ATTRACTORS FOR FITZHUGH-NAGUMO LATTICE SYSTEMS WITH ALMOST PERIODIC NONLINEAR PARTS

For FitzHugh-Nagumo lattice dynamical systems (LDSs) many authors studied the existence of global attractors for deterministic systems [1, 34, 41, 43] and the existence of global random attractors for stochastic systems [23, J4, 27, 48, 49], where for non-autonomous cases, the nonlinear parts are considered of the form f (u). Here we study the existence of the uniform global attractor for a new family of non-autonomous FitzHugh-Nagumo LDSs with nonlinear parts of the form f (u, t), where we introduce a suitable Banach space of functions W and we assume that f is an element of the hull of an almost periodic function f(0) (., t) with values in W.