Collective frequency variation in network synchronization and reverse PageRank.

@article{Skardal2016CollectiveFV,
  title={Collective frequency variation in network synchronization and reverse PageRank.},
  author={Per Sebastian Skardal and Dane Taylor and Jie Sun and Alex Arenas},
  journal={Physical review. E},
  year={2016},
  volume={93},
  pages={
          042314
        }
}
A wide range of natural and engineered phenomena rely on large networks of interacting units to reach a dynamical consensus state where the system collectively operates. Here we study the dynamics of self-organizing systems and show that for generic directed networks the collective frequency of the ensemble is not the same as the mean of the individuals' natural frequencies. Specifically, we show that the collective frequency equals a weighted average of the natural frequencies, where the… 

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