Chaos in driven Alfvén systems

Unstable periodic orbits and chaotic saddles

A. C.L. Chian, W. M. Santana, E. L. Rempel, F. A. Borotto, Tohru Hada, Y. Kamide

    Research output: Contribution to journalArticle

    14 Citations (Scopus)

    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 languageEnglish
    Pages (from-to)17-29
    Number of pages13
    JournalNonlinear Processes in Geophysics
    Volume14
    Issue number1
    DOIs
    Publication statusPublished - Jan 1 2007

    Fingerprint

    Time varying systems
    saddles
    chaotic dynamics
    Chaos theory
    chaos
    Orbits
    orbits
    bifurcation
    Solar wind
    Nonlinear equations
    Explosions
    Turbulence
    Derivatives
    Plasmas
    explosion
    solar wind
    space plasmas
    turbulence
    diagram
    intermittency

    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, Tohru; Kamide, Y.

    In: Nonlinear Processes in Geophysics, Vol. 14, No. 1, 01.01.2007, p. 17-29.

    Research output: Contribution to journalArticle

    Chian, A. C.L. ; Santana, W. M. ; Rempel, E. L. ; Borotto, F. A. ; Hada, Tohru ; Kamide, Y. / Chaos in driven Alfvén systems : Unstable periodic orbits and chaotic saddles. In: Nonlinear Processes in Geophysics. 2007 ; Vol. 14, No. 1. pp. 17-29.
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    abstract = "The chaotic dynamics of Alfv{\'e}n waves in space plasmas governed by the derivative nonlinear Schr{\"o}dinger 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 Alfv{\'e}n intermittent turbulence observed in the solar wind is discussed.",
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    AU - Santana, W. M.

    AU - Rempel, E. L.

    AU - Borotto, F. A.

    AU - Hada, Tohru

    AU - Kamide, Y.

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