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At least 19 recordsLinked to original sources
PubMed2006

Inference for nonlinear dynamical systems.

Nonlinear stochastic dynamical systems are widely used to model systems across the sciences and engineering. Such models are natural to formulate and can be analyzed mathematically and numerically. However, difficulties associated with inference from time-series data about unknown parameters in these models have been a constraint on their application. We present a new method that makes maximum likelihood estimation feasible for partially-observed nonlinear stochastic dynamical systems (also known as state-space models) where this was not previously the case. The method is based on a sequence of filtering operations which are shown to converge to a maximum likelihood parameter estimate. We make use of recent advances in nonlinear filtering in the implementation of the algorithm. We apply the method to the study of cholera in Bangladesh. We construct confidence intervals, perform residual analysis, and apply other diagnostics. Our analysis, based upon a model capturing the intrinsic nonlinear dynamics of the system, reveals some effects overlooked by previous studies.

Cholera↗
PubMed1999

Robustness of supersensitivity to small signals in nonlinear dynamical systems.

Nonlinear dynamical systems possessing an invariant subspace can display interesting dynamical behavior, such as on-off intermittency and bubbling. This Rapid Communication shows that a class of such systems has amazing features of (1) supersensitivity to small input signals and (2) robustness of the supersensitivity in the presence of noise. These features make the systems very promising as small signal detectors.

Journal Article↗
PubMed2005

Nonlinear dynamical analysis of noisy time series.

Empirical time series in the life sciences are often nonstationary and have small signal-to-noise ratios, making it difficult to accurately detect and characterize dynamical structure. The usual response to high noise is averaging, but time domain averaging is inappropriate, especially when the dynamics are nonlinear. We review alternative delay-space averaging methods based on the topology and short-term predictability of nonlinear dynamics and illustrate their application using the TISEAN software (Hegger, Kantz & Schreiber, 1999). The methods were applied to a Lorenz series, which resembles the dynamics found by Kelly, Heathcote, Heath and Longstaff (2001) in series of decision times. The Lorenz series was corrupted with up to 80% additive Gaussian noise, a lower signal-to-noise ratio than has been used in any previous test of these methods, but consistent with Kelly et al.'s data. Prediction methods performed the best for detecting nonstationarity and nonlinear dynamics, and optimal predictability provided an objective criterion for setting the parameters required by the analyses. Local linear filtering methods performed best for characterization, producing informative plots that revealed the nature of the underlying dynamics. These results suggest that a methodology based on delay-space averaging and prediction could be useful with noisy empirical data series.

Animals↗
PubMed2006

Adjusting behavioral methods when applying nonlinear dynamical measures to stimulus rate.

A nonlinear dynamical perspective addresses an area of behavior that tends to be ignored: trial-to-trial variability under seemingly identical conditions. Data exhibiting sequence effects are excellent candidates for a nonlinear dynamical analysis, because of their dependence on previous trial events. When applying nonlinear dynamical tools to behavioral data, the assumptions underlying the tools may require changes in experimental methodology. In this paper, the assumptions of trial timing and their potential impact on nonlinear dynamical analysis are explored. This is done with the intent of initiating a discussion on the appropriate control of trial timing. To examine these issues, each participant's response times on simple two-choice tasks were treated as a time series and submitted along with two comparisons to two nonlinear dynamical measures. Two experimental variables, stimulus rate and stimulus-response mapping, were manipulated in order to examine the issue of controlling trial timing via stimulus rate. Significant differences between the observed and comparison time series were found for estimated dimensionalities(m). Differences in dimensionality(m) estimates were also found between the experimental variables. Of the two methods for controlling stimulus rate, response-stimulus-interval and inter-stimulus-interval, the latter is recommended when applying nonlinear dynamical measures.

Analysis of Variance↗
PubMed2000

Nonlinear dynamics: chaos and catastrophe theory.

Nonlinear relationships are attracting much attention in nursing. Nonlinear dynamics are used abstractly as theory and also may be applied in a concrete sense to explain data. There is often confusion and misunderstanding about aspects of nonlinear dynamics. This article explores two of the more well known areas of nonlinear dynamics--chaos and catastrophe theory. A summary of each is given, areas of commonality and distinction are explored, and guidelines for application are identified.

Humans↗
PubMed1998

Social contagion, adolescent sexual behavior, and pregnancy: a nonlinear dynamic EMOSA model.

Nonlinear dynamic modeling has useful developmental applications. The authors introduce this class of models and contrast them with traditional linear models. Epidemic models of the onset of social activities (EMOSA models) are a special case, motivated by J. L. Rodgers and D. C. Rowe's (1993) social contagion theory, which predict the spread of adolescent behaviors like smoking, drinking, delinquency, and sexuality. In this article, a biological outcome, pregnancy, is added to an earlier EMOSA sexuality model. Parameters quantify likelihood of pregnancy for girls of different sexuality statuses. Five different sexuality/pregnancy models compete to explain variance in national prevalence curves. One finding was that, in the context of the authors' simplified model, adolescent girls have an approximately constant probability of pregnancy across age and time since virginity.

