Co-existence of a Period Annulus and a Limit Cycle in a Class of Predator–Prey Models with Group Defense

For a family of two-dimensional predator–prey models Gause type, we investigate the simultaneous occurrence center singularity and limit cycle. The is characterized by fact that functional response nonanalytical exhibits group defense. We prove existence uniqueness cycle using new theorem for Liénard systems. gives conditions which surrounds period annulus. results this paper provide mechanism studying global behavior solutions to systems through bifurcation an integrable system contains