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截断误差导致的非双曲不动点邻域拓扑变异

盛利元 张刚

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截断误差导致的非双曲不动点邻域拓扑变异

盛利元, 张刚

The topological variance of neighborhood of a non-hyperbolic fixed point produced by truncation error

Sheng Li-Yuan, Zhang Gang
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  • 提供一个关于截断误差使简单系统复杂化的直接实验证据,以此证明存在混沌抗退化机理.分别构造了一个一维圆弧迭代系统和一个一维抛物线迭代系统,两者均有一个非双曲不动点,其迭代序列被证明是简单极限序列,数字计算实验显示这两个迭代系统都存在可以越过不动点的序列.采用计算"元胞"分析方法清晰地展示了截断误差导致非双曲不动点邻域拓扑变异:形成第I类阵发混沌通道,或产生纹波分岔.
    In the paper,a direct evidence for truncation error to complicate a simple system is provided,which proves the existence of anti-degradation mechanism in chaotic systems. Both one-dimensional circular arc iterated system and one-dimensional parabola iterated system are constructed,respectively. In each system,there is a non-hyperbolic fixed point. The corresponding iterative sequences are theoretically proved to be simple convergent sequences. However,there are a lot of iterative sequences that could jump over the fixed point in digital experiments. It is clearly revealed by digital-cell analysis that the topological variance of neighborhood of a non-hyperbolic fixed point is produced by truncation error,either a channel of type-I intermittency or a ripple bifurcation is configured from the fixed point.
    • 基金项目: 国家自然科学基金(批准号:60672041)资助的课题.
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    Baptista M S 1998 Phys. Lett. A 240 50

    [2]

    Kocarev L,Jakimoski G 2001 Phys. Lett. A 289 199

    [3]

    Stojanoski T,Kovarev L 2001 IEEE Trans. CAS-I 48 281

    [4]

    Palacios A,Juarez H 2002 Phys. Lett. A 303 345

    [5]

    Wang X M,Zhang J S,Zhang W F 2003 Acta Phys. Sin. 52 2737 (in Chinese) [王小敏、张家树、张文芳 2003 物理学报 52 2737 ]

    [6]

    Zhan H,Wang X F,Li C H,Liu D H 2005 Acta Phys. Sin. 54 4006 (in Chinese) [张 瀚、王秀峰、李朝晖、刘大海 2005 物理学报 54 4006]

    [7]

    Sheng L Y,Cao L L,Sun K H,Wen J 2005 Acta Phys. Sin. 54 4031 (in Chinese) [盛利元、曹莉凌、孙克辉、闻 姜 2005 物理学报 54 4031]

    [8]

    Wang L,Wang F P,Wang Z J 2006 Acta Phys. Sin. 55 3964 (in Chinese) [王 蕾、汪芙平、王赞基 2006 物理学报 55 3964 ]

    [9]

    Sheng L Y,Li G Q,Li Z W 2006 Acta Phys. Sin. 55 5700 (in Chinese) [盛利元、李更强、李志炜 2006 物理学报 55 5700]

    [10]

    Curiac D I,Iercan D,Dranga O,Dragan F,Banias O 2007 Proceedings of International Conference on Emerging Security Information,Systems and Technologies (SECURWARE 2007),Valencia,Spain,October 14—20,2007 p71

    [11]

    Levy Y E 1982 Phys. Lett. A 53 1

    [12]

    Beck C,Roepstorff G 1987 Physica D 25 173

    [13]

    Binder P M 1992 Physica 57 31

    [14]

    Li S J,Mou X Q,Cai Y L,Ji Z,Zhang J H 2003 Comput. Phys. Commun. 153 52

    [15]

    Alvarez G,Li S J 2006 Int. J. Bifurc. Chaos. 16 2129

    [16]

    Sheng L Y,Wen J,Cao L L,Xiao Y Y 2007 Acta Phys. Sin. 56 0078 (in Chinese) [盛利元、闻 姜、曹莉凌、肖燕予 2007 物理学报 56 0078]

    [17]

    Sheng L Y,Jia W Y 2005 Acta Phys. Sin. 54 5574 (in Chinese) [盛利元、贾伟尧 2005 物理学报 54 5574]

    [18]

