Bifurcation Dynamics of a Pest Management System With Cooperative Predation, Fear Effect, and Impulsive Density‐Dependent Nonlinear Effects

ABSTRACT Effective integrated pest management should control pests while safeguarding the environment and human health. This study proposes a novel pest management system incorporating cooperative predation, fear effect, impulsive density‐dependent nonlinear prey (pest) trapping and predator (natural enemy) release. The conditions for global asymptotic stability of the prey extinction periodic solution and system permanence are established. A supercritical bifurcation occurs when the impulsive control period serves as a bifurcation parameter. This implies that a transition from a prey extinction periodic solution to a positive periodic solution of prey–predator coexistence when the impulsive period exceeds a critical value. Meanwhile, simulations are conducted to verify the theoretical results, determine the key factors influencing pest extinction threshold condition, and explore the complex dynamics of the system. This analysis will aid future research and the development of effective pest control strategies.