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Lyapunov Exponents (lyapunov + exponent)
Selected AbstractsLinear and nonlinear measures of blood pressure variability: Increased chaos of blood pressure time series in patients with panic disorderDEPRESSION AND ANXIETY, Issue 2 2004Vikram K. Yeragani M.B.B.S. Abstract Arterial blood pressure (BP) variability increases progressively with the development of hypertension and an increase in BP variability is associated with end organ damage and cardiovascular morbidity. On the other hand, a decrease in heart rate (HR) variability is associated with significant cardiovascular mortality. There is a strong association between cardiovascular mortality and anxiety. Several previous studies have shown decreased HR variability in patients with anxiety. In this study, we investigated beat-to-beat variability of systolic and diastolic BP (SBP and DBP) in normal controls and patients with panic disorder during normal breathing and controlled breathing at 12, and 20 breaths per minute using linear as well as nonlinear techniques. Finger BP signal was obtained noninvasively using Finapres. Standing SBPvi and DBP BPvi (log value of BP variance corrected for mean BP divided by HR variance corrected for mean HR) were significantly higher in patients compared to controls. Largest Lyapunov exponent (LLE) of SBP and DBP, a measure of chaos, was significantly higher in patients in supine as well as standing postures. The ratios of LLE (SBP/HR) and LLE (DBP/HR) were also significantly higher (P < .001) in patients compared to controls. These findings further suggest dissociation between HR and BP variability and a possible relative increase in sympathetic function in anxiety. This increase in BP variability may partly explain the increase in cardiovascular mortality in this group of patients. Depression and Anxiety 19:85-95, 2004. © 2004 Wiley-Liss, Inc. [source] Isolating the root cause of propagated oscillations in process plantsINTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 4 2005Xiaoyun Zang Abstract Oscillations are a common type of propagated disturbance, whose sources might be attributable to a number of different phenomena such as poor controller tuning or actuator nonlinearity. A number of data-driven methods have already been proposed to isolate the source loop of nonlinearity induced plant-wide oscillations. Amongst these the bi-amplitude ratio index, correlation dimension, maximal Lyapunov exponent, nonlinearity index and spectral ICA show promise. The propagation of oscillations is first examined in order to gain an understanding of how this might affect the performances of the various techniques. The various methods are then described and their performance on a set of simulation generated data and two industrial case studies are compared. Copyright © 2004 John Wiley & Sons, Ltd. [source] CHAOTIC FORECASTING OF DISCHARGE TIME SERIES: A CASE STUDY,JOURNAL OF THE AMERICAN WATER RESOURCES ASSOCIATION, Issue 2 2001Francesco Lisi ABSTRACT: This paper considers the problem of forecasting the discharge time series of a river by means of a chaotic approach. To this aim, we first check for some evidence of chaotic behavior in the dynamic by considering a set of different procedures, namely, the phase portrait of the attractor, the correlation dimension, and the largest Lyapunov exponent. Their joint application seems to confirm the presence of a nonlinear deterministic dynamic of chaotic type. Second, we consider the so-called nearest neighbors predictor and we compare it with a classical linear model. By comparing these two predictors, it seems that nonlinear river flow modeling, and in particular chaotic modeling, is an effective method to improve predictions. [source] Fine structure of the zeros of orthogonal polynomials IV: A priori bounds and clock behavior,COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 4 2008Yoram Last We prove locally uniform spacing for the zeros of orthogonal polynomials on the real line under weak conditions (Jacobi parameters approach the free ones and are of bounded variation). We prove that for ergodic discrete Schrödinger operators, Poisson behavior implies a positive Lyapunov exponent. Both results depend on a priori bounds on eigenvalue spacings for which we provide several proofs. © 2007 Wiley Periodicals, Inc. [source] Modified mixture of experts employing eigenvector methods and Lyapunov exponents for analysis of electroencephalogram signalsEXPERT SYSTEMS, Issue 4 2009Elif Derya ÜbeyliArticle first published online: 2 SEP 200 Abstract: The use of diverse features in detecting variability of electroencephalogram (EEG) signals is presented. The classification accuracies of the modified mixture of experts (MME), which was trained on diverse features, were obtained. Eigenvector methods (Pisarenko, multiple signal classification , MUSIC, and minimum-norm) were selected to generate the power spectral density estimates. The features from the power spectral density estimates and Lyapunov exponents of the EEG signals were computed and statistical features were calculated to depict their distribution. The statistical features, which were used for obtaining the diverse features of the EEG signals, were then input into the implemented neural network models for training and testing purposes. The present study demonstrated that the MME trained on the diverse features achieved high accuracy rates (total classification accuracy of the MME is 98.33%). [source] Chaotic analysis of predictability versus knowledge discovery techniques: case study of the Polish stock marketEXPERT SYSTEMS, Issue 5 2002Hak Chun Increasing evidence over the past decade indicates that financial markets exhibit nonlinear dynamics in the form of chaotic behavior. Traditionally, the prediction of stock markets has relied on statistical methods including multivariate statistical methods, autoregressive integrated moving average models and autoregressive conditional heteroskedasticity models. In recent years, neural networks and other knowledge techniques have been applied extensively to the task of predicting financial variables. This paper examines the relationship between chaotic models and learning techniques. In particular, chaotic analysis indicates the upper limits of predictability for a time series. The learning techniques involve neural networks and case,based reasoning. The chaotic models take the form of R/S analysis to measure persistence in a time series, the correlation dimension to encapsulate system complexity, and Lyapunov exponents to indicate predictive horizons. The concepts are illustrated in the context of a major emerging market, namely the Polish stock market. [source] Lyapunov spectrum determination from the FEM simulation of a chaotic advecting flowINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 5 2006Philippe CarrièreArticle first published online: 7 SEP 200 Abstract The problem of the