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arXiv · 1208.1513

Dynamics on Networks of Manifolds

Lee DeVille·Eugene Lerman
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Abstract

We propose a precise definition of a continuous time dynamical system made up of interacting open subsystems. The interconnections of subsystems are coded by directed graphs. We prove that the appropriate maps of graphs called graph fibrations give rise to maps of dynamical systems. Consequently surjective graph fibrations give rise to invariant subsystems and injective graph fibrations give rise to projections of dynamical systems.

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Lee DeVille, Eugene Lerman. 2015-03-12. Dynamics on Networks of Manifolds. https://doi.org/10.3842/sigma.2015.022

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