2011/12/20 by Valentín Flunkert, V. Flunkert, Serhiy Yanchuk +8
Computer Science · Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Neural Networks Stability and Synchronization #Nonlinear Dynamics and Pattern Formation #nlin.CD #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.1112.4711
18 pages, 7 figures. arXiv admin note: substantial text overlap with arXiv:1009.6120
arxiv created 2011/12/20 · openalex publication_date 2011/12/20 · arxiv updated 2011/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.