Adolescent↗
PubMed1994

Analysis of vocal disorders with methods from nonlinear dynamics.

Several authors have recently demonstrated the intimate relationship between nonlinear dynamics and observations in vocal fold vibration (Herzel, 1993; Mende, Herzel, & Wermke, 1990; Titze, Baken, & Herzel, 1993). The aim of this paper is to analyze vocal disorders from a nonlinear dynamics point of view. Basic concepts and analysis techniques from nonlinear dynamics are reviewed and related to voice. The voices of several patients with vocal disorders are analyzed using traditional voice analysis techniques and methods from nonlinear dynamics. The two methods are shown to complement each other in many ways. Likely physiological mechanisms of the observed nonlinear phenomena are presented, and it is shown how much of the terminology in the literature describing rough voice can be unified within the framework of nonlinear dynamics.

Electroencephalography↗
PubMed2001

Nonlinear-dynamical arrhythmia control in humans.

Nonlinear-dynamical control techniques, also known as chaos control, have been used with great success to control a wide range of physical systems. Such techniques have been used to control the behavior of in vitro excitable biological tissue, suggesting their potential for clinical utility. However, the feasibility of using such techniques to control physiological processes has not been demonstrated in humans. Here we show that nonlinear-dynamical control can modulate human cardiac electrophysiological dynamics by rapidly stabilizing an unstable target rhythm. Specifically, in 52/54 control attempts in five patients, we successfully terminated pacing-induced period-2 atrioventricular-nodal conduction alternans by stabilizing the underlying unstable steady-state conduction. This proof-of-concept demonstration shows that nonlinear-dynamical control techniques are clinically feasible and provides a foundation for developing such techniques for more complex forms of clinical arrhythmia.

Adult↗
PubMed1999

[A primary clinical study of HRV analysis of nonlinear dynamics].

We observed the changes of nonlinear dynamic parameters in the patients with diabetes and old myocardial infarction with the methods of nonlinear dynamics. The results indicate that the correlation dimension of the patients with old myocardial infarction is higher than that of the normal, their Lyapunov exponent is lower than the normal's; that the correlation dimension of the patients with diabetes is also higher than that of the normal, their Lyapunov exponent is lower than the normal's; and that the values of the entropy of the two patient groups are basically identical to the entropy of the normal. Therefore the correlation dimension can indicate the changes in the function of autonomic nerve of the patients with diabetes and old myocardial infarction.

Autonomic Nervous System↗
PubMedDate not supplied

Evaluation of nonlinear dynamics in postural steadiness time series.

Fractal and correlation dimensions have been computed for time series obtained from tests of balance (postural steadiness). Although these measures appear to be reliable and differentiate subject groups, it has become clear that random (noise) time series may have finite dimensions and appear to demonstrate dynamics characteristic of nonlinear systems. Consequently, it is necessary to apply a test to distinguish a time series with putative nonlinear dynamics from random noise. A simple predictor was utilized to compare center of pressure (COP) time series with surrogate data constructed to have similar time and frequency domain characteristics. It was found that the original time series was more predictable than the surrogate data, suggesting that the COP data is derived from a nonlinear system.

Adult↗
PubMed2001

Neurodynamics: nonlinear dynamics and neurobiology.

The use of methods from contemporary nonlinear dynamics in studying neurobiology has been rather limited.Yet, nonlinear dynamics has become a practical tool for analyzing data and verifying models. This has led to productive coupling of nonlinear dynamics with experiments in neurobiology in which the neural circuits are forced with constant stimuli, with slowly varying stimuli, with periodic stimuli, and with more complex information-bearing stimuli. Analysis of these more complex stimuli of neural circuits goes to the heart of how one is to understand the encoding and transmission of information by nervous systems.

Animals↗
PubMedDate not supplied

The role of nonlinear dynamics in cardiac arrhythmia control.

The field of nonlinear dynamics has made important contributions toward a mechanistic understanding of cardiac arrhythmias. In recent years, many of these advancements have been in the area of arrhythmia control. This paper reviews the literature on analytical, modeling, and experimental nonlinear dynamical arrhythmia control with a focus on stimulation and pharmacologic techniques that have been developed, and in some cases used in experiments, to control reentrant rhythms (including spiral and scroll waves) and fibrillation. Although such approaches currently have practical limitations, they offer hope that nonlinear dynamical control techniques will be clinically useful in the coming years.

Animals↗
PubMed2001

Nonlinear dynamics and chaos theory: concepts and applications relevant to pharmacodynamics.

The theory of nonlinear dynamical systems (chaos theory), which deals with deterministic systems that exhibit a complicated, apparently random-looking behavior, has formed an interdisciplinary area of research and has affected almost every field of science in the last 20 years. Life sciences are one of the most applicable areas for the ideas of chaos because of the complexity of biological systems. It is widely appreciated that chaotic behavior dominates physiological systems. This is suggested by experimental studies and has also been encouraged by very successful modeling. Pharmacodynamics are very tightly associated with complex physiological processes, and the implications of this relation demand that the new approach of nonlinear dynamics should be adopted in greater extent in pharmacodynamic studies. This is necessary not only for the sake of more detailed study, but mainly because nonlinear dynamics suggest a whole new rationale, fundamentally different from the classic approach. In this work the basic principles of dynamical systems are presented and applications of nonlinear dynamics in topics relevant to drug research and especially to pharmacodynamics are reviewed. Special attention is focused on three major fields of physiological systems with great importance in pharmacotherapy, namely cardiovascular, central nervous, and endocrine systems, where tools and concepts from nonlinear dynamics have been applied.

