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Scholarly Research Exchange / 2009 / Article

Research Article | Open Access

Volume 2009 |Article ID 854060 | 7 pages | https://doi.org/10.3814/2009/854060

Formulas for the Amplitude of the van der Pol Limit Cycle through the Homotopy Analysis Method

Received01 Sep 2008
Revised17 Feb 2009
Accepted03 Apr 2009
Published22 Apr 2009

Abstract

The limit cycle of the van der Pol oscillator, x¨+ε(x21)x˙+x=0, is studied in the plane (x,x˙) by applying the homotopy analysis method. A recursive set of formulas that approximate the amplitude and form of this limit cycle for the whole range of the parameter ε is obtained. These formulas generate the amplitude with an error less than 0.1%. To our knowledge, this is the first time where an analytical approximation of the amplitude of the van der Pol limit cycle, with validity from the weakly up to the strongly nonlinear regime, is given.

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Copyright © 2009 J. L. López et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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