id	sid	eid	entity	type
ejpam-6097	1	1	european journal	ORG
ejpam-6097	1	2	2025	DATE
ejpam-6097	1	3	18	CARDINAL
ejpam-6097	1	4	2	CARDINAL
ejpam-6097	1	5	6097	CARDINAL
ejpam-6097	1	6	1307-5543	DATE
ejpam-6097	1	7	new york	GPE
ejpam-6097	1	8	1	CARDINAL
ejpam-6097	1	9	random3 immigration4	ORG
ejpam-6097	1	10	mohammed1	GPE
ejpam-6097	1	11	jawdat alebraheem	ORG
ejpam-6097	1	12	1,∗	DATE
ejpam-6097	1	13	ismail m. tayel1,5 muhamad hifzhudin	PERSON
ejpam-6097	1	14	majmaah university	ORG
ejpam-6097	1	15	al-majmaah	PERSON
ejpam-6097	1	16	arabia8 2 institute of mathematical sciences	ORG
ejpam-6097	1	17	science universiti malaya 50603,9 kuala lumpur	ORG
ejpam-6097	1	18	11	CARDINAL
ejpam-6097	7	1	2020	DATE
ejpam-6097	7	2	92-11	CARDINAL
ejpam-6097	7	3	60h10	DATE
ejpam-6097	7	4	34d2012	CARDINAL
ejpam-6097	7	5	introduction16	ORG
ejpam-6097	7	6	dynamical17	ORG
ejpam-6097	8	1	in18	PRODUCT
ejpam-6097	8	2	lotka	ORG
ejpam-6097	8	3	1	CARDINAL
ejpam-6097	8	4	2	CARDINAL
ejpam-6097	9	1	this19	PERSON
ejpam-6097	9	2	instantaneous,20	ORG
ejpam-6097	9	3	presupposes21	GPE
ejpam-6097	10	1	lotka-voltera	ORG
ejpam-6097	10	2	model22	ORG
ejpam-6097	10	3	dynamics23 ∗corresponding	ORG
ejpam-6097	11	1	m. mohammed	PERSON
ejpam-6097	11	2	j.alebraheem@mu.edu.sa	PERSON
ejpam-6097	11	3	j. alebraheem	PERSON
ejpam-6097	11	4	i.tayel.edu.sa	ORG
ejpam-6097	11	5	i. m. tayel	PERSON
ejpam-6097	12	1	1	CARDINAL
ejpam-6097	12	2	2025	CARDINAL
ejpam-6097	13	1	m. mohamed et al	PERSON
ejpam-6097	14	1	j. pure	PERSON
ejpam-6097	14	2	18	CARDINAL
ejpam-6097	14	3	2	CARDINAL
ejpam-6097	14	4	2025	CARDINAL
ejpam-6097	14	5	6097 2	DATE
ejpam-6097	14	6	19	CARDINAL
ejpam-6097	15	1	3–9	CARDINAL
ejpam-6097	16	1	such25	GPE
ejpam-6097	16	2	fear26	ORG
ejpam-6097	17	1	10–13].27 one	CARDINAL
ejpam-6097	17	2	crucial28	ORG
ejpam-6097	18	1	to29	ORG
ejpam-6097	18	2	14	CARDINAL
ejpam-6097	18	3	15	CARDINAL
ejpam-6097	18	4	16	CARDINAL
ejpam-6097	19	1	affect33	ORG
ejpam-6097	20	1	17–21	CARDINAL
ejpam-6097	20	2	such36	ORG
ejpam-6097	21	1	22	CARDINAL
ejpam-6097	22	1	as37	PRODUCT
ejpam-6097	24	1	complete46	ORG
ejpam-6097	24	2	simulation.48 2	ORG
ejpam-6097	24	3	ii50	ORG
ejpam-6097	25	1	23–26	CARDINAL
ejpam-6097	26	1	equations51	ORG
ejpam-6097	27	1	1−	TIME
ejpam-6097	28	1	1	CARDINAL
ejpam-6097	28	2	53	CARDINAL
ejpam-6097	28	3	1 +	DATE
ejpam-6097	29	1	2	CARDINAL
ejpam-6097	29	2	54	CARDINAL
ejpam-6097	29	3	3	CARDINAL
ejpam-6097	30	1	et55 al	PERSON
ejpam-6097	31	1	26	CARDINAL
ejpam-6097	31	2	1)-(3	CARDINAL
ejpam-6097	32	1	model’s56	DATE
ejpam-6097	33	1	were58	ORG
ejpam-6097	34	1	system59	GPE
ejpam-6097	36	1	j. pure	PERSON
ejpam-6097	36	2	18	CARDINAL
ejpam-6097	36	3	2	CARDINAL
ejpam-6097	36	4	2025	CARDINAL
ejpam-6097	36	5	6097 3	DATE
ejpam-6097	36	6	19	CARDINAL
ejpam-6097	36	7	1)-(3	CARDINAL
ejpam-6097	38	1	1−	TIME
ejpam-6097	38	2	1 +	QUANTITY
ejpam-6097	39	1	1 +	DATE
ejpam-6097	40	1	v(0	PERSON
ejpam-6097	40	2	4	CARDINAL
ejpam-6097	40	3	5	CARDINAL
ejpam-6097	40	4	6	CARDINAL
ejpam-6097	40	5	4)-(6	CARDINAL
ejpam-6097	40	6	1−	TIME
ejpam-6097	40	7	1+βu	DATE
ejpam-6097	40	8	func-63	FAC
ejpam-6097	40	9	−σv	PRODUCT
ejpam-6097	40	10	1+βu	DATE
ejpam-6097	40	11	λv2	ORG
ejpam-6097	42	1	to67	PRODUCT
ejpam-6097	42	2	popu-68	DATE
ejpam-6097	44	1	•	CARDINAL
ejpam-6097	44	2	the predator.74 • σ	EVENT
ejpam-6097	44	3	• γ	GPE
ejpam-6097	44	4	• δdb1 and ϵdb2	WORK_OF_ART
ejpam-6097	44	5	•	CARDINAL
ejpam-6097	44	6	0.82 •	CARDINAL
ejpam-6097	44	7	1	CARDINAL
ejpam-6097	45	1	0	CARDINAL
