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Travelable Period-1 Motions to Chaos in a Periodically Excited Pendulum

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Regularity and Stochasticity of Nonlinear Dynamical Systems

Part of the book series: Nonlinear Systems and Complexity ((NSCH,volume 21))

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Abstract

In this chapter, the analytical bifurcation trees of travelable period-1 motions to chaos in a periodically excited pendulum will be presented with varying excitation amplitude. The analytical prediction is based on the implicit discrete maps obtained from the midpoint scheme of the corresponding differential equation. Using the discrete maps, mapping structures will be developed for various periodic motions, and analytical bifurcation trees of periodic motions to chaos can be obtained.

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Authors and Affiliations

  1. McCoy School of Engineering, Midwestern State University, Wichita Falls, TX, 76308, USA

    Yu Guo

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

    Albert C. J. Luo

Authors
  1. Yu Guo
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  2. Albert C. J. Luo
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Correspondence to Yu Guo .

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Editors and Affiliations

  1. Department of Mathematics and Statistics, Texas Tech University, Lubbock, Texas, USA

    Dimitri Volchenkov

  2. Centre de Physique Théorique, Aix-Marseille Université, Marseille, France

    Xavier Leoncini

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Guo, Y., Luo, A.C.J. (2018). Travelable Period-1 Motions to Chaos in a Periodically Excited Pendulum. In: Volchenkov, D., Leoncini, X. (eds) Regularity and Stochasticity of Nonlinear Dynamical Systems. Nonlinear Systems and Complexity, vol 21. Springer, Cham. https://doi.org/10.1007/978-3-319-58062-3_11

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  • DOI: https://doi.org/10.1007/978-3-319-58062-3_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-58061-6

  • Online ISBN: 978-3-319-58062-3

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