Influence of Noise on the Phase and Amplitude of Second-Order Oscillators

We investigate noise effects in second-order oscillators described in terms of amplitude and phase. We show that phase noise in an oscillator is a convection-diffusion problem, i.e., noise is responsible for both phase diffusion and frequency shift. The magnitude of a noise-induced frequency shift depends on both the noise intensity and on the curvature of iscohrons, i.e., manifolds describing the phase of a nonlinear oscillator. We discuss this dependence and to what extent amplitude fluctuations can be neglected. In the case of additive noise, ignoring amplitude fluctuations gives a trivial phase macromodel that can be integrated directly, and the resulting phase variable is a Gaussian-distributed random process.