因特网拓扑演化及其节点平均连接度的分形研究

Research on Internet Topology Evolution and the Fractal of Average Degree of Nodes

针对因特网(Internet)的复杂网络特征,通过计算Internet标准结构熵和时间的关系,揭示了Inter-net的拓扑结构向着更有序方向演化的规律,并利用协同学原理求出了影响其演化的序参量.另外,通过对Inter-net节点平均连接度时间序列进行相空间重构,计算了其分形维数、最大Lyapunov指数和Kolmologorov熵,从理论上分析了这组数据可预测的时间尺度.最后,根据分析的结果,通过对时间序列进行预处理,运用混沌预测方法对未来一段时间内Internet节点的平均连接度进行了预测.

In view of the complex network character of Internet, the computing result of the relation of Internet standard entropy with time shows that Internet evolves from low level order to high level one. Furthermore, the order parameter was also obtained by computing according to the synergetics theory. However, the time series data of average nodes degree were reconstructed in phase space. The fractal dimension, maximum Lyapunov parameter and Kolmologor ov entropy were also computed. The predictable time scale of the serial data was get from the above computation. Finally, in means of the analytical results the time series data were preprocessed, and the average nodes degree of Internet in near months was predicated by means of chaos predicting.