Turing patterns in a p-adic FitzHugh-Nagumo system on the unit ball

TL;DR

This paper explores Turing pattern formation in p-adic FitzHugh-Nagumo systems, demonstrating the existence of traveling wave patterns through theoretical criteria and extensive simulations on the p-adic unit ball.

Contribution

It introduces discrete and p-adic continuous models of the FitzHugh-Nagumo system and establishes criteria for Turing pattern existence in these non-Archimedean settings.

Findings

Turing patterns are traveling waves in the p-adic unit ball.

Criteria for Turing pattern existence are provided.

Simulations confirm pattern formation in p-adic systems.

Abstract

We introduce discrete and p-adic continuous versions of the FitzHugh-Nagumo system on the one-dimensional p-adic unit ball. We provide criteria for the existence of Turing patterns. We present extensive simulations of some of these systems. The simulations show that the Turing patterns are traveling waves in the p-adic unit ball.