Dynamics on Networks of Manifolds

[摘要] 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.

[关键词] coupled cell networks;open dynamical systems;control systems;morphisms of dynamical systems