ejpam-6097	45	2	•	CARDINAL
ejpam-6097	45	3	zero	CARDINAL
ejpam-6097	46	1	m. mohamed et al	PERSON
ejpam-6097	47	1	j. pure	PERSON
ejpam-6097	47	2	18	CARDINAL
ejpam-6097	47	3	2	CARDINAL
ejpam-6097	47	4	2025	CARDINAL
ejpam-6097	47	5	6097 4 of 19 3	DATE
ejpam-6097	47	6	boundedness87	ORG
ejpam-6097	47	7	probabilistic88	NORP
ejpam-6097	48	1	4)-(6	CARDINAL
ejpam-6097	48	2	m(t	PERSON
ejpam-6097	48	3	x)db x0	PERSON
ejpam-6097	49	1	x(0	PERSON
ejpam-6097	49	2	7	CARDINAL
ejpam-6097	49	3	8)	CARDINAL
ejpam-6097	49	4	0	CARDINAL
ejpam-6097	49	5	2	CARDINAL
ejpam-6097	49	6	0	CARDINAL
ejpam-6097	49	7	2	CARDINAL
ejpam-6097	49	8	m(t	PERSON
ejpam-6097	49	9	m(t	PERSON
ejpam-6097	50	1	1−	TIME
ejpam-6097	50	2	1+βu	CARDINAL
ejpam-6097	50	3	1+βu	CARDINAL
ejpam-6097	57	1	1	CARDINAL
ejpam-6097	58	1	m(t	PERSON
ejpam-6097	58	2	satisfy92	GPE
ejpam-6097	58	3	condition93 e∥m(t	ORG
ejpam-6097	58	4	x)∥2 +	DATE
ejpam-6097	60	1	9	CARDINAL
ejpam-6097	61	1	4	CARDINAL
ejpam-6097	66	1	one	CARDINAL
ejpam-6097	67	1	10	CARDINAL
ejpam-6097	68	1	1−	LANGUAGE
ejpam-6097	68	2	1 + βu ∥2	DATE
ejpam-6097	70	1	1 +	DATE
ejpam-6097	70	2	+ ∥v∥2	MONEY
ejpam-6097	70	3	ce∥u∥2(1	ORG
ejpam-6097	70	4	11	CARDINAL
ejpam-6097	70	5	m. mohamed et al	PERSON
ejpam-6097	71	1	j. pure	PERSON
ejpam-6097	71	2	18	CARDINAL
ejpam-6097	71	3	2	CARDINAL
ejpam-6097	71	4	2025	CARDINAL
ejpam-6097	71	5	6097 5	DATE
ejpam-6097	71	6	19	DATE
ejpam-6097	71	7	10	CARDINAL
ejpam-6097	71	8	11	CARDINAL
ejpam-6097	72	1	12	CARDINAL
ejpam-6097	72	2	that99	GPE
ejpam-6097	74	1	13	CARDINAL
ejpam-6097	74	2	12	CARDINAL
ejpam-6097	74	3	13	CARDINAL
ejpam-6097	74	4	1	CARDINAL
ejpam-6097	75	1	1	CARDINAL
ejpam-6097	75	2	0	CARDINAL
ejpam-6097	75	3	0≤t≤t ∥x∥p	QUANTITY
ejpam-6097	75	4	14	CARDINAL
ejpam-6097	76	1	7	CARDINAL
ejpam-6097	78	1	x)ds+ ∫	ORG
ejpam-6097	80	1	15	CARDINAL
ejpam-6097	80	2	27	CARDINAL
ejpam-6097	80	3	∈	ORG
ejpam-6097	80	4	∈	ORG
ejpam-6097	81	1	0,∞	DATE
ejpam-6097	81	2	1 ≤	MONEY
ejpam-6097	86	1	16	CARDINAL
ejpam-6097	86	2	16	CARDINAL
ejpam-6097	86	3	0	CARDINAL
ejpam-6097	86	4	0≤t≤t	CARDINAL
ejpam-6097	88	1	0≤t≤t	CARDINAL
ejpam-6097	89	1	∣∣∣∣q	ORG
ejpam-6097	90	1	17	CARDINAL
ejpam-6097	90	2	1	CARDINAL
ejpam-6097	91	1	1	CARDINAL
ejpam-6097	91	2	0≤t≤t	CARDINAL
ejpam-6097	91	3	x)dt	ORG
ejpam-6097	91	4	1	CARDINAL
ejpam-6097	91	5	1	CARDINAL
ejpam-6097	94	1	18	CARDINAL
ejpam-6097	94	2	m. mohamed et al	PERSON
ejpam-6097	95	1	j. pure	PERSON
ejpam-6097	95	2	18	CARDINAL
ejpam-6097	95	3	2	CARDINAL
ejpam-6097	95	4	2025	CARDINAL
ejpam-6097	95	5	6097 6	DATE
ejpam-6097	95	6	19	DATE
ejpam-6097	95	7	1	CARDINAL
ejpam-6097	95	8	16	CARDINAL
ejpam-6097	98	1	2 dt ≤	QUANTITY
ejpam-6097	98	2	ec	ORG
ejpam-6097	98	3	2	CARDINAL
ejpam-6097	99	1	2 2	CARDINAL
ejpam-6097	99	2	2	CARDINAL
ejpam-6097	99	3	2 2	CARDINAL
ejpam-6097	99	4	2	CARDINAL
ejpam-6097	99	5	t + e	DATE
ejpam-6097	100	1	19	CARDINAL
ejpam-6097	100	2	18	CARDINAL
ejpam-6097	100	3	19	CARDINAL
ejpam-6097	100	4	0≤t≤t	CARDINAL
ejpam-6097	101	1	2 2	CARDINAL
ejpam-6097	101	2	2	CARDINAL
ejpam-6097	102	1	2 2	CARDINAL
ejpam-6097	102	2	2	CARDINAL
ejpam-6097	104	1	20	CARDINAL
ejpam-6097	104	2	burkholder-davis-gundyand	PERSON
ejpam-6097	105	1	0≤t≤t	CARDINAL
ejpam-6097	106	1	∣∣∣∣q	ORG
ejpam-6097	106	2	2	CARDINAL
ejpam-6097	106	3	1	CARDINAL
ejpam-6097	107	1	2	CARDINAL
ejpam-6097	107	2	2	CARDINAL
ejpam-6097	108	1	x)|qdt.	GPE
ejpam-6097	109	1	21	CARDINAL
ejpam-6097	109	2	1	CARDINAL
ejpam-6097	109	3	16	CARDINAL
ejpam-6097	109	4	2	CARDINAL
