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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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
PII: S 0002-9947(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