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Dynamics of Duffing-Holmes oscillator with fractional order nonlinearity

Author

Listed:
  • Khaled Aledealat

    (Physics Department, Jordan University of Science and Technology)

  • Abdalla Obeidat

    (Physics Department, Jordan University of Science and Technology)

  • Maen Gharaibeh

    (Physics Department, Jordan University of Science and Technology)

  • Adnan Jaradat

    (Physics Department, Jordan University of Science and Technology)

  • Khitam Khasawinah

    (Physics Department, Yarmouk University)

  • Mohammad-Khair Hasan

    (Physics Department, Jordan University of Science and Technology)

  • Akram Rousan

    (Physics Department, Jordan University of Science and Technology)

Abstract

In this work, the dynamics of Duffing-Holmes oscillator with fractional order nonlinearity is explored. Basically, a fractional spatial derivative is introduced to the cubic term, and the order of the derivative α is varied between zero and two. The evolution of the dynamics of the system from nonlinear behavior to linear behavior is investigated using multiple tools such as phase portraits, Poincare maps, and bifurcation diagrams. We have demonstrated that as α increases the system can alternate between chaotic and periodic states depending on the parameters setting. However, the overall impact transforms the system into simpler dynamics and eventually causes the chaotic regions to fade out regardless of the system settings. The largest α at which the system still exhibits chaotic behavior is estimated to be around 1.17 and for transient chaos is estimated to be 1.25. Graphical abstract

Suggested Citation

  • Khaled Aledealat & Abdalla Obeidat & Maen Gharaibeh & Adnan Jaradat & Khitam Khasawinah & Mohammad-Khair Hasan & Akram Rousan, 2019. "Dynamics of Duffing-Holmes oscillator with fractional order nonlinearity," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 92(10), pages 1-6, October.
    • Handle: RePEc:spr:eurphb:v:92:y:2019:i:10:d:10.1140_epjb_e2019-100299-8
    DOI: 10.1140/epjb/e2019-100299-8
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