Stochastic dynamics for the solutions of a modified Holling–Tanner model with random perturbation

Abstract

In this paper, we consider a stochastic nonautonomous predator–prey model with modified Leslie–Gower and Holling II schemes in the presence of environmental forcing. The deterministic model is the modified Holling–Tanner model which is an extension of the classical Leslie–Gower model. We show that there is a unique positive solution to the stochastic system for any positive initial value. Sufficient conditions for strong persistence in mean and extinction to the stochastic system are established.