# 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:

- Institute of Aeronautical Technology (ITA) and World Institute for Space Environment Research (WISER), Sao Jose dos Campos, SP 12228-900 (Brazil)
- (INPE) and World Institute for Space Environment Research (WISER), P.O. Box 515, Sao Jose dos Campos, SP 12227-010 (Brazil)
- (UnB), Gama Campus, and Plasma Physics Laboratory, Institute of Physics, Brasilia, DF 70910-900 (Brazil)
- (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}

}