  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.
