Bifurcations of the van der Pol-Duffing oscillator

The incremental harmonic balance method has proved to be an efficient tool for computing periodic oscillations in the analysis of nonlinear dynamical systems. It was developed into a form that enables the computing of steady-state periodic response with a dependence on various variable parameters. When the bifurcation process follows a sequence of period doublings, then the periodic response is composed of subharmonic solutions of higher orders. When no more subharmonic solutions exist in the process of periodic doublings, then the periodic response becomes chaotic. The changing of the amplitudes of the periodic oscillation in dependence of the variable system parameters and the possible transition into chaos is shown in bifurcation diagrams. A general procedure for the construction of a bifurcation diagram is the used in van der Pol-Duffing oscillator for various kinds of parameters. It is proved that the van der Pol-Duffing oscillator possesses various kinds of bifurcations, which can be analyzed by using suitable strategies. (C) 2003 Journal of Mechanical Engineering. All rights reserved.