基于区间脉冲控制的害虫治理模型研究

发布时间：2018-01-29 07:13

本文关键词： 害虫综合治理模型区间状态反馈控制 x~k型增长周期解稳定性　出处：《大连大学》2017年硕士论文　论文类型：学位论文

【摘要】：害虫治理是农业可持续发展的重要组成部分.传统的害虫治理手段主要包括化学控制和生物防治两种.害虫综合治理是综合利用农业、生物、化学、物理等方法来控制害虫浓度,使其控制在一个合理的经济阙值内.以往基于状态反馈的控制策略均是假设化学控制和生物控制在同一害虫密度水平被激发,但考虑到在实际的害虫治理中,生物控制一般较早于化学控制,为了更能反映实际的害虫治理过程,我们提出了基于区间状态反馈控制的害虫治理策略,即当害虫的浓度达到第一个监测浓度时,我们采取生物控制方法;一旦害虫浓度达到或高于第二个监测浓度时,我们采取化学控制的方法.首先,我们建立了一类基于区间状态反馈控制的Gompertz捕食-食饵害虫治理模型.借助于Poincaré定理和后继函数方法分析了系统阶一周期解的存在性.同时运用Bendixson理论分析了阶一周期解的稳定性.最后利用Matlab软件对所建立的模型进行数值模拟,进一步验证理论分析结果的准确性.其次,建立了两类基于区间状态反馈控制的x~k型捕食-食饵害虫治理模型.第一类是区间可调节控制水平x~k型Lotka-Volterra捕食-食饵害虫治理模型.应用雅克比矩阵证明了连续系统解的全局渐进稳定性.应用Dulac函数证明了系统不存在极限环.通过Poincaré映射和后继函数方法分析了控制系统阶一周期解的存在性和稳定性.同时以害虫控制浓度为优化变量,以控制成本为目标进行了优化处理.第二类是区间状态反馈控制的x~k型Gompertz捕食-食饵害虫综合治理模型.应用特征根的方法和Bendixson-Dulac定理证明了连续系统解的全局渐进稳定性.然后通过Poincaré映射和后继函数方法分析了控制系统阶一周期解的存在性和稳定性.最后利用Matlab软件对所建立的模型进行数值模拟,进一步验证了理论结果的正确性.
[Abstract]:Pest control is an important part of the sustainable development of agriculture. The traditional pest control methods mainly include chemical control and biological control. Two kinds of integrated pest management is the comprehensive utilization of agricultural, biological, chemical, physical and other methods to control pest concentration, make its control in a reasonable economic threshold. Based on previous control strategy state feedback is that chemical control and biological control are excited at the same level of pest density in pest control, but considering the actual biological control, general earlier in chemical control, pest control process in order to better reflect the actual, we propose a pest control strategy based on state feedback control interval, i.e. when the pest concentration reached first monitoring concentration, we adopt biological control methods; once the concentration reaches second or higher pest monitoring concentration, we adopt chemical control. Method. First, we establish a class of state feedback control interval Gompertz predator prey on pest control model. By the Poincar theorem and the successor function method for the analysis of the existence of solutions for a system of order cycle. At the same time using the Bendixson theory to analyze the stability of periodic solution of order one. Finally, numerical simulation is carried out on the the establishment of the model using the Matlab software, to further verify the accuracy of the results of theoretical analysis. Secondly, a two x~k type predator feedback control interval based on the state of prey pest control model. The first is the interval adjustable control level x~k type Lotka-Volterra predator-prey pest control model. Application of Jacobian matrix prove global asymptotic stability the solution of continuous system. The application of Dulac function to prove the nonexistence of limit cycles. Through Poincar mapping and subsequent function analysis for control system of order cycle The existence and stability of solutions. At the same time to control the concentration of pests as optimization variables, to control the cost of the target was optimized. The second is the interval state feedback control of x~k type Gompertz predator prey model. The comprehensive management of the pest method and the application of Bendixson-Dulac eigenvalue theory prove the global asymptotic stability of the solution of the continuous system and then through the Poincar mapping and the successor function method to analyze the existence and stability of solution control system order cycle. Finally, the numerical simulation of the model established by Matlab software, further verified the theoretical results.

【学位授予单位】：大连大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175;O231

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