Publication Type:

Journal Article

Source:

Physica Scripta, Volume 89, Number 7 (2014)

URL:

http://www.scopus.com/inward/record.url?eid=2-s2.0-84903584277&partnerID=40&md5=0192e833832ac8b0293563ffd0c38977

Keywords:

limit Cycle solutions, modified HAM, nonlinear oscillators, quasi-periodic solutions

Abstract:

In this paper we propose a technique to obtain limit cycles and quasi-periodic solutions of forced nonlinear oscillators. We apply this technique to the forced Van der Pol oscillator and the forced Van der Pol Duffing oscillator and obtain for the first time their limit cycles (periodic) and quasi-periodic solutions analytically. We introduce a modification of the homotopy analysis method to obtain these solutions. We minimize the square residual error to obtain accurate approximations to these solutions. The obtained analytical solutions are convergent and agree well with numerical solutions even at large times. Time trajectories of the solution, its first derivative and phase plots are presented to confirm the validity of the proposed approach. We also provide rough criteria for the determination of parameter regimes which lead to limit cycle or quasi-periodic behaviour. © 2014 The Royal Swedish Academy of Sciences.

Cite this Research Publication

A.K. Shukla, Ramamohan, T. R., and Srinivas, S., “A new analytical approach for limit cycles and quasi-periodic solutions of nonlinear oscillators: The example of the forced Van der Pol Duffing oscillator”, Physica Scripta, vol. 89, 2014.