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截断误差导致的非双曲不动点邻域拓扑变异
引用本文:盛利元,张刚.截断误差导致的非双曲不动点邻域拓扑变异[J].海洋学报,2010,32(9):5972-5978.
作者姓名:盛利元  张刚
作者单位:中南大学物理科学与技术学院,长沙 410083;中南大学物理科学与技术学院,长沙 410083
基金项目:国家自然科学基金(批准号:60672041)资助的课题.
摘    要: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.

关 键 词:截断误差  非双曲不动点  抗退化机理  拓扑结构变异
修稿时间:1/5/2010 12:00:00 AM

The topological variance of neighborhood of a non-hyperbolicfixed point produced by truncation error
Sheng Li-Yuan and Zhang Gang.The topological variance of neighborhood of a non-hyperbolicfixed point produced by truncation error[J].Acta Oceanologica Sinica (in Chinese),2010,32(9):5972-5978.
Authors:Sheng Li-Yuan and Zhang Gang
Institution:School of Physics Science and Technology,Central South University,Changsha 410083,China;School of Physics Science and Technology,Central South University,Changsha 410083,China
Abstract: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.
Keywords:truncation error  non-hyperbolic fixed point  anti-degradation mechanism  variance of topological configuration
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