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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.

MSC:

60H30 Applications of stochastic analysis (to PDEs, etc.)
92D25 Population dynamics (general)
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