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.
"Existence, Stationary Distribution, and Extinction of Predator-Prey System of Prey Dispersal with Stochastic Perturbation." Abstr. Appl. Anal. 2012 (SI07) 1 - 24, 2012. https://doi.org/10.1155/2012/547152