Dresden 2011 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 14: Delay Dynamics

DY 14.3: Talk

Tuesday, March 15, 2011, 14:30–14:45, ZEU 255

Synchronizing distant nodes: a universal classification of networks — •Valentin Flunkert¹, Serhiy Yanchuk², Thomas Dahms¹, and Eckehard Schöll¹ — ¹Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, 10623 Berlin, Germany — ²Institut für Mathematik, Humboldt Universität Berlin, Unter den Linden 6, 10099 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 [1]. 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.

[1] V. Flunkert, S. Yanchuk, T. Dahms, and E. Schöll, Phys. Rev. Lett. (2010) in print.