A NOVEL MODEL FOR THE SIMULATION OF CHAOS IN LOW-FLOW-RATE CSTR EXPERIMENTS WITH THE BELOUSOV ZHABOTINSKY REACTION - A CHEMICAL MECHANISM FOR 2 FREQUENCY OSCILLATIONS

Continuous-flow, stirred tank reactor (CSTR) experiments with the oscillatory Belousov-Zhabotinsky (BZ) reaction provide the most important examples of chemical chaos. Experiments performed at low flow rates at the University of Texas in Austin are particularly important because of the large amount of data accumulated and the apparent low dimensionality of the attractor. Although the mechanism of the BZ reaction is largely elucidated, it has not been previously possible to simulate this aperiodicity by using realistic models of the homogeneous dynamics of the BZ system. We present here such a model based on the interaction of two frequency sources within the homogeneous flow system. One frequency is that of the Oregonator core of the model. The other originates in the dynamics of the major bromide ion precursor, bromomalonic acid (BrMA), which is a product of the overall reaction as well as a bifurcation parameter of the Oregonator core. Its concentration remains high but undergoes small-amplitude oscillations. There is a critical value of [BrMA] above which the reduced steady state of the Oregonator core becomes stable, causing [BrMA] to decrease because it is not produced in significant amounts in this state but is still washed out in a first-order manner by the flow. This negative feedback of [BrMA] on itself establishes a second frequency source within the homogeneous BZ dynamics. The interaction of the two frequencies creates the complex dynamics observed. The model, consisting of 11 dynamic variables and 19 reactions, simulates very well for the experimental conditions the observed series of major periodic states, the bifurcations of these states to chaos, and the presence of periodic-chaotic windows. Both the simulated waveforms and their next-maximum maps agree well with the measured ones. Several regions of hysteresis and very long transients also are observed in the simulations.