Hopf bifurcation in chemical kinetics

We study Hopf bifurcations in chemical reaction systems for their potential use in quantitative experimental analysis of the kinetics of oscillatory reactions. Three models of the Belousov–Zhabotinsky reaction are investigated as examples. For these we have determined and characterized the sub- and supercritical Hopf bifurcations in their dependence on parameters of the models. For supercritical bifurcations we calculate a number of parameters that can be used for quantitative comparison of models and experiment. In particular, we calculate expansion coefficients of the flow rate, the frequency of oscillation, and a Floquet exponent; the small parameter of the expansions is the square of the amplitude of the fundamental Fourier component of the oscillations. We also calculate quenching amplitudes from an adjoint eigenvector of the Jacobi matrix of the kinetics. They determine the conditions under which the small amplitude oscillations can be quenched by addition of the species participating in the reaction. The model properties are compared with experiment. They show qualitative, but not quantitative agreement.