Periodic Solution of a Stochastic Non-Autonomous Lotka-Volterra Cooperative System with Impulsive Perturbations

Abstract

This paper is concerned with a stochastic non-autonomous Lotka-Volterra cooperative model with impulsive effects. The main purpose of this paper is to explore the existence of periodic solution of the system provided the coefficients of the system are continuous periodic functions. By constructing appropriate Lyapunov functions and using the theory of Khasminskii, sufficient conditions under which the existence of the periodic solution of the system are obtained, and our results illustrate that the existence of the periodic solution has close relations with the white noise and the impulsive perturbations.