A key point in the analysis of dynamical models of biological systems is to handle systems of relatively high dimensions. In the present paper we propose a method to hierarchically organize a certain type of piecewise affine (PWA) differential systems. This specific class of systems has been extensively studied for the past few years, as it provides a good framework to model gene regulatory networks. The method, shown on several examples, allows a qualitative analysis of the asymptotic behavior of a PWA system, decomposing it into several smaller subsystems. This technique, based on the well-known strongly connected components decomposition, is not new. However, its adaptation to the non-smooth PWA differential equations turns out to be quite relevant because of the strong discrete structure underlying these equations. Its biological relevance is shown on a 7-dimensional PWA system modeling the gene network responsible for the carbon starvation response in Escherichia coli.

中文翻译：

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基因调控网络分段仿射模型的层次分析。

生物系统动力学模型分析的一个关键点是处理相对高维的系统。在本文中，我们提出了一种分层组织某种类型的分段仿射 (PWA) 差分系统的方法。过去几年对这一特定类别的系统进行了广泛的研究，因为它提供了一个很好的框架来模拟基因调控网络。该方法显示在几个示例中，允许对 PWA 系统的渐近行为进行定性分析，将其分解为几个较小的子系统。这种基于众所周知的强连通分量分解的技术并不新鲜。然而，由于这些方程具有很强的离散结构，因此它对非光滑 PWA 微分方程的适应证明是非常相关的。