Abstract
In this paper, we investigate the dynamics of a chemostat model with single-species growth on two nutrients, which is disturbed by the telegraph noise. Switching between different environmental states is achieved by Markov chain. Firstly, we prove the existence and uniqueness of the positive solution. Then the threshold between extinction and persistence in the mean of the microorganism is obtained. Moreover, in the case of persistence, we establish sufficient conditions for the existence of positive recurrence. Finally, some simulations are carried out to demonstrate our theoretical results. Our main effort is to build the suitable Lyapunov functions with regime switching.
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