Synchronization properties of network motifs: Influence of coupling delay and symmetry

Otti D'Huys*, Raul Vicente, Thomas Erneux, Jan Danckaert, Ingo Fischer

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

98 Citations (Web of Science)


We investigate the effect of coupling delays on the synchronization properties of several network motifs. In particular, we analyze the synchronization patterns of unidirectionally coupled rings, bidirectionally coupled rings, and open chains of Kuramoto oscillators. Our approach includes an analytical and semianalytical study of the existence and stability of different in-phase and out-of-phase periodic solutions, complemented by numerical simulations. The delay is found to act differently on networks possessing different symmetries. While for the unidirectionally coupled ring the coupling delay is mainly observed to induce multistability, its effect on bidirectionally coupled rings is to enhance the most symmetric solution. We also study the influence of feedback and conclude that it also promotes the in-phase solution of the coupled oscillators. We finally discuss the relation between our theoretical results on delay-coupled Kuramoto oscillators and the synchronization properties of networks consisting of real-world delay-coupled oscillators, such as semiconductor laser arrays and neuronal circuits.
Original languageEnglish
Article number037116
Issue number3
Publication statusPublished - 1 Sept 2008
Externally publishedYes


  • Semiconductor lasers
  • laser diodes
  • Synchronization
  • coupled oscillators

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