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