The autoresonance threshold into a system of weakly coupled oscillators

TL;DR

This paper studies how a weakly coupled oscillator system can be driven into resonance by an external periodic force, providing explicit formulas for the threshold amplitude needed for autoresonance through asymptotic analysis and simulations.

Contribution

It introduces an explicit formula for the autoresonance threshold in weakly coupled oscillators, combining asymptotic methods with numerical validation.

Findings

Explicit threshold formula derived for autoresonance

Asymptotic analysis matches numerical simulations

External forcing can induce resonance in weakly coupled oscillators

Abstract

We investigate a system of two weakly coupled oscillators. It is shown that an external periodic perturbation can lead to the capture into resonance. Asymptotic description and numerical simulations are presented. We have obtained the explicit formula for the threshold value for the amplitude of the perturbation that leads to the autoresonance.