Multiple steady states for chemical reaction networks of deficiency one
This paper is an addendum to the author's paper ibid., 311-370 (1995; see the preceding review Zbl 0853.92024). Readers are presumed to be familiar with the terminology and notation used there. In the foregoing paper a subclass of so called deficiency one networks was characterized for which the corresponding system of mass action equations can admit no more than one equilibrium for any choice of positive values for the rate constants. Now, the main purpose is to provide a theory for determining when a deficiency one reaction network has the capacity to admit multiple positive equilibria. For so called regular networks in this class of networks (to which all systems belong that arise when heterogeneous catalysis is involved) an algorithm is derived that allows to decide about the existence of multiple positive equilibria. This algorithm translates questions about systems of nonlinear polynomial equations in several variables into questions about systems of linear inequalities.
systems of nonlinear polynomial equations in several variables
scientific article; zbMATH DE number 880578