延遲性微分方程的穩定區域

Abstract

本篇論文主要是探討含兩個時間延遲參數的一階線性微分方程，其係數和兩個參數對零解穩定性的影響。 第一章中，我們介紹所要討論的延遲性微分方程，以及它的來源和基本性質性質還有Mr. Jack K.Hale, Mr.Wenzhang Huang對這個微分方程所提出的論述 第二章是把微分方程所產生的特徵方程去做初步的分類。用幾何的觀點分析特徵根和係數的關係。 第三章以及第四章討論兩種基本類型，並且在平面上繪出在此條件下穩定和不穩定的分野。以此類型去衍生出其它類型，並指出所產生的特殊現象。

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.