翻訳と辞書 Words near each other ・ Lyanco ・ Lyangar ・ Lyanka Gryu ・ Lyantonde ・ Lyantonde District ・ Lyantor ・ LYAO ・ LYaPAS ・ Lyapin River ・ Lyapis Trubetskoy ・ Lyappa arm ・ Lyapunov ・ Lyapunov (crater) ・ Lyapunov equation ・ Lyapunov exponent ・ Lyapunov fractal ・ Lyapunov function ・ Lyapunov optimization ・ Lyapunov redesign ・ Lyapunov stability ・ Lyapunov theorem ・ Lyapunov time ・ Lyapunov vector ・ Lyapunov–Malkin theorem ・ Lyapunov–Schmidt reduction ・ LYAR ・ Lyari ・ Lyari Development Authority ・ Lyari Expressway ・ Lyari Expressway Resettlement Project Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Lyapunov fractal ： ウィキペディア英語版 Lyapunov fractal In mathematics, Lyapunov fractals (also known as Markus–Lyapunov fractals) are bifurcational fractals derived from an extension of the logistic map in which the degree of the growth of the population, ''r'', periodically switches between two values ''A'' and ''B''. A Lyapunov fractal is constructed by mapping the regions of stability and chaotic behaviour (measured using the Lyapunov exponent $\backslash lambda$) in the ''a''−''b'' plane for given periodic sequences of ''a'' and ''b''. In the images, yellow corresponds to (stability), and blue corresponds to $\backslash lambda\; >\; 0$ (chaos). ==Properties== Lyapunov fractals are generally drawn for values of ''A'' and ''B'' in the interval $()$. For larger values, the interval () is no longer stable, and the sequence is likely to be attracted by infinity, although convergent cycles of finite values continue to exist for some parameters. For all iteration sequences, the diagonal ''a = b'' is always the same as for the standard one parameter logistic function. The sequence is usually started at the value 0.5, which is a critical point of the iterative function. The other (even complex valued) critical points of the iterative function during one entire round are those that pass through the value 0.5 in the first round. A convergent cycle must attract at least one critical point; therefore all convergent cycles can be obtained by just shifting the iteration sequence, and keeping the starting value 0.5. In practice, shifting this sequence leads to changes in the fractal, as some branches get covered by others; notice for instance how the Lyapunov fractal for the iteration sequence AB is not perfectly symmetric with respect to ''a'' and ''b''. 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「Lyapunov fractal」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.