Trend prediction of chaotic time series
Li Aiguo; Zhao Cai; Li Zhanhuai
2007-01-01
To predict the trend of chaotic time series in time series analysis and time series data mining fields, a novel predicting algorithm of chaotic time series trend is presented, and an on-line segmenting algorithm is proposed to convert a time series into a binary string according to ascending or descending trend of each subsequence. The on-line segmenting algorithm is independent of the prior knowledge about time series. The naive Bayesian algorithm is then employed to predict the trend of chaotic time series according to the binary string. The experimental results of three chaotic time series demonstrate that the proposed method predicts the ascending or descending trend of chaotic time series with few error.
Combination prediction method of chaotic time series
ZHAO DongHua; RUAN Jiong; CAI ZhiJie
2007-01-01
In the present paper, we propose an approach of combination prediction of chaotic time series. The method is based on the adding-weight one-rank local-region method of chaotic time series. The method allows us to define an interval containing a future value with a given probability, which is obtained by studying the prediction error distribution. Its effectiveness is shown with data generated by Logistic map.
Improving the prediction of chaotic time series
李克平; 高自友; 陈天仑
2003-01-01
One of the features of deterministic chaos is sensitive to initial conditions. This feature limits the prediction horizons of many chaotic systems. In this paper, we propose a new prediction technique for chaotic time series. In our method, some neighbouring points of the predicted point, for which the corresponding local Lyapunov exponent is particularly large, would be discarded during estimating the local dynamics, and thus the error accumulated by the prediction algorithm is reduced. The model is tested for the convection amplitude of Lorenz systems. The simulation results indicate that the prediction technique can improve the prediction of chaotic time series.
Building Chaotic Model From Incomplete Time Series
Siek, Michael; Solomatine, Dimitri
2010-05-01
This paper presents a number of novel techniques for building a predictive chaotic model from incomplete time series. A predictive chaotic model is built by reconstructing the time-delayed phase space from observed time series and the prediction is made by a global model or adaptive local models based on the dynamical neighbors found in the reconstructed phase space. In general, the building of any data-driven models depends on the completeness and quality of the data itself. However, the completeness of the data availability can not always be guaranteed since the measurement or data transmission is intermittently not working properly due to some reasons. We propose two main solutions dealing with incomplete time series: using imputing and non-imputing methods. For imputing methods, we utilized the interpolation methods (weighted sum of linear interpolations, Bayesian principle component analysis and cubic spline interpolation) and predictive models (neural network, kernel machine, chaotic model) for estimating the missing values. After imputing the missing values, the phase space reconstruction and chaotic model prediction are executed as a standard procedure. For non-imputing methods, we reconstructed the time-delayed phase space from observed time series with missing values. This reconstruction results in non-continuous trajectories. However, the local model prediction can still be made from the other dynamical neighbors reconstructed from non-missing values. We implemented and tested these methods to construct a chaotic model for predicting storm surges at Hoek van Holland as the entrance of Rotterdam Port. The hourly surge time series is available for duration of 1990-1996. For measuring the performance of the proposed methods, a synthetic time series with missing values generated by a particular random variable to the original (complete) time series is utilized. There exist two main performance measures used in this work: (1) error measures between the actual
Time Series Prediction Based on Chaotic Attractor
LIKe-Ping; CHENTian-Lun; GAOZi-You
2003-01-01
A new prediction technique is proposed for chaotic time series. The usefulness of the technique is that it can kick off some false neighbor points which are not suitable for the local estimation of the dynamics systems. A time-delayed embedding is used to reconstruct the underlying attractor, and the prediction model is based on the time evolution of the topological neighboring in the phase space. We use a feedforward neural network to approximate the local dominant Lyapunov exponent, and choose the spatial neighbors by the Lyapunov exponent. The model is tested for the Mackey-Glass equation and the convection amplitude of lorenz systems. The results indicate that this prediction technique can improve the prediction of chaotic time series.
Application of a Local Polynomial Approximation Chaotic Time Series Prediction
Orzeszko, Witold
2004-01-01
Chaos theory has become a new approach to financial processes analysis. Due to complicated dynamics, chaotic time series seem to be random and, in consequence, unpredictable. In fact, unlike truly random processes, chaotic dynamics can be forecasted very precisely in a short run. In this paper, a local polynomial approximation is presented. Its efficiency, as a method of building short-term predictors of chaotic time series, has been examined. The presented method has been applied to forecast...
Chaotic time series prediction using artificial neural networks
Bartlett, E.B.
1991-01-01
This paper describes the use of artificial neural networks to model the complex oscillations defined by a chaotic Verhuist animal population dynamic. A predictive artificial neural network model is developed and tested, and results of computer simulations are given. These results show that the artificial neural network model predicts the chaotic time series with various initial conditions, growth parameters, or noise.
Chaotic time series prediction using artificial neural networks
Bartlett, E.B.
1991-12-31
This paper describes the use of artificial neural networks to model the complex oscillations defined by a chaotic Verhuist animal population dynamic. A predictive artificial neural network model is developed and tested, and results of computer simulations are given. These results show that the artificial neural network model predicts the chaotic time series with various initial conditions, growth parameters, or noise.
A data-fitting procedure for chaotic time series
McDonough, J.M.; Mukerji, S. [Univ. of Kentucky, Lexington, KY (United States). Dept. of Mechanical Engineering; Chung, S. [Univ. of Illinois, Urbana, IL (United States)
1998-10-01
In this paper the authors introduce data characterizations for fitting chaotic data to linear combinations of one-dimensional maps (say, of the unit interval) for use in subgrid-scale turbulence models. They test the efficacy of these characterizations on data generated by a chaotically-forced Burgers` equation and demonstrate very satisfactory results in terms of modeled time series, power spectra and delay maps.
A Novel Adaptive Predictor for Chaotic Time Series
BU Yun; WEN Guang-Jun; ZHOU Xiao-Jia; ZHANG Qiang
2009-01-01
Many chaotic time series show non-Gaussian distribution, and non-Gaussianity can be characterized not only by higher-order cumulants but also by negative entropy.Since negative entropy can be accurately approximated by some special non-polynomial functions, which also can form an orthogonal system, these functions are used to construct an adaptive predictor to replace higher-order cumulants.Simulation shows the algorithm performs well for different chaotic systems.
Chaotic time series. Part II. System Identification and Prediction
Bjørn Lillekjendlie
1994-10-01
Full Text Available This paper is the second in a series of two, and describes the current state of the art in modeling and prediction of chaotic time series. Sample data from deterministic non-linear systems may look stochastic when analysed with linear methods. However, the deterministic structure may be uncovered and non-linear models constructed that allow improved prediction. We give the background for such methods from a geometrical point of view, and briefly describe the following types of methods: global polynomials, local polynomials, multilayer perceptrons and semi-local methods including radial basis functions. Some illustrative examples from known chaotic systems are presented, emphasising the increase in prediction error with time. We compare some of the algorithms with respect to prediction accuracy and storage requirements, and list applications of these methods to real data from widely different areas.
Chaotic time series analysis in economics: Balance and perspectives
The aim of the paper is not to review the large body of work concerning nonlinear time series analysis in economics, about which much has been written, but rather to focus on the new techniques developed to detect chaotic behaviours in economic data. More specifically, our attention will be devoted to reviewing some of these techniques and their application to economic and financial data in order to understand why chaos theory, after a period of growing interest, appears now not to be such an interesting and promising research area
Chaotic time series analysis in economics: Balance and perspectives
Faggini, Marisa, E-mail: mfaggini@unisa.it [Dipartimento di Scienze Economiche e Statistiche, Università di Salerno, Fisciano 84084 (Italy)
2014-12-15
The aim of the paper is not to review the large body of work concerning nonlinear time series analysis in economics, about which much has been written, but rather to focus on the new techniques developed to detect chaotic behaviours in economic data. More specifically, our attention will be devoted to reviewing some of these techniques and their application to economic and financial data in order to understand why chaos theory, after a period of growing interest, appears now not to be such an interesting and promising research area.
PREDICTING CHAOTIC TIME SERIES WITH IMPROVED LOCAL APPROXIMATIONS
MU Xiaowu; LIN Lan; ZHOU Xiangdong
2004-01-01
In this paper, new approaches for chaotic time series prediction are introduced.We first summarize and evaluate the existing local prediction models, then propose optimization models and new algorithms to modify procedures of local approximations. The modification to the choice of sample sets is given, and the zeroth-order approximation is improved by a linear programming method. Four procedures of first-order approximation are compared, and corresponding modified methods are given. Lastly, the idea of nonlinear feedback to raise predicting accuracy is put forward. In the end, we discuss two important examples, i.e. Lorenz system and Rossler system, and the simulation experiments indicate that the modified algorithms are effective.
The improved local linear prediction of chaotic time series
Meng Qing-Fang; Peng Yu-Hua; Sun Jia
2007-01-01
Based on the Bayesian information criterion, this paper proposes the improved local linear prediction method to predict chaotic time aeries. This method uses spatial correlation and temporal correlation simultaneously. Simulation results show that the improved local linear prediction method can effectively make multi-step and one-step prediction of chaotic time aeries and the multi-step prediction performance and one-step prediction accuracy of the improved local linear prediction method are superior to those of the traditional local linear prediction method.
Local discrete cosine transformation domain Volterra prediction of chaotic time series
张家树; 李恒超; 肖先赐
2005-01-01
In this paper a local discrete cosine transformation (DCT) domain Volterra prediction method is proposed to predict chaotic time series, where the DCT is used to lessen the complexity of solving the coefficient matrix. Numerical simulation results show that the proposed prediction method can effectively predict chaotic time series and improve the prediction accuracy compared with the traditional local linear prediction methods.
PREDICTION TECHNIQUES OF CHAOTIC TIME SERIES AND ITS APPLICATIONS AT LOW NOISE LEVEL
MA Jun-hai; WANG Zhi-qiang; CHEN Yu-shu
2006-01-01
The paper not only studies the noise reduction methods of chaotic time series with noise and its reconstruction techniques, but also discusses prediction techniques of chaotic time series and its applications based on chaotic data noise reduction. In the paper, we first decompose the phase space of chaotic time series to range space and null noise space. Secondly we restructure original chaotic time series in range space. Lastly on the basis of the above, we establish order of the nonlinear model and make use of the nonlinear model to predict some research. The result indicates that the nonlinear modelhas very strong ability of approximation function, and Chaos predict method has certain tutorial significance to the practical problems.
Regular nonlinear response of the driven Duffing oscillator to chaotic time series
Nonlinear response of the driven Duffing oscillator to periodic or quasi-periodic signals has been well studied. In this paper, we investigate the nonlinear response of the driven Duffing oscillator to non-periodic, more specifically, chaotic time series. Through numerical simulations, we find that the driven Duffing oscillator can also show regular nonlinear response to the chaotic time series with different degree of chaos as generated by the same chaotic series generating model, and there exists a relationship between the state of the driven Duffing oscillator and the chaoticity of the input signal of the driven Duffing oscillator. One real-world and two artificial chaotic time series are used to verify the new feature of Duffing oscillator. A potential application of the new feature of Duffing oscillator is also indicated. (general)
Predicting Hyper-Chaotic Time Series Using Adaptive Higher-Order Nonlinear Filter
Zhang, Jia-Shu; Xiao, Xian-Ci
2001-03-01
A newly proposed method, i.e. the adaptive higher-order nonlinear finite impulse response (HONFIR) filter based on higher-order sparse Volterra series expansions, is introduced to predict hyper-chaotic time series. The effectiveness of using the adaptive HONFIR filter for making one-step and multi-step predictions is tested based on very few data points by computer-generated hyper-chaotic time series including the Mackey-Glass equation and four-dimensional nonlinear dynamical system. A comparison is made with some neural networks for predicting the Mackey-Glass hyper-chaotic time series. Numerical simulation results show that the adaptive HONFIR filter proposed here is a very powerful tool for making prediction of hyper-chaotic time series.
STUDY ON PREDICTION METHODS FOR DYNAMIC SYSTEMS OF NONLINEAR CHAOTIC TIME SERIES
马军海; 陈予恕; 辛宝贵
2004-01-01
The prediction methods for nonlinear dynamic systems which are decided by chaotic time series are mainly studied as well as structures of nonlinear self-related chaotic models and their dimensions.By combining neural networks and wavelet theories,the structures of wavelet transform neural networks were studied and also a wavelet neural networks learning method was given.Based on wavelet networks,a new method for parameter identification was suggested,which can be used selectively to extract different scales of frequency and time in time series in order to realize prediction of tendencies or details of original time series.Through pre-treatment and comparison of results before and after the treatment,several useful conclusions are reached:High accurate identification can be guaranteed by applying wavelet networks to identify parameters of self-related chaotic models and more valid prediction of the chaotic time series including noise can be achieved accordingly.
Prediction of chaotic time series based on modified minimax probability machine regression
Sun Jian-Cheng
2007-01-01
Long-term prediction of chaotic time series is very difficult, for the chaos restricts predictability. In thie paper a new method is studied to model and predict chaotic time series based on minimax probability machine regression (MPMR). Since the positive global Lyapunov exponents lead the errors to increase exponentially in modelling the chaotic time series, a weighted term is introduced to compensate a cost function. Using mean square error (MSE) and absolute error (AE) as a criterion, simulation results show that the proposed method is more effective and accurate for multistep prediction. It can identify the system characteristics quite well and provide a new way to make long-term predictions of the chaotic time series.
Multi-step-prediction of chaotic time series based on co-evolutionary recurrent neural network
This paper proposes a co-evolutionary recurrent neural network (CERNN) for the multi-step-prediction of chaotic time series, it estimates the proper parameters of phase space reconstruction and optimizes the structure of recurrent neural networks by co-evolutionary strategy. The searching space was separated into two subspaces and the individuals are trained in a parallel computational procedure. It can dynamically combine the embedding method with the capability of recurrent neural network to incorporate past experience due to internal recurrence. The effectiveness of CERNN is evaluated by using three benchmark chaotic time series data sets: the Lorenz series, Mackey-Glass series and real-world sun spot series. The simulation results show that CERNN improves the performances of multi-step-prediction of chaotic time series
Chaotic Characteristic of Time Series of Partial Discharge in Oil-Paper Insulation
The chaotic characteristics of time series of five partial discharge (PD) patterns in oil-paper insulation are studied. The results verify obvious chaotic characteristic of the time series of discharge signals and the fact that PD is a chaotic process. These time series have distinctive features, and the chaotic attractors obtained from time series differed greatly from each other by shapes in the phase space, so they could be used to qualitatively identify the PD patterns. The phase space parameters are selected, then the chaotic characteristic quantities can be extracted. These quantities could quantificationally characterize the PD patterns. The effects on pattern recognition of PRPD and CAPD are compared by using the neural network of radial basis function. The results show that both of the two recognition methods work well and have their respective advantages. Then, both the statistical operators under PRPD mode and the chaotic characteristic quantities under CAPD mode are selected comprehensively as the input vectors of neural network, and the PD pattern recognition accuracy is thereby greatly improved. (15th asian conference on electrical discharge)
Prediction and analysis of chaotic time series on the basis of support vector
Li Tianliang; He Liming; Li Haipeng
2008-01-01
Based on discussion on the theories of support vector machines(SVM),an one-step prediction model for time series prediction is presented,wherein the chaos theory is incorporated.Chaotic character of the time series is taken into account in the prediction procedure;parameters of reconstruction-delay and embedding-dimension for phase-space reconstruction are calculated in light of mutual-information and false-nearest-neighbor method,respectively.Precision and functionality have been demonstrated by the experimental results on the basis of the prediction of Lorenz chaotic time series.
Mackey-Glass noisy chaotic time series prediction by a swarm-optimized neural network
López-Caraballo, C. H.; Salfate, I.; Lazzús, J. A.; Rojas, P.; Rivera, M.; Palma-Chilla, L.
2016-05-01
In this study, an artificial neural network (ANN) based on particle swarm optimization (PSO) was developed for the time series prediction. The hybrid ANN+PSO algorithm was applied on Mackey-Glass noiseless chaotic time series in the short-term and long-term prediction. The performance prediction is evaluated and compared with similar work in the literature, particularly for the long-term forecast. Also, we present properties of the dynamical system via the study of chaotic behaviour obtained from the time series prediction. Then, this standard hybrid ANN+PSO algorithm was complemented with a Gaussian stochastic procedure (called stochastic hybrid ANN+PSO) in order to obtain a new estimator of the predictions that also allowed us compute uncertainties of predictions for noisy Mackey-Glass chaotic time series. We study the impact of noise for three cases with a white noise level (σ N ) contribution of 0.01, 0.05 and 0.1.
柳景青; 张士乔; 俞申凯
2004-01-01
The chaotic characteristics and maximum predictable time scale of the observation series of hourly water consumption in Hangzhou were investigated using the advanced algorithm presented here is based on the conventional Wolf's algorithm for the largest Lyapunov exponent. For comparison, the largest Lyapunov exponents of water consumption series with one-hour and 24-hour intervals were calculated respectively. The results indicated that chaotic characteristics obviously exist in the hourly water consumption system; and that observation series with 24-hour interval have longer maximum predictable scale than hourly series. These findings could have significant practical application for better prediction of urban hourly water consumption.
Long Range Dependence Prognostics for Bearing Vibration Intensity Chaotic Time Series
Qing Li
2016-01-01
Full Text Available According to the chaotic features and typical fractional order characteristics of the bearing vibration intensity time series, a forecasting approach based on long range dependence (LRD is proposed. In order to reveal the internal chaotic properties, vibration intensity time series are reconstructed based on chaos theory in phase-space, the delay time is computed with C-C method and the optimal embedding dimension and saturated correlation dimension are calculated via the Grassberger–Procaccia (G-P method, respectively, so that the chaotic characteristics of vibration intensity time series can be jointly determined by the largest Lyapunov exponent and phase plane trajectory of vibration intensity time series, meanwhile, the largest Lyapunov exponent is calculated by the Wolf method and phase plane trajectory is illustrated using Duffing-Holmes Oscillator (DHO. The Hurst exponent and long range dependence prediction method are proposed to verify the typical fractional order features and improve the prediction accuracy of bearing vibration intensity time series, respectively. Experience shows that the vibration intensity time series have chaotic properties and the LRD prediction method is better than the other prediction methods (largest Lyapunov, auto regressive moving average (ARMA and BP neural network (BPNN model in prediction accuracy and prediction performance, which provides a new approach for running tendency predictions for rotating machinery and provide some guidance value to the engineering practice.
New prediction of chaotic time series based on local Lyapunov exponent
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 reconstructing 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 local Lyapunov exponent. Numerical simulations are carried 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. (general)
Time series cross prediction in a single transistor chaotic circuit using neural networks
L. Magafas
2009-01-01
Full Text Available In this paper we will be trying to cross predict a multivariate time series of a single transistor chaotic circuit using neural networks. For this purpose we investigate the influence of a number of first and second order near neighbors in predicting chaotic time series using a back propagation neural network. This influence is examined by changing the number of neurons in the hidden layer of a backprogation neural network with one hidden layer. The number of neurons at the input layer were equal to the embedding dimension of the corresponding strange attractor.
This paper introduces a novel algorithm for determining the structure of a radial basis function (RBF) network (the number of hidden units) while it is used for dynamic modeling of chaotic time series. It can be seen that the hidden units in the RBF network can form hyperplanes to partition the input space into various regions in each of which it is possible to approximate the dynamics with a basis function. The number of regions corresponds to the number of hidden units. The basic idea of the proposed algorithm is to partition the input space by fractal scaling of the chaotic time series being modeled. By fractal scaling process, the number of basis functions (hidden units) as well as the number of input variables can be specified. Accordingly, the network topology is efficiently determined based on the complexity of the underlying dynamics as reflected in the observed time series. The feasibility of the proposed scheme is examined through dynamic modeling of the well-known chaotic time series. The results show that the new method can improve the predictability of chaotic time series with a suitable number of hidden units compared to that of reported in the literature
Multi-Scale Gaussian Processes: a Novel Model for Chaotic Time Series Prediction
ZHOU Ya-Tong; ZHANG Tai-Yi; SUN Jian-Cheng
2007-01-01
@@ Based on the classical Gaussian process (GP) model, we propose a multi-scale Gaussian process (MGP) model to predict the existence of chaotic time series. The MGP employs a covariance function that is constructed by a scaling function with its different dilations and translations, ensuring that the optimal hyperparameter is easy to determine.
无
2006-01-01
Nonlinear time series prediction is studied by using an improved least squares support vector machine (LSSVM) regression based on chaotic mutation evolutionary programming (CMEP) approach for parameter optimization.We analyze how the prediction error varies with different parameters (σ, γ) in LS-SVM. In order to select appropriate parameters for the prediction model, we employ CMEP algorithm. Finally, Nasdaq stock data are predicted by using this LS-SVM regression based on CMEP, and satisfactory results are obtained.
Chaotic time series prediction using mean-field theory for support vector machine
Cui Wan-Zhao; Zhu Chang-Chun; Bao Wen-Xing; Liu Jun-Hua
2005-01-01
This paper presents a novel method for predicting chaotic time series which is based on the support vector machines approach, and it uses the mean-field theory for developing an easy and efficient learning procedure for the support vector machine. The proposed method approximates the distribution of the support vector machine parameters to a Gaussian process and uses the mean-field theory to estimate these parameters easily, and select the weights of the mixture of kernels used in the support vector machine estimation more accurately and faster than traditional quadratic programming-based algorithms. Finally, relationships between the embedding dimension and the predicting performance of this method are discussed, and the Mackey-Glass equation is applied to test this method. The stimulations show that the mean-field theory for support vector machine can predict chaotic time series accurately, and even if the embedding dimension is unknown, the predicted results are still satisfactory. This result implies that the mean-field theory for support vector machine is a good tool for studying chaotic time series.
