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Detection of Dynamical Complexity Changes in Dst Time Series Using Entropy Concepts and Rescaled Range Analysis

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The Dynamic Magnetosphere

Part of the book series: IAGA Special Sopron Book Series ((IAGA,volume 3))

Abstract

Using an array of diagnostic tools including entropy concepts and rescaled range analysis, we establish that the Dst index time series exhibits long-range correlations, and that the underlying stochastic process can be modeled as fractional Brownian motion. We show the emergence of two distinct patterns in the geomagnetic variability of the terrestrial magnetosphere: (1) a pattern associated with intense magnetic storms, which is characterized by a higher degree of organization (i.e., lower complexity or higher predictability for the system) and persistent behavior, and (2) a pattern associated with normal periods, which is characterized by a lower degree of organization (i.e., higher complexity or lower predictability for the system) and anti-persistent behavior.

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References

  • Balasis G, Eftaxias K (2009) A study of non-extensivity in the Earth’s magnetosphere. Eur Phys J Special Topics 174:219–225

    Article  Google Scholar 

  • Balasis G, Daglis IA, Kapiris P, Mandea M, Vassiliadis D, Eftaxias K (2006) From prestorm activity to magnetic storms: a transition described in terms of fractal dynamics. Ann Geophys 24:3557–3567

    Article  Google Scholar 

  • Balasis G, Daglis IA, Papadimitriou C, Kalimeri M, Anastasiadis A, Eftaxias K (2008) Dynamical complexity in Dst time series using non-extensive Tsallis entropy. Geophys Res Lett. doi:10.1029/2008GL034743

    Google Scholar 

  • Balasis G, Daglis IA, Papadimitriou C, Kalimeri M, Anastasiadis A, Eftaxias K (2009) Investigating dynamical complexity in the magnetosphere using various entropy measures. J Geophys Res. doi:10.1029/2008JA014035

    Google Scholar 

  • Carbone A, Stanley H (2007) Scaling properties and entropy of long-range correlated time series. Physica A 384:267–271

    Article  Google Scholar 

  • Daglis IA, Baker DN, Galperin Y, Kappenman JG, Lanzerotti LJ (2001) Technological impacts of space storms: outstanding issues. Eos Trans AGU. doi:10.1029/01EO00340

    Google Scholar 

  • Daglis IA, Kozyra J, Kamide Y, Vassiliadis D, Sharma A, Liemohn M, Gonzalez W, Tsurutani B, Lu G (2003) Intense space storms: critical issues and open disputes. J Geophys Res. doi:10.1029/2002JA009722

    Google Scholar 

  • Daglis IA, Balasis G, Ganushkina N, Metallinou F-A, Palmroth M, Pirjola R, Tsagouri IA (2009) Investigating dynamic coupling in geospace through the combined use of modeling, simulations and data analysis. Acta Geophys. doi:10.2478/s11600-008-0055-5

    Google Scholar 

  • Ebeling W, Nicolis G (1992) Word frequency and entropy of symbolic sequences: a dynamical Perspective. Chaos Solitons Fractals 2:635–650

    Article  Google Scholar 

  • Ebeling W, Steuer R, Titchener M (2001) Partition-based entropies of deterministic and stochastic maps. Stochast Dyn 1:45–61

    Article  Google Scholar 

  • Graben P, Kurths J (2003) Detecting subthreshold events in noisy data by symbolic dynamics. Phys Rev Lett 90:100602(1–4).

    Article  Google Scholar 

  • Grassberger P, Procaccia I (1983) Estimation of the Kolmogorov entropy from a chaotic signal. Phys Rev A 28:2591–2593

    Article  Google Scholar 

  • Hao B-L (1989) Elementary symbolic dynamics and chaos in dissipative systems. World Scientific, Singapore

    Google Scholar 

  • Henegham C, McDarby G (2000) Establishing the relation between detrended fluctuation analysis and power spectral density analysis for stochastic processes. Phys Rev E 62:6103–6110

    Article  Google Scholar 

  • Hurst HE (1951) Long-term storage of reservoirs: an experimental study. Trans Am Soc Civ Eng 116:770–799

    Google Scholar 

  • Karamanos K (2000) From symbolic dynamics to a digital approach: chaos and transcendence. Lect Notes Phys 550:357–371

    Article  Google Scholar 

  • Karamanos K (2001) Entropy analysis of substitutive sequences revisited. J Phys A: Math Gen 34:9231–9241

