Clustering in Globally Coupled Oscillators Near a Hopf Bifurcation: Theory and Experiments

摘要

A theoretical analysis is presented to show the general occurrence of phaseclusters in weakly, globally coupled oscillators close to a Hopf bifurcation.Through a reductive perturbation method, we derive the amplitude equation witha higher order correction term valid near a Hopf bifurcation point. Thisamplitude equation allows us to calculate analytically the phase couplingfunction from given limit-cycle oscillator models. Moreover, using the phasecoupling function, the stability of phase clusters can be analyzed. Wedemonstrate our theory with the Brusselator model. Experiments are carried outto confirm the presence of phase clusters close to Hopf bifurcations withelectrochemical oscillators.