Abstract

GARZON, Diego A.; RAMIREZ, Angélica M.  and  DUQUE, Carlos A.. TURING PATTERNS ON SPHERES WITH CONTINUOUS GROWTH. Rev.EIA.Esc.Ing.Antioq [online]. 2012, n.17, pp.39-46. ISSN 1794-1237.

We have developed several numerical examples of reaction-diffusion equations with growth surface domain. In this research we use the Schnakenberg reaction model, with parameters in the Turing space. Therefore, numerical tests are performed on the appearence of Turing patterns in spherical surfaces. For the solution of reaction diffusion equations provides a method of settling on surfaces in three dimensions using the finite element method under the total Lagrangian formulation. The results show that the formation of Turing patterns depends on the growth rate of the surface, the type of wave number predicted in the theory of square domains and their stabilization time. These results may explain some phenomena of pattern change on the surface of the skin of animals that exhibit characteristic spots.

Keywords : reaction-diffusion; Turing; total Lagrangian; finite elements; deformation of surfaces.

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