Abstract and Applied Analysis
Volume 2013 (2013), Article ID 912579, 9 pages
http://dx.doi.org/10.1155/2013/912579
Research Article

Effects of Dispersal for a Logistic Growth Population in Random Environments

Xiaoling Zou,1 Dejun Fan,1 and Ke Wang1,2

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

Received 23 November 2012; Accepted 12 February 2013

Academic Editor: Julio Rossi

Copyright © 2013 Xiaoling Zou 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 study a stochastic logistic model with diffusion between two patches in this paper. Using the definition of stationary distribution, we discuss the effect of dispersal in detail. If the species are able to have nontrivial stationary distributions when the patches are isolated, then they continue to do so for small diffusion rates. In addition, we use some examples and numerical experiments to reflect that diffusions are capable of both stabilizing and destabilizing a given ecosystem.