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The asymptotic amplitudes for a three-parameter oscillator has been determined both analytically and numerically. The differential equation representing the oscillator establishes a generalization of both the van der Pol equation and the so called Scott- Murata equation. Moreover, the limit cycle behavior for a wide set of the involved parameters has been illustrated. For large nonlinearities, it resulted that the autooscillation amplitude is a smooth function of the parameters representing the properties of the amplifier. With these conditions a characteristic similarity of the limit cycles has also been shown.