4	)	)	PUNCT
ejpam-5458	211	5	=	=	SYM
ejpam-5458	211	6	(	(	PUNCT
ejpam-5458	211	7	β	β	X
ejpam-5458	211	8	+	+	X
ejpam-5458	211	9	i)u+	i)u+	NUM
ejpam-5458	211	10	su|u|2	su|u|2	PROPN
ejpam-5458	211	11	+	+	NOUN
ejpam-5458	211	12	o(|u|4	o(|u|4	NOUN
ejpam-5458	211	13	)	)	PUNCT
ejpam-5458	211	14	(	(	PUNCT
ejpam-5458	211	15	26	26	NUM
ejpam-5458	211	16	)	)	PUNCT
ejpam-5458	211	17	where	where	SCONJ
ejpam-5458	211	18	u	u	NOUN
ejpam-5458	211	19	is	be	AUX
ejpam-5458	211	20	a	a	DET
ejpam-5458	211	21	new	new	ADJ
ejpam-5458	211	22	complex	complex	ADJ
ejpam-5458	211	23	coordinate	coordinate	NOUN
ejpam-5458	211	24	,	,	PUNCT
ejpam-5458	211	25	and	and	CCONJ
ejpam-5458	211	26	θ	θ	PROPN
ejpam-5458	211	27	is	be	AUX
ejpam-5458	211	28	the	the	DET
ejpam-5458	211	29	time	time	NOUN
ejpam-5458	211	30	and	and	CCONJ
ejpam-5458	211	31	β	β	X
ejpam-5458	211	32	is	be	AUX
ejpam-5458	211	33	a	a	DET
ejpam-5458	211	34	new	new	ADJ
ejpam-5458	211	35	parameter	parameter	NOUN
ejpam-5458	211	36	,	,	PUNCT
ejpam-5458	211	37	and	and	CCONJ
ejpam-5458	211	38	s	s	NOUN
ejpam-5458	211	39	=	=	NOUN
ejpam-5458	211	40	sign	sign	PROPN
ejpam-5458	211	41	l1(0	l1(0	PROPN
ejpam-5458	211	42	)	)	PUNCT
ejpam-5458	211	43	=	=	PUNCT
ejpam-5458	211	44	sign	sign	VERB
ejpam-5458	211	45	re(c1(0	re(c1(0	NOUN
ejpam-5458	211	46	)	)	PUNCT
ejpam-5458	211	47	)	)	PUNCT
ejpam-5458	212	1	=	=	PRON
ejpam-5458	212	2	±1	±1	VERB
ejpam-5458	212	3	.	.	PUNCT
ejpam-5458	213	1	the	the	DET
ejpam-5458	213	2	real	real	ADJ
ejpam-5458	213	3	function	function	NOUN
ejpam-5458	213	4	l1(β	l1(β	PROPN
ejpam-5458	213	5	)	)	PUNCT
ejpam-5458	213	6	is	be	AUX
ejpam-5458	213	7	called	call	VERB
ejpam-5458	213	8	the	the	DET
ejpam-5458	213	9	first	first	ADJ
ejpam-5458	213	10	lyapunov	lyapunov	ADJ
ejpam-5458	213	11	coefficient	coefficient	NOUN
ejpam-5458	214	1	[	[	X
ejpam-5458	214	2	4	4	NUM
ejpam-5458	214	3	,	,	PUNCT
ejpam-5458	214	4	definition	definition	NOUN
ejpam-5458	214	5	3.3,p	3.3,p	NUM
ejpam-5458	214	6	99	99	NUM
ejpam-5458	214	7	]	]	PUNCT
ejpam-5458	214	8	.	.	PUNCT
ejpam-5458	215	1	to	to	PART
ejpam-5458	215	2	describe	describe	VERB
ejpam-5458	215	3	bifurcation	bifurcation	NOUN
ejpam-5458	215	4	analytically	analytically	ADV
ejpam-5458	215	5	,	,	PUNCT
ejpam-5458	215	6	we	we	PRON
ejpam-5458	215	7	present	present	VERB
ejpam-5458	215	8	an	an	DET
ejpam-5458	215	9	example	example	NOUN
ejpam-5458	215	10	of	of	ADP
ejpam-5458	215	11	the	the	DET
ejpam-5458	215	12	first	first	ADJ
ejpam-5458	215	13	lyapunov	lyapunov	ADJ
ejpam-5458	215	14	coefficient	coefficient	NOUN
ejpam-5458	215	15	l1	l1	PROPN
ejpam-5458	215	16	in	in	ADP
ejpam-5458	215	17	the	the	DET
ejpam-5458	215	18	complex	complex	ADJ
ejpam-5458	215	19	form	form	NOUN
ejpam-5458	215	20	of	of	ADP
ejpam-5458	215	21	the	the	DET
ejpam-5458	215	22	dynamical	dynamical	ADJ
ejpam-5458	215	23	system	system	NOUN
ejpam-5458	215	24	near	near	ADP
ejpam-5458	215	25	the	the	DET
ejpam-5458	215	26	original	original	ADJ
ejpam-5458	215	27	equilibrium	equilibrium	NOUN
ejpam-5458	215	28	point	point	NOUN
ejpam-5458	215	29	.	.	PUNCT
ejpam-5458	216	1	example	example	NOUN
ejpam-5458	217	1	1	1	NUM
ejpam-5458	217	2	.	.	X
ejpam-5458	217	3	consider	consider	VERB
ejpam-5458	217	4	the	the	DET
ejpam-5458	217	5	two	two	NUM
ejpam-5458	217	6	differential	differential	ADJ
ejpam-5458	217	7	equations	equation	NOUN
ejpam-5458	217	8	which	which	PRON
ejpam-5458	217	9	depend	depend	VERB
ejpam-5458	217	10	on	on	ADP
ejpam-5458	217	11	one	one	NUM
ejpam-5458	217	12	parameter	parameter	NOUN
ejpam-5458	217	13	:	:	PUNCT
ejpam-5458	217	14	ẋ	ẋ	PROPN
ejpam-5458	218	1	=	=	PUNCT
ejpam-5458	218	2	αx−	αx−	NUM
ejpam-5458	218	3	y	y	NOUN
ejpam-5458	218	4	−	−	NOUN
ejpam-5458	218	5	x(x2	x(x2	NOUN
ejpam-5458	218	6	+	+	CCONJ
ejpam-5458	218	7	y2	y2	NOUN
ejpam-5458	218	8	)	)	PUNCT
ejpam-5458	218	9	ẏ	ẏ	PROPN
ejpam-5458	219	1	=	=	NOUN
ejpam-5458	219	2	x+	x+	PROPN
ejpam-5458	219	3	αy	αy	ADP
ejpam-5458	219	4	−	−	NUM
ejpam-5458	219	5	y(x2	y(x2	NOUN
ejpam-5458	219	6	+	+	CCONJ
ejpam-5458	219	7	y2	y2	NOUN
ejpam-5458	219	8	)	)	PUNCT
ejpam-5458	219	9	(	(	PUNCT
ejpam-5458	219	10	27	27	NUM
ejpam-5458	219	11	)	)	PUNCT
ejpam-5458	219	12	this	this	DET
ejpam-5458	219	13	equation	equation	NOUN
ejpam-5458	219	14	has	have	VERB
ejpam-5458	219	15	the	the	DET
ejpam-5458	219	16	equilibrium	equilibrium	NOUN
ejpam-5458	219	17	(	(	PUNCT
ejpam-5458	219	18	x	x	NOUN
ejpam-5458	219	19	,	,	PUNCT
ejpam-5458	219	20	y	y	NOUN
ejpam-5458	219	21	)	)	PUNCT
ejpam-5458	219	22	=	=	SYM
ejpam-5458	220	1	(	(	PUNCT
ejpam-5458	220	2	0	0	NUM
ejpam-5458	220	3	,	,	PUNCT
ejpam-5458	220	4	0	0	NUM
ejpam-5458	220	5	)	)	PUNCT
ejpam-5458	220	6	with	with	ADP
ejpam-5458	220	7	eigenvalues	eigenvalue	VERB
ejpam-5458	220	8	λ1,2	λ1,2	PROPN
ejpam-5458	220	9	=	=	SYM
ejpam-5458	220	10	α	α	PROPN
ejpam-5458	220	11	±	±	NOUN
ejpam-5458	220	12	i.	i.	NOUN
ejpam-5458	220	13	for	for	ADP
ejpam-5458	220	14	bifurcations	bifurcation	NOUN
ejpam-5458	220	15	of	of	ADP
ejpam-5458	220	16	equilibria	equilibrium	NOUN
ejpam-5458	220	17	,	,	PUNCT
ejpam-5458	220	18	topological	topological	ADJ
ejpam-5458	220	19	normal	normal	ADJ
ejpam-5458	220	20	forms	form	NOUN
ejpam-5458	220	21	present	present	ADJ
ejpam-5458	220	22	general	general	ADJ
ejpam-5458	220	23	bifurcation	bifurcation	NOUN
ejpam-5458	220	24	diagrams	diagram	NOUN
ejpam-5458	220	25	.	.	PUNCT
ejpam-5458	221	1	together	together	ADV
ejpam-5458	221	2	with	with	ADP
ejpam-5458	221	3	system	system	NOUN
ejpam-5458	221	4	(	(	PUNCT
ejpam-5458	221	5	27	27	NUM
ejpam-5458	221	6	)	)	PUNCT
ejpam-5458	221	7	,	,	PUNCT
ejpam-5458	221	8	let	let	VERB
ejpam-5458	221	9	us	we	PRON
ejpam-5458	221	10	introduce	introduce	VERB
ejpam-5458	221	11	a	a	DET
ejpam-5458	221	12	new	new	ADJ
ejpam-5458	221	13	variable	variable	NOUN
ejpam-5458	221	14	z	z	NOUN
ejpam-5458	221	15	=	=	PUNCT
ejpam-5458	221	16	x	x	SYM
ejpam-5458	222	1	+	+	CCONJ
ejpam-5458	222	2	iy	iy	PROPN
ejpam-5458	222	3	,	,	PUNCT
ejpam-5458	222	4	z̄	z̄	X
ejpam-5458	222	5	=	=	PUNCT
ejpam-5458	222	6	x	x	PROPN
ejpam-5458	222	7	−	−	PROPN
ejpam-5458	222	8	iy	iy	PROPN
ejpam-5458	222	9	,	,	PUNCT
ejpam-5458	222	10	|z|2	|z|2	PROPN
ejpam-5458	222	11	=	=	SYM
ejpam-5458	222	12	zz̄	zz̄	X
ejpam-5458	222	13	=	=	PUNCT
ejpam-5458	223	1	x2	x2	PROPN
ejpam-5458	224	1	+	+	CCONJ
ejpam-5458	224	2	y2	y2	PROPN
ejpam-5458	224	3	and	and	CCONJ
ejpam-5458	224	4	the	the	DET
ejpam-5458	224	5	differential	differential	ADJ
ejpam-5458	224	6	equation	equation	NOUN
ejpam-5458	224	7	as	as	ADP
ejpam-5458	224	8	ż	ż	NOUN
ejpam-5458	224	9	=	=	SYM
ejpam-5458	224	10	ẋ+	ẋ+	PROPN
ejpam-5458	224	11	iẏ	iẏ	PUNCT
ejpam-5458	225	1	=	=	PUNCT
ejpam-5458	225	2	α(x+	α(x+	NUM
ejpam-5458	225	3	iy	iy	X
ejpam-5458	225	4	)	)	PUNCT
ejpam-5458	226	1	+	+	CCONJ
ejpam-5458	226	2	i(x+	i(x+	ADP
ejpam-5458	226	3	iy)−	iy)−	VERB
ejpam-5458	226	4	(	(	PUNCT
ejpam-5458	226	5	x+	x+	X
ejpam-5458	226	6	iy)(x2	iy)(x2	NOUN
ejpam-5458	226	7	+	+	CCONJ
ejpam-5458	226	8	y2	y2	NOUN
ejpam-5458	226	9	)	)	PUNCT
ejpam-5458	226	10	(	(	PUNCT
ejpam-5458	226	11	28	28	NUM
ejpam-5458	226	12	)	)	PUNCT
ejpam-5458	226	13	now	now	ADV
ejpam-5458	226	14	we	we	PRON
ejpam-5458	226	15	can	can	AUX
ejpam-5458	226	16	rewrite	rewrite	VERB
ejpam-5458	226	17	system	system	NOUN
ejpam-5458	226	18	(	(	PUNCT
ejpam-5458	226	19	27	27	NUM
ejpam-5458	226	20	)	)	PUNCT
ejpam-5458	226	21	in	in	ADP
ejpam-5458	226	22	the	the	DET
ejpam-5458	226	23	following	follow	VERB
ejpam-5458	226	24	complex	complex	ADJ
ejpam-5458	226	25	form	form	NOUN
ejpam-5458	226	26	:	:	PUNCT
ejpam-5458	226	27	ż	ż	NOUN
ejpam-5458	226	28	=	=	SYM
ejpam-5458	226	29	(	(	PUNCT
ejpam-5458	226	30	α+	α+	X
ejpam-5458	226	31	i)z	i)z	ADJ
ejpam-5458	226	32	−	−	PROPN
ejpam-5458	226	33	z|z|2	z|z|2	PROPN
ejpam-5458	226	34	.	.	PUNCT
ejpam-5458	227	1	(	(	PUNCT
ejpam-5458	227	2	29	29	NUM
ejpam-5458	227	3	)	)	PUNCT
ejpam-5458	227	4	i.	i.	NOUN
ejpam-5458	227	5	alraddadi	alraddadi	PROPN
ejpam-5458	227	6	/	/	SYM
ejpam-5458	227	7	eur	eur	PROPN
ejpam-5458	227	8	.	.	PUNCT
ejpam-5458	228	1	j.	j.	PROPN
ejpam-5458	228	2	pure	pure	PROPN
ejpam-5458	228	3	appl	appl	PROPN
ejpam-5458	228	4	.	.	PROPN
ejpam-5458	228	5	math	math	PROPN
ejpam-5458	228	6	,	,	PUNCT
ejpam-5458	228	7	17	17	NUM
ejpam-5458	228	8	(	(	PUNCT
ejpam-5458	228	9	4	4	NUM
ejpam-5458	228	10	)	)	PUNCT
ejpam-5458	228	11	(	(	PUNCT
ejpam-5458	228	12	2024	2024	NUM
ejpam-5458	228	13	)	)	PUNCT
ejpam-5458	228	14	,	,	PUNCT
ejpam-5458	228	15	3708	3708	NUM
ejpam-5458	228	16	-	-	SYM
ejpam-5458	228	17	3729	3729	NUM
ejpam-5458	228	18	3721	3721	NUM
ejpam-5458	228	19	this	this	PRON
ejpam-5458	228	20	is	be	AUX
ejpam-5458	228	21	the	the	DET
ejpam-5458	228	22	normal	normal	ADJ
ejpam-5458	228	23	form	form	NOUN
ejpam-5458	228	24	of	of	ADP
ejpam-5458	228	25	(	(	PUNCT
ejpam-5458	228	26	27	27	NUM
ejpam-5458	228	27	)	)	PUNCT
ejpam-5458	228	28	.	.	PUNCT
ejpam-5458	229	1	to	to	PART
ejpam-5458	229	2	present	present	VERB
ejpam-5458	229	3	the	the	DET
ejpam-5458	229	4	polar	polar	ADJ
ejpam-5458	229	5	form	form	NOUN
ejpam-5458	229	6	,	,	PUNCT
ejpam-5458	229	7	let	let	VERB
ejpam-5458	229	8	z	z	NOUN
ejpam-5458	229	9	=	=	SYM
ejpam-5458	229	10	reiθ(t	reiθ(t	PROPN
ejpam-5458	229	11	)	)	PUNCT
ejpam-5458	229	12	ż	ż	NOUN
ejpam-5458	229	13	=	=	PUNCT
ejpam-5458	229	14	ṙeiθ(t	ṙeiθ(t	NUM
ejpam-5458	229	15	)	)	PUNCT
ejpam-5458	230	1	+	+	NUM
ejpam-5458	230	2	riθ̇eiθ(t	riθ̇eiθ(t	NOUN
ejpam-5458	230	3	)	)	PUNCT
ejpam-5458	230	4	(	(	PUNCT
ejpam-5458	230	5	30	30	X
ejpam-5458	230	6	)	)	PUNCT
ejpam-5458	230	7	substituting	substitute	VERB
ejpam-5458	230	8	into	into	ADP
ejpam-5458	230	9	(	(	PUNCT
ejpam-5458	230	10	6.12	6.12	NUM
ejpam-5458	230	11	)	)	PUNCT
ejpam-5458	230	12	,	,	PUNCT
ejpam-5458	230	13	we	we	PRON
ejpam-5458	230	14	obtain	obtain	VERB
ejpam-5458	230	15	the	the	DET
ejpam-5458	230	16	polar	polar	ADJ
ejpam-5458	230	17	form	form	NOUN
ejpam-5458	230	18	:	:	PUNCT
ejpam-5458	230	19	ṙeiθ(t	ṙeiθ(t	NUM
ejpam-5458	230	20	)	)	PUNCT
ejpam-5458	230	21	+	+	NUM
ejpam-5458	230	22	riθ̇eiθ(t	riθ̇eiθ(t	NOUN
ejpam-5458	230	23	)	)	PUNCT
ejpam-5458	230	24	=	=	PUNCT
ejpam-5458	230	25	reiθ(α+	reiθ(α+	NUM
ejpam-5458	230	26	i−	i−	PROPN
ejpam-5458	230	27	r2	r2	NOUN
ejpam-5458	230	28	)	)	PUNCT
ejpam-5458	230	29	(	(	PUNCT
ejpam-5458	230	30	31	31	NUM
ejpam-5458	230	31	)	)	PUNCT
ejpam-5458	230	32	now	now	ADV
ejpam-5458	230	33	we	we	PRON
ejpam-5458	230	34	can	can	AUX
ejpam-5458	230	35	rewrite	rewrite	VERB
ejpam-5458	230	36	(	(	PUNCT
ejpam-5458	230	37	6.14	6.14	NUM
ejpam-5458	230	38	)	)	PUNCT
ejpam-5458	230	39	as	as	ADP
ejpam-5458	230	40	:	:	PUNCT
ejpam-5458	230	41	ṙ	ṙ	NOUN
ejpam-5458	230	42	=	=	SYM
ejpam-5458	230	43	r(α−	r(α−	ADJ
ejpam-5458	230	44	r2	r2	NOUN
ejpam-5458	230	45	)	)	PUNCT
ejpam-5458	230	46	θ̇	θ̇	NOUN
ejpam-5458	230	47	=	=	SYM
ejpam-5458	230	48	1	1	NUM
ejpam-5458	230	49	(	(	PUNCT
ejpam-5458	230	50	32	32	NUM
ejpam-5458	230	51	)	)	PUNCT
ejpam-5458	230	52	where	where	SCONJ
ejpam-5458	230	53	r	r	NOUN
ejpam-5458	230	54	and	and	CCONJ
ejpam-5458	230	55	θ	θ	PROPN
ejpam-5458	230	56	are	be	AUX
ejpam-5458	230	57	independent	independent	ADJ
ejpam-5458	230	58	in	in	ADP
ejpam-5458	230	59	uncouple	uncouple	ADJ
ejpam-5458	230	60	system	system	NOUN
ejpam-5458	230	61	(	(	PUNCT
ejpam-5458	230	62	32	32	NUM
ejpam-5458	230	63	)	)	PUNCT
ejpam-5458	230	64	.	.	PUNCT
ejpam-5458	231	1	the	the	DET
ejpam-5458	231	2	first	first	ADJ
ejpam-5458	231	3	equation	equation	NOUN
ejpam-5458	231	4	has	have	VERB
ejpam-5458	231	5	the	the	DET
ejpam-5458	231	6	equilibrium	equilibrium	NOUN
ejpam-5458	231	7	of	of	ADP
ejpam-5458	231	8	(	(	PUNCT
ejpam-5458	231	9	32	32	NUM
ejpam-5458	231	10	)	)	PUNCT
ejpam-5458	231	11	at	at	ADP
ejpam-5458	231	12	r	r	NOUN
ejpam-5458	231	13	=	=	SYM
ejpam-5458	231	14	0	0	NUM
ejpam-5458	231	15	and	and	CCONJ
ejpam-5458	231	16	α	α	NOUN
ejpam-5458	231	17	=	=	ADJ
ejpam-5458	231	18	0	0	PROPN
ejpam-5458	231	19	.	.	PUNCT
ejpam-5458	232	1	this	this	DET
ejpam-5458	232	2	equilibrium	equilibrium	NOUN
ejpam-5458	232	3	is	be	AUX
ejpam-5458	232	4	a	a	DET
ejpam-5458	232	5	stable	stable	ADJ
ejpam-5458	232	6	spiral	spiral	NOUN
ejpam-5458	232	7	for	for	ADP
ejpam-5458	232	8	α	α	PRON
ejpam-5458	232	9	<	<	X
ejpam-5458	232	10	0	0	PROPN
ejpam-5458	232	11	and	and	CCONJ
ejpam-5458	232	12	an	an	DET
ejpam-5458	232	13	unstable	unstable	ADJ
ejpam-5458	232	14	spiral	spiral	NOUN
ejpam-5458	232	15	for	for	ADP
ejpam-5458	232	16	α	α	PROPN
ejpam-5458	232	17	>	>	X
ejpam-5458	232	18	0	0	NUM
ejpam-5458	232	19	.	.	PUNCT
ejpam-5458	233	1	it	it	PRON
ejpam-5458	233	2	is	be	AUX
ejpam-5458	233	3	possible	possible	ADJ
ejpam-5458	233	4	to	to	PART
ejpam-5458	233	5	notice	notice	VERB
ejpam-5458	233	6	from	from	ADP
ejpam-5458	233	7	(	(	PUNCT
ejpam-5458	233	8	32	32	NUM
ejpam-5458	233	9	)	)	PUNCT
ejpam-5458	233	10	that	that	SCONJ
ejpam-5458	233	11	the	the	DET
ejpam-5458	233	12	system	system	NOUN
ejpam-5458	233	13	has	have	AUX
ejpam-5458	233	14	a	a	DET
ejpam-5458	233	15	unique	unique	ADJ
ejpam-5458	233	16	and	and	CCONJ
ejpam-5458	233	17	stable	stable	ADJ
ejpam-5458	233	18	limit	limit	NOUN
ejpam-5458	233	19	cycle	cycle	NOUN
ejpam-5458	233	20	for	for	ADP
ejpam-5458	233	21	any	any	DET
ejpam-5458	233	22	α	α	NOUN
ejpam-5458	233	23	>	>	X
ejpam-5458	233	24	0	0	NUM
ejpam-5458	233	25	of	of	ADP
ejpam-5458	233	26	radius	radius	NOUN
ejpam-5458	233	27	r	r	NOUN
ejpam-5458	233	28	=	=	PUNCT
ejpam-5458	233	29	√	√	NUM
ejpam-5458	233	30	α	α	X
ejpam-5458	233	31	.	.	PUNCT
ejpam-5458	234	1	more	more	ADV
ejpam-5458	234	2	generally	generally	ADV
ejpam-5458	234	3	,	,	PUNCT
ejpam-5458	234	4	when	when	SCONJ
ejpam-5458	234	5	α	α	PROPN
ejpam-5458	234	6	passes	pass	VERB
ejpam-5458	234	7	through	through	ADP
ejpam-5458	234	8	zero	zero	NUM
ejpam-5458	234	9	,	,	PUNCT
ejpam-5458	234	10	under	under	ADP
ejpam-5458	234	11	certain	certain	ADJ
ejpam-5458	234	12	non	non	ADJ
ejpam-5458	234	13	-	-	ADJ
ejpam-5458	234	14	degeneracy	degeneracy	ADJ
ejpam-5458	234	15	conditions	condition	NOUN
ejpam-5458	234	16	,	,	PUNCT
ejpam-5458	234	17	we	we	PRON
ejpam-5458	234	18	have	have	VERB
ejpam-5458	234	19	a	a	DET
ejpam-5458	234	20	bifurcation	bifurcation	NOUN
ejpam-5458	234	21	in	in	ADP
ejpam-5458	234	22	system	system	NOUN
ejpam-5458	234	23	(	(	PUNCT
ejpam-5458	234	24	27	27	NUM
ejpam-5458	234	25	)	)	PUNCT
ejpam-5458	234	26	called	call	VERB
ejpam-5458	234	27	the	the	DET
ejpam-5458	234	28	andronov	andronov	NOUN
ejpam-5458	234	29	-	-	PUNCT
ejpam-5458	234	30	hopf	hopf	ADJ
ejpam-5458	234	31	bifurcation	bifurcation	NOUN
ejpam-5458	234	32	[	[	X
ejpam-5458	234	33	14	14	NUM
ejpam-5458	234	34	]	]	PUNCT
ejpam-5458	234	35	.	.	PUNCT
ejpam-5458	235	1	a	a	DET
ejpam-5458	235	2	cubic	cubic	ADJ
ejpam-5458	235	3	coefficient	coefficient	NOUN
ejpam-5458	235	4	(	(	PUNCT
ejpam-5458	235	5	called	call	VERB
ejpam-5458	235	6	the	the	DET
ejpam-5458	235	7	first	first	ADJ
ejpam-5458	235	8	lyapunov	lyapunov	ADJ
ejpam-5458	235	9	coefficient	coefficient	NOUN
ejpam-5458	235	10	)	)	PUNCT
ejpam-5458	235	11	in	in	ADP
ejpam-5458	235	12	the	the	DET
ejpam-5458	235	13	complex	complex	ADJ
ejpam-5458	235	14	form	form	NOUN
ejpam-5458	235	15	(	(	PUNCT
ejpam-5458	235	16	29	29	NUM
ejpam-5458	235	17	)	)	PUNCT
ejpam-5458	235	18	,	,	PUNCT
ejpam-5458	235	19	determines	determine	VERB
ejpam-5458	235	20	the	the	DET
ejpam-5458	235	21	behaviour	behaviour	NOUN
ejpam-5458	235	22	of	of	ADP
ejpam-5458	235	23	(	(	PUNCT
ejpam-5458	235	24	27	27	NUM
ejpam-5458	235	25	)	)	PUNCT
ejpam-5458	235	26	in	in	ADP
ejpam-5458	235	27	the	the	DET
ejpam-5458	235	28	neighbourhood	neighbourhood	NOUN
ejpam-5458	235	29	of	of	ADP
ejpam-5458	235	30	a	a	DET
ejpam-5458	235	31	hopf	hopf	ADJ
ejpam-5458	235	32	bifurcation	bifurcation	NOUN
ejpam-5458	235	33	point	point	NOUN
ejpam-5458	235	34	,	,	PUNCT
ejpam-5458	235	35	if	if	SCONJ
ejpam-5458	235	36	it	it	PRON
ejpam-5458	235	37	is	be	AUX
ejpam-5458	235	38	non	non	ADJ
