Kuramoto dynamics in Hamiltonian systems.

  title={Kuramoto dynamics in Hamiltonian systems.},
  author={Dirk Witthaut and Marc Timme},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  volume={90 3},
  • D. Witthaut, M. Timme
  • Published 2014
  • Mathematics, Physics, Medicine
  • Physical review. E, Statistical, nonlinear, and soft matter physics
The Kuramoto model constitutes a paradigmatic model for the dissipative collective dynamics of coupled oscillators, characterizing in particular the emergence of synchrony (phase locking). 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 locking of the phase of one oscillator on a Kuramoto manifold to the average phase emerges… Expand
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