Electron. J. Diff. Equ., Vol. 2013 (2013), No. 262, pp. 1-16.

Persistence and extinction for a stochastic logistic model with infinite delay

Chun Lu, Xiaohua Ding

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.

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Chun Lu
Department of Mathematics
Harbin Institute of Technology
Weihai 264209, China
email: mathlc@163.com
Xiaohua Ding
Department of Mathematics
Harbin Institute of Technology
Weihai 264209, China
email: mathlc@126.com

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