| 基于脉冲控制的害虫管理模型 |
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| 引用本文： | 宋 燕,张庭婷,姜 威.基于脉冲控制的害虫管理模型[J].福州大学学报(自然科学版),2016,44(2):156-163. |
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| 作者姓名： | 宋 燕 张庭婷 姜 威 |
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| 作者单位： | 渤海大学数理学院，辽宁 锦州 121000,渤海大学数理学院，辽宁 锦州 121000,渤海大学数理学院，辽宁 锦州 121000 |
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| 摘 要： | 基于喷洒杀虫剂及投放病虫的综合控制害虫策略,建立了具有脉冲控制的微分方程模型.利用脉冲微分方程的Floquet定理、比较定理,证明了害虫灭绝周期解的全局渐近稳定性与系统的持久性,并利用分支理论给出了正周期解存在的分支参数.
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| 关 键 词： | 脉冲控制 害虫灭绝 全局渐近稳定 持久性 正周期解 |
The pest management model with impulsive control |
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| SONG Yan,ZHANG Tingting and JIANG Wei.The pest management model with impulsive control[J].Journal of Fuzhou University(Natural Science Edition),2016,44(2):156-163. |
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| Authors: | SONG Yan ZHANG Tingting and JIANG Wei |
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| Institution: | College of Mathematics and Physics, Bohai University, Liaoning, Jinzhou 121000,College of Mathematics and Physics, Bohai University, Liaoning, Jinzhou 121000 and College of Mathematics and Physics, Bohai University, Liaoning, Jinzhou 121000 |
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| Abstract: | Based on the integrated control strategy with spraying pesticides and releasing infective pests to control pests, we establish a model of differential equations with impulsive control. Using the Floquet Theorem of impulsive differential equations and the comparison Theorem, the globally asymptotical stability of the periodic solution of susceptible pest eradication and the permanence of the system are proven, and using bifurcation theory the bifurcation parameter for existence of the positive periodic solution is given. |
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| Keywords: | impulsive control pest eradication globally asymptotical stability permanence positive periodic solution |
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