  We obtain the phase diagram of random Boolean networks with nested canalizing
functions. Using the annealed approximation, we obtain the evolution of the
number $b_t$ of nodes with value one, and the network sensitivity $\lambda$,
and we compare with numerical simulations of quenched networks. We find that,
contrary to what was reported by Kauffman et al. [Proc. Natl. Acad. Sci. 2004
101 49 17102-7], these networks have a rich phase diagram, were both the
"chaotic" and frozen phases are present, as well as an oscillatory regime of
the value of $b_t$. We argue that the presence of only the frozen phase in the
work of Kauffman et al. was due simply to the specific parametrization used,
and is not an inherent feature of this class of functions. However, these
networks are significantly more stable than the variants where all possible
Boolean functions are allowed.
