lyapunov exponent 中文意思是什麼
lyapunov exponent
解釋
李雅普諾夫指數-
We describe the meaning of chaos > future idea of chaotic theory and influence on forecast ; introduce the character of chaotic time series, and point out the problem and shortage of the methods already existed computing character value which are fractal dimension and the largest lyapunov exponent and improve on it ; present the forecast principle of forecast method based on chaotic attractor, and point out the shortage of local field forecast method based on chaotic attractor and bring forward improved on methodo at the same time, we put forward a banausic algorithm and compare two models using practical example
論述了混飩的含義與混淪理論的未來觀及其對預測的影響；介紹了。混飩時間序列的特徵，指出了己有的計算分形維及最大李雅譜諾夫指數這兩個特徵量的方法存在的問題與不足，並對此進行了改進；給出了基於混飩吸引子的預測方法的預測原理，指出了常用的基於混燉吸引子預測的局域法的不足並給出了改進方法，同時，給出了其實用演算法，並用實例進行了比較。 -
We give a brief theoretic analysis of using delayed self - controlling feedback to control beam halo. s ( the length of one period of focusing channel ) is selected as the delay parameter of the controller and the maximal lyapunov exponent is calculated
經分析，確定了延遲反饋控制器的延遲參數為s （一個聚焦磁場通道周期） ；而後，計算了系統的最大李雅普諾夫指數。 -
Lyapunov exponent depict the discrete extent of chaotic dynamic system. there propose an estimation of one step prediction error based on lyapunov exponent, the estimation express the reliability of prediction numerically. at the same time, in order to improve the predictive precision it drew out an error complement methods creatively to correct one step prediction
Lyapunov指數定量刻畫混沌離散動力系統的平均發散程度，基於lyapunov指數作出了一步預測的誤差估計，以此來定量反映預測的可靠性；根據奇異吸引子流形的性質，創造性的提出殘差補充法，對預測值作出修正以降低誤差，提高預測精確性。 -
As a reliable statistical index to describe chaos lyapunov exponent is applied extensively. the definition and algorithm are discussed in this paper. only in the one - mass hamiltonian system lyapunov exponent equals to the eigenvalue
作為描述混沌的一種可靠的統計指標， lyapunov指數被廣泛應用於電力系統混沌的判斷，本文介紹了其定義及演算法，指出在一般情況下，該指數不同於系統jacobi矩陣的特徵根。 -
The chaotic invariants of measured time series of dams such as correlation dimension, the lyapunov exponent and the kolmogorov entropy, are calculated
對大壩觀測時間序列進行了相空間重構，計算其混沌特徵量，即吸引子維數（關聯維數） 、 lyapunov指數和kolmogorov熵。 -
After the discussion of the algorithm of complexity parameters, lyapunov exponent and apen, the pressure fluctuation in fluidized beds is analyzed quantitatively. the effect of different operating conditions, such as variant gas superficial velocities, axial positions and static bed heights, is discussed
在討論復雜性參數、 lyapunov指數、近似熵的演算法基礎上，對流化床壓力脈動進行定量分析，討論了表觀氣速、軸向位置、靜床高等不同操作條件對混沌特徵參數的影響及其對應的動力學規律。 -
We reconstructed the phase space and calculated the nonlinear parameters such as correlation dimension, the largest lyapunov exponent, approximate entropy, and l - z complexity of the data. it can be conclud from the results that the reconstruction of heart beat rate signal is strange, its correlation dimension is between 5 to 7 and have the character of fractal dimension, its largest lyapunov exponent is larger than zero, its approximate entropy and l - z complexity are obviously differ from noise. we can draw a conclusion from all above : the heart beat rate signal is n ' t simple noise, it is high dimensional chaos obeys certain dynamical law
