Allee Effect in Prey versus Hunting Cooperation on Predator — Enhancement of Stable Coexistence

Abstract

Predator foraging facilitation or cooperative hunting increases per predator consumption rate as predator density increases. This affects predator extinction in a prey–predator interaction model when the predator density is low. This is an indication of Allee effect in predator’s growth rate. Here, we take a Gause type model with a generalized type II functional response which depends on both prey and predator densities. We also assume that prey’s growth is subjected to Allee effect. Strong Allee effect in prey’s growth rate enhances the stability of the coexisting steady state. A region is found in a two-parameter plane where the coexisting steady state is a global attractor when the prey’s growth is subjected to weak Allee effect. In addition, codimension two bifurcation points (cusp and Bogdanov–Takens points) have also been found in the bifurcation diagram.