ejpam-5458	235	39	-	-	ADJ
ejpam-5458	235	40	zero	zero	NUM
ejpam-5458	235	41	.	.	PUNCT
ejpam-5458	236	1	we	we	PRON
ejpam-5458	236	2	recall	recall	VERB
ejpam-5458	236	3	this	this	PRON
ejpam-5458	236	4	in	in	ADP
ejpam-5458	236	5	the	the	DET
ejpam-5458	236	6	following	following	NOUN
ejpam-5458	236	7	theorem	theorem	NOUN
ejpam-5458	236	8	:	:	PUNCT
ejpam-5458	236	9	theorem	theorem	NOUN
ejpam-5458	236	10	1	1	NUM
ejpam-5458	236	11	.	.	PUNCT
ejpam-5458	237	1	[	[	X
ejpam-5458	237	2	4	4	NUM
ejpam-5458	237	3	,	,	PUNCT
ejpam-5458	237	4	topological	topological	ADJ
ejpam-5458	237	5	normal	normal	ADJ
ejpam-5458	237	6	form	form	NOUN
ejpam-5458	237	7	for	for	ADP
ejpam-5458	237	8	the	the	DET
ejpam-5458	237	9	hopf	hopf	ADJ
ejpam-5458	237	10	bifurcation	bifurcation	NOUN
ejpam-5458	237	11	,	,	PUNCT
ejpam-5458	237	12	p100	p100	PROPN
ejpam-5458	237	13	]	]	PUNCT
ejpam-5458	237	14	suppose	suppose	VERB
ejpam-5458	237	15	twodimensional	twodimensional	ADJ
ejpam-5458	237	16	dynamical	dynamical	ADJ
ejpam-5458	237	17	system	system	NOUN
ejpam-5458	237	18	,	,	PUNCT
ejpam-5458	237	19	ẋ	ẋ	PROPN
ejpam-5458	238	1	=	=	SYM
ejpam-5458	238	2	f(x	f(x	PROPN
ejpam-5458	238	3	,	,	PUNCT
ejpam-5458	238	4	α	α	NOUN
ejpam-5458	238	5	)	)	PUNCT
ejpam-5458	238	6	,	,	PUNCT
ejpam-5458	238	7	x	x	PUNCT
ejpam-5458	238	8	∈	∈	NOUN
ejpam-5458	238	9	r2	r2	NOUN
ejpam-5458	238	10	,	,	PUNCT
ejpam-5458	238	11	α	α	PROPN
ejpam-5458	238	12	∈	∈	NOUN
ejpam-5458	238	13	r	r	NOUN
ejpam-5458	238	14	(	(	PUNCT
ejpam-5458	238	15	33	33	NUM
ejpam-5458	238	16	)	)	PUNCT
ejpam-5458	238	17	with	with	ADP
ejpam-5458	238	18	smooth	smooth	ADJ
ejpam-5458	238	19	f	f	PROPN
ejpam-5458	238	20	,	,	PUNCT
ejpam-5458	238	21	has	have	VERB
ejpam-5458	238	22	for	for	ADP
ejpam-5458	238	23	all	all	DET
ejpam-5458	238	24	sufficiently	sufficiently	ADV
ejpam-5458	238	25	small	small	ADJ
ejpam-5458	238	26	|α|	|α|	PROPN
ejpam-5458	238	27	the	the	DET
ejpam-5458	238	28	equilibrium	equilibrium	NOUN
ejpam-5458	238	29	x	x	PUNCT
ejpam-5458	239	1	=	=	SYM
ejpam-5458	239	2	0	0	NUM
ejpam-5458	239	3	with	with	ADP
ejpam-5458	239	4	eigenvalues	eigenvalue	VERB
ejpam-5458	239	5	λ1,2	λ1,2	PROPN
ejpam-5458	239	6	=	=	SYM
ejpam-5458	239	7	µ(α)±	µ(α)±	PROPN
ejpam-5458	239	8	iω(α	iω(α	PROPN
ejpam-5458	239	9	)	)	PUNCT
ejpam-5458	239	10	where	where	SCONJ
ejpam-5458	239	11	µ(0	µ(0	NOUN
ejpam-5458	239	12	)	)	PUNCT
ejpam-5458	239	13	=	=	SYM
ejpam-5458	239	14	0	0	NUM
ejpam-5458	239	15	,	,	PUNCT
ejpam-5458	239	16	ω(0	ω(0	PROPN
ejpam-5458	239	17	)	)	PUNCT
ejpam-5458	239	18	=	=	PUNCT
ejpam-5458	239	19	ω0	ω0	CCONJ
ejpam-5458	239	20	>	>	X
ejpam-5458	239	21	0	0	X
ejpam-5458	239	22	.	.	PUNCT
ejpam-5458	240	1	let	let	VERB
ejpam-5458	240	2	the	the	DET
ejpam-5458	240	3	following	follow	VERB
ejpam-5458	240	4	conditions	condition	NOUN
ejpam-5458	240	5	be	be	AUX
ejpam-5458	240	6	satisfied	satisfied	ADJ
ejpam-5458	240	7	:	:	PUNCT
ejpam-5458	240	8	(	(	PUNCT
ejpam-5458	240	9	h.1	h.1	X
ejpam-5458	240	10	)	)	PUNCT
ejpam-5458	240	11	l1(0	l1(0	PROPN
ejpam-5458	240	12	)	)	PUNCT
ejpam-5458	240	13	̸=	̸=	PROPN
ejpam-5458	240	14	0	0	NUM
ejpam-5458	240	15	,	,	PUNCT
ejpam-5458	240	16	where	where	SCONJ
ejpam-5458	240	17	l1	l1	PROPN
ejpam-5458	240	18	is	be	AUX
ejpam-5458	240	19	the	the	DET
ejpam-5458	240	20	first	first	ADJ
ejpam-5458	240	21	lyapunov	lyapunov	ADJ
ejpam-5458	240	22	coefficient	coefficient	NOUN
ejpam-5458	240	23	(	(	PUNCT
ejpam-5458	240	24	h.2	h.2	NOUN
ejpam-5458	240	25	)	)	PUNCT
ejpam-5458	240	26	µ′(0	µ′(0	NOUN
ejpam-5458	240	27	)	)	PUNCT
ejpam-5458	240	28	̸=	̸=	PROPN
ejpam-5458	240	29	0	0	NUM
ejpam-5458	240	30	.	.	PUNCT
ejpam-5458	241	1	then	then	ADV
ejpam-5458	241	2	there	there	PRON
ejpam-5458	241	3	are	be	VERB
ejpam-5458	241	4	invertible	invertible	ADJ
ejpam-5458	241	5	coordinate	coordinate	NOUN
ejpam-5458	241	6	and	and	CCONJ
ejpam-5458	241	7	parameter	parameter	NOUN
ejpam-5458	241	8	changes	change	NOUN
ejpam-5458	241	9	and	and	CCONJ
ejpam-5458	241	10	a	a	DET
ejpam-5458	241	11	time	time	NOUN
ejpam-5458	241	12	reparametrization	reparametrization	NOUN
ejpam-5458	241	13	transforming	transform	VERB
ejpam-5458	241	14	(	(	PUNCT
ejpam-5458	241	15	33	33	NUM
ejpam-5458	241	16	)	)	PUNCT
ejpam-5458	241	17	into	into	ADP
ejpam-5458	241	18	the	the	DET
ejpam-5458	241	19	complex	complex	ADJ
ejpam-5458	241	20	form	form	NOUN
ejpam-5458	241	21	ż	ż	NOUN
ejpam-5458	241	22	=	=	PUNCT
ejpam-5458	241	23	(	(	PUNCT
ejpam-5458	241	24	l0	l0	NOUN
ejpam-5458	241	25	+	+	CCONJ
ejpam-5458	241	26	i)z	i)z	ADJ
ejpam-5458	242	1	+	+	CCONJ
ejpam-5458	242	2	l1z|z|2	l1z|z|2	NOUN
ejpam-5458	243	1	+	+	ADV
ejpam-5458	243	2	o(|z|4	o(|z|4	ADJ
ejpam-5458	244	1	)	)	PUNCT
ejpam-5458	244	2	(	(	PUNCT
ejpam-5458	244	3	34	34	NUM
ejpam-5458	244	4	)	)	PUNCT
ejpam-5458	244	5	where	where	SCONJ
ejpam-5458	244	6	l0	l0	NOUN
ejpam-5458	244	7	=	=	SYM
ejpam-5458	244	8	0	0	PROPN
ejpam-5458	245	1	and	and	CCONJ
ejpam-5458	245	2	l1	l1	PROPN
ejpam-5458	245	3	̸=	̸=	PROPN
ejpam-5458	245	4	0	0	NUM
ejpam-5458	245	5	.	.	PUNCT
ejpam-5458	246	1	i.	i.	PROPN
ejpam-5458	246	2	alraddadi	alraddadi	PROPN
ejpam-5458	246	3	/	/	SYM
ejpam-5458	246	4	eur	eur	PROPN
ejpam-5458	246	5	.	.	PUNCT
ejpam-5458	247	1	j.	j.	PROPN
ejpam-5458	247	2	pure	pure	PROPN
ejpam-5458	247	3	appl	appl	PROPN
ejpam-5458	247	4	.	.	PROPN
ejpam-5458	247	5	math	math	PROPN
ejpam-5458	247	6	,	,	PUNCT
ejpam-5458	247	7	17	17	NUM
ejpam-5458	247	8	(	(	PUNCT
ejpam-5458	247	9	4	4	NUM
ejpam-5458	247	10	)	)	PUNCT
ejpam-5458	247	11	(	(	PUNCT
ejpam-5458	247	12	2024	2024	NUM
ejpam-5458	247	13	)	)	PUNCT
ejpam-5458	247	14	,	,	PUNCT
ejpam-5458	247	15	3708	3708	NUM
ejpam-5458	247	16	-	-	SYM
ejpam-5458	247	17	3729	3729	NUM
ejpam-5458	247	18	3722	3722	NUM
ejpam-5458	247	19	4.2	4.2	NUM
ejpam-5458	247	20	.	.	PUNCT
ejpam-5458	248	1	the	the	DET
ejpam-5458	248	2	normal	normal	ADJ
ejpam-5458	248	3	form	form	NOUN
ejpam-5458	248	4	of	of	ADP
ejpam-5458	248	5	the	the	DET
ejpam-5458	248	6	bautin	bautin	ADJ
ejpam-5458	248	7	bifurcation	bifurcation	NOUN
ejpam-5458	248	8	the	the	DET
ejpam-5458	248	9	bautin	bautin	ADJ
ejpam-5458	248	10	bifurcation	bifurcation	NOUN
ejpam-5458	248	11	(	(	PUNCT
ejpam-5458	248	12	or	or	CCONJ
ejpam-5458	248	13	generalised	generalise	VERB
ejpam-5458	248	14	hopf	hopf	ADJ
ejpam-5458	248	15	bifurcation	bifurcation	NOUN
ejpam-5458	248	16	)	)	PUNCT
ejpam-5458	248	17	is	be	AUX
ejpam-5458	248	18	codimension-2	codimension-2	NUM
ejpam-5458	248	19	of	of	ADP
ejpam-5458	248	20	an	an	DET
ejpam-5458	248	21	equilibrium	equilibrium	NOUN
ejpam-5458	248	22	.	.	PUNCT
ejpam-5458	249	1	the	the	DET
ejpam-5458	249	2	bautin	bautin	PROPN
ejpam-5458	249	3	point	point	NOUN
ejpam-5458	249	4	separates	separate	VERB
ejpam-5458	249	5	branches	branch	NOUN
ejpam-5458	249	6	of	of	ADP
ejpam-5458	249	7	subcritical	subcritical	ADJ
ejpam-5458	249	8	and	and	CCONJ
ejpam-5458	249	9	supercritical	supercritical	ADJ
ejpam-5458	249	10	andronov	andronov	NOUN
ejpam-5458	249	11	-	-	PUNCT
ejpam-5458	249	12	hopf	hopf	ADJ
ejpam-5458	249	13	bifurcations	bifurcation	NOUN
ejpam-5458	249	14	in	in	ADP
ejpam-5458	249	15	the	the	DET
ejpam-5458	249	16	parameter	parameter	NOUN
ejpam-5458	249	17	plane	plane	NOUN
ejpam-5458	249	18	.	.	PUNCT
ejpam-5458	250	1	in	in	ADP
ejpam-5458	250	2	particular	particular	ADJ
ejpam-5458	250	3	,	,	PUNCT
ejpam-5458	250	4	the	the	DET
ejpam-5458	250	5	equilibrium	equilibrium	NOUN
ejpam-5458	250	6	has	have	VERB
ejpam-5458	250	7	purely	purely	ADV
ejpam-5458	250	8	imaginary	imaginary	ADJ
ejpam-5458	250	9	eigenvalues	eigenvalue	NOUN
ejpam-5458	250	10	and	and	CCONJ
ejpam-5458	250	11	the	the	DET
ejpam-5458	250	12	first	first	ADJ
ejpam-5458	250	13	lyapunov	lyapunov	ADJ
ejpam-5458	250	14	coefficient	coefficient	NOUN
ejpam-5458	250	15	for	for	ADP
ejpam-5458	250	16	hopf	hopf	ADJ
ejpam-5458	250	17	bifurcation	bifurcation	NOUN
ejpam-5458	250	18	vanishes	vanish	VERB
ejpam-5458	250	19	as	as	ADP
ejpam-5458	250	20	bautin	bautin	ADJ
ejpam-5458	250	21	bifurcation	bifurcation	NOUN
ejpam-5458	250	22	conditions	condition	NOUN
ejpam-5458	250	23	.	.	PUNCT
ejpam-5458	251	1	note	note	VERB
ejpam-5458	251	2	when	when	SCONJ
ejpam-5458	251	3	two	two	NUM
ejpam-5458	251	4	limit	limit	NOUN
ejpam-5458	251	5	cycles	cycle	NOUN
ejpam-5458	251	6	which	which	PRON
ejpam-5458	251	7	collide	collide	VERB
ejpam-5458	251	8	and	and	CCONJ
ejpam-5458	251	9	disappear	disappear	VERB
ejpam-5458	251	10	via	via	ADP
ejpam-5458	251	11	a	a	DET
ejpam-5458	251	12	saddlenode	saddlenode	ADJ
ejpam-5458	251	13	bifurcation	bifurcation	NOUN
ejpam-5458	251	14	of	of	ADP
ejpam-5458	251	15	limit	limit	NOUN
ejpam-5458	251	16	cycles	cycle	NOUN
ejpam-5458	251	17	.	.	PUNCT
ejpam-5458	252	1	we	we	PRON
ejpam-5458	252	2	can	can	AUX
ejpam-5458	252	3	review	review	VERB
ejpam-5458	252	4	the	the	DET
ejpam-5458	252	5	analysis	analysis	NOUN
ejpam-5458	252	6	of	of	ADP
ejpam-5458	252	7	the	the	DET
ejpam-5458	252	8	bautin	bautin	ADJ
ejpam-5458	252	9	bifurcation	bifurcation	NOUN
ejpam-5458	252	10	by	by	ADP
ejpam-5458	252	11	stating	state	VERB
ejpam-5458	252	12	the	the	DET
ejpam-5458	252	13	following	follow	VERB
ejpam-5458	252	14	theorem	theorem	NOUN
ejpam-5458	252	15	.	.	PUNCT
ejpam-5458	252	16	theorem	theorem	NOUN
ejpam-5458	252	17	2	2	NUM
ejpam-5458	252	18	.	.	PUNCT
ejpam-5458	253	1	[	[	X
ejpam-5458	253	2	4	4	NUM
ejpam-5458	253	3	,	,	PUNCT
ejpam-5458	253	4	topological	topological	ADJ
ejpam-5458	253	5	normal	normal	ADJ
ejpam-5458	253	6	form	form	NOUN
ejpam-5458	253	7	for	for	ADP
ejpam-5458	253	8	the	the	DET
ejpam-5458	253	9	bautin	bautin	PROPN
ejpam-5458	253	10	bifurcation	bifurcation	NOUN
ejpam-5458	253	11	,	,	PUNCT
ejpam-5458	253	12	p308	p308	PROPN
ejpam-5458	253	13	]	]	PUNCT
ejpam-5458	253	14	suppose	suppose	VERB
ejpam-5458	253	15	twodimensional	twodimensional	ADJ
ejpam-5458	253	16	dynamical	dynamical	ADJ
ejpam-5458	253	17	system	system	NOUN
ejpam-5458	253	18	,	,	PUNCT
ejpam-5458	253	19	ẋ	ẋ	PROPN
ejpam-5458	254	1	=	=	SYM
ejpam-5458	254	2	f(x	f(x	PROPN
ejpam-5458	254	3	,	,	PUNCT
ejpam-5458	254	4	α	α	NOUN
ejpam-5458	254	5	)	)	PUNCT
ejpam-5458	254	6	,	,	PUNCT
ejpam-5458	254	7	x	x	PUNCT
ejpam-5458	254	8	∈	∈	NOUN
ejpam-5458	254	9	r2	r2	NOUN
ejpam-5458	254	10	,	,	PUNCT
ejpam-5458	254	11	α	α	PROPN
ejpam-5458	254	12	∈	∈	PROPN
ejpam-5458	254	13	r2	r2	NOUN
ejpam-5458	254	14	(	(	PUNCT
ejpam-5458	254	15	35	35	NUM
ejpam-5458	254	16	)	)	PUNCT
ejpam-5458	254	17	with	with	ADP
ejpam-5458	254	18	smooth	smooth	ADJ
ejpam-5458	254	19	f	f	PROPN
ejpam-5458	254	20	,	,	PUNCT
ejpam-5458	254	21	has	have	VERB
ejpam-5458	254	22	for	for	ADP
ejpam-5458	254	23	all	all	DET
ejpam-5458	254	24	sufficiently	sufficiently	ADV
ejpam-5458	254	25	small	small	ADJ
ejpam-5458	254	26	|α|	|α|	PROPN
ejpam-5458	254	27	the	the	DET
ejpam-5458	254	28	equilibrium	equilibrium	NOUN
ejpam-5458	254	29	x	x	PUNCT
ejpam-5458	255	1	=	=	SYM
ejpam-5458	255	2	0	0	NUM
ejpam-5458	255	3	with	with	ADP
ejpam-5458	255	4	eigenvalues	eigenvalue	VERB
ejpam-5458	255	5	λ1,2	λ1,2	PROPN
ejpam-5458	255	6	=	=	SYM
ejpam-5458	255	7	µ(α)±	µ(α)±	PROPN
ejpam-5458	255	8	iω(α	iω(α	PROPN
ejpam-5458	255	9	)	)	PUNCT
ejpam-5458	255	10	where	where	SCONJ
ejpam-5458	255	11	µ(0	µ(0	NOUN
ejpam-5458	255	12	)	)	PUNCT
ejpam-5458	255	13	=	=	SYM
ejpam-5458	255	14	0	0	NUM
ejpam-5458	255	15	,	,	PUNCT
ejpam-5458	255	16	ω(0	ω(0	PROPN
ejpam-5458	255	17	)	)	PUNCT
ejpam-5458	255	18	=	=	PUNCT
ejpam-5458	255	19	ω0	ω0	CCONJ
ejpam-5458	255	20	>	>	PUNCT
ejpam-5458	255	21	0	0	PUNCT
ejpam-5458	256	1	for	for	ADP
ejpam-5458	256	2	α	α	NOUN
ejpam-5458	256	3	=	=	SYM
ejpam-5458	256	4	0	0	NUM
ejpam-5458	256	5	,	,	PUNCT
ejpam-5458	256	6	let	let	VERB
ejpam-5458	256	7	bautin	bautin	ADJ
ejpam-5458	256	8	bifurcation	bifurcation	NOUN
ejpam-5458	256	9	conditions	condition	NOUN
ejpam-5458	256	10	hold	hold	VERB
ejpam-5458	256	11	:	:	PUNCT
ejpam-5458	256	12	µ(0	µ(0	NUM
ejpam-5458	256	13	)	)	PUNCT
ejpam-5458	256	14	=	=	SYM
ejpam-5458	256	15	0	0	NUM
ejpam-5458	256	16	,	,	PUNCT
ejpam-5458	256	17	l1(0	l1(0	PROPN
ejpam-5458	256	18	)	)	PUNCT
ejpam-5458	257	1	=	=	SYM
ejpam-5458	257	2	0	0	NUM
ejpam-5458	257	3	where	where	SCONJ
ejpam-5458	257	4	l1(α)is	l1(α)is	ADP
ejpam-5458	257	5	the	the	DET
ejpam-5458	257	6	first	first	ADJ
ejpam-5458	257	7	lyapunov	lyapunov	ADJ
ejpam-5458	257	8	coefficient	coefficient	NOUN
ejpam-5458	257	9	.	.	PUNCT
ejpam-5458	258	1	let	let	VERB
ejpam-5458	258	2	the	the	DET
ejpam-5458	258	3	following	follow	VERB
ejpam-5458	258	4	conditions	condition	NOUN
ejpam-5458	258	5	be	be	AUX
ejpam-5458	258	6	satisfied	satisfied	ADJ
ejpam-5458	258	7	:	:	PUNCT
ejpam-5458	258	8	(	(	PUNCT
ejpam-5458	258	9	b.1	b.1	NOUN
ejpam-5458	258	10	)	)	PUNCT
ejpam-5458	258	11	l2(0	l2(0	NOUN
ejpam-5458	258	12	)	)	PUNCT
ejpam-5458	258	13	̸=	̸=	PROPN
ejpam-5458	258	14	0	0	NUM
ejpam-5458	258	15	,	,	PUNCT
ejpam-5458	258	16	where	where	SCONJ
ejpam-5458	258	17	l2	l2	NOUN
ejpam-5458	258	18	is	be	AUX
ejpam-5458	258	19	the	the	DET
ejpam-5458	258	20	second	second	ADJ
ejpam-5458	258	21	lyapunov	lyapunov	ADJ
ejpam-5458	258	22	coefficient	coefficient	NOUN
ejpam-5458	258	23	.	.	PUNCT
ejpam-5458	259	1	(	(	PUNCT
ejpam-5458	259	2	b.2	b.2	X
ejpam-5458	259	3	)	)	PUNCT
ejpam-5458	259	4	the	the	DET
ejpam-5458	259	5	map	map	NOUN
ejpam-5458	259	6	→	→	SYM
ejpam-5458	259	7	(	(	PUNCT
ejpam-5458	259	8	µ(α	µ(α	NOUN
ejpam-5458	259	9	)	)	PUNCT
ejpam-5458	259	10	,	,	PUNCT
ejpam-5458	259	11	l1(α	l1(α	X
ejpam-5458	259	12	)	)	PUNCT
ejpam-5458	259	13	)	)	PUNCT
ejpam-5458	260	1	t	t	PROPN
ejpam-5458	260	2	is	be	AUX
ejpam-5458	260	3	regular	regular	ADJ
ejpam-5458	260	4	at	at	ADP
ejpam-5458	260	5	α	α	PROPN
ejpam-5458	260	6	=	=	SYM
ejpam-5458	260	7	0	0	PROPN
ejpam-5458	260	8	.	.	PUNCT
ejpam-5458	261	1	then	then	ADV
ejpam-5458	261	2	there	there	PRON
ejpam-5458	261	3	are	be	VERB
ejpam-5458	261	4	invertible	invertible	ADJ
ejpam-5458	261	5	coordinate	coordinate	NOUN
ejpam-5458	261	6	and	and	CCONJ
ejpam-5458	261	7	parameter	parameter	NOUN
ejpam-5458	261	8	changes	change	NOUN
ejpam-5458	261	9	and	and	CCONJ
ejpam-5458	261	10	a	a	DET
ejpam-5458	261	11	time	time	NOUN
ejpam-5458	261	12	reparametrization	reparametrization	NOUN
ejpam-5458	261	13	transforming	transform	VERB
ejpam-5458	261	14	(	(	PUNCT
ejpam-5458	261	15	35	35	NUM
ejpam-5458	261	16	)	)	PUNCT
ejpam-5458	261	17	into	into	ADP
ejpam-5458	261	18	the	the	DET
ejpam-5458	261	19	complex	complex	ADJ
ejpam-5458	261	20	form	form	NOUN
ejpam-5458	261	21	ż	ż	NOUN
ejpam-5458	261	22	=	=	PUNCT
ejpam-5458	261	23	(	(	PUNCT
ejpam-5458	261	24	l0	l0	NOUN
ejpam-5458	261	25	+	+	CCONJ
ejpam-5458	261	26	i)z	i)z	ADJ
ejpam-5458	261	27	+	+	CCONJ
ejpam-5458	261	28	l1z|z|2	l1z|z|2	NOUN
ejpam-5458	261	29	+	+	CCONJ
ejpam-5458	261	30	l2z|z|4	l2z|z|4	ADJ
ejpam-5458	261	31	+	+	ADV
ejpam-5458	261	32	o(|z|6	o(|z|6	ADV
ejpam-5458	261	33	)	)	PUNCT
ejpam-5458	261	34	(	(	PUNCT
ejpam-5458	261	35	36	36	NUM
ejpam-5458	261	36	)	)	PUNCT
ejpam-5458	261	37	where	where	SCONJ
ejpam-5458	261	38	l0	l0	PROPN
ejpam-5458	261	39	=	=	PROPN
ejpam-5458	261	40	l1	l1	PROPN
ejpam-5458	261	41	=	=	SYM
ejpam-5458	261	42	0	0	NUM
ejpam-5458	261	43	,	,	PUNCT
ejpam-5458	261	44	l2	l2	VERB
ejpam-5458	261	45	̸=	̸=	PROPN
ejpam-5458	261	46	0	0	NUM
ejpam-5458	261	47	.	.	PUNCT
ejpam-5458	262	1	computation	computation	NOUN
ejpam-5458	262	2	of	of	ADP
ejpam-5458	262	3	lyapunov	lyapunov	ADJ
ejpam-5458	262	4	numbers	number	NOUN
ejpam-5458	262	5	when	when	SCONJ
ejpam-5458	262	6	a	a	DET
ejpam-5458	262	7	hopf	hopf	ADJ
ejpam-5458	262	8	bifurcation	bifurcation	NOUN
ejpam-5458	262	9	point	point	NOUN
ejpam-5458	262	10	is	be	AUX
ejpam-5458	262	11	detected	detect	VERB
ejpam-5458	262	12	as	as	ADP
ejpam-5458	262	13	l0	l0	PROPN
ejpam-5458	262	14	=	=	SYM
ejpam-5458	262	15	0	0	PROPN
ejpam-5458	262	16	,	,	PUNCT
ejpam-5458	262	17	the	the	DET
ejpam-5458	262	18	type	type	NOUN
ejpam-5458	262	19	of	of	ADP
