Quasi-projective synchronization of fractional-order quaternion-valued inertial neural networks with application to image encryption.

Authors

Yanxia Hu, Xiaofang Meng, Zhouhong Li, Jinde Cao

Published in

ISA transactions. Jul 21, 2026. Epub Jul 21, 2026.

Abstract

Fractional-order quaternion inertial neural networks have shown great potential for secure communications, as evidenced by the capability of efficiently capturing the dynamic characteristics of high-dimensional data. This article focuses on studying the quasi-projective synchronization problem of a class of delayed fractional-order quaternion-valued inertial neural networks. Firstly, a simple and efficient controller is designed without decomposing the quaternion-valued neural networks into multiple subsystems. Moreover, unlike previous studies, the non-reduced order method is adopted to analyze inertial neural networks directly. Secondly, a class of Lyapunov functions for quaternion states and their fractional-order derivatives is constructed, along with several inequalities. On this basis, a sufficient criterion for achieving quasi-projective synchronization of the constructed model, and an upper bound on the system synchronization error are estimated. A more complex form of controller is also proposed, and the synchronization of the studied system is achieved using the same proof method as before. Finally, the validity of the theoretical results is verified through a numerical example. This research has been successfully applied to the encryption and decryption of color images, demonstrating strong practical application prospects.

PMID:
42498580
Bibliographic data and abstract were imported from PubMed on 25 Jul 2026.

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