Improved Correlation Dimension Calculation
Improved Correlation Dimension Calculation
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DOI：
10.1142/s021812740100305x
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发表时间：
2000-07
期刊：
影响因子：
--
通讯作者：
J. Sprott;G. Rowlands
中科院分区：
文献类型：
--
作者：
J. Sprott;G. Rowlands
对于许多混沌系统，由于随着尺度的减小，关联维数的收敛速度非常慢，因此很难从测量数据中准确地计算关联维数。这个问题通常是由吸引子上的高度不均匀的度量引起的。本文提出了一种大比例尺数据采集和零比例尺外推的方法。其结果是大大减少了测量维度中给定精度所需的数据点数量。以一维地图为例，详细说明了该方法，并将其应用于更复杂的地图和流动。给出了许多标准混沌系统的关联维值。
For many chaotic systems, accurate calculation of the correlation dimension from measured data is difficult because of very slow convergence as the scale size is reduced. This problem is often caused by the highly nonuniform measure on the attractor. This paper proposes a method for collecting data at large scales and extrapolating to the limit of zero scale. The result is a vastly reduced required number of data points for a given accuracy in the measured dimension. The method is illustrated in detail for one-dimensional maps and then applied to more complicated maps and flows. Values are given for the correlation dimension of many standard chaotic systems.