On Complex Periodic Motions in a Time-Delayed, Double-Well Duffing Oscillator With Strong Excitation
The time-delayed double-well Duffing oscillator is extensively applied in engineering and particle physics. Determination of periodic motions in such a system is significant. Thus, in this paper, period-1 motions in the time-delayed double-well Duffing oscillator are discussed through a semi-analytical method. The semi-analytical method is based on the implicit mappings constructed by discretization of the corresponding differential equation. Complex period-1 motions are predicted and the corresponding stability and bifurcation analysis are completed. From predictions, complex periodic motions are simulated numerically, and the harmonic amplitudes and phases are presented. Through this study, the complexity of periodic motions in the time-delayed Duffing oscillator can be better understood.