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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