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

Guoqi Zhang and Zhiqiang Wu

Chaos, Solitons & Fractals, 2019, vol. 127, issue C, 342-353

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.

Keywords: Duffing oscillator; Homotopy analysis method; Dual frequency excitations; Quasi-period solution (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:127:y:2019:i:c:p:342-353

DOI: 10.1016/j.chaos.2019.07.024

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