Nonlinear dynamics of plasma oscillations modeled by an anharmonic oscillator

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 x+e(1+x2)x+x+κx2+δx3=FcosΩt. 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.

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