Phase model reduction for oscillatory networks subject to stochastic inputs

Oscillatory networks represent a circuit architecture for image and information processing, that can be used to realize associative and dynamic memories. Phase noise is often a limiting key factors for the performances of oscillatory networks. The ideal framework to investigate phase noise effect in nonlinear oscillators are phase models. Classical phase models lead to the conclusion that, in presence of random disturbances such as white noise, the phase noise problem is simply a diffusion process. In this paper we develop a reduced order model for phase noise analysis in nonlinear oscillators. We derive a reduced Fokker-Planck equation for the phase variable and the corresponding reduced phase equations. We show that the phase noise problem is a convection-diffusion process, proving that white noise produces both phase diffusion and frequency shift.