Before revision:  In particular we develop a combinatorial models for the categories of modular continuous time dynamical systems on manifolds .
After revision:  In particular we develop a combinatorial models for the categories of modular continuous time dynamical systems . Each such model, as a category, is a fibration over an appropriate category of labeled directed graphs. This makes precise the relation between dynamical systems living on networks and the combinatorial structure of the underlying directed graphs, allowing us to exploit the relation in new and interesting ways .