Periodic Motions and Bifurcation Trees in a Parametric Duffing Oscillator

This paper studies bifurcation trees of periodic motions in a parametric, damped Duffing oscillator. From the semi-analytic method, the corresponding differential equation is discretized to obtain the implicit mapping. From implicit mapping structure, the periodic nodes of periodic motions are computed, and the bifurcation trees of period-1 to period-4 motions are presented and the corresponding stability and bifurcation are carried out by eigenvalue analysis. From the analytical predictions, numerical simulations are completed, and the trajectory, harmonic amplitudes and phases of period-1 to period-4 motions are illustrated.