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

Abstract

This paper considers the oscillations of system modeled by a forced Van der Pol generalized oscillator. These oscillations are described by a nonlinear differential equation. The amplitudes of the forced harmonic, primary resonance super-harmonic and sub-harmonic oscillatory states are obtained using the harmonic balance technique and the multiple time scales methods. Hysteresis and jump phenomena in the system oscillations are obtained. Bifurcation sequences displayed by the model for each type of oscillatory states are performed numerically through the fourth-order Runge-Kutta scheme.