Critical result on the break-even concentration in a single-species stochastic chemostat model

In this paper, the strictly critical parameter λ˜ is identified as the break-even concentration for the stochastic chemostat model. λ˜>S0 suffices for extinction of the microorganism for any noise intensity σ2>0 is proved firstly, which completely solves the open problem proposed in [10]. Then, by using the Feller test, we show that the microorganism will go extinct in probability if λ˜=S0, which has not been studied in the known literature. When λ˜