Bifurcation Dynamics of a Pest Management System with Group Defense, Interspecific Cooperative Hunting and Impulsive Effects

In this study, we propose a novel three-species pest management system. The system incorporates group defense by the prey (pest), interspecific cooperative hunting among predators (natural enemies), and impulsive pesticide applications combined with the release of two predator species at different fixed moments. The conditions for global asymptotic stability of the prey extinction periodic solution and for system permanence are derived. By considering the impulsive period as the bifurcation parameter, the condition for a supercritical bifurcation is established. This bifurcation results in the emergence of a positive periodic solution from the prey extinction periodic solution, allowing coexistence of the prey and two predators. Moreover, numerical analysis is conducted to illustrate the theoretical results. Sensitivity and two-parameter analyses indicate that the interspecific cooperative hunting intensity, the impulsive release quantities of the two predators, and the impulsive period significantly impact the prey extinction threshold condition. This research provides important theoretical insights for effective integrated pest management and biodiversity conservation strategies.