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Application of the Conditional Nonlinear Local Lyapunov Exponent to Second-Kind Predictability
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作者 Ming ZHANG Ruiqiang DING +2 位作者 Quanjia ZHONG Jianping LI Deyu LU 《Advances in Atmospheric Sciences》 SCIE CAS CSCD 2024年第9期1769-1786,共18页
In order to quantify the influence of external forcings on the predictability limit using observational data,the author introduced an algorithm of the conditional nonlinear local Lyapunov exponent(CNLLE)method.The eff... In order to quantify the influence of external forcings on the predictability limit using observational data,the author introduced an algorithm of the conditional nonlinear local Lyapunov exponent(CNLLE)method.The effectiveness of this algorithm is validated and compared with the nonlinear local Lyapunov exponent(NLLE)and signal-to-noise ratio methods using a coupled Lorenz model.The results show that the CNLLE method is able to capture the slow error growth constrained by external forcings,therefore,it can quantify the predictability limit induced by the external forcings.On this basis,a preliminary attempt was made to apply this method to measure the influence of ENSO on the predictability limit for both atmospheric and oceanic variable fields.The spatial distribution of the predictability limit induced by ENSO is similar to that arising from the initial conditions calculated by the NLLE method.This similarity supports ENSO as the major predictable signal for weather and climate prediction.In addition,a ratio of predictability limit(RPL)calculated by the CNLLE method to that calculated by the NLLE method was proposed.The RPL larger than 1 indicates that the external forcings can significantly benefit the long-term predictability limit.For instance,ENSO can effectively extend the predictability limit arising from the initial conditions of sea surface temperature over the tropical Indian Ocean by approximately four months,as well as the predictability limit of sea level pressure over the eastern and western Pacific Ocean.Moreover,the impact of ENSO on the geopotential height predictability limit is primarily confined to the troposphere. 展开更多
关键词 conditional nonlinear local lyapunov exponent second-kind predictability coupled Lorenz model ENSO
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General mapping of one-dimensional non-Hermitian mosaic models to non-mosaic counterparts:Mobility edges and Lyapunov exponents
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作者 蒋盛莲 刘彦霞 郎利君 《Chinese Physics B》 SCIE EI CAS CSCD 2023年第9期79-86,共8页
We establish a general mapping from one-dimensional non-Hermitian mosaic models to their non-mosaic counterparts.This mapping can give rise to mobility edges and even Lyapunov exponents in the mosaic models if critica... We establish a general mapping from one-dimensional non-Hermitian mosaic models to their non-mosaic counterparts.This mapping can give rise to mobility edges and even Lyapunov exponents in the mosaic models if critical points of localization or Lyapunov exponents of localized states in the corresponding non-mosaic models have already been analytically solved.To demonstrate the validity of this mapping,we apply it to two non-Hermitian localization models:an Aubry-Andre-like model with nonreciprocal hopping and complex quasiperiodic potentials,and the Ganeshan-Pixley-Das Sarma model with nonreciprocal hopping.We successfully obtain the mobility edges and Lyapunov exponents in their mosaic models.This general mapping may catalyze further studies on mobility edges,Lyapunov exponents,and other significant quantities pertaining to localization in non-Hermitian mosaic models. 展开更多
关键词 non-Hermitian mosaic model mosaic-to-non-mosaic mapping mobility edge lyapunov exponent
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Lagrangian-based investigation of multiphase flows by finite-timeLyapunov exponents 被引量:12
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作者 Jia-Ning Tang Chien-Chou Tseng Ning-FeiWang 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2012年第3期612-624,共13页
Multiphase flows are ubiquitous in our daily life and engineering applications. It is important to investigate the flow structures to predict their dynamical behaviors ef- fectively. Lagrangian coherent structures (... Multiphase flows are ubiquitous in our daily life and engineering applications. It is important to investigate the flow structures to predict their dynamical behaviors ef- fectively. Lagrangian coherent structures (LCS) defined by the ridges of the finite-time Lyapunov exponent (FTLE) is utilized in this study to elucidate the multiphase interactions in gaseous jets injected into water and time-dependent turbu- lent cavitation under the framework of Navier-Stokes flow computations. For the gaseous jets injected into water, the highlighted phenomena of the jet transportation can be observed by the LCS method, including expansion, bulge, necking/breaking, and back-attack. Besides, the observation of the LCS reveals that the back-attack phenomenon arises from the fact that the injected gas has difficulties to move toward downstream re- gion after the necking/breaking. For the turbulent cavitating flow, the ridge of the FTLE field can form a LCS to capture the front and boundary of the re-entraint jet when the ad- verse pressure gradient is strong enough. It represents a bar- rier between particles trapped inside the circulation region and those moving downstream. The results indicate that the FFLE field has the potential to identify the structures of mul- tiphase flows, and the LCS can capture the interface/barrier or the vortex/circulation region. 展开更多
