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Determining Lyapunov Exponents from a Time Series
 Physica
, 1985
"... We present the first algorithms that allow the estimation of nonnegative Lyapunov exponents from an experimental time series. Lyapunov exponents, which provide a qualitative and quantitative characterization of dynamical behavior, are related to the exponentially fast divergence or convergence of n ..."
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We present the first algorithms that allow the estimation of nonnegative Lyapunov exponents from an experimental time series. Lyapunov exponents, which provide a qualitative and quantitative characterization of dynamical behavior, are related to the exponentially fast divergence or convergence of nearby orbits in phase space. A system with one or more positive Lyapunov exponents is defined to be chaotic. Our method is rooted conceptually in a previously developed technique that could only be applied to analytically defined model systems: we monitor the longterm growth rate of small volume elements in an attractor. The method is tested on model systems with known Lyapunov spectra, and applied to data for the BelousovZhabotinskii reaction and CouetteTaylor flow. Contents 1.
Application of Chaos Methods to Helicopter Vibration Reduction Using Higher Harmonic Control
 Naval Postgraduate School
, 1990
"... ~9 ~STACT(Continue on reverse if necessarv and identf bv$(IQck numbctr ~Chaos is ad!&cipJ~in4oUsed 4,45 understandi+j"'complex nonlinear dynamics. The geometric and topological methods of Chaos theory are applied, for the first time, to the study of flight test data. Data analyzed is ..."
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~9 ~STACT(Continue on reverse if necessarv and identf bv$(IQck numbctr ~Chaos is ad!&cipJ~in4oUsed 4,45 understandi+j"'complex nonlinear dynamics. The geometric and topological methods of Chaos theory are applied, for the first time, to the study of flight test data. Data analyzed is from the McDMnia4ll uq1a6 OH6A Higher Harmonic Control (HHC) test aircraft. HHC is an active control system used to suppress helicopter vibrations. Some of the first practical applications of Chaos methods are demonstrated with the HHC data.
Fractional Derivative Reconstruction of Forced Oscillators
"... Fractional derivatives are applied in the reconstruction, from a single observable, of the dynamics of a Duffing oscillator and a twowell experiment. The fractional derivatives of time series data are obtained in the frequency domain. The derivative fraction is evaluated using the average mutual in ..."
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Fractional derivatives are applied in the reconstruction, from a single observable, of the dynamics of a Duffing oscillator and a twowell experiment. The fractional derivatives of time series data are obtained in the frequency domain. The derivative fraction is evaluated using the average mutual information between the observable and its fractional derivative. The ability of this reconstruction method to unfold the data is assessed by the method of global false nearest neighbors. The reconstructed data is used to compute recurrences and fractal dimensions. The reconstruction is compared to the true phase space and the delay reconstruction in order to assess the reconstruction parameters and the quality of results.
2008): Downward causation in fluid convection
 Synthese
"... Recent developments in nonlinear dynamics have found wide application in many areas of science from physics to neuroscience. Nonlinear phenomena such as feedback loops, interlevel relations, wholes constraining and modifying the behavior of their parts, and memory effects are interesting candidates ..."
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Recent developments in nonlinear dynamics have found wide application in many areas of science from physics to neuroscience. Nonlinear phenomena such as feedback loops, interlevel relations, wholes constraining and modifying the behavior of their parts, and memory effects are interesting candidates for emergence and downward causation. RayleighBénard convection is an example of a nonlinear system that, I suggest, yields important insights for metaphysics and philosophy of science. In this paper I propose convection as a model for downward causation in classical mechanics, far more robust and less speculative than the examples typically provided in the philosophy of mind literature. Although the physics of RayleighBénard convection is quite complicated, this model provides a much more realistic and concrete example for examining various assumptions and arguments found in emergence and philosophy of mind debates. After reviewing some key concepts of nonlinear dynamics, complex systems and the basic physics of RayleighBénard convection, I begin that examination here by (1) assessing a recently proposed definition for emergence and downward causation, (2) discussing some typical objections to downward causation and (3) comparing this model with Sperry’s examples. 2The aim of science is not things themselves, as the dogmatists in their simplicity imagine, but the relations among things; outside these relations there is no reality knowable. Poincaré 1.
Fractional Derivatives Applied to Phase Space Reconstructions
, 2004
"... The concept and application of phasespace reconstructions are reviewed. Fractional derivatives are then proposed for the purpose of reconstructing dynamics from a single observed time history. A procedure is presented in which the fractional derivatives of time series data are obtained in the frequ ..."
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The concept and application of phasespace reconstructions are reviewed. Fractional derivatives are then proposed for the purpose of reconstructing dynamics from a single observed time history. A procedure is presented in which the fractional derivatives of time series data are obtained in the frequency domain. The method is applied to the Lorenz system. The ability of the method to unfold the data is assessed by the method of global false nearest neighbors. The reconstructed data is used to compute recurrences and correlation dimensions. The reconstruction is compared to the commonly used method of delays in order to assess the choice of reconstruction parameters, and also the quality of results.
Forecasting of Chaotic Cloud Absorption Time Series for Meteorological and Plume Dispersion Modeling
 J. APPL. METEOR
, 1998
"... A nonlinear forecasting method based on the reconstruction of a chaotic strange attractor from about 1.5 years of cloud absorption data obtained from halfhourly Meteosat infrared images was used to predict the behavior of the time series 24 h in advance. The forecast values are then used by a met ..."
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A nonlinear forecasting method based on the reconstruction of a chaotic strange attractor from about 1.5 years of cloud absorption data obtained from halfhourly Meteosat infrared images was used to predict the behavior of the time series 24 h in advance. The forecast values are then used by a meteorological model for daily prediction of plume transport from the As Pontes 1400MW power plant in northwestern Spain. Results from the meteorological model, using the cloud absorption predictions, are compared with measurements obtained from meteorological towers and a Remtech PA3 sodar. The effects of cloud absorption on SO 2 groundlevel concentration forecasts are analyzed for two different days.
APPLICATION OF CHAOS METHODS TO HELICOPTER VIBRATION REDUCTION USING HIGHER HARMONIC CONTROL
, 1990
"... la REPORT SECURITY ' CLASSIF (A'1(0 % it RESTP&CThi ' VAR %'S ..."
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la REPORT SECURITY ' CLASSIF (A'1(0 % it RESTP&CThi ' VAR %'S