ejpam-5458	262	20	hopf	hopf	ADJ
ejpam-5458	262	21	bifurcation	bifurcation	NOUN
ejpam-5458	262	22	of	of	ADP
ejpam-5458	262	23	(	(	PUNCT
ejpam-5458	262	24	33	33	NUM
ejpam-5458	262	25	)	)	PUNCT
ejpam-5458	262	26	corresponds	correspond	VERB
ejpam-5458	262	27	to	to	ADP
ejpam-5458	262	28	the	the	DET
ejpam-5458	262	29	sign	sign	NOUN
ejpam-5458	262	30	of	of	ADP
ejpam-5458	262	31	the	the	DET
ejpam-5458	262	32	first	first	ADJ
ejpam-5458	262	33	lyapunov	lyapunov	ADJ
ejpam-5458	262	34	coefficient	coefficient	NOUN
ejpam-5458	262	35	l1	l1	PROPN
ejpam-5458	262	36	.	.	PUNCT
ejpam-5458	263	1	we	we	PRON
ejpam-5458	263	2	review	review	VERB
ejpam-5458	263	3	the	the	DET
ejpam-5458	263	4	technique	technique	NOUN
ejpam-5458	263	5	for	for	ADP
ejpam-5458	263	6	computing	compute	VERB
ejpam-5458	263	7	the	the	DET
ejpam-5458	263	8	first	first	ADJ
ejpam-5458	263	9	and	and	CCONJ
ejpam-5458	263	10	second	second	ADJ
ejpam-5458	263	11	lyapunov	lyapunov	ADJ
ejpam-5458	263	12	coefficients	coefficient	NOUN
ejpam-5458	263	13	at	at	ADP
ejpam-5458	263	14	the	the	DET
ejpam-5458	263	15	bifurcation	bifurcation	NOUN
ejpam-5458	263	16	point	point	NOUN
ejpam-5458	263	17	.	.	PUNCT
ejpam-5458	264	1	also	also	ADV
ejpam-5458	264	2	,	,	PUNCT
ejpam-5458	264	3	the	the	DET
ejpam-5458	264	4	taylor	taylor	PROPN
ejpam-5458	264	5	coefficients	coefficient	NOUN
ejpam-5458	264	6	formula	formula	NOUN
ejpam-5458	264	7	gkl	gkl	NOUN
ejpam-5458	264	8	of	of	ADP
ejpam-5458	264	9	the	the	DET
ejpam-5458	264	10	quadratic	quadratic	ADJ
ejpam-5458	264	11	terms	term	NOUN
ejpam-5458	264	12	in	in	ADP
ejpam-5458	264	13	g(z	g(z	PROPN
ejpam-5458	264	14	,	,	PUNCT
ejpam-5458	264	15	z̄	z̄	X
ejpam-5458	264	16	,	,	PUNCT
ejpam-5458	264	17	0	0	NUM
ejpam-5458	264	18	)	)	PUNCT
ejpam-5458	264	19	can	can	AUX
ejpam-5458	264	20	be	be	AUX
ejpam-5458	264	21	expressed	express	VERB
ejpam-5458	264	22	by	by	ADP
ejpam-5458	264	23	the	the	DET
ejpam-5458	264	24	following	following	NOUN
ejpam-5458	264	25	[	[	X
ejpam-5458	264	26	4	4	NUM
ejpam-5458	264	27	,	,	PUNCT
ejpam-5458	264	28	p311	p311	PROPN
ejpam-5458	264	29	]	]	X
ejpam-5458	264	30	:	:	PUNCT
ejpam-5458	264	31	l1(α	l1(α	X
ejpam-5458	264	32	)	)	PUNCT
ejpam-5458	264	33	=	=	SYM
ejpam-5458	264	34	1	1	NUM
ejpam-5458	264	35	2ω2	2ω2	NUM
ejpam-5458	264	36	0	0	NUM
ejpam-5458	265	1	re(ig20g11	re(ig20g11	ADJ
ejpam-5458	265	2	+	+	PUNCT
ejpam-5458	265	3	ω0g21	ω0g21	NUM
ejpam-5458	265	4	)	)	PUNCT
ejpam-5458	265	5	,	,	PUNCT
ejpam-5458	265	6	g20	g20	NOUN
ejpam-5458	265	7	=	=	SYM
ejpam-5458	265	8	⟨p	⟨p	PROPN
ejpam-5458	265	9	,	,	PUNCT
ejpam-5458	265	10	b(q	b(q	PROPN
ejpam-5458	265	11	,	,	PUNCT
ejpam-5458	265	12	q)⟩	q)⟩	NOUN
ejpam-5458	265	13	,	,	PUNCT
ejpam-5458	265	14	g11	g11	X
ejpam-5458	265	15	=	=	SYM
ejpam-5458	265	16	⟨p	⟨p	PROPN
ejpam-5458	265	17	,	,	PUNCT
ejpam-5458	265	18	b(q	b(q	PROPN
ejpam-5458	265	19	,	,	PUNCT
ejpam-5458	265	20	q̄)⟩	q̄)⟩	PROPN
ejpam-5458	265	21	,	,	PUNCT
ejpam-5458	265	22	g02	g02	NOUN
ejpam-5458	265	23	=	=	SYM
ejpam-5458	265	24	⟨p	⟨p	NOUN
ejpam-5458	265	25	,	,	PUNCT
ejpam-5458	265	26	b(q̄	b(q̄	NOUN
ejpam-5458	265	27	,	,	PUNCT
ejpam-5458	265	28	q̄)⟩	q̄)⟩	PROPN
ejpam-5458	265	29	(	(	PUNCT
ejpam-5458	265	30	37	37	NUM
ejpam-5458	265	31	)	)	PUNCT
ejpam-5458	265	32	i.	i.	NOUN
ejpam-5458	265	33	alraddadi	alraddadi	PROPN
ejpam-5458	265	34	/	/	SYM
ejpam-5458	265	35	eur	eur	PROPN
ejpam-5458	265	36	.	.	PUNCT
ejpam-5458	266	1	j.	j.	PROPN
ejpam-5458	266	2	pure	pure	PROPN
ejpam-5458	266	3	appl	appl	PROPN
ejpam-5458	266	4	.	.	PROPN
ejpam-5458	266	5	math	math	PROPN
ejpam-5458	266	6	,	,	PUNCT
ejpam-5458	266	7	17	17	NUM
ejpam-5458	266	8	(	(	PUNCT
ejpam-5458	266	9	4	4	NUM
ejpam-5458	266	10	)	)	PUNCT
ejpam-5458	266	11	(	(	PUNCT
ejpam-5458	266	12	2024	2024	NUM
ejpam-5458	266	13	)	)	PUNCT
ejpam-5458	266	14	,	,	PUNCT
ejpam-5458	266	15	3708	3708	NUM
ejpam-5458	266	16	-	-	SYM
ejpam-5458	266	17	3729	3729	NUM
ejpam-5458	266	18	3723	3723	NUM
ejpam-5458	266	19	and	and	CCONJ
ejpam-5458	266	20	g21	g21	PROPN
ejpam-5458	266	21	=	=	SYM
ejpam-5458	266	22	⟨p	⟨p	PROPN
ejpam-5458	266	23	,	,	PUNCT
ejpam-5458	266	24	c(q	c(q	PROPN
ejpam-5458	266	25	,	,	PUNCT
ejpam-5458	266	26	q	q	X
ejpam-5458	266	27	,	,	PUNCT
ejpam-5458	266	28	q̄)⟩	q̄)⟩	PROPN
ejpam-5458	266	29	−	−	NOUN
ejpam-5458	266	30	2⟨p	2⟨p	NUM
ejpam-5458	266	31	,	,	PUNCT
ejpam-5458	266	32	b(q	b(q	PROPN
ejpam-5458	266	33	,	,	PUNCT
ejpam-5458	266	34	a−1b(q	a−1b(q	PROPN
ejpam-5458	266	35	,	,	PUNCT
ejpam-5458	266	36	q̄)))⟩+	q̄)))⟩+	PROPN
ejpam-5458	266	37	⟨p	⟨p	NOUN
ejpam-5458	266	38	,	,	PUNCT
ejpam-5458	266	39	b(q̄	b(q̄	PROPN
ejpam-5458	266	40	,	,	PUNCT
ejpam-5458	266	41	(	(	PUNCT
ejpam-5458	266	42	2iω0e	2iω0e	NUM
ejpam-5458	266	43	−a)−1b(q	−a)−1b(q	NOUN
ejpam-5458	266	44	,	,	PUNCT
ejpam-5458	266	45	q))⟩	q))⟩	VERB
ejpam-5458	266	46	+	+	CCONJ
ejpam-5458	266	47	1	1	NUM
ejpam-5458	266	48	iω0	iω0	PROPN
ejpam-5458	266	49	⟨p	⟨p	PROPN
ejpam-5458	266	50	,	,	PUNCT
ejpam-5458	266	51	b(q	b(q	PROPN
ejpam-5458	266	52	,	,	PUNCT
ejpam-5458	266	53	q)⟩⟨p	q)⟩⟨p	NOUN
ejpam-5458	266	54	,	,	PUNCT
ejpam-5458	266	55	b(q	b(q	PROPN
ejpam-5458	266	56	,	,	PUNCT
ejpam-5458	266	57	q̄)⟩	q̄)⟩	PROPN
ejpam-5458	266	58	−	−	PROPN
ejpam-5458	266	59	2	2	NUM
ejpam-5458	266	60	iω0	iω0	NOUN
ejpam-5458	266	61	|⟨p	|⟨p	NOUN
ejpam-5458	266	62	,	,	PUNCT
ejpam-5458	266	63	b(q	b(q	PROPN
ejpam-5458	266	64	,	,	PUNCT
ejpam-5458	266	65	q̄)⟩|2	q̄)⟩|2	NOUN
ejpam-5458	266	66	−	−	PROPN
ejpam-5458	266	67	1	1	NUM
ejpam-5458	266	68	3iω0	3iω0	NUM
ejpam-5458	266	69	|⟨p	|⟨p	NOUN
ejpam-5458	266	70	,	,	PUNCT
ejpam-5458	266	71	b(q̄	b(q̄	NOUN
ejpam-5458	266	72	,	,	PUNCT
ejpam-5458	266	73	q̄)⟩|2	q̄)⟩|2	NOUN
ejpam-5458	266	74	at	at	ADP
ejpam-5458	266	75	the	the	DET
ejpam-5458	266	76	bautin	bautin	PROPN
ejpam-5458	266	77	bifurcation	bifurcation	NOUN
ejpam-5458	266	78	point	point	NOUN
ejpam-5458	266	79	l1(0	l1(0	PROPN
ejpam-5458	266	80	,	,	PUNCT
ejpam-5458	266	81	0	0	NUM
ejpam-5458	266	82	)	)	PUNCT
ejpam-5458	266	83	=	=	SYM
ejpam-5458	266	84	0	0	NUM
ejpam-5458	266	85	,	,	PUNCT
ejpam-5458	266	86	the	the	DET
ejpam-5458	266	87	formula	formula	NOUN
ejpam-5458	266	88	gives	give	VERB
ejpam-5458	266	89	l2(0	l2(0	NOUN
ejpam-5458	266	90	,	,	PUNCT
ejpam-5458	266	91	0	0	NUM
ejpam-5458	266	92	):	):	PUNCT
ejpam-5458	266	93	12l2(0	12l2(0	NOUN
ejpam-5458	266	94	,	,	PUNCT
ejpam-5458	266	95	0	0	NUM
ejpam-5458	266	96	)	)	PUNCT
ejpam-5458	266	97	=	=	SYM
ejpam-5458	266	98	1	1	NUM
ejpam-5458	266	99	ω0	ω0	NOUN
ejpam-5458	266	100	reg32	reg32	NOUN
ejpam-5458	266	101	+	+	CCONJ
ejpam-5458	266	102	1	1	NUM
ejpam-5458	266	103	ω2	ω2	NUM
ejpam-5458	266	104	0	0	NUM
ejpam-5458	267	1	i	i	PRON
ejpam-5458	267	2	m	m	VERB
ejpam-5458	267	3	[	[	PUNCT
ejpam-5458	267	4	g20ḡ31	g20ḡ31	NOUN
ejpam-5458	267	5	−	−	NOUN
ejpam-5458	267	6	g11(4g31	g11(4g31	X
ejpam-5458	267	7	+	+	CCONJ
ejpam-5458	267	8	3ḡ22)−	3ḡ22)−	NUM
ejpam-5458	267	9	1	1	NUM
ejpam-5458	267	10	3	3	NUM
ejpam-5458	267	11	g02(g40	g02(g40	NOUN
ejpam-5458	267	12	+	+	CCONJ
ejpam-5458	267	13	ḡ13)−	ḡ13)−	NOUN
ejpam-5458	267	14	g30g12	g30g12	NOUN
ejpam-5458	267	15	]	]	PUNCT
ejpam-5458	268	1	+	+	CCONJ
ejpam-5458	268	2	1	1	NUM
ejpam-5458	268	3	ω3	ω3	NOUN
ejpam-5458	268	4	0	0	NUM
ejpam-5458	268	5	{	{	PUNCT
ejpam-5458	268	6	re	re	X
ejpam-5458	268	7	[	[	PUNCT
ejpam-5458	268	8	g20	g20	NOUN
ejpam-5458	268	9	(	(	PUNCT
ejpam-5458	268	10	ḡ11(3g12	ḡ11(3g12	NOUN
ejpam-5458	268	11	−	−	PROPN
ejpam-5458	268	12	ḡ30	ḡ30	PROPN
ejpam-5458	268	13	)	)	PUNCT
ejpam-5458	268	14	+	+	CCONJ
ejpam-5458	268	15	g02	g02	NOUN
ejpam-5458	268	16	(	(	PUNCT
ejpam-5458	268	17	ḡ12	ḡ12	ADJ
ejpam-5458	268	18	−	−	PROPN
ejpam-5458	268	19	1	1	NUM
ejpam-5458	268	20	3	3	NUM
ejpam-5458	268	21	g30	g30	NOUN
ejpam-5458	268	22	)	)	PUNCT
ejpam-5458	269	1	+	+	CCONJ
ejpam-5458	269	2	1	1	NUM
ejpam-5458	269	3	3	3	NUM
ejpam-5458	269	4	ḡ02g03	ḡ02g03	NOUN
ejpam-5458	269	5	)	)	PUNCT
ejpam-5458	270	1	+	+	NOUN
ejpam-5458	270	2	g11	g11	X
ejpam-5458	270	3	(	(	PUNCT
ejpam-5458	270	4	ḡ02	ḡ02	PROPN
ejpam-5458	270	5	(	(	PUNCT
ejpam-5458	270	6	3	3	NUM
ejpam-5458	270	7	5	5	NUM
ejpam-5458	270	8	ḡ30	ḡ30	PROPN
ejpam-5458	270	9	+	+	NUM
ejpam-5458	270	10	3g12	3g12	NUM
ejpam-5458	270	11	)	)	PUNCT
ejpam-5458	271	1	+	+	CCONJ
ejpam-5458	271	2	1	1	NUM
ejpam-5458	271	3	3	3	NUM
ejpam-5458	271	4	g02ḡ03	g02ḡ03	VERB
ejpam-5458	271	5	−	−	PROPN
ejpam-5458	271	6	4g11g30	4g11g30	NOUN
ejpam-5458	271	7	)	)	PUNCT
ejpam-5458	271	8	]	]	PUNCT
ejpam-5458	272	1	+	+	CCONJ
ejpam-5458	272	2	3im(g20g11)img21	3im(g20g11)img21	NUM
ejpam-5458	272	3	}	}	PUNCT
ejpam-5458	272	4	+	+	CCONJ
ejpam-5458	272	5	1	1	NUM
ejpam-5458	272	6	ω4	ω4	NUM
ejpam-5458	272	7	0	0	NUM
ejpam-5458	273	1	{	{	PUNCT
ejpam-5458	274	1	i	i	PRON
ejpam-5458	274	2	m	m	VERB
ejpam-5458	274	3	[	[	PUNCT
ejpam-5458	274	4	g11ḡ02(ḡ	g11ḡ02(ḡ	NUM
ejpam-5458	274	5	2	2	NUM
ejpam-5458	274	6	20	20	NUM
ejpam-5458	274	7	−	−	PROPN
ejpam-5458	274	8	3ḡ20g11	3ḡ20g11	NUM
ejpam-5458	274	9	−	−	PROPN
ejpam-5458	274	10	4g211	4g211	NUM
ejpam-5458	274	11	)	)	PUNCT
ejpam-5458	274	12	]	]	PUNCT
ejpam-5458	275	1	+	+	CCONJ
ejpam-5458	275	2	im(g20g11	im(g20g11	X
ejpam-5458	275	3	)	)	PUNCT
ejpam-5458	275	4	[	[	PUNCT
ejpam-5458	275	5	3re(g20g11)−	3re(g20g11)−	NUM
ejpam-5458	275	6	2|g02|2	2|g02|2	NUM
ejpam-5458	275	7	]	]	SYM
ejpam-5458	275	8	}	}	PUNCT
ejpam-5458	275	9	(	(	PUNCT
ejpam-5458	275	10	38	38	NUM
ejpam-5458	275	11	)	)	PUNCT
ejpam-5458	275	12	where	where	SCONJ
ejpam-5458	275	13	g12	g12	PROPN
ejpam-5458	275	14	=	=	SYM
ejpam-5458	275	15	⟨p	⟨p	PROPN
ejpam-5458	275	16	,	,	PUNCT
ejpam-5458	275	17	c(q	c(q	PROPN
ejpam-5458	275	18	,	,	PUNCT
ejpam-5458	275	19	q	q	X
ejpam-5458	275	20	,	,	PUNCT
ejpam-5458	275	21	q̄)⟩	q̄)⟩	PROPN
ejpam-5458	275	22	,	,	PUNCT
ejpam-5458	275	23	g30	g30	NOUN
ejpam-5458	275	24	=	=	SYM
ejpam-5458	275	25	⟨p	⟨p	PROPN
ejpam-5458	275	26	,	,	PUNCT
ejpam-5458	275	27	c(q	c(q	PROPN
ejpam-5458	275	28	,	,	PUNCT
ejpam-5458	275	29	q	q	X
ejpam-5458	275	30	,	,	PUNCT
ejpam-5458	275	31	q)⟩	q)⟩	NOUN
ejpam-5458	275	32	,	,	PUNCT
ejpam-5458	275	33	g03	g03	NOUN
ejpam-5458	275	34	=	=	SYM
ejpam-5458	275	35	⟨p	⟨p	NOUN
ejpam-5458	275	36	,	,	PUNCT
ejpam-5458	275	37	c(q̄	c(q̄	NOUN
ejpam-5458	275	38	,	,	PUNCT
ejpam-5458	275	39	q̄	q̄	ADJ
ejpam-5458	275	40	,	,	PUNCT
ejpam-5458	275	41	q̄)⟩	q̄)⟩	PROPN
ejpam-5458	275	42	this	this	PRON
ejpam-5458	275	43	explains	explain	VERB
ejpam-5458	275	44	the	the	DET
ejpam-5458	275	45	general	general	ADJ
ejpam-5458	275	46	method	method	NOUN
ejpam-5458	275	47	for	for	ADP
ejpam-5458	275	48	determining	determine	VERB
ejpam-5458	275	49	the	the	DET
ejpam-5458	275	50	critical	critical	ADJ
ejpam-5458	275	51	normal	normal	ADJ
ejpam-5458	275	52	form	form	NOUN
ejpam-5458	275	53	coefficients	coefficient	NOUN
ejpam-5458	275	54	,	,	PUNCT
ejpam-5458	275	55	which	which	PRON
ejpam-5458	275	56	include	include	VERB
ejpam-5458	275	57	third	third	ADJ
ejpam-5458	275	58	-	-	PUNCT
ejpam-5458	275	59	order	order	NOUN
ejpam-5458	275	60	coefficients	coefficient	NOUN
ejpam-5458	275	61	for	for	ADP
ejpam-5458	275	62	the	the	DET
ejpam-5458	275	63	hopf	hopf	ADJ
ejpam-5458	275	64	bifurcation	bifurcation	NOUN
ejpam-5458	275	65	and	and	CCONJ
ejpam-5458	275	66	fifth	fifth	ADJ
ejpam-5458	275	67	-	-	PUNCT
ejpam-5458	275	68	order	order	NOUN
ejpam-5458	275	69	coefficients	coefficient	NOUN
ejpam-5458	275	70	for	for	ADP
ejpam-5458	275	71	the	the	DET
ejpam-5458	275	72	bautin	bautin	ADJ
ejpam-5458	275	73	bifurcation	bifurcation	NOUN
ejpam-5458	275	74	.	.	PUNCT
ejpam-5458	276	1	the	the	DET
ejpam-5458	276	2	other	other	ADJ
ejpam-5458	276	3	formula	formula	NOUN
ejpam-5458	276	4	for	for	ADP
ejpam-5458	276	5	computation	computation	NOUN
ejpam-5458	276	6	of	of	ADP
ejpam-5458	276	7	the	the	DET
ejpam-5458	276	8	coefficients	coefficient	NOUN
ejpam-5458	276	9	of	of	ADP
ejpam-5458	276	10	the	the	DET
ejpam-5458	276	11	normal	normal	ADJ
ejpam-5458	276	12	form	form	NOUN
ejpam-5458	276	13	are	be	AUX
ejpam-5458	276	14	derived	derive	VERB
ejpam-5458	276	15	in	in	ADP
ejpam-5458	276	16	[	[	X
ejpam-5458	276	17	3	3	NUM
ejpam-5458	276	18	]	]	PUNCT
ejpam-5458	276	19	.	.	PUNCT
ejpam-5458	277	1	5	5	X
ejpam-5458	277	2	.	.	X
ejpam-5458	277	3	the	the	DET
ejpam-5458	277	4	normal	normal	ADJ
ejpam-5458	277	5	form	form	NOUN
ejpam-5458	277	6	of	of	ADP
ejpam-5458	277	7	bifurcations	bifurcation	NOUN
ejpam-5458	277	8	for	for	ADP
ejpam-5458	277	9	rothman	rothman	PROPN
ejpam-5458	277	10	’s	’s	PART
ejpam-5458	277	11	carbon	carbon	NOUN
ejpam-5458	277	12	cycle	cycle	NOUN
ejpam-5458	277	13	model	model	NOUN
ejpam-5458	277	14	in	in	ADP
ejpam-5458	277	15	this	this	DET
ejpam-5458	277	16	section	section	NOUN
ejpam-5458	277	17	,	,	PUNCT
ejpam-5458	277	18	we	we	PRON
ejpam-5458	277	19	present	present	VERB
ejpam-5458	277	20	the	the	DET
ejpam-5458	277	21	normal	normal	ADJ
ejpam-5458	277	22	form	form	NOUN
ejpam-5458	277	23	of	of	ADP
ejpam-5458	277	24	hopf	hopf	ADJ
ejpam-5458	277	25	and	and	CCONJ
ejpam-5458	277	26	bautin	bautin	ADJ
ejpam-5458	277	27	bifurcations	bifurcation	NOUN
ejpam-5458	277	28	for	for	ADP
ejpam-5458	277	29	rothman	rothman	PROPN
ejpam-5458	277	30	’s	’s	PART
ejpam-5458	277	31	carbon	carbon	NOUN
ejpam-5458	277	32	cycle	cycle	NOUN
ejpam-5458	277	33	model	model	NOUN
ejpam-5458	277	34	(	(	PUNCT
ejpam-5458	277	35	7	7	NUM
ejpam-5458	277	36	)	)	PUNCT
ejpam-5458	277	37	.	.	PUNCT
ejpam-5458	278	1	our	our	PRON
ejpam-5458	278	2	analysis	analysis	NOUN
ejpam-5458	278	3	is	be	AUX
ejpam-5458	278	4	based	base	VERB
ejpam-5458	278	5	on	on	ADP
ejpam-5458	278	6	the	the	DET
ejpam-5458	278	7	normal	normal	ADJ
ejpam-5458	278	8	form	form	NOUN
ejpam-5458	278	9	theory	theory	NOUN
ejpam-5458	278	10	of	of	ADP
ejpam-5458	278	11	hopf	hopf	ADJ
ejpam-5458	278	12	and	and	CCONJ
ejpam-5458	278	13	bautin	bautin	ADJ
ejpam-5458	278	14	bifurcations	bifurcation	NOUN
ejpam-5458	278	15	(	(	PUNCT
ejpam-5458	278	16	see	see	VERB
ejpam-5458	278	17	subsection	subsection	NOUN
ejpam-5458	278	18	5.1	5.1	NUM
ejpam-5458	278	19	and	and	CCONJ
ejpam-5458	278	20	section	section	NOUN
ejpam-5458	278	21	4.2	4.2	NUM
ejpam-5458	278	22	)	)	PUNCT
ejpam-5458	278	23	.	.	PUNCT
ejpam-5458	279	1	we	we	PRON
ejpam-5458	279	2	use	use	VERB
ejpam-5458	279	3	the	the	DET
ejpam-5458	279	4	conditions	condition	NOUN
ejpam-5458	279	5	and	and	CCONJ
ejpam-5458	279	6	highlight	highlight	VERB
ejpam-5458	279	7	the	the	DET
ejpam-5458	279	8	lyapunov	lyapunov	ADJ
ejpam-5458	279	9	coefficients	coefficient	NOUN
ejpam-5458	279	10	that	that	PRON
ejpam-5458	279	11	appear	appear	VERB
ejpam-5458	279	12	in	in	ADP
ejpam-5458	279	13	this	this	DET
ejpam-5458	279	14	normal	normal	ADJ
ejpam-5458	279	15	form	form	NOUN
ejpam-5458	279	16	.	.	PUNCT
ejpam-5458	280	1	we	we	PRON
ejpam-5458	280	2	use	use	VERB
ejpam-5458	280	3	theorems	theorem	NOUN
ejpam-5458	280	4	1	1	NUM
ejpam-5458	280	5	and	and	CCONJ
ejpam-5458	280	6	2	2	NUM
ejpam-5458	280	7	to	to	PART
ejpam-5458	280	8	identify	identify	VERB
ejpam-5458	280	9	the	the	DET
ejpam-5458	280	10	topological	topological	ADJ
ejpam-5458	280	11	normal	normal	ADJ
ejpam-5458	280	12	form	form	NOUN
ejpam-5458	280	13	for	for	ADP
ejpam-5458	280	14	hopf	hopf	ADJ
ejpam-5458	280	15	and	and	CCONJ
ejpam-5458	280	16	bautin	bautin	ADJ
ejpam-5458	280	17	bifurcations	bifurcation	NOUN
ejpam-5458	280	18	,	,	PUNCT
ejpam-5458	280	19	and	and	CCONJ
ejpam-5458	280	20	we	we	PRON
ejpam-5458	280	21	aim	aim	VERB
ejpam-5458	280	22	to	to	PART
ejpam-5458	280	23	identify	identify	VERB
ejpam-5458	280	24	the	the	DET
ejpam-5458	280	25	bautin	bautin	ADJ
ejpam-5458	280	26	bifurcation	bifurcation	NOUN
ejpam-5458	280	27	and	and	CCONJ
ejpam-5458	280	28	classify	classify	VERB
ejpam-5458	280	29	its	its	PRON
ejpam-5458	280	30	criticality	criticality	NOUN
ejpam-5458	280	31	by	by	ADP
ejpam-5458	280	32	finding	find	VERB
ejpam-5458	280	33	the	the	DET
ejpam-5458	280	34	appropriate	appropriate	ADJ
ejpam-5458	280	35	coefficients	coefficient	NOUN
