A bifurcation analysis of pattern formation in a diffusion governed morphogenetic field

We discuss from an analytical point of view the mechanism of pre-pattern formation in a diffusion governed morphogenetic field. The model here considered is a normalized form of one of the models, proposed by Gierer and Meinhardt, based on the general principle of lateral inhibition. The results, obtained in the framework of bifurcation theory, shows that there is a spontaneous formation of a gradient both for activator and inhibitor concentrations if the ratio between the mean squares of the diffusion ranges of inhibitor and activator is greater than a well defined critical value.