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

ABSTRACT This paper investigates a generalized stochastic predator‐prey model consisting of two differential equations with a general nonlinear functional response denoted as , driven by both standard Brownian motion and Lévy 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 Lévy‐type perturbation by not requiring that the Lévy noise be bounded; that is, we do not assume .