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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.
Social Processes As Dynamical Processes: Qualitative Dynamical Systems. . .
, 1996
"... We present an alternative view to the dominant discourse in scientific psychology, where researchers are concerned primarily with predictability of phenomena based largely on simple tests of linear relation. Instead, the timedependent and evolving nature of social experience and interaction can be ..."
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We present an alternative view to the dominant discourse in scientific psychology, where researchers are concerned primarily with predictability of phenomena based largely on simple tests of linear relation. Instead, the timedependent and evolving nature of social experience and interaction can be examined using the methodology of nonlinear dynamical systems theory (NDS). We review relevant concepts from key content areas ("chaos" theory, catastrophe models and selforganising networks) and assess their applicability to the modelling of social psychological phenomena. In addition, we offer a guide to reanalysing existing "between subjects" data for nonlinearity, and "within subjects" data for dynamical change. NDS provides useful metaphors, models and analytical tools for developing qualitative process as opposed to quantitative outcome models. INTRODUCTION Two of the implicit assumptions in many areas of scientific endeavour have been that apparently simple events have simple expl...
NorthHolland, Amsterdam CHARACTERIZATION OF HYDRODYNAMIC STRANGE ATrRACTORS
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C Elsevier Science Publishers B.V., 1990 CHAOTIC STRUCTURES IN INFORMETRICS
"... A sample space o f the number o f publ icat ions i n polymer chemistry over a f i ve year period has been subjected t o t ime ser ies data analysis. The technique uses autocorre lat ion and a subsequent FFT ( f as t Four ier transform). The analysis shows t h a t the sample space i s small but the d ..."
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A sample space o f the number o f publ icat ions i n polymer chemistry over a f i ve year period has been subjected t o t ime ser ies data analysis. The technique uses autocorre lat ion and a subsequent FFT ( f as t Four ier transform). The analysis shows t h a t the sample space i s small but the data appears t o have chaotic behaviour. Recomnendations f o r f u tu re work and appl icat ions are i den t i f i ed. 1.