Models of reactions with diffusion and their analysis

2 Models of reactions with diffusion and their analysis 

The models of reactions with diffusion will be described below. The Brusselator with diffusion is a model system while the Oregonator with diffusion corresponds to the Belousov-Zhabotinskii reaction. First we shall describe the Fisher-Kolmogorov model with diffusion which, as will be shown later, may be regarded as a special case of the Oregonator with diffusion. 

Catastrophes occurring in these models in the presence of diffusion will be examined next. We shall investigate wave phenomena in the Fisher-Kolmogorov model and in the Oregonator as well as dissipative structures in the Brusselator. The studies of systems of reactions with diffusion, both experimental and theoretical, have not led yet to the formulation of a complete theory. Consequently, only fundamental results concerning the phenomena of a loss of stability type in these models will be presented. 

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