Necessary and sufficient conditions for complex balancing in chemical kinetics

Summary

In a recent publication (Horn & Jackson [1]) it was shown that complex balancing together with mass action type rate laws ensures certain stability properties of a kinetic system, thereby precluding sustained oscillations, bistability and other types of irregular dynamics. In this paper a necessary condition for complex balancing in general kinetics and necessary and sufficient conditions for complex balancing in mass action systems are derived. A theorem is stated which excludes the occurence of equilibria in certain composition regions of general kinetic systems. For mass action systems it is shown that it is sometimes true that the algebraic structure of the reactions suffices to ensure complex balancing, while in other cases complex balancing occurs only if certain relations between the rate constants are satisfied. The number of these relations, called the deficiency of the mass action system is determined by the algebraic structure of the set of reactions underlying that system.