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Clustering and Synchronization of Oscillator Networks

Patrick N. McGraw·Michael Menzinger
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Abstract

Using a recently described technique for manipulating the clustering coefficient of a network without changing its degree distribution, we examine the effect of clustering on the synchronization of phase oscillators on networks with Poisson and scale-free degree distributions. For both types of network, increased clustering hinders global synchronization as the network splits into dynamical clusters that oscillate at different frequencies. Surprisingly, in scale-free networks, clustering promotes the synchronization of the most connected nodes (hubs) even though it inhibits global synchronization. As a result, scale-free networks show an additional, advanced transition instead of a single synchronization threshold. This cluster-enhanced synchronization of hubs may be relevant to the brain with its scale-free and highly clustered structure.

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Patrick N. McGraw, Michael Menzinger. 2005-06-09. Clustering and Synchronization of Oscillator Networks. https://doi.org/10.1103/physreve.72.015101

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