一种最大李雅普诺夫指数估计的稳健算法

最大李雅普诺夫指数是诊断和描述动态系统混沌的重要参数.在深入研究相空间重构技术和轨道跟踪法的基础上,提出了一种从标量混沌时间序列中估计最大李雅普诺夫指数的新算法.该算法能够克服现有算法的不足,主要有以下三个优点:1)很高的精度;2)几乎不受噪声的影响;3)所需的计算时间和存贮空间小, 能进行在线计算.     

一种最大李雅普诺夫指数估计的稳健算法

最大李雅普诺夫指数是诊断和描述动态系统混沌的重要参数.在深入研究相空间重构技术和轨道跟踪法的基础上,提出了一种从标量混沌时间序列中估计最大李雅普诺夫指数的新算法.该算法能够克服现有算法的不足,主要有以下三个优点:1)很高的精度 2)几乎不受噪声的影响 3)所需的计算时间和存贮空间小,能进行在线计算 关键词：     

常微分方程系统李雅普诺夫特性指数的研究

讨论常微分方程系统李雅普诺夫特性指数的一些基本问题,包括数值计算技术和常微分方程系统任何平衡点以外极限集的李雅普诺夫指数必有一个为零的结论.给出超混沌吸引子必超出3维的结论,指出基于常微分方程求解李雅普诺夫指数的Wolf程序使用中初值的选取对结果的影响.同时提出一种简便可行的计算条件李雅普诺夫指数方法.通过数值研究一些重要模型进一步说明本文的观点及提出的方法.对常微分方程系统任何平衡点以外极限集的李雅普诺夫指数必有一个为零的结论进行了讨论,可以作为分析结果和计算方法的有利工具,在一些工作中被忽视. 关键词：     

嗓音多频带非线性分析的声带病变识别

提出了一种嗓音多频带非线性分析的声带病变识别方法,以提高声带病变嗓音的识别率。首先采用Gammatone听觉滤波器组对嗓音信号进行滤波,求取每个频带下的最大李雅普诺夫指数;对映射到核空间的数据采用高斯最大似然度准则优化核函数,然后采用优化核主成分分析算法实现特征抽取。识别实验表明,多频带最大李雅普诺夫指数的识别率比传统的MFCC和最大李雅普诺夫指数分别有6.52%和8.45%的提高,且采用优化核主成分分析算法比传统核主成分分析算法有更好的抽取效果.将多频带非线性分析和优化核主成分分析算法结合,识别率提升至97.82%。      

一类四维超混沌系统的界及同步的研究

文章研究了一类四维连续自治系统,在一定条件下它只有一个平衡点,却表现出复杂的动力学行为. 文章首先分析了系统的平衡点及李雅普诺夫指数;其次对该系统的界进行了估计,给出了界的表达式.通过设计一个控制器,研究了该四维超混沌系统的完全同步,并做出了相应的数值模拟. 关键词： 超混沌系统 李雅普诺夫指数 混沌系统的界 同步     

声光双稳态系统混沌的周期扰动控制

声光双稳混沌系统的参量受到进行周期扰动,在一定扰动强度下,可实现对混沌的控制.通过数值模拟,证明该方法的有效性,并计算了系统随扰动强度的状态演化和李雅普诺夫指数演化,揭示了扰动强度与系统状态的关系.在此基础上的实验研究,实验证实了对声光双稳混沌系统进行参量扰动可以有效控制混沌.     

V型阵发李雅普诺夫指数标度律的验证

报道在一个张弛振荡电路中获得的V型阵发李雅普诺夫指数标度律的实验证据.对这个电路的理论模型进行了数值计算，所得结果与实验一致. 关键词：     

用常数周期脉冲方法控制耦合标准映象的混沌

将用常数周期脉冲方法控制保守系统的混沌运动的方法，用于控制高维系统耦合标准映象的混沌运动，计算了系统参数k=0.8和耦合常数β=0.04的有限时间李雅普诺夫指数，考察了不同系统参数和耦合常数下的有限时间李雅普诺夫指数随迭代次数的演化规律，从各次迭代的有限时间收敛区选择满足期望动力学特征的轨道片段，施加适当的脉冲强度找出其对应的周期不动点，从而得到期望的周期转道。     

