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**Existence, stationary distribution, and extinction of predator-prey system of prey dispersal with stochastic perturbation.**
*(English)*
Zbl 1253.60078

Summary: We consider a predator-prey model in which the preys disperse among \(n\) patches \((n \geq 2)\) 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.

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\textit{L. Zu} et al., Abstr. Appl. Anal. 2012, Article ID 547152, 24 p. (2012; Zbl 1253.60078)

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