Multiple time scale analysis of two models for the peroxidase-oxidase reaction

A multiple time scale analysis of two four-variable models of the peroxidase-oxidase reaction, the DOP, and the Olsen model, is carried out. It is shown that autonomous limit cycle oscillations are exhibited by the fast subsets of these two models, but only in certain regions of parameter space, confirming the prior suggestion that the slow variable (NADH) is not essential for oscillatory behavior. However, it is found that the slow variable is essential for oscillatory behavior over other ranges of parameter values, and is always essential for complex oscillatory and chaotic behavior. This latter conclusion is based on a study involving driving the fast subset with a sinusoidally varying (NADH). This study suggests the level of coupling between fast and slow variables of an autonomous system necessary to cause the chaos observed in the DOP model. Further study of the driven system allows for the identification of a natural period of the nonoscillatory but bistable fast subsystem and a set of rules for applying a parametric driving in such a way as to generate a more complete Farey sequence from a truncated Farey sequence. These conclusions are used to compare the very similar DOP and Olsen models, which, nevertheless, exhibit quite different Farey sequences and routes to chaos. (c) 1995 American Institute of Physics.