损伤尺寸分布下功能有向网络的复杂性阈值
Complexity Threshold for Functioning Directed Networks in Damage Size Distribution
摘要：
提出了一个确定的复杂度阈值，它定义了RSN的术语“复杂网络”，例如s>=2的考夫曼网络-两个以上的等概率状态变量。这样的考夫曼网络不再是布尔网络。RSN不同于RWN和RNS。这篇文章是第二个三个步骤中的“结构趋势”，这是复杂的RSN的适应性进化的影响的描述。这个复杂性阈值是基于网络随机增长和小网络效应消失期间出现的混沌特征。利用仿真研究了在一小部分受损节点中测量的受损尺寸（小扰动后）的分布，或受损外部输出的数量和混沌度。它是在不同的增长（N=4000个节点）过程中完成的：网络类型（包括无标度），节点输入的数量（K= 2，3，4，对于网络是固定的）和信号变量的数量（s= 2，3，4，16）。在该分布中出现两个峰值，并且在它们之间出现零频率区域-这是在调查中发现的复杂性阈值的最佳实用标准。在新出现的复杂性领域没有发现临界点。使用一种特殊的简化算法（“反向退火”），它省略了圆形吸引子的问题。调查的“过渡”到混乱的N是不同的，从已知的相变K=2附近的s=2。
英文摘要：
A certain complexity threshold is proposed which defines the term `complex network' for RSN, e.g. Kauffman networks with s>=2 - more than two equally probable state variants. Such Kauffman networks are no longer Boolean networks. RSN are different than RWN and RNS. This article is the second one of three steps in description of `structural tendencies' which are an effect of adaptive evolution of complex RSN. This complexity threshold is based on the appearances of chaotic features of a network during its random growth and disappearance of small network effects. Distribution of damage size (after small disturbance) measured in a fraction of damaged nodes, or in number of damaged external outputs and degree of chaos is investigated using simulation. It is done during growth (up to N=4000 nodes) for different: network types (including scale-free), numbers of node inputs (K=2,3,4, fixed for a network) and numbers of signal variants (s=2,3,4,16). In this distribution two peaks emerge and in-between them there appears an area of zero frequency - this is the best practical criterion of complexity threshold found in the investigation. No critical points are found in the area of emerging complexity. A special simplified algorithm (`reversed-annealed') is used which omits the problem of circular attractors. The investigated `transition' to chaos in respect to N is different from the known phase transition near K=2 for s=2.
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