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Control of synchrony by delay coupling in complex networks

Pages: 292 - 301, Issue Special, September 2011

 Abstract        Full Text (1014.8K)              

Chol-Ung Choe - Department of Physics, University of Science, Unjong-District, Pyongyang, DPR, North Korea (email)
Thomas Dahms - Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, 10623 Berlin, Germany (email)
Philipp Hövel - Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, 10623 Berlin, Germany (email)
Eckehard Schöll - Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, 10623 Berlin, Germany (email)

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.

Keywords:  Dynamics of networks, delay differential equations, master stability function
Mathematics Subject Classification:  Primary: 34H15, 70K20; Secondary: 70K50, 05C82

Received: July 2010;      Revised: August 2010;      Published: October 2011.