Deriving Information about Architecture from Activity Patterns in Coupled Cell Systems

In coupled networks, the properties of the constituent elements (cells), their interactions, and the coupling architecture combine to determine the possible coherent states that may arise. In this work, we examine what can be said about the coupling architecture of a network based on an observed polysynchronous 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 polysynchronous state. We analyze this relation under the assumption that the network consists of either a ring of identical cells or a double ring of two interacting 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.