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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 Master stability function ： ウィキペディア英語版 Master stability function In mathematics, the master stability function is a tool used to analyse the stability of the synchronous state in a dynamical system consisting of many identical oscillators which are coupled together, such as the Kuramoto model. The setting is as follows. Consider a system with $N$ identical oscillators. Without the coupling, they evolve according to the same differential equation, say $\backslash dot\_i\; =\; f(x\_i)$ where $x\_i$ denotes the state of oscillator $i$. A synchronous state of the system of oscillators is where all the oscillators are in the same state. The coupling is defined by a coupling strength $\backslash sigma$, a matrix $A\_$ which describes how the oscillators are coupled together, and a function $g$ of the state of a single oscillator. Including the coupling leads to the following equation: :$\backslash dot\_i\; =\; f(x\_i)\; +\; \backslash sigma\; \backslash sum\_^N\; A\_\; g(x\_j).$ It is assumed that the row sums $\backslash sum\_j\; A\_$ vanish so that the manifold of synchronous states is neutrally stable. The master stability function is now defined as the function which maps the complex number $z$ to the greatest Lyapunov exponent of the equation :$\backslash dot\; =\; (Df\; +\; \backslash gamma\; Dg)\; y.$ The synchronous state of the system of coupled oscillators is stable if the master stability function is negative at $\backslash sigma\; \backslash lambda\_k$ where $\backslash lambda\_k$ ranges over the eigenvalues of the coupling matrix $A$. ==References== * . * . 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「Master stability function」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.