Real ecological systems are inevitably stochastic and usually affected by environmental noises. Considering the fact that the continuous culture of microorganism in the chemostat may be influenced by environmental noises, in this talk, I will introduce some stochastic chemostat models and their dynamics. For a simple chemostat model with white noise, we find that a defined stochastic break-even concentration can determine the destiny of microorganism, and the noise plays a negative role on the persistence of microorganism. For a simple chemostat model with telegraph noise, we find that the destiny of microorganism is completely determined by an average break-even concentration which depends on the probability distribution of the switching process. For the special and general competition chemostat models with white noises, we show that the competitive exclusion principle (CEP) holds, and the destinies can be exchanged between two microorganism species in the chemostat due to the white noise. All the theoretical results are illustrated by numerical simulations.

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