By considering the classical Oregonator model, the effect of the main reactants, i.e., bromate and malonic acid, on the behavior of the Belousov-Zhabotinskii system is studied. This analysis is a prerequisite for the understanding of the occurrence and disappearance of oscillations in batch reactors. A parametric analysis of the Oregonator in the three-dimensional space spanned by the bromate concentration, the malonic acid concentration, and the stoichiometric coefficient f is performed. Through asymptotic stability analysis the Hopf bifurcation set in the parameter space is determined analytically, whereas its character is defined through normal form analysis. In this study the most plausible values of the kinetic parameters, namely the ''Lo'' values proposed by Tyson (Tyson, J. J. In Oscillations and Traveling Waves in Chemical Systems; Field, R. J., Burger, M., Eds.; Wiley-Interscience: New York, 1985), are used. The system may exhibit both sub- and supercritical Hopf bifurcations, and near the latter the phenomenon of canard explosion has been observed. The results obtained with the ''Hi'' values are also reported for a comparison with previous studies in the literature.
Bifurcation-analysis of the Oregonator Model In the 3-d Space Bromate Malonic-acid Stoichiometric Coefficient
MAZZOTTI, MARCO GIUSEPPE;MORBIDELLI, MASSIMO;
1995-01-01
Abstract
By considering the classical Oregonator model, the effect of the main reactants, i.e., bromate and malonic acid, on the behavior of the Belousov-Zhabotinskii system is studied. This analysis is a prerequisite for the understanding of the occurrence and disappearance of oscillations in batch reactors. A parametric analysis of the Oregonator in the three-dimensional space spanned by the bromate concentration, the malonic acid concentration, and the stoichiometric coefficient f is performed. Through asymptotic stability analysis the Hopf bifurcation set in the parameter space is determined analytically, whereas its character is defined through normal form analysis. In this study the most plausible values of the kinetic parameters, namely the ''Lo'' values proposed by Tyson (Tyson, J. J. In Oscillations and Traveling Waves in Chemical Systems; Field, R. J., Burger, M., Eds.; Wiley-Interscience: New York, 1985), are used. The system may exhibit both sub- and supercritical Hopf bifurcations, and near the latter the phenomenon of canard explosion has been observed. The results obtained with the ''Hi'' values are also reported for a comparison with previous studies in the literature.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
