Drossel Barbara, Greil Florian
Institut für Festkörperphysik, Technische Universität Darmstadt, 64289 Darmstadt, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Aug;80(2 Pt 2):026102. doi: 10.1103/PhysRevE.80.026102. Epub 2009 Aug 4.
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 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 in-degree distribution. These and ensuing results explain various findings obtained earlier by computer simulations.
我们通过解析和数值方法研究了具有幂律入度分布的临界布尔网络的动力学特性，并针对两种更新函数选择进行了研究。当入度分布的指数大于3时，我们得到的结果与固定入度网络所得到的结果等效，例如，非冻结节点的数量随系统规模N按N(2/3)缩放。当分布指数在2到3之间时，非冻结节点的数量随N(x)增加，其中x在0到2/3之间，且取决于指数和入度分布的截止值。这些以及后续结果解释了早期通过计算机模拟获得的各种发现。
