scholarly journals Quantifying Dynamical Complexity of Magnetic Storms and Solar Flares via Nonextensive Tsallis Entropy

Entropy ◽  
2011 ◽  
Vol 13 (10) ◽  
pp. 1865-1881 ◽  
Author(s):  
Georgios Balasis ◽  
Ioannis A. Daglis ◽  
Constantinos Papadimitriou ◽  
Anastasios Anastasiadis ◽  
Ingmar Sandberg ◽  
...  
Keyword(s):  
Solar Flares ◽  
Magnetic Storms ◽  
Tsallis Entropy ◽  
Dynamical Complexity

scholarly journals Similarities between extreme events in the solar-terrestrial system by means of nonextensivity

2011 ◽  
Vol 18 (5) ◽  
pp. 563-572 ◽  
Author(s):  
G. Balasis ◽  
C. Papadimitriou ◽  
I. A. Daglis ◽  
A. Anastasiadis ◽  
I. Sandberg ◽  
...  
Keyword(s):  
Extreme Events ◽  
Solar Flares ◽  
Particle Physics ◽  
Building Blocks ◽  
Magnetic Storms ◽  
Earthquake Dynamics ◽  
Magnitude Distribution ◽  
Terrestrial System ◽  
Universal Principles ◽  
Elementary Building

Abstract. The dynamics of complex systems are founded on universal principles that can be used to describe disparate problems ranging from particle physics to economies of societies. A corollary is that transferring ideas and results from investigators in hitherto disparate areas will cross-fertilize and lead to important new results. In this contribution, we investigate the existence of a universal behavior, if any, in solar flares, magnetic storms, earthquakes and pre-seismic electromagnetic (EM) emissions, extending the work recently published by Balasis et al. (2011a). A common characteristic in the dynamics of the above-mentioned phenomena is that their energy release is basically fragmentary, i.e. the associated events are being composed of elementary building blocks. By analogy with earthquakes, the magnitude of the magnetic storms, solar flares and pre-seismic EM emissions can be appropriately defined. Then the key question we can ask in the frame of complexity is whether the magnitude distribution of earthquakes, magnetic storms, solar flares and pre-fracture EM emissions obeys the same law. We show that these apparently different extreme events, which occur in the solar-terrestrial system, follow the same energy distribution function. The latter was originally derived for earthquake dynamics in the framework of nonextensive Tsallis statistics.

scholarly journals The transient variation in the complexes of the low-latitude ionosphere within the equatorial ionization anomaly region of Nigeria

2015 ◽  
Vol 22 (5) ◽  
pp. 527-543 ◽  
Author(s):  
A. B. Rabiu ◽  
B. O. Ogunsua ◽  
I. A. Fuwape ◽  
J. A. Laoye
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Lyapunov Exponents ◽  
Correlation Dimension ◽  
Tsallis Entropy ◽  
Variation Pattern ◽  
Dynamical Complexity ◽  
Equatorial Ionization Anomaly ◽  
Non Linear ◽  
Anomaly Region

Abstract. The quest to find an index for proper characterization and description of the dynamical response of the ionosphere to external influences and its various internal irregularities has led to the study of the day-to-day variations of the chaoticity and dynamical complexity of the ionosphere. This study was conducted using Global Positioning System (GPS) total electron content (TEC) time series, measured in the year 2011, from five GPS receiver stations in Nigeria, which lies within the equatorial ionization anomaly region. The non-linear aspects of the TEC time series were obtained by detrending the data. The detrended TEC time series were subjected to various analyses to obtain the phase space reconstruction and to compute the chaotic quantifiers, which are Lyapunov exponents LE, correlation dimension, and Tsallis entropy, for the study of dynamical complexity. Considering all the days of the year, the daily/transient variations show no definite pattern for each month, but day-to-day values of Lyapunov exponents for the entire year show a wavelike semiannual variation pattern with lower values around March, April, September and October. This can be seen from the correlation dimension with values between 2.7 and 3.2, with lower values occurring mostly during storm periods, demonstrating a phase transition from higher dimension during the quiet periods to lower dimension during storms for most of the stations. The values of Tsallis entropy show a similar variation pattern to that of the Lyapunov exponent, with both quantifiers correlating within the range of 0.79 to 0.82. These results show that both quantifiers can be further used together as indices in the study of the variations of the dynamical complexity of the ionosphere. The presence of chaos and high variations in the dynamical complexity, even in quiet periods in the ionosphere, may be due to the internal dynamics and inherent irregularities of the ionosphere which exhibit non-linear properties. However, this inherent dynamics may be complicated by external factors like geomagnetic storms. This may be the main reason for the drop in the values of the Lyapunov exponent and Tsallis entropy during storms. The dynamical behaviour of the ionosphere throughout the year, as described by these quantifiers, was discussed in this work.

