Turing patterns in systems with high-order interactions

TL;DR

This paper extends Turing pattern theory to systems with high-order, many-body interactions modeled via hypergraphs, revealing how these interactions can influence pattern formation in complex systems.

Contribution

It introduces a framework for analyzing Turing patterns in systems with higher-order interactions, expanding the classical theory to include group interactions.

Findings

High-order interactions can both promote and inhibit Turing pattern formation.

The hypergraph-based approach generalizes classical reaction-diffusion models.

Results provide insights into pattern mechanisms in systems with many-body interactions.

Abstract

Turing theory of pattern formation is among the most popular theoretical means to account for the variety of spatio-temporal structures observed in Nature and, for this reason, finds applications in many different fields. While Turing patterns have been thoroughly investigated on continuous support and on networks, only a few attempts have been made towards their characterization in systems with higher-order interactions. In this paper, we propose a way to include group interactions in reaction-diffusion systems, and we study their effects on the formation of Turing patterns. To achieve this goal, we rewrite the problem originally studied by Turing in a general form that accounts for a microscropic description of interactions of any order in the form of a hypergraph, and we prove that the interplay between the different orders of interaction may either enhance or repress the emergence of Turing patterns. Our results shed light on the mechanisms of pattern-formation in systems with many-body interactions and pave the way for further extensions of Turing original framework.