id	sid	tid	token	lemma	pos
ejpam-1901	1	1	compiles/6a43080106cbd1fa83482983593961c6	compiles/6a43080106cbd1fa83482983593961c6	PROPN
ejpam-1901	1	2	/	/	SYM
ejpam-1901	1	3	output.dvi	output.dvi	PROPN
ejpam-1901	1	4	european	european	ADJ
ejpam-1901	1	5	journal	journal	NOUN
ejpam-1901	1	6	of	of	ADP
ejpam-1901	1	7	pure	pure	ADJ
ejpam-1901	1	8	and	and	CCONJ
ejpam-1901	1	9	applied	apply	VERB
ejpam-1901	1	10	mathematics	mathematic	NOUN
ejpam-1901	1	11	vol	vol	NOUN
ejpam-1901	1	12	.	.	PUNCT
ejpam-1901	2	1	7	7	NUM
ejpam-1901	2	2	,	,	PUNCT
ejpam-1901	2	3	no	no	INTJ
ejpam-1901	2	4	.	.	NOUN
ejpam-1901	2	5	1	1	NUM
ejpam-1901	2	6	,	,	PUNCT
ejpam-1901	2	7	2014	2014	NUM
ejpam-1901	2	8	,	,	PUNCT
ejpam-1901	2	9	37	37	NUM
ejpam-1901	2	10	-	-	SYM
ejpam-1901	2	11	44	44	NUM
ejpam-1901	2	12	issn	issn	PROPN
ejpam-1901	2	13	1307	1307	NUM
ejpam-1901	2	14	-	-	SYM
ejpam-1901	2	15	5543	5543	NUM
ejpam-1901	2	16	–	–	PUNCT
ejpam-1901	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-1901	2	18	modeling	model	VERB
ejpam-1901	2	19	the	the	DET
ejpam-1901	2	20	prey	prey	NOUN
ejpam-1901	2	21	predator	predator	NOUN
ejpam-1901	2	22	problem	problem	NOUN
ejpam-1901	2	23	by	by	ADP
ejpam-1901	2	24	a	a	DET
ejpam-1901	2	25	graph	graph	NOUN
ejpam-1901	2	26	differential	differential	ADJ
ejpam-1901	2	27	equation	equation	NOUN
ejpam-1901	2	28	j.	j.	PROPN
ejpam-1901	2	29	vasundhara	vasundhara	PROPN
ejpam-1901	2	30	devi∗	devi∗	PROPN
ejpam-1901	2	31	,	,	PUNCT
ejpam-1901	2	32	r.	r.	PROPN
ejpam-1901	2	33	v.	v.	PROPN
ejpam-1901	2	34	g.	g.	PROPN
ejpam-1901	2	35	ravi	ravi	PROPN
ejpam-1901	2	36	kumar	kumar	PROPN
ejpam-1901	2	37	department	department	PROPN
ejpam-1901	2	38	of	of	ADP
ejpam-1901	2	39	mathematics	mathematics	PROPN
ejpam-1901	2	40	,	,	PUNCT
ejpam-1901	2	41	gvp-prof.v.lakshmikantham	gvp-prof.v.lakshmikantham	PROPN
ejpam-1901	2	42	institute	institute	VERB
ejpam-1901	2	43	for	for	ADP
ejpam-1901	2	44	advanced	advanced	ADJ
ejpam-1901	2	45	studies	study	NOUN
ejpam-1901	2	46	,	,	PUNCT
ejpam-1901	2	47	gvp	gvp	PROPN
ejpam-1901	2	48	college	college	PROPN
ejpam-1901	2	49	of	of	ADP
ejpam-1901	2	50	engineering	engineering	PROPN
ejpam-1901	2	51	,	,	PUNCT
ejpam-1901	2	52	visakhapatnam	visakhapatnam	PROPN
ejpam-1901	2	53	,	,	PUNCT
ejpam-1901	2	54	ap	ap	PROPN
ejpam-1901	2	55	,	,	PUNCT
ejpam-1901	2	56	india	india	PROPN
ejpam-1901	2	57	.	.	PUNCT
ejpam-1901	3	1	abstract	abstract	PROPN
ejpam-1901	3	2	.	.	PUNCT
ejpam-1901	4	1	in	in	ADP
ejpam-1901	4	2	this	this	DET
ejpam-1901	4	3	paper	paper	NOUN
ejpam-1901	4	4	,	,	PUNCT
ejpam-1901	4	5	we	we	PRON
ejpam-1901	4	6	introduce	introduce	VERB
ejpam-1901	4	7	new	new	ADJ
ejpam-1901	4	8	concepts	concept	NOUN
ejpam-1901	4	9	like	like	ADP
ejpam-1901	4	10	a	a	DET
ejpam-1901	4	11	pseudo	pseudo	NOUN
ejpam-1901	4	12	simple	simple	ADJ
ejpam-1901	4	13	graph	graph	NOUN
ejpam-1901	4	14	,	,	PUNCT
ejpam-1901	4	15	product	product	NOUN
ejpam-1901	4	16	of	of	ADP
ejpam-1901	4	17	two	two	NUM
ejpam-1901	4	18	graphs	graph	NOUN
ejpam-1901	4	19	and	and	CCONJ
ejpam-1901	4	20	obtain	obtain	VERB
ejpam-1901	4	21	a	a	DET
ejpam-1901	4	22	sufficient	sufficient	ADJ
ejpam-1901	4	23	condition	condition	NOUN
ejpam-1901	4	24	which	which	PRON
ejpam-1901	4	25	will	will	AUX
ejpam-1901	4	26	guarantee	guarantee	VERB
ejpam-1901	4	27	that	that	SCONJ
ejpam-1901	4	28	the	the	DET
ejpam-1901	4	29	solution	solution	NOUN
ejpam-1901	4	30	of	of	ADP
ejpam-1901	4	31	the	the	DET
ejpam-1901	4	32	ivp	ivp	NOUN
ejpam-1901	4	33	of	of	ADP
ejpam-1901	4	34	a	a	DET
ejpam-1901	4	35	graph	graph	NOUN
ejpam-1901	4	36	differential	differential	ADJ
ejpam-1901	4	37	equation	equation	NOUN
ejpam-1901	4	38	has	have	VERB
ejpam-1901	4	39	the	the	DET
ejpam-1901	4	40	same	same	ADJ
ejpam-1901	4	41	nature	nature	NOUN
ejpam-1901	4	42	as	as	ADP
ejpam-1901	4	43	its	its	PRON
ejpam-1901	4	44	graph	graph	NOUN
ejpam-1901	4	45	of	of	ADP
ejpam-1901	4	46	initial	initial	ADJ
ejpam-1901	4	47	conditions	condition	NOUN
ejpam-1901	4	48	.	.	PUNCT
ejpam-1901	5	1	further	far	ADV
ejpam-1901	5	2	,	,	PUNCT
ejpam-1901	5	3	we	we	PRON
ejpam-1901	5	4	model	model	VERB
ejpam-1901	5	5	the	the	DET
ejpam-1901	5	6	well	well	ADV
ejpam-1901	5	7	known	know	VERB
ejpam-1901	5	8	prepredator	prepredator	NOUN
ejpam-1901	5	9	problem	problem	NOUN
ejpam-1901	5	10	by	by	ADP
ejpam-1901	5	11	graph	graph	NOUN
ejpam-1901	5	12	differential	differential	ADJ
ejpam-1901	5	13	equations	equation	NOUN
ejpam-1901	5	14	and	and	CCONJ
ejpam-1901	5	15	show	show	VERB
ejpam-1901	5	16	that	that	SCONJ
ejpam-1901	5	17	the	the	DET
ejpam-1901	5	18	nonlinearity	nonlinearity	NOUN
ejpam-1901	5	19	is	be	AUX
ejpam-1901	5	20	naturally	naturally	ADV
ejpam-1901	5	21	preserved	preserve	VERB
ejpam-1901	5	22	.	.	PUNCT
ejpam-1901	6	1	2010	2010	NUM
ejpam-1901	6	2	mathematics	mathematic	NOUN
ejpam-1901	6	3	subject	subject	NOUN
ejpam-1901	6	4	classifications	classification	NOUN
ejpam-1901	6	5	:	:	PUNCT
ejpam-1901	6	6	05c20	05c20	NUM
ejpam-1901	6	7	05c22	05c22	NOUN
ejpam-1901	6	8	05c50	05c50	NUM
ejpam-1901	6	9	34ab2	34ab2	NUM
ejpam-1901	6	10	92d25	92d25	NUM
ejpam-1901	6	11	key	key	ADJ
ejpam-1901	6	12	words	word	NOUN
ejpam-1901	6	13	and	and	CCONJ
ejpam-1901	6	14	phrases	phrase	NOUN
ejpam-1901	6	15	:	:	PUNCT
ejpam-1901	6	16	simple	simple	ADJ
ejpam-1901	6	17	graph	graph	NOUN
ejpam-1901	6	18	,	,	PUNCT
ejpam-1901	6	19	pseudo	pseudo	NOUN
ejpam-1901	6	20	simple	simple	ADJ
ejpam-1901	6	21	graph	graph	NOUN
ejpam-1901	6	22	,	,	PUNCT
ejpam-1901	6	23	product	product	NOUN
ejpam-1901	6	24	of	of	ADP
ejpam-1901	6	25	graphs	graph	NOUN
ejpam-1901	6	26	,	,	PUNCT
ejpam-1901	6	27	graph	graph	NOUN
ejpam-1901	6	28	differential	differential	ADJ
ejpam-1901	6	29	equation	equation	NOUN
ejpam-1901	6	30	and	and	CCONJ
ejpam-1901	6	31	prey	prey	VERB
ejpam-1901	6	32	predator	predator	NOUN
ejpam-1901	6	33	model	model	NOUN
ejpam-1901	6	34	.	.	PUNCT
ejpam-1901	7	1	1	1	X
ejpam-1901	7	2	.	.	X
ejpam-1901	7	3	introduction	introduction	NOUN
ejpam-1901	7	4	any	any	DET
ejpam-1901	7	5	natural	natural	ADJ
ejpam-1901	7	6	or	or	CCONJ
ejpam-1901	7	7	a	a	DET
ejpam-1901	7	8	man	man	NOUN
ejpam-1901	7	9	made	make	VERB
ejpam-1901	7	10	system	system	NOUN
ejpam-1901	7	11	involves	involve	VERB
ejpam-1901	7	12	interconnections	interconnection	NOUN
ejpam-1901	7	13	between	between	ADP
ejpam-1901	7	14	its	its	PRON
ejpam-1901	7	15	constituents	constituent	NOUN
ejpam-1901	7	16	,	,	PUNCT
ejpam-1901	7	17	thus	thus	ADV
ejpam-1901	7	18	forming	form	VERB
ejpam-1901	7	19	a	a	DET
ejpam-1901	7	20	network	network	NOUN
ejpam-1901	7	21	,	,	PUNCT
ejpam-1901	7	22	which	which	PRON
ejpam-1901	7	23	can	can	AUX
ejpam-1901	7	24	be	be	AUX
ejpam-1901	7	25	expressed	express	VERB
ejpam-1901	7	26	by	by	ADP
ejpam-1901	7	27	a	a	DET
ejpam-1901	7	28	graph	graph	NOUN
ejpam-1901	8	1	[	[	X
ejpam-1901	8	2	2	2	NUM
ejpam-1901	8	3	,	,	PUNCT
ejpam-1901	8	4	3	3	NUM
ejpam-1901	8	5	]	]	PUNCT
ejpam-1901	8	6	.	.	PUNCT
ejpam-1901	9	1	graphs	graph	NOUN
ejpam-1901	9	2	arise	arise	VERB
ejpam-1901	9	3	naturally	naturally	ADV
ejpam-1901	9	4	when	when	SCONJ
ejpam-1901	9	5	trying	try	VERB
ejpam-1901	9	6	to	to	PART
ejpam-1901	9	7	model	model	VERB
ejpam-1901	9	8	organizational	organizational	ADJ
ejpam-1901	9	9	structures	structure	NOUN
ejpam-1901	9	10	in	in	ADP
ejpam-1901	9	11	social	social	ADJ
ejpam-1901	9	12	sciences	science	NOUN
ejpam-1901	9	13	.	.	PUNCT
ejpam-1901	10	1	it	it	PRON
ejpam-1901	10	2	has	have	AUX
ejpam-1901	10	3	been	be	AUX
ejpam-1901	10	4	noted	note	VERB
ejpam-1901	10	5	that	that	SCONJ
ejpam-1901	10	6	a	a	DET
ejpam-1901	10	7	graph	graph	NOUN
ejpam-1901	10	8	which	which	PRON
ejpam-1901	10	9	is	be	AUX
ejpam-1901	10	10	static	static	ADJ
ejpam-1901	10	11	in	in	ADP
ejpam-1901	10	12	nature	nature	NOUN
ejpam-1901	10	13	is	be	AUX
ejpam-1901	10	14	not	not	PART
ejpam-1901	10	15	suitable	suitable	ADJ
ejpam-1901	10	16	for	for	ADP
ejpam-1901	10	17	social	social	ADJ
ejpam-1901	10	18	phenomena	phenomenon	NOUN
ejpam-1901	10	19	whose	whose	DET
ejpam-1901	10	20	changes	change	NOUN
ejpam-1901	10	21	with	with	ADP
ejpam-1901	10	22	time	time	NOUN
ejpam-1901	10	23	are	be	AUX
ejpam-1901	10	24	natural	natural	ADJ
ejpam-1901	10	25	.	.	PUNCT
ejpam-1901	11	1	this	this	PRON
ejpam-1901	11	2	led	lead	VERB
ejpam-1901	11	3	to	to	ADP
ejpam-1901	11	4	the	the	DET
ejpam-1901	11	5	introduction	introduction	NOUN
ejpam-1901	11	6	of	of	ADP
ejpam-1901	11	7	a	a	DET
ejpam-1901	11	8	dynamic	dynamic	ADJ
ejpam-1901	11	9	graph	graph	NOUN
ejpam-1901	11	10	and	and	CCONJ
ejpam-1901	11	11	a	a	DET
ejpam-1901	11	12	graph	graph	NOUN
ejpam-1901	11	13	differential	differential	ADJ
ejpam-1901	11	14	equation	equation	NOUN
ejpam-1901	11	15	(	(	PUNCT
ejpam-1901	11	16	gde	gde	NOUN
ejpam-1901	11	17	)	)	PUNCT
ejpam-1901	11	18	in	in	ADP
ejpam-1901	11	19	[	[	X
ejpam-1901	11	20	3	3	NUM
ejpam-1901	11	21	]	]	PUNCT
ejpam-1901	11	22	.	.	PUNCT
ejpam-1901	12	1	the	the	DET
ejpam-1901	12	2	introduced	introduce	VERB
ejpam-1901	12	3	concepts	concept	NOUN
ejpam-1901	12	4	were	be	AUX
ejpam-1901	12	5	successfully	successfully	ADV
ejpam-1901	12	6	utilized	utilize	VERB
ejpam-1901	12	7	to	to	PART
ejpam-1901	12	8	study	study	VERB
ejpam-1901	12	9	stability	stability	NOUN
ejpam-1901	12	10	of	of	ADP
ejpam-1901	12	11	complex	complex	ADJ
ejpam-1901	12	12	dynamic	dynamic	ADJ
ejpam-1901	12	13	systems	system	NOUN
ejpam-1901	12	14	through	through	ADP
ejpam-1901	12	15	its	its	PRON
ejpam-1901	12	16	associated	associated	ADJ
ejpam-1901	12	17	adjacency	adjacency	NOUN
ejpam-1901	12	18	matrix	matrix	NOUN
ejpam-1901	13	1	[	[	X
ejpam-1901	13	2	3	3	NUM
ejpam-1901	13	3	]	]	PUNCT
ejpam-1901	13	4	.	.	PUNCT
ejpam-1901	14	1	in	in	ADP
ejpam-1901	14	2	[	[	X
ejpam-1901	14	3	2	2	X
ejpam-1901	14	4	]	]	PUNCT
ejpam-1901	14	5	we	we	PRON
ejpam-1901	14	6	have	have	AUX
ejpam-1901	14	7	utilized	utilize	VERB
ejpam-1901	14	8	the	the	DET
ejpam-1901	14	9	concepts	concept	NOUN
ejpam-1901	14	10	defined	define	VERB
ejpam-1901	14	11	in	in	ADP
ejpam-1901	14	12	[	[	X
ejpam-1901	14	13	3	3	NUM
ejpam-1901	14	14	]	]	PUNCT
ejpam-1901	14	15	including	include	VERB
ejpam-1901	14	16	a	a	DET
ejpam-1901	14	17	graph	graph	NOUN
ejpam-1901	14	18	linear	linear	ADJ
ejpam-1901	14	19	space	space	NOUN
ejpam-1901	14	20	and	and	CCONJ
ejpam-1901	14	21	its	its	PRON
ejpam-1901	14	22	associated	associated	ADJ
ejpam-1901	14	23	matrix	matrix	NOUN
ejpam-1901	14	24	linear	linear	NOUN
ejpam-1901	14	25	space	space	NOUN
ejpam-1901	14	26	.	.	PUNCT
ejpam-1901	15	1	using	use	VERB
ejpam-1901	15	2	the	the	DET
ejpam-1901	15	3	notion	notion	NOUN
ejpam-1901	15	4	of	of	ADP
ejpam-1901	15	5	a	a	DET
ejpam-1901	15	6	dynamic	dynamic	ADJ
ejpam-1901	15	7	graph	graph	NOUN
ejpam-1901	15	8	and	and	CCONJ
ejpam-1901	15	9	the	the	DET
ejpam-1901	15	10	graph	graph	NOUN
ejpam-1901	15	11	differential	differential	ADJ
ejpam-1901	15	12	equations	equation	NOUN
ejpam-1901	15	13	we	we	PRON
ejpam-1901	15	14	observed	observe	VERB
ejpam-1901	15	15	that	that	SCONJ
ejpam-1901	15	16	the	the	DET
ejpam-1901	15	17	study	study	NOUN
ejpam-1901	15	18	of	of	ADP
ejpam-1901	15	19	gdes	gdes	PROPN
ejpam-1901	15	20	falls	fall	VERB
ejpam-1901	15	21	into	into	ADP
ejpam-1901	15	22	the	the	DET
ejpam-1901	15	23	realm	realm	NOUN
ejpam-1901	15	24	of	of	ADP
ejpam-1901	15	25	differential	differential	ADJ
ejpam-1901	15	26	equations	equation	NOUN
ejpam-1901	15	27	in	in	ADP
ejpam-1901	15	28	abstract	abstract	ADJ
ejpam-1901	15	29	spaces	space	NOUN
ejpam-1901	15	30	.	.	PUNCT
ejpam-1901	16	1	this	this	DET
ejpam-1901	16	2	study	study	NOUN
ejpam-1901	16	3	,	,	PUNCT
ejpam-1901	16	4	through	through	ADP
ejpam-1901	16	5	highly	highly	ADV
ejpam-1901	16	6	mathematical	mathematical	ADJ
ejpam-1901	16	7	,	,	PUNCT
ejpam-1901	16	8	would	would	AUX
ejpam-1901	16	9	be	be	AUX
ejpam-1901	16	10	of	of	ADP
ejpam-1901	16	11	little	little	ADJ
ejpam-1901	16	12	use	use	NOUN
ejpam-1901	16	13	for	for	ADP
