The mean field analysis of the kuramoto model on graphs Ⅱ. asymptotic stability of the incoherent state, center manifold reduction, and bifurcations

  title={The mean field analysis of the kuramoto model on graphs Ⅱ. asymptotic stability of the incoherent state, center manifold reduction, and bifurcations},
  author={Hayato Chiba and Georgi S. Medvedev},
  journal={Discrete \& Continuous Dynamical Systems - A},
In our previous work [Chiba, Medvedev, arXiv:1612.06493], we initiated a mathematical investigation of the onset of synchronization in the Kuramoto model (KM) of coupled phase oscillators on convergent graph sequences. There, we derived and rigorously justified the mean field limit for the KM on graphs. Using linear stability analysis, we identified the critical values of the coupling strength, at which the incoherent state looses stability, thus, determining the onset of synchronization in… 

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