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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 125089, 9 pages
http://dx.doi.org/10.1155/2013/125089
Research Article

Persistence and Nonpersistence of a Food Chain Model with Stochastic Perturbation

1School of Mathematics, Jilin University, Changchun, Jilin 130024, China
2Department of Basic Courses, Air Force Aviation University, Changchun, Jilin 130022, China
3School of Mathematics, Northeast Normal University, Changchun, Jilin 130024, China

Received 3 June 2013; Accepted 21 September 2013

Academic Editor: Mark McKibben

Copyright © 2013 Haihong Li 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

We analyze a three species predator-prey chain model with stochastic perturbation. First, we show that this system has a unique positive solution and its th moment is bounded. Then, we deduce conditions that the system is persistent in time average. After that, conditions for the system going to be extinction in probability are established. At last, numerical simulations are carried out to support our results.