Critical Boolean networks with scale-free in-degree distribution

Details Critical Boolean networks with scale-free in-degree distribution Critical Boolean networks with scale-free in-degree distribution

2009-01-04

arxiv.org/abs/0901.0387v1

Phys. Rev. E 80, 026102 (2009)

Physics

Condensed Matter

Disordered Systems and Neural Networks

5 pages, 1 graph, 1 sketch, submitted

Scientific paper

10.1103/PhysRevE.80.026102

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.

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