    Article  Google Scholar 

  • Karamanos K, Nicolis G (1999) Symbolic dynamics and entropy analysis of Feigenbaum limit sets. Chaos Solitons Fractals 10(7):1135–1150

    Article  Google Scholar 

  • Khinchin AI (1957) Mathematical foundations of information theory. Dover, New York, NY

    Google Scholar 

  • Nicolis G, Gaspard P (1994) Toward a probabilistic approach to complex systems. Chaos Solitons Fractals 4(1):41–57

    Article  Google Scholar 

  • Pincus S (1991) Approximate entropy: a complexity measure for biologic time series data. In: Proceedings of IEEE 17th annual northeast bioengineering conference, IEE Press, New York, NY, p 35–36

    Google Scholar 

  • Pincus S, Keefe D (1992) Quantification of hormone pulsatility via an approximate entropy algorithm. Am J Physiol (Endocrinol Metab) 262: E741–E754

    Google Scholar 

  • Pincus S, Goldberger A (1994) Physiological time-series analysis: what does regularity quantify? Am J Physiol 266:H1643–H1656

    Google Scholar 

  • Pincus S, Singer B (1996) Randomness and degree of irregularity. Proc Natl Acad Sci USA 93:2083–2088

    Article  Google Scholar 

  • Shannon CE (1948) A mathematical theory of communication. Bell Syst Tech J 27:379–423

    Google Scholar 

  • Titchener M, Nicolescu R, Staiger L, Gulliver A, Speidel U (2005) Deterministic complexity and entropy. Fund Inform 64:443–461

    Google Scholar 

  • Tsallis C (1988) Possible generalization of Boltzmann-Gibbs statistics. J Stat Phys 52:479–487

    Article  Google Scholar 

  • Tsallis C (2009) Introduction to nonextensive statistical mechanics, approaching a complex word. Springer, Berlin

    Google Scholar 

  • Vanouplines P (1995) Rescaled range analysis and the fractal dimension of pi. University library, Free University Brussels, Brussels, Belgium. http://ftp.vub.ac.be/_pvouplin/pi/rswhat.htm

  • Wanliss JA (2005) Fractal properties of SYM-H during quiet and active times. J Geophys Res. doi:10.1029/2004JA010544.

    Google Scholar 

  • Wanliss JA, Dobias P (2007) Space storm as a dynamic phase transition. J Atmos Sol Terr Phys 69:675–684

    Article  Google Scholar 

  • Wing S, Johnson J.R. (2010) Introduction to special section on entropy properties and constraints related to space plasma transport. J Geophys Res. doi:10.1029/2009JA014911

    Google Scholar 

  • Zunino L, Perez D, Kowalski A, Martin M, Garavaglia M, Plastino A, Rosso O (2008) Fractional Brownian motion, fractional Gaussian noise and Tsallis permutation entropy. Physica A 387:6057–6068

    Article  Google Scholar 

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Acknowledgements

The Dst data are provided by the World Data Center for Geomagnetism, Kyoto (http://swdcwww.kugi.kyoto-u.ac.jp/).

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Authors and Affiliations

  1. Institute for Space Applications and Remote Sensing, National Observatory of Athens, Athens, Greece

    Georgios Balasis, Ioannis A. Daglis & Anastasios Anastasiadis

  2. Section of Solid State Physics, Department of Physics, University of Athens, Athens, Greece

    Konstantinos Eftaxias

Authors
  1. Georgios Balasis
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  2. Ioannis A. Daglis
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  3. Anastasios Anastasiadis
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  4. Konstantinos Eftaxias
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Corresponding author

Correspondence to Georgios Balasis .

Editor information

Editors and Affiliations

  1. Spacecraft Engineering, Canadian Space Agency, route de l'Aeroport 6767, St.-Hubert, J3Y 8Y9, Québec, Canada

    William Liu

  2. Astronautical Science (ISAS), Institute of Space &, Yoshinodai 3-1-1, Sagamihara, Kanagawa, 229-8510, Japan

    Masaki Fujimoto

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Balasis, G., Daglis, I.A., Anastasiadis, A., Eftaxias, K. (2011). Detection of Dynamical Complexity Changes in Dst Time Series Using Entropy Concepts and Rescaled Range Analysis. In: Liu, W., Fujimoto, M. (eds) The Dynamic Magnetosphere. IAGA Special Sopron Book Series, vol 3. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0501-2_12

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