18,873 research outputs found

    The Control of Dynamical Systems - Recovering Order from Chaos -

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    Following a brief historical introduction of the notions of chaos in dynamical systems, we will present recent developments that attempt to profit from the rich structure and complexity of the chaotic dynamics. In particular, we will demonstrate the ability to control chaos in realistic complex environments. Several applications will serve to illustrate the theory and to highlight its advantages and weaknesses. The presentation will end with a survey of possible generalizations and extensions of the basic formalism as well as a discussion of applications outside the field of the physical sciences. Future research avenues in this rapidly growing field will also be addressed.Comment: 18 pages, 9 figures. Invited Talk at the XXIth International Conference on the Physics of Electronic and Atomic Collisions (ICPEAC), July 22-27, 1999 (Sendai, Japan

    Maximum approximate entropy and r threshold: A new approach for regularity changes detection

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    Approximate entropy (ApEn) has been widely used as an estimator of regularity in many scientific fields. It has proved to be a useful tool because of its ability to distinguish different system's dynamics when there is only available short-length noisy data. Incorrect parameter selection (embedding dimension mm, threshold rr and data length NN) and the presence of noise in the signal can undermine the ApEn discrimination capacity. In this work we show that rmaxr_{max} (ApEn(m,rmax,N)=ApEnmaxApEn(m,r_{max},N)=ApEn_{max}) can also be used as a feature to discern between dynamics. Moreover, the combined use of ApEnmaxApEn_{max} and rmaxr_{max} allows a better discrimination capacity to be accomplished, even in the presence of noise. We conducted our studies using real physiological time series and simulated signals corresponding to both low- and high-dimensional systems. When ApEnmaxApEn_{max} is incapable of discerning between different dynamics because of the noise presence, our results suggest that rmaxr_{max} provides additional information that can be useful for classification purposes. Based on cross-validation tests, we conclude that, for short length noisy signals, the joint use of ApEnmaxApEn_{max} and rmaxr_{max} can significantly decrease the misclassification rate of a linear classifier in comparison with their isolated use

    Practical implementation of nonlinear time series methods: The TISEAN package

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    Nonlinear time series analysis is becoming a more and more reliable tool for the study of complicated dynamics from measurements. The concept of low-dimensional chaos has proven to be fruitful in the understanding of many complex phenomena despite the fact that very few natural systems have actually been found to be low dimensional deterministic in the sense of the theory. In order to evaluate the long term usefulness of the nonlinear time series approach as inspired by chaos theory, it will be important that the corresponding methods become more widely accessible. This paper, while not a proper review on nonlinear time series analysis, tries to make a contribution to this process by describing the actual implementation of the algorithms, and their proper usage. Most of the methods require the choice of certain parameters for each specific time series application. We will try to give guidance in this respect. The scope and selection of topics in this article, as well as the implementational choices that have been made, correspond to the contents of the software package TISEAN which is publicly available from http://www.mpipks-dresden.mpg.de/~tisean . In fact, this paper can be seen as an extended manual for the TISEAN programs. It fills the gap between the technical documentation and the existing literature, providing the necessary entry points for a more thorough study of the theoretical background.Comment: 27 pages, 21 figures, downloadable software at http://www.mpipks-dresden.mpg.de/~tisea

    A maximum likelihood based technique for validating detrended fluctuation analysis (ML-DFA)

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    Detrended Fluctuation Analysis (DFA) is widely used to assess the presence of long-range temporal correlations in time series. Signals with long-range temporal correlations are typically defined as having a power law decay in their autocorrelation function. The output of DFA is an exponent, which is the slope obtained by linear regression of a log-log fluctuation plot against window size. However, if this fluctuation plot is not linear, then the underlying signal is not self-similar, and the exponent has no meaning. There is currently no method for assessing the linearity of a DFA fluctuation plot. Here we present such a technique, called ML-DFA. We scale the DFA fluctuation plot to construct a likelihood function for a set of alternative models including polynomial, root, exponential, logarithmic and spline functions. We use this likelihood function to determine the maximum likelihood and thus to calculate values of the Akaike and Bayesian information criteria, which identify the best fit model when the number of parameters involved is taken into account and over-fitting is penalised. This ensures that, of the models that fit well, the least complicated is selected as the best fit. We apply ML-DFA to synthetic data from FARIMA processes and sine curves with DFA fluctuation plots whose form has been analytically determined, and to experimentally collected neurophysiological data. ML-DFA assesses whether the hypothesis of a linear fluctuation plot should be rejected, and thus whether the exponent can be considered meaningful. We argue that ML-DFA is essential to obtaining trustworthy results from DFA.Comment: 22 pages, 7 figure

    Neighbourhood detection and indentification of spatio-temporal dynamical systems using a coarse-to-fine approach

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    A novel approach to the determination of the neighbourhood and the identification of spatio-temporal dynamical systems is investigated. It is shown that thresholding to convert the pattern to a binary pattern and then applying cellular automata (CA) neighbourhood detection methods can provide an initial estimate of the neighbourhood. A coupled map lattice model can then be identified using the CA detected neighbourhood as the initial conditions. This provides a coarse-to-fine approach for neighbourhood detection and identification of coupled map lattice models. Three examples are used to demonstrate the application of the new approach

    Computational Intelligence in Exchange-Rate Forecasting

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    This paper applies computational intelligence methods to exchange rate forecasting. In particular, it employs neural network methodology in order to predict developments of the Euro exchange rate versus the U.S. Dollar and the Japanese Yen. Following a study of our series using traditional as well as specialized, non-parametric methods together with Monte Carlo simulations we employ selected Neural Networks (NNs) trained to forecast rate fluctuations. Despite the fact that the data series have been shown by the Rescaled Range Statistic (R/S) analysis to exhibit random behaviour, their internal dynamics have been successfully captured by certain NN topologies, thus yielding accurate predictions of the two exchange-rate series.Exchange - rate forecasting, Neural networks
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