A Hopf bifurcation in the Kuramoto-Daido model
Dynamical Systems
2016-10-11 v1
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 distributions. 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.
Keywords
Cite
@article{arxiv.1610.02834,
title = {A Hopf bifurcation in the Kuramoto-Daido model},
author = {Hayato Chiba},
journal= {arXiv preprint arXiv:1610.02834},
year = {2016}
}
Comments
arXiv admin note: substantial text overlap with arXiv:1609.04126