A special kind of Poisson stable trajectory, which is called unpredictable and leads to sensitivity in the quasi-minimal set, was proposed by Akhmet and Fen (2016) for semiflows. In the present paper we carry this finding one step further by defining a new kind of trajectory, called asymptotically unpredictable. We prove that such motions also lead to sensitivity in the dynamics. This feature is now achieved under a weaker hypothesis. Benefiting from the Bebutov dynamical system, continuous asymptotically unpredictable functions on the real axis are defined, and it is shown that the set of these functions properly includes the set of unpredictable ones. Moreover, results on producing new asymptotically unpredictable functions from a given one are obtained. The existence and uniqueness of bounded asymptotically unpredictable solutions of quasi-linear systems are also investigated, and an application to Hopfield neural networks is provided.

中文翻译：

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半流中渐近不可预测的轨迹

Akhmet 和 Fen (2016) 针对半流提出了一种特殊的泊松稳定轨迹，称为不可预测并导致准最小集的敏感性。在本文中，我们通过定义一种新的轨迹（称为渐近不可预测的轨迹）将这一发现更进一步。我们证明这种运动也会导致动力学的敏感性。现在，该功能是在较弱的假设下实现的。受益于Bebutov动力系统，定义了实轴上的连续渐近不可预测函数，并表明这些函数的集合适当地包含了不可预测函数的集合。此外，还获得了从给定函数产生新的渐近不可预测函数的结果。还研究了拟线性系统有界渐近不可预测解的存在性和唯一性，并提供了在 Hopfield 神经网络中的应用。