The 12 subharmonic resonance and its transition to chaotic motion in a non-linear oscillator

Abstract A theoretical study of periodic solutions, their local stability and period doubling bifurcations in a non-linear oscillator made by the aid of approximate analytical methods is completed by a computer simulation analysis to verify theoretical results and observe chaotic behaviour. Thus the chaotic motion is observed against a background of the classical resonance curves, stability limits and jump phenomena. It has been shown that the chaotic motion appears in the neighbourhood of the stability limit of the 1 2 subharmonic resonance and forms a transition zone between the subharmonic and principal resonance solution. Because the averaged power spectrum in this case shows only one narrow continuous segment, an essence of an irregularity of the motion has been roughly interpreted as random-like fluctuation of the amplitude and frequency of the 1 2 subharmonic component.