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

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, ẋ)=(1−x 2−ẋ 2)ẋ are studied in detail. The relation between the amplitude and frequency and modulus of the elliptic function is obtained.

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