Global dynamics of a Leslie–Gower predator–prey model with square root response function

Abstract

A Leslie–Gower predator–prey model with square root response function is considered. We prove that the origin is unstable using blow-up method, and show that if the positive equilibrium is locally stable, then it is globally asymptotically stable based on the divergency criterion. Also, if the positive equilibrium is unstable, the system admits a unique stable limit cycle. A conclusion is finally given to show the influence of the square root response function on the dynamic behaviors of the system.