Global dynamics in stochastic n‐species food chain systems with white noise and Lévy jumps

Abstract

This paper is concerned with a n-species stochastic food chain model with white noise and Lévy 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.

Global dynamics in a stochastic two predators-one prey system with regime-switching and ratio-dependent functional response

“…Therefore, the remaining challenge is how to generalize our conclusions in this paper to a n-species predator-prey stochastic model with regime switching. On the flip side, more intricate models need to be explored, for example, stochastic models with Allee effect (as studied in [38]), delays (as presented in [39]) and Lévy jumps (as seen in [40]). These topics may warrant further investigation.…”