  In this work we analyze scale-free networks with different power law spectra
$N(k) \sim k^{-\gamma}$ under a boolean dynamic, where the boolean rule that
each node obeys is a function of its connectivity $k$. This is done by using
only two logical functions (AND and XOR) which are controlled by a parameter
$q$. Using damage spreading technique we show that the Hamming distance and the
number of 1's exhibit power law behavior as a function of $q$. The exponents
appearing in the power laws depend on the value of $\gamma$.
