Abstract
Nonlinear oscillations and its applications in physics, chemistry, engineering, biophysics, communications are studied with some analytical, numerical and experimental methods. In the present paper, hysteresis, resonant oscillations and bifurcation mode of a system modeled by a forced modified Van der Pol-Duffing oscillator are considered. The plasma oscillations are considered and are described by a nonlinear differential equation. By using the harmonic balance technique and the multiple time scales methods, the amplitudes of the forced harmonic, superharmonic and subharmonic oscillatory states are obtained. Then, we derived admissible values of the amplitude of the external strength. Some bifurcation structures and transition to chaos of the model have been investigated. The model presented several dynamics motions which are influenced by nonlinear parameters. It can be concluded that the nonlinear parameters have a real impact on the dynamics of the model.
Highlights
The theory of oscillators has shown that many dynamics phenomena can be modeled by oscillators in engineering, biochemistry, biophysics, communications
We focus our studies on the model and equation of motion, the resonant states, the chaotic behavior through hysteresis and bifurcation mode
We have investigated hysteresis, resonant oscillations and bifurcation mode of a system modeled by a forced modified Van der Pol-Duffng oscillator
Summary
The theory of oscillators has shown that many dynamics phenomena can be modeled by oscillators in engineering, biochemistry, biophysics, communications. The paper is structured as follows: Section 2 gives the equation of motion and amplitude of the forced harmonic oscillatory states of nonlinear dynamics of plasma oscillations. The aim of this section is to find some bifurcation structures in the nonlinear dynamics of plasma oscillations described by Equation 3 for resonant states since they are of interest in this system For this purpose, we numerically solve this equation using the fourth-order Runge Kutta algorithm (Piskunov, 1980). It can be concluded that α contributes to the fractalization of the basins and accentuates the chaos in the system
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