Bifurcation Dynamics of Periodic Motions in a Duffing Oscillator under Multiple Periodic Excitations
DOI:
https://doi.org/10.5890/JVTSD.2026.06.007Abstract
In this paper, periodic motions in a Duffing oscillator under two external periodic forces are obtained through the corresponding discrete implicit maps. Using specific mapping structure, the bifurcation trees of periodic motions to chaos are developed semi-analytically, and the corresponding stability and bifurcation analysis of periodic motions are carried out through the corresponding eigenvalue analysis. From discrete nodes on periodic motions, the frequency-amplitude characteristics of periodic motions are computed through the discrete Fourier series, and the bifurcation trees of periodic motions are also presented through frequency-amplitude curves. For a better understanding of periodic motions in nonlinear systems under multiple excitations, numerical illustrations of period-2 and period-4 motions are presented.References
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