Complicated quasiperiodic oscillations and chaos from driven piecewise-constant circuit: Chenciner bubbles do not necessarily occur via simple phase-locking

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書誌事項

公開日
2017-02
資源種別
journal article
権利情報
  • https://www.elsevier.com/tdm/userlicense/1.0/
DOI
  • 10.1016/j.physd.2016.09.008
公開者
Elsevier BV

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説明

Abstract 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.

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