Bringing memory to Boolean networks: a unifying framework
Abstract
Boolean networks are extensively applied as models of complex dynamical systems, aiming at capturing essential features related to causality and synchronicity of the state changes of components along time. Dynamics of Boolean networks result from the application of their Boolean map according to a so-called update mode, specifying the possible transitions between network configurations. In this paper, we explore update modes that possess a memory on past configurations, and provide a generic framework to define them. We show that recently introduced modes such as the most permissive and interval modes can be naturally expressed in this framework, and we propose novel update modes, the history-based, trapping, and subcube-based modes. Building on the unified definitions, we provide a comprehensive comparison of memory-based update modes, resulting in their hierarchy by simulation and weak simulation. Finally, we highlight consequences of introducing memory on the notions of trajectory and attractors.
Cite
@article{arxiv.2404.03553,
title = {Bringing memory to Boolean networks: a unifying framework},
author = {Maximilien Gadouleau and Loïc Paulevé and Sara Riva},
journal= {arXiv preprint arXiv:2404.03553},
year = {2026}
}