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Title: Chaotic saddles in nonlinear modulational interactions in a plasma

Abstract

A nonlinear model of modulational processes in the subsonic regime involving a linearly unstable wave and two linearly damped waves with different damping rates in a plasma is studied numerically. We compute the maximum Lyapunov exponent as a function of the damping rates in a two-parameter space, and identify shrimp-shaped self-similar structures in the parameter space. By varying the damping rate of the low-frequency wave, we construct bifurcation diagrams and focus on a saddle-node bifurcation and an interior crisis associated with a periodic window. We detect chaotic saddles and their stable and unstable manifolds, and demonstrate how the connection between two chaotic saddles via coupling unstable periodic orbits can result in a crisis-induced intermittency. The relevance of this work for the understanding of modulational processes observed in plasmas and fluids is discussed.

Authors:
 [1];  [2];  [3];  [1];  [2];  [1];  [2];  [4]
  1. Institute of Aeronautical Technology (ITA) and World Institute for Space Environment Research (WISER), Sao Jose dos Campos, SP 12228-900 (Brazil)
  2. (INPE) and World Institute for Space Environment Research (WISER), P.O. Box 515, Sao Jose dos Campos, SP 12227-010 (Brazil)
  3. (UnB), Gama Campus, and Plasma Physics Laboratory, Institute of Physics, Brasilia, DF 70910-900 (Brazil)
  4. (France)
Publication Date:
OSTI Identifier:
22068884
Resource Type:
Journal Article
Journal Name:
Physics of Plasmas
Additional Journal Information:
Journal Volume: 19; Journal Issue: 11; Other Information: (c) 2012 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1070-664X
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; BIFURCATION; CHAOS THEORY; DAMPING; INTERACTIONS; LYAPUNOV METHOD; MATHEMATICAL SPACE; NONLINEAR PROBLEMS; PERIODICITY; PLASMA

Citation Formats

Miranda, Rodrigo A., National Institute for Space Research, University of Brasilia, Rempel, Erico L., National Institute for Space Research, Chian, Abraham C.-L., National Institute for Space Research, and Observatoire de Paris, LESIA, CNRS, 92195 Meudon. Chaotic saddles in nonlinear modulational interactions in a plasma. United States: N. p., 2012. Web. doi:10.1063/1.4766472.
Miranda, Rodrigo A., National Institute for Space Research, University of Brasilia, Rempel, Erico L., National Institute for Space Research, Chian, Abraham C.-L., National Institute for Space Research, & Observatoire de Paris, LESIA, CNRS, 92195 Meudon. Chaotic saddles in nonlinear modulational interactions in a plasma. United States. doi:10.1063/1.4766472.
Miranda, Rodrigo A., National Institute for Space Research, University of Brasilia, Rempel, Erico L., National Institute for Space Research, Chian, Abraham C.-L., National Institute for Space Research, and Observatoire de Paris, LESIA, CNRS, 92195 Meudon. Thu . "Chaotic saddles in nonlinear modulational interactions in a plasma". United States. doi:10.1063/1.4766472.
@article{osti_22068884,
title = {Chaotic saddles in nonlinear modulational interactions in a plasma},
author = {Miranda, Rodrigo A. and National Institute for Space Research and University of Brasilia and Rempel, Erico L. and National Institute for Space Research and Chian, Abraham C.-L. and National Institute for Space Research and Observatoire de Paris, LESIA, CNRS, 92195 Meudon},
abstractNote = {A nonlinear model of modulational processes in the subsonic regime involving a linearly unstable wave and two linearly damped waves with different damping rates in a plasma is studied numerically. We compute the maximum Lyapunov exponent as a function of the damping rates in a two-parameter space, and identify shrimp-shaped self-similar structures in the parameter space. By varying the damping rate of the low-frequency wave, we construct bifurcation diagrams and focus on a saddle-node bifurcation and an interior crisis associated with a periodic window. We detect chaotic saddles and their stable and unstable manifolds, and demonstrate how the connection between two chaotic saddles via coupling unstable periodic orbits can result in a crisis-induced intermittency. The relevance of this work for the understanding of modulational processes observed in plasmas and fluids is discussed.},
doi = {10.1063/1.4766472},
journal = {Physics of Plasmas},
issn = {1070-664X},
number = 11,
volume = 19,
place = {United States},
year = {2012},
month = {11}
}