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2011, Volume 2011: 292-301. Doi: 10.3934/proc.2011.2011.292 open access
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Control of synchrony by delay coupling in complex networks

  • 1.

    Department of Physics, University of Science, Unjong-District, Pyongyang, DPR

  • 2.

    Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, 10623 Berlin

Received:  June 30, 2010
Revised:  July 31, 2010
Published:  August 2017
Abstract Related Papers Cited by
    Abstract
  • Using a master stability function approach, we study synchronization in delay-coupled oscillator networks. The oscillators are modeled by a complex normal form of super- or subcritical Hopf bifurcation. We derive analytical stability conditions and demonstrate that by tuning the phase of the complex coupling constant one can easily control the stability of synchronous periodic states. The phase is identified as a crucial control parameter to switch between in-phase synchronization or desynchronization for general network topologies. For unidirectionally coupled rings or more general networks described by circulant matrices the coupling phase controls in-phase, cluster, or splay states. Our results are robust even for slightly nonidentical oscillators.
    Mathematics Subject Classification: Primary: 34H15, 70K20; Secondary: 70K50, 05C82.

    Citation:
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