CHARACTERISTIC MODES OF OSCILLATORY CHEMICAL-REACTIONS

We show how eigenvectors of the Jacobi matrix J and its transpose J T at a supercritical Hopf bifurcation can be used for quantitative characterization and analysis of models of oscillatory chemical reactions. Eigenvectors of J determine the oscillations and the principal transients and can be expressed in terms of concentrations or reaction currents. Important reactions of a system can be easily identified this way. A pair of complex conjugate eigenvectors of JT associated with the bifurcation determines all independent quenchings of the oscillations. It can be used for quantitative comparison with experiment and in systematic search for better models. We combine the two sets of eigenvectors in a quantitative analysis of the effect of using a phase space of reduced dimension as an approximation to the full phase space. The analysis is illustrated by an explicit reduction of a five-dimensional Oregonator based model of the Belousov-Zhabotinskii reaction to a four-dimensional phase space involving a "quasi-species." The reduced phase space is tangent to a slow manifold at the bifurcating stationary point. Reconstruction of amplitudes and phases of the oscillations from incomplete quenching data is explained in terms of the reduced phase space. © 1990 American Institute of Physics.