Synchronizing distant nodes: a universal classification of networks
arXiv:1009.6120 · doi:10.1103/PhysRevLett.105.254101
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 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.
4 pages, 1 figure, 1 table. Phys. Rev. Lett. in print, v2 has minor changes in response to PRL referee comments