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首页> 外文会议>Transactions on petri nets and other models of concurrency V. >Cycle Structure in SR and DSR Graphs: Implications for Multiple Equilibria and Stable Oscillation in Chemical Reaction Networks
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Cycle Structure in SR and DSR Graphs: Implications for Multiple Equilibria and Stable Oscillation in Chemical Reaction Networks

机译：SR和DSR图中的循环结构：对化学反应网络中的多个平衡和稳定振荡的影响

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Associated with a chemical reaction network is a natural labelled bipartite multigraph termed an SR graph, and its directed version, the DSR graph. These objects are closely related to Petri nets, but encode weak assumptions on the reaction kinetics, and are more generally associated with continuous-time, continuous-state models rather than discrete-event systems. The construction of SR and DSR graphs for chemical reaction networks is presented. Conclusions about asymptotic behaviour of the associated dynamical systems which can be drawn easily from the graphs are discussed. In particular, theorems on ruling out the possibility of multiple equilibria or stable oscillation based on computations on SR/DSR graphs are presented. These include both published and new results. The power and limitations of such results are illustrated via several examples.
机译：与化学反应网络相关联的是称为SR图的自然标记的二元多重图，其有向图为DSR图。这些对象与Petri网密切相关，但编码了对反应动力学的较弱假设，并且更一般地与连续时间，连续状态模型而不是离散事件系统相关。介绍了化学反应网络的SR和DSR图的构建。讨论了有关动力学系统渐近行为的结论，这些结论可以很容易地从图中得出。特别是，提出了基于SR / DSR图的计算来排除多重平衡或稳定振荡可能性的定理。这些包括已发布结果和新结果。通过几个例子说明了这种结果的力量和局限性。

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