Characterization of Strange Attractors

Grassberger, Peter; Procaccia, Itamar

doi:10.1103/physrevlett.50.346

Cited by 4,414 publications

(2,193 citation statements)

References 13 publications

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“…The algorithm employed for ApEn estimation is from Grassberger and Procaccia. [8][9][10][11] ApEn is close to 0 for time series with pronounced regularity and shows increasing values to 1 with increasing irregularity of the time series.…”

Section: Definition Of End Point and Follow-upmentioning

confidence: 87%

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Prediction of hypertensive crisis based on average, variability and approximate entropy of 24-h ambulatory blood pressure monitoring

Schoenenberger

Erné²,

Ammann

et al. 2007

J Hum Hypertens

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Approximate entropy (ApEn) of blood pressure (BP) can be easily measured based on software analysing 24-h ambulatory BP monitoring (ABPM), but the clinical value of this measure is unknown. In a prospective study we investigated whether ApEn of BP predicts, in addition to average and variability of BP, the risk of hypertensive crisis. In 57 patients with known hypertension we measured ApEn, average and variability of systolic and diastolic BP based on 24-h ABPM. Eight of these fiftyseven patients developed hypertensive crisis during follow-up (mean follow-up duration 726 days). In bivariate regression analysis, ApEn of systolic BP (Po0.01), average of systolic BP (P ¼ 0.02) and average of diastolic BP (P ¼ 0.03) were significant predictors of hypertensive crisis. The incidence rate ratio of hypertensive crisis was 14.0 (95% confidence interval (CI) 1.8, 631.5; Po0.01) for high ApEn of systolic BP as compared to low values. In multivariable regression analysis, ApEn of systolic (P ¼ 0.01) and average of diastolic BP (Po0.01) were independent predictors of hypertensive crisis. A combination of these two measures had a positive predictive value of 75%, and a negative predictive value of 91%, respectively. ApEn, combined with other measures of 24-h ABPM, is a potentially powerful predictor of hypertensive crisis. If confirmed in independent samples, these findings have major clinical implications since measures predicting the risk of hypertensive crisis define patients requiring intensive follow-up and intensified therapy.

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Section: Definition Of End Point and Follow-upmentioning

confidence: 87%

“…ApEn describes the irregularity of a time series. [8][9][10][11] Animal studies detected chaotic components in the time series of BP. [12][13][14][15] One property inherent in chaotic systems is the possibility of a sudden dissipation.…”

Section: Introductionmentioning

confidence: 99%

Prediction of hypertensive crisis based on average, variability and approximate entropy of 24-h ambulatory blood pressure monitoring

Schoenenberger

Erné²,

Ammann

et al. 2007

J Hum Hypertens

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“…The amount of data required for meaningful results is beyond the experimental possibilities for physiological data (Eckmann and Ruelle, 1992) and the Grassberger and Procaccia algorithm or its modifications used to estimate the D 2 assume the time series to be stationary (Grassberger and Procaccia, 1983b), something generally not true with biological data. Therefore, it becomes necessary to apply other non-linear methods to study the EEG background activity.…”

Section: Introductionmentioning

confidence: 99%

Analysis of regularity in the EEG background activity of Alzheimer's disease patients with Approximate Entropy

Abásolo

Hornero

Espino

et al. 2005

Clinical Neurophysiology

217

159

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“…The dimension of this state space has to be at least as large as the dimension of the given time series. Various methods exist to calculate the dimension of an experimental time series [21].…”

Section: '-Jmentioning

confidence: 99%

Modeling experimental time series with ordinary differential equations

et al. 1991

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Abstract. Recently some methods have been presented to extract ordinary differential equations (ODE) directly from an experimental time series. Here, we introduce a new method to find an ODE which models both the short time and the long time dynamics. The experimental data are represented in a state space and the corresponding flow vectors are approximated by polynomials of the state vector components. We apply these methods both to simulated data and experimental data from human limb movements, which like many other biological systems can exhibit limit cycle dynamics. In systems with only one oscillator there is excellent agreement between the limit cycling displayed by the experimental system and the reconstructed model, even if the data are very noisy. Furthermore we study systems of two coupled limit cycle oscillators. There, a reconstruction was only successful for data with a sufficently long transient trajectory and relatively low noise level.

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Characterization of Strange Attractors

Cited by 4,414 publications

References 13 publications

Prediction of hypertensive crisis based on average, variability and approximate entropy of 24-h ambulatory blood pressure monitoring

Prediction of hypertensive crisis based on average, variability and approximate entropy of 24-h ambulatory blood pressure monitoring

Analysis of regularity in the EEG background activity of Alzheimer's disease patients with Approximate Entropy

Modeling experimental time series with ordinary differential equations

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