Periodic solution for a non-autonomous Lotka–Volterra predator–prey model with random perturbation

This paper studies a stochastic non-autonomous Lotka–Volterra predator–prey model. We prove that there exists at least one positive periodic solution under some simple and reasonable conditions. In addition we obtain sufficient conditions for persistence in mean and extinction for the stochastic non-autonomous system. Our method and results are new and the ideas could be used to study other types of non-autonomous stochastic predator–prey systems.