scholarly journals Nonlinear analysis of magnetospheric data Part II. Dynamical characteristics of the AE index time series and comparison with nonlinear surrogate data

1999 ◽  
Vol 6 (2) ◽  
pp. 79-98 ◽  
Author(s):  
G. P. Pavlos ◽  
D. Kugiumtzis ◽  
M. A. Athanasiu ◽  
N. Hatzigeorgiu ◽  
D. Diamantidis ◽  
...  
Keyword(s):  
Time Series ◽  
Nonlinear Analysis ◽  
Dynamic Models ◽  
Surrogate Data ◽  
Dynamical Characteristics ◽  
Ae Index ◽  
The Family ◽  
Nonlinear Dynamic Models ◽  
Original Time ◽  
Index Time Series

Abstract. In this study we have used dynamical characteristies such as Lyapunov exponents, nonlinear dynamic models and mutual information for the nonlinear analysis of the magnetospheric AE index time series. Similarly with the geometrical characteristic studied in Pavlos et al. (1999b), we have found significant differences between the original time series and its surrogate data. These results also suggest the rejection of the null hypothesis that the AE index belongs to the family of stochastic linear signals undergoing a static nonlinear distortion. Finally, we believe that these results support the hypothesis of nonlinearity and chaos for the magnetospheric dynamics.

scholarly journals Nonlinear analysis of magnetospheric data Part I. Geometric characteristics of the AE index time series and comparison with nonlinear surrogate data

1999 ◽  
Vol 6 (1) ◽  
pp. 51-65 ◽  
Author(s):  
G. P. Pavlos ◽  
M. A. Athanasiu ◽  
D. Kugiumtzis ◽  
N. Hatzigeorgiu ◽  
A. G. Rigas ◽  
...  
Keyword(s):  
Time Series ◽  
State Space ◽  
Null Hypothesis ◽  
Surrogate Data ◽  
Statistical Testing ◽  
Geometrical Parameters ◽  
Geometric Characteristics ◽  
Geometrical Characteristics ◽  
Ae Index ◽  
Index Time Series

Abstract. A long AE index time series is used as a crucial magnetospheric quantity in order to study the underlying dynainics. For this purpose we utilize methods of nonlinear and chaotic analysis of time series. Two basic components of this analysis are the reconstruction of the experimental tiine series state space trajectory of the underlying process and the statistical testing of an null hypothesis. The null hypothesis against which the experimental time series are tested is that the observed AE index signal is generated by a linear stochastic signal possibly perturbed by a static nonlinear distortion. As dis ' ' ating statistics we use geometrical characteristics of the reconstructed state space (Part I, which is the work of this paper) and dynamical characteristics (Part II, which is the work a separate paper), and "nonlinear" surrogate data, generated by two different techniques which can mimic the original (AE index) signal. lie null hypothesis is tested for geometrical characteristics which are the dimension of the reconstructed trajectory and some new geometrical parameters introduced in this work for the efficient discrimination between the nonlinear stochastic surrogate data and the AE index. Finally, the estimated geometric characteristics of the magnetospheric AE index present new evidence about the nonlinear and low dimensional character of the underlying magnetospheric dynamics for the AE index.

scholarly journals SVD analysis of the magnetospheric AE index time series and comparison with low-dimensional chaotic dynamics

2001 ◽  
Vol 8 (1/2) ◽  
pp. 95-125 ◽  
Author(s):  
M. A. Athanasiu ◽  
G. P. Pavlos
Keyword(s):  
Time Series ◽  
Colored Noise ◽  
External Noise ◽  
Original Time Series ◽  
Svd Analysis ◽  
Ae Index ◽  
Low Dimensional ◽  
Original Time ◽  
Value Decomposition ◽  
Index Time Series

