Electron. J. Diff. Eqns., Vol. 2002(2002), No. 84, pp. 112.
Constructing universal pattern formation processes
governed by reactiondiffusion systems
SenZhong Huang
Abstract:
For a given connected compact subset
in
we construct a smooth map
on
in such a way that the corresponding
reactiondiffusion system
of
components
,
accompanying with the
homogeneous Neumann boundary condition, has an attractor
which is isomorphic to
.
This implies the following
universality: The makeup of a pattern with arbitrary complexity
(e.g., a fractal pattern) can be realized by a reactiondiffusion
system once the vector supply term
has been previously
properly constructed.
Submitted August 28, 2002. Published October 4, 2002.
Math Subject Classifications: 35B40, 70G60, 35Q99
Key Words: Attractor, pattern formation.
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SenZhong Huang
Fachbereich Mathematik
Universitat Rostock
Universitatsplatz 1
D18055 Rostock, F. R. Germany
email: senzhong.huang@mathematik.unirostock.de

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