二维滞后logistic映射的混沌行为、控制和混沌同步  

Chaos,chaos control and synchronization 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：《西北师范大学学报（自然科学版）》2009年第6期26-31,53,共7页Journal of Northwest Normal University(Natural Science)

基　　金：河北省教育厅研究项目(Z2008128)

摘　　要：利用分岔图、Lyapunov指数、相图等方法研究了二维滞后logistic映射通向混沌的道路,应用逃逸时间算法构造二维滞后logistic映射的彩色广义M-J集,分析了广义M-J集的对称性问题.以此为基础,基于离散系统稳定性理论和Pecora-Carroll混沌同步定理,设计非线性反馈控制器,分别实现了二维滞后logistic映射的不稳定单周期点的镇定和混沌同步.通过分析受控系统的Jacobi矩阵对应的特征方程和计算响应系统的最大条件Lyapunov指数,分别得到了离散系统的不稳定单周期点的镇定条件和混沌同步条件.基于Matlab软件的数值模拟结果证明了上述方法的有效性.By using phase maps,bifurcation graphics and Lyapunov exponent,the paper reveals the transition of two-dimensional lagged logistic system from regularity to chaos.When Lyapunov dimension is calculated based on Lyapunov exponent and the color general Mandelbrot-Julia sets is constructed by using escape time algorithm,the fractal characterization of strange attractors is described quantitatively and qualitatively respectively.Based on the stability theory of discrete systems and Pecora-Carrol chaotic synchronization theorem, the nonlinear controller which can suppress chaos to unstable equilibrium points and the nonlinear controller which can synchronize identical system are proposed respectively. Through analyzing the eigenvalue of Jacobi matrix of the controlled system and calculating the maximum conditional Lyapunov exponent of the response system, the suppression region and the synchronization region of control parameter are gained respectively. The numerical simulation based on Matlab software shows their effectiveness.

关 键 词：二维滞后logistic映射 HOPF分岔 逃逸时间算法 广义M-J集 混沌控制 混沌同步 

分 类 号：TP301.5[自动化与计算机技术—计算机系统结构]