关键词 Finite-time lyapunov exponents Lagrangiancoherent structures Multiphase flow Gaseous jets injectedinto water CAVITATION
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Determining the Spectrum of the Nonlinear Local Lyapunov Exponents in a Multidimensional Chaotic System 被引量:6
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作者 Ruiqiang DING Jianping LI Baosheng LI 《Advances in Atmospheric Sciences》 SCIE CAS CSCD 2017年第9期1027-1034,共8页
For an n-dimensional chaotic system, we extend the definition of the nonlinear local Lyapunov exponent (NLLE) from one- to n-dimensional spectra, and present a method for computing the NLLE spectrum. The method is t... For an n-dimensional chaotic system, we extend the definition of the nonlinear local Lyapunov exponent (NLLE) from one- to n-dimensional spectra, and present a method for computing the NLLE spectrum. The method is tested on three chaotic systems with different complexity. The results indicate that the NLLE spectrum realistically characterizes the growth rates of initial error vectors along different directions from the linear to nonlinear phases of error growth. This represents an improvement over the traditional Lyapunov exponent spectrum, which only characterizes the error growth rates during the linear phase of error growth. In addition, because the NLLE spectrum can effectively separate the slowly and rapidly growing perturbations, it is shown to be more suitable for estimating the predictability of chaotic systems, as compared to the traditional Lyapunov exponent spectrum. 展开更多
关键词 lyapunov exponent nonlinear local lyapunov exponent PREDICTABILITY
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New prediction of chaotic time series based on local Lyapunov exponent 被引量:9
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作者 张勇 《Chinese Physics B》 SCIE EI CAS CSCD 2013年第5期191-197,共7页
A new method of predicting chaotic time series is presented based on a local Lyapunov exponent, by quantitatively measuring the exponential rate of separation or attraction of two infinitely close trajectories in stat... A new method of predicting chaotic time series is presented based on a local Lyapunov exponent, by quantitatively measuring the exponential rate of separation or attraction of two infinitely close trajectories in state space. After recon- structing state space from one-dimensional chaotic time series, neighboring multiple-state vectors of the predicting point are selected to deduce the prediction formula by using the definition of the locaI Lyapunov exponent. Numerical simulations are carded out to test its effectiveness and verify its higher precision over two older methods. The effects of the number of referential state vectors and added noise on forecasting accuracy are also studied numerically. 展开更多
关键词 chaotic time series prediction of chaotic time series local lyapunov exponent least squaresmethod
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Estimating the largest Lyapunov exponent in a multibody system with dry friction by using chaos synchronization 被引量:6
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作者 Shihui Fu Qi Wang 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2006年第3期277-283,共7页
Using the properties of chaos synchronization, the method for estimating the largest Lyapunov exponent in a multibody system with dry friction is presented in this paper. The Lagrange equations with multipliers of the... Using the properties of chaos synchronization, the method for estimating the largest Lyapunov exponent in a multibody system with dry friction is presented in this paper. The Lagrange equations with multipliers of the systems are given in matrix form, which is adequate for numerical calculation. The approach for calculating the generalized velocity and acceleration of the slider is given to determine slipping or sticking of the slider in the systems. For slip-slip and stick-slip multibody systems, their largest Lyapunov exponents are calculated to characterize their dynamics. 展开更多
关键词 Multibody system Dry friction lyapunov exponent Chaos synchronization
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A perturbation method to the tent map based on Lyapunov exponent and its application 被引量:4
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作者 曹绿晨 罗玉玲 +1 位作者 丘森辉 刘俊秀 《Chinese Physics B》 SCIE EI CAS CSCD 2015年第10期78-85,共8页
