Abstract and Applied Analysis
Volume 2011 (2011), Article ID 518719, 16 pages
http://dx.doi.org/10.1155/2011/518719
Research Article

Analysis on a Stochastic Predator-Prey Model with Modified Leslie-Gower Response

Jingliang Lv1 and Ke Wang1,2

1Department of Mathematics, Harbin Institute of Technology, Weihai 264209, China
2School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China

Received 30 October 2010; Accepted 30 March 2011

Academic Editor: Wing-Sum Cheung

Copyright © 2011 Jingliang Lv and Ke Wang. 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

This paper presents an investigation of asymptotic properties of a stochastic predator-prey model with modified Leslie-Gower response. We obtain the global existence of positive unique solution of the stochastic model. That is, the solution of the system is positive and not to explode to infinity in a finite time. And we show some asymptotic properties of the stochastic system. Moreover, the sufficient conditions for persistence in mean and extinction are obtained. Finally we work out some figures to illustrate our main results.