ejpam-1901	16	14	practical	practical	ADJ
ejpam-1901	16	15	problems	problem	NOUN
ejpam-1901	16	16	.	.	PUNCT
ejpam-1901	17	1	on	on	ADP
ejpam-1901	17	2	the	the	DET
ejpam-1901	17	3	other	other	ADJ
ejpam-1901	17	4	hand	hand	NOUN
ejpam-1901	17	5	,	,	PUNCT
ejpam-1901	17	6	if	if	SCONJ
ejpam-1901	17	7	we	we	PRON
ejpam-1901	17	8	consider	consider	VERB
ejpam-1901	17	9	the	the	DET
ejpam-1901	17	10	associated	associated	ADJ
ejpam-1901	17	11	matrix	matrix	NOUN
ejpam-1901	17	12	differential	differential	NOUN
ejpam-1901	17	13	equation(mde	equation(mde	NOUN
ejpam-1901	17	14	)	)	PUNCT
ejpam-1901	17	15	then	then	ADV
ejpam-1901	17	16	the	the	DET
ejpam-1901	17	17	approach	approach	NOUN
ejpam-1901	17	18	appeared	appear	VERB
ejpam-1901	17	19	more	more	ADV
ejpam-1901	17	20	reasonable	reasonable	ADJ
ejpam-1901	17	21	and	and	CCONJ
ejpam-1901	17	22	practical	practical	ADJ
ejpam-1901	17	23	for	for	ADP
ejpam-1901	17	24	the	the	DET
ejpam-1901	17	25	study	study	NOUN
ejpam-1901	17	26	of	of	ADP
ejpam-1901	17	27	gdes	gde	NOUN
ejpam-1901	17	28	.	.	PUNCT
ejpam-1901	18	1	hence	hence	ADV
ejpam-1901	18	2	in	in	ADP
ejpam-1901	18	3	[	[	X
ejpam-1901	18	4	2	2	NUM
ejpam-1901	18	5	]	]	PUNCT
ejpam-1901	18	6	,	,	PUNCT
ejpam-1901	18	7	we	we	PRON
ejpam-1901	18	8	considered	consider	VERB
ejpam-1901	18	9	a	a	DET
ejpam-1901	18	10	weighted	weight	VERB
ejpam-1901	18	11	directed	direct	VERB
ejpam-1901	18	12	simple	simple	ADJ
ejpam-1901	18	13	graph	graph	NOUN
ejpam-1901	18	14	as	as	ADP
ejpam-1901	18	15	the	the	DET
ejpam-1901	18	16	basic	basic	ADJ
ejpam-1901	18	17	element	element	NOUN
ejpam-1901	18	18	and	and	CCONJ
ejpam-1901	18	19	developed	develop	VERB
ejpam-1901	18	20	∗corresponding	∗corresponde	VERB
ejpam-1901	18	21	author	author	NOUN
ejpam-1901	18	22	.	.	PUNCT
ejpam-1901	19	1	email	email	NOUN
ejpam-1901	19	2	address	address	NOUN
ejpam-1901	19	3	:	:	PUNCT
ejpam-1901	19	4	jvdevi@gmail.com	jvdevi@gmail.com	X
ejpam-1901	19	5	(	(	PUNCT
ejpam-1901	19	6	j.	j.	PROPN
ejpam-1901	19	7	vasundhara	vasundhara	PROPN
ejpam-1901	19	8	devi	devi	PROPN
ejpam-1901	19	9	)	)	PUNCT
ejpam-1901	19	10	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-1901	20	1	37	37	NUM
ejpam-1901	21	1	c	c	X
ejpam-1901	21	2	©	©	PROPN
ejpam-1901	21	3	2014	2014	NUM
ejpam-1901	21	4	ejpam	ejpam	NOUN
ejpam-1901	21	5	all	all	DET
ejpam-1901	21	6	rights	right	NOUN
ejpam-1901	21	7	reserved	reserve	VERB
ejpam-1901	21	8	.	.	PUNCT
ejpam-1901	22	1	j.	j.	PROPN
ejpam-1901	22	2	devi	devi	PROPN
ejpam-1901	22	3	,	,	PUNCT
ejpam-1901	22	4	r.	r.	PROPN
ejpam-1901	22	5	kumar	kumar	PROPN
ejpam-1901	22	6	/	/	SYM
ejpam-1901	22	7	eur	eur	PROPN
ejpam-1901	22	8	.	.	PUNCT
ejpam-1901	23	1	j.	j.	PROPN
ejpam-1901	23	2	pure	pure	PROPN
ejpam-1901	23	3	appl	appl	PROPN
ejpam-1901	23	4	.	.	PROPN
ejpam-1901	23	5	math	math	PROPN
ejpam-1901	23	6	,	,	PUNCT
ejpam-1901	23	7	7	7	NUM
ejpam-1901	23	8	(	(	PUNCT
ejpam-1901	23	9	2014	2014	NUM
ejpam-1901	23	10	)	)	PUNCT
ejpam-1901	23	11	,	,	PUNCT
ejpam-1901	23	12	37	37	NUM
ejpam-1901	23	13	-	-	SYM
ejpam-1901	23	14	44	44	NUM
ejpam-1901	23	15	38	38	NUM
ejpam-1901	23	16	the	the	DET
ejpam-1901	23	17	theory	theory	NOUN
ejpam-1901	23	18	.	.	PUNCT
ejpam-1901	24	1	we	we	PRON
ejpam-1901	24	2	have	have	AUX
ejpam-1901	24	3	obtained	obtain	VERB
ejpam-1901	24	4	existence	existence	NOUN
ejpam-1901	24	5	and	and	CCONJ
ejpam-1901	24	6	uniqueness	uniqueness	NOUN
ejpam-1901	24	7	of	of	ADP
ejpam-1901	24	8	solutions	solution	NOUN
ejpam-1901	24	9	of	of	ADP
ejpam-1901	24	10	a	a	DET
ejpam-1901	24	11	gde	gde	NOUN
ejpam-1901	24	12	through	through	ADP
ejpam-1901	24	13	its	its	PRON
ejpam-1901	24	14	associated	associated	ADJ
ejpam-1901	24	15	mde	mde	NOUN
ejpam-1901	24	16	using	use	VERB
ejpam-1901	24	17	the	the	DET
ejpam-1901	24	18	monotone	monotone	ADJ
ejpam-1901	24	19	iterative	iterative	NOUN
ejpam-1901	24	20	technique	technique	NOUN
ejpam-1901	24	21	.	.	PUNCT
ejpam-1901	25	1	in	in	ADP
ejpam-1901	25	2	[	[	X
ejpam-1901	25	3	2	2	NUM
ejpam-1901	25	4	]	]	PUNCT
ejpam-1901	25	5	through	through	ADP
ejpam-1901	25	6	we	we	PRON
ejpam-1901	25	7	have	have	AUX
ejpam-1901	25	8	developed	develop	VERB
ejpam-1901	25	9	significant	significant	ADJ
ejpam-1901	25	10	results	result	NOUN
ejpam-1901	25	11	,	,	PUNCT
ejpam-1901	25	12	the	the	DET
ejpam-1901	25	13	basic	basic	ADJ
ejpam-1901	25	14	concept	concept	NOUN
ejpam-1901	25	15	involved	involve	VERB
ejpam-1901	25	16	was	be	AUX
ejpam-1901	25	17	weighted	weight	VERB
ejpam-1901	25	18	directed	direct	VERB
ejpam-1901	25	19	simple	simple	ADJ
ejpam-1901	25	20	graph	graph	NOUN
ejpam-1901	25	21	.	.	PUNCT
ejpam-1901	26	1	since	since	SCONJ
ejpam-1901	26	2	a	a	DET
ejpam-1901	26	3	simple	simple	ADJ
ejpam-1901	26	4	graph	graph	NOUN
ejpam-1901	26	5	has	have	VERB
ejpam-1901	26	6	no	no	DET
ejpam-1901	26	7	loops	loop	NOUN
ejpam-1901	26	8	,	,	PUNCT
ejpam-1901	26	9	this	this	DET
ejpam-1901	26	10	fact	fact	NOUN
ejpam-1901	26	11	when	when	SCONJ
ejpam-1901	26	12	translated	translate	VERB
ejpam-1901	26	13	into	into	ADP
ejpam-1901	26	14	differential	differential	ADJ
ejpam-1901	26	15	equations	equation	NOUN
ejpam-1901	26	16	frame	frame	VERB
ejpam-1901	26	17	work	work	NOUN
ejpam-1901	26	18	states	state	VERB
ejpam-1901	26	19	that	that	SCONJ
ejpam-1901	26	20	there	there	PRON
ejpam-1901	26	21	is	be	VERB
ejpam-1901	26	22	no	no	DET
ejpam-1901	26	23	way	way	NOUN
ejpam-1901	26	24	to	to	PART
ejpam-1901	26	25	accommodate	accommodate	VERB
ejpam-1901	26	26	the	the	DET
ejpam-1901	26	27	rate	rate	NOUN
ejpam-1901	26	28	of	of	ADP
ejpam-1901	26	29	change	change	NOUN
ejpam-1901	26	30	of	of	ADP
ejpam-1901	26	31	an	an	DET
ejpam-1901	26	32	edge	edge	NOUN
ejpam-1901	26	33	eii	eii	PROPN
ejpam-1901	26	34	and	and	CCONJ
ejpam-1901	26	35	its	its	PRON
ejpam-1901	26	36	relation	relation	NOUN
ejpam-1901	26	37	with	with	ADP
ejpam-1901	26	38	other	other	ADJ
ejpam-1901	26	39	edges	edge	NOUN
ejpam-1901	26	40	including	include	VERB
ejpam-1901	26	41	the	the	DET
ejpam-1901	26	42	edge	edge	NOUN
ejpam-1901	26	43	eii	eii	PROPN
ejpam-1901	26	44	.	.	PUNCT
ejpam-1901	27	1	this	this	PRON
ejpam-1901	27	2	is	be	AUX
ejpam-1901	27	3	a	a	DET
ejpam-1901	27	4	drawback	drawback	NOUN
ejpam-1901	27	5	that	that	PRON
ejpam-1901	27	6	had	have	VERB
ejpam-1901	27	7	to	to	PART
ejpam-1901	27	8	be	be	AUX
ejpam-1901	27	9	handled	handle	VERB
ejpam-1901	27	10	to	to	PART
ejpam-1901	27	11	model	model	VERB
ejpam-1901	27	12	physical	physical	ADJ
ejpam-1901	27	13	phenomena	phenomenon	NOUN
ejpam-1901	27	14	using	use	VERB
ejpam-1901	27	15	graph	graph	NOUN
ejpam-1901	27	16	differential	differential	ADJ
ejpam-1901	27	17	equations	equation	NOUN
ejpam-1901	27	18	,	,	PUNCT
ejpam-1901	27	19	which	which	PRON
ejpam-1901	27	20	called	call	VERB
ejpam-1901	27	21	for	for	ADP
ejpam-1901	27	22	a	a	DET
ejpam-1901	27	23	new	new	ADJ
ejpam-1901	27	24	concept	concept	NOUN
ejpam-1901	27	25	that	that	SCONJ
ejpam-1901	27	26	we	we	PRON
ejpam-1901	27	27	plan	plan	VERB
ejpam-1901	27	28	to	to	PART
ejpam-1901	27	29	introduce	introduce	VERB
ejpam-1901	27	30	in	in	ADP
ejpam-1901	27	31	this	this	DET
ejpam-1901	27	32	paper	paper	NOUN
ejpam-1901	27	33	.	.	PUNCT
ejpam-1901	28	1	further	far	ADV
ejpam-1901	28	2	,	,	PUNCT
ejpam-1901	28	3	since	since	SCONJ
ejpam-1901	28	4	there	there	PRON
ejpam-1901	28	5	exists	exist	VERB
ejpam-1901	28	6	an	an	DET
ejpam-1901	28	7	isomorphism	isomorphism	NOUN
ejpam-1901	28	8	between	between	ADP
ejpam-1901	28	9	graphs	graph	NOUN
ejpam-1901	28	10	and	and	CCONJ
ejpam-1901	28	11	their	their	PRON
ejpam-1901	28	12	adjacency	adjacency	NOUN
ejpam-1901	28	13	matrices	matrix	NOUN
ejpam-1901	28	14	,	,	PUNCT
ejpam-1901	28	15	we	we	PRON
ejpam-1901	28	16	successfully	successfully	ADV
ejpam-1901	28	17	exploited	exploit	VERB
ejpam-1901	28	18	it	it	PRON
ejpam-1901	28	19	and	and	CCONJ
ejpam-1901	28	20	defined	define	VERB
ejpam-1901	28	21	the	the	DET
ejpam-1901	28	22	product	product	NOUN
ejpam-1901	28	23	of	of	ADP
ejpam-1901	28	24	two	two	NUM
ejpam-1901	28	25	graphs	graph	NOUN
ejpam-1901	28	26	.	.	PUNCT
ejpam-1901	29	1	a	a	DET
ejpam-1901	29	2	good	good	ADJ
ejpam-1901	29	3	example	example	NOUN
ejpam-1901	29	4	,	,	PUNCT
ejpam-1901	29	5	will	will	AUX
ejpam-1901	29	6	go	go	VERB
ejpam-1901	29	7	a	a	DET
ejpam-1901	29	8	long	long	ADJ
ejpam-1901	29	9	way	way	NOUN
ejpam-1901	29	10	in	in	ADP
ejpam-1901	29	11	support	support	NOUN
ejpam-1901	29	12	of	of	ADP
ejpam-1901	29	13	the	the	DET
ejpam-1901	29	14	theory	theory	NOUN
ejpam-1901	29	15	,	,	PUNCT
ejpam-1901	29	16	we	we	PRON
ejpam-1901	29	17	have	have	AUX
ejpam-1901	29	18	considered	consider	VERB
ejpam-1901	29	19	the	the	DET
ejpam-1901	29	20	prey	prey	NOUN
ejpam-1901	29	21	predator	predator	NOUN
ejpam-1901	29	22	problem	problem	NOUN
ejpam-1901	29	23	and	and	CCONJ
ejpam-1901	29	24	developed	develop	VERB
ejpam-1901	29	25	the	the	DET
ejpam-1901	29	26	corresponding	corresponding	ADJ
ejpam-1901	29	27	matrix	matrix	NOUN
ejpam-1901	29	28	differential	differential	NOUN
ejpam-1901	29	29	equation	equation	NOUN
ejpam-1901	29	30	and	and	CCONJ
ejpam-1901	29	31	showed	show	VERB
ejpam-1901	29	32	how	how	SCONJ
ejpam-1901	29	33	the	the	DET
ejpam-1901	29	34	nonlinearity	nonlinearity	NOUN
ejpam-1901	29	35	is	be	AUX
ejpam-1901	29	36	preserved	preserve	VERB
ejpam-1901	29	37	in	in	ADP
ejpam-1901	29	38	this	this	DET
ejpam-1901	29	39	set	set	VERB
ejpam-1901	29	40	up	up	ADP
ejpam-1901	29	41	.	.	PUNCT
ejpam-1901	30	1	the	the	DET
ejpam-1901	30	2	rest	rest	NOUN
ejpam-1901	30	3	of	of	ADP
ejpam-1901	30	4	the	the	DET
ejpam-1901	30	5	paper	paper	NOUN
ejpam-1901	30	6	is	be	AUX
ejpam-1901	30	7	as	as	SCONJ
ejpam-1901	30	8	follows	follow	VERB
ejpam-1901	30	9	.	.	PUNCT
ejpam-1901	31	1	in	in	ADP
ejpam-1901	31	2	section	section	NOUN
ejpam-1901	31	3	two	two	NUM
ejpam-1901	31	4	,	,	PUNCT
ejpam-1901	31	5	we	we	PRON
ejpam-1901	31	6	introduce	introduce	VERB
ejpam-1901	31	7	the	the	DET
ejpam-1901	31	8	concepts	concept	NOUN
ejpam-1901	31	9	of	of	ADP
ejpam-1901	31	10	pseudo	pseudo	NOUN
ejpam-1901	31	11	simple	simple	ADJ
ejpam-1901	31	12	graph	graph	NOUN
ejpam-1901	31	13	and	and	CCONJ
ejpam-1901	31	14	product	product	NOUN
ejpam-1901	31	15	of	of	ADP
ejpam-1901	31	16	two	two	NUM
ejpam-1901	31	17	graphs	graph	NOUN
ejpam-1901	31	18	and	and	CCONJ
ejpam-1901	31	19	have	have	AUX
ejpam-1901	31	20	obtained	obtain	VERB
ejpam-1901	31	21	a	a	DET
ejpam-1901	31	22	result	result	NOUN
ejpam-1901	31	23	,	,	PUNCT
ejpam-1901	31	24	that	that	PRON
ejpam-1901	31	25	can	can	AUX
ejpam-1901	31	26	be	be	AUX
ejpam-1901	31	27	of	of	ADP
ejpam-1901	31	28	practical	practical	ADJ
ejpam-1901	31	29	importance	importance	NOUN
ejpam-1901	31	30	in	in	ADP
ejpam-1901	31	31	this	this	DET
ejpam-1901	31	32	set	set	VERB
ejpam-1901	31	33	up	up	ADP
ejpam-1901	31	34	.	.	PUNCT
ejpam-1901	32	1	in	in	ADP
ejpam-1901	32	2	section	section	NOUN
ejpam-1901	32	3	three	three	NUM
ejpam-1901	32	4	we	we	PRON
ejpam-1901	32	5	obtained	obtain	VERB
ejpam-1901	32	6	the	the	DET
ejpam-1901	32	7	matrix	matrix	NOUN
ejpam-1901	32	8	differential	differential	NOUN
ejpam-1901	32	9	equation	equation	NOUN
ejpam-1901	32	10	for	for	ADP
ejpam-1901	32	11	prey	prey	NOUN
ejpam-1901	32	12	predator	predator	NOUN
ejpam-1901	32	13	problem	problem	NOUN
ejpam-1901	32	14	and	and	CCONJ
ejpam-1901	32	15	extended	extend	VERB
ejpam-1901	32	16	it	it	PRON
ejpam-1901	32	17	to	to	ADP
ejpam-1901	32	18	three	three	NUM
ejpam-1901	32	19	species	specie	NOUN
ejpam-1901	32	20	and	and	CCONJ
ejpam-1901	32	21	further	far	ADV
ejpam-1901	32	22	generalized	generalize	VERB
ejpam-1901	32	23	it	it	PRON
ejpam-1901	32	24	.	.	PUNCT
ejpam-1901	33	1	in	in	ADP
ejpam-1901	33	2	section	section	NOUN
ejpam-1901	33	3	four	four	NUM
ejpam-1901	33	4	we	we	PRON
ejpam-1901	33	5	conclude	conclude	VERB
ejpam-1901	33	6	our	our	PRON
ejpam-1901	33	7	work	work	NOUN
ejpam-1901	33	8	.	.	PUNCT
ejpam-1901	34	1	2	2	X
ejpam-1901	34	2	.	.	X
ejpam-1901	34	3	main	main	ADJ
