Stability and bifurcation analysis of discrete predator-prey model with nonlinear prey harvesting and prey refuge

In this paper, a discrete Leslie-Gower model with nonlinear prey harvesting and prey refuge is proposed. We prove the existence and stability of an interior equilibrium of the model. In addition, the existence of flip bifurcation and Neimark-Sacker bifurcation at the interior equilibrium is studied by applying central manifold theory and bifurcation theory. Using Pontryagin's maximum principle, we propose an optimal harvesting problem.