Journal of Applied Mathematics
Volume 2012 (2012), Article ID 692742, 21 pages
http://dx.doi.org/10.1155/2012/692742
Research Article

Survival Analysis of a Nonautonomous Logistic Model with Stochastic Perturbation

Chun Lu1,2 and Xiaohua Ding1

1Department of Mathematics, Harbin Institute of Technology, Weihai 264209, China
2Department of Mathematics, Qingdao Technological University, Qingdao 266520, China

Received 23 March 2012; Revised 13 May 2012; Accepted 13 May 2012

Academic Editor: Kai Diethelm

Copyright © 2012 Chun Lu and Xiaohua Ding. 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

Taking white noise into account, a stochastic nonautonomous logistic model is proposed and investigated. Sufficient conditions for extinction, nonpersistence in the mean, weak persistence, stochastic permanence, and global asymptotic stability are established. Moreover, the threshold between weak persistence and extinction is obtained. Finally, we introduce some numerical simulink graphics to illustrate our main results.