一类混沌系统全局指数吸引集的新结果及应用  

New results of globally exponentially attractive set of a class of chaotic system and their application

作　　者：蹇继贵[1] 涂正文[1] 王建凤[1] 

机构地区：[1]三峡大学非线性与复杂系统研究所,湖北宜昌443002

出　　处：《华中科技大学学报（自然科学版）》2010年第6期12-14,27,共4页Journal of Huazhong University of Science and Technology(Natural Science Edition)

基　　金：湖北省高等学校优秀中青年团队计划资助项目(T200809);湖北省自然科学基金资助项目(2008CDB316;2008CDZ046);湖北省教育厅重点项目(D20091305)

摘　　要：研究了一类新混沌系统的全局指数吸引集与全局指数同步的问题.首先,根据全局指数吸引集的定义及李雅普诺夫稳定性理论,在没有任何存在性的假设下,对于系统所给参数构造了广义正定、径向无界的李雅普诺夫函数簇,给出了新混沌系统的全局指数吸引集和正向不变集的新估计.其次,对于两个混沌系统,采用线性反馈同步方法给出了两个混沌系统全局指数同步的充分性代数判据.最后,通过数值仿真给出了系统的同步误差图,结果表明此方法是可行有效的.The globally exponentially attractive set and synchronization problem of a new chaotic system was researched.Firstly,based on the definition of globally exponentially attractive set and Lyapunov stability theory, by constructing a family of generalized positive definite Lyapunov functions with radially unbound with respect to the parameters of the system,some new estimations of the globally exponentially attractive set of the new chaotic system were obtained without any existence assumptions.Secondly,a sufficient algebraic criterion for the globally exponential synchronization of two chaotic systems is obtained analytically via linear feedback approach.The figure of synchronous errors is given and the numerical simulation results indicate the effectiveness of the proposed methods.

关 键 词：混沌系统 线性反馈控制 全局指数吸引集 全局指数同步 广义李雅普诺夫函数 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]