title: Clustering in globally coupled oscillators near a Hopf bifurcation: theory and experiments.
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.
authors.affiliation: Department of Information Sciences, Ochanomizu University, Tokyo 112-8610, Japan and CREST, Japan Science and Technology Agency, Kawaguchi 332-0012, Japan.
authors.forename: Hiroshi
authors.initials: H
authors.lastname: Kori
authors.affiliation: International Institute for Advanced Studies, Kyoto 619-0225, Japan.
authors.forename: Yoshiki
authors.initials: Y
authors.lastname: Kuramoto
authors.affiliation: Department of Chemical Engineering, University of Virginia, Charlottesville, Virginia 22904, USA.
authors.forename: Swati
authors.initials: S
authors.lastname: Jain
authors.affiliation: Department of Chemistry, Saint Louis University, St. Louis, Missouri 63103, USA.
authors.forename: István Z
authors.initials: IZ
authors.lastname: Kiss
authors.affiliation: Department of Chemical Engineering, University of Virginia, Charlottesville, Virginia 22904, USA.
authors.forename: John L
authors.initials: JL
authors.lastname: Hudson
mesh_terms: D016000:Cluster Analysis; D008962:Models, Theoretical; D017711:Nonlinear Dynamics; D010507:Periodicity