English

Exact dynamics of the critical Kauffman model with connectivity one

Statistical Mechanics 2023-04-03 v2 Molecular Networks

Abstract

The critical Kauffman model with connectivity one is the simplest class of critical Boolean networks. Nevertheless, it exhibits intricate behavior at the boundary of order and chaos. We introduce a formalism for expressing the dynamics of multiple loops as a product of the dynamics of individual loops. Using it, we prove that the number of attractors scales as 2m2^m, where mm is the number of nodes in loops - as fast as possible, and much faster than previously believed.

Keywords

Cite

@article{arxiv.2302.05314,
  title  = {Exact dynamics of the critical Kauffman model with connectivity one},
  author = {T. M. A. Fink},
  journal= {arXiv preprint arXiv:2302.05314},
  year   = {2023}
}