A family of sparse polynomial systems arising in chemical reaction systems
Please always quote using this URN: urn:nbn:de:0297-zib-4150
- A class of sparse polynomial systems is investigated which is defined by a weighted directed graph and a weighted bipartite graph. They arise in the model of mass action kinetics for chemical reaction systems. In this application the number of real positive solutions within a certain affine subspace is of particular interest. We show that the simplest cases are equivalent to binomial systems while in general the solution structure is highly determined by the properties of the two graphs. First we recall results by Feinberg and give rigorous proofs. Secondly, we explain how the graphs determine the Newton polytopes of the system of sparse polynomials and thus determine the solution structure. The results on positive solutions from real algebraic geometry are applied to this particular situation. Examples illustrate the theoretical results.
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| Author: | Karin Gatermann, Birkett Huber |
|---|---|
| Document Type: | ZIB-Report |
| Tag: | mass action kinetics; positive solutions; sparse polynomial systems |
| MSC-Classification: | 14-XX ALGEBRAIC GEOMETRY / 14Mxx Special varieties / 14M25 Toric varieties, Newton polyhedra [See also 52B20] |
| Date of first Publication: | 1999/08/09 |
| Series (Serial Number): | ZIB-Report (SC-99-27) |
| ZIB-Reportnumber: | SC-99-27 |
| Published in: | Appeared in: Journal of Symbolic Computation 33 (2002) 275-305 |
