Impacts of hunting cooperation among predators on predator-prey dynamics

It is well established that hunting cooperation among predators can significantly influence the dynamic behavior of predator-prey interactions. In this paper, we present a qualitative analysis of a basic predator-prey model with hunting cooperation, including the existence and local stability of all feasible equilibria, and the global dynamics under certain conditions. Explicit expressions of the corresponding conditions are provided through ingenious and technical deduction. The obtained theoretical results reveal the effects of both the strength of hunting cooperation and the basic reproduction number on the population dynamics. Combining the qualitative analysis with quantitative analysis, we demonstrate the distribution of all possible asymptotic states of the model and give the corresponding biological interpretations. Notably, beyond the Allee effect and collapse in predators reported in existing works, we identify and discuss novel phenomena such as the inverse Allee effect and relaxation oscillations. These findings are instrumental for understanding predator-prey interactions with hunting cooperation and mitigating the risk of predator extinction.