Perturbation imposed on a chaos system is an effective way to maintain its chaotic features. A novel parameter perturbation method for the tent map based on the Lyapunov exponent is proposed in this paper. The pseudo-... Perturbation imposed on a chaos system is an effective way to maintain its chaotic features. A novel parameter perturbation method for the tent map based on the Lyapunov exponent is proposed in this paper. The pseudo-random sequence generated by the tent map is sent to another chaos function - the Chebyshev map for the post processing. If the output value of the Chebyshev map falls into a certain range, it will be sent back to replace the parameter of the tent map. As a result, the parameter of the tent map keeps changing dynamically. The statistical analysis and experimental results prove that the disturbed tent map has a highly random distribution and achieves good cryptographic properties of a pseudo-random sequence. As a result, it weakens the phenomenon of strong correlation caused by the finite precision and effectively compensates for the digital chaos system dynamics degradation. 展开更多
关键词 PERTURBATION tent map lyapunov exponent finite precision
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Coherent structures over riblets in turbulent boundary layer studied by combining time-resolved particle image velocimetry(TRPIV),proper orthogonal decomposition(POD),and finite-time Lyapunov exponent(FTLE) 被引量:4
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作者 Shan Li Nan Jiang +2 位作者 Shaoqiong Yang Yongxiang Huang Yanhua Wu 《Chinese Physics B》 SCIE EI CAS CSCD 2018年第10期395-404,共10页
Time-resolved particle image velocimetry(TRPIV) experiments are performed to investigate the coherent structure's performance of riblets in a turbulent boundary layer(TBL) at a friction Reynolds number of 185. To... Time-resolved particle image velocimetry(TRPIV) experiments are performed to investigate the coherent structure's performance of riblets in a turbulent boundary layer(TBL) at a friction Reynolds number of 185. To visualize the energetic large-scale coherent structures(CSs) over a smooth surface and riblets, the proper orthogonal decomposition(POD) and finite-time Lyapunov exponent(FTLE) are used to identify the CSs in the TBL. Spatial-temporal correlation is implemented to obtain the characters and transport properties of typical CSs in the FTLE fields. The results demonstrate that the generic flow structures, such as hairpin-like vortices, are also observed in the boundary layer flow over the riblets, consistent with its smooth counterpart. Low-order POD modes are more sensitive to the riblets in comparison with the high-order ones,and the wall-normal movement of the most energy-containing structures are suppressed over riblets. The spatial correlation analysis of the FTLE fields indicates that the evolution process of the hairpin vortex over riblets are inhibited. An apparent decrease of the convection velocity over riblets is noted, which is believed to reduce the ejection/sweep motions associated with high shear stress from the viscous sublayer. These reductions exhibit inhibition of momentum transfer among the structures near the wall in the TBL flows. 展开更多
关键词 turbulent boundary layer RIBLETS proper orthogonal decomposition finite-time lyapunov exponent
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Trend Prediction Method Based on the Largest Lyapunov Exponent for Large Rotating Machine Equipments 被引量:5
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作者 徐小力 朱春梅 张建民 《Journal of Beijing Institute of Technology》 EI CAS 2009年第4期433-436,共4页
In order to predict electromechanical equipments' nonlinear and non-stationary condition effectively, max Lyapunov exponent is introduced to the fault trend prediction of large rotating mechanical equipments based on... In order to predict electromechanical equipments' nonlinear and non-stationary condition effectively, max Lyapunov exponent is introduced to the fault trend prediction of large rotating mechanical equipments based on chaos theory. The predict method of chaos time series and two methods of proposing f and F are dis- cussed. The arithmetic of max prediction time of chaos time series is provided. Aiming at the key part of large rotating mechanical equipments-bearing, used this prediction method the simulation experiment is carried out. The result shows that this method has excellent performance for condition trend prediction. 展开更多
关键词 largest lyapunov exponent large rotating machine equipments developing condition prediction
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Lyapunov exponent calculation of a two-degree-of-freedom vibro-impact system with symmetrical rigid stops 被引量:3
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作者 李群宏 谭洁燕 《Chinese Physics B》 SCIE EI CAS CSCD 2011年第4期123-131,共9页
