标题： 代数方法用于反应网络的分解以及稳态的存在性和数量的确定 显示英文标题

标题： Algebraic approaches for the decomposition of reaction networks and the determination of existence and number of steady states

摘要： 化学反应网络理论为严格理解化学反应以及表示它们的动力系统和微分方程提供了强大的工具。 这些网络的数学分析中经常出现的问题是依赖于显式参数值，而在许多情况下这些参数值无法通过实验确定。 这可能使得对动力系统进行分析变得不可行，尤其是在系统规模较大的情况下。 一种方法是分析整个网络的子网络，并利用这些结果进行整体分析。 我们的重点是反应网络的平衡点。 Gröbner基计算是解决与动力系统平衡点对应的多项式方程的一种有用方法。 我们确定了一类网络，其中子网络的Gröbner基计算可以用于重建整个网络的更昂贵的Gröbner基计算。 我们还补充了确定稳态是否存在以及如果存在的话有多少个的工具。 显示英文摘要

摘要： Chemical reaction network theory provides powerful tools for rigorously understanding chemical reactions and the dynamical systems and differential equations that represent them. A frequent issue with mathematical analyses of these networks is the reliance on explicit parameter values which in many cases cannot be determined experimentally. This can make analyzing a dynamical system infeasible, particularly when the size of the system is large. One approach is to analyze subnetworks of the full network and use the results for a full analysis. Our focus is on the equilibria of reaction networks. Gr\"obner basis computation is a useful approach for solving the polynomial equations which correspond to equilibria of a dynamical system. We identify a class of networks for which Gr\"obner basis computations of subnetworks can be used to reconstruct the more expensive Gr\"obner basis computation of the whole network. We compliment this result with tools to determine if a steady state can exist, and if so, how many.