Stroboscopic Phase Portrait of a Forced Nonlinear Oscillator

Abstract

The computer simulation on the behaviour of a forced nonlinear oscillator is extended to cases of nonfundamental bands of entrainment and of strong excitation. As a result an extensive phase diagram is obtained including the regions of harmonic cascade of bifurcations and of chaotic decolation, in addition to those of various bands for entrainment and the quasi-periodic oscillation. The transition between different regions in the phase diagram, in particular that between quasi-periodic motion and subharmonic entrainment, has been investigated quantitatively by the method of Fourier analysis. Three kinds of transition have been found.