Dynamical behavior of a classical stochastic delayed chemostat model

In this paper, we formulate a classical stochastic delayed chemostat model and verify that this model has a unique global positive solution. Furthermore, we investigate the dynamical behavior of this solution. We find that the solution of stochastic delayed system will oscillate around the equilibriums of the corresponding deterministic delayed model, moreover, analytical findings reveal that time delay has very significant effects on the extinction and persistence of the microorganism, that is to say, when the time delay is smaller, microorganism will be persistent; when the time delay is larger, microorganism will be extinct. Finally, computer simulations are carried out to illustrate the obtained results. In addition, we can also find by the computer simulation that larger noise may lead to microorganism become extinct, although microorganism is persistent in the deterministic delayed system when the time delay is smaller.