{"title":"Application of He\u2019s Parameter-Expansion Method to a Coupled Van Der Pol oscillators with Two Kinds of Time-delay Coupling","authors":"Mohammad Taghi Darvishi, Samad Kheybari","volume":50,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":145,"pagesEnd":151,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/7039","abstract":"
In this paper, the dynamics of a system of two van der Pol oscillators with delayed position and velocity is studied. We provide an approximate solution for this system using parameterexpansion method. Also, we obtain approximate values for frequencies of the system. The parameter-expansion method is more efficient than the perturbation method for this system because the method is independent of perturbation parameter assumption.<\/p>\r\n","references":"[1] J.H. He, Variational iteration method-a kind of non-linear analytical\r\ntechnique: some examples, Int. J. Non-linear Mech. 34(4) (1999) 699-\r\n708.\r\n[2] M.T. Darvishi, F. Khani, A.A. Soliman, The numerical simulation for stiff\r\nsystems of ordinary differential equations, Comput. Math. Appl. 54(7-8)\r\n(2007) 1055-1063.\r\n[3] M.T. Darvishi, F. Khani, Numerical and explicit solutions of the fifth-order\r\nKorteweg-de Vries equations, Chaos, Solitons and Fractals 39 (2009)\r\n2484-2490.\r\n[4] S. Abbasbandy, M.T. 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