Biopharmaceutics↗
PubMed1998

[Nonlinear dynamic analysis of heart rate variability during exercise].

Nonlinear dynamic analysis was used to examine the changes of complexity of heart rate variability (HRV) under rest and exercise. Nine healthy male subjects participated in the test. Each subject had a rest in supine position for 10 min, and then exercised on a cycle ergometer (10 min at 50 W and 10 min at 100 W). The results showed that R-R interval and its standard deviation reduced, and at the same time the values of nonlinear dynamics indices (complexity, entropy, correlation dimension, capacity dimension) also decreased during exercise. Moreover, at 100W work load the decrease of these indices was greater than that of 50W. It shows that physical exercise may reduce the complexity of HRV, and nonlinear dynamic indices could be used in distinguishing the complexity of heart rate variability under different physiological conditions.

Adult↗
PubMed2001

Investigation of brain dynamics in Parkinson's disease by methods derived from nonlinear dynamics.

EEGs were recorded from patients in early stages of Parkinson's disease (17 patients, 9 females) and healthy controls (12 subjects, 8 females) during rest and during execution/imagining of a complex motor task. The prediction that Parkinson's disease patients compared to controls would show more complex brain dynamics during performance of a complex motor task and imagination of the movements was confirmed by methods derived from nonlinear dynamics. In the resting state, analysis of correlation dimension of EEG time series revealed only slight topographical differences between the groups. During performance of a complex motor task, however, data from Parkinson's disease patients showed higher dimensionality than data from controls, indicating more complex EEG time series. The same difference was found when subjects did not perform any motor movements but imagined the complex movements they had just performed. The data are consistent with the hypothesis that the disturbances in Parkinson's disease result in the recruitment of superfluous cortical networks due to failed inhibition of alternative motor programs in the striatum and thus increase the complexity of cortical representation in motor conditions.

Aged↗
PubMed1991

Can the analytic techniques of nonlinear dynamics distinguish periodic, random and chaotic signals?

Recent advances in the mathematical discipline of nonlinear dynamics have led to its use in the analysis of many biologic processes. But the ability of the tools of nonlinear dynamic analysis to identify chaotic behavior has not been determined. We analyzed a series of signals--periodic, chaotic and random--with five tools of nonlinear dynamics. Periodic signals were sine, square, triangular, sawtooth, modulated sine waves and quasiperiodic, generated at multiple amplitudes and frequencies. Chaotic signals were generated by solving sets of nonlinear equations including the logistic map, Duffing's equation, Lorenz equations and the Silnikov attractor. Random signals were both discontinuous and continuous. Gaussian noise was added to some signals at magnitudes of 1, 2, 5, 10 and 20% of the signal's amplitude. Each signal was then subjected to tools of nonlinear dynamics (phase plane plot, return map, Poincaré section, correlation dimension and spectral analysis) to determine the relative ability of each to characterize the underlying system as periodic, chaotic or random. In the absence of noise, phase plane plots and return maps were the most sensitive detectors of chaotic and periodic processes. Spectral analysis could determine if a process was periodic or quasiperiodic, but could not distinguish between chaotic and random signals. Correlation dimension was useful to determine the overall complexity of a signal, but could not be used in isolation to identify a chaotic process. Noise at any level effaced the structure of the phase plane plot. Return maps were relatively immune to noise at levels of up to 5%. Spectral analysis and correlation dimension were insensitive to noise. Accordingly, we recommend that unknown signals be subjected to all of the techniques to increase the accuracy of identification of the underlying process. Based on these data, we conclude that no single test is sufficiently sensitive or specific to categorize an unknown signal as chaotic.

Fourier Analysis↗
PubMed2005

Comparison of nonlinear dynamic methods and perturbation methods for voice analysis.

Nonlinear dynamic methods and perturbation methods are compared in terms of the effects of signal length, sampling rate, and noise. Results of theoretical and experimental studies quantitatively show that measurements representing frequency and amplitude perturbations are not applicable to chaotic signals because of difficulties in pitch tracking and sensitivity to initial state differences. Perturbation analyses are only reliable when applied to nearly periodic voice samples of sufficiently long signal lengths that were obtained at high sampling rates and low noise levels. In contrast, nonlinear dynamic methods, such as correlation dimension, allow the quantification of chaotic time series. Additionally, the correlation dimension method presents a more stable analysis of nearly periodic voice samples for shorter signal lengths, lower sampling rates, and higher noise levels. The correlation dimension method avoids some of the methodological issues associated with perturbation methods, and may potentially improve the ability for real time analysis as well as reduce costs in experimental designs for objectively assessing voice disorders.

Adult↗