Adaptive Strategies and its Application in the Mittag-Leffler Synchronization of Delayed Fractional-Order Complex-Valued Reaction-Diffusion Neural Networks

Abstract

This paper addresses the Mittag-Leffler synchronization problem of fractional-order reaction-diffusion complex-valued neural networks (FRDCVNNs) with delays. New Mittag-Leffler synchronization (MLS) criteria in the form of the $p$ -norm for an error model derived from the drive-response model are constructed. In the design of the adaptive feedback controller, the Lyapunov approach is considered in the framework of the $p$ -norm technique, and less conservative algebraic conditions that guarantee MLS for the considered model are given. Moreover, the MLS of the considered model without reaction diffusion effect is investigated using adaptive control. Finally, an example is used to validate the proposed control scheme. To demonstrate the advantages and superiority of the proposed technique over existing methods, an image encryption method based on MLS of FRDCVNNs is considered and solved using the proposed method.