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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]).
On démontre grâce à l’usage de la dynamique symbolique en dimension un que la transition vers le chaos dans un oscillateur non-linéaire de relaxation avec terme de contrainte périodique se produit à travers un “Devil Staircase” dans le diagramme de bifurcation.
@article{AIF_1994__44_1_109_0,
author = {Alsed\`a, Lluis and Falc\'o, Antonio},
title = {Devil's staircase route to chaos in a forced relaxation oscillator},
journal = {Annales de l'Institut Fourier},
pages = {109--128},
publisher = {Institut Fourier},
address = {Grenoble},
volume = {44},
number = {1},
year = {1994},
doi = {10.5802/aif.1391},
mrnumber = {95b:58098},
zbl = {0793.34028},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.5802/aif.1391/}
}
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 SP - 109 EP - 128 VL - 44 IS - 1 PB - Institut Fourier PP - Grenoble UR - http://geodesic.mathdoc.fr/articles/10.5802/aif.1391/ DO - 10.5802/aif.1391 LA - en ID - AIF_1994__44_1_109_0 ER -
%0 Journal Article %A Alsedà, Lluis %A Falcó, Antonio %T Devil's staircase route to chaos in a forced relaxation oscillator %J Annales de l'Institut Fourier %D 1994 %P 109-128 %V 44 %N 1 %I Institut Fourier %C Grenoble %U http://geodesic.mathdoc.fr/articles/10.5802/aif.1391/ %R 10.5802/aif.1391 %G en %F AIF_1994__44_1_109_0
Alsedà, Lluis; Falcó, Antonio. Devil's staircase route to chaos in a forced relaxation oscillator. Annales de l'Institut Fourier, Tome 44 (1994) no. 1, pp. 109-128. doi: 10.5802/aif.1391
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