2016 Fiscal Year Final Research Report
Investigation of Diverse Bifurcation Structures in Differential Dynamical Systems
| 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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| Project Period (FY) |
2013-04-01 – 2017-03-31
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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 |
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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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| Free Research Field |
力学系理論
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