14 Reaction–Diffusion, Travelling Waves and Review

Diffusion alone spreads and flattens. Combined with local reactions, growth, chemical kinetics, the firing of a nerve, it produces fronts that advance at a definite speed and patterns that arise from a uniform state. Fisher (1937) used such an equation for the spread of an advantageous gene, Kolmogorov, Petrovsky and Piskunov analysed it in the same year, and Turing (1952) showed how two diffusing chemicals could create the spots and stripes of animal coats. This last section treats the scalar and the two-species problems, and then reviews the course.

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