Energy constraints in pulsed phase control of chaos
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; Università Vita-Salute San Raffaele, Via Olgettina 58, Milano, 20132, Italy; Dipartimento di Scienze della Terra, Università di Firenze, Via G. La Pira 4, Firenze, 50100, Italy; Università 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 controlDOI: 10.1016/j.physleta.2016.09.041Citations: 5data from “WEB OF SCIENCE” (of Thomson Reuters) are update at: 2019-09-15References taken from IsiWeb of Knowledge: (subscribers only)Connecting to view paper tab on IsiWeb: Click hereConnecting to view citations from IsiWeb: Click here