• Corpus ID: 235624290

Forget Partitions: Cluster Synchronization in Directed Networks Generate Hierarchies

  title={Forget Partitions: Cluster Synchronization in Directed Networks Generate Hierarchies},
  author={Fiona M. Brady and Yuanzhao Zhang and Adilson E. Motter},
We present a scalable approach for simplifying the stability analysis of cluster synchronization patterns on directed networks. When a network has directional couplings, decomposition of the coupling matrix into independent blocks (which in turn decouples the variational equation) is no longer adequate to reveal the full relations among perturbation modes. Instead, it is often necessary to introduce directional dependencies among the blocks and establish hierarchies among perturbation modes… 

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