标题: 延迟性微分方程的稳定区域
Stable Region of Two Delay Equations
作者: 陈铭峰
CHen, Ming-Fong
陈福祥
Tsen, Fu-Shiang
应用数学系所
关键字: 延迟性;微分方程;?定区域
公开日期: 1996
摘要: 本篇论文主要是探讨含两个时间延迟参数的一阶线性微分方程,其系数和两个参数对零解稳定性的影响。
第一章中,我们介绍所要讨论的延迟性微分方程,以及它的来源和基本性质性质还有Mr. Jack K.Hale, Mr.Wenzhang Huang对这个微分方程所提出的论述
第二章是把微分方程所产生的特征方程去做初步的分类。用几何的观点分析特征根和系数的关系。
第三章以及第四章讨论两种基本类型,并且在平面上绘出在此条件下稳定和不稳定的分野。以此类型去衍生出其它类型,并指出所产生的特殊现象。
In this thesis, we study the problem of stability region of a linear two delay differential equation. This region is determined by the three constant coefficients and two delay parameters.
In the first chapter, we will introduce the historical background of the two delay equation and some basic properties of the two delay equation. The well known results of Hale and Huang on two delay differential equation will be stated.
In the second chapter, we classified the relation between the coefficients of the equation into four types of situations. By using the special eigenvalue in characteristic equation, we could tell the relation between parameters and the stability region.
In the third chapter, we concentrate on studying the two basic types, so that the boundary curve of the stability region could be described in terms of a function relation between two delay parameters.
In the fourth chapter, we used the results of the third chapter to study the remaining types of the stability region through both the theoretical analysis and numerical computations. Finally we presented all the computer graph results corresponding to all types and some special type of situations.
URI: http://140.113.39.130/cdrfb3/record/nctu/#NT853507001
http://hdl.handle.net/11536/62436
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