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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Kuramoto model ： ウィキペディア英語版 Kuramoto model The Kuramoto model, first proposed by Yoshiki Kuramoto (蔵本 由紀 ''Kuramoto Yoshiki'') , is a mathematical model used to describe synchronization. More specifically, it is a model for the behavior of a large set of coupled oscillators . Its formulation was motivated by the behavior of systems of chemical and biological oscillators, and it has found widespread applications such as in neuroscience . Kuramoto was quite surprised when the behavior of some physical systems, namely coupled arrays of Josephson junctions followed his model.〔Steven Strogatz, ''Sync: The Emerging Science of Spontaneous Order'', Hyperion, 2003.〕 The model makes several assumptions, including that there is weak coupling, that the oscillators are identical or nearly identical, and that interactions depend sinusoidally on the phase difference between each pair of objects. == Definition == In the most popular version of the Kuramoto model, each of the oscillators is considered to have its own intrinsic natural frequency $\backslash omega\_i$, and each is coupled equally to all other oscillators. Surprisingly, this fully nonlinear model can be solved exactly, in the infinite-''N'' limit, with a clever transformation and the application of self-consistency arguments. The most popular form of the model has the following governing equations: :$\backslash frac\; =\; \backslash omega\_i\; +\; \backslash frac\; \backslash sum\_^\; \backslash sin(\backslash theta\_j\; -\; \backslash theta\_i),\; \backslash qquad\; i\; =\; 1\; \backslash ldots\; N$, where the system is composed of ''N'' limit-cycle oscillators. Noise can be added to the system. In that case, the original equation is altered to: :$$ \frac = \omega_+\zeta_+\dfrac\sum_^N\sin(\theta_-\theta_) , where $\backslash zeta\_$ is the fluctuation and a function of time. If we consider the noise to be white noise, then :$$ \langle\zeta_(t)\rangle=0 , :$$ \langle\zeta_(t)\zeta_(t')\rangle=2D\delta_\delta(t-t') with $D$ denoting the strength of noise. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Kuramoto model」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.