ejpam-6097	109	5	∣∣∣∣ ≤ cbt	QUANTITY
ejpam-6097	109	6	2	CARDINAL
ejpam-6097	109	7	2 2	CARDINAL
ejpam-6097	109	8	2	CARDINAL
ejpam-6097	110	1	2	CARDINAL
ejpam-6097	110	2	2 2	CARDINAL
ejpam-6097	110	3	2	CARDINAL
ejpam-6097	110	4	t + e	DATE
ejpam-6097	110	5	2c	CARDINAL
ejpam-6097	110	6	2 2	CARDINAL
ejpam-6097	110	7	2	CARDINAL
ejpam-6097	110	8	q−2 2	PRODUCT
ejpam-6097	110	9	2 2	CARDINAL
ejpam-6097	110	10	2	CARDINAL
ejpam-6097	111	1	22	CARDINAL
ejpam-6097	111	2	17	CARDINAL
ejpam-6097	111	3	21	CARDINAL
ejpam-6097	111	4	22	CARDINAL
ejpam-6097	111	5	one	CARDINAL
ejpam-6097	111	6	4	CARDINAL
ejpam-6097	111	7	4)-(6	CARDINAL
ejpam-6097	111	8	1)-(3	CARDINAL
ejpam-6097	112	1	three	CARDINAL
ejpam-6097	112	2	1	CARDINAL
ejpam-6097	113	1	0)116 m. mohamed et al	PERSON
ejpam-6097	114	1	j. pure	PERSON
ejpam-6097	114	2	18	CARDINAL
ejpam-6097	114	3	2	CARDINAL
ejpam-6097	114	4	2025	CARDINAL
ejpam-6097	114	5	6097 7	DATE
ejpam-6097	118	1	αu∗v∗ 1 +	DATE
ejpam-6097	118	2	0	CARDINAL
ejpam-6097	119	1	2	CARDINAL
ejpam-6097	119	2	0	CARDINAL
ejpam-6097	120	1	23	CARDINAL
ejpam-6097	120	2	24	CARDINAL
ejpam-6097	120	3	1−	TIME
ejpam-6097	122	1	−σv + γuv	ORG
ejpam-6097	122	2	1 +	DATE
ejpam-6097	124	1	v(0	PERSON
ejpam-6097	125	1	25	CARDINAL
ejpam-6097	125	2	26	CARDINAL
ejpam-6097	125	3	27	CARDINAL
ejpam-6097	125	4	g(t	GPE
ejpam-6097	125	5	28	CARDINAL
ejpam-6097	127	1	123	CARDINAL
ejpam-6097	137	1	k + αβv∗	GPE
ejpam-6097	137	2	1+βu)2	CARDINAL
ejpam-6097	137	3	1+βu∗)γ−γβu∗	CARDINAL
ejpam-6097	137	4	1+βu∗)2	CARDINAL
ejpam-6097	138	1	g(t	NORP
ejpam-6097	142	1	φ ∈	ORG
ejpam-6097	143	1	28	CARDINAL
ejpam-6097	143	2	markov128 m. mohamed et al	PERSON
ejpam-6097	144	1	j. pure	PERSON
ejpam-6097	144	2	18	CARDINAL
ejpam-6097	144	3	2	CARDINAL
ejpam-6097	144	4	2025	CARDINAL
ejpam-6097	144	5	6097 8	DATE
ejpam-6097	144	6	19	CARDINAL
ejpam-6097	144	7	28	CARDINAL
ejpam-6097	144	8	by129 lφ(t	PERSON
ejpam-6097	146	1	g(t	PERSON
ejpam-6097	147	1	29	CARDINAL
ejpam-6097	147	2	28)130	CARDINAL
ejpam-6097	147	3	2	CARDINAL
ejpam-6097	148	1	1 +	CARDINAL
ejpam-6097	148	2	2	CARDINAL
ejpam-6097	148	3	2	CARDINAL
ejpam-6097	148	4	30	CARDINAL
ejpam-6097	148	5	31	CARDINAL
ejpam-6097	148	6	23)-(27	CARDINAL
ejpam-6097	149	1	1 2	CARDINAL
ejpam-6097	149	2	2 + a2y 2	DATE
ejpam-6097	149	3	1	CARDINAL
ejpam-6097	149	4	2	CARDINAL
ejpam-6097	149	5	deter-134	GPE
ejpam-6097	151	1	0	CARDINAL
ejpam-6097	152	1	32	CARDINAL
ejpam-6097	152	2	136	CARDINAL
ejpam-6097	153	1	2	CARDINAL
ejpam-6097	153	2	k + αβv∗	ORG
ejpam-6097	153	3	1 +bu∗)2	QUANTITY
ejpam-6097	153	4	∗	CARDINAL
ejpam-6097	153	5	1 +	CARDINAL
ejpam-6097	153	6	− a2λv ∗v∗	ORG
ejpam-6097	153	7	33	CARDINAL
ejpam-6097	153	8	1 2	CARDINAL
ejpam-6097	153	9	g(t	NORP
ejpam-6097	154	1	1 2	CARDINAL
ejpam-6097	154	2	2	CARDINAL
ejpam-6097	154	3	2ϵ2	CARDINAL
ejpam-6097	155	1	34	CARDINAL
ejpam-6097	155	2	32)-(34	CARDINAL
ejpam-6097	155	3	29	CARDINAL
ejpam-6097	155	4	get138 l(φ(t	PERSON
ejpam-6097	158	1	1 +bu∗)2	QUANTITY
ejpam-6097	158	2	1 +	CARDINAL
ejpam-6097	159	1	2u2	CARDINAL
ejpam-6097	160	1	k u∗ −	ORG
ejpam-6097	160	2	1 +bu∗)2	QUANTITY
ejpam-6097	160	3	1 2	CARDINAL
ejpam-6097	160	4	2	CARDINAL
ejpam-6097	160	5	2	CARDINAL
ejpam-6097	160	6	1 +	CARDINAL
ejpam-6097	161	1	35	CARDINAL
ejpam-6097	161	2	m. mohamed et al	PERSON
ejpam-6097	162	1	j. pure	PERSON
ejpam-6097	162	2	18	CARDINAL
ejpam-6097	162	3	2	CARDINAL
ejpam-6097	162	4	2025	CARDINAL
ejpam-6097	162	5	6097 9	DATE
ejpam-6097	162	6	19	CARDINAL
