Non-monotony and Boolean automata networks

TL;DR

This paper explores the impact of non-monotone interactions in Boolean automata networks, aiming to understand their role in biological regulation complexity through preliminary analysis of XOR circulant networks.

Contribution

It introduces the study of non-monotony in Boolean automata networks and provides initial results on their dynamical behaviors, highlighting phenomena beyond monotone models.

Findings

Non-monotony contributes to increased dynamical complexity.

Preliminary analysis of XOR circulant networks shows diverse behaviors.

Non-monotone interactions can explain biological phenomena not captured by monotone models.

Abstract

This paper aims at setting the keystone of a prospective theoretical study on the role of non-monotone interactions in biological regulation networks. Focusing on discrete models of these networks, namely, Boolean automata networks, we propose to analyse the contribution of non-monotony to the diversity and complexity in their dynamical behaviours. More precisely, in this paper, we start by detailing some motivations, both mathematical and biological, for our interest in non-monotony, and we discuss how it may account for phenomena that cannot be produced by monotony only. Then, to build some understanding in this direction, we propose some preliminary results on the dynamical behaviour of some specific non-monotone Boolean automata networks called XOR circulant networks.