Abstract
The application of chaos theory has become popular to understand the nature of various features of solar activity because most of them are far from regular. The usual approach, however, that is based on finding low-dimensional structures of the underlying processes seems to be successful only in a few exceptional cases, such as in rather coherent phenomena as coronal pulsations. It is important to note that most phenomena in solar radio emission are more complex. We present two kinds of techniques from nonlinear dynamics which can be useful to analyse such phenomena:
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Fragmentation processes observed in solar spike events are studied by means of symbolic dynamics methods. Different measures of complexity calculated from such observations reveal that there is some order in this fragmentation.
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Bursts are a typical transient phenomenon. To study energization processes causing impulsive microwave bursts, the wavelet analysis is applied. It exhibits structural differences of the pre- and post-impulsive phase in cases where the power spectra of both are not distinct.
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References
Chaitin, G.J.: 1987, Algorithmic Information Theory, Cambridge University Press
Farmer, J.D.: 1982, Information Dimension and the Probabilistic Structure of Chaos, Z. Naturforsch 37a, 1304–1325
Grassberger, P.: 1986, How to Measure Self-generated Complexity, Physica A 140, 319–325
Grassberger, P. and Procaccia, I.: 1983, Characterization of Strange Attractors, Phys. Rev. Lett. 50, 346–349
Hao, B.-L.: 1991, Symbolic Dynamics and Characterization of Complexity, Physica D 51, 161–176
Hempelmann, A. and Kurths, J.: 1990, Dynamics of the Outburst Series of SS Cygni, Astron. and Astrophys. 232, 356–366
Isliker, H.: 1993, Non-linear Properties of Bursts and Flares, (this issue)
Kaspar, F. and Schuster, H.G.: 1987, Easily Calculable Measures for the Complexity of Spatio-Temporal Patterns, Phys. Rev. A 36, 842–846
Kolmogorov, A. N.: 1965, Three Approaches to the Quantitative Definition of Information, Probl. of Inform. Theory 1, 3–11
Krüger, A., Urpo, S., Kliem, B. and Schwarz, U.: 1993, Time Structures of Solar Radio Bursts at 37 and 87 GHz, XXIVth General Assembly of the International Union of Radio Science, Kyoto, Japan, August 25 – September 2, 1993, URSI, Section J5, Solar Radio Astronomy
Kurths, J., Benz, A.O. and Aschwanden, M.: 1991, The Attractor Dimension of Solar Decimetric Radio Pulsations, Astron. Astrophys. 248, 270–276
Kurths, J. and Herzel, H.: 1987, An Attractor in a Solar Time Series, Physica D 25, 165–172
Kurths, J. and Karlicky, M.: 1989, The Route to Chaos during a Pulsation Event, Solar Physics 119, 399–411
Mandelbrot, B.: 1977, The Fractal Geometry of Nature, W.H.Freeman and Co., San Francisco
May, R. M.: 1976, Simple Mathematical Models with very Complicated Dynamics, Nature 261, 459–467
Meyer, Y. and Ryan, R.D.: 1993, Wavelets. Algorithms and Applications, Society for Industrial and Applied Mathematics, Philadelphia
Osborne, A.R. and Provenzale, A.: 1989, Finite Correlation Dimension for Stochastic Systems with Power-law Spectra, Physica D 35, 357–381
Ott, E.: 1993, Chaos in Dynamical Systems, Cambridge University Press
Saparin, P., Witt, A., Kurths, J. and Anishchenko, V.: 1994, The Renormalized Entropy, Chaos, Solitons & Fractals (subm.)
Scargle, J. D.: 1993, Wavelet Methods in Astronomical Time Series Analysis, in: Lessi, O. (Ed.) 1993 International Conference on Applications of Time Series Analysis in Astronomy and Meteorology, Padua
Schuster, H.G.: 1988, Deterministic Chaos. An Introduction, VCH, Physik-Verlag, Weinheim
Schwarz, U., Benz, A.O., Kurths, J. and Witt, A.: 1993, Analysis of Solar Spike Events by Means of Symbolic Dynamics Methods, Astron. and Astrophys. 277, 215–224
Schwarz, U., Kurths, J., Witt, A. and Benz, A.O.: 1993, Analysis of Solar Spike Events by Means of Symbolic Dynamics Methods, (this issue)
Takens, F.,: 1981, Detecting Strange Attractors in Turbulence, Warwick 1980, Lecture Notes in Mathematics 898, Springer-Verlag, Berlin
Theiler, J., Eubank, S., Longtin, A., Galdrikian, B. and Farmer, J.D.: 1992, Test for Nonlinearity in Time Series: The Method of Surrogate Data, Physica D 58, 77–94
Wackerbauer, R., Witt, A., Atmanspacher, H., Kurths, J. and Scheingraber, H.: 1993, A Comparative Classification of Complexity Measures, Chaos, Solitons & Fractals (in press)
Witt, A., Kurths, J., Krause, F. and Fischer, K.: 1994, On Validity of a Model for the Reversals of the Earth’s Magnetic Field, Geophys. and Astrophys. Fluid Dynamics (in press)
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© 1994 Springer Science+Business Media Dordrecht
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Kurths, J., Schwarz, U. (1994). Chaos Theory and Radio Emission. In: Van den Oord, G.H.J. (eds) Fragmented Energy Release in Sun and Stars. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1014-3_24
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DOI: https://doi.org/10.1007/978-94-011-1014-3_24
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-4441-7
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