Preassigned-Time Projective Lag Synchronization of Octonion-Valued BAM Neural Networks via Exponential Quantized Event-Triggered Control

This study addresses the preassigned-time (PDT) projective lag synchronization of octonion-valued BAM neural networks (OV-BAMNNs) through exponential quantized event-triggered control (ETC). First, an OV-BAMNN model incorporating discontinuous activation functions and time-varying delays is established. Subsequently, by introducing the octonion-valued sign function, several exponential quantized ETC schemes are designed, which employ solely a single exponential term while eliminating traditional linear and power-law components. Compared with conventional ETC designs, the proposed control schemes are simpler in form. Furthermore, within the framework of the non-separation method, several criteria for PDT projective lag synchronization are derived based on the Lyapunov method and Taylor expansion, proving that Zeno behavior is excluded. Finally, two simulation examples are given to verify the correctness of the theoretical results and to apply these results to image encryption.