The European Physical Journal Special Topics

, Volume 225, Issue 1, pp 171–186 | Cite as

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

  • M. BonninEmail author
  • F. Corinto
  • V. Lanza
Regular Article Synchronization, Control and Dynamics of Chaotic Models
Part of the following topical collections:
  1. Synchronization and Control in Time-Delayed Complex Networks and Spatio-Temporal Patterns


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.


Chaotic System European Physical Journal Special Topic Noise Intensity Couple Oscillator Amplitude Deviation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© EDP Sciences and Springer 2016

Authors and Affiliations

  1. 1.Politecnico di Torino, Department of Electronics and TelecommunicationsTurinItaly
  2. 2.Normandie Univ. ULH, LMAH, CNRS 3335, ISCNLe HavreFrance

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