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

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 pr...

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Bibliographic Details
Published in:Complexity (New York, N.Y.) N.Y.), 2017-01, Vol.2017 (2017), p.1-18
Main Authors: Yue, Rong, Song, Yi, Zhao, Wencai, Bian, Feifei
Format: Article
Language:English
Subjects:
Applied mathematics
Economic models
Ecosystems
Endangered & extinct species
Extinction
Food
Growth rate
Markov processes
Mathematical models
Neural networks
Nutrition
Ordinary differential equations
Perturbation methods
Pollutants
Pollution
Population
Predation
Predator-prey simulation
Stochastic models
Stochastic systems
White noise
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Summary: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.
ISSN:1076-2787
1099-0526
DOI:10.1155/2017/3742197