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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