耦合逻辑斯蒂映射中的一个混沌吸引子  

A CHAOTIC ATTRACTOR IN THE COUPLED LOGISTIC MAP

作　　者：孟湛祥[1] 

机构地区：[1]天津大学理学院

出　　处：《天津大学学报》1999年第6期711-715,共5页Journal of Tianjin University(Science and Technology)

摘　　要：研究一个二维耦合逻辑斯蒂映射，发现一个混沌吸引子，采用跟踪正交矢量和Ｇｒａｍ －Ｓｃｈｍ ｉｄｔ重新正交归一化方法计算了该吸引子的李雅普诺夫指数，按分维定义计算该吸引子的各种维数，为卡普兰和约克的猜测提供又一例证，还观察了它的自相似结构和倍周期分岔过程．The regularity of the two dimensional coupled logistic map is studied and a chaotic attractor is discovered in this paper.The Lyapunov exponents of the attractor are obtained by the repeated use of the Gram Schmidt reorthonormalization (GSR) procedure on the traced vector frame.We calculated various fractal dimensions of the attractor by relative definitions,which provide a new illustration for the conjecture of Kaplan and Yorke.Its selfsimilar structure and the process of period doubling bifurcations are also observed.

关 键 词：逻辑斯蒂映射 混沌吸引子 李雅普诺夫指数 分岔 

分 类 号：O411[理学—理论物理] O414.2[理学—物理]