Fixed/Preassigned-Time Synchronization of Quaternion-Valued Stochastic BAM Neural Networks with Discontinuous Activations Using Impulsive Control Technique

In this study, a comprehensive analysis of the fixed/preassigned-time synchronization of a class of quaternion-valued BAM (QBAM) neural networks with stochastic and impulsive effects is conducted. Unlike previous analysis methods, our method features a direct analysis approach. First, to clarify the combined impact of impulsive and stochastic phenomena on synchronization behavior, we establish a QBAM neural network system incorporating stochastic and impulsive effects. Notably, differing from prior relevant studies, we assume that the activation function is discontinuous, thereby enhancing the practical relevance of this research. Second, leveraging the quaternion-valued sign function and its properties, we implement impulsive control via the direct analysis method to achieve Fixed/Predefined-Time synchronization of the considered system. Finally, numerical simulations are performed to verify the ability of the theoretical analysis and the proposed control protocol to realize synchronization under impulsive and stochastic effects.