A family of sparse polynomial systems arising in chemical reaction systems
A family of sparse polynomial systems arising in chemical reaction systems
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DOI：
10.1006/jsco.2001.0512
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发表时间：
2002-03-01
影响因子：
0.7
通讯作者：
Huber, B
中科院分区：
文献类型：
--
作者：
Gatermann, K;Huber, B
研究了质量作用动力学模型化学反应系统的正定态问题。这个稀疏多项式系统由一个加权有向图和一个加权二部图给出。在这个应用程序中的真实的正解的数量在某些仿射子空间的R-m是特别感兴趣的。我们表明，最简单的情况下是等价的二项式系统和解释的帮助下，复曲面品种。论证是建设性的，并提出了算法。一般来说，解的结构是由两个图的性质决定的。我们解释了如何确定稀疏多项式系统的牛顿多面体的图形，从而确定解决方案的结构。从真实的代数几何正解的结果适用于这种特殊情况。实例说明了理论结果。(C)2002 Elsevier Science Ltd.
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.