Role of delay for the symmetry in the dynamics of networks

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

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


The symmetry in a network of oscillators determines the spatiotemporal patterns of activity that can emerge. We study how a delay in the coupling affects symmetry-breaking and -restoring bifurcations. We are able to draw general conclusions in the limit of long delays. For one class of networks we derive a criterion that predicts that delays have a symmetrizing effect. Moreover, we demonstrate that for any network admitting a steady-state solution, a long delay can solely advance the first bifurcation point as compared to the instantaneous-coupling regime.
Original languageEnglish
Article number046223
JournalPhysical Review E
Issue number4
Publication statusPublished - 1 Apr 2011
Externally publishedYes


  • Synchronization
  • coupled oscillators
  • Patterns
  • Networks and genealogical trees
  • Delay and functional equations

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