ejpam-1901	34	4	results	result	NOUN
ejpam-1901	34	5	in	in	ADP
ejpam-1901	34	6	this	this	DET
ejpam-1901	34	7	section	section	NOUN
ejpam-1901	34	8	,	,	PUNCT
ejpam-1901	34	9	we	we	PRON
ejpam-1901	34	10	begin	begin	VERB
ejpam-1901	34	11	with	with	ADP
ejpam-1901	34	12	the	the	DET
ejpam-1901	34	13	concept	concept	NOUN
ejpam-1901	34	14	of	of	ADP
ejpam-1901	34	15	a	a	DET
ejpam-1901	34	16	pseudo	pseudo	NOUN
ejpam-1901	34	17	simple	simple	ADJ
ejpam-1901	34	18	and	and	CCONJ
ejpam-1901	34	19	later	later	ADV
ejpam-1901	34	20	introduce	introduce	VERB
ejpam-1901	34	21	the	the	DET
ejpam-1901	34	22	product	product	NOUN
ejpam-1901	34	23	of	of	ADP
ejpam-1901	34	24	two	two	NUM
ejpam-1901	34	25	graphs	graph	NOUN
ejpam-1901	34	26	.	.	PUNCT
ejpam-1901	35	1	definition	definition	NOUN
ejpam-1901	35	2	1	1	NUM
ejpam-1901	35	3	(	(	PUNCT
ejpam-1901	35	4	pseudo	pseudo	NOUN
ejpam-1901	35	5	simple	simple	ADJ
ejpam-1901	35	6	graph	graph	NOUN
ejpam-1901	35	7	)	)	PUNCT
ejpam-1901	35	8	.	.	PUNCT
ejpam-1901	36	1	a	a	DET
ejpam-1901	36	2	simple	simple	ADJ
ejpam-1901	36	3	graph	graph	NOUN
ejpam-1901	36	4	having	have	VERB
ejpam-1901	36	5	loops	loop	NOUN
ejpam-1901	36	6	is	be	AUX
ejpam-1901	36	7	called	call	VERB
ejpam-1901	36	8	as	as	ADP
ejpam-1901	36	9	a	a	DET
ejpam-1901	36	10	pseudo	pseudo	NOUN
ejpam-1901	36	11	simple	simple	ADJ
ejpam-1901	36	12	graph	graph	NOUN
ejpam-1901	36	13	.	.	PUNCT
ejpam-1901	37	1	parallel	parallel	NOUN
ejpam-1901	37	2	to	to	ADP
ejpam-1901	37	3	the	the	DET
ejpam-1901	37	4	definitions	definition	NOUN
ejpam-1901	37	5	and	and	CCONJ
ejpam-1901	37	6	theory	theory	NOUN
ejpam-1901	37	7	developed	develop	VERB
ejpam-1901	37	8	in	in	ADP
ejpam-1901	37	9	[	[	X
ejpam-1901	37	10	2	2	X
ejpam-1901	37	11	]	]	PUNCT
ejpam-1901	37	12	we	we	PRON
ejpam-1901	37	13	proceed	proceed	VERB
ejpam-1901	37	14	to	to	PART
ejpam-1901	37	15	state	state	VERB
ejpam-1901	37	16	the	the	DET
ejpam-1901	37	17	results	result	NOUN
ejpam-1901	37	18	in	in	ADP
ejpam-1901	37	19	this	this	DET
ejpam-1901	37	20	set	set	NOUN
ejpam-1901	37	21	up	up	ADP
ejpam-1901	37	22	.	.	PUNCT
ejpam-1901	38	1	we	we	PRON
ejpam-1901	38	2	avoid	avoid	VERB
ejpam-1901	38	3	the	the	DET
ejpam-1901	38	4	details	detail	NOUN
ejpam-1901	38	5	for	for	ADP
ejpam-1901	38	6	fear	fear	NOUN
ejpam-1901	38	7	of	of	ADP
ejpam-1901	38	8	repetition	repetition	NOUN
ejpam-1901	38	9	.	.	PUNCT
ejpam-1901	39	1	let	let	VERB
ejpam-1901	39	2	v1	v1	NOUN
ejpam-1901	39	3	,	,	PUNCT
ejpam-1901	39	4	v2	v2	NOUN
ejpam-1901	39	5	,	,	PUNCT
ejpam-1901	39	6	.	.	PUNCT
ejpam-1901	39	7	.	.	PUNCT
ejpam-1901	40	1	.	.	PUNCT
ejpam-1901	41	1	,	,	PUNCT
ejpam-1901	41	2	vn	vn	PROPN
ejpam-1901	41	3	be	be	AUX
ejpam-1901	41	4	n	n	PRON
ejpam-1901	41	5	verticess	verticess	ADJ
ejpam-1901	41	6	,	,	PUNCT
ejpam-1901	41	7	n	n	PRON
ejpam-1901	41	8	fixed	fix	VERB
ejpam-1901	41	9	.	.	PUNCT
ejpam-1901	42	1	let	let	VERB
ejpam-1901	42	2	dn	dn	PART
ejpam-1901	42	3	be	be	AUX
ejpam-1901	42	4	the	the	DET
ejpam-1901	42	5	set	set	NOUN
ejpam-1901	42	6	of	of	ADP
ejpam-1901	42	7	all	all	DET
ejpam-1901	42	8	weighted	weight	VERB
ejpam-1901	42	9	directed	direct	VERB
ejpam-1901	42	10	pseudo	pseudo	NOUN
ejpam-1901	42	11	simple	simple	ADJ
ejpam-1901	42	12	graphs	graph	NOUN
ejpam-1901	42	13	d	d	NOUN
ejpam-1901	42	14	=	=	SYM
ejpam-1901	42	15	(	(	PUNCT
ejpam-1901	42	16	v	v	NOUN
ejpam-1901	42	17	,	,	PUNCT
ejpam-1901	42	18	e	e	NOUN
ejpam-1901	42	19	)	)	PUNCT
ejpam-1901	42	20	.	.	PUNCT
ejpam-1901	43	1	then	then	ADV
ejpam-1901	43	2	(	(	PUNCT
ejpam-1901	43	3	dn	dn	INTJ
ejpam-1901	43	4	,	,	PUNCT
ejpam-1901	43	5	+	+	PROPN
ejpam-1901	43	6	,	,	PUNCT
ejpam-1901	43	7	.	.	PUNCT
ejpam-1901	43	8	)	)	PUNCT
ejpam-1901	43	9	is	be	AUX
ejpam-1901	43	10	a	a	DET
ejpam-1901	43	11	linear	linear	ADJ
ejpam-1901	43	12	space	space	NOUN
ejpam-1901	43	13	with	with	ADP
ejpam-1901	43	14	the	the	DET
ejpam-1901	43	15	definitions	definition	NOUN
ejpam-1901	43	16	given	give	VERB
ejpam-1901	43	17	in	in	ADP
ejpam-1901	43	18	[	[	X
ejpam-1901	43	19	3	3	NUM
ejpam-1901	43	20	]	]	PUNCT
ejpam-1901	43	21	and	and	CCONJ
ejpam-1901	43	22	[	[	X
ejpam-1901	43	23	2	2	NUM
ejpam-1901	43	24	]	]	PUNCT
ejpam-1901	43	25	.	.	PUNCT
ejpam-1901	44	1	let	let	VERB
ejpam-1901	44	2	the	the	DET
ejpam-1901	44	3	set	set	NOUN
ejpam-1901	44	4	of	of	ADP
ejpam-1901	44	5	all	all	DET
ejpam-1901	44	6	corresponding	correspond	VERB
ejpam-1901	44	7	adjacency	adjacency	NOUN
ejpam-1901	44	8	matrices	matrix	NOUN
ejpam-1901	44	9	be	be	VERB
ejpam-1901	44	10	en	en	ADP
ejpam-1901	44	11	.	.	PUNCT
ejpam-1901	45	1	then	then	ADV
ejpam-1901	45	2	(	(	PUNCT
ejpam-1901	45	3	en	en	X
ejpam-1901	45	4	,	,	PUNCT
ejpam-1901	45	5	+	+	PROPN
ejpam-1901	45	6	,	,	PUNCT
ejpam-1901	45	7	.	.	PUNCT
ejpam-1901	45	8	)	)	PUNCT
ejpam-1901	45	9	is	be	AUX
ejpam-1901	45	10	a	a	DET
ejpam-1901	45	11	matrix	matrix	NOUN
ejpam-1901	45	12	linear	linear	NOUN
ejpam-1901	45	13	space	space	NOUN
ejpam-1901	45	14	where	where	SCONJ
ejpam-1901	45	15	’	'	PUNCT
ejpam-1901	45	16	+	+	ADJ
ejpam-1901	45	17	’	'	PUNCT
ejpam-1901	45	18	denotes	denote	NOUN
ejpam-1901	45	19	matrix	matrix	VERB
ejpam-1901	45	20	addition	addition	NOUN
ejpam-1901	45	21	and	and	CCONJ
ejpam-1901	45	22	’	'	PUNCT
ejpam-1901	45	23	.	.	PUNCT
ejpam-1901	45	24	’	'	PUNCT
ejpam-1901	46	1	indicates	indicate	VERB
ejpam-1901	46	2	scalar	scalar	ADJ
ejpam-1901	46	3	multiplication	multiplication	NOUN
ejpam-1901	46	4	.	.	PUNCT
ejpam-1901	47	1	with	with	ADP
ejpam-1901	47	2	this	this	DET
ejpam-1901	47	3	basic	basic	ADJ
ejpam-1901	47	4	structures	structure	NOUN
ejpam-1901	47	5	defined	define	VERB
ejpam-1901	47	6	,	,	PUNCT
ejpam-1901	47	7	the	the	DET
ejpam-1901	47	8	comparison	comparison	NOUN
ejpam-1901	47	9	theorems	theorem	NOUN
ejpam-1901	47	10	,	,	PUNCT
ejpam-1901	47	11	existence	existence	NOUN
ejpam-1901	47	12	and	and	CCONJ
ejpam-1901	47	13	uniqueness	uniqueness	NOUN
ejpam-1901	47	14	results	result	NOUN
ejpam-1901	47	15	of	of	ADP
ejpam-1901	47	16	solutions	solution	NOUN
ejpam-1901	47	17	of	of	ADP
ejpam-1901	47	18	mde	mde	PROPN
ejpam-1901	47	19	and	and	CCONJ
ejpam-1901	47	20	the	the	DET
ejpam-1901	47	21	corresponding	correspond	VERB
ejpam-1901	47	22	gde	gde	PROPN
ejpam-1901	47	23	follow	follow	VERB
ejpam-1901	47	24	as	as	ADP
ejpam-1901	47	25	in	in	ADP
ejpam-1901	47	26	[	[	X
ejpam-1901	47	27	2	2	NUM
ejpam-1901	47	28	]	]	PUNCT
ejpam-1901	47	29	.	.	PUNCT
ejpam-1901	48	1	taking	take	VERB
ejpam-1901	48	2	cue	cue	NOUN
ejpam-1901	48	3	from	from	ADP
ejpam-1901	48	4	matrix	matrix	NOUN
ejpam-1901	48	5	multiplication	multiplication	NOUN
ejpam-1901	48	6	we	we	PRON
ejpam-1901	48	7	define	define	VERB
ejpam-1901	48	8	the	the	DET
ejpam-1901	48	9	product	product	NOUN
ejpam-1901	48	10	of	of	ADP
ejpam-1901	48	11	two	two	NUM
ejpam-1901	48	12	graphs	graph	NOUN
ejpam-1901	48	13	as	as	SCONJ
ejpam-1901	48	14	follows	follow	VERB
ejpam-1901	48	15	.	.	PUNCT
ejpam-1901	49	1	product	product	NOUN
ejpam-1901	49	2	of	of	ADP
ejpam-1901	49	3	graphs	graph	NOUN
ejpam-1901	49	4	:	:	PUNCT
ejpam-1901	49	5	let	let	VERB
ejpam-1901	49	6	g1	g1	PROPN
ejpam-1901	49	7	and	and	CCONJ
ejpam-1901	49	8	g2	g2	PROPN
ejpam-1901	49	9	be	be	VERB
ejpam-1901	49	10	two	two	NUM
ejpam-1901	49	11	graphs	graph	NOUN
ejpam-1901	49	12	with	with	ADP
ejpam-1901	49	13	edges	edge	NOUN
ejpam-1901	49	14	(	(	PUNCT
ejpam-1901	49	15	ei	ei	ADP
ejpam-1901	49	16	j)n×n	j)n×n	ADJ
ejpam-1901	49	17	and	and	CCONJ
ejpam-1901	49	18	(	(	PUNCT
ejpam-1901	49	19	di	di	NOUN
ejpam-1901	49	20	j)n×n	j)n×n	PROPN
ejpam-1901	49	21	respectively	respectively	ADV
ejpam-1901	49	22	.	.	PUNCT
ejpam-1901	50	1	then	then	ADV
ejpam-1901	50	2	the	the	DET
ejpam-1901	50	3	product	product	NOUN
ejpam-1901	50	4	of	of	ADP
ejpam-1901	50	5	the	the	DET
ejpam-1901	50	6	two	two	NUM
ejpam-1901	50	7	graphs	graph	NOUN
ejpam-1901	50	8	g1	g1	NOUN
ejpam-1901	50	9	and	and	CCONJ
ejpam-1901	50	10	g2	g2	PROPN
ejpam-1901	50	11	is	be	AUX
ejpam-1901	50	12	the	the	DET
ejpam-1901	50	13	graph	graph	NOUN
ejpam-1901	50	14	g	g	NOUN
ejpam-1901	50	15	in	in	ADP
ejpam-1901	50	16	which	which	PRON
ejpam-1901	50	17	the	the	DET
ejpam-1901	50	18	weight	weight	NOUN
ejpam-1901	50	19	gi	gi	X
ejpam-1901	50	20	j	j	PROPN
ejpam-1901	50	21	of	of	ADP
ejpam-1901	50	22	the	the	DET
ejpam-1901	50	23	edge	edge	NOUN
ejpam-1901	50	24	from	from	ADP
ejpam-1901	50	25	v	v	NUM
ejpam-1901	50	26	j	j	PROPN
ejpam-1901	50	27	to	to	ADP
ejpam-1901	50	28	vi	vi	PROPN
ejpam-1901	50	29	is	be	AUX
ejpam-1901	50	30	the	the	DET
ejpam-1901	50	31	dot	dot	NOUN
ejpam-1901	50	32	product	product	NOUN
ejpam-1901	50	33	of	of	ADP
ejpam-1901	50	34	the	the	DET
ejpam-1901	50	35	vectors	vector	NOUN
ejpam-1901	50	36	one	one	NOUN
ejpam-1901	50	37	having	have	VERB
ejpam-1901	50	38	the	the	DET
ejpam-1901	50	39	weights	weight	NOUN
ejpam-1901	50	40	of	of	ADP
ejpam-1901	50	41	the	the	DET
ejpam-1901	50	42	edges	edge	NOUN
ejpam-1901	50	43	inwards	inward	NOUN
ejpam-1901	50	44	to	to	ADP
ejpam-1901	50	45	vi	vi	PROPN
ejpam-1901	50	46	and	and	CCONJ
ejpam-1901	50	47	the	the	DET
ejpam-1901	50	48	other	other	ADJ
ejpam-1901	50	49	having	have	VERB
ejpam-1901	50	50	weights	weight	NOUN
ejpam-1901	50	51	of	of	ADP
ejpam-1901	50	52	the	the	DET
ejpam-1901	50	53	edges	edge	NOUN
ejpam-1901	50	54	outwards	outward	VERB
ejpam-1901	50	55	from	from	ADP
ejpam-1901	50	56	v	v	NUM
ejpam-1901	50	57	j	j	PROPN
ejpam-1901	50	58	.	.	PUNCT
ejpam-1901	51	1	we	we	PRON
ejpam-1901	51	2	now	now	ADV
ejpam-1901	51	3	proceed	proceed	VERB
ejpam-1901	51	4	to	to	PART
ejpam-1901	51	5	develop	develop	VERB
ejpam-1901	51	6	a	a	DET
ejpam-1901	51	7	result	result	NOUN
ejpam-1901	51	8	on	on	ADP
ejpam-1901	51	9	the	the	DET
ejpam-1901	51	10	nature	nature	NOUN
ejpam-1901	51	11	of	of	ADP
ejpam-1901	51	12	solutions	solution	NOUN
ejpam-1901	51	13	of	of	ADP
ejpam-1901	51	14	a	a	DET
ejpam-1901	51	15	graph	graph	NOUN
ejpam-1901	51	16	differential	differential	ADJ
ejpam-1901	51	17	equation	equation	NOUN
ejpam-1901	51	18	.	.	PUNCT
ejpam-1901	52	1	j.	j.	PROPN
ejpam-1901	52	2	devi	devi	PROPN
ejpam-1901	52	3	,	,	PUNCT
ejpam-1901	52	4	r.	r.	PROPN
ejpam-1901	52	5	kumar	kumar	PROPN
ejpam-1901	52	6	/	/	SYM
ejpam-1901	52	7	eur	eur	PROPN
ejpam-1901	52	8	.	.	PUNCT
ejpam-1901	53	1	j.	j.	PROPN
ejpam-1901	53	2	pure	pure	PROPN
ejpam-1901	53	3	appl	appl	PROPN
ejpam-1901	53	4	.	.	PROPN
ejpam-1901	53	5	math	math	PROPN
ejpam-1901	53	6	,	,	PUNCT
ejpam-1901	53	7	7	7	NUM
ejpam-1901	53	8	(	(	PUNCT
ejpam-1901	53	9	2014	2014	NUM
ejpam-1901	53	10	)	)	PUNCT
ejpam-1901	53	11	,	,	PUNCT
ejpam-1901	53	12	37	37	NUM
ejpam-1901	53	13	-	-	SYM
ejpam-1901	53	14	44	44	NUM
ejpam-1901	53	15	39	39	NUM
ejpam-1901	53	16	let	let	VERB
ejpam-1901	53	17	d′	d′	PRON
ejpam-1901	53	18	=	=	SYM
ejpam-1901	53	19	g(t	g(t	PROPN
ejpam-1901	53	20	,	,	PUNCT
ejpam-1901	53	21	d	d	NOUN
ejpam-1901	53	22	)	)	PUNCT
ejpam-1901	53	23	(	(	PUNCT
ejpam-1901	53	24	1	1	X
ejpam-1901	53	25	)	)	PUNCT
ejpam-1901	53	26	be	be	AUX
ejpam-1901	53	27	a	a	DET
ejpam-1901	53	28	graph	graph	NOUN
ejpam-1901	53	29	differential	differential	ADJ
ejpam-1901	53	30	equation	equation	NOUN
ejpam-1901	53	31	.	.	PUNCT
ejpam-1901	54	1	now	now	ADV
ejpam-1901	54	2	if	if	SCONJ
ejpam-1901	54	3	possible	possible	ADJ
ejpam-1901	54	4	suppose	suppose	VERB
ejpam-1901	54	5	g(t	g(t	PROPN
ejpam-1901	54	6	,	,	PUNCT
ejpam-1901	54	7	d	d	NOUN
ejpam-1901	54	8	)	)	PUNCT
ejpam-1901	54	9	can	can	AUX
ejpam-1901	54	10	be	be	AUX
ejpam-1901	54	11	written	write	VERB
ejpam-1901	54	12	as	as	ADP
ejpam-1901	54	13	a	a	DET
ejpam-1901	54	14	product	product	NOUN
ejpam-1901	54	15	of	of	ADP
ejpam-1901	54	16	two	two	NUM
ejpam-1901	54	17	graphs	graph	NOUN
ejpam-1901	54	18	c	c	NOUN
ejpam-1901	54	19	d	d	NOUN
ejpam-1901	54	20	where	where	SCONJ
ejpam-1901	54	21	c	c	NOUN
ejpam-1901	54	22	is	be	AUX
ejpam-1901	54	23	a	a	DET
ejpam-1901	54	24	graph	graph	NOUN
ejpam-1901	54	25	having	have	VERB
ejpam-1901	54	26	constant	constant	ADJ
