Abstract
Several numerical examples of reaction–diffusion equations with increasing dominance are presented. Schnakenberg reaction model is solved with parameters in the Turing space. Therefore, numerical tests are performed in spherical and cylindrical surfaces. For the solution of the reaction–diffusion equations we provide a method of solution on surfaces in three dimensions using the finite element method with 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 the stabilization time of the same. These results may explain some phenomena of change of pattern on the surface of the skin of animals that exhibit characteristic spots and stripes.
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