Amplitude and phase dynamics of noisy oscillators

摘要

A description in terms of phase and amplitude variables is given for nonlinear oscillators subject to white Gaussian noise described by Ito stochastic differential equations. The stochastic differential equations derived for the amplitude and the phase are rigorous, and their validity is not limited to the weak noise limit. It is shown that if Floquet vectors are used, then in the neighborhood of a limit cycle the phase variable coincides with the asymptotic phase defined through isochrons. Two techniques for the analysis of the phase and amplitude equations are discussed, that is, asymptotic expansion method and a phase reduction procedure based on projection operators technique. Formulas for the expected angular frequency, expected oscillation amplitude, and amplitude variance are derived using Ito calculus. Copyright (c) 2016 John Wiley & Sons, Ltd.