ejpam-5458	280	36	in	in	ADP
ejpam-5458	280	37	the	the	DET
ejpam-5458	280	38	normal	normal	ADJ
ejpam-5458	280	39	form	form	NOUN
ejpam-5458	280	40	.	.	PUNCT
ejpam-5458	281	1	we	we	PRON
ejpam-5458	281	2	rewrite	rewrite	VERB
ejpam-5458	281	3	(	(	PUNCT
ejpam-5458	281	4	7	7	NUM
ejpam-5458	281	5	)	)	PUNCT
ejpam-5458	281	6	here	here	ADV
ejpam-5458	281	7	in	in	ADP
ejpam-5458	281	8	the	the	DET
ejpam-5458	281	9	following	follow	VERB
ejpam-5458	281	10	complex	complex	ADJ
ejpam-5458	281	11	form	form	NOUN
ejpam-5458	281	12	(	(	PUNCT
ejpam-5458	281	13	36	36	NUM
ejpam-5458	281	14	):	):	PUNCT
ejpam-5458	281	15	ż	ż	NOUN
ejpam-5458	281	16	=	=	SYM
ejpam-5458	281	17	(	(	PUNCT
ejpam-5458	281	18	l0	l0	PROPN
ejpam-5458	281	19	±	±	NUM
ejpam-5458	281	20	iw)z	iw)z	PROPN
ejpam-5458	281	21	+	+	NUM
ejpam-5458	281	22	l1z|z|2	l1z|z|2	NOUN
ejpam-5458	281	23	+	+	CCONJ
ejpam-5458	281	24	l2z|z|4	l2z|z|4	ADJ
ejpam-5458	281	25	+	+	ADV
ejpam-5458	281	26	o(|z|6	o(|z|6	NOUN
ejpam-5458	281	27	)	)	PUNCT
ejpam-5458	281	28	(	(	PUNCT
ejpam-5458	281	29	39	39	NUM
ejpam-5458	281	30	)	)	PUNCT
ejpam-5458	281	31	where	where	SCONJ
ejpam-5458	281	32	z	z	PROPN
ejpam-5458	281	33	∈	∈	PROPN
ejpam-5458	281	34	c	c	NOUN
ejpam-5458	281	35	is	be	AUX
ejpam-5458	281	36	a	a	DET
ejpam-5458	281	37	complex	complex	ADJ
ejpam-5458	281	38	variable	variable	NOUN
ejpam-5458	281	39	,	,	PUNCT
ejpam-5458	281	40	and	and	CCONJ
ejpam-5458	281	41	l0	l0	PROPN
ejpam-5458	281	42	,	,	PUNCT
ejpam-5458	281	43	l1,and	l1,and	NOUN
ejpam-5458	281	44	l2	l2	NOUN
ejpam-5458	281	45	are	be	AUX
ejpam-5458	281	46	real	real	ADJ
ejpam-5458	281	47	parameters	parameter	NOUN
ejpam-5458	281	48	.	.	PUNCT
ejpam-5458	282	1	we	we	PRON
ejpam-5458	282	2	now	now	ADV
ejpam-5458	282	3	use	use	VERB
ejpam-5458	282	4	the	the	DET
ejpam-5458	282	5	method	method	NOUN
ejpam-5458	282	6	discussed	discuss	VERB
ejpam-5458	282	7	in	in	ADP
ejpam-5458	282	8	sections	section	NOUN
ejpam-5458	282	9	4.1	4.1	NUM
ejpam-5458	282	10	-	-	SYM
ejpam-5458	282	11	4.2	4.2	NUM
ejpam-5458	282	12	to	to	PART
ejpam-5458	282	13	determine	determine	VERB
ejpam-5458	282	14	the	the	DET
ejpam-5458	282	15	bautin	bautin	ADJ
ejpam-5458	282	16	bifurcation	bifurcation	NOUN
ejpam-5458	282	17	in	in	ADP
ejpam-5458	282	18	rothman	rothman	PROPN
ejpam-5458	282	19	’s	’s	PART
ejpam-5458	282	20	model	model	NOUN
ejpam-5458	282	21	(	(	PUNCT
ejpam-5458	282	22	7	7	NUM
ejpam-5458	282	23	)	)	PUNCT
ejpam-5458	282	24	.	.	PUNCT
ejpam-5458	283	1	we	we	PRON
ejpam-5458	283	2	implement	implement	VERB
ejpam-5458	283	3	this	this	DET
ejpam-5458	283	4	formula	formula	NOUN
ejpam-5458	283	5	by	by	ADP
ejpam-5458	283	6	using	use	VERB
ejpam-5458	283	7	maple	maple	NOUN
ejpam-5458	283	8	to	to	PART
ejpam-5458	283	9	compute	compute	VERB
ejpam-5458	283	10	the	the	DET
ejpam-5458	283	11	normal	normal	ADJ
ejpam-5458	283	12	form	form	NOUN
ejpam-5458	283	13	coefficients	coefficient	NOUN
ejpam-5458	283	14	of	of	ADP
ejpam-5458	283	15	hopf	hopf	ADJ
ejpam-5458	283	16	and	and	CCONJ
ejpam-5458	283	17	bautin	bautin	ADJ
ejpam-5458	283	18	bifurcations	bifurcation	NOUN
ejpam-5458	283	19	for	for	ADP
ejpam-5458	283	20	(	(	PUNCT
ejpam-5458	283	21	7	7	NUM
ejpam-5458	283	22	)	)	PUNCT
ejpam-5458	283	23	[	[	X
ejpam-5458	283	24	6	6	NUM
ejpam-5458	283	25	]	]	PUNCT
ejpam-5458	283	26	.	.	PUNCT
ejpam-5458	284	1	i.	i.	PROPN
ejpam-5458	284	2	alraddadi	alraddadi	PROPN
ejpam-5458	284	3	/	/	SYM
ejpam-5458	284	4	eur	eur	PROPN
ejpam-5458	284	5	.	.	PUNCT
ejpam-5458	285	1	j.	j.	PROPN
ejpam-5458	285	2	pure	pure	PROPN
ejpam-5458	285	3	appl	appl	PROPN
ejpam-5458	285	4	.	.	PROPN
ejpam-5458	285	5	math	math	PROPN
ejpam-5458	285	6	,	,	PUNCT
ejpam-5458	285	7	17	17	NUM
ejpam-5458	285	8	(	(	PUNCT
ejpam-5458	285	9	4	4	NUM
ejpam-5458	285	10	)	)	PUNCT
ejpam-5458	285	11	(	(	PUNCT
ejpam-5458	285	12	2024	2024	NUM
ejpam-5458	285	13	)	)	PUNCT
ejpam-5458	285	14	,	,	PUNCT
ejpam-5458	285	15	3708	3708	NUM
ejpam-5458	285	16	-	-	SYM
ejpam-5458	285	17	3729	3729	NUM
ejpam-5458	285	18	3724	3724	NUM
ejpam-5458	285	19	figure	figure	NOUN
ejpam-5458	285	20	9	9	NUM
ejpam-5458	285	21	:	:	PUNCT
ejpam-5458	285	22	this	this	PRON
ejpam-5458	285	23	shows	show	VERB
ejpam-5458	285	24	the	the	DET
ejpam-5458	285	25	first	first	ADJ
ejpam-5458	285	26	l1	l1	PROPN
ejpam-5458	285	27	and	and	CCONJ
ejpam-5458	285	28	second	second	ADJ
ejpam-5458	285	29	l2	l2	NOUN
ejpam-5458	285	30	lyapunov	lyapunov	NOUN
ejpam-5458	285	31	coefficients	coefficient	VERB
ejpam-5458	285	32	along	along	ADP
ejpam-5458	285	33	the	the	DET
ejpam-5458	285	34	two	two	NUM
ejpam-5458	285	35	hopf	hopf	ADJ
ejpam-5458	285	36	branches	branch	NOUN
ejpam-5458	285	37	of	of	ADP
ejpam-5458	285	38	(	(	PUNCT
ejpam-5458	285	39	7	7	NUM
ejpam-5458	285	40	)	)	PUNCT
ejpam-5458	285	41	for	for	ADP
ejpam-5458	285	42	varying	vary	VERB
ejpam-5458	285	43	cx	cx	PROPN
ejpam-5458	285	44	(	(	PUNCT
ejpam-5458	285	45	(	(	PUNCT
ejpam-5458	285	46	a)-(b	a)-(b	NOUN
ejpam-5458	285	47	)	)	PUNCT
ejpam-5458	285	48	)	)	PUNCT
ejpam-5458	285	49	and	and	CCONJ
ejpam-5458	285	50	µ	µ	X
ejpam-5458	285	51	(	(	PUNCT
ejpam-5458	285	52	(	(	PUNCT
ejpam-5458	285	53	c)-(d	c)-(d	NOUN
ejpam-5458	285	54	)	)	PUNCT
ejpam-5458	285	55	)	)	PUNCT
ejpam-5458	285	56	.	.	PUNCT
ejpam-5458	286	1	we	we	PRON
ejpam-5458	286	2	use	use	VERB
ejpam-5458	286	3	maple	maple	NOUN
ejpam-5458	286	4	to	to	PART
ejpam-5458	286	5	compute	compute	VERB
ejpam-5458	286	6	the	the	DET
ejpam-5458	286	7	l1	l1	PROPN
ejpam-5458	286	8	and	and	CCONJ
ejpam-5458	286	9	l2	l2	NOUN
ejpam-5458	286	10	in	in	ADP
ejpam-5458	286	11	the	the	DET
ejpam-5458	286	12	normal	normal	ADJ
ejpam-5458	286	13	form	form	NOUN
ejpam-5458	286	14	at	at	ADP
ejpam-5458	286	15	hopf	hopf	ADJ
ejpam-5458	286	16	bifurcation	bifurcation	NOUN
ejpam-5458	286	17	point	point	NOUN
ejpam-5458	286	18	where	where	SCONJ
ejpam-5458	286	19	l0	l0	NOUN
ejpam-5458	286	20	=	=	NOUN
ejpam-5458	286	21	0	0	PROPN
ejpam-5458	286	22	.	.	PUNCT
ejpam-5458	287	1	the	the	DET
ejpam-5458	287	2	type	type	NOUN
ejpam-5458	287	3	of	of	ADP
ejpam-5458	287	4	hopf	hopf	ADJ
ejpam-5458	287	5	bifurcation	bifurcation	NOUN
ejpam-5458	287	6	corresponds	correspond	VERB
ejpam-5458	287	7	to	to	ADP
ejpam-5458	287	8	the	the	DET
ejpam-5458	287	9	sign	sign	NOUN
ejpam-5458	287	10	of	of	ADP
ejpam-5458	287	11	the	the	DET
ejpam-5458	287	12	l1	l1	PROPN
ejpam-5458	287	13	.	.	PUNCT
ejpam-5458	288	1	the	the	DET
ejpam-5458	288	2	black	black	ADJ
ejpam-5458	288	3	stars	star	NOUN
ejpam-5458	288	4	indicate	indicate	VERB
ejpam-5458	288	5	bautin	bautin	ADJ
ejpam-5458	288	6	bifurcation	bifurcation	NOUN
ejpam-5458	288	7	points	point	NOUN
ejpam-5458	288	8	.	.	PUNCT
ejpam-5458	289	1	we	we	PRON
ejpam-5458	289	2	follow	follow	VERB
ejpam-5458	289	3	the	the	DET
ejpam-5458	289	4	technique	technique	NOUN
ejpam-5458	289	5	in	in	ADP
ejpam-5458	289	6	the	the	DET
ejpam-5458	289	7	previous	previous	ADJ
ejpam-5458	289	8	section	section	NOUN
ejpam-5458	289	9	4.1	4.1	NUM
ejpam-5458	289	10	to	to	PART
ejpam-5458	289	11	compute	compute	VERB
ejpam-5458	289	12	numerical	numerical	ADJ
ejpam-5458	289	13	values	value	NOUN
ejpam-5458	289	14	of	of	ADP
ejpam-5458	289	15	of	of	ADP
ejpam-5458	289	16	l1	l1	PROPN
ejpam-5458	289	17	and	and	CCONJ
ejpam-5458	289	18	l2	l2	NOUN
ejpam-5458	289	19	.	.	PUNCT
ejpam-5458	290	1	we	we	PRON
ejpam-5458	290	2	write	write	VERB
ejpam-5458	290	3	the	the	DET
ejpam-5458	290	4	right	right	ADJ
ejpam-5458	290	5	-	-	PUNCT
ejpam-5458	290	6	hand	hand	NOUN
ejpam-5458	290	7	side	side	NOUN
ejpam-5458	290	8	of	of	ADP
ejpam-5458	290	9	(	(	PUNCT
ejpam-5458	290	10	7	7	NUM
ejpam-5458	290	11	)	)	PUNCT
ejpam-5458	290	12	as	as	ADP
ejpam-5458	290	13	functions	function	NOUN
ejpam-5458	290	14	f1,2	f1,2	PROPN
ejpam-5458	290	15	.	.	PUNCT
ejpam-5458	291	1	we	we	PRON
ejpam-5458	291	2	fix	fix	VERB
ejpam-5458	291	3	all	all	DET
ejpam-5458	291	4	parameters	parameter	NOUN
ejpam-5458	291	5	except	except	SCONJ
ejpam-5458	291	6	µ	µ	NOUN
ejpam-5458	291	7	or	or	CCONJ
ejpam-5458	291	8	cx	cx	NOUN
ejpam-5458	291	9	as	as	ADP
ejpam-5458	291	10	bifurcation	bifurcation	NOUN
ejpam-5458	291	11	parameters	parameter	NOUN
ejpam-5458	291	12	,	,	PUNCT
ejpam-5458	291	13	and	and	CCONJ
ejpam-5458	291	14	f1,2	f1,2	PROPN
ejpam-5458	291	15	is	be	AUX
ejpam-5458	291	16	then	then	ADV
ejpam-5458	291	17	solved	solve	VERB
ejpam-5458	291	18	in	in	ADP
ejpam-5458	291	19	order	order	NOUN
ejpam-5458	291	20	to	to	PART
ejpam-5458	291	21	get	get	VERB
ejpam-5458	291	22	an	an	DET
ejpam-5458	291	23	equilibrium	equilibrium	NOUN
ejpam-5458	291	24	point	point	NOUN
ejpam-5458	291	25	(	(	PUNCT
ejpam-5458	291	26	c	c	X
ejpam-5458	291	27	,	,	PUNCT
ejpam-5458	291	28	w	w	NOUN
ejpam-5458	291	29	)	)	PUNCT
ejpam-5458	291	30	.	.	PUNCT
ejpam-5458	292	1	then	then	ADV
ejpam-5458	292	2	we	we	PRON
ejpam-5458	292	3	compute	compute	VERB
ejpam-5458	292	4	the	the	DET
ejpam-5458	292	5	jacobian	jacobian	ADJ
ejpam-5458	292	6	matrix	matrix	NOUN
ejpam-5458	292	7	j	j	PROPN
ejpam-5458	292	8	and	and	CCONJ
ejpam-5458	292	9	its	its	PRON
ejpam-5458	292	10	transpose	transpose	NOUN
ejpam-5458	292	11	k	k	PROPN
ejpam-5458	292	12	at	at	ADP
ejpam-5458	292	13	this	this	DET
ejpam-5458	292	14	point	point	NOUN
ejpam-5458	292	15	to	to	PART
ejpam-5458	292	16	get	get	VERB
ejpam-5458	292	17	a	a	DET
ejpam-5458	292	18	value	value	NOUN
ejpam-5458	292	19	µ	µ	NOUN
ejpam-5458	292	20	when	when	SCONJ
ejpam-5458	292	21	the	the	DET
ejpam-5458	292	22	equilibrium	equilibrium	NOUN
ejpam-5458	292	23	point	point	NOUN
ejpam-5458	292	24	(	(	PUNCT
ejpam-5458	292	25	c	c	X
ejpam-5458	292	26	,	,	PUNCT
ejpam-5458	292	27	w	w	NOUN
ejpam-5458	292	28	)	)	PUNCT
ejpam-5458	292	29	has	have	AUX
ejpam-5458	292	30	purely	purely	ADV
ejpam-5458	292	31	imaginary	imaginary	ADJ
ejpam-5458	292	32	eigenvalues	eigenvalue	VERB
ejpam-5458	292	33	±iω	±iω	PROPN
ejpam-5458	292	34	.	.	PUNCT
ejpam-5458	293	1	we	we	PRON
ejpam-5458	293	2	find	find	VERB
ejpam-5458	293	3	the	the	DET
ejpam-5458	293	4	critical	critical	ADJ
ejpam-5458	293	5	eigenvectors	eigenvector	NOUN
ejpam-5458	293	6	p	p	ADJ
ejpam-5458	293	7	of	of	ADP
ejpam-5458	293	8	j	j	PROPN
ejpam-5458	293	9	and	and	CCONJ
ejpam-5458	293	10	the	the	DET
ejpam-5458	293	11	critical	critical	ADJ
ejpam-5458	293	12	eigenvectors	eigenvector	NOUN
ejpam-5458	293	13	q	q	PROPN
ejpam-5458	293	14	of	of	ADP
ejpam-5458	293	15	k	k	PRON
ejpam-5458	293	16	such	such	ADJ
ejpam-5458	293	17	that	that	SCONJ
ejpam-5458	293	18	the	the	DET
ejpam-5458	293	19	normalisation	normalisation	NOUN
ejpam-5458	293	20	⟨p	⟨p	NOUN
ejpam-5458	293	21	,	,	PUNCT
ejpam-5458	293	22	q⟩	q⟩	X
ejpam-5458	293	23	=	=	NOUN
ejpam-5458	294	1	1	1	X
ejpam-5458	294	2	.	.	X
ejpam-5458	294	3	we	we	PRON
ejpam-5458	294	4	introduce	introduce	VERB
ejpam-5458	294	5	new	new	ADJ
ejpam-5458	294	6	complex	complex	ADJ
ejpam-5458	294	7	variables	variable	NOUN
ejpam-5458	294	8	x1,2	x1,2	ADJ
ejpam-5458	294	9	to	to	PART
ejpam-5458	294	10	evaluate	evaluate	VERB
ejpam-5458	294	11	the	the	DET
ejpam-5458	294	12	complex	complex	ADJ
ejpam-5458	294	13	function	function	NOUN
ejpam-5458	294	14	h(z	h(z	NOUN
ejpam-5458	294	15	,	,	PUNCT
ejpam-5458	294	16	z̄	z̄	NOUN
ejpam-5458	294	17	)	)	PUNCT
ejpam-5458	294	18	as	as	SCONJ
ejpam-5458	294	19	presented	present	VERB
ejpam-5458	294	20	in	in	ADP
ejpam-5458	294	21	(	(	PUNCT
ejpam-5458	294	22	39	39	NUM
ejpam-5458	294	23	)	)	PUNCT
ejpam-5458	294	24	.	.	PUNCT
ejpam-5458	295	1	we	we	PRON
ejpam-5458	295	2	need	need	VERB
ejpam-5458	295	3	to	to	PART
ejpam-5458	295	4	expand	expand	VERB
ejpam-5458	295	5	h(z	h(z	NOUN
ejpam-5458	295	6	,	,	PUNCT
ejpam-5458	295	7	z̄	z̄	NOUN
ejpam-5458	295	8	)	)	PUNCT
ejpam-5458	295	9	to	to	ADP
ejpam-5458	295	10	the	the	DET
ejpam-5458	295	11	fifthorder	fifthorder	NOUN
ejpam-5458	295	12	at	at	ADP
ejpam-5458	295	13	(	(	PUNCT
ejpam-5458	295	14	z	z	NOUN
ejpam-5458	295	15	,	,	PUNCT
ejpam-5458	295	16	z̄	z̄	NOUN
ejpam-5458	295	17	)	)	PUNCT
ejpam-5458	295	18	=	=	SYM
ejpam-5458	295	19	(	(	PUNCT
ejpam-5458	295	20	0	0	NUM
ejpam-5458	295	21	,	,	PUNCT
ejpam-5458	295	22	0	0	NUM
ejpam-5458	295	23	)	)	PUNCT
ejpam-5458	295	24	.	.	PUNCT
ejpam-5458	296	1	using	use	VERB
ejpam-5458	296	2	(	(	PUNCT
ejpam-5458	296	3	37	37	NUM
ejpam-5458	296	4	)	)	PUNCT
ejpam-5458	296	5	and	and	CCONJ
ejpam-5458	296	6	(	(	PUNCT
ejpam-5458	296	7	38	38	NUM
ejpam-5458	296	8	)	)	PUNCT
ejpam-5458	296	9	we	we	PRON
ejpam-5458	296	10	are	be	AUX
ejpam-5458	296	11	able	able	ADJ
ejpam-5458	296	12	to	to	PART
ejpam-5458	296	13	calculate	calculate	VERB
ejpam-5458	296	14	numerical	numerical	ADJ
ejpam-5458	296	15	values	value	NOUN
ejpam-5458	296	16	of	of	ADP
ejpam-5458	296	17	l1	l1	PROPN
ejpam-5458	296	18	and	and	CCONJ
ejpam-5458	296	19	l2	l2	NOUN
ejpam-5458	296	20	are	be	AUX
ejpam-5458	296	21	evaluated	evaluate	VERB
ejpam-5458	296	22	at	at	ADP
ejpam-5458	296	23	the	the	DET
ejpam-5458	296	24	hopf	hopf	ADJ
ejpam-5458	296	25	bifurcation	bifurcation	NOUN
ejpam-5458	296	26	point	point	NOUN
ejpam-5458	296	27	.	.	PUNCT
ejpam-5458	297	1	figure	figure	NOUN
ejpam-5458	297	2	9	9	NUM
ejpam-5458	297	3	shows	show	VERB
ejpam-5458	297	4	the	the	DET
ejpam-5458	297	5	first	first	ADJ
ejpam-5458	297	6	l1	l1	PROPN
ejpam-5458	297	7	and	and	CCONJ
ejpam-5458	297	8	second	second	ADJ
ejpam-5458	297	9	l2	l2	NOUN
ejpam-5458	297	10	lyapunov	lyapunov	NOUN
ejpam-5458	297	11	coefficients	coefficient	VERB
ejpam-5458	297	12	along	along	ADP
ejpam-5458	297	13	the	the	DET
ejpam-5458	297	14	two	two	NUM
ejpam-5458	297	15	hopf	hopf	ADJ
ejpam-5458	297	16	branches	branch	NOUN
ejpam-5458	297	17	of	of	ADP
ejpam-5458	297	18	(	(	PUNCT
ejpam-5458	297	19	7	7	NUM
ejpam-5458	297	20	)	)	PUNCT
ejpam-5458	297	21	for	for	ADP
ejpam-5458	297	22	varying	vary	VERB
ejpam-5458	297	23	cx	cx	PROPN
ejpam-5458	297	24	(	(	PUNCT
ejpam-5458	297	25	a)-(b	a)-(b	NOUN
ejpam-5458	297	26	)	)	PUNCT
ejpam-5458	297	27	)	)	PUNCT
ejpam-5458	297	28	and	and	CCONJ
ejpam-5458	297	29	µ	µ	X
ejpam-5458	297	30	(	(	PUNCT
ejpam-5458	297	31	(	(	PUNCT
ejpam-5458	297	32	c)-(d	c)-(d	NOUN
ejpam-5458	297	33	)	)	PUNCT
ejpam-5458	297	34	)	)	PUNCT
ejpam-5458	297	35	.	.	PUNCT
ejpam-5458	298	1	figure	figure	NOUN
ejpam-5458	298	2	10	10	NUM
ejpam-5458	298	3	shows	show	VERB
ejpam-5458	298	4	the	the	DET
ejpam-5458	298	5	first	first	ADJ
ejpam-5458	298	6	l1	l1	PROPN
ejpam-5458	298	7	against	against	ADP
ejpam-5458	298	8	second	second	ADJ
ejpam-5458	298	9	l2	l2	NOUN
ejpam-5458	299	1	lyapunov	lyapunov	NOUN
ejpam-5458	299	2	coefficients	coefficient	VERB
ejpam-5458	299	3	along	along	ADP
ejpam-5458	299	4	the	the	DET
ejpam-5458	299	5	two	two	NUM
ejpam-5458	299	6	hopf	hopf	ADJ
ejpam-5458	299	7	branches	branch	NOUN
ejpam-5458	299	8	of	of	ADP
ejpam-5458	299	9	(	(	PUNCT
ejpam-5458	299	10	7	7	NUM
ejpam-5458	299	11	)	)	PUNCT
ejpam-5458	299	12	for	for	ADP
ejpam-5458	299	13	varying	vary	VERB
ejpam-5458	299	14	cx	cx	PROPN
ejpam-5458	299	15	and	and	CCONJ
ejpam-5458	299	16	µ.	µ.	NOUN
ejpam-5458	299	17	in	in	ADP
ejpam-5458	299	18	figure	figure	NOUN
ejpam-5458	299	19	11	11	NUM
ejpam-5458	299	20	,	,	PUNCT
ejpam-5458	299	21	the	the	DET
ejpam-5458	299	22	first	first	ADJ
ejpam-5458	299	23	l1	l1	PROPN
ejpam-5458	299	24	and	and	CCONJ
ejpam-5458	299	25	second	second	ADJ
ejpam-5458	299	26	l2	l2	NOUN
ejpam-5458	299	27	lyapunov	lyapunov	NOUN
ejpam-5458	299	28	coefficients	coefficient	NOUN
ejpam-5458	299	29	of	of	ADP
ejpam-5458	299	30	(	(	PUNCT
ejpam-5458	299	31	7	7	NUM
ejpam-5458	299	32	)	)	PUNCT
ejpam-5458	299	33	at	at	ADP
ejpam-5458	299	34	a	a	DET
ejpam-5458	299	35	hopf	hopf	ADJ
ejpam-5458	299	36	bifurcation	bifurcation	NOUN
ejpam-5458	299	37	point	point	NOUN
ejpam-5458	299	38	when	when	SCONJ
ejpam-5458	299	39	cx	cx	PROPN
ejpam-5458	299	40	and	and	CCONJ
ejpam-5458	299	41	µ	µ	NOUN
ejpam-5458	299	42	as	as	ADP
ejpam-5458	299	43	the	the	DET
ejpam-5458	299	44	bifurcation	bifurcation	NOUN
ejpam-5458	299	45	parameters	parameter	NOUN
