Synchronization and symmetry breaking of delay-coupled oscillators: on the role of phase and amplitude instabilities

Otti D'Huys; Raul Vicente; Jan Danckaert; Ingo Fischer

doi:10.1117/12.854522

Synchronization and symmetry breaking of delay-coupled oscillators: on the role of phase and amplitude instabilities

Otti D'Huys^*, Raul Vicente, Jan Danckaert, Ingo Fischer

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceeding › Academic › peer-review

Abstract

We study the synchronization behavior of Stuart-Landau oscillators coupled with delay, using analytical and numerical methods. We compare the dynamics of one oscillator with delayed feedback, two mutually oscillators coupled with delay, and two delay-coupled elements with feedback. Taking only the phase dynamics into account, no chaotic dynamics has been observed. Moreover, the stability of the symmetric (identical synchronization) solution is the same in each of the three studied networks of delay-coupled elements. When allowing 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 is accompanied by a symmetry breaking, leading to the in lasers observed leader-laggard behavior in the chaotic regime. Adding self-feedback (with the same strength and delay as the coupling), stabilizes the system in transverse direction.

Original language	English
Title of host publication	Proceedings SPIE Photonics Europe
Subtitle of host publication	Semiconductor Lasers and Laser Dynamics IV
Publisher	SPIE
Volume	7720
DOIs	https://doi.org/10.1117/12.854522
Publication status	Published - 1 Apr 2010
Externally published	Yes

Publication series

Series	SPIE Proceedings
Volume	7720

Access to Document

10.1117/12.854522

http://adsabs.harvard.edu/abs/2010SPIE.7720E..23D

Cite this

@inproceedings{c8d67705435445f0b70d9ad07ad8c34a,

title = "Synchronization and symmetry breaking of delay-coupled oscillators: on the role of phase and amplitude instabilities",

abstract = "We study the synchronization behavior of Stuart-Landau oscillators coupled with delay, using analytical and numerical methods. We compare the dynamics of one oscillator with delayed feedback, two mutually oscillators coupled with delay, and two delay-coupled elements with feedback. Taking only the phase dynamics into account, no chaotic dynamics has been observed. Moreover, the stability of the symmetric (identical synchronization) solution is the same in each of the three studied networks of delay-coupled elements. When allowing 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 is accompanied by a symmetry breaking, leading to the in lasers observed leader-laggard behavior in the chaotic regime. Adding self-feedback (with the same strength and delay as the coupling), stabilizes the system in transverse direction.",

author = "Otti D'Huys and Raul Vicente and Jan Danckaert and Ingo Fischer",

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Synchronization and symmetry breaking of delay-coupled oscillators: on the role of phase and amplitude instabilities. / D'Huys, Otti; Vicente, Raul; Danckaert, Jan et al.
Proceedings SPIE Photonics Europe: Semiconductor Lasers and Laser Dynamics IV. Vol. 7720 SPIE, 2010. 772023 (SPIE Proceedings, Vol. 7720).

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceeding › Academic › peer-review

TY - GEN

T1 - Synchronization and symmetry breaking of delay-coupled oscillators: on the role of phase and amplitude instabilities

AU - D'Huys, Otti

AU - Vicente, Raul

AU - Danckaert, Jan

AU - Fischer, Ingo

PY - 2010/4/1

Y1 - 2010/4/1

N2 - We study the synchronization behavior of Stuart-Landau oscillators coupled with delay, using analytical and numerical methods. We compare the dynamics of one oscillator with delayed feedback, two mutually oscillators coupled with delay, and two delay-coupled elements with feedback. Taking only the phase dynamics into account, no chaotic dynamics has been observed. Moreover, the stability of the symmetric (identical synchronization) solution is the same in each of the three studied networks of delay-coupled elements. When allowing 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 is accompanied by a symmetry breaking, leading to the in lasers observed leader-laggard behavior in the chaotic regime. Adding self-feedback (with the same strength and delay as the coupling), stabilizes the system in transverse direction.

AB - We study the synchronization behavior of Stuart-Landau oscillators coupled with delay, using analytical and numerical methods. We compare the dynamics of one oscillator with delayed feedback, two mutually oscillators coupled with delay, and two delay-coupled elements with feedback. Taking only the phase dynamics into account, no chaotic dynamics has been observed. Moreover, the stability of the symmetric (identical synchronization) solution is the same in each of the three studied networks of delay-coupled elements. When allowing 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 is accompanied by a symmetry breaking, leading to the in lasers observed leader-laggard behavior in the chaotic regime. Adding self-feedback (with the same strength and delay as the coupling), stabilizes the system in transverse direction.

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DO - 10.1117/12.854522

M3 - Conference article in proceeding

VL - 7720

T3 - SPIE Proceedings

BT - Proceedings SPIE Photonics Europe

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