Critical Boolean networks with scalefree indegree distribution
Abstract
We investigate analytically and numerically the dynamical properties of critical Boolean networks with powerlaw indegree distributions and for two choices of update functions. When the exponent of the indegree distribution is larger than 3, we obtain results equivalent to those obtained for networks with fixed indegree, e.g., the number of the nonfrozen 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 nonfrozen nodes increases as N^{x} , with x being between 0 and 2/3 and depending on the exponent and on the cutoff of the indegree 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
 EPrint:
 5 pages, 1 graph, 1 sketch, submitted