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

Fu, H. X.; Qian, Y. H.

Int. J. Bifurcation Chaos Appl. Sci. Eng. 28, No. 4, Article ID 1850049, 11 p. (2018).

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:

BVPh

References:

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