Robustness of Attractor States in Complex Networks

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∼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.