Universality, multiplicity, and the effect of iron impurities in the Belousov–Zhabotinskii reaction

Abstract

In experiments on the Belousov–Zhabotinskii reaction in a flow reactor we have observed dynamical behavior that is described well by one-dimensional maps with a single maximum. A sequence of period doubling bifurcations was observed as a parameter was varied, and beyond the accumulation point for the period doubling sequence there was a sequence of periodic states that has the same symbolic dynamics as the states of the U (universal) sequence of Metropolis, Stein, and Stein (1973). However, in another experiment with malonic acid from a different vendor, we found that some states with particular symbol sequences occurred in three different parameter ranges rather than in one range as in the U sequence. Analysis of the effect of impurities in the reagents showed that some impurities (e.g., Fe3+ and esters of malonic acid) at concentrations of only a few ppm produced dramatic changes in the dynamics; such impurities are contained in commercially available malonic acid. Experiments with purified malonic acid indicate that the Fe2+/Fe3+ and Cu+/Cu2+ redox couples act as co-catalysts of the Belousov–Zhabotinskii reaction; their effect can be explained by a free radical mechanism. Other metal ions (e.g., Ni2+ and Co2+) at low concentrations have negligible effect on the dynamics. Finally, both the sequences with universal ordering and the sequences with multiplicity are described well by indented trapezoid maps of the type analyzed by Beyer, Mauldin, and Stein (1986).