Cycle Structure in SR and DSR Graphs: Implications for Multiple Equilibria and Stable Oscillation in Chemical Reaction Networks

摘要

Associated with a chemical reaction network is a natural labelled bipartitemultigraph termed an SR graph, and its directed version, the DSR graph. Theseobjects are closely related to Petri nets. The construction of SR and DSRgraphs for chemical reaction networks is presented. Conclusions aboutasymptotic behaviour of the associated dynamical systems which can be drawneasily from the graphs are discussed. In particular, theorems on ruling out thepossibility of multiple equilibria or stable oscillation in chemical reactionnetworks based on computations on SR/DSR graphs are presented. These includeboth published and new results. The power and limitations of such results areillustrated via several examples.