Dynamics of a stochastic Holling type II predator–prey model with hyperbolic mortality

This paper considers a stochastic predator–prey model with hyperbolic mortality and Holling type II response. Firstly, we show that there is a critical value which can easily determine the extinction and persistence in the mean of the predator population. Then by constructing appropriate Lyapunov functions, we prove that there is a stationary distribution to this model and it has the ergodic property. Finally, a numerical example is introduced to illustrate the results developed.