A two-degree-of-freedom vibro-impact system having symmetrical rigid stops and subjected to periodic excitation is investigated in this paper. By introducing local maps between different stages of motion in the whole ... A two-degree-of-freedom vibro-impact system having symmetrical rigid stops and subjected to periodic excitation is investigated in this paper. By introducing local maps between different stages of motion in the whole impact process, the Poincare map of the system is constructed. Using the Poincare map and the Gram Schmidt orthonormalization, a method of calculating the spectrum of Lyapunov exponents of the above vibro-impact system is presented. Then the phase portraits of periodic and chaotic attractors for the system and the corresponding convergence diagrams of the spectrum of Lyapunov exponents are given out through the numerical simulations. To further identify the validity of the aforementioned computation method, the bifurcation diagram of the system with respect to the bifurcation parameter and the corresponding largest Lyapunov exponents are shown. 展开更多
关键词 vibro-impact system Poincare map Gram-Schmidt orthonormalization lyapunov exponent
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Optimization of support vector machine power load forecasting model based on data mining and Lyapunov exponents 被引量:7
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作者 牛东晓 王永利 马小勇 《Journal of Central South University》 SCIE EI CAS 2010年第2期406-412,共7页
According to the chaotic and non-linear characters of power load data,the time series matrix is established with the theory of phase-space reconstruction,and then Lyapunov exponents with chaotic time series are comput... According to the chaotic and non-linear characters of power load data,the time series matrix is established with the theory of phase-space reconstruction,and then Lyapunov exponents with chaotic time series are computed to determine the time delay and the embedding dimension.Due to different features of the data,data mining algorithm is conducted to classify the data into different groups.Redundant information is eliminated by the advantage of data mining technology,and the historical loads that have highly similar features with the forecasting day are searched by the system.As a result,the training data can be decreased and the computing speed can also be improved when constructing support vector machine(SVM) model.Then,SVM algorithm is used to predict power load with parameters that get in pretreatment.In order to prove the effectiveness of the new model,the calculation with data mining SVM algorithm is compared with that of single SVM and back propagation network.It can be seen that the new DSVM algorithm effectively improves the forecast accuracy by 0.75%,1.10% and 1.73% compared with SVM for two random dimensions of 11-dimension,14-dimension and BP network,respectively.This indicates that the DSVM gains perfect improvement effect in the short-term power load forecasting. 展开更多
关键词 power load forecasting support vector machine (SVM) lyapunov exponent data mining embedding dimension feature classification
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Oil–water two-phase flow pattern analysis with ERT based measurement and multivariate maximum Lyapunov exponent 被引量:8
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作者 谭超 王娜娜 董峰 《Journal of Central South University》 SCIE EI CAS CSCD 2016年第1期240-248,共9页
Oil–water two-phase flow patterns in a horizontal pipe are analyzed with a 16-electrode electrical resistance tomography(ERT) system. The measurement data of the ERT are treated as a multivariate time-series, thus th... Oil–water two-phase flow patterns in a horizontal pipe are analyzed with a 16-electrode electrical resistance tomography(ERT) system. The measurement data of the ERT are treated as a multivariate time-series, thus the information extracted from each electrode represents the local phase distribution and fraction change at that location. The multivariate maximum Lyapunov exponent(MMLE) is extracted from the 16-dimension time-series to demonstrate the change of flow pattern versus the superficial velocity ratio of oil to water. The correlation dimension of the multivariate time-series is further introduced to jointly characterize and finally separate the flow patterns with MMLE. The change of flow patterns with superficial oil velocity at different water superficial velocities is studied with MMLE and correlation dimension, respectively, and the flow pattern transition can also be characterized with these two features. The proposed MMLE and correlation dimension map could effectively separate the flow patterns, thus is an effective tool for flow pattern identification and transition analysis. 展开更多
关键词 oil-water two-phase flow flow patterns electrical resistance tomography (ERT) multivariate time-series multivariate maximum lyapunov exponent correlation dimension
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A METHOD FOR CALCULATING THE LYAPUNOV EXPONENT SPECTRUM OF A PERIODICALLY EXCITED NON-AUTONOMOUS DYNAMICAL SYSTEM 被引量:1
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作者 Cheng Changjun Fan Xiaojun 《Acta Mechanica Solida Sinica》 SCIE EI 2000年第3期254-261,共8页
