Abstract
A bifurcation theory for a system of globally coupled phase oscillators is developed based on the theory of rigged Hilbert spaces. It is shown that there exists a finite-dimensional center manifold on a space of generalized functions. The dynamics on the manifold is derived for any coupling functions. When the coupling function is sin θ, a bifurcation diagram conjectured by Kuramoto is rigorously obtained. When it is not sin θ, a new type of bifurcation phenomenon is found due to the discontinuity of the projection operator to the center subspace.
Original language | English |
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Article number | 043103 |
Journal | Chaos |
Volume | 21 |
Issue number | 4 |
DOIs | |
Publication status | Published - 2011 Dec 12 |
Externally published | Yes |
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)
- Applied Mathematics