| | |
Summary: Canalizing Kauffman Networks: Nonergodicity and Its Effect on Their Critical Behavior
Andre´ Auto Moreira1,* and Lui´s A. Nunes Amaral1,
1
Department of Chemical and Biological Engineering, Northwestern University, Evanston, Illinois 60208, USA
(Received 18 November 2004; published 3 June 2005)
Boolean networks have been used to study numerous phenomena, including gene regulation, neural
networks, social interactions, and biological evolution. Here, we propose a general method for determin-
ing the critical behavior of Boolean systems built from arbitrary ensembles of Boolean functions. In
particular, we solve the critical condition for systems of units operating according to canalizing functions
and present strong numerical evidence that our approach correctly predicts the phase transition from order
to chaos in such systems.
DOI: 10.1103/PhysRevLett.94.218702 PACS numbers: 89.75.Hc, 05.45.-a, 64.60.Cn
Biological and social systems typically comprise a large
number of interacting units coupled through a nontrivial
network of interactions. Examples of such systems include
the metabolic processes in living cells [1] and social inter-
actions in human groups [2,3]. Remarkably, these systems
exhibit a high degree of self-organization that ensures their
continued functioning and allows them to respond to en-
vironmental changes. A challenging aspect in the study of
|
