Dynamics on Networks of Manifolds

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.

References in corpus (2)

• Algebras of Open Dynamical Systems on the Operad of Wiring Diagrams
• Dynamics on networks I. Combinatorial categories of modular continuous-time systems

Cited by in corpus (11)

• Sheaves, Cosheaves and Applications
• Algebras of Open Dynamical Systems on the Operad of Wiring Diagrams
• The operad of temporal wiring diagrams: formalizing a graphical language for discrete-time processes
• A bicategory of decorated cospans
• Networks of hybrid open systems
• Networks of open systems
• A category of hybrid systems
• Amplified steady state bifurcations in feedforward networks
• An algebra of open continuous time dynamical systems and networks
• Runge-Kutta and Networks
• Morphisms of Networks of Hybrid Open Systems