Dynamic of a pest management system with hibernation of pests and impulsive nonlinear release of natural enemies

Considering the hibernation of pests and impulsive nonlinear release of natural enemies, we construct a pest management system with hibernation of pests and impulsive nonlinear release of natural enemies. Using Floquet theory and the comparison theorem of impulsive differential equations, we derive the conditions under which the pest-eradication periodic solution is globally asymptotically stable (GAS) and the system is permanent. Furthermore, we obtain a control threshold that is critical for managing pest population. The validity of these conditions is rigorously tested and confirmed through numerical simulations. Our work provides ways to pest management.