Periodic solutions and stationary distribution for a stochastic predator-prey system with impulsive perturbations

Abstract

In this paper, we consider a stochastic predator-prey system with Beddington-DeAngelis functional response and impulsive perturbations. First, we prove that the model admits a unique global positive solution by constructing the equivalent system without impulsive perturbations. Second, we establish a sufficient condition which allows the existence of a positive periodic solution using stochastic Lyapunov functions. Finally, for the predator-prey system with Beddington-DeAngelis functional response disturbed by both white noise and telephone noise, we give the sufficient conditions for the stationary distribution which is ergodic and positive recurrent of the solution. The conclusion implies that the stochastic system has a positive T-periodic Markov process in a certain condition when the corresponding deterministic system has at least one positive T-periodic solution.