Suppression of chaos by incommensurate excitations: Theory and experimental confirmations

Year: 2020

Authors: Martinez P.J., Euzzor S., Meucci R., Chacon R.

Autors Affiliation: Univ Zaragoza, Dept Fis Aplicada, EINA, E-50018 Zaragoza, Spain; CNR, Ist Nazl Ott, Largo E Fermi 6, Florence, Italy;‎ Univ Extremadura, Dept Fis Aplicada, EII, Apartado Postal 382, E-06006 Badajoz, Spain; Univ Zaragoza, Inst Ciencia Mat Aragon, CSIC, E-50009 Zaragoza, Spain;‎ Univ Extremadura, Inst Comp Cient Avanzada ICCAEx, E-06006 Badajoz, Spain

Abstract: We experimentally, numerically, and theoretically characterize the effectiveness of incommensurate excitations at suppressing chaos in damped driven systems. Specifically, we consider an inertial Brownian particle moving in a prototypical two-well potential and subjected to a primary (chaos-inducing) harmonic excitation and a suppressory incommensurategeneric (non-harmonic) excitation. We show that the effective amplitude of the suppressory excitation is minimal when the impulse transmitted by it is near its maximum, while its value is rather insensitive to higher-order convergents of the irrational ratio between the involved driving periods. Remarkably, the number and values of the effective initial phase difference between the two excitations are independent of the impulse while they critically depend on each particular convergent in a complex way involving both the approximate frustration of chaos-inducing homoclinic bifurcations and the maximum survival of relevant spatio-temporal symmetries of the dynamical equation. (C) 2019 Published by Elsevier B.V.

Journal/Review: COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION

Volume: 83      Pages from: 105137-1  to: 105137-16

KeyWords: Chaos control in a prototypical nolinear oscillator via Incommensurate drivings; Experimental; Theoretical and numerical study
DOI: 10.1016/j.cnsns.2019.105137

Citations: 6
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