    Sheng L Y,Jia W Y,Wu S C,Xia G R 2007 Acta Phys. Sin. 56 3753 (in Chinese) [盛利元、贾伟尧、吴舒辞、夏国荣 2007 物理学报 56 3753]

    [19]

    Murakami K 2005 J. Math. Anal. Appl. 310 492

    [20]

    Li S J 2003 Ph. D. Dissertation (Xian:Xian Jiaotong University) (in Chinese) [李树钧 2003 博士学位论文(西安:西安交通大学)]

    [21]

    Pomeau Y,Manneville P 1980 Commun. Math. Phys. 74 189

    [22]

    Oteo J A,Ros J 2007 Phys. Rev. E 76 036214

  • [1]

    Baptista M S 1998 Phys. Lett. A 240 50

    [2]

    Kocarev L,Jakimoski G 2001 Phys. Lett. A 289 199

    [3]

    Stojanoski T,Kovarev L 2001 IEEE Trans. CAS-I 48 281

    [4]

    Palacios A,Juarez H 2002 Phys. Lett. A 303 345

    [5]

    Wang X M,Zhang J S,Zhang W F 2003 Acta Phys. Sin. 52 2737 (in Chinese) [王小敏、张家树、张文芳 2003 物理学报 52 2737 ]

    [6]

    Zhan H,Wang X F,Li C H,Liu D H 2005 Acta Phys. Sin. 54 4006 (in Chinese) [张 瀚、王秀峰、李朝晖、刘大海 2005 物理学报 54 4006]

    [7]

    Sheng L Y,Cao L L,Sun K H,Wen J 2005 Acta Phys. Sin. 54 4031 (in Chinese) [盛利元、曹莉凌、孙克辉、闻 姜 2005 物理学报 54 4031]

    [8]

    Wang L,Wang F P,Wang Z J 2006 Acta Phys. Sin. 55 3964 (in Chinese) [王 蕾、汪芙平、王赞基 2006 物理学报 55 3964 ]

    [9]

    Sheng L Y,Li G Q,Li Z W 2006 Acta Phys. Sin. 55 5700 (in Chinese) [盛利元、李更强、李志炜 2006 物理学报 55 5700]

    [10]

    Curiac D I,Iercan D,Dranga O,Dragan F,Banias O 2007 Proceedings of International Conference on Emerging Security Information,Systems and Technologies (SECURWARE 2007),Valencia,Spain,October 14—20,2007 p71

    [11]

    Levy Y E 1982 Phys. Lett. A 53 1

    [12]

    Beck C,Roepstorff G 1987 Physica D 25 173

    [13]

    Binder P M 1992 Physica 57 31

    [14]

    Li S J,Mou X Q,Cai Y L,Ji Z,Zhang J H 2003 Comput. Phys. Commun. 153 52

    [15]

    Alvarez G,Li S J 2006 Int. J. Bifurc. Chaos. 16 2129

    [16]

    Sheng L Y,Wen J,Cao L L,Xiao Y Y 2007 Acta Phys. Sin. 56 0078 (in Chinese) [盛利元、闻 姜、曹莉凌、肖燕予 2007 物理学报 56 0078]

    [17]

    Sheng L Y,Jia W Y 2005 Acta Phys. Sin. 54 5574 (in Chinese) [盛利元、贾伟尧 2005 物理学报 54 5574]

    [18]

    Sheng L Y,Jia W Y,Wu S C,Xia G R 2007 Acta Phys. Sin. 56 3753 (in Chinese) [盛利元、贾伟尧、吴舒辞、夏国荣 2007 物理学报 56 3753]

    [19]

    Murakami K 2005 J. Math. Anal. Appl. 310 492

    [20]

    Li S J 2003 Ph. D. Dissertation (Xian:Xian Jiaotong University) (in Chinese) [李树钧 2003 博士学位论文(西安:西安交通大学)]

    [21]

    Pomeau Y,Manneville P 1980 Commun. Math. Phys. 74 189

    [22]

    Oteo J A,Ros J 2007 Phys. Rev. E 76 036214

计量
  • 文章访问数:  8010
  • PDF下载量:  757
  • 被引次数: 0
出版历程
  • 收稿日期:  2009-12-02
  • 修回日期:  2010-01-05
  • 刊出日期:  2010-09-15

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