Geodesic
Constructing universal pattern formation processes governed by reaction-diffusion systems
Electronic journal of differential equations, Tome 2002 (2002)
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 
@article{EJDE_2002__2002__a207,
     author = {Huang,  Sen-Zhong},
     title = {Constructing universal pattern formation processes governed by reaction-diffusion systems},
     journal = {Electronic journal of differential equations},
     year = {2002},
     volume = {2002},
     zbl = {1024.35018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a207/}
}
TY  - JOUR
AU  - Huang,  Sen-Zhong
TI  - Constructing universal pattern formation processes governed by reaction-diffusion systems
JO  - Electronic journal of differential equations
PY  - 2002
VL  - 2002
UR  - http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a207/
LA  - en
ID  - EJDE_2002__2002__a207
ER  - 
%0 Journal Article
%A Huang,  Sen-Zhong
%T Constructing universal pattern formation processes governed by reaction-diffusion systems
%J Electronic journal of differential equations
%D 2002
%V 2002
%U http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a207/
%G en
%F EJDE_2002__2002__a207
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__a207/