2023 Fiscal Year Final Research Report
Inherent time-delay structure and its extraction: Development and evolution of dynamics research using time-delay structure
| Project/Area Number |
19K14565
|
|---|
| Research Category |
Grant-in-Aid for Early-Career Scientists
|
| Allocation Type | Multi-year Fund |
|---|
| Review Section |
Basic Section 12020:Mathematical analysis-related
|
|---|
| Research Institution | Tohoku University |
|---|
Principal Investigator |
|
|---|
| Project Period (FY) |
2019-04-01 – 2024-03-31
|
| Keywords | 遅延微分方程式 / 遅れ型関数微分方程式 / 無限次元力学系 / 特性方程式 / 定数変化法公式 |
|---|
| Outline of Final Research Achievements |
In a delay differential equation (DDE), where the time derivative of an unknown function also depends on the past information of the unknown function, its dynamics can be viewed as the time evolution of the history segment in the space of continuous functions. The mathematical formulation of DDE using this concept is called a retarded functional differential equation (RFDE).
1. Study on the smooth dependence of solutions of DDEs on the delay parameter; 2. Study to understand the asymptotic behavior of solutions of differential equations with respect to time and space variables in the framework of topological dynamical systems and their global attractors; 3. Study on the time delay parameter dependence of the linear stability of equilibrium points; 4. Introduction of the concept of mild solutions of autonomous linear RFDEs and study of their properties.
|
| Free Research Field |
遅延微分方程式
|
| Academic Significance and Societal Importance of the Research Achievements |
制御におけるむだ時間，情報の伝播速度の有限性，個体成熟に要する期間，政策ラグなど，遅延微分方程式(DDE)としての考察が不可欠な現象が数多く存在する．DDEにおいてはそれに含まれる時間遅れのパラメータの大きさというものが問題となり，DDEの解が時間遅れパラメータにどのように依存するかを調べることは，上に述べたDDEとしての解析が不可欠なさまざまな現象の理解につながる．また，DDEと常微分方程式(ODE)との差異を調べることは，DDEのダイナミクスの特性を理解する上で重要である．本研究における軟解概念の導入は，DDEとODEとの差異を明らかにするものである．
|
