Emission of autoresonant trajectories and thresholds of resonant pumping

TL;DR

This paper investigates the conditions under which nonlinear oscillators exhibit autoresonant behavior, deriving formulas for resonance thresholds and analyzing capture and emission dynamics.

Contribution

It provides new formulas for autoresonance thresholds and studies the capture and emission phenomena in nonlinear oscillators under slowly varying external parameters.

Findings

Formulas for autoresonant threshold values of amplitude and frequency.

Analysis of capture into and emission out of resonance.

Quantitative measure of autoresonant asymptotic behavior.

Abstract

We study an autoresonant asymptotic behaviour for nonlinear oscillators under slowly changing frequency and amplitude of external driver. As a result we obtain formulas for threshold values of amplitude and frequency of the driver when autoresonant behaviour for the nonlinear oscillator is observed. Also we study a capture into resonance and emission out of the resonance for trajectories of the oscillator. A measure of autoresonant asymptotic behaviours for nonlinear oscillator is obtained.