Dynamics of a stochastic predator–prey model with distributed delay and Markovian switching

Abstract

In this paper, we study a stochastic predator–prey model with distributed delay and Markovian switching. Firstly, we obtain sufficient criteria for weak persistence of the predator population. Then in the case of weak persistence, we establish sufficient conditions for the existence of positive recurrence of the solutions to the model by constructing a suitable stochastic Lyapunov function with regime switching. Finally, we establish sufficient conditions for extinction of the predator population.