Periodic solutions for a stochastic non-autonomous Holling–Tanner predator–prey system with impulses

Abstract

A stochastic non-autonomous Holling–Tanner predator–prey system with impulsive effect is investigated. First, we prove the existence and uniqueness of the global positive solution by constructing the equivalent system without impulse. Second, we give the sufficient condition for the existence of positive T-periodic solution by choosing a suitable Lyapunov function. Third, we prove the existence and global attraction of the boundary periodic solution by using the comparison theorem under a certain condition. Finally, numerical simulations illustrate our theoretical results, which show that the impulse or the white noises can result in the extinction of the predator in a certain condition.