Impulse-induced optimum control of chaos in dissipative driven systems

TL;DR

This paper demonstrates that controlling the impulse of generic periodic excitations can optimally suppress chaos in dissipative driven systems, supported by experiments, simulations, and theoretical analysis.

Contribution

It introduces a novel approach of impulse control to enhance chaos suppression effectiveness in nonlinear systems.

Findings

Impulse control effectively suppresses chaos.

Experimental and numerical results confirm the approach.

Theoretical analysis links impulse variation to energy transmission.

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. This is demonstrated experimentally by means of an analog version of a universal 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 correlative variation of the energy transmitted by the suppressory excitation.