Analytic representation of oscillations, excitability, and traveling waves in a realistic model of the Belousov–Zhabotinskii reaction

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Abstract
On the basis of their thorough investigation of the mechanism of the malonic acid–bromate–cerium reaction, Field and Noyes have proposed a simple model for the sustained oscillations observed in this system. In this paper, I present a scheme of analysis of their differential equations which yields simple analytic formulae characterizing: (a) the domain in parameter space of local asymptotic stability of the steady state solution, (b) the amplitude, period, and waveform of limit cycle oscillations, (c) the direction of bifurcation of small amplitude periodic solutions, (d) the existence of large amplitude stable periodic solutions simultaneously with a locally stable constant solution, (e) the threshold of excitation and transient response to perturbations from a globally, asymptotically stable solution, and (f) the spatial and temporal development of the concentrations of key intermediates in periodic traveling waves (plane, axisymmetric, and rotating‐spiral waves). These formulae facilitate the choice of parameter values to give reasonable agreement between model calculations and observed oscillations.