Volume 99, Number 2, July 2012
|Number of page(s)||6|
|Published online||19 July 2012|
Global dynamics of oscillator populations under common noise
1 Department of Physics and Astronomy, Potsdam University - 14476 Potsdam-Golm, Germany, EU
2 Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Centre for Mathematical Sciences - Cambridge CB3 0WA, UK, EU
3 IFISC, CSIC-UIB - Campus UIB, 07122 Palma de Mallorca, Spain, EU
Received: 14 May 2012
Accepted: 24 June 2012
Common noise acting on a population of identical oscillators can synchronize them. We develop a description of this process which is not limited to the states close to synchrony, but provides a global picture of the evolution of the ensembles. The theory is based on the Watanabe-Strogatz transformation, allowing us to obtain closed stochastic equations for the global variables. We show that at the initial stage, the order parameter grows linearly in time, while at the later stages the convergence to synchrony is exponentially fast. Furthermore, we extend the theory to nonidentical ensembles with the Lorentzian distribution of natural frequencies and determine the stationary values of the order parameter in dependence on driving noise and mismatch.
PACS: 05.40.Ca – Noise / 05.45.Xt – Synchronization; coupled oscillators
© EPLA, 2012
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.