| Project/Area Number |
15K21424
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Communication/Network engineering
Control engineering/System engineering
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| Research Institution | The University of Tokyo (2016-2017)
Meiji University (2015) |
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Principal Investigator |
Kamiyama Kyohei 東京大学, 生産技術研究所, 特任助教 (50738383)
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2017: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 準周期解 / リアプノフバンドル / リアプノフ指数 / 局所分岐 / 分岐解析 / 支配的リアプノフバンドル / 支配的リアプノフ指数 |
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| Outline of Final Research Achievements |
In this study, we developed Lyapunov bundle which is a classification tool for quasi-periodic bifurcations, and we found and classified many bifurcations. Then, we explained them by the simple discrete-time dynamical systems and the continuous time dynamical systems of the electric circuits.
With this approach, we succeeded in classifying the local bifurcations of quasi-periodic solutions into four types by the Lyapunov bundle topology before and after bifurcation: saddle-node, period-doubling, double covering, and Neimark-Sacker bifurcations.
Moreover, the bifurcation structure of the Arnold resonance web which is a complicated synchronization region of quasi-periodic solution in bifurcation diagram was clarified by Newton's method and topology analysis by Lyapunov bundle.
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