A Hopf bifurcation in the Kuramoto-Daido model

Hayato Chiba

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arXiv · 1610.02834

A Hopf bifurcation in the Kuramoto-Daido model

Hayato Chiba

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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 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.

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Hayato Chiba. 2016-10-10. A Hopf bifurcation in the Kuramoto-Daido model. https://arxiv.org/abs/1610.02834

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