Arnol'd resonance webs and Chenciner bubbles from a three-dimensional piecewise-constant hysteresis oscillator

Tri Quoc Truong, Tadashi Tsubone, Munehisa Sekikawa, Naohiko Inaba, Tetsuro Endo

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1 Citation (Scopus)

Abstract

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.

Original languageEnglish
Article number053A04
JournalProgress of Theoretical and Experimental Physics
Volume2017
Issue number5
DOIs
Publication statusPublished - 1 May 2017

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