American Institute of Mathematical Sciences

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2011, 2011(Special): 292-301. doi: 10.3934/proc.2011.2011.292

Control of synchrony by delay coupling in complex networks

Chol-Ung Choe 1, , Thomas Dahms 2, , Philipp Hövel 2, and  Eckehard Schöll 2,

1. 

Department of Physics, University of Science, Unjong-District, Pyongyang, DPR, North Korea
2. 

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

Received  July 2010 Revised  August 2010 Published  October 2011

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.
Keywords: master stability function, delay differential equations, Dynamics of networks.
Mathematics Subject Classification: Primary: 34H15, 70K20; Secondary: 70K50, 05C82.
Citation: Chol-Ung Choe, Thomas Dahms, Philipp Hövel, Eckehard Schöll. Control of synchrony by delay coupling in complex networks. Conference Publications, 2011, 2011 (Special) : 292-301. doi: 10.3934/proc.2011.2011.292
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