ON THE 3RD SUPERHARMONIC RESONANCE IN THE DUFFING OSCILLATOR

The third order superharmonic resonance in two versions of a harmonically excited Duffing oscillator is investigated by analytical and numerical methods. It is shown that even in situations for which a non-linear oscillator may be though a priori to satisfy the 'small perturbation' requirements, the analytical results obtained by the amplitude-expansion method of perturbation analysis may lead to incomplete and/or erroneous results. For harmonically excited, non-linear oscillators, equivalence of the approximate solutions obtained by two fundamentally different perturbation schemes is questioned: and for the Duffing-Ueda oscillator, it is shown that a sudden transition into chaos is the results of a saddle-node bifurcation of the third superharmonic response; and a sudden transition out of chaos is the result of a boundary crisis. © 1994 Academic Press Limited.