Ergodic stationary distribution of a stochastic chemostat model with regime switching

Abstract

In this paper, a stochastic chemostat model with single-species growth on two perfectly substitutable nutrients under telegraph noise is investigated. Firstly, we prove the solution of the system is positive and global. Then we establish sufficient conditions for the existence of ergodic stationary distribution of the model by constructing suitable Lyapunov functions with regime switching. Finally, numerical simulations are carried out to demonstrate our theoretical results.