Survival analysis of a stochastic predator–prey model with prey refuge and fear effect

Abstract

In this paper, we propose and investigate a stochastic Holling type-II predator–prey model with prey refuge and fear effect. We first prove the existence and uniqueness of the global positive solution. Then we perform the survival analysis of the model, including the existence of a unique ergodic stationary distribution and the extinction of the model. Numerical simulations are carried out to validate our analytical results. Our findings indicate that the white noise is adverse to the growth of predator and prey populations, and the increase of fear effect will lead to the decrease of predator density, but with no obvious effect on prey density.