ejpam-5458	299	46	.	.	PUNCT
ejpam-5458	300	1	we	we	PRON
ejpam-5458	300	2	highlight	highlight	VERB
ejpam-5458	300	3	the	the	DET
ejpam-5458	300	4	red	red	ADJ
ejpam-5458	300	5	curve	curve	NOUN
ejpam-5458	300	6	(	(	PUNCT
ejpam-5458	300	7	l1	l1	PROPN
ejpam-5458	300	8	<	<	X
ejpam-5458	300	9	0	0	NUM
ejpam-5458	300	10	)	)	PUNCT
ejpam-5458	300	11	and	and	CCONJ
ejpam-5458	300	12	the	the	DET
ejpam-5458	300	13	blue	blue	ADJ
ejpam-5458	300	14	curve	curve	NOUN
ejpam-5458	300	15	(	(	PUNCT
ejpam-5458	300	16	l1	l1	PROPN
ejpam-5458	300	17	>	>	X
ejpam-5458	300	18	0	0	NUM
ejpam-5458	300	19	)	)	PUNCT
ejpam-5458	300	20	correspond	correspond	VERB
ejpam-5458	300	21	to	to	ADP
ejpam-5458	300	22	the	the	DET
ejpam-5458	300	23	supercritical	supercritical	ADJ
ejpam-5458	300	24	hopf	hopf	ADJ
ejpam-5458	300	25	bifurcation	bifurcation	NOUN
ejpam-5458	300	26	and	and	CCONJ
ejpam-5458	300	27	the	the	DET
ejpam-5458	300	28	subcritical	subcritical	ADJ
ejpam-5458	300	29	hopf	hopf	ADJ
ejpam-5458	300	30	bifurcation	bifurcation	NOUN
ejpam-5458	300	31	respectively	respectively	ADV
ejpam-5458	300	32	.	.	PUNCT
ejpam-5458	301	1	the	the	DET
ejpam-5458	301	2	two	two	NUM
ejpam-5458	301	3	bautin	bautin	ADJ
ejpam-5458	301	4	bifurcation	bifurcation	NOUN
ejpam-5458	301	5	points	point	NOUN
ejpam-5458	301	6	are	be	AUX
ejpam-5458	301	7	represented	represent	VERB
ejpam-5458	301	8	by	by	ADP
ejpam-5458	301	9	black	black	ADJ
ejpam-5458	301	10	i.	i.	PROPN
ejpam-5458	301	11	alraddadi	alraddadi	PROPN
ejpam-5458	301	12	/	/	SYM
ejpam-5458	301	13	eur	eur	PROPN
ejpam-5458	301	14	.	.	PUNCT
ejpam-5458	302	1	j.	j.	PROPN
ejpam-5458	302	2	pure	pure	PROPN
ejpam-5458	302	3	appl	appl	PROPN
ejpam-5458	302	4	.	.	PROPN
ejpam-5458	302	5	math	math	PROPN
ejpam-5458	302	6	,	,	PUNCT
ejpam-5458	302	7	17	17	NUM
ejpam-5458	302	8	(	(	PUNCT
ejpam-5458	302	9	4	4	NUM
ejpam-5458	302	10	)	)	PUNCT
ejpam-5458	302	11	(	(	PUNCT
ejpam-5458	302	12	2024	2024	NUM
ejpam-5458	302	13	)	)	PUNCT
ejpam-5458	302	14	,	,	PUNCT
ejpam-5458	302	15	3708	3708	NUM
ejpam-5458	302	16	-	-	SYM
ejpam-5458	302	17	3729	3729	NUM
ejpam-5458	302	18	3725	3725	NUM
ejpam-5458	302	19	figure	figure	NOUN
ejpam-5458	302	20	10	10	NUM
ejpam-5458	302	21	:	:	PUNCT
ejpam-5458	302	22	this	this	PRON
ejpam-5458	302	23	shows	show	VERB
ejpam-5458	302	24	the	the	DET
ejpam-5458	302	25	first	first	ADJ
ejpam-5458	302	26	l1	l1	PROPN
ejpam-5458	302	27	against	against	ADP
ejpam-5458	302	28	second	second	ADJ
ejpam-5458	302	29	l2	l2	NOUN
ejpam-5458	303	1	lyapunov	lyapunov	NOUN
ejpam-5458	303	2	coefficients	coefficient	VERB
ejpam-5458	303	3	along	along	ADP
ejpam-5458	303	4	the	the	DET
ejpam-5458	303	5	two	two	NUM
ejpam-5458	303	6	hopf	hopf	ADJ
ejpam-5458	303	7	branches	branch	NOUN
ejpam-5458	303	8	of	of	ADP
ejpam-5458	303	9	(	(	PUNCT
ejpam-5458	303	10	7	7	NUM
ejpam-5458	303	11	)	)	PUNCT
ejpam-5458	303	12	for	for	ADP
ejpam-5458	303	13	varying	vary	VERB
ejpam-5458	303	14	cx	cx	PROPN
ejpam-5458	303	15	and	and	CCONJ
ejpam-5458	303	16	µ.	µ.	NOUN
ejpam-5458	303	17	we	we	PRON
ejpam-5458	303	18	use	use	VERB
ejpam-5458	303	19	maple	maple	NOUN
ejpam-5458	303	20	to	to	PART
ejpam-5458	303	21	compute	compute	VERB
ejpam-5458	303	22	the	the	DET
ejpam-5458	303	23	l1	l1	PROPN
ejpam-5458	303	24	and	and	CCONJ
ejpam-5458	303	25	l2	l2	NOUN
ejpam-5458	303	26	in	in	ADP
ejpam-5458	303	27	the	the	DET
ejpam-5458	303	28	normal	normal	ADJ
ejpam-5458	303	29	form	form	NOUN
ejpam-5458	303	30	at	at	ADP
ejpam-5458	303	31	hopf	hopf	ADJ
ejpam-5458	303	32	bifurcation	bifurcation	NOUN
ejpam-5458	303	33	point	point	NOUN
ejpam-5458	303	34	where	where	SCONJ
ejpam-5458	303	35	l0	l0	NOUN
ejpam-5458	303	36	=	=	NOUN
ejpam-5458	303	37	0	0	PROPN
ejpam-5458	303	38	.	.	PUNCT
ejpam-5458	304	1	the	the	DET
ejpam-5458	304	2	type	type	NOUN
ejpam-5458	304	3	of	of	ADP
ejpam-5458	304	4	hopf	hopf	ADJ
ejpam-5458	304	5	bifurcation	bifurcation	NOUN
ejpam-5458	304	6	corresponds	correspond	VERB
ejpam-5458	304	7	to	to	ADP
ejpam-5458	304	8	the	the	DET
ejpam-5458	304	9	sign	sign	NOUN
ejpam-5458	304	10	of	of	ADP
ejpam-5458	304	11	the	the	DET
ejpam-5458	304	12	l1	l1	PROPN
ejpam-5458	304	13	.	.	PUNCT
ejpam-5458	305	1	the	the	DET
ejpam-5458	305	2	two	two	NUM
ejpam-5458	305	3	black	black	ADJ
ejpam-5458	305	4	stars	star	NOUN
ejpam-5458	305	5	indicate	indicate	VERB
ejpam-5458	305	6	bautin	bautin	ADJ
ejpam-5458	305	7	bifurcation	bifurcation	NOUN
ejpam-5458	305	8	points	point	NOUN
ejpam-5458	305	9	.	.	PUNCT
ejpam-5458	306	1	points	point	NOUN
ejpam-5458	306	2	at	at	ADP
ejpam-5458	306	3	l1	l1	PROPN
ejpam-5458	306	4	=	=	SYM
ejpam-5458	306	5	0	0	PROPN
ejpam-5458	306	6	,	,	PUNCT
ejpam-5458	306	7	and	and	CCONJ
ejpam-5458	306	8	we	we	PRON
ejpam-5458	306	9	display	display	VERB
ejpam-5458	306	10	these	these	PRON
ejpam-5458	306	11	by	by	ADP
ejpam-5458	306	12	leading	lead	VERB
ejpam-5458	306	13	at	at	ADP
ejpam-5458	306	14	the	the	DET
ejpam-5458	306	15	sign	sign	NOUN
ejpam-5458	306	16	of	of	ADP
ejpam-5458	306	17	l2	l2	NOUN
ejpam-5458	306	18	.	.	PUNCT
ejpam-5458	307	1	5.1	5.1	NUM
ejpam-5458	307	2	.	.	PUNCT
ejpam-5458	307	3	saddle	saddle	NOUN
ejpam-5458	307	4	-	-	PUNCT
ejpam-5458	307	5	node	node	NOUN
ejpam-5458	307	6	bifurcation	bifurcation	NOUN
ejpam-5458	307	7	of	of	ADP
ejpam-5458	307	8	limit	limit	NOUN
ejpam-5458	307	9	cycles	cycle	NOUN
ejpam-5458	307	10	this	this	DET
ejpam-5458	307	11	complex	complex	ADJ
ejpam-5458	307	12	form	form	NOUN
ejpam-5458	307	13	(	(	PUNCT
ejpam-5458	307	14	39	39	NUM
ejpam-5458	307	15	)	)	PUNCT
ejpam-5458	307	16	undergoes	undergo	VERB
ejpam-5458	307	17	saddle	saddle	NOUN
ejpam-5458	307	18	-	-	PUNCT
ejpam-5458	307	19	node	node	NOUN
ejpam-5458	307	20	bifurcation	bifurcation	NOUN
ejpam-5458	307	21	of	of	ADP
ejpam-5458	307	22	limit	limit	NOUN
ejpam-5458	307	23	cycles	cycle	NOUN
ejpam-5458	308	1	if	if	SCONJ
ejpam-5458	308	2	l1l2	l1l2	X
ejpam-5458	308	3	<	<	X
ejpam-5458	308	4	0	0	PUNCT
ejpam-5458	308	5	and	and	CCONJ
ejpam-5458	308	6	l21	l21	NOUN
ejpam-5458	308	7	−	−	PROPN
ejpam-5458	308	8	4l0l2	4l0l2	NUM
ejpam-5458	308	9	=	=	SYM
ejpam-5458	308	10	0	0	PUNCT
ejpam-5458	308	11	(	(	PUNCT
ejpam-5458	308	12	40	40	NUM
ejpam-5458	308	13	)	)	PUNCT
ejpam-5458	308	14	then	then	ADV
ejpam-5458	308	15	,	,	PUNCT
ejpam-5458	308	16	we	we	PRON
ejpam-5458	308	17	attempt	attempt	VERB
ejpam-5458	308	18	to	to	PART
ejpam-5458	308	19	approximate	approximate	VERB
ejpam-5458	308	20	the	the	DET
ejpam-5458	308	21	location	location	NOUN
ejpam-5458	308	22	of	of	ADP
ejpam-5458	308	23	the	the	DET
ejpam-5458	308	24	saddle	saddle	NOUN
ejpam-5458	308	25	-	-	PUNCT
ejpam-5458	308	26	node	node	NOUN
ejpam-5458	308	27	limit	limit	NOUN
ejpam-5458	308	28	cycles	cycle	NOUN
ejpam-5458	308	29	.	.	PUNCT
ejpam-5458	309	1	in	in	ADP
ejpam-5458	309	2	figure	figure	NOUN
ejpam-5458	309	3	12	12	NUM
ejpam-5458	309	4	,	,	PUNCT
ejpam-5458	309	5	we	we	PRON
ejpam-5458	309	6	used	use	VERB
ejpam-5458	309	7	a	a	DET
ejpam-5458	309	8	numerical	numerical	ADJ
ejpam-5458	309	9	continuation	continuation	NOUN
ejpam-5458	309	10	software	software	NOUN
ejpam-5458	309	11	xppaut	xppaut	PRON
ejpam-5458	310	1	[	[	X
ejpam-5458	310	2	2	2	X
ejpam-5458	310	3	]	]	PUNCT
ejpam-5458	310	4	to	to	PART
ejpam-5458	310	5	plot	plot	VERB
ejpam-5458	310	6	the	the	DET
ejpam-5458	310	7	bifurcation	bifurcation	NOUN
ejpam-5458	310	8	diagram	diagram	NOUN
ejpam-5458	310	9	of	of	ADP
ejpam-5458	310	10	rothman	rothman	PROPN
ejpam-5458	310	11	’s	’s	PART
ejpam-5458	310	12	carbon	carbon	NOUN
ejpam-5458	310	13	cycle	cycle	NOUN
ejpam-5458	310	14	model	model	NOUN
ejpam-5458	310	15	(	(	PUNCT
ejpam-5458	310	16	7	7	NUM
ejpam-5458	310	17	)	)	PUNCT
ejpam-5458	310	18	in	in	ADP
ejpam-5458	310	19	the	the	DET
ejpam-5458	310	20	parameter	parameter	NOUN
ejpam-5458	310	21	plane	plane	NOUN
ejpam-5458	310	22	(	(	PUNCT
ejpam-5458	310	23	cx	cx	PROPN
ejpam-5458	310	24	,	,	PUNCT
ejpam-5458	310	25	µ	µ	NOUN
ejpam-5458	310	26	)	)	PUNCT
ejpam-5458	310	27	,	,	PUNCT
ejpam-5458	310	28	and	and	CCONJ
ejpam-5458	310	29	we	we	PRON
ejpam-5458	310	30	illustrated	illustrate	VERB
ejpam-5458	310	31	the	the	DET
ejpam-5458	310	32	fold	fold	ADJ
ejpam-5458	310	33	limit	limit	NOUN
ejpam-5458	310	34	cycle	cycle	NOUN
ejpam-5458	310	35	and	and	CCONJ
ejpam-5458	310	36	the	the	DET
ejpam-5458	310	37	hopf	hopf	ADJ
ejpam-5458	310	38	bifurcation	bifurcation	NOUN
ejpam-5458	310	39	of	of	ADP
ejpam-5458	310	40	(	(	PUNCT
ejpam-5458	310	41	7	7	NUM
ejpam-5458	310	42	)	)	PUNCT
ejpam-5458	310	43	.	.	PUNCT
ejpam-5458	311	1	we	we	PRON
ejpam-5458	311	2	illustrate	illustrate	VERB
ejpam-5458	311	3	the	the	DET
ejpam-5458	311	4	approximation	approximation	NOUN
ejpam-5458	311	5	using	use	VERB
ejpam-5458	311	6	the	the	DET
ejpam-5458	311	7	two	two	NUM
ejpam-5458	311	8	methods	method	NOUN
ejpam-5458	311	9	in	in	ADP
ejpam-5458	311	10	figure	figure	NOUN
ejpam-5458	311	11	13	13	NUM
ejpam-5458	311	12	.	.	PUNCT
ejpam-5458	312	1	figure	figure	VERB
ejpam-5458	312	2	13	13	NUM
ejpam-5458	312	3	shows	show	NOUN
ejpam-5458	312	4	in	in	ADP
ejpam-5458	312	5	the	the	DET
ejpam-5458	312	6	parameter	parameter	NOUN
ejpam-5458	312	7	plane	plane	NOUN
ejpam-5458	312	8	(	(	PUNCT
ejpam-5458	312	9	cx	cx	PROPN
ejpam-5458	312	10	,	,	PUNCT
ejpam-5458	312	11	µ	µ	NOUN
ejpam-5458	312	12	)	)	PUNCT
ejpam-5458	312	13	the	the	DET
ejpam-5458	312	14	curves	curve	NOUN
ejpam-5458	312	15	of	of	ADP
ejpam-5458	312	16	bifurcation	bifurcation	NOUN
ejpam-5458	312	17	of	of	ADP
ejpam-5458	312	18	periodic	periodic	ADJ
ejpam-5458	312	19	orbits	orbit	NOUN
ejpam-5458	312	20	near	near	ADP
ejpam-5458	312	21	the	the	DET
ejpam-5458	312	22	bautin	bautin	ADJ
ejpam-5458	312	23	bifurcation	bifurcation	NOUN
ejpam-5458	312	24	(	(	PUNCT
ejpam-5458	312	25	indicated	indicate	VERB
ejpam-5458	312	26	by	by	ADP
ejpam-5458	312	27	the	the	DET
ejpam-5458	312	28	red	red	PROPN
ejpam-5458	312	29	star	star	PROPN
ejpam-5458	312	30	)	)	PUNCT
ejpam-5458	312	31	.	.	PUNCT
ejpam-5458	313	1	the	the	DET
ejpam-5458	313	2	saddle	saddle	NOUN
ejpam-5458	313	3	-	-	PUNCT
ejpam-5458	313	4	node	node	NOUN
ejpam-5458	313	5	bifurcation	bifurcation	NOUN
ejpam-5458	313	6	of	of	ADP
ejpam-5458	313	7	limit	limit	NOUN
ejpam-5458	313	8	cycles	cycle	NOUN
ejpam-5458	313	9	are	be	AUX
ejpam-5458	313	10	both	both	PRON
ejpam-5458	313	11	of	of	ADP
ejpam-5458	313	12	the	the	DET
ejpam-5458	313	13	hopf	hopf	ADJ
ejpam-5458	313	14	curve	curve	NOUN
ejpam-5458	313	15	.	.	PUNCT
ejpam-5458	314	1	figures	figure	NOUN
ejpam-5458	314	2	13(a	13(a	NUM
ejpam-5458	314	3	)	)	PUNCT
ejpam-5458	314	4	and	and	CCONJ
ejpam-5458	314	5	13(b	13(b	NUM
ejpam-5458	314	6	)	)	PUNCT
ejpam-5458	314	7	consider	consider	VERB
ejpam-5458	314	8	the	the	DET
ejpam-5458	314	9	left	left	ADJ
ejpam-5458	314	10	and	and	CCONJ
ejpam-5458	314	11	right	right	ADJ
ejpam-5458	314	12	side	side	NOUN
ejpam-5458	314	13	of	of	ADP
ejpam-5458	314	14	the	the	DET
ejpam-5458	314	15	bautin	bautin	ADJ
ejpam-5458	314	16	bifurcation	bifurcation	NOUN
ejpam-5458	314	17	from	from	ADP
ejpam-5458	314	18	figure	figure	NOUN
ejpam-5458	314	19	12	12	NUM
ejpam-5458	314	20	.	.	PUNCT
ejpam-5458	315	1	these	these	PRON
ejpam-5458	315	2	are	be	AUX
ejpam-5458	315	3	computed	compute	VERB
ejpam-5458	315	4	in	in	ADP
ejpam-5458	315	5	two	two	NUM
ejpam-5458	315	6	ways	way	NOUN
ejpam-5458	315	7	:	:	PUNCT
ejpam-5458	315	8	for	for	ADP
ejpam-5458	315	9	the	the	DET
ejpam-5458	315	10	hopf	hopf	ADJ
ejpam-5458	315	11	bifurcation	bifurcation	NOUN
ejpam-5458	315	12	curve	curve	NOUN
ejpam-5458	315	13	,	,	PUNCT
ejpam-5458	315	14	the	the	DET
ejpam-5458	315	15	xppaut	xppaut	PROPN
ejpam-5458	315	16	calculations	calculation	NOUN
ejpam-5458	315	17	and	and	CCONJ
ejpam-5458	315	18	the	the	DET
ejpam-5458	315	19	maple	maple	NOUN
ejpam-5458	315	20	calculations	calculation	NOUN
ejpam-5458	315	21	agree	agree	VERB
ejpam-5458	315	22	very	very	ADV
ejpam-5458	315	23	well	well	ADV
ejpam-5458	315	24	.	.	PUNCT
ejpam-5458	316	1	on	on	ADP
ejpam-5458	316	2	the	the	DET
ejpam-5458	316	3	other	other	ADJ
ejpam-5458	316	4	hand	hand	NOUN
ejpam-5458	316	5	,	,	PUNCT
ejpam-5458	316	6	the	the	DET
ejpam-5458	316	7	curve	curve	NOUN
ejpam-5458	316	8	of	of	ADP
ejpam-5458	316	9	the	the	DET
ejpam-5458	316	10	saddle	saddle	NOUN
ejpam-5458	316	11	-	-	PUNCT
ejpam-5458	316	12	node	node	NOUN
ejpam-5458	316	13	bifurcation	bifurcation	NOUN
ejpam-5458	316	14	of	of	ADP
ejpam-5458	316	15	limit	limit	NOUN
ejpam-5458	316	16	cycles	cycle	NOUN
ejpam-5458	316	17	is	be	AUX
ejpam-5458	316	18	calculated	calculate	VERB
ejpam-5458	316	19	by	by	ADP
ejpam-5458	316	20	two	two	NUM
ejpam-5458	316	21	methods	method	NOUN
ejpam-5458	316	22	.	.	PUNCT
ejpam-5458	317	1	for	for	ADP
ejpam-5458	317	2	the	the	DET
ejpam-5458	317	3	hopf	hopf	ADJ
ejpam-5458	317	4	curve	curve	NOUN
ejpam-5458	317	5	,	,	PUNCT
ejpam-5458	317	6	two	two	NUM
ejpam-5458	317	7	method	method	NOUN
ejpam-5458	317	8	calculations	calculation	NOUN
ejpam-5458	317	9	have	have	VERB
ejpam-5458	317	10	the	the	DET
ejpam-5458	317	11	same	same	ADJ
ejpam-5458	317	12	criticality	criticality	NOUN
ejpam-5458	317	13	and	and	CCONJ
ejpam-5458	317	14	are	be	AUX
ejpam-5458	317	15	lying	lie	VERB
ejpam-5458	317	16	on	on	ADP
ejpam-5458	317	17	the	the	DET
ejpam-5458	317	18	same	same	ADJ
ejpam-5458	317	19	side	side	NOUN
ejpam-5458	317	20	of	of	ADP
ejpam-5458	317	21	the	the	DET
ejpam-5458	317	22	hopf	hopf	ADJ
ejpam-5458	317	23	curve	curve	NOUN
ejpam-5458	317	24	in	in	ADP
ejpam-5458	317	25	figures	figure	NOUN
ejpam-5458	317	26	13(a	13(a	NUM
ejpam-5458	317	27	)	)	PUNCT
ejpam-5458	317	28	and	and	CCONJ
ejpam-5458	317	29	13(b	13(b	NUM
ejpam-5458	317	30	)	)	PUNCT
ejpam-5458	317	31	,	,	PUNCT
ejpam-5458	317	32	showing	show	VERB
ejpam-5458	317	33	that	that	SCONJ
ejpam-5458	317	34	both	both	DET
ejpam-5458	317	35	calculations	calculation	NOUN
ejpam-5458	317	36	indicate	indicate	VERB
ejpam-5458	317	37	this	this	PRON
ejpam-5458	317	38	is	be	AUX
ejpam-5458	317	39	the	the	DET
ejpam-5458	317	40	subcritical	subcritical	ADJ
ejpam-5458	317	41	hopf	hopf	ADJ
ejpam-5458	317	42	bifurcation	bifurcation	NOUN
ejpam-5458	317	43	curve	curve	NOUN
ejpam-5458	317	44	which	which	PRON
ejpam-5458	317	45	lies	lie	VERB
ejpam-5458	317	46	to	to	ADP
ejpam-5458	317	47	the	the	DET
ejpam-5458	317	48	left	left	NOUN
ejpam-5458	317	49	and	and	CCONJ
ejpam-5458	317	50	to	to	ADP
ejpam-5458	317	51	the	the	DET
ejpam-5458	317	52	right	right	NOUN
ejpam-5458	317	53	of	of	ADP
ejpam-5458	317	54	the	the	DET
ejpam-5458	317	55	bautin	bautin	ADJ
ejpam-5458	317	56	bifurcation	bifurcation	NOUN
ejpam-5458	317	57	from	from	ADP
ejpam-5458	317	58	figure	figure	NOUN
ejpam-5458	317	59	12	12	NUM
ejpam-5458	317	60	.	.	PUNCT
ejpam-5458	318	1	i.	i.	PROPN
ejpam-5458	318	2	alraddadi	alraddadi	PROPN
ejpam-5458	318	3	/	/	SYM
ejpam-5458	318	4	eur	eur	PROPN
ejpam-5458	318	5	.	.	PUNCT
ejpam-5458	319	1	j.	j.	PROPN
ejpam-5458	319	2	pure	pure	PROPN
ejpam-5458	319	3	appl	appl	PROPN
ejpam-5458	319	4	.	.	PROPN
ejpam-5458	319	5	math	math	PROPN
ejpam-5458	319	6	,	,	PUNCT
ejpam-5458	319	7	17	17	NUM
ejpam-5458	319	8	(	(	PUNCT
ejpam-5458	319	9	4	4	NUM
ejpam-5458	319	10	)	)	PUNCT
ejpam-5458	319	11	(	(	PUNCT
ejpam-5458	319	12	2024	2024	NUM
ejpam-5458	319	13	)	)	PUNCT
ejpam-5458	319	14	,	,	PUNCT
ejpam-5458	319	15	3708	3708	NUM
ejpam-5458	319	16	-	-	SYM
ejpam-5458	319	17	3729	3729	NUM
ejpam-5458	319	18	3726	3726	NUM
ejpam-5458	319	19	60	60	NUM
ejpam-5458	319	20	70	70	NUM
ejpam-5458	319	21	80	80	NUM
ejpam-5458	319	22	90	90	NUM
ejpam-5458	319	23	100	100	NUM
ejpam-5458	319	24	110	110	NUM
ejpam-5458	319	25	cx	cx	NOUN
ejpam-5458	319	26	50	50	NUM
ejpam-5458	319	27	100	100	NUM
ejpam-5458	319	28	150	150	NUM
ejpam-5458	319	29	200	200	NUM
ejpam-5458	319	30	250	250	NUM
ejpam-5458	319	31	300	300	NUM
ejpam-5458	319	32	350	350	NUM
ejpam-5458	319	33	400	400	NUM
ejpam-5458	319	34	450	450	NUM
ejpam-5458	319	35	500	500	NUM
