Before revision:  This papercontains the results from computational experiments aimed at investigating the attractor structure of Boolean networks defined by functions of a given canalizing depth. We observe that Boolean networks with higher canalizing depth have generally fewer attractors, the attractors are smaller, and the basins are larger, with implications for the stability and robustness of the models.
After revision:  In this paper, we investigate the dynamics of a random Boolean network with such properties using analytical methods and simulations. From our simulations, we observe that Boolean networks with higher canalizing depth have generally fewer attractors, the attractors are smaller, and the basins are larger, with implications for the stability and robustness of the models.