ejpam-1901	54	27	weights	weight	NOUN
ejpam-1901	54	28	.	.	PUNCT
ejpam-1901	55	1	then	then	ADV
ejpam-1901	55	2	the	the	DET
ejpam-1901	55	3	gde	gde	NOUN
ejpam-1901	55	4	(	(	PUNCT
ejpam-1901	55	5	1	1	X
ejpam-1901	55	6	)	)	PUNCT
ejpam-1901	55	7	can	can	AUX
ejpam-1901	55	8	be	be	AUX
ejpam-1901	55	9	written	write	VERB
ejpam-1901	55	10	in	in	ADP
ejpam-1901	55	11	the	the	DET
ejpam-1901	55	12	form	form	NOUN
ejpam-1901	55	13	d′	d′	X
ejpam-1901	56	1	=	=	NOUN
ejpam-1901	56	2	c	c	NOUN
ejpam-1901	56	3	d	d	X
ejpam-1901	56	4	dt0	dt0	X
ejpam-1901	56	5	=	=	NOUN
ejpam-1901	56	6	d0	d0	NOUN
ejpam-1901	56	7	(	(	PUNCT
ejpam-1901	56	8	2	2	NUM
ejpam-1901	56	9	)	)	PUNCT
ejpam-1901	56	10	where	where	SCONJ
ejpam-1901	56	11	c	c	NOUN
ejpam-1901	56	12	is	be	AUX
ejpam-1901	56	13	a	a	DET
ejpam-1901	56	14	graph	graph	NOUN
ejpam-1901	56	15	called	call	VERB
ejpam-1901	56	16	a	a	DET
ejpam-1901	56	17	coefficient	coefficient	NOUN
ejpam-1901	56	18	graph	graph	NOUN
ejpam-1901	56	19	and	and	CCONJ
ejpam-1901	56	20	d	d	NOUN
ejpam-1901	56	21	0	0	NUM
ejpam-1901	56	22	is	be	AUX
ejpam-1901	56	23	the	the	DET
ejpam-1901	56	24	initial	initial	ADJ
ejpam-1901	56	25	graph	graph	NOUN
ejpam-1901	56	26	.	.	PUNCT
ejpam-1901	57	1	let	let	VERB
ejpam-1901	57	2	e′	e′	X
ejpam-1901	57	3	=	=	VERB
ejpam-1901	57	4	ae	ae	PROPN
ejpam-1901	57	5	et0	et0	NOUN
ejpam-1901	57	6	=	=	SYM
ejpam-1901	57	7	e0	e0	PROPN
ejpam-1901	57	8	(	(	PUNCT
ejpam-1901	57	9	3	3	X
ejpam-1901	57	10	)	)	PUNCT
ejpam-1901	57	11	be	be	AUX
ejpam-1901	57	12	the	the	DET
ejpam-1901	57	13	corresponding	corresponding	ADJ
ejpam-1901	57	14	ivp	ivp	NOUN
ejpam-1901	57	15	of	of	ADP
ejpam-1901	57	16	the	the	DET
ejpam-1901	57	17	mde	mde	PROPN
ejpam-1901	57	18	where	where	SCONJ
ejpam-1901	57	19	e	e	NOUN
ejpam-1901	57	20	0	0	PROPN
ejpam-1901	57	21	is	be	AUX
ejpam-1901	57	22	the	the	DET
ejpam-1901	57	23	adjacency	adjacency	NOUN
ejpam-1901	57	24	matrix	matrix	NOUN
ejpam-1901	57	25	corresponding	correspond	VERB
ejpam-1901	57	26	to	to	ADP
ejpam-1901	57	27	the	the	DET
ejpam-1901	57	28	initial	initial	ADJ
ejpam-1901	57	29	graph	graph	NOUN
ejpam-1901	57	30	d	d	NOUN
ejpam-1901	57	31	0	0	PROPN
ejpam-1901	57	32	.	.	PUNCT
ejpam-1901	58	1	then	then	ADV
ejpam-1901	58	2	we	we	PRON
ejpam-1901	58	3	have	have	VERB
ejpam-1901	58	4	the	the	DET
ejpam-1901	58	5	following	following	ADJ
ejpam-1901	58	6	result	result	NOUN
ejpam-1901	58	7	relating	relate	VERB
ejpam-1901	58	8	to	to	ADP
ejpam-1901	58	9	the	the	DET
ejpam-1901	58	10	solutions	solution	NOUN
ejpam-1901	58	11	of	of	ADP
ejpam-1901	58	12	mde	mde	PROPN
ejpam-1901	58	13	and	and	CCONJ
ejpam-1901	58	14	hence	hence	ADV
ejpam-1901	58	15	to	to	ADP
ejpam-1901	58	16	that	that	PRON
ejpam-1901	58	17	of	of	ADP
ejpam-1901	58	18	gdes	gde	NOUN
ejpam-1901	58	19	.	.	PUNCT
ejpam-1901	59	1	theorem	theorem	NOUN
ejpam-1901	59	2	1	1	NUM
ejpam-1901	59	3	.	.	PUNCT
ejpam-1901	60	1	let	let	AUX
ejpam-1901	60	2	e(t	e(t	VERB
ejpam-1901	60	3	)	)	PUNCT
ejpam-1901	60	4	be	be	AUX
ejpam-1901	60	5	a	a	DET
ejpam-1901	60	6	solution	solution	NOUN
ejpam-1901	60	7	of	of	ADP
ejpam-1901	60	8	the	the	DET
ejpam-1901	60	9	ivp	ivp	NOUN
ejpam-1901	60	10	(	(	PUNCT
ejpam-1901	60	11	3	3	NUM
ejpam-1901	60	12	)	)	PUNCT
ejpam-1901	60	13	.	.	PUNCT
ejpam-1901	61	1	suppose	suppose	VERB
ejpam-1901	61	2	there	there	PRON
ejpam-1901	61	3	exists	exist	VERB
ejpam-1901	61	4	a	a	DET
ejpam-1901	61	5	non	non	ADJ
ejpam-1901	61	6	singular	singular	NOUN
ejpam-1901	61	7	matrix	matrix	NOUN
ejpam-1901	61	8	p	p	NOUN
ejpam-1901	61	9	such	such	DET
ejpam-1901	61	10	that	that	DET
ejpam-1901	61	11	p−1ap	p−1ap	NOUN
ejpam-1901	61	12	=	=	PUNCT
ejpam-1901	61	13	h	h	NOUN
ejpam-1901	61	14	is	be	AUX
ejpam-1901	61	15	a	a	DET
ejpam-1901	61	16	diagonal	diagonal	ADJ
ejpam-1901	61	17	matrix	matrix	NOUN
ejpam-1901	61	18	.	.	PUNCT
ejpam-1901	62	1	then	then	ADV
ejpam-1901	62	2	the	the	DET
ejpam-1901	62	3	solution	solution	NOUN
ejpam-1901	62	4	e(t	e(t	NOUN
ejpam-1901	62	5	)	)	PUNCT
ejpam-1901	62	6	has	have	VERB
ejpam-1901	62	7	the	the	DET
ejpam-1901	62	8	same	same	ADJ
ejpam-1901	62	9	nature	nature	NOUN
ejpam-1901	62	10	as	as	ADP
ejpam-1901	62	11	that	that	PRON
ejpam-1901	62	12	of	of	ADP
ejpam-1901	62	13	e	e	PROPN
ejpam-1901	62	14	0	0	PUNCT
ejpam-1901	62	15	.	.	PUNCT
ejpam-1901	63	1	in	in	ADP
ejpam-1901	63	2	other	other	ADJ
ejpam-1901	63	3	words	word	NOUN
ejpam-1901	63	4	,	,	PUNCT
ejpam-1901	63	5	the	the	DET
ejpam-1901	63	6	solution	solution	NOUN
ejpam-1901	63	7	of	of	ADP
ejpam-1901	63	8	the	the	DET
ejpam-1901	63	9	ivp	ivp	NOUN
ejpam-1901	63	10	of	of	ADP
ejpam-1901	63	11	the	the	DET
ejpam-1901	63	12	gde	gde	NOUN
ejpam-1901	63	13	(	(	PUNCT
ejpam-1901	63	14	2	2	NUM
ejpam-1901	63	15	)	)	PUNCT
ejpam-1901	63	16	has	have	VERB
ejpam-1901	63	17	the	the	DET
ejpam-1901	63	18	same	same	ADJ
ejpam-1901	63	19	nature	nature	NOUN
ejpam-1901	63	20	as	as	ADP
ejpam-1901	63	21	that	that	PRON
ejpam-1901	63	22	of	of	ADP
ejpam-1901	63	23	the	the	DET
ejpam-1901	63	24	initial	initial	ADJ
ejpam-1901	63	25	graph	graph	NOUN
ejpam-1901	63	26	d	d	NOUN
ejpam-1901	63	27	0	0	NUM
ejpam-1901	63	28	.	.	PUNCT
ejpam-1901	64	1	proof	proof	NOUN
ejpam-1901	64	2	.	.	PUNCT
ejpam-1901	65	1	suppose	suppose	VERB
ejpam-1901	65	2	there	there	PRON
ejpam-1901	65	3	exist	exist	VERB
ejpam-1901	65	4	a	a	DET
ejpam-1901	65	5	matrix	matrix	NOUN
ejpam-1901	65	6	p	p	NOUN
ejpam-1901	66	1	such	such	DET
ejpam-1901	66	2	that	that	DET
ejpam-1901	66	3	p−1ap	p−1ap	NOUN
ejpam-1901	66	4	=	=	SYM
ejpam-1901	66	5	h.	h.	PROPN
ejpam-1901	67	1	then	then	ADV
ejpam-1901	67	2	we	we	PRON
ejpam-1901	67	3	know	know	VERB
ejpam-1901	67	4	from	from	ADP
ejpam-1901	67	5	the	the	DET
ejpam-1901	67	6	theory	theory	NOUN
ejpam-1901	67	7	of	of	ADP
ejpam-1901	67	8	linear	linear	PROPN
ejpam-1901	67	9	algebra	algebra	NOUN
ejpam-1901	67	10	that	that	PRON
ejpam-1901	67	11	a	a	PRON
ejpam-1901	67	12	and	and	CCONJ
ejpam-1901	67	13	h	h	NOUN
ejpam-1901	67	14	have	have	AUX
ejpam-1901	67	15	the	the	DET
ejpam-1901	67	16	same	same	ADJ
ejpam-1901	67	17	eigen	eigen	PROPN
ejpam-1901	67	18	values	value	NOUN
ejpam-1901	67	19	.	.	PUNCT
ejpam-1901	68	1	further	far	ADV
ejpam-1901	68	2	we	we	PRON
ejpam-1901	68	3	know	know	VERB
ejpam-1901	68	4	that	that	SCONJ
ejpam-1901	68	5	the	the	DET
ejpam-1901	68	6	solution	solution	NOUN
ejpam-1901	68	7	of	of	ADP
ejpam-1901	68	8	the	the	DET
ejpam-1901	68	9	ivp	ivp	NOUN
ejpam-1901	68	10	of	of	ADP
ejpam-1901	68	11	mde	mde	PROPN
ejpam-1901	68	12	(	(	PUNCT
ejpam-1901	68	13	3	3	X
ejpam-1901	68	14	)	)	PUNCT
ejpam-1901	68	15	is	be	AUX
ejpam-1901	68	16	same	same	ADJ
ejpam-1901	68	17	as	as	ADP
ejpam-1901	68	18	the	the	DET
ejpam-1901	68	19	solution	solution	NOUN
ejpam-1901	68	20	of	of	ADP
ejpam-1901	68	21	the	the	DET
ejpam-1901	68	22	mde	mde	NOUN
ejpam-1901	68	23	e′	e′	X
ejpam-1901	69	1	=	=	SYM
ejpam-1901	69	2	he	he	PRON
ejpam-1901	69	3	,	,	PUNCT
ejpam-1901	69	4	et0	et0	NOUN
ejpam-1901	69	5	=	=	SYM
ejpam-1901	69	6	e0	e0	PROPN
ejpam-1901	69	7	.	.	PUNCT
ejpam-1901	70	1	the	the	DET
ejpam-1901	70	2	solution	solution	NOUN
ejpam-1901	70	3	of	of	ADP
ejpam-1901	70	4	the	the	DET
ejpam-1901	70	5	mde	mde	PROPN
ejpam-1901	70	6	(	(	PUNCT
ejpam-1901	70	7	3	3	X
ejpam-1901	70	8	)	)	PUNCT
ejpam-1901	70	9	is	be	AUX
ejpam-1901	70	10	given	give	VERB
ejpam-1901	70	11	by	by	ADP
ejpam-1901	70	12	e(t	e(t	NOUN
ejpam-1901	70	13	)	)	PUNCT
ejpam-1901	70	14	=	=	SYM
ejpam-1901	70	15	eht	eht	PROPN
ejpam-1901	70	16	e	e	PROPN
ejpam-1901	70	17	0	0	PROPN
ejpam-1901	70	18	,	,	PUNCT
ejpam-1901	70	19	where	where	SCONJ
ejpam-1901	70	20	eht	eht	PROPN
ejpam-1901	70	21	is	be	AUX
ejpam-1901	70	22	a	a	DET
ejpam-1901	70	23	diagonal	diagonal	ADJ
ejpam-1901	70	24	matrix	matrix	NOUN
ejpam-1901	70	25	.	.	PUNCT
ejpam-1901	71	1	thus	thus	ADV
ejpam-1901	71	2	it	it	PRON
ejpam-1901	71	3	is	be	AUX
ejpam-1901	71	4	clear	clear	ADJ
ejpam-1901	71	5	that	that	SCONJ
ejpam-1901	71	6	e(t	e(t	PROPN
ejpam-1901	71	7	)	)	PUNCT
ejpam-1901	71	8	enjoys	enjoy	VERB
ejpam-1901	71	9	the	the	DET
ejpam-1901	71	10	same	same	ADJ
ejpam-1901	71	11	character	character	NOUN
ejpam-1901	71	12	as	as	ADP
ejpam-1901	71	13	of	of	ADP
ejpam-1901	71	14	e	e	NOUN
ejpam-1901	71	15	0	0	PUNCT
ejpam-1901	71	16	.	.	PUNCT
ejpam-1901	72	1	using	use	VERB
ejpam-1901	72	2	the	the	DET
ejpam-1901	72	3	fact	fact	NOUN
ejpam-1901	72	4	that	that	SCONJ
ejpam-1901	72	5	there	there	PRON
ejpam-1901	72	6	exists	exist	VERB
ejpam-1901	72	7	an	an	DET
ejpam-1901	72	8	isomorphism	isomorphism	NOUN
ejpam-1901	72	9	between	between	ADP
ejpam-1901	72	10	matrices	matrix	NOUN
ejpam-1901	72	11	and	and	CCONJ
ejpam-1901	72	12	graphs	graph	NOUN
ejpam-1901	72	13	.	.	PUNCT
ejpam-1901	73	1	we	we	PRON
ejpam-1901	73	2	can	can	AUX
ejpam-1901	73	3	easily	easily	ADV
ejpam-1901	73	4	conclude	conclude	VERB
ejpam-1901	73	5	that	that	SCONJ
ejpam-1901	73	6	the	the	DET
ejpam-1901	73	7	ivp	ivp	NOUN
ejpam-1901	73	8	of	of	ADP
ejpam-1901	73	9	gde	gde	PROPN
ejpam-1901	73	10	(	(	PUNCT
ejpam-1901	73	11	2	2	NUM
ejpam-1901	73	12	)	)	PUNCT
ejpam-1901	73	13	has	have	VERB
ejpam-1901	73	14	a	a	DET
ejpam-1901	73	15	solution	solution	NOUN
ejpam-1901	73	16	d(t	d(t	NOUN
ejpam-1901	73	17	)	)	PUNCT
ejpam-1901	73	18	having	have	VERB
ejpam-1901	73	19	the	the	DET
ejpam-1901	73	20	same	same	ADJ
ejpam-1901	73	21	nature	nature	NOUN
ejpam-1901	73	22	as	as	ADP
ejpam-1901	73	23	that	that	PRON
ejpam-1901	73	24	of	of	ADP
ejpam-1901	73	25	d0	d0	NOUN
ejpam-1901	73	26	.	.	PUNCT
ejpam-1901	74	1	remark	remark	NOUN
ejpam-1901	74	2	1	1	NUM
ejpam-1901	74	3	.	.	PUNCT
ejpam-1901	75	1	corresponding	correspond	VERB
ejpam-1901	75	2	to	to	ADP
ejpam-1901	75	3	the	the	DET
ejpam-1901	75	4	matrices	matrix	NOUN
ejpam-1901	75	5	p−1	p−1	PROPN
ejpam-1901	75	6	and	and	CCONJ
ejpam-1901	75	7	p	p	NOUN
ejpam-1901	75	8	we	we	PRON
ejpam-1901	75	9	can	can	AUX
ejpam-1901	75	10	find	find	VERB
ejpam-1901	75	11	two	two	NUM
ejpam-1901	75	12	graphs	graph	NOUN
ejpam-1901	75	13	gp−1	gp−1	VERB
ejpam-1901	75	14	and	and	CCONJ
ejpam-1901	75	15	gp	gp	NOUN
ejpam-1901	75	16	such	such	ADJ
ejpam-1901	75	17	that	that	SCONJ
ejpam-1901	75	18	gp−1	gp−1	PROPN
ejpam-1901	75	19	gagp=	gagp=	PROPN
ejpam-1901	75	20	gh	gh	PROPN
ejpam-1901	75	21	is	be	AUX
ejpam-1901	75	22	a	a	DET
ejpam-1901	75	23	graph	graph	NOUN
ejpam-1901	75	24	having	have	VERB
ejpam-1901	75	25	only	only	ADJ
ejpam-1901	75	26	loops	loop	NOUN
ejpam-1901	75	27	.	.	PUNCT
ejpam-1901	76	1	please	please	INTJ
ejpam-1901	76	2	see	see	VERB
ejpam-1901	76	3	figures	figure	NOUN
ejpam-1901	76	4	1a	1a	PROPN
ejpam-1901	76	5	through	through	ADP
ejpam-1901	76	6	1d	1d	NUM
ejpam-1901	76	7	.	.	PUNCT
ejpam-1901	77	1	j.	j.	PROPN
ejpam-1901	77	2	devi	devi	PROPN
ejpam-1901	77	3	,	,	PUNCT
ejpam-1901	77	4	r.	r.	PROPN
ejpam-1901	77	5	kumar	kumar	PROPN
ejpam-1901	77	6	/	/	SYM
ejpam-1901	77	7	eur	eur	PROPN
ejpam-1901	77	8	.	.	PUNCT
ejpam-1901	78	1	j.	j.	PROPN
ejpam-1901	78	2	pure	pure	PROPN
ejpam-1901	78	3	appl	appl	PROPN
ejpam-1901	78	4	.	.	PROPN
ejpam-1901	78	5	math	math	PROPN
ejpam-1901	78	6	,	,	PUNCT
ejpam-1901	78	7	7	7	NUM
ejpam-1901	78	8	(	(	PUNCT
ejpam-1901	78	9	2014	2014	NUM
ejpam-1901	78	10	)	)	PUNCT
ejpam-1901	78	11	,	,	PUNCT
ejpam-1901	78	12	37	37	NUM
ejpam-1901	78	13	-	-	SYM
ejpam-1901	78	14	44	44	NUM
ejpam-1901	78	15	40	40	NUM
ejpam-1901	78	16	(	(	PUNCT
ejpam-1901	78	17	a	a	NOUN
ejpam-1901	78	18	)	)	PUNCT
ejpam-1901	78	19	gp	gp	NOUN
ejpam-1901	78	20	(	(	PUNCT
ejpam-1901	78	21	b	b	NOUN
ejpam-1901	78	22	)	)	PUNCT
ejpam-1901	78	23	gp	gp	NOUN
ejpam-1901	78	24	−1	−1	NOUN
ejpam-1901	78	25	(	(	PUNCT
ejpam-1901	78	26	c	c	X
ejpam-1901	78	27	)	)	PUNCT
ejpam-1901	78	28	ga	ga	NOUN
ejpam-1901	78	29	(	(	PUNCT
ejpam-1901	78	30	d	d	NOUN
ejpam-1901	78	31	)	)	PUNCT
ejpam-1901	78	32	gp	gp	NOUN
ejpam-1901	79	1	−1gag	−1gag	NOUN
ejpam-1901	79	2	figure	figure	NOUN
ejpam-1901	79	3	1	1	NUM
ejpam-1901	79	4	:	:	PUNCT
ejpam-1901	79	5	graphs	graphs	PROPN
