Asymptotic Solutions of the Field-Noyes Model for the Belousov Reaction—I. Homogeneous Oscillations

Multiple-time-scale techniques are used to solve the non-linear autonomous system used by Field and Noyes to model the chemical oscillations of the Belousov reaction. An asymptotic representation, valid for a wide range of parameters, is found for a spatially homogeneous limit-cycle solution. For certain values of the parameters, two limit-cycle solutions are shown (asymptotically) to exist. For parameter values for which the limit cycle appears to be unique, it is shown to be linearly stable. The asymptotic solution is shown to correspond excellently to the numerical solution calculated by Field and Noyes for one set of parameters.