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Existence, Stationary Distribution, and Extinction of Predator-Prey System of Prey Dispersal with Stochastic Perturbation

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  • Li Zu
  • Daqing Jiang
  • Fuquan Jiang

Abstract

We consider a predator-prey model in which the preys disperse among patches ( ) with stochastic perturbation. We show that there is a unique positive solution and find out the sufficient conditions for the extinction to the system with any given positive initial value. In addition, we investigate that there exists a stationary distribution for the system and it has ergodic property. Finally, we illustrate the dynamic behavior of the system with via numerical simulation.

Suggested Citation

  • Li Zu & Daqing Jiang & Fuquan Jiang, 2012. "Existence, Stationary Distribution, and Extinction of Predator-Prey System of Prey Dispersal with Stochastic Perturbation," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-24, October.
    • Handle: RePEc:hin:jnlaaa:547152
    DOI: 10.1155/2012/547152
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