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Kuramoto dynamics in Hamiltonian systems

2013/05/08 by Dirk Witthaut, Marc Timme · 1 citation
Physics and Astronomy · #nlin.CD

paper · pdf · doi:10.1103/physreve.90.032917

10 pages, 4 figures

arxiv created 2013/05/08 · arxiv updated 2015/06/15

Abstract

The Kuramoto model constitutes a paradigmatic model for the dissipative collective dynamics of coupled oscillators, characterizing in particular the emergence of synchrony. Here we present a classical Hamiltonian (and thus conservative) system with 2N state variables that in its action-angle representation exactly yields Kuramoto dynamics on N-dimensional invariant manifolds. We show that the synchronization transition on a Kuramoto manifold emerges where the transverse Hamiltonian action dynamics becomes unstable. The uncovered Kuramoto dynamics in Hamiltonian systems thus distinctly links dissipative to conservative dynamics.

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