Groupoids, Fibrations, and Balanced Colorings of Networks
Ian Stewart
Abstract:Robust synchrony in network dynamics is governed by balanced colorings and the corresponding quotient network, also formalized in terms of graph fibrations. Dynamics and bifurcations are constrained — often in surprising ways — by the associated synchrony subspaces, which are invariant under all admissible ordinary differential equations (ODEs). The class of admissible ODEs is determined by a groupoid, whose objects are the input sets of nodes and whose morphisms are input isomorphisms between those sets. We d… Show more
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