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

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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 languageEnglish
Title of host publicationProceedings SPIE Photonics Europe
Subtitle of host publicationSemiconductor Lasers and Laser Dynamics IV
PublisherSPIE
Volume7720
DOIs
Publication statusPublished - 1 Apr 2010
Externally publishedYes

Publication series

SeriesSPIE Proceedings
Volume7720

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