离散动力系统无退化-配置N个正Lyapunov指数  

Discrete Dynamic System without Degradation-configure N Positive Lyapunov Exponents

作　　者：赵耿[1,2] 李红[1,2] 马英杰 秦晓宏[2] ZHAO Geng;LI Hong;MA Yingjie;QIN Xiaohong(Xidian University,Xi’an 710071,China;Beijing Electronic Science and Technology Institute,Beijing 100070,China)

机构地区：[1]西安电子科技大学,西安710071 [2]北京电子科技学院,北京100070

出　　处：《电子与信息学报》2019年第9期2280-2286,共7页Journal of Electronics & Information Technology

基　　金：国家自然科学基金(61772047)~~

摘　　要：针对离散时间混沌动力学系统,该文提出一种基于矩阵特征值以及特征向量配置Lyapunov指数为正的新算法。计算离散受控矩阵的特征值以及特征向量,设计一类具有正Lyapunov指数的通用控制器,理论证明系统轨道的有界性和Lyapunov指数的有限性。对线性反馈算子以及微扰反馈算子进行数值仿真分析,验证了算法的正确性、通用性和有效性。性能评估表明,与Chen-Lai算法相比,该方法可以构建较低计算复杂度的混沌系统,并且运行时间较短,其输出序列也具有较强的随机性,实现了无退化、无兼并的离散混沌系统。Considering discrete-time chaotic dynamics systems,a new algorithm is proposed which is based on matrix eigenvalues and eigenvectors to configure Lyapunov exponents to be positive.The eigenvalues and eigenvectors of the discrete controlled matrix are calculated to design a general controller with positive Lyapunov exponents.The theory proves the boundedness of the system orbit and the finiteness of the Lyapunov exponents.The numerical simulation analysis of the linear feedback operator and the perturbation feedback operator verifies the correctness,versatility and effectiveness of the algorithm.Performance evaluations show that,compared with Chen-Lai methods,the proposed method can construct chaotic system with lower computation complexity and the running time is shorter and the outputs demonstrate strong randomness.Thus,a discrete chaotic system with no degradation and no merger is realized.

关 键 词：混沌系统 无退化 LYAPUNOV指数 矩阵特征值 线性反馈算子 微扰反馈算子 

分 类 号：TP309.7[自动化与计算机技术—计算机系统结构]