کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1897084 1044487 2009 9 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Synchronization of a large number of continuous one-dimensional stochastic elements with time-delayed mean-field coupling
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
Synchronization of a large number of continuous one-dimensional stochastic elements with time-delayed mean-field coupling
چکیده انگلیسی

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. For a large number of one-dimensional continuous stochastic elements coupled non-homogeneously through the mean field with delay we developed an approach to find a boundary of synchronization domain and the frequency of the mean-field oscillations on it. Namely, the 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 in the mean-field behavior are observed in the stochastic network at finite noise intensities. In the limit of small noise intensities the critical coupling strength is shown to remain finite, provided that the delay in the coupling function is not infinitely small. Delay in the coupling term can be used as a control parameter that manipulates the location of the synchronization threshold.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Physica D: Nonlinear Phenomena - Volume 238, Issue 2, 15 January 2009, Pages 175–183
نویسندگان
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