Asymptotic property of solutions of delay equations and spectral analysis

延迟方程解的渐近性及谱分析

• 批准号: 21740103
• 负责人: MATSUNAGA Hideaki
• 金额: $ 1.91万
• 依托单位: Osaka Prefecture University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 财政年份: 2009
• 资助国家: 日本
• 起止时间: 2009 至 2011
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21740103/
• 关键词: 時間遅れ; 微分方程式; 差分方程式; 漸近安定性; 特性根; Volterra差分方程式; 相空間の直和分解; 射影作用素; 積分微分方程式; 形式的随伴方程式; 相空間; 解作用素; 特性方程式

In this research we have studied the asymptotic property of solutions of delay equations and spectral analysis, and have presented the following main results.(1) We have established some asymptotic stability conditions for the zero solution of linear integro-differential systems and linear difference systems with diagonal or off-diagonal delays. In particular, we have showed that stability switches appear in linear integro-differential systems as a parameter of diagonal delays increases under certain conditions.(2) For linear Volterra difference equations with infinite delay, we have obtained an explicit representation form of the projection on the center-unstable subspace in the phase space to get an asymptotic formula of the solutions. As an application, we have easily calculated some asymptotic periodic solutions of concrete equations.

本研究研究了时滞方程解的渐近性质和谱分析，得到了以下主要结果：(1)建立了线性积分微分系统和具有对角或非对角时滞的线性差分系统的零解的渐近稳定条件。特别是，我们证明了在一定条件下，随着对角时滞参数的增加，线性积分微分系统中会出现稳定性切换。(2)对于具有无限时滞的线性Volterra差分方程，我们得到了相空间中中心不稳定子空间上的投影的显式表示形式，从而得到了解的渐近公式。作为一个应用，我们很容易计算出具体方程的一些渐近周期解。

项目成果

Asymptotic stability conditions for a delay difference system

时滞差分系统的渐近稳定性条件

• 发表时间: 2009
• 期刊: Advanced Studies in Pure Mathematics 53
• 作者: F. Kawahigashi;H. Matsunaga
• 通讯作者: H. Matsunaga

Stability regions for linear delay differential equations with four parameters

具有四个参数的线性时滞微分方程的稳定区域

• 期刊: International Journal of Qualitative Theory of Differential Equations and Applications (掲載決定済)
• 作者: J. Sugie;Y. Ogami;藤解和也;N. Yamaoka;藤解和也;H. Matsunaga
• 通讯作者: H. Matsunaga

Global behavior of a two-dimensional monotone difference system

二维单调差分系统的全局行为

• 发表时间: 2009
• 期刊: Advanced Studies in Pure Mathematics 53
• 作者: M. Inoue;H. Matsunaga
• 通讯作者: H. Matsunaga