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.
Li Zu. Daqing Jiang. Fuquan Jiang. "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