Complete optimization of models of the Belousov–Zhabotinsky reaction at a Hopf bifurcation

Abstract

We analyze two reaction networks for the Belousov–Zhabotinsky reaction at a Hopf bifurcation by methods developed in a previous paper. One network is equivalent to the oregonator, the other is an extended oregonator with seven species and eleven reactions. For each model the current polytope has a simple geometry and the paper serves to illustrate the analytic methods and explain their relation to the chemistry of the reactions. All possible models based on each network are compared with experimental quenching results and other experimental data at a supercritical Hopf bifurcation. The best possible fit is obtained through a systematic search of the current cone and concentration space. For the oregonator, the optimization is essentially complete and results in a determination from scratch of all six rate constants of the model. The agreement of the optimum with the experiments is very good, and the agreement of the deduced rate constants with the most recent set determined from kinetic measurements on subsystems seems quite remarkable. The larger model is too big for a really complete search, but the best point found shows a significant improvement over our previous results based on continuation methods. Despite the good agreement with the experiments, a graphical eigenvector analysis definitively shows that perfect agreement is impossible for any of the models, no matter how the rate constants are chosen; additional reactions are needed.