一类IFS吸引子界与动力学特征定量观测  

Quantitative observation of boundary and dynamic characteristics of a class IFS attractors

作　　者：王兴元[1] 梁庆永[1] 马洪连[1] 

机构地区：[1]大连理工大学电子与信息工程学院,辽宁大连116024

出　　处：《大连理工大学学报》2004年第1期132-136,共5页Journal of Dalian University of Technology

基　　金：国家自然科学基金资助项目(69974008);中国博士后科学基金资助项目;辽宁省自然科学基金资助项目(972194).

摘　　要：阐述了迭代函数系(iteratedfunctionsystem,IFS)理论及随机迭代算法,通过理论解析给出了求由两个仿射映射所构造的一类IFS吸引子的界的方法,介绍了IFS吸引子的Lyapunov指数和关联维数的算法.分析了IFS吸引子的动力学特征.The iterated function systems (it is called IFS for short) theory and the random iteration algorithm are expounded. By the theoretical analysis, the method by which the boundary of a class attractors of IFS using two affine maps can be evaluated is given out. The algorithm of determining the Lyapunov exponent and the correlation dimension of the attractors of IFS is introduced. Utilizing the computer simulated a class two-dimensional, three-dimensional attractors of IFS, the boundary, the Lyapunov exponent and the correlation dimension of the attractors of IFS are calculated, and the dynamic characteristics of the attractors of IFS are analyzed.

关 键 词：IFS吸引子 动力学 随机迭代算法 界 LYAPUNOV指数 关联维数 迭代函数系 非空紧子集空间 不动点 

分 类 号：O177.91[理学—数学]