ejpam-1901	79	6	j.	j.	PROPN
ejpam-1901	79	7	devi	devi	PROPN
ejpam-1901	79	8	,	,	PUNCT
ejpam-1901	79	9	r.	r.	PROPN
ejpam-1901	79	10	kumar	kumar	PROPN
ejpam-1901	79	11	/	/	SYM
ejpam-1901	79	12	eur	eur	PROPN
ejpam-1901	79	13	.	.	PUNCT
ejpam-1901	80	1	j.	j.	PROPN
ejpam-1901	80	2	pure	pure	PROPN
ejpam-1901	80	3	appl	appl	PROPN
ejpam-1901	80	4	.	.	PROPN
ejpam-1901	80	5	math	math	PROPN
ejpam-1901	80	6	,	,	PUNCT
ejpam-1901	80	7	7	7	NUM
ejpam-1901	80	8	(	(	PUNCT
ejpam-1901	80	9	2014	2014	NUM
ejpam-1901	80	10	)	)	PUNCT
ejpam-1901	80	11	,	,	PUNCT
ejpam-1901	80	12	37	37	NUM
ejpam-1901	80	13	-	-	SYM
ejpam-1901	80	14	44	44	NUM
ejpam-1901	80	15	41	41	NUM
ejpam-1901	80	16	3	3	NUM
ejpam-1901	80	17	.	.	PUNCT
ejpam-1901	81	1	modeling	modeling	NOUN
ejpam-1901	81	2	of	of	ADP
ejpam-1901	81	3	the	the	DET
ejpam-1901	81	4	prey	prey	NOUN
ejpam-1901	81	5	-	-	PUNCT
ejpam-1901	81	6	predator	predator	NOUN
ejpam-1901	81	7	problem	problem	NOUN
ejpam-1901	81	8	in	in	ADP
ejpam-1901	81	9	this	this	DET
ejpam-1901	81	10	section	section	NOUN
ejpam-1901	81	11	,	,	PUNCT
ejpam-1901	81	12	we	we	PRON
ejpam-1901	81	13	formulate	formulate	VERB
ejpam-1901	81	14	a	a	DET
ejpam-1901	81	15	matrix	matrix	NOUN
ejpam-1901	81	16	differential	differential	NOUN
ejpam-1901	81	17	equation	equation	NOUN
ejpam-1901	81	18	for	for	ADP
ejpam-1901	81	19	the	the	DET
ejpam-1901	81	20	famous	famous	ADJ
ejpam-1901	81	21	prey	prey	NOUN
ejpam-1901	81	22	predator	predator	NOUN
ejpam-1901	81	23	model	model	NOUN
ejpam-1901	81	24	and	and	CCONJ
ejpam-1901	81	25	later	later	ADV
ejpam-1901	81	26	extend	extend	VERB
ejpam-1901	81	27	it	it	PRON
ejpam-1901	81	28	to	to	ADP
ejpam-1901	81	29	three	three	NUM
ejpam-1901	81	30	species	specie	NOUN
ejpam-1901	81	31	and	and	CCONJ
ejpam-1901	81	32	n	n	DET
ejpam-1901	81	33	-species	-specie	NOUN
ejpam-1901	81	34	.	.	PUNCT
ejpam-1901	82	1	let	let	VERB
ejpam-1901	82	2	x	x	PRON
ejpam-1901	82	3	denote	denote	VERB
ejpam-1901	82	4	the	the	DET
ejpam-1901	82	5	prey	prey	NOUN
ejpam-1901	82	6	population	population	NOUN
ejpam-1901	82	7	and	and	CCONJ
ejpam-1901	82	8	y	y	PROPN
ejpam-1901	82	9	denote	denote	VERB
ejpam-1901	82	10	the	the	DET
ejpam-1901	82	11	predator	predator	NOUN
ejpam-1901	82	12	population	population	NOUN
ejpam-1901	82	13	,	,	PUNCT
ejpam-1901	82	14	then	then	ADV
ejpam-1901	82	15	the	the	DET
ejpam-1901	82	16	rate	rate	NOUN
ejpam-1901	82	17	of	of	ADP
ejpam-1901	82	18	change	change	NOUN
ejpam-1901	82	19	of	of	ADP
ejpam-1901	82	20	prey	prey	NOUN
ejpam-1901	82	21	and	and	CCONJ
ejpam-1901	82	22	that	that	PRON
ejpam-1901	82	23	of	of	ADP
ejpam-1901	82	24	predator	predator	NOUN
ejpam-1901	82	25	gives	give	VERB
ejpam-1901	82	26	rise	rise	NOUN
ejpam-1901	82	27	to	to	ADP
ejpam-1901	82	28	a	a	DET
ejpam-1901	82	29	system	system	NOUN
ejpam-1901	82	30	of	of	ADP
ejpam-1901	82	31	nonlinear	nonlinear	ADJ
ejpam-1901	82	32	differential	differential	ADJ
ejpam-1901	82	33	equations	equation	NOUN
ejpam-1901	82	34	given	give	VERB
ejpam-1901	82	35	by	by	ADP
ejpam-1901	82	36	d	d	PROPN
ejpam-1901	82	37	x	x	PROPN
ejpam-1901	82	38	d	d	NOUN
ejpam-1901	82	39	t	t	NOUN
ejpam-1901	82	40	=	=	NOUN
ejpam-1901	82	41	ax	ax	NOUN
ejpam-1901	82	42	+	+	CCONJ
ejpam-1901	82	43	bx	bx	PROPN
ejpam-1901	82	44	y	y	PROPN
ejpam-1901	82	45	,	,	PUNCT
ejpam-1901	82	46	a	a	PRON
ejpam-1901	82	47	>	>	X
ejpam-1901	82	48	0	0	NUM
ejpam-1901	82	49	,	,	PUNCT
ejpam-1901	82	50	b	b	X
ejpam-1901	82	51	<	<	X
ejpam-1901	82	52	0	0	NUM
ejpam-1901	82	53	,	,	PUNCT
ejpam-1901	82	54	(	(	PUNCT
ejpam-1901	82	55	4	4	X
ejpam-1901	82	56	)	)	PUNCT
ejpam-1901	83	1	d	d	NOUN
ejpam-1901	83	2	y	y	PROPN
ejpam-1901	83	3	d	d	X
ejpam-1901	83	4	t	t	PROPN
ejpam-1901	83	5	=	=	PUNCT
ejpam-1901	84	1	c	c	NOUN
ejpam-1901	84	2	y	y	NOUN
ejpam-1901	84	3	x	x	PUNCT
ejpam-1901	85	1	+	+	CCONJ
ejpam-1901	85	2	d	d	X
ejpam-1901	85	3	y	y	PROPN
ejpam-1901	85	4	,	,	PUNCT
ejpam-1901	85	5	c	c	X
ejpam-1901	85	6	>	>	X
ejpam-1901	85	7	0	0	PROPN
ejpam-1901	85	8	,	,	PUNCT
ejpam-1901	85	9	d	d	X
ejpam-1901	85	10	<	<	X
ejpam-1901	85	11	0	0	NUM
ejpam-1901	85	12	.	.	PUNCT
ejpam-1901	86	1	(	(	PUNCT
ejpam-1901	86	2	5	5	X
ejpam-1901	86	3	)	)	PUNCT
ejpam-1901	86	4	it	it	PRON
ejpam-1901	86	5	is	be	AUX
ejpam-1901	86	6	well	well	ADV
ejpam-1901	86	7	known	know	VERB
ejpam-1901	86	8	that	that	SCONJ
ejpam-1901	86	9	the	the	DET
ejpam-1901	86	10	above	above	ADJ
ejpam-1901	86	11	differential	differential	ADJ
ejpam-1901	86	12	equations	equation	NOUN
ejpam-1901	86	13	are	be	AUX
ejpam-1901	86	14	linearized	linearize	VERB
ejpam-1901	86	15	and	and	CCONJ
ejpam-1901	86	16	solved	solve	VERB
ejpam-1901	86	17	as	as	ADP
ejpam-1901	86	18	a	a	DET
ejpam-1901	86	19	linear	linear	ADJ
ejpam-1901	86	20	system	system	NOUN
ejpam-1901	86	21	of	of	ADP
ejpam-1901	86	22	differential	differential	ADJ
ejpam-1901	86	23	equations	equation	NOUN
ejpam-1901	86	24	.	.	PUNCT
ejpam-1901	87	1	we	we	PRON
ejpam-1901	87	2	now	now	ADV
ejpam-1901	87	3	express	express	VERB
ejpam-1901	87	4	the	the	DET
ejpam-1901	87	5	above	above	ADJ
ejpam-1901	87	6	system	system	NOUN
ejpam-1901	87	7	as	as	ADP
ejpam-1901	87	8	a	a	DET
ejpam-1901	87	9	graph	graph	NOUN
ejpam-1901	87	10	differential	differential	ADJ
ejpam-1901	87	11	equation	equation	NOUN
ejpam-1901	87	12	and	and	CCONJ
ejpam-1901	87	13	consider	consider	VERB
ejpam-1901	87	14	the	the	DET
ejpam-1901	87	15	corresponding	corresponding	ADJ
ejpam-1901	87	16	matrix	matrix	NOUN
ejpam-1901	87	17	differential	differential	NOUN
ejpam-1901	87	18	equation	equation	NOUN
ejpam-1901	87	19	.	.	PUNCT
ejpam-1901	88	1	we	we	PRON
ejpam-1901	88	2	show	show	VERB
ejpam-1901	88	3	that	that	SCONJ
ejpam-1901	88	4	the	the	DET
ejpam-1901	88	5	nonlinearity	nonlinearity	NOUN
ejpam-1901	88	6	is	be	AUX
ejpam-1901	88	7	preserved	preserve	VERB
ejpam-1901	88	8	in	in	ADP
ejpam-1901	88	9	this	this	DET
ejpam-1901	88	10	set	set	VERB
ejpam-1901	88	11	up	up	ADP
ejpam-1901	88	12	.	.	PUNCT
ejpam-1901	89	1	let	let	VERB
ejpam-1901	89	2	the	the	DET
ejpam-1901	89	3	vertex	vertex	NOUN
ejpam-1901	89	4	v1	v1	NOUN
ejpam-1901	89	5	denote	denote	VERB
ejpam-1901	89	6	the	the	DET
ejpam-1901	89	7	prey	prey	NOUN
ejpam-1901	89	8	and	and	CCONJ
ejpam-1901	89	9	v2	v2	PROPN
ejpam-1901	89	10	denote	denote	VERB
ejpam-1901	89	11	the	the	DET
ejpam-1901	89	12	predator	predator	NOUN
ejpam-1901	89	13	.	.	PUNCT
ejpam-1901	90	1	set	set	VERB
ejpam-1901	90	2	e11	e11	NOUN
ejpam-1901	90	3	=	=	NOUN
ejpam-1901	91	1	x	x	PUNCT
ejpam-1901	91	2	as	as	ADP
ejpam-1901	91	3	population	population	NOUN
ejpam-1901	91	4	of	of	ADP
ejpam-1901	91	5	the	the	DET
ejpam-1901	91	6	prey	prey	NOUN
ejpam-1901	91	7	and	and	CCONJ
ejpam-1901	91	8	e22	e22	X
ejpam-1901	91	9	=	=	SYM
ejpam-1901	91	10	y	y	PROPN
ejpam-1901	91	11	as	as	ADP
ejpam-1901	91	12	the	the	DET
ejpam-1901	91	13	population	population	NOUN
ejpam-1901	91	14	of	of	ADP
ejpam-1901	91	15	the	the	DET
ejpam-1901	91	16	predator	predator	NOUN
ejpam-1901	91	17	.	.	PUNCT
ejpam-1901	92	1	it	it	PRON
ejpam-1901	92	2	can	can	AUX
ejpam-1901	92	3	be	be	AUX
ejpam-1901	92	4	seen	see	VERB
ejpam-1901	92	5	that	that	SCONJ
ejpam-1901	92	6	e12	e12	NOUN
ejpam-1901	92	7	is	be	AUX
ejpam-1901	92	8	the	the	DET
ejpam-1901	92	9	edge	edge	NOUN
ejpam-1901	92	10	going	go	VERB
ejpam-1901	92	11	outward	outward	ADV
ejpam-1901	92	12	from	from	ADP
ejpam-1901	92	13	v2	v2	NOUN
ejpam-1901	92	14	and	and	CCONJ
ejpam-1901	92	15	is	be	AUX
ejpam-1901	92	16	incident	incident	NOUN
ejpam-1901	92	17	on	on	ADP
ejpam-1901	92	18	v1	v1	NOUN
ejpam-1901	92	19	.	.	PUNCT
ejpam-1901	93	1	this	this	PRON
ejpam-1901	93	2	means	mean	VERB
ejpam-1901	93	3	that	that	SCONJ
ejpam-1901	93	4	e12	e12	NOUN
ejpam-1901	93	5	denotes	denote	VERB
ejpam-1901	93	6	the	the	DET
ejpam-1901	93	7	interaction	interaction	NOUN
ejpam-1901	93	8	between	between	ADP
ejpam-1901	93	9	predator	predator	NOUN
ejpam-1901	93	10	and	and	CCONJ
ejpam-1901	93	11	prey	prey	NOUN
ejpam-1901	93	12	.	.	PUNCT
ejpam-1901	94	1	actually	actually	ADV
ejpam-1901	94	2	,	,	PUNCT
ejpam-1901	94	3	e12	e12	NOUN
ejpam-1901	94	4	gives	give	VERB
ejpam-1901	94	5	the	the	DET
ejpam-1901	94	6	status	status	NOUN
ejpam-1901	94	7	of	of	ADP
ejpam-1901	94	8	predators	predator	NOUN
ejpam-1901	94	9	finding	find	VERB
ejpam-1901	94	10	the	the	DET
ejpam-1901	94	11	prey	prey	NOUN
ejpam-1901	94	12	.	.	PUNCT
ejpam-1901	95	1	similarly	similarly	ADV
ejpam-1901	95	2	e21	e21	X
ejpam-1901	95	3	denotes	denote	NOUN
ejpam-1901	95	4	the	the	DET
ejpam-1901	95	5	edge	edge	NOUN
ejpam-1901	95	6	outward	outward	ADV
ejpam-1901	95	7	from	from	ADP
ejpam-1901	95	8	v1	v1	NOUN
ejpam-1901	95	9	and	and	CCONJ
ejpam-1901	95	10	incident	incident	NOUN
ejpam-1901	95	11	on	on	ADP
ejpam-1901	95	12	v2	v2	PROPN
ejpam-1901	95	13	.	.	PUNCT
ejpam-1901	96	1	in	in	ADP
ejpam-1901	96	2	terms	term	NOUN
ejpam-1901	96	3	of	of	ADP
ejpam-1901	96	4	our	our	PRON
ejpam-1901	96	5	model	model	NOUN
ejpam-1901	96	6	,	,	PUNCT
ejpam-1901	96	7	this	this	DET
ejpam-1901	96	8	edge	edge	NOUN
ejpam-1901	96	9	indicates	indicate	VERB
ejpam-1901	96	10	the	the	DET
ejpam-1901	96	11	status	status	NOUN
ejpam-1901	96	12	of	of	ADP
ejpam-1901	96	13	prey	prey	NOUN
ejpam-1901	96	14	that	that	PRON
ejpam-1901	96	15	fall	fall	VERB
ejpam-1901	96	16	prey	prey	NOUN
ejpam-1901	96	17	to	to	ADP
ejpam-1901	96	18	predators	predator	NOUN
ejpam-1901	96	19	.	.	PUNCT
ejpam-1901	97	1	now	now	ADV
ejpam-1901	97	2	the	the	DET
ejpam-1901	97	3	graph	graph	NOUN
ejpam-1901	97	4	of	of	ADP
ejpam-1901	97	5	the	the	DET
ejpam-1901	97	6	prey	prey	NOUN
ejpam-1901	97	7	predator	predator	NOUN
ejpam-1901	97	8	model	model	NOUN
ejpam-1901	97	9	is	be	AUX
ejpam-1901	97	10	of	of	ADP
ejpam-1901	97	11	the	the	DET
ejpam-1901	97	12	form	form	NOUN
ejpam-1901	97	13	figure	figure	NOUN
ejpam-1901	97	14	2	2	NUM
ejpam-1901	97	15	:	:	PUNCT
ejpam-1901	97	16	the	the	DET
ejpam-1901	97	17	graph	graph	NOUN
ejpam-1901	97	18	of	of	ADP
ejpam-1901	97	19	the	the	DET
ejpam-1901	97	20	prey	prey	NOUN
ejpam-1901	97	21	-	-	PUNCT
ejpam-1901	97	22	predator	predator	NOUN
ejpam-1901	97	23	problem	problem	NOUN
ejpam-1901	97	24	and	and	CCONJ
ejpam-1901	97	25	its	its	PRON
ejpam-1901	97	26	adjacency	adjacency	NOUN
ejpam-1901	97	27	matrix	matrix	NOUN
ejpam-1901	97	28	is	be	AUX
ejpam-1901	97	29	given	give	VERB
ejpam-1901	97	30	by	by	ADP
ejpam-1901	97	31	�	�	PROPN
ejpam-1901	97	32	e11	e11	PROPN
ejpam-1901	97	33	e12	e12	NOUN
ejpam-1901	97	34	e21	e21	X
ejpam-1901	97	35	e22	e22	PROPN
ejpam-1901	97	36	�	�	PROPN
ejpam-1901	97	37	.	.	PUNCT
ejpam-1901	98	1	the	the	DET
ejpam-1901	98	2	equations	equation	NOUN
ejpam-1901	98	3	(	(	PUNCT
ejpam-1901	98	4	4	4	NUM
ejpam-1901	98	5	)	)	PUNCT
ejpam-1901	98	6	and	and	CCONJ
ejpam-1901	98	7	(	(	PUNCT
ejpam-1901	98	8	5	5	X
ejpam-1901	98	9	)	)	PUNCT
ejpam-1901	98	10	reduce	reduce	VERB
ejpam-1901	98	11	to	to	ADP
ejpam-1901	98	12	the	the	DET
ejpam-1901	98	13	form	form	NOUN
ejpam-1901	98	14	e′11	e′11	NOUN
ejpam-1901	98	15	=	=	SYM
ejpam-1901	98	16	ae11	ae11	PROPN
ejpam-1901	98	17	+	+	CCONJ
ejpam-1901	98	18	be21	be21	PROPN
ejpam-1901	98	19	,	,	PUNCT
ejpam-1901	98	20	(	(	PUNCT
ejpam-1901	98	21	6	6	NUM
ejpam-1901	98	22	)	)	PUNCT
ejpam-1901	98	23	j.	j.	PROPN
ejpam-1901	98	24	devi	devi	PROPN
ejpam-1901	98	25	,	,	PUNCT
ejpam-1901	98	26	r.	r.	PROPN
ejpam-1901	98	27	kumar	kumar	PROPN
ejpam-1901	98	28	/	/	SYM
ejpam-1901	98	29	eur	eur	PROPN
ejpam-1901	98	30	.	.	PUNCT
ejpam-1901	99	1	j.	j.	PROPN
ejpam-1901	99	2	pure	pure	PROPN
ejpam-1901	99	3	appl	appl	PROPN
ejpam-1901	99	4	.	.	PROPN
ejpam-1901	99	5	math	math	PROPN
ejpam-1901	99	6	,	,	PUNCT
ejpam-1901	99	7	7	7	NUM
ejpam-1901	99	8	(	(	PUNCT
ejpam-1901	99	9	2014	2014	NUM
ejpam-1901	99	10	)	)	PUNCT
ejpam-1901	99	11	,	,	PUNCT
ejpam-1901	99	12	37	37	NUM
ejpam-1901	99	13	-	-	SYM
ejpam-1901	99	14	44	44	NUM
ejpam-1901	99	15	42	42	NUM
ejpam-1901	99	16	e′22	e′22	ADJ
ejpam-1901	99	17	=	=	SYM
ejpam-1901	99	18	ae12	ae12	PROPN
