Nonlinear dynamics of plasma oscillations modeled by a forced modified Van der Pol-Duffing oscillator

Understand

This paper considers nonlinear dynamics of plasma oscillations modeled by a forced modified Van der Pol-Duffing oscillator.

• These plasma oscillations are described by a nonlinear differential equation of the form $ \ddot{x}+ \epsilon (1 +{x}^{2}){\dot{x}} + x+ \alpha \epsilon{x}{\dot{x}} + {\beta}x^{2}+\gamma x^{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 methods.
• Bifurcation sequences displayed by the model for each type of oscillatory states are performed numerically through the fourth order Runge- Kutta scheme.
• The influences of the differents parameters and of amplitude of external forced have been found.