Detection of dynamical regime transitions with lacunarity as a multiscale recurrence quantification measure
- We propose lacunarity as a novel recurrence quantification measure and illustrate its efficacy to detect dynamical regime transitions which are exhibited by many complex real-world systems. We carry out a recurrence plot-based analysis for different paradigmatic systems and nonlinear empirical data in order to demonstrate the ability of our method to detect dynamical transitions ranging across different temporal scales. It succeeds to distinguish states of varying dynamical complexity in the presence of noise and non-stationarity, even when the time series is of short length. In contrast to traditional recurrence quantifiers, no specification of minimal line lengths is required and geometric features beyond linear structures in the recurrence plot can be accounted for. This makes lacunarity more broadly applicable as a recurrence quantification measure. Lacunarity is usually interpreted as a measure of heterogeneity or translational invariance of an arbitrary spatial pattern. In application to recurrence plots, it quantifies theWe propose lacunarity as a novel recurrence quantification measure and illustrate its efficacy to detect dynamical regime transitions which are exhibited by many complex real-world systems. We carry out a recurrence plot-based analysis for different paradigmatic systems and nonlinear empirical data in order to demonstrate the ability of our method to detect dynamical transitions ranging across different temporal scales. It succeeds to distinguish states of varying dynamical complexity in the presence of noise and non-stationarity, even when the time series is of short length. In contrast to traditional recurrence quantifiers, no specification of minimal line lengths is required and geometric features beyond linear structures in the recurrence plot can be accounted for. This makes lacunarity more broadly applicable as a recurrence quantification measure. Lacunarity is usually interpreted as a measure of heterogeneity or translational invariance of an arbitrary spatial pattern. In application to recurrence plots, it quantifies the degree of heterogeneity in the temporal recurrence patterns at all relevant time scales. We demonstrate the potential of the proposed method when applied to empirical data, namely time series of acoustic pressure fluctuations from a turbulent combustor. Recurrence lacunarity captures both the rich variability in dynamical complexity of acoustic pressure fluctuations and shifting time scales encoded in the recurrence plots. Furthermore, it contributes to a better distinction between stable operation and near blowout states of combustors.…
Author details: | Tobias BraunORCiD, Vishnu R. Unni, Raman I. SujithORCiD, Jürgen KurthsORCiDGND, Norbert MarwanORCiDGND |
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DOI: | https://doi.org/10.1007/s11071-021-06457-5 |
ISSN: | 0924-090X |
ISSN: | 1573-269X |
Title of parent work (English): | Nonlinear dynamics : an international journal of nonlinear dynamics and chaos in engineering systems |
Publisher: | Springer Science + Business Media B.V |
Place of publishing: | Dordrecht [u.a.] |
Publication type: | Article |
Language: | English |
Date of first publication: | 2021/04/27 |
Publication year: | 2021 |
Release date: | 2024/09/13 |
Tag: | Lacunarity; Nonlinear time series; Recurrence plots; Regime shifts; Thermoacoustic instability |
Volume: | 104 |
Issue: | 4 |
Number of pages: | 19 |
First page: | 3955 |
Last Page: | 3973 |
Funding institution: | Deutsche Forschungsgemeinschaft in the context of the DFG projectGerman Research Foundation (DFG) [MA4759/11-1, MA4759/9-1]; European UnionEuropean Commission [820970]; Science and Engineering Research Board (SERB) of the Department of Science and Technology, Government of India [DST/SF/1(EC)/2006, JCB/2018/000034/SSC]; University of California San DiegoUniversity of California System |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Geowissenschaften |
DDC classification: | 5 Naturwissenschaften und Mathematik / 50 Naturwissenschaften / 500 Naturwissenschaften und Mathematik |
Peer review: | Referiert |
Publishing method: | Open Access / Hybrid Open-Access |
License (German): | CC-BY - Namensnennung 4.0 International |