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Synchronization of a large number of continuous one-dimensional stochastic elements with time delayed mean field coupling

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journal contribution
posted on 22.07.2013, 11:51 authored by Andrey Pototsky, Natalia JansonNatalia Janson
We study synchronization as a means of control of collective behavior of an ensemble of coupled stochastic units in which oscillations are induced merely by external noise. We determine the boundary of the synchronization domain of a large number of onedimensional continuous stochastic elements with time delayed non-homogeneous mean-field coupling. Exact location of the synchronization threshold is shown to be a solution of the boundary value problem (BVP) which was derived from the linearized Fokker-Planck equation. Here the synchronization threshold is found by solving this BVP numerically. Approximate analytics is obtained by expanding the solution of the linearized Fokker-Planck equation into a series of eigenfunctions of the stationary Fokker-Planck operator. Bistable systems with a polynomial and piece-wise linear potential are considered as examples. Multistability and hysteresis is observed in the Langevin equations for finite noise intensity. In the limit of small noise intensities the critical coupling strength was shown to remain finite.

History

School

  • Science

Department

  • Mathematical Sciences

Citation

POTOTSKY, A. and JANSON, N.B., 2009. Synchronization of a large number of continuous one-dimensional stochastic elements with time delayed mean field coupling. Physica D: Nonlinear Phenomena, 238 (2), pp.175-183.

Publisher

© Elsevier

Version

AM (Accepted Manuscript)

Publication date

2009

Notes

This article was accepted for publication in the journal Physica D: Nonlinear Phenomena, and the definitive version can be found at: http://dx.doi.org/10.1016/j.physd.2008.09.010

ISSN

0167-2789

Language

en