强迫布鲁塞尔振子奇异吸引子的柯尔莫哥洛夫容量和李雅普诺夫维数

本文用周期采样降低吸引子维数的办法,计算和讨论了强迫布鲁塞尔振子的几种典型吸引子的柯尔莫哥洛夫容量d_C和李雅普诺夫维数d_L。结果表明,人们关于d_C和d_L关系的推测是正确的。这些推测是:当最大李雅普诺夫指数λ₁>0时d_C=d_L关系成立,当λ₁=0时d_C=d_L关系不一定成立。文中指出和论证了强迫布鲁塞尔振子的Runge-Kutta差分方程使上述算法给出的d_C不收敛的原因和克服办法。文中还指出:可能是类似的微分方程的差分化的原因,使得用单个观察量的时间系列来计算容量的办法遇到了发散困难。 关键词：     

非线性反馈控制单模激光Haken-Lorenz混沌系统

提出一种变量非线性反馈（VNF）方法控制混沌系统.介绍了该方法的控制原理以及反馈系数的选取原则,以单模激光Haken-Lorenz系统为例对非线性反馈控制方法进行了理论研究.仿真结果显示,通过恰当的选择反馈系数k,使系统的最大李雅普诺夫（Lyapunov）指数由正值转变为负值,相图中系统的轨迹由混沌吸引子转变为周期数为2n×3mp(n、m为整数)的周期轨道.通过与线性反馈控制结果对比发现,非线性反馈控制方法简便有效,控制速度快.     

New method for computing finite-time Lyapunov exponents

We present a novel method for computing finite-time Lyapunov exponents and vectors, via generalizing a correction given by Goldhirsch, Sulem, and Orszag [Physica (Amsterdam) 27D, 311 (1987)]] into higher-order corrections. This method is a generalized LR method, which is, in contrast to the existing methods, applicable to multidimensional systems with degenerate spectra. The efficiency and accuracy is demonstrated by applying it to multidimensional dynamical systems. Without these corrections, we could not accurately detect, as an example, the coexistence of qualitatively different Lyapunov instabilities along a trajectory for a multidimensional oscillator system.     

Determining Lyapunov exponents from a time series

We present the first algorithms that allow the estimation of non-negative Lyapunov exponents from an experimental time series. Lyapunov exponents, which provide a qualitative and quantitative characterization of dynamical behavior, are related to the exponentially fast divergence or convergence of nearby orbits in phase space. A system with one or more positive Lyapunov exponents is defined to be chaotic. Our method is rooted conceptually in a previously developed technique that could only be applied to analytically defined model systems: we monitor the long-term growth rate of small volume elements in an attractor. The method is tested on model systems with known Lyapunov spectra, and applied to data for the Belousov-Zhabotinskii reaction and Couette-Taylor flow.     

基于非线性控制的超混沌Chen系统混沌同步

研究了基于非线性控制的超混沌Chen系统的混沌同步问题.基于Lyapunov稳定性理论，设计了非线性控制器，改进了Jiang和Huang等设计的同步误差系统的Lyapunov函数形式，理论证明了超混沌Chen系统的自同步和超混沌Chen系统与超混沌R?ssler系统的异结构同步.数值模拟进一步验证了所提出方案的有效性. 关键词： 超混沌Chen系统 自同步 异结构同步 非线性控制器     

Scaling and interleaving of subsystem Lyapunov exponents for spatio-temporal systems

The computation of the entire Lyapunov spectrum for extended dynamical systems is a very time consuming task. If the system is in a chaotic spatio-temporal regime it is possible to approximately reconstruct the Lyapunov spectrum from the spectrum of a subsystem by a suitable rescaling in a very cost effective way. We compute the Lyapunov spectrum for the subsystem by truncating the original Jacobian without modifying the original dynamics and thus taking into account only a portion of the information of the entire system. In doing so we notice that the Lyapunov spectra for consecutive subsystem sizes are interleaved and we discuss the possible ways in which this may arise. We also present a new rescaling method, which gives a significantly better fit to the original Lyapunov spectrum. We evaluate the performance of our rescaling method by comparing it to the conventional rescaling (dividing by the relative subsystem volume) for one- and two-dimensional lattices in spatio-temporal chaotic regimes. Finally, we use the new rescaling to approximate quantities derived from the Lyapunov spectrum (largest Lyapunov exponent, Lyapunov dimension, and Kolmogorov-Sinai entropy), finding better convergence as the subsystem size is increased than with conventional rescaling. (c) 1999 American Institute of Physics.     

