Study on Dynamic Behavior of a Stochastic Predator–Prey System with Beddington–DeAngelis Functional Response and Regime Switching

In this paper, by introducing environmental white noise and telegraph noise, we proposed a stochastic predator–prey model with the Beddington–DeAngelis type functional response investigated its dynamical behavior. Persistence extinction are two core contents of population research, so analyzed these properties. The sufficient conditions strong persistence in mean were established threshold between them was obtained. Moreover, took stability into account and, means structuring suitable Lyapunov function regime switching, proved that system has unique stationary distribution. Finally, numerical simulations used to illustrate our theoretical results.