CHAOTICITY AND DYNAMICAL COMPLEXITY OF THE IONOSPHERE OVER NIGERIA WITHIN THE EQUATORIAL IONIZATION ANOMALY REGION

Abstract

A proper description of the dynamical response of the ionosphere to external influences and its various internal irregularities requires an index for the characterization of this behaviour. Therefore this work has been focused on determining the dynamical complexity of the equatorial ionosphere in the low latitude region of Nigeria during quiet, disturbed and storm periods; the seasonal variability of the chaotic behaviours in the ionosphere; and evaluating the use of chaotic and dynamical measures as indices for ionospheric studies. This study was conducted using Total Electron Content (TEC) time series, measured in the year 2011, from 5 Global Positioning System (GPS) receiver stations in Nigeria which lies within the Equatorial Ionization Anomaly region, namely: Birnin Kebbi (geographic coordinates 12°32′𝑁,4°12′𝐸; dip latitude 0.62°𝑁), Torro (geographic coordinates 10° 03′𝑁,9°04′𝐸; dip latitude −0.82°𝑁), Enugu (geographic coordinates 6°26′𝑁,7°30′𝐸; dip latitude −3.21°𝑁), Lagos (geographic coordinates 6°27′𝑁,3°23′𝐸; dip latitude −3.07°𝑁) and Yola (geographic coordinates 9° 12′𝑁,12°30°𝐸; dip latitude −1.39°𝑁). 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 the 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 3.5 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 activity and in its internal dynamics. The dynamical behavior of the ionosphere throughout the year as described by these quantifiers, were discussed in this work. The study concluded that the variations in the ionospheric chaoticity is to the modification of the systems internal dynamics due to variations in energy input at different geophysical conditions and that both Lyapunov exponents and Tsallis entropy can be used interchangeably for the for the study of ionospheric processes and dynamics.