title: Synchronizing distant nodes: a universal classification of networks.
abstract: 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.
authors.affiliation: Institut für Theoretische Physik, TU Berlin, Hardenbergstrasse 36, 10623 Berlin, Germany. schoell@physik.tu-berlin.de
authors.forename: V
authors.initials: V
authors.lastname: Flunkert
authors.forename: S
authors.initials: S
authors.lastname: Yanchuk
authors.forename: T
authors.initials: T
authors.lastname: Dahms
authors.forename: E
authors.initials: E
authors.lastname: Schöll