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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 547152, 24 pages
http://dx.doi.org/10.1155/2012/547152
Research Article

Existence, Stationary Distribution, and Extinction of Predator-Prey System of Prey Dispersal with Stochastic Perturbation

1School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China
2School of Science, Changchun University, Changchun 130022, China
3Department of Foundation, Harbin Finance University, Harbin 150030, China

Received 24 July 2012; Accepted 13 September 2012

Academic Editor: Yonghui Xia

Copyright © 2012 Li Zu 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 consider a predator-prey model in which the preys disperse among patches ( ) with stochastic perturbation. We show that there is a unique positive solution and find out the sufficient conditions for the extinction to the system with any given positive initial value. In addition, we investigate that there exists a stationary distribution for the system and it has ergodic property. Finally, we illustrate the dynamic behavior of the system with via numerical simulation.