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

Automated summary

The paper investigates a diffusive predator-prey model with two delays, proving the existence of limit cycle in the weak cooperation model and identifying a loop of heteroclinic orbits connecting two equilibria by studying stable and unstable manifolds of saddles. When the conversion rate exceeds a threshold, both species go extinct.