ejpam-1901	99	19	+	+	NUM
ejpam-1901	99	20	be22	be22	PROPN
ejpam-1901	99	21	.	.	PUNCT
ejpam-1901	100	1	(	(	PUNCT
ejpam-1901	100	2	7	7	X
ejpam-1901	100	3	)	)	PUNCT
ejpam-1901	100	4	our	our	PRON
ejpam-1901	100	5	aim	aim	NOUN
ejpam-1901	100	6	is	be	AUX
ejpam-1901	100	7	to	to	PART
ejpam-1901	100	8	obtain	obtain	VERB
ejpam-1901	100	9	a	a	DET
ejpam-1901	100	10	matrix	matrix	NOUN
ejpam-1901	100	11	differential	differential	NOUN
ejpam-1901	100	12	equations	equation	NOUN
ejpam-1901	100	13	of	of	ADP
ejpam-1901	100	14	the	the	DET
ejpam-1901	100	15	form	form	NOUN
ejpam-1901	100	16	�	�	PROPN
ejpam-1901	100	17	e11	e11	PROPN
ejpam-1901	100	18	e12	e12	NOUN
ejpam-1901	100	19	e21	e21	PROPN
ejpam-1901	100	20	e22	e22	PROPN
ejpam-1901	100	21	�	�	PROPN
ejpam-1901	100	22	′	′	NUM
ejpam-1901	100	23	=	=	PUNCT
ejpam-1901	100	24	a	a	DET
ejpam-1901	100	25	�	�	PROPN
ejpam-1901	100	26	e11	e11	PROPN
ejpam-1901	100	27	e12	e12	NOUN
ejpam-1901	100	28	e21	e21	X
ejpam-1901	100	29	e22	e22	PROPN
ejpam-1901	100	30	�	�	PROPN
ejpam-1901	100	31	where	where	SCONJ
ejpam-1901	100	32	a2×2	a2×2	NOUN
ejpam-1901	100	33	is	be	AUX
ejpam-1901	100	34	the	the	DET
ejpam-1901	100	35	coefficient	coefficient	NOUN
ejpam-1901	100	36	matrix	matrix	NOUN
ejpam-1901	100	37	.	.	PUNCT
ejpam-1901	101	1	it	it	PRON
ejpam-1901	101	2	can	can	AUX
ejpam-1901	101	3	be	be	AUX
ejpam-1901	101	4	easily	easily	ADV
ejpam-1901	101	5	seen	see	VERB
ejpam-1901	101	6	that	that	SCONJ
ejpam-1901	101	7	�	�	PROPN
ejpam-1901	101	8	e11	e11	PROPN
ejpam-1901	101	9	e22	e22	PROPN
ejpam-1901	101	10	�	�	PROPN
ejpam-1901	101	11	′	′	NOUN
ejpam-1901	101	12	=	=	PUNCT
ejpam-1901	101	13	�	�	PROPN
ejpam-1901	101	14	a	a	DET
ejpam-1901	101	15	b	b	PROPN
ejpam-1901	101	16	c	c	NOUN
ejpam-1901	101	17	d	d	X
ejpam-1901	101	18	�	�	PROPN
ejpam-1901	101	19	�	�	PROPN
ejpam-1901	101	20	e11	e11	PROPN
ejpam-1901	101	21	e22	e22	PROPN
ejpam-1901	101	22	�	�	PROPN
ejpam-1901	101	23	and	and	CCONJ
ejpam-1901	101	24	hence	hence	ADV
ejpam-1901	101	25	we	we	PRON
ejpam-1901	101	26	propose	propose	VERB
ejpam-1901	101	27	to	to	PART
ejpam-1901	101	28	choose	choose	VERB
ejpam-1901	101	29	a=	a=	ADV
ejpam-1901	101	30	�	�	PROPN
ejpam-1901	101	31	a	a	DET
ejpam-1901	101	32	b	b	PROPN
ejpam-1901	101	33	c	c	NOUN
ejpam-1901	101	34	d	d	X
ejpam-1901	101	35	�	�	PROPN
ejpam-1901	101	36	and	and	CCONJ
ejpam-1901	101	37	obtain	obtain	VERB
ejpam-1901	101	38	matrix	matrix	NOUN
ejpam-1901	101	39	differential	differential	NOUN
ejpam-1901	101	40	equation	equation	NOUN
ejpam-1901	101	41	of	of	ADP
ejpam-1901	101	42	the	the	DET
ejpam-1901	101	43	form	form	NOUN
ejpam-1901	101	44	�	�	PROPN
ejpam-1901	101	45	e11	e11	PROPN
ejpam-1901	101	46	e12	e12	NOUN
ejpam-1901	101	47	e21	e21	PROPN
ejpam-1901	101	48	e22	e22	PROPN
ejpam-1901	101	49	�	�	PROPN
ejpam-1901	101	50	′	′	NOUN
ejpam-1901	101	51	=	=	PUNCT
ejpam-1901	101	52	�	�	PROPN
ejpam-1901	101	53	a	a	DET
ejpam-1901	101	54	b	b	PROPN
ejpam-1901	101	55	c	c	NOUN
ejpam-1901	101	56	d	d	X
ejpam-1901	101	57	�	�	PROPN
ejpam-1901	101	58	�	�	PROPN
ejpam-1901	101	59	e11	e11	PROPN
ejpam-1901	101	60	e12	e12	NOUN
ejpam-1901	101	61	e21	e21	X
ejpam-1901	101	62	e22	e22	X
ejpam-1901	101	63	�	�	PROPN
ejpam-1901	101	64	(	(	PUNCT
ejpam-1901	101	65	8)	8)	NUM
ejpam-1901	101	66	the	the	DET
ejpam-1901	101	67	system	system	NOUN
ejpam-1901	101	68	(	(	PUNCT
ejpam-1901	101	69	8)	8)	NUM
ejpam-1901	101	70	yields	yield	VERB
ejpam-1901	101	71	the	the	DET
ejpam-1901	101	72	equations	equation	NOUN
ejpam-1901	101	73	(	(	PUNCT
ejpam-1901	101	74	6	6	NUM
ejpam-1901	101	75	)	)	PUNCT
ejpam-1901	101	76	,	,	PUNCT
ejpam-1901	101	77	(	(	PUNCT
ejpam-1901	101	78	7	7	X
ejpam-1901	101	79	)	)	PUNCT
ejpam-1901	101	80	and	and	CCONJ
ejpam-1901	101	81	the	the	DET
ejpam-1901	101	82	following	follow	VERB
ejpam-1901	101	83	two	two	NUM
ejpam-1901	101	84	differential	differential	ADJ
ejpam-1901	101	85	equations	equation	NOUN
ejpam-1901	101	86	given	give	VERB
ejpam-1901	101	87	by	by	ADP
ejpam-1901	101	88	e′12	e′12	PRON
ejpam-1901	101	89	=	=	PUNCT
ejpam-1901	101	90	ae12	ae12	PROPN
ejpam-1901	101	91	+	+	SYM
ejpam-1901	101	92	be22	be22	PROPN
ejpam-1901	101	93	,	,	PUNCT
ejpam-1901	101	94	(	(	PUNCT
ejpam-1901	101	95	9	9	X
ejpam-1901	101	96	)	)	PUNCT
ejpam-1901	101	97	e′21	e′21	NOUN
ejpam-1901	101	98	=	=	SYM
ejpam-1901	101	99	ce11	ce11	PROPN
ejpam-1901	101	100	+	+	CCONJ
ejpam-1901	101	101	de21	de21	PROPN
ejpam-1901	101	102	.	.	PUNCT
ejpam-1901	102	1	(	(	PUNCT
ejpam-1901	102	2	10	10	NUM
ejpam-1901	102	3	)	)	PUNCT
ejpam-1901	102	4	the	the	DET
ejpam-1901	102	5	equation	equation	NOUN
ejpam-1901	102	6	(	(	PUNCT
ejpam-1901	102	7	9	9	X
ejpam-1901	102	8	)	)	PUNCT
ejpam-1901	102	9	describe	describe	VERB
ejpam-1901	102	10	the	the	DET
ejpam-1901	102	11	rate	rate	NOUN
ejpam-1901	102	12	of	of	ADP
ejpam-1901	102	13	change	change	NOUN
ejpam-1901	102	14	of	of	ADP
ejpam-1901	102	15	predator	predator	NOUN
ejpam-1901	102	16	finding	find	VERB
ejpam-1901	102	17	prey	prey	NOUN
ejpam-1901	102	18	and	and	CCONJ
ejpam-1901	102	19	it	it	PRON
ejpam-1901	102	20	is	be	AUX
ejpam-1901	102	21	positively	positively	ADV
ejpam-1901	102	22	proportional	proportional	ADJ
ejpam-1901	102	23	to	to	ADP
ejpam-1901	102	24	the	the	DET
ejpam-1901	102	25	predator	predator	NOUN
ejpam-1901	102	26	finding	find	VERB
ejpam-1901	102	27	prey	prey	NOUN
ejpam-1901	102	28	and	and	CCONJ
ejpam-1901	102	29	negatively	negatively	ADV
ejpam-1901	102	30	proportional	proportional	ADJ
ejpam-1901	102	31	to	to	ADP
ejpam-1901	102	32	the	the	DET
ejpam-1901	102	33	predator	predator	NOUN
ejpam-1901	102	34	population	population	NOUN
ejpam-1901	102	35	.	.	PUNCT
ejpam-1901	103	1	the	the	DET
ejpam-1901	103	2	equation	equation	NOUN
ejpam-1901	103	3	(	(	PUNCT
ejpam-1901	103	4	10	10	NUM
ejpam-1901	103	5	)	)	PUNCT
ejpam-1901	103	6	gives	give	VERB
ejpam-1901	103	7	the	the	DET
ejpam-1901	103	8	rate	rate	NOUN
ejpam-1901	103	9	of	of	ADP
ejpam-1901	103	10	change	change	NOUN
ejpam-1901	103	11	prey	prey	NOUN
ejpam-1901	103	12	coming	come	VERB
ejpam-1901	103	13	in	in	ADP
ejpam-1901	103	14	way	way	NOUN
ejpam-1901	103	15	of	of	ADP
ejpam-1901	103	16	predator	predator	NOUN
ejpam-1901	103	17	and	and	CCONJ
ejpam-1901	103	18	this	this	PRON
ejpam-1901	103	19	is	be	AUX
ejpam-1901	103	20	positively	positively	ADV
ejpam-1901	103	21	proportional	proportional	ADJ
ejpam-1901	103	22	to	to	PART
ejpam-1901	103	23	prey	prey	VERB
ejpam-1901	103	24	available	available	ADJ
ejpam-1901	103	25	and	and	CCONJ
ejpam-1901	103	26	negatively	negatively	ADV
ejpam-1901	103	27	proportional	proportional	ADJ
ejpam-1901	103	28	to	to	ADP
ejpam-1901	103	29	prey	prey	VERB
ejpam-1901	103	30	falling	fall	VERB
ejpam-1901	103	31	to	to	PART
ejpam-1901	103	32	predator	predator	VERB
ejpam-1901	103	33	.	.	PUNCT
ejpam-1901	104	1	hence	hence	ADV
ejpam-1901	104	2	it	it	PRON
ejpam-1901	104	3	can	can	AUX
ejpam-1901	104	4	be	be	AUX
ejpam-1901	104	5	seen	see	VERB
ejpam-1901	104	6	that	that	SCONJ
ejpam-1901	104	7	all	all	DET
ejpam-1901	104	8	the	the	DET
ejpam-1901	104	9	four	four	NUM
ejpam-1901	104	10	equations	equation	NOUN
ejpam-1901	104	11	given	give	VERB
ejpam-1901	104	12	by	by	ADP
ejpam-1901	104	13	(	(	PUNCT
ejpam-1901	104	14	6	6	NUM
ejpam-1901	104	15	)	)	PUNCT
ejpam-1901	104	16	,	,	PUNCT
ejpam-1901	104	17	(	(	PUNCT
ejpam-1901	104	18	7	7	NUM
ejpam-1901	104	19	)	)	PUNCT
ejpam-1901	104	20	,	,	PUNCT
ejpam-1901	104	21	(	(	PUNCT
ejpam-1901	104	22	9	9	NUM
ejpam-1901	104	23	)	)	PUNCT
ejpam-1901	104	24	and	and	CCONJ
ejpam-1901	104	25	(	(	PUNCT
ejpam-1901	104	26	10	10	NUM
ejpam-1901	104	27	)	)	PUNCT
ejpam-1901	104	28	are	be	AUX
ejpam-1901	104	29	consistent	consistent	ADJ
ejpam-1901	104	30	with	with	ADP
ejpam-1901	104	31	the	the	DET
ejpam-1901	104	32	standard	standard	ADJ
ejpam-1901	104	33	prey	prey	NOUN
ejpam-1901	104	34	predator	predator	NOUN
ejpam-1901	104	35	problem	problem	NOUN
ejpam-1901	104	36	.	.	PUNCT
ejpam-1901	105	1	the	the	DET
ejpam-1901	105	2	beauty	beauty	NOUN
ejpam-1901	105	3	in	in	ADP
ejpam-1901	105	4	this	this	PRON
ejpam-1901	105	5	set	set	VERB
ejpam-1901	105	6	up	up	ADP
ejpam-1901	105	7	is	be	AUX
ejpam-1901	105	8	that	that	SCONJ
ejpam-1901	105	9	the	the	DET
ejpam-1901	105	10	nonlinearity	nonlinearity	NOUN
ejpam-1901	105	11	is	be	AUX
ejpam-1901	105	12	preserved	preserve	VERB
ejpam-1901	105	13	and	and	CCONJ
ejpam-1901	105	14	effectively	effectively	ADV
ejpam-1901	105	15	used	use	VERB
ejpam-1901	105	16	.	.	PUNCT
ejpam-1901	106	1	the	the	DET
ejpam-1901	106	2	system	system	NOUN
ejpam-1901	106	3	obtained	obtain	VERB
ejpam-1901	106	4	reduces	reduce	VERB
ejpam-1901	106	5	to	to	ADP
ejpam-1901	106	6	a	a	DET
ejpam-1901	106	7	matrix	matrix	NOUN
ejpam-1901	106	8	linear	linear	NOUN
ejpam-1901	106	9	differential	differential	NOUN
ejpam-1901	106	10	equation	equation	NOUN
ejpam-1901	106	11	and	and	CCONJ
ejpam-1901	106	12	the	the	DET
ejpam-1901	106	13	solution	solution	NOUN
ejpam-1901	106	14	is	be	AUX
ejpam-1901	106	15	immediately	immediately	ADV
ejpam-1901	106	16	given	give	VERB
ejpam-1901	106	17	by	by	ADP
ejpam-1901	106	18	�	�	PROPN
ejpam-1901	106	19	e11(t	e11(t	NOUN
ejpam-1901	106	20	)	)	PUNCT
ejpam-1901	106	21	e12(t	e12(t	NOUN
ejpam-1901	106	22	)	)	PUNCT
ejpam-1901	106	23	e21(t	e21(t	PROPN
ejpam-1901	106	24	)	)	PUNCT
ejpam-1901	106	25	e22(t	e22(t	NOUN
ejpam-1901	106	26	)	)	PUNCT
ejpam-1901	106	27	�	�	PROPN
ejpam-1901	106	28	=	=	SYM
ejpam-1901	106	29	ea(t−t0	ea(t−t0	PROPN
ejpam-1901	106	30	)	)	PUNCT
ejpam-1901	106	31	e0	e0	NOUN
ejpam-1901	106	32	where	where	SCONJ
ejpam-1901	106	33	e0	e0	PROPN
ejpam-1901	106	34	is	be	AUX
ejpam-1901	106	35	the	the	DET
ejpam-1901	106	36	given	give	VERB
ejpam-1901	106	37	matrix	matrix	NOUN
ejpam-1901	106	38	of	of	ADP
ejpam-1901	106	39	initial	initial	ADJ
ejpam-1901	106	40	conditions	condition	NOUN
ejpam-1901	106	41	at	at	ADP
ejpam-1901	106	42	t	t	PROPN
ejpam-1901	106	43	=	=	SYM
ejpam-1901	106	44	t0	t0	PROPN
ejpam-1901	106	45	,	,	PUNCT
ejpam-1901	106	46	see	see	VERB
ejpam-1901	106	47	[	[	X
ejpam-1901	106	48	1	1	NUM
ejpam-1901	106	49	]	]	PUNCT
ejpam-1901	106	50	.	.	PUNCT
ejpam-1901	107	1	observe	observe	VERB
ejpam-1901	107	2	that	that	SCONJ
ejpam-1901	107	3	ea(t−t0	ea(t−t0	NOUN
ejpam-1901	107	4	)	)	PUNCT
ejpam-1901	107	5	is	be	AUX
ejpam-1901	107	6	a	a	DET
ejpam-1901	107	7	matrix	matrix	NOUN
ejpam-1901	107	8	.	.	PUNCT
ejpam-1901	108	1	if	if	SCONJ
ejpam-1901	108	2	a	a	PRON
ejpam-1901	108	3	is	be	AUX
ejpam-1901	108	4	diagonalizable	diagonalizable	ADJ
ejpam-1901	108	5	then	then	ADV
ejpam-1901	108	6	ea(t−t0	ea(t−t0	NOUN
ejpam-1901	108	7	)	)	PUNCT
ejpam-1901	108	8	can	can	AUX
ejpam-1901	108	9	be	be	AUX
ejpam-1901	108	10	replaced	replace	VERB
ejpam-1901	108	11	by	by	ADP
ejpam-1901	108	12	the	the	DET
ejpam-1901	108	13	diagonal	diagonal	ADJ
ejpam-1901	108	14	matrix	matrix	NOUN
ejpam-1901	108	15	eh(t−t0	eh(t−t0	PROPN
ejpam-1901	108	16	)	)	PUNCT
ejpam-1901	108	17	,	,	PUNCT
ejpam-1901	108	18	where	where	SCONJ
ejpam-1901	108	19	h	h	NOUN
ejpam-1901	108	20	=	=	SYM
ejpam-1901	108	21	diag[λ1,λ2	diag[λ1,λ2	PROPN
ejpam-1901	108	22	]	]	PUNCT
ejpam-1901	108	23	where	where	SCONJ
ejpam-1901	108	24	λ1	λ1	ADJ
ejpam-1901	108	25	and	and	CCONJ
ejpam-1901	108	26	λ2	λ2	NOUN
ejpam-1901	108	27	are	be	AUX
ejpam-1901	108	28	the	the	DET
ejpam-1901	108	29	eigen	eigen	PROPN
ejpam-1901	108	30	values	value	NOUN
ejpam-1901	108	31	of	of	ADP
ejpam-1901	108	32	a	a	PRON
ejpam-1901	108	33	and	and	CCONJ
ejpam-1901	108	34	the	the	DET
ejpam-1901	108	35	matrix	matrix	NOUN
ejpam-1901	108	36	has	have	VERB
ejpam-1901	108	37	the	the	DET
ejpam-1901	108	38	form	form	NOUN
ejpam-1901	108	39	eh(t−t0	eh(t−t0	NOUN
ejpam-1901	108	40	)	)	PUNCT
ejpam-1901	108	41	=	=	SYM
ejpam-1901	108	42	�	�	PROPN
ejpam-1901	108	43	eλ1(t−t0	eλ1(t−t0	PROPN
ejpam-1901	108	44	)	)	PUNCT
ejpam-1901	108	45	0	0	NUM
ejpam-1901	108	46	0	0	NUM
ejpam-1901	108	47	eλ2(t−t0	eλ2(t−t0	NOUN