Jun Wang
2015-01-01
Full Text Available The paper proposes a novel function expression method to forecast chaotic time series, using an improved genetic-simulated annealing (IGSA algorithm to establish the optimum function expression that describes the behavior of time series. In order to deal with the weakness associated with the genetic algorithm, the proposed algorithm incorporates the simulated annealing operation which has the strong local search ability into the genetic algorithm to enhance the performance of optimization; besides, the fitness function and genetic operators are also improved. Finally, the method is applied to the chaotic time series of Quadratic and Rossler maps for validation. The effect of noise in the chaotic time series is also studied numerically. The numerical results verify that the method can forecast chaotic time series with high precision and effectiveness, and the forecasting precision with certain noise is also satisfactory. It can be concluded that the IGSA algorithm is energy-efficient and superior.
Power Forecasting of Combined Heating and Cooling Systems Based on Chaotic Time Series
Liu Hai
2015-01-01
Full Text Available Theoretic analysis shows that the output power of the distributed generation system is nonlinear and chaotic. And it is coupled with the microenvironment meteorological data. Chaos is an inherent property of nonlinear dynamic system. A predicator of the output power of the distributed generation system is to establish a nonlinear model of the dynamic system based on real time series in the reconstructed phase space. Firstly, chaos should be detected and quantified for the intensive studies of nonlinear systems. If the largest Lyapunov exponent is positive, the dynamical system must be chaotic. Then, the embedding dimension and the delay time are chosen based on the improved C-C method. The attractor of chaotic power time series can be reconstructed based on the embedding dimension and delay time in the phase space. By now, the neural network can be trained based on the training samples, which are observed from the distributed generation system. The neural network model will approximate the curve of output power adequately. Experimental results show that the maximum power point of the distributed generation system will be predicted based on the meteorological data. The system can be controlled effectively based on the prediction.
Modelling of chaotic time series using a variable-length windowing approach
A multidimensional feature extraction method for chaotic time series is presented. The method uses a variable-length windowing approach. Mackey-Glass delay-difference equation is used to create chaotic sample signals. Among many possible alternatives, the length of the data segment having the smallest variance fractal dimension (VFD) value is found and used as the feature value. Multidimensional feature vectors are formed to model each sample signal. A probabilistic neural network (PNN) is trained and tested with these vectors. It is shown that the application of the new feature extraction method improves the classification performance of the PNN as compared to a VFD based feature extraction method using a fix-length windowing approach
The Application of Direction Basis Function Neural Networks to the Prediction of Chaotic Time Series
CAOWenming
2004-01-01
In this paper we have examined the ability of Direction basis function networks (DBFN) to predict the output of a chaotic time series generated from a model of a physical system. DBFNs are known to be universal approximators, and chaotic systems are known to exhibit “random” behavior. Therefore the challenge is to apply the DBFN to the prediction of the output of a chaotic system, which we have chosen here to be the Mackey-Glass delay differential equation. The DBFN has been trained with off-line supervised learning using a Recursive Least Squares optimization for obtaining weights. Key issues which are addressed are the estimation of the order of the system and dependence of prediction error on various factors such as placement of DBF centers, selection of perceptive widths, and number of training samples. Included in this study is an implementation of Moody and Darken's K Means Clustering approach to optimally place DBF centers and a heuristic nearest neighbor method for determining perceptive widths.
Future mission studies: Forecasting solar flux directly from its chaotic time series
Ashrafi, S.
1991-01-01
The mathematical structure of the programs written to construct a nonlinear predictive model to forecast solar flux directly from its time series without reference to any underlying solar physics is presented. This method and the programs are written so that one could apply the same technique to forecast other chaotic time series, such as geomagnetic data, attitude and orbit data, and even financial indexes and stock market data. Perhaps the most important application of this technique to flight dynamics is to model Goddard Trajectory Determination System (GTDS) output of residues between observed position of spacecraft and calculated position with no drag (drag flag = off). This would result in a new model of drag working directly from observed data.
Shen, Meie; Chen, Wei-Neng; Zhang, Jun; Chung, Henry Shu-Hung; Kaynak, Okyay
2013-04-01
The optimal selection of parameters for time-delay embedding is crucial to the analysis and the forecasting of chaotic time series. Although various parameter selection techniques have been developed for conventional uniform embedding methods, the study of parameter selection for nonuniform embedding is progressed at a slow pace. In nonuniform embedding, which enables different dimensions to have different time delays, the selection of time delays for different dimensions presents a difficult optimization problem with combinatorial explosion. To solve this problem efficiently, this paper proposes an ant colony optimization (ACO) approach. Taking advantage of the characteristic of incremental solution construction of the ACO, the proposed ACO for nonuniform embedding (ACO-NE) divides the solution construction procedure into two phases, i.e., selection of embedding dimension and selection of time delays. In this way, both the embedding dimension and the time delays can be optimized, along with the search process of the algorithm. To accelerate search speed, we extract useful information from the original time series to define heuristics to guide the search direction of ants. Three geometry- or model-based criteria are used to test the performance of the algorithm. The optimal embeddings found by the algorithm are also applied in time-series forecasting. Experimental results show that the ACO-NE is able to yield good embedding solutions from both the viewpoints of optimization performance and prediction accuracy. PMID:23144038
Phase Space Prediction of Chaotic Time Series with Nu-Support Vector Machine Regression
YE Mei-Ying; WANG Xiao-Dong
2005-01-01
A new class of support vector machine, nu-support vector machine, is discussed which can handle both classification and regression. We focus on nu-support vector machine regression and use it for phase space prediction of compares nu-support vector machine with back propagation (BP) networks in order to better evaluate the performance of the proposed methods. The experimental results show that the nu-support vector machine regression obtains lower root mean squared error than the BP networks and provides an accurate chaotic time series prediction. These results can be attributable to the fact that nu-support vector machine implements the structural risk minimization principle and this leads to better generalization than the BP networks.
Research on Optimize Prediction Model and Algorithm about Chaotic Time Series
JIANG Wei-jin; XU Yu-sheng
2004-01-01
We put forward a chaotic estimating model.by using the parameter of the chaotic system, sensitivity of the parameter to inching and control the disturbance of the system, and estimated the parameter of the model by using the best update option.In the end, we forecast the intending series value in its mutually space.The example shows that it can increase the precision in the estimated process by selecting the best model steps.It not only conquer the abuse of using detention inlay technology alone, but also decrease blindness of using forecast error to decide the input model directly, and the result of it is better than the method of statistics and other series means.
An iterative optimization method is used to uncover unobserved initial state (t = 0), historical evolutionary path (t 0) and parameters of a chaotic process from a segment of scalar time series (t0 ≤ t ≤ t1, t0 > 0). Given the system structure, we can precisely estimate the model parameters, recover the trajectory components unobserved, identify the state of all variables at the beginning (t = t0) of the observed time series, and trace the historical evolution of the system back to a long time interval (0 ≤ t 0). Chaotic time series of Lorenz system and Roessler system are utilized for illustration. The results show that the method is effective and tolerant to large mismatches between the guessed and actual values of the initial state and parameters
A finite impulse response neural network, with tap delay lines after each neuron in hidden layer, is used. Genetic algorithm with arithmetic decimal crossover and Roulette selection with normal probability mutation method with linear combination rule is used for optimization of FIR neural network. The method is applied for prediction of several important and benchmarks chaotic time series such as: geomagnetic activity index natural time series and famous Mackey-Glass time series. The results of simulations shows that applying dynamic neural models for modeling of highly nonlinear chaotic systems is more satisfactory with respect to feed forward neural networks. Likewise, global optimization method such as genetic algorithm is more efficient in comparison of nonlinear gradient based optimization methods like momentum term, conjugate gradient.
A method to improve the precision of chaotic time series prediction by using a non-trajectory
Yan Hua; Wei Ping; Xiao Xian-Ci
2009-01-01
Due to the error in the measured value of the initial state and the sensitive dependence on initial conditions of chaotic dynamical systems,the error of chaotic time series prediction increases with the prediction step.This paper provides a method to improve the prediction precision by adjusting the predicted value in the course of iteration according to the evolution information of small intervals on the Lett and right sides of the predicted value.The adjusted predicted result is a non-trajectory which can provide a better prediction performance than the usual result based on the trajectory.Numerical simulations of two typical chaotic maps demonstrate its effectiveness.When the prediction step gets relatively larger,the effect is more pronounced.
A method to improve the precision of chaotic time series prediction by using a non-trajectory
Due to the error in the measured value of the initial state and the sensitive dependence on initial conditions of chaotic dynamical systems, the error of chaotic time series prediction increases with the prediction step. This paper provides a method to improve the prediction precision by adjusting the predicted value in the course of iteration according to the evolution information of small intervals on the left and right sides of the predicted value. The adjusted predicted result is a non-trajectory which can provide a better prediction performance than the usual result based on the trajectory. Numerical simulations of two typical chaotic maps demonstrate its effectiveness. When the prediction step gets relatively larger, the effect is more pronounced. (general)
Xu, Xijin; Tang, Qian; Xia, Haiyue; Zhang, Yuling; Li, Weiqiu; Huo, Xia
2016-01-01
Chaotic time series prediction based on nonlinear systems showed a superior performance in prediction field. We studied prenatal exposure to polychlorinated biphenyls (PCBs) by chaotic time series prediction using the least squares self-exciting threshold autoregressive (SEATR) model in umbilical cord blood in an electronic waste (e-waste) contaminated area. The specific prediction steps basing on the proposal methods for prenatal PCB exposure were put forward, and the proposed scheme’s validity was further verified by numerical simulation experiments. Experiment results show: 1) seven kinds of PCB congeners negatively correlate with five different indices for birth status: newborn weight, height, gestational age, Apgar score and anogenital distance; 2) prenatal PCB exposed group at greater risks compared to the reference group; 3) PCBs increasingly accumulated with time in newborns; and 4) the possibility of newborns suffering from related diseases in the future was greater. The desirable numerical simulation experiments results demonstrated the feasibility of applying mathematical model in the environmental toxicology field. PMID:27118260
Xu, Xijin; Tang, Qian; Xia, Haiyue; Zhang, Yuling; Li, Weiqiu; Huo, Xia
2016-04-01
Chaotic time series prediction based on nonlinear systems showed a superior performance in prediction field. We studied prenatal exposure to polychlorinated biphenyls (PCBs) by chaotic time series prediction using the least squares self-exciting threshold autoregressive (SEATR) model in umbilical cord blood in an electronic waste (e-waste) contaminated area. The specific prediction steps basing on the proposal methods for prenatal PCB exposure were put forward, and the proposed scheme’s validity was further verified by numerical simulation experiments. Experiment results show: 1) seven kinds of PCB congeners negatively correlate with five different indices for birth status: newborn weight, height, gestational age, Apgar score and anogenital distance; 2) prenatal PCB exposed group at greater risks compared to the reference group; 3) PCBs increasingly accumulated with time in newborns; and 4) the possibility of newborns suffering from related diseases in the future was greater. The desirable numerical simulation experiments results demonstrated the feasibility of applying mathematical model in the environmental toxicology field.
Highlights: • Impact of meteorological factors on wind speed forecasting is taken into account. • Forecasted wind speed results are corrected by the associated rules. • Forecasting accuracy is improved by the new wind speed forecasting strategy. • Robust of the proposed model is validated by data sampled from different sites. - Abstract: Wind energy has been the fastest growing renewable energy resource in recent years. Because of the intermittent nature of wind, wind power is a fluctuating source of electrical energy. Therefore, to minimize the impact of wind power on the electrical grid, accurate and reliable wind power forecasting is mandatory. In this paper, a new wind speed forecasting approach based on based on the chaotic time series modelling technique and the Apriori algorithm has been developed. The new approach consists of four procedures: (I) Clustering by using the k-means clustering approach; (II) Employing the Apriori algorithm to discover the association rules; (III) Forecasting the wind speed according to the chaotic time series forecasting model; and (IV) Correcting the forecasted wind speed data using the associated rules discovered previously. This procedure has been verified by 31-day-ahead daily average wind speed forecasting case studies, which employed the wind speed and other meteorological data collected from four meteorological stations located in the Hexi Corridor area of China. The results of these case studies reveal that the chaotic forecasting model can efficiently improve the accuracy of the wind speed forecasting, and the Apriori algorithm can effectively discover the association rules between the wind speed and other meteorological factors. In addition, the correction results demonstrate that the association rules discovered by the Apriori algorithm have powerful capacities in handling the forecasted wind speed values correction when the forecasted values do not match the classification discovered by the association rules
Detection of chaotic determinism in time series from randomly forced maps
Chon, K H; Kanters, J K; Cohen, R J; Holstein-Rathlou, N H
1997-01-01
Time series from biological system often display fluctuations in the measured variables. Much effort has been directed at determining whether this variability reflects deterministic chaos, or whether it is merely "noise". Despite this effort, it has been difficult to establish the presence of chaos...... in time series from biological sytems. The output from a biological system is probably the result of both its internal dynamics, and the input to the system from the surroundings. This implies that the system should be viewed as a mixed system with both stochastic and deterministic components. We...... the time series followed by an estimation of the characteristic exponents of the model over the observed probability distribution of states for the system. The method is tested by computer simulations, and applied to heart rate variability data....
Prediction of Gas Emission Based on Information Fusion and Chaotic Time Series
无
2006-01-01
In order to make more exact predictions of gas emissions, information fusion and chaos time series are combined to predict the amount of gas emission in pits. First, a multi-sensor information fusion frame is established. The frame includes a data level, a character level and a decision level. Functions at every level are interpreted in detail in this paper. Then, the process of information fusion for gas emission is introduced. On the basis of those data processed at the data and character levels, the chaos time series and neural network are combined to predict the amount of gas emission at the decision level. The weights of the neural network are gained by training not by manual setting, in order to avoid subjectivity introduced by human intervention. Finally, the experimental results were analyzed in Matlab 6.0 and prove that the method is more accurate in the prediction of the amount of gas emission than the traditional method.
Fathian Baneh, A.; Sarkhosh, L.
2013-12-01
Before August 11th, 2012 Arasbaran twin earthquakes (Mw 6.4 and Mw 6.3), no seismogenic fault has been fully recognized within the meizoseismal area of the events, neither there were obvious evidence on the microseismicity pattern of the region showing potentials of such activities for an earthquake to occur. In the present study, we tried to investigate the seismic activity of the area in a time period between 2006 and 2012 to verify whether symptoms are detectable in the seismicity of the region or not. In this case, we profited from two different approaches: a statistical method (considering which as a linear system) and Chaos theory (considering it as a non-linear system). We analyzed firstly the seismic time series based on magnitude/number of earthquakes versus time, using ARIMA modeling which refutes the linear behavior of the system. Therefore, we discussed the nonlinear behavior of earthquake time series of the study area to simply explain the complexities in the system using chaos theory for a time interval of six years. Moreover, the calculation of Lyapunov exponent was put into practice. Although results derived from ARIMA modeling indicate non-stability of the studied system and reveal the system undergoes a non-periodicity behavior, yet the positive estimated Lyapunov exponent obviously denotes the chaotic dynamics in the system. Such results could be used as a marker for more detailed further surveys of the areas which seem safe in terms of seismic hazard, as Arasbaran area was once deemed.
Gaussian小波SVM及其混沌时间序列预测%Gaussian Wavelet SVM and Its Applications to Chaotic Time Series Forecasting
郑永康; 陈维荣; 戴朝华; 王维博
2009-01-01
To improve the accuracy of chaotic time series forecasting,Gaussiun wavelet support vector machine (SVM) forecasting model is proposed,which combines the wavelet technology with SVM kernel function method,and based on that the wavelet is beneficial to extracting imperceptible features of signal.It is proved that the even order derivative Ganssian wavelet function is an admissible translation-invariant kernel of SVM,and corresponding Ganssian wavelet SVM is constructed.The chaotic time series is reconstructed in phase space,and the vector in phase space reconstruction is used as the input of SVM.The experiments of forecasting Chen's chaotic time series and load chaotic time series are conducted using the proposed SVM,the conventional radial basis SVM and the Morlet wavelet SVM respectively.The comparison results show that Gaussian wavelet SVM has better performance than the other two SVMs.%为了提高混沌时间序列的预测精度,针对小波有利于信号细微特征提取的优点,结合小波技术和SVM的核函数方法,提出基于Gaussian小波SVM的混沌时间序列预测模型.证明了偶数阶Ganssian小波函数满足SVM平移不变核条件,并构建相应的Gaussian小波SVM.时混沌时间序列进行相空间重构,将重构相空间中的向量作为SVM的输入参量.用Ganssian小波SVM与常用的径向基SVM及Morlet小渡SVM进行对比实验,通过对Chen's混沌时间序列和负荷混沌时间序列的预测,结果表明,Ganssian小波SVM的效果比其他两种SVM更好.
Vaughan, Adam; Bohac, Stanislav V
2015-10-01
Fuel efficient Homogeneous Charge Compression Ignition (HCCI) engine combustion timing predictions must contend with non-linear chemistry, non-linear physics, period doubling bifurcation(s), turbulent mixing, model parameters that can drift day-to-day, and air-fuel mixture state information that cannot typically be resolved on a cycle-to-cycle basis, especially during transients. In previous work, an abstract cycle-to-cycle mapping function coupled with ϵ-Support Vector Regression was shown to predict experimentally observed cycle-to-cycle combustion timing over a wide range of engine conditions, despite some of the aforementioned difficulties. The main limitation of the previous approach was that a partially acasual randomly sampled training dataset was used to train proof of concept offline predictions. The objective of this paper is to address this limitation by proposing a new online adaptive Extreme Learning Machine (ELM) extension named Weighted Ring-ELM. This extension enables fully causal combustion timing predictions at randomly chosen engine set points, and is shown to achieve results that are as good as or better than the previous offline method. The broader objective of this approach is to enable a new class of real-time model predictive control strategies for high variability HCCI and, ultimately, to bring HCCI's low engine-out NOx and reduced CO2 emissions to production engines. PMID:26164437
The Levenberg-Marquardt learning algorithm is applied for training a multilayer perception with three hidden layer each with ten neurons in order to carefully map the structure of chaotic time series such as Mackey-Glass time series. First the MLP network is trained with 1000 data, and then it is tested with next 500 data. After that the trained and tested network is applied for long-term prediction of next 120 data which come after test data. The prediction is such a way that, the first inputs to network for prediction are the four last data of test data, then the predicted value is shifted to the regression vector which is the input to the network, then after first four-step of prediction, the input regression vector to network is fully predicted values and in continue, each predicted data is shifted to input vector for subsequent prediction.
Xiang Yuanpeng; Cao Biao; Zeng Min; Huang Shisheng; Shao Lanjuan
2008-01-01
The experimental time series of welding current produced by carbon dioxide gas metal arc welding with shortcircuiting transfer were recorded and subsequently evaluated. Based on phase space reconstruction, the correlation dimensions and Kolmogorov entropies of the corresponding system have been numerically calculated using the Grassberger-Procaccia algorithm at different time delays. It was found out that the time delay has little effect on the estimation of correlation dimension; conversely,it plays a key role in producing precise results on the estimation of Kolmogorov entropy.
Regular transport dynamics produce chaotic travel times.
Villalobos, Jorge; Muñoz, Víctor; Rogan, José; Zarama, Roberto; Johnson, Neil F; Toledo, Benjamín; Valdivia, Juan Alejandro
2014-06-01
In the hope of making passenger travel times shorter and more reliable, many cities are introducing dedicated bus lanes (e.g., Bogota, London, Miami). Here we show that chaotic travel times are actually a natural consequence of individual bus function, and hence of public transport systems more generally, i.e., chaotic dynamics emerge even when the route is empty and straight, stops and lights are equidistant and regular, and loading times are negligible. More generally, our findings provide a novel example of chaotic dynamics emerging from a single object following Newton's laws of motion in a regularized one-dimensional system. PMID:25019866
Behavioural analysis of a time series–A chaotic approach
T A Fathima; V Jothiprakash
2014-06-01
Out of the various methods available to study the chaotic behaviour, correlation dimension method (CDM) derived from Grassberger-Procaccia algorithm and False Nearest Neighbour method (FNN) are widely used. It is aimed to study the adaptability of those techniques for Indian rainfall data that is dominated by monsoon. In the present study, five sets of time series data are analyzed using correlation dimension method (CDM) based upon Grassberger-Procaccia algorithm for studying their behaviour. In order to confirm the results arrived from correlation dimension method, FNN and phase randomisation method is also applied to the time series used in the present study to fix the optimum embedding dimension. First series is a deterministic natural number series, the next two series are random number series with two types of distributions; one is uniform and another is normal distributed random number series. The fourth series is Henon data, an erratic data generated from a deterministic non linear equation (classified as chaotic series). After checking the applicability of correlation dimension method for deterministic, stochastic and chaotic data (known series) the method is applied to a rainfall time series observed at Koyna station, Maharashtra, India for its behavioural study. The results obtained from the chaotic analysis revealed that CDM is an efficient method for behavioural study of a time series. It also provides first hand information on the number of dimensions to be considered for time series prediction modelling. The CDM applied to real life rainfall data brings out the nature of rainfall at Koyna station as chaotic. For the rainfall data, CDM resulted in a minimum correlation dimension of one and optimum dimension as five. FNN method also resulted in five dimensions for the rainfall data. The behaviour of the rainfall time series is further confirmed by phase randomisation technique also. The surrogate data derived from randomisation gives entirely different
Chaotic time series prediction based on wavelet echo state network%基于小波回声状态网络的混沌时间序列预测
宋彤; 李菡
2012-01-01
混沌现象普遍存在于自然界及人类社会中，因此混沌时间序列预测具有重要意义．提出了一种新的混沌时间序列预测模型—小波回声状态网络，该模型可以有效克服传统回声状态网络模型中普遍存在的病态矩阵问题，提高了混沌时间序列预测精度．通过对Lorenz、含噪声Lorenz及间歇式反应釜釜温三个时间序列的预测，将小波回声状态网络与传统回声状态网络进行了比较．结果表明，小波回声状态网络与传统回声状态网络相比，预测精度提高一倍以上且预测结果更加稳定．%Chaos is widespread in nature and human society, so the prediction of chaotic time series is very important. In this paper, we propose a new chaotic time series prediction model - echo state network based on wavelet, which can effectively overcome the ill-posed problem that exists in traditional echo state networks. And it also has a good generalization ability. Three time series are used to test the new model, i.e., Lorenz time series, Lorenz time series with added noise and batch reactor vessel temperature time series. Results suggest that the new proposed method can achieve a higher predictable accuracy, better generalization and more stable prediction results than traditional echo state networks.
