Qualitative analysis of a predator–prey model with Holling type II functional response incorporating a constant prey refuge

A predator–prey model with Holling type II functional response incorporating a constant prey refuge is investigated. Depending on a constant prey refuge mm, which provides a condition for protecting mm of prey from predation, we show the instability and global stability properties of the equilibria and the existence and uniqueness of limit cycles for the model. Two examples are carried out to illustrate the validity of our results.