ejpam-6097	162	7	γv∗ 1+βu∗a2	DATE
ejpam-6097	162	8	l(φ(t	PERSON
ejpam-6097	164	1	−ρu∗ k −	PERSON
ejpam-6097	164	2	1 +bu∗)2	QUANTITY
ejpam-6097	164	3	1 2	CARDINAL
ejpam-6097	164	4	2	CARDINAL
ejpam-6097	165	1	2	CARDINAL
ejpam-6097	165	2	36	CARDINAL
ejpam-6097	165	3	l(φ(t	PERSON
ejpam-6097	166	1	then140 −ρu∗ k > αβu∗v∗	PERSON
ejpam-6097	166	2	1 +	CARDINAL
ejpam-6097	166	3	+ 1 2	QUANTITY
ejpam-6097	166	4	1 2	CARDINAL
ejpam-6097	167	1	1	CARDINAL
ejpam-6097	168	1	30	CARDINAL
ejpam-6097	168	2	31	CARDINAL
ejpam-6097	168	3	4)-(6	CARDINAL
ejpam-6097	168	4	1	CARDINAL
ejpam-6097	169	1	5.1	CARDINAL
ejpam-6097	170	1	29].152	CARDINAL
ejpam-6097	170	2	2	CARDINAL
ejpam-6097	171	1	lim	PERSON
ejpam-6097	171	2	0≤t≤t	CARDINAL
ejpam-6097	171	3	1	CARDINAL
ejpam-6097	172	1	37	CARDINAL
ejpam-6097	172	2	3	CARDINAL
ejpam-6097	173	1	2	CARDINAL
ejpam-6097	173	2	0	CARDINAL
ejpam-6097	175	1	0	CARDINAL
ejpam-6097	175	2	1	CARDINAL
ejpam-6097	175	3	38	CARDINAL
ejpam-6097	177	1	39	CARDINAL
ejpam-6097	177	2	m. mohamed et al	PERSON
ejpam-6097	178	1	j. pure	PERSON
ejpam-6097	178	2	18	CARDINAL
ejpam-6097	178	3	2	CARDINAL
ejpam-6097	178	4	2025	CARDINAL
ejpam-6097	178	5	6097 10 of 19 and157	DATE
ejpam-6097	178	6	1 2	CARDINAL
ejpam-6097	178	7	0	CARDINAL
ejpam-6097	178	8	0	CARDINAL
ejpam-6097	180	1	40	CARDINAL
ejpam-6097	182	1	2 + γû]dt+	MONEY
ejpam-6097	183	1	0	CARDINAL
ejpam-6097	183	2	t ≤ 1	CARDINAL
ejpam-6097	183	3	2	CARDINAL
ejpam-6097	183	4	1	CARDINAL
ejpam-6097	183	5	0	CARDINAL
ejpam-6097	184	1	1	CARDINAL
ejpam-6097	185	1	2 +	QUANTITY
ejpam-6097	185	2	1	CARDINAL
ejpam-6097	185	3	0	CARDINAL
ejpam-6097	186	1	1	CARDINAL
ejpam-6097	187	1	41	CARDINAL
ejpam-6097	187	2	get161 lim	PERSON
ejpam-6097	187	3	2 +	QUANTITY
ejpam-6097	187	4	42	CARDINAL
ejpam-6097	187	5	lim	PERSON
ejpam-6097	190	1	ρ k û−	PERSON
ejpam-6097	190	2	1 2	CARDINAL
ejpam-6097	191	1	43	CARDINAL
ejpam-6097	191	2	give163	GPE
ejpam-6097	192	1	1	CARDINAL
ejpam-6097	193	1	t ∫	ORG
ejpam-6097	193	2	0	CARDINAL
ejpam-6097	195	1	1 2	CARDINAL
ejpam-6097	195	2	t ∫	ORG
ejpam-6097	195	3	0	CARDINAL
ejpam-6097	197	1	the lim supt→∞	ORG
ejpam-6097	197	2	39	CARDINAL
ejpam-6097	197	3	40	CARDINAL
ejpam-6097	197	4	we164 obtain165 lim	PERSON
ejpam-6097	197	5	1	CARDINAL
ejpam-6097	197	6	2	CARDINAL
ejpam-6097	197	7	− ρ k	PERSON
ejpam-6097	197	8	0	CARDINAL
ejpam-6097	198	1	44	DATE
ejpam-6097	198	2	2	CARDINAL
ejpam-6097	199	1	0	CARDINAL
ejpam-6097	200	1	5.2	CARDINAL
ejpam-6097	201	1	4	CARDINAL
ejpam-6097	202	1	2	CARDINAL
ejpam-6097	203	1	45	CARDINAL
ejpam-6097	203	2	m. mohamed et al	PERSON
ejpam-6097	204	1	j. pure	PERSON
ejpam-6097	204	2	18	CARDINAL
ejpam-6097	204	3	2	CARDINAL
ejpam-6097	204	4	2025	CARDINAL
ejpam-6097	204	5	6097 11	DATE
ejpam-6097	204	6	19	CARDINAL
ejpam-6097	205	1	φ(t	ORG
ejpam-6097	206	1	1 2	CARDINAL
ejpam-6097	207	1	46	CARDINAL
ejpam-6097	207	2	0	CARDINAL
ejpam-6097	207	3	1	CARDINAL
ejpam-6097	208	1	1 2	CARDINAL
ejpam-6097	208	2	1	CARDINAL
ejpam-6097	209	1	47	DATE
ejpam-6097	209	2	one	CARDINAL
ejpam-6097	209	3	gets172 lim	PERSON
ejpam-6097	209	4	1	CARDINAL
ejpam-6097	209	5	0	CARDINAL
ejpam-6097	209	6	48	CARDINAL
ejpam-6097	209	7	lim	PERSON
ejpam-6097	209	8	t→∞	CARDINAL
ejpam-6097	209	9	1 2	CARDINAL
ejpam-6097	210	1	49	CARDINAL
ejpam-6097	210	2	1	CARDINAL
ejpam-6097	210	3	lim t→∞	FAC
ejpam-6097	210	4	0	CARDINAL
ejpam-6097	210	5	5.3	CARDINAL
ejpam-6097	210	6	5	CARDINAL
ejpam-6097	211	1	2	CARDINAL
ejpam-6097	211	2	2	CARDINAL
ejpam-6097	211	3	50	CARDINAL
