Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 262, pp. 1-16.

Title: Persistence and extinction for a stochastic logistic model with
       infinite delay

Authors: Chun Lu (Harbin Institute of Technology, Weihai, China)
         Xiaohua Ding (Harbin Institute of Technology, Weihai, China)

Abstract:
 This article, studies a stochastic logistic model with infinite
 delay. Using a phase space, we  establish sufficient conditions for
 the  extinction,  nonpersistence in the mean,  weak persistence, and
 stochastic permanence. A threshold between weak persistence and
 extinction is obtained. Our results state that different types of
 environmental noises have different effects on the persistence and
 extinction, and that the delay has no impact on the persistence
 and extinction for the stochastic model in the autonomous case.
 Numerical simulations illustrate the theoretical results.

Submitted September 19, 2013. Published November 26, 2013.
Math Subject Classifications: 64H40, 92D25, 60H10, 34K50.
Key Words: White noise; persistence; extinction; delay.