[1] In this paper, we compare the local and global dynamics of total electron content (TEC) by analyzing Lyapunov exponents and correlation dimensions. The internal structure of the underlying system is studied using TEC data from the solar minimum years [2007][2008]. The mutual information, false nearest neighbors, and space-time separation of both local and global snapshots are estimated and analyzed. It indicates that although the internal dynamics changes with season, the pattern of variation over the seasons remains identical for both the years, suggesting that the characteristics of these changes might be predictable. We report the evidence of a linear scaling with slope 0.00187 and a periodicity with period of 1 year on measures of global and local scale complexities of TEC dynamics. This behavior appears to be a universal phenomenon unaffected by change of cycles and amount of information influencing the complexity, since they are almost constant over the 2 years. The global Lyapunov exponent increases linearly over a year, whereas the local Lyapunov exponent increases up to the middle of the year, attains greatest local complexity, and then decreases. This suggests that local prediction is more reliable than the global one. The estimated invariants characterize the complex dynamics as it evolve from local time to global time and also provide information to the system's heterogeneity. The features such as presence of multiple attractors, linear scaling, and nearly regular seasonal periodicity may have practical consequences and could yield insights into the internal dynamics of TEC and the modeling of its variations.Citation: Kumar, C. V. A., and S. Eapen (2013), Linear scaling and periodicity on the measures of global and local scale complexities of total electron content dynamics,

We analyze the underlying dynamics at three different latitudes of ionosphere through total electron content‐series for 4 months. The global dynamics reconstructed from the data is shown to be deterministic with low dimensional chaotic attractors at all the locations, and the dynamics is seen to be less complex at the midlatitude station with smaller dimension of correlation (CD) and maximum Lyapunov exponent (MLE). The influence of geomagnetic storms on the ionospheric dynamics is studied, by analyzing the local dynamics during disturbed and quiet periods, reconstructed from segments of total electron content‐series of shorter duration. With positive MLEs and smaller CDs, the local dynamics is seen to be deterministic and chaotic at the low latitude, midlatitude, and high latitude during both the disturbed and quiet days. However, it is interesting to observe that the dynamics is less chaotic and complex during the disturbed days of the entire period of observation compared to the adjacent quiet days at the three locations. This is further evidenced by sample predictions made using nonlinear tools, yielding better predictions during storms. The smaller CD value during disturbed periods indicates that the geomagnetic activities tend to make a few of the variables dominant enough to control the essential dynamics of the system. Further, the MLEs of the disturbed days are found to increase nearly in a linear fashion from beginning to end of the observation period at all the locations considered. This is an indication of the strong influence of geomagnetic activities on the ionosphere and might have caused the restructuring of the ionospheric dynamics.