Conditions for persistence and ergodicity of a stochastic Lotka-Volterra predator-prey model with regime switching

A stochastic Lotka-Volterra predator-prey model with regime switching is investigated. We examine when the system is persistence in mean and the extinction under some appropriate conditions, and we discuss the threshold between them. Sufficient conditions for the stationary distribution which is ergodic and positive recurrent of the solution is established using stochastic Lyapunov functions. Simulations are also carried out to illustrate our analytical results.