Hierarchical Wilson–Cowan Models and Connection Matrices

Authors

Wilson A. Zuniga-Galindo, The University of Texas Rio Grande Valley
Brian A. Zambrano-Luna, The University of Texas Rio Grande Valley

Document Type

Article

Publication Date

6-16-2023

Abstract

This work aims to study the interplay between the Wilson–Cowan model and connection matrices. These matrices describe cortical neural wiring, while Wilson–Cowan equations provide a dynamical description of neural interaction. We formulate Wilson–Cowan equations on locally compact Abelian groups. We show that the Cauchy problem is well posed. We then select a type of group that allows us to incorporate the experimental information provided by the connection matrices. We argue that the classical Wilson–Cowan model is incompatible with the small-world property. A necessary condition to have this property is that the Wilson–Cowan equations be formulated on a compact group. We propose a p-adic version of the Wilson–Cowan model, a hierarchical version in which the neurons are organized into an infinite rooted tree. We present several numerical simulations showing that the p-adic version matches the predictions of the classical version in relevant experiments. The p-adic version allows the incorporation of the connection matrices into the Wilson–Cowan model. We present several numerical simulations using a neural network model that incorporates a p-adic approximation of the connection matrix of the cat cortex.

Comments

© 2023 by the authors.

Recommended Citation

Zúñiga-Galindo WA, Zambrano-Luna BA. Hierarchical Wilson–Cowan Models and Connection Matrices. Entropy. 2023; 25(6):949. https://doi.org/10.3390/e25060949

Creative Commons License

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

Publication Title

Entropy

DOI

https://doi.org/10.3390/e25060949