Periodic Solutions in the van der Pol Oscillator: A Comparison

An expansion of the periodic solution of the van der Pol oscillator for small values of the damping parameter epsilon is shown via a frequency domain method and harmonic balancing technique. An approximation of the amplitude of the first harmonic and the frequency omega in terms of epsilon is obtained by an analytical form instead of the conventional algorithmic approach used before with this methodology. Its decomposition under different harmonics sin k theta and cos k theta where k = 3, 5, 7 is written in terms of their leading coefficients in power series of epsilon to make easy comparisons with other methods in the literature.