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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 Brusselator ： ウィキペディア英語版 Brusselator The Brusselator is a theoretical model for a type of autocatalytic reaction. The Brusselator model was proposed by Ilya Prigogine and his collaborators at the Université Libre de Bruxelles.〔(【引用サイトリンク】 IDEA - Internet Differential Equations Activities )〕 It is a portmanteau of Brussels and oscillator. It is characterized by the reactions :$A\; \backslash rightarrow\; X$ :$2X\; +\; Y\; \backslash rightarrow\; 3X$ :$B\; +\; X\; \backslash rightarrow\; Y\; +\; D$ :$X\; \backslash rightarrow\; E$ Under conditions where A and B are in vast excess and can thus can be modeled at constant concentration, the rate equations become :$\backslash left\backslash \; =\; \backslash left\backslash \; +\; \backslash left\backslash ^2\; \backslash left\backslash \; -\; \backslash left\backslash \; \backslash left\backslash \; -\; \backslash left\backslash \; \backslash ,$ :$\backslash left\backslash \; =\; \backslash left\backslash \; \backslash left\backslash \; -\; \backslash left\backslash ^2\; \backslash left\backslash \; \backslash ,$ where, for convenience, the rate constants have been set to 1. The Brusselator has a fixed point at :$\backslash left\backslash \; =\; A\; \backslash ,$ :$\backslash left\backslash \; =\; \backslash ,$. The fixed point becomes unstable when :$B>1+A^2\; \backslash ,$ leading to an oscillation of the system. Unlike the Lotka–Volterra equation, the oscillations of the Brusselator do not depend on the amount of reactant present initially. Instead, after sufficient time, the oscillations approach a limit cycle.〔http://www.bibliotecapleyades.net/archivos_pdf/brusselator.pdf Dynamics of the Brusselator 〕 The best-known example is the clock reaction, the Belousov–Zhabotinsky reaction (BZ reaction). It can be created with a mixture of potassium bromate $(KBrO\_3)$, malonic acid $(CH\_2(COOH)\_2)$, and manganese sulfate $(MnSO\_4)$ prepared in a heated solution of sulfuric acid $(H\_2SO\_4)$.〔(BZ reaction )〕 ==See also== *Lotka–Volterra equation *Oregonator 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「Brusselator」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.