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.

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 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 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)

scholarly journals Wavelet filtering of chaotic data

2000 ◽  
Vol 7 (1/2) ◽  
pp. 111-116 ◽  
Author(s):  
M. Grzesiak
Keyword(s):  
Time Series ◽  
Dynamical Systems ◽  
Finite Impulse Response ◽  
Gaussian White Noise ◽  
Noisy Data ◽  
Singular Value ◽  
Filter Methods ◽  
Satisfactory Method ◽  
Low Dimensional ◽  
Value Decomposition

Abstract. Satisfactory method of removing noise from experimental chaotic data is still an open problem. Normally it is necessary to assume certain properties of the noise and dynamics, which one wants to extract, from time series. The wavelet based method of denoising of time series originating from low-dimensional dynamical systems and polluted by the Gaussian white noise is considered. Its efficiency is investigated by comparing the correlation dimension of clean and noisy data generated for some well-known dynamical systems. The wavelet method is contrasted with the singular value decomposition (SVD) and finite impulse response (FIR) filter methods.

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 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.

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

2003 ◽  
Vol 21 (9) ◽  
pp. 1975-1993 ◽  
Author(s):  
G. P. Pavlos ◽  
M. A. Athanasiu ◽  
A. G. Rigas ◽  
D. V. Sarafopoulos ◽  
E. T. Sarris
Keyword(s):  
Time Series ◽  
Nonlinear Distortion ◽  
Lorenz System ◽  
Nonlinear Phenomena ◽  
Coloured Noise ◽  
Radio Science ◽  
Geometrical Characteristics ◽  
Noise Perturbation ◽  
Reconstructed Phase Space ◽  
Low Dimensional

Abstract. In the first part of the paper we study the geometrical characteristics of the magnetospheric ions’ time series in the reconstructed phase space by using the SVD extended chaotic analysis, and we test the strong null hypothesis supposing that the ions’ time series is caused by a linear stochastic process perturbed by a static nonlinear distortion. The SVD reconstructed spectrum of the ions’ signal reveals a strong component of high dimensional, external coloured noise, as well as an internal low dimensional nonlinear deterministic component. Also, the stochastic Lorenz system produced by coloured noise perturbation of the deterministic Lorenz system was used as an archetype model in comparison with the dynamics of the magnetrospheric ions.Key words. Magnetospheric physics (energetic particles) – Radio science (nonlinear phenomena)

Randomness in Geomagnetic Storms

Fractals ◽  
1997 ◽  
Vol 05 (01) ◽  
pp. 169-173
Author(s):  
M. A. Foti ◽  
C. M. Arizmendi
Keyword(s):  
Neural Networks ◽  
Time Series ◽  
Gaussian Noise ◽  
Chaotic Dynamics ◽  
Degrees Of Freedom ◽  
Geomagnetic Storms ◽  
Basic Question ◽  
Geomagnetic Index ◽  
Deterministic Systems ◽  
Index Time Series

Although geomagnetic forecasting is extremely important, geomagnetic predictions usually rely on forecasters' experience in distinguishing events expected to be geoeffective. Initial investigations with powerful forecasting techniques such as neural networks have recently been applied to geomagnetic prediction, but these are based on the assumption that the phenomenon to be forecasted has only several degrees of freedom. Thus a basic question related to geomagnetic forecasting is whether the randomness associated with geomagnetic evolution is produced by linear Gaussian noise or by nonlinear chaotic dynamics with only a few degrees of freedom. In order to try to answer this important question, we took a geomagnetic index time series and applied a recently developed technique which distinguishes nonlinear deterministic systems from linear ones.

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