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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 Rössler attractor ： ウィキペディア英語版 Rössler attractor The Rössler attractor is the attractor for the Rössler system, a system of three non-linear ordinary differential equations originally studied by Otto Rössler.〔.〕〔.〕 These differential equations define a continuous-time dynamical system that exhibits chaotic dynamics associated with the fractal properties of the attractor.〔.〕 Some properties of the Rössler system can be deduced via linear methods such as eigenvectors, but the main features of the system require non-linear methods such as Poincaré maps and bifurcation diagrams. The original Rössler paper states the Rössler attractor was intended to behave similarly to the Lorenz attractor, but also be easier to analyze qualitatively.〔 An orbit within the attractor follows an outward spiral close to the $x,\; y$ plane around an unstable fixed point. Once the graph spirals out enough, a second fixed point influences the graph, causing a rise and twist in the $z$-dimension. In the time domain, it becomes apparent that although each variable is oscillating within a fixed range of values, the oscillations are chaotic. This attractor has some similarities to the Lorenz attractor, but is simpler and has only one manifold. Otto Rössler designed the Rössler attractor in 1976,〔 but the originally theoretical equations were later found to be useful in modeling equilibrium in chemical reactions. ==Definition== The defining equations of the Rössler system are:〔 $\backslash begin\; \backslash frac\; =\; -y\; -\; z\; \backslash \backslash \; \backslash frac\; =\; x\; +\; ay\; \backslash \backslash \; \backslash frac\; =\; b\; +\; z(x-c)\; \backslash end$ Otto E. Rössler studied the chaotic attractor with $a\; =\; 0.2$, $b\; =\; 0.2$, and $c\; =\; 5.7$, though properties of $a\; =\; 0.1$, $b\; =\; 0.1$, and $c\; =\; 14$ have been more commonly used since. Another line of the parameter space was investigated using the topological analysis. It corresponds to $b\; =\; 2$, $c\; =\; 4$, and $a$ was chosen as the bifurcation parameter. How Rössler discovered this set of equations was investigated by Letellier and Messager. 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「Rössler attractor」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.