Spatial chaotic structure of attractors of reaction-diffusion systems

Authors:
V. Afraimovich, A. Babin and S.-N. Chow

Journal:
Trans. Amer. Math. Soc. **348** (1996), 5031-5063

MSC (1991):
Primary 35K57; Secondary 34C35

MathSciNet review:
1344202

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Abstract: The dynamics described by a system of reaction-diffusion equations with a nonlinear potential exhibits complicated spatial patterns. These patterns emerge from preservation of homotopy classes of solutions with bounded energies. Chaotically arranged stable patterns exist because of realizability of all elements of a fundamental homotopy group of a fixed degree. This group corresponds to level sets of the potential. The estimates of homotopy complexity of attractors are obtained in terms of geometric characteristics of the potential and other data of the problem.

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Additional Information

**V. Afraimovich**

Affiliation:
CDSNS, Georgia Institute of Technology, Atlanta, Georgia 30332-0190

**A. Babin**

Affiliation:
Moscow State University of Communications, Obraztsova 15, 101475 Moscow, Russia

**S.-N. Chow**

Affiliation:
CDSNS and School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332-0160

DOI:
http://dx.doi.org/10.1090/S0002-9947-96-01578-4

Keywords:
Reaction-diffusion system; potential; homotopy complexity; symbolic dynamics

Received by editor(s):
July 18, 1994

Received by editor(s) in revised form:
June 22, 1995

Additional Notes:
The first and third authors were partially supported by ARO DAAH04-93G-0199.

Research was partially supported by NIST Grant 60NANB2D1276.

Article copyright:
© Copyright 1996
American Mathematical Society