Dynamics of a stochastic predator-prey coupled system with modified Leslie-Gower and Holling type II schemes

We study a stochastic predator-prey system with modified Leslie-Gower and Holling type II functional response among n patches. The existence and uniqueness as well as boundedness of solution are obtained. Furthermore, we obtain sufficient conditions for stochastic permanence, and by the Lyapunov functional technique we obtain sufficient conditions for the existence of the stationary distribution. Finally, we illustrate our conclusions through numerical simulation.