A New Consideration of the Influence of Shelter on the Kinetic Behavior of the Leslie-Gower Predator Prey System with Fear Effect

Abstract

In this study, a Leslie-Gower predator-prey model that incorporates both fear effect and shelter is presented and investigated. It is assumed that predator species only capture and cause fear in prey species outside the refuge, but have no impact on prey species inside the refuge. We demonstrate that the fear effect and the refuge have no impact on the positive equilibrium’s existence and local stability. Next, we explore the system’s persistence characteristic. By applying the Bendixson-Dulac criterion, we demonstrate that the requirement assures the system’s permanence is enough to guarantee the global attractivity of the positive equilibrium. According to our investigation, the birth rate of prey species and the refuge are two of the most critical factors in ensuring the sustainable development of the system.