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 [Formula: see text] is shown via a frequency domain method and harmonic balancing technique. An approximation of the amplitude of the first harmonic and the frequency [Formula: see text] in terms of [Formula: see text] is obtained by an analytical form instead of the conventional algorithmic approach used before with this methodology. Its decomposition under different harmonics [Formula: see text] and [Formula: see text] where [Formula: see text] is written in terms of their leading coefficients in power series of [Formula: see text] to make easy comparisons with other methods in the literature.