Complex dynamics of a generalist predator–prey model with hunting cooperation in predator

The predator–prey models with hunting cooperation have a great significance in ecology. Hunting cooperation by predators represents more realism in an ecological environment when group defense is shown by the prey species. Ecological models can be divided into two types of predators, depending upon the nature of predators, namely specialist and generalist predators. The present study examines the role of hunting cooperation in the dynamics of predator–prey systems where the predator is a generalist. We discuss complex dynamics of the system, like bistability along with local and global bifurcations, viz., Transcritical, Saddle-node, Hopf, Bogdanov–Takens, homoclinic bifurcation, etc. We also find that the system exists up to six equilibria with bistability, limit cycles and several local, global bifurcations. We discuss two parametric bifurcation diagram. And finally, all the theoretical results are displayed numerically.