Stability and complex balancing in mass-action systems with three short complexes

Abstract General methods developed previously (Feinberg 1973; Horn Horn 1973 a, b, c) are used in order to analyse all mass-action systems with three short complexes. It is shown that there exist in all 43 different isomorphism classes of collections of three short complexes and that the weakly reversible mass-action systems which are associated with 41 of these classes are unconditionally complex balanced. For the remaining mass-action systems the condition on the rate constants is given, which is necessary and sufficient to ensure complex balancing. It is also shown that all weakly reversible mass-action systems with three short complexes are quasithermodynamic and, therefore, exhibit the dynamic regularity which is associated with that condition.