Clustering limit cycle oscillators by spectral analysis of the synchronisation matrix with an additional phase sensitive rotation

Abstract

Synchrony is a phenomenon present in many complex systems of coupled oscillators. It is often important to cluster those systems into subpopulations of oscillators, and characterise the interactions therein. This article derives the clustering information, based on an eigen-value decomposition of the complex synchronisation matrix. A phase sensitive post-rotation is proposed, to separate classes of oscillators with similar frequencies, but with no physical interaction. © Springer-Verlag Berlin Heidelberg 2007.