Identification of minimal parameters for optimal suppression of chaos in dissipative driven systems
Authors: Martinez PJ., Euzzor S., Gallas JAC., Meucci R., Charon R.
Autors Affiliation: [Martinez, Pedro J.] Univ Zaragoza, EINA, Dept Fis Aplicada, E-50018 Zaragoza, Spain and Univ Zaragoza, CSIC, Inst Ciencia Mat Aragon, E-50009 Zaragoza, Spain.
[Euzzor, Stefano; Meucci, Riccardo] CNR, Ist Nazl Ott, Largo E Fermi 6, Florence, Italy.
[Gallas, Jason A. C.] Univ Fed Paraiba, Dept Fis, BR-58051970 Joao Pessoa, Paraiba, Brazil.
[Chacon, Ricardo] Univ Extremadura, EII, Dept Fis Aplicada, Apartado Postal 382, E-06006 Badajoz, Spain and Univ Extremadura, Inst Comp Cient Avanzada ICCAEx, E-06006 Badajoz, Spain.
Abstract: Taming chaos arising from dissipative non-autonomous nonlinear systems by applying additional harmonic excitations is a reliable and widely used procedure nowadays. But the suppressory effectiveness of generic non-harmonic periodic excitations continues to be a significant challenge both to our theoretical understanding and in practical applications. Here we show how the effectiveness of generic suppressory excitations is optimally enhanced when the impulse transmitted by them (time integral over two consecutive zeros) is judiciously controlled in a not obvious way. Specifically, the effective amplitude of the suppressory excitation is minimal when the impulse transmitted is maximum. Also, by lowering the impulse transmitted one obtains larger regularization areas in the initial phase difference-amplitude control plane, the price to be paid being the requirement of larger amplitudes. These two remarkable features, which constitute our definition of optimum control, are demonstrated experimentally by means of an analog version of a paradigmatic model, and confirmed numerically by simulations of such a damped driven system including the presence of noise. Our theoretical analysis shows that the controlling effect of varying the impulse is due to a subsequent variation of the energy transmitted by the suppressory excitation.
Journal/Review: SCIENTIFIC REPORTS
Volume: 7 Pages from: 17988-1 to: 17988-7
KeyWords: Article; Case report; Clinical article; Controlled study; Excitation; Human; Noise; SimulationDOI: 10.1038/s41598-017-17969-9Citations: 1data from “WEB OF SCIENCE” (of Thomson Reuters) are update at: 2019-09-15References taken from IsiWeb of Knowledge: (subscribers only)