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www.nonlin-processes-geophys.net/14/17/2007/
doi:10.5194/npg-14-17-2007
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under a Creative Commons License.
Chaos in driven Alfvén systems: unstable periodic orbits and chaotic saddles
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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Citation: Chian, A. C.-L., Santana, W. M., Rempel, E. L., Borotto, F. A., Hada, T., and Kamide, Y.: Chaos in driven Alfvén systems: unstable periodic orbits and chaotic saddles, Nonlin. Processes Geophys., 14, 17-29, doi:10.5194/npg-14-17-2007, 2007. Bibtex EndNote Reference Manager XML
