期刊
JOURNAL OF SYMBOLIC COMPUTATION
卷 33, 期 3, 页码 275-305出版社
ACADEMIC PRESS LTD ELSEVIER SCIENCE LTD
DOI: 10.1006/jsco.2001.0512
关键词
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The positive steady states of chemical reaction systems modeled by mass action kinetics are investigated. This sparse polynomial system is given by a weighted directed graph and a weighted bipartite graph. In this application the number of real positive solutions within certain affine subspaces of R-m is of particular interest. We show that the simplest cases are equivalent to binomial systems and are explained with the help of toric varieties. The argumentation is constructive and suggests algorithms. In general the solution structure is highly determined by the properties of the two graphs. We explain how the graphs determine the Newton polytopes of the system of sparse polynomials and thus determine the solution structure. Results on positive solutions from real algebraic geometry are applied to this particular situation. Examples illustrate the theoretical results. (C) 2002 Elsevier Science Ltd.
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