A stochastic predator–prey model with Holling II increasing function in the predator

Abstract

This paper is concerned with a stochastic predator–prey model with Holling II increasing function in the predator. By applying the Lyapunov analysis method, we demonstrate the existence and uniqueness of the global positive solution. Then we show there is a stationary distribution which implies the stochastic persistence of the predator and prey in the model. Moreover, we obtain respectively sufficient conditions for weak persistence in the mean and extinction of the prey and extinction of the predator. Finally, some numerical simulations are given to illustrate our main results and the discussion and conclusion are presented.