The relation between the Lyapunov exponent spectrum of a periodically excited non-autonomous dynamical system and the Lyapunov exponent spectrum of the corresponding autonomous system is given and the validity of the ... The relation between the Lyapunov exponent spectrum of a periodically excited non-autonomous dynamical system and the Lyapunov exponent spectrum of the corresponding autonomous system is given and the validity of the relation is verified theoretically and computationally. A direct method for calculating the Lyapunov exponent spectrum of non-autonomous dynamical systems is suggested in this paper, which makes it more convenient to calculate the Lyapunov exponent spectrum of the dynamical system periodically excited. Following the definition of the Lyapunov dimension D-L((A)) of the autonomous system, the definition of the Lyapunov dimension D-L of the non-autonomous dynamical system is also given, and the difference between them is the integer 1, namely, D-L((A)) - D-L = 1. For a quasi-periodically excited dynamical system, similar conclusions are formed. 展开更多
关键词 periodically excited dynamical system lyapunov exponent spectrum lyapunov dimension Duffing equation van der Pol equation
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Quantitative Comparison of Predictabilities of Warm and Cold Events Using the Backward Nonlinear Local Lyapunov Exponent Method 被引量:1
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作者 Xuan LI Ruiqiang DING Jianping LI 《Advances in Atmospheric Sciences》 SCIE CAS CSCD 2020年第9期951-958,共8页
The backward nonlinear local Lyapunov exponent method(BNLLE)is applied to quantify the predictability of warm and cold events in the Lorenz model.Results show that the maximum prediction lead times of warm and cold ev... The backward nonlinear local Lyapunov exponent method(BNLLE)is applied to quantify the predictability of warm and cold events in the Lorenz model.Results show that the maximum prediction lead times of warm and cold events present obvious layered structures in phase space.The maximum prediction lead times of each warm(cold)event on individual circles concentric with the distribution of warm(cold)regime events are roughly the same,whereas the maximum prediction lead time of events on other circles are different.Statistical results show that warm events are more predictable than cold events. 展开更多
关键词 backward nonlinear local lyapunov exponent maximum prediction lead time layered structure statistical result
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Application of Lyapunov exponent algorithm in balise signal chaotic oscillator detection 被引量:1
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作者 ZHANG Hongyan WANG Ruifeng 《Journal of Measurement Science and Instrumentation》 CAS CSCD 2021年第3期281-286,共6页
To improve the detection accuracy of the balise uplink signal transmitted in a strong noise environment,we use chaotic oscillator to detect the balise uplink signal based on the characteristics of the chaotic system t... To improve the detection accuracy of the balise uplink signal transmitted in a strong noise environment,we use chaotic oscillator to detect the balise uplink signal based on the characteristics of the chaotic system that is sensitive to initial conditions and immune to noise.Combining with the principle of Duffing oscillator system used in weak signal detection and uplink signal feature,the methods and steps of using Duffing oscillator to detect the balise signal are presented.Furthermore,the Lyapunov exponent algorithm is used to calculate the critical threshold of the Duffing oscillator detection system.Thus,the output states of the system can be quantitatively judged to achieve demodulation of the balise signal.The simulation results show that the chaotic oscillator detection method for balise signal based on Lyapunov exponent algorithm not only improves the accuracy and efficiency of threshold setting,but also ensures the reliability of balise signal detection. 展开更多
关键词 Duffing oscillator lyapunov exponent Jacobian algorithm small data sets balise uplink signal
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Forecasting available parking space with largest Lyapunov exponents method 被引量:3
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作者 季彦婕 汤斗南 +2 位作者 郭卫红 BLYTHE T.Phil 王炜 《Journal of Central South University》 SCIE EI CAS 2014年第4期1624-1632,共9页
