Periodic solution for a non-autonomous Lotka-Volterra predator-prey model with random perturbation

被引：49

作者：

Zu, Li ^{[1
]}

Jiang, Daqing ^{[2
]}

O'Regan, Donal ^{[3
,4
]}

Ge, Bin ^{[5
]}

机构：

[1] Hainan Normal Univ, Coll Math & Stat, Hainan 571158, Peoples R China

[2] China Univ Petr East China, Sch Sci, Qingdao 266580, Peoples R China

[3] Natl Univ Ireland, Sch Math Stat & Appl Math, Galway, Ireland

[4] King Abdulaziz Univ, Nonlinear Anal & Appl Math NAAM Res Grp, Jeddah 21413, Saudi Arabia

[5] Harbin Engn Univ, Dept Appl Math, Harbin 150001, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2015年 / 430卷 / 01期

关键词：

Lotka-Volterra predator-prey system; Periodic solution; White noise; Non-autonomous; Persistence in mean; FUNCTIONAL-RESPONSE; HARVESTING TERMS; SYSTEM; PERSISTENCE; BEHAVIOR; DELAYS;

D O I：

10.1016/j.jmaa.2015.04.058

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper studies a stochastic non-autonomous Lotka-Volterra predator-prey model. We prove that there exists at least one positive periodic solution under some simple and reasonable conditions. In addition we obtain sufficient conditions for persistence in mean and extinction for the stochastic non-autonomous system. Our method and results are new and the ideas could be used to study other types of non-autonomous stochastic predator prey systems. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：428 / 437

页数：10

共 50 条

[1] Almost periodic solution of non-autonomous Lotka-Volterra predator-prey dispersal system with delays
Meng, Xinzhu
Chen, Lansun
[J]. JOURNAL OF THEORETICAL BIOLOGY, 2006, 243 (04) : 562 - 574
[2] MULTIPLE POSITIVE PERIODIC SOLUTIONS TO A NON-AUTONOMOUS LOTKA-VOLTERRA PREDATOR-PREY SYSTEM WITH HARVESTING TERMS
Zhao, Kaihong
Li, Yongkun
[J]. ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2011,
[3] Permanence and stability in non-autonomous predator-prey Lotka-Volterra systems with feedback controls
Nie, Linfei
Teng, Zhidong
Hu, Lin
Peng, Jigen
[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2009, 58 (03) : 436 - 448
[4] Periodic solution of a Lotka-Volterra predator-prey model with dispersion and time delays
Xu, R
Chaplain, MAJ
Davidson, FA
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2004, 148 (02) : 537 - 560
[5] THE PERIODIC PREDATOR-PREY LOTKA-VOLTERRA MODEL WITH IMPULSIVE EFFECT
Tang, Sanyi
Chen, Lansun
[J]. JOURNAL OF MECHANICS IN MEDICINE AND BIOLOGY, 2002, 2 (3-4) : 267 - 296
[6] On the existence of almost periodic solutions of impulsive non-autonomous Lotka-Volterra predator-prey system with harvesting terms
Wang, Li
Zhang, Hui
Liu, Suying
[J]. AIMS MATHEMATICS, 2022, 7 (01): : 925 - 938
[7] PERMANENCE IN GENERAL NON-AUTONOMOUS LOTKA-VOLTERRA PREDATOR-PREY SYSTEMS WITH DISTRIBUTED DELAYS AND IMPULSES
Muhammadhaji, Ahmadjan
Teng, Zhidong
Zhang, Long
[J]. JOURNAL OF BIOLOGICAL SYSTEMS, 2013, 21 (02)
[8] Multiple positive almost periodic solutions to an impulsive non-autonomous Lotka-Volterra predator-prey system with harvesting terms
Li, Yongkun
Ye, Yuan
[J]. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2013, 18 (11) : 3190 - 3201
[9] FOUR POSITIVE ALMOST PERIODIC SOLUTIONS TO AN IMPULSIVE NON-AUTONOMOUS LOTKA-VOLTERRA PREDATOR-PREY SYSTEM WITH HARVESTING TERMS
Zhang, Chunhua
Zhang, Yuying
Chen, Xiaoxing
[J]. COMMUNICATIONS IN MATHEMATICAL BIOLOGY AND NEUROSCIENCE, 2015,
[10] A note on stability criteria in the periodic Lotka-Volterra predator-prey model
Ortega, Victor
Rebelo, Carlota
[J]. APPLIED MATHEMATICS LETTERS, 2023, 145

← 1 2 3 4 5 →