具有状态依赖脉冲控制的害虫综合治理模型分析

发布时间：2018-05-07 17:11

  本文选题：状态依赖 + 周期解　； 参考：《兰州理工大学》2017年硕士论文

【摘要】：作为数学和生物学相结合的新兴交叉学科,生物数学模型的研究近百年来得到了长足的发展.由于脉冲可以准确地描述某种数量在某些定时刻的快速变化或跳跃的特性,脉冲微分方程普遍用于生物种群生长发展的控制建模分析中.本文主要研究具有二次状态依赖脉冲控制的捕食-食饵模型,分析在不同状态依赖脉冲控制下的害虫治理模型的动力学行为.首先研究了一种基于Leslie-Gower修改的具有Holling-II型功能反应函数的状态依赖脉冲控制的捕食-食饵模型,分别研究了不加脉冲控制的情况下的解的存在性以及具有状态依赖脉冲控制下动力学行为.其次研究了一种带有二次状态依赖脉冲控制的Holling-Ⅲ型的捕食者食饵模型,利用后继函数、几何分析方法、脉冲微分方程的Poincare-Bendixson环域定理分析了系统周期解的存在性,进一步利用脉冲微分方程周期解的稳定性理论和类庞加莱准则给出了系统周期解稳定的充分条件.
[Abstract]:As a new interdisciplinary subject which combines mathematics and biology, the research of biological mathematical model has been greatly developed in the past hundred years. Because impulses can accurately describe the characteristics of a certain number of rapid changes or jumps at certain fixed times, impulsive differential equations are widely used in the control modeling and analysis of the growth and development of biological populations. In this paper, the predator-prey model with quadratic state dependent impulse control is studied, and the dynamic behavior of pest control model with different state dependent impulse control is analyzed. Firstly, a prey-prey model with state dependent impulse control with Holling-II type functional response function modified by Leslie-Gower is studied. The existence of solutions without impulsive control and the dynamic behavior under state-dependent impulsive control are studied respectively. Secondly, a predator-prey model of Holling- 鈪，

本文编号：1857759