Dynamics of a stochastic delayed predator-prey system with regime switching and jumps

In this article, a stochastic predator-prey system with regime switching and Lévy jumps is formulated. First, the extinction and persistence in mean of each species are investigated by use of the stochastic differential comparison theorem and some stochastic inequalities. Second, the sufficient criteria for the stochastic permanence are established by constructing some Lyapunov functionals. In the end, simulation examples are given to illustrate the theoretical results and reveal the impacts of regime switching, distributed time delays and Lévy jumps on the dynamics, respectively.