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- W2009659872 abstract "Abstract The limit cycle of the Duffing–van der Pol equation x ¨ + x + e ( x 2 - 1 ) x ˙ + δ x 3 = 0 is studied. By considering the product of the frequency ω of the limit cycle and the coefficient e as an independent parameter μ = e ω , an equivalent equation is obtained and then solved by Liao’s homotopy analysis method. The frequency ω is deduced as a function of μ and δ . This function provides us with an algebraic equation for ω , according to which we have an analytical approximation for the frequency. Numerical examples show that the attained approximation is very accurate. More importantly, the results are uniformly valid for all positive values of e ." @default.
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- W2009659872 date "2009-10-01" @default.
- W2009659872 modified "2023-09-25" @default.
- W2009659872 title "Uniformly valid solution of limit cycle of the Duffing–van der Pol equation" @default.
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- W2009659872 doi "https://doi.org/10.1016/j.mechrescom.2009.06.001" @default.
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