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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 Zubov's method ： ウィキペディア英語版 Zubov's method Zubov's method is a technique for computing the basin of attraction for a set of ordinary differential equations (a dynamical system). The domain of attraction is the set $\backslash$, where $v(x)$ is the solution to a partial differential equation known as the Zubov equation. 'Zubov's method' can be used in a number of ways. Zubov's theorem states that: :If $x\text{'}\; =\; f(x),\; t\; \backslash in\; \backslash R$ is an ordinary differential equation in $\backslash R^n$ with $f(0)=0$, a set $A$ containing 0 in its interior is the domain of attraction of zero if and only if there exist continuous functions $v,\; h$ such that: : * $v(0)\; =\; h(0)\; =\; 0$, for $x\; \backslash in\; A\; \backslash setminus\; \backslash$, $h\; >\; 0$ on $\backslash R^n\; \backslash setminus\; \backslash$ : * for every $\backslash gamma\_2\; >\; 0$ there exist $\backslash gamma\_1\; >\; 0,\; \backslash alpha\_1\; >\; 0$ such that $v(x)\; >\; \backslash gamma\_1,\; h(x)\; >\; \backslash alpha\_1$ , if $||x||>\backslash gamma\_2$ : * $v(x\_n)\; \backslash rightarrow\; 1$ for $x\_n\; \backslash rightarrow\; \backslash partial\; A$ or $||x\_n||\; \backslash rightarrow\; \backslash infty$ : * $\backslash nabla\; v(x)\; \backslash cdot\; f(x)\; =\; -h(x)(1-v(x))\; \backslash sqrt$ If f is continuously differentiable, then the differential equation has at most one continuously differentiable solution satisfying $v(0)\; =\; 0$. ==References== Vladimir Ivanovich Zubov, ''Methods of A.M. Lyapunov and their application'', Izdatel'stvo Leningradskogo Universiteta, 1961. (Translated by the United States Atomic Energy Commission, 1964.) ASIN B0007F2CDQ. 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「Zubov's method」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.