Discrete Dynamic System without Degradation -configure N Positive Lyapunov Exponents
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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。Abstract: 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.
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表 1 两种算法配置Lyapunov指数效果比较
期望配置的李氏指数 Chen-Lai算法 本文算法 0.1 1.4112; 1.8741 0.1261; 0.1101 0.6 1.5732; 1.9542 0.6612; 0.6213 3.0 3.1392; 3.2317 3.0201; 3.0131 
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表 2 2种算法运行速度的比较(s)
混沌系统的维数 Chen-Lai算法 本文算法 3 0.0517 0.0279 4 0.0579 0.0287 5 0.1025 0.0587 6 0.1534 0.6640
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