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

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  • Pavlos, G.P.
  • Karakatsanis, L.P.
  • Xenakis, M.N.

Abstract

In this study, the non-linear analysis of the sunspot index is embedded in the non-extensive statistical theory of Tsallis (1988, 2004, 2009) [7,9,10]. The q-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 f(a), the generalized Renyi dimension spectrum D(q) and the spectrum J(p) of the structure function exponents were estimated experimentally and theoretically by using the q-entropy principle included in Tsallis non-extensive statistical theory, following Arimitsu and Arimitsu (2001, 2000) [76,77]. 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 a phase transition to low dimensional chaos in accordance to Ruzmaikin, Zeleny and Milovanov’s studies (Zelenyi and Milovanov (1991) [21]); Milovanov and Zelenyi (1993) [22]; Ruzmakin et al. (1996) [26]) (c) faithful agreement of Tsallis non-equilibrium statistical theory with the experimental estimations of (i) non-Gaussian probability distribution function P(x), (ii) multifractal scaling exponent spectrum f(a) and generalized Renyi dimension spectrum Dq, (iii) exponent spectrum J(p) of the structure functions estimated for the sunspot index and its underlying non equilibrium solar dynamics.

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  • Pavlos, G.P. & Karakatsanis, L.P. & Xenakis, M.N., 2012. "Tsallis non-extensive statistics, intermittent turbulence, SOC and chaos in the solar plasma, Part one: Sunspot dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(24), pages 6287-6319.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:24:p:6287-6319
    DOI: 10.1016/j.physa.2012.07.066
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    1. Arimitsu, Toshihico & Arimitsu, Naoko, 2001. "Analysis of turbulence by statistics based on generalized entropies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 295(1), pages 177-194.
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    4. Pavlos, G.P. & Karakatsanis, L.P. & Xenakis, M.N. & Sarafopoulos, D. & Pavlos, E.G., 2012. "Tsallis statistics and magnetospheric self-organization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(11), pages 3069-3080.
    5. McCauley, Joseph L., 1997. "Nonintegrability, chaos, and complexity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 237(3), pages 387-404.
    6. Ferri, G.L. & Reynoso Savio, M.F. & Plastino, A., 2010. "Tsallis’ q-triplet and the ozone layer," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(9), pages 1829-1833.
    7. Pavlos, G.P. & Iliopoulos, A.C. & Tsoutsouras, V.G. & Sarafopoulos, D.V. & Sfiris, D.S. & Karakatsanis, L.P. & Pavlos, E.G., 2011. "First and second order non-equilibrium phase transition and evidence for non-extensive Tsallis statistics in Earth’s magnetosphere," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(15), pages 2819-2839.
    8. Lenzi, E.K. & Mendes, R.S. & da Silva, L.R., 2000. "Statistical mechanics based on Renyi entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 280(3), pages 337-345.
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    Cited by:

    1. Emad E. Mahmoud & M. Higazy & Turkiah M. Al-Harthi, 2019. "A New Nine-Dimensional Chaotic Lorenz System with Quaternion Variables: Complicated Dynamics, Electronic Circuit Design, Anti-Anticipating Synchronization, and Chaotic Masking Communication Applicatio," Mathematics, MDPI, vol. 7(10), pages 1-26, September.
    2. Pavlos, G.P. & Iliopoulos, A.C. & Zastenker, G.N. & Zelenyi, L.M. & Karakatsanis, L.P. & Riazantseva, M.O. & Xenakis, M.N. & Pavlos, E.G., 2015. "Tsallis non-extensive statistics and solar wind plasma complexity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 422(C), pages 113-135.
    3. Pavlos, G.P. & Karakatsanis, L.P. & Xenakis, M.N. & Pavlos, E.G. & Iliopoulos, A.C. & Sarafopoulos, D.V., 2014. "Universality of non-extensive Tsallis statistics and time series analysis: Theory and applications," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 395(C), pages 58-95.
    4. Pavlos, G.P. & Malandraki, O.E. & Pavlos, E.G. & Iliopoulos, A.C. & Karakatsanis, L.P., 2016. "Non-extensive statistical analysis of magnetic field during the March 2012 ICME event using a multi-spacecraft approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 464(C), pages 149-181.
    5. Iliopoulos, A.C. & Aifantis, E.C., 2018. "Tsallis q-triplet, intermittent turbulence and Portevin–Le Chatelier effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 498(C), pages 17-32.
    6. Karakatsanis, L.P. & Pavlos, G.P. & Xenakis, M.N., 2013. "Tsallis non-extensive statistics, intermittent turbulence, SOC and chaos in the solar plasma. Part two: Solar flares dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(18), pages 3920-3944.
    7. Pavlos, G.P. & Karakatsanis, L.P. & Iliopoulos, A.C. & Pavlos, E.G. & Xenakis, M.N. & Clark, Peter & Duke, Jamie & Monos, D.S., 2015. "Measuring complexity, nonextensivity and chaos in the DNA sequence of the Major Histocompatibility Complex," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 438(C), pages 188-209.

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