Devil's staircase route to chaos in a forced relaxation oscillator
Annales de l'Institut Fourier, Tome 44 (1994) no. 1, p. 109-128
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.
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]).
@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},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {44},
     number = {1},
     year = {1994},
     pages = {109-128},
     doi = {10.5802/aif.1391},
     zbl = {0793.34028},
     mrnumber = {95b:58098},
     language = {en},
     url = {http://www.numdam.org/item/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. http://www.numdam.org/item/AIF_1994__44_1_109_0/

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