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Proceedings Paper

Synchronization and symmetry breaking of delay-coupled oscillators: on the role of phase and amplitude instabilities
Author(s): Otti D'Huys; Raul Vicente; Jan Danckaert; Ingo Fischer
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Paper 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.

Paper Details

Date Published: 27 April 2010
PDF: 11 pages
Proc. SPIE 7720, Semiconductor Lasers and Laser Dynamics IV, 772023 (27 April 2010); doi: 10.1117/12.854522
Show Author Affiliations
Otti D'Huys, Vrije Univ. Brussel (Belgium)
Raul Vicente, Max-Planck-Institute for Brain Research (Germany)
Frankfurt Institute for Advanced Studies (Germany)
Jan Danckaert, Vrije Univ. Brussel (Belgium)
Ingo Fischer, Instituto de Física Interdisciplinar y Sistemas Complejos (Spain)

Published in SPIE Proceedings Vol. 7720:
Semiconductor Lasers and Laser Dynamics IV
Krassimir Panajotov; Marc Sciamanna; Angel A. Valle; Rainer Michalzik, Editor(s)

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