李雅普诺夫指数

结果非线性动力学研究方法对糖尿病患者HRV分析的结果表现出很强的特异性，尤其是李雅普诺夫指数、近似熵和非线性能量算子。

Results The nonlinear indices of both DAN patients and patients without obvious DAN were significantly different from those of the normal subjects , especially in terms of Lyapunov exponent , approximate entropy , and nonlinear energy operator .

本文通过相关维检验、李雅普诺夫指数检验、BDS检验和返回临近（CR）检验对中国股票市场的混沌特征进行了分析，获得中国股票市场是混沌的有力证据。

We have tested the chaotic characteristics by using correlation dimension test , Lyapunov exponent test , BDS test and close return ( CR ) test . The conclusion indicates that Chinese stock market is chaotic .

冠心患者与健康人同步12导联ECG信号的李雅普诺夫指数谱比较研究

A comparative study of Lyapunov spectra of CAD patients ' and healthy people 's synchronous 12-lead ECG signals

通过计算N台激光阵列的李雅普诺夫指数表明，当激光系统出现混沌同步时，系统的最大李雅普诺夫指数大于零，激光系统的参数范围完全处于混沌状态。

The calculation of the Lyapunov exponents in the array of N lasers shows that the laser system is in the chaotic states when the largest Lyapunov exponents are greater than zero . The parameters in the laser system are in the chaotic states .

机械设备故障信号的李雅普诺夫指数识别

Lyapunov exponent recognition for the fault signal of mechanical equipment

李雅普诺夫指数降低开关模式电源电磁干扰水平研究

Research to Reduce Electromagnetic Interference Level of Switching-Mode Power Supply with Different Lyapunov Exponents

用时间序列的李雅普诺夫指数计算预报电力系统中的某些失稳现象

Predicting some collapses in power systems by computing windowed Lyapunov exponents of time series

李雅普诺夫指数谱的研究与仿真

Research and Simulation of Lyapunov 's Exponents

热线温度场稳定性的实验研究&李雅普诺夫指数和分形数

An experimental research on thermal stability of hot wire & lyapunov exponent and fractal dimension

混沌的存在是由李雅普诺夫指数的计算和分析所确定。

The existence of the chaos is confirmed by calculation and analysis of its Lyapunov exponents .

提出了通过改变离散混沌系统的李雅普诺夫指数对离散混沌系统进行控制的一种方法。

It is proved that chaotic systems could be controlled by changing the Lyapunov exponents of the systems and setting it to be negative .

通过相图分析、李雅普诺夫指数分析和分维分析，本文得到了二维超声速自由剪切层流动由线性到非线性失稳过程的数学特征。

Upon the analyses on the phase mapping , Lyapunov exponents and fractal dimension , the mathematical feature of nonlinear instability development have been described .

通过功率谱分析、李雅普诺夫指数、分形维数及柯熵的研究，确立了微振动与混沌的关系。

The relationship between the micro-vibration and chaos was confirmed under the research of analyzing power spectrum , Lyapunov exponent , fractal dimension and Kolmogorov entropy .

方法利用庞加莱截面、李雅普诺夫指数、关联维等工具分别对抛物方程和椭圆方程的非线性动力学行为进行描述。

Methods Nonlinear dynamical behavior of both parabolic equation and elliptic equation were investigated by several tools such as Poincare section , Lyapunov exponent , and correlation dimension .

通过数值模拟，模拟了该系统的时间演化图、相图、分岔图、庞加莱映射图以及最大李雅普诺夫指数谱图，并进行了分析。

Time evolution , phase diagrams , bifurcation diagram , Poincare map , and largest Lyapunov in-dex spectrogram of the system are plotted by means of numerical simulations .

根据这一地点的李雅普诺夫指数，算出理论上有效预测点数为144个。

According to the Lyapunov exponent in this area , we reckon the efficient time points are 144 in theory . In this score , our prediction is successful .

在以往的研究中，人们强调弱噪声引起的神经元同步，发现同步时李雅普诺夫指数为负值。

In previous research , people focus on the effect of weak noise on the neurons , and find when synchronization occurs , the leading Lyapunov exponents is negative .

延迟混沌系统是无限维系统，能生成多个正的李雅普诺夫指数，对其分析和控制都比较困难。

The time-delayed chaotic system is infinite dimensional systems , and it can generate multiple positive Lyapunov exponents , and it is more difficult to be analysised and controled .

此处所谓的亚超混沌振荡，是指相空间轨线的吸引子具有（＋，0，0，－）类型的李雅普诺夫指数谱的振荡制式而言的。

The so called quasi - hyperchaos is defined as a chaos corresponding to a strange attractor with the Lyapunov exponent spectrum of the type ( + , 0,0 , - ) .

介绍了混沌时间序列分析中根据单个时间序列重建相空间，用关联维方法和李雅普诺夫指数来辨识观测数据中存在混沌的可能性，以及全局和局部预测方法。

This paper introduces the reconstruction of phase space in one time series , the identification of possible existence of chaos by the correlation dimension method and Lyapunov exponent , and the global and local method of predication of chaotic time series .

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。

Some basic problems of Lyapunov Characteristic Exponents ( LCE ) are discussed , including the computational method and the fact that the Lyapunov exponent of any limit set other than an equilibrium point must be zero , namely one of the Lyapunov exponents should vanishes .