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

Abstract

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.

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

“…Coraddu et al (2005) showed the Tsallis entropy generalization for Lyapunov exponents. Further details can be found in Ogunsua et al (2014); they were able to investigate the similarities in their response to the complex dynamics of the ionosphere, and this informs the further use of the two quantities as indices to study the day-to-day variation of ionospheric behaviour in this work.…”

“…A similar approach to the computation of the correlation dimension was used by Unnikrishnan and Ravindran (2010) to determine the correlation dimension of detrended TEC data for some stations in India, which lies within the equatorial region, like Nigeria. Ogunsua et al (2014) also used similar methods for some detrended TEC from Nigerian stations.…”

“…The equatorial ionization anomaly and other natural processes which include various ionization processes and recombination, influx of solar wind, photoionization processes and so many other factors that occur due to variations in solar activities, have a great influence on the systems of the ionosphere, due to their effects on internal dynamics of the ionosphere. This portrays the ionosphere as a typical natural system with continuous interaction with its external environment, which led to the study of the influence of the Sun on the ionosphere (Ogunsua et al, 2014). The ionosphere possesses a significant level of non-linear variations that requires more investigation, which can be studied and characterized using a non-linear approach like the chaoticity and dynamical complexity for the study of its dynamics.…”

“…Most investigations have been based on quiet and storm conditions only for all studies carried out, and none of the previous works involved the use of quiet and disturbed day classification of geophysical conditions until recently by Ogunsua et al (2014), where we considered the comparative use of Lyapunov exponents and Tsallis entropy as proxies for the internal dynamics of the ionosphere. This is the main reason for the consideration of day-to-day variation of these parameters in this work.…”

“…Further studies on the chaotic behaviour and non-linear dynamics of the ionosphere over the low-latitude African region is however required for the improvement of our understanding and characterization of its dynamical behaviour. Recently, Ogunsua et al (2014) studied comparatively the chaoticity of the equatorial ionosphere over Nigeria using TEC data, considering five quietest day classifications and five most disturbed day classifications. They were able to show the presence of chaos as indicated the positive Lyapunov exponents and also were able to show that Tsallis entropy can be used as a viable measure of dynamical complexity in the ionosphere, with portions showing lower values of Tsallis entropy indicating lower dynamical complexity, with a good relationship with Lyapunov exponents.…”