Evolution of Arnold's Tongues in a Z2-Symmetric Electronic Circuit

Antonio ALGABA  Manuel MERINO  Alejandro J. RODRIGUEZ-LUIS  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E82-A   No.9   pp.1714-1721
Publication Date: 1999/09/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Nonlinear Theory and Its Applications)
Arnold's tongues,  oscillations,  bifurcation,  autonomous circuits,  

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In this paper we study the evolution of the resonance zones that appear in connection with a Hopf-pitchfork bifurcation exhibited by a Z2-symmetric electronic circuit. These regions, bounded by curves of folds (saddle-node bifurcations) may be closed or open depending on the values of the parameters. An angular degeneracy on the torus bifurcation curve originates the banana shape of Arnold's tongues. The presence of homoclinic bifurcations is also pointed out.