NSC Seminar Effects of nonisochronicity and heterogeneity in systems of phase synchronized oscillators

2008-04-25 15:00 - 2008-04-25 16:30
Ralf Toenjes
Recent years have seen a growing interest in the analysis of theKuramoto model in spatially extended and heterogeneous systems ofcoupled phase oscillators. In general, autonomous oscillators arenot isochronous with respect to perturbations of their amplitude.The nonlinear effect of nonisochronicity translates to phase equationsas a break in the symmetry of the phase coupling function in discretesystems or as a nonlinearty in the Kuramoto phase diffusion equations.This break in the coupling symmetry has an ordering effect onthe system which can strengthen the influence of fasteroscillators over slower ones. For sufficiently weak heterogeneity,attractively coupled phase oscillators synchronize. The relative phasesbecome stationary and quasi-regular concentric waves form arounda self-organized pacemaker center. By means of an approximation anda nonlinear transformation it is possible to analyze the synchronizedstate as an eigenvalue problem. By perturbation methods we derivedispersion relations between nonisochronicity, heterogeneity in form offrequency variance and the synchronization frequency. Finally we showthat the location of the pace maker region can change fundamentallyat critical parameter values.