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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union
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Volume 14, issue 1 | Copyright

Special issue: Nonlinear dynamics of Earth-Oceans-Space (EOS2005)

Nonlin. Processes Geophys., 14, 17-29, 2007
https://doi.org/10.5194/npg-14-17-2007
© Author(s) 2007. This work is licensed under
the Creative Commons Attribution-NonCommercial-ShareAlike 2.5 License.

  24 Jan 2007

24 Jan 2007

Chaos in driven Alfvén systems: unstable periodic orbits and chaotic saddles

A. C.-L. Chian1, W. M. Santana1, E. L. Rempel2, F. A. Borotto3, T. Hada4, and Y. Kamide5 A. C.-L. Chian et al.
  • 1National Institute for Space Research (INPE) and World Institute for Space Environment Research (WISER), P.O. Box 515, São José dos Campos – SP, CEP 12227-010, Brazil
  • 2Institute of Aeronautical Technology (ITA), São José dos Campos – SP, CEP 12228-900, Brazil
  • 3Universidad de Concepción, Departamento de Física, Concepción, Chile
  • 4Kyushu University, Department of Earth Sciences and Technology, Fukuoka 8168580, Japan
  • 5Solar-Terrestrial Environment Laboratory, Nagoya University, Toyokawa 4428507, Japan

Abstract. The chaotic dynamics of Alfvén waves in space plasmas governed by the derivative nonlinear Schrödinger equation, in the low-dimensional limit described by stationary spatial solutions, is studied. A bifurcation diagram is constructed, by varying the driver amplitude, to identify a number of nonlinear dynamical processes including saddle-node bifurcation, boundary crisis, and interior crisis. The roles played by unstable periodic orbits and chaotic saddles in these transitions are analyzed, and the conversion from a chaotic saddle to a chaotic attractor in these dynamical processes is demonstrated. In particular, the phenomenon of gap-filling in the chaotic transition from weak chaos to strong chaos via an interior crisis is investigated. A coupling unstable periodic orbit created by an explosion, within the gaps of the chaotic saddles embedded in a chaotic attractor following an interior crisis, is found numerically. The gap-filling unstable periodic orbits are responsible for coupling the banded chaotic saddle (BCS) to the surrounding chaotic saddle (SCS), leading to crisis-induced intermittency. The physical relevance of chaos for Alfvén intermittent turbulence observed in the solar wind is discussed.

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