【作者】 黄郑；

【导师】 蒋威；

【作者基本信息】 安徽大学 ， 应用数学， 2013， 硕士

【摘要】 在实际系统中,退化、时滞现象总是普遍存在的,例如控制系统、金融系统、化工系统、工业工程系统、生态系统、电力系统等,稳定性理论是退化时滞微分系统的一个基础结构特征,自从俄国数学力学家Lyapunov建立了常微分方程稳定性理论以来,很多学者在此基础上研究了退化时滞微分系统的稳定性理论,极大地推动了稳定性理论和方法的不断发展和创新,已经取得了大量的研究成果.同时在实际系统中,周期现象也经常出现,因而周期问题也是一个重要的研究方向.本文对退化时滞微分系统的周期解及稳定性进行了研究并得出了一些结论.全文共分为如下四章.第一章主要介绍问题的一些背景知识及本文所做的主要工作,给出本文所需的一些预备知识.第二章研究了如下退化中立型系统的周期解问题.第三章研究了n维退化时滞微分系统Ex(t)=Ax(t)+Bx(t-τ)全时滞稳定的代数判据.第四章研究了一类具有分布时滞的Lurie直接控制系统：和一类具有分布时滞的Lurie间接控制系统：的绝对稳定性.更多还原

【Abstract】 There were many degenerate and time delay phenomena existing in many practi-cal fields, such as control system,financial system,chemical system,industrial project sys-tem,ecosystem,power system and so on.Stability is a basic structure characteristic of de-generate differential systems with delays.Since the Russian mathematician mechanics Lya-punov found stability theory of ordinary differential equations,many scholars have studied the stability theory of degenerate differential systems with delays,which promoted the con-tinuous development and innovation of degenerate differential systems and has obtained a lot of research achievement.At the same time, periodic phenomena often occur in practical fields, and thus the periodic problem is also an important aspect of the study.This paper deals with periodic solution and stability of degenerate differential systems with delays, many important results are also given in it. There are four chapters in this paper.In chapter1, some background knowledge of degenerate differential systems with delays is introduced, and the preliminary knowledge which is necessary in the paper is given.In chapter2, we consider the periodic solution of the following system:In chapter3,we investigate the stability of the following system: Ex(t)=Ax(t)+Bx(t-τ)In chapter4, we study the stability of the following two systems: and更多还原