季节变化下害虫综合治理切换模型的动力学性质研究

Study on Dynamics of a Switching Model of Integrated Pest Management under Seasonal Variation

考虑害虫一周期的两个阶段,建立季节变换下害虫综合治理切换模型.利用脉冲微分方程的比较定理和分析方法,给出害虫灭绝周期解全局渐近稳定的充分条件.通过数值模拟,给出害虫灭绝阈值与害虫休眠时间、害虫控制周期、杀虫剂对害虫瞬时杀死率以及投放天敌数量之间的关系.

In this paper, based on the phenomena that the pests go through two stages in each cycle, a switching model of integrated pest management under seasonal variation is established.By using the comparison theorem of impulsive differential equations and analysis method, the sufficient conditions for the global asymptotic stability of pest extinction periodic solution are given.The relationship between the pest extinction threshold and dormancy time, pest control period, instantaneous killing rate of pesticides to pests and the amount of natural enemies is given by numerical simulations.