Bifurcations of a predator–prey system with cooperative hunting and Holling III functional response

In this paper, we consider the dynamics of a predator–prey system Gause type with cooperative hunting among predators and Holling III functional response. The known work numerically shows that exhibits saddle-node Hopf bifurcations except homoclinic bifurcation for some special parameter values. Our results show there are weak focus multiplicity three degenerate equilibrium double zero eigenvalues (i.e., cusp codimension two) general conditions can exhibit various as perturbing parameters appropriately, such transcritical pitchfork at boundary equilibrium, Bogdanov–Takens positive around focus. comparative study demonstrates far richer more complex than without predators. analysis reveal appropriate intensity is beneficial persistence diversity ecosystem.