### 抜粋

In this study, we analyze quasiperiodic oscillations generated by a three-coupled autonomous piecewise-constant hysteresis oscillator. These oscillations generate three-dimensional tori and Arnol'd resonance webs in which two-dimensional tori-partial-entrainment regions extend in a number of directions in a manner similar to webs in three-dimensional tori-generating regions. Detailed Lyapunov analysis clearly shows that hysteresis phenomena significantly Erode Chenciner bubbles. This phenomenon is significant because full-mode entrainment regions do not occur as a result of simple phase-locking of two-dimensional tori. To clarify the mechanism underlying the hysteresis phenomenon observed in electric circuits, we analyze a two-coupled delayed logistic map as one of the simplest discrete dynamics that generate Arnol'd resonance webs and confirm the generation of hysteresis around Chenciner bubbles in a manner similar to that in an autonomous oscillator. By analyzing the Chenciner bubbles produced under these discrete dynamics, we partially explain hysteresis as a result of subcritical Neimark-Sacker bifurcations.

元の言語 | English |
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記事番号 | 053A04 |

ジャーナル | Progress of Theoretical and Experimental Physics |

巻 | 2017 |

発行部数 | 5 |

DOI | |

出版物ステータス | Published - 1 5 2017 |

## フィンガープリント Arnol'd resonance webs and Chenciner bubbles from a three-dimensional piecewise-constant hysteresis oscillator' の研究トピックを掘り下げます。これらはともに一意のフィンガープリントを構成します。

## これを引用

*Progress of Theoretical and Experimental Physics*,

*2017*(5), [053A04]. https://doi.org/10.1093/ptep/ptx058