ejpam-5458	319	36	550	550	NUM
ejpam-5458	319	37	600	600	NUM
ejpam-5458	319	38	supercritical	supercritical	ADJ
ejpam-5458	319	39	hopf	hopf	ADJ
ejpam-5458	319	40	bifurcation	bifurcation	NOUN
ejpam-5458	319	41	l	l	NOUN
ejpam-5458	319	42	1	1	NUM
ejpam-5458	319	43	<	<	SYM
ejpam-5458	319	44	0	0	NUM
ejpam-5458	319	45	subcritical	subcritical	ADJ
ejpam-5458	319	46	hopf	hopf	ADJ
ejpam-5458	319	47	bifurcation	bifurcation	NOUN
ejpam-5458	319	48	l	l	NOUN
ejpam-5458	319	49	1	1	NUM
ejpam-5458	319	50	>	>	SYM
ejpam-5458	319	51	0	0	NUM
ejpam-5458	319	52	l	l	NOUN
ejpam-5458	319	53	2	2	NUM
ejpam-5458	319	54	>	>	SYM
ejpam-5458	319	55	0	0	NUM
ejpam-5458	319	56	bautin	bautin	ADJ
ejpam-5458	319	57	bifurcation	bifurcation	NOUN
ejpam-5458	319	58	l	l	NOUN
ejpam-5458	319	59	1	1	NUM
ejpam-5458	319	60	=	=	SYM
ejpam-5458	319	61	0	0	NUM
ejpam-5458	319	62	figure	figure	NOUN
ejpam-5458	319	63	11	11	NUM
ejpam-5458	319	64	:	:	PUNCT
ejpam-5458	319	65	this	this	PRON
ejpam-5458	319	66	illustrates	illustrate	VERB
ejpam-5458	319	67	the	the	DET
ejpam-5458	319	68	bifurcation	bifurcation	NOUN
ejpam-5458	319	69	diagram	diagram	NOUN
ejpam-5458	319	70	of	of	ADP
ejpam-5458	319	71	(	(	PUNCT
ejpam-5458	319	72	7	7	NUM
ejpam-5458	319	73	)	)	PUNCT
ejpam-5458	319	74	for	for	ADP
ejpam-5458	319	75	the	the	DET
ejpam-5458	319	76	parameter	parameter	NOUN
ejpam-5458	319	77	plane	plane	NOUN
ejpam-5458	319	78	(	(	PUNCT
ejpam-5458	319	79	cx	cx	PROPN
ejpam-5458	319	80	,	,	PUNCT
ejpam-5458	319	81	µ	µ	NOUN
ejpam-5458	319	82	)	)	PUNCT
ejpam-5458	319	83	.	.	PUNCT
ejpam-5458	320	1	two	two	NUM
ejpam-5458	320	2	types	type	NOUN
ejpam-5458	320	3	of	of	ADP
ejpam-5458	320	4	hopf	hopf	ADJ
ejpam-5458	320	5	bifurcation	bifurcation	NOUN
ejpam-5458	320	6	are	be	AUX
ejpam-5458	320	7	presented	present	VERB
ejpam-5458	320	8	by	by	ADP
ejpam-5458	320	9	blue	blue	ADJ
ejpam-5458	320	10	(	(	PUNCT
ejpam-5458	320	11	subcritical	subcritical	ADJ
ejpam-5458	320	12	)	)	PUNCT
ejpam-5458	320	13	and	and	CCONJ
ejpam-5458	320	14	red	red	ADJ
ejpam-5458	320	15	(	(	PUNCT
ejpam-5458	320	16	supercritical	supercritical	ADJ
ejpam-5458	320	17	)	)	PUNCT
ejpam-5458	320	18	curves	curve	NOUN
ejpam-5458	320	19	.	.	PUNCT
ejpam-5458	321	1	bautin	bautin	ADJ
ejpam-5458	321	2	bifurcation	bifurcation	NOUN
ejpam-5458	321	3	points	point	NOUN
ejpam-5458	321	4	are	be	AUX
ejpam-5458	321	5	indicated	indicate	VERB
ejpam-5458	321	6	by	by	ADP
ejpam-5458	321	7	black	black	ADJ
ejpam-5458	321	8	stars	star	NOUN
ejpam-5458	321	9	.	.	PUNCT
ejpam-5458	322	1	l2	l2	NOUN
ejpam-5458	322	2	is	be	AUX
ejpam-5458	322	3	negative	negative	ADJ
ejpam-5458	322	4	along	along	ADP
ejpam-5458	322	5	red	red	ADJ
ejpam-5458	322	6	parts	part	NOUN
ejpam-5458	322	7	of	of	ADP
ejpam-5458	322	8	curve	curve	NOUN
ejpam-5458	322	9	and	and	CCONJ
ejpam-5458	322	10	l2	l2	NOUN
ejpam-5458	322	11	is	be	AUX
ejpam-5458	322	12	positive	positive	ADJ
ejpam-5458	322	13	along	along	ADP
ejpam-5458	322	14	yellow	yellow	ADJ
ejpam-5458	322	15	parts	part	NOUN
ejpam-5458	322	16	of	of	ADP
ejpam-5458	322	17	curve	curve	NOUN
ejpam-5458	322	18	.	.	PUNCT
ejpam-5458	323	1	all	all	DET
ejpam-5458	323	2	calculations	calculation	NOUN
ejpam-5458	323	3	were	be	AUX
ejpam-5458	323	4	computed	compute	VERB
ejpam-5458	323	5	with	with	ADP
ejpam-5458	323	6	maple	maple	NOUN
ejpam-5458	323	7	then	then	ADV
ejpam-5458	323	8	matlab	matlab	PROPN
ejpam-5458	323	9	was	be	AUX
ejpam-5458	323	10	used	use	VERB
ejpam-5458	323	11	to	to	PART
ejpam-5458	323	12	plot	plot	VERB
ejpam-5458	323	13	the	the	DET
ejpam-5458	323	14	bifurcation	bifurcation	NOUN
ejpam-5458	323	15	diagram	diagram	NOUN
ejpam-5458	323	16	in	in	ADP
ejpam-5458	323	17	the	the	DET
ejpam-5458	323	18	parameter	parameter	NOUN
ejpam-5458	323	19	space	space	NOUN
ejpam-5458	323	20	(	(	PUNCT
ejpam-5458	323	21	cx	cx	PROPN
ejpam-5458	323	22	,	,	PUNCT
ejpam-5458	323	23	µ	µ	NOUN
ejpam-5458	323	24	)	)	PUNCT
ejpam-5458	323	25	.	.	PUNCT
ejpam-5458	324	1	in	in	ADP
ejpam-5458	324	2	figure	figure	NOUN
ejpam-5458	324	3	13(a	13(a	NUM
ejpam-5458	324	4	)	)	PUNCT
ejpam-5458	324	5	,	,	PUNCT
ejpam-5458	324	6	there	there	PRON
ejpam-5458	324	7	is	be	VERB
ejpam-5458	324	8	reasonable	reasonable	ADJ
ejpam-5458	324	9	agreement	agreement	NOUN
ejpam-5458	324	10	between	between	ADP
ejpam-5458	324	11	the	the	DET
ejpam-5458	324	12	xppaut	xppaut	PROPN
ejpam-5458	324	13	and	and	CCONJ
ejpam-5458	324	14	maple	maple	PROPN
ejpam-5458	324	15	calculations	calculation	NOUN
ejpam-5458	324	16	.	.	PUNCT
ejpam-5458	325	1	for	for	ADP
ejpam-5458	325	2	the	the	DET
ejpam-5458	325	3	hopf	hopf	ADJ
ejpam-5458	325	4	bifurcation	bifurcation	NOUN
ejpam-5458	325	5	curve	curve	NOUN
ejpam-5458	325	6	,	,	PUNCT
ejpam-5458	325	7	the	the	DET
ejpam-5458	325	8	maple	maple	NOUN
ejpam-5458	325	9	calculations	calculation	NOUN
ejpam-5458	325	10	are	be	AUX
ejpam-5458	325	11	closer	close	ADJ
ejpam-5458	325	12	to	to	ADP
ejpam-5458	325	13	the	the	DET
ejpam-5458	325	14	hopf	hopf	ADJ
ejpam-5458	325	15	line	line	NOUN
ejpam-5458	325	16	than	than	ADP
ejpam-5458	325	17	the	the	DET
ejpam-5458	325	18	xppaut	xppaut	PROPN
ejpam-5458	325	19	calculations	calculation	NOUN
ejpam-5458	325	20	which	which	PRON
ejpam-5458	325	21	are	be	AUX
ejpam-5458	325	22	presumably	presumably	ADV
ejpam-5458	325	23	more	more	ADV
ejpam-5458	325	24	accurate	accurate	ADJ
ejpam-5458	325	25	.	.	PUNCT
ejpam-5458	326	1	the	the	DET
ejpam-5458	326	2	curve	curve	NOUN
ejpam-5458	326	3	of	of	ADP
ejpam-5458	326	4	the	the	DET
ejpam-5458	326	5	saddle	saddle	NOUN
ejpam-5458	326	6	-	-	PUNCT
ejpam-5458	326	7	node	node	NOUN
ejpam-5458	326	8	bifurcation	bifurcation	NOUN
ejpam-5458	326	9	of	of	ADP
ejpam-5458	326	10	limit	limit	NOUN
ejpam-5458	326	11	cycles	cycle	NOUN
ejpam-5458	326	12	is	be	AUX
ejpam-5458	326	13	plausible	plausible	ADJ
ejpam-5458	326	14	by	by	ADP
ejpam-5458	326	15	using	use	VERB
ejpam-5458	326	16	maple	maple	NOUN
ejpam-5458	326	17	calculations	calculation	NOUN
ejpam-5458	326	18	.	.	PUNCT
ejpam-5458	327	1	this	this	DET
ejpam-5458	327	2	curve	curve	NOUN
ejpam-5458	327	3	ends	end	VERB
ejpam-5458	327	4	up	up	ADP
ejpam-5458	327	5	being	be	AUX
ejpam-5458	327	6	tangent	tangent	NOUN
ejpam-5458	327	7	to	to	ADP
ejpam-5458	327	8	the	the	DET
ejpam-5458	327	9	xppaut	xppaut	PROPN
ejpam-5458	327	10	curve	curve	NOUN
ejpam-5458	327	11	that	that	PRON
ejpam-5458	327	12	is	be	AUX
ejpam-5458	327	13	presumably	presumably	ADV
ejpam-5458	327	14	the	the	DET
ejpam-5458	327	15	correct	correct	ADJ
ejpam-5458	327	16	curve	curve	NOUN
ejpam-5458	327	17	,	,	PUNCT
ejpam-5458	327	18	and	and	CCONJ
ejpam-5458	327	19	then	then	ADV
ejpam-5458	327	20	they	they	PRON
ejpam-5458	327	21	meet	meet	VERB
ejpam-5458	327	22	at	at	ADP
ejpam-5458	327	23	the	the	DET
ejpam-5458	327	24	bautin	bautin	ADJ
ejpam-5458	327	25	bifurcation	bifurcation	NOUN
ejpam-5458	327	26	point	point	NOUN
ejpam-5458	327	27	.	.	PUNCT
ejpam-5458	328	1	in	in	ADP
ejpam-5458	328	2	figure	figure	NOUN
ejpam-5458	328	3	13(b	13(b	NUM
ejpam-5458	328	4	)	)	PUNCT
ejpam-5458	328	5	,	,	PUNCT
ejpam-5458	328	6	the	the	DET
ejpam-5458	328	7	maple	maple	NOUN
ejpam-5458	328	8	calculations	calculation	NOUN
ejpam-5458	328	9	appear	appear	VERB
ejpam-5458	328	10	to	to	PART
ejpam-5458	328	11	be	be	AUX
ejpam-5458	328	12	reasonable	reasonable	ADJ
ejpam-5458	328	13	for	for	ADP
ejpam-5458	328	14	the	the	DET
ejpam-5458	328	15	hopf	hopf	ADJ
ejpam-5458	328	16	curve	curve	NOUN
ejpam-5458	328	17	that	that	PRON
ejpam-5458	328	18	agrees	agree	VERB
ejpam-5458	328	19	very	very	ADV
ejpam-5458	328	20	well	well	ADV
ejpam-5458	328	21	with	with	ADP
ejpam-5458	328	22	xppaut	xppaut	PROPN
ejpam-5458	328	23	.	.	PUNCT
ejpam-5458	329	1	however	however	ADV
ejpam-5458	329	2	,	,	PUNCT
ejpam-5458	329	3	the	the	DET
ejpam-5458	329	4	maple	maple	NOUN
ejpam-5458	329	5	calculations	calculation	NOUN
ejpam-5458	329	6	of	of	ADP
ejpam-5458	329	7	saddle	saddle	NOUN
ejpam-5458	329	8	-	-	PUNCT
ejpam-5458	329	9	node	node	NOUN
ejpam-5458	329	10	bifurcation	bifurcation	NOUN
ejpam-5458	329	11	of	of	ADP
ejpam-5458	329	12	limit	limit	NOUN
ejpam-5458	329	13	cycles	cycle	NOUN
ejpam-5458	329	14	are	be	AUX
ejpam-5458	329	15	less	less	ADV
ejpam-5458	329	16	capable	capable	ADJ
ejpam-5458	329	17	of	of	ADP
ejpam-5458	329	18	resolving	resolve	VERB
ejpam-5458	329	19	their	their	PRON
ejpam-5458	329	20	behaviour	behaviour	NOUN
ejpam-5458	329	21	near	near	ADP
ejpam-5458	329	22	the	the	DET
ejpam-5458	329	23	second	second	ADJ
ejpam-5458	329	24	bautin	bautin	ADJ
ejpam-5458	329	25	bifurcation	bifurcation	NOUN
ejpam-5458	329	26	.	.	PUNCT
ejpam-5458	330	1	this	this	PRON
ejpam-5458	330	2	could	could	AUX
ejpam-5458	330	3	possibly	possibly	ADV
ejpam-5458	330	4	be	be	AUX
ejpam-5458	330	5	due	due	ADJ
ejpam-5458	330	6	to	to	ADP
ejpam-5458	330	7	the	the	DET
ejpam-5458	330	8	normal	normal	ADJ
ejpam-5458	330	9	form	form	NOUN
ejpam-5458	330	10	coefficients	coefficient	NOUN
ejpam-5458	330	11	being	be	AUX
ejpam-5458	330	12	much	much	ADV
ejpam-5458	330	13	smaller	small	ADJ
ejpam-5458	330	14	in	in	ADP
ejpam-5458	330	15	this	this	DET
ejpam-5458	330	16	case	case	NOUN
ejpam-5458	330	17	.	.	PUNCT
ejpam-5458	331	1	6	6	X
ejpam-5458	331	2	.	.	X
ejpam-5458	331	3	conclusion	conclusion	NOUN
ejpam-5458	331	4	these	these	DET
ejpam-5458	331	5	nonlinear	nonlinear	ADJ
ejpam-5458	331	6	oscillator	oscillator	NOUN
ejpam-5458	331	7	models	model	NOUN
ejpam-5458	331	8	is	be	AUX
ejpam-5458	331	9	the	the	DET
ejpam-5458	331	10	long	long	ADJ
ejpam-5458	331	11	timescale	timescale	NOUN
ejpam-5458	331	12	carbon	carbon	NOUN
ejpam-5458	331	13	cycle	cycle	NOUN
ejpam-5458	331	14	model	model	NOUN
ejpam-5458	331	15	of	of	ADP
ejpam-5458	331	16	rothman	rothman	PROPN
ejpam-5458	331	17	for	for	ADP
ejpam-5458	331	18	long	long	ADJ
ejpam-5458	331	19	term	term	NOUN
ejpam-5458	331	20	oscillations	oscillation	NOUN
ejpam-5458	331	21	in	in	ADP
ejpam-5458	331	22	the	the	DET
ejpam-5458	331	23	global	global	ADJ
ejpam-5458	331	24	marine	marine	PROPN
ejpam-5458	331	25	carbon	carbon	NOUN
ejpam-5458	331	26	cycle	cycle	NOUN
ejpam-5458	331	27	.	.	PUNCT
ejpam-5458	332	1	we	we	PRON
ejpam-5458	332	2	have	have	AUX
ejpam-5458	332	3	confirmed	confirm	VERB
ejpam-5458	332	4	the	the	DET
ejpam-5458	332	5	bifurcation	bifurcation	NOUN
ejpam-5458	332	6	behaviour	behaviour	NOUN
ejpam-5458	332	7	found	find	VERB
ejpam-5458	332	8	by	by	ADP
ejpam-5458	332	9	rothman	rothman	PROPN
ejpam-5458	333	1	[	[	X
ejpam-5458	333	2	12	12	NUM
ejpam-5458	333	3	]	]	PUNCT
ejpam-5458	333	4	using	use	VERB
ejpam-5458	333	5	analytical	analytical	ADJ
ejpam-5458	333	6	approximation	approximation	NOUN
ejpam-5458	333	7	.	.	PUNCT
ejpam-5458	334	1	in	in	ADP
ejpam-5458	334	2	section	section	NOUN
ejpam-5458	334	3	4	4	NUM
ejpam-5458	334	4	,	,	PUNCT
ejpam-5458	334	5	we	we	PRON
ejpam-5458	334	6	derive	derive	VERB
ejpam-5458	334	7	the	the	DET
ejpam-5458	334	8	normal	normal	ADJ
ejpam-5458	334	9	form	form	NOUN
ejpam-5458	334	10	of	of	ADP
ejpam-5458	334	11	hopf	hopf	ADJ
ejpam-5458	334	12	and	and	CCONJ
ejpam-5458	334	13	bautin	bautin	ADJ
ejpam-5458	334	14	bifurcations	bifurcation	NOUN
ejpam-5458	334	15	for	for	ADP
ejpam-5458	334	16	rothman	rothman	PROPN
ejpam-5458	334	17	’s	’s	PART
ejpam-5458	334	18	carbon	carbon	NOUN
ejpam-5458	334	19	cycle	cycle	NOUN
ejpam-5458	334	20	model	model	NOUN
ejpam-5458	334	21	(	(	PUNCT
ejpam-5458	334	22	7	7	NUM
ejpam-5458	334	23	)	)	PUNCT
ejpam-5458	334	24	.	.	PUNCT
ejpam-5458	335	1	our	our	PRON
ejpam-5458	335	2	analysis	analysis	NOUN
ejpam-5458	335	3	is	be	AUX
ejpam-5458	335	4	based	base	VERB
ejpam-5458	335	5	on	on	ADP
ejpam-5458	335	6	the	the	DET
ejpam-5458	335	7	normal	normal	ADJ
ejpam-5458	335	8	form	form	NOUN
ejpam-5458	335	9	theory	theory	NOUN
ejpam-5458	335	10	of	of	ADP
ejpam-5458	335	11	hopf	hopf	ADJ
ejpam-5458	335	12	and	and	CCONJ
ejpam-5458	335	13	bautin	bautin	ADJ
ejpam-5458	335	14	bifurcations	bifurcation	NOUN
ejpam-5458	335	15	(	(	PUNCT
ejpam-5458	335	16	see	see	VERB
ejpam-5458	335	17	subsection	subsection	NOUN
ejpam-5458	335	18	5.1	5.1	NUM
ejpam-5458	335	19	and	and	CCONJ
ejpam-5458	335	20	4.2	4.2	NUM
ejpam-5458	335	21	)	)	PUNCT
ejpam-5458	335	22	.	.	PUNCT
ejpam-5458	336	1	we	we	PRON
ejpam-5458	336	2	use	use	VERB
ejpam-5458	336	3	the	the	DET
ejpam-5458	336	4	conditions	condition	NOUN
ejpam-5458	336	5	and	and	CCONJ
ejpam-5458	336	6	highlight	highlight	VERB
ejpam-5458	336	7	the	the	DET
ejpam-5458	336	8	lyapunov	lyapunov	ADJ
ejpam-5458	336	9	coefficients	coefficient	NOUN
ejpam-5458	336	10	that	that	PRON
ejpam-5458	336	11	appear	appear	VERB
ejpam-5458	336	12	in	in	ADP
ejpam-5458	336	13	this	this	DET
ejpam-5458	336	14	normal	normal	ADJ
ejpam-5458	336	15	form	form	NOUN
ejpam-5458	336	16	.	.	PUNCT
ejpam-5458	337	1	we	we	PRON
ejpam-5458	337	2	use	use	VERB
ejpam-5458	337	3	theorems	theorem	NOUN
ejpam-5458	337	4	1	1	NUM
ejpam-5458	337	5	and	and	CCONJ
ejpam-5458	337	6	2	2	NUM
ejpam-5458	337	7	to	to	ADP
ejpam-5458	337	8	i.	i.	PROPN
ejpam-5458	337	9	alraddadi	alraddadi	PROPN
ejpam-5458	337	10	/	/	SYM
ejpam-5458	337	11	eur	eur	PROPN
ejpam-5458	337	12	.	.	PUNCT
ejpam-5458	338	1	j.	j.	PROPN
ejpam-5458	338	2	pure	pure	PROPN
ejpam-5458	338	3	appl	appl	PROPN
ejpam-5458	338	4	.	.	PROPN
ejpam-5458	338	5	math	math	PROPN
ejpam-5458	338	6	,	,	PUNCT
ejpam-5458	338	7	17	17	NUM
ejpam-5458	338	8	(	(	PUNCT
ejpam-5458	338	9	4	4	NUM
ejpam-5458	338	10	)	)	PUNCT
ejpam-5458	338	11	(	(	PUNCT
ejpam-5458	338	12	2024	2024	NUM
ejpam-5458	338	13	)	)	PUNCT
ejpam-5458	338	14	,	,	PUNCT
ejpam-5458	338	15	3708	3708	NUM
ejpam-5458	338	16	-	-	SYM
ejpam-5458	338	17	3729	3729	NUM
ejpam-5458	338	18	3727	3727	NUM
ejpam-5458	338	19	figure	figure	NOUN
ejpam-5458	338	20	12	12	NUM
ejpam-5458	338	21	:	:	PUNCT
ejpam-5458	338	22	bifurcation	bifurcation	NOUN
ejpam-5458	338	23	diagram	diagram	NOUN
ejpam-5458	338	24	for	for	ADP
ejpam-5458	338	25	(	(	PUNCT
ejpam-5458	338	26	7	7	X
ejpam-5458	338	27	)	)	PUNCT
ejpam-5458	338	28	computed	compute	VERB
ejpam-5458	338	29	with	with	ADP
ejpam-5458	338	30	xppaut	xppaut	PROPN
ejpam-5458	338	31	in	in	ADP
ejpam-5458	338	32	the	the	DET
ejpam-5458	338	33	parameter	parameter	NOUN
ejpam-5458	338	34	plane	plane	NOUN
ejpam-5458	338	35	(	(	PUNCT
ejpam-5458	338	36	cx	cx	PROPN
ejpam-5458	338	37	,	,	PUNCT
ejpam-5458	338	38	µ	µ	NOUN
ejpam-5458	338	39	)	)	PUNCT
ejpam-5458	338	40	.	.	PUNCT
ejpam-5458	339	1	hopf	hopf	ADJ
ejpam-5458	339	2	bifurcation	bifurcation	NOUN
ejpam-5458	339	3	for	for	ADP
ejpam-5458	339	4	(	(	PUNCT
ejpam-5458	339	5	7	7	NUM
ejpam-5458	339	6	)	)	PUNCT
ejpam-5458	339	7	is	be	AUX
ejpam-5458	339	8	represented	represent	VERB
ejpam-5458	339	9	by	by	ADP
ejpam-5458	339	10	blue	blue	ADJ
ejpam-5458	339	11	curve	curve	NOUN
ejpam-5458	339	12	.	.	PUNCT
ejpam-5458	340	1	two	two	NUM
ejpam-5458	340	2	branches	branch	NOUN
ejpam-5458	340	3	of	of	ADP
ejpam-5458	340	4	saddle	saddle	NOUN
ejpam-5458	340	5	-	-	PUNCT
ejpam-5458	340	6	node	node	NOUN
ejpam-5458	340	7	bifurcation	bifurcation	NOUN
ejpam-5458	340	8	of	of	ADP
ejpam-5458	340	9	limit	limit	NOUN
ejpam-5458	340	10	cycles	cycle	NOUN
ejpam-5458	340	11	for	for	ADP
ejpam-5458	340	12	(	(	PUNCT
ejpam-5458	340	13	7	7	X
ejpam-5458	340	14	)	)	PUNCT
ejpam-5458	340	15	are	be	AUX
ejpam-5458	340	16	represented	represent	VERB
ejpam-5458	340	17	by	by	ADP
ejpam-5458	340	18	black	black	ADJ
ejpam-5458	340	19	lines	line	NOUN
ejpam-5458	340	20	.	.	PUNCT
ejpam-5458	341	1	identify	identify	VERB
ejpam-5458	341	2	the	the	DET
ejpam-5458	341	3	topological	topological	ADJ
ejpam-5458	341	4	normal	normal	ADJ
ejpam-5458	341	5	form	form	NOUN
ejpam-5458	341	6	for	for	ADP
ejpam-5458	341	7	hopf	hopf	ADJ
ejpam-5458	341	8	and	and	CCONJ
ejpam-5458	341	9	bautin	bautin	ADJ
ejpam-5458	341	10	bifurcations	bifurcation	NOUN
ejpam-5458	341	11	.	.	PUNCT
ejpam-5458	342	1	from	from	ADP
ejpam-5458	342	2	our	our	PRON
