Determination of periodic solution for the Helmholtz-Duffing oscillators by Hamiltonian approach and coupled homotopy-variational formulation

International Journal of Physical Sciences

Mehdi Akbarzade¹ 

关键词: Helmholtz-Duffing oscillator;    nonlinear oscillation;    analytical methods;    periodic solution.;   

DOI  :  10.5897/IJPS11.1518

学科分类：物理（综合）

来源: Academic Journals

【 摘 要 】

This paper aims to directly extend theHamiltonian approach and coupled homotopy-variational formulationto study theperiodic solutions of the Helmholtz-Duffing oscillator.The results of numerical example are presented and only a few terms are required to obtain accurate solutions. Results derived from this method are shown graphically.The behaviors of the solutions in the positive and negative directions are quite different, the asymmetric equation is separated into two auxiliary equations and the auxiliary equations are solved by two different method. Finally, the phase plane to show the stability of systems is plotted and discussed. An excellent agreement between the approximate periods with the exact period is achieved.The numerical results presented show that thesemethods arevery accurate.

【 授权许可】

CC BY