Cluster synchronization and isolated desynchronization in complex networks with symmetries

By L. Pecora, F. Sorrentino, A. Hagerstrom, Thomas E. Murphy, Rajarshi Roy. Nature Communications, 2013

561 citations recorded by the source corpus.

Synchronization is of central importance in power distribution, telecommunication, neuronal and biological networks. Many networks are observed to produce patterns of synchronized clusters, but it has been difficult to predict these clusters or understand the conditions under which they form. Here we present a new framework and develop techniques for the analysis of network dynamics that shows the connection between network symmetries and cluster formation. The connection between symmetries and cluster synchronization is experimentally confirmed in the context of real networks with heterogeneities and noise using an electro-optic network. We experimentally observe and theoretically predict a surprising phenomenon in which some clusters lose synchrony without disturbing the others. Our analysis shows that such behaviour will occur in a wide variety of networks and node dynamics. The results could guide the design of new power grid systems or lead to new understanding of the dynamical behaviour of networks ranging from neural to social. Many networks exhibit patterns of synchronized clusters, but the conditions under which this occurs are poorly understood. Pecora et al. develop an analytical approach based on computational group theory to predict the emergence and disappearance of synchrony among local clusters in complex networks.

Subfields: Cellular and Molecular Neuroscience, Computer Networks and Communications, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/265b802fa10a6a7f18f3e9e0240c20534313e2d6

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In Cellular and Molecular Neuroscience

M. A. Porter

In Computer Networks and Communications

In Statistical and Nonlinear Physics

Citations in the corpus

Random walks and diffusion on networks (2016, background): “s in a way that preserves the spectral properties of relevant matrices [411, 412], external equitable partitions [413], and using computational group theory to nd \hidden" symmetries in networks [414]. More generally, RWs are at the heart of ow-based algorithms, and they have been exploited to ”
Networks beyond pairwise interactions: structure and dynamics (2020, background): “[363] Louis M Pecora, Francesco Sorrentino, Aaron M Hagerstrom, Thomas E Murphy, and Rajarshi Roy.”