Dynamics on networks I. Combinatorial categories of modular continuous-time systems

Understand

We develop a new framework for the study of complex continuous time dynamical systems based on viewing them as collections of interacting control modules.

• This framework is inspired by and builds upon the groupoid formalism of Golubitsky, Stewart and their collaborators.
• Our approach uses the tools and --- more importantly ---the stance of category theory.
• This enables us to put the groupoid formalism in a coordinate-free setting and to extend it from ordinary differential equations to vector fields on manifolds.