SIMPLE-MODELS OF DETERMINISTIC CHAOS IN THE BELOUSOV-ZHABOTINSKY REACTION

A recently developed, chemically accurate, 11-variable model of the Belousov-Zhabotinsky reaction previously has been shown to reproduce essentially all details of the low-flow-rate complexity and deterministic chaos observed when the reaction is run in a continuous-flow, stirred tank reactor. However, this model is large enough that extracting the skeletal source of the complexity in its dynamic structure was not possible. That is done here by reducing the number of variables in the model by means of rate sensitivity analysis as well as the conventional methods of chemical kinetics, e.g., the rate-determining step, equilibrium, and quasi-steady-state approximations. A 7-variable model retaining mass-action kinetics form is obtained first. It is then reduced to two 4-variable models of nonpolynomial form, which may finally be reduced to a 3-variable model. All models with four or more variables reproduce the major features of the experimentally observed chaos at low flow rates. Agreement with experiment is less good with the 3-variable model. The 4-variable models also are able to reproduce many features of the experimentally observed complex oscillations and chaos at high CSTR flow rates that previously has not been possible in a chemically accurate model. The source of complexity at both high and low flow rates is found in the complex interaction of two frequencies, one related to a negative feedback loop solely within the homogeneous kinetics of the BZ reaction and the other related to the coupling of a feedback loop involving BrMA, a product of the reaction, with the CSTR flow.