Critical Kauffman networks under deterministic asynchronous update

TL;DR

This paper studies how deterministic asynchronous updates affect the dynamics of critical Kauffman networks, revealing that delays reduce attractor counts and can cause very long periods, impacting network stability.

Contribution

It provides a detailed analysis of how delays influence attractor properties in critical Boolean networks, a novel focus on non-synchronous updates.

Findings

Delays decrease the number of attractors.

Non-integer delays can lead to very long periods.

Attractor length and count are significantly affected by delays.

Abstract

We investigate the influence of a deterministic but non-synchronous update on Random Boolean Networks, with a focus on critical networks. Knowing that ``relevant components'' determine the number and length of attractors, we focus on such relevant components and calculate how the length and number of attractors on these components are modified by delays at one or more nodes. The main findings are that attractors decrease in number when there are more delays, and that periods may become very long when delays are not integer multiples of the basic update step.