Critical Boolean networks with scale-free in-degree distribution

Abstract

We investigate analytically and numerically the dynamical properties of critical Boolean networks with power-law in-degree distributions. When the exponent of the in-degree distribution is larger than 3, we obtain results equivalent to those obtained for networks with fixed in-degree, e.g., the number of the non-frozen nodes scales as $N^{2/3}$ with the system size $N$. When the exponent of the distribution is between 2 and 3, the number of the non-frozen nodes increases as $N^x$, with $x$ being between 0 and 2/3 and depending on the exponent and on the cutoff of the in-degree distribution. These and ensuing results explain various findings obtained earlier by computer simulations.

5 pages, 1 graph, 1 sketch, submitted

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Cited by in corpus (9)

• Colloquium: Criticality and dynamical scaling in living systems
• Degree correlations in directed scale-free networks
• The effect of scale-free topology on the robustness and evolvability of genetic regulatory networks
• Impact of individual nodes in Boolean network dynamics
• The phase diagram of random Boolean networks with nested canalizing functions
• Intrinsic noise and deviations from criticality in Boolean gene-regulatory networks
• Formation of the frozen core in critical Boolean Networks
• Scaling laws in critical random Boolean networks with general in- and out-degree distributions
• Mean-Field and Non-Mean-Field Behaviors in Scale-free Networks with Random Boolean Dynamics