Role of delay for the symmetry in the dynamics of networks

Ottilde D'Huys, I. Fischer, Jan Danckaert, R. Vicente

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

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
Pages (from-to)46223
Number of pages1
JournalPhys. Rev. E
Volume83
Publication statusPublished - 26 Apr 2011

Keywords

  • SEMICONDUCTOR-LASERS; OPTICAL FEEDBACK
  • HOPF-BIFURCATION; TIME-DELAY; BREAKING;
  • CHAOS; SYNCHRONIZATION; STABILIZATION;
  • OSCILLATORS; SYSTEMS

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