ejpam-5458	342	3	results	result	NOUN
ejpam-5458	342	4	in	in	ADP
ejpam-5458	342	5	this	this	DET
ejpam-5458	342	6	subsection	subsection	NOUN
ejpam-5458	342	7	,	,	PUNCT
ejpam-5458	342	8	we	we	PRON
ejpam-5458	342	9	are	be	AUX
ejpam-5458	342	10	able	able	ADJ
ejpam-5458	342	11	to	to	PART
ejpam-5458	342	12	identify	identify	VERB
ejpam-5458	342	13	the	the	DET
ejpam-5458	342	14	bautin	bautin	ADJ
ejpam-5458	342	15	bifurcation	bifurcation	NOUN
ejpam-5458	342	16	and	and	CCONJ
ejpam-5458	342	17	classify	classify	VERB
ejpam-5458	342	18	its	its	PRON
ejpam-5458	342	19	criticality	criticality	NOUN
ejpam-5458	342	20	by	by	ADP
ejpam-5458	342	21	finding	find	VERB
ejpam-5458	342	22	the	the	DET
ejpam-5458	342	23	appropriate	appropriate	ADJ
ejpam-5458	342	24	coefficients	coefficient	NOUN
ejpam-5458	342	25	in	in	ADP
ejpam-5458	342	26	the	the	DET
ejpam-5458	342	27	normal	normal	ADJ
ejpam-5458	342	28	form	form	NOUN
ejpam-5458	342	29	.	.	PUNCT
ejpam-5458	343	1	we	we	PRON
ejpam-5458	343	2	review	review	VERB
ejpam-5458	343	3	the	the	DET
ejpam-5458	343	4	technique	technique	NOUN
ejpam-5458	343	5	for	for	ADP
ejpam-5458	343	6	computing	compute	VERB
ejpam-5458	343	7	lyapunov	lyapunov	ADJ
ejpam-5458	343	8	coefficients	coefficient	NOUN
ejpam-5458	343	9	.	.	PUNCT
ejpam-5458	344	1	we	we	PRON
ejpam-5458	344	2	use	use	VERB
ejpam-5458	344	3	maple	maple	NOUN
ejpam-5458	344	4	to	to	PART
ejpam-5458	344	5	compute	compute	VERB
ejpam-5458	344	6	the	the	DET
ejpam-5458	344	7	first	first	ADJ
ejpam-5458	344	8	and	and	CCONJ
ejpam-5458	344	9	second	second	ADJ
ejpam-5458	344	10	lyapunov	lyapunov	ADJ
ejpam-5458	344	11	coefficients	coefficient	VERB
ejpam-5458	344	12	l1	l1	PROPN
ejpam-5458	344	13	and	and	CCONJ
ejpam-5458	344	14	l2	l2	NOUN
ejpam-5458	344	15	in	in	ADP
ejpam-5458	344	16	the	the	DET
ejpam-5458	344	17	normal	normal	ADJ
ejpam-5458	344	18	form	form	NOUN
ejpam-5458	344	19	at	at	ADP
ejpam-5458	344	20	a	a	DET
ejpam-5458	344	21	bifurcation	bifurcation	NOUN
ejpam-5458	344	22	point	point	NOUN
ejpam-5458	344	23	where	where	SCONJ
ejpam-5458	344	24	l0	l0	NOUN
ejpam-5458	344	25	=	=	NOUN
ejpam-5458	344	26	0	0	PROPN
ejpam-5458	344	27	.	.	PUNCT
ejpam-5458	345	1	the	the	DET
ejpam-5458	345	2	type	type	NOUN
ejpam-5458	345	3	of	of	ADP
ejpam-5458	345	4	hopf	hopf	ADJ
ejpam-5458	345	5	bifurcation	bifurcation	NOUN
ejpam-5458	345	6	corresponds	correspond	VERB
ejpam-5458	345	7	to	to	ADP
ejpam-5458	345	8	the	the	DET
ejpam-5458	345	9	sign	sign	NOUN
ejpam-5458	345	10	of	of	ADP
ejpam-5458	345	11	the	the	DET
ejpam-5458	345	12	first	first	ADJ
ejpam-5458	345	13	lyapunov	lyapunov	ADJ
ejpam-5458	345	14	coefficient	coefficient	NOUN
ejpam-5458	345	15	l1	l1	PROPN
ejpam-5458	345	16	.	.	PUNCT
ejpam-5458	346	1	in	in	ADP
ejpam-5458	346	2	figure	figure	NOUN
ejpam-5458	346	3	11	11	NUM
ejpam-5458	346	4	,	,	PUNCT
ejpam-5458	346	5	we	we	PRON
ejpam-5458	346	6	highlight	highlight	VERB
ejpam-5458	346	7	the	the	DET
ejpam-5458	346	8	red	red	ADJ
ejpam-5458	346	9	curve	curve	NOUN
ejpam-5458	346	10	(	(	PUNCT
ejpam-5458	346	11	l1	l1	PROPN
ejpam-5458	346	12	<	<	X
ejpam-5458	346	13	0	0	NUM
ejpam-5458	346	14	)	)	PUNCT
ejpam-5458	346	15	and	and	CCONJ
ejpam-5458	346	16	the	the	DET
ejpam-5458	346	17	blue	blue	ADJ
ejpam-5458	346	18	curve	curve	NOUN
ejpam-5458	346	19	(	(	PUNCT
ejpam-5458	346	20	l1	l1	PROPN
ejpam-5458	346	21	>	>	X
ejpam-5458	346	22	0	0	NUM
ejpam-5458	346	23	)	)	PUNCT
ejpam-5458	346	24	correspond	correspond	VERB
ejpam-5458	346	25	to	to	ADP
ejpam-5458	346	26	the	the	DET
ejpam-5458	346	27	supercritical	supercritical	ADJ
ejpam-5458	346	28	hopf	hopf	ADJ
ejpam-5458	346	29	bifurcation	bifurcation	NOUN
ejpam-5458	346	30	and	and	CCONJ
ejpam-5458	346	31	the	the	DET
ejpam-5458	346	32	subcritical	subcritical	ADJ
ejpam-5458	346	33	hopf	hopf	ADJ
ejpam-5458	346	34	bifurcation	bifurcation	NOUN
ejpam-5458	346	35	respectively	respectively	ADV
ejpam-5458	346	36	.	.	PUNCT
ejpam-5458	347	1	the	the	DET
ejpam-5458	347	2	bautin	bautin	ADJ
ejpam-5458	347	3	bifurcation	bifurcation	NOUN
ejpam-5458	347	4	points	point	NOUN
ejpam-5458	347	5	are	be	AUX
ejpam-5458	347	6	represented	represent	VERB
ejpam-5458	347	7	by	by	ADP
ejpam-5458	347	8	black	black	ADJ
ejpam-5458	347	9	points	point	NOUN
ejpam-5458	347	10	at	at	ADP
ejpam-5458	347	11	l1	l1	PROPN
ejpam-5458	347	12	=	=	SYM
ejpam-5458	347	13	0	0	PROPN
ejpam-5458	347	14	,	,	PUNCT
ejpam-5458	347	15	and	and	CCONJ
ejpam-5458	347	16	calculate	calculate	VERB
ejpam-5458	347	17	the	the	DET
ejpam-5458	347	18	sign	sign	NOUN
ejpam-5458	347	19	of	of	ADP
ejpam-5458	347	20	l2	l2	NOUN
ejpam-5458	347	21	at	at	ADP
ejpam-5458	347	22	these	these	DET
ejpam-5458	347	23	points	point	NOUN
ejpam-5458	347	24	to	to	PART
ejpam-5458	347	25	determine	determine	VERB
ejpam-5458	347	26	the	the	DET
ejpam-5458	347	27	bautin	bautin	ADJ
ejpam-5458	347	28	bifurcation	bifurcation	NOUN
ejpam-5458	347	29	scenario	scenario	NOUN
ejpam-5458	347	30	.	.	PUNCT
ejpam-5458	348	1	the	the	DET
ejpam-5458	348	2	main	main	ADJ
ejpam-5458	348	3	results	result	NOUN
ejpam-5458	348	4	are	be	AUX
ejpam-5458	348	5	compared	compare	VERB
ejpam-5458	348	6	in	in	ADP
ejpam-5458	348	7	figure	figure	NOUN
ejpam-5458	348	8	13	13	NUM
ejpam-5458	348	9	,	,	PUNCT
ejpam-5458	348	10	showing	show	VERB
ejpam-5458	348	11	the	the	DET
ejpam-5458	348	12	two	two	NUM
ejpam-5458	348	13	-	-	PUNCT
ejpam-5458	348	14	parameter	parameter	NOUN
ejpam-5458	348	15	bifurcation	bifurcation	NOUN
ejpam-5458	348	16	diagrams	diagram	NOUN
ejpam-5458	348	17	of	of	ADP
ejpam-5458	348	18	rothman	rothman	PROPN
ejpam-5458	348	19	’s	’s	PART
ejpam-5458	348	20	carbon	carbon	NOUN
ejpam-5458	348	21	cycle	cycle	NOUN
ejpam-5458	348	22	model	model	NOUN
ejpam-5458	348	23	(	(	PUNCT
ejpam-5458	348	24	7	7	NUM
ejpam-5458	348	25	)	)	PUNCT
ejpam-5458	348	26	,	,	PUNCT
ejpam-5458	348	27	with	with	ADP
ejpam-5458	348	28	one	one	NUM
ejpam-5458	348	29	of	of	ADP
ejpam-5458	348	30	the	the	DET
ejpam-5458	348	31	diagrams	diagram	NOUN
ejpam-5458	348	32	computed	compute	VERB
ejpam-5458	348	33	with	with	ADP
ejpam-5458	348	34	maple	maple	NOUN
ejpam-5458	348	35	and	and	CCONJ
ejpam-5458	348	36	the	the	DET
ejpam-5458	348	37	other	other	ADJ
ejpam-5458	348	38	with	with	ADP
ejpam-5458	348	39	xppaut	xppaut	PROPN
ejpam-5458	348	40	.	.	PUNCT
ejpam-5458	349	1	we	we	PRON
ejpam-5458	349	2	use	use	VERB
ejpam-5458	349	3	maple	maple	NOUN
ejpam-5458	349	4	to	to	PART
ejpam-5458	349	5	compute	compute	VERB
ejpam-5458	349	6	l2	l2	NOUN
ejpam-5458	349	7	at	at	ADP
ejpam-5458	349	8	both	both	DET
ejpam-5458	349	9	points	point	NOUN
ejpam-5458	349	10	and	and	CCONJ
ejpam-5458	349	11	find	find	VERB
ejpam-5458	349	12	its	its	PRON
ejpam-5458	349	13	negative	negative	NOUN
ejpam-5458	349	14	for	for	SCONJ
ejpam-5458	349	15	the	the	DET
ejpam-5458	349	16	parameters	parameter	NOUN
ejpam-5458	349	17	used	use	VERB
ejpam-5458	349	18	,	,	PUNCT
ejpam-5458	349	19	which	which	PRON
ejpam-5458	349	20	confirms	confirm	VERB
ejpam-5458	349	21	that	that	SCONJ
ejpam-5458	349	22	both	both	PRON
ejpam-5458	349	23	of	of	ADP
ejpam-5458	349	24	the	the	DET
ejpam-5458	349	25	bautin	bautin	ADJ
ejpam-5458	349	26	bifurcations	bifurcation	NOUN
ejpam-5458	349	27	are	be	AUX
ejpam-5458	349	28	of	of	ADP
ejpam-5458	349	29	supercritical	supercritical	ADJ
ejpam-5458	349	30	type	type	NOUN
ejpam-5458	349	31	,	,	PUNCT
ejpam-5458	349	32	then	then	ADV
ejpam-5458	349	33	we	we	PRON
ejpam-5458	349	34	confirm	confirm	VERB
ejpam-5458	349	35	this	this	PRON
ejpam-5458	349	36	using	use	VERB
ejpam-5458	349	37	xppaut	xppaut	PROPN
ejpam-5458	349	38	.	.	PUNCT
ejpam-5458	350	1	also	also	ADV
ejpam-5458	350	2	,	,	PUNCT
ejpam-5458	350	3	we	we	PRON
ejpam-5458	350	4	attempt	attempt	VERB
ejpam-5458	350	5	to	to	PART
ejpam-5458	350	6	approximate	approximate	VERB
ejpam-5458	350	7	the	the	DET
ejpam-5458	350	8	location	location	NOUN
ejpam-5458	350	9	of	of	ADP
ejpam-5458	350	10	the	the	DET
ejpam-5458	350	11	saddle	saddle	NOUN
ejpam-5458	350	12	-	-	PUNCT
ejpam-5458	350	13	node	node	NOUN
ejpam-5458	350	14	bifurcation	bifurcation	NOUN
ejpam-5458	350	15	of	of	ADP
ejpam-5458	350	16	limit	limit	NOUN
ejpam-5458	350	17	cycles	cycle	NOUN
ejpam-5458	350	18	.	.	PUNCT
ejpam-5458	351	1	we	we	PRON
ejpam-5458	351	2	illustrate	illustrate	VERB
ejpam-5458	351	3	the	the	DET
ejpam-5458	351	4	approximation	approximation	NOUN
ejpam-5458	351	5	using	use	VERB
ejpam-5458	351	6	the	the	DET
ejpam-5458	351	7	two	two	NUM
ejpam-5458	351	8	methods	method	NOUN
ejpam-5458	351	9	in	in	ADP
ejpam-5458	351	10	figure	figure	NOUN
ejpam-5458	351	11	13	13	NUM
ejpam-5458	351	12	.	.	PUNCT
ejpam-5458	352	1	we	we	PRON
ejpam-5458	352	2	compute	compute	VERB
ejpam-5458	352	3	the	the	DET
ejpam-5458	352	4	hopf	hopf	ADJ
ejpam-5458	352	5	bifurcation	bifurcation	NOUN
ejpam-5458	352	6	and	and	CCONJ
ejpam-5458	352	7	saddle	saddle	NOUN
ejpam-5458	352	8	-	-	PUNCT
ejpam-5458	352	9	node	node	NOUN
ejpam-5458	352	10	bifurcation	bifurcation	NOUN
ejpam-5458	352	11	of	of	ADP
ejpam-5458	352	12	limit	limit	NOUN
ejpam-5458	352	13	cycles	cycle	NOUN
ejpam-5458	352	14	using	use	VERB
ejpam-5458	352	15	xppaut	xppaut	PROPN
ejpam-5458	352	16	and	and	CCONJ
ejpam-5458	352	17	also	also	ADV
ejpam-5458	352	18	using	use	VERB
ejpam-5458	352	19	the	the	DET
ejpam-5458	352	20	value	value	NOUN
ejpam-5458	352	21	of	of	ADP
ejpam-5458	352	22	l2	l2	NOUN
ejpam-5458	352	23	computed	compute	VERB
ejpam-5458	352	24	using	use	VERB
ejpam-5458	352	25	maple	maple	NOUN
ejpam-5458	352	26	,	,	PUNCT
ejpam-5458	352	27	and	and	CCONJ
ejpam-5458	352	28	then	then	ADV
ejpam-5458	352	29	we	we	PRON
ejpam-5458	352	30	find	find	VERB
ejpam-5458	352	31	that	that	SCONJ
ejpam-5458	352	32	for	for	ADP
ejpam-5458	352	33	one	one	NUM
ejpam-5458	352	34	of	of	ADP
ejpam-5458	352	35	these	these	PRON
ejpam-5458	352	36	,	,	PUNCT
ejpam-5458	352	37	the	the	DET
ejpam-5458	352	38	saddle	saddle	NOUN
ejpam-5458	352	39	-	-	PUNCT
ejpam-5458	352	40	node	node	NOUN
ejpam-5458	352	41	bifurcation	bifurcation	NOUN
ejpam-5458	352	42	of	of	ADP
ejpam-5458	352	43	limit	limit	NOUN
ejpam-5458	352	44	cycles	cycle	NOUN
ejpam-5458	352	45	was	be	AUX
ejpam-5458	352	46	approximated	approximate	VERB
ejpam-5458	352	47	reasonably	reasonably	ADV
ejpam-5458	352	48	well	well	ADV
ejpam-5458	352	49	in	in	ADP
ejpam-5458	352	50	maple	maple	NOUN
ejpam-5458	352	51	using	use	VERB
ejpam-5458	352	52	the	the	DET
ejpam-5458	352	53	fifth	fifth	ADJ
ejpam-5458	352	54	order	order	NOUN
ejpam-5458	352	55	normal	normal	ADJ
ejpam-5458	352	56	form	form	NOUN
ejpam-5458	352	57	for	for	ADP
ejpam-5458	352	58	one	one	NUM
ejpam-5458	352	59	of	of	ADP
ejpam-5458	352	60	them	they	PRON
ejpam-5458	352	61	(	(	PUNCT
ejpam-5458	352	62	the	the	DET
ejpam-5458	352	63	saddle	saddle	NOUN
ejpam-5458	352	64	-	-	PUNCT
ejpam-5458	352	65	node	node	NOUN
ejpam-5458	352	66	bifurcation	bifurcation	NOUN
ejpam-5458	352	67	of	of	ADP
ejpam-5458	352	68	limit	limit	NOUN
ejpam-5458	352	69	cycles	cycle	NOUN
ejpam-5458	352	70	)	)	PUNCT
ejpam-5458	352	71	but	but	CCONJ
ejpam-5458	352	72	not	not	PART
ejpam-5458	352	73	the	the	DET
ejpam-5458	352	74	other	other	ADJ
ejpam-5458	352	75	.	.	PUNCT
ejpam-5458	353	1	references	reference	NOUN
ejpam-5458	353	2	3728	3728	NUM
ejpam-5458	353	3	figure	figure	NOUN
ejpam-5458	353	4	13	13	NUM
ejpam-5458	353	5	:	:	PUNCT
ejpam-5458	353	6	this	this	DET
ejpam-5458	353	7	shows	show	VERB
ejpam-5458	353	8	(	(	PUNCT
ejpam-5458	353	9	cx	cx	PROPN
ejpam-5458	353	10	,	,	PUNCT
ejpam-5458	353	11	µ	µ	NOUN
ejpam-5458	353	12	)	)	PUNCT
ejpam-5458	353	13	two	two	NUM
ejpam-5458	353	14	-	-	PUNCT
ejpam-5458	353	15	parameter	parameter	NOUN
ejpam-5458	353	16	bifurcation	bifurcation	NOUN
ejpam-5458	353	17	diagrams	diagram	NOUN
ejpam-5458	353	18	of	of	ADP
ejpam-5458	353	19	(	(	PUNCT
ejpam-5458	353	20	7	7	NUM
ejpam-5458	353	21	)	)	PUNCT
ejpam-5458	353	22	.	.	PUNCT
ejpam-5458	354	1	left	leave	VERB
ejpam-5458	354	2	(	(	PUNCT
ejpam-5458	354	3	a	a	NOUN
ejpam-5458	354	4	)	)	PUNCT
ejpam-5458	354	5	and	and	CCONJ
ejpam-5458	354	6	right	right	ADJ
ejpam-5458	354	7	(	(	PUNCT
ejpam-5458	354	8	b	b	NOUN
ejpam-5458	354	9	)	)	PUNCT
ejpam-5458	354	10	show	show	VERB
ejpam-5458	354	11	curves	curve	NOUN
ejpam-5458	354	12	of	of	ADP
ejpam-5458	354	13	bifurcations	bifurcation	NOUN
ejpam-5458	354	14	of	of	ADP
ejpam-5458	354	15	periodic	periodic	ADJ
ejpam-5458	354	16	orbits	orbit	NOUN
ejpam-5458	354	17	near	near	ADP
ejpam-5458	354	18	the	the	DET
ejpam-5458	354	19	bautin	bautin	ADJ
ejpam-5458	354	20	bifurcation	bifurcation	NOUN
ejpam-5458	354	21	(	(	PUNCT
ejpam-5458	354	22	indicated	indicate	VERB
ejpam-5458	354	23	by	by	ADP
ejpam-5458	354	24	the	the	DET
ejpam-5458	354	25	red	red	PROPN
ejpam-5458	354	26	star	star	PROPN
ejpam-5458	354	27	)	)	PUNCT
ejpam-5458	354	28	.	.	PUNCT
ejpam-5458	355	1	these	these	DET
ejpam-5458	355	2	bifurcation	bifurcation	NOUN
ejpam-5458	355	3	curves	curve	NOUN
ejpam-5458	355	4	are	be	AUX
ejpam-5458	355	5	computed	compute	VERB
ejpam-5458	355	6	using	use	VERB
ejpam-5458	355	7	two	two	NUM
ejpam-5458	355	8	methods	method	NOUN
ejpam-5458	355	9	:	:	PUNCT
ejpam-5458	355	10	maple	maple	NOUN
ejpam-5458	355	11	and	and	CCONJ
ejpam-5458	355	12	xppaut	xppaut	PROPN
ejpam-5458	355	13	.	.	PUNCT
ejpam-5458	356	1	hopf	hopf	ADJ
ejpam-5458	356	2	bifurcation	bifurcation	NOUN
ejpam-5458	356	3	and	and	CCONJ
ejpam-5458	356	4	saddle	saddle	NOUN
ejpam-5458	356	5	-	-	PUNCT
ejpam-5458	356	6	node	node	NOUN
ejpam-5458	356	7	bifurcation	bifurcation	NOUN
ejpam-5458	356	8	of	of	ADP
ejpam-5458	356	9	limit	limit	NOUN
ejpam-5458	356	10	cycles	cycle	NOUN
ejpam-5458	356	11	are	be	AUX
ejpam-5458	356	12	computed	compute	VERB
ejpam-5458	356	13	using	use	VERB
ejpam-5458	356	14	maple	maple	NOUN
ejpam-5458	356	15	and	and	CCONJ
ejpam-5458	356	16	represented	represent	VERB
ejpam-5458	356	17	by	by	ADP
ejpam-5458	356	18	dashed	dash	VERB
ejpam-5458	356	19	(	(	PUNCT
ejpam-5458	356	20	blue	blue	ADJ
ejpam-5458	356	21	)	)	PUNCT
ejpam-5458	356	22	and	and	CCONJ
ejpam-5458	356	23	red	red	ADJ
ejpam-5458	356	24	lines	line	NOUN
ejpam-5458	356	25	.	.	PUNCT
ejpam-5458	357	1	from	from	ADP
ejpam-5458	357	2	the	the	DET
ejpam-5458	357	3	xppaut	xppaut	PROPN
ejpam-5458	357	4	calculations	calculation	NOUN
ejpam-5458	357	5	,	,	PUNCT
ejpam-5458	357	6	the	the	DET
ejpam-5458	357	7	hopf	hopf	ADJ
ejpam-5458	357	8	bifurcation	bifurcation	NOUN
ejpam-5458	357	9	and	and	CCONJ
ejpam-5458	357	10	saddle	saddle	NOUN
ejpam-5458	357	11	-	-	PUNCT
ejpam-5458	357	12	node	node	NOUN
ejpam-5458	357	13	bifurcation	bifurcation	NOUN
ejpam-5458	357	14	of	of	ADP
ejpam-5458	357	15	limit	limit	NOUN
ejpam-5458	357	16	cycles	cycle	NOUN
ejpam-5458	357	17	are	be	AUX
ejpam-5458	357	18	respectively	respectively	ADV
ejpam-5458	357	19	shown	show	VERB
ejpam-5458	357	20	using	use	VERB
ejpam-5458	357	21	blue	blue	ADJ
ejpam-5458	357	22	and	and	CCONJ
ejpam-5458	357	23	red	red	ADJ
ejpam-5458	357	24	circles	circle	NOUN
ejpam-5458	357	25	.	.	PUNCT
ejpam-5458	358	1	conflict	conflict	NOUN
ejpam-5458	358	2	of	of	ADP
ejpam-5458	358	3	interest	interest	NOUN
ejpam-5458	358	4	:	:	PUNCT
ejpam-5458	358	5	the	the	DET
ejpam-5458	358	6	authors	author	NOUN
ejpam-5458	358	7	of	of	ADP
ejpam-5458	358	8	the	the	DET
ejpam-5458	358	9	paper	paper	NOUN
ejpam-5458	358	10	state	state	NOUN
ejpam-5458	358	11	that	that	SCONJ
ejpam-5458	358	12	there	there	PRON
ejpam-5458	358	13	is	be	VERB
ejpam-5458	358	14	no	no	DET
ejpam-5458	358	15	conflict	conflict	NOUN
ejpam-5458	358	16	of	of	ADP
ejpam-5458	358	17	interest	interest	NOUN
ejpam-5458	358	18	.	.	PUNCT
ejpam-5458	359	1	data	datum	NOUN
ejpam-5458	359	2	availability	availability	NOUN
ejpam-5458	359	3	statement	statement	NOUN
ejpam-5458	359	4	:	:	PUNCT
ejpam-5458	359	5	all	all	DET
ejpam-5458	359	6	data	datum	NOUN
ejpam-5458	359	7	generated	generate	VERB
ejpam-5458	359	8	or	or	CCONJ
ejpam-5458	359	9	analyzed	analyze	VERB
