混沌动力系统小波变换模数的关联维数  

Calculating the correlation dimension of dynamical system with wavelet analysis

作　　者：刘海峰 代正华[1] 陈峰[1] 龚欣[1] 于遵宏[1] 

机构地区：[1]华东理工大学资源与环境工程学院,上海200237

出　　处：《物理学报》2002年第6期1186-1192,共7页Acta Physica Sinica

基　　金：国家重点基础研究发展规划 (批准号 :G19990 2 2 10 3);教育部骨干教师基金资助的课题~~

摘　　要：关联维数是描述动力系统混沌的重要参数 .在仿真计算的基础上 ,发现尽管小尺度小波变换时 ,奇异吸引子的整体形状发生了改变 ,但小波变换模数的关联维数与动力系统本身是一致的 .同时仿真计算还表明 ,随尺度的增加 ,关联积分与距离的标度关系逐渐变差 ,但在一定范围内仍可较准确地计算出关联维数 .The correlation dimension is an important parameter of detecting and characterizing chaos produced from a dynamical system. Based on emulation calculation, it has been found that the correlation dimension of the small-scale wavelet transform modulus of discrete and continuous chaotic dynamical system is the same as the system's, though the attractor shape changed after wavelet transform. At the same time, the influences of wavelet transform scale on the scaling law between integral sum and distance has been investigated.

关 键 词：混沌 动力系统 小波变换模数 关联维数 小波分析 尺度 相空间 

分 类 号：O415.5[理学—理论物理] O174.2[理学—物理]