Suppression of chaos by incommensurate excitations: Theory and experimental confirmations

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.