Dynamics of stochastic predator-prey models with Holling II functional response

被引：43

作者：

Liu, Qun ^{[1
]}

Zu, Li ^{[2
]}

Jiang, Daqing ^{[3
,4
]}

机构：

[1] Yulin Normal Univ, Sch Math & Informat Sci, Guangxi Univ Key Lab Complex Syst Optimizat & Big, Yulin 537000, Guangxi, Peoples R China

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

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

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

来源：

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2016年 / 37卷

关键词：

Stochastic predator-prey model; Pathwise estimation; Ultimate boundedness; Stationary distribution and ergodicity; GLOBAL ASYMPTOTICAL STABILITY; POSITIVE PERIODIC-SOLUTION; MUTUAL INTERFERENCE; STATIONARY DISTRIBUTION; VOLTERRA MODEL; PERSISTENCE; PERMANENCE; SYSTEM; ATTRACTIVITY; ERGODICITY;

D O I：

10.1016/j.cnsns.2016.01.005

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider the dynamics of stochastic predator-prey models with Holling II functional response. For the stochastic systems, we firstly establish sufficient conditions for the existence of the globally positive solutions. Then we investigate the asymptotic moment estimations of the positive solutions and study the ultimately bounded in the mean of them. Thirdly, by constructing some suitable Lyapunov functions, we verify that there are unique stationary distributions and they are ergodic. The obtained results show that the systems still retain some stability in the sense of weak stability provided that the intensity of the white noise is relatively small. Finally, some numerical simulations are introduced to illustrate our main results. (C) 2016 Elsevier B.V. All rights reserved.

引用

页码：62 / 76

页数：15

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