Abstract and Applied Analysis
Volume 2013 (2013), Article ID 256249, 13 pages
http://dx.doi.org/10.1155/2013/256249
Research Article

Persistence and Nonpersistence of a Nonautonomous Stochastic Mutualism System

Peiyan Xia,1,2 Xiaokun Zheng,2 and Daqing Jiang2

1School of Basic Sciences, Changchun University of Technology, Changchun, Jilin 130021, China
2School of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin 130024, China

Received 22 October 2012; Accepted 29 November 2012

Academic Editor: Jifeng Chu

Copyright © 2013 Peiyan Xia 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

In this paper, a two-species nonautonomous stochastic mutualism system is investigated. The intrinsic growth rates of the two species at time are estimated by respectively. Viewing the different intensities of the noises , as two parameters at time , we conclude that there exists a global positive solution and the th moment of the solution is bounded. We also show that the system is permanent, including stochastic permanence, persistence in mean, and asymptotic boundedness in time average. Besides, we show that the large white noise will make the system nonpersistent. Finally, we establish sufficient criteria for the global attractivity of the system.