ejpam-5458	359	10	during	during	ADP
ejpam-5458	359	11	the	the	DET
ejpam-5458	359	12	research	research	NOUN
ejpam-5458	359	13	investigation	investigation	NOUN
ejpam-5458	359	14	have	have	AUX
ejpam-5458	359	15	been	be	AUX
ejpam-5458	359	16	included	include	VERB
ejpam-5458	359	17	in	in	ADP
ejpam-5458	359	18	the	the	DET
ejpam-5458	359	19	paper	paper	NOUN
ejpam-5458	359	20	.	.	PUNCT
ejpam-5458	360	1	references	reference	NOUN
ejpam-5458	360	2	[	[	X
ejpam-5458	360	3	1	1	NUM
ejpam-5458	360	4	]	]	X
ejpam-5458	360	5	michel	michel	PROPN
ejpam-5458	360	6	crucifix	crucifix	PROPN
ejpam-5458	360	7	.	.	PUNCT
ejpam-5458	361	1	oscillators	oscillator	NOUN
ejpam-5458	361	2	and	and	CCONJ
ejpam-5458	361	3	relaxation	relaxation	NOUN
ejpam-5458	361	4	phenomena	phenomenon	NOUN
ejpam-5458	361	5	in	in	ADP
ejpam-5458	361	6	pleistocene	pleistocene	PROPN
ejpam-5458	361	7	climate	climate	NOUN
ejpam-5458	361	8	theory	theory	NOUN
ejpam-5458	361	9	.	.	PUNCT
ejpam-5458	362	1	trans	trans	PROPN
ejpam-5458	362	2	.	.	PUNCT
ejpam-5458	362	3	r.	r.	PROPN
ejpam-5458	362	4	soc	soc	PROPN
ejpam-5458	362	5	.	.	PUNCT
ejpam-5458	363	1	a	a	DET
ejpam-5458	363	2	,	,	PUNCT
ejpam-5458	363	3	370:1140–1165	370:1140–1165	NUM
ejpam-5458	363	4	,	,	PUNCT
ejpam-5458	363	5	2012	2012	NUM
ejpam-5458	363	6	.	.	PUNCT
ejpam-5458	364	1	[	[	X
ejpam-5458	364	2	2	2	NUM
ejpam-5458	364	3	]	]	PUNCT
ejpam-5458	364	4	bard	bard	ADJ
ejpam-5458	364	5	ermentrout	ermentrout	NOUN
ejpam-5458	364	6	.	.	PUNCT
ejpam-5458	365	1	simulating	simulate	VERB
ejpam-5458	365	2	,	,	PUNCT
ejpam-5458	365	3	analyzing	analyzing	NOUN
ejpam-5458	365	4	,	,	PUNCT
ejpam-5458	365	5	and	and	CCONJ
ejpam-5458	365	6	animating	animate	VERB
ejpam-5458	365	7	dynamical	dynamical	ADJ
ejpam-5458	365	8	systems	system	NOUN
ejpam-5458	365	9	:	:	PUNCT
ejpam-5458	365	10	a	a	DET
ejpam-5458	365	11	guide	guide	NOUN
ejpam-5458	365	12	to	to	ADP
ejpam-5458	365	13	xppaut	xppaut	PRON
ejpam-5458	365	14	for	for	ADP
ejpam-5458	365	15	researchers	researcher	NOUN
ejpam-5458	365	16	and	and	CCONJ
ejpam-5458	365	17	students	student	NOUN
ejpam-5458	365	18	.	.	PUNCT
ejpam-5458	366	1	siam	siam	PROPN
ejpam-5458	366	2	,	,	PUNCT
ejpam-5458	366	3	2002	2002	NUM
ejpam-5458	366	4	.	.	PUNCT
ejpam-5458	367	1	[	[	X
ejpam-5458	367	2	3	3	NUM
ejpam-5458	367	3	]	]	X
ejpam-5458	367	4	yu	yu	PROPN
ejpam-5458	367	5	.	.	PUNCT
ejpam-5458	367	6	a.	a.	PROPN
ejpam-5458	367	7	kuznetsov	kuznetsov	PROPN
ejpam-5458	367	8	.	.	PUNCT
ejpam-5458	368	1	numerical	numerical	PROPN
ejpam-5458	368	2	normalization	normalization	PROPN
ejpam-5458	368	3	techniques	technique	NOUN
ejpam-5458	368	4	for	for	ADP
ejpam-5458	368	5	all	all	DET
ejpam-5458	368	6	codim	codim	NOUN
ejpam-5458	368	7	2	2	NUM
ejpam-5458	368	8	bifurcations	bifurcation	NOUN
ejpam-5458	368	9	of	of	ADP
ejpam-5458	368	10	equilibria	equilibrium	NOUN
ejpam-5458	368	11	in	in	ADP
ejpam-5458	368	12	ode	ode	PROPN
ejpam-5458	368	13	’s	’s	NOUN
ejpam-5458	368	14	.	.	PUNCT
ejpam-5458	369	1	siam	siam	PROPN
ejpam-5458	369	2	journal	journal	PROPN
ejpam-5458	369	3	on	on	ADP
ejpam-5458	369	4	numerical	numerical	ADJ
ejpam-5458	369	5	analysis	analysis	NOUN
ejpam-5458	369	6	,	,	PUNCT
ejpam-5458	369	7	36(4):1104–1124	36(4):1104–1124	NUM
ejpam-5458	369	8	,	,	PUNCT
ejpam-5458	369	9	1999	1999	NUM
ejpam-5458	369	10	.	.	PUNCT
ejpam-5458	370	1	references	reference	NOUN
ejpam-5458	370	2	3729	3729	NUM
ejpam-5458	370	3	[	[	X
ejpam-5458	370	4	4	4	X
ejpam-5458	370	5	]	]	PUNCT
ejpam-5458	370	6	yuri	yuri	PROPN
ejpam-5458	370	7	a.	a.	PROPN
ejpam-5458	370	8	kuznetsov	kuznetsov	PROPN
ejpam-5458	370	9	.	.	PUNCT
ejpam-5458	371	1	elements	element	NOUN
ejpam-5458	371	2	of	of	ADP
ejpam-5458	371	3	applied	apply	VERB
ejpam-5458	371	4	bifurcation	bifurcation	NOUN
ejpam-5458	371	5	theory	theory	NOUN
ejpam-5458	371	6	,	,	PUNCT
ejpam-5458	371	7	second	second	ADJ
ejpam-5458	371	8	edition	edition	NOUN
ejpam-5458	371	9	.	.	PUNCT
ejpam-5458	372	1	library	library	PROPN
ejpam-5458	372	2	,	,	PUNCT
ejpam-5458	372	3	page	page	NOUN
ejpam-5458	372	4	591	591	NUM
ejpam-5458	372	5	,	,	PUNCT
ejpam-5458	372	6	1998	1998	NUM
ejpam-5458	372	7	.	.	PUNCT
ejpam-5458	373	1	[	[	X
ejpam-5458	373	2	5	5	X
ejpam-5458	373	3	]	]	X
ejpam-5458	373	4	timothy	timothy	PROPN
ejpam-5458	373	5	m.	m.	PROPN
ejpam-5458	373	6	lenton	lenton	PROPN
ejpam-5458	373	7	,	,	PUNCT
ejpam-5458	373	8	hermann	hermann	PROPN
ejpam-5458	373	9	held	hold	VERB
ejpam-5458	373	10	,	,	PUNCT
ejpam-5458	373	11	elmar	elmar	PROPN
ejpam-5458	373	12	kriegler	kriegler	PROPN
ejpam-5458	373	13	,	,	PUNCT
ejpam-5458	373	14	jim	jim	PROPN
ejpam-5458	373	15	w.	w.	PROPN
ejpam-5458	373	16	hall	hall	PROPN
ejpam-5458	373	17	,	,	PUNCT
ejpam-5458	373	18	wolfgang	wolfgang	PROPN
ejpam-5458	373	19	lucht	lucht	PROPN
ejpam-5458	373	20	,	,	PUNCT
ejpam-5458	373	21	stefan	stefan	PROPN
ejpam-5458	373	22	rahmstorf	rahmstorf	PROPN
ejpam-5458	373	23	,	,	PUNCT
ejpam-5458	373	24	and	and	CCONJ
ejpam-5458	373	25	hans	hans	PROPN
ejpam-5458	373	26	joachim	joachim	PROPN
ejpam-5458	373	27	schellnhuber	schellnhuber	PROPN
ejpam-5458	373	28	.	.	PUNCT
ejpam-5458	374	1	tipping	tip	VERB
ejpam-5458	374	2	elements	element	NOUN
ejpam-5458	374	3	in	in	ADP
ejpam-5458	374	4	the	the	DET
ejpam-5458	374	5	earth	earth	NOUN
ejpam-5458	374	6	’s	’s	PART
ejpam-5458	374	7	climate	climate	NOUN
ejpam-5458	374	8	system	system	NOUN
ejpam-5458	374	9	.	.	PUNCT
ejpam-5458	375	1	proceedings	proceeding	NOUN
ejpam-5458	375	2	of	of	ADP
ejpam-5458	375	3	the	the	DET
ejpam-5458	375	4	national	national	PROPN
ejpam-5458	375	5	academy	academy	PROPN
ejpam-5458	375	6	of	of	ADP
ejpam-5458	375	7	sciences	sciences	PROPN
ejpam-5458	375	8	,	,	PUNCT
ejpam-5458	375	9	105(6):1786–1793	105(6):1786–1793	NUM
ejpam-5458	375	10	,	,	PUNCT
ejpam-5458	375	11	2008	2008	NUM
ejpam-5458	375	12	.	.	PUNCT
ejpam-5458	376	1	[	[	X
ejpam-5458	376	2	6	6	NUM
ejpam-5458	376	3	]	]	PUNCT
ejpam-5458	376	4	stephen	stephen	PROPN
ejpam-5458	376	5	lynch	lynch	PROPN
ejpam-5458	376	6	.	.	PUNCT
ejpam-5458	377	1	dynamical	dynamical	ADJ
ejpam-5458	377	2	systems	system	NOUN
ejpam-5458	377	3	with	with	ADP
ejpam-5458	377	4	applications	application	NOUN
ejpam-5458	377	5	using	use	VERB
ejpam-5458	377	6	matlab	matlab	PROPN
ejpam-5458	377	7	®	®	PROPN
ejpam-5458	377	8	.	.	PUNCT
ejpam-5458	378	1	springer	springer	PROPN
ejpam-5458	378	2	international	international	ADJ
ejpam-5458	378	3	publishing	publishing	NOUN
ejpam-5458	378	4	,	,	PUNCT
ejpam-5458	378	5	2014	2014	NUM
ejpam-5458	378	6	.	.	PUNCT
ejpam-5458	379	1	[	[	X
ejpam-5458	379	2	7	7	X
ejpam-5458	379	3	]	]	X
ejpam-5458	379	4	kirk	kirk	PROPN
ejpam-5458	379	5	a.	a.	PROPN
ejpam-5458	379	6	maasch	maasch	PROPN
ejpam-5458	379	7	and	and	CCONJ
ejpam-5458	379	8	barry	barry	PROPN
ejpam-5458	379	9	saltzman	saltzman	PROPN
ejpam-5458	379	10	.	.	PUNCT
ejpam-5458	380	1	a	a	DET
ejpam-5458	380	2	low	low	ADJ
ejpam-5458	380	3	-	-	PUNCT
ejpam-5458	380	4	order	order	NOUN
ejpam-5458	380	5	dynamical	dynamical	ADJ
ejpam-5458	380	6	model	model	NOUN
ejpam-5458	380	7	of	of	ADP
ejpam-5458	380	8	global	global	ADJ
ejpam-5458	380	9	climatic	climatic	ADJ
ejpam-5458	380	10	variability	variability	NOUN
ejpam-5458	380	11	over	over	ADP
ejpam-5458	380	12	the	the	DET
ejpam-5458	380	13	full	full	ADJ
ejpam-5458	380	14	pleistocene	pleistocene	NOUN
ejpam-5458	380	15	.	.	PUNCT
ejpam-5458	381	1	journal	journal	PROPN
ejpam-5458	381	2	of	of	ADP
ejpam-5458	381	3	geophysical	geophysical	ADJ
ejpam-5458	381	4	research	research	NOUN
ejpam-5458	381	5	:	:	PUNCT
ejpam-5458	381	6	atmospheres	atmosphere	NOUN
ejpam-5458	381	7	,	,	PUNCT
ejpam-5458	381	8	95(d2):1955–1963	95(d2):1955–1963	NUM
ejpam-5458	381	9	,	,	PUNCT
ejpam-5458	381	10	1990	1990	NUM
ejpam-5458	381	11	.	.	PUNCT
ejpam-5458	382	1	[	[	X
ejpam-5458	382	2	8	8	NUM
ejpam-5458	382	3	]	]	SYM
ejpam-5458	382	4	j.murray	j.murray	NOUN
ejpam-5458	382	5	mitchell	mitchell	PROPN
ejpam-5458	382	6	.	.	PUNCT
ejpam-5458	383	1	an	an	DET
ejpam-5458	383	2	overview	overview	NOUN
ejpam-5458	383	3	of	of	ADP
ejpam-5458	383	4	climatic	climatic	ADJ
ejpam-5458	383	5	variability	variability	NOUN
ejpam-5458	383	6	and	and	CCONJ
ejpam-5458	383	7	its	its	PRON
ejpam-5458	383	8	causal	causal	ADJ
ejpam-5458	383	9	mechanisms	mechanism	NOUN
ejpam-5458	383	10	.	.	PUNCT
ejpam-5458	384	1	quaternary	quaternary	ADJ
ejpam-5458	384	2	research	research	NOUN
ejpam-5458	384	3	,	,	PUNCT
ejpam-5458	384	4	6(4):481–493	6(4):481–493	NUM
ejpam-5458	384	5	,	,	PUNCT
ejpam-5458	384	6	1976	1976	NUM
ejpam-5458	384	7	.	.	PUNCT
ejpam-5458	385	1	[	[	X
ejpam-5458	385	2	9	9	NUM
ejpam-5458	385	3	]	]	PUNCT
ejpam-5458	385	4	didier	didier	NOUN
ejpam-5458	385	5	paillard	paillard	NOUN
ejpam-5458	385	6	and	and	CCONJ
ejpam-5458	385	7	frédéric	frédéric	ADJ
ejpam-5458	385	8	parrenin	parrenin	NOUN
ejpam-5458	385	9	.	.	PUNCT
ejpam-5458	386	1	the	the	DET
ejpam-5458	386	2	antarctic	antarctic	ADJ
ejpam-5458	386	3	ice	ice	NOUN
ejpam-5458	386	4	sheet	sheet	NOUN
ejpam-5458	386	5	and	and	CCONJ
ejpam-5458	386	6	the	the	DET
ejpam-5458	386	7	triggering	triggering	NOUN
ejpam-5458	386	8	of	of	ADP
ejpam-5458	386	9	deglaciations	deglaciation	NOUN
ejpam-5458	386	10	.	.	PUNCT
ejpam-5458	387	1	earth	earth	NOUN
ejpam-5458	387	2	and	and	CCONJ
ejpam-5458	387	3	planetary	planetary	ADJ
ejpam-5458	387	4	science	science	NOUN
ejpam-5458	387	5	letters	letter	NOUN
ejpam-5458	387	6	,	,	PUNCT
ejpam-5458	387	7	227(3):263–271	227(3):263–271	NUM
ejpam-5458	387	8	,	,	PUNCT
ejpam-5458	387	9	2004	2004	NUM
ejpam-5458	387	10	.	.	PUNCT
ejpam-5458	388	1	[	[	X
ejpam-5458	388	2	10	10	NUM
ejpam-5458	388	3	]	]	X
ejpam-5458	388	4	daniel	daniel	PROPN
ejpam-5458	388	5	rothman	rothman	PROPN
ejpam-5458	388	6	.	.	PUNCT
ejpam-5458	389	1	earth	earth	PROPN
ejpam-5458	389	2	’s	’s	PART
ejpam-5458	389	3	carbon	carbon	NOUN
ejpam-5458	389	4	cycle	cycle	NOUN
ejpam-5458	389	5	:	:	PUNCT
ejpam-5458	389	6	a	a	DET
ejpam-5458	389	7	mathematical	mathematical	ADJ
ejpam-5458	389	8	perspective	perspective	NOUN
ejpam-5458	389	9	.	.	PUNCT
ejpam-5458	390	1	bulletin	bulletin	NOUN
ejpam-5458	390	2	of	of	ADP
ejpam-5458	390	3	the	the	DET
ejpam-5458	390	4	american	american	PROPN
ejpam-5458	390	5	mathematical	mathematical	PROPN
ejpam-5458	390	6	society	society	NOUN
ejpam-5458	390	7	,	,	PUNCT
ejpam-5458	390	8	52(1):47–64	52(1):47–64	NUM
ejpam-5458	390	9	,	,	PUNCT
ejpam-5458	390	10	2015	2015	NUM
ejpam-5458	390	11	.	.	PUNCT
ejpam-5458	391	1	[	[	X
ejpam-5458	391	2	11	11	NUM
ejpam-5458	391	3	]	]	X
ejpam-5458	391	4	daniel	daniel	PROPN
ejpam-5458	391	5	h.	h.	PROPN
ejpam-5458	391	6	rothman	rothman	PROPN
ejpam-5458	391	7	.	.	PUNCT
ejpam-5458	392	1	thresholds	threshold	NOUN
ejpam-5458	392	2	of	of	ADP
ejpam-5458	392	3	catastrophe	catastrophe	NOUN
ejpam-5458	392	4	in	in	ADP
ejpam-5458	392	5	the	the	DET
ejpam-5458	392	6	earth	earth	NOUN
ejpam-5458	392	7	system	system	NOUN
ejpam-5458	392	8	.	.	PUNCT
ejpam-5458	393	1	science	science	NOUN
ejpam-5458	393	2	advances	advance	NOUN
ejpam-5458	393	3	,	,	PUNCT
ejpam-5458	393	4	3(9):e1700906	3(9):e1700906	NUM
ejpam-5458	393	5	,	,	PUNCT
ejpam-5458	393	6	2017	2017	NUM
ejpam-5458	393	7	.	.	PUNCT
ejpam-5458	394	1	[	[	X
ejpam-5458	394	2	12	12	NUM
ejpam-5458	394	3	]	]	X
ejpam-5458	394	4	daniel	daniel	PROPN
ejpam-5458	394	5	h.	h.	PROPN
ejpam-5458	394	6	rothman	rothman	PROPN
ejpam-5458	394	7	.	.	PUNCT
ejpam-5458	395	1	characteristic	characteristic	ADJ
ejpam-5458	395	2	disruptions	disruption	NOUN
ejpam-5458	395	3	of	of	ADP
ejpam-5458	395	4	an	an	DET
ejpam-5458	395	5	excitable	excitable	ADJ
ejpam-5458	395	6	carbon	carbon	NOUN
ejpam-5458	395	7	cycle	cycle	NOUN
ejpam-5458	395	8	.	.	PUNCT
ejpam-5458	396	1	proceedings	proceeding	NOUN
ejpam-5458	396	2	of	of	ADP
ejpam-5458	396	3	the	the	DET
ejpam-5458	396	4	national	national	PROPN
ejpam-5458	396	5	academy	academy	PROPN
ejpam-5458	396	6	of	of	ADP
ejpam-5458	396	7	sciences	sciences	PROPN
ejpam-5458	396	8	,	,	PUNCT
ejpam-5458	396	9	116(30):14813–14822	116(30):14813–14822	NUM
ejpam-5458	396	10	,	,	PUNCT
ejpam-5458	396	11	2019	2019	NUM
ejpam-5458	396	12	.	.	PUNCT
ejpam-5458	397	1	[	[	X
ejpam-5458	397	2	13	13	NUM
ejpam-5458	397	3	]	]	X
ejpam-5458	397	4	daniel	daniel	PROPN
ejpam-5458	397	5	h.	h.	PROPN
ejpam-5458	397	6	rothman	rothman	PROPN
ejpam-5458	397	7	,	,	PUNCT
ejpam-5458	397	8	john	john	PROPN
ejpam-5458	397	9	m.	m.	PROPN
ejpam-5458	397	10	hayes	hayes	PROPN
ejpam-5458	397	11	,	,	PUNCT
ejpam-5458	397	12	and	and	CCONJ
ejpam-5458	397	13	roger	roger	PROPN
ejpam-5458	397	14	e.	e.	PROPN
ejpam-5458	397	15	summons	summons	PROPN
ejpam-5458	397	16	.	.	PUNCT
ejpam-5458	398	1	dynamics	dynamic	NOUN
ejpam-5458	398	2	of	of	ADP
ejpam-5458	398	3	the	the	DET
ejpam-5458	398	4	neoproterozoic	neoproterozoic	ADJ
ejpam-5458	398	5	carbon	carbon	NOUN
ejpam-5458	398	6	cycle	cycle	NOUN
ejpam-5458	398	7	.	.	PUNCT
ejpam-5458	399	1	proceedings	proceeding	NOUN
ejpam-5458	399	2	of	of	ADP
ejpam-5458	399	3	the	the	DET
ejpam-5458	399	4	national	national	PROPN
ejpam-5458	399	5	academy	academy	PROPN
ejpam-5458	399	6	of	of	ADP
ejpam-5458	399	7	sciences	sciences	PROPN
ejpam-5458	399	8	,	,	PUNCT
ejpam-5458	399	9	100(14):8124	100(14):8124	NUM
ejpam-5458	399	10	–	–	PUNCT
ejpam-5458	399	11	8129	8129	NUM
ejpam-5458	399	12	,	,	PUNCT
ejpam-5458	399	13	2003	2003	NUM
ejpam-5458	399	14	.	.	PUNCT
ejpam-5458	400	1	[	[	X
ejpam-5458	400	2	14	14	NUM
ejpam-5458	400	3	]	]	X
ejpam-5458	400	4	h	h	NOUN
ejpam-5458	400	5	strogatz	strogatz	PROPN
ejpam-5458	400	6	steven	steven	PROPN
ejpam-5458	400	7	.	.	PUNCT
ejpam-5458	401	1	nonlinear	nonlinear	ADJ
ejpam-5458	401	2	dynamics	dynamic	NOUN
ejpam-5458	401	3	and	and	CCONJ
ejpam-5458	401	4	chaos	chaos	NOUN
ejpam-5458	401	5	:	:	PUNCT
ejpam-5458	401	6	with	with	ADP
ejpam-5458	401	7	applications	application	NOUN
ejpam-5458	401	8	to	to	ADP
ejpam-5458	401	9	physics	physics	NOUN
ejpam-5458	401	10	,	,	PUNCT
ejpam-5458	401	11	biology	biology	NOUN
ejpam-5458	401	12	,	,	PUNCT
ejpam-5458	401	13	chemistry	chemistry	NOUN
ejpam-5458	401	14	,	,	PUNCT
ejpam-5458	401	15	and	and	CCONJ
ejpam-5458	401	16	engineering	engineering	NOUN
ejpam-5458	401	17	,	,	PUNCT
ejpam-5458	401	18	1994	1994	NUM
ejpam-5458	401	19	.	.	PUNCT
ejpam-5458	402	1	[	[	X
ejpam-5458	402	2	15	15	NUM
ejpam-5458	402	3	]	]	X
ejpam-5458	402	4	anna	anna	PROPN
ejpam-5458	402	5	s	s	PROPN
ejpam-5458	402	6	von	von	PROPN
ejpam-5458	402	7	der	der	PROPN
ejpam-5458	402	8	heydt	heydt	PROPN
ejpam-5458	402	9	,	,	PUNCT
ejpam-5458	402	10	peter	peter	PROPN
ejpam-5458	402	11	ashwin	ashwin	PROPN
ejpam-5458	402	12	,	,	PUNCT
ejpam-5458	402	13	charles	charles	PROPN
ejpam-5458	402	14	d	d	PROPN
ejpam-5458	402	15	camp	camp	PROPN
ejpam-5458	402	16	,	,	PUNCT
ejpam-5458	402	17	michel	michel	PROPN
ejpam-5458	402	18	crucifix	crucifix	PROPN
ejpam-5458	402	19	,	,	PUNCT
ejpam-5458	402	20	henk	henk	PROPN
ejpam-5458	402	21	a	a	DET
ejpam-5458	402	22	dijkstra	dijkstra	PROPN
ejpam-5458	402	23	,	,	PUNCT
ejpam-5458	402	24	peter	peter	PROPN
ejpam-5458	402	25	ditlevsen	ditlevsen	PROPN
ejpam-5458	402	26	,	,	PUNCT
ejpam-5458	402	27	and	and	CCONJ
ejpam-5458	402	28	timothy	timothy	PROPN
ejpam-5458	402	29	m	m	PROPN
ejpam-5458	402	30	lenton	lenton	PROPN
ejpam-5458	402	31	.	.	PUNCT
ejpam-5458	403	1	quantification	quantification	NOUN
ejpam-5458	403	2	and	and	CCONJ
ejpam-5458	403	3	interpretation	interpretation	NOUN
ejpam-5458	403	4	of	of	ADP
ejpam-5458	403	5	the	the	DET
ejpam-5458	403	6	climate	climate	NOUN
ejpam-5458	403	7	variability	variability	NOUN
ejpam-5458	403	8	record	record	NOUN
ejpam-5458	403	9	.	.	PUNCT
ejpam-5458	404	1	global	global	ADJ
ejpam-5458	404	2	and	and	CCONJ
ejpam-5458	404	3	planetary	planetary	ADJ
ejpam-5458	404	4	change	change	NOUN
ejpam-5458	404	5	,	,	PUNCT
ejpam-5458	404	6	197:103399	197:103399	NUM
ejpam-5458	404	7	,	,	PUNCT
ejpam-5458	404	8	2021	2021	NUM
ejpam-5458	404	9	.	.	PUNCT