scholarly journals Weakly Reversible Mass-Action Systems With Infinitely Many Positive Steady States

2020 ◽  
Vol 80 (4) ◽  
pp. 1936-1946 ◽  
Author(s):  
Balázs Boros ◽  
Gheorghe Craciun ◽  
Polly Y. Yu
Keyword(s):  
Steady States ◽  
Mass Action ◽  
Action Systems ◽  
Positive Steady States

scholarly journals A generalization of Birch's theorem and vertex-balanced steady states for generalized mass-action systems

2019 ◽  
Vol 16 (6) ◽  
pp. 8243-8267 ◽  
Author(s):  
Gheorghe Craciun ◽  
◽  
Stefan Muller ◽  
Casian Pantea ◽  
Polly Y. Yu ◽  
...  
Keyword(s):  
Steady States ◽  
Mass Action ◽  
Action Systems

scholarly journals Zero Eigenvalue Analysis for the Determination of Multiple Steady States in Reaction Networks

1998 ◽  
Vol 53 (3-4) ◽  
pp. 171-177
Author(s):  
Hsing-Ya Li
Keyword(s):  
Steady State ◽  
Rate Constants ◽  
Reaction Network ◽  
Steady States ◽  
Eigenvalue Analysis ◽  
Zero Eigenvalue ◽  
Positive Steady State ◽  
Positive Steady States ◽  
Positive Rate ◽  
System Of Inequalities

Abstract A chemical reaction network can admit multiple positive steady states if and only if there exists a positive steady state having a zero eigenvalue with its eigenvector in the stoichiometric subspace. A zero eigenvalue analysis is proposed which provides a necessary and sufficient condition to determine the possibility of the existence of such a steady state. The condition forms a system of inequalities and equations. If a set of solutions for the system is found, then the network under study is able to admit multiple positive steady states for some positive rate constants. Otherwise, the network can exhibit at most one steady state, no matter what positive rate constants the system might have. The construction of a zero-eigenvalue positive steady state and a set of positive rate constants is also presented. The analysis is demonstrated by two examples.

scholarly journals Complex-balanced equilibria of generalized mass-action systems: necessary conditions for linear stability

2020 ◽  
Vol 17 (1) ◽  
pp. 442-459
Author(s):  
Balázs Boros ◽  
◽  
Stefan Müller ◽  
Georg Regensburger ◽  
Keyword(s):  
Linear Stability ◽  
Necessary Conditions ◽  
Mass Action ◽  
Action Systems

scholarly journals Toric ideals and graph theory to analyze Hopf bifurcations in mass action systems

2005 ◽  
Vol 40 (6) ◽  
pp. 1361-1382 ◽  
Author(s):  
Karin Gatermann ◽  
Markus Eiswirth ◽  
Anke Sensse
Keyword(s):  
Graph Theory ◽  
Mass Action ◽  
Hopf Bifurcations ◽  
Toric Ideals ◽  
Action Systems

scholarly journals Families of toric chemical reaction networks

2020 ◽  
Vol 58 (9) ◽  
pp. 2061-2093
Author(s):  
Michael F. Adamer ◽  
Martin Helmer
Keyword(s):  
Chemical Reaction ◽  
Chemical Reaction Networks ◽  
Steady States ◽  
Reaction Networks ◽  
Core Network ◽  
Entire Family ◽  
Data Set ◽  
The Family ◽  
Positive Steady States ◽  
State Behaviour

Abstract We study families of chemical reaction networks whose positive steady states are toric, and therefore can be parameterized by monomials. Families are constructed algorithmically from a core network; we show that if a family member is multistationary, then so are all subsequent networks in the family. Further, we address the questions of model selection and experimental design for families by investigating the algebraic dependencies of the chemical concentrations using matroids. Given a family with toric steady states and a constant number of conservation relations, we construct a matroid that encodes important information regarding the steady state behaviour of the entire family. Among other things, this gives necessary conditions for the distinguishability of families of reaction networks with respect to a data set of measured chemical concentrations. We illustrate our results using multi-site phosphorylation networks.

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