Sudden transition to chaos in plasma wave interactions

López-Rebollal, O.; Sanmartin, J. R.; Río, Ezequiel del

doi:10.1063/1.873006

Cited by 7 publications

(4 citation statements)

References 22 publications

(25 reference statements)

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“…17 Also, one can verify that once reached the line rϭ1 in that plane all trajectories keep r less than unity. The entire flow in ͑30͒ tends to the stable focus at rϽ1.…”

Section: ͑28͒mentioning

confidence: 99%

“…14 For quadratic coupling ͑corresponding to qϭ1 in the two-oscillator case͒, the hard transition and the effects of noise have been experimentally verified using electronic oscillators; 15 also, the hard transition was found to persist when the daughter waves had unequal dampings, the flow then being 4D rather than 3D. 16,17 Cubic interaction, corresponding to qϭ2 ͑or 1:1 frequency ratio͒ in the two-oscillator case, allows a variety of coupling structures. A reduced 3-wave truncation of the nonlinear Schrödinger equation showed chaotic behavior at finite ⌫; 18 a hard transition was encountered in a two-oscillator model of a spherical swing.…”

Section: Introductionmentioning

confidence: 99%

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Hard transition to chaotic dynamics in Alfvén wave fronts

et al. 2004

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The derivative nonlinear Schrödinger ͑DNLS͒ equation, describing propagation of circularly polarized Alfvén waves of finite amplitude in a cold plasma, is truncated to explore the coherent, weakly nonlinear, cubic coupling of three waves near resonance, one wave being linearly unstable and the other waves damped. In a reduced three-wave model ͑equal dampings of daughter waves, three-dimensional flow for two wave amplitudes and one relative phase͒, no matter how small the growth rate of the unstable wave there exists a parametric domain with the flow exhibiting chaotic relaxation oscillations that are absent for zero growth rate. This hard transition in phase-space behavior occurs for left-hand ͑LH͒ polarized waves, paralleling the known fact that only LH time-harmonic solutions of the DNLS equation are modulationally unstable, with damping less than about ͑unstable wave frequency͒ 2 /4ϫion cyclotron frequency. The structural stability of the transition was explored by going into a fully 3-wave model ͑different dampings of daughter waves, four-dimensional flow͒; both models differ in significant phase-space features but keep common features essential for the transition.

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“…17 Also, one can verify that once reached the line rϭ1 in that plane all trajectories keep r less than unity. The entire flow in ͑30͒ tends to the stable focus at rϽ1.…”

Section: ͑28͒mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Hard transition to chaotic dynamics in Alfvén wave fronts

et al. 2004

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“…(3)- (5) exhibits rich dynamical behaviors, such as fixed point, divergence, limit cycle and strange attractor (Wersinger et al, 1980;Meunier et al, 1982;Lopes and Chian, 1996b;Lopez et al, 1998;Chian et al, 2000). The system dynamics can be studied by constructing a bifurcation diagram which shows the birth, evolution, and death of attracting sets (Alligood et al, 1996).…”

Section: Bifurcation Diagrammentioning

confidence: 99%

Chaos in magnetospheric radio emissions

Chian

Rempel

Borotto

2002

Nonlin. Processes Geophys.

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Abstract.A three-wave model of auroral radio emissions near the electron plasma frequency was proposed by Chian et al. (1994) involving resonant interactions of Langmuir, whistler and Alfvén waves. Chaos can occur in the nonlinear evolution of this three-wave process in the magnetosphere. In particular, two types of intermittency, due to either local or global bifurcations, can be observed. We analyze the type-I Pomeau-Manneville intermittency, arising from a saddlenode bifurcation, and the crisis-induced intermittency, arising from an interior crisis associated with a global bifurcation. Examples of time series, power spectrum, phasespace trajectory for both types of intermittency are presented through computer simulations. The degree of chaoticity of this three-wave process is characterized by calculating the maximum Lyapunov exponent. We suggest that the intermittent phenomena discussed in this paper may be observed in the temporal signal of magnetospheric radio emissions.

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“…This led to exactly ID, noninvertible maps, with vanishing Cantor structures and to chaotic dynamics with vanishing Lyapunov exponents. The transition has been recently shown to be structurally stable [Lopez-Rebollal et al, 1998]. …”

Section: Introductionmentioning

confidence: 99%

Experimental Evidence of a Hard Transition to Chaos

Río

Sanmartin

López-Rebollal

1998

Int. J. Bifurcation Chaos

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A generic, sudden transition to chaos has been experimentally verified using electronic circuits. The particular system studied involves the near resonance of two coupled oscillators at 2 : 1 frequency ratio when the damping of the first oscillator becomes negative. We identified in the experiment all types of orbits described by theory. We also found that a theoretical, ID limit map fits closely a map of the experimental attractor which, however, could be strongly disturbed by noise. In particular, we found noisy periodic orbits, in good agreement with noise theory.

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Sudden transition to chaos in plasma wave interactions

Cited by 7 publications

References 22 publications

Hard transition to chaotic dynamics in Alfvén wave fronts

Hard transition to chaotic dynamics in Alfvén wave fronts

Chaos in magnetospheric radio emissions

Experimental Evidence of a Hard Transition to Chaos

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