2005
DOI: 10.1103/physreve.72.046220
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Visualization of coupling in time series by order recurrence plots

Abstract: We introduce a new method to visualize dependencies between two time series applying the concept of cross recurrence plots to the local ordinal structure. We derive a measure of the coupling strength which is robust against observational noise, nonlinear distortion of the amplitude and lowfrequency trends. Connections to the instantaneous phase and the determination of phase coupling of two coupled Rössler systems in standard and funnel regime are shown. An application to EEG data demonstrates that the method … Show more

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Cited by 101 publications
(67 citation statements)
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“…From these order patterns we form a new symbolic time series p i , and define the order patterns recurrence plot (OPRP) as (Groth 2005):…”
Section: Wavelet Transformmentioning
confidence: 99%
See 1 more Smart Citation
“…From these order patterns we form a new symbolic time series p i , and define the order patterns recurrence plot (OPRP) as (Groth 2005):…”
Section: Wavelet Transformmentioning
confidence: 99%
“…What is more, Bian et al have shown that MA at ST36 can increase the complexity of EEG signals, which can be regards as a characteristic parameter to distinguish the states during acupuncture and before acupuncture (Bian et al 2011). One of the most widely used methods to analyze EEG complexity is order recurrence quantification analysis (ORQA) (Groth 2005). The ORQA method based on the order recurrence plot (ORP) can not only describe the distribution character of the recursive state points, but also reveal more significant information during transitions in the brain processes due to the surprising stimuli and to distinguish ERPs between single electrodes (Marwan et al 2007).…”
Section: Introductionmentioning
confidence: 99%
“…These recurrence-based methods of signal analysis have been used to compute nonlinear dynamical properties of signals, 3 quantify nonstationarity, [3][4][5][6][7][8][9] detect unstable periodic orbits ͑UPOs͒, 10-14 estimate dynamical invariants, 15,16 and measure levels of synchrony. 8,17 Other statistics quantifying visually apparent structures in the recurrence plots, such as, the lengths of diagonal or horizontal lines, have been used to measure percent recurrence and percent determinism, 4,18 but the relationship between these statistics and features derived from visual inspection of the original signal is often unclear. 19 It is also not known if any of these statistics uncover new dynamical information, or are simply reflective of time-frequency-energy signal changes, as is likely the case with correlation dimension and Lyapunov exponent.…”
Section: Introductionmentioning
confidence: 99%
“…Let us consider embedding dimension m = 3, which is related to the phase of an oscillator [16], discussed in Section 5. Here the phase space is nicely decomposed into m!…”
Section: Order Patterns Of Lengthmentioning
confidence: 99%
“…The average recurrence rate RR = RR x,y is determined as in (16). It depends not only on ε, but also indicates whether trajectories of the two systems often visit the same phase space regions.…”
Section: Auto-recurrencementioning
confidence: 99%