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.