ejpam-1901	108	48	)	)	PUNCT
ejpam-1901	108	49	�	�	PROPN
ejpam-1901	108	50	.	.	PUNCT
ejpam-1901	109	1	j.	j.	PROPN
ejpam-1901	109	2	devi	devi	PROPN
ejpam-1901	109	3	,	,	PUNCT
ejpam-1901	109	4	r.	r.	PROPN
ejpam-1901	109	5	kumar	kumar	PROPN
ejpam-1901	109	6	/	/	SYM
ejpam-1901	109	7	eur	eur	PROPN
ejpam-1901	109	8	.	.	PUNCT
ejpam-1901	110	1	j.	j.	PROPN
ejpam-1901	110	2	pure	pure	PROPN
ejpam-1901	110	3	appl	appl	PROPN
ejpam-1901	110	4	.	.	PROPN
ejpam-1901	110	5	math	math	PROPN
ejpam-1901	110	6	,	,	PUNCT
ejpam-1901	110	7	7	7	NUM
ejpam-1901	110	8	(	(	PUNCT
ejpam-1901	110	9	2014	2014	NUM
ejpam-1901	110	10	)	)	PUNCT
ejpam-1901	110	11	,	,	PUNCT
ejpam-1901	110	12	37	37	NUM
ejpam-1901	110	13	-	-	SYM
ejpam-1901	110	14	44	44	NUM
ejpam-1901	110	15	43	43	NUM
ejpam-1901	110	16	thus	thus	ADV
ejpam-1901	110	17	it	it	PRON
ejpam-1901	110	18	has	have	AUX
ejpam-1901	110	19	been	be	AUX
ejpam-1901	110	20	effectively	effectively	ADV
ejpam-1901	110	21	shown	show	VERB
ejpam-1901	110	22	that	that	SCONJ
ejpam-1901	110	23	a	a	DET
ejpam-1901	110	24	physical	physical	ADJ
ejpam-1901	110	25	phenomena	phenomena	NOUN
ejpam-1901	110	26	can	can	AUX
ejpam-1901	110	27	be	be	AUX
ejpam-1901	110	28	described	describe	VERB
ejpam-1901	110	29	through	through	ADP
ejpam-1901	110	30	a	a	DET
ejpam-1901	110	31	graph	graph	NOUN
ejpam-1901	110	32	and	and	CCONJ
ejpam-1901	110	33	using	use	VERB
ejpam-1901	110	34	the	the	DET
ejpam-1901	110	35	standard	standard	ADJ
ejpam-1901	110	36	models	model	NOUN
ejpam-1901	110	37	we	we	PRON
ejpam-1901	110	38	can	can	AUX
ejpam-1901	110	39	preserve	preserve	VERB
ejpam-1901	110	40	the	the	DET
ejpam-1901	110	41	nonlinearity	nonlinearity	NOUN
ejpam-1901	110	42	and	and	CCONJ
ejpam-1901	110	43	obtain	obtain	VERB
ejpam-1901	110	44	more	more	ADJ
ejpam-1901	110	45	information	information	NOUN
ejpam-1901	110	46	using	use	VERB
ejpam-1901	110	47	its	its	PRON
ejpam-1901	110	48	associated	associated	ADJ
ejpam-1901	110	49	matrix	matrix	NOUN
ejpam-1901	110	50	differential	differential	NOUN
ejpam-1901	110	51	equation	equation	NOUN
ejpam-1901	110	52	.	.	PUNCT
ejpam-1901	111	1	next	next	ADV
ejpam-1901	111	2	we	we	PRON
ejpam-1901	111	3	consider	consider	VERB
ejpam-1901	111	4	a	a	DET
ejpam-1901	111	5	three	three	NUM
ejpam-1901	111	6	species	specie	NOUN
ejpam-1901	111	7	model	model	NOUN
ejpam-1901	111	8	given	give	VERB
ejpam-1901	111	9	by	by	ADP
ejpam-1901	111	10	d	d	PROPN
ejpam-1901	111	11	x	x	PROPN
ejpam-1901	111	12	d	d	NOUN
ejpam-1901	111	13	t	t	NOUN
ejpam-1901	111	14	=	=	NOUN
ejpam-1901	111	15	ax	ax	NOUN
ejpam-1901	112	1	+	+	CCONJ
ejpam-1901	112	2	bx	bx	NOUN
ejpam-1901	112	3	y	y	PROPN
ejpam-1901	112	4	+	+	CCONJ
ejpam-1901	112	5	cxz	cxz	ADJ
ejpam-1901	112	6	,	,	PUNCT
ejpam-1901	112	7	d	d	PROPN
ejpam-1901	112	8	y	y	PROPN
ejpam-1901	112	9	d	d	X
ejpam-1901	112	10	t	t	PROPN
ejpam-1901	112	11	=	=	PUNCT
ejpam-1901	113	1	d	d	X
ejpam-1901	113	2	y	y	PROPN
ejpam-1901	113	3	x	x	PUNCT
ejpam-1901	114	1	+	+	PUNCT
ejpam-1901	114	2	e	e	X
ejpam-1901	114	3	y	y	PROPN
ejpam-1901	114	4	+	+	CCONJ
ejpam-1901	114	5	f	f	PROPN
ejpam-1901	114	6	yz	yz	PROPN
ejpam-1901	114	7	,	,	PUNCT
ejpam-1901	114	8	dz	dz	PROPN
ejpam-1901	114	9	d	d	X
ejpam-1901	114	10	t	t	PROPN
ejpam-1901	114	11	=	=	PUNCT
ejpam-1901	114	12	gzx	gzx	NOUN
ejpam-1901	115	1	+	+	CCONJ
ejpam-1901	115	2	hz	hz	VERB
ejpam-1901	115	3	y	y	PROPN
ejpam-1901	115	4	+	+	PROPN
ejpam-1901	115	5	kz	kz	PROPN
ejpam-1901	115	6	.	.	PUNCT
ejpam-1901	115	7	working	work	VERB
ejpam-1901	115	8	parallel	parallel	NOUN
ejpam-1901	115	9	to	to	ADP
ejpam-1901	115	10	the	the	DET
ejpam-1901	115	11	prey	prey	NOUN
ejpam-1901	115	12	predator	predator	NOUN
ejpam-1901	115	13	problem	problem	NOUN
ejpam-1901	115	14	,	,	PUNCT
ejpam-1901	115	15	we	we	PRON
ejpam-1901	115	16	consider	consider	VERB
ejpam-1901	115	17	three	three	NUM
ejpam-1901	115	18	vertices	vertex	NOUN
ejpam-1901	115	19	v1	v1	NOUN
ejpam-1901	115	20	,	,	PUNCT
ejpam-1901	115	21	v2	v2	PROPN
ejpam-1901	115	22	and	and	CCONJ
ejpam-1901	115	23	v3	v3	PROPN
ejpam-1901	115	24	representing	represent	VERB
ejpam-1901	115	25	x	x	SYM
ejpam-1901	115	26	,	,	PUNCT
ejpam-1901	115	27	y	y	PROPN
ejpam-1901	115	28	and	and	CCONJ
ejpam-1901	115	29	z	z	NOUN
ejpam-1901	115	30	respectively	respectively	ADV
ejpam-1901	115	31	.	.	PUNCT
ejpam-1901	116	1	proceeding	proceed	VERB
ejpam-1901	116	2	as	as	ADP
ejpam-1901	116	3	in	in	ADP
ejpam-1901	116	4	the	the	DET
ejpam-1901	116	5	prey	prey	NOUN
ejpam-1901	116	6	predator	predator	NOUN
ejpam-1901	116	7	problem	problem	NOUN
ejpam-1901	116	8	,	,	PUNCT
ejpam-1901	116	9	we	we	PRON
ejpam-1901	116	10	arrive	arrive	VERB
ejpam-1901	116	11	at	at	ADP
ejpam-1901	116	12	the	the	DET
ejpam-1901	116	13	linear	linear	ADJ
ejpam-1901	116	14	matrix	matrix	NOUN
ejpam-1901	116	15	differential	differential	NOUN
ejpam-1901	116	16	equation	equation	NOUN
ejpam-1901	116	17	of	of	ADP
ejpam-1901	116	18	the	the	DET
ejpam-1901	116	19	form	form	NOUN
ejpam-1901	116	20			NOUN
ejpam-1901	116	21			ADJ
ejpam-1901	116	22			NUM
ejpam-1901	116	23	e11	e11	PROPN
ejpam-1901	116	24	e12	e12	NOUN
ejpam-1901	116	25	e13	e13	NOUN
ejpam-1901	116	26	e21	e21	PROPN
ejpam-1901	116	27	e22	e22	X
ejpam-1901	116	28	e23	e23	PROPN
ejpam-1901	116	29	e31	e31	PROPN
ejpam-1901	116	30	e32	e32	PROPN
ejpam-1901	116	31	e33	e33	PROPN
ejpam-1901	116	32			PROPN
ejpam-1901	117	1			PROPN
ejpam-1901	117	2			PROPN
ejpam-1901	117	3	′	′	NOUN
ejpam-1901	117	4	=	=	NOUN
ejpam-1901	117	5			NOUN
ejpam-1901	117	6			NOUN
ejpam-1901	117	7			NOUN
ejpam-1901	118	1	a	a	DET
ejpam-1901	118	2	b	b	NOUN
ejpam-1901	118	3	c	c	NOUN
ejpam-1901	118	4	d	d	X
ejpam-1901	118	5	e	e	X
ejpam-1901	118	6	f	f	PROPN
ejpam-1901	118	7	g	g	PROPN
ejpam-1901	118	8	h	h	PROPN
ejpam-1901	119	1	k	k	PROPN
ejpam-1901	119	2			PROPN
ejpam-1901	119	3			PROPN
ejpam-1901	119	4			PROPN
ejpam-1901	119	5			NOUN
ejpam-1901	119	6			ADJ
ejpam-1901	119	7			NUM
ejpam-1901	119	8	e11	e11	PROPN
ejpam-1901	119	9	e12	e12	NOUN
ejpam-1901	119	10	e13	e13	NOUN
ejpam-1901	119	11	e21	e21	PROPN
ejpam-1901	119	12	e22	e22	X
ejpam-1901	119	13	e23	e23	PROPN
ejpam-1901	119	14	e31	e31	PROPN
ejpam-1901	119	15	e32	e32	PROPN
ejpam-1901	119	16	e33	e33	PROPN
ejpam-1901	119	17	.	.	PUNCT
ejpam-1901	120	1			PROPN
ejpam-1901	120	2			PROPN
ejpam-1901	120	3			PROPN
ejpam-1901	120	4	it	it	PRON
ejpam-1901	120	5	can	can	AUX
ejpam-1901	120	6	be	be	AUX
ejpam-1901	120	7	observed	observe	VERB
ejpam-1901	120	8	that	that	SCONJ
ejpam-1901	120	9	we	we	PRON
ejpam-1901	120	10	will	will	AUX
ejpam-1901	120	11	get	get	VERB
ejpam-1901	120	12	six	six	NUM
ejpam-1901	120	13	additional	additional	ADJ
ejpam-1901	120	14	equations	equation	NOUN
ejpam-1901	120	15	and	and	CCONJ
ejpam-1901	120	16	hence	hence	ADV
ejpam-1901	120	17	more	more	ADJ
ejpam-1901	120	18	information	information	NOUN
ejpam-1901	120	19	is	be	AUX
ejpam-1901	120	20	known	know	VERB
ejpam-1901	120	21	.	.	PUNCT
ejpam-1901	121	1	the	the	DET
ejpam-1901	121	2	solution	solution	NOUN
ejpam-1901	121	3	for	for	ADP
ejpam-1901	121	4	this	this	DET
ejpam-1901	121	5	system	system	NOUN
ejpam-1901	121	6	can	can	AUX
ejpam-1901	121	7	be	be	AUX
ejpam-1901	121	8	immediately	immediately	ADV
ejpam-1901	121	9	given	give	VERB
ejpam-1901	121	10	by	by	ADP
ejpam-1901	121	11	e(t	e(t	NOUN
ejpam-1901	121	12	)	)	PUNCT
ejpam-1901	121	13	=	=	SYM
ejpam-1901	121	14	ea(t−t0)c	ea(t−t0)c	NOUN
ejpam-1901	121	15	,	,	PUNCT
ejpam-1901	121	16	where	where	SCONJ
ejpam-1901	121	17	c	c	PROPN
ejpam-1901	121	18	is	be	AUX
ejpam-1901	121	19	the	the	DET
ejpam-1901	121	20	matrix	matrix	NOUN
ejpam-1901	121	21	of	of	ADP
ejpam-1901	121	22	initial	initial	ADJ
ejpam-1901	121	23	conditions	condition	NOUN
ejpam-1901	121	24	.	.	PUNCT
ejpam-1901	122	1	clearly	clearly	ADV
ejpam-1901	122	2	,	,	PUNCT
ejpam-1901	122	3	this	this	DET
ejpam-1901	122	4	approach	approach	NOUN
ejpam-1901	122	5	can	can	AUX
ejpam-1901	122	6	be	be	AUX
ejpam-1901	122	7	extended	extend	VERB
ejpam-1901	122	8	suitably	suitably	ADV
ejpam-1901	122	9	to	to	ADP
ejpam-1901	122	10	a	a	DET
ejpam-1901	122	11	n	n	NUM
ejpam-1901	122	12	-species	-specie	NOUN
ejpam-1901	122	13	model	model	NOUN
ejpam-1901	122	14	.	.	PUNCT
ejpam-1901	123	1	remark	remark	PROPN
ejpam-1901	123	2	2	2	NUM
ejpam-1901	123	3	.	.	PUNCT
ejpam-1901	124	1	it	it	PRON
ejpam-1901	124	2	can	can	AUX
ejpam-1901	124	3	be	be	AUX
ejpam-1901	124	4	observed	observe	VERB
ejpam-1901	124	5	that	that	SCONJ
ejpam-1901	124	6	if	if	SCONJ
ejpam-1901	124	7	the	the	DET
ejpam-1901	124	8	rate	rate	NOUN
ejpam-1901	124	9	of	of	ADP
ejpam-1901	124	10	change	change	NOUN
ejpam-1901	124	11	of	of	ADP
ejpam-1901	124	12	an	an	DET
ejpam-1901	124	13	edge	edge	NOUN
ejpam-1901	124	14	ei	ei	X
ejpam-1901	124	15	j	j	PROPN
ejpam-1901	124	16	is	be	AUX
ejpam-1901	124	17	proportional	proportional	ADJ
ejpam-1901	124	18	only	only	ADV
ejpam-1901	124	19	to	to	ADP
ejpam-1901	124	20	the	the	DET
ejpam-1901	124	21	edges	edge	NOUN
ejpam-1901	124	22	that	that	PRON
ejpam-1901	124	23	are	be	AUX
ejpam-1901	124	24	incident	incident	NOUN
ejpam-1901	124	25	outward	outward	ADV
ejpam-1901	124	26	from	from	ADP
ejpam-1901	124	27	v	v	NUM
ejpam-1901	125	1	j	j	NOUN
ejpam-1901	126	1	then	then	ADV
ejpam-1901	126	2	we	we	PRON
ejpam-1901	126	3	obtain	obtain	VERB
ejpam-1901	126	4	a	a	DET
ejpam-1901	126	5	matrix	matrix	NOUN
ejpam-1901	126	6	differential	differential	NOUN
ejpam-1901	126	7	equation	equation	NOUN
ejpam-1901	126	8	.	.	PUNCT
ejpam-1901	127	1	on	on	ADP
ejpam-1901	127	2	the	the	DET
ejpam-1901	127	3	other	other	ADJ
ejpam-1901	127	4	hand	hand	NOUN
ejpam-1901	127	5	,	,	PUNCT
ejpam-1901	127	6	if	if	SCONJ
ejpam-1901	127	7	the	the	DET
ejpam-1901	127	8	rate	rate	NOUN
ejpam-1901	127	9	of	of	ADP
ejpam-1901	127	10	change	change	NOUN
ejpam-1901	127	11	of	of	ADP
ejpam-1901	127	12	edge	edge	NOUN
ejpam-1901	127	13	ei	ei	X
ejpam-1901	127	14	j	j	PROPN
ejpam-1901	127	15	is	be	AUX
ejpam-1901	127	16	proportional	proportional	ADJ
ejpam-1901	127	17	to	to	ADP
ejpam-1901	127	18	all	all	DET
ejpam-1901	127	19	the	the	DET
ejpam-1901	127	20	n	n	NUM
ejpam-1901	127	21	×	×	NOUN
ejpam-1901	127	22	n	n	PRON
ejpam-1901	127	23	edges	edge	NOUN
ejpam-1901	127	24	or	or	CCONJ
ejpam-1901	127	25	to	to	ADP
ejpam-1901	127	26	some	some	PRON
ejpam-1901	127	27	of	of	ADP
ejpam-1901	127	28	them	they	PRON
ejpam-1901	127	29	(	(	PUNCT
ejpam-1901	127	30	without	without	ADP
ejpam-1901	127	31	any	any	DET
ejpam-1901	127	32	structure	structure	NOUN
ejpam-1901	127	33	)	)	PUNCT
ejpam-1901	127	34	then	then	ADV
ejpam-1901	127	35	we	we	PRON
ejpam-1901	127	36	can	can	AUX
ejpam-1901	127	37	treat	treat	VERB
ejpam-1901	127	38	the	the	DET
ejpam-1901	127	39	n	n	NUM
ejpam-1901	127	40	×	×	NOUN
ejpam-1901	127	41	n	n	PRON
ejpam-1901	127	42	edges	edge	NOUN
ejpam-1901	127	43	as	as	ADP
ejpam-1901	127	44	an	an	DET
ejpam-1901	127	45	n2	n2	ADJ
ejpam-1901	127	46	vector	vector	NOUN
ejpam-1901	127	47	and	and	CCONJ
ejpam-1901	127	48	consider	consider	VERB
ejpam-1901	127	49	a	a	DET
ejpam-1901	127	50	vector	vector	NOUN
ejpam-1901	127	51	differential	differential	NOUN
ejpam-1901	127	52	equation	equation	NOUN
ejpam-1901	127	53	of	of	ADP
ejpam-1901	127	54	the	the	DET
ejpam-1901	127	55	x	x	NOUN
ejpam-1901	127	56	′	′	NOUN
ejpam-1901	127	57	=	=	NOUN
ejpam-1901	127	58	ax	ax	NOUN
ejpam-1901	127	59	where	where	SCONJ
ejpam-1901	127	60	a	a	PRON
ejpam-1901	127	61	is	be	AUX
ejpam-1901	127	62	an	an	DET
ejpam-1901	127	63	n	n	NUM
ejpam-1901	127	64	×	×	NOUN
ejpam-1901	127	65	n	n	PRON
ejpam-1901	127	66	matrix	matrix	NOUN
ejpam-1901	127	67	.	.	PUNCT
ejpam-1901	128	1	4	4	X
ejpam-1901	128	2	.	.	X
ejpam-1901	128	3	conclusion	conclusion	NOUN
ejpam-1901	128	4	in	in	ADP
ejpam-1901	128	5	this	this	DET
ejpam-1901	128	6	paper	paper	NOUN
ejpam-1901	128	7	we	we	PRON
ejpam-1901	128	8	have	have	AUX
ejpam-1901	128	9	introduced	introduce	VERB
ejpam-1901	128	10	the	the	DET
