Periodic solutions of the Van der Pol equation with moderate values of damping coefficient

An analytic approach which combines the harmonic balance method and perturbation techniques is used for calculation of the periodic solutions of the van der Pol equation with . An approximate solution which includes a few main harmonics can be found by the harmonic balance method. Then the van der Pol equation is reduced to an equivalent small parameter form. Perturbation techniques are applied to find the correction equations. These are linear differential equations and their steady-state solutions are used to calculate higher harmonics, the amplitude correction terms for the initial main harmonics, and the correction of the oscillation frequency.