Resonance Clustering in Globally Coupled Electrochemical Oscillators with External Forcing

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.