Oscillations in chemical systems. XII. Applicability to closed systems of models with two and three variables

Most computations on models of chemical oscillators have maintained constant concentrations of major reactants while concentrations of intermediates were allowed to vary. Such simplified computations are applicable to closed chemical systems only if reactants are depleted by small fractions during each cycle. Existing models that involve only two intermediate species are generally unsatisfactory for modeling closed systems. Thus, the Lotka mechanism (which does not generate a true limit cycle) can not model even infinitesimally small oscillations in a closed system unless the rate constant for predator–prey interaction is very large. The Brusselator model can not model closed system oscillations unless the various rate constants are confined to very restricted ranges. Any other model with only two intermediates must contain a step at least third order in those intermediates. By contrast, the Oregonator model with three variables and only first- and second-order processes, can model a closed system in which the major reactants are depleted by only a small fraction during each cycle. By suitable coupling approximations, some of the mathematical advantages of models involving only two variables can be retained when the Oregonator is used as a model.