Chaotic behavior of ionospheric scintillation: Modeling and observations

Wernik, A. W.; Yeh, K. C.

doi:10.1029/93rs01828

Cited by 20 publications

(18 citation statements)

References 19 publications

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“…The presence of chaos is indicated by the positive values of the Lyapunov exponent found in all the computations for all the TEC values obtained for the selected days for all the measuring stations used in this work. This can be expected, as it agrees with results from previous works that show that there is a reasonable presence of chaos in the ionosphere, even in the midst of the influence of stochastic drivers like solar winds (Bhattacharyya, 1990;Wernik and Yeh, 1994;Kumar et al, 2004;Unnikrishnan et al, 2006a, b;Unnikrishnan, 2010).…”

Section: Discussionsupporting

confidence: 81%

“…Also, Wernik and Yeh (1994) further revealed the chaotic behavior of the ionospheric turbulence using scintillation data and numerical modeling of scintillation at high latitudes. They showed that the ionospheric turbulence attractor (if it exists) cannot be reconstructed from amplitude scintillation data, and their measured phase scintillation data adequately reproduce the assumed chaotic structure in the ionosphere.…”

Section: Introductionmentioning

confidence: 99%

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

Ogunsua

Laoye

Fuwape

et al. 2014

Nonlin. Processes Geophys.

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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.

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Section: Discussionsupporting

confidence: 81%

Section: Introductionmentioning

confidence: 99%

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

Ogunsua

Laoye

Fuwape

et al. 2014

Nonlin. Processes Geophys.

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“…Bhattacharyya (1990) had studied the chaotic behavior of ionospheric density fluctuations, using amplitude and phase scintillation data, and found the existence of lowdimensional chaos. Also, Wernik and Yeh (1994) have studied chaotic behavior of ionospheric turbulence using scintillation data and numerical modeling of scintillation at high latitude. Kumar et al (2004) reported the evidence of low dimensional chaos in a set of TEC data, obtained by Faraday rotation technique, measured at a high-latitude station, Goose Bay (47 • N, 286 • E), during the period, February to April 1976.…”

Section: Introductionmentioning

confidence: 99%

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

Unnikrishnan

2008

Ann. Geophys.

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Abstract. The deterministic chaotic behaviour of magnetosphere was analyzed, using AE index time series. The significant chaotic quantifiers like, Lyapunov exponent, spatiotemporal 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 D st 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.Correspondence to: K. Unnikrishnan (kaleekkal unni@yahoo.com) 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.

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“…The largest Lyapunov exponent (λ 1 ) can be used to determine the rate of divergence as indicated by Wolf et al (1985), where…”

Section: Lyapunov Exponentsmentioning

confidence: 99%

“…These previous efforts made by the aforementioned researchers has led to the development of the concept of investigating and revealing the chaoticity and the complex dynamics of the ionosphere, and as a result, studies on the chaoticity of the ionosphere have been conducted, by some investigators like Bhattacharyya (1990), who studied chaotic behaviour of ionospheric diversity fluctuation using amplitude and phase scintillation data, and found the existence of low-dimension chaos. Also, Wernik and Yeh (1994) further revealed the chaotic behaviour of the ionospheric turbulence using scintillation data and numerical modelling of scintillation at high latitude. They showed that the ionospheric turbulence attractor (if it exists) cannot be reconstructed from amplitude scintillation data, and their measured phase scintillation data adequately reproduce the assumed chaotic structure in the ionosphere.…”

mentioning

confidence: 99%

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

Rabiu

Ogunsua

Fuwape

et al. 2015

Nonlin. Processes Geophys.

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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.

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Chaotic behavior of ionospheric scintillation: Modeling and observations

Cited by 20 publications

References 19 publications

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

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

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

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

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