| Project/Area Number |
08640285
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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 |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Okayama University |
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Principal Investigator |
WATANABE Masaji The faculty of environmental science and technology, Okayama University, Professor, 環境理工学部, 教授 (30243546)
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| Co-Investigator(Kenkyū-buntansha) |
SASAKI Tooru The faculty of environmental science and technology, Okayama University, Lecture, 環境理工学部, 講師 (20260664)
KAJIWARA Tsuyoshi The faculty of environmental science and technology, Okayama University, Associa, 環境理工学部, 助教授 (50169447)
ISHIKAWA Hirofumi The faculty of environmental science and technology, Okayama University, Profess, 環境理工学部, 教授 (00108101)
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| Project Period (FY) |
1996 – 1998
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| Project Status |
Completed (Fiscal Year 1998)
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| Budget Amount *help |
¥2,200,000 (Direct Cost: ¥2,200,000)
Fiscal Year 1998: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 1997: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 1996: ¥800,000 (Direct Cost: ¥800,000)
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| Keywords | circadian rhythm / nonlinear oscillator / ordinary differential equation / periodic solution / numerical analysis / mathematical model / 常微分方程式系 / 常微分方程式系のダイナミクス / 同調 / 分岐 |
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| Research Abstract |
Sleep-wake rhythm and periodic body temperature change persist with period close to 24-hour even in isolation from 24-hour environmental change, which shows that these periodic changes are generated by some endogenous mechanism. These periodic changes observed in living things are called circadian rhythms. In order to help finding the mechanism of circadian rhythms, we set up mathematical models, analyze them, and verify analytical results with numerical analysis. Besides circadian rhythms, oscillations of some glycolytic intermediates are other periodic phenomena observed in living things. The period of biochemical oscillations ranges a few minutes to 10 minutes, and the period of circadian rhythms are more than 100 times as long. In spite of the significant difference, one can not deny some sort of relation between circadian rhythms and biochemical reactions, because circadian rhythms are observed in variety of living things, and because biochemical reactions are essential for living things to obtain energy. In this study, we suppose that a part of a living thing is surrounded by another part. In case there is no transport of substances between them, the change of concentrations of substances in the inner part is governed by a nonlinear oscillator. Then we assume that there is transport of the substances between the parts. The assumption leads to a system in which a system governing the concentrations in the inner part and a system governing the concentrations in the outer part are coupled. Assuming that a non oscillator has some characteristics, we show that periodic solutions of the coupled system can exist. Moreover, we analyze the system to find conditions under which oscillations of long period can be generated from oscillations of relatively short period. We analyze a model for a electrical circuit anda model for a biochemical reactions, numerically, and verify the results of analysis.
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