Synchronizability of networks with strongly delayed links: A universal classification

Details Synchronizability of networks with strongly delayed links: A universal classification Synchronizability of networks with strongly delayed links: A universal classification

2011-12-20

arxiv.org/abs/1112.4711v1

Nonlinear Sciences

Chaotic Dynamics

18 pages, 7 figures. arXiv admin note: substantial text overlap with arXiv:1009.6120

Scientific paper

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.

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