Minimal model for oscillatory dynamics of a nonlinear chemical reaction network

Since Bray's pioneering discovery exactly 100 years ago of the first oscillating reaction, more than 25 families of nonlinear oscillating reaction networks have been identified. The B–Z reaction network has been expanded, and complex models considering a score of chemical reactions and species have been developed. Here we look at the inverse problem and ask how the complexity of the models can be reduced. We quantify the dynamics of a minimal model by linear stability techniques and direct integration of the set of ODEs, and show that essential oscillatory and excitability features are satisfactorily captured. Reasons for the success of the minimal model are explained. Extensions of the model to fundamental chemical and biological processes are discussed, and application of the chemical reaction network to mathematically model nerve conduction is illustrated.