Tsallis non-extensive statistics, intermittent turbulence, SOC and chaos in the solar plasma. Part one: Sunspot dynamics

Abstract

In this study, the nonlinear analysis of the sunspot index is embedded in the non-extensive statistical theory of Tsallis. The triplet of Tsallis, as well as the correlation dimension and the Lyapunov exponent spectrum were estimated for the SVD components of the sunspot index timeseries. Also the multifractal scaling exponent spectrum, the generalized Renyi dimension spectrum and the spectrum of the structure function exponents were estimated experimentally and theoretically by using the entropy principle included in Tsallis non extensive statistical theory, following Arimitsu and Arimitsu. Our analysis showed clearly the following: a) a phase transition process in the solar dynamics from high dimensional non Gaussian SOC state to a low dimensional non Gaussian chaotic state, b) strong intermittent solar turbulence and anomalous (multifractal) diffusion solar process, which is strengthened as the solar dynamics makes phase transition to low dimensional chaos in accordance to Ruzmaikin, Zeleny and Milovanov studies c) faithful agreement of Tsallis non equilibrium statistical theory with the experimental estimations of i) non-Gaussian probability distribution function, ii) multifractal scaling exponent spectrum and generalized Renyi dimension spectrum, iii) exponent spectrum of the structure functions estimated for the sunspot index and its underlying non equilibrium solar dynamics.

40 pages, 11 figures

References in corpus (6)

• Fractional Vector Calculus and Fractional Maxwell's Equations
• Universality in solar flare and earthquake occurrence
• Fractional Variations for Dynamical Systems: Hamilton and Lagrange Approaches
• Fractional Liouville and BBGKI Equations
• A generalization of the central limit theorem consistent with nonextensive statistical mechanics
• Multivariate Generalizations of the q--Central Limit Theorem

Cited by in corpus (8)

• A free energy principle for a particular physics
• 25 Years of Self-Organized Criticality: Solar and Astrophysics
• Path integrals, particular kinds, and strange things
• A Fractional Fokker-Planck Model for Anomalous Diffusion
• Tsallis non-extensive statistics, intermittent turbulence, SOC and chaos in the solar plasma. Part two: Solar Flares dynamics
• Non-Linear Langevin and Fractional Fokker-Planck Equations for Anomalous Diffusion by Levy Stable Processes
• Spatial-temporal forecasting the sunspot diagram
• Evidence of Nonlinear Signatures in Solar Wind Proton Density at the L1 Lagrange point