The general theory of stoichiometric number by Juro Horiuti—Application to the analysis of the stoichiometries of chemical oscillation systems

Abstract

A criterion for preserving overall stoichiometry in reduced mechanisms of the Belousov–Zhabotinski (BZ) reaction was expressed by the stoichimetric numbers, ν j A ,ν k A ,ν j B ,ν k B ,ν j C , and ν k C of steps j and k of the BZ reaction which are combined in the reduced mechanism as, ν j A −=rνk A ,ν j B =rνk B , and ν j C =rνk C , where superscripts A , B and C imply three reaction routes of the BZ reaction and a constant r is the ratio of the net rates of steps j and k . The stoichiometric relations of complex reaction networks were discussed with the general theory of stoichiometric number introduced and developed by Horiuti et al. Horiuti introduced the concept of reaction route in the theory, in which the reaction route was expressed by a set of stoichiometric numbers. The theory was applied to analyses of the stoichiometries in the reaction network of the 11 pseudo-elementary reactions (steps) of the Belousov–Zhabotinski (BZ) reaction and its reduced mechanism called the amplified Oregonator. Both of the mechanisms were developed by Noyes et al. for analysis of the oscillatory phenomena of the BZ reaction. The amplified Oregonator was concluded sufficiently to describe the stoichiometries of the original network of 11 steps by using the general theory of stoichometric number. In comparison of these analyses of the stoichiometries in the above two mechanisms, a criterion for preserving overall stoichiometry in reduced mechanisms was introduced.