Cycle Structure in SR and DSR Graphs: Implications for Multiple Equilibria and Stable Oscillation in Chemical Reaction Networks
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.
KeywordsMultiple Equilibrium Stoichiometric Matrix Cycle Structure Nonnegative Orthant Extremal Vector
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