周期环境下脉冲微分方程的定性分析及应用
发布时间：2018-10-08 14:10
【摘要】：本文主要利用脉冲微分方程比较定理和Floquet引理对周期环境下害虫综合治理模型进行定性分析,并对害虫综合治理策略在农业生产中的应用进行深入研究。第一章介绍了基于害虫综合治理策略的害虫-天敌系统的研究背景和研究现状,提供论文中常用的基本概念以及重要引理等基础知识,它们是后续章节讨论的基础。第二章研究了一类具有不同频率脉冲控制的周期环境下的捕食系统,利用Floquet引理和小扰动技巧,分别给出了不同策略下根除害虫周期解的存在性与全局渐近稳定的充分条件,通过数值模拟分析了系统参数对临界值的影响。第三章研究了周期环境下具有抗性发展且喷洒农药和投放天敌具有不同频率但周期相同的害虫控制模型,利用脉冲微分方程相关理论对所建生物模型进行定性分析,得到了系统害虫根除周期解全局渐近稳定的临界值以及系统一致持续生存和永久持续生存的充分条件,数值模拟结果为实际生产提供理论依据。第四章在第三章的基础上将更具有实际生产意义的Monod-Haldane型功能反应函数引入到系统中,通过定性分析得到了系统害虫根除周期解的稳定性以及持久生存。最后,对本文的研究工作进行总结,展望了自己在害虫综合治理方面将进一步研究的课题。
[Abstract]:In this paper, the comparison theorem of impulsive differential equation and Floquet Lemma are used to qualitatively analyze the integrated pest management model in periodic environment, and the application of integrated pest management strategy in agricultural production is deeply studied. The first chapter introduces the research background and present situation of the pest natural enemy system based on the integrated pest management strategy, and provides the basic concepts and important Lemma, which are the basis of the discussion in the following chapters. In chapter 2, we study a class of predator-prey systems with impulsive control at different frequencies. By using Floquet Lemma and small perturbation technique, we give sufficient conditions for the existence and global asymptotic stability of periodic solutions of pest eradication under different strategies. The influence of system parameters on critical value is analyzed by numerical simulation. In chapter 3, the pest control model with resistance development and different frequency of spraying pesticide and natural enemy is studied, and the biological model is analyzed qualitatively by using the theory of pulse differential equation. The critical value of the global asymptotic stability of the periodic solution of pest eradication and the sufficient conditions for the consistent and permanent survival of the system are obtained. The numerical simulation results provide a theoretical basis for practical production. In chapter 4, based on the third chapter, the Monod-Haldane type functional response function is introduced into the system, and the stability and persistence of the periodic solution of pest eradication are obtained by qualitative analysis. Finally, the research work of this paper is summarized, and the future research topics in integrated pest management are prospected.
【学位授予单位】：温州大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O175
本文编号：2257055
[Abstract]:In this paper, the comparison theorem of impulsive differential equation and Floquet Lemma are used to qualitatively analyze the integrated pest management model in periodic environment, and the application of integrated pest management strategy in agricultural production is deeply studied. The first chapter introduces the research background and present situation of the pest natural enemy system based on the integrated pest management strategy, and provides the basic concepts and important Lemma, which are the basis of the discussion in the following chapters. In chapter 2, we study a class of predator-prey systems with impulsive control at different frequencies. By using Floquet Lemma and small perturbation technique, we give sufficient conditions for the existence and global asymptotic stability of periodic solutions of pest eradication under different strategies. The influence of system parameters on critical value is analyzed by numerical simulation. In chapter 3, the pest control model with resistance development and different frequency of spraying pesticide and natural enemy is studied, and the biological model is analyzed qualitatively by using the theory of pulse differential equation. The critical value of the global asymptotic stability of the periodic solution of pest eradication and the sufficient conditions for the consistent and permanent survival of the system are obtained. The numerical simulation results provide a theoretical basis for practical production. In chapter 4, based on the third chapter, the Monod-Haldane type functional response function is introduced into the system, and the stability and persistence of the periodic solution of pest eradication are obtained by qualitative analysis. Finally, the research work of this paper is summarized, and the future research topics in integrated pest management are prospected.
【学位授予单位】：温州大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O175
【参考文献】
相关硕士学位论文 前1条
1 张方方;具有抗性发展的害虫控制模型的研究[D];陕西师范大学;2012年
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