Quaternions provide expressive power beyond real numbers, allowing neural networks to capture and process correlations and patterns in data with greater complexity. Besides, event-triggering mechanism has significant advantages in reducing redundant data transmission and control costs, since the sampling instant is determined by preset trigger conditions. Based on these fact, this article investigates the fixed-time and preassigned-time synchronization of quaternion-valued Bidirectional Associative Memory (BAM) neural networks via event-triggered control. Firstly, based on a dual-layer network structure with different number of nodes, a type of BAM neural network with generalized time-varying delays is established in the quaternion domain. Secondly, four kinds of Zeno-free dynamic event-triggered control mechanisms are designed, and the trigger condition can be dynamically adjusted according to the changing requirements. In the framework of non-separation analysis, the synchronization the controlled network can be guaranteed within a fixed time, and the upper bound of the setting time is provided explicitly. Furthermore, to better meet practical needs, the above event-triggered mechanism and the criteria are extended to the PAT synchronization. Two illustrate examples are presented at last to validate the developed event-triggered mechanism and synchronization results.

中文翻译：

---

四元数BAM神经网络的固定/预分配时间同步：一种基于事件的非分离控制方法


四元数提供了超越实数的表达能力，使神经网络能够捕获和处理更复杂的数据中的相关性和模式。此外，事件触发机制由于采样时刻是由预设的触发条件决定的，因此在减少冗余数据传输和控制成本方面具有显着的优势。基于这些事实，本文通过事件触发控制研究了四元数双向关联记忆（BAM）神经网络的固定时间和预分配时间同步。首先，基于不同节点数的双层网络结构，在四元数域建立了一类具有广义时变时滞的BAM神经网络。其次，设计了四种Zeno-free动态事件触发控制机制，并且可以根据需求的变化动态调整触发条件。在非分离分析的框架下，可以保证固定时间内受控网络的同步，并明确规定了设定时间的上限。此外，为了更好地满足实际需要，将上述事件触发机制和准则扩展到PAT同步中。最后给出了两个示例来验证所开发的事件触发机制和同步结果。