Surrogate for nonlinear time series analysis

Dolan, Kevin; Spano, Mark L.

doi:10.1103/physreve.64.046128

Cited by 82 publications

(68 citation statements)

References 12 publications

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“…There are some limitations of the Schreiber and Schmitz [2000] surrogate data test for nonlinearity: The different realizations may not be completely independent of each other and thus not uniformly span the probability space [see Dolan and Spano, 2001]. We also applied more advanced techniques that handle this technical problem and obtained similar results.…”

Section: Appendix B: Surrogate Test For Nonlinearitysupporting

confidence: 54%

Simple stochastic models for glacial dynamics

2005

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[1] Glacial-interglacial events have several nonlinear and stochastic characteristics. Recent studies suggested additional stochastic nonlinear features (not necessarily related to the large-scale dynamics of the glacial cycle) in the timescale of 1-100 kyr including (1) strong long-range correlations in the magnitude of climate variable increments as well as (2) a wide multifractal spectrum. Realistic climate models should reproduce these properties of the natural system. We first study several previously proposed stochastic models for glacial-interglacial dynamics and demonstrate that they do not reproduce some of the nonlinear properties of the paleoclimate proxy data. We then suggest two nonlinear stochastic models for glacial-interglacial dynamics that exhibit similar stochastic nonlinear properties to those seen in the natural data. We conjecture that interaction between fast random fluctuations (representing atmospheric variability) and slowly varying fluctuations (representing oceanic variability) may underlie the observed stochastic nonlinearity of time series for glacial-interglacial oscillations.

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Section: Appendix B: Surrogate Test For Nonlinearitysupporting

confidence: 54%

Simple stochastic models for glacial dynamics

2005

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“…. ; s N g by randomly shuffling it (Dolan and Spano 2001). Then, all of the original data were included in a completely random order.…”

Section: Pe and Oimentioning

confidence: 99%

Complexity of resting-state EEG activity in the patients with early-stage Parkinson’s disease

Wang

Deng

et al. 2016

Cogn Neurodyn

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To investigate the abnormal brain activities in the early stage of Parkinson's disease (PD), the electroencephalogram (EEG) signals were recorded with 20 channels from non-dementia PD patients (18 patients, 8 females) and age matched healthy controls (18 subjects, 8 females) during the resting state. Two methods based on the ordinal patterns of the recorded series, i.e., permutation entropy (PE) and order index (OI), were introduced to characterize the complexity of the cortical activities for two groups. It was observed that the resting-state EEG of PD patients showed lower PE and higher OI than healthy controls, which indicated that the early-stage PD caused the reduced complexity of EEG. We further applied two methods to determine the complexity of EEG rhythms in five sub-bands. The results showed that the gamma, beta and alpha rhythms of PD patients were characterized by lower PE and higher OI, i.e., reduced complexity, than healthy subjects. No significant differences were observed in theta or delta rhythms between two groups. The findings suggested that PE and OI were promising methods to detect the abnormal changes in the dynamics of EEG signals associated with early-stage PD. Further, such changes in EEG complexity may be the early markers of the cortical or subcortical dysfunction caused by PD.

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“…For these set of parameter values and ǫ = 0, the true values characterizing the UPOs are: λ s = 0.178, λ us = −1.69, and fixed point at X * = 0.6667 [39]. Hénon map has been analyzed earlier using only the Level 0 topological recurrence method combined with a matrix fit algorithm [39]. The dynamical parameters were estimated and analyzed with or without noise.…”

Section: Resultsmentioning

confidence: 99%

“…To determine whether the detected UPOs actually originate from deterministic and not from stochastic dynamics, surrogate analysis methods have been proposed [15,30,34,35,41] . In the topological recurrence method [35], the K value…”

Section: B Statistical Significance Of Uposmentioning

confidence: 99%

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Reliability of unstable periodic orbit based control strategies in biological systems

Mishra

Hasse

Biswal

et al. 2015

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Presence of recurrent and statistically significant unstable periodic orbits (UPOs) in time series obtained from biological systems are now routinely used as evidence for low dimensional chaos . Extracting accurate dynamical information from the detected UPO trajectories are vital for successful control strategies that either aim to stabilize the system near the fixed point or steer the system away from the periodic orbits. A hybrid UPO detection method from return maps that combines topological recurrence criterion, matrix fit algorithm and stringent criterion for fixed point location gives accurate and statistically significant UPOs even in the presence of significant noise. Geometry of the return map, frequency of UPOs visiting the same trajectory, length of the data set, strength of the noise and degree of nonstationarity affect the efficacy of the proposed method. Results suggest that establishing determinism from unambiguous UPO detection is often possible in short data sets with significant noise, but derived dynamical properties are rarely accurate and adequate for controlling the dynamics around these UPOs. A repeat chaos control experiment on epileptic hippocampal slices through more stringent control strategy and adaptive UPO tracking is reinterpreted in this context through simulation of similar control experiments on an analogous but stochastic computer model of epileptic brain slices. Reproduction of equivalent results suggests that far more stringent criteria are needed for linking apparent success of control in such experiments with possible determinism in the underlying dynamics. Unstable periodic orbits (UPOs) analysis has now become an established tool for detecting determinism in biological systems. If the system is truly deterministic, accurate UPO characteristics can be further used for application of control or anti control strategies with potential medical application. However, accurate biological time series analysis for UPOs critically depend on the length of data set, strength of noise, type of geometry, nonstationarity etc. In this work we show that it is possible to establish determinism through UPO analysis in presence of all these factors. However, the inaccuracy in the measured UPO parameters and non-stationarity nature of biological systems mean only adaptive control strategies are useful for successful chaos control in such systems. At the same time, comparable success of adaptive control strategies on a stochastic neural network model of epileptic slices demand more stringent criteria for linking adaptive control success with determinism.

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Surrogate for nonlinear time series analysis

Cited by 82 publications

References 12 publications

Simple stochastic models for glacial dynamics

Simple stochastic models for glacial dynamics

Complexity of resting-state EEG activity in the patients with early-stage Parkinson’s disease

Reliability of unstable periodic orbit based control strategies in biological systems

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