Autoresonance in a Dissipative System
Sergei Glebov, Oleg Kiselev, Nikolai Tarkhanov
TL;DR
This paper investigates the autoresonant behavior of a dissipative Duffing oscillator, proving its stability as an attracting set and analyzing amplitude limits and transition times through analytical and numerical methods.
Contribution
It provides a rigorous proof of autoresonance as an attracting solution in a dissipative system and quantifies key dynamical parameters.
Findings
Autoresonant solution is an attracting set.
Maximum amplitude of autoresonance is evaluated.
Transition time from growth to fast oscillations is determined.
Abstract
We study the autoresonant solution of Duffing's equation in the presence of dissipation. This solution is proved to be an attracting set. We evaluate the maximal amplitude of the autoresonant solution and the time of transition from autoresonant growth of the amplitude to the mode of fast oscillations. Analytical results are illustrated by numerical simulations.
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