Resonating Delay Equation

TL;DR

This paper introduces a delay differential equation that demonstrates a novel resonant oscillatory behavior, where oscillations appear and vanish with increasing delay, highlighting a unique dynamical phenomenon distinct from typical delay effects.

Contribution

The study presents a new delay differential equation model exhibiting resonant oscillations that are optimally enhanced at specific delays, contrasting with conventional delay-induced dynamics.

Findings

Oscillatory dynamics appear and disappear with delay changes.

Optimal power spectrum height occurs at a specific delay.

Resonant behavior differs from typical delay effects.

Abstract

We propose here a delay differential equation that exhibits a new type of resonating oscillatory dynamics. The oscillatory transient dynamics appear and disappear as the delay is increased between zero to asymptotically large delay. The optimal height of the power spectrum of the dynamical trajectory is observed with the suitably tuned delay. This resonant behavior contrasts itself against the general behaviors where an increase of delay parameter leads to the persistence of oscillations or more complex dynamics.