Before revision: It is a common expectation in chemistry that a chemical transformation which takes place in the presence of a catalyst must also take place in its absence , though perhaps at a much slower rate. We say a reaction network is " saturated " if it satisfies such an expectation.
After revision: A "critical siphon" is a subset of the species in a chemical reaction network whose absence is forward invariant and stoichiometrically compatible with a positive point. We define "catalytic networks" as networks with an essentially catalytic reaction pathway: one which is " saturated " if it satisfies such an expectation.