In this paper, inertial neural networks are under investigation, that is, the second order differential equations. The recently introduced new type of motions, unpredictable oscillations, are considered for the models. The motions continue a line of periodic and almost periodic oscillations. The research is of very strong importance for neuroscience, since the existence of unpredictable solutions proves Poincaré chaos. Sufficient conditions have been determined for the existence, uniqueness, and exponential stability of unpredictable solutions. The results can significantly extend the role of oscillations for artificial neural networks exploitation, since they provide strong new theoretical and practical opportunities for implementation of methods of chaos extension, synchronization, stabilization, and control of periodic motions in various types of neural networks. Numerical simulations are presented to demonstrate the validity of the theoretical results.

中文翻译：

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具有不可预测振荡的惯性神经网络

本文正在研究惯性神经网络，即二阶微分方程。模型考虑了最近引入的新型运动，即不可预测的振荡。运动继续出现周期性的和几乎周期性的振荡。该研究对于神经科学非常重要，因为存在不可预测的解决方案证明了庞加莱的混乱。已经确定了不可预测解的存在性，唯一性和指数稳定性的充分条件。结果可以显着扩展振荡在人工神经网络开发中的作用，因为它们为实现混沌扩展，同步，稳定化，各种神经网络中周期运动的控制。数值模拟表明了理论结果的有效性。