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

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 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

Dynamical complexity detection in pre-seismic emissions using nonadditive Tsallis entropy

2008 ◽  
Vol 387 (5-6) ◽  
pp. 1161-1172 ◽  
Author(s):  
M. Kalimeri ◽  
C. Papadimitriou ◽  
G. Balasis ◽  
K. Eftaxias
Keyword(s):  
Tsallis Entropy ◽  
Dynamical Complexity

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

2014 ◽  
Vol 1 (2) ◽  
pp. 1855-1903
Author(s):  
A. B. Rabiu ◽  
B. O. Ogunsua ◽  
I. A. Fuwape ◽  
J. A. Laoye
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Correlation Dimension ◽  
Tsallis Entropy ◽  
Internal Dynamics ◽  
Variation Pattern ◽  
Dynamical Complexity ◽  
Equatorial Ionization Anomaly ◽  
Definite Pattern ◽  
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 5 GPS receiver stations in Nigeria which lies within the Equatorial Ionization Anomaly region. The nonlinear aspect of the TEC time series were 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 which are Lyapunov exponents LE, correlation dimension, and Tsallis entropy for the study of dynamical complexity. The results show positive Lyapunov exponents for all days which indicate chaoticity of the ionosphere with no definite pattern for both quiet and disturbed days. However values of LE were lower for the storm period compared to its nearest relative quiet periods for all the stations. 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 exponent for the entire year show a wavelike semiannual variation pattern with lower values around March, April, September and October, a change in pattern which demonstrates the self-organized critical phenomenon of the system. 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 similar variation pattern with that of Lyapunov exponent with a lot of agreement in their comparison, with all computed values of Lyapunov exponent correlating with values of Tsallis entropy within the range of 0.79 to 0.82. These results show that Lyapunov quantifiers can be 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 at 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 Lyapunov exponent and Tsallis entropy during storms. The results also show a strong interplay between determinism and stochasticity, as the ionosphere shows its response to changes in solar activities and in its internal dynamics. The dynamical behavior of the ionosphere throughout the year as described by these quantifiers, were discussed in this work.

Detection of Objects in Underwater Images Based on the Two-Dimensional Tsallis Entropy

ROBOT ◽  
2010 ◽  
Vol 32 (3) ◽  
pp. 289-297
Author(s):  
Xudong TANG ◽  
Yongjie PANG ◽  
Tiedong ZHANG ◽  
Ye LI
Keyword(s):  
Tsallis Entropy ◽  
Two Dimensional ◽  
Detection Of Objects

scholarly journals Assessing Machine Learning versus a Mathematical Model to Estimate the Transverse Shear Stress Distribution in a Rectangular Channel

Mathematics ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 596
Author(s):  
Babak Lashkar-Ara ◽  
Niloofar Kalantari ◽  
Zohreh Sheikh Khozani ◽  
Amir Mosavi
Keyword(s):  
Shear Stress ◽  
Stress Distribution ◽  
Fuzzy Inference ◽  
Rectangular Channel ◽  
Tsallis Entropy ◽  
Shear Stress Distribution ◽  
Data Series ◽  
Shear Stresses ◽  
Inference System ◽  
Aspect Ratios

One of the most important subjects of hydraulic engineering is the reliable estimation of the transverse distribution in the rectangular channel of bed and wall shear stresses. This study makes use of the Tsallis entropy, genetic programming (GP) and adaptive neuro-fuzzy inference system (ANFIS) methods to assess the shear stress distribution (SSD) in the rectangular channel. To evaluate the results of the Tsallis entropy, GP and ANFIS models, laboratory observations were used in which shear stress was measured using an optimized Preston tube. This is then used to measure the SSD in various aspect ratios in the rectangular channel. To investigate the shear stress percentage, 10 data series with a total of 112 different data for were used. The results of the sensitivity analysis show that the most influential parameter for the SSD in smooth rectangular channel is the dimensionless parameter B/H, Where the transverse coordinate is B, and the flow depth is H. With the parameters (b/B), (B/H) for the bed and (z/H), (B/H) for the wall as inputs, the modeling of the GP was better than the other one. Based on the analysis, it can be concluded that the use of GP and ANFIS algorithms is more effective in estimating shear stress in smooth rectangular channels than the Tsallis entropy-based equations.

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