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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 Tikhonov's theorem (dynamical systems) ： ウィキペディア英語版 Tikhonov's theorem (dynamical systems) In applied mathematics, Tikhonov's theorem on dynamical systems is a result on stability of solutions of systems of differential equations. It has applications to chemical kinetics.〔http://www.math.bme.hu/~jtoth/frk/Roussel.pdf〕 The theorem is named after Andrey Nikolayevich Tikhonov. == Statement == Consider this system of differential equations: : $$ \begin \frac & = \mathbf(\mathbf,\mathbf,t), \\ \mu\frac & = \mathbf(\mathbf,\mathbf,t). \end Taking the limit as $\backslash mu\backslash to\; 0$, this becomes the "degenerate system": : $$ \begin \frac & = \mathbf(\mathbf,\mathbf,t), \\ \mathbf & = \varphi(\mathbf,t), \end where the second equation is the solution of the algebraic equation : $\backslash mathbf(\backslash mathbf,\backslash mathbf,t)\; =\; 0.\; \backslash ,$ Note that there may be more than one such function ''φ''. Tikhonov's theorem states that as $\backslash mu\backslash to\; 0,\backslash ,$ the solution of the system of two differential equations above approaches the solution of the degenerate system if $\backslash mathbf\; =\; \backslash varphi(\backslash mathbf,t)$ is a stable root of the "adjoined system" : $\backslash frac\; =\; \backslash mathbf(\backslash mathbf,\backslash mathbf,t).$ 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「Tikhonov's theorem (dynamical systems)」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.