Finding attractors in asynchronous Boolean dynamics

TL;DR

This paper introduces a computational method to efficiently identify attractors in asynchronous Boolean networks by transforming the state transition graph into an acyclic form, enabling easier enumeration of fixed points.

Contribution

The method systematically removes transitions to find attractors in asynchronous Boolean networks, extending fixed points from the simplified graph to the original dynamics.

Findings

Efficient attractor enumeration in Kauffman networks

Moderate growth in state vectors visited with network size

Applicable to standard Boolean network models

Abstract

We present a computational method for finding attractors (ergodic sets of states) of Boolean networks under asynchronous update. The approach is based on a systematic removal of state transitions to render the state transition graph acyclic. In this reduced state transition graph, all attractors are fixed points that can be enumerated with little effort in most instances. This attractor set is then extended to the attractor set of the original dynamics. Our numerical tests on standard Kauffman networks indicate that the method is efficient in the sense that the total number of state vectors visited grows moderately with the number of states contained in attractors.