On a connexion between stability and graphs in chemical kinetics. I. Stability and the reaction diagram

Abstract

In a previous publication (Horn & Jackson 1972) there was defined a class of open reaction systems, called quasi-thermodynamic mass-action systems, whose statics and dynamics exhibit a regularity similar to that which can be found with closed systems. For instance, it was shown that in quasi-thermodynamic systems all equilibria are asymptotically stable and satisfy conditions of existence and uniqueness relative to certain subsets of the composition space. In this paper quasi-thermodynamic behaviour is related to the properties of a digraph ('reaction diagram') and a set of vectors ('complexes') that may be associated with certain open reaction systems. The results presented allow the determination of the qualitative statics and dynamics of a large class of open reaction systems by simple computational procedures.