Qualitative analysis of a predator–prey model with constant-rate prey harvesting incorporating a constant prey refuge

We consider a predator–prey model with Holling type II functional response incorporating a constant prey refuge and a constant-rate prey harvesting. Depending on the constant prey refuge m, which provides a condition for protecting m of prey from predation, and the constant-rate prey harvesting, some sufficient conditions for the instability and global stability of the equilibria, and the existence and uniqueness of limit cycles of the model are obtained. We also show the influences of prey refuge and harvesting efforts on equilibrium density values. Numerical simulations are carried out to illustrate the feasibility of the obtained results and the dependence of the dynamic behavior on the harvesting efforts or prey refuge.