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Clustering in globally coupled oscillators near a Hopf bifurcation: theory and experiments
Hiroshi Kori1, Yoshiki Kuramoto2, Swati Jain3
1Department of Information Sciences, Ochanomizu University, Tokyo 112-8610, Japan and CREST, Japan Science and Technology Agency, Kawaguchi 332-0012, Japan.
Abstract:
A theoretical analysis is presented to show the general occurrence of phase clusters in weakly, globally coupled oscillators close to a Hopf bifurcation. Through a reductive perturbation method, we derive the amplitude equation with a higher-order correction term valid near a Hopf bifurcation point. This amplitude equation allows us to calculate analytically the phase coupling function from given limit-cycle oscillator models. Moreover, using the phase coupling function, the stability of phase clusters can be analyzed. We demonstrate our theory with the Brusselator model. Experiments are carried out to confirm the presence of phase clusters close to Hopf bifurcations with electrochemical oscillators.
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