Robustness of Attractor States in Complex Networks with Scale-free Topology

TL;DR

This study investigates the robustness and properties of attractor states in Boolean dynamics within scale-free complex networks, revealing differences from random networks and sensitivity to node connectivity.

Contribution

It provides a comparative analysis of attractor robustness in scale-free networks versus random Kauffman networks, highlighting the influence of node connectivity.

Findings

Higher fraction of frozen nodes in scale-free networks.

Attractors are more sensitive to flips in highly connected nodes.

Scale-free topology affects attractor stability and node influence.

Abstract

We study the intrinsic properties of attractors in the Boolean dynamics in complex network with scale-free topology, comparing with those of the so-called random Kauffman networks. We have numerically investigated the frozen and relevant nodes for each attractor, and the robustness of the attractors to the perturbation that flips the state of a single node of attractors in the relatively small network ($N=30 \sim 200$). It is shown that the rate of frozen nodes in the complex networks with scale-free topology is larger than that in the random Kauffman model. Furthermore, we have found that in the complex scale-free networks with fluctuations of in-degree number the attractors are more sensitive to the state flip of a highly connected node than to the state flip of a less connected node.