Abstract:
A new impulsive system with integrated control effects is presented based on Lotka-Volterra predator-prey systems. Impulsive differential equations with three impulsive effects in one period are used to simulate the behaviors of releasing sick pests and predators, spraying pesticides, and putting viruses for pest control. By using Floquet theorem and small amplitude perturbation methods, it is proved that there exists a globally stable pest eradication solution when the control parameters are larger than some critical values. The condition for the uniform permanence of this system is also presented.