Influencia de la curvatura en la formación de patrones: el mecanismo de Turing en el círculo

Palabras clave: Patrones de Turing, reacción-difusión, variedades de curvas


En este trabajo estudiamos la influencia de la curvatura del medio sobre la formaci´on de patrones mediante el mecanismo de inestabilidad de Turing generada por difusi´on. Para analizar el efecto de la curvatura consideramos la variedad curva cerrada m´as simple, una circunferencia. Presentamos el operador de Laplace-Beltrami, que es la generalizaci´on del Laplaciano sobre variedades, con el fin de resolver la ecuaci´on de difusi´on y describir las modificaciones que induce la curvatura en la funci´on de distribuci´on y en el camino cuadr´atico medio. Como un caso particular de estudio empleamos el modelo de Gierer-Meinhardt. Se muestra que el rango de modos inestables donde ser´a posible hallar los patrones espacio-temporales depende del radio y, por lo tanto, de la curvatura del c´ırculo espec´ıfico.


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Cómo citar
Núñez-López, M., & Chacón-Acosta, G. (2022). Influencia de la curvatura en la formación de patrones: el mecanismo de Turing en el círculo. Pädi Boletín Científico De Ciencias Básicas E Ingenierías Del ICBI, 10(Especial), 42-51.