Analysis of a stochastic predator–prey system with fear effect and Lévy noise

Abstract

This paper studies a stochastic predator–prey model with Beddington–DeAngelis functional response, fear effect, and Lévy noise, where the fear is of prey induced by predator. First, we use Itô’s formula to prove the existence and uniqueness of a global positive solution and its moment boundedness. Next, sufficient conditions for the persistence and extinction of both species are given. We further investigate the stability in distribution of our system. Finally, we verify our analytical results by exhaustive numerical simulations.