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Parametric Perturbations of a Duffing–Type Equation with Nonmonotonic Rotation

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Mathematical Modeling and Supercomputer Technologies (MMST 2023)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1914))

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Abstract

Quasiperiodic parametric perturbations of a Duffing–type equation with nonmonotonic rotation are studied. It is assumed that the perturbations are nonconservative. The solutions behavior in the neighborhood of nearly degenerate resonance levels of energy is described and conditions for the existence of new resonance three–dimensional invariant tori in the extended phase space are found. Bifurcations that lead to the appearance of these solutions are also studied.

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Notes

  1. 1.

    Details on action–angle variables can be found in [11].

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Acknowledgements

Authors acknowledge a financial support from the Russian Science Foundation [grant 24–21–00050]. Numerical simulations of the paper were supported by the Ministry of Science and Higher Education of the Russian Federation [grant FSWR-2020-0036]. K.E. Morozov was partially supported by the RSciF [grant number 19–11–00280] (Section 3, Theorem 2).

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Authors and Affiliations

  1. Lobachevsky State University of Nizniy Novgorod, Nizniy Novgorod, Russia

    K. E. Morozov & A. D. Morozov

Authors
  1. K. E. Morozov
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  2. A. D. Morozov
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Correspondence to K. E. Morozov .

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Editors and Affiliations

  1. Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia

    Dmitry Balandin

  2. Lobachevsky State University, Nizhny Novgorod, Russia

    Konstantin Barkalov

  3. Lobachevsky State University, Nizhny Novgorod, Russia

    Iosif Meyerov

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Morozov, K.E., Morozov, A.D. (2024). Parametric Perturbations of a Duffing–Type Equation with Nonmonotonic Rotation. In: Balandin, D., Barkalov, K., Meyerov, I. (eds) Mathematical Modeling and Supercomputer Technologies. MMST 2023. Communications in Computer and Information Science, vol 1914. Springer, Cham. https://doi.org/10.1007/978-3-031-52470-7_7

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  • DOI: https://doi.org/10.1007/978-3-031-52470-7_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-52469-1

  • Online ISBN: 978-3-031-52470-7

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