ejpam-6097	211	4	surely.178	NORP
ejpam-6097	212	1	two	CARDINAL
ejpam-6097	212	2	2	CARDINAL
ejpam-6097	214	1	41	CARDINAL
ejpam-6097	214	2	2 +	QUANTITY
ejpam-6097	215	1	51	CARDINAL
ejpam-6097	215	2	then181 lim	PERSON
ejpam-6097	216	1	2	CARDINAL
ejpam-6097	216	2	t).182 m. mohamed et al	PERSON
ejpam-6097	217	1	j. pure	PERSON
ejpam-6097	217	2	18	CARDINAL
ejpam-6097	217	3	2	CARDINAL
ejpam-6097	217	4	2025	CARDINAL
ejpam-6097	217	5	6097 12	DATE
ejpam-6097	217	6	2	CARDINAL
ejpam-6097	217	7	0	CARDINAL
ejpam-6097	218	1	0	CARDINAL
ejpam-6097	221	1	2	CARDINAL
ejpam-6097	221	2	ds− ρ k	ORG
ejpam-6097	225	1	2 + ϱ2	DATE
ejpam-6097	226	1	30	CARDINAL
ejpam-6097	226	2	2.2	CARDINAL
ejpam-6097	227	1	2 + ϱ2	DATE
ejpam-6097	229	1	2	CARDINAL
ejpam-6097	230	1	17	CARDINAL
ejpam-6097	230	2	lim	PERSON
ejpam-6097	230	3	1	CARDINAL
ejpam-6097	230	4	2 + γul ≤	QUANTITY
ejpam-6097	231	1	2	CARDINAL
ejpam-6097	232	1	0.186	CARDINAL
ejpam-6097	232	2	2	CARDINAL
ejpam-6097	233	1	50).188 6	CARDINAL
ejpam-6097	236	1	mathematica 11.1	PERSON
ejpam-6097	237	1	0.9	CARDINAL
ejpam-6097	237	2	0.8	CARDINAL
ejpam-6097	238	1	1)-(3	CARDINAL
ejpam-6097	238	2	0.4	CARDINAL
ejpam-6097	238	3	0.75	CARDINAL
ejpam-6097	238	4	0.5	CARDINAL
ejpam-6097	238	5	0.2	CARDINAL
ejpam-6097	238	6	0.6	CARDINAL
ejpam-6097	238	7	0.1	CARDINAL
ejpam-6097	239	1	52	CARDINAL
ejpam-6097	239	2	m. mohamed et al	PERSON
ejpam-6097	240	1	j. pure	PERSON
ejpam-6097	240	2	18	CARDINAL
ejpam-6097	240	3	2	CARDINAL
ejpam-6097	240	4	2025	CARDINAL
ejpam-6097	240	5	6097 13	DATE
ejpam-6097	240	6	19	CARDINAL
ejpam-6097	240	7	4)-(6	CARDINAL
ejpam-6097	241	1	0.5254	CARDINAL
ejpam-6097	242	1	0	CARDINAL
ejpam-6097	242	2	0.05	CARDINAL
ejpam-6097	242	3	0.05	CARDINAL
ejpam-6097	242	4	0.4	CARDINAL
ejpam-6097	242	5	0.4	CARDINAL
ejpam-6097	242	6	0.4	CARDINAL
ejpam-6097	242	7	1.2	CARDINAL
ejpam-6097	242	8	1.0	CARDINAL
ejpam-6097	242	9	199	CARDINAL
ejpam-6097	242	10	1.2 1.4	CARDINAL
ejpam-6097	242	11	o	DATE
ejpam-6097	242	12	0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4	QUANTITY
ejpam-6097	242	13	1.2 1.4	CARDINAL
ejpam-6097	242	14	1	CARDINAL
ejpam-6097	242	15	1)-(3	CARDINAL
ejpam-6097	242	16	0.9	CARDINAL
ejpam-6097	242	17	0.8	CARDINAL
ejpam-6097	243	1	52	CARDINAL
ejpam-6097	244	1	figure1	PERSON
ejpam-6097	244	2	1)-(3	CARDINAL
ejpam-6097	244	3	≈	CARDINAL
ejpam-6097	244	4	0.5254	CARDINAL
ejpam-6097	244	5	25].202	CARDINAL
ejpam-6097	244	6	20 40	DATE
ejpam-6097	244	7	1.2 1.4	CARDINAL
ejpam-6097	244	8	o	DATE
ejpam-6097	244	9	0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4	QUANTITY
ejpam-6097	244	10	1.2 1.4	CARDINAL
ejpam-6097	244	11	2	CARDINAL
ejpam-6097	244	12	4)-(6	CARDINAL
ejpam-6097	244	13	0.9	CARDINAL
ejpam-6097	244	14	0.8	CARDINAL
ejpam-6097	244	15	0.05	CARDINAL
ejpam-6097	244	16	0.05	CARDINAL
ejpam-6097	244	17	52	CARDINAL
ejpam-6097	245	1	2	CARDINAL
ejpam-6097	245	2	4)-(6	CARDINAL
ejpam-6097	245	3	0.05	CARDINAL
ejpam-6097	245	4	0.05	CARDINAL
ejpam-6097	245	5	the204	ORG
ejpam-6097	245	6	the following:205 • ρu∗	TIME
ejpam-6097	245	7	k −	ORG
ejpam-6097	245	8	1+bu∗)2	DATE
ejpam-6097	246	1	2 ≈ 0.0425	QUANTITY
ejpam-6097	246	2	0.206	CARDINAL
ejpam-6097	246	3	m. mohamed et al	PERSON
ejpam-6097	247	1	j. pure	PERSON
ejpam-6097	247	2	18	CARDINAL
ejpam-6097	247	3	2	CARDINAL
ejpam-6097	247	4	2025	CARDINAL
ejpam-6097	247	5	6097 14	DATE
ejpam-6097	247	6	19 •	CARDINAL
ejpam-6097	249	1	2	CARDINAL
ejpam-6097	250	1	0.207 •	CARDINAL
ejpam-6097	250	2	2 ≈ 0.3988	QUANTITY
