具有状态依赖脉冲控制的害虫管理SI模型的动力学性质

何志龙,聂麟飞

系统科学与数学 ›› 2017, Vol. 37 ›› Issue (11) : 2163-2177.

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系统科学与数学 ›› 2017, Vol. 37 ›› Issue (11) : 2163-2177. DOI: 10.12341/jssms13274
论文

具有状态依赖脉冲控制的害虫管理SI模型的动力学性质

    何志龙1,聂麟飞2
作者信息 +

The Dynamics of Pest Management SI Model with Impulsive State Feedback Control

    HE Zhilong1 ,NIE Linfei2
Author information +
文章历史 +

摘要

考虑到过量使用农药对环境和农作物造成的危害, 文章提出了一类具有 状态脉冲反馈控制策略的害虫管理SI控制模型, 即, 当易感害虫的数量到达经济危害水平时, 施加生物和化学控制策略(例如, 释放染病害虫且按易感害虫的比例喷洒杀虫剂), 使得易感害虫的数量在极短的时间内低于危害阈值, 从而达到控制病虫害的目的. 通过使用微分几何理论, Poincar\'e 映射, 不动点定理等方法和技巧, 建立了该控制模型系统正周期解存在性和稳定性的判别准则.

Abstract

Considering the harm caused by excessive use of pesticides on the environment and crops, we propose a pest management SI model with state feedback impulsive control strategies, that is, when the quantity of susceptible pests population reaches the economic damage level, biological and chemical tactics (for example, the releasing infective pests, and spraying pesticides by rate of susceptible pest population) are taken such that the quantity of susceptible pest population below the threshold value in a very short time, so as to achieve the purpose of insect pest control. By using the method and skill of the geometry theory of differential equation, Poincar\'e map and fixed point theorem, some criterions for the existence and stability of positive periodic solution are obtained.

关键词

害虫管理SI模型 / 状态反馈控制 / Poincar\'e 映射 / 周期解 / 存在性和稳定性.

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何志龙 , 聂麟飞. 具有状态依赖脉冲控制的害虫管理SI模型的动力学性质. 系统科学与数学, 2017, 37(11): 2163-2177. https://doi.org/10.12341/jssms13274
HE Zhilong1 , NIE Linfei. The Dynamics of Pest Management SI Model with Impulsive State Feedback Control. Journal of Systems Science and Mathematical Sciences, 2017, 37(11): 2163-2177 https://doi.org/10.12341/jssms13274
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