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Journal of Applied Mathematics
Volume 2005 (2005), Issue 3, Pages 273-288
http://dx.doi.org/10.1155/JAM.2005.273

Upper semicontinuity of the attractor for lattice dynamical systems of partly dissipative reaction diffusion systems

Department of Mathematics, University of Jordan, Amman 11942, Jordan

Received 12 July 2004; Revised 7 December 2004

Copyright © 2005 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We investigate the existence of a global attractor and its upper semicontinuity for the infinite-dimensional lattice dynamical system of a partly dissipative reaction diffusion system in the Hilbert space l2×l2. Such a system is similar to the discretized FitzHugh-Nagumo system in neurobiology, which is an adequate justification for its study.