An analogue of break-even concentration in a simple stochastic chemostat model

This paper deals with the problem of a single-species stochastic chemostat model in which the maximal growth rate is influenced by the white noise in environment. When the noise is small, we obtain an analogue, λ̃, of the break-even concentration (λλ) of the corresponding deterministic model, which completely determines the persistence or extinction of the microorganism: if λ̃S0, then the microorganism becomes extinct in the chemostat. We find that this analogue λ̃ is larger than the break-even concentration λλ, which means that the noise plays a negative role on the persistence of the microorganism. In addition, we obtain that the large noise can make the microorganism go extinct in the chemostat.