Delay-Induced Resonance in the Time-Delayed Duffing Oscillator

TL;DR

This paper investigates delay-induced resonance in the Duffing oscillator, revealing how time-delay can enhance oscillations and introduce a conjugate phenomenon where delay-driven oscillations are amplified by forcing.

Contribution

It explores new features of delay-induced resonance in both overdamped and underdamped Duffing oscillators, including a conjugate phenomenon and alternative resonance mechanisms.

Findings

Delay can enhance oscillations caused by external forcing.

A conjugate phenomenon where delay-induced oscillations are amplified without changing frequency.

Resonance can occur even without sustained oscillations induced by delay.

Abstract

The phenomenon of delay-induced resonance implies that in a nonlinear system a time-delay term may be used as an effective enhancer of the oscillations caused by an external forcing maintaining the same frequency. This is possible for the parameters for which the time-delay induces sustained oscillations. Here, we study this type of resonance in the overdamped and underdamped time-delayed Duffing oscillators, and we explore some new features. One of them is the conjugate phenomenon: the oscillations caused by the time-delay may be enhanced by means of the forcing without modifying their frequency. The resonance takes place when the frequency of the oscillations induced by the time-delay matches the ones caused by the forcing and vice versa. This is an interesting result as the nature of both perturbations is different. Even for the parameters for which the time-delay does not induce sustained oscillations, we show that a resonance may appear following a different mechanism.