Linear scaling and periodicity on the measures of global and local scale complexities of total electron content dynamics

Abstract

[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.