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Complexity
Volume 2017, Article ID 3742197, 18 pages
https://doi.org/10.1155/2017/3742197
Research Article

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

1College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China
2State Key Laboratory of Mining Disaster Prevention and Control Co-Founded by Shandong Province and the Ministry of Science and Technology, Shandong University of Science and Technology, Qingdao 266590, China

Correspondence should be addressed to Wencai Zhao; nc.ude.tsuds@iacnewoahz

Received 1 July 2017; Revised 8 October 2017; Accepted 17 October 2017; Published 5 December 2017

Academic Editor: Dimitri Volchenkov

Copyright © 2017 Feifei Bian et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.