混沌吸引子的维数研究  

The Dimension Research of Chaotic Attractor

作　　者：李亚安[1] 张效民[1] 徐德民[1] 

机构地区：[1]西北工业大学航海工程学院,陕西西安710072

出　　处：《探测与控制学报》2002年第4期43-46,共4页Journal of Detection & Control

基　　金：国防科技预研基金资助项目 (99J42 .1 .5 )

摘　　要：维数的分析与计算在混沌信号处理中有着重要的作用。而基于 Hausdorff维数理论的 G-P算法在计算混沌吸引子的关联维数时存在抗噪声干扰能力差、运算时间长等缺点。通过对重构空间引入奇异谱分析 ,将状态矢量变换到一组正交的坐标系 ,进而计算其关联维数。克服了原算法的不足 ,同时具有可靠性高 。The calculation of dimension has taken an very important role in the chaotic signal processing. The traditional G P algorithm based on the Hausdorff dimension thereom has follow drawbacks: poor robustness to noise and more calculation time. By means of the Singular Spectrum Analysis (SSA), We transform the reconstructed space to an orthogonal coordinate and then calculate its correlation dimension. The results are superior to the results from traditional algorithm because of its greater robustness to noise , higher stability and more easy to realize.

关 键 词：吸引子 维数 HAUSDORFF维数 最小嵌入维数 混沌 相空间重构 关联维数 

分 类 号：TN911.23[电子电信—通信与信息系统] O415.5[电子电信—信息与通信工程]