异结构系统混沌同步的新方法

基于Lyapunov稳定性理论, 结合反馈控制和自适应控制方法, 提出了一种异结构混沌系统同步的新方法. 该方法适用范围广, 不仅能为人们提供控制器的一般选取办法，而且对于具体的误差系统还可进一步简化控制器结构, 具有稳健、易于实现等优点. 通过对Lorenz系统与Liu系统、超混沌的R?ssler系统与广义Lorenz系统的同步数值仿真, 证实了该方法的有效性. 关键词： 混沌同步 Lorenz系统 R?ssler系统 Lyapunov函数     

级联混沌及其动力学特性研究

初值敏感性是混沌的本质,混沌的随机性来源于其对初始条件的高度敏感性,而Lyapunov指数又是这种初值敏感性的一种度量.本文的研究发现,混沌系统的级联可明显提高级联混沌的Lyapunov指数,改善其动力学特性.因此,本文研究了混沌系统的级联和级联混沌对动力学特性的影响,提出了混沌系统级联的定义及条件,从理论上证明了级联混沌的Lyapunov指数为各个级联子系统Lyapunov指数之和;适当的级联可增加系统参数、扩展混沌映射和满映射的参数区间,由此可提高混沌映射的初值敏感性和混沌伪随机序列的安全性.以Logistic映射、Cubic映射和Tent映射为例,研究了Logistic-Logistic级联、Logistic-Cubic级联和Logistic-Tent级联的动力学特性,验证了级联混沌动力学性能的改善.级联混沌可作为伪随机数发生器的随机信号源,用以产生初值敏感性更高、安全性更好的伪随机序列.     

One Lyapunov control for quantum systems and its application to entanglement generation

In this Letter, we investigate the control of finite dimensional ideal quantum systems in which the quantum states are represented by the density operators. A new Lyapunov function based on the Hilbert–Schmidt distance and mechanical quantity of the quantum system is given. We present a theoretical convergence result using LaSalle invariance principle. Applying the proposed Lyapunov method, the generation of the maximally entangled quantum states of two qubits is obtained.     

切换系统Lyapunov指数的算法及应用

Lyapunov指数是判定系统非线性行为的重要工具,然而目前的大多算法并不适用于切换系统.在传统Jacobi法的基础上,提出了一种新算法,可以直接计算得到n维切换系统的n个Lyapunov指数.首先,根据切换面处相邻轨线的动态变化规律,从相空间几何推导出切换面处轨线变化的Jacobi矩阵;然后,对该矩阵进行QR分解,从而利用R的对角线元素实现Lyapunov指数的切换补偿;最后,将新算法应用到平面双螺旋混沌系统、Glass网络和航天器供电系统三个实例中,并将计算结果与Poincaré映射方法的计算结果进行比较,对新算法的有效性进行验证.     

The adaptive synchronization of fractional-order Liu chaotic system with unknown parameters

In this paper, the chaos control and the synchronization of two fractional-order Liu chaotic systems with unknown parameters are studied. According to the Lyapunov stabilization theory and the adaptive control theorem, the adaptive control rule is obtained for the described error dynamic stabilization. Using the adaptive rule and a proper Lyapunov candidate function, the unknown coefficients of the system are estimated and the stabilization of the synchronizer system is demonstrated. Finally, the numerical simulation illustrates the efficiency of the proposed method in synchronizing two chaotic systems.     

Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy methods for sums of Lyapunov exponents for dilute gases

We consider a general method for computing the sum of positive Lyapunov exponents for moderately dense gases. This method is based upon hierarchy techniques used previously to derive the generalized Boltzmann equation for the time-dependent spatial and velocity distribution functions for such systems. We extend the variables in the generalized Boltzmann equation to include a new set of quantities that describe the separation of trajectories in phase space needed for a calculation of the Lyapunov exponents. The method described here is especially suitable for calculating the sum of all of the positive Lyapunov exponents for the system, and may be applied to equilibrium as well as nonequilibrium situations. For low densities we obtain an extended Boltzmann equation, from which, under a simplifying approximation, we recover the sum of positive Lyapunov exponents for hard-disk and hard-sphere systems, obtained before by a simpler method. In addition we indicate how to improve these results by avoiding the simplifying approximation. The restriction to hard-sphere systems in d dimensions is made to keep the somewhat complicated formalism as clear as possible, but the method can be easily generalized to apply to gases of particles that interact with strong short-range forces. (c) 1998 American Institute of Physics.