Reaction 7 is an empirical relationship including a factor, f, which relates the number of ions released by the reduction of two Ce(IV) ions and the concomitant oxidation of malonic acid and its brominated derivatives. The concentration of brominated derivatives depends on the time course of the reaction via the production of in reaction 1. Thus, f also depends on time. To account for this complete mechanism, the seven reactions employed in this paper must be expanded to 21 elementary steps. As employed, however, f plays a pivotal role. If f is much below 2, then an insufficient amount of is produced to remove completely. In this case, the steady-state  is high and depends upon the competition between an autocatalytic cycle (reactions 5 and 6) and a second-order disproportionation reaction (4). When f is much above 2, then  is sufficient at all times that reaction 2 is important. This sink for competes with an autocatalytic cycle (reactions 5 and 6). The result is a low steady-state . Chemical oscillations occur when f is near 2 because the dominant chemical mode alternates.
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