Deriving information about architecture from activity patterns in coupled cell systems

In this work, we examine what can be said about the coupling architecture of a network based on an observed multisynchronous activity pattern, in which cells form multiple synchronized clusters. Specifically, we derive a linear relation, the solutions of which are precisely those coupling architectures that are robustly compatible with a given multisynchronous state. We analyze this relation under the assumption that the network consists of a ring of identical cells, or a ring of two interleaved cell populations. Comparison of these cases shows that coupling of an "observed" layer of cells to a second "hidden" layer can significantly broaden the range of architectures that support certain clustering patterns in the observed cells.

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