Dynamics of a stochastic food chain chemostat model with Monod-Haldane functional response and Ornstein-Uhlenbeck process

In the present paper, a novel stochastic food chain chemostat model with Monod-Haldane functional response is proposed and studied, incorporating the mean-reversion Ornstein- Uhlenbeck process to simulate stochastic perturbation on the growth of microorganisms by environmental fluctuations. Firstly, the existence and uniqueness of the global positive solution are proved, and the stochastic boundedness of the solution is obtained. Secondly, the conditions for controlling exponential extinction and persistence in the mean of microorganisms are delved. Finally, a large number of representative numerical examples are provided to validate the theoretical results. The results show that the stochastic noise measured by the regression speed and the fluctuation intensity has significant effects on the dynamics of the model.