Bifurcation analysis of chemical reaction mechanisms. I. Steady state bifurcation structure

Abstract

The vocabulary and techniques of numerical bifurcation analysis are described, with an emphasis on steady state bifurcations of codimension one and two. The direct computation of bifurcation sets is shown to be of considerable utility in analyzing and comparing complex chemical reaction mechanisms. The systems chosen for analysis are the chlorite–iodide and the mixed Landolt reactions. The calculation of a simple hysteresis loop for a mechanism of the chlorite–iodide reaction using both numerical bifurcation analysis and numerical integration begins an extended comparison between the methods advocated in this paper and more familiar methods. The systematic identification of the existence of isolated branches of steady states is described for a second mechanism of the chlorite–iodide reaction. Two mechanisms for the mixed Landolt system are contrasted. It is found that the alternative negative feedback pathway mechanism, which reproduces the periodic behavior more successfully at a selected point in parameter space, is less satisfactory than the EOE mechanism in describing the overall bifurcation behavior of the system in the parameter plane for which experimental data are available. Finally, we examine another mechanism for the chlorite–iodide reaction. This mechanism was designed with the intent of suppressing oscillatory behavior on a subset of parameter space. Numerical integration revealed only bistability of steady states, as desired, but numerical bifurcation analysis reveals a sizeable region in the previously investigated subset of parameter space on which oscillatory behavior exists.