Exponential Synchronization of Quaternion-Valued Inertial Neural Networks with Mixed Delays Under Aperiodically Intermittent Control

This paper investigates the problem of exponential synchronization for a class of quaternion-valued inertial neural networks with mixed time delays under aperiodic intermittent control. First, a neural network model incorporating both discrete and distributed delays is established. To overcome the limitations of conventional approaches, a novel quaternion-based controller is proposed, which operates without relying on model order reduction or quaternion decomposition techniques, thereby achieving global exponential synchronization of the system. Furthermore, by constructing an appropriate Lyapunov function and combining the algebraic properties of quaternions with inequality techniques, sufficient conditions for synchronization are rigorously derived within the Lyapunov stability framework. Numerical simulations are conducted to demonstrate the effectiveness of the proposed control strategy and validate the theoretical results. Finally, an image encryption application is developed to further corroborate the practical viability of the proposed scheme, wherein the original image is encrypted into a noise-like pattern without information leakage and perfectly recovered upon synchronization, with quantitative error analysis confirming high-precision exponential synchronization.