Asymptotic behavior of a stochastic non-autonomous predator-prey system with jumps

In this paper, a two-species stochastic non-autonomous food chain predator-prey system with jumps is proposed and studied. The asymptotic properties of the system are examined. Sufficient conditions for extinction, non-persistence in the mean, weak persistence in the mean and weak persistence of the system are established. Results show that Lévy jumps are disadvantageous for the persistence of the populations. Furthermore, we also show that the solution is stochastically ultimate bounded under certain conditions. Some examples together with numerical simulations are introduced to illustrate our main results.