Kuramoto dynamics in Hamiltonian systems
arXiv:1305.1742 · doi:10.1103/PhysRevE.90.032917
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.
10 pages, 4 figures
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