Dynamics on Networks of Manifolds

Understand

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.