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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 limit cycle ： ウィキペディア英語版 limit cycle In mathematics, in the study of dynamical systems with two-dimensional phase space, a limit cycle is a closed trajectory in phase space having the property that at least one other trajectory spirals into it either as time approaches infinity or as time approaches negative infinity. Such behavior is exhibited in some nonlinear systems. Limit cycles have been used to model the behavior of a great many real world oscillatory systems. The study of limit cycles was initiated by Henri Poincaré (1854-1912). ==Definition== We consider a two-dimensional dynamical system of the form :$x\text{'}(t)=V(x(t))$ where :$V:\backslash mathbb^2\backslash to\backslash mathbb^2$ is a smooth function. A ''trajectory'' of this system is some smooth function $x(t)$ with values in $\backslash mathbb^2$ which satisfies this differential equation. Such a trajectory is called ''closed'' (or ''periodic'') if it is not constant but returns to its starting point, i.e. if there exists some $t\_0>0$ such that $x(t+t\_0)=x(t)$ for all $t\backslash in\backslash mathbb$. An orbit is the image of a trajectory, a subset of $\backslash mathbb^2$. A ''closed orbit'', or ''cycle'', is the image of a closed trajectory. A ''limit cycle'' is a cycle which is the limit set of some other trajectory. 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「limit cycle」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.