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

D'Huys, O., Vicente, R., Danckaert, J. and Fischer, I. (2010). Amplitude and phase effects on the synchronization of delay-coupled oscillators. Chaos, 20 (4),

Abstract

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.

Publication DOI: https://doi.org/10.1063/1.3518363
Divisions: Engineering & Applied Sciences
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 https://doi.org/10.1063/1.3518363
Uncontrolled Keywords: Statistical and Nonlinear Physics,Mathematical Physics,Physics and Astronomy(all),Applied Mathematics
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Related URLs: http://www.scop ... tnerID=8YFLogxK (Scopus URL)
https://aip.sci ... .1063/1.3518363 (Publisher URL)
Published Date: 2010-12-30
Authors: D'Huys, O. ( 0000-0001-7498-6771)
Vicente, R.
Danckaert, J.
Fischer, I.

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