An Itô-Stratonovich dilemma-free treatment for nonlinear oscillators with colored noise

We present here an innovative treatment of nonlinear oscillators subject to colored noise sources, namely Lorentzian fluctuations. Exploiting averaging techniques, the full system is transformed into an equivalent oscillator with white noise sources in the limit of small noise correlation time, thus avoiding the Itô-Stratonovich ambiguity. The equivalent noisy oscillator is then transformed into a phase-amplitude model, thus simplifying phase noise analysis. The soundness of the approach is demonstrated for a 2 dimensional example.