Dynamical Behaviors Of Stochastic Ratio-dependent Chemostat Model

In this paper, we investigate the dynamical behaviors of stochastic ratio-dependent model which maximal growth rate is subject to stochastic perturbation using the method of stochastic Lyapunov analysis. The existence and uniqueness of a global positive solution are obtained first of all. Then the sufficient conditions of extinction are given. This reveals the large environmental noise may lead to the population ex-tinction. Furthermore, we show that the stochastic system exhibits similar asymptotic behaviors near the disease-free equilibrium point of the corresponding deterministic system under some conditions. Moreover, we show that the concentration of the mi-croorganism is persistent in time average, and the system is ergodic and has a unique stationary distribution.