The Fisher-Kolmogorov model of reactions with diffusion

2 The Fisher-Kolmogorov model of reactions with diffusion 

An equation of a reaction with diffusion for one variable is of the form 

In the case when P(x) = ax(l — x), a = const, we obtain a model used by Fisher and Kolmogorov for the description of some biological processes (more specifically, the model may represent spread of an epidemic in a certain region or propagation of a favourable gene in a population)  

Note that equation (6.123b) is also obtained by accounting for diffusion in the kinetic equation (6.28) for a reversible autocatalytic reaction and renormalizing the x-variable, x - (ki/k i)x. 

This model also appears in a description of the Belousov-Zhabotinskii reaction as a special case of the Oregonator with diffusion, see Section 6.3.2.3. 

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