The dynamics of critical Kauffman networks under asynchronous stochastic update

TL;DR

This paper investigates how the behavior of critical Kauffman networks changes under asynchronous stochastic updates, revealing power-law growth in attractor count and stretched exponential growth in attractor size, contrasting with synchronous updates.

Contribution

It provides a detailed analysis of the attractor dynamics in critical Boolean networks under asynchronous updates, highlighting significant differences from synchronous cases.

Findings

Mean number of attractors grows as a power law

Mean attractor size increases as a stretched exponential

Contrasts with faster growth in synchronous updates

Abstract

We show that the mean number of attractors in a critical Boolean network under asynchronous stochastic update grows like a power law and that the mean size of the attractors increases as a stretched exponential with the system size. This is in strong contrast to the synchronous case, where the number of attractors grows faster than any power law.