Abstract. The singular value decomposition (SVD) analysis is used at different stages in this paper in order to extract useful information concerning the underlying dynamics of the magnetospheric AE index. As a frame of reference we use the dynamics of the Lorenz system perturbed by external noise, white or colored. One of the critical results is that the colored noise can be differentiated from the white noise when we study their perturbation upon the eigenvalue spectrum of the trajectory matrix, the SVD reconstructed components of the original time series and other characteristics. This result is used in order to conclude the existence of strong component of colored noise included in the magnetospheric AE index time series. Moreover, the study of the SVD reconstructed components of the original time series can confirm the low-dimensionality of a dynamical system strongly perturbed by external colored noise. Finally, the results of this study strengthen the hypothesis of the magnetospheric chaos.

scholarly journals Dynamical characteristics of magnetospheric energetic ion time series: evidence for low dimensional chaos

2003 ◽  
Vol 21 (9) ◽  
pp. 1995-2010 ◽  
Author(s):  
M. A. Athanasiu ◽  
G. P. Pavlos ◽  
D. V. Sarafopoulos ◽  
E. T. Sarris
Keyword(s):  
Time Series ◽  
Chaotic Dynamics ◽  
Lorenz System ◽  
Prediction Models ◽  
Surrogate Data ◽  
Nonlinear Phenomena ◽  
Energetic Ions ◽  
Dynamical Characteristics ◽  
Noise Perturbation ◽  
Low Dimensional

Abstract. This paper is a companion to the first work (Pavlos et al., 2003), which contains significant results concerning the dynamical characteristics of the magnetospheric energetic ions’ time series. The low dimensional and nonlinear deterministic characteristics of the same time series were described in Pavlos et al. (2003). In this second work we present significant results concerning the Lyapunov spectrum, the mutual information and prediction models. The dynamical characteristics of the magnetospheric ions’ signals are compared with corresponding characteristics obtained for the stochastic Lorenz system when a coloured noise perturbation is present. In addition, the null hypothesis is tested for the dynamical characteristics of the magnetospheric ions’ signal by using nonlinear surrogate data. The results of the above comparisons provide significant evidence for the existence of low dimensional chaotic dynamics underlying the energetic ions’ time series.Key words. Magnetospheric physics (energetic particles) – Radio sciences (nonlinear phenomena)

Human fetuses have nonlinear cardiac dynamics

1999 ◽  
Vol 87 (2) ◽  
pp. 530-537 ◽  
Author(s):  
Lynn J. Groome ◽  
Donna M. Mooney ◽  
Scherri B. Holland ◽  
Lisa A. Smith ◽  
Jana L. Atterbury ◽  
...  
Keyword(s):  
Time Series ◽  
Dynamic Models ◽  
Time Series Data ◽  
Low Risk ◽  
Series Data ◽  
Correlated Noise ◽  
Human Fetuses ◽  
Original Time Series ◽  
Uncorrelated Noise ◽  
Original Time

Approximate entropy (ApEn) is a statistic that quantifies regularity in time series data, and this parameter has several features that make it attractive for analyzing physiological systems. In this study, ApEn was used to detect nonlinearities in the heart rate (HR) patterns of 12 low-risk human fetuses between 38 and 40 wk of gestation. The fetal cardiac electrical signal was sampled at a rate of 1,024 Hz by using Ag-AgCl electrodes positioned across the mother’s abdomen, and fetal R waves were extracted by using adaptive signal processing techniques. To test for nonlinearity, ApEn for the original HR time series was compared with ApEn for three dynamic models: temporally uncorrelated noise, linearly correlated noise, and linearly correlated noise with nonlinear distortion. Each model had the same mean and SD in HR as the original time series, and one model also preserved the Fourier power spectrum. We estimated that noise accounted for 17.2–44.5% of the total between-fetus variance in ApEn. Nevertheless, ApEn for the original time series data still differed significantly from ApEn for the three dynamic models for both group comparisons and individual fetuses. We concluded that the HR time series, in low-risk human fetuses, could not be modeled as temporally uncorrelated noise, linearly correlated noise, or static filtering of linearly correlated noise.

