Threshold of a stochastic two‐species competition chemostat model with saturated growth rate and Lévy jumps

Abstract

In this paper, a stochastic two‐species competition chemostat model with saturated growth rate, which is randomly disturbed by Gaussian white noise and Lévy jumps, is proposed and investigated. First, the existence and uniqueness of the positive global solution of the model are discussed. Then, the thresholds of the microorganisms for the persistence in the mean and the extinction are established. To be more specific, the mild condition for the coexistence of microorganisms and is obtained. Finally, we give some numerical examples to support the theoretical analysis results. The results show that strong enough environmental noise will inhibit the growth of microorganisms, and the model with both Gaussian white noise and Lévy jumps can better characterize environmental variability in biological systems compared with the model with only Gaussian white noise.