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Chaotic Dynamics of an Extended Duffing Oscillator Under Periodic Excitation

Received: 29 June 2018     Accepted: 12 July 2018     Published: 6 August 2018
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Abstract

In this paper, chaotic dynamics of a cubic-quintic-septic Duffing oscillator subjected to periodic excitation is investigated. The multiple scales method is used to determine the various resonance states of the model. It is found that the considered model posses thirteen resonance states whose seven are thoroughly studied. The steady-state solutions and theirs stabilities are determined. The frequency-amplitude curves show that the considered system presents mixed behavior, limit cycles, hysteresis, jump and bifurcation phenomena. It is also noticed that these phenomena are strongly influenced by quintic-septic nonlinearity and excitation amplitude. Bifurcation structures displayed by the model for each considered type of resonant states are investigated numerically using the fourth-order Runge-Kutta algorithm. As results, the quintic-septic nonlinearity, linear dissipation and excitation amplitude can be used to control the chaotic behavior of the system.

Published in World Journal of Applied Physics (Volume 3, Issue 2)
DOI 10.11648/j.wjap.20180302.13
Page(s) 34-50
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2018. Published by Science Publishing Group

Keywords

Extended Duffing Oscillator, Resonance States, Stability, Limit Cycles, Bifurcation and Jump Phenomena, Periodic and Quasi-periodic Oscillations, Chaos

References
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Cite This Article
  • APA Style

    Hervé Lucas Koudahoun, Yélomè Judicaël Fernando Kpomahou, Jean Akande, Damien Kêgnidé Kolawolé Adjaï. (2018). Chaotic Dynamics of an Extended Duffing Oscillator Under Periodic Excitation. World Journal of Applied Physics, 3(2), 34-50. https://doi.org/10.11648/j.wjap.20180302.13

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    ACS Style

    Hervé Lucas Koudahoun; Yélomè Judicaël Fernando Kpomahou; Jean Akande; Damien Kêgnidé Kolawolé Adjaï. Chaotic Dynamics of an Extended Duffing Oscillator Under Periodic Excitation. World J. Appl. Phys. 2018, 3(2), 34-50. doi: 10.11648/j.wjap.20180302.13

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    AMA Style

    Hervé Lucas Koudahoun, Yélomè Judicaël Fernando Kpomahou, Jean Akande, Damien Kêgnidé Kolawolé Adjaï. Chaotic Dynamics of an Extended Duffing Oscillator Under Periodic Excitation. World J Appl Phys. 2018;3(2):34-50. doi: 10.11648/j.wjap.20180302.13

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  • @article{10.11648/j.wjap.20180302.13,
      author = {Hervé Lucas Koudahoun and Yélomè Judicaël Fernando Kpomahou and Jean Akande and Damien Kêgnidé Kolawolé Adjaï},
      title = {Chaotic Dynamics of an Extended Duffing Oscillator Under Periodic Excitation},
      journal = {World Journal of Applied Physics},
      volume = {3},
      number = {2},
      pages = {34-50},
      doi = {10.11648/j.wjap.20180302.13},
      url = {https://doi.org/10.11648/j.wjap.20180302.13},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.wjap.20180302.13},
      abstract = {In this paper, chaotic dynamics of a cubic-quintic-septic Duffing oscillator subjected to periodic excitation is investigated. The multiple scales method is used to determine the various resonance states of the model. It is found that the considered model posses thirteen resonance states whose seven are thoroughly studied. The steady-state solutions and theirs stabilities are determined. The frequency-amplitude curves show that the considered system presents mixed behavior, limit cycles, hysteresis, jump and bifurcation phenomena. It is also noticed that these phenomena are strongly influenced by quintic-septic nonlinearity and excitation amplitude. Bifurcation structures displayed by the model for each considered type of resonant states are investigated numerically using the fourth-order Runge-Kutta algorithm. As results, the quintic-septic nonlinearity, linear dissipation and excitation amplitude can be used to control the chaotic behavior of the system.},
     year = {2018}
    }
    

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  • TY  - JOUR
    T1  - Chaotic Dynamics of an Extended Duffing Oscillator Under Periodic Excitation
    AU  - Hervé Lucas Koudahoun
    AU  - Yélomè Judicaël Fernando Kpomahou
    AU  - Jean Akande
    AU  - Damien Kêgnidé Kolawolé Adjaï
    Y1  - 2018/08/06
    PY  - 2018
    N1  - https://doi.org/10.11648/j.wjap.20180302.13
    DO  - 10.11648/j.wjap.20180302.13
    T2  - World Journal of Applied Physics
    JF  - World Journal of Applied Physics
    JO  - World Journal of Applied Physics
    SP  - 34
    EP  - 50
    PB  - Science Publishing Group
    SN  - 2637-6008
    UR  - https://doi.org/10.11648/j.wjap.20180302.13
    AB  - In this paper, chaotic dynamics of a cubic-quintic-septic Duffing oscillator subjected to periodic excitation is investigated. The multiple scales method is used to determine the various resonance states of the model. It is found that the considered model posses thirteen resonance states whose seven are thoroughly studied. The steady-state solutions and theirs stabilities are determined. The frequency-amplitude curves show that the considered system presents mixed behavior, limit cycles, hysteresis, jump and bifurcation phenomena. It is also noticed that these phenomena are strongly influenced by quintic-septic nonlinearity and excitation amplitude. Bifurcation structures displayed by the model for each considered type of resonant states are investigated numerically using the fourth-order Runge-Kutta algorithm. As results, the quintic-septic nonlinearity, linear dissipation and excitation amplitude can be used to control the chaotic behavior of the system.
    VL  - 3
    IS  - 2
    ER  - 

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Author Information
  • Department of Physics, University of Abomey-Calavi, Abomey-Calavi, Benin

  • Department of Physics, University of Abomey-Calavi, Abomey-Calavi, Benin

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