Eur. Phys. J. B 43, 243-250 (2005)
https://doi.org/10.1140/epjb/e2005-00046-2

Frequency clustering of coupled phase oscillators on small-world networks

¹ Abdus Salam International Center for Theoretical Physics, P.O. Box 586, 34100 Trieste, Italy
² Consejo Nacional de Investigaciones Científicas y Técnicas, Centro Atómico Bariloche and Instituto Balseiro, 8400 Bariloche, Argentina

Corresponding author: ^a morelli@mpipks-dresden.mpg.de

Received: 9 July 2004
Revised: 10 December 2004
Published online: 25 February 2005

Abstract

We analyze the phenomenon of frequency clustering in a system of coupled phase oscillators. The oscillators, which in the absence of coupling have uniformly distributed natural frequencies, are coupled through a small-world network, built according to the Watts-Strogatz model. We study the time evolution and determine variations in the transient times depending on the disorder of the network and on the coupling strength. We investigate the effects of fluctuations in the average frequencies, and discuss the definition of the threshold for synchronization. We characterize the structure of clusters and the distribution of cluster sizes in the synchronization transition, and define suitable order parameters to describe the aggregation of the oscillators as the network disorder and the coupling strength change. The non-monotonic behavior observed in some order parameters is related to fluctuations in the mean frequencies.