我們還對信號進行了相空間重構，計算了信號的關聯維數、最大lyapunov指數、近似熵和復雜度這幾個非線性特徵量，我們發現，心率信號的吸引子是奇怪吸引子，關聯維數介於5到7之間，具有分維的特徵，其最大lyapunov指數大於0 ，其近似熵值和復雜度值明顯區別于噪聲，這說明心率信號不是隨機噪聲，它是服從確定性動力學規律的高維混沌信號。 -
At first, construct ten sets of surrogate data for each emg data, then calculate the correlation dimension ( dcorr ), correlation time, maximum lyapunov exponent ( a, ), l - z complexity and approximate entropy ( apen ) of both the original emg data and surrogate data, and then compare them
構造這四例肌電信號的代替數據（各十組） ，分別計算原數據及其代替數據的關聯維、關聯時間、最大李雅普諾夫指數、 l - z復雜度和近似熵，我們發現，四例原數據的以上所有特徵量都與各自所對應的十組代替數據存在明顯差別。 -
It testifies that chaos is existed in the sonic signal of boiler tube leak, according to the chaos theory and the correlative contents about the sky dynamics, and illustrates the physical meanings of the lyapunov exponent ( the change at the place of the boiler tube leak ), based on the calculational methods of the lyapunov exponent and the peculiarities of boiler tube leak detection and diagnosis
根據混沌理論與空氣動力學的有關理論，確定了爐管泄漏聲信號中存在著混沌，在討論如lyapunov指數的演算法的基礎上，針對鍋爐爐管泄漏檢測與診斷的特點，明確了lyapunov指數的實際物理含義（爐管泄漏點處狀態的變化） 。 -
As an example, the time series of china composite stock index is considered firstly, the distribution of five day ' s return on china composite stock index is studied. secondly, based on the r / s analysis hurst exponent is worked out and determination detecting can be done. lastly, the topological characteristics such as correlation dimension and maximum lyapunov exponent are extracted from time series
作為例子，本文對中國股票指數時間序列做了實證分析，首先研究了中國股票指數的五天收益率的分佈規律，然後運用重標極差分析方法計算出赫斯特指數，並以此為基礎進行確定性檢驗，最後在相空間重構的基礎上提取吸引子的拓撲特徵指數。 -
At first, a method for controlling chaos is studied, which is based on phase switching modulation. the n - scroll chua ' s circuit is controlled to its fixed point as well as periodic orbits by using switching modulation on one its phase. its mechanism of control is analysed using the change of the max lyapunov exponent when the system is controlled
首先，通過對多渦卷蔡氏電路中非線性特性函數的相位進行開關調制，把多渦卷蔡氏電路由混沌狀態控制到其平衡態和周期軌道，並用控制后系統的最大lyapunov指數隨時間的轉變闡述了其控制機制。 -
It is constructed that radial impact and rubbing dynamics differential equations of the rotor system having the nonlinear rigidity on the unsteady and non - linear oil film. the bifurcation and chaos behavior of impact and rubbing fault rotor system caused by the parameters of nonlinear rigidity, rotor rotating speed, eccentric mass is analyzed, in the numerical value analysis method. the bifurcation diagrams, maximum lyapunov exponent diagrams, poincar maps, phase plane portraits, trajectories of journal center, time - history curve, amplitude spectra diagrams of the rotor motion are used
（ 2 ）建立了具有非線性剛度的轉子系統在非穩態非線性油膜力作用下的徑向碰摩動力學微分方程，並應用含高階余項的非線性動力方程的線性化數值法研究了此類系統響應的復雜動力學行為，利用轉子響應的分岔圖、最大lyapunov指數曲線、 poincar截面映射、時域波形、相軌線、軸心軌跡、幅值譜等圖形分析了系統響應的周期運動、擬周期運動、倍周期分岔、混沌等運動形式的轉化與演變過程，重點研究了非線性剛度、轉子轉速、偏心質量等系統參數對碰摩故障轉子系統的分岔和混沌行為的影響。 -
We try to use the proposed method to understand of information processes in brain. main works of the dissertation are as follows : firstly, introduced the model of wang - smith cnn, and its dynamics characteristics, such as lyapunov exponent ( le ), bifurcation and dissipative have been analyzed thoroughly. based on this, an improved wang - smith cnn is proposed, whose dynamics characteristics also have been analyzed thoroughly
