Stability of the bromate–cerium–malonic acid network. I. Theoretical formulation

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Abstract
The steady state stability problem for the detailed mechanism of the bromate–cerium–malonic acid system (Belousov–Zhabotinskii system) is set up mathematically. Justification for examining a reduced network with four independent reactants and eight reactions is based on recently developed theorems on the stability of topologically similar chemical networks. The reduced network’s possible steady state currents are found to lie in a convex cone whose cross section is a three dimensional ’’current polytope’’ Πc with seven vertices—each vertex being one of the extremal ’’framing current loops’’ of the network. The number of steady states is proven to be either one or three and in several special cases is proven to be one. The graphs of possible arrows are then constructed for each of the framing current loops and the feedback cycles which can destabilize are discussed. The network is proven to be stable in each of several simplices of a decomposition of Πc. The stability problem is subdivided into units which will be analyzed in detail in subsequent publications.