中文摘要：

最近发展了一些将时间序列转化为复杂网络的方法，从而可以通过研究网络的拓扑性质来分析原始时间序列的性质．本文用递归图方法将分数布朗运动（FBM）时间序列转化为复杂网络，并研究其对应递归网络的拓扑性质．我们发现，对固定的Hurst指数日，在网络连通率首次增长到1之前，随着递归图的参数阂值的增大，网络的平均路径长度L也随之递增，之后反而递减．我们也发现由FBM时间序列转化得到的网络是无标度网络．我们采用节点覆盖盒计数法分析发现FBM的递归网络为分形网络，具有自相似特性，其分形维数dB随Hurst指数日的增大而减小，特别当H≥0．4时，有近似关系dB=H^2—2．1×H＋2．

英文摘要：

Some methods have been proposed recently to convert a single time series to a complex network so that the properties of the original time series can be understood by investigating the topological properties of the network. Here we convert fractional Brownian motion （FBM） time series to complex networks using recurrence plot method, and then we investigate the topological properties of the corresponding recurrence networks. It is found that for fixed Hurst exponent H, before the connectivity rate of corresponding networks increases to about 1 for the first time, the average length L of the shortest paths increases with the increase of parameter threshold in the recurrence plot, and then decreases. It is also found that the converted networks from FBM time series are scale-free. The analysis using the node-covering box-counting method shows that the recurrence networks axe fractals with self-similaxity property, and the fractal dimension dB decreases with Hurst index H. Especially, when H 〉 0.4, there is a approximately relationship dB= H^2 - 2.1 × H ＋ 2.