A graphical approach to estimate the critical coupling strength for Kuramoto networks

Brady Gilg, Dieter Armbruster

Research output: Contribution to journalArticlepeer-review


The Kuramoto model is an archetypal model for studying synchronization in groups of nonidentical oscillators. Each oscillator is imbued with its own personal inherent driving frequency and experiences attractive coupling forces toward all the other oscillators in the system. As the coupling increases, there exists a minimal coupling strength called the critical coupling beyond which the system moves in a collective rhythm. A unified approach for creating approximations of the critical coupling is created. It is based on an interpretation of a measurement of phase synchronization among the oscillators (the order parameter) as a function of the coupling strength. The approach allows a graphical way to develop new approximations that are provably, strict lower bounds. It is shown that several of the critical coupling bounds that have been previously studied can be interpreted in this unified framework. In addition, a process based on fixed point sampling is introduced that converts upper bounds for the critical coupling into associated lower bounds.

Original languageEnglish (US)
Article number053122
Issue number5
StatePublished - May 1 2019

ASJC Scopus subject areas

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


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