Academic Journals Database
Disseminating quality controlled scientific knowledge

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

Author(s): J. L. López | S. Abbasbandy | R. López-Ruiz

Journal: Scholarly Research Exchange
ISSN 1687-8299

Volume: 2009;
Date: 2009;
Original page

The limit cycle of the van der Pol oscillator, x¨+ε(x2−1)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.

HR software für Hotellerie

Automatische Erstellung
von Personaldokumente
und Anmeldungen bei Behörden

RPA Switzerland

RPA Switzerland

Robotic process automation