Extinction and stationary distribution of an impulsive stochastic chemostat model with nonlinear perturbation

This paper investigates a new impulsive stochastic chemostat model with nonlinear perturbation in a polluted environment. We present the analysis and the criteria of the extinction of the microorganisms, and establish sufficient conditions for the existence of a unique ergodic stationary distribution of the model via Lyapunov functions method. The results show that both stochastic noise and impulsive toxicant input have great effects on the survival and extinction of the microorganisms. Moreover, we provide a series of numerical simulations to illustrate the analytical results.