Stability of Twisted States in the Kuramoto Model on Cayley and Random Graphs

@article{Medvedev2015StabilityOT,
  title={Stability of Twisted States in the Kuramoto Model on Cayley and Random Graphs},
  author={Georgi S. Medvedev and Xuezhi Tang},
  journal={Journal of Nonlinear Science},
  year={2015},
  volume={25},
  pages={1169-1208}
}
The Kuramoto model of coupled phase oscillators on complete, Paley, and Erdős–Rényi (ER) graphs is analyzed in this work. As quasirandom graphs, the complete, Paley, and ER graphs share many structural properties. For instance, they exhibit the same asymptotics of the edge distributions, homomorphism densities, graph spectra, and have constant graph limits. Nonetheless, we show that the asymptotic behavior of solutions in the Kuramoto model on these graphs can be qualitatively different… 
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