# Nonlinear dynamics of plasma oscillations modeled by an anharmonic oscillator

## Abstract

This paper considers nonlinear dynamics of plasma oscillations modeled by an anharmonic oscillator. These plasma oscillations are described by a nonlinear differential equation of the form xe+{epsilon}(1+x{sup 2})x+x+{kappa}x{sup 2}+{delta}x{sup 3}=F cos {omega}t. The amplitudes of the forced harmonic, superharmonic, and subharmonic oscillatory states are obtained using the harmonic balance technique and the multiple time scales method. Admissible values of the amplitude of the external strength are derived. Bifurcation sequences displayed by the model for each type of oscillatory states are performed numerically through the fourth-order Runge-Kutta scheme.

- Authors:

- Institut de Mathematiques et de Sciences Physiques, B.P. 613, Porto-Novo (Benin)
- (Cameroon)
- Laboratory of Modelling and Simulation in Engineering and Biological Physics, Faculty of Science, University of Yaounde I, Box 812, Yaounde (Cameroon)
- Faculty of Sciences, University of Dschang, Box 67, Dschang (Cameroon)

- Publication Date:

- OSTI Identifier:
- 21106163

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physics of Plasmas; Journal Volume: 15; Journal Issue: 3; Other Information: DOI: 10.1063/1.2841032; (c) 2008 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; AMPLITUDES; ANHARMONIC OSCILLATORS; BIFURCATION; DIFFERENTIAL EQUATIONS; HARMONIC OSCILLATORS; NONLINEAR PROBLEMS; PLASMA WAVES; RUNGE-KUTTA METHOD

### Citation Formats

```
Enjieu Kadji, H. G., Laboratory of Modelling and Simulation in Engineering and Biological Physics, Faculty of Science, University of Yaounde I, Box 812, Yaounde, Nana Nbendjo, B. R., Chabi Orou, J. B., and Talla, P. K.
```*Nonlinear dynamics of plasma oscillations modeled by an anharmonic oscillator*. United States: N. p., 2008.
Web. doi:10.1063/1.2841032.

```
Enjieu Kadji, H. G., Laboratory of Modelling and Simulation in Engineering and Biological Physics, Faculty of Science, University of Yaounde I, Box 812, Yaounde, Nana Nbendjo, B. R., Chabi Orou, J. B., & Talla, P. K.
```*Nonlinear dynamics of plasma oscillations modeled by an anharmonic oscillator*. United States. doi:10.1063/1.2841032.

```
Enjieu Kadji, H. G., Laboratory of Modelling and Simulation in Engineering and Biological Physics, Faculty of Science, University of Yaounde I, Box 812, Yaounde, Nana Nbendjo, B. R., Chabi Orou, J. B., and Talla, P. K. Sat .
"Nonlinear dynamics of plasma oscillations modeled by an anharmonic oscillator". United States.
doi:10.1063/1.2841032.
```

```
@article{osti_21106163,
```

title = {Nonlinear dynamics of plasma oscillations modeled by an anharmonic oscillator},

author = {Enjieu Kadji, H. G. and Laboratory of Modelling and Simulation in Engineering and Biological Physics, Faculty of Science, University of Yaounde I, Box 812, Yaounde and Nana Nbendjo, B. R. and Chabi Orou, J. B. and Talla, P. K.},

abstractNote = {This paper considers nonlinear dynamics of plasma oscillations modeled by an anharmonic oscillator. These plasma oscillations are described by a nonlinear differential equation of the form xe+{epsilon}(1+x{sup 2})x+x+{kappa}x{sup 2}+{delta}x{sup 3}=F cos {omega}t. The amplitudes of the forced harmonic, superharmonic, and subharmonic oscillatory states are obtained using the harmonic balance technique and the multiple time scales method. Admissible values of the amplitude of the external strength are derived. Bifurcation sequences displayed by the model for each type of oscillatory states are performed numerically through the fourth-order Runge-Kutta scheme.},

doi = {10.1063/1.2841032},

journal = {Physics of Plasmas},

number = 3,

volume = 15,

place = {United States},

year = {Sat Mar 15 00:00:00 EDT 2008},

month = {Sat Mar 15 00:00:00 EDT 2008}

}

DOI: 10.1063/1.2841032

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