Global dynamics in stochastic n-species food chain systems with white noise and Levy jumps

This paper is concerned with a n-species stochastic food chain model with white noise and Levy jumps. The global stochastic dynamics are established, including the existence of the global and positive solutions, stochastic ultimate boundedness, extinction with probability one, and the permanence and global stability in the mean by developing a new research method, using the auxiliary functions and theory of stochastic differential equations. Furthermore, the numerical simulations are presented to verify the theoretical results and illustrate the proposed open problems.