Energy constraints in pulsed phase control of chaos

Year: 2017

Authors: Meucci R., Euzzor S., Zambrano S., Pugliese E., Francini F., Arecchi F.T.

Autors Affiliation: Istituto Nazionale di Ottica, Consiglio Nazionale delle Ricerche, Largo E. Fermi 6, Firenze, 50125, Italy; Universitą Vita-Salute San Raffaele, Via Olgettina 58, Milano, 20132, Italy; Dipartimento di Scienze della Terra, Universitą di Firenze, Via G. La Pira 4, Firenze, 50100, Italy; Universitą di Firenze, Firenze, Italy

Abstract: Phase control of chaos is a powerful technique but little is known about its physical constraints, relevant for real systems. As a fact, it has not been explored whether this technique can also be applied when the controlling perturbation is not harmonic. Here we apply phase control on a driven double well Duffing oscillator using periodic rectangular pulsed perturbations instead of the classical sinusoidal perturbations. Experimental measurements and numerical simulations show that this kind of perturbation is also able to stabilize the chaotic orbits for an adequate selection of the phase. Furthermore, as the duty cycle of the perturbation (that is, the fraction of the time that the periodically pulsed control is active) is increased, two separate regimes occur. In the first one, the perturbations leading to stabilization of periodic solutions are of constant energy (taken as the product of the duty cycle and the amplitude) and in the second one, a saturation phenomenon occurs, implying that increasing energy values of the perturbations are wasted. Our results unveil the versatility of the pulsed phase control scheme and the importance of energy constraints.

Journal/Review: PHYSICS LETTERS A

Volume: 381 (2)      Pages from: 82  to: 86

KeyWords: Chaos control; Duffing oscillator; Phase control
DOI: 10.1016/j.physleta.2016.09.041

Citations: 7
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