Adaptive synchronization in delay-coupled networks of Stuart-Landau oscillators

Anton A. Selivanov, Judith Lehnert, Thomas Dahms, Philipp Hövel, Alexander L. Fradkov, and Eckehard Schöll
Phys. Rev. E 85, 016201 – Published 3 January 2012

Abstract

We consider networks of delay-coupled Stuart-Landau oscillators. In these systems, the coupling phase has been found to be a crucial control parameter. By proper choice of this parameter one can switch between different synchronous oscillatory states of the network. Applying the speed-gradient method, we derive an adaptive algorithm for an automatic adjustment of the coupling phase such that a desired state can be selected from an otherwise multistable regime. We propose goal functions based on both the difference of the oscillators and a generalized order parameter and demonstrate that the speed-gradient method allows one to find appropriate coupling phases with which different states of synchronization, e.g., in-phase oscillation, splay, or various cluster states, can be selected.

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  • Received 1 July 2011

DOI:https://doi.org/10.1103/PhysRevE.85.016201

©2012 American Physical Society

Authors & Affiliations

Anton A. Selivanov1, Judith Lehnert2, Thomas Dahms2, Philipp Hövel2, Alexander L. Fradkov1,3, and Eckehard Schöll2,*

  • 1Department of Theoretical Cybernetics, Saint-Petersburg State University, Saint-Petersburg, Russia
  • 2Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, 10623 Berlin, Germany
  • 3Institute of Problems in Mechanical Engineering, St. Petersburg, Russia

  • *schoell@physik.tu-berlin.de

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Vol. 85, Iss. 1 — January 2012

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