%0 Journal Article
%T Bifurcation and fractal of the coupled logistic maps<br>二维Logistic映射的分岔与分形
%A Wang Xingyuan Luo Chao
%A <br>王兴元
%A 骆超
%J 力学学报
%D 2005
%I 
%X The bifurcation of the coupled Logistic map is analyzed theoretically. By using phase graphics, bifurcation graphics, power spectra, the computation of the fractal dimension and the Lyapunov exponent, the paper reveals the general features of the coupled Logistic map transition from regularity to chaos, the following conclusions are shown: (1) Chaotic patterns of the map may emerge out of double-periodic bifurcation and Hopf bifurcation, respectively; (2) During the process of double-period bifurcation, the system exhibits the self-similar structure and invariance which is under scale variety in both parameter space and phase space. Prom the research on attractor basin of the coupled Logistic map and Mandelbrot-Julia set, the following conclusions are indicated: (1) The boundary between periodic and non-periodic regions is fractal, and that indicates the impossibility to predict the moving end-result of the points in phase plane; (2) The structures of the Mandelbrot-Julia sets are determined by the control parameters, and their boundaries have the fractal characteristic.
%K coupled Logistic map
%K bifurcation
%K chaos
%K Mandelbrot-Julia set
%K fractal<br>Logistic映射
%K 二维
%K 分形
%K Lyapunov
%K 倍周期分岔
%K Hopf分岔
%K Julia集
%K M-J集
%K 维数计算
%K 尺度变换
%K 自相似性
%K 参数空间
%K 控制参数
%K 吸引盆
%K 分岔图
%K 功率谱
%K 指数和
%K 非周期
%K 不变性
%K 相空间
%K 相平面
%K 边界
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=6E709DC38FA1D09A4B578DD0906875B5B44D4D294832BB8E&cid=5D344E2AD54D14F8&jid=4100DA4A1A3BA1B0CE5AD99AE1DFB420&aid=675B20414D4253EE&yid=2DD7160C83D0ACED&vid=42425781F0B1C26E&iid=38B194292C032A66&sid=C7DDDE86E6286CD9&eid=26AEEED215BE97D0&journal_id=0459-1879&journal_name=力学学报&referenced_num=6&reference_num=22