Devil's staircase route to chaos in a forced relaxation oscillator
type: Item
instance of: scholarly article
title: Devil's staircase route to chaos in a forced relaxation oscillator
zbMATH Open document ID: 0793.34028
author: Lluís Alsedà
author: Antonio Falcó
publication date: 1994-06-16T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/75051
review text: We use one-dimensional techniques to characterize the Devil's staircase route to chaos in a relaxation oscillator of the Van der Pol type with periodic forcing term. In particular, by using symbolic dynamics, we give the behaviour for certain range of parameters values of a Cantor set of solutions having a certain rotation set associated to a rational number. Finally, we explain the phenomena observed experimentally in the system by \textit{M. P. Kennedy}, \textit{K. R. Krieg} and \textit{L. O. Chua} [IEEE Trans. Circuits Syst. 36, 1133-1139 (1989)] related with the appearance of secondary staircases intercalated into the primary staircases which were found by \textit{B. Van der Pol} and \textit{J. Van der Mark} [Nature 120 (1927)].
Mathematics Subject Classification ID: 37-XX
Mathematics Subject Classification ID: 34C15
Mathematics Subject Classification ID: 54H20
zbMATH DE Number: 566966
zbMATH Keywords: Devil's staircase route to chaos
zbMATH Keywords: relaxation oscillator of the Van der Pol type
zbMATH Keywords: symbolic dynamics
MaRDI profile type: Publication
OpenAlex ID: W2333379342
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DOI: 10.5802/AIF.1391
published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 566966