A linear stability and bifurcation analysis is carried out on the improved mathematical model proposed by Franck and FitzHugh for the oscillations observed during the electrodissolution of iron in sulphuric acid solutions. For the improved Franck-FitzHugh model a logarithmic instead of a linear dependence of the Flade potential on H+ concentration is considered. Also a correcting function, phi, related to the transference number of the H+, is incorporated into the Nernst-Planck equation, which is applied between the bulk of the solution and the diffusion layer, to account for the effect of the charge transport by Fe2+ and SO4(2-). This type of analysis together with the inherent physico-chemical constraints gives the conditions and the limits of the control parameters for stable, decaying or periodic solutions of the dynamical equations which describe the system. The transition to periodic solutions occurs through a Hopf bifurcation. The advantage provided by the improved model is that the control parameters which are involved in the bifurcation condition include the H+ concentration of the solution, h0, the applied potential, E(p), and a function related to the transference number of the H+ ions, phi. Therefore, a direct comparison of the bifurcation results with the experimental data can be made to determine more explicitly the parameters for which the model provides not only qualitatively but also quantitatively reasonable predictions. The kinetics equations for the periodically forced improved and simplified Franck-FitzHugh model are derived.
