Socolar J E S, Kauffman S A
Bios Group and Santa Fe Institute, Santa Fe, New Mexico 87501, USA.
Phys Rev Lett. 2003 Feb 14;90(6):068702. doi: 10.1103/PhysRevLett.90.068702. Epub 2003 Feb 13.
Random Boolean networks, originally invented as models of genetic regulatory networks, are simple models for a broad class of complex systems that show rich dynamical structures. From a biological perspective, the most interesting networks lie at or near a critical point in parameter space that divides "ordered" from "chaotic" attractor dynamics. We study the scaling of the average number of dynamically relevant nodes and the median number of distinct attractors in such networks. Our calculations indicate that the correct asymptotic scalings emerge only for very large systems.
随机布尔网络最初是作为基因调控网络的模型而发明的，是一类广泛的复杂系统的简单模型，这些系统展现出丰富的动力学结构。从生物学角度来看，最有趣的网络位于参数空间中的临界点或其附近，该临界点将“有序”吸引子动力学与“混沌”吸引子动力学区分开来。我们研究了此类网络中动态相关节点的平均数量和不同吸引子的中位数数量的标度。我们的计算表明，只有对于非常大的系统才会出现正确的渐近标度。
