Pathological tremors: Deterministic chaos or nonlinear stochastic oscillators?

Timmer, Jens; Häußler, SM; Lauk, M.; Lücking, Carl Hermann

doi:10.1063/1.166494

Cited by 118 publications

(69 citation statements)

References 43 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Since a straight line is tantamount to a constant slope, the local slopes α(s) of log 10 F (s) vs. log 10 s have to be evaluated for constancy in a sufficient range (Kantz and Schreiber, 1995;Tsonis and Elsner, 1995;Timmer et al, 2000). The extend of a sufficient range is still a matter of debate (see e.g.…”

Section: Two Example Processesmentioning

confidence: 99%

Tempting long-memory - on the interpretation of DFA results

Maraun

Rust

Timmer

2004

Nonlin. Processes Geophys.

Self Cite

172

179

View full text Add to dashboard Cite

Abstract.We study the inference of long-range correlations by means of Detrended Fluctuation Analysis (DFA) and argue that power-law scaling of the fluctuation function and thus long-memory may not be assumed a priori but have to be established. This requires the investigation of the local slopes. We account for the variability characteristic for stochastic processes by calculating empirical confidence regions. Comparing a long-memory with a short-memory model shows that the inference of long-range correlations from a finite amount of data by means of DFA is not specific. We remark that scaling cannot be concluded from a straight line fit to the fluctuation function in a log-log representation. Furthermore, we show that a local slope larger than α=0.5 for large scales does not necessarily imply longmemory. We also demonstrate, that it is not valid to conclude from a finite scaling region of the fluctuation function to an equivalent scaling region of the autocorrelation function. Finally, we review DFA results for the Prague temperature data set and show that long-range correlations cannot not be concluded unambiguously.

show abstract

Section: Two Example Processesmentioning

confidence: 99%

Tempting long-memory - on the interpretation of DFA results

Maraun

Rust

Timmer

2004

Nonlin. Processes Geophys.

Self Cite

172

179

View full text Add to dashboard Cite

show abstract

“…Regarding the behavior of wind speed and wind power in figures 1 and 2, what is important for us, figure 3 more closely, one should note that existence of the higher harmonics in the spectra indicates that the processes underlying the time series are not linear processes, but there is some kind of nonlinearity [21,24]. As another point, consider the frequency content of the plots.…”

Section: The Power Spectral Densitymentioning

confidence: 99%

“…From this figure, with increasing the wind speed, some type of bifurcation occurs in the corresponding wind power values. This bifurcation diagram may, however, be due to a chaotic or stochastic nature of a nonlinear process [20][21]. To distinguish between these two types of processes, several methods such as power spectrum analysis, phase space reconstruction, surrogate testing, test of the fractional dimension and the slope of integral sums, the δ-ε method, and recurrence plots will be performed using the TISEAN package [22] and CRP toolbox of MATLAB [23] as our tools.…”

Section: The Experimental Data and Time Series Analysismentioning

confidence: 99%

Dynamic characterization and predictability analysis of wind speed and wind power time series in Spain wind farm

Bigdeli

Lafmejani

2016

JAIDM

View full text Add to dashboard Cite

The renewable energy resources such as wind power have recently attracted more researchers' attention. It is mainly due to the aggressive energy consumption, high pollution and cost of fossil fuels. In this era, the future fluctuations of these time series should be predicted to increase the reliability of the power network. In this paper, the dynamic characteristics and short-term predictability of hourly wind speed and power time series are investigated via nonlinear time series analysis methods such as power spectral density analysis, time series histogram, phase space reconstruction, the slope of integral sums, the − method, the recurrence plot and the recurrence quantification analysis. Moreover, the interactive behavior of the wind speed and wind power time series is studied via the cross correlation, the cross and joint recurrence plots as well as the cross and joint recurrence quantification analyses. The results imply stochastic nature of these time series. Besides, a measure of the short-term mimic predictability of the wind speed and the underlying wind power has been derived for the experimental data of Spain's wind farm.

show abstract

“…At this point, we wish to emphasize that we have applied the noise titration technique to some experimental data, including pathological tremors [57][58][59] and velocity signals measured in the near wake of a circular cylinder of low-Reynolds number [60]. Both types of data have been found not to be chaotic, but like stochastic oscillations.…”

Section: Detecting Chaos In Continuous Dynamical Systems Using the Nomentioning

confidence: 99%

Detecting low-dimensional chaos by the “noise titration” technique: Possible problems and remedies

Gao¹,

Hu²,

Mao³

et al. 2012

Chaos, Solitons & Fractals

View full text Add to dashboard Cite

a b s t r a c tDistinguishing low-dimensional chaos from noise is an important issue in time series analysis. Among the many methods proposed for this purpose is the noise titration technique, which quantifies the amount of noise that needs to be added to the signal to fully destroy its nonlinearity. Two groups of researchers recently have questioned the validity of the technique. In this paper, we report a broad range of situations where the noise titration technique fails, and offer solutions to fix the problems identified.

show abstract

Pathological tremors: Deterministic chaos or nonlinear stochastic oscillators?

Cited by 118 publications

References 43 publications

Tempting long-memory - on the interpretation of DFA results

Tempting long-memory - on the interpretation of DFA results

Dynamic characterization and predictability analysis of wind speed and wind power time series in Spain wind farm

Detecting low-dimensional chaos by the “noise titration” technique: Possible problems and remedies

Contact Info

Product

Resources

About