期刊
NONLINEAR DYNAMICS
卷 100, 期 2, 页码 1689-1704出版社
SPRINGER
DOI: 10.1007/s11071-020-05581-y
关键词
Chaotic oscillator; Complexity; Dynamical system; Holder exponents; Multifractal analysis; Multifractal spectrum; Singularity; Time-series analysis
资金
- World Research Hub Initiative (WRHI), Institute of Innovative Research (IIR), Tokyo Institute of Technology, Tokyo, Japan
- Argentinean Consejo Nacional de Investigaciones Cientificas y Tecnicas (CONICET)
The robustness of two widespread multifractal analysis methods, one based on detrended fluctuation analysis and one on wavelet leaders, is discussed in the context of time-series containing non-uniform structures with only isolated singularities. Signals generated by simulated and experimentally-realized chaos generators, together with synthetic data addressing particular aspects, are taken into consideration. The results reveal essential limitations affecting the ability of both methods to correctly infer the non-multifractal nature of signals devoid of a cascade-like hierarchy of singularities. Namely, signals harboring only isolated singularities are found to artefactually give rise to broad multifractal spectra, resembling those expected in the presence of a well-developed underlying multifractal structure. Hence, there is a real risk of incorrectly inferring multifractality due to isolated singularities. The careful consideration of local scaling properties and the distribution of Holder exponent obtained, for example, through wavelet analysis, is indispensable for rigorously assessing the presence or absence of multifractality.
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