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Time-Delay Effects on Periodic Motions in a Duffing Oscillator

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Chaotic, Fractional, and Complex Dynamics: New Insights and Perspectives

Part of the book series: Understanding Complex Systems ((UCS))

Abstract

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.

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Author information

Authors and Affiliations

  1. Department of Mechanical and Industrial Engineering, Southern Illinois University Edwardsville, Edwardsville, IL, 62026-1805, USA

    Albert C. J. Luo & Siyuan Xing

Authors
  1. Albert C. J. Luo
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  2. Siyuan Xing
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Corresponding author

Correspondence to Albert C. J. Luo .

Editor information

Editors and Affiliations

  1. Stern College for Women, Yeshiva University, New York, New York, USA

    Mark Edelman

  2. INPE/LAC, Instituto Nacional de Pesquisas Espaciai, São José dos Campos, São Paulo, Brazil

    Elbert E. N. Macau

  3. Departamento de Fisica, Universidad Rey Juan Carlos, Móstoles, Madrid, Spain

    Miguel A. F. Sanjuan

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Luo, A.C.J., Xing, S. (2018). Time-Delay Effects on Periodic Motions in a Duffing Oscillator. In: Edelman, M., Macau, E., Sanjuan, M. (eds) Chaotic, Fractional, and Complex Dynamics: New Insights and Perspectives. Understanding Complex Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-68109-2_5

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