利用改进的小波函数控制(超)混沌离散系统  

Control discrete(hyper-) chaotic system using improved wavelet functions

作　　者：李险峰[1] 褚衍东[1] 刘晓君[2] 张建刚[1] 

机构地区：[1]兰州交通大学数理与软件工程学院,甘肃兰州730070 [2]天水师范学院数学与统计学院,甘肃天水741001

出　　处：《华中科技大学学报（自然科学版）》2009年第5期72-74,共3页Journal of Huazhong University of Science and Technology(Natural Science Edition)

基　　金：国家自然科学基金资助项目(50475109);甘肃省自然科学基金资助项目(3ZS042-B25-049)

摘　　要：基于二次的Box-within-a-box分叉理论,得到二维离散混沌系统二参数分叉结构.通过穷尽计算离散(超)混沌系统在二参数平面上的李雅普洛夫指数和Kaplan-Yorke维数,求出系统在二维参数平面上的最复杂混沌吸引子.利用简单的小波函数及其改进形式,构造非线性压缩映射,对(超)混沌系统最复杂混沌吸引子进行了有效、快速的控制,得到了满意的控制结果.数值结果验证了方法的有效性.On the basis of theory of quadratic Box-within-a-box bifurcation, the two-parameter bifurcation structure of a two-dimensional discrete chaotic system was obained numerically. The maximally complex （hyper-） chaotic attractor was fixed by limited computing the Lyapunov exponents and the Kaplan-Yorke dimension of a two-parameter （hyper-） chaotic discrete system. The maximally complex （hyper-） chaotic attractor could be controlled effectively and fleetly by nonlinear contraction maps, which were composed of wavelet functions and their improved form, abundant control results were obtained. The effectiveness of this new method was validated by numerical simulation.

关 键 词：离散混沌系统 小波函数 吸引子 非线性映射 混沌控制 

分 类 号：TP301.5[自动化与计算机技术—计算机系统结构]