ejpam-6097	250	3	0.208 •	CARDINAL
ejpam-6097	251	1	2	CARDINAL
ejpam-6097	252	1	0.209	CARDINAL
ejpam-6097	252	2	2	CARDINAL
ejpam-6097	252	3	3	CARDINAL
ejpam-6097	252	4	214	CARDINAL
ejpam-6097	253	1	o	DATE
ejpam-6097	253	2	0.0 0.5 1.0 1.5	QUANTITY
ejpam-6097	253	3	2.5	CARDINAL
ejpam-6097	253	4	2.5 3.0	CARDINAL
ejpam-6097	253	5	3	CARDINAL
ejpam-6097	253	6	4)-(6	CARDINAL
ejpam-6097	253	7	0.9	CARDINAL
ejpam-6097	253	8	0.8	CARDINAL
ejpam-6097	253	9	0.4	CARDINAL
ejpam-6097	253	10	0.4	CARDINAL
ejpam-6097	253	11	52	CARDINAL
ejpam-6097	254	1	3	CARDINAL
ejpam-6097	254	2	4)-(6	CARDINAL
ejpam-6097	254	3	0.4	CARDINAL
ejpam-6097	254	4	0.4	CARDINAL
ejpam-6097	254	5	the following:216 •	PRODUCT
ejpam-6097	254	6	k −	ORG
ejpam-6097	254	7	1+bu∗)2	DATE
ejpam-6097	255	1	2 ≈	QUANTITY
ejpam-6097	255	2	0.217 •	CARDINAL
ejpam-6097	255	3	2 ≈ 0− 0.0305	QUANTITY
ejpam-6097	255	4	0.218 •	CARDINAL
ejpam-6097	255	5	2 ≈ 0.32	QUANTITY
ejpam-6097	255	6	0.219 •	CARDINAL
ejpam-6097	256	1	2	CARDINAL
ejpam-6097	256	2	≈ 0.096	CARDINAL
ejpam-6097	256	3	0.220	CARDINAL
ejpam-6097	256	4	2	CARDINAL
ejpam-6097	257	1	3	CARDINAL
ejpam-6097	258	1	5	CARDINAL
ejpam-6097	259	1	227	CARDINAL
ejpam-6097	259	2	m. mohamed et al	PERSON
ejpam-6097	260	1	j. pure	PERSON
ejpam-6097	260	2	18	CARDINAL
ejpam-6097	260	3	2	CARDINAL
ejpam-6097	260	4	2025	CARDINAL
ejpam-6097	260	5	6097 15	DATE
ejpam-6097	260	6	o	DATE
ejpam-6097	260	7	0 1 2 3 4 5 0.0 0.5 1.0 1.5	QUANTITY
ejpam-6097	260	8	2.5 3.0	CARDINAL
ejpam-6097	260	9	4	CARDINAL
ejpam-6097	260	10	4)-(6	CARDINAL
ejpam-6097	260	11	0.9	CARDINAL
ejpam-6097	260	12	0.8	CARDINAL
ejpam-6097	260	13	0.4	CARDINAL
ejpam-6097	260	14	1.2	CARDINAL
ejpam-6097	260	15	52	CARDINAL
ejpam-6097	261	1	4	CARDINAL
ejpam-6097	261	2	4)-(6	CARDINAL
ejpam-6097	261	3	0.4	CARDINAL
ejpam-6097	261	4	1.2	CARDINAL
ejpam-6097	261	5	the228	ORG
ejpam-6097	261	6	the following:229 •	LAW
ejpam-6097	262	1	k −	ORG
ejpam-6097	262	2	1+bu∗)2	DATE
ejpam-6097	263	1	2 ≈	QUANTITY
ejpam-6097	263	2	2 ≈ 0− 0.6704	QUANTITY
ejpam-6097	263	3	0.231 •	CARDINAL
ejpam-6097	263	4	2 ≈ 0.32	QUANTITY
ejpam-6097	263	5	0.232 •	CARDINAL
ejpam-6097	263	6	2	CARDINAL
ejpam-6097	264	1	≈	CARDINAL
ejpam-6097	264	2	0.233	CARDINAL
ejpam-6097	264	3	2	CARDINAL
ejpam-6097	265	1	3	CARDINAL
ejpam-6097	265	2	238	CARDINAL
ejpam-6097	265	3	o	DATE
ejpam-6097	265	4	0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4	QUANTITY
ejpam-6097	265	5	1.2 1.4	CARDINAL
ejpam-6097	265	6	5	CARDINAL
ejpam-6097	265	7	4)-(6	CARDINAL
ejpam-6097	265	8	0.9	CARDINAL
ejpam-6097	265	9	0.8	CARDINAL
ejpam-6097	265	10	1.0	CARDINAL
ejpam-6097	265	11	0.1	CARDINAL
ejpam-6097	265	12	52	CARDINAL
ejpam-6097	266	1	m. mohamed et al	PERSON
ejpam-6097	267	1	j. pure	PERSON
ejpam-6097	267	2	18	CARDINAL
ejpam-6097	267	3	2	CARDINAL
ejpam-6097	267	4	2025	CARDINAL
ejpam-6097	267	5	6097 16	DATE
ejpam-6097	267	6	19	CARDINAL
ejpam-6097	267	7	5	CARDINAL
ejpam-6097	267	8	4)-(6	CARDINAL
ejpam-6097	267	9	1.0	CARDINAL
ejpam-6097	267	10	0.1	CARDINAL
ejpam-6097	267	11	the239	NORP
ejpam-6097	267	12	k −	ORG
ejpam-6097	267	13	1+bu∗)2	DATE
ejpam-6097	268	1	2 ≈	QUANTITY
ejpam-6097	268	2	0.241 •	CARDINAL
ejpam-6097	268	3	2 ≈ 00.0447	QUANTITY
ejpam-6097	268	4	0.242 •	CARDINAL
ejpam-6097	268	5	2	CARDINAL
ejpam-6097	269	1	−0.1	ORG
ejpam-6097	269	2	0.243 •	MONEY
ejpam-6097	269	3	2	CARDINAL
ejpam-6097	270	1	≈	CARDINAL
ejpam-6097	270	2	0.244	CARDINAL
ejpam-6097	270	3	2	CARDINAL
ejpam-6097	270	4	3	CARDINAL