Matías Rafti
2010-01-01
Full Text Available Se estudia la influencia del procedimiento de filtrado aplicado sobre series temporales para su uso en la caracterización y detección de regímenes no-lineales. Para esto, se toma como ejemplo de dichos métodos, un algoritmo ampliamente utilizado para el cálculo de la dimensión de correlación de la trayectoria en el espacio de las fases (el algoritmo de Grassberger-Procaccia. El interés de este ejemplo de estudio radica en la similitud con el procedimiento que se aplica al analizar imágenes experimentales de sistemas fisicoquímicos de reacción-difusión, provenientes de técnicas de análisis superficial como la microscopía de emisión de fotoelectrones. Los resultados de las simulaciones realizadas muestran como el uso de un parámetro de filtrado inadecuado puede conducir a caracterizar erróneamente estados como no lineales o caóticos.The influence of the filtering scheme on time series for their use in the characterization and detection of non lineal regimes. As an example, the Grassberger-Procaccia algorithm for phase-space trajectory correlation dimension is used The main interest of such analysis is to study the similarities with the processing of experimental images from reaction-diffusion systems obtained via surface science standard tools such as photoelectron emission microscopy. Simulation results show how inadequate filtering parameter choice may lead to erroneous characterization of systems as non-linear or chaotic.
Synchronization of complex chaotic systems in series expansion form
This paper studies the synchronization of complex chaotic systems in series expansion form by Lyapunov asymptotical stability theorem. A sufficient condition is given for the asymptotical stability of an error dynamics, and is applied to guiding the design of the secure communication. Finally, numerical results are studied for the Quantum-CNN oscillators synchronizing with unidirectional/bidirectional linear coupling to show the effectiveness of the proposed synchronization strategy
Synchronization of complex chaotic systems in series expansion form
Ge Zhengming [Department of Mechanical Engineering, National Chiao Tung University, 1001 Ta Hsueh Road, Hsinchu 300, Taiwan (China)]. E-mail: zmg@cc.nctu.edu.tw; Yang Chenghsiung [Department of Mechanical Engineering, National Chiao Tung University, 1001 Ta Hsueh Road, Hsinchu 300, Taiwan (China)
2007-12-15
This paper studies the synchronization of complex chaotic systems in series expansion form by Lyapunov asymptotical stability theorem. A sufficient condition is given for the asymptotical stability of an error dynamics, and is applied to guiding the design of the secure communication. Finally, numerical results are studied for the Quantum-CNN oscillators synchronizing with unidirectional/bidirectional linear coupling to show the effectiveness of the proposed synchronization strategy.
多元混沌时间序列的相关状态机预测模型研究%Research on Multivariate Chaotic Time Series Prediction Using mRSM Model
韩敏; 许美玲; 任伟杰
2014-01-01
Considering that there may be overfitting problem, as well as the problem of high dimensional redundant input variables in multivariate chaotic time series prediction, we introduce a novel multivariate prediction model based on relevance vector machine and echo state network, named multivariate relevance state machine (mRSM). The proposed model reconstructs the multivariate chaotic time series into the phase space, then reduces the dimension of input variables with the principal component analysis method. Subsequently, the mRSM uses a reservoir, replacing kernel functions of relevance vector machine, to map the dynamic features of multivariate time series suﬃciently. Therefore, the mRSM presents rich dynamics and good sparsity. Furthermore, it avoids overfitting, and improves the predictive accuracy. Simulation results, based on two multivariate time series, substantiate the effectiveness of the mRSM.%针对多元混沌时间序列预测存在的过拟合问题及高维输入变量冗余问题，提出一种新型的多变量稀疏化预测模型—多元相关状态机。该模型采用主成分分析方法对相空间重构后的高维输入变量进行低维表示，将动态储备池作为相关向量机的核函数，充分映射多元混沌时间序列的动力学特性，使得模型具有丰富的动态机制和良好的稀疏性能，有效避免过拟合问题，提高预测精度。基于两组多元混沌时间序列的仿真实验验证了模型的有效性。
Parameter identification of time-delay chaotic system using chaotic ant swarm
The identification problem of delay time as well as parameters of time-delay chaotic system is investigated in this paper. The identification problem is converted to that of parameter optimization by constructing suitable fitness function. A novel optimization method, called CAS (chaotic ant swarm), which simulates the chaotic behavior of single ant and the self-organization behavior of ant colony, is used to solve this optimization problem. Illustrative example demonstrates the effectiveness of the proposed method.
Detecting temporal and spatial correlations in pseudoperiodic time series
Zhang, Jie; Luo, Xiaodong; Nakamura, Tomomichi; Sun, Junfeng; Small, Michael
2007-01-01
Recently there has been much attention devoted to exploring the complicated possibly chaotic dynamics in pseudoperiodic time series. Two methods [Zhang , Phys. Rev. E 73, 016216 (2006); Zhang and Small, Phys. Rev. Lett. 96, 238701 (2006)] have been forwarded to reveal the chaotic temporal and spatial correlations, respectively, among the cycles in the time series. Both these methods treat the cycle as the basic unit and design specific statistics that indicate the presence of chaotic dynamics. In this paper, we verify the validity of these statistics to capture the chaotic correlation among cycles by using the surrogate data method. In particular, the statistics computed for the original time series are compared with those from its surrogates. The surrogate data we generate is pseudoperiodic type (PPS), which preserves the inherent periodic components while destroying the subtle nonlinear (chaotic) structure. Since the inherent chaotic correlations among cycles, either spatial or temporal (which are suitably characterized by the proposed statistics), are eliminated through the surrogate generation process, we expect the statistics from the surrogate to take significantly different values than those from the original time series. Hence the ability of the statistics to capture the chaotic correlation in the time series can be validated. Application of this procedure to both chaotic time series and real world data clearly demonstrates the effectiveness of the statistics. We have found clear evidence of chaotic correlations among cycles in human electrocardiogram and vowel time series. Furthermore, we show that this framework is more sensitive to examine the subtle changes in the dynamics of the time series due to the match between PPS surrogate and the statistics adopted. It offers a more reliable tool to reveal the possible correlations among cycles intrinsic to the chaotic nature of the pseudoperiodic time series.
Projective Synchronization in Time-Delayed Chaotic Systems
FENG Cun-Fang; ZHANG Yan; WANG Ying-Hai
2006-01-01
For the first time, we report on projective synchronization between two time delay chaotic systems with single time delays. It overcomes some limitations of the previous wort, where projective synchronization has been investigated only in finite-dimensional chaotic systems, so we can achieve projective synchronization in infinite-dimensional chaotic systems. We give a general method with which we can achieve projective synchronization in time-delayed chaotic systems. The method is illustrated using the famous delay-differential equations related to optical bistability. Numerical simulations fully support the analytical approach.
Phase synchronization of coupled chaotic multiple time scales systems
The brushless dc motor (BLDCM) with multi-time scales is an electric machine. By coupled BLDCM, it is discovered that chaotic routes of the uncoupled systems influence synchronous result of coupled identical and nonidentical chaotic systems. Another multi-time scales form, Hindmarsh-Rose (HR) neurons, when the chaotic parameter is selected only in the range of the period-doubling route to chaos, phase synchronization can be predicted via Laypunov exponent. Finally, Laypunov exponent however cannot be used as a criterion for phase synchronization of coupled chaotic systems with either single or multi-time scales in our study
Yulmetyev, R M; Emelyanova, N; Gafarov, F; Hänggi, P; Yulmetyev, Renat; Demin, Sergey; Emelyanova, Natalya; Gafarov, Fail; Hanggi, Peter
2003-01-01
In this work we develop a new method of diagnosing the nervous system diseases and a new approach in studying human gait dynamics with the help of the theory of discrete non-Markov random processes. The stratification of the phase clouds and the statistical non-Markov effects in the time series of the dynamics of human gait are considered. We carried out the comparative analysis of the data of four age groups of healthy people: children (from 3 to 10 year olds), teenagers (from 11 to 14 year oulds), young people (from 21 up to 29 year oulds), elderly persons (from 71 to 77 year olds) and Parkinson patients. The full data set are analyzed with the help of the phase portraits of the four dynamic variables, the power spectra of the initial time correlation function and the memory functions of junior orders, the three first points in the spectra of the statistical non-Markov parameter. The received results allow to define the predisposition of the probationers to deflections in the central nervous system caused b...
李瑞国; 张宏立; 范文慧; 王雅
2015-01-01
Chaos phenomenon which exists widely in nature and society affects people’s production and life. It has great important significance to find out the regularity of chaotic time series from a chaotic system. Since chaotic system has extremely complex dynamic characteristics and unpredictability, and chaotic time series prediction through traditional methods has low prediction precision, slow convergence speed and complex model structure, a prediction model about Hermite orthogonal basis neural network based on improved teaching-learning-based optimization algorithm is proposed. Firstly, according to the chaotic time series, autocorrelation method and Cao method are used to determine the best delay time and the minimum embedding dimension respectively, then a phase space is reconstructed to obtain the refactoring delay time vector. Secondly, on the basis of phase space reconstruction and best square approximation theory, combined with the neural network topology, a prediction model about Hermite orthogonal basis neural network with excitation functions based on the Hermite orthogonal basis functions is put forward. Thirdly, in order to optimize the parameters of the prediction model, an improved teaching-learning-based optimization algorithm is proposed, where a feedback stage is introduced at the end of the learning stage based on the teaching-learning-based optimization algorithm. Finally, the parameter optimization problem is transformed into a function optimization problem in the multidimensional space, then the improved teaching-learning-based optimization algorithm is used for parameter optimization of the prediction model so as to establish it and analyze it. Lorenz and Liu chaotic systems are taken as models respectively, then the chaotic time series which will be used as simulation object is produced by the fourth order Runge-Kutta method. The comparison experiments with other prediction models are conducted on single-step and multi-step prediction for the
Linear generalized synchronization of continuous-time chaotic systems
This paper develops a general approach for constructing a response system to implement linear generalized synchronization (GS) with the drive continuous-time chaotic system. Some sufficient conditions of global asymptotic linear GS between the drive and response continuous-time chaotic systems are attained from rigorously modern control theory. Finally, we take Chua's circuit as an example for illustration and verification
Linear generalized synchronization of continuous-time chaotic systems
Lu Jun
2003-01-01
This paper develops a general approach for constructing a response system to implement linear generalized synchronization (GS) with the drive continuous-time chaotic system. Some sufficient conditions of global asymptotic linear GS between the drive and response continuous-time chaotic systems are attained from rigorously modern control theory. Finally, we take Chua's circuit as an example for illustration and verification.
Linear generalized synchronization of continuous-time chaotic systems
Lu Junguo E-mail: jglu@sjtu.edu.cn; Xi Yugeng
2003-08-01
This paper develops a general approach for constructing a response system to implement linear generalized synchronization (GS) with the drive continuous-time chaotic system. Some sufficient conditions of global asymptotic linear GS between the drive and response continuous-time chaotic systems are attained from rigorously modern control theory. Finally, we take Chua's circuit as an example for illustration and verification.
Towards pattern generation and chaotic series prediction with photonic reservoir computers
Antonik, Piotr; Hermans, Michiel; Duport, François; Haelterman, Marc; Massar, Serge
2016-03-01
Reservoir Computing is a bio-inspired computing paradigm for processing time dependent signals that is particularly well suited for analog implementations. Our team has demonstrated several photonic reservoir computers with performance comparable to digital algorithms on a series of benchmark tasks such as channel equalisation and speech recognition. Recently, we showed that our opto-electronic reservoir computer could be trained online with a simple gradient descent algorithm programmed on an FPGA chip. This setup makes it in principle possible to feed the output signal back into the reservoir, and thus highly enrich the dynamics of the system. This will allow to tackle complex prediction tasks in hardware, such as pattern generation and chaotic and financial series prediction, which have so far only been studied in digital implementations. Here we report simulation results of our opto-electronic setup with an FPGA chip and output feedback applied to pattern generation and Mackey-Glass chaotic series prediction. The simulations take into account the major aspects of our experimental setup. We find that pattern generation can be easily implemented on the current setup with very good results. The Mackey-Glass series prediction task is more complex and requires a large reservoir and more elaborate training algorithm. With these adjustments promising result are obtained, and we now know what improvements are needed to match previously reported numerical results. These simulation results will serve as basis of comparison for experiments we will carry out in the coming months.
An Optimized Multikeying Chaotic Encryption for Real Time Applications
R. Tamijetchelvy
2013-12-01
Full Text Available In recent years, the availability of wireless technologies has become prominent solution for next generation wireless networks (NGWN. Hence the demand for secure communication is an important research issue. Cryptography is recognized as the best method of data protection against active and passive attacks. Therefore a novel chaotic cryptographic scheme is proposed for real time communication. Chaos signals are random behaviour, continuous and sensitive dependence on initial conditions. However, it has been shown that most of these chaotic methods have a low level of security because of single keying concept. In this paper an optimized fast encryption scheme based on chaotic signal with multi key is justified for video frame. Simulation results show that the proposed chaotic encryption scheme outperforms the existing scheme in terms of considerable reduction in encryption and decryption time. The security of the proposed scheme is also analysed by various cryptanalysis attacks.
Recurrence time statistics in chaotic dynamics. I. Discrete time maps
The dynamics of transitions between the cells of a finite-phase-space partition in a variety of systems giving rise to chaotic behavior is analyzed, with special emphasis on the statistics of recurrence times. In the case of one-dimensional piecewise Markov maps the recurrence problem is cast into a renewal process. In the presence of intermittency, transitions between cells define a non-Markovian, non-renewal process reflected in the presence of power-law probability distributions and of divergent variances and mean values
Impulsive Control of Memristive Chaotic Systems with Impulsive Time Window
FuLi Chen
2015-01-01
Full Text Available The problem of impulsive control for memristor-based chaotic circuit systems with impulsive time windows is investigated. Based on comparison principle, several novel criteria which guarantee the asymptotic stabilization of the memristor-based chaotic circuit systems are obtained. In comparison with previous results, the present results are easily verified. Numerical simulations are given to further illustrate the effectiveness of the theoretical results.
Characterizing Weak Chaos using Time Series of Lyapunov Exponents
da Silva, R. M.; Manchein, C.; Beims, M. W.; Altmann, E. G.
2015-01-01
We investigate chaos in mixed-phase-space Hamiltonian systems using time series of the finite- time Lyapunov exponents. The methodology we propose uses the number of Lyapunov exponents close to zero to define regimes of ordered (stickiness), semi-ordered (or semi-chaotic), and strongly chaotic motion. The dynamics is then investigated looking at the consecutive time spent in each regime, the transition between different regimes, and the regions in the phase-space associated to them. Applying ...
Moskowitz, Tobias J.; Ooi, Yao Hua; Heje Pedersen, Lasse
2012-01-01
We document significant “time series momentum” in equity index, currency, commodity, and bond futures for each of the 58 liquid instruments we consider. We find persistence in returns for one to 12 months that partially reverses over longer horizons, consistent with sentiment theories of initial...... under-reaction and delayed over-reaction. A diversified portfolio of time series momentum strategies across all asset classes delivers substantial abnormal returns with little exposure to standard asset pricing factors and performs best during extreme markets. Examining the trading activities...... of speculators and hedgers, we find that speculators profit from time series momentum at the expense of hedgers....
Loredo, Thomas
The key, central objectives of the proposed Time Series Explorer project are to develop an organized collection of software tools for analysis of time series data in current and future NASA astrophysics data archives, and to make the tools available in two ways: as a library (the Time Series Toolbox) that individual science users can use to write their own data analysis pipelines, and as an application (the Time Series Automaton) providing an accessible, data-ready interface to many Toolbox algorithms, facilitating rapid exploration and automatic processing of time series databases. A number of time series analysis methods will be implemented, including techniques that range from standard ones to state-of-the-art developments by the proposers and others. Most of the algorithms will be able to handle time series data subject to real-world problems such as data gaps, sampling that is otherwise irregular, asynchronous sampling (in multi-wavelength settings), and data with non-Gaussian measurement errors. The proposed research responds to the ADAP element supporting the development of tools for mining the vast reservoir of information residing in NASA databases. The tools that will be provided to the community of astronomers studying variability of astronomical objects (from nearby stars and extrasolar planets, through galactic and extragalactic sources) will revolutionize the quality of timing analyses that can be carried out, and greatly enhance the scientific throughput of all NASA astrophysics missions past, present, and future. The Automaton will let scientists explore time series - individual records or large data bases -- with the most informative and useful analysis methods available, without having to develop the tools themselves or understand the computational details. Both elements, the Toolbox and the Automaton, will enable deep but efficient exploratory time series data analysis, which is why we have named the project the Time Series Explorer. Science
Multivariate Time Series Search
National Aeronautics and Space Administration — Multivariate Time-Series (MTS) are ubiquitous, and are generated in areas as disparate as sensor recordings in aerospace systems, music and video streams, medical...
Hisdal, H.; Holmqvist, E.; Hyvärinen, V.; Jónsson, P.; Kuusisto, E.; Larsen, S. E.; Lindström, G.; Ovesen, N. B.; Roald, L. A.
Awareness that emission of greenhouse gases will raise the global temperature and change the climate has led to studies trying to identify such changes in long-term climate and hydrologic time series. This report, written by the......Awareness that emission of greenhouse gases will raise the global temperature and change the climate has led to studies trying to identify such changes in long-term climate and hydrologic time series. This report, written by the...
Fischer, Paul; Hilbert, Astrid
2012-01-01
We introduce a platform which supplies an easy-to-handle, interactive, extendable, and fast analysis tool for time series analysis. In contrast to other software suits like Maple, Matlab, or R, which use a command-line-like interface and where the user has to memorize/look-up the appropriate...... commands, our application is select-and-click-driven. It allows to derive many different sequences of deviations for a given time series and to visualize them in different ways in order to judge their expressive power and to reuse the procedure found. For many transformations or model-ts, the user may...... choose between manual and automated parameter selection. The user can dene new transformations and add them to the system. The application contains efficient implementations of advanced and recent techniques for time series analysis including techniques related to extreme value analysis and filtering...
Madsen, Henrik
2007-01-01
""In this book the author gives a detailed account of estimation, identification methodologies for univariate and multivariate stationary time-series models. The interesting aspect of this introductory book is that it contains several real data sets and the author made an effort to explain and motivate the methodology with real data. … this introductory book will be interesting and useful not only to undergraduate students in the UK universities but also to statisticians who are keen to learn time-series techniques and keen to apply them. I have no hesitation in recommending the book.""-Journa
Woodward, Wayne A; Elliott, Alan C
2011-01-01
""There is scarcely a standard technique that the reader will find left out … this book is highly recommended for those requiring a ready introduction to applicable methods in time series and serves as a useful resource for pedagogical purposes.""-International Statistical Review (2014), 82""Current time series theory for practice is well summarized in this book.""-Emmanuel Parzen, Texas A&M University""What an extraordinary range of topics covered, all very insightfully. I like [the authors'] innovations very much, such as the AR factor table.""-David Findley, U.S. Census Bureau (retired)""…
Network structure of multivariate time series
Lacasa, Lucas; Nicosia, Vincenzo; Latora, Vito
2015-10-01
Our understanding of a variety of phenomena in physics, biology and economics crucially depends on the analysis of multivariate time series. While a wide range tools and techniques for time series analysis already exist, the increasing availability of massive data structures calls for new approaches for multidimensional signal processing. We present here a non-parametric method to analyse multivariate time series, based on the mapping of a multidimensional time series into a multilayer network, which allows to extract information on a high dimensional dynamical system through the analysis of the structure of the associated multiplex network. The method is simple to implement, general, scalable, does not require ad hoc phase space partitioning, and is thus suitable for the analysis of large, heterogeneous and non-stationary time series. We show that simple structural descriptors of the associated multiplex networks allow to extract and quantify nontrivial properties of coupled chaotic maps, including the transition between different dynamical phases and the onset of various types of synchronization. As a concrete example we then study financial time series, showing that a multiplex network analysis can efficiently discriminate crises from periods of financial stability, where standard methods based on time-series symbolization often fail.
Liang, X San
2014-01-01
Given two time series, can one tell, in a rigorous and quantitative way, the cause and effect between them? Based on a recently rigorized physical notion namely information flow, we arrive at a concise formula and give this challenging question, which is of wide concern in different disciplines, a positive answer. Here causality is measured by the time rate of change of information flowing from one series, say, X2, to another, X1. The measure is asymmetric between the two parties and, particularly, if the process underlying X1 does not depend on X2, then the resulting causality from X2 to X1 vanishes. The formula is tight in form, involving only the commonly used statistics, sample covariances. It has been validated with touchstone series purportedly generated with one-way causality. It has also been applied to the investigation of real world problems; an example presented here is the cause-effect relation between two climate modes, El Ni\\~no and Indian Ocean Dipole, which have been linked to the hazards in f...
Minati, Ludovico, E-mail: lminati@ieee.org, E-mail: ludovico.minati@unitn.it [MR-Lab, Center for Mind/Brain Science, University of Trento, Trento, Italy and Scientific Department, Fondazione IRCCS Istituto Neurologico Carlo Besta, Milan (Italy)
2014-09-01
In this paper, an experimental characterization of the dynamical properties of five autonomous chaotic oscillators, based on bipolar-junction transistors and obtained de-novo through a genetic algorithm in a previous study, is presented. In these circuits, a variable resistor connected in series to the DC voltage source acts as control parameter, for a range of which the largest Lyapunov exponent, correlation dimension, approximate entropy, and amplitude variance asymmetry are calculated, alongside bifurcation diagrams and spectrograms. Numerical simulations are compared to experimental measurements. The oscillators can generate a considerable variety of regular and chaotic sine-like and spike-like signals.
