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 and for two choices of update functions. 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 nonfrozen nodes scales as N2/3 with the system size N . When the exponent of the distribution is between 2 and 3, the number of the nonfrozen nodes increases as Nx , 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.
- Publication:
-
Physical Review E
- Pub Date:
- August 2009
- DOI:
- 10.1103/PhysRevE.80.026102
- arXiv:
- arXiv:0901.0387
- Bibcode:
- 2009PhRvE..80b6102D
- Keywords:
-
- 89.75.Hc;
- 64.60.aq;
- 02.50.-r;
- Networks and genealogical trees;
- Networks;
- Probability theory stochastic processes and statistics;
- Condensed Matter - Disordered Systems and Neural Networks;
- Condensed Matter - Statistical Mechanics
- E-Print:
- 5 pages, 1 graph, 1 sketch, submitted