Persistence of activity in threshold contact processes, an Annealed approximation of random Boolean networks
We consider a model for gene regulatory networks that is a modification of Kauffmann's J Theor Biol 22 (1969), 437467 random Boolean networks. There are three parameters: number of nodes, number of inputs to each node, and expected fraction of 1'sin the Boolean functions at each node. Following a standard practice in thephysics literature, we use a threshold contact process on a random graph on n nodes, in which each node has in degree r, to approximate its dynamics. We show that if and , then the threshold contact process persists for a long time, which correspond to chaotic behavior of the Boolean network. Unfortunately, we are only able to prove the persistence time is with when , and when .  2011 Wiley Periodicals, Inc. Random Struct. Alg., 2011
threshold contact process random boolean networks gene regulatory networks random graphs phase transition