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Homotopy analysis method for approximations of Duffing oscillator with dual frequency excitations

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  • Zhang, Guoqi
  • Wu, Zhiqiang

Abstract

In this paper, the classical Duffing oscillator under dual frequency excitations is studied by the homotopy analysis method(HAM). Analytical study of the low-order approximations is firstly conducted and the saddle node(SN) bifurcation boundary for the initial guess solution is obtained. The maximum value bifurcation plot of the high order approximations with the bifurcation parameters f1 and λ1 are obtained and compared with the numerical solutions based on the Runge–Kutta method. The results show that the initial guess solution can qualitatively reflect the trend of the numerical solution, and the high order approximations agree well with the numerical solutions. The maximum value bifurcation plots of high order approximations show periodic and quasi-periodic solutions, which agree well with the numerical ones.

Suggested Citation

  • Zhang, Guoqi & Wu, Zhiqiang, 2019. "Homotopy analysis method for approximations of Duffing oscillator with dual frequency excitations," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 342-353.
    • Handle: RePEc:eee:chsofr:v:127:y:2019:i:c:p:342-353
    DOI: 10.1016/j.chaos.2019.07.024
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    References listed on IDEAS

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    1. Li, Xian-Feng & Chu, Yan-Dong & Leung, Andrew Y.T. & Zhang, Hui, 2017. "Synchronization of uncertain chaotic systems via complete-adaptive-impulsive controls," Chaos, Solitons & Fractals, Elsevier, vol. 100(C), pages 24-30.
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    Cited by:

    1. Zhu, Jue & Yuan, Wei-bin & Li, Long-yuan, 2021. "Cross-sectional flattening-induced nonlinear damped vibration of elastic tubes subjected to transverse loads," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).

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