Bifurcation Analysis of Quasi-Periodic Solution and Its Application for Electronic Circuit

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K21424
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Communication/Network engineering; Control engineering/System engineering
• Research Institution: The University of Tokyo (2016-2017); Meiji University (2015)
• Principal Investigator: Kamiyama Kyohei 東京大学, 生産技術研究所, 特任助教 (50738383)
• Project Period (FY): 2015-04-01 – 2018-03-31
• 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

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.

Free Research Field

電気電子工学