p-adic Cellular Neural Networks

Authors

B. A. Zambrano-Luna
Wilson A. Zuniga-Galindo, The University of Texas Rio Grande ValleyFollow

Document Type

Article

Publication Date

3-2023

Abstract

In this article we introduce the p-adic cellular neural networks which are mathematical generalizations of the classical cellular neural networks (CNNs) introduced by Chua and Yang. The new networks have infinitely many cells which are organized hierarchically in rooted trees, and also they have infinitely many hidden layers. Intuitively, the p-adic CNNs occur as limits of large hierarchical discrete CNNs. More precisely, the new networks can be very well approximated by hierarchical discrete CNNs. Mathematically speaking, each of the new networks is modeled by one integro-differential equation depending on several p-adic spatial variables and the time. We study the Cauchy problem associated to these integro-differential equations and also provide numerical methods for solving them.

Comments

Copyright © 2022, The Author(s)

Recommended Citation

Zambrano-Luna, B. A., and Wilson A. Zuniga-Galindo. "p-Adic cellular neural networks." Journal of Nonlinear Mathematical Physics 30, no. 1 (2023): 34-70. https://doi.org/10.1007/s44198-022-00071-8

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Publication Title

Journal of Nonlinear Mathematical Physics

DOI

10.1007/s44198-022-00071-8