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

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

    Research output: Contribution to journalArticlepeer-review

    15 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 - 2007

    All Science Journal Classification (ASJC) codes

    • Statistical and Nonlinear Physics
    • Geophysics
    • Geochemistry and Petrology

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