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

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 $l^2\times l^2$. Such a system is similar to the discretized FitzHugh-Nagumo system in neurobiology, which is an adequate justification for its study.