Bifurcation Analysis of a Predator-Prey Model with Allee Effect and Cooperative Hunting

TL;DR

This paper develops a predator-prey model incorporating the Allee effect and cooperative hunting, analyzing its stability and bifurcations to understand complex ecological dynamics.

Contribution

It introduces a novel predator-prey model with Allee effect and cooperative hunting, providing comprehensive bifurcation analysis and stability results.

Findings

Multiple equilibria identified

Transitions in stability observed

Complex dynamical patterns emerge

Abstract

We propose a novel predator-prey model that integrate two ecologically significant mechanisms: the Allee effect in the prey population and cooperative hunting behavior among predators. Building upon the Rosenzweig-MacArthur framework, our model modifies the prey growth term to incorporate the Allee effect and introduces a nonlinear functional response reflecting predator cooperation. We establish the existence and boundedness of global solutions for the system and analyze the local and global stability of its equilibria. In addition, we perform a comprehensive bifurcation analysis, including transcritical, saddle-node, Hopf, and heteroclinic bifurcations, to explore how system dynamics change with key parameters. These results reveal rich and biologically relevant behaviors, such as multiple equilibria, transitions in stability, and the emergence of complex dynamical patterns.