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Mathematical Problems in Engineering
Volume 2015, Article ID 479326, 10 pages
http://dx.doi.org/10.1155/2015/479326
Research Article

The Stationary Distribution and Extinction of Generalized Multispecies Stochastic Lotka-Volterra Predator-Prey System

College of Sciences, Hohai University, Nanjing 210098, China

Received 19 May 2015; Revised 21 August 2015; Accepted 30 August 2015

Academic Editor: Leonid Shaikhet

Copyright © 2015 Fancheng Yin and Xiaoyan Yu. 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 is concerned with the existence of stationary distribution and extinction for multispecies stochastic Lotka-Volterra predator-prey system. The contributions of this paper are as follows. (a) By using Lyapunov methods, the sufficient conditions on existence of stationary distribution and extinction are established. (b) By using the space decomposition technique and the continuity of probability, weaker conditions on extinction of the system are obtained. Finally, a numerical experiment is conducted to validate the theoretical findings.