Dynamics of stochastic chemostat models with mixed nonlinear incidence

In this paper, we proposes a stochastic chemostat model with mixed nonlinear incidence. Firstly, the existence and uniqueness of the global positive solutions are proved. Secondly, we demonstrate that the chemostat model is persistence in mean and the solution of this stochastic chemostat model is bounded for any initial condition by constructing the Lyapunov function. Then we obtain the sufficient condition for the existence of an ergodic stationary distribution in this system. Finally, the numerical simulation results of the model are given. The simulation results show that a particular random perturbation can change the fate of microorganisms.