Response of Van Der Pol's oscillator to random excitation

This paper considers the response of Van der Pol's oscillator to random excitation. It is shown that the output of the oscillator consists of a periodic term, plus a narrow band noise term centered at the natural frequency of the oscillator. The root-mean-square amplitude of this noise term is shown to be proportional to the square root of the spectral density of the excitation, and inversely proportional to the amplittude of self-oscillation.