Stationary distribution of a stochastic chemostat model with Beddington–DeAngelis functional response

Abstract In this paper, we study a stochastic chemostat model with Beddington–DeAngelis functional response. By constructing a suitable stochastic Lyapunov function, we establish sufficient conditions for the existence of a unique ergodic stationary distribution to the model. The existence of a stationary distribution implies stochastic weak stability.