Analysis of a stochastic predator-prey system with mixed functional responses and Lévy jumps

Abstract

In this paper, we consider a stochastic two predator-one prey system consisting of prey, intermediate predator and top predator with Lévy jumps. Here we consider Ratio-dependent function response between intermediate predator and top predator and other function responses are assumed to be linear. Firstly, we prove that the existence and boundedness of pth moment of the positive solution. Then under some assumptions, we establish sufficient criteria for the extinction of the system. The results reveal an important property that the Lévy jumps are unfavorable for the existence of species. Furthermore, we establish sufficient condition for the asymptotically stable in distribution under certain conditions. Finally, some numerical simulations are introduced to demonstrate the theoretical results.

Keywords

• mixed functional response
• lévy jumps
• extinction
• asymptotically stable in distribution