Break-even concentration and periodic behavior of a stochastic chemostat model with seasonal fluctuation

This paper formulates a single-species stochastic chemostat model with periodic coefficients due to seasonal fluctuation. When the noise is small, a modified break-even concentration is identified, whose value below or above the averaged concentration of the input nutrient can completely determine whether the microorganism will persist or not, where an accuracy decay rate is given for extinction. In case of persistence, existence of the random positive periodic solution is proved for the considered model. Further, the random periodic solution is shown to be globally attractive under some mild extra condition. The periodic dynamics obtained in this paper are supported by computer simulations.