Mean-field and non-mean-field behaviors in scale-free networks with random Boolean dynamics

We study two types of simplified Boolean dynamics in scale-free networks, both with a synchronous update. Assigning only the Boolean functions AND and XOR to the nodes with probabilities 1 - p and p, respectively, we are able to analyze the density of 1's and the Hamming distance on the network...

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Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2010-06, Vol.43 (22), p.225101-225101
Main Authors: Silva, A Castro e, da Silva, J Kamphorst Leal
Format: Article
Language:English
Subjects:
Approximation
Boolean algebra
Computer simulation
Density
Dynamics
Exact sciences and technology
Mathematical analysis
Mathematical models
Networks
Physics
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Summary:We study two types of simplified Boolean dynamics in scale-free networks, both with a synchronous update. Assigning only the Boolean functions AND and XOR to the nodes with probabilities 1 - p and p, respectively, we are able to analyze the density of 1's and the Hamming distance on the network by numerical simulations and by a mean-field approximation (annealed approximation). We show that the behavior is quite different if the node always enters in the dynamics as its own input (self-regulation) or not. The same conclusion holds for the Kauffman NK model. Moreover, the simulation results and the mean-field ones (i) agree well when there is no self-regulation and (ii) disagree for small p when self-regulation is present in the model.
ISSN:1751-8121
1751-8113
1751-8121
DOI:10.1088/1751-8113/43/22/225101