We investigate analytically and numerically the dynamical properties of
critical Boolean networks with power-law in-degree distributions. When the
exponent of the in-degree distribution is larger than 3, we obtain results
equivalent to those obtained for networks with fixed in-degree, e.g., the
number of the non-frozen nodes scales as N2/3 with the system size N.
When the exponent of the distribution is between 2 and 3, the number of the
non-frozen nodes increases as Nx, with x being between 0 and 2/3 and
depending on the exponent and on the cutoff of the in-degree distribution.
These and ensuing results explain various findings obtained earlier by computer
simulations.Comment: 5 pages, 1 graph, 1 sketch, submitte