Abstract
Taking levy jumps into account, a Lotka-Volterra food chain chemostat model in random environment is proposed and investigated. We first prove the existence and uniqueness of the global positive solution. Then conditions for extinction of the microorganisms are derived in two cases. Furthermore, we establish sufficient conditions for persistence in the mean of the system. Theoretical analysis indicates that the dynamics of the considered model are determined by two threshold parameters R-0(s), and R-1(s) and both white noise and levy noise are disadvantageous to the system. Finally, numerical simulations are given to illustrate the results. (C) 2019 Elsevier B.V. All rights reserved.