Periodic Solutions in the van der Pol Oscillator: A Comparison

Abstract

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