ejpam-6097	270	5	5	CARDINAL
ejpam-6097	271	1	which248	ORG
ejpam-6097	272	1	destabiliza-249	GPE
ejpam-6097	273	1	7	CARDINAL
ejpam-6097	275	1	solu-255 tion	PERSON
ejpam-6097	276	1	2	CARDINAL
ejpam-6097	276	2	1	CARDINAL
ejpam-6097	277	1	3	CARDINAL
ejpam-6097	277	2	2	CARDINAL
ejpam-6097	278	1	1-5	CARDINAL
ejpam-6097	279	1	52	CARDINAL
ejpam-6097	281	1	•	CARDINAL
ejpam-6097	281	2	2	CARDINAL
ejpam-6097	282	1	50	CARDINAL
ejpam-6097	283	1	45	CARDINAL
ejpam-6097	283	2	50)together268	CARDINAL
ejpam-6097	284	1	in270	CARDINAL
ejpam-6097	284	2	5.271	CARDINAL
ejpam-6097	284	3	first	ORDINAL
ejpam-6097	284	4	22	CARDINAL
ejpam-6097	284	5	m. mohamed et al	PERSON
ejpam-6097	285	1	j. pure	PERSON
ejpam-6097	285	2	18	CARDINAL
ejpam-6097	285	3	2	CARDINAL
ejpam-6097	285	4	2025	CARDINAL
ejpam-6097	285	5	6097 17	DATE
ejpam-6097	285	6	19	CARDINAL
ejpam-6097	286	1	general275	PRODUCT
ejpam-6097	287	1	majmaah university	ORG
ejpam-6097	287	2	the283	ORG
ejpam-6097	287	3	icr-2025-1724).284	DATE
ejpam-6097	288	1	1	CARDINAL
ejpam-6097	288	2	alfred james lotka	PERSON
ejpam-6097	290	1	williams & wilkins	ORG
ejpam-6097	290	2	1925.286	CARDINAL
ejpam-6097	290	3	2	CARDINAL
ejpam-6097	290	4	vito volterra	PERSON
ejpam-6097	291	1	variazioni e	PERSON
ejpam-6097	291	2	del numero	FAC
ejpam-6097	292	1	anonima tipografica	PERSON
ejpam-6097	292	2	leonardo da vinci	PERSON
ejpam-6097	292	3	1926.288	CARDINAL
ejpam-6097	292	4	3	CARDINAL
ejpam-6097	293	1	35(3/4):213–245	CARDINAL
ejpam-6097	293	2	1948.290	CARDINAL
ejpam-6097	294	1	canadian	NORP
ejpam-6097	294	2	91(7):385–398	CARDINAL
ejpam-6097	294	3	1959.292	CARDINAL
ejpam-6097	294	4	5	CARDINAL
ejpam-6097	294	5	michael l rosenzweig	PERSON
ejpam-6097	294	6	robert h macarthur	PERSON
ejpam-6097	296	1	american	NORP
ejpam-6097	296	2	97(895):209–294 223	CARDINAL
ejpam-6097	296	3	1963.295	CARDINAL
ejpam-6097	296	4	6	CARDINAL
ejpam-6097	296	5	robert m	PERSON
ejpam-6097	298	1	177(4052):900–296 902	CARDINAL
ejpam-6097	298	2	7	CARDINAL
ejpam-6097	300	1	m.298 dekker	PERSON
ejpam-6097	300	2	1980.299	CARDINAL
ejpam-6097	301	1	8	CARDINAL
ejpam-6097	301	2	yang kuang	PERSON
ejpam-6097	303	1	j. biomath,300	PRODUCT
ejpam-6097	304	1	2002.301	CARDINAL
ejpam-6097	304	2	9	CARDINAL
ejpam-6097	304	3	salah boulaaras	ORG
ejpam-6097	306	1	applied303	ORG
ejpam-6097	306	2	33(1):2483728	CARDINAL
ejpam-6097	306	3	2025.304	CARDINAL
ejpam-6097	306	4	10	CARDINAL
ejpam-6097	306	5	zhihui ma	PERSON
ejpam-6097	306	6	shufan wang	PERSON
ejpam-6097	306	7	weide li	PERSON
ejpam-6097	306	8	zizhen li	PERSON
ejpam-6097	307	1	a305	GPE
ejpam-6097	308	1	2013.306	CARDINAL
ejpam-6097	309	1	11	CARDINAL
ejpam-6097	309	2	kumar mandal	PERSON
ejpam-6097	310	1	a307 competitive prey	ORG
ejpam-6097	311	1	biosystems	ORG
ejpam-6097	311	2	110(3):133–148,308 2012.309	CARDINAL
ejpam-6097	312	1	12	CARDINAL
ejpam-6097	312	2	wang	ORG
ejpam-6097	312	3	liana zanette	PERSON
ejpam-6097	312	4	xingfu zou	PERSON
ejpam-6097	314	1	73(5):1179–1204	CARDINAL
ejpam-6097	314	2	2016.311	CARDINAL
ejpam-6097	314	3	m. mohamed et al	PERSON
ejpam-6097	315	1	j. pure	PERSON
ejpam-6097	315	2	18	CARDINAL
ejpam-6097	315	3	2	CARDINAL
ejpam-6097	315	4	2025	CARDINAL
ejpam-6097	315	5	6097 18 of 19	DATE
ejpam-6097	315	6	13	CARDINAL
ejpam-6097	315	7	fengde chen	PERSON
ejpam-6097	315	8	zhenliang zhu	PERSON
ejpam-6097	315	9	zhong li	PERSON
ejpam-6097	317	1	2019:1–17	CARDINAL
ejpam-6097	317	2	2019.313	CARDINAL
ejpam-6097	318	1	14	CARDINAL
ejpam-6097	318	2	takeru tahara	PERSON
