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奇异吸引子


一个吸引集,在嵌入相空间中具有零测度,并具有分形维数。奇异吸引子内的轨迹似乎随机跳跃。

StrangeAttractors1
StrangeAttractors2

上面展示了一般二次映射的一些奇异吸引子

x_(n+1)=a_1+a_2x_n+a_3x_n^2+a_4x_ny_n+a_5y_n+a_6y_n^2
(1)
y_(n+1)=a_7+a_8x_n+a_9x_n^2+a_(10)x_ny_n+a_(11)y_n+a_(12)y_n^2
(2)

,其中字母 AY 代表二次方的系数,从 -1.2 到 1.2,步长为 0.1 (Sprott 1993c)。这些代表了大约 1.6% 的所有可能的 25^(12) approx 6×10^(16) 这种混沌映射的一小部分 (Sprott 1993bc)。


另请参阅

吸引盆, 关联指数, 分形, 姜饼人映射, Hénon-Heiles 方程, Hénon 映射, Lorenz 吸引子, Lozi 映射, 相空间, Rössler 吸引子, 标准映射, Wada 盆

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参考文献

Benmizrachi, A.; Procaccia, I.; and Grassberger, P. "Characterization of Experimental (Noisy) Strange Attractors." Phys. Rev. A 29, 975-977, 1984.Dewdney, A. K. "Probing the Strange Attractors of Chaos." Sci. Amer. 235, 90-93, 1976.Farmer, J. D.; Ott, E.; and Yorke, J. A. "The Dimension of Chaotic Attractors." Physica 7D, 153, 1983.Gleick, J. "Strange Attractors." Chaos: Making a New Science. New York: Penguin Books, pp. 119-153, 1988.Grassberger, P. "On the Hausdorff Dimension of Fractal Attractors." J. Stat. Phys. 26, 173-179, 1981.Grassberger, P. and Procaccia, I. "Measuring the Strangeness of Strange Attractors." Physica D 9, 189-208, 1983a.Grassberger, P. and Procaccia, I. "Characterization of Strange Attractors." Phys. Rev. Let. 50, 346-349, 1983b.Lauwerier, H. Fractals: Endlessly Repeated Geometric Figures. Princeton, NJ: Princeton University Press, pp. 137-138, 1991.Peitgen, H.-O. and Richter, D. H. The Beauty of Fractals: Images of Complex Dynamical Systems. New York: Springer-Verlag, 1986.Pickover, C. "A Note on Rendering 3-D Strange-Attractors." Comput. & Graphics 12, 263, 1988.Sprott, J. C. Strange Attractors: Creating Patterns in Chaos. New York: Henry Holt, 1993a.Sprott, J. C. "How Common Is Chaos?" Phys. Lett. A 173, 21, 1993b.Sprott, J. C. "Automatic Generation of Strange Attractors." Comput. & Graphics 17, 325-332, 1993c. Reprinted in Chaos and Fractals, A Computer Graphical Journey: Ten Year Compilation of Advanced Research (Ed. C. A. Pickover). Amsterdam, Netherlands: Elsevier, pp. 53-60, 1998.Viana, M. "What's New on Lorenz Strange Attractors." Math. Intell. 22, 6-19.

引用

奇异吸引子

引用为

Weisstein, Eric W. "奇异吸引子。" 来自 MathWorld——Wolfram 网络资源。 https://mathworld.net.cn/StrangeAttractor.html

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