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曲面迭代混沌特性研究

于万波 赵斌

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曲面迭代混沌特性研究

于万波, 赵斌

A new chaotic attractor graphics drawing method based on the curved iteration

Yu Wan-Bo, Zhao Bin
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  • 研究了空间单位区域内两个曲面映射构成的动力系统的混沌特性. 研究发现两个曲面中有一个曲面振荡剧烈,另外一个曲面随机生成时系统更容易出现混沌,能生成众多有特点的混沌吸引子. 如果调整随机曲面使其成为满射,那么所构成的动力系统是混沌的概率可以达到1/2或者更高. 通过计算Lyapunov 指数以及绘制分岔图等方法对系统的混沌特性进行分析,同时给出了由两个曲面构造的系统出现混沌的必要条件. 和二维情形一样,一个三维正弦函数与两个三维多项式函数构造的动力系统是混沌的概率也很高,通过计算可以得到众多的具有观赏和实用价值的三维吸引子.
    In this paper, we continue to study the chaotic characteristics of two curved surface mapping which forms a function in a unit area, and find that when one of the two curved surfaces is a standard curved surface and subjected to strong oscillation, and the other is randomly generate, the occurrence of chaos is more prone. Many different chaotic attractors are drawn by this method, adjusting the random surface to become subjective, the probability of chaotic attractor appearing can reach a half or more, which means that when certain conditions are meet, chaos is extremely common. Through calculating Lyapunov exponent and drawing the bifurcation diagram to analyze characteristics of chaos of the function, according to the bifurcation diagram of parameters and the Lyapunov exponent curve to look for more chaotic mapping function, a lot of chaotic attractors can be obtained. Finally a three-dimensional trigonometric function and two randomly generated three-dimensional polynomial functions are iterated, and many fancy three-dimensional attractors are obtained.
    [1]

    Li T Y, Yorke J A 1975 Am. Math. Mon. 82 984

    [2]

    Oprocha P 2009 Nonlinear Anal. 71 5835

    [3]

    He Y X, He Y L, Li H 1999 Comput. Graph. 23 547

    [4]

    Viswanath D 2004 Physica D 190 115

    [5]

    Kin D W, Chang P H 2013 Results Phys. 3 14

    [6]

    Li C P, Chen G 2008 Chaos Solitons Fract. 18 807

    [7]

    Reza M S 2012 Commun. Nonlinear Sci. Numer. Simul. 17 3857

    [8]

    Yu W B, Zhou Y 2013 Acta Phys. Sin. 62 220501 (in Chinese) [于万波, 周洋 2013 物理学报 62 220501]

    [9]

    Yu W B, Yang L Z 2013 Acta Phys. Sin. 62 020503 (in Chinese) [于万波, 杨灵芝 2013 物理学报 62 020503]

    [10]

    Yu W B, Yang X S, Wei X P 2011 Application Research of Computers 28 3837 (in Chinese) [于万波, 杨雪松, 魏小鹏 2011 计算机应用研究 28 3837]

    [11]

    Jin Y Q, Liang Z C 2003 Acta Phys. Sin. 52 1319 (in Chinese) [金亚秋, 梁子长 2003 物理学报 52 1319]

    [12]

    Mo J Q, Lin W T 2000 Acta Phys. Sin. 49 1648 (in Chinese) [莫嘉琪, 林万涛 2000 物理学报 49 1648]

    [13]

    Li C A 2005 Acta Phys. Sin. 54 1081 (in Chinese) [李传安 2005 物理学报 54 1081]

    [14]

    Ge Y Z, Mi J C 2013 Acta Phys. Sin. 62 024704 (in Chinese) [戈阳祯, 米建春 2013 物理学报 62 024704]

    [15]

    Yuan R S, Ma Y A, Yuan B, Ao P 2014 Chin. Phys. B 23 010505

    [16]

    Gao W, Zha F S, Song B Y, Li M T 2014 Chin. Phys. B 23 010701

    [17]

    Qin H, Xue P 2014 Chin. Phys. B 23 010301

  • [1]

    Li T Y, Yorke J A 1975 Am. Math. Mon. 82 984

    [2]

    Oprocha P 2009 Nonlinear Anal. 71 5835

    [3]

    He Y X, He Y L, Li H 1999 Comput. Graph. 23 547

    [4]

    Viswanath D 2004 Physica D 190 115

    [5]

    Kin D W, Chang P H 2013 Results Phys. 3 14

    [6]

    Li C P, Chen G 2008 Chaos Solitons Fract. 18 807

    [7]

    Reza M S 2012 Commun. Nonlinear Sci. Numer. Simul. 17 3857

    [8]

    Yu W B, Zhou Y 2013 Acta Phys. Sin. 62 220501 (in Chinese) [于万波, 周洋 2013 物理学报 62 220501]

    [9]

    Yu W B, Yang L Z 2013 Acta Phys. Sin. 62 020503 (in Chinese) [于万波, 杨灵芝 2013 物理学报 62 020503]

    [10]

    Yu W B, Yang X S, Wei X P 2011 Application Research of Computers 28 3837 (in Chinese) [于万波, 杨雪松, 魏小鹏 2011 计算机应用研究 28 3837]

    [11]

    Jin Y Q, Liang Z C 2003 Acta Phys. Sin. 52 1319 (in Chinese) [金亚秋, 梁子长 2003 物理学报 52 1319]

    [12]

    Mo J Q, Lin W T 2000 Acta Phys. Sin. 49 1648 (in Chinese) [莫嘉琪, 林万涛 2000 物理学报 49 1648]

    [13]

    Li C A 2005 Acta Phys. Sin. 54 1081 (in Chinese) [李传安 2005 物理学报 54 1081]

    [14]

    Ge Y Z, Mi J C 2013 Acta Phys. Sin. 62 024704 (in Chinese) [戈阳祯, 米建春 2013 物理学报 62 024704]

    [15]

    Yuan R S, Ma Y A, Yuan B, Ao P 2014 Chin. Phys. B 23 010505

    [16]

    Gao W, Zha F S, Song B Y, Li M T 2014 Chin. Phys. B 23 010701

    [17]

    Qin H, Xue P 2014 Chin. Phys. B 23 010301

计量
  • 文章访问数:  4569
  • PDF下载量:  527
  • 被引次数: 0
出版历程
  • 收稿日期:  2013-12-11
  • 修回日期:  2014-01-08
  • 刊出日期:  2014-06-05

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