Topological properties and fractal analysis of a recurrence network constructed from fractional Brownian motions.
Topological properties and fractal analysis of a recurrence network constructed from fractional Brownian motions.
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DOI：
10.1103/physreve.89.032814
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发表时间：
2014-03
期刊：
影响因子：
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通讯作者：
Jin-long Liu;Zuguo Yu;V. Anh
中科院分区：
文献类型：
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作者：
Jin-long Liu;Zuguo Yu;V. Anh
许多研究表明，我们可以通过研究时间序列的复杂网络来获得更多的信息。在这项工作中，我们研究的基本拓扑和分形性质的递归网络构造的分数布朗运动（FBM）。首先，我们的研究结果表明，所构造的递归网络具有指数度分布，平均度指数<$λ <$随着相关FBM的Hurst指数H的增大先增大后减小，H与<$λ <$的关系可用三次多项式函数表示.接下来，我们将重点关注递归网络的模序秩分布，以便我们可以更好地在局部结构水平上理解网络。我们发现了有趣的超家族现象，即，具有相同模序排列模式的递归网络被分成两个超家族。最后，我们数值分析了递归网络的分形和多重分形性质。我们发现递归网络的平均分形维数随关联FBM的Hurst指数H的增大而减小，并且它们之间的关系近似满足线性关系式<$dB <$<$2-H，这意味着关联递归网络的分形维数与FBM图的分形维数接近.此外，多重分形分析的数值结果表明，这些递归网络中存在多重分形性，并且当相关时间序列的Hurst指数从0.4增大到0.95时，这些递归网络的多重分形性先增强后减弱.特别地，Hurst指数H=0.5的递归网络具有最强的多重分形性。此外，平均信息维<D（1）>和平均关联维<D（2）>对赫斯特指数H的依赖关系也可以很好地用线性函数拟合。我们的研究结果强烈表明，递归网络继承了相关的FBM系列的基本特征和分形性质。
Many studies have shown that we can gain additional information on time series by investigating their accompanying complex networks. In this work, we investigate the fundamental topological and fractal properties of recurrence networks constructed from fractional Brownian motions (FBMs). First, our results indicate that the constructed recurrence networks have exponential degree distributions; the average degree exponent 〈λ〉 increases first and then decreases with the increase of Hurst index H of the associated FBMs; the relationship between H and 〈λ〉 can be represented by a cubic polynomial function. We next focus on the motif rank distribution of recurrence networks, so that we can better understand networks at the local structure level. We find the interesting superfamily phenomenon, i.e., the recurrence networks with the same motif rank pattern being grouped into two superfamilies. Last, we numerically analyze the fractal and multifractal properties of recurrence networks. We find that the average fractal dimension 〈dB〉 of recurrence networks decreases with the Hurst index H of the associated FBMs, and their dependence approximately satisfies the linear formula 〈dB〉≈2-H, which means that the fractal dimension of the associated recurrence network is close to that of the graph of the FBM. Moreover, our numerical results of multifractal analysis show that the multifractality exists in these recurrence networks, and the multifractality of these networks becomes stronger at first and then weaker when the Hurst index of the associated time series becomes larger from 0.4 to 0.95. In particular, the recurrence network with the Hurst index H=0.5 possesses the strongest multifractality. In addition, the dependence relationships of the average information dimension 〈D(1)〉 and the average correlation dimension 〈D(2)〉 on the Hurst index H can also be fitted well with linear functions. Our results strongly suggest that the recurrence network inherits the basic characteristic and the fractal nature of the associated FBM series.