本文所作的工作主要有：首先，簡要介紹wang - smith混沌神經網路模型並深入分析該模型的動力學特性，這主要包括兩個方面：一方面是分析只含有一個神經元時系統的lyapunov特徵指數、分岔現象以及系統的耗散性；另一方面是分析含有多個神經元時系統的lyapunov特徵指數和系統的耗散性。 -
In addition the h. kantz method is applied to analyze the time series of the motor current, the maximal lyapunov exponent calculation is realized, the criterion for the motor chaos is brought forward, the existence of chaotic phenomenon in the induction motor is verified by the characteristic exponents, which proves theoretically that the chaotic movement is one of the reasons that results in the low frequency oscillation of the induction motor system
應用h . kantz方法對電機電流信號的時間序列分析，實現了最大李亞普諾夫指數的具體演算法，提出了電機出現混沌運動的判定根據，通過特徵指數驗證了異步電動機現象的存在，從理論上說明混沌運動是異步電動機系統產生低頻振蕩的原因之一。第三部分深入研究了系統低頻振蕩的主要影響因素。 -
Application of maximal lyapunov exponent to weak signal detection
匹配追蹤時頻分解演算法的點檢測方法 -
Finally, the results are compared with periodic and random chains. then we studied acoustic wave propagation in 1d quasiperiodic and aperiodic systems by means of he transfer matrix. transmission rate, reflection rate, energy flow, logarithmic energy flow, energy density and lyapunov exponent are computed numerically, and compared with periodic and random system
其次研究了聲波在幾種一維準周期和非周期系統中的傳播，通過轉移矩陣的方法，數值地得到了系統的傳播系數t _ n 、反射系數r _ n 、能流密度j _ n ，能量密度e _ n和lyapunov指數，給出了以上各量與傳播長度n以及頻率之間的關系，同時發現能流及能量密度都具有分形結構，並與周期和隨機系統的結果作了比較。 -
Firstly, acoustic waves propagation in id quasi - periodic system is studied by means of the transfer matrix method. the transmission rate, reflection rate, energy flow, logarithmic energy flow, energy density and lyapunov exponent are obtained numerically. we explain all these parameters " relations with frequency and the size of system, and compare these p arameters with those o f periodic system. we find that these parameters are fractal in this quasi - period system
通過轉移矩陣的方法，數值地得到了系統的傳播系數t _ n 、反射系數r _ n ，能流密度j _ n 、能量密度e _ n 、李雅譜諾大指數_ n ，給出了以上各量與系統大小n以及頻率之間的關系，發現這些量存在著與周期系統不同的準周期性質，其能量會出現局域化現象，能流以及能量密度都具有分形結構，給出了相應的理論解釋。 -
The main contents of this dissertation are follows : the mathematical model of chaos is discussed deeply from mathematical map, statistical viewpoint for the purpose of analysis and synthesis chaotic signal. the dissertation analysis chaotic signals deeply, mainly about the correlation property ( including auto - correlation and cross correlation ) and lyapunov exponent. the study shows the ideal auto correlation and cross correlation of the chaotic signals by using theoretical derives and computer simulations
本文首先對混沌信號的數學模型進行了深入的討論，並分別從數學映射、統計學角度對其數學模型進行了全面的研究，特別是全面總結了混沌系統的統計學模型的研究成果，討論並給出了混沌與噪聲的區別與相似之處；雷達信號處理的重要一步是雜波中的信號檢測問題。 -
These include two keys problem in phase space reconstruction theory, that is embedding dimension and optimal delay time, and numeric recognition of chaos, that is lyapunov exponent, as well as numeric recognition of fractal, that is correlative dimension of chaotic attractors
其中重點講述了非線性動力學的數值研究實驗方法：相空間重構的兩個關鍵問題，即嵌入維數和最佳延遲時間；混沌的數值識別，即李雅普諾夫指數；分形的數值識別，即吸引子的關聯維數。 -
The one dimension lyapunov exponent mode of boiler tube leak prediction is confirmed
確定了爐管泄漏預報的一維lyapunov指數模式。
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