Dynamics of a stochastic predator-prey system in a polluted environment with pulse toxicant input and impulsive perturbations

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• 作者：Shuwen Zhang^a ; ^{anzsw_123@163.com" class="auth_mail" title="E-mail the corresponding author} ; Dejun Tan^b
• 关键词：Impulsive effect ; Extinction ; Predator&ndash ; prey system ; Stochastic perturbation ; Weak persistence in the mean
• 刊名：Applied Mathematical Modelling
• 出版年：2015
• 出版时间：15 October 2015
• 年：2015
• 卷：39
• 期：20
• 页码：6319-6331
• 全文大小：798 K

文摘

In this study, we consider a stochastic predator–prey system in a polluted environment with pulse toxicant input and impulsive perturbations. By constructing a suitable Lyapunov function and using comparison theorem with an impulsive differential equation and stochastic differential equation, we obtain a set of sufficient conditions for extinction, with weak persistence in the mean and global attraction to any positive solution of the system. We also estimate the conditions for the upper boundedness of the expectations of this system solution. Finally, the results are verified based on computer simulations.