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Russian Mathematical Surveys, 2004, Volume 59, Issue 3, Pages 481–513
DOI: https://doi.org/10.1070/RM2004v059n03ABEH000737 (Mi rm737) 		 
This article is cited in 19 scientific papers (total in 19 papers)

Some physical models of the reaction-diffusion equation, and coupled map lattices

Ya. B. Pesina, A. A. Yurchenkob

a Pennsylvania State University
b Georgia Institute of Technology
English version PDF (485 kB) Citations (19)
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DOI: https://doi.org/10.1070/RM2004v059n03ABEH000737
Abstract: A number of models are surveyed which appear in physics, biology, chemistry, and other areas and which are described by a reaction-diffusion equation. The corresponding coupled map lattice (CML) system is obtained by discretizing this equation. These CMLs are classified by the type of the dynamics of the local map. Several different types of behavior are observed: Morse–Smale type systems, systems with attractors, and systems with Smale horseshoes.
Received: 24.06.2003
Russian version:
Uspekhi Matematicheskikh Nauk, 2004, Volume 59, Issue 3(357), Pages 81–114
DOI: https://doi.org/10.4213/rm737
Bibliographic databases:
Document Type: Article
UDC: 517.91/.93
MSC: Primary 35K57; Secondary 37D15, 37D45, 37N25, 37N10
Language: English
Original paper language: Russian
Citation: Ya. B. Pesin, A. A. Yurchenko, “Some physical models of the reaction-diffusion equation, and coupled map lattices”, Uspekhi Mat. Nauk, 59:3(357) (2004), 81–114; Russian Math. Surveys, 59:3 (2004), 481–513
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/rm/v59/i3/p81
    • This publication is cited in the following 19 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Russian version PDF:326
    English version PDF:11
    References:58
    First page:2
     
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