This paper is concerned with finite-time and fixed-time synchronization of complex-valued recurrent neural networks with discontinuous activations and time-varying delays. First, by separating the complex-valued recurrent neural networks into real and imaginary parts, we get subsystems with real values covered by the framework of differential inclusions, and novel time-delays feedback controllers are constructed to understand the synchronization problem in finite time and fixed time of error system. Second, by creating Lyapunov functions and applying some differential inequalities, several new criteria are derived to get the synchronization in finite time and fixed time of the studied neural networks. Finally, two numerical examples are presented to justify the effectiveness of our results.

中文翻译：

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具有不连续激活和时变延迟的复值循环神经网络的有限时间和固定时间同步

本文涉及具有不连续激活和时变延迟的复值递归神经网络的有限时间和固定时间同步。首先，通过将复值递归神经网络分为实部和虚部，得到微分包含框架覆盖的实值子系统，并构造新颖的时滞反馈控制器来理解有限时间和固定的同步问题。错误系统的时间。其次，通过创建李雅普诺夫函数并应用一些微分不等式，推导出了几个新准则来获得所研究神经网络在有限时间和固定时间的同步。最后，给出了两个数值例子来证明我们结果的有效性。