A Hopf bifurcation in the Kuramoto-Daido model

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Abstract

A Hopf bifurcation in the Kuramoto-Daido model is investigated based on the generalized spectral theory and the center manifold reduction for a certain class of frequency densities. The dynamical system of the order parameter on a four-dimensional center manifold is derived. It is shown that the dynamical system undergoes a Hopf bifurcation as the coupling strength increases, which proves the existence of a periodic two-cluster state of oscillators.

Original languageEnglish
Pages (from-to)546-570
Number of pages25
JournalJournal of Differential Equations
Volume280
DOIs
Publication statusPublished - 2021 Apr 15

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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