Synchronization transition of identical phase oscillators in a directed small-world network

Ralf Tönjes, Naoki Masuda, Hiroshi Kori

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)

Abstract

We numerically study a directed small-world network consisting of attractively coupled, identical phase oscillators. While complete synchronization is always stable, it is not always reachable from random initial conditions. Depending on the shortcut density and on the asymmetry of the phase coupling function, there exists a regime of persistent chaotic dynamics. By increasing the density of shortcuts or decreasing the asymmetry of the phase coupling function, we observe a discontinuous transition in the ability of the system to synchronize. Using a control technique, we identify the bifurcation scenario of the order parameter. We also discuss the relation between dynamics and topology and remark on the similarity of the synchronization transition to directed percolation.

Original languageEnglish
Article number033108
JournalChaos
Volume20
Issue number3
DOIs
Publication statusPublished - 2010 Jul 13
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

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