The threshold of stochastic chemostat model with Monod-Haldane response function

This paper deals with problem of a stochastic chemostat model with Monod-Haldane response function. Firstly, we confirm the truth of the existence and uniqueness of the positive solution to the system. Then, we show the condition for the microorganism to be extinct. Moreover, we investigate there is a stationary distribution of this stochastic system and finally, we derive the expression for its invariant density.