Long-time analysis of a stochastic chemostat model with instantaneous nutrient recycling

This paper presents long-time analysis of a stochastic chemostat model with instantaneous nutrient recycling. We focus on the investigation of the sufficient and almost necessary conditions of the exponential extinction and persistence for the model. The convergence to the invariant measure is also established under total variation norm. Our work generalizes and improves many existing results. One of the interesting findings is that random disturbance can suppress microorganism growth, which can provide us some useful control strategies to microbiological cultivation. Finally, some numerical simulations partly based on the stochastic sensitive function technique are given to illustrate theoretical results.