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          Institute: Fritz-Haber-Institut     Collection: Physical Chemistry     Display Documents



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ID: 429900.0, Fritz-Haber-Institut / Physical Chemistry
Application of quotient rings for stability analysis in chemical systems
Authors:Sauerbrei, Sonja; Sensse, Anke; Eiswirth, Markus
Language:English
Date of Publication (YYYY-MM-DD):2011
Title of Journal:Zeitschrif für Naturforschung A
Journal Abbrev.:Z. Naturfors. Sect. A
Volume:66
Start Page:231
End Page:241
Review Status:Peer-review
Audience:Experts Only
Abstract / Description: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.
Free Keywords:toric geometry; quotient rings; mass action kinetics; chemical reaction networks; stoichiometric network analysis
External Publication Status:published
Document Type:Article
Communicated by:Martin Wolf
Affiliations:Fritz-Haber-Institut/Physical Chemistry
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