Note that a deterministic Petri net is a kind of dynamical system - our topics are connected!

In this case, the state space is a subset of \\(\mathbb{R^n}\\), with all components non-negative. The ODEs are of course the rate equations, which are predicated on the mass-action kinetics, under which the rate at which a reaction takes place is proportional to the product of its input values (input concentrations).