The techniques to forecast available parking space(APS) are indispensable components for parking guidance systems(PGS). According to the data collected in Newcastle upon Tyne, England, the changing characteristics of ... The techniques to forecast available parking space(APS) are indispensable components for parking guidance systems(PGS). According to the data collected in Newcastle upon Tyne, England, the changing characteristics of APS were studied. Thereafter, aiming to build up a multi-step APS forecasting model that provides richer information than a conventional one-step model, the largest Lyapunov exponents(largest LEs) method was introduced into PGS. By experimental tests conducted using the same dataset, its prediction performance was compared with traditional wavelet neural network(WNN) method in both one-step and multi-step processes. Based on the results, a new multi-step forecasting model called WNN-LE method was proposed, where WNN, which enjoys a more accurate performance along with a better learning ability in short-term forecasting, was applied in the early forecast steps while the Lyapunov exponent prediction method in the latter steps precisely reflect the chaotic feature in latter forecast period. The MSE of APS forecasting for one hour time period can be reduced from 83.1 to 27.1(in a parking building with 492 berths) by using largest LEs method instead of WNN and further reduced to 19.0 by conducted the new method. 展开更多
关键词 available parking space lyapunov exponents wavelet neural network multi-step forecasting method
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Improved algorithm for calculating Lyapunov exponent and distinguishing chaos from noise 被引量:1
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作者 谢忠玉 王科俊 张立 《Journal of Harbin Institute of Technology(New Series)》 EI CAS 2010年第1期101-104,共4页
An improved algorithm for calculating the largest Lyapunov exponents (λ1) is presented based on Kantz algorithm. The presented algorithm can select a neighborhood in a certain extent according to the variety of the c... An improved algorithm for calculating the largest Lyapunov exponents (λ1) is presented based on Kantz algorithm. The presented algorithm can select a neighborhood in a certain extent according to the variety of the curves for calculating the largest Lyapunov exponent. And it can determine the linear zone based on the curves where branch is generated, thus, the largest Lyapunov exponent is obtained. The numerical experiments for the Hénon map prove that the proposed method is a direct method to identify whether a linear envelope to the curves exists in distinguishing chaos from noise, and it is superior to the Kantz algorithm. 展开更多
关键词 chaos lyapunov exponent noise
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Moment Lyapunov exponent for three-dimensional system under real noise excitation
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作者 李胜宏 刘先斌 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2013年第5期613-626,共14页
The pth moment Lyapunov exponent of a two-codimension bifurcation systern excited parametrically by a real noise is investigated. By a linear stochastic transformation, the differential operator of the system is obtai... The pth moment Lyapunov exponent of a two-codimension bifurcation systern excited parametrically by a real noise is investigated. By a linear stochastic transformation, the differential operator of the system is obtained. In order to evaluate the asymptotic expansion of the moment Lyapunov exponent, via a perturbation method, a ralevant eigenvalue problem is obtained. The eigenvalue problem is then solved by a Fourier cosine series expansion, and an infinite matrix is thus obtained, whose leading eigenvalue is the second-order of the asymptotic expansion of the moment Lyapunov exponent. Finally, the convergence of procedure is numerically illustrated, and the effects of the system and the noise parameters on the moment Lyapunov exponent are discussed. 展开更多
关键词 moment lyapunov exponent perturbation method real noise diffusion process Fourier series
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THE MATRIC ALGORITHM OF LYAPUNOV EXPONENT FOR THE EXPERIMENTAL DATA OBTAINED IN DYNAMIC ANALYSIS
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作者 马军海 陈予恕 刘曾荣 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1999年第9期985-993,共9页
The Lyapunov exponent is important quantitative index for describing chaotic attractors. Since Wolf put up the trajectory algorithm to Lyapunov exponent in 1985, how to calculate the Lyapunov exponent with accuracy ha... The Lyapunov exponent is important quantitative index for describing chaotic attractors. Since Wolf put up the trajectory algorithm to Lyapunov exponent in 1985, how to calculate the Lyapunov exponent with accuracy has become a very important question. Based on the theoretical algorithm of Zuo Binwu, the matric algorithm of Lyapunov exponent is given, and the results with the results of Wolf's algorithm are compared. The calculating results validate that the matric algorithm has sufficient accuracy, and the relationship between the character of attractor and the value of Lyapunov exponent is studied in this paper. The corresponding conclusions are given in this paper. 展开更多
关键词 nonlinear chaotic timeseries lyapunov exponent matric algorithm
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Study of Lyapunov exponent spectra for axial-flow compression system 被引量:1
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作者 ZHANG Jian DONG Fu-an WU You-li WU Xue-hui 《通讯和计算机(中英文版)》 2008年第6期61-65,共5页
关键词 李雅普诺夫指数 压缩技术 计算机技术 混沌系统
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