Testing for an attractor in the solar wind flow

Physica D: Nonlinear Phenomena

Volumn 122, Issue 1-4, 1998, Pages 254-264

  Macek, Wieslaw M ^a  

^a Department of Earth Observation   (Poland)

Author keywords

Nonlinear plasma physics; Signal processing; Solar wind; Turbulence

Indexed keywords

EID: 0000035712     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(98)00098-0     Document Type: Article

References (30)

1. S.H. Strogatz, Nonlinear Dynamics and Chaos, Addison-Wesley, Reading, MA, 1994.
2. E. Ott, Chaos in Dynamical Systems, Cambridge University Press, Cambridge, 1993.
3. F. Takens, Detecting strange attractors in turbulence, in: D.A. Rand, L.S. Young (Eds.), Lecture Notes in Mathematics, vol. 898, Springer, Berlin, 1981, pp. 366-381.
4. T. Sauer, J.A. Yorke, M. Casgali, Embedology, J. Stat. Phys. 65 (1991) 579-616.
5. H.D.I. Abarbanel, R. Brown, J.J. Sidorowich, L.S. Tsimring, The analysis of observed chaotic data in physical systems, Rev. Modern Phys. 65 (1993) 1331-1392.
6. J. Kurths, H. Herzel, An attractor in a solar time series, Physica D 25 (1987) 165-172.
7. N.O. Weiss, Chaotic modulation of the solar cycle, Philos. Trans. R. Soc. A 348 (1994) 445-447.
8. D.V. Vassiliadis, A.S Sharma, T.E. Eastman, K. Papadopoulos, Low-dimensional chaos in magnetospheric activity from AE time series, Geophys. Res. Lett. 17 (1990) 1841-1844.
9. D.A. Roberts, Is there a strange attractor in the magnetosphere?, J. Geophys. Res. 96 (1991) 16031-16046.
10. R. Schwenn, Large-scale structure of the interplanetary medium, in: R. Schwenn, E. Marsch (Eds.), Physics of the Inner Heliosphere, vol. 20, Springer, Berlin, 1990, pp. 99-182.
11. W.M. Macek, L. Obojska, Fractal analysis of the low-speed solar wind flow, in: A. Hilgers, T.-D. Guyenne (Eds.), ESA Symposium Proceedings on Environment Modelling for Space-based Applications, SP-392, ESTEC, Noordwijk, December 1996, pp. 247-252.
12. W.M. Macek, L. Obojska, Fractal analysis of the solar wind flow in the inner heliosphere, Chaos, Solitons and Fractals 8 (1997) 1601-1607.
13. W.M. Macek, L. Obqjska, Testing for nonlinearity in the solar wind flow, in: T. Kapitaniak, J. Brindley (Eds.), Proceedings of Third International Conference on Applied Chaotic Systems, Chaos, Solitons and Fractals 9 (1998) 221-229.
14. R. Badii, G. Broggi, B. Derighetti, M. Ravani, S. Ciliberto, A. Politi, M.A. Rubio, Dimension increase in filtered chaotic signals, Phys. Rev. Lett. 60 (1988) 979-982.
15. E. Ott, T. Sauer, J.A. Yorke, Coping with Chaos, Wiley, New York, 1994.
16. P. Grassberger, I. Procaccia, Measuring the strangeness of strange attractors, Physica D 9 (1983) 189-208.
17. J. Theiler, Spurious dimension from correlation algorithms applied to limited time-series data, Phys. Rev. A 34 (1986) 2427-2432.
18. P. Grassberger, I. Procaccia, Estimation of the Kolmogorov entropy from a chaotic signal, Phys. Rev. A 28 (1983) 2591-2593.
19. E. Marsch, C.Y. Tu, Non-Gaussian probability distributions of solar wind fluctuations, Ann. Geophys. 12 (1994) 1127-1138.
20. F. Kaspar, H.G. Schuster, Easily calculable measure for the complexity of spatiotemporal patterns, Phys. Rev. A 36 (1987) 842-848.
21. D.S. Broomhead, G.P. King, Extracting qualitative dynamics from experimental data, Physica D 20 (1986) 217-236.
22. A.M Albano, J. Muench, C. Schwartz, A.I. Mess, P.E. Rapp, Singular-value decomposition and the Grassberger-Procaccia algorithm, Phys. Rev. A 38 (1988) 3017-3026.
23. H.G. Schuster, Deterministic Chaos, VCH, Weinheim, Germany, 1989.
24. J.-P. Eckmann, D. Ruelle, Fundamental limitations for estimating dimensions and Lyapunov exponents in dynamical systems, Physica D 56 (1992) 185-187.
25. M. Ding, C. Grebogi, E. Ott, T. Sauer, J.A. Yorke, Plateau onset for correlation dimension: When does it occur? Phys. Rev. Lett. 70 (1993) 3872-3875.
26. T. Sauer, J.A. Yorke, How many delay coordinates do you need?, Int. J. Bifurcation Chaos 3 (1993) 737-744.
27. J. -P. Eckmann, D. Ruelle, Ergodic theory of chaos and strange attractors, Rev. Mod. Phys. 57 (1985) 617-656.
28. E. Marsch, S. Liu, Structure functions and intermittency of velocity fluctuations in the inner solar wind, Ann. Geophys. 11 (1993) 227-238.
29. J. Theiler, S. Eubank, A. Longtin, B. Galdrikian, J.D. Farmer, Testing for nonlinearity in time series: The method of surrogate data, Physica D 58 (1992) 77-94.
30. A. Wolf, J.B. Swift, H.L. Swinney, J.A. Vastano, Determining Lyapunov exponents from a time series, Physica D 16 (1985) 285-317.