For a given connected compact subset in we construct a smooth map on in such a way that the corresponding reaction-diffusion system
of components , accompanying with the homogeneous Neumann boundary condition, has an attractor which is isomorphic to . 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 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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|Sen-Zhong Huang |
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