Chaos in driven Alfvén systems

Tohru Hada, C. F. Kennel, B. Buti, E. Mjølhus

    Research output: Contribution to journalArticle

    45 Citations (Scopus)

    Abstract

    The chaos in a one-dimensional system, which would be nonlinear stationary Alfvén waves in the absence of an external driver, is characterized. The evolution equations are numerically integrated for the transverse wave magnetic field amplitude and phase using the derivative nonlinear Schrödinger equation (DNLS), including resistive wave damping and a long-wavelength monochromatic, circularly polarized driver. A Poincaré map analysis shows that, for the nondissipative (Hamiltonian) case, the solutions near the phase space (soliton) separatrices of this system become chaotic as the driver amplitude increases, and "strong" chaos appears when the driver amplitude is large. The dissipative system exhibits a wealth of dynamical behavior, including quasiperiodic orbits, period-doubling bifurcations leading to chaos, sudden transitions to chaos, and several types of strange attractors.

    Original languageEnglish
    Pages (from-to)2581-2590
    Number of pages10
    JournalPhysics of Fluids B
    Volume2
    Issue number11
    DOIs
    Publication statusPublished - Jan 1 1990

    Fingerprint

    Chaos theory
    chaos
    Hamiltonians
    strange attractors
    transverse waves
    period doubling
    Chaotic systems
    Solitons
    Nonlinear equations
    nonlinear equations
    Orbits
    Damping
    solitary waves
    damping
    Magnetic fields
    Derivatives
    orbits
    Wavelength
    magnetic fields
    wavelengths

    All Science Journal Classification (ASJC) codes

    • Computational Mechanics
    • Condensed Matter Physics
    • Mechanics of Materials
    • Physics and Astronomy(all)
    • Fluid Flow and Transfer Processes

    Cite this

    Hada, T., Kennel, C. F., Buti, B., & Mjølhus, E. (1990). Chaos in driven Alfvén systems. Physics of Fluids B, 2(11), 2581-2590. https://doi.org/10.1063/1.859383

    Chaos in driven Alfvén systems. / Hada, Tohru; Kennel, C. F.; Buti, B.; Mjølhus, E.

    In: Physics of Fluids B, Vol. 2, No. 11, 01.01.1990, p. 2581-2590.

    Research output: Contribution to journalArticle

    Hada, T, Kennel, CF, Buti, B & Mjølhus, E 1990, 'Chaos in driven Alfvén systems', Physics of Fluids B, vol. 2, no. 11, pp. 2581-2590. https://doi.org/10.1063/1.859383
    Hada T, Kennel CF, Buti B, Mjølhus E. Chaos in driven Alfvén systems. Physics of Fluids B. 1990 Jan 1;2(11):2581-2590. https://doi.org/10.1063/1.859383
    Hada, Tohru ; Kennel, C. F. ; Buti, B. ; Mjølhus, E. / Chaos in driven Alfvén systems. In: Physics of Fluids B. 1990 ; Vol. 2, No. 11. pp. 2581-2590.
    @article{d55638dc63274e5bb41b45ca9017c3c1,
    title = "Chaos in driven Alfv{\'e}n systems",
    abstract = "The chaos in a one-dimensional system, which would be nonlinear stationary Alfv{\'e}n waves in the absence of an external driver, is characterized. The evolution equations are numerically integrated for the transverse wave magnetic field amplitude and phase using the derivative nonlinear Schr{\"o}dinger equation (DNLS), including resistive wave damping and a long-wavelength monochromatic, circularly polarized driver. A Poincar{\'e} map analysis shows that, for the nondissipative (Hamiltonian) case, the solutions near the phase space (soliton) separatrices of this system become chaotic as the driver amplitude increases, and {"}strong{"} chaos appears when the driver amplitude is large. The dissipative system exhibits a wealth of dynamical behavior, including quasiperiodic orbits, period-doubling bifurcations leading to chaos, sudden transitions to chaos, and several types of strange attractors.",
    author = "Tohru Hada and Kennel, {C. F.} and B. Buti and E. Mj{\o}lhus",
    year = "1990",
    month = "1",
    day = "1",
    doi = "10.1063/1.859383",
    language = "English",
    volume = "2",
    pages = "2581--2590",
    journal = "Physics of Fluids B",
    issn = "0899-8221",
    publisher = "American Institute of Physics Publising LLC",
    number = "11",

    }

    TY - JOUR

    T1 - Chaos in driven Alfvén systems

    AU - Hada, Tohru

    AU - Kennel, C. F.

    AU - Buti, B.

    AU - Mjølhus, E.

    PY - 1990/1/1

    Y1 - 1990/1/1

    N2 - The chaos in a one-dimensional system, which would be nonlinear stationary Alfvén waves in the absence of an external driver, is characterized. The evolution equations are numerically integrated for the transverse wave magnetic field amplitude and phase using the derivative nonlinear Schrödinger equation (DNLS), including resistive wave damping and a long-wavelength monochromatic, circularly polarized driver. A Poincaré map analysis shows that, for the nondissipative (Hamiltonian) case, the solutions near the phase space (soliton) separatrices of this system become chaotic as the driver amplitude increases, and "strong" chaos appears when the driver amplitude is large. The dissipative system exhibits a wealth of dynamical behavior, including quasiperiodic orbits, period-doubling bifurcations leading to chaos, sudden transitions to chaos, and several types of strange attractors.

    AB - The chaos in a one-dimensional system, which would be nonlinear stationary Alfvén waves in the absence of an external driver, is characterized. The evolution equations are numerically integrated for the transverse wave magnetic field amplitude and phase using the derivative nonlinear Schrödinger equation (DNLS), including resistive wave damping and a long-wavelength monochromatic, circularly polarized driver. A Poincaré map analysis shows that, for the nondissipative (Hamiltonian) case, the solutions near the phase space (soliton) separatrices of this system become chaotic as the driver amplitude increases, and "strong" chaos appears when the driver amplitude is large. The dissipative system exhibits a wealth of dynamical behavior, including quasiperiodic orbits, period-doubling bifurcations leading to chaos, sudden transitions to chaos, and several types of strange attractors.

    UR - http://www.scopus.com/inward/record.url?scp=0001669915&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=0001669915&partnerID=8YFLogxK

    U2 - 10.1063/1.859383

    DO - 10.1063/1.859383

    M3 - Article

    AN - SCOPUS:0001669915

    VL - 2

    SP - 2581

    EP - 2590

    JO - Physics of Fluids B

    JF - Physics of Fluids B

    SN - 0899-8221

    IS - 11

    ER -