Properties of two-component bimolecular and trimolecular chemical reaction systems

Abstract

By a very simple argument we show that for chemical reaction mechanisms containing only bimolecular steps, which are open to a flow of matter so that there are only two time‐dependent concentrations (X and Y), the steady state is either a saddle point, a center, or a stable node or focus. For mechanisms containing trimolecular steps we identify two processes which can lead to instability: A + 2X → 3X, and 2X + Y → 3X. The autocatalytic step A + 2X → 3X, where A is maintained at constant concentration, is explosive and it is very hard, if not impossible, to obtain limit cycle oscillations based on such an instability though we give an interesting example of conservative oscillations in a mechanism containing this step. There already exists a well‐characterized mechanism admitting limit cycle oscillations which depend on the destabilizing self‐limiting autocatalytic step 2X + Y → 3X, and these results suggest that this is the simplest example of chemical limit cycle oscillations. When the chemical reactions are coupled with diffusive processes, we also find that for bimolecular kinetics the nodes and foci are stable.