Influence of noise intensity on the spectrum of an oscillator

This paper investigates the influence of high-intensity noise on the correlation spectrum of a two-dimensional (2-D) non-linear oscillator. An exact analytical solution for the correlation spectrum of this 2-D oscillator is provided. The analytical derivations are well suited for oscillators with white noise of any intensity, but computational constraints on the solution of the partial differential equation may make it impractical for cases where the number of state variables exceeds three. The spectral results predicted by our analytical method are verified by numerical simulations of the noisy oscillator in the time domain. We find that the peak of the oscillator spectrum shifts toward higher frequencies as the noise intensity is increased, as opposed to the fixed oscillation frequency predicted in the existing literature. This phenomenon does not appear to have been reported previously in the context of phase noise in oscillators.