Synchronization properties of network motifs:Influence of coupling delay and symmetry


We investigate the effect of coupling delays on the synchronization properties of several network motifs. In particular, we analyze the synchronization patterns of unidirectionally coupled rings, bidirectionally coupled rings, and open chains of Kuramoto oscillators. Our approach includes an analytical and semianalytical study of the existence and stability of different in-phase and out-of-phase periodic solutions, complemented by numerical simulations. The delay is found to act differently on networks possessing different symmetries. While for the unidirectionally coupled ring the coupling delay is mainly observed to induce multistability, its effect on bidirectionally coupled rings is to enhance the most symmetric solution. We also study the influence of feedback and conclude that it also promotes the in-phase solution of the coupled oscillators. We finally discuss the relation between our theoretical results on delay-coupled Kuramoto oscillators and the synchronization properties of networks consisting of real-world delay-coupled oscillators, such as semiconductor laser arrays and neuronal circuits.

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Divisions: College of Engineering & Physical Sciences
Funding Information: Part of this work has been performed at the Instituto de Fisica Interdisciplinar y Sistemas Complejos (IFISC), Universtitat de les Illes Balears, Palma de Mallorca, Spain, and we wish to thank Claudio Mirasso for his hospitality and guidance. We thank Pau
Additional Information: Copyright © 2008 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Synchronization properties of network motifs: Influence of coupling delay and symmetry Chaos 18, 037116 (2008) and may be found at
Uncontrolled Keywords: Statistical and Nonlinear Physics,Mathematical Physics,Physics and Astronomy(all),Applied Mathematics
Publication ISSN: 1089-7682
Last Modified: 01 Apr 2024 07:29
Date Deposited: 31 Jan 2019 16:01
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Related URLs: http://www.scop ... tnerID=8YFLogxK (Scopus URL)
https://aip.sci ... .1063/1.2953582 (Publisher URL)
PURE Output Type: Article
Published Date: 2008-09-22
Authors: D'Huys, O. (ORCID Profile 0000-0001-7498-6771)
Vicente, R.
Erneux, T.
Danckaert, J.
Fischer, I.



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