ejpam-6097	318	3	maica krizna	PERSON
ejpam-6097	318	4	jerrold m	PERSON
ejpam-6097	318	5	hiromu ito	PERSON
ejpam-6097	318	6	satoru morita	PERSON
ejpam-6097	318	7	genki ichinose	PERSON
ejpam-6097	318	8	tatsuya togashi	PERSON
ejpam-6097	318	9	lotka-volterra	PERSON
ejpam-6097	319	1	2018.317	CARDINAL
ejpam-6097	319	2	15	CARDINAL
ejpam-6097	319	3	debasis mukherjee	PERSON
ejpam-6097	321	1	world319 applications	PERSON
ejpam-6097	321	2	31:277–287	CARDINAL
ejpam-6097	321	3	2016.320	DATE
ejpam-6097	322	1	16	CARDINAL
ejpam-6097	324	1	2021.322	CARDINAL
ejpam-6097	324	2	17	CARDINAL
ejpam-6097	324	3	leonid	PERSON
ejpam-6097	324	4	andrei korobeinikov	PERSON
ejpam-6097	326	1	mathematics,324 12(10):1588	ORG
ejpam-6097	326	2	2024.325	DATE
ejpam-6097	326	3	18	CARDINAL
ejpam-6097	326	4	qiuyue zhao	PERSON
ejpam-6097	326	5	xinglong niu	PERSON
ejpam-6097	328	1	2024.327	CARDINAL
ejpam-6097	328	2	19	CARDINAL
ejpam-6097	328	3	feng rao	PERSON
ejpam-6097	328	4	yun kang	PERSON
ejpam-6097	330	1	175:113935	CARDINAL
ejpam-6097	330	2	2023.330	CARDINAL
ejpam-6097	330	3	20	CARDINAL
ejpam-6097	330	4	karam allali	PERSON
ejpam-6097	330	5	kottakkaran	PERSON
ejpam-6097	330	6	covid-19	PRODUCT
ejpam-6097	330	7	lévy	PRODUCT
ejpam-6097	331	1	21	CARDINAL
ejpam-6097	332	1	the standard brownian335	ORG
ejpam-6097	332	2	lévy	PRODUCT
ejpam-6097	333	1	37:105477	CARDINAL
ejpam-6097	333	2	2022.336	CARDINAL
ejpam-6097	334	1	22	CARDINAL
ejpam-6097	334	2	mogtaba mohammed	GPE
ejpam-6097	334	3	ismail m	PERSON
ejpam-6097	334	4	hifzhudin noor aziz	PERSON
ejpam-6097	336	1	9(6):14982–14996	DATE
ejpam-6097	336	2	2024.339	CARDINAL
ejpam-6097	336	3	23	CARDINAL
ejpam-6097	336	4	castillo-alvino	PERSON
ejpam-6097	336	5	marcos marvá.	PERSON
ejpam-6097	337	1	14(1):222–244	CARDINAL
ejpam-6097	337	2	2020.342	CARDINAL
ejpam-6097	338	1	24	CARDINAL
ejpam-6097	339	1	functional343	PERSON
ejpam-6097	340	1	conference344 series	ORG
ejpam-6097	340	2	062025	DATE
ejpam-6097	341	1	iop publishing	ORG
ejpam-6097	341	2	2019.345	CARDINAL
ejpam-6097	342	1	25	CARDINAL
ejpam-6097	344	1	10(10):532,347	CARDINAL
ejpam-6097	346	1	26	CARDINAL
ejpam-6097	346	2	qasim ibrahim	PERSON
ejpam-6097	346	3	ghassan ezzulddin arif	PERSON
ejpam-6097	346	4	hamdi	PERSON
ejpam-6097	346	5	omar bazighifan	PERSON
ejpam-6097	346	6	ali hasan ali	PERSON
ejpam-6097	348	1	30(1):605–625	DATE
ejpam-6097	348	2	2024.352	CARDINAL
ejpam-6097	348	3	27	CARDINAL
ejpam-6097	348	4	doina cioranescu	PERSON
ejpam-6097	348	5	patrizia donato	PERSON
ejpam-6097	348	6	marian p roque	PERSON
ejpam-6097	350	1	m. mohamed et al	PERSON
ejpam-6097	351	1	j. pure	PERSON
ejpam-6097	351	2	18	CARDINAL
ejpam-6097	351	3	2	CARDINAL
ejpam-6097	351	4	2025	CARDINAL
ejpam-6097	351	5	6097 19	DATE
ejpam-6097	351	6	19	CARDINAL
ejpam-6097	351	7	2018.355	CARDINAL
ejpam-6097	352	1	28	CARDINAL
ejpam-6097	352	2	nikolaevich afanasiev	PERSON
ejpam-6097	354	1	springer science & business media	ORG
ejpam-6097	354	2	2013.357	CARDINAL
ejpam-6097	354	3	29	CARDINAL
ejpam-6097	354	4	youlin huang	PERSON
ejpam-6097	354	5	wanying shi	PERSON
ejpam-6097	354	6	chunjin wei	PERSON
ejpam-6097	354	7	shuwen zhang	PERSON
ejpam-6097	356	1	biological359 dynamics	ORG
ejpam-6097	356	2	15(1):1–18	CARDINAL
ejpam-6097	356	3	2021.360	CARDINAL
ejpam-6097	356	4	30	CARDINAL
ejpam-6097	356	5	nirav dalal	PERSON
ejpam-6097	356	6	david greenhalgh	PERSON
ejpam-6097	356	7	xuerong mao	PERSON
ejpam-6097	358	1	341(2):1084–362 1101	DATE
ejpam-6097	358	2	2008.363	CARDINAL