Phase-locked patterns of the Kuramoto model on 3-regular graphs

Lee DeVille, Bard Ermentrout

Research output: Contribution to journalArticlepeer-review


We consider the existence of non-synchronized fixed points to the Kuramoto model defined on sparse networks: specifically, networks where each vertex has degree exactly three. We show that "most" such networks support multiple attracting phase-locked solutions that are not synchronized and study the depth and width of the basins of attraction of these phase-locked solutions. We also show that it is common in "large enough" graphs to find phase-locked solutions where one or more of the links have angle difference greater than π/2.

Original languageEnglish (US)
Article number094820
Issue number9
StatePublished - Sep 1 2016

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • General Physics and Astronomy
  • Applied Mathematics


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