Dynamical Analysis of a Class of Prey-Predator Model with Beddington-DeAngelis Functional Response, Stochastic Perturbation, and Impulsive Toxicant Input

作者：Bian, Feifei; Zhao, Wencai^*; Song, Yi; Yue, Rong

来源：Complexity, 2017, 2017: 3742197.

DOI：10.1155/2017/3742197

• DELAY-DIFFERENTIAL EQUATIONS
• LOTKA-VOLTERRA MODEL
• STATIONARY DISTRIBUTION
• QUALITATIVE APPROACH
• PERIODIC-SOLUTION
• LOGISTIC MODEL
• ASYMPTOTIC PROPERTIES
• STABILITY ANALYSIS
• SURVIVAL ANALYSIS
• GLOBAL STABILITY

A stochastic prey-predator system in a polluted environment with Beddington-DeAngelis functional response is proposed and analyzed. Firstly, for the system with white noise perturbation, by analyzing the limit system, the existence of boundary periodic solutions and positive periodic solutions is proved and the sufficient conditions for the existence of boundary periodic solutions and positive periodic solutions are derived. And then for the stochastic system, by introducing Markov regime switching, the sufficient conditions for extinction or persistence of such system are obtained. Furthermore, we proved that the system is ergodic and has a stationary distribution when the concentration of toxicant is a positive constant. Finally, two examples with numerical simulations are carried out in order to illustrate the theoretical results.

• 出版日期2017
• 单位山东科技大学