scholarly journals The comparative study of chaoticity and dynamical complexity of the low-latitude ionosphere, over Nigeria, during quiet and disturbed days

2014 ◽  
Vol 21 (1) ◽  
pp. 127-142 ◽  
Author(s):  
B. O. Ogunsua ◽  
J. A. Laoye ◽  
I. A. Fuwape ◽  
A. B. Rabiu
Keyword(s):  
Time Series ◽  
Lyapunov Exponents ◽  
Correlation Dimension ◽  
Chaotic Behavior ◽  
Surrogate Data ◽  
Tsallis Entropy ◽  
Electron Content ◽  
Total Electron ◽  
Dynamical Complexity ◽  
Definite Pattern

Abstract. The deterministic chaotic behavior and dynamical complexity of the space plasma dynamical system over Nigeria are analyzed in this study and characterized. The study was carried out using GPS (Global Positioning System) TEC (Total Electron Content) time series, measured in the year 2011 at three GPS receiver stations within Nigeria, which lies within the equatorial ionization anomaly region. The TEC time series for the five quietest and five most disturbed days of each month of the year were selected for the study. The nonlinear aspect of the TEC time series was obtained by detrending the data. The detrended TEC time series were subjected to various analyses for phase space reconstruction and to obtain the values of chaotic quantifiers like Lyapunov exponents, correlation dimension and also Tsallis entropy for the measurement of dynamical complexity. The observations made show positive Lyapunov exponents (LE) for both quiet and disturbed days, which indicates chaoticity, and for different days the chaoticity of the ionosphere exhibits no definite pattern for either quiet or disturbed days. However, values of LE were lower for the storm period compared with its nearest relative quiet periods for all the stations. The monthly averages of LE and entropy also show no definite pattern for the month of the year. The values of the correlation dimension computed range from 2.8 to 3.5, with the lowest values recorded at the storm period of October 2011. The surrogate data test shows a significance of difference greater than 2 for all the quantifiers. The entropy values remain relatively close, with slight changes in these values during storm periods. The values of Tsallis entropy show similar variation patterns to those of Lyapunov exponents, with a lot of agreement in their comparison, with all computed values of Lyapunov exponents correlating with values of Tsallis entropy within the range of 0.79 to 0.81. These results show that both quantifiers can be used together as indices in the study of the variation of the dynamical complexity of the ionosphere. The results also show a strong play between determinism and stochasticity. The behavior of the ionosphere during these storm and quiet periods for the seasons of the year are discussed based on the results obtained from the chaotic quantifiers.

scholarly journals Dynamical complexity inDsttime series using non-extensive Tsallis entropy

2008 ◽  
Vol 35 (14) ◽  
Author(s):  
Georgios Balasis ◽  
Ioannis A. Daglis ◽  
Constantinos Papadimitriou ◽  
Maria Kalimeri ◽  
Anastasios Anastasiadis ◽  
...  
Keyword(s):  
Tsallis Entropy ◽  
Dynamical Complexity

Recurrence-Based Quantification of Multi-Scale Dynamical Complexity in the Earth’s Magnetosphere

2021 ◽  
Author(s):  
Reik Donner
Keyword(s):  
Network Analysis ◽  
Space Weather ◽  
Geomagnetic Field ◽  
Magnetic Storms ◽  
Temporal Organization ◽  
Geophysical Research ◽  
Multi Scale ◽  
Dynamical Complexity ◽  
The Earth ◽  
Relevant Effect

