Optimal Phase-Control Strategy for Damped-Driven Duffing Oscillators

Year: 2016

Authors: Meucci R., Euzzor S., Pugliese E., Zambrano S., Gallas M.R., Gallas J.A.C.

Autors Affiliation: Istituto Nazionale di Ottica, Consiglio Nazionale delle Ricerche, Largo E. Fermi 6, Firenze, Italy;
Departamento de Física, Universidade Federal da Paraíba, 58051-970 João Pessoa, Brazil;
Instituto de Altos Estudos da Paraíba, Rua Infante Dom Henrique 100-1801, 58039-150 João Pessoa, Brazil;
Dipartimento di Scienze della Terra, Università degli Studi di Firenze, Via G. La Pira 4, Firenze, Italy;
Università Vita–Salute San Raffaele, Via Olgettina 58, 20132 Milano, Italy

Abstract: Phase-control techniques of chaos aim to extract periodic behaviors from chaotic systems by applying weak harmonic perturbations with a suitably chosen phase. However, little is known about the best strategy for selecting adequate perturbations to reach desired states. Here we use experimental measures and numerical simulations to assess the benefits of controlling individually the three terms of a Duffing oscillator. Using a real-time analog indicator able to discriminate on-the-fly periodic behaviors from chaos, we reconstruct experimentally the phase versus perturbation strength stability areas when periodic perturbations are applied to different terms governing the oscillator. We verify the system to be more sensitive to perturbations applied to the quadratic term of the double-well Duffing oscillator and to the quartic term of the single-well Duffing oscillator.


Volume: 116 (4)      Pages from: 044101-1  to: 044101-5

More Information: We thank Professor F. T. Arecchi for many helpful discussions. S. Z. thanks the Intra-European Fellowships for career development, Grant No. 2011-298447NonLinKB. M. R. G. and J. A. C. G. thank CNPq, Brazil for support. Bitmaps were computed at the CESUP-UFRGS clusters.
KeyWords: Chaotic systems; Phase control, Double well; Duffing oscillator; Harmonic perturbations; On the flies; Periodic behavior; Periodic perturbation; Perturbation strength; Quartic terms, Oscillators (mechanical)
DOI: 10.1103/PhysRevLett.116.044101

Citations: 27
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