首先应用状态脉冲反馈控制的理论,建立了无公害害虫治理中的数学模型,并且对所建的模型进行定性分析,利用微分方程几何理论中后续函数法得到系统的阶一周期解存在的充分条件,证明该周期解是轨道渐近稳定的,同时利用数值模拟的手段讨论了系统在害虫治理中的应用意义. Firstly, the state impulsive feedback control theory is applied to establish the mathematical model of pollution-free pest management, and the qualitative analysis of the model is made. The sufficient condition for the existence of the order-periodic solution of the system is obtained by using the follow-up function method in the differential equation geometric theory It is proved that the periodic solution is asymptotically stable orbit, and the application of the system in pest management is discussed by means of numerical simulation.