  We determine stability and attractor properties of random Boolean genetic
network models with canalyzing rules for a variety of architectures. For all
power law, exponential, and flat in-degree distributions, we find that the
networks are dynamically stable. Furthermore, for architectures with few inputs
per node, the dynamics of the networks is close to critical. In addition, the
fraction of genes that are active decreases with the number of inputs per node.
These results are based upon investigating ensembles of networks using
analytical methods. Also, for different in-degree distributions, the numbers of
fixed points and cycles are calculated, with results intuitively consistent
with stability analysis; fewer inputs per node implies more cycles, and vice
versa. There are hints that genetic networks acquire broader degree
distributions with evolution, and hence our results indicate that for single
cells, the dynamics should become more stable with evolution. However, such an
effect is very likely compensated for by multicellular dynamics, because one
expects less stability when interactions among cells are included. We verify
this by simulations of a simple model for interactions among cells.
