Fixed/Preassigned-time synchronization of quaternion-valued BAM neural networks: An event-based non-separation control method

Abstract

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.