| Project/Area Number |
14540193
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Osaka Electro-Communication University |
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Principal Investigator |
SAKATA Sadahisa Osaka Electro-Communication University, Faculty of Engineering, Professor, 工学部, 助教授 (60175362)
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| Co-Investigator(Kenkyū-buntansha) |
YAMAHARA Hideo Osaka Electro-Communication University, Faculty of Engineering, Associate Professor, 工学部, 助教授 (30103344)
MANDAI Takesi Osaka Electro-Communication University, Faculty of Engineering, Professor, 工学部, 教授 (10181843)
ASAKURA Fumioki Osaka Electro-Communication University, Faculty of Engineering, Professor, 工学部, 教授 (20140238)
NAGABUCHI Yutaka Anan National College of Technology, Department of Systems and Control Engineering, Associate Professor, 助教授 (60252607)
HARA Tdayuki Osaka Prefecture University, Graduate School of Engineering, Professor, 大学院・工学研究科, 教授 (20029565)
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| Project Period (FY) |
2002 – 2003
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| Project Status |
Completed (Fiscal Year 2003)
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| Budget Amount *help |
¥2,400,000 (Direct Cost: ¥2,400,000)
Fiscal Year 2003: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2002: ¥1,400,000 (Direct Cost: ¥1,400,000)
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| Keywords | Linear Differential Equations / Two Kinds of Time Lags / Asymptotic Stability / Characteristic Equations / Influence on Characteristic roots by Parameters / 0 |
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| Research Abstract |
We studied the influence on behavior of solutions of linear differential equation (1) x´=ax(t-r)+b∫^t_<t-h> x(s)ds by four parameters, namely time lags r, h and two coefficients a, b. It is well known that the zero solution of linear differential equation is asymptotically stable if and only if all roots of the associated characteristic equation have negative real parts. Therefore we need to investigate the influence on the characteristic roots by the parameters. These parameters are not independent one another. So, we investigated the influence by parameters a and b under fixing r and h. But it is very difficult to analyze the distribution of characteristic roots. Therefore we assumed that the ratio of r to h is 1 to n (a positive integer) or n to 1, and showed ab-regions which mean the sets of (a, b) in the ab-plane for which the zero solution of (1) is asymptotically stable. On the other hand, for fixed a and b, we can classify the choice of the ratio of a to b into seven typical cases. We found with regret the rh-regions for only four cases, but have not arrived at the conclusive results yet.
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