The Kauffman model on Small-World Topology

TL;DR

This paper investigates how small-world network topology influences the dynamics of Kauffman's automata, revealing that long-range connections increase damage spread and reduce fractal dimensions, bridging short-range and infinite-range behaviors.

Contribution

It provides a detailed analysis of the effects of small-world topology on Kauffman automata, including critical exponents and fractal dimensions, which was not previously explored.

Findings

Damage propagation increases with long-range connections.

Fractal dimensions decrease as long-range links are added.

Critical exponents are characterized for small-world networks.

Abstract

We apply Kauffman's automata on small-world networks to study the crossover between the short-range and the infinite-range case. We perform accurate calculations on square lattices to obtain both critical exponents and fractal dimensions. Particularly, we find an increase of the damage propagation and a decrease in the fractal dimensions when adding long-range connections.