Chaos synchronization and chaotization of complex chaotic systems in series form by optimal control
By the method of quadratic optimum control, a quadratic optimal regulator is used for synchronizing two complex chaotic systems in series form. By this method the least error with less control energy is achieved, and the optimization on both energy and error is realized synthetically. The simulation results of two Quantum-CNN chaos systems in series form prove the effectiveness of this method. Finally, chaotization of the system is given by optimal control.
Complete chaotic synchronization in mutually coupled time-delay systems.
Landsman, Alexandra S; Schwartz, Ira B
2007-02-01
Complete chaotic synchronization of end lasers has been observed in a line of mutually coupled, time-delayed system of three lasers, with no direct communication between the end lasers. The present paper uses ideas from generalized synchronization to explain the complete synchronization in the presence of long coupling delays, applied to a model of mutually coupled semiconductor lasers in a line. These ideas significantly simplify the analysis by casting the stability in terms of the local dynamics of each laser. The variational equations near the synchronization manifold are analyzed, and used to derive the synchronization condition that is a function of parameters. The results explain and predict the dependence of synchronization on various parameters, such as time delays, strength of coupling and dissipation. The ideas can be applied to understand complete synchronization in other chaotic systems with coupling delays and no direct communication between synchronized subsystems. PMID:17358399
Many human-related activities show power-law decaying interevent time distribution with exponents usually varying between 1 and 2. We study a simple task-queuing model, which produces bursty time series due to the non-trivial dynamics of the task list. The model is characterized by a priority distribution as an input parameter, which describes the choice procedure from the list. We give exact results on the asymptotic behaviour of the model and we show that the interevent time distribution is power-law decaying for any kind of input distributions that remain normalizable in the infinite list limit, with exponents tunable between 1 and 2. The model satisfies a scaling law between the exponents of interevent time distribution (β) and autocorrelation function (α): α + β = 2. This law is general for renewal processes with power-law decaying interevent time distribution. We conclude that slowly decaying autocorrelation function indicates long-range dependence only if the scaling law is violated. (paper)
The synchronization for time-delay of linearly bidirectional coupled chaotic system
Based on Lyapunov stability theory and matrix measure, this paper presents a new generic criterion of global chaotic synchronization for bidirectional coupled chaotic system with time-delay. A new chaotic system with four-scroll attractor is chosen as an example to verify the effectiveness of the criterion. Numerical simulation are shown for demonstration
Time evolution of frequency components in a chaotic digital signal
Martin-Pereda, Jose A.; Gonzalez-Marcos, Ana P.
2001-11-01
The type of signals obtained has conditioned chaos analysis tools. Almost in every case, they have analogue characteristics. But in certain cases, a chaotic digital signal is obtained and theses signals need a different approach than conventional analogue ones. The main objective of this paper will be to present some possible approaches to the study of this signals and how information about their characteristics may be obtained in the more straightforward possible way. We have obtained digital chaotic signals from an Optical Logic Cell with some feedback between output and one of the possible control gates. This chaos has been reported in several papers and its characteristics have been employed as a possible method to secure communications and as a way to encryption. In both cases, the influence of some perturbation in the transmission medium gave problems both for the synchronization of chaotic generators at emitter and receiver and for the recovering of information data. A proposed way to analyze the presence of some perturbation is to study the noise contents of transmitted signal and to implement a way to eliminate it. In our present case, the digital signal will be converted to a multilevel one by grouping bits in packets of 8 bits and applying conventional methods of time-frequency analysis to them. The results give information about the change in signals characteristics and hence some information about the noise or perturbations present. Equivalent representations to the phase and to the Feigenbaum diagrams for digital signals are employed in this case.
Determination of Optimal Control Strength of Delayed Feedback Control Using Time Series
YIN Hua-Wei; LU Wei-Ping; WANG Peng-Ye
2004-01-01
@@ We study controlling chaos using time-delayed feedback control based on chaotic time series without prior knowl edge of dynamical systems, and determine the optimal control parameters for stabilizing unstable periodic orbits with maximal stability.
Application of bootstrap to detecting chaos in financial time series
Brzozowska-Rup, Katarzyna; Orłowski, Arkadiusz
2004-12-01
A moving blocks bootstrap procedure is used to investigate the dynamics of nominal exchange rates and the return rates of the US Dollar against the Polish Zloty. The problem if these financial time series exhibit chaotic behavior is undertaken. A possibility of detecting the presence of a positive Lyapunov exponent is studied.
Attractors of relaxation discrete-time systems with chaotic dynamics on a fast time scale
Maslennikov, Oleg V.; Nekorkin, Vladimir I.
2016-07-01
In this work, a new type of relaxation systems is considered. Their prominent feature is that they comprise two distinct epochs, one is slow regular motion and another is fast chaotic motion. Unlike traditionally studied slow-fast systems that have smooth manifolds of slow motions in the phase space and fast trajectories between them, in this new type one observes, apart the same geometric objects, areas of transient chaos. Alternating periods of slow regular motions and fast chaotic ones as well as transitions between them result in a specific chaotic attractor with chaos on a fast time scale. We formulate basic properties of such attractors in the framework of discrete-time systems and consider several examples. Finally, we provide an important application of such systems, the neuronal electrical activity in the form of chaotic spike-burst oscillations.
GPS Position Time Series @ JPL
Owen, Susan; Moore, Angelyn; Kedar, Sharon; Liu, Zhen; Webb, Frank; Heflin, Mike; Desai, Shailen
2013-01-01
Different flavors of GPS time series analysis at JPL - Use same GPS Precise Point Positioning Analysis raw time series - Variations in time series analysis/post-processing driven by different users. center dot JPL Global Time Series/Velocities - researchers studying reference frame, combining with VLBI/SLR/DORIS center dot JPL/SOPAC Combined Time Series/Velocities - crustal deformation for tectonic, volcanic, ground water studies center dot ARIA Time Series/Coseismic Data Products - Hazard monitoring and response focused center dot ARIA data system designed to integrate GPS and InSAR - GPS tropospheric delay used for correcting InSAR - Caltech's GIANT time series analysis uses GPS to correct orbital errors in InSAR - Zhen Liu's talking tomorrow on InSAR Time Series analysis
Synchronization of Discrete-Time Chaotic Systems in Bandlimited Channels
Marcio Eisencraft
2009-01-01
Full Text Available Over the last couple of decades, many methods for synchronizing chaotic systems have been proposed with communications applications in view. Yet their performance has proved disappointing in face of the nonideal character of usual channels linking transmitter and receiver, that is, due to both noise and signal propagation distortion. Here we consider a discrete-time master-slave system that synchronizes despite channel bandwidth limitations and an allied communication system. Synchronization is achieved introducing a digital filter that limits the spectral content of the feedback loop responsible for producing the transmitted signal.
A NEW SLIDING MODE CONTROL FOR A CLASS OF UNCERTAIN TIME-DELAY CHAOTIC SYSTEMS
LI LI-XIANG; PENG HAI-PENG; GUAN BAO-ZHU; XU JIN-MING
2001-01-01
We propose a new sliding mode control scheme for a class of uncertain time-delay chaotic systems. It is shown that a linear time invariant system with the desired system dynamics is used as a reference model for the output of a time-delay chaotic system to track. A sliding mode controller is then designed to drive the output of the time-delay chaotic system to track the desired linear system. On the sliding mode, the output of the controlled time-delay chaotic system can behave like the desired linear system. A simulation example is given in support of the proposed control scheme.
Time scales and species coexistence in chaotic flows
Galla, Tobias
2016-01-01
Empirical observations in marine ecosystems have suggested a balance of biological and advection time scales as a possible explanation of species coexistence. To characterise this scenario, we measure the time to fixation in neutrally evolving populations in chaotic flows. Contrary to intuition the variation of time scales does not interpolate straightforwardly between the no-flow and well-mixed limits; instead we find that fixation is the slowest at intermediate Damk\\"ohler numbers, indicating long-lasting coexistence of species. Our analysis shows that this slowdown is due to spatial organisation on an increasingly modularised network. We also find that diffusion can either slow down or speed up fixation, depending on the relative time scales of flow and evolution.
多元混沌时间序列的因子回声状态网络预测模型%Factor Echo State Network for Multivariate Chaotic Time Series Prediction
许美玲; 韩敏
2015-01-01
When an echo state network is used to predict mul-tivariate time series, there may exist ill-posed problem. This pa-per proposes a novel prediction model, named factor echo state network, to solve the problem. It uses a factor analysis (FA) al-gorithm to extract the common factors of the reservoir matrix, and to remove the redundancies and noises. Then the unknown output weights are calculated by linear regression of the output and common factors. The model is used to predict Lorenz series and monthly average temperature-rainfall time series in Dalian, and simulation results substantiate its effectiveness.%针对采用回声状态网络预测多元混沌时间序列时存在的病态解问题,本文建立了因子回声状态网络模型,通过因子分析(Factor analysis, FA)方法提取高维储备池状态矩阵的公因子,去除冗余和噪声成分。利用降维后的因子变量与期望输出之间的线性回归关系,求解网络未知参数。基于Lorenz 序列和大连月平均气温–降雨量的仿真实验验证了本文所提模型的有效性。
Finite-Time Synchronizing Control for Chaotic Neural Networks
Chao Zhang
2014-01-01
Full Text Available This paper addresses the finite-time synchronizing problem for a class of chaotic neural networks. In a real communication network, parameters of the master system may be time-varying and the system may be perturbed by external disturbances. A simple high-gain observer is designed to track all the nonlinearities, unknown system functions, and disturbances. Then, a dynamic active compensatory controller is proposed and by using the singular perturbation theory, the control method can guarantee the finite-time stability of the error system between the master system and the slave system. Finally, two illustrative examples are provided to show the effectiveness and applicability of the proposed scheme.
Recovery of the Time-Evolution Equation of Time-Delay Systems from Time Series
Bünner, M J; Kittel, A; Parisi, J; Meyer, Th.
1997-01-01
We present a method for time series analysis of both, scalar and nonscalar time-delay systems. If the dynamics of the system investigated is governed by a time-delay induced instability, the method allows to determine the delay time. In a second step, the time-delay differential equation can be recovered from the time series. The method is a generalization of our recently proposed method suitable for time series analysis of {\\it scalar} time-delay systems. The dynamics is not required to be settled on its attractor, which also makes transient motion accessible to the analysis. If the motion actually takes place on a chaotic attractor, the applicability of the method does not depend on the dimensionality of the chaotic attractor - one main advantage over all time series analysis methods known until now. For demonstration, we analyze time series, which are obtained with the help of the numerical integration of a two-dimensional time-delay differential equation. After having determined the delay time, we recover...
On the detection of superdiffusive behaviour in time series
Gottwald, Georg A
2016-01-01
We present a new method for detecting superdiffusive behaviour and for determining rates of superdiffusion in time series data. Our method applies equally to stochastic and deterministic time series data and relies on one realisation (ie one sample path) of the process. Linear drift effects are automatically removed without any preprocessing. We show numerical results for time series constructed from i.i.d. $\\alpha$-stable random variables and from deterministic weakly chaotic maps. We compare our method with the standard method of estimating the growth rate of the mean-square displacement as well as the $p$-variation method.
LM algorithm in echo state network for chaotic time series prediction%回声状态网络LM算法及混沌时间序列预测
韩敏; 穆大芸
2011-01-01
The problem of sigular solution in echo state network（ESN） learning algorithm is existed,which is easy to cause ill issue.Especially when training samples are less than the dimenssions of the output,the solution of the ESN must be singular.Therefore,Levenberg Marquardt（LM） algorithm is used to learn ESN instead of linear regression method,which can effectively control the amplitude of the output weight result in improved predictive performance.The presented model is tested on the Lorenz time series and applied to some real life time series such as Dalian monthly average temprture time series.Actual simulation results show that the predictive model has higher predictive accuracy,and is of great practicality and effectiveness.%回声状态网络（ESN）学习算法中可能存在解的奇异问题,在时间序列预测时易导致病态解问题,且伴随着具有较大幅值的输出权值,尤其是当训练样本个数小于输出权值维数时,ESN的解必为奇异的.鉴于此,考虑使用LM（Levenberg Marquardt）算法代替常用的线性回归方法,自适应选择LM参数,从而有效地控制输出权值的幅值,提高ESN的预测性能.通过Lorenz混沌时间序列进行预测研究,对大连月平均气温实际数据进行仿真研究,取得了较好的预测效果.
Bootstrapping High Dimensional Time Series
Zhang, Xianyang; Cheng, Guang
2014-01-01
This article studies bootstrap inference for high dimensional weakly dependent time series in a general framework of approximately linear statistics. The following high dimensional applications are covered: (1) uniform confidence band for mean vector; (2) specification testing on the second order property of time series such as white noise testing and bandedness testing of covariance matrix; (3) specification testing on the spectral property of time series. In theory, we first derive a Gaussi...
Autoencoding Time Series for Visualisation
Gianniotis, Nikolaos; Kügler, Dennis; Tino, Peter; Polsterer, Kai; Misra, Ranjeev
2015-01-01
We present an algorithm for the visualisation of time series. To that end we employ echo state networks to convert time series into a suitable vector representation which is capable of capturing the latent dynamics of the time series. Subsequently, the obtained vector representations are put through an autoencoder and the visualisation is constructed using the activations of the bottleneck. The crux of the work lies with defining an objective function that quantifies the reconstruction error ...
Allan, Alasdair
2014-06-01
FROG performs time series analysis and display. It provides a simple user interface for astronomers wanting to do time-domain astrophysics but still offers the powerful features found in packages such as PERIOD (ascl:1406.005). FROG includes a number of tools for manipulation of time series. Among other things, the user can combine individual time series, detrend series (multiple methods) and perform basic arithmetic functions. The data can also be exported directly into the TOPCAT (ascl:1101.010) application for further manipulation if needed.
Multi-target real-time ranging with chaotic laser radar
Bingjie Wang; Yuncai Wang; Lingqin Kong; Anbang Wang
2008-01-01
We demonstrate the feasibility of multi-target real-time ranging with a chaotic laser radar. The used chaotic laser is emitted by a semiconductor laser with optical feedback. We design a proof-of-concept experiment based on the correlation detection and realize the range measurements of two targets simultaneously. The range resolution of 9 cm between two targets is achieved, which is limited by the bandwidth of the used real-time oscilloscope. A preliminary experiment of chaotic laser coherence is carried out to verify the high resolution of the chaotic lidar.
Advances in time series forecasting
Cagdas, Hakan Aladag
2012-01-01
Readers will learn how these methods work and how these approaches can be used to forecast real life time series. The hybrid forecasting model is also explained. Data presented in this e-book is problem based and is taken from real life situations. It is a valuable resource for students, statisticians and working professionals interested in advanced time series analysis.
A unified approach for impulsive lag synchronization of chaotic systems with time delay
In this paper, we propose a unified approach for impulsive lag-synchronization of a class of chaotic systems with time delay by employing the stability theory of impulsive delayed differential equations. Three well-known delayed chaotic systems are presented to illustrate our results. Also, the estimates of the stable regions for these systems are given, respectively
Models for dependent time series
Tunnicliffe Wilson, Granville; Haywood, John
2015-01-01
Models for Dependent Time Series addresses the issues that arise and the methodology that can be applied when the dependence between time series is described and modeled. Whether you work in the economic, physical, or life sciences, the book shows you how to draw meaningful, applicable, and statistically valid conclusions from multivariate (or vector) time series data.The first four chapters discuss the two main pillars of the subject that have been developed over the last 60 years: vector autoregressive modeling and multivariate spectral analysis. These chapters provide the foundational mater
Autoencoding Time Series for Visualisation
Gianniotis, Nikolaos; Tino, Peter; Polsterer, Kai; Misra, Ranjeev
2015-01-01
We present an algorithm for the visualisation of time series. To that end we employ echo state networks to convert time series into a suitable vector representation which is capable of capturing the latent dynamics of the time series. Subsequently, the obtained vector representations are put through an autoencoder and the visualisation is constructed using the activations of the bottleneck. The crux of the work lies with defining an objective function that quantifies the reconstruction error of these representations in a principled manner. We demonstrate the method on synthetic and real data.
Time Series with Tailored Nonlinearities
Raeth, C
2015-01-01
It is demonstrated how to generate time series with tailored nonlinearities by inducing well- defined constraints on the Fourier phases. Correlations between the phase information of adjacent phases and (static and dynamic) measures of nonlinearities are established and their origin is explained. By applying a set of simple constraints on the phases of an originally linear and uncor- related Gaussian time series, the observed scaling behavior of the intensity distribution of empirical time series can be reproduced. The power law character of the intensity distributions being typical for e.g. turbulence and financial data can thus be explained in terms of phase correlations.
A Chaotic Block Cipher for Real-Time Multimedia
M. Venkatesulu
2012-01-01
Full Text Available Problem statement: The widespread use of image, audio and video data makes media content protection increasingly necessary and important. We propose a naive approach which treats the multimedia signal to be protected as a text and use proposed encryption design to encrypt the whole data stream. Upon reception, the entire cipher text data stream would be decrypted and playback can be performed at the client end with an initial time delay. Approach: We introduce a block cipher algorithm, which encrypts and decrypts a block size of 512 bits regardless of the file format. In this, a permutation algorithm using a chaotic system is employed to provide the shuffler function. A shuffler operator is defined using the shuffler function. A random key generator generates key sequences and the scheme employs key-dependant transformations based on distance in the shuffling operator. The process of encryption/decryption is governed by the shuffler function, shuffler operator and the pseudorandom key. Results: The basic operation used is logical XOR and so the algorithm has a very high encryption/decryption speed. The execution time shows the proposed scheme is faster than the existing cryptographic schemes. Conclusion: The proposal of the algorithm is to manage the tradeoffs between the speed and security and hence appropriate for real-time image and video communication applications.
Lag synchronization of chaotic systems with time-delayed linear terms via impulsive control
Ranchao Wu; Dongxu Cao
2013-11-01
In this paper, the lag synchronization of chaotic systems with time-delayed linear terms via impulsive control is investigated. Based on the stability theory of impulsive delayed differential equations, some sufficient conditions are obtained guaranteeing the synchronized behaviours between two delayed chaotic systems. Numerical simulations on time-delayed Lorenz and hyperchaotic Chen systems are also carried out to show the effectiveness of the proposed scheme. Note that under the scheme the chaotic system is controlled only at discrete time instants, and so it reduces the control cost in real applications.
Synchronisation of fractional-order time delayed chaotic systems with ring connection
He, S.; Sun, K.; Wang, H.
2016-02-01
In this paper, synchronisation of fractional-order time delayed chaotic systems in ring networks is investigated. Based on Lyapunov stability theory, a new generic synchronisation criterion for N-coupled chaotic systems with time delay is proposed. The synchronisation scheme is applied to N-coupled fractional-order time delayed simplified Lorenz systems, and the Adomian decomposition method (ADM) is developed for solving these chaotic systems. Performance analysis of the synchronisation network is carried out. Numerical experiments demonstrate that synchronisation realises in both state variables and intermediate variables, which verifies the effectiveness of the proposed method.
Novaes, Marcel [Instituto de Física, Universidade Federal de Uberlândia, Av. João Naves de Ávila, 2121, Uberlândia, MG 38408-100 (Brazil)
2015-06-15
We consider S-matrix correlation functions for a chaotic cavity having M open channels, in the absence of time-reversal invariance. Relying on a semiclassical approximation, we compute the average over E of the quantities Tr[S{sup †}(E − ϵ) S(E + ϵ)]{sup n}, for general positive integer n. Our result is an infinite series in ϵ, whose coefficients are rational functions of M. From this, we extract moments of the time delay matrix Q = − iħS{sup †}dS/dE and check that the first 8 of them agree with the random matrix theory prediction from our previous paper [M. Novaes, J. Math. Phys. 56, 062110 (2015)].
Multivariate Time Series Similarity Searching
Jimin Wang; Yuelong Zhu; Shijin Li; Dingsheng Wan; Pengcheng Zhang
2014-01-01
Multivariate time series (MTS) datasets are very common in various financial, multimedia, and hydrological fields. In this paper, a dimension-combination method is proposed to search similar sequences for MTS. Firstly, the similarity of single-dimension series is calculated; then the overall similarity of the MTS is obtained by synthesizing each of the single-dimension similarity based on weighted BORDA voting method. The dimension-combination method could use the existing similarity searchin...
马军海; 陈予恕
2001-01-01
The prediction methods and its applications of the nonlinear dynamic systems determined from chaotic time series of low-dimension are discussed mainly. Based on the work of the foreign researchers, the chaotic time series in the phase space adopting one kind of nonlinear chaotic model were reconstructed. At first, the model parameters were estimated by using the improved least square method. Then as the precision was satisfied,the optimization method was used to estimate these parameters. At the end by using the obtained chaotic model, the future data of the chaotic time series in the phase space was predicted. Some representative experimental examples were analyzed to testify the models and the algorithms developed in this paper. The results show that if the algorithms developed here are adopted, the parameters of the corresponding chaotic model will be easily calculated well and true. Predictions of chaotic series in phase space make the traditional methods change from outer iteration to interpolations. And if the optimal model rank is chosen, the prediction precision will increase notably. Long term superior predictability of nonlinear chaotic models is proved to be irrational and unreasonable.
Random time series in astronomy.
Vaughan, Simon
2013-02-13
Progress in astronomy comes from interpreting the signals encoded in the light received from distant objects: the distribution of light over the sky (images), over photon wavelength (spectrum), over polarization angle and over time (usually called light curves by astronomers). In the time domain, we see transient events such as supernovae, gamma-ray bursts and other powerful explosions; we see periodic phenomena such as the orbits of planets around nearby stars, radio pulsars and pulsations of stars in nearby galaxies; and we see persistent aperiodic variations ('noise') from powerful systems such as accreting black holes. I review just a few of the recent and future challenges in the burgeoning area of time domain astrophysics, with particular attention to persistently variable sources, the recovery of reliable noise power spectra from sparsely sampled time series, higher order properties of accreting black holes, and time delays and correlations in multi-variate time series. PMID:23277606
Symplectic geometry spectrum regression for prediction of noisy time series
Xie, Hong-Bo; Dokos, Socrates; Sivakumar, Bellie; Mengersen, Kerrie
2016-05-01
We present the symplectic geometry spectrum regression (SGSR) technique as well as a regularized method based on SGSR for prediction of nonlinear time series. The main tool of analysis is the symplectic geometry spectrum analysis, which decomposes a time series into the sum of a small number of independent and interpretable components. The key to successful regularization is to damp higher order symplectic geometry spectrum components. The effectiveness of SGSR and its superiority over local approximation using ordinary least squares are demonstrated through prediction of two noisy synthetic chaotic time series (Lorenz and Rössler series), and then tested for prediction of three real-world data sets (Mississippi River flow data and electromyographic and mechanomyographic signal recorded from human body).
