Dynamics of a stochastic modified Leslie–Gower predator–prey system with hunting cooperation

Abstract

In this paper, we consider a stochastic two-species predator–prey system with modified Leslie–Gower. Meanwhile, we assume that hunting cooperation occurs in the predators. By using Itô formula and constructing a proper Lyapunov function, we first show that there is a unique global positive solution for any given positive initial value. Furthermore, based on Chebyshev inequality, the stochastic ultimate boundedness and stochastic permanence are discussed. Then, under some conditions, we prove the persistence in mean and extinction of system. Finally, we verify our results by numerical simulations.