ON THE RELIABILITY OF THE SURROGATE DATA TEST FOR NONLINEARITY IN THE ANALYSIS OF NOISY TIME SERIES

2001 ◽  
Vol 11 (07) ◽  
pp. 1881-1896 ◽  
Author(s):  
D. KUGIUMTZIS
Keyword(s):  
Time Series ◽  
Null Hypothesis ◽  
Volterra Series ◽  
Simulated Data ◽  
Real Data ◽  
Surrogate Data ◽  
Largest Lyapunov Exponent ◽  
Real World Data ◽  
Original Time ◽  
False Nearest Neighbors

In the analysis of real world data, the surrogate data test is often performed in order to investigate nonlinearity in the data. The null hypothesis of the test is that the original time series is generated from a linear stochastic process possibly undergoing a nonlinear static transform. We argue against reported rejection of the null hypothesis and claims of evidence of nonlinearity based on a single nonlinear statistic. In particular, two schemes for the generation of surrogate data are examined, the amplitude adjusted Fourier transform (AAFT) and the iterated AAFT (IAFFT) and many nonlinear discriminating statistics are used for testing, i.e. the fit with the Volterra series of polynomials and the fit with local average mappings, the mutual information, the correlation dimension, the false nearest neighbors, the largest Lyapunov exponent and simple nonlinear averages (the three point autocorrelation and the time reversal asymmetry). The results on simulated data and real data (EEG and exchange rates) suggest that the test depends on the method and its parameters, the algorithm generating the surrogate data and the observational data of the examined process.

scholarly journals Chaos and magnetospheric dynamics

1994 ◽  
Vol 1 (2/3) ◽  
pp. 124-135 ◽  
Author(s):  
G. P. Pavlos ◽  
D. Diamandidis ◽  
A. Adamopoulos ◽  
A. G. Rigas ◽  
I. A. Daglis ◽  
...  
Keyword(s):  
Time Series ◽  
Chaotic Dynamics ◽  
Electric Circuit ◽  
Dynamical Chaos ◽  
Ae Index ◽  
Reconstructed Phase Space ◽  
Magnetospheric Dynamics ◽  
Low Dimensional ◽  
Value Decomposition ◽  
Index Time Series

Abstract. Our intention in this work is to show, by using two different methods, that magnetospheric dynamics reveal low dimensional chaos. In the first method we extend the chaotic analysis for the AE index time series by including singular value decomposition (SVD) analysis in combination with Theiler's test in order to discriminate dynamical chaos from self-affinity or "crinkliness". The estimated fractality of the AE index time series which is obtained belongs to a strange attractor structure with close returns in the reconstructed phase space. In the second method we extend the linear equivalent magnetospheric electric circuit to a nonlinear one, the arithmetic solution of which reveals low dimensional chaotic dynamics. Both methods strongly support the existence of low dimensional magnetospheric chaos.

Historical SAM index time series: linear and nonlinear analysis

2018 ◽  
Vol 38 ◽  
pp. e1091-e1106 ◽  
Author(s):  
Mariana G. Barrucand ◽  
Miguel E. Zitto ◽  
Rosa Piotrkowski ◽  
Pablo Canziani ◽  
Alan O'Neill
Keyword(s):  
Time Series ◽  
Nonlinear Analysis ◽  
Linear And Nonlinear ◽  
Index Time Series

scholarly journals Detecting nonlinearity in time series driven by non-Gaussian noise: the case of river flows

2004 ◽  
Vol 11 (4) ◽  
pp. 463-470 ◽  
Author(s):  
F. Laio ◽  
A. Porporato ◽  
L. Ridolfi ◽  
S. Tamea
Keyword(s):  
Time Series ◽  
Gaussian Noise ◽  
Driving Force ◽  
Surrogate Data ◽  
Rainfall Runoff ◽  
River Flows ◽  
Dynamical Characteristics ◽  
Univariate Time Series ◽  
Poissonian Noise ◽  
Non Gaussian

Abstract. Several methods exist for the detection of nonlinearity in univariate time series. In the present work we consider riverflow time series to infer the dynamical characteristics of the rainfall-runoff transformation. It is shown that the non-Gaussian nature of the driving force (rainfall) can distort the results of such methods, in particular when surrogate data techniques are used. Deterministic versus stochastic (DVS) plots, conditionally applied to the decay phases of the time series, are instead proved to be a suitable tool to detect nonlinearity in processes driven by non-Gaussian (Poissonian) noise. An application to daily discharges from three Italian rivers provides important clues to the presence of nonlinearity in the rainfall-runoff transformation.