Self-organization in Trees and Motifs of Two-Dimensional Chaotic Maps with Time Delay
Levnajić, Zoran; Tadić, Bosiljka
2007-01-01
We study two-dimensional chaotic standard maps coupled along the edges of scale-free trees and tree-like subgraph (4-star) with a non-symplectic coupling and time delay between the nodes. Apart from the chaotic and regular 2-periodic motion, the coupled map system exhibits variety of dynamical effects in a wide range of coupling strengths. This includes dynamical localization, emergent periodicity, and appearance of strange non-chaotic attractors. Near the strange attractors we find long-rang...
Adaptive control of chaotic systems with stochastic time varying unknown parameters
In this paper based on the Lyapunov stability theorem, an adaptive control scheme is proposed for stabilizing the unstable periodic orbits (UPO) of chaotic systems. It is assumed that the chaotic system has some linearly dependent unknown parameters which are stochastically time varying. The stochastic parameters are modeled through the Weiner process derivative. To demonstrate the effectiveness of the proposed technique it has been applied to the Lorenz, Chen and Rossler dynamical systems, as some case studies. Simulation results indicate that the proposed adaptive controller has a high performance in stabilizing the UPO of chaotic systems in noisy environment
Estimating measurement noise in a time series by exploiting nonstationarity
A measured time series is always corrupted by noise to some degree. Even a rough estimation of the level of noise contained in an experimental time series is valuable. This is so, for example, when one wishes to apply techniques from nonlinear dynamics theory to analyze a time series. However, this is a very difficult problem. It becomes even harder when the measured signal is nonstationary, which is often true in practice. Detecting nonstationarity has been a hot research topic in recent years. However, many researchers stop when they find the time series under study is indeed nonstationary. Here, we exploit the very nature of nonstationarity in a signal to formulate a method for quantitatively estimating the amount of noise contained in the signal. The approach is first verified using computer simulated signals based on the chaotic Lorenz attractors and the Mackey-Glass equations with different parameters and then applied to the clinically measured intracranial EEG signals. It is found that the amount of noise in the EEG signals is around 8.0-8.5% in terms of amplitude. Implications to whether EEG signals are chaotic or not are discussed
Global synchronization criteria with channel time-delay for chaotic time-delay system
Based on the Lyapunov stabilization theory, matrix measure, and linear matrix inequality (LMIs), this paper studies the chaos synchronization of time-delay system using the unidirectional linear error feedback coupling with time-delay. Some generic conditions of chaos synchronization with time-delay in the transmission channel is established. The chaotic Chua's circuit is used for illustration, where the coupling parameters are determined according to the criteria under which the global chaos synchronization of the time-delay coupled systems is achieved
Global synchronization criteria with channel time-delay for chaotic time-delay system
Sun Jitao E-mail: sunjt@sh163.net
2004-08-01
Based on the Lyapunov stabilization theory, matrix measure, and linear matrix inequality (LMIs), this paper studies the chaos synchronization of time-delay system using the unidirectional linear error feedback coupling with time-delay. Some generic conditions of chaos synchronization with time-delay in the transmission channel is established. The chaotic Chua's circuit is used for illustration, where the coupling parameters are determined according to the criteria under which the global chaos synchronization of the time-delay coupled systems is achieved.
Stochastic Time-Series Spectroscopy
Scoville, John
2015-01-01
Spectroscopically measuring low levels of non-equilibrium phenomena (e.g. emission in the presence of a large thermal background) can be problematic due to an unfavorable signal-to-noise ratio. An approach is presented to use time-series spectroscopy to separate non-equilibrium quantities from slowly varying equilibria. A stochastic process associated with the non-equilibrium part of the spectrum is characterized in terms of its central moments or cumulants, which may vary over time. This parameterization encodes information about the non-equilibrium behavior of the system. Stochastic time-series spectroscopy (STSS) can be implemented at very little expense in many settings since a series of scans are typically recorded in order to generate a low-noise averaged spectrum. Higher moments or cumulants may be readily calculated from this series, enabling the observation of quantities that would be difficult or impossible to determine from an average spectrum or from prinicipal components analysis (PCA). This meth...
Expanded boundary integral method and chaotic time-reversal doublets in quantum billiards
Veble, G.; Prosen, T.; Robnik, M.
2007-01-01
We present the expanded boundary integral method for solving the planar Helmholtz problem, which combines the ideas of the boundary integral method and the scaling method and is applicable to arbitrary shapes. We apply the method to a chaotic billiard with unidirectional transport, where we demonstrate the existence of doublets of chaotic eigenstates, which are quasi-degenerate due to time-reversal symmetry, and a very particular level spacing distribution that attains a chaotic Shnirelman peak at short energy ranges and exhibits Gaussian Unitary Ensemble (GUE) like statistics for large energy ranges. We show that, as a consequence of such particular level statistics or algebraic tunnelling between disjoint chaotic components connected by time-reversal operation, the system exhibits quantum current reversals.
Chaotic anti-control for the bounded linear continuous-time system
Li Jianfen; Lin Hui; Li Nong
2008-01-01
With regard to the bounded linear continuous-time system, a universal chaotic anti-controlling method was presented on the basis of tracking control. A tracking controller is designed to such an extent that it can track any chaotic reference input, thus making it possible to chaotify the linear system. The controller is identical in structure for different controlled linear systems. Computer simulations proved the effectiveness of the proposed method.
Y. Saiki
2007-09-01
Full Text Available An infinite number of unstable periodic orbits (UPOs are embedded in a chaotic system which models some complex phenomenon. Several algorithms which extract UPOs numerically from continuous-time chaotic systems have been proposed. In this article the damped Newton-Raphson-Mees algorithm is reviewed, and some important techniques and remarks concerning the practical numerical computations are exemplified by employing the Lorenz system.
Time evolution of frequency components In a chaotic digital signal
Martín Pereda, José Antonio; González Marcos, Ana
2001-01-01
The type of signals obtained has conditioned chaos analysis tools. Almost in every case, they have analogue characteristics. But in certain cases, a chaotic digital signal is obtained and theses signals need a different approach than conventional analogue ones. The main objective of this paper will be to present some possible approaches to the study of this signals and how information about their characteristics may be obtained in the more straightforward possible way. We have obtained digita...
Lyapunov exponents from CHUA's circuit time series using artificial neural networks
Gonzalez, J. Jesus; Espinosa, Ismael E.; Fuentes, Alberto M.
1995-01-01
In this paper we present the general problem of identifying if a nonlinear dynamic system has a chaotic behavior. If the answer is positive the system will be sensitive to small perturbations in the initial conditions which will imply that there is a chaotic attractor in its state space. A particular problem would be that of identifying a chaotic oscillator. We present an example of three well known different chaotic oscillators where we have knowledge of the equations that govern the dynamical systems and from there we can obtain the corresponding time series. In a similar example we assume that we only know the time series and, finally, in another example we have to take measurements in the Chua's circuit to obtain sample points of the time series. With the knowledge about the time series the phase plane portraits are plotted and from them, by visual inspection, it is concluded whether or not the system is chaotic. This method has the problem of uncertainty and subjectivity and for that reason a different approach is needed. A quantitative approach is the computation of the Lyapunov exponents. We describe several methods for obtaining them and apply a little known method of artificial neural networks to the different examples mentioned above. We end the paper discussing the importance of the Lyapunov exponents in the interpretation of the dynamic behavior of biological neurons and biological neural networks.
Detection of "noisy" chaos in a time series
Chon, K H; Kanters, J K; Cohen, R J; Holstein-Rathlou, N H
Time series from biological system often displays fluctuations in the measured variables. Much effort has been directed at determining whether this variability reflects deterministic chaos, or whether it is merely "noise". The output from most biological systems is probably the result of both the...... internal dynamics of the systems, and the input to the system from the surroundings. This implies that the system should be viewed as a mixed system with both stochastic and deterministic components. We present a method that appears to be useful in deciding whether determinism is present in a time series......, and if this determinism has chaotic attributes. The method relies on fitting a nonlinear autoregressive model to the time series followed by an estimation of the characteristic exponents of the model over the observed probability distribution of states for the system. The method is tested by computer...
张学清; 梁军
2013-01-01
According to the chaotic feature of wind power time series, a combined short-term wind power forecasting approach based on ensemble empirical mode decomposition (EEMD)-approximate entropy and echo state network (ESN) is proposed. Firstly, in order to reduce the calculation scale of partial analysis for wind power and improve the wind power prediction accuracy, the wind power time series is decomposed into a series of wind power subsequences with obvious differences in complex degree by using EEMD-approximate entropy. Then, the forecasting model of each subsequence is created with least squares support vector machine (LSSVM), ESN and EEMD-ESN improved with the regularized high frequency parts. Finally, the simulation is performed by using the real data collected from a certain wind farm, the results show that the EEMD-ESN model is better in the training speed and forecasting accuracy, than those obtained from the least square support vector machine (LSSVM) model, which provides a new useful reference for the short-term forecasting of wind power in online engineering application.% 针对风电功率时间序列的混沌特性,提出了一种基于集成经验模态分解(ensemble empirical mode decomposition, EEMD)-近似熵和回声状态网络(echo state network, ESN)的风电功率混沌时间序列组合预测模型。首先为降低对风电功率局部分析的计算规模以及提高预测的准确性,利用EEMD-近似熵将风电功率时间序列分解为一系列复杂度差异明显的风电子序列；然后对各子序列分别建立ESN、经过高频分量正则化改进的EEMD-ESN模型和最小二乘支持向量机预测模型；最后以某一风电场实际采集的数据为算例,仿真结果表明EEMD-ESN模型在训练速度和预测精度上优于最小二乘支持向量机模型,为实现风电功率短期预测的在线工程应用提供了新的有益参考。
Response of the parameters of a neural network to pseudoperiodic time series
Zhao, Yi; Weng, Tongfeng; Small, Michael
2014-02-01
We propose a representation plane constructed from parameters of a multilayer neural network, with the aim of characterizing the dynamical character of a learned time series. We find that fluctuation of this plane reveals distinct features of the time series. Specifically, a periodic representation plane corresponds to a periodic time series, even when contaminated with strong observational noise or dynamical noise. We present a theoretical explanation for how the neural network training algorithm adjusts parameters of this representation plane and thereby encodes the specific characteristics of the underlying system. This ability, which is intrinsic to the architecture of the neural network, can be employed to distinguish the chaotic time series from periodic counterparts. It provides a new path toward identifying the dynamics of pseudoperiodic time series. Furthermore, we extract statistics from the representation plane to quantify its character. We then validate this idea with various numerical data generated by the known periodic and chaotic dynamics and experimentally recorded human electrocardiogram data.
The brief time-reversibility of the local Lyapunov exponents for a small chaotic Hamiltonian system
Highlights: •We consider the local Lyapunov spectrum for a four-dimensional Hamilton system. •Its stable periodic motion can be reversed for long times. •In the chaotic motion, time reversal occurs only for a short time. •Perturbations will change this short unstable case into a different stable case. •These observations might relate chaos to the Second Law of Thermodynamics. - Abstract: We consider the local (instantaneous) Lyapunov spectrum for a four-dimensional Hamiltonian system. Its stable periodic motion can be reversed for long times. Its unstable chaotic motion, with two symmetric pairs of exponents, cannot. In the latter case reversal occurs for more than a thousand fourth-order Runge–Kutta time steps, followed by a transition to a new set of paired Lyapunov exponents, unrelated to those seen in the forward time direction. The relation of the observed chaotic dynamics to the Second Law of Thermodynamics is discussed
Adaptive control of uncertain time-delay chaotic systems
Zhuhong ZHANG
2005-01-01
This work investigates adaptive control of a large class of uncertain me-delay chaotic systems (UTCSs) with unknown general perturbation terms bounded by a polynomial ( unknown gains). Associated with the different cases of known and unknown system matrices, two corresponding adaptive controllers are proposed to stabilize unstable fixed points of the systems by means of Lyapunov stability theory and linear matrix inequalities (LMI) which can be solved easily by convex optimization algorithms. Two examples are used for examining the effectiveness of the proposed methods.
Learning time series evolution by unsupervised extraction of correlations
As a consequence, we are able to model chaotic and nonchaotic time series. Furthermore, one critical point in modeling time series is the determination of the dimension of the embedding vector used, i.e., the number of components of the past that are needed to predict the future. With this method we can detect the embedding dimension by extracting the influence of the past on the future, i.e., the correlation of remote past and future. Optimal embedding dimensions are obtained for the Henon map and the Mackey-Glass series. When noisy data corrupted by colored noise are used, a model is still possible. The noise will then be decorrelated by the network. In the case of modeling a chemical reaction, the most natural architecture that conserves the volume is a symplectic network which describes a system that conserves the entropy and therefore the transmitted information
Lee, C; Zhu, X; Gao, K; Hai, W; Duan Yi Shi; Liu, W K; Lee, Chaohong; Shi, Lei; Zhu, Xiwen; Gao, Kelin; Hai, Wenhua; Duan, Yiwu; Liu, Wing-Ki
2001-01-01
We have investigated the chaotic atomic population oscillations between two coupled Bose-Einstein condensates (BEC) with time-dependent asymmetric trap potential. In the perturbative regime, the population oscillations can be described by the Duffing equation, and the chaotic oscillations near the separatrix solution are analyzed. The sufficient-necessary conditions for stable oscillations depend on the physical parameters and initial conditions sensitively. The first-order necessary condition indicates that the Melnikov function is equal to zero, so the stable oscillations are Melnikov chaotic. For the ordinary parameters and initial conditions, the chaotic dynamics is simulated with numerical calculation. If the damping is absent, with the increasing of the trap asymmetry, the regular oscillations become chaotic gradually, the corresponding stroboscopic Poincare sections (SPS) vary from a single island to more islands, and then the chaotic sea. For the completely chaotic oscillations, the long-term localiza...
Parameter estimation for time-delay chaotic system by particle swarm optimization
The knowledge about time delays and parameters is very important for control and synchronization of time-delay chaotic system. In this paper, parameter estimation for time-delay chaotic system is given by treating the time delay as an additional parameter. The parameter estimation is converted to an optimization problem, which finds a best parameter combination such that an objective function is minimized. Particle swarm optimization (PSO) is used to optimize the objective function through particles' cooperation and evolution. Two illustrative examples are given to show the validity of the proposed method.
ACCURATE TIME SERIES CLASSIFICATION USING SHAPELETS
M. Arathi; A. GOVARDHAN
2014-01-01
Time series data are sequences of values measured o ver time. One of the most recent approaches to classification of time series data is to find shape lets within a data set. Time series shapelets are time series subsequences which represent a class. In order to compare two time series sequences, existing work use s Euclidean distance measure. The problem with Euclid ean distance is that it requires data to be standardized if scales ...
Nonlinear time series analysis methods and applications
Diks, Cees
1999-01-01
Methods of nonlinear time series analysis are discussed from a dynamical systems perspective on the one hand, and from a statistical perspective on the other. After giving an informal overview of the theory of dynamical systems relevant to the analysis of deterministic time series, time series generated by nonlinear stochastic systems and spatio-temporal dynamical systems are considered. Several statistical methods for the analysis of nonlinear time series are presented and illustrated with applications to physical and physiological time series.
Experimental observation of Loschmidt time reversal of a Quantum Chaotic System
Ullah, A; Hoogerland, M. D.
2009-01-01
We have performed an experiment to demonstrate the approximate time reversal of a "chaotic" time evolution of atomic deBroglie waves. We use ultra cold atoms from a Bose-Einstein condensate in a quantum $\\delta$-kicked rotor experiment, and show that an initial state can be approximately re-created even after a period of "chaotic" evolution (a number of kicks). As this mechanism only works for a very narrow range of momenta, the net effect is a narrowing of the momentum distribution after the...
P. Siricharuanun
2016-01-01
Full Text Available A second-order sliding mode control for chaotic synchronization with bounded disturbance is studied. A robust finite-time controller is designed based on super twisting algorithm which is a popular second-order sliding mode control technique. The proposed controller is designed by combining an adaptive law with super twisting algorithm. New results based on adaptive super twisting control for the synchronization of identical Qi three-dimensional four-wing chaotic system are presented. The finite-time convergence of synchronization is ensured by using Lyapunov stability theory. The simulations results show the usefulness of the developed control method.
Reconstruction of Ordinary Differential Equations From Time Series Data
Mai, Manuel; O'Hern, Corey S
2016-01-01
We develop a numerical method to reconstruct systems of ordinary differential equations (ODEs) from time series data without {\\it a priori} knowledge of the underlying ODEs using sparse basis learning and sparse function reconstruction. We show that employing sparse representations provides more accurate ODE reconstruction compared to least-squares reconstruction techniques for a given amount of time series data. We test and validate the ODE reconstruction method on known 1D, 2D, and 3D systems of ODEs. The 1D system possesses two stable fixed points; the 2D system possesses an oscillatory fixed point with closed orbits; and the 3D system displays chaotic dynamics on a strange attractor. We determine the amount of data required to achieve an error in the reconstructed functions to less than $0.1\\%$. For the reconstructed 1D and 2D systems, we are able to match the trajectories from the original ODEs even at long times. For the 3D system with chaotic dynamics, as expected, the trajectories from the original an...
Yang, Dong-Sheng; Liu, Zhen-Wei; Zhao, Yan; Liu, Zhao-Bing
2012-04-01
The networked synchronization problem of a class of master-slave chaotic systems with time-varying communication topologies is investigated in this paper. Based on algebraic graph theory and matrix theory, a simple linear state feedback controller is designed to synchronize the master chaotic system and the slave chaotic systems with a time-varying communication topology connection. The exponential stability of the closed-loop networked synchronization error system is guaranteed by applying Lyapunov stability theory. The derived novel criteria are in the form of linear matrix inequalities (LMIs), which are easy to examine and tremendously reduce the computation burden from the feedback matrices. This paper provides an alternative networked secure communication scheme which can be extended conveniently. An illustrative example is given to demonstrate the effectiveness of the proposed networked synchronization method.
The networked synchronization problem of a class of master-slave chaotic systems with time-varying communication topologies is investigated in this paper. Based on algebraic graph theory and matrix theory, a simple linear state feedback controller is designed to synchronize the master chaotic system and the slave chaotic systems with a time-varying communication topology connection. The exponential stability of the closed-loop networked synchronization error system is guaranteed by applying Lyapunov stability theory. The derived novel criteria are in the form of linear matrix inequalities (LMIs), which are easy to examine and tremendously reduce the computation burden from the feedback matrices. This paper provides an alternative networked secure communication scheme which can be extended conveniently. An illustrative example is given to demonstrate the effectiveness of the proposed networked synchronization method. (general)
Finite-time synchronization of a class of autonomous chaotic systems
Huini Lin; Jianping Cai
2014-03-01
Some criteria for achieving the finite-time synchronization of a class of autonomous chaotic systems are derived by the finite-time stability theory and Gerschgorin disc theorem. Numerical simulations are shown to illustrate the effectiveness of the proposed method.
Chaos analysis of the electrical signal time series evoked by acupuncture
This paper employs chaos theory to analyze the time series of electrical signal which are evoked by different acupuncture methods applied to the Zusanli point. The phase space is reconstructed and the embedding parameters are obtained by the mutual information and Cao's methods. Subsequently, the largest Lyapunov exponent is calculated. From the analyses we can conclude that the time series are chaotic. In addition, differences between various acupuncture methods are discussed
Chaos analysis of the electrical signal time series evoked by acupuncture
Wang Jiang [School of Electrical Engineering, Tianjin University, Tianjin 300072 (China)]. E-mail: jiangwang@tju.edu.cn; Sun Li [School of Electrical Engineering, Tianjin University, Tianjin 300072 (China); Fei Xiangyang [School of Electrical Engineering, Tianjin University, Tianjin 300072 (China); Zhu Bing [Institute of Acupuncture and Moxibustion, China Academy of Traditional Chinese Medicine, Beijing 100700 (China)
2007-08-15
This paper employs chaos theory to analyze the time series of electrical signal which are evoked by different acupuncture methods applied to the Zusanli point. The phase space is reconstructed and the embedding parameters are obtained by the mutual information and Cao's methods. Subsequently, the largest Lyapunov exponent is calculated. From the analyses we can conclude that the time series are chaotic. In addition, differences between various acupuncture methods are discussed.
Yang Dong-Sheng; Liu Zhen-Wei; Zhao Yan; Liu Zhao-Bing
2012-01-01
The networked synchronization problem of a class of master-slave chaotic systems with time-varying communication topologies is investigated in this paper. Based on algebraic graph theory and matrix theory,a simple linear state feedback controller is designed to synchronize the master chaotic system and the slave chaotic systems with a timevarying communication topology connection.The exponential stability of the closed-loop networked synchronization error system is guaranteed by applying Lyapunov stability theory.The derived novel criteria are in the form of linear matrix inequalities (LMIs),which are easy to examine and tremendously reduce the computation burden from the feedback matrices.This paper provides an alternative networked secure communication scheme which can be extended conveniently.An illustrative example is given to demonstrate the effectiveness of the proposed networked synchronization method.
