Dynamics of predator-prey models with refuge, harvesting and dispersal

Abstract

The dynamics of predator-prey models with different prey harvesting functions and prey refuge is studied. This study includes a three-dimensional model to account for the dispersal of prey to a habitat where it is unavailable to the predator. Besides local stability analysis, one central question is how harvesting, refuge and dispersal could directly affect the dynamics of the ecosystem, such as existence and dynamics of coexistence equilibria and periodic solutions. Theoretical and numerical methods are used to prove the existence and to study the role played by several bifurcations in the mathematical models. (2010): 37N25, 92D25. Mathematics Subject Classification

The Effects of Varying Predator Dispersal Strength on Prey-Predator Dynamics with Refuge Process

“…The study also revealed that bold but less vigilant prey remained in the open habitat at the expense of their stock, while more apprehensive and less vigilant prey chose the refuge, compromising their foraging and mating opportunities. Some prior studies, [20][21][22] examined different aspects of prey-predator dynamics incorporating various factors such as time delay, refuge, harvesting, and prey dispersal. Alidousti and Ghahfarokhi [20] focused on a time-delay fractional predator-prey system with prey dispersal and demonstrated that the fractional system exhibited periodic solutions with shorter periods compared to the classical case, expanding the stability domain under the fractional order.…”

“…Alidousti and Ghahfarokhi [20] focused on a time-delay fractional predator-prey system with prey dispersal and demonstrated that the fractional system exhibited periodic solutions with shorter periods compared to the classical case, expanding the stability domain under the fractional order. In contrast, Hare and Rebaza [21] investigated the dynamics of a predator-prey system with refuge, harvesting, and dispersal. They introduced two patches in a three-dimensional model to represent unavailable prey habitat and a classical predator-prey relationship, including refuge and harvesting.…”