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

Abstract

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