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Application of quotient rings for stability analysis in chemical systems

MPG-Autoren
http://pubman.mpdl.mpg.de/cone/persons/resource/persons22050

Sauerbrei,  Sonja
Physical Chemistry, Fritz Haber Institute, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons22104

Sensse,  Anke
Physical Chemistry, Fritz Haber Institute, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons21488

Eiswirth,  Markus
Physical Chemistry, Fritz Haber Institute, Max Planck Society;

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sauerbrei_pv_revised.pdf
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Zitation

Sauerbrei, S., Sensse, A., & Eiswirth, M. (2011). Application of quotient rings for stability analysis in chemical systems. Zeitschrift für Naturforschung Section A, 66, 231-241. Retrieved from http://www.znaturforsch.com/aa/v66a/66a0231.pdf.


Zitierlink: http://hdl.handle.net/11858/00-001M-0000-000F-4130-0
Zusammenfassung
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.