Geodesic
Constructing universal pattern formation processes governed by reaction-diffusion systems
Electronic Journal of Differential Equations, Tome 2002 (2002).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: For a given connected compact subset $K$ in $\mathbb{R}^n$ we construct a smooth map $F$ on $\mathbb{R}^{1+n}$ in such a way that the corresponding reaction-diffusion system $u_t=D\Delta u+F(u)$ of $n+1$ components $u=(u_0,u_1,\dots ,u_n)$, accompanying with the homogeneous Neumann boundary condition, has an attractor which is isomorphic to $K$. This implies the following universality: The make-up of a pattern with arbitrary complexity (e.g., a fractal pattern) can be realized by a reaction-diffusion system once the vector supply term $F$ has been previously properly constructed.
Classification : 35B40, 70G60, 35Q99
Keywords: attractor, pattern formation 
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     author = {Huang, Sen-Zhong},
     title = {Constructing universal pattern formation processes governed by reaction-diffusion systems},
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     year = {2002},
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     url = {http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a107/}
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Huang, Sen-Zhong. Constructing universal pattern formation processes governed by reaction-diffusion systems. Electronic Journal of Differential Equations, Tome 2002 (2002). http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a107/