Analogous Dynamics of Boolean Network

TL;DR

This paper investigates the invariant properties of Boolean networks' dynamics, showing how different networks can exhibit similar behavior and identifying structural features that remain unchanged under certain conditions.

Contribution

It introduces a formal framework for understanding the invariance of Boolean network dynamics via graph isomorphisms and mode variations, providing new insights into their structural properties.

Findings

Invariant structural properties of interaction graphs identified

Conditions for maintaining equivalence under mode variation established

Group of isomorphism preserving the mode characterized

Abstract

Different Boolean networks may reveal similar dynamics although their definition differs, then preventing their distinction from the observations. This raises the question about the sufficiency of a particular Boolean network for properly reproducing a modeled phenomenon to make realistic predictions. The question actually depends on the invariant properties of behaviorally similar Boolean networks. In this article, we address this issue by considering that the similarity is formalized by isomorphism on graphs modeling their dynamics. The similarity also depends on the parameter governing the updating policy, called the mode. We define a general characterization of the group of isomorphism preserving the mode. From this characterization, we deduce invariant structural properties of the interaction graph and conditions to maintain an equivalence through mode variation.