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

Abstract EN

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.