Synchronizability of networks with strongly delayed links: A universal classification

We show that for large coupling delays the synchronizability of delay-coupled networks of identical units 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 li...

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Bibliographic Details
Published in:arXiv.org 2011-12
Main Authors: Flunkert, V, Yanchuk, S, Dahms, T, Schöll, E
Format: Article
Language:English
Subjects:
Classification
Delay
Network topologies
Networks
Synchronism
Online Access:Get full text
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Description
Summary:We show that for large coupling delays the synchronizability of delay-coupled networks of identical units 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. We give details of the proof of this structure and discuss the resulting universal classification of networks with respect to their synchronization properties. We illustrate this classification by means of several prototype network topologies.
ISSN:2331-8422