Resonance Clustering in Globally Coupled Electrochemical Oscillators with External Forcing

TL;DR

This paper investigates how globally coupled electrochemical oscillators under external forcing form resonance clusters with discretized frequencies following a specific resonance rule, revealing the role of coupling strength in cluster formation.

Contribution

It demonstrates the emergence of resonance clustering in electrochemical oscillators due to the interaction of mutual and forced entrainment, highlighting the importance of optimal coupling strength.

Findings

Resonance clusters follow a specific frequency discretization rule.

Optimal intermediate coupling strength is necessary for resonance clustering.

Strong coupling leads to collective behavior similar to a single oscillator.

Abstract

Experiments are carried out with a globally coupled, externally forced population of limit-cycle electrochemical oscillators with an approximately unimodal distribution of heterogeneities. Global coupling induces mutually entrained (at frequency $\omega_{1}$) states; periodic forcing produces forced-entrained ($\omega_{\mathrm{F}}$) states. As a result of the interaction of mutual and forced entrainment, resonant cluster states occur with equal spacing of frequencies that have discretized frequencies following a resonance rule $\omega_{n}\cong n\omega_{1}-(n-1)\omega_{\mathrm{F}}$. Resonance clustering requires an optimal, intermediate global coupling strength; at weak coupling the clusters have smaller sizes and do not strictly follow the resonance rule, while at strong coupling the population behaves similar to a single, giant oscillator.