多重分形序列的可见图分析

Visibility graph approach for multi-fractal series analysis

可见图方法将多重分形时间序列映射为相应的网络,研究并对比了由不同机制产生的多重分形序列的非平凡特征,发现单分形时间序列的简单叠加得到的混合序列有多分形性质,对应的可见图是无尺度网络;而通过模型产生的多分形序列对应的可见图一般不具有无标度性质.为了辨别不同机制生成的多分形时间序列,小波分析和可见图必须联合运用才能识别这两种不同的分形结构,可见图算法作为传统时间序列分析方法的补充在揭示序列产生机制时具有重要的用途.

Visibility graph method is used to map multi-fractal series to complex networks. Intrin- sic traits of multi-fractal series generated by different dynamical mechanisms were compared. It is found that mixture series constructed by superposition of several mono-fractal Brownian motions behave generally with multi-fractal character and the corresponding networks are scale-free. While for the multi-fractal series generated by theoretical models, the corresponding visibility graphs dis- play complicated behaviors rather than scale-free. In order to distinguish between these different generators, joint use of wavelet analysis and visibility graph is required to make clear the dynamical mechanisms embedded in multi-fractal time series. Visibility graph method is a necessary complement to traditional time series analysis approaches, which has potential use in detecting dynamical mechanisms of complex systems from output series.