Eur. Phys. J. B 78, 187-192 (2010)
https://doi.org/10.1140/epjb/e2010-10559-0

The phase diagram of random Boolean networks with nested canalizing functions

Institut für Festkörperphysik, TU Darmstadt, Hochschulstrasse 6, 64289 Darmstadt, Germany

Corresponding author: ^a tiago@fkp.tu-darmstadt.de

Received: 20 July 2010
Revised: 28 September 2010
Published online: 17 November 2010

Abstract

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 λ, and compare with numerical simulations of quenched networks. We find that, contrary to what was reported by Kauffman et al. [Proc. Natl. Acad. Sci. 101, 17102 (2004)], 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 variant where all possible Boolean functions are allowed.