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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December 2010
Research Article|
December 03 2010
Amplitude and phase effects on the synchronization of delay-coupled oscillators
O. D’Huys;
O. D’Huys
a)
1Department of Physics (DNTK),
Vrije Universiteit Brussel
, Pleinlaan 2, 1050 Brussel, Belgium
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R. Vicente;
R. Vicente
2
Max-Planck-Institute for Brain Research
, Deutschordenstraße 46, 60528 Frankfurt am Main, Germany
and Frankfurt Institute for Advanced Studies (FIAS)
, Ruth-Moufang-Straße 1, 60438 Frankfurt, Germany
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J. Danckaert;
J. Danckaert
1Department of Physics (DNTK),
Vrije Universiteit Brussel
, Pleinlaan 2, 1050 Brussel, Belgium
3Department of Applied Physics and Photonics (TONA),
Vrije Universiteit Brussel
, Pleinlaan 2, 1050 Brussel, Belgium
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I. Fischer
I. Fischer
4Instituto de Fisica Interdisciplinar y Sistemas Complejos,
IFISC (UIB-CSIC)
, Campus Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain
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a)
Electronic mail: [email protected].
Chaos 20, 043127 (2010)
Article history
Received:
September 24 2010
Accepted:
November 01 2010
Citation
O. D’Huys, R. Vicente, J. Danckaert, I. Fischer; Amplitude and phase effects on the synchronization of delay-coupled oscillators. Chaos 1 December 2010; 20 (4): 043127. https://doi.org/10.1063/1.3518363
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