Nonlinear dynamics of a predator–prey system with kleptoparasitic interactions

Abstract

This study explores a predator–prey model featuring one prey and two competing predators linked through kleptoparasitism. Unlike traditional approaches, we introduce a nonlinear formulation where the interaction simultaneously suppresses the host predator’s growth while boosting the kleptoparasite. We determine the system’s equilibrium points and evaluate their stability through the Routh–Hurwitz criteria and Lyapunov methods. Our findings reveal that the system’s dynamics are highly sensitive to parameter shifts. Numerical simulations reveal three main results: full species coexistence, competitive elimination, and bistability. Importantly, the environmental carrying capacity serves as a key factor that initiates changes among these varying dynamic states. Additionally, the presence of bistability highlights that the system’s long-term fate can be completely reliant on the numbers of initial populations. These findings imply that our proposed formulation presents a novel viewpoint compared to traditional interference-based models. By addressing these complex responses, this framework delivers a more refined comprehension of how kleptoparasitic behavior influence predator-prey relationships across various ecological environments.