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**Study on a multi-frequency homotopy analysis method for period-doubling solutions of nonlinear systems.**
*(English)*
Zbl 1391.34034

Summary: In this paper, a modification of homotopy analysis method (HAM) is applied to study the two-degree-of-freedom coupled Duffing system. Firstly, the process of calculating the two-degree-of-freedom coupled Duffing system is presented. Secondly, the single periodic solutions and double periodic solutions are obtained by solving the constructed nonlinear algebraic equations. Finally, comparing the periodic solutions obtained by the multi-frequency homotopy analysis method (MFHAM) and the fourth-order Runge-Kutta method, it is found that the approximate solution agrees well with the numerical solution.

### MSC:

34A45 | Theoretical approximation of solutions to ordinary differential equations |

34C15 | Nonlinear oscillations and coupled oscillators for ordinary differential equations |

37C60 | Nonautonomous smooth dynamical systems |

34C25 | Periodic solutions to ordinary differential equations |

34C23 | Bifurcation theory for ordinary differential equations |

### Keywords:

multi-frequency homotopy analysis method; Duffing system; period-doubling; approximation solution### Software:

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\textit{H. X. Fu} and \textit{Y. H. Qian}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 28, No. 4, Article ID 1850049, 11 p. (2018; Zbl 1391.34034)

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### References:

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