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1999 (1)
1998 (1)
1Author    Hsing-Ya LiRequires cookie*
 Title    Zero Eigenvalue Analysis for the Determination of Multiple Steady States in Reaction Networks  
 Abstract    A chemical reaction network can admit multiple positive steady states if and only if there exists a pos-itive 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 equa-tions. If a set of solutions for the system is found, then the network under study is able to admit multi-ple 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. 
  Reference    Z. Naturforsch. 53a, 171—177 (1998); received December 31 1997 
  Published    1998 
  Keywords    Reaction Network, Multiple Steady States, Zero Eigenvalue Analysis 
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 TEI-XML for    default:Reihe_A/53/ZNA-1998-53a-0171.pdf 
 Identifier    ZNA-1998-53a-0171 
 Volume    53 
2Author    Hsing-Ya LiRequires cookie*
 Title    Determination of Multiple Steady States in an Active Membrane Transport Model  
 Abstract    A necessary and sufficient condition is applied to determine the possibility of multiple positive steady states in a complex, active membrane transport model with a cycle, which is performed by pump pro-teins coupled to a source of metabolic energy. A set of rate constants and two corresponding steady states are computed. Hysteresis phenomena are observed. A signature of multiplicity is derived, which can be applied in mechanism identifications if steady-state concentrations for some species are measured. The bifurcation of multiple steady states is also displayed. 
  Reference    Z. Naturforsch. 54a, 245—250 (1999); received September 11 1998 
  Published    1999 
  Keywords    Multiple Steady States, Bifurcation, Active Membrane Transport Models 
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 TEI-XML for    default:Reihe_A/54/ZNA-1999-54a-0245.pdf 
 Identifier    ZNA-1999-54a-0245 
 Volume    54