A stochastic chemostat model with mean-reverting Ornstein-Uhlenbeck process and Monod-Haldane response function

Abstract

In this paper, we mainly construct and analyze a stochastic chemostat model with mean-reverting Ornstein-Uhlenbeck process and Monod-Haldane response function, which is a stochastic non-autonomous system. We first study the existence of global unique positive solution with any initial value for stochastic chemostat system. After that, the sufficient conditions are established for extinction exponentially and persistence in the mean of microorganism. Finally, we also give numerical simulations to illustrate our main conclusions. Our results show that the mean-reverting process is an effective and reasonable method to introduce environmental noise into the continuous culture model of microorganism, and we also find that the reversion speed and volatility intensity have an important influence on the extinction and persistence of microorganism.