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Journal of the London Mathematical Society 2006 74(2):453-474; doi:10.1112/S0024610706023015
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© The London Mathematical Society 2006

LOWER ESTIMATE OF THE ATTRACTOR DIMENSION FOR A CHEMOTAXIS GROWTH SYSTEM

Masashi Aida, Tohru Tsujikawa, Messoud Efendiev, Atsushi Yagi and Masayasu Mimura

Department of Applied Physics, Osaka University Suita Osaka 565-0871, Japan
Faculty of Engineering Miyazaki University Miyazaki 889-2192, Japan
University of Stuttgart Mathematisches Institut A, Pfaffenwaldring 57, 70569 Stuttgart, Germany
Department of Applied Physics, Osaka University Suita Osaka 565-0871, Japan yagi{at}ap.eng.osaka-u.ac.jp
Department of Mathematics, Meiji University Kawasaki, Kanagawa 214-8571, Japan

Received 30 May 2005. Revision received 9 November 2005.

This paper estimates from below the attractor dimension of the dynamical system determined from a chemotaxis growth model which was presented by Mimura and Tsujikawa. It is already known that the dynamical system has exponential attractors and it is also known by numerical computations that the model contains various pattern solutions. This paper is then devoted to estimating the attractor dimension from below and in fact to showing that, as the parameter of chemotaxis increases and tends to infinity, so does the attractor dimension. Such a result is in a good correlation with the numerical results.


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