Electronic Journal of Differential Equations,
Vol. 2002(2002), No. 84, pp. 1-12.

Title: Constructing universal pattern formation processes
       governed by reaction-diffusion systems 
        
Author: Sen-Zhong Huang (Univ. Rostock, Germany)
         
Abstract: 
 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.
     
Submitted August 28, 2002. Published October 4, 2002.
Math Subject Classifications: 35B40, 70G60, 35Q99
Key Words: Attractor; pattern formation.