Belousov–Zhabotinskii Reaction Models

Abstract

This chapter is devoted to studying reaction–diffusion models for the Belousov–Zhabotinskii reaction. The reaction which consists of more than ten elementary chemical reactions arising simultaneously and which does not tend to any chemical equilibrium is known as one of typical self-organization phenomena in chemistry. In 1974, Field–Noyes presented a simple mathematical model for describing the complicated mechanism from a global point of view. Their reaction–diffusion model of dimensionless form is given by

$$\begin{cases}\frac{\partial u}{\partial t}=a\varDelta u+\varepsilon^{-1}(qw-uw+u-u^2)&\text{in}\ \varOmega\times(0,\infty), \\\noalign{\vspace{3pt}}\frac{\partial v}{\partial t}=b\varDelta v+u-v&\text{in}\ \varOmega\times(0,\infty), \\\frac{\partial w}{\partial t}=d\varDelta w+\delta^{-1}(-qw-uw+cv)&\text{in}\ \varOmega\times(0,\infty).\end{cases}$$

Here, u denotes the concentration of HBrO₂, v the concentration of Ce⁴⁺, and w the concentration of Br⁻, respectively, in a vessel represented by Ω. The positive constants δ, ε, q, and c are chemical parameters, where especially δ, ε, and q are considered to be small.