Differential equations to represent electronic amplifier oscillators have been developed by van der Pol and Scott using a cubic and an arctangent approximation for the amplifier transfer characteristic, respectively. Using a piecewise linear approximation for the transfer characteristic results in more accurate solutions, independently of the amplitude of the oscillations and does not require to determine the coefficients for the approximations, usually a difficult problem.
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R.M. Iñigo (1975) studied this question.