Average break-even concentration in a simple chemostat model with telegraph noise. (August 2018) - Xu, Chaoqun; Yuan, Sanling; Zhang, Tonghua
Abstract: In this paper, we aim to investigate the effect of telegraph noise on the continuous culture of microorganism in a chemostat. With the help of a finite-state Markov chain, we first construct a regime-switching chemostat model and then establish conditions for extinction and persistence of the microorganism. It is shown that the particular outcome of the chemostat is completely determined by a defined average break-even concentration λ A : The microorganism becomes extinct in the chemostat when λ A > S 0, the input substrate concentration; it will persist when λ A < S 0 . In the case of persistence, we also investigate some further dynamic behaviors of the solution including the recurrent level and eventually existent domain. The theoretical results are illustrated by simulations at the end of the paper.