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Free keywords:
Recurrence Plots; Regime Shifts; Lacunarity; Nonlinear time series; Thermoacoustic
Instability
Abstract:
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 nonstationarity, even when the time series is of short length. In contrast to traditional recurrence quantifiers, no specification of minimal line lengths is required and rather
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 heterogenity 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.
