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 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)

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.

scholarly journals Nonlinear time series analysis of geomagnetic pulsations

1994 ◽  
Vol 1 (2/3) ◽  
pp. 145-155 ◽  
Author(s):  
Z. Vörös ◽  
J. Verö ◽  
J. Kristek
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Correlation Dimension ◽  
Deterministic Chaos ◽  
Nonlinear Time Series ◽  
Surrogate Data ◽  
Nonlinear Time Series Analysis ◽  
Geomagnetic Pulsations ◽  
Series Analysis ◽  
Low Dimensional

Abstract. A detailed nonlinear time series analysis has been made of two daytime geomagnetic pulsation events being recorded at L'Aquila (Italy, L ≈ 1.6) and Niemegk (Germany, L ≈ 2.3). Grassberger and Procaccia algorithm has been used to investigate the dimensionality of physical processes. Surrogate data test and self affinity (fractal) test have been used to exclude coloured noise with power law spectra. Largest Lyapunow exponents have been estimated using the methods of Wolf et al. The problems of embedding, stability of estimations, spurious correlations and nonlinear noise reduction have also been discussed. The main conclusions of this work, which include some new results on the geomagnetic pulsations, are (1) that the April 26, 1991 event, represented by two observatory time series LAQ1 and NGK1 is probably due to incoherent waves; no finite correlation dimension was found in this case, and (2) that the June 18, 1991 event represented by observatory time series LAQ2 and NGK2, is due to low dimensional nonlinear dynamics, which include deterministic chaos with correlation dimension D2(NGK2) = 2.25 ± 0.05 and D2(NDK2) = 2.02 ± 0.03, and with positive Lyapunov exponents λmax (LAQ2) = 0.055 ± 0.003 bits/s and λmax (NGK2) = 0.052 ± 0.003 bits/s; the predictability time in both cases is ≈ 13 s.

Validity of Dimensional Complexity Measures of EEG Signals

1997 ◽  
Vol 07 (01) ◽  
pp. 173-186 ◽  
Author(s):  
N. Pradhan ◽  
P. K. Sadasivan
Keyword(s):  
Time Series ◽  
Gaussian Noise ◽  
Chaotic Systems ◽  
Surrogate Data ◽  
Data Sets ◽  
Eeg Signals ◽  
Complexity Measures ◽  
Dimensional Complexity ◽  
Colored Gaussian Noise ◽  
Low Dimensional

The measure of dimensional complexity has the potential for feature extraction, modeling and prediction of EEG signals. However, the nonlinear dynamics of neuronal processes is under criticism that EEG signals may have a simpler stochastic description and chaotic dynamical measures of EEG may be spurious or unnecessary. Surrogate-data testing has been propounded to detect nonlinearity and chaos in experimental time series and to differentiate it from linear stochastic processes or colored noises. The surrogate data tests of brain signals (EEG) have produced equivocal results. Therefore, we examine the surrogate testing procedure using numerical data of classical chaotic systems, mixed sine waves, white Gaussian and colored Gaussian noises and typical EEGs. White Gaussian noise and classical chaotic time series are easily discerned by the surrogate-data test. However, a colored Gaussian noise data of low correlation dimensions (D2) or mixed sine waves containing less number of sinusoids show behaviors similar to the low dimensional deterministic chaotic systems. There are significant differences in D2 values between the original and surrogate data sets. The colored Gaussian noise appears linear and stochastic only when there is an increased randomness in its pattern and the signal is high dimensional. Our results clearly indicate that the "surrogate testing" alone may not be a sufficient test for distinguishing colored noises from low dimensional chaos. The EEG time series produce finite correlation dimensions. The surrogate testing of 8 independent realizations of different forms of EEG activities produce significantly different D2 values than the original data sets. Apparently many natural phenomena follow deterministic chaos and as the dimensional complexity of the system increases (D2 > 5) it may approximate a stochastic process. Thus EEG appears unlikely to have originated from a linear system driven by white noise.

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.

A NEW COLOR IMAGE ENCRYPTION BASED ON HIGH-DIMENSIONAL CHAOTIC SYSTEMS

2014 ◽  
Vol 28 (07) ◽  
pp. 1450024 ◽  
Author(s):  
PI LI ◽  
XING-YUAN WANG ◽  
HONG-JING FU ◽  
DA-HAI XU ◽  
XIU-KUN WANG
Keyword(s):  
Time Series ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Color Image ◽  
High Dimensional ◽  
Encryption Scheme ◽  
Color Image Encryption ◽  
System Variable ◽  
Key Space ◽  
Low Dimensional

The high-dimensional chaotic systems (HDCS) have a lot of advantages as more multifarious mechanism, greater the key space, more ruleless for the time series of the system variable than with the low-dimensional chaotic systems (LDCS), etc. Thus, a novel encryption scheme using Lorenz system is suggested. Moreover, we use substitution–diffusion architecture to advance the security of the scheme. The theoretical and experimental results show that the suggested cryptosystem has higher security.

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 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 Realization of a Novel Chaotic System Using Coupling Dual Chaotic System

2021 ◽  
Author(s):  
Salam K. Mousa ◽  
Raied K. Jamal
Keyword(s):  
Time Series ◽  
Chaotic System ◽  
Optical Communications ◽  
Chaotic Dynamics ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Fourier Transforms ◽  
Optical Coupling ◽  
Before And After ◽  
The Lorenz System

Abstract This paper establishes coupling between two various chaotic systems for Lorenz and Rössler circuits. The x-dynamics of Lorenz circuit was coupled numerically with the x dynamics of Rössler circuit. As a result of the optical coupling between these two chaotic systems, it has been observed an exceptional variation in the time series and attractors, which exhibits a novel behavior, leading to a promises method for controlling the chaotic systems. However, performing fast Fourier transforms (FFT) of chaotic dynamics before and after coupling showed an increase in the bandwidth of the Rössler system after its coupling with the Lorenz system, which, in turn increases the possibility of using this system for secure and confidential optical communications.

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