Attractors for lattice FitzHugh–Nagumo systems

Abstract: The FitzHugh–Nagumo system on infinite lattices is studied. By means of “tail ends” estimates on solutions, it is proved that the system is asymptotically compact in a weighted space and has a compact global attractor containing traveling wave solutions. The singular limiting behavior of global attractors is also investigated as a singular parameter . It is shown that the limiting system for has no global attractor, but all the global attractors for perturbed systems are contained in a common compact subset of the phase space when is positive but small. Further, a compact local attractor for the limiting system is constructed, and the upper semicontinuity of global attractors is established when . [Copyright &y& Elsevier]