Asymptotic behavior of a stochastic delayed chemostat model with nonmonotone uptake function

In this paper, a stochastic delay differential equations chemostat model with nonmonotone uptake function is considered, and the nutrient conversion process involves time delay. First, we verify that there is a unique global positive solution of the stochastic system. Second, we find that the solutions of stochastic system will oscillate around the equilibria of the corresponding deterministic model, moreover, results show that time delay has critical effects on the extinction and persistence of the microorganism, that is to say, under small noise, when the time delay is small, microorganism is persistent; when the time delay is large, microorganism will be extinct. In addition, we can find by the computer simulation that large noise may lead to microorganism become extinct, although microorganism is persistent in the deterministic systems when the time delay is small. Finally, computer simulations are carried out to illustrate the obtained results and the existence of bistability is observed.