Existence and persistence of positive solution for a stochastic turbidostat model

Abstract

A novel stochastic turbidostat model is investigated in this paper. The stochasticity in the model comes from the maximal growth rate influenced by white noise. Firstly, the existence and uniqueness of the positive solution for the system are demonstrated. Secondly, we analyze the persistence in mean and stochastic persistence of the system, respectively. Sufficient conditions about the extinction of the microorganism are obtained. Finally, numerical simulation results are given to support the theoretical conclusions.