The stability of fixed points for a Kuramoto model with Hebbian interactions

Jared C. Bronski, Yizhang He, Xinye Li, Yue Liu, Danielle Rae Sponseller, Seth Wolbert

Research output: Contribution to journalArticlepeer-review

Abstract

We consider a variation of the Kuramoto model with dynamic coupling, where the coupling strengths are allowed to evolve in response to the phase difference between the oscillators, a model first considered by Ha, Noh, and Park. We demonstrate that the fixed points of this model, as well as their stability, can be completely expressed in terms of the fixed points and stability of the analogous classical Kuramoto problem where the coupling strengths are fixed to a constant (the same for all edges). In particular, for the "all-to-all" network, where the underlying graph is the complete graph, the problem reduces to the problem of understanding the fixed points and stability of the all-to-all Kuramoto model with equal edge weights, a problem that is well understood.

Original languageEnglish (US)
Article number053110
JournalChaos
Volume27
Issue number5
DOIs
StatePublished - May 1 2017

ASJC Scopus subject areas

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

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