Abstract and Applied Analysis
Volume 2012 (2012), Article ID 801812, 14 pages
http://dx.doi.org/10.1155/2012/801812
Research Article

The Asymptotic Behavior of a Stochastic Predator-Prey System with Holling II Functional Response

Zhenwen Liu,1,2 Ningzhong Shi,1 Daqing Jiang,1 and Chunyan Ji1,3

1School of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin 130024, China
2School of Science, Changchun University of Science and Technology, Changchun, Jilin 130022, China
3Department of Mathematics, Changshu Institute of Technology, Changshu, Jiangsu 215500, China

Received 21 October 2012; Accepted 14 December 2012

Academic Editor: Ivanka Stamova

Copyright © 2012 Zhenwen Liu 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 discuss a stochastic predator-prey system with Holling II functional response. First, we show that this system has a unique positive solution as this is essential in any population dynamics model. Then, we deduce the conditions that there is a stationary distribution of the system, which implies that the system is permanent. At last, we give the conditions for the system that is going to be extinct.