一类综合脉冲控制系统的动力学分析

Dynamic Analysis of an Impulsive Model with Integrated Control

  • 摘要: 针对Lotka-Volterra的捕食-食饵系统提出了一个新的综合控制系统,利用三次脉冲微分方程拟合在一周期内不同时刻释放病虫和捕食者、喷洒农药以及投放病毒的动力学过程,从而达到控制害虫(食饵)的目的.根据Floquet定理和小振幅扰动方法,证明了当脉冲参数大于某个临界值时,系统存在一个全局渐近稳定的害虫灭绝周期解,并进一步获得了系统持续生存的条件.

     

    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.

     

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