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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 320460, 14 pages
http://dx.doi.org/10.1155/2014/320460
Research Article

Stochastic Permanence, Stationary Distribution and Extinction of a Single-Species Nonlinear Diffusion System with Random Perturbation

1School of Science, Changchun University, Changchun 130022, China
2School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China
3School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland

Received 5 October 2013; Accepted 22 November 2013; Published 22 January 2014

Academic Editor: Weiming Wang

Copyright © 2014 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 analyze the influence of stochastic perturbations on a single-species logistic model with the population’s nonlinear diffusion among patches. First, we show that this system has a unique positive solution. Then we obtain sufficient conditions for stochastic permanence and persistence in mean, stationary distribution, and extinction. Finally, we illustrate our conclusions through numerical simulation.