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A mathematical framework for amplitude and phase noise analysis of coupled oscillators

  • Regular Article
  • Synchronization, Control and Dynamics of Chaotic Models
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Abstract

Synchronization 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.

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Authors and Affiliations

  1. Politecnico di Torino, Department of Electronics and Telecommunications, Corso Duca degli Abruzzi 24, 10129, Turin, Italy

    M. Bonnin & F. Corinto

  2. Normandie Univ. ULH, LMAH, CNRS 3335, ISCN, 25 rue Philippe Lebon, 76600, Le Havre, France

    V. Lanza

Authors
  1. M. Bonnin
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  2. F. Corinto
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  3. V. Lanza
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Correspondence to M. Bonnin.

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Bonnin, M., Corinto, F. & Lanza, V. A mathematical framework for amplitude and phase noise analysis of coupled oscillators. Eur. Phys. J. Spec. Top. 225, 171–186 (2016). https://doi.org/10.1140/epjst/e2016-02617-8

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  • DOI: https://doi.org/10.1140/epjst/e2016-02617-8

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