Closing probabilities in the Kauffman model: an annealed computation

TL;DR

This paper introduces an annealed approximation method to analyze the probabilistic distributions of periods, transients, and attraction basin weights in Kauffman networks, providing insights into their dynamics.

Contribution

It presents a novel probabilistic scheme within the annealed approximation to compute key dynamical properties of Kauffman networks.

Findings

Numerical results agree with theoretical exponents of average periods.

Some features observed cannot be explained by the annealed approximation.

The method offers a new way to analyze complex network dynamics.

Abstract

We define a probabilistic scheme to compute the distributions of periods, transients and weigths of attraction basins in Kauffman networks. These quantities are obtained in the framework of the annealed approximation, first introduced by Derrida and Pomeau. Numerical results are in good agreement with the computed values of the exponents of average periods, but show also some interesting features which can not be explained whithin the annealed approximation.