Abstract
In this chapter, bifurcation trees of periodic motions in a periodically forced, time-delayed, Duffing oscillator are predicted by a semi-analytical method. From the finite discrete Fourier series, harmonic frequency–amplitude curves for stable and unstable period-1 to period-4 motions are developed for a better understanding of quantity levels, singularity and catastrophes of harmonic amplitudes in the frequency domain.
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Luo ACJ, Xing S (2016) Multiple bifurcation trees of period-1 motions to chaos in a periodically forced, time-delayed, hardening Duffing oscillator. Chaos, Solitons Fractals 89:405–434
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Luo, A.C.J. (2017). Time-Delayed Duffing Oscillator. In: Memorized Discrete Systems and Time-delay. Nonlinear Systems and Complexity, vol 17. Springer, Cham. https://doi.org/10.1007/978-3-319-42778-2_5
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DOI: https://doi.org/10.1007/978-3-319-42778-2_5
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-42777-5
Online ISBN: 978-3-319-42778-2
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