Analysis of a predator-prey model with Lévy jumps

This paper deals with a predator-prey model of Beddington-DeAngelis type functional response with Lévy jumps. The proposed mathematical model consists of a system of two stochastic differential equations to stimulate the interactions between predator population and prey population. The dynamics of the system is discussed mainly from the point of view of persistence and extinction. To begin with, the global positivity, stochastically boundedness and other asymptotic properties have been derived. In addition, sufficient conditions for extinction, nonpersistence in the mean and weak persistence are obtained. It is proved that the variation of Lévy jumps can affect the asymptotic property of the system.