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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.show moreshow less

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Metadaten
Author details:Tobias BraunORCiD, Vishnu R. Unni, Raman I. SujithORCiD, Jürgen KurthsORCiDGND, Norbert MarwanORCiDGND
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):License LogoCC-BY - Namensnennung 4.0 International
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