Diffusion and chemical oscillations—theory and calculations on a mechanism for the bromate-cerium-malonic acid system

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Abstract
An approach to the calculation of the boundary of stability of chemically oscillating systems with diffusion has been developed. The method uses the fact that the Routh‐Hurwitz stability criterion has an absolute minimum of zero at the boundary of stability. The condition for this minimum can be used to obtain the shape of the boundary of stability in concentration space, the wavelength and frequency of the undamped perturbation, and the oscillating normal modes of the reaction system. The method is developed using a model mechanism derived from the one discussed by Glansdorff and Prigogine for the bromate‐cerium‐malonic acid instability. The difficulties to be encountered if this method is extended to the much more complicated mechanism of Noyes, Field, and Körös appear great. Calculations done for the model mechanism produced a boundary of stability with a very complex shape which was dependent on only two parameters and would serve to verify the reaction mechanism.