Devil's staircase route to chaos in a forced relaxation oscillator

Lluis Alsedà; Antonio Falcó

Annales de l'institut Fourier (1994)

  • Volume: 44, Issue: 1, page 109-128
  • ISSN: 0373-0956

Abstract

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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 parameter 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 Kennedy, Krieg and Chua (in [10]) related with the appearance of secondary staircases intercalated into the primary staircases which were found by van der Pol and van der Mark (in [17]).

How to cite

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Alsedà, Lluis, and Falcó, Antonio. "Devil's staircase route to chaos in a forced relaxation oscillator." Annales de l'institut Fourier 44.1 (1994): 109-128. <http://eudml.org/doc/75051>.

@article{Alsedà1994,
abstract = {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 parameter 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 Kennedy, Krieg and Chua (in [10]) related with the appearance of secondary staircases intercalated into the primary staircases which were found by van der Pol and van der Mark (in [17]).},
author = {Alsedà, Lluis, Falcó, Antonio},
journal = {Annales de l'institut Fourier},
keywords = {Devil's staircase route to chaos; relaxation oscillator of the Van der Pol type; symbolic dynamics},
language = {eng},
number = {1},
pages = {109-128},
publisher = {Association des Annales de l'Institut Fourier},
title = {Devil's staircase route to chaos in a forced relaxation oscillator},
url = {http://eudml.org/doc/75051},
volume = {44},
year = {1994},
}

TY - JOUR
AU - Alsedà, Lluis
AU - Falcó, Antonio
TI - Devil's staircase route to chaos in a forced relaxation oscillator
JO - Annales de l'institut Fourier
PY - 1994
PB - Association des Annales de l'Institut Fourier
VL - 44
IS - 1
SP - 109
EP - 128
AB - 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 parameter 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 Kennedy, Krieg and Chua (in [10]) related with the appearance of secondary staircases intercalated into the primary staircases which were found by van der Pol and van der Mark (in [17]).
LA - eng
KW - Devil's staircase route to chaos; relaxation oscillator of the Van der Pol type; symbolic dynamics
UR - http://eudml.org/doc/75051
ER -

References

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