Bringing memory to Boolean networks: a unifying framework

TL;DR

This paper introduces a unifying framework for Boolean network update modes with memory, compares existing modes, proposes new ones, and analyzes their impact on system dynamics.

Contribution

It provides a generic framework to define and compare memory-based update modes, including new modes, and studies their effects on Boolean network dynamics.

Findings

Existing modes like permissive and interval are expressed within the framework.

New modes such as history-based, trapping, and subcube-based are proposed.

Memory influences trajectories and attractor structures in Boolean networks.

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.