Asymptotic properties of a stochastic predator–prey system with Holling II functional response

A stochastic predator–prey system with Holling II functional response is proposed and investigated. We show that there is a unique positive solution to the model for any positive initial value. And we show that the positive solution to the stochastic system is stochastically bounded. Moreover, under some conditions, we conclude that the stochastic model is stochastically permanent and persistent in mean.

Research highlights
► A stochastic predator-prey model with Holling II functional response is studied.
► The existence, uniqueness of global solution are obtained.
► We obtain that the stochastic system is stochastically bounded.
► Extinction and two types of stochastic permanence are investigated.
► We make out some figures to confirm our conclusions.