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 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 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

The Determination of Multiple Steady States in Two Families of Biological Systems

2004 ◽  
Vol 59 (3) ◽  
pp. 136-146
Author(s):  
Guo-Syong Chuang ◽  
Pang-Yen Ho ◽  
Hsing-Ya Li
Keyword(s):  
Steady State ◽  
Transport Model ◽  
Biological Systems ◽  
Linear Equations ◽  
Steady States ◽  
Metabolic Energy ◽  
Mass Action ◽  
Multiple Steady States ◽  
Mass Action Kinetics ◽  
Subnetwork Analysis

The capacity of computational multiple steady states in two biological systems are determined by the Deficiency One Algorithm and the Subnetwork Analysis. One is a bacterial glycolysis model involving the generation of ATP, and the other one is an active membrane transport model, which is performed by pump proteins coupled to a source of metabolic energy. Mass action kinetics, is assumed and both models consist of eight coupled non-linear equations. A set of rate constants and two corresponding steady states are computed. The phenomena of bistability and hysteresis are discussed. The bifurcation of multiple steady states is also displayed. A signature of multiplicity is derived, which can be applied to mechanism identifications if steady state concentrations for some species are measured. The capacity of steady state multiplicity is extended to their families of reaction networks.

Kinetic investigation of complex pseudo mass action systems by use of the pulse method

1980 ◽  
Vol 58 (4) ◽  
pp. 513-516 ◽  
Author(s):  
Erhard G. Christoffel ◽  
Indarto T. Surjo ◽  
Karl-H. Robschlager
Keyword(s):  
Pulse Method ◽  
Mass Action ◽  
Kinetic Investigation ◽  
Action Systems
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