Journal of Applied Mathematics
Volume 2005 (2005), Issue 3, Pages 273-288
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 Ahmed Y. Abdallah. 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.
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 . Such a system
is similar to the discretized FitzHugh-Nagumo system in
neurobiology, which is an adequate justification for its study.