Computations simulating experimental observations of complex bursting patterns in the Belousov–Zhabotinsky system

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Abstract
A model based on five independent composition variables has been tested by simulating the complex bursting patterns observed experimentally for a Belousov–Zhabotinsky system in a flow reactor. If the system is in a region of constraint space where all stationary states are locally unstable, and if malonic acid concentration in the feed is decreased at constant flow of bromide ion, simple limit‐cycle oscillations persist until the system reaches the Hopf bifurcation which generates a stable stationary state with low concentration of bromide ion. If bromide ion concentration in the feed is increased at constant flow of malonic acid, more and more small‐amplitude oscillations are interspersed between trains of fewer and fewer large‐amplitude excursions until a Hopf bifurcation leads to a stable stationary state with a high concentration of bromide ion. Patterns may be quite complex but usually repeat regularly. If a firing number is defined as ΣS/(ΣS+ΣL), where the summations represent the numbers of small‐ and large‐amplitude oscillations in a complete pattern, then this firing number increases monotonically with increasing bromide ion in the feed. Narrow regions of chaotic mixing of patterns are also observed. The computations agree spectacularly with the careful experimental observations of Maselko and Swinney. Two separate curves are generated by the Hopf bifurcations which limit local stabilities of stationary states containing low and high concentrations of bromide ion, and the intersection of these curves provides a rationale for the ‘‘cross‐shaped phase diagrams’’ which define regions of bistability and of oscillations in constraint spaces for such systems.