Bifurcation Analysis and Spatio-Temporal Patterns of a Prey-Predator Model with Hunting Cooperation

Understanding the effects of cooperative hunting among the predators is an important topic in ecology. We explore a prey-predator model with cooperative hunting among predators modeled by a Holling type-II functional response having saturated encounter rate. Bifurcation analysis is carried out on the temporal model to detect local bifurcations such as transcritical, saddle-node, Hopf bifurcation and global homoclinic bifurcation. A comprehensive numerical bifurcation analysis is performed on the Turing solutions of the corresponding diffusive model. Stable and unstable branches of mode specific Turing solutions and their dependence on parameters are identified. For suitable values of parameters, spatio-temporal chaos via period doubling cascade is observed when a given parameter traverses the Turing-Hopf region.