title: Cluster synchronization and isolated desynchronization in complex networks with symmetries.
abstract: 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.
authors.affiliation: US Naval Research Laboratory, Department of Material Science and Technology, Washington, District of Columbia 20375, USA.
authors.forename: Louis M
authors.initials: LM
authors.lastname: Pecora
authors.affiliation: Department of Mechanical Engineering, University of New Mexico, Albuquerque, New Mexico 87131, USA.
authors.forename: Francesco
authors.initials: F
authors.lastname: Sorrentino
authors.affiliation: 1] Department of Physics, University of Maryland, College Park, Maryland 20742, USA [2] Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland 20742, USA.
authors.forename: Aaron M
authors.initials: AM
authors.lastname: Hagerstrom
authors.affiliation: 1] Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland 20742, USA [2] Department of Electrical and Computer Engineering, University of Maryland, College Park, Maryland 20742, USA.
authors.forename: Thomas E
authors.initials: TE
authors.lastname: Murphy
authors.affiliation: 1] Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland 20742, USA [2] Department of Physics, University of Maryland, College Park, Maryland 20742, USA [3] Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA.
authors.forename: Rajarshi
authors.initials: R
authors.lastname: Roy