<p>The Earth’s magnetosphere is characterized by a considerable degree of dynamical complexity resulting from the interaction of different multiscale processes, which can be both directly driven/triggered by changes of the interplanetary medium condition, and due to internal processes of the magnetosphere. This complexity can be characterized by following both “classical” and “new” dynamical system tools. Recent work has demonstrated that recurrence plot based techniques may play a pivotal role in such an assessment.</p><p>In this presentation, I will summarize some recent results on applications of recurrence quantification analysis and recurrence network analysis to different geomagnetic indices (Dst, SYM-H, ASY-H, AE) reflecting the variability of the Earth’s electromagnetic environment at different time-scales and magnetic latitudes. In addition, the same techniques are applied to some essential properties of the solar wind which are likely to have a relevant effect on geomagnetic field fluctuations and might serve as triggers of instability leading to geospace magnetic storms and/or magnetospheric substorms. The obtained findings underline that dynamical fluctuations of the geomagnetic field during periods of magnetospheric quiescence and storminess indeed exhibit distinctively different levels of dynamical complexity. Moreover, they provide additional evidence for a time-scale separation in magnetospheric dynamics that is further characterized by employing some multi-scale version of recurrence analysis utilizing a continuous wavelet transform of the signals of interest. The corresponding results can be of potential relevance for the development of improved approaches for space weather modelling and forecasting.</p><p> </p><p>References:</p><p>R.V. Donner, V. Stolbova, G. Balasis, J.F. Donges, M. Georgiou, S. Potirakis, J. Kurths: Temporal organization of magnetospheric fluctuations unveiled by recurrence patterns in the Dst index. Chaos, 28, 085716 (2018)</p><p>R.V. Donner, G. Balasis, V. Stolbova, M. Georgiou, M. Wiedermann, J. Kurths: Recurrence based quantification of dynamical complexity in the Earth's magnetosphere at geospace storm timescales. Journal of Geophysical Research - Space Physics, 124, 90-108 (2019)</p><p>J. Lekscha, R.V. Donner: Areawise significance tests for windowed recurrence network analysis. Proceedings of the Royal Society A, 475 (2228), 20190161 (2019)</p><p>T. Alberti, J. Lekscha, G. Consolini, P. De Michelis, R.V. Donner: Disentangling nonlinear geomagnetic variability during magnetic storms and quiescence by timescale dependent recurrence properties. Journal of Space Weather and Space Climate, 10, 25 (2020)</p>

scholarly journals Correlation-based characterisation of time-varying dynamical complexity in the Earth's magnetosphere

2013 ◽  
Vol 20 (6) ◽  
pp. 965-975 ◽  
Author(s):  
R. V. Donner ◽  
G. Balasis
Keyword(s):  
Dynamical Behaviour ◽  
Magnetic Storms ◽  
Time Varying ◽  
Temporal Complexity ◽  
Multi Scale ◽  
Dynamical Complexity ◽  
Geophysical Time Series ◽  
Recorded Data ◽  
Different Characteristics ◽  
High Degree

Abstract. The dynamical behaviour of the magnetosphere is known to be a sensitive indicator for the response of the system to solar wind coupling. Since the solar activity commonly displays very interesting non-stationary and multi-scale dynamics, the magnetospheric response also exhibits a high degree of dynamical complexity associated with fundamentally different characteristics during periods of quiescence and magnetic storms. The resulting temporal complexity profile has been explored using several approaches from applied statistics, dynamical systems theory and statistical mechanics. Here, we propose an alternative way of looking at time-varying dynamical complexity of nonlinear geophysical time series utilising subtle but significant changes in the linear autocorrelation structure of the recorded data. Our approach is demonstrated to sensitively trace the dynamic signatures associated with intense magnetic storms, and to display reasonable skills in distinguishing between quiescence and storm periods. The potentials and methodological limitations of this new viewpoint are discussed in some detail.

scholarly journals Cosmic-Ray Effects from Solar Flares and Magnetic Storms

1948 ◽  
Vol 20 (1) ◽  
pp. 350-352 ◽  
Author(s):  
H. V. Neher ◽  
W. C. Roesch
Keyword(s):  
Solar Flares ◽  
Cosmic Ray ◽  
Magnetic Storms ◽  
Ray Effects ◽  
Cosmic Ray Effects

Dynamical Complexity of Magnetic Storms at Swarm Altitudes Using Entropy Measures

2020 ◽  
Author(s):  
Constantinos Papadimitriou ◽  
Georgios Balasis ◽  
Adamantia-Zoe Boutsi ◽  
Omiros GIannakis ◽  
Anastasios Anastasiadis ◽  
...  
Keyword(s):  
Information Theory ◽  
Time Series ◽  
Magnetic Storms ◽  
Topside Ionosphere ◽  
Dynamical Response ◽  
Electromagnetic Environment ◽  
Dynamical Complexity ◽  
Coupling System ◽  
Entropy Measures ◽  
Earth’S System

<p>Recently, many novel concepts originated in dynamical systems or information theory have been developed, partly motivated by specific research questions linked to geosciences, and found a variety of different applications. This continuously extending toolbox of nonlinear time series analysis highlights the importance of the dynamical complexity to understand the behavior of the complex solar wind – magnetosphere – ionosphere - thermosphere coupling system and its components. Here, we propose to apply such new approaches, mainly a series of entropy methods to the time series of the Earth's magnetic field measured by the Swarm constellation. Swarm is an ESA mission launched on November 22, 2013, comprising three satellites at low Earth polar orbits. The mission delivers data that provide new insight into the Earth's system by improving our understanding of the Earth's interior as well as the near-Earth electromagnetic environment. We show successful applications of methods originated in information theory to quantitatively studying complexity in the dynamical response of the topside ionosphere, at Swarm altitudes, focusing on the most intense magnetic storms of the present solar cycle.</p>

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