Since the unsaturating activation function is unbounded, more complex dynamics may exist in neural networks with this kind of activation function. In this article, monostability and multistability results of almost-periodic solutions are developed for fractional-order neural networks with unsaturating piecewise linear activation functions. Some globally Mittag-Leffler attractive sets are given, and the existence of globally Mittag-Leffler stable almost-periodic solution is demonstrated by using Ascoli-Arzela theorem. In particular, some sufficient conditions are provided to ascertain the multistability of almost-periodic solutions based on locally positively invariant set. It shows that there exists an almost-periodic solution in each positively invariant set, and all trajectories converge to this periodic trajectory in that rectangular area. Two illustrative examples are provided to demonstrate the effectiveness of the proposed sufficient criteria.

中文翻译：

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具有不饱和分段线性激活函数的分数阶神经网络的概周期解的单稳定性和多重稳定性。

由于不饱和激活函数是无穷大的，因此在具有这种激活函数的神经网络中可能存在更复杂的动力学。在本文中，针对具有不饱和分段线性激活函数的分数阶神经网络，开发了几乎周期解的单稳定性和多稳定性结果。给出了一些全局Mittag-Leffler吸引集，并通过使用Ascoli-Arzela定理证明了全局Mittag-Leffler稳定的概周期解的存在。特别地，提供了一些充分的条件来基于局部正不变集确定几乎周期解的多重稳定性。它表明在每个正不变量集中都存在一个几乎周期的解，并且在该矩形区域中所有轨迹都收敛到该周期轨迹。