Ergodic stationary distribution of a stochastic chemostat model with regime switching.

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. • A stochastic chemostat model with two nutrients under telegraph noise is considered. • We establish sufficient conditions for the existence of stationary distribution. • The existence of stationary distribution implies stochastic weak stability. • Numerical simulations are carried out to illustrate the results. [ABSTRACT FROM AUTHOR]