p-Adic Cellular Neural Networks With Delay

Abstract

This dissertation presents a novel framework for p-adic reaction-diffusion cellular neural networks (CNNs) with delay, offering new insights into the stability and dynamic behavior of these networks. Through numerical simulations, we explore their response to various conditions, highlighting their capability to model complex systems. Additionally, this work reviews cutting-edge developments in p-adic CNNs, particularly their application to advanced image processing tasks such as edge detection and noise filtering, demonstrating their effectiveness in preserving critical image features while filtering out noise. This dissertation is written in collaboration with my Ph.D supervisor and Dr. Zambrano-Luna, Brian.