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Free keywords:
toric geometry; quotient rings; mass action kinetics; chemical reaction networks; stoichiometric network analysis
Abstract:
Concepts from algebraic geometry (polynomial rings) can be used to determine analytically the stationary solutions in chemical reaction systems, more generally, systems of ordinary differential aligns of polynomial form. The stability analysis via the Jacobian matrix often leads to complicated expressions which can hardly be analyzed. It is shown that these expressions can be simplified by forming quotient rings of the corresponding polynomial ring. The coefficients in the characteristic aligns of the Jacobian can be represented by the normal forms obtained by generating the quotient rings so that their sign changes in dependence of a kinetic parameter and hence the stability can be determined. The procedure is illustrated using a well-known surface reaction.
