In this article, sufficient conditions for fixed-time synchronization of time-delayed quaternion-valued neural networks (QVNNs) are derived. Firstly, QVNNs are decomposed into four real-valued systems. Then using the available lemmas and by constructing the Lyapunov function, the synchronization criterion for the neural networks is proposed. Activation functions satisfy the Lipschitz condition. A suitable controller has been designed to synchronize the master–slave systems. The effectiveness of the proposed result is validated through a comparison of the settling time obtained by applying two different existing lemmas to a particular problem of synchronization of two identical QVNNs with time-varying delay with the help of suitable controllers.

中文翻译：

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具有时变延迟的四元数值神经网络的固定时间同步

在本文中，推导出了时滞四元数值神经网络 (QVNN) 的固定时间同步的充分条件。首先，QVNNs 被分解为四个实值系统。然后使用可用的引理并通过构造Lyapunov 函数，提出了神经网络的同步准则。激活函数满足 Lipschitz 条件。设计了一个合适的控制器来同步主从系统。通过在合适的控制器的帮助下将两个不同的现有引理应用于具有时变延迟的两个相同 QVNN 同步的特定问题所获得的稳定时间的比较，验证了所提出结果的有效性。