Kuramoto model with frequency-degree correlations on complex networks

@article{Coutinho2013KuramotoMW,
  title={Kuramoto model with frequency-degree correlations on complex networks},
  author={Bruno Coutinho and Alexander V. Goltsev and Sergey N. Dorogovtsev and Jos{\'e} F. F. Mendes},
  journal={Physical Review E},
  year={2013},
  volume={87},
  pages={032106}
}
We study the Kuramoto model on complex networks, in which natural frequencies of phase oscillators and the vertex degrees are correlated. Using the annealed network approximation and numerical simulations, we explore a special case in which the natural frequencies of the oscillators and the vertex degrees are linearly coupled. We find that in uncorrelated scale-free networks with the degree distribution exponent $2l\ensuremath{\gamma}l3$, the model undergoes a first-order phase transition… 

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