Graph-theoretic methods for the analysis of chemical and biochemical networks. I. Multistability and oscillations in ordinary differential equation models
Graph-theoretic methods for the analysis of chemical and biochemical networks. I. Multistability and oscillations in ordinary differential equation models
复制标题
DOI：
10.1007/s00285-007-0099-1
复制
发表时间：
2007-07-01
影响因子：
1.9
通讯作者：
Roussel, Marc R.
中科院分区：
文献类型：
--
作者：
Mincheva, Maya;Roussel, Marc R.
化学机理是化学反应网络的模型，由一组表示分子如何相互反应的基元反应组成。在经典的质量作用动力学中，一个机制意味着一组常微分方程（ODE），它控制着浓度的时间演化。在这篇文章中，化学动力学的常微分方程模型，有潜在的多个正平衡或振荡进行了研究。我们开始考虑一些方法的稳定性分析的基础上的有向图的雅可比矩阵。然后我们证明了两个定理最初由A。N. Ivanova将质量作用模型的分叉结构与具有代表化学物种和反应的节点的二分图的属性关联起来。我们提供了几个例子，这些定理的应用。
A chemical mechanism is a model of a chemical reaction network consisting of a set of elementary reactions that express how molecules react with each other. In classical mass-action kinetics, a mechanism implies a set of ordinary differential equations (ODEs) which govern the time evolution of the concentrations. In this article, ODE models of chemical kinetics that have the potential for multiple positive equilibria or oscillations are studied. We begin by considering some methods of stability analysis based on the digraph of the Jacobian matrix. We then prove two theorems originally given by A. N. Ivanova which correlate the bifurcation structure of a mass-action model to the properties of a bipartite graph with nodes representing chemical species and reactions. We provide several examples of the application of these theorems.