An analysis of phase noise and Fokker–Planck equations

A local moving orthonormal transformation has been introduced to rigorously study phase noise in stochastic differential equations (SDEs) arising from nonlinear oscillators. A general theory of phase and amplitude noise equations and its corresponding Fokker–Planck equations are derived to characterize the dynamics of phase and amplitude error. As an example, a van der Pol oscillator is considered by using the general theory.