# Colored noise in oscillators. Phase-amplitude analysis and a method to avoid the Ito-Stratonovich dilemma

## TL;DR

This paper analyzes how colored noise affects oscillator phase fluctuations, introduces a transformation method to handle the Ito-Stratonovich dilemma, and improves phase noise modeling accuracy.

## Contribution

It presents a novel transformation technique to convert colored noise into white noise for better phase noise analysis in oscillators.

## Key findings

- Phase noise is a drift-diffusion process influenced by noise variance and correlation time.
- The method reduces modeling errors compared to previous phase reduced models.
- A new approach avoids the Ito-Stratonovich dilemma in stochastic oscillator analysis.

## Abstract

We investigate the effect of time-correlated noise on the phase fluctuations of nonlinear oscillators. The analysis is based on a methodology that transforms a system subject to colored noise, modeled as an Ornstein-Uhlenbeck process, into an equivalent system subject to white Gaussian noise. A description in terms of phase and amplitude deviation is given for the transformed system. Using stochastic averaging technique, the equations are reduced to a phase model that can be analyzed to characterize phase noise. We find that phase noise is a drift-diffusion process, with a noise-induced frequency shift related to the variance and to the correlation time of colored noise. The proposed approach improves the accuracy of previous phase reduced models.