Multiple steady states for chemical reaction networks of deficiency one
type: Item
instance of: scholarly article
title: Multiple steady states for chemical reaction networks of deficiency one
zbMATH Open document ID: 0853.92025
DOI: 10.1007/BF00375615
author: Martin Feinberg
published in: Archive for Rational Mechanics and Analysis
publication date: 1997-01-06T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 92E20
Mathematics Subject Classification ID: 92E10
zbMATH DE Number: 880578
zbMATH Keywords: deficiency one reaction network
zbMATH Keywords: multiple positive equilibria
zbMATH Keywords: regular networks
zbMATH Keywords: systems of nonlinear polynomial equations in several variables
zbMATH Keywords: systems of linear inequalities
reviewed by: Dietmar Dorninger
describes a project that uses: crntwin
MaRDI profile type: Publication
cites work: The existence and uniqueness of steady states for a class of chemical reaction networks
cites work: Traveling composition waves on isothermal catalyst surfaces
description: scientific article; zbMATH DE number 880578