DYNAMIC BEHAVIOR OF A STOCHASTIC NON-AUTONOMOUS PREDATOR–PREY MODEL WITH CROWLEY–MARTIN FUNCTIONAL RESPONSE AND IMPULSES

Abstract

A stochastic non-autonomous one-prey two-predator model with Crowley–Martin functional response and impulses is proposed in this paper. First, by constructing the equivalent system without impulses, we investigate the existence and uniqueness of the global positive solution of the system. Second, by using Itô formula, strong law of large numbers and Chebyshev’s inequality, some sufficient conditions are established to ensure the extinction, non-persistence in the mean, persistence in the mean and stochastic permanence of the system. Third, we prove the system is globally attractive under some conditions. Finally, we choose different white noise intensities and impulsive parameters to illustrate the analytical results by numerical simulations.