Dynamics in a Predator–Prey Model with Cooperative Hunting and Allee Effect

This paper deals with a diffusive predator–prey model with two delays. First, we consider the local bifurcation and global dynamical behavior of the kinetic system, which is a predator–prey model with cooperative hunting and Allee effect. For the model with weak cooperation, we prove the existence of limit cycle, and a loop of heteroclinic orbits connecting two equilibria at a threshold of conversion rate p=p#, by investigating stable and unstable manifolds of saddles. When p>p#, both species go extinct, and when p