Filtered noise can mimic low-dimensional chaotic attractors

Rapp, Paul E.; Albano, A. M.; Schmah, Tanya; Farwell, Lawrence A.

doi:10.1103/physreve.47.2289

Cited by 228 publications

(106 citation statements)

References 31 publications

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“…The method of surrogate data is a powerful statistical procedure for examining hypotheses about the structure of dynamical systems (Theiler et al 1992;Rapp et al 1993). An investigation with surrogate data has three components.…”

Section: First Order Markov Surrogates: Probing the Fine Structure Ofmentioning

confidence: 99%

Quantitative characterization of animal behavior following blast exposure

Rapp

2007

Cogn Neurodyn

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The simplest approach to quantifying animal behavior begins by identifying a list of discrete behaviors and observing the animal's behavior at regular intervals for a specified period of time. The behavioral distribution (the fraction of observations corresponding to each behavior) is then determined. This is an incomplete characterization of behavior, and in some instances, mild injury is not reflected by statistically significant changes in the distribution even though a human observer can confidently and correctly assert that the animal is not behaving normally. In these circumstances, an examination of the sequential structure of the animal's behavior may, however, show significant alteration. This contribution describes procedures derived from symbolic dynamics for quantifying the sequential structure of animal behavior. Normalization procedures for complexity estimates are presented, and the limitations of complexity measures are discussed.

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Section: First Order Markov Surrogates: Probing the Fine Structure Ofmentioning

confidence: 99%

Quantitative characterization of animal behavior following blast exposure

Rapp

2007

Cogn Neurodyn

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“…Time series taken at time intervals of different length, so called unevenly sampled time series, are also quite common (Schreiber and Schmitz, 1999). So far as systems variables are coupled a single component contains essential information about the dynamics of the whole system (Castro and Sauer, 1997;Kantz and Schreiber, 1997;Rapp and Farwell, 1993). Therefore the trajectory reconstructed from this scalar time series is expected to have the same properties as the trajectory embedded in the original phase space, formed by all m state variables.…”

Section: Phase Space Structures As Image Of Dynamicsmentioning

confidence: 99%

“…Phase randomized surrogate sets (PR -obtained by destroying the nonlinear structure through randomization of the phases of a Fourier transform of the original time series and the following inverse transformation) is often used to test the null hypothesis that the time series are linearly correlated with Gaussian noise (Theiler and Farmer, 1992). Also the Gaussian scaled random phase (GSRP) surrogate set can be generated to address a null hypothesis that the original time series is linearly correlated noise that has been transformed by a static, monotone nonlinearity (Rapp and Jumenez-Montero, 1994;Rapp and Farwell, 1993). GSRP surrogates are generated in a three-step procedure.…”

Section: Phase Space Structures As Image Of Dynamicsmentioning

confidence: 99%

“…In spite of the popularity of the d 2 calculation method, GPA results must be interpreted with great care as it is well known that linear stochastic processes can also mimic low-dimensional dynamics (Rapp and Farwell, 1993;Theiler and Prichard, ). In other words, the saturation of a correlation dimension and the existence of positive Lyapunov exponents cannot always be considered as decisive proof of deterministic chaos, a dynamical regime which is predictable in the sense of patterns, and is closest to quasiperiodicity (Kantz and Schreiber, 1997;Rapp and Farwell, 1993). Since linear correlations lead to many spurious conclusions in nonlinear time series analyses, it is important to verify results obtained using the so-called surrogate data approach.…”

Section: Phase Space Structures As Image Of Dynamicsmentioning

confidence: 99%

“…This is why in different fields of science and practice there has been an explosion of papers searching for methods aiming at detection of peculiarities of complex systems evolution in order to achieve reliable identification of processes by their dynamics. At present a time series nonlinear analysis technique is elaborated (Abarbanel and Tsimring, 1993;Berge and Vidal, 1984;Eckman and Ruelle, 1985;Kantz and Schreiber, 1997;Packard and Shaw, 1980;Rapp and Farwell, 1993), which often (but not always due to the same cause -complexity of nature) enables us to achieve correct qualitative and quantitative assessment of complex processes by measuring their dynamical characteristics. These methods aiming to measure the complexity of both local and global spatial and temporal scales are universal and applicable to a very broad range of complicated processes.…”

Section: Introductionmentioning

confidence: 99%

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Identification of Complex Processes Based on Analysis of Phase Space Structures

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Abstract. The problem of investigation of temporal and/or spatial behavior of highly nonlinear or complex natural systems has long been of fundamental scientific interest. At the same time it is presently well understood that identification of dynamics of processes in complex natural systems, through their qualitative description and quantitative evaluation, is far from a purely academic question and has an essential practical importance. This is quite understandable as systems with complex dynamics abound in nature and examples can be found in very different areas such as medicine and biology (rhythms, physiological cycles, epidemics), atmosphere (climate and weather change), geophysics (tides, earthquakes, volcanoes, magnetic field variations), economy (financial markets behavior, exchange rates), engineering (friction, fracturing), communication (electronic networks, internet packet dynamics) etc. The past two decades of research on qualitative and especially quantitative investigations of dynamics of real processes of different origin brought significant progress in the understanding of behavior of natural processes. At the same time serious drawbacks have also been revealed. This is why exhaustive investigation of dynamical properties of complex processes for scientific, engineering or practical purposes is now recognized as one of the main scientific challenges. Much attention is paid to elaboration of appropriate methods aiming to measuring the complexity of both global and local dynamical behaviors from the observed data sets -time series. This chapter presents a short overview of modern methods of qualitative and quantitative evaluation of dynamics of complex natural processes such as calculation of Lyapunov exponents and fractal dimensions, recurrence plots and recurrence quantification analysis. Other related methods are also described. The traditional approach to studying dynamical behavior of complex nonlinear systems is to reconstruct from observation scalar time series state or phase space plot. This graph indicates how the systems behavior changes over the time. We focus on the methods of identification and quantitative evaluation of complex dynamics that are based on the testing of evolutionary and geometric properties of phase space graphs as images of investigated complex dynamics. For practical examples of the application c 2006 Springer. Printed in the Netherlands.of nonlinear methods for identification of complex natural processes, our results on medical, geophysical, hydrological, and stick-slip time series analysis are presented.

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Chaos and Complexity

Ehlers

1995

Arch Gen Psychiatry

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Filtered noise can mimic low-dimensional chaotic attractors

Cited by 228 publications

References 31 publications

Quantitative characterization of animal behavior following blast exposure

Quantitative characterization of animal behavior following blast exposure

Identification of Complex Processes Based on Analysis of Phase Space Structures

Chaos and Complexity

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