Quaternion-Valued Fuzzy Cellular Neural Networks with time-mixed delays: Stability of measure pseudo almost periodic solutions

This study applies measure theory to analyze Quaternion-Valued Fuzzy Cellular Neural Networks (QVFCNNs) with time-mixed delays, focusing on the extension of pseudo almost periodic solutions. Specifically, we extend the theory of measure pseudo almost periodicity (σ-pseudo almost periodicity) to characterize the dynamical behavior of QVFCNNs. Using the Banach fixed-point theorem, we investigate the existence, uniqueness, and global exponential stability of σ-pseudo almost periodic solutions for the proposed model. The Lebesgue–Radon–Nikodym theorem is employed to construct a suitable measure σ for the analysis. To illustrate the practical relevance of the theoretical results, two examples are provided to demonstrate the applicability and effectiveness of the proposed approach. Overall, this study yields novel insights into the behavior of QVFCNNs in measurable spaces and contributes to a deeper understanding of dynamical systems with time delays.