Amplitude and phase effects on the synchronization of delay-coupled oscillators

O. D'Huys, R. Vicente, J. Danckaert, I. Fischer

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

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.
Original languageEnglish
Article number043127
JournalChaos: An Interdisciplinary Journal of Nonlinear Science
Volume20
Issue number4
DOIs
Publication statusPublished - 1 Dec 2010
Externally publishedYes

Keywords

  • chaos
  • numerical analysis
  • oscillators
  • phase transformations
  • spontaneous symmetry breaking
  • synchronisation
  • Synchronization
  • coupled oscillators
  • Spontaneous and radiative symmetry breaking
  • Numerical approximation and analysis
  • Phase transitions: general studies

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