Energy-based theory of autoresonance in chains of coupled damped-driven generic oscillators

TL;DR

This paper develops an energy-based variational theory for autoresonance in coupled dissipative oscillators, analyzing the effects of time-delay and feedback, and confirming predictions through numerical experiments.

Contribution

It introduces a novel energy functional approach to analyze autoresonance in chains of coupled oscillators, including delayed and feedback effects, with analytical solutions and numerical validation.

Findings

Time-delayed feedback alters autoresonance behavior.

Analytical solutions for autoresonance in delayed Duffing-Ueda oscillators.

Numerical results confirm theoretical predictions.

Abstract

An energy-based theory of autoresonance in driven dissipative chains of coupled generic oscillators is discussed on the basis of a variational principle concerning the energy functional. The theory is applied to chains of delayed Duffing-Ueda oscillators and the equations that together govern the autoresonance forces and solutions are derived and solved analytically for generic values of parameters and initial conditions, including the case of quenched time-delay disorder. Remarkably, the presence of retarded potentials with time-delayed feedback drastically modify the autoresonance scenario preventing the growth of the energy oscillation over specific regions of the parameter space. Additionally, effective harmonic forces with a slowly varying frequency are derived from the exact autoresonant excitations and the effectiveness of the theory is demonstrated at suppressing the chaos induced by homogeneous periodic excitations in such oscillator chains. Numerical experiments confirmed all the theoretical predictions.