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 $.

中文翻译：

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具有几乎周期非线性部分的FitzHugh-Nagumo晶格系统的吸引子

对于FitzHugh-Nagumo晶格动力学系统（LDS），许多作者研究了确定性系统的全局吸引子的存在[4，34，41，43]和随机系统的全局随机吸引子的存在[23，24，27，48，49]，其中对于非自治情况，非线性部分的形式为$ f \ left（u \ right）$。在这里，我们研究具有非线性部分$ f \ left（u，t \ right）$的非自治FitzHugh-Nagumo LDS新族的一致全局吸引子的存在，在此我们引入合适的Banach函数空间$ W $，我们假定$ f $是几乎周期函数$ f_ {0} \ left（\ cdot，t \ right）$的外壳元素，其值在$ W $中。