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

27 April 2010 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

Author Affiliations +

Proceedings Volume 7720, Semiconductor Lasers and Laser Dynamics IV; 772023 (2010) https://doi.org/10.1117/12.854522
Event: SPIE Photonics Europe, 2010, Brussels, Belgium

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.

Citation Download Citation

Otti D'Huys, Raul Vicente, Jan Danckaert, and Ingo Fischer "Synchronization and symmetry breaking of delay-coupled oscillators: on the role of phase and amplitude instabilities", Proc. SPIE 7720, Semiconductor Lasers and Laser Dynamics IV, 772023 (27 April 2010); https://doi.org/10.1117/12.854522

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