Dynamics Analysis of a Predator–Prey Model with Hunting Cooperative and Nonlinear Stochastic Disturbance

Abstract

This paper proposes a stochastic predator–prey model with hunting cooperation and nonlinear stochastic disturbance, and focuses on the effects of nonlinear white noise and hunting cooperation on the populations. First, we present the thresholds R1 and R2 for extinction and persistence in mean of the predator. When R1 is less than 0, the predator population is extinct; when R2 is greater than 0, the predator population is persistent in mean. Moreover, by establishing suitable Lyapunov functions, we investigate the threshold R0 for the existence of a unique ergodic stationary distribution. At last, we carry out the numerical simulations. The results show that white noise is harmful to the populations and hunting cooperation is beneficial to the predator population.