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

Li Zu, Daqing Jiang and Fuquan Jiang

Abstract and Applied Analysis, 2012, vol. 2012, issue 1

Abstract: We consider a predator‐prey model in which the preys disperse among n patches (n ≥ 2) 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 n = 2 via numerical simulation.

Date: 2012
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https://doi.org/10.1155/2012/547152

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:547152

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