论文标题
反应网络的复曲面动力系统模量空间的结构
The structure of the moduli space of toric dynamical systems of a reaction network
论文作者
论文摘要
我们认为感谢您的动力学系统也称为复杂平衡的质量成分系统。这些是非常稳定的多项式动力学系统，它是由对反应网络的数学模型分析产生的，当时，在质量表演动力学的假设下，它们可以引起复杂的平衡平衡。给定一个反应网络，我们研究了该网络生成的复曲面动力学系统的模量空间，也称为网络的复曲基因座。复曲基因座是一个代数品种，我们对其拓扑特性特别感兴趣。我们表明，复杂平衡的平衡不连续取决于复合曲线基因座中的参数值，并且，使用此结果，我们证明了复合物位基因座具有出色的产品结构：它对一组复杂平衡的磁通量的产物是同构的，并且网络的封装不变型多面体。特别是，因此，图意的基因座是可缩度的歧管。最后，我们表明，相对于生成反应网络的两种植物仿射转化，图意的基因座是不变的。
We consider toric dynamical systems, which are also called complex-balanced mass-action systems. These are remarkably stable polynomial dynamical systems that arise from the analysis of mathematical models of reaction networks when, under the assumption of mass-action kinetics, they can give rise to complex-balanced equilibria. Given a reaction network, we study the moduli space of toric dynamical systems generated by this network, also called the toric locus of the network. The toric locus is an algebraic variety, and we are especially interested in its topological properties. We show that complex-balanced equilibria depend continuously on the parameter values in the toric locus, and, using this result, we prove that the toric locus has a remarkable product structure: it is homeomorphic to the product of the set of complex-balanced flux vectors and the affine invariant polyhedron of the network. In particular, it follows that the toric locus is a contractible manifold. Finally, we show that the toric locus is invariant with respect to bijective affine transformations of the generating reaction network.
