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Synchronizability of Networks with Strongly Delayed Links: A Universal Classification

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Abstract

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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Authors and Affiliations

  1. Institut für Theoretische Physik, TU Berlin, Hardenbergstrase 36, 10623, Berlin, Germany

    V. Flunkert, T. Dahms & E. Schöll

  2. Instituto de Fisica Interdisciplinar y Sistemas Complejos, IFISC (UIB-CSIC), Campus Universitat de les Illes Balears, E-07122, Palma de Mallorca, Spain

    V. Flunkert

  3. Institut für Mathematik, Humboldt Universität Berlin, Unter den Linden 6, 10099, Berlin, Germany

    S. Yanchuk

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Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 48, Proceedings of the Sixth International Conference on Differential and Functional Differential Equations and International Workshop “Spatio-Temporal Dynamical Systems” (Moscow, Russia, 14–21 August, 2011). Part 4, 2013.

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Flunkert, V., Yanchuk, S., Dahms, T. et al. Synchronizability of Networks with Strongly Delayed Links: A Universal Classification. J Math Sci 202, 809–824 (2014). https://doi.org/10.1007/s10958-014-2078-6

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