Persistence and periodic measure of a stochastic predator–prey model with Beddington–DeAngelis functional response

In this paper, we study a stochastic predator–prey model with Beddington–DeAngelis functional response and time-periodic coefficients. By analyzing the stability of the solution on the boundary and some stochastic estimates, the threshold conditions for the time-average persistence in probability and extinction of each population are established. Furthermore, the existence of a unique periodic measure of the model is also presented under the condition of the time-average persistence in probability of the model. Several numerical simulations are given to verify the effectiveness of the theoretical results and to illustrate the effects of the white noises on the persistence and periodic measure of the model.