Symmetry Groupoids and Patterns of Synchrony in Coupled Cell Networks

By Ian Stewart, Martin Golubitsky, Marcus Pivato. SIAM Journal on Applied Dynamical Systems, 2003

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What are higher-order networks? (2021, background): “2) have been considered as coupled cell systems [4, 250].”
Polychronization: Computation with Spikes (2006, background): “It is also different from the notion of clustering, partial synchrony (Hoppensteadt and Izhikevich 1997), or polysynchrony (Stewart et al. 2003), in which some neurons oscillate synchronously while others do not.”
Multilayer networks (2013, background): “Indeed, in order to conduct a generic bifurcation analysis in a coupled-cell network, it is first necessary to classify its “patterns of synchrony”30 [140,317].”
Bifurcations from regular quotient networks: A first insight (2009, background): “A theory for coupled cell networks has been developed in [12,8,7].”
State Agreement for Continuous-Time Coupled Nonlinear Systems (2007, background): “Most existing work has dealt with static graphs with a particular topology, such as rings [6, 30], cyclic digraphs [32], and fully-connected graphs [12, 13, 34], or with static graphs having an unspecified topology but a certain connectedness.”