Long-Time Behavior of Non-Autonomous FitzHugh-Nagumo Lattice Systems

In Abdallah (J Appl Math 3: 273-288, 2005), Boughoufala and Abdallah (Disc Cont Dyn Ays B), Li and Wang (J Math Anal Appl 325: 141-156, 2007), Vleck and Wang (PhysicaD212: 317-336, 2005), Wang (Int J Bifurcation Chaos 17: 1673-1685, 2007) the existence of global attractors for autonomous and non-autonomous deterministic FitzHugh-Nagumo lattice dynamical systems (LDSs) with nonlinear parts of the form G(i) (u(i)) have been studied. Here the existence of the uniform global attractor for such non-autonomous systemswith nonlinear parts of the form G(i) (u(k) vertical bar k is an element of I-iq) is carefully investigated, where such nonlinear parts present the main difficulty of this work.