Nonlinear dynamics of system oscillations modeled by a forced Van der Pol generalized oscillator

摘要

This paper considers the oscillations modeled by a forced Van der Polgeneralized oscillator. These oscillations are described by a nonlineardifferential equation of the form $\ddot{x}+x-\varepsilon\left(1-ax^2-b\dot{x}^2\right)\dot{x}=E\sin{{\Omega}t}.$The amplitudes of the forced harmonic, primary resonance superharmonic andsubharmonic oscillatory states are obtained using the harmonic balancetechnique and the multiple time scales methods. We obtain also the hysteresisand jump phenomena in the system oscillations. Bifurcation sequences displayedby the model for each type of oscillatory states are performed numericallythrough the fourth-order Runge- Kutta scheme.