基于lnC(r)～lnr关系曲线最小曲率值的无标度区的识别  

The Identification of Non-scale Range Based on least Curvature value About ln C(r)～ln r curve

作　　者：唐依民[1] 雷鸣[1] 聂重军[1] 肖江[2] 

机构地区：[1]长沙学院土木工程系,湖南长沙410003 [2]湖南科技大学土木工程学院,湖南湘潭411201

出　　处：《湖南科技大学学报（自然科学版）》2008年第4期48-52,共5页Journal of Hunan University of Science And Technology：Natural Science Edition

基　　金：湖南省自然科学基金项目(06JJ4071)

摘　　要：为计算关联维数D2,应确定G.P算法过程中的无标度区.从ln C(r)～ln r关系曲线的几何特征出发,分析关系曲线最小曲率的分形意义,结果表明:以最小曲率点作为计算无标度区的基点,以曲线上两点间夹角的大小作为线性相关性的判断依据,能够准确判断关联维数计算时的无标度区上下限.编制Matlab计算程序,对Lorenz混沌系统进行计算,表明该方法的适用性.Non-scale range GP calculation should be ascertained for calculating correlation dimension D2. Minimum curvature of ln Cm （r） ～ ln r curve was studied in geometry feature of this curve. Results showed that, if the minimum curvature point is treated as basic point of non-scale rang calculation and if the size of the included angle between two points on the curve is treated as judgment for linear relativity, the most and least value of non-scale rang of correlation dimension calculation can be estimated accurately. Matlab program was constructed and was applied in calculating lorenz chaos system, which has showed that the calculation method was feasible. 2figs., 2tabs., 1 lrefs.

关 键 词：无标度区 关联维数 G.P算法 曲率 

分 类 号：O415.5[理学—理论物理]