Synchronization and clustering of phase oscillators with heterogeneous couplingG. H. Paissan and D. H. Zanette
Consejo Nacional de Investigaciones Científicas y Técnicas, Centro Atómico Bariloche and Instituto Balseiro 8400 Bariloche, Río Negro, Argentina
received 13 September 2006; accepted in final form 14 November 2006; published January 2007
published online 8 January 2007
We generalize Kuramoto's theory for the synchronization transition of globally coupled phase oscillators to populations where each oscillator has a different coupling strength. We show that, beyond the transition, even those oscillators with very small couplings may participate in the synchronized ensemble, provided that their natural frequencies are close enough to the synchronization frequency. In finite systems, numerical realizations reveal that the transition is preceded by a regime of clustering where the population splits into internally synchronized groups of various sizes. The appearance of these clusters may be qualitatively understood in terms of fluctuations in the distribution of natural frequencies.
05.45.Xt - Synchronization; coupled oscillators .
89.75.Fb - Structures and organization in complex systems .
05.70.Fh - Phase transitions: general studies .
© Europhysics Letters Association 2007