Influence of Prey Reserves, Cooperative Predator Hunting and Herd Behavior on Species Coexistence and Population...

The coexistence of species in predator-prey systems is a critical ecological issue due to the intricate interactions among multiple influencing factors. In this study, we develop a predator-prey model that incorporates prey herd behavior, cooperative hunting strategies among predators, and the establishment of a reserved area for prey protection. We establish conditions for the positivity and boundedness of the system to ensure long-term biological feasibility. The existence and stability of equilibrium points, along with the conditions for Hopf and saddle-node bifurcations, are rigorously analyzed. Numerical simulations are performed to validate the analytical findings. Global sensitivity analysis reveals that key parameters, including the size of the reserved area, predator cooperation, and migration rates, significantly affect system dynamics and species coexistence. Our numerical results suggest that expanding the reserved area promotes prey recovery, with predator populations initially growing but eventually declining towards extinction. Increased hunting cooperation among predators initially boosts predator populations but ultimately accelerates prey depletion, leading to predator collapse due to overhunting.