Amplitude and phase effects on the synchronization of delay-coupled oscillators


We consider the behavior of Stuart-Landau oscillators as generic limit-cycle oscillators when they are interacting with delay. We investigate the role of amplitude and phase instabilities in producing symmetry-breaking/restoring transitions. Using analytical and numerical methods we compare the dynamics of one oscillator with delayed feedback, two oscillators mutually coupled with delay, and two delay-coupled elements with self-feedback. Taking only the phase dynamics into account, no chaotic dynamics is observed, and the stability of the identical synchronization solution is the same in each of the three studied networks of delay-coupled elements. When allowing for a variable oscillation amplitude, the delay can induce amplitude instabilities. We provide analytical proof that, in case of two mutually coupled elements, the onset of an amplitude instability always results in antiphase oscillations, leading to a leader-laggard behavior in the chaotic regime. Adding self-feedback with the same strength and delay as the coupling stabilizes the system in the transverse direction and, thus, promotes the onset of identically synchronized behavior.

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Divisions: College of Engineering & Physical Sciences
Funding Information: We would like to thank T. Erneux, E. Schöll, S. Yanchuk, and P. Perlikowski for helpful discussions. O.D. acknowledges the Research Foundation Flanders (FWO-Vlaanderen) for a fellowship and for project support. This work was partially supported by the Int
Additional Information: Copyright © 2010 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 Amplitude and phase effects on the synchronization of delay-coupled oscillators Chaos 20, 043127 (2010) 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: 10 Apr 2024 07:15
Date Deposited: 31 Jan 2019 13:09
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Related URLs: http://www.scop ... tnerID=8YFLogxK (Scopus URL)
https://aip.sci ... .1063/1.3518363 (Publisher URL)
PURE Output Type: Article
Published Date: 2010-12-30
Authors: D'Huys, O. (ORCID Profile 0000-0001-7498-6771)
Vicente, R.
Danckaert, J.
Fischer, I.



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