Periodic patterns in a ring of delay-coupled oscillators

P. Perlikowski, S. Yanchuk, O. V. Popovych, and P. A. Tass
Phys. Rev. E 82, 036208 – Published 20 September 2010

Abstract

We describe the appearance and stability of spatiotemporal periodic patterns (rotating waves) in unidirectional rings of coupled oscillators with delayed couplings. We show how delays in the coupling lead to the splitting of each rotating wave into several new ones. The appearance of rotating waves is mediated by the Hopf bifurcations of the symmetric equilibrium. We also conclude that the coupling delays can be effectively replaced by increasing the number of oscillators in the chain. The phenomena are shown for the Stuart-Landau oscillators as well as for the coupled FitzHugh-Nagumo systems modeling an ensemble of spiking neurons interacting via excitatory chemical synapses.

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  • Received 16 April 2010

DOI:https://doi.org/10.1103/PhysRevE.82.036208

©2010 American Physical Society

Authors & Affiliations

P. Perlikowski1,2, S. Yanchuk1, O. V. Popovych3, and P. A. Tass3,4

  • 1Institute of Mathematics, Humboldt University of Berlin, 10099 Berlin, Germany
  • 2Division of Dynamics, Technical University of Lodz, 90-924 Lodz, Poland
  • 3Institute of Neuroscience and Medicine–Neuromodulation (INM-7), Research Center Jülich, 52425 Jülich, Germany
  • 4Department of Stereotaxic and Functional Neurosurgery, University Hospital, 50924 Cologne, Germany

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Issue

Vol. 82, Iss. 3 — September 2010

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