Design and analysis of quaternion-valued neural networks for storing and retrieving color images

In this paper, we address the global exponential stability (GES) issue for the quaternion-valued neural networks (QVNNs) with non-differentiable distributed delays using the matrix measure method (MMM). Given the complex nature of quaternion algebra, the QVNNs are first transformed into similar four-dimensional real-valued neural networks (RVNNs) to overcome the complexities of quaternion multiplication. Through the construction of applicable Lyapunov functions and the application of MMM, rigorous stability conditions are established. Furthermore, the study presents novel and easily verifiable results, offering new perspectives into the GES of QVNNs. The proposed conditions are also applicable when QVNNs are reformulated as complex-valued neural networks (CVNNs) or RVNNs. To validate the obtained findings, some numerical examples with graphical analysis are presented, along with their application to storing and retrieving color image patterns.