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Transition from low to high dimensional chaos in a group of pulsations recorded in a broad radiowave interval

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Abstract

We examined the dynamic characteristics of the time series regarding a group of pulsations in broadband spectrum at metric waveband solar radio emission. The data were recorded with the radio polarimeter of the INAF-Trieste Astronomical Observatory at July 17, 2002. The aim is to determine if the underlying process of these pulsations can be describe as a periodic, deterministic chaos or stochastic. The pulsations under inquiry in present paper are rather rare, as we found only one example of similar ones reported in the literature. Unlike most of the previously works where the analyses was done to a broadband pulsating events at one single frequency, we examine the pulsation event as it evolves both in time and in frequency. We found that the dynamics underlying the generation of pulsations can be characterized by a deterministic chaotic process which increases the dimension of chaos with frequency showing a transition from low-dimensional to high-dimensional deterministic chaotic system.

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References

  • Aschwanden, M.J.: The polarization of decimetric pulsations. Sol. Phys. 104, 57–65 (1986)

    Article  ADS  Google Scholar 

  • Aschwanden, M.J.: Theory of radio pulsations in coronal loops. Sol. Phys. 111, 113–136 (1987)

    Article  ADS  Google Scholar 

  • Farmer, J.D.: Chaotic attractors of an infinite-dimensional dynamical system. Physica D 4, 366–393 (1982)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  • Farmer, J.D., Ott, J.: The dimension of chaotic attractors. Physica D 7, 153–180 (1983)

    Article  MathSciNet  ADS  Google Scholar 

  • Fraser, A.M., Swinney, H.L.: Independent coordinates for strange attractors from mutual information. Phys. Rev. A 33, 1134–1140 (1986)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  • Harrison, M.A., Lai, Y.-C.: Route to high-dimensional chaos. Phys. Rev. E 59, 3799–3802 (1999)

    Article  ADS  Google Scholar 

  • Hurst, H.E.: Long term storage capacity of reservoirs. Trans. Am. Soc. Eng. 116, 770–799 (1951)

    Google Scholar 

  • Isliker, H.: A scaling test for correlation dimensions. Phys. Lett. A 169, 313–322 (1992)

    Article  ADS  Google Scholar 

  • Kaplan, T., Glass, L.: Direct test for determinism in a time series. Phys. Rev. Lett. 68, 427–430 (1992)

    Article  ADS  Google Scholar 

  • Kennel, M.B., Brown, R., Abarbanel, H.D.I.: Determining embedding dimension for phase space reconstruction using a geometrical construction. Phys. Rev. A 45, 3403–3411 (1992)

    Article  ADS  Google Scholar 

  • Kilcik, A., Anderson, C.N.K., Rozelot, J.P., Ye, H., Sugihara, G., Ozguc, A.: Nonlinear prediction of solar cycle 24. Astrophys. J. 693, 1173–1177 (2009)

    Article  ADS  Google Scholar 

  • Kurths, J., Herzel, H.: Can a solar pulsation event be characterized by a low-dimensional chaotic attractor? Sol. Phys. 107, 39–45 (1987a)

    Article  ADS  Google Scholar 

  • Kurths, J., Herzel, H.: An attractor in a solar time series. Physica D 27, 165–172 (1987b)

    Article  ADS  Google Scholar 

  • Kurths, J., Karlický, M.: The route to chaos during a pulsation event. Sol. Phys. 119, 399–411 (1989)

    Article  ADS  Google Scholar 

  • Kurths, J., Benz, A.O., Aschwanden, M.J.: The attractor dimension of solar decimetric radio pulsations. Astron. Astrophys. 248, 270–276 (1991)

    ADS  Google Scholar 

  • Mandelbrot, B.B., Wallis, J.R.: Robustness of the rescaled range R/S in the measurement of noncyclic long run statistical dependence. Water Resour. Res. 5, 967–987 (1969)

    Article  ADS  Google Scholar 

  • Méndez Berhondo, A.L., Díaz Rodríguez, A.K., Zlobec, P., Cuendias, L.: Deterministic behavior in the dynamics of solar metric radio bursts with intermediate drifting patterns. Astrophys. Space Sci. 346, 301–306 (2013)

    Article  Google Scholar 

  • Messerotti, M.: TSRS as a solar radio noise monitor for communication and navigation systems. Earth Moon Planets 104, 51–54 (2009)

    Article  ADS  Google Scholar 

  • Messerotti, M., Zlobec, P., Coretti, I., Jurcev, M., Padovan, S.: TSRS diagnostics for space weather effects analysis. Mem. Soc. Astron. Ital. Suppl. 3, 36–39 (2003)

    ADS  Google Scholar 

  • Robert, B., Edwin, P.M., Benz, A.O.: On coronal oscillations. Astrophys. J. 279, 857–865 (1984)

    Article  ADS  Google Scholar 

  • Takens, F.: Detecting strange attractors in turbulence. Lect. Notes Math. 898, 366–381 (1981)

    MathSciNet  Google Scholar 

  • Turcotte, D.L.: Fractals and Chaos in Geology and Geophysics, 2nd edn. Cambridge University Press, Cambridge (1997) 398 pp.

    Book  Google Scholar 

  • Veronig, A., Messerotti, M., Hanslmeier, A.: Determination of fractal dimensions of solar radio bursts. Astron. Astrophys. 327, 337–350 (2000)

    ADS  Google Scholar 

  • Zlobec, P., Messerotti, M., Li, H.-W., Barry, M.B., Comari, M.: Analysis of the polarization of pulsating structures at m-dm wavelengths. Sol. Phys. 114, 375–384 (1987)

    Article  ADS  Google Scholar 

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Acknowledgements

A.L. Méndez Berhondo acknowledges Prof. Matjaž Perc (Dept. of Physics, University of Maribor, Slovenia) for his software and comments. The authors acknowledge Henry Aurass for the radio spectra recorded at the Potsdam Observatory. A.L. Méndez Berhondo expresses his gratitude to the Basovizza Observing Station (INAF-Trieste Astronomical Observatory) staff for their hospitality, and the support of ICTP-TRIL Program, in particular to Prof. S.M. Radicella. Authors acknowledge the fruitful revision of the manuscript and suggestions of the anonymous reviewer.

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Correspondence to Adolfo L. Méndez Berhondo.

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Méndez Berhondo, A.L., Zlobec, P. & Díaz Rodríguez, A.K. Transition from low to high dimensional chaos in a group of pulsations recorded in a broad radiowave interval. Astrophys Space Sci 357, 150 (2015). https://doi.org/10.1007/s10509-015-2380-x

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