Abstract In this study we use Tsallis non-extensive statistics for a new understanding the magnetospheric dynamics and the magnetospheric self-organization during quiet and intensive superstorm periods. The q s e n s , q s t a t , and q r e l indices set known as the Tsallis q -triplet was estimated during both quiet and strongly active periods, as well as the correlation dimensions and Lyapunov exponents spectrum for magnetospheric bulk plasma flows data. The results obtained by our analysis clearly indicate the magnetospheric phase transition process from a high-dimensional quiet SOC state to a low-dimensional global chaotic state when superstorm events are developed. During such a phase transition process the non-extensive statistical character of the magnetospheric plasma is strengthened as the values of the q -triplet indices changes obtaining higher values than their values during the quiet periods.