A Course in Time Series Analysis
Peña, Daniel; Tsay, Ruey S
2011-01-01
New statistical methods and future directions of research in time series A Course in Time Series Analysis demonstrates how to build time series models for univariate and multivariate time series data. It brings together material previously available only in the professional literature and presents a unified view of the most advanced procedures available for time series model building. The authors begin with basic concepts in univariate time series, providing an up-to-date presentation of ARIMA models, including the Kalman filter, outlier analysis, automatic methods for building ARIMA models, a
Analysis of the time structure of synchronization in multidimensional chaotic systems
Makarenko, A. V., E-mail: avm.science@mail.ru [Constructive Cybernetics Research Group (Russian Federation)
2015-05-15
A new approach is proposed to the integrated analysis of the time structure of synchronization of multidimensional chaotic systems. The method allows one to diagnose and quantitatively evaluate the intermittency characteristics during synchronization of chaotic oscillations in the T-synchronization mode. A system of two identical logistic mappings with unidirectional coupling that operate in the developed chaos regime is analyzed. It is shown that the widely used approach, in which only synchronization patterns are subjected to analysis while desynchronization areas are considered as a background signal and removed from analysis, should be regarded as methodologically incomplete.
Isochronal synchronization of time delay and delay-coupled chaotic systems
Grzybowski, J. M. V.; Macau, E. E. N.; Yoneyama, T.
2011-04-01
This paper studies the problem of isochronal synchronization of time-delay chaotic systems featuring also coupling delay. Based on the Lyapunov-Krasovskii stability theory, sufficient conditions are derived for the stability of isochronal synchronization between a pair of identical chaotic systems. Such criteria permit the proper design of stable proportional linear feedback controller, more specifically, the design of adequate proportional feedback gain matrices. The proposed criteria are suited to systems with (i) intrinsic delay, (ii) coupling delay or (iii) both. Numerical simulations of the synchronization of delay-coupled systems are presented as examples of the application of the criteria.
Sabavath, Gopi Kishan; Banerjee, I.; Mahapatra, S. K., E-mail: skmahapatra@bitmesra.ac.in [Plasma Laboratory, Department of Physics, Birla Institute of Technology-Mesra, Ranchi 835215 (India); Shaw, Pankaj Kumar; Sekar Iyengar, A. N. [Plasma Physics Division, Saha Institute of Nuclear Physics, 1/AF, Bidhannagar, Kolkata 700064 (India)
2015-08-15
Floating potential fluctuations from a direct current magnetron sputtering plasma have been analysed using time series analysis techniques like phase space plots, power spectra, frequency bifurcation plot, etc. The system exhibits quasiperiodic-chaotic-quasiperiodic-chaotic transitions as the discharge voltage was increased. The transitions of the fluctuations, quantified using the largest Lyapunov exponent, have been corroborated by Hurst exponent and the Shannon entropy. The Shannon entropy is high for quasiperiodic and low for chaotic oscillations.
LMI optimization approach to stabilization of time-delay chaotic systems
Based on the Lyapunov stability theory and linear matrix inequality (LMI) technique, this paper proposes a novel control method for stabilization of a class of time-delay chaotic systems. A stabilization criterion is derived in terms of LMIs which can be easily solved by efficient convex optimization algorithms. A numerical example is included to show the advantage of the result derived
A novel criterion for delayed feedback control of time-delay chaotic systems
This paper investigated stability criterion of time-delay chaotic systems via delayed feedback control (DFC) using the Lyapunov stability theory and linear matrix inequality (LMI) technique. A stabilization criterion is derived in terms of LMIs which can be easily solved by efficient convex optimization algorithms. A numerical example is given to illuminate the design procedure and advantage of the result derived
Time averaged properties along unstable periodic orbits and chaotic orbits in two map systems
Y. Saiki
2008-08-01
Full Text Available Unstable periodic orbit (UPO recently has become a keyword in analyzing complex phenomena in geophysical fluid dynamics and space physics. In this paper, sets of UPOs in low dimensional maps are theoretically or systematically found, and time averaged properties along UPOs are studied, in relation to those of chaotic orbits.
Effective Feature Preprocessing for Time Series Forecasting
Zhao, Junhua; Dong, Zhaoyang; Xu, Zhao
2006-01-01
Time series forecasting is an important area in data mining research. Feature preprocessing techniques have significant influence on forecasting accuracy, therefore are essential in a forecasting model. Although several feature preprocessing techniques have been applied in time series forecasting...
Effective Feature Preprocessing for Time Series Forecasting
Zhao, Junhua; Dong, Zhaoyang; Xu, Zhao
Time series forecasting is an important area in data mining research. Feature preprocessing techniques have significant influence on forecasting accuracy, therefore are essential in a forecasting model. Although several feature preprocessing techniques have been applied in time series forecasting...
Application of chaotic noise reduction techniques to chaotic data trained by ANN
C Chandra Shekara Bhat; M R Kaimal; T R Ramamohan
2001-10-01
We propose a novel method of combining artiﬁcial neural networks (ANNs) with chaotic noise reduction techniques that captures the metric and dynamic invariants of a chaotic time series, e.g. a time series obtained by iterating the logistic map in chaotic regimes. Our results indicate that while the feedforward neural network is capable of capturing the dynamical and metric invariants of chaotic time series within an error of about 25%, ANNs along with chaotic noise reduction techniques, such as Hammel’s method or the local projective method, can signiﬁcantly improve these results. This further suggests that the effort on the ANN to train data corresponding to complex structures can be signiﬁcantly reduced. This technique can be applied in areas like signal processing, data communication, image processing etc.
A novel memristive time-delay chaotic system without equilibrium points
Pham, V.-T.; Vaidyanathan, S.; Volos, C. K.; Jafari, S.; Kuznetsov, N. V.; Hoang, T. M.
2016-02-01
Memristor and time-delay are potential candidates for constructing new systems with complex dynamics and special features. A novel time-delay system with a presence of memristive device is proposed in this work. It is worth noting that this memristive time-delay system can generate chaotic attractors although it possesses no equilibrium points. In addition, a circuitry implementation of such time-delay system has been introduced to show its feasibility.
This Letter investigates chaos synchronization of chaotic and hyperchaotic systems. Based on finite-time stability theory, a simple adaptive control method for realizing chaos synchronization in a finite time is proposed. In comparison with previous methods, the present method is not only simple, but could also be easily utilized in application. Numerical simulations are given to illustrate the effectiveness and validity of the proposed approach. -- Highlights: → Optimizing the synchronization time is essential for chaotic synchronization application. → This is particularly important in communication system for recovering encoded message/data. → This Letter proposes an adaptive control method for realizing finite-time chaos synchronization. → The method gives simple control inputs that guarantee finite-time synchronization. → It could be exploited for experimental realization of finite-time synchronization.
The synchronization of chaotic neurons coupled with gap junction with time delays is investigated. In this paper, the coupled model is based on the nonlinear cable model of neuron. The influences of the strength of gap junction and the time delay on the synchronization are discussed in detail. The so called delay-dependent criteria for the synchronization of two coupled neurons which contain the information of the time delay and the coupling strength is given
This paper investigates a novel stability criterion for interval time-delay chaotic systems via the evolutionary programming (EP) approach. First a delay-dependent criterion is derived for ensuring the stability of degenerate time-delay systems, and then by solving eigenvalue location optimization problems, which will be defined later, the robust stability of interval time-delay systems can be guaranteed. An example is given to verify our method that yields less conservative results than those appeared in the literature
GENERAL: Synchronization of time-delay chaotic systems on small-world networks with delayed coupling
Qi, Wei; Wang, Ying-Hai
2009-04-01
By using the well-known Ikeda model as the node dynamics, this paper studies synchronization of time-delay systems on small-world networks where the connections between units involve time delays. It shows that, in contrast with the undelayed case, networks with delays can actually synchronize more easily. Specifically, for randomly distributed delays, time-delayed mutual coupling suppresses the chaotic behaviour by stabilizing a fixed point that is unstable for the uncoupled dynamical system.
Wang Jiang [School of Electrical and Automation Engineering, Tianjin University, 300072, Tianjin (China)], E-mail: jiangwang@tju.edu.cn; Deng Bin; Fei Xiangyang [School of Electrical and Automation Engineering, Tianjin University, 300072, Tianjin (China)
2008-02-15
The synchronization of chaotic neurons coupled with gap junction with time delays is investigated. In this paper, the coupled model is based on the nonlinear cable model of neuron. The influences of the strength of gap junction and the time delay on the synchronization are discussed in detail. The so called delay-dependent criteria for the synchronization of two coupled neurons which contain the information of the time delay and the coupling strength is given.
Time Series Analysis and Forecasting by Example
Bisgaard, Soren
2011-01-01
An intuition-based approach enables you to master time series analysis with ease Time Series Analysis and Forecasting by Example provides the fundamental techniques in time series analysis using various examples. By introducing necessary theory through examples that showcase the discussed topics, the authors successfully help readers develop an intuitive understanding of seemingly complicated time series models and their implications. The book presents methodologies for time series analysis in a simplified, example-based approach. Using graphics, the authors discuss each presented example in
A review of subsequence time series clustering.
Zolhavarieh, Seyedjamal; Aghabozorgi, Saeed; Teh, Ying Wah
2014-01-01
Clustering of subsequence time series remains an open issue in time series clustering. Subsequence time series clustering is used in different fields, such as e-commerce, outlier detection, speech recognition, biological systems, DNA recognition, and text mining. One of the useful fields in the domain of subsequence time series clustering is pattern recognition. To improve this field, a sequence of time series data is used. This paper reviews some definitions and backgrounds related to subsequence time series clustering. The categorization of the literature reviews is divided into three groups: preproof, interproof, and postproof period. Moreover, various state-of-the-art approaches in performing subsequence time series clustering are discussed under each of the following categories. The strengths and weaknesses of the employed methods are evaluated as potential issues for future studies. PMID:25140332
Highlights: → A chaotic model of spontaneous neuron firing. → Mapping the irregular spiking time-series into telegraph signals. → Fundamental frequency of the Rossler attractor provides periodic component. → Spiking time-series from spontaneous activity of hippocampal neurons. → Comparison shows good agreement between the model and the experiment. - Abstract: A chaotic model of spontaneous (without external stimulus) neuron firing has been analyzed by mapping the irregular spiking time-series into telegraph signals. In this model the fundamental frequency of chaotic Roessler attractor provides (with a period doubling) the strong periodic component of the generated irregular signal. The exponentially decaying broad-band part of the spectrum of the Roessler attractor has been transformed by the threshold firing mechanism into a scaling tale. These results are compared with irregular spiking time-series obtained in vitro from a spontaneous activity of hippocampal (CA3) singular neurons (rat's brain slice culture). The comparison shows good agreement between the model and experimentally obtained spectra.
Learning time series evolution by unsupervised extraction of correlations
Deco, Gustavo; Schürmann, Bernd
1995-03-01
We focus on the problem of modeling time series by learning statistical correlations between the past and present elements of the series in an unsupervised fashion. This kind of correlation is, in general, nonlinear, especially in the chaotic domain. Therefore the learning algorithm should be able to extract statistical correlations, i.e., higher-order correlations between the elements of the time signal. This problem can be viewed as a special case of factorial learning. Factorial learning may be formulated as an unsupervised redundancy reduction between the output components of a transformation that conserves the transmitted information. An information-theoretic-based architecture and learning paradigm are introduced. The neural architecture has only one layer and a triangular structure in order to transform elements by observing only the past and to conserve the volume. In this fashion, a transformation that guarantees transmission of information without loss is formulated. The learning rule decorrelates the output components of the network. Two methods are used: higher-order decorrelation by explicit evaluation of higher-order cumulants of the output distributions, and minimization of the sum of entropies of each output component in order to minimize the mutual information between them, assuming that the entropies have an upper bound given by Gibbs second theorem. After decorrelation between the output components, the correlation between the elements of the time series can be extracted by analyzing the trained neural architecture. As a consequence, we are able to model chaotic and nonchaotic time series. Furthermore, one critical point in modeling time series is the determination of the dimension of the embedding vector used, i.e., the number of components of the past that are needed to predict the future. With this method we can detect the embedding dimension by extracting the influence of the past on the future, i.e., the correlation of remote past and future
Numerical test for hyperbolicity of chaotic dynamics in time-delay systems.
Kuptsov, Pavel V; Kuznetsov, Sergey P
2016-07-01
We develop a numerical test of hyperbolicity of chaotic dynamics in time-delay systems. The test is based on the angle criterion and includes computation of angle distributions between expanding, contracting, and neutral manifolds of trajectories on the attractor. Three examples are tested. For two of them, previously predicted hyperbolicity is confirmed. The third one provides an example of a time-delay system with nonhyperbolic chaos. PMID:27575062
Numerical test for hyperbolicity of chaotic dynamics in time-delay systems
Kuptsov, Pavel V.; Kuznetsov, Sergey P.
2016-01-01
We develop the numerical test of hyperbolicity of chaotic dynamics in time-delay systems. The test is based on the angle criterion and includes the computation of angle distribution between expanding, contracting and neutral manifolds of trajectories on the attractor. Three examples are tested. For two of them previously predicted hyperbolicity is confirmed. The third one provides an example of time-delay system with non-hyperbolic chaos.
Chaotic Scattering and Escape Times of Marginally Trapped Ultracold Neutrons
Coakley, K. J.; Doyle, J. M.; Dzhosyuk, S. N.; Yang, L.; Huffman, P. R.
2005-01-01
We compute classical trajectories of Ultracold neutrons (UCNs) in a superconducting Ioffe-type magnetic trap using a symplectic integration method. We find that the computed escape time for a particular set of initial conditions (momentum and position) does not generally stabilize as the time step parameter is reduced unless the escape time is short (less than approximately 10 s). For energy intervals where more than half of the escape times computed for UCN realizations are numerically well determined, we predict the median escape time as a function of the midpoint of the interval.
Data mining in time series databases
Kandel, Abraham; Bunke, Horst
2004-01-01
Adding the time dimension to real-world databases produces Time SeriesDatabases (TSDB) and introduces new aspects and difficulties to datamining and knowledge discovery. This book covers the state-of-the-artmethodology for mining time series databases. The novel data miningmethods presented in the book include techniques for efficientsegmentation, indexing, and classification of noisy and dynamic timeseries. A graph-based method for anomaly detection in time series isdescribed and the book also studies the implications of a novel andpotentially useful representation of time series as strings. Theproblem of detecting changes in data mining models that are inducedfrom temporal databases is additionally discussed.
International Work-Conference on Time Series
Pomares, Héctor
2016-01-01
This volume presents selected peer-reviewed contributions from The International Work-Conference on Time Series, ITISE 2015, held in Granada, Spain, July 1-3, 2015. It discusses topics in time series analysis and forecasting, advanced methods and online learning in time series, high-dimensional and complex/big data time series as well as forecasting in real problems. The International Work-Conferences on Time Series (ITISE) provide a forum for scientists, engineers, educators and students to discuss the latest ideas and implementations in the foundations, theory, models and applications in the field of time series analysis and forecasting. It focuses on interdisciplinary and multidisciplinary research encompassing the disciplines of computer science, mathematics, statistics and econometrics.
Coupling between time series: a network view
Mehraban, Saeed; Zamani, Maryam; Jafari, Gholamreza
2013-01-01
Recently, the visibility graph has been introduced as a novel view for analyzing time series, which maps it to a complex network. In this paper, we introduce new algorithm of visibility, "cross-visibility", which reveals the conjugation of two coupled time series. The correspondence between the two time series is mapped to a network, "the cross-visibility graph", to demonstrate the correlation between them. We applied the algorithm to several correlated and uncorrelated time series, generated by the linear stationary ARFIMA process. The results demonstrate that the cross-visibility graph associated with correlated time series with power-law auto-correlation is scale-free. If the time series are uncorrelated, the degree distribution of their cross-visibility network deviates from power-law. For more clarifying the process, we applied the algorithm to real-world data from the financial trades of two companies, and observed significant small-scale coupling in their dynamics.
Sliding-Mode Synchronization Control for Uncertain Fractional-Order Chaotic Systems with Time Delay
Haorui Liu
2015-06-01
Full Text Available Specifically setting a time delay fractional financial system as the study object, this paper proposes a single controller method to eliminate the impact of model uncertainty and external disturbances on the system. The proposed method is based on the stability theory of Lyapunov sliding-mode adaptive control and fractional-order linear systems. The controller can fit the system state within the sliding-mode surface so as to realize synchronization of fractional-order chaotic systems. Analysis results demonstrate that the proposed single integral, sliding-mode control method can control the time delay fractional power system to realize chaotic synchronization, with strong robustness to external disturbance. The controller is simple in structure. The proposed method was also validated by numerical simulation.
In this Letter we consider modified function projective synchronization of unidirectionally coupled multiple time-delayed Rossler chaotic systems using adaptive controls. Recently, delay differential equations have attracted much attention in the field of nonlinear dynamics. The high complexity of the multiple time-delayed systems can provide a new architecture for enhancing message security in chaos based encryption systems. Adaptive control can be used for synchronization when the parameters of the system are unknown. Based on Lyapunov stability theory, the adaptive control law and the parameter update law are derived to make the state of two chaotic systems are function projective synchronized. Numerical simulations are presented to demonstrate the effectiveness of the proposed adaptive controllers.
Cristian Rodriguez Rivero
2016-03-01
Full Text Available A new predictor algorithm based on Bayesian enhanced approach (BEA for long-term chaotic time series using artificial neural networks (ANN is presented. The technique based on stochastic models uses Bayesian inference by means of Fractional Brownian Motion as model data and Beta model as prior information. However, the need of experimental data for specifying and estimating causal models has not changed. Indeed, Bayes method provides another way to incorporate prior knowledge in forecasting models; the simplest representations of prior knowledge in forecasting models are hard to beat in many forecasting situations, either because prior knowledge is insufficient to improve on models or because prior knowledge leads to the conclusion that the situation is stable. This work contributes with long-term time series prediction, to give forecast horizons up to 18 steps ahead. Thus, the forecasted values and validation data are presented by solutions of benchmark chaotic series such as Mackey-Glass, Lorenz, Henon, Logistic, Rössler, Ikeda, Quadratic one-dimensional map series and monthly cumulative rainfall collected from Despeñaderos, Cordoba, Argentina. The computational results are evaluated against several non-linear ANN predictors proposed before on high roughness series that shows a better performance of Bayesian Enhanced approach in long-term forecasting.
Semiclassical matrix model for quantum chaotic transport with time-reversal symmetry
Novaes, Marcel, E-mail: marcel.novaes@gmail.com
2015-10-15
We show that the semiclassical approach to chaotic quantum transport in the presence of time-reversal symmetry can be described by a matrix model. In other words, we construct a matrix integral whose perturbative expansion satisfies the semiclassical diagrammatic rules for the calculation of transport statistics. One of the virtues of this approach is that it leads very naturally to the semiclassical derivation of universal predictions from random matrix theory.
Lag-generalized synchronization of time-delay chaotic systems with stochastic perturbation
Zhang, Shuo; Yu, Yongguang; Wen, Guoguang; Rahmani, Ahmed
2016-01-01
The lag-generalized synchronization of coupled time-delay chaotic systems with unknown parameters and stochastic perturbation is investigated. Based on the LaSalle-type invariance principle of stochastic differential equation, the synchronization is realized by analyzing stochastic stability of the error system. In order to achieve the synchronization, the unknown parameter update laws and the control laws are proposed. At last, two numerical examples are presented to show the effectiveness of the obtained theoretical results.
Discrete-Time Chaotic Circuits for Implementation of Tent Map and Bernoulli Map
LI Zhi-zhong; QIU Shui-sheng
2005-01-01
Discrete-time chaotic circuit implementations of a tent map and a Bernoulli map using switched-current (SI) techniques are presented. The two circuits can be constructed with 16MOSFET's and 2 capacitors. The simulations and experiments built with commercially available IC's for the circuits have demonstrated the validity of the circuit designs. The experiment results also indicate that the proposed circuits are integrable by a standard CMOS technology. The implementations are useful for studies and applications of chaos.
Detecting Dynamical States from Noisy Time Series using Bicoherence
George, Sandip V; Misra, R
2016-01-01
Deriving meaningful information from observational data is often restricted by many limiting factors, the most important of which is the presence of noise. In this work, we present the use of the bicoherence function to extract information about the underlying nonlinearity from noisy time series. We show that a system evolving in the presence of noise which has its dynamical state concealed from quantifiers like the power spectrum and correlation dimension D2, can be revealed using the bicoherence function. We define an index called main peak bicoherence function as the bicoherence associated with the maximal power spectral peak. We show that this index is extremely useful while dealing with quasi-periodic data as it can distinguish strange non chaos from quasi periodicity even with added noise. We demonstrate this in a real world scenario, by taking the bicoherence of variable stars showing period doubling and strange non-chaotic behavior. Our results indicate that bicoherence analysis can also bypass the me...
A Chaotic Block Cipher for Real-Time Multimedia
M. Venkatesulu; N.Radha
2012-01-01
Problem statement: The widespread use of image, audio and video data makes media content protection increasingly necessary and important. We propose a naive approach which treats the multimedia signal to be protected as a text and use proposed encryption design to encrypt the whole data stream. Upon reception, the entire cipher text data stream would be decrypted and playback can be performed at the client end with an initial time delay. Approach: We introduce a block cipher algorithm, which ...
Detecting dynamical complexity changes in time series using the base-scale entropy
Li Jin; Ning Xin-Bao; Wu Wei; Ma Xiao-Fei
2005-01-01
Timely detection of dynamical complexity changes in natural and man-made systems has deep scientific and practical meanings. We introduce a complexity measure for time series: the base-scale entropy. The definition directly applies to arbitrary real-word data. We illustrate our method on a practical speech signal and in a theoretical chaotic system. The results show that the simple and easily calculated measure of base-scale entropy can be effectively used to detect qualitative and quantitative dynamical changes.
Random time series in Astronomy
Vaughan, Simon
2013-01-01
Progress in astronomy comes from interpreting the signals encoded in the light received from distant objects: the distribution of light over the sky (images), over photon wavelength (spectrum), over polarization angle, and over time (usually called light curves by astronomers). In the time domain we see transient events such as supernovae, gamma-ray bursts, and other powerful explosions; we see periodic phenomena such as the orbits of planets around nearby stars, radio pulsars, and pulsations...
