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

1994; Association of the Annals of the Fourier Institute; Volume: 44; Issue: 1 Linguagem: Inglês

10.5802/aif.1391

1777-5310

Lluı́s Alsedà, Antonio Falcó,

Advanced Thermodynamics and Statistical Mechanics

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]).