On Modelling Pattern Formation by Activator-Inhibitor Systems.

摘要

The formation of spatially patterned structures in biological organisms has been modelled in recent years by various mechanisms, including pairs of reaction-diffusion equations u sub t = D1 laplacian u + f(u,v), v sub t = D2 laplacian v + g(u,v). Their analysis has been by computer simulation. In some cases, u can be interpreted as an activator and v an inhibitor. The following problem is treated: given a pattern u = phi(x) v = psi(x), find a system which has it as a stable stationary solution (stability is used in various senses in the paper). This inverse problem is shown to have solutions for reasonable phi and psi. The solutions constructed are of activator-inhibitor type with D2 > D1. (Author)