一个二维滞后Logistic映射的分岔与分形  

Bifurcation and Fractal of Two-Dimensional Lagged Logistic System

作　　者：王立明[1] 

机构地区：[1]廊坊师范学院物理系,河北廊坊065000

出　　处：《河南师范大学学报（自然科学版）》2010年第1期86-89,共4页Journal of Henan Normal University(Natural Science Edition)

基　　金：廊坊师范学院科学研究项目(LSZQ200906)

摘　　要：利用理论推导分析了二维滞后Logistic映射周期解的稳定性和分岔,利用相图、分岔图、Lyapunov指数和分维数等计算方法,证明了二维滞后Logistic映射依次经叉形分岔和Hopf分岔通向混沌.对二维滞后Logistic映射的吸引盆及其广义M-J集的研究表明:不同周期轨道的吸引盆形状相似,大小不同,每个吸引盆中周期和非周期区域之间的边界是分形的;广义M集的结构与a,R和有N关,广义J集的结构与a,R,N,和Cx,Cy有关,并且广义M-J集具有分形特征.The bifurcation of Two-dimensional Lagged Logistic System is analyzed theoretically and numerically. By using phase maps,bifurcation graphics,fractal dimension and Lyapunov exponent,the paper reveals the general features of two-dimensional lagged Logistic system transition from regularity to chaos and the fractal configuration of Periodic attraction basin and general Mandelbrot-Julia sets,the following conclusions are shown：（1）Chaotic patterns of the map may emerge out of fork bifurcation and Hopf bifurcation in turn;（2）shape is similar and size is different among different periodic attractor basins,the boundaries between periodic and non-periodic regions is fractal that indicates the moving end-result of the points in phase plane is predicted impossibly;（3）The boundaries of the general Mandelbrot-Julia sets are fractal,The structures of the general Mandelbrot sets are determined by the control parameters a,R and N ,The structures of the general Julia sets are determined by the control parameters a,R,N,Cx and Cy.

关 键 词：二维滞后Logistic映射 HOPF分岔 吸引盆 逃逸时间算法 广义M-J集 分形 

分 类 号：TP301.5[自动化与计算机技术—计算机系统结构]