Event-triggered control for exponential synchronization of reaction–diffusion fractional-order Clifford-valued delayed neural networks and its application to image encryption

Abstract

This paper investigates the $\alpha$-exponential synchronization problem for reaction–diffusion fractional-order Clifford-valued delayed neural networks (RDFOCLVDNNs) using an event-triggered control (ETC) strategy. First, a general form of neural networks (NNs), namely RDFOCLVDNNs is considered, which provides deeper insights into the dynamics of Clifford-valued neural networks (CLVNNs). To address the challenges posed by the non-commutative nature of Clifford algebra, the RDFOCLVDNNs are decomposed into multi-dimensional real-valued neural networks (RVNNs), which avoid the complexities of Clifford number multiplication and also simplify the analysis. Then, by constructing a suitable Lyapunov–Krasovskii functional (LKF) and applying appropriate inequalities new robust conditions are derived to guarantee the $\alpha$-exponential synchronization of RDFOCLVDNNs under the proposed ETC strategy. To validate the synchronization criteria, a numerical example is presented along with graphical analysis. Furthermore, proposed theoretical framework is utilized to develop an effective color image encryption algorithm for secure image transmission. Finally, the effectiveness and security of the proposed encryption scheme are verified through simulations and various performance analyses.