Chaos in driven Alfvén systems

T. Hada; C. F. Kennel; B. Buti; E. Mjølhus

doi:10.1063/1.859383

Chaos in driven Alfvén systems

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

Research output: Contribution to journal › Article › peer-review

11 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 language	English
Pages (from-to)	2581-2590
Number of pages	10
Journal	Physics of Fluids B
Volume	2
Issue number	11
DOIs	https://doi.org/10.1063/1.859383
Publication status	Published - 1990

All Science Journal Classification (ASJC) codes

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

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10.1063/1.859383

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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.",

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T1 - Chaos in driven Alfvén systems

AU - Hada, T.

AU - Kennel, C. F.

AU - Buti, B.

AU - Mjølhus, E.

PY - 1990

Y1 - 1990

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.

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Chaos in driven Alfvén systems

Abstract

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