determination of the Lyapunov spectrum in chaotic advection using approximated velocity fields resulting from a standard FEM method is investigated. A fourth order Runge,Kutta scheme for trajectory integration is combined with a third order Jacobian matrix method with QR -factorization. After checking the algorithm on the standard Lorenz and coupled quartic oscillator systems, the method is applied to a model 3-D steady flow for which an analytical expression is known. Both linear and quadratic approximated velocity fields succeed in predicting the Lyapunov exponents as well as describing the chaotic or regular regions inside the flow with satisfactory accuracy. A more realistic flow is then studied in order to delineate the possible limitations of the approach. Copyright © 2005 John Wiley & Sons, Ltd. [source] Hyperchaotic behaviour of two bi-directionally coupled Chua's circuitsINTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS, Issue 6 2002Barbara Cannas Abstract In this paper, a non-linear bi-directional coupling of two Chua's circuits is presented. The coupling is obtained by using polynomial functions that are symmetric with respect to the state variables of the two Chua's circuits. Both a transverse and a tangent system are studied to ensure a global validity of the results in the state space. First, it is shown that the transverse system is an autonomous Chua's circuit, which directly allows the evaluation of the conditions on its chaotic behaviour, i.e. the absence of synchronization between the coupled circuits. Moreover, it is demonstrated that the tangent system is also a Chua's circuit, forced by the transverse system; therefore, its dynamics is ruled by a time-dependent equation. Thus, the calculus of conditional Lyapunov exponents is necessary in order to exclude antisynchronization along the tangent manifold. The properties of the transverse and tangent systems simplify the study of the coupled Chua's circuits and the determination of the conditions on their hyperchaotic behaviour. In particular, it is shown that hyperchaotic behaviour occurs for proper values of the coupling strength between the two Chua's circuits. Finally, numerical examples are given and discussed. Copyright © 2002 John Wiley & Sons, Ltd. [source] Switching contact task control in hydraulic actuators: Stability analysis and experimental evaluationINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 17 2009P. Sekhavat Abstract A switching contact task control for hydraulic actuators is proposed. The controller is built upon three individually designed control laws for three phases of motion: (1) position regulation in free space, (2) impact suppression and stable transition from free to constrained motion and (3) force regulation in sustained-contact motion. The position and force control schemes are capable of asymptotic set-point regulation in the presence of actuator friction and without the complexity of sliding mode or adaptive control techniques. The intermediate impact control scheme is included for the first time to dampen the undesirable impacts and dissipate the impact energy that could potentially drive the whole system unstable. The solution concept and the stability of the complete switching control system are analyzed rigorously using the Filippov's solution concept and the concept of Lyapunov exponents. Both computer simulations and experiments are carried out to demonstrate the efficacy of the designed switching control law. Copyright © 2009 John Wiley & Sons, Ltd. [source] The dynamical stability of a Kuiper Belt-like regionMONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 3 2007A. Celletti ABSTRACT The dynamics of the Kuiper Belt region between 33 and 63 au is investigated just taking into account the gravitational influence of Neptune. Indeed the aim is to analyse the information which can be drawn from the actual exoplanetary systems, where typically physical and orbital data of just one or two planets are available. Under this perspective we start our investigation using the simplest three-body model (with Sun and Neptune as primaries), adding at a later stage the eccentricity of Neptune and the inclinations of the orbital planes to evaluate their effects on the Kuiper Belt dynamics. Afterwards we remove the assumption that the orbit of Neptune is Keplerian by adding the effect of Uranus through the Lagrange,Laplace solution or through a suitable resonant normal form. Finally, different values of the mass ratios of the primary to the host star are considered in order to perform a preliminary analysis of the behaviour of exoplanetary systems. In all cases, the stability is investigated by means of classical tools borrowed from dynamical system theory, like Poincaré mappings and Lyapunov exponents. [source] Data assimilation with regularized nonlinear instabilitiesTHE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 648 2010Henry D. I. Abarbanel Abstract In variational formulations of data assimilation, the estimation of parameters or initial state values by a search for a minimum of a cost function can be hindered by the numerous local minima in the dependence of the cost function on those quantities. We argue that this is a result of instability on the synchronization manifold where the observations are required to match the model outputs in the situation where the data and the model are chaotic. The solution to this impediment to estimation is given as controls moving the positive conditional Lyapunov exponents on the synchronization manifold to negative values and adding to the cost function a penalty that drives those controls to zero as a result of the optimization process implementing the assimilation. This is seen as the solution to the proper size of ,nudging' terms: they are zero once the estimation has been completed, leaving only the physics of the problem to govern forecasts after the assimilation window. We show how this procedure, called Dynamical State and Parameter Estimation (DSPE), works in the case of the Lorenz96 model with nine dynamical variables. Using DSPE, we are able to accurately estimate the fixed parameter of this model and all of the state variables, observed and unobserved, over an assimilation time interval [0, T]. Using the state variables at T and the estimated fixed parameter, we are able to accurately forecast the state of the model for t > T to those times where the chaotic behaviour of the system interferes with forecast accuracy. Copyright © 2010 Royal Meteorological Society [source] Sternberg theorems for random dynamical systemsCOMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 7 2005Weigu Li In this paper, we prove the smooth conjugacy theorems of Sternberg type for random dynamical systems based on their Lyapunov exponents. We also present a stable and unstable manifold theorem with tempered estimates that are used to construct conjugacy. © 2005 Wiley Periodicals, Inc. [source] | ||||||||||