The Stochastic Periodic Behavior of a Chemostat Model with Periodic Nutrient Input

In this paper, we study the stochastic periodic behavior of a chemostat model with periodic nutrient input. We first prove the existence of global unique positive solution with any initial value for stochastic non-autonomous periodic chemostat system. After that, the sufficient conditions are established for the existence of nontrivial positive T-periodic solution. Moreover, we also analyze the conditions for extinction exponentially of microorganism, and we find that there exists a unique boundary periodic solution for stochastic chemostat model, which is globally attractive. At the same time, in the end of this paper, we also give some numerical simulations to illustrate our main conclusions.