相互作用元素系统内射性和多重平衡的图论方法
Graph-theoretic approaches to injectivity and multiple equilibria in systems of interacting elements
摘要：
我们将以前化学反应网络中的内射性的工作扩展到一般的相互作用网络。矩阵和图论条件，这些系统的内射性。一个特定的签署，定向，标记，二部多重图，称为“DSR图”，是一个有用的表示的互动网络时，讨论问题的注入性。一个图论的条件，以前开发的化学反应网络的背景下，被证明是足够的，以保证一个大类的系统的注入性。图论条件很容易陈述，而且往往很容易检验。最后通过实例说明了该理论的广泛适用性。
英文摘要：
We extend previous work on injectivity in chemical reaction networks to general interaction networks. Matrix- and graph-theoretic conditions for injectivity of these systems are presented. A particular signed, directed, labelled, bipartite multigraph, termed the ``DSR graph'', is shown to be a useful representation of an interaction network when discussing questions of injectivity. A graph-theoretic condition, developed previously in the context of chemical reaction networks, is shown to be sufficient to guarantee injectivity for a large class of systems. The graph-theoretic condition is simple to state and often easy to check. Examples are presented to illustrate the wide applicability of the theory developed.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
