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Stochastic Permanence, Stationary Distribution and Extinction of a Single-Species Nonlinear Diffusion System with Random Perturbation

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  • Li Zu
  • Daqing Jiang
  • Donal O’Regan

Abstract

We analyze the influence of stochastic perturbations on a single-species logistic model with the population’s nonlinear diffusion among patches. First, we show that this system has a unique positive solution. Then we obtain sufficient conditions for stochastic permanence and persistence in mean, stationary distribution, and extinction. Finally, we illustrate our conclusions through numerical simulation.

Suggested Citation

  • Li Zu & Daqing Jiang & Donal O’Regan, 2014. "Stochastic Permanence, Stationary Distribution and Extinction of a Single-Species Nonlinear Diffusion System with Random Perturbation," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-14, January.
    • Handle: RePEc:hin:jnlaaa:320460
    DOI: 10.1155/2014/320460
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    Cited by:

    1. Xiangjun Dai & Hui Jiao & Jianjun Jiao & Qi Quan, 2023. "Survival Analysis of a Predator–Prey Model with Seasonal Migration of Prey Populations between Breeding and Non-Breeding Regions," Mathematics, MDPI, vol. 11(18), pages 1-19, September.

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