Fixed-time synchronization of quaternion-valued memristive neural networks with time-varying delays and impulsive effect

This study explored the fixed-time synchronization (FTS) problem for quaternion-valued memristive neural networks (QVMNNs) incorporating time-varying delays and impulsive disturbances. Initially, we established a model for QVMNNs incorporating these characteristics, namely time-varying delays, memristor behavior, impulsive effects, and quaternion-valued neural network properties. Given that QVMNNs do not obey the commutative law of multiplication, we decomposed them into four real-valued memristor neural networks for analysis. Second, due to the potential disruption of instantaneous impulsive disturbances to neural network synchronization, it was crucial to design an appropriate controller to manage these effects. Therefore, we devised a suitable feedback controller to effectively regulate the system. Next, we established the FTS conditions for QVMNNs using fixed-time stability theory combined with multiple inequality methods. Numerical experiments were performed to validate the theoretical results, demonstrating the effectiveness of our approach.