Numerical and experimental exploration of phase control of chaos

Year: 2006

Authors: Zambrano S., Allaria E., Brugioni S., Leyva I., Meucci R., Sanjuan M.A.F., Arecchi F.T.

Autors Affiliation: Nonlinear Dynamics and Chaos Group, Departamento de Mathematicas y Fisica Aplicadas y Ciencias de la Naturaleza, Universidad Rey Juan Carlos, Tulipan, s/n, 28933 Mostoles, Madrid, Spain; CNR – Istituto Nazionale di Ottica Applicata, Largo E. Fermi 6, 50125 Firenze, Italy; Department of Physics, Università di Firenze, Firenze, Italy

Abstract: A well-known method to suppress chaos in a periodically forced chaotic system is to add a harmonic perturbation. The phase control of chaos scheme uses the phase difference between a small added harmonic perturbation and the main driving to suppress chaos, leading the system to different periodic orbits. Using the Duffing oscillator as a paradigm, we present here an in-depth study of this technique. A thorough numerical exploration has been made focused in the important role played by the phase, from which new interesting patterns in parameter space have appeared. On the other hand, our novel experimental implementation of phase control in an electronic circuit confirms both the well-known features of this method and the new ones detected numerically. All this may help in future implementations of phase control of chaos, which is globally confirmed here to be robust and easy to implement experimentally. (C) 2006 American Institute of Physics.

Journal/Review: CHAOS

Volume: 16 (1)      Pages from: 013111-1  to: 013111-9

More Information: This work has been supported by the Spanish Ministry of Science and Technology under Project No. BFM2003-03081 and by the Universidad Rey Juan Carlos under Project No. PPR-2004-28. E.A. was supported by FIRB Contract No. RBAU01B49F_002. Partial support from Azione Integrata Italia Spagna IT1348 and Acción Integrada Hispano-italiana HI03-207 is also acknowledged.
KeyWords: Resonant parametric perturbations; Weak harmonc perturbations; Suppression
DOI: 10.1063/1.2161437

Citations: 27
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