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

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

Ahmed Y. Abdallah

 Department of Mathematics, University of Jordan, Amman 11942, Jordan
Received 12 July 2004; Revised 7 December 2004

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.