Abstract
In this paper, a stochastic chemostat model with variable yield is investigated. The environment noises are given by independent standard Brownian motions, and the yield coefficient reflecting the conversion of nutrient to microorganism varies depending on the ambient nutrient. First, we give that the stochastic system has a unique global positive solution. Second, the sufficient conditions for the extinction and strong persistence in the mean of the microorganism are established. Third, by using stochastic Lyapunov function, the existence of a unique stationary distribution to the stochastic model is studied. In addition, some numerical simulations are carried to illustrate the theoretical results and the influence of the variable yield on the microorganism.
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