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Phys Rev Lett. 2010 Dec 17;105(25):254101. Epub 2010 Dec 13.

Synchronizing distant nodes: a universal classification of networks.

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  • 1Institut für Theoretische Physik, TU Berlin, Hardenbergstrasse 36, 10623 Berlin, Germany.


Stability of synchronization in delay-coupled networks of identical units generally depends in a complicated way on the coupling topology. We show that for large coupling delays synchronizability relates in a simple way to the spectral properties of the network topology. The master stability function used to determine the stability of synchronous solutions has a universal structure in the limit of large delay: It is rotationally symmetric around the origin and increases monotonically with the radius in the complex plane. This allows a universal classification of networks with respect to their synchronization properties and solves the problem of complete synchronization in networks with strongly delayed coupling.

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