2017年2月
Complicated quasiperiodic oscillations and chaos from driven piecewise-constant circuit: Chenciner bubbles do not necessarily occur via simple phase-locking
PHYSICA D-NONLINEAR PHENOMENA
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- ,
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- 巻
- 341
- 号
- 0
- 開始ページ
- 1
- 終了ページ
- 9
- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.1016/j.physd.2016.09.008
- 出版者・発行元
- ELSEVIER SCIENCE BV
We analyze the complex quasiperiodic oscillations and chaos generated by two coupled piecewise-constant hysteresis oscillators driven by a rectangular wave force. Oscillations generate Arnol'd resonance webs wherein lower dimensional resonance tongues extend such as that of a web in numerous directions. We provide the fundamental tools for bifurcation analysis of nonautonomous piecewise-constant oscillators. To optimize the outstanding simplicity of piecewise-constant circuits, we formulate a generalized procedure for calculating the Lyapunov exponents in nonautonomous piecewise-constant dynamics. The Lyapunov exponents in these dynamics can be calculated with a precision approximately similar to that of maps. We observe two-parameter Lyapunov diagrams near the fundamental resonance region called Chenciner bubbles, wherein the oscillation frequencies of the two oscillators and the force are synchronized with a ratio of 1:1:1. Inevitably, the hysteresis considerably distorts the Chenciner bubbles. This result suggests that the Chenciner bubbles do not necessarily occur due to simple phase locking of two-dimensional tori that can be explained by homeomorphism on the circle. Furthermore, we observe the Farey sequence in the experimental measurements. (C) 2016 Elsevier B.V. All rights reserved.
- リンク情報
- ID情報
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- DOI : 10.1016/j.physd.2016.09.008
- ISSN : 0167-2789
- eISSN : 1872-8022
- Web of Science ID : WOS:000392899800001