Delay-induced resonance suppresses damping-induced unpredictability

TL;DR

This paper investigates how delay-induced resonance can counteract damping effects in a time-delayed Duffing oscillator, restoring oscillations suppressed by dissipation through specific forcing parameters.

Contribution

It introduces the concept of delay-induced resonance as a mechanism to suppress damping-induced unpredictability in a time-delayed nonlinear oscillator.

Findings

Delay-induced resonance can restore interwell oscillations.

Minimal forcing amplitude and frequency are identified for different delays.

Delay replaces vibrational forcing to control dissipation effects.

Abstract

Combined effects of the damping and forcing in the underdamped time-delayed Duffing oscillator are considered in this paper. We analyze the generation of a certain damping-induced unpredictability, due to the gradual suppression of interwell oscillations. We find the minimal amount of the forcing amplitude and the right forcing frequency to revert the effect of the dissipation, so that the interwell oscillations can be restored, for different time delay values. This is achieved by using the delay-induced resonance, in which the time delay replaces one of the two periodic forcings present in the vibrational resonance. A discussion in terms of the time delay of the critical values of the forcing for which the delay-induced resonance can tame the dissipation effect is finally carried out.