We study the statistical response of stochastic nonlinear radial oscillations of self-gravitating poly-, tropic masses, assuming the small-scale turbulence to be representable by a Gaussian white noise. For highly nonlinear radial oscillator systems with dissipation proportional to velocity, we observe (ⅰ) the variance of the response to be the same as that of the linear oscillator with low values of the noise strength parameter D, (ⅱ) that for larger values of D the power spectra suggest a widening of the bandwidth of the fundamental mode and also a slight shift of the power peak toward higher frequencies, and (ⅲ) that various statistical moments of dynamical variables depend on the polytropic index, n. For noisy self-excited nonlinear oscillations in a given polytrope, on the other hand, no appreciable change in the variance occurs with an increase in D. The peak power of the principal mode shifts toward higher frequencies due to the presence of nonlinear terms in the stiffness part of the oscillator. Furthermore, the increase in noise strength parameter D not only increases the bandwidth but also lowers the peak power of the principal mode and related harmonics. This is shown to be caused primarily by the increase in random dephasing of the trajectories brought about by the increase in the noise level.
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