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Exponential attractors for Belousov-Zhabotinskii reaction model

Pages: 846 - 856, Issue Special, September 2009

 Abstract        Full Text (191.3K)              

Atsushi Yagi - Department of Applied Physics, Osaka University, Suita, Osaka, 565-0871, Japan (email)
Koichi Osaki - Department of Business Adminstration, Ube National College of Technology, Ube, Yamaguchi 755-8555, Japan (email)
Tatsunari Sakurai - Department of Physics, Chiba University, Chiba 263-8522, Japan (email)

Abstract: This paper is concerned with the Belousov-Zhabotinskii reaction model. We consider the reaction-diffusion model due to Keener-Tyson. After constructing a dynamical system, we will construct exponential attractors and will estimate the attractor dimension from below. In particular, it will be shown that, as the excitability $\epsilon > 0$ tends to zero, the attractor dimension tends to infinity, although the exponential attractor can depend on the excitability continuously.

Keywords:  Belousov-Zhabotinskii reaction, Reaction-diffusion model, Exponential attractors
Mathematics Subject Classification:  Primary: 37L25; Secondary: 35K57

Received: July 2008;      Revised: April 2009;      Published: September 2009.