ejpam-1901	128	11	notions	notion	NOUN
ejpam-1901	128	12	of	of	ADP
ejpam-1901	128	13	a	a	DET
ejpam-1901	128	14	pseudo	pseudo	NOUN
ejpam-1901	128	15	simple	simple	ADJ
ejpam-1901	128	16	graph	graph	NOUN
ejpam-1901	128	17	and	and	CCONJ
ejpam-1901	128	18	the	the	DET
ejpam-1901	128	19	product	product	NOUN
ejpam-1901	128	20	of	of	ADP
ejpam-1901	128	21	two	two	NUM
ejpam-1901	128	22	graphs	graph	NOUN
ejpam-1901	128	23	we	we	PRON
ejpam-1901	128	24	have	have	AUX
ejpam-1901	128	25	given	give	VERB
ejpam-1901	128	26	sufficient	sufficient	ADJ
ejpam-1901	128	27	conditions	condition	NOUN
ejpam-1901	128	28	under	under	ADP
ejpam-1901	128	29	which	which	PRON
ejpam-1901	128	30	a	a	DET
ejpam-1901	128	31	solution	solution	NOUN
ejpam-1901	128	32	of	of	ADP
ejpam-1901	128	33	a	a	DET
ejpam-1901	128	34	graph	graph	NOUN
ejpam-1901	128	35	differential	differential	ADJ
ejpam-1901	128	36	equation	equation	NOUN
ejpam-1901	128	37	has	have	VERB
ejpam-1901	128	38	the	the	DET
ejpam-1901	128	39	same	same	ADJ
ejpam-1901	128	40	nature	nature	NOUN
ejpam-1901	128	41	as	as	ADP
ejpam-1901	128	42	its	its	PRON
ejpam-1901	128	43	graph	graph	NOUN
ejpam-1901	128	44	of	of	ADP
ejpam-1901	128	45	initial	initial	ADJ
ejpam-1901	128	46	conditions	condition	NOUN
ejpam-1901	128	47	.	.	PUNCT
ejpam-1901	129	1	further	far	ADV
ejpam-1901	129	2	,	,	PUNCT
ejpam-1901	129	3	we	we	PRON
ejpam-1901	129	4	have	have	AUX
ejpam-1901	129	5	obtained	obtain	VERB
ejpam-1901	129	6	a	a	DET
ejpam-1901	129	7	matrix	matrix	NOUN
ejpam-1901	129	8	differential	differential	NOUN
ejpam-1901	129	9	equation	equation	NOUN
ejpam-1901	129	10	for	for	ADP
ejpam-1901	129	11	a	a	DET
ejpam-1901	129	12	prey	prey	NOUN
ejpam-1901	129	13	predator	predator	NOUN
ejpam-1901	129	14	probleml	probleml	NOUN
ejpam-1901	129	15	and	and	CCONJ
ejpam-1901	129	16	explicitly	explicitly	ADV
ejpam-1901	129	17	gave	give	VERB
ejpam-1901	129	18	its	its	PRON
ejpam-1901	129	19	solutions	solution	NOUN
ejpam-1901	129	20	preserving	preserve	VERB
ejpam-1901	129	21	the	the	DET
ejpam-1901	129	22	nonlinearity	nonlinearity	NOUN
ejpam-1901	129	23	.	.	PUNCT
ejpam-1901	130	1	from	from	ADP
ejpam-1901	130	2	the	the	DET
ejpam-1901	130	3	model	model	NOUN
ejpam-1901	130	4	,	,	PUNCT
ejpam-1901	130	5	it	it	PRON
ejpam-1901	130	6	is	be	AUX
ejpam-1901	130	7	clear	clear	ADJ
ejpam-1901	130	8	that	that	SCONJ
ejpam-1901	130	9	the	the	DET
ejpam-1901	130	10	nonlinearity	nonlinearity	NOUN
ejpam-1901	130	11	in	in	ADP
ejpam-1901	130	12	the	the	DET
ejpam-1901	130	13	prey	prey	NOUN
ejpam-1901	130	14	predator	predator	NOUN
ejpam-1901	130	15	problem	problem	NOUN
ejpam-1901	130	16	is	be	AUX
ejpam-1901	130	17	preserved	preserve	VERB
ejpam-1901	130	18	by	by	ADP
ejpam-1901	130	19	using	use	VERB
ejpam-1901	130	20	a	a	DET
ejpam-1901	130	21	graph	graph	NOUN
ejpam-1901	130	22	differential	differential	ADJ
ejpam-1901	130	23	equation	equation	NOUN
ejpam-1901	130	24	.	.	PUNCT
ejpam-1901	131	1	as	as	ADV
ejpam-1901	131	2	long	long	ADV
ejpam-1901	131	3	as	as	ADP
ejpam-1901	131	4	the	the	DET
ejpam-1901	131	5	rate	rate	NOUN
ejpam-1901	131	6	of	of	ADP
ejpam-1901	131	7	change	change	NOUN
ejpam-1901	131	8	of	of	ADP
ejpam-1901	131	9	the	the	DET
ejpam-1901	131	10	species	specie	NOUN
ejpam-1901	131	11	x	x	INTJ
ejpam-1901	131	12	i	i	PRON
ejpam-1901	131	13	is	be	AUX
ejpam-1901	131	14	proportional	proportional	ADJ
ejpam-1901	131	15	to	to	PART
ejpam-1901	131	16	linear	linear	VERB
ejpam-1901	131	17	interactions	interaction	NOUN
ejpam-1901	131	18	between	between	ADP
ejpam-1901	131	19	itself	itself	PRON
ejpam-1901	131	20	and	and	CCONJ
ejpam-1901	131	21	x	x	SYM
ejpam-1901	131	22	j	j	PROPN
ejpam-1901	131	23	species	specie	NOUN
ejpam-1901	131	24	it	it	PRON
ejpam-1901	131	25	will	will	AUX
ejpam-1901	131	26	be	be	AUX
ejpam-1901	131	27	possible	possible	ADJ
ejpam-1901	131	28	to	to	PART
ejpam-1901	131	29	obtain	obtain	VERB
ejpam-1901	131	30	a	a	DET
ejpam-1901	131	31	linear	linear	ADJ
ejpam-1901	131	32	graph	graph	NOUN
ejpam-1901	131	33	differential	differential	ADJ
ejpam-1901	131	34	equation	equation	NOUN
ejpam-1901	131	35	.	.	PUNCT
ejpam-1901	132	1	in	in	ADP
ejpam-1901	132	2	other	other	ADJ
ejpam-1901	132	3	words	word	NOUN
ejpam-1901	132	4	,	,	PUNCT
ejpam-1901	132	5	in	in	ADP
ejpam-1901	132	6	the	the	DET
ejpam-1901	132	7	above	above	ADJ
ejpam-1901	132	8	discussed	discuss	VERB
ejpam-1901	132	9	prey	prey	NOUN
ejpam-1901	132	10	-	-	PUNCT
ejpam-1901	132	11	predator	predator	NOUN
ejpam-1901	132	12	problem	problem	NOUN
ejpam-1901	132	13	if	if	SCONJ
ejpam-1901	132	14	the	the	DET
ejpam-1901	132	15	rate	rate	NOUN
ejpam-1901	132	16	of	of	ADP
ejpam-1901	132	17	change	change	NOUN
ejpam-1901	132	18	of	of	ADP
ejpam-1901	132	19	prey	prey	PROPN
ejpam-1901	132	20	population	population	NOUN
ejpam-1901	132	21	x	x	PUNCT
ejpam-1901	132	22	w.r.t	w.r.t	ADJ
ejpam-1901	132	23	time	time	NOUN
ejpam-1901	132	24	is	be	AUX
ejpam-1901	132	25	proportional	proportional	ADJ
ejpam-1901	132	26	to	to	ADP
ejpam-1901	132	27	the	the	DET
ejpam-1901	132	28	interaction	interaction	NOUN
ejpam-1901	132	29	of	of	ADP
ejpam-1901	132	30	the	the	DET
ejpam-1901	132	31	square	square	NOUN
ejpam-1901	132	32	of	of	ADP
ejpam-1901	132	33	prey	prey	PROPN
ejpam-1901	132	34	population	population	NOUN
ejpam-1901	132	35	(	(	PUNCT
ejpam-1901	132	36	x	x	NOUN
ejpam-1901	132	37	2	2	X
ejpam-1901	132	38	)	)	PUNCT
ejpam-1901	132	39	and	and	CCONJ
ejpam-1901	132	40	square	square	ADJ
ejpam-1901	132	41	references	reference	NOUN
ejpam-1901	132	42	44	44	NUM
ejpam-1901	132	43	of	of	ADP
ejpam-1901	132	44	product	product	NOUN
ejpam-1901	132	45	population	population	NOUN
ejpam-1901	132	46	(	(	PUNCT
ejpam-1901	132	47	y	y	PROPN
ejpam-1901	132	48	2	2	NUM
ejpam-1901	132	49	)	)	PUNCT
ejpam-1901	132	50	and	and	CCONJ
ejpam-1901	132	51	similarly	similarly	ADV
ejpam-1901	132	52	with	with	ADP
ejpam-1901	132	53	predator	predator	NOUN
ejpam-1901	132	54	population	population	NOUN
ejpam-1901	132	55	then	then	ADV
ejpam-1901	132	56	the	the	DET
ejpam-1901	132	57	problem	problem	NOUN
ejpam-1901	132	58	reduces	reduce	VERB
ejpam-1901	132	59	to	to	ADP
ejpam-1901	132	60	the	the	DET
ejpam-1901	132	61	form	form	NOUN
ejpam-1901	133	1	d	d	X
ejpam-1901	133	2	x	x	SYM
ejpam-1901	133	3	d	d	NOUN
ejpam-1901	133	4	t	t	NOUN
ejpam-1901	133	5	=	=	NOUN
ejpam-1901	133	6	ax	ax	NOUN
ejpam-1901	133	7	+	+	CCONJ
ejpam-1901	133	8	bx2	bx2	NOUN
ejpam-1901	133	9	y2	y2	PROPN
ejpam-1901	133	10	,	,	PUNCT
ejpam-1901	134	1	d	d	PROPN
ejpam-1901	134	2	y	y	PROPN
ejpam-1901	134	3	d	d	X
ejpam-1901	134	4	t	t	PROPN
ejpam-1901	134	5	=	=	PUNCT
ejpam-1901	134	6	c	c	NOUN
ejpam-1901	134	7	y2	y2	NOUN
ejpam-1901	135	1	x2	x2	PROPN
ejpam-1901	136	1	+	+	CCONJ
ejpam-1901	136	2	d	d	PROPN
ejpam-1901	136	3	y.	y.	NOUN
ejpam-1901	136	4	this	this	PRON
ejpam-1901	136	5	can	can	AUX
ejpam-1901	136	6	not	not	PART
ejpam-1901	136	7	be	be	AUX
ejpam-1901	136	8	immediately	immediately	ADV
ejpam-1901	136	9	modeled	model	VERB
ejpam-1901	136	10	by	by	ADP
ejpam-1901	136	11	a	a	DET
ejpam-1901	136	12	linear	linear	ADJ
ejpam-1901	136	13	graph	graph	NOUN
ejpam-1901	136	14	differential	differential	ADJ
ejpam-1901	136	15	equation	equation	NOUN
ejpam-1901	136	16	and	and	CCONJ
ejpam-1901	136	17	needs	need	VERB
ejpam-1901	136	18	further	further	ADJ
ejpam-1901	136	19	investigations	investigation	NOUN
ejpam-1901	136	20	.	.	PUNCT
ejpam-1901	137	1	acknowledgements	acknowledgement	NOUN
ejpam-1901	137	2	this	this	DET
ejpam-1901	137	3	work	work	NOUN
ejpam-1901	137	4	was	be	AUX
ejpam-1901	137	5	done	do	VERB
ejpam-1901	137	6	under	under	ADP
ejpam-1901	137	7	the	the	DET
ejpam-1901	137	8	project	project	NOUN
ejpam-1901	137	9	no	no	INTJ
ejpam-1901	137	10	.	.	PUNCT
ejpam-1901	138	1	2/48(8)/2011/-r&d	2/48(8)/2011/-r&d	NUM
ejpam-1901	138	2	ii/1600	ii/1600	SCONJ
ejpam-1901	138	3	sanctioned	sanction	VERB
ejpam-1901	138	4	by	by	ADP
ejpam-1901	138	5	national	national	PROPN
ejpam-1901	138	6	board	board	PROPN
ejpam-1901	138	7	of	of	ADP
ejpam-1901	138	8	higher	high	ADJ
ejpam-1901	138	9	mathematics	mathematic	NOUN
ejpam-1901	138	10	,	,	PUNCT
ejpam-1901	138	11	department	department	NOUN
ejpam-1901	138	12	of	of	ADP
ejpam-1901	138	13	atomic	atomic	ADJ
ejpam-1901	138	14	energy	energy	NOUN
ejpam-1901	138	15	,	,	PUNCT
ejpam-1901	138	16	government	government	NOUN
ejpam-1901	138	17	of	of	ADP
ejpam-1901	138	18	india	india	PROPN
ejpam-1901	138	19	.	.	PUNCT
ejpam-1901	139	1	the	the	DET
ejpam-1901	139	2	authors	author	NOUN
ejpam-1901	139	3	acknowledge	acknowledge	VERB
ejpam-1901	139	4	their	their	PRON
ejpam-1901	139	5	support	support	NOUN
ejpam-1901	139	6	.	.	PUNCT
ejpam-1901	140	1	references	reference	NOUN
ejpam-1901	140	2	[	[	X
ejpam-1901	140	3	1	1	NUM
ejpam-1901	140	4	]	]	X
ejpam-1901	140	5	s.g	s.g	PROPN
ejpam-1901	140	6	.	.	PROPN
ejpam-1901	140	7	deo	deo	PROPN
ejpam-1901	140	8	,	,	PUNCT
ejpam-1901	140	9	v.	v.	ADP
ejpam-1901	140	10	lakshmikantham	lakshmikantham	NOUN
ejpam-1901	140	11	,	,	PUNCT
ejpam-1901	140	12	and	and	CCONJ
ejpam-1901	140	13	v.	v.	PROPN
ejpam-1901	140	14	raghavendra	raghavendra	PROPN
ejpam-1901	140	15	.	.	PROPN
ejpam-1901	140	16	textbook	textbook	NOUN
ejpam-1901	140	17	of	of	ADP
ejpam-1901	140	18	ordinary	ordinary	ADJ
ejpam-1901	140	19	differential	differential	ADJ
ejpam-1901	140	20	equations	equation	NOUN
ejpam-1901	140	21	,	,	PUNCT
ejpam-1901	140	22	2nd	2nd	PROPN
ejpam-1901	140	23	edition	edition	NOUN
ejpam-1901	140	24	.	.	PUNCT
ejpam-1901	141	1	tata	tata	PROPN
ejpam-1901	141	2	mcgraw	mcgraw	PROPN
ejpam-1901	141	3	hill	hill	PROPN
ejpam-1901	141	4	education	education	PROPN
ejpam-1901	141	5	private	private	ADJ
ejpam-1901	141	6	limited	limited	ADJ
ejpam-1901	141	7	,	,	PUNCT
ejpam-1901	141	8	new	new	ADJ
ejpam-1901	141	9	delhi	delhi	PROPN
ejpam-1901	141	10	.	.	PUNCT
ejpam-1901	142	1	1998	1998	NUM
ejpam-1901	142	2	.	.	PUNCT
ejpam-1901	143	1	[	[	X
ejpam-1901	143	2	2	2	NUM
ejpam-1901	143	3	]	]	X
ejpam-1901	143	4	j.v	j.v	PROPN
ejpam-1901	143	5	.	.	PUNCT
ejpam-1901	143	6	devi	devi	PROPN
ejpam-1901	143	7	,	,	PUNCT
ejpam-1901	143	8	r.v.g.r	r.v.g.r	PROPN
ejpam-1901	143	9	.	.	PROPN
ejpam-1901	143	10	kumar	kumar	PROPN
ejpam-1901	143	11	,	,	PUNCT
ejpam-1901	143	12	and	and	CCONJ
ejpam-1901	143	13	n.g	n.g	PROPN
ejpam-1901	143	14	.	.	PROPN
ejpam-1901	143	15	babu	babu	PROPN
ejpam-1901	143	16	.	.	PUNCT
ejpam-1901	144	1	on	on	ADP
ejpam-1901	144	2	graph	graph	NOUN
ejpam-1901	144	3	differential	differential	ADJ
ejpam-1901	144	4	equations	equation	NOUN
ejpam-1901	144	5	and	and	CCONJ
ejpam-1901	144	6	its	its	PRON
ejpam-1901	144	7	associated	associated	ADJ
ejpam-1901	144	8	matrix	matrix	NOUN
ejpam-1901	144	9	differential	differential	NOUN
ejpam-1901	144	10	equations	equation	NOUN
ejpam-1901	144	11	.	.	PUNCT
ejpam-1901	145	1	malaya	malaya	PROPN
ejpam-1901	145	2	journal	journal	PROPN
ejpam-1901	145	3	of	of	ADP
ejpam-1901	145	4	mathematik	mathematik	PROPN
ejpam-1901	145	5	1	1	NUM
ejpam-1901	145	6	(	(	PUNCT
ejpam-1901	145	7	1	1	NUM
ejpam-1901	145	8	)	)	PUNCT
ejpam-1901	145	9	82	82	NUM
ejpam-1901	145	10	-	-	SYM
ejpam-1901	145	11	90	90	NUM
ejpam-1901	145	12	.	.	PUNCT
ejpam-1901	145	13	2012	2012	NUM
ejpam-1901	145	14	.	.	PUNCT
ejpam-1901	146	1	[	[	X
ejpam-1901	146	2	3	3	X
ejpam-1901	146	3	]	]	X
ejpam-1901	146	4	d.d	d.d	PROPN
ejpam-1901	146	5	.	.	PROPN
ejpam-1901	146	6	siljak	siljak	PROPN
ejpam-1901	146	7	.	.	PUNCT
ejpam-1901	147	1	dynamic	dynamic	ADJ
ejpam-1901	147	2	graphs	graph	NOUN
ejpam-1901	147	3	,	,	PUNCT
ejpam-1901	147	4	nonlinear	nonlinear	ADJ
ejpam-1901	147	5	analysis	analysis	NOUN
ejpam-1901	147	6	,	,	PUNCT
ejpam-1901	147	7	hybrid	hybrid	ADJ
ejpam-1901	147	8	systems	system	NOUN
ejpam-1901	147	9	2	2	NUM
ejpam-1901	147	10	,	,	PUNCT
ejpam-1901	147	11	544	544	NUM
ejpam-1901	147	12	-	-	SYM
ejpam-1901	147	13	567	567	NUM
ejpam-1901	147	14	.	.	NUM
ejpam-1901	147	15	2008	2008	NUM
ejpam-1901	147	16	.	.	PUNCT