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

J. L. López, S. Abbasbandy, R. López-Ruiz
2009 Scholarly Research Exchange  
The limit cycle of the van der Pol oscillator,ẍ + ε(x 2 − 1)ẋ + x = 0, is studied in the plane (x,ẋ) 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
more » ... akly up to the strongly nonlinear regime, is given.
doi:10.3814/2009/854060 fatcat:qkfbwkyp4ff37lc3ffq3qshhwm