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Periodic patterns in a ring of delay-coupled oscillators and spiking neurons

Please always quote using this URN:urn:nbn:de:0296-matheon-6884
  • We describe the appearance and stability of spatio-temporal periodic patterns (rotating waves) in unidirectional rings of coupled oscillators with delayed couplings. We show how delays in the coupling lead to a splitting of each rotating wave into several new ones. The appearance of rotating waves is mediated by 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 Stuart-Landau oscillators as well as for coupled FitzHugh-Nagumo systems interacting via excitatory chemical synapses.

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Metadaten
Author:Przemyslaw Perlikowski, Serhiy Yanchuk, Tass P. A., Popovych O. V.
URN:urn:nbn:de:0296-matheon-6884
Referee:Alexander Mielke
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2010/04/13
Release Date:2010/12/04
Tag:
Institute:Humboldt-Universität zu Berlin
MSC-Classification:05-XX COMBINATORICS (For finite fields, see 11Txx) / 05Cxx Graph theory (For applications of graphs, see 68R10, 81Q30, 81T15, 82B20, 82C20, 90C35, 92E10, 94C15) / 05C82 Small world graphs, complex networks [See also 90Bxx, 91D30]
92-XX BIOLOGY AND OTHER NATURAL SCIENCES
Preprint Number:694
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