Universality of Tsallis Non-Extensive Statistics and Fractal Dynamics for Complex Systems

Abstract: Tsallis q-extension of statistics and fractal generalization of dynamics are two faces of the same physical reality, as well as the Kernel modern complexity theory. The fractal generalization dynamics is based at the multiscale - multifractal characters of complex dynamics in the physical space-time and the complex system's dynamical phase space. Tsallis q-triplet of non-extensive statistics can be used for the experiment test of q-statistic as well as of the fractal dynamics. In this study we present indicative experimental verifications of Tsallis theory in various complex systems such as solar plasmas, (planetic magnetospheres, cosmic stars and cosmic rays), atmospheric dynamics, seismogenesis and brain dynamics.