| Project/Area Number |
25400168
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Mathematical analysis
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| Research Institution | Kyoto University (2014-2016)
Hiroshima University (2013) |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
柴山 允瑠 京都大学, 情報学研究科, 准教授 (40467444)
伊藤 秀一 金沢大学, 数物科学系, 教授 (90159905)
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| Project Period (FY) |
2013-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2015: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2013: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
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| Keywords | 力学系 / 偏微分方程式系 / 不規則摂動系 / 周期摂動系 / 区分的に滑らかな系 / 分岐 / カオス / 非可積分性 / 微分方程式 / 反転可能系 |
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| Outline of Final Research Achievements |
Dynamical systems described by ordinary and partial differential equations were considered and complicated behaviors such as bifurcation structures occurring in these systems were theoretically investigated. Especially, bifurcations and stability of solitary waves in partial differential equations, unique existence and bifurcations of radial symmetric, positive solutions in elliptic partial differential equations, control of microcantilevers in atomic force microscopy, nonintegrability of general differential equations, and chaos in periodic perturbations of conservative systems and random perturbed systems were discussed. Appropriate numerical analyses and simulations were also carried out to demonstrate these theoretical results numerically and graphically.
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