In this chapter, time-delay effects on periodic motions in a periodically forced, time-delayed, hardening Duffing oscillator are reviewed and further discussed. Bifurcation trees of periodic motions to chaos varying with time-delay are presented for such a time-delayed, Duffing oscillator. From the analytical prediction, periodic motions in the time-delayed, hardening Duffing oscillator are simulated numerically. Through numerical illustrations, time-delay effects on period-1 motions to chaos in nonlinear dynamical systems are strongly related to the distributions and quantity levels of harmonic amplitudes.
CITATION STYLE
Luo, A. C. J., & Xing, S. (2018). Time-delay effects on periodic motions in a duffing oscillator. In Understanding Complex Systems (pp. 77–100). Springer Verlag. https://doi.org/10.1007/978-3-319-68109-2_5
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