Asymptotic Properties of a Stochastic Predator-Prey Model With a General Functional Response Driven by Dual Stochastic Perturbations

This paper investigates a generalized stochastic predator-prey model consisting of two differential equations with a general nonlinear functional response denoted as F(u,v), driven by both standard Brownian motion and Levy noise. Unlike prior research, the main objective of this manuscript is to investigate the long-term behavior of the system while placing only mild assumptions on the functional response. Our analysis establishes the existence and uniqueness of a global positive solution. Moreover, we derive sufficient conditions for the extinction and persistence of the two species by employing novel threshold parameters. Notably, these outcomes are derived and substantiated using a Levy-type perturbation by not requiring that the Levy noise be bounded; that is, we do not assume nu(Upsilon) < infinity.