For any linear circulant gathering protocol the state space decomposes identically into stable invariant subspaces whose convergence rates alone depend on the weights; a similar decomposition holds after speed normalization in the nonlinear case.
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On the Dynamical Hierarchy in Gathering Protocols with Circulant Topologies
For any linear circulant gathering protocol the state space decomposes identically into stable invariant subspaces whose convergence rates alone depend on the weights; a similar decomposition holds after speed normalization in the nonlinear case.