Hurst Exponent Analysis of Financial Time Series
无
2001-01-01
Statistical properties of stock market time series and the implication of their Hurst exponents are discussed. Hurst exponents of DJ1A (Dow Jones Industrial Average) components are tested using re-scaled range analysis. In addition to the original stock return series, the linear prediction errors of the daily returns are also tested. Numerical results show that the Hurst exponent analysis can provide some information about the statistical properties of the financial time series.
The Foundations of Modern Time Series Analysis
Mills, Professor Terence C
2011-01-01
This book develops the analysis of Time Series from its formal beginnings in the 1890s through to the publication of Box and Jenkins' watershed publication in 1970, showing how these methods laid the foundations for the modern techniques of Time Series analysis that are in use today.
Lag space estimation in time series modelling
Goutte, Cyril
1997-01-01
The purpose of this article is to investigate some techniques for finding the relevant lag-space, i.e. input information, for time series modelling. This is an important aspect of time series modelling, as it conditions the design of the model through the regressor vector a.k.a. the input layer...
Delay-dependent stability criteria for time-delay chaotic systems via time-delay feedback control
This paper studies delay-dependent stability of time-delay chaotic systems via time-delayed feedback control (DFC). The delay-dependent stability criteria via DFC are derived from the results based on standard feedback control (SFC), the method can be obtained to stabilize the system to an unstable fixed point. A numerical example is discussed to illustrate the advantage of the obtained result
Cherrier, Estelle; M'Saad, Mohammed; Farza, Mondher
2010-01-01
This work investigates high gain observer design to synchronize a time-delay chaotic system. It is shown that the underlying class of nonlinear systems can be put into the canonical observable form, and thus high gain observer design framework can be extended to chaotic synchronization problem. Our approach is motivated by its simplicity of implementation: the observer gain synthesis relies on the explicit resolution of a time-invariant algebraic Lyapunov equation, which leads to a single par...
Cherrier, Estelle; M'Saad, Mohammed
2009-01-01
This work investigates high gain observer design to synchronize a time-delay chaotic system. It is shown that the underlying class of nonlinear systems can be put into the canonical observable form, and thus high gain observer design framework can be extended to chaotic synchronization problem. Our approach is motivated by its simplicity of implementation: the observer gain synthesis relies on the explicit resolution of a time-invariant algebraic Lyapunov equation, which leads to a single par...
Zhang, Guodong; Shen, Yi
2015-07-01
This paper is concerned with the global exponential stabilization of memristor-based chaotic neural networks with both time-varying delays and general activation functions. Here, we adopt nonsmooth analysis and control theory to handle memristor-based chaotic neural networks with discontinuous right-hand side. In particular, several new sufficient conditions ensuring exponential stabilization of memristor-based chaotic neural networks are obtained via periodically intermittent control. In addition, the proposed results here are easy to verify and they also extend the earlier publications. Finally, numerical simulations illustrate the effectiveness of the obtained results. PMID:25148672
Novaes, Marcel [Instituto de Física, Universidade Federal de Uberlândia, Ave. João Naves de Ávila, 2121, Uberlândia, MG 38408-100 (Brazil)
2015-06-15
We consider the statistics of time delay in a chaotic cavity having M open channels, in the absence of time-reversal invariance. In the random matrix theory approach, we compute the average value of polynomial functions of the time delay matrix Q = − iħS{sup †}dS/dE, where S is the scattering matrix. Our results do not assume M to be large. In a companion paper, we develop a semiclassical approximation to S-matrix correlation functions, from which the statistics of Q can also be derived. Together, these papers contribute to establishing the conjectured equivalence between the random matrix and the semiclassical approaches.
We consider the statistics of time delay in a chaotic cavity having M open channels, in the absence of time-reversal invariance. In the random matrix theory approach, we compute the average value of polynomial functions of the time delay matrix Q = − iħS†dS/dE, where S is the scattering matrix. Our results do not assume M to be large. In a companion paper, we develop a semiclassical approximation to S-matrix correlation functions, from which the statistics of Q can also be derived. Together, these papers contribute to establishing the conjectured equivalence between the random matrix and the semiclassical approaches
Comparing entropy with tests for randomness as a measure of complexity in time series
Gan, Chee Chun
2015-01-01
Entropy measures have become increasingly popular as an evaluation metric for complexity in the analysis of time series data, especially in physiology and medicine. Entropy measures the rate of information gain, or degree of regularity in a time series e.g. heartbeat. Ideally, entropy should be able to quantify the complexity of any underlying structure in the series, as well as determine if the variation arises from a random process. Unfortunately current entropy measures mostly are unable to perform the latter differentiation. Thus, a high entropy score indicates a random or chaotic series, whereas a low score indicates a high degree of regularity. This leads to the observation that current entropy measures are equivalent to evaluating how random a series is, or conversely the degree of regularity in a time series. This raises the possibility that existing tests for randomness, such as the runs test or permutation test, may have similar utility in diagnosing certain conditions. This paper compares various t...
Homogenising time series: beliefs, dogmas and facts
Domonkos, P.
2011-06-01
In the recent decades various homogenisation methods have been developed, but the real effects of their application on time series are still not known sufficiently. The ongoing COST action HOME (COST ES0601) is devoted to reveal the real impacts of homogenisation methods more detailed and with higher confidence than earlier. As a part of the COST activity, a benchmark dataset was built whose characteristics approach well the characteristics of real networks of observed time series. This dataset offers much better opportunity than ever before to test the wide variety of homogenisation methods, and analyse the real effects of selected theoretical recommendations. Empirical results show that real observed time series usually include several inhomogeneities of different sizes. Small inhomogeneities often have similar statistical characteristics than natural changes caused by climatic variability, thus the pure application of the classic theory that change-points of observed time series can be found and corrected one-by-one is impossible. However, after homogenisation the linear trends, seasonal changes and long-term fluctuations of time series are usually much closer to the reality than in raw time series. Some problems around detecting multiple structures of inhomogeneities, as well as that of time series comparisons within homogenisation procedures are discussed briefly in the study.
Searching of Chaotic Elements in Hydrology
Sorin VLAD
2014-03-01
Full Text Available Chaos theory offers new means of understanding and prediction of phenomena otherwise considered random and unpredictable. The signatures of chaos can be isolated by performing nonlinear analysis of the time series available. The paper presents the results obtained by conducting a nonlinear analysis of the time series of daily Siret river flow (located in the North-Eastern part of Romania. The time series analysis is recorded starting with January 1999 to July 2009. The attractor is embedded in the reconstructed phase space then the chaotic dynamics is revealed computing the chaotic invariants - correlation dimension and the maximum Lyapunov Exponent.
Testing Mean Stability of Heteroskedastic Time Series
Violetta Dalla; Liudas Giraitis; Phillips, Peter C. B.
2015-01-01
Time series models are often fitted to the data without preliminary checks for stability of the mean and variance, conditions that may not hold in much economic and financial data, particularly over long periods. Ignoring such shifts may result in fitting models with spurious dynamics that lead to unsupported and controversial conclusions about time dependence, causality, and the effects of unanticipated shocks. In spite of what may seem as obvious differences between a time series of indepen...
Testing mean stability of heteroskedastic time series
Dalla, Violetta; Giraitis, Liudas; Phillips, Peter C. B.
2015-01-01
Time series models are often fitted to the data without preliminary checks for stability of the mean and variance, conditions that may not hold in much economic and financial data, particularly over long periods. Ignoring such shifts may result in fitting models with spurious dynamics that lead to unsupported and controversial conclusions about time dependence, causality, and the effects of unanticipated shocks. In spite of what may seem as obvious differences between a time series of indepen...
Time Series Analysis Using Composite Multiscale Entropy
Kung-Yen Lee; Chun-Chieh Wang; Shiou-Gwo Lin; Chiu-Wen Wu; Shuen-De Wu
2013-01-01
Multiscale entropy (MSE) was recently developed to evaluate the complexity of time series over different time scales. Although the MSE algorithm has been successfully applied in a number of different fields, it encounters a problem in that the statistical reliability of the sample entropy (SampEn) of a coarse-grained series is reduced as a time scale factor is increased. Therefore, in this paper, the concept of a composite multiscale entropy (CMSE) is introduced to overcome this difficulty. S...
Projective synchronization in modulated time-delayed systems is studied by applying an active control method. Based on the Lyapunov asymptotical stability theorem, the controller and sufficient condition for projective synchronization are calculated analytically. We give a general method with which we can achieve projective synchronization in modulated time-delayed chaotic systems. This method allows us to adjust the desired scaling factor arbitrarily. The effectiveness of our method is confirmed by using the famous delay-differential equations related to optical bistable or hybrid optical bistable devices. Numerical simulations fully support the analytical approach. (general)
Lee, Chaohong; Shi, Lei; Zhu, Xiwen; Gao, Kelin; Hai, Wenhua; Duan, Yiwu; Liu, Wing-Ki
2000-01-01
We have investigated the chaotic atomic population oscillations between two coupled Bose-Einstein condensates (BEC) with time-dependent asymmetric trap potential. In the perturbative regime, the population oscillations can be described by the Duffing equation, and the chaotic oscillations near the separatrix solution are analyzed. The sufficient-necessary conditions for stable oscillations depend on the physical parameters and initial conditions sensitively. The first-order necessary conditio...
Wu Wei; Cui Bao-Tong
2007-01-01
In this paper, a synchronization scheme for a class of chaotic neural networks with time-varying delays is presented.This class of chaotic neural networks covers several well-known neural network, such a Hopfield neural networks, cellular neural networks, and bidirectional associative memory networks. The obtained criteria are expressed in terms of linear matrix inequalities, thus they can be efficiently verified. A comparison between our results and the previous results shows that our results are less restrictive.
Time series modeling, computation, and inference
Prado, Raquel
2010-01-01
The authors systematically develop a state-of-the-art analysis and modeling of time series. … this book is well organized and well written. The authors present various statistical models for engineers to solve problems in time series analysis. Readers no doubt will learn state-of-the-art techniques from this book.-Hsun-Hsien Chang, Computing Reviews, March 2012My favorite chapters were on dynamic linear models and vector AR and vector ARMA models.-William Seaver, Technometrics, August 2011… a very modern entry to the field of time-series modelling, with a rich reference list of the current lit
Time Series Analysis Forecasting and Control
Box, George E P; Reinsel, Gregory C
2011-01-01
A modernized new edition of one of the most trusted books on time series analysis. Since publication of the first edition in 1970, Time Series Analysis has served as one of the most influential and prominent works on the subject. This new edition maintains its balanced presentation of the tools for modeling and analyzing time series and also introduces the latest developments that have occurred n the field over the past decade through applications from areas such as business, finance, and engineering. The Fourth Edition provides a clearly written exploration of the key methods for building, cl
Visibility Graph Based Time Series Analysis.
Mutua Stephen
Full Text Available Network based time series analysis has made considerable achievements in the recent years. By mapping mono/multivariate time series into networks, one can investigate both it's microscopic and macroscopic behaviors. However, most proposed approaches lead to the construction of static networks consequently providing limited information on evolutionary behaviors. In the present paper we propose a method called visibility graph based time series analysis, in which series segments are mapped to visibility graphs as being descriptions of the corresponding states and the successively occurring states are linked. This procedure converts a time series to a temporal network and at the same time a network of networks. Findings from empirical records for stock markets in USA (S&P500 and Nasdaq and artificial series generated by means of fractional Gaussian motions show that the method can provide us rich information benefiting short-term and long-term predictions. Theoretically, we propose a method to investigate time series from the viewpoint of network of networks.
Forecasting Daily Time Series using Periodic Unobserved Components Time Series Models
Koopman, Siem Jan; Ooms, Marius
2004-01-01
We explore a periodic analysis in the context of unobserved components time series models that decompose time series into components of interest such as trend and seasonal. Periodic time series models allow dynamic characteristics to depend on the period of the year, month, week or day. In the stand
Measuring nonlinear behavior in time series data
Wai, Phoong Seuk; Ismail, Mohd Tahir
2014-12-01
Stationary Test is an important test in detect the time series behavior since financial and economic data series always have missing data, structural change as well as jumps or breaks in the data set. Moreover, stationary test is able to transform the nonlinear time series variable to become stationary by taking difference-stationary process or trend-stationary process. Two different types of hypothesis testing of stationary tests that are Augmented Dickey-Fuller (ADF) test and Kwiatkowski-Philips-Schmidt-Shin (KPSS) test are examine in this paper to describe the properties of the time series variables in financial model. Besides, Least Square method is used in Augmented Dickey-Fuller test to detect the changes of the series and Lagrange multiplier is used in Kwiatkowski-Philips-Schmidt-Shin test to examine the properties of oil price, gold price and Malaysia stock market. Moreover, Quandt-Andrews, Bai-Perron and Chow tests are also use to detect the existence of break in the data series. The monthly index data are ranging from December 1989 until May 2012. Result is shown that these three series exhibit nonlinear properties but are able to transform to stationary series after taking first difference process.
Complex network approach to fractional time series
In order to extract correlation information inherited in stochastic time series, the visibility graph algorithm has been recently proposed, by which a time series can be mapped onto a complex network. We demonstrate that the visibility algorithm is not an appropriate one to study the correlation aspects of a time series. We then employ the horizontal visibility algorithm, as a much simpler one, to map fractional processes onto complex networks. The degree distributions are shown to have parabolic exponential forms with Hurst dependent fitting parameter. Further, we take into account other topological properties such as maximum eigenvalue of the adjacency matrix and the degree assortativity, and show that such topological quantities can also be used to predict the Hurst exponent, with an exception for anti-persistent fractional Gaussian noises. To solve this problem, we take into account the Spearman correlation coefficient between nodes' degrees and their corresponding data values in the original time series
Advanced spectral methods for climatic time series
Ghil, M.; Allen, M.R.; Dettinger, M.D.; Ide, K.; Kondrashov, D.; Mann, M.E.; Robertson, A.W.; Saunders, A.; Tian, Y.; Varadi, F.; Yiou, P.
2002-01-01
The analysis of univariate or multivariate time series provides crucial information to describe, understand, and predict climatic variability. The discovery and implementation of a number of novel methods for extracting useful information from time series has recently revitalized this classical field of study. Considerable progress has also been made in interpreting the information so obtained in terms of dynamical systems theory. In this review we describe the connections between time series analysis and nonlinear dynamics, discuss signal- to-noise enhancement, and present some of the novel methods for spectral analysis. The various steps, as well as the advantages and disadvantages of these methods, are illustrated by their application to an important climatic time series, the Southern Oscillation Index. This index captures major features of interannual climate variability and is used extensively in its prediction. Regional and global sea surface temperature data sets are used to illustrate multivariate spectral methods. Open questions and further prospects conclude the review.
Complex network approach to fractional time series
Manshour, Pouya
2015-10-01
In order to extract correlation information inherited in stochastic time series, the visibility graph algorithm has been recently proposed, by which a time series can be mapped onto a complex network. We demonstrate that the visibility algorithm is not an appropriate one to study the correlation aspects of a time series. We then employ the horizontal visibility algorithm, as a much simpler one, to map fractional processes onto complex networks. The degree distributions are shown to have parabolic exponential forms with Hurst dependent fitting parameter. Further, we take into account other topological properties such as maximum eigenvalue of the adjacency matrix and the degree assortativity, and show that such topological quantities can also be used to predict the Hurst exponent, with an exception for anti-persistent fractional Gaussian noises. To solve this problem, we take into account the Spearman correlation coefficient between nodes' degrees and their corresponding data values in the original time series.
Applied time series analysis and innovative computing
Ao, Sio-Iong
2010-01-01
This text is a systematic, state-of-the-art introduction to the use of innovative computing paradigms as an investigative tool for applications in time series analysis. It includes frontier case studies based on recent research.
Detecting nonlinear structure in time series
We describe an approach for evaluating the statistical significance of evidence for nonlinearity in a time series. The formal application of our method requires the careful statement of a null hypothesis which characterizes a candidate linear process, the generation of an ensemble of ''surrogate'' data sets which are similar to the original time series but consistent with the null hypothesis, and the computation of a discriminating statistic for the original and for each of the surrogate data sets. The idea is to test the original time series against the null hypothesis by checking whether the discriminating statistic computed for the original time series differs significantly from the statistics computed for each of the surrogate sets. While some data sets very cleanly exhibit low-dimensional chaos, there are many cases where the evidence is sketchy and difficult to evaluate. We hope to provide a framework within which such claims of nonlinearity can be evaluated. 5 refs., 4 figs
Arturo C Martí; Marcelo Ponce; Cristina Masoller
2008-06-01
We review our recent work on the synchronization of a network of delay-coupled maps, focusing on the interplay of the network topology and the delay times that take into account the finite velocity of propagation of interactions. We assume that the elements of the network are identical ( logistic maps in the regime where the individual maps, without coupling, evolve in a chaotic orbit) and that the coupling strengths are uniform throughout the network. We show that if the delay times are su±ciently heterogeneous, for adequate coupling strength the network synchronizes in a spatially homogeneous steady state, which is unstable for the individual maps without coupling. This synchronization behavior is referred to as `suppression of chaos by random delays' and is in contrast with the synchronization when all the interaction delay times are homogeneous, because with homogeneous delays the network synchronizes in a state where the elements display in-phase time-periodic or chaotic oscillations. We analyze the influence of the network topology considering four different types of networks: two regular (a ring-type and a ring-type with a central node) and two random (free-scale Barabasi-Albert and small-world Newman-Watts). We find that when the delay times are sufficiently heterogeneous the synchronization behavior is largely independent of the network topology but depends on the network's connectivity, i.e., on the average number of neighbors per node.
Bayes linear variance adjustment for time series
Wilkinson, Darren J
2008-01-01
This paper exhibits quadratic products of linear combinations of observables which identify the covariance structure underlying the univariate locally linear time series dynamic linear model. The first- and second-order moments for the joint distribution over these observables are given, allowing Bayes linear learning for the underlying covariance structure for the time series model. An example is given which illustrates the methodology and highlights the practical implications of the theory.
FATS: Feature Analysis for Time Series
Nun, Isadora; Sim, Brandon; Zhu, Ming; Dave, Rahul; Castro, Nicolas; Pichara, Karim
2015-01-01
In this paper, we present the FATS (Feature Analysis for Time Series) library. FATS is a Python library which facilitates and standardizes feature extraction for time series data. In particular, we focus on one application: feature extraction for astronomical light curve data, although the library is generalizable for other uses. We detail the methods and features implemented for light curve analysis, and present examples for its usage.
Nonlinear time series: semiparametric and nonparametric methods
Gao, Jiti
2007-01-01
Useful in the theoretical and empirical analysis of nonlinear time series data, semiparametric methods have received extensive attention in the economics and statistics communities over the past twenty years. Recent studies show that semiparametric methods and models may be applied to solve dimensionality reduction problems arising from using fully nonparametric models and methods. Answering the call for an up-to-date overview of the latest developments in the field, "Nonlinear Time Series: S...
The underlying requirements for successful implementation of any efficient tumour motion management strategy are regularity and reproducibility of a patient's breathing pattern. The physiological act of breathing is controlled by multiple nonlinear feedback and feed-forward couplings. It would therefore be appropriate to analyse the breathing pattern of lung cancer patients in the light of nonlinear dynamical system theory. The purpose of this paper is to analyse the one-dimensional respiratory time series of lung cancer patients based on nonlinear dynamics and delay coordinate state space embedding. It is very important to select a suitable pair of embedding dimension 'm' and time delay 'τ' when performing a state space reconstruction. Appropriate time delay and embedding dimension were obtained using well-established methods, namely mutual information and the false nearest neighbour method, respectively. Establishing stationarity and determinism in a given scalar time series is a prerequisite to demonstrating that the nonlinear dynamical system that gave rise to the scalar time series exhibits a sensitive dependence on initial conditions, i.e. is chaotic. Hence, once an appropriate state space embedding of the dynamical system has been reconstructed, we show that the time series of the nonlinear dynamical systems under study are both stationary and deterministic in nature. Once both criteria are established, we proceed to calculate the largest Lyapunov exponent (LLE), which is an invariant quantity under time delay embedding. The LLE for all 16 patients is positive, which along with stationarity and determinism establishes the fact that the time series of a lung cancer patient's breathing pattern is not random or irregular, but rather it is deterministic in nature albeit chaotic. These results indicate that chaotic characteristics exist in the respiratory waveform and techniques based on state space dynamics should be employed for tumour motion management.
H∞ synchronization of chaotic neural networks with time-varying delays
In this paper, we investigate the problem of H∞ synchronization for chaotic neural networks with time-varying delays. A new model of the networks with disturbances in both master and slave systems is presented. By constructing a suitable Lyapunov—Krasovskii functional and using a reciprocally convex approach, a novel H∞ synchronization criterion for the networks concerned is established in terms of linear matrix inequalities (LMIs) which can be easily solved by various effective optimization algorithms. Two numerical examples are given to illustrate the effectiveness of the proposed method
A constructional method for generalized synchronization of coupled time-delay chaotic systems
A constructional method for detecting the existence and determining the functional relationship of generalized synchronization is introduced in this paper. Based on the stability theory of fixed points of dynamical systems, we show theoretically and numerically that an appropriate coupling scheme allows us to find the synchronization functional relationship between the states of coupled time-delay chaotic systems. On the other hand, given a synchronization function, this approach may help us to design the coupling scheme. To demonstrate the proposed method, Ikeda system is presented as an example.
