Global Mittag-Leffler stability and synchronization of fractional-order Clifford-valued delayed neural networks with reaction-diffusion terms and its application to image encryption

With the rapid progress in modern engineering and the increasing complexity of real-world problems, the demand for studying Clifford-valued neural networks (CLVNNs) has grown significantly. Therefore, this paper aims to investigate the global Mittag-Leffler (GML) stability and synchronization problem for a class of CLVNNs. By incorporating fractional calculus and reaction-diffusion terms (RDTs) into CLVNNs, we first introduce a novel class of fractional-order Clifford-valued delayed neural networks (FOCLVDNNs) with RDTs to provide a robust framework for realistic understanding of CLVNN dynamics. To address non-commutativity in Clifford number multiplication, we decompose the original CLVNNs into real-valued neural networks (RVNNs) using the decomposition method. This simplifies the structure of the Clifford algebra and makes it easier to apply standard methods to its dynamical analysis. Then, by employing Lyapunov functions and novel inequality techniques, we establish sufficient conditions to guarantee the GML stability of the networks under investigation. Furthermore, we derive robust criteria to ensure the GML synchronization of the networks under linear feedback control. To validate the obtained theoretical conditions, we provide two numerical examples accompanied by graphical analysis. Furthermore, we propose an image encryption algorithm for color images based on FOCLVDNNs and demonstrate its effectiveness through simulations and performance analyses.