Attractors for FitzHugh-Nagumo lattice systems with almost periodic nonlinear parts

Abstract

For FitzHugh-Nagumo lattice dynamical systems (LDSs) many authors studied the existence of global attractors for deterministic systems [4,34,41,43] and the existence of global random attractors for stochastic systems [23,24,27,48,49], where for non-autonomous cases, the nonlinear parts are considered of the form $ f\left( u\right) $. 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\left( u,t\right) $, 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}\left( \cdot ,t\right) $ with values in $ W $.