Abstract
Two nonlinear dynamos have been analyzed by numerical means: 3D-simulation of the magneto-hydrodynamic equations and qualitative analysis of a simplified low-dimensional mean field model. It turns out that both are capable of deterministic chaos in a certain parameter range. As the basic tool the calculation of Lyapunov exponents has been used.
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References
Brandenburg, A., Jennings, R. L., Nordlund, Å. and Stein, R.F.: 1991, in T. Riste and D. Sherrington, ed(s)., Spontaneous formation of space-time structures and criticality, Nato ASI Series, Dordrecht, 371.
Eddy, J.A.: 1976, Science 286, 1198.
Feudel, U. and Jansen, W.: 1992, Int. J. Bifurcation & Chaos 2.
Feudel, U., Jansen, W., and Kurths, J.: 1993, Int. J. Bifurcation & Chaos 3, in press.
Jones, C. A. and Weiss, N. O. and Cattaneo, F.: 1985, Physica 14D, 161.
Krause, F. and Rädler, K.-H.: 1980, Mean-Field Magnetohydrodynamics and Dynamo Theory, Akademie-Verlag, Berlin.
Kurths, J. and Brandenburg, A.: 1991, Phys. Rev. A44, R3427.
Malinetzky, G.G., Ruzmaikin, A.A. and Samarsky, A.A.: 1986, A Model for Long Variations of the Solar Activity, Preprint.
Meneguzzi, M. and Pouquet, A.: 1989, J. Fluid Mech. 205, 297.
Nordlund, Å., Brandenburg, A., Jennings, R. L., Rieutord, M., Ruokolainen, J., Stein, R. F. and Tuominen, I.: 1992, Astrophys. J. 392, 647.
Ruelle, D.: 1989, Chaotic Evolution and Strange Attractors, Cambridge University Press.
Schuster, H.G.: 1984, Deterministic Chaos, VCH, Weinheim.
Zeldovich, Ya. B., Ruzmaikin, A. A. and Sokoloff, D. D.: 1983, Magnetic Fields in Astrophysics, Gordon & Breach, New York.
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© 1993 Springer Science+Business Media Dordrecht
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Kurths, J., Brandenburg, A., Feudel, U., Jansen, W. (1993). Chaos in Nonlinear Dynamo Models. In: Krause, F., Rädler, KH., Rüdiger, G. (eds) The Cosmic Dynamo. International Astronomical Union Symposia / Union Astronomique Internationale, vol 157. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0772-3_14
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DOI: https://doi.org/10.1007/978-94-011-0772-3_14
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