二维logistic映射的动力学行为和奇怪吸引子的分形特征  

The dynamic behavior of two-dimensional logistic system and the fractal characterization of strange attractors

作　　者：王立明[1] 

机构地区：[1]廊坊师范学院物理系,河北廓坊065000

出　　处：《大学物理》2010年第2期21-25,共5页College Physics

基　　金：河北省廊坊市科学技术与发展指导计划资助项目(2009011002)

摘　　要：研究了二维logistic映射的动力学行为和奇怪吸引子的分形特征.利用分岔图、相图和Lyapunov指数谱分析系统的分岔过程,研究系统通向混沌的道路并确定系统处于混沌运动的参数区间;采用G-P算法计算奇怪吸引子的关联维数和Kolmogorov熵,对奇怪吸引子的分形特征定量刻画;采用逃逸时间算法构造奇怪吸引子的彩色广义M-J集,对奇怪吸引子的分形特征定性表征.结果表明,这些分析方法的配合使用可以更全面、形象地描述奇怪吸引子的分形特征.The dynamic behaviors of the two-dimensional logistic system are analyzed and the fractal characterization of strange attractors is researched. By using phase maps, bifurcation graphics and Lyapunov exponent, the paper reveals the transition of two-dimensional logistic system from regularity to chaos. By using G-P algorithm, the correlation dimension and Kolmogorov entropy of strange attractors are calculated, so the fractal characterization of strange attractors is described qualitatively. By using escape time algorithm, the color general Mandelbrot-Julia sets of strange attractors are construeted, so the fractal characterization of strange attractors is described quantitatively. The results show that the fractal characterization of strange attractors is explained clearly when these methods are used altogether.

关 键 词：二维LOGISTIC映射 HOPF分岔 关联维数 Kolmogorov熵 逃逸时间算法 广义M—J集 

分 类 号：O415.5[理学—理论物理]