Detection of Dynamical Regime Transitions with Lacunarity as a Multiscale Recurrence Quantification Measure

We propose Lacunarity as a novel recurrence quantification measure and apply it in the context of dynamical regime transitions. Many complex real-world systems exhibit abrupt regime shifts. We carry out a recurrence plot based analysis for different paradigmatic systems and thermoacoustic combustion time series in order to demonstrate the ability of our method to detect dynamical transitions on variable temporal scales. Lacunarity is usually interpreted as a measure of ‘gappiness’ of an arbitrary spatial pattern. In application to recurrence plots, it quantifies the degree of heterogenity in the temporal recurrent patterns. Our method succeeds to distinguish states of varying dynamical complexity in presence of noise and short time series length. In contrast to traditional recurrence quantifiers, no specification of minimal line lengths is required and features beyond the scope of line structures can be accounted for. Applied to acoustic pressure fluctuation time series, it captures both the rich variability in dynamical complexity and detects shifts of characteristic time scales.