  We present a renormalization-grouplike method performed in the state space
for detecting the dynamical behaviors of large scale-free Boolean networks,
especially for the chaotic regime as well as the edge of chaos. Numerical
simulations with different coarse-graining level show that the state space
networks of scale-free Boolean networks follow universal power-law
distributions of in and out strength, in and out degree, as well as weight.
These interesting results indicate scale-free Boolean networks still possess
self-organized mechanism near the edge of chaos in the chaotic regime. The
number of state nodes as a function of biased parameter for distinct
coarse-graining level also demonstrates that the power-law behaviors are not
the artifact of coarse-graining procedure. Our work may also shed some light on
the investigation of brain dynamics.