scholarly journals Comparison of chaotic aspects of magnetosphere under various physical conditions using AE index time series

2008 ◽  
Vol 26 (4) ◽  
pp. 941-953 ◽  
Author(s):  
K. Unnikrishnan
Keyword(s):  
Time Series ◽  
Solar Activity ◽  
Lyapunov Exponent ◽  
Degrees Of Freedom ◽  
High Solar Activity ◽  
Nonlinear Prediction ◽  
Physical Conditions ◽  
Ae Index ◽  
Significant Difference ◽  
Index Time Series

Abstract. The deterministic chaotic behaviour of magnetosphere was analyzed, using AE index time series. The significant chaotic quantifiers like, Lyapunov exponent, spatio-temporal entropy and nonlinear prediction error for AE index time series under various physical conditions were estimated and compared. During high solar activity (1991), the values of Lyapunov exponent for AE index time series representing quiet conditions (yearly mean = 0.5±0.1 min−1) have no significant difference from those values for corresponding storm conditions (yearly mean = 0.5±0.17 min−1). This implies that, for the cases considered here, geomagnetic storms may not be an additional source to increase or decrease the deterministic chaotic aspects of magnetosphere, especially during high solar activity. During solar minimum period (1994), the seasonal mean value of Lyapunov exponent for AE index time series belong to quiet periods in winter (0.7±0.11 min−1) is higher compared to corresponding value of storm periods in winter (0.36±0.09 min−1). This may be due to the fact that, stochastic part, which is Dst dependent could be more prominent during storms, thereby increasing fluctuations/stochasticity and reducing determinism in AE index time series during storms. It is observed that, during low solar active period (1994), the seasonal mean value of entropy for time series representing storm periods of equinox is greater than that for quiet periods. However, significant difference is not observed between storm and quiet time values of entropy during high solar activity (1991), which is also true for nonlinear prediction error for both low and high solar activities. In the case of both high and low solar activities, the higher standard deviations of yearly mean Lyapunov exponent values for AE index time series for storm periods compared to those for quiet periods might be due to the strong interplay between stochasticity and determinism during storms. It is inferred that, the external driving forces, mainly due to solar wind, make the solar-magnetosphere-ionosphere coupling more complex, which generates many active degrees of freedom with various levels of coupling among them, under various physical conditions. Hence, the superposition of a large number of active degrees of freedom can modify the stability/instability conditions of magnetosphere.

GLOBAL LOW DIMENSIONAL SEISMIC CHAOS IN THE HELLENIC REGION

2010 ◽  
Vol 20 (07) ◽  
pp. 2071-2095 ◽  
Author(s):  
A. C. ILIOPOULOS ◽  
G. P. PAVLOS
Keyword(s):  
Time Series ◽  
Theoretical Models ◽  
Surrogate Data ◽  
Threshold Dynamics ◽  
Seismic Process ◽  
Dynamical Characteristics ◽  
Low Dimensionality ◽  
Low Dimensional ◽  
Intermittent Chaos ◽  
Of Greece

In this study, we present results concerning seismogenesis in the Hellenic region (land and sea of Greece), applying nonlinear analysis to an earthquake time series. The model of the dripping faucet is used as a physical interpretation of the seismic process and the construction of inter-event seismic time series. Geometrical and dynamical characteristics estimated in the reconstructed state space support the low dimensional, chaotic character of the global seismic process in the Hellenic region. The method of stochastic surrogate data was employed to the exclusion of "pseudo chaos" caused by the nonlinear distortion of a purely stochastic process. These results are in agreement with general theoretical models concerning distributed driven threshold dynamics applied to the case of seismic processes. Moreover, the observed global character of low dimensionality and chaoticity over such a complex system of faults supports the hypothesis that seismogenesis is characterized by spatiotemporal intermittent chaos throughout the Hellenic region.

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