Abstract
A non-linear stability analysis using a multi-scale perturbation procedure is carried out on the practical Thomas reaction-diffusion mechanism which exhibits bifurcation to non-uniform states. The analytical results compare favourably with the numerical solutions. The sequential patterns generated by this model by variations in a parameter related to the reaction-diffusion domain indicate its capacity to represent certain key morphogenetic features required in a recent model by Kauffman for pattern formation in theDrosophila embryo.
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Ochoa, F.L., Murray, J.D. A non-linear analysis for spatial structure in a reaction-diffusion model. Bltn Mathcal Biology 45, 917–930 (1983). https://doi.org/10.1007/BF02458822
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DOI: https://doi.org/10.1007/BF02458822