Global Dynamics of a Predator-Prey System with Cooperative Hunting

We consider a predator-prey system with cooperative hunting. The parameter space of the system is divided into several mutually exclusive regions. Based on the investigation of the dynamical properties in each parameter region, we provide a complete description of the global dynamics, including stability, Hopf bifurcation and its directions, and the existence of limit cycles. By comparing this system's dynamics to those of a system without cooperative hunting, it is found that cooperative hunting is beneficial to the coexistence of the prey and predator. When the mortality of the predator is small, hunting cooperation does not affect the coexistence of populations but it affects the pattern of coexistence.