Chaos in driven Alfvén systems: unstable periodic orbits and chaotic saddles
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 nonlinea...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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Copernicus Publications
2007-01-01
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| Series: | Nonlinear Processes in Geophysics |
| Online Access: | http://www.nonlin-processes-geophys.net/14/17/2007/npg-14-17-2007.pdf |
| _version_ | 1811327559710801920 |
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| author | A. C.-L. Chian W. M. Santana E. L. Rempel F. A. Borotto T. Hada Y. Kamide |
| author_facet | A. C.-L. Chian W. M. Santana E. L. Rempel F. A. Borotto T. Hada Y. Kamide |
| author_sort | A. C.-L. Chian |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-13T15:10:04Z |
| format | Article |
| id | doaj.art-8303424213e14f138b74737bfaac45a7 |
| institution | Directory Open Access Journal |
| issn | 1023-5809 1607-7946 |
| language | English |
| last_indexed | 2024-04-13T15:10:04Z |
| publishDate | 2007-01-01 |
| publisher | Copernicus Publications |
| record_format | Article |
| series | Nonlinear Processes in Geophysics |
| spelling | doaj.art-8303424213e14f138b74737bfaac45a72022-12-22T02:42:02ZengCopernicus PublicationsNonlinear Processes in Geophysics1023-58091607-79462007-01-011411729Chaos in driven Alfvén systems: unstable periodic orbits and chaotic saddlesA. C.-L. ChianW. M. SantanaE. L. RempelF. A. BorottoT. HadaY. KamideThe 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.http://www.nonlin-processes-geophys.net/14/17/2007/npg-14-17-2007.pdf |
| spellingShingle | A. C.-L. Chian W. M. Santana E. L. Rempel F. A. Borotto T. Hada Y. Kamide Chaos in driven Alfvén systems: unstable periodic orbits and chaotic saddles Nonlinear Processes in Geophysics |
| title | Chaos in driven Alfvén systems: unstable periodic orbits and chaotic saddles |
| title_full | Chaos in driven Alfvén systems: unstable periodic orbits and chaotic saddles |
| title_fullStr | Chaos in driven Alfvén systems: unstable periodic orbits and chaotic saddles |
| title_full_unstemmed | Chaos in driven Alfvén systems: unstable periodic orbits and chaotic saddles |
| title_short | Chaos in driven Alfvén systems: unstable periodic orbits and chaotic saddles |
| title_sort | chaos in driven alfven systems unstable periodic orbits and chaotic saddles |
| url | http://www.nonlin-processes-geophys.net/14/17/2007/npg-14-17-2007.pdf |
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