Department of Computer Science, International Computer Science Institute, University of California Berkeley, California 94704, USA.
Chaos. 2013 Mar;23(1):013135. doi: 10.1063/1.4793782.
We show that in networks with a hierarchical architecture, critical dynamical behaviors can emerge even when the underlying dynamical processes are not critical. This finding provides explicit insight into current studies of the brain's neuronal network showing power-law avalanches in neural recordings, and provides a theoretical justification of recent numerical findings. Our analysis shows how the hierarchical organization of a network can itself lead to power-law distributions of avalanche sizes and durations, scaling laws between anomalous exponents, and universal functions-even in the absence of self-organized criticality or critical points. This hierarchy-induced phenomenon is independent of, though can potentially operate in conjunction with, standard dynamical mechanisms for generating power laws.
我们表明，在具有层次结构的网络中，即使基础动力学过程不是临界的，也可能出现关键的动力学行为。这一发现为当前研究大脑神经元网络提供了明确的见解，这些研究显示在神经记录中存在幂律级联，为最近的数值发现提供了理论依据。我们的分析表明，网络的层次结构如何本身导致级联大小和持续时间的幂律分布、异常指数之间的标度律以及通用函数——即使在没有自组织临界性或临界点的情况下也是如此。这种由层次结构引起的现象与产生幂律的标准动力学机制无关，但可能与之同时发生。
