Persistence and extinction for a stochastic logistic model with infinite delay

Article English OPEN
Chun Lu ; Xiaohua Ding (2013)
  • Publisher: Texas State University
  • Journal: Electronic Journal of Differential Equations (issn: 1072-6691)
  • Subject: White noise | extinction | delay | Mathematics | persistence | QA1-939
    arxiv: Quantitative Biology::Populations and Evolution

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.
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