Pseudo-periodic surrogate test to sample time series in stochastic softening Duffing oscillator
Identification of typical noise-contaminated sample response is a hard task in a nonlinear system under stochastic background since irregularity of the sample response may come from measure noise, dynamical noise, or nonlinear effect, etc., and conventional dynamical methods are generally not useful. Here, the pseudo-periodic surrogate algorithm by Small is employed to test the sample time series in the softening Duffing oscillator under the Gaussian white noise excitation. The correlation dimensions of the noisy periodic and the noise-induced chaotic time series of the system are compared with those of their corresponding surrogate data respectively, the leading Lyapunov exponents by Rosenstein's algorithm are also presented for comparison
冯存芳; 汪映海
2011-01-01
Projective synchronization in modulated time-delayed systems is studied by applying an active control method. Based on the Lyapunov asymptotical stability theorem, the controller and sufficient condition for projective synchronization are calculated analytically. We give a genera./ method with which we can achieve projective synchronization in modulated time-delayed chaotic systems. This method allows us to adjust the desired scaling factor arbitrarily. The effectiveness of our method is confirmed by using the famous delay-differential equations related to optical bistable or hybrid optical bistable devices. Numerical simulations fully support the analytical approach.%Projective synchronization in modulated time-delayed systems is studied by applying an active control method.Based on the Lyapunov asymptotical stability theorem,the controller and sufficient condition for projective synchronization are calculated analytically.We give a general method with which we can achieve projective synchronization in modulated time-delayed chaotic systems.This method allows us to adjust the desired scaling factor arbitrarily.The effectiveness of our method is confirmed by using the famous delay-differential equations related to optical bistable or hybrid optical bistable devices.Numerical simulations fully support the analytical approach.
Introduction to time series analysis and forecasting
Montgomery, Douglas C; Kulahci, Murat
2008-01-01
An accessible introduction to the most current thinking in and practicality of forecasting techniques in the context of time-oriented data. Analyzing time-oriented data and forecasting are among the most important problems that analysts face across many fields, ranging from finance and economics to production operations and the natural sciences. As a result, there is a widespread need for large groups of people in a variety of fields to understand the basic concepts of time series analysis and forecasting. Introduction to Time Series Analysis and Forecasting presents the time series analysis branch of applied statistics as the underlying methodology for developing practical forecasts, and it also bridges the gap between theory and practice by equipping readers with the tools needed to analyze time-oriented data and construct useful, short- to medium-term, statistically based forecasts.
Time series irreversibility: a visibility graph approach
Lacasa, Lucas; Roldán, Édgar; Parrondo, Juan M R; Luque, Bartolo
2011-01-01
We propose a method to measure real-valued time series irreversibility which combines two differ- ent tools: the horizontal visibility algorithm and the Kullback-Leibler divergence. This method maps a time series to a directed network according to a geometric criterion. The degree of irreversibility of the series is then estimated by the Kullback-Leibler divergence (i.e. the distinguishability) between the in and out degree distributions of the associated graph. The method is computationally effi- cient, does not require any ad hoc symbolization process, and naturally takes into account multiple scales. We find that the method correctly distinguishes between reversible and irreversible station- ary time series, including analytical and numerical studies of its performance for: (i) reversible stochastic processes (uncorrelated and Gaussian linearly correlated), (ii) irreversible stochastic pro- cesses (a discrete flashing ratchet in an asymmetric potential), (iii) reversible (conservative) and irreversible (di...
Multiscale entropy analysis of electroseismic time series
L. Guzmán-Vargas; Ramírez-Rojas, A.; Angulo-Brown, F.
2008-01-01
In this work we use the multiscale entropy method to analyse the variability of geo-electric time series monitored in two sites located in Mexico. In our analysis we consider a period of time from January 1995 to December 1995. We systematically calculate the sample entropy of electroseismic time series. Important differences in the entropy profile for several time scales are observed in records from the same station. In particular, a complex behaviour is observed in the vicinity of a
Time Series Forecasting with Missing Values
Shin-Fu Wu
2015-11-01
Full Text Available Time series prediction has become more popular in various kinds of applications such as weather prediction, control engineering, financial analysis, industrial monitoring, etc. To deal with real-world problems, we are often faced with missing values in the data due to sensor malfunctions or human errors. Traditionally, the missing values are simply omitted or replaced by means of imputation methods. However, omitting those missing values may cause temporal discontinuity. Imputation methods, on the other hand, may alter the original time series. In this study, we propose a novel forecasting method based on least squares support vector machine (LSSVM. We employ the input patterns with the temporal information which is defined as local time index (LTI. Time series data as well as local time indexes are fed to LSSVM for doing forecasting without imputation. We compare the forecasting performance of our method with other imputation methods. Experimental results show that the proposed method is promising and is worth further investigations.
Testing time symmetry in time series using data compression dictionaries
Kennel, Matthew B.
2004-01-01
Time symmetry, often called statistical time reversibility, in a dynamical process means that any segment of time-series output has the same probability of occurrence in the process as its time reversal. A technique, based on symbolic dynamics, is proposed to distinguish such symmetrical processes from asymmetrical ones, given a time-series observation of the otherwise unknown process. Because linear stochastic Gaussian processes, and static nonlinear transformations of them, are statisticall...
Feature Matching in Time Series Modelling
Xia, Yingcun
2011-01-01
Using a time series model to mimic an observed time series has a long history. However, with regard to this objective, conventional estimation methods for discrete-time dynamical models are frequently found to be wanting. In the absence of a true model, we prefer an alternative approach to conventional model fitting that typically involves one-step-ahead prediction errors. Our primary aim is to match the joint probability distribution of the observable time series, including long-term features of the dynamics that underpin the data, such as cycles, long memory and others, rather than short-term prediction. For want of a better name, we call this specific aim {\\it feature matching}. The challenges of model mis-specification, measurement errors and the scarcity of data are forever present in real time series modelling. In this paper, by synthesizing earlier attempts into an extended-likelihood, we develop a systematic approach to empirical time series analysis to address these challenges and to aim at achieving...
Analysis of Rattleback Chaotic Oscillations
Michael Hanias
2014-01-01
Full Text Available Rattleback is a canoe-shaped object, already known from ancient times, exhibiting a nontrivial rotational behaviour. Although its shape looks symmetric, its kinematic behaviour seems to be asymmetric. When spun in one direction it normally rotates, but when it is spun in the other direction it stops rotating and oscillates until it finally starts rotating in the other direction. It has already been reported that those oscillations demonstrate chaotic characteristics. In this paper, rattleback’s chaotic dynamics are studied by applying Kane’s model for different sets of (experimentally decided parameters, which correspond to three different experimental prototypes made of wax, gypsum, and lead-solder. The emerging chaotic behaviour in all three cases has been studied and evaluated by the related time-series analysis and the calculation of the strange attractors’ invariant parameters.
Analysis of rattleback chaotic oscillations.
Hanias, Michael; Stavrinides, Stavros G; Banerjee, Santo
2014-01-01
Rattleback is a canoe-shaped object, already known from ancient times, exhibiting a nontrivial rotational behaviour. Although its shape looks symmetric, its kinematic behaviour seems to be asymmetric. When spun in one direction it normally rotates, but when it is spun in the other direction it stops rotating and oscillates until it finally starts rotating in the other direction. It has already been reported that those oscillations demonstrate chaotic characteristics. In this paper, rattleback's chaotic dynamics are studied by applying Kane's model for different sets of (experimentally decided) parameters, which correspond to three different experimental prototypes made of wax, gypsum, and lead-solder. The emerging chaotic behaviour in all three cases has been studied and evaluated by the related time-series analysis and the calculation of the strange attractors' invariant parameters. PMID:24511290
Schlick, Conor P., E-mail: conorschlick2015@u.northwestern.edu [Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, Illinois 60208 (United States); Umbanhowar, Paul B. [Department of Mechanical Engineering, Northwestern University, Evanston, Illinois 60208 (United States); Ottino, Julio M. [Department of Chemical and Biological Engineering, Northwestern University, Evanston, Illinois 60208 (United States); Department of Mechanical Engineering, Northwestern University, Evanston, Illinois 60208 (United States); The Northwestern Institute on Complex Systems (NICO), Northwestern University, Evanston, Illinois 60208 (United States); Lueptow, Richard M., E-mail: r-lueptow@northwestern.edu [Department of Mechanical Engineering, Northwestern University, Evanston, Illinois 60208 (United States); The Northwestern Institute on Complex Systems (NICO), Northwestern University, Evanston, Illinois 60208 (United States)
2014-03-15
We investigate chaotic advection and diffusion in autocatalytic reactions for time-periodic sine flow computationally using a mapping method with operator splitting. We specifically consider three different autocatalytic reaction schemes: a single autocatalytic reaction, competitive autocatalytic reactions, which can provide insight into problems of chiral symmetry breaking and homochirality, and competitive autocatalytic reactions with recycling. In competitive autocatalytic reactions, species B and C both undergo an autocatalytic reaction with species A such that A+B→2B and A+C→2C. Small amounts of initially spatially localized B and C and a large amount of spatially homogeneous A are advected by the velocity field, diffuse, and react until A is completely consumed and only B and C remain. We find that local finite-time Lyapunov exponents (FTLEs) can accurately predict the final average concentrations of B and C after the reaction completes. The species that starts in the region with the larger FTLE has, with high probability, the larger average concentration at the end of the reaction. If B and C start in regions with similar FTLEs, their average concentrations at the end of the reaction will also be similar. When a recycling reaction is added, the system evolves towards a single species state, with the FTLE often being useful in predicting which species fills the entire domain and which is depleted. The FTLE approach is also demonstrated for competitive autocatalytic reactions in journal bearing flow, an experimentally realizable flow that generates chaotic dynamics.
Area-preserving maps models of gyro-averaged ${\\bf E} \\times {\\bf B}$ chaotic transport
da Fonseca, J D; Caldas, I L
2014-01-01
Discrete maps have been extensively used to model 2-dimensional chaotic transport in plasmas and fluids. Here we focus on area-preserving maps describing finite Larmor radius (FLR) effects on ${\\bf E} \\times {\\bf B}$ chaotic transport in magnetized plasmas with zonal flows perturbed by electrostatic drift waves. FLR effects are included by gyro-averaging the Hamiltonians of the maps which, depending on the zonal flow profile, can have monotonic or non-monotonic frequencies. In the limit of zero Larmor radius, the monotonic frequency map reduces to the standard Chirikov-Taylor map, and, in the case of non-monotonic frequency, the map reduces to the standard nontwist map. We show that in both cases FLR leads to chaos suppression, changes in the stability of fixed points, and robustness of transport barriers. FLR effects are also responsible for changes in the phase space topology and zonal flow bifurcations. Dynamical systems methods based on recurrence time statistics are used to quantify the dependence on the...
Introduction to time series analysis and forecasting
Montgomery, Douglas C; Kulahci, Murat
2015-01-01
Praise for the First Edition ""…[t]he book is great for readers who need to apply the methods and models presented but have little background in mathematics and statistics."" -MAA Reviews Thoroughly updated throughout, Introduction to Time Series Analysis and Forecasting, Second Edition presents the underlying theories of time series analysis that are needed to analyze time-oriented data and construct real-world short- to medium-term statistical forecasts. Authored by highly-experienced academics and professionals in engineering statistics, the Second Edition features discussions on both
Fractal and natural time analysis of geoelectrical time series
Ramirez Rojas, A.; Moreno-Torres, L. R.; Cervantes, F.
2013-05-01
In this work we show the analysis of geoelectric time series linked with two earthquakes of M=6.6 and M=7.4. That time series were monitored at the South Pacific Mexican coast, which is the most important active seismic subduction zone in México. The geolectric time series were analyzed by using two complementary methods: a fractal analysis, by means of the detrended fluctuation analysis (DFA) in the conventional time, and the power spectrum defined in natural time domain (NTD). In conventional time we found long-range correlations prior to the EQ-occurrences and simultaneously in NTD, the behavior of the power spectrum suggest the possible existence of seismo electric signals (SES) similar with the previously reported in equivalent time series monitored in Greece prior to earthquakes of relevant magnitude.
Layered Ensemble Architecture for Time Series Forecasting.
Rahman, Md Mustafizur; Islam, Md Monirul; Murase, Kazuyuki; Yao, Xin
2016-01-01
Time series forecasting (TSF) has been widely used in many application areas such as science, engineering, and finance. The phenomena generating time series are usually unknown and information available for forecasting is only limited to the past values of the series. It is, therefore, necessary to use an appropriate number of past values, termed lag, for forecasting. This paper proposes a layered ensemble architecture (LEA) for TSF problems. Our LEA consists of two layers, each of which uses an ensemble of multilayer perceptron (MLP) networks. While the first ensemble layer tries to find an appropriate lag, the second ensemble layer employs the obtained lag for forecasting. Unlike most previous work on TSF, the proposed architecture considers both accuracy and diversity of the individual networks in constructing an ensemble. LEA trains different networks in the ensemble by using different training sets with an aim of maintaining diversity among the networks. However, it uses the appropriate lag and combines the best trained networks to construct the ensemble. This indicates LEAs emphasis on accuracy of the networks. The proposed architecture has been tested extensively on time series data of neural network (NN)3 and NN5 competitions. It has also been tested on several standard benchmark time series data. In terms of forecasting accuracy, our experimental results have revealed clearly that LEA is better than other ensemble and nonensemble methods. PMID:25751882
Climate Time Series Analysis and Forecasting
Young, P. C.; Fildes, R.
2009-04-01
This paper will discuss various aspects of climate time series data analysis, modelling and forecasting being carried out at Lancaster. This will include state-dependent parameter, nonlinear, stochastic modelling of globally averaged atmospheric carbon dioxide; the computation of emission strategies based on modern control theory; and extrapolative time series benchmark forecasts of annual average temperature, both global and local. The key to the forecasting evaluation will be the iterative estimation of forecast error based on rolling origin comparisons, as recommended in the forecasting research literature. The presentation will conclude with with a comparison of the time series forecasts with forecasts produced from global circulation models and a discussion of the implications for climate modelling research.
CALENDAR EFFECTS IN MONTHLY TIME SERIES MODELS
Gerhard THURY; Mi ZHOU
2005-01-01
It is not unusual for the level of a monthly economic time series, such as industrial production,retail and wholesale sales, monetary aggregates, telephone calls or road accidents, to be influenced by calendar effects. Such effects arise when changes occur in the level of activity resulting from differences in the composition of calendar between years. The two main sources of calendar effects are trading day variations and moving festivals. Ignoring such calendar effects will lead to substantial distortions in the identification stage of time series modeling. Therefore, it is mandatory to introduce calendar effects, when they are present in a time series, as the component of the model which one wants to estimate.
Chaotic Dynamics of Comet 1P/Halley; Lyapunov Exponent and Survival Time Expectancy
Muñoz-Gutiérrez, M A; Pichardo, B
2014-01-01
The orbital elements of comet Halley are known to a very high precision, suggesting that the calculation of its future dynamical evolution is straightforward. In this paper we seek to characterize the chaotic nature of the present day orbit of comet Halley and to quantify the timescale over which its motion can be predicted confidently. In addition, we attempt to determine the timescale over which its present day orbit will remain stable. Numerical simulations of the dynamics of test particles in orbits similar to that of comet Halley are carried out with the Mercury 6.2 code. On the basis of these we construct survival time maps to assess the absolute stability of Halley's orbit, frequency analysis maps, to study the variability of the orbit and we calculate the Lyapunov exponent for the orbit for variations in initial conditions at the level of the present day uncertainties in our knowledge of its orbital parameters. On the basis of our calculations of the Lyapunov exponent for comet Halley, the chaotic nat...
Spending too much time at the Galactic bar: chaotic fanning of the Ophiuchus stream
Price-Whelan, Adrian M; Johnston, Kathryn V; Rix, Hans-Walter
2016-01-01
The Ophiuchus stellar stream is peculiar: (1) its length is short given the age of its constituent stars, and (2) several probable member stars that lie close in both sky position and velocity have dispersions in these dimensions that far exceed those seen within the stream. The stream's proximity to the Galactic center suggests that the bar must have a significant influence on its dynamical history: The triaxiality and time-dependence of the bar may generate chaotic orbits in the vicinity of the stream that can greatly affect its morphology. We explore this hypothesis with models of stream formation along orbits consistent with Ophiuchus' properties in a Milky Way potential model that includes a rotating bar. We find that in all choices for the rotation parameters of the bar, orbits fit to the stream are strongly chaotic. Mock streams generated along these orbits qualitatively match the observed properties of the stream: because of chaos, stars stripped early generally form low-density, high-dispersion "fans...
Fuzzy Information Granules in Time Series Data
HEIKO HOFER; ORTOLANI M; DAVID PATTERSON; FRANK HOEPPNER; ONDINE CALLAN; Berthold, Michael R
2004-01-01
Often, it is desirable to represent a set of time series through typical shapes in order to detect common patterns. The algorithm presented here compares pieces of a different time series in order to find such similar shapes. The use of a fuzzy clustering technique based on fuzzy c-means allows us to detect shapes that belong to a certain group of typical shapes with a degree of membership. Modifications to the original algorithm also allow this matching to be invariant with respect to a scal...
Case study in time series analysis
Zhongjie, Xie
1993-01-01
This book is a monograph on case studies using time series analysis, which includes the main research works applied to practical projects by the author in the past 15 years. The works cover different problems in broad fields, such as: engineering, labour protection, astronomy, physiology, endocrinology, oil development, etc. The first part of this book introduces some basic knowledge of time series analysis which is necessary for the reader to understand the methods and the theory used in the procedure for solving problems. The second part is the main part of this book - case studies in differ
Lecture notes for Advanced Time Series Analysis
Madsen, Henrik; Holst, Jan
1997-01-01
A first version of this notes was used at the lectures in Grenoble, and they are now extended and improved (together with Jan Holst), and used in Ph.D. courses on Advanced Time Series Analysis at IMM and at the Department of Mathematical Statistics, University of Lund, 1994, 1997, ......A first version of this notes was used at the lectures in Grenoble, and they are now extended and improved (together with Jan Holst), and used in Ph.D. courses on Advanced Time Series Analysis at IMM and at the Department of Mathematical Statistics, University of Lund, 1994, 1997, ...
Dynamical networks reconstructed from time series
Levnajić, Zoran
2012-01-01
Novel method of reconstructing dynamical networks from empirically measured time series is proposed. By statistically examining the correlations between motions displayed by network nodes, we derive a simple equation that directly yields the adjacency matrix, assuming the intra-network interaction functions to be known. We illustrate the method's implementation on a simple example and discuss the dependence of the reconstruction precision on the properties of time series. Our method is applicable to any network, allowing for reconstruction precision to be maximized, and errors to be estimated.
Introduction to time series and forecasting
Brockwell, Peter J
2016-01-01
This book is aimed at the reader who wishes to gain a working knowledge of time series and forecasting methods as applied to economics, engineering and the natural and social sciences. It assumes knowledge only of basic calculus, matrix algebra and elementary statistics. This third edition contains detailed instructions for the use of the professional version of the Windows-based computer package ITSM2000, now available as a free download from the Springer Extras website. The logic and tools of time series model-building are developed in detail. Numerous exercises are included and the software can be used to analyze and forecast data sets of the user's own choosing. The book can also be used in conjunction with other time series packages such as those included in R. The programs in ITSM2000 however are menu-driven and can be used with minimal investment of time in the computational details. The core of the book covers stationary processes, ARMA and ARIMA processes, multivariate time series and state-space mod...
The distribution of "time of flight" in 3D stationary chaotic advection
Raynal, Florence
2014-01-01
The distributions of "time of flight" (time spent by a single fluid particle between two crossings of the Poincar\\'e section) are investigated for five different 3D stationary chaotic mixers. Above all, we study the large tails of those distributions, and show that mainly two types of behaviors are encountered. In the case of slipping walls, as expected, we obtain an exponential decay, which, however, does not scale with the Lyapunov exponent. Using a simple model, we suggest that this decay is related to the negative eigenvalues of the fixed points of the flow. When no-slip walls are considered, as predicted by the model, the behavior is radically dfferent, with a very large tail following a power law with an exponent close to -3.
The distribution of “time of flight” in three dimensional stationary chaotic advection
Raynal, Florence; Carrière, Philippe [LMFA, UMR CNRS–Université de Lyon, École Centrale de Lyon–Université Lyon 1–INSA Lyon, École Centrale de Lyon, 36 Avenue Guy de Collongue, 69134 Écully cédex (France)
2015-04-15
The distributions of “time of flight” (time spent by a single fluid particle between two crossings of the Poincaré section) are investigated for five different three dimensional stationary chaotic mixers. Above all, we study the large tails of those distributions and show that mainly two types of behaviors are encountered. In the case of slipping walls, as expected, we obtain an exponential decay, which, however, does not scale with the Lyapunov exponent. Using a simple model, we suggest that this decay is related to the negative eigenvalues of the fixed points of the flow. When no-slip walls are considered, as predicted by the model, the behavior is radically different, with a very large tail following a power law with an exponent close to −3.
Exploring sensitive dependence and transitivity to optimize travel time in chaotic systems
Transitivity and sensitive dependence on initial conditions are the main characteristics of chaotic behavior. The latter one can be exploited so that small controlled perturbations in system parameters may imply a faster transfer in time from a desired start point to a neighborhood of a desired final state. In this study three targeting approaches are evaluated: The first one uses a geometric approach to find the proper perturbation which allows a faster transfer between two desired points; The second, an evolutionary algorithm called GEO (Generalized External Optimization), is adapted to search for optimized orbits; The third one, uses successive perturbations along the path in order to direct the orbits to the final desired point in a short time interval. These three methods are evaluated regarding performance and implementation complexity
The distribution of “time of flight” in three dimensional stationary chaotic advection
The distributions of “time of flight” (time spent by a single fluid particle between two crossings of the Poincaré section) are investigated for five different three dimensional stationary chaotic mixers. Above all, we study the large tails of those distributions and show that mainly two types of behaviors are encountered. In the case of slipping walls, as expected, we obtain an exponential decay, which, however, does not scale with the Lyapunov exponent. Using a simple model, we suggest that this decay is related to the negative eigenvalues of the fixed points of the flow. When no-slip walls are considered, as predicted by the model, the behavior is radically different, with a very large tail following a power law with an exponent close to −3
Time series tapering for short data samples
Kaimal, J.C.; Kristensen, L.
We explore the effect of applying tapered windows on atmospheric data to eliminate overestimation inherent in spectra computed from short time series. Some windows are more effective than others in correcting this distortion. The Hamming window gave the best results with experimental data. The Ha...