Chemical reaction network theory and the problem of reaction rate

A chemical system can be described at different levels. When we focus on the population of chemical species, it is convenient to consider the system as consisting of a number of chemical reactions, which assumes the structure of a (hyper)graph together with the species. The chemical reaction network theory studies chemical systems described in such a way. It aims to elucidate the dynamics of overall chemical composition in terms of the associated graph structure. Notably, it applies not only to chemical systems but also to more general systems as long as the mathematical structure is compatible. In the first part of this talk, we will review the basic concepts and results of the theory, which mainly concern the existence and stability of the equilibrium. From the viewpoint of chemical kinetics, it is interesting to consider the rate of the overall reaction, which may be obtained by the total balance of chemical species. The second part of the talk will be devoted to this topic. Formulation of the problem and some results will be presented. In particular, chemical reaction networks with first-order reactions will be considered in detail.