Abstract
In this chapter, periodic motions in a periodically excited Duffing oscillator with a time-delayed displacement are investigated through the Fourier series, and the stability and bifurcation of such periodic motions are discussed through eigenvalue analysis.
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References
Luo, A. C. J. (2012). Continuous dynamical systems. Beijing/Glen Carbon: Higher Education Press/L&H Scientific.
Luo, A. C. J. (2013). Analytical solutions for periodic motions to chaos in dynamical systems with/without time-delay. International Journal of Dynamics and Control, 1(4), 330–350.
Luo, A. C. J., & Jin, H. X. (2014). Period-1 motion to chaos in a periodically forced, Duffing oscillator with a time-delay displacement. International Journal of Bifucration and Chaos, 24(10), 1450126.
Luo, A. C. J., & Jin, H. X. (2015). Period-3 motion to chaos in a periodically forced, Duffing oscillator with a time-delay displacement. International Journal of Dynamics and Control, 3(4), 371–388.
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Luo, A.C.J. (2017). Time-Delay Duffing Oscillators. In: Periodic Flows to Chaos in Time-delay Systems. Nonlinear Systems and Complexity, vol 16. Springer, Cham. https://doi.org/10.1007/978-3-319-42664-8_5
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DOI: https://doi.org/10.1007/978-3-319-42664-8_5
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Publisher Name: Springer, Cham
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Online ISBN: 978-3-319-42664-8
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