Echo Phenomena in Large Systems of Coupled Oscillators

TL;DR

This paper investigates echo phenomena in large coupled oscillator systems like the Kuramoto model, revealing how successive stimuli can induce predictable response pulses below the phase coherence transition.

Contribution

It demonstrates the existence of echo phenomena in large oscillator systems below the critical coupling, providing theoretical analysis and numerical validation.

Findings

Echoes occur at multiples of the stimulus interval

Echo phenomena appear below the phase transition point

Numerical experiments confirm theoretical predictions

Abstract

As exemplified by the Kuramoto model, large systems of coupled oscillators may undergo a transition to phase coherence with increasing coupling strength. It is shown that below the critical coupling strength for this transition such systems may be expected to exhibit `echo' phenomena: a stimulation by two successive pulses separated by a time interval tau leads to the spontaneous formation of response pulses at a time tau, 2 tau, 3 tau ..., after the second stimulus pulse. Analysis of this phenomenon, as well as illustrative numerical experiments, are presented. The theoretical significance and potential uses of echoes in such systems are discussed.