Further results on global stability of Clifford-valued neural networks subject to time-varying delays

Abstract

This paper investigates the global exponential and asymptotic stability of Clifford-valued neural networks (CLVNNs) with multiple time-varying delays. Due to the non-commutative nature of Clifford algebra, analyzing the stability and other dynamical properties of CLVNNs becomes challenging. To address this issue, we separate the CLVNNs into equivalent real-valued neural networks (RVNNs). This separation simplifies the study of CLVNNs through their RVNN components. By constructing a suitable Lyapunov–Krasovskii functionals (LKFs) and applying inequality techniques, we establish several sufficient conditions that guarantee the existence and uniqueness of the equilibrium point (EP), as well as the global exponential and asymptotic stability of the considered neural networks (NNs). These conditions are expressed as linear matrix inequalities (LMIs), which can be efficiently verified using MATLAB LMI toolbox. To validate the analytical results, we present three numerical examples. Additionally, we propose a novel color image encryption algorithm, and demonstrate its effectiveness through simulation results and detailed performance analysis.