https://hal-normandie-univ.archives-ouvertes.fr/hal-02047749Bonnin, MicheleMicheleBonninDET - Department of Electronics and Telecommunications [Torino] - Polito - Politecnico di Torino = Polytechnic of Turin Corinto, FernandoFernandoCorintoDET - Department of Electronics and Telecommunications [Torino] - Polito - Politecnico di Torino = Polytechnic of Turin Lanza, ValentinaValentinaLanzaLMAH - Laboratoire de Mathématiques Appliquées du Havre - ULH - Université Le Havre Normandie - NU - Normandie UniversitéA mathematical framework for amplitude and phase noise analysis of coupled oscillatorsHAL CCSD2016Chaotic SystemEuropean Physical Journal Special TopicNoise IntensityAmplitude DeviationCouple Oscillator[MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS]Lanza, Valentina2019-02-25 11:09:012022-04-01 13:40:012019-02-25 11:09:01enJournal articles10.1140/epjst/e2016-02617-81Synchronization of coupled oscillators is a paradigm for complexity in many areas of science and engineering. Any realistic network model should include noise effects. We present a description in terms of phase and amplitude deviation for nonlinear oscillators coupled together through noisy interactions. In particular, the coupling is assumed to be modulated by white Gaussian noise. The equations derived for the amplitude deviation and the phase are rigorous, and their validity is not limited to the weak noise limit. We show that using Floquet theory, a partial decoupling between the amplitude and the phase is obtained. The decoupling can be exploited to describe the oscillator’s dynamics solely by the phase variable. We discuss to what extent the reduced model is appropriate and some implications on the role of noise on the frequency of the oscillators.