Study on dynamics of fractional-order random diffusion cellular neural networks with time delays

We present a comprehensive analysis of a class of fractional-order cellular neural networks incorporating reaction-diffusion mechanisms, time-varying delays, and random perturbations. We establish the existence and uniqueness of mean-square weighted pseudo S-asymptotically ω-periodic solution, extending classical periodicity concepts to a more flexible stochastic framework. Furthermore, sufficient conditions are derived to guarantee finite-time stability, ensuring rapid and precise convergence within a predefined time horizon. By integrating fractional calculus, spatial diffusion, time delays, and random effects into a model, this work provides a realistic and rigorous framework for modeling neural dynamics under uncertainty and spatial heterogeneity. Finally, numerical simulations validate the theoretical results, illustrating both the periodic-like behavior and finite-time stability of the system. The findings contribute significantly to the neuromorphic computing field and establish a foundation for future applications in image processing, robotic vision, and biological system modeling.