Boolean networks synchronism sensitivity and XOR circulant networks convergence time

TL;DR

This paper investigates how non-monotone interactions, specifically XOR circulant networks, influence the dynamical behaviors and synchronism sensitivity of Boolean automata networks, providing initial theoretical insights.

Contribution

It offers the first theoretical analysis of non-monotony's impact on synchronism sensitivity and convergence times in XOR circulant Boolean networks.

Findings

Non-monotony affects synchronism sensitivity in Boolean networks.

Preliminary results on convergence times of XOR circulant networks.

Insights into the role of non-monotone interactions in network dynamics.

Abstract

In this paper are presented first results of a theoretical study on the role of non-monotone interactions in Boolean automata networks. We propose to analyse the contribution of non-monotony to the diversity and complexity in their dynamical behaviours according to two axes. The first one consists in supporting the idea that non-monotony has a peculiar influence on the sensitivity to synchronism of such networks. It leads us to the second axis that presents preliminary results and builds an understanding of the dynamical behaviours, in particular concerning convergence times, of specific non-monotone Boolean automata networks called XOR circulant networks.