Entrainment in van der Pol's oscillator in the presence of noise

The response of Van der Pol's oscillator to a combination of harmonic and white noise excitations is considered. The harmonic excitation frequency is taken to be in the neighbourhood of the system limit cycle frequency. The effect of addition of noise on the entrainment behaviour is investigated using a combination of methods of stochastic averaging and equivalent nonlinearization. Results based on the gaussian closure technique are also obtained and the theoretical solutions are compared with digital simulations