Periodic solution of the Duffing-Van der Pol oscillator by homotopy perturbation method

Abstract

In this paper, the homotopy perturbation method proposed by J.-H. He is adopted for determining the limit cycle motion of the Duffing-Van der Pol oscillator. Approximate analytic solving methods based on homotopy and Jacobian elliptic functions are introduced. Three types of strongly nonlinear Duffing-Van der Pol oscillator equation with f(x, [xdot])=(1−x ²−[xdot] ²)[xdot] are studied in detail. The relation between the amplitude and frequency and modulus of the elliptic function is obtained.

Keywords:

• homotopy
• He's homotopy perturbation method
• Jacobian elliptic function
• Duffing-Van der Pol oscillator
• periodic solution

2000 AMS Subject Classifications :

• 34E05
• 34E10

Acknowledgements

The authors wish to thank the anonymous reviewers for their helpful comments and suggestions. This work was supported by the Science Foundation of Guangxi (0832244) and Science Foundation of the Education Office of Guangxi Province (D2008007).