Multiple Time Scale Analysis of a Model Belousov--Zhabotinskii Reaction

This paper discusses the dynamics of a seven dimensional model of the Belousov--Zhabotinskii (BZ) reaction. The model was proposed by Györgyi and Field as a system of rate equations with mass-action kinetics that reproduce the complex dynamics displayed by the BZ reaction in a stirred tank reactor. We investigate the geometric mechanisms that shape the behavior of this model and the bifurcations which occur as the flow rate of the reactor is varied. Our perspective is that of geometric singular perturbation theory, and we use recent results from this theory as a foundation for mathematical analysis of the model. In particular, we examine qualitative differences in the two families of mixed-mode oscillations observed in the model.