Analysis of a stochastic predator–prey system with modified Leslie–Gower and Holling-type IV schemes

Abstract

In this paper, we investigate the dynamics of a stochastic predator–prey system with modified Leslie–Gower and Holling-type IV schemes. We first show the existence and uniqueness of the global positive solution to the system with positive initial values. In some case, the stochastic boundedness and stochastic permanence are obtained. Then, under some conditions, we prove the persistence in mean and extinction of the stochastic system. Moreover, under certain parametric restrictions, we obtain that the system has a stationary distribution which is ergodic. Finally, some numerical simulations are carried out to support our results.