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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 401031, 24 pages
http://dx.doi.org/10.1155/2012/401031
Research Article

The Complex Dynamics of a Stochastic Predator-Prey Model

1College of Mathematics and Information Science, Wenzhou University, Wenzhou 325035, China
2School of Mathematics and Computational Science, Sun Yat-sen University, Guangzhou 510275, China

Received 19 May 2012; Accepted 29 July 2012

Academic Editor: Sergey V. Zelik

Copyright © 2012 Xixi Wang 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 modified stochastic ratio-dependent Leslie-Gower predator-prey model is formulated and analyzed. For the deterministic model, we focus on the existence of equilibria, local, and global stability; for the stochastic model, by applying Itô formula and constructing Lyapunov functions, some qualitative properties are given, such as the existence of global positive solutions, stochastic boundedness, and the global asymptotic stability. Based on these results, we perform a series of numerical simulations and make a comparative analysis of the stability of the model system within deterministic and stochastic environments.