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.
| Original language | English |
|---|---|
| Pages (from-to) | 17-29 |
| Number of pages | 13 |
| Journal | Nonlinear Processes in Geophysics |
| Volume | 14 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - Jan 1 2007 |
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All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Geophysics
- Geochemistry and Petrology
Cite this
Chaos in driven Alfvén systems : Unstable periodic orbits and chaotic saddles. / Chian, A. C.L.; Santana, W. M.; Rempel, E. L.; Borotto, F. A.; Hada, T.; Kamide, Y.
In: Nonlinear Processes in Geophysics, Vol. 14, No. 1, 01.01.2007, p. 17-29.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Chaos in driven Alfvén systems
T2 - Unstable periodic orbits and chaotic saddles
AU - Chian, A. C.L.
AU - Santana, W. M.
AU - Rempel, E. L.
AU - Borotto, F. A.
AU - Hada, T.
AU - Kamide, Y.
PY - 2007/1/1
Y1 - 2007/1/1
N2 - 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.
AB - 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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UR - http://www.scopus.com/inward/citedby.url?scp=33846590536&partnerID=8YFLogxK
U2 - 10.5194/npg-14-17-2007
DO - 10.5194/npg-14-17-2007
M3 - Article
AN - SCOPUS:33846590536
VL - 14
SP - 17
EP - 29
JO - Nonlinear Processes in Geophysics
JF - Nonlinear Processes in Geophysics
SN - 1023-5809
IS - 1
ER -