SEARCH · PubMed Health

Results for “Nonlinear Dynamics”

Explore indexed PubMed citations for clinical trials, systematic reviews and public health research. Read source abstracts and follow each citation to its original PubMed record.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,045 records · Page 58Linked to original sources

PubMed1997

Tracking controlled chaos: Theoretical foundations and applications.

Tracking controlled states over a large range of accessible parameters is a process which allows for the experimental continuation of unstable states in both chaotic and non-chaotic parameter regions of interest. In algorithmic form, tracking allows experimentalists to examine many of the unstable states responsible for much of the observed nonlinear dynamic phenomena. Here we present a theoretical foundation for tracking controlled states from both dynamical systems as well as control theoretic viewpoints. The theory is constructive and shows explicitly how to track a curve of unstable states as a parameter is changed. Applications of the theory to various forms of control currently used in dynamical system experiments are discussed. Examples from both numerical and physical experiments are given to illustrate the wide range of tracking applications. (c) 1997 American Institute of Physics.

Journal Article↗

PubMed1998

On the evidence of deterministic chaos in ECG: Surrogate and predictability analysis.

The question whether the human cardiac system is chaotic or not has been an open one. Recent results in chaos theory have shown that the usual methods, such as saturation of correlation dimension D(2) or the existence of positive Lyapunov exponent, alone do not provide sufficient evidence to confirm the presence of deterministic chaos in an experimental system. The results of surrogate data analysis together with the short-term prediction analysis can be used to check whether a given time series is consistent with the hypothesis of deterministic chaos. In this work nonlinear dynamical tools such as surrogate data analysis, short-term prediction, saturation of D(2) and positive Lyapunov exponent have been applied to measured ECG data for several normal and pathological cases. The pathology presently studied are PVC (Premature Ventricular Contraction), VTA (Ventricular Tachy Arrhythmia), AV (Atrio-Ventricular) block and VF (Ventricular Fibrillation). While these results do not prove that ECG time series is definitely chaotic, they are found to be consistent with the hypothesis of chaotic dynamics. (c) 1998 American Institute of Physics.

Journal Article↗

PubMed1998

Exponential asymptotic expansions and approximations of the unstable and stable manifolds of singularly perturbed systems with the Henon map as an example.

The subject of this paper is the construction of the exponential asymptotic expansions of the unstable and stable manifolds of the area-preserving Henon map. The approach that is taken enables one to capture the exponentially small effects that result from what is known as the Stokes phenomenon in the analytic theory of equations with irregular singular points. The exponential asymptotic expansions were then used to obtain explicit functional approximations for the stable and unstable manifolds. These approximations are compared with numerical simulations and the agreement is excellent. Several of the main results of the paper have been previously announced in A. Tovbis, M. Tsuchiya, and C. Jaffe ["Chaos-integrability transition in nonlinear dynamical systems: exponential asymptotic approach," Differential Equations and Applications to Biology and to Industry, edited by M. Martelli, K. Cooke, E. Cumberbatch, B. Tang, and H. Thieme (World Scientific, Singapore, 1996), pp. 495-507, and A. Tovbis, M. Tsuchiya, and C. Jaffe, "Exponential asymptotic expansions and approximations of the unstable and stable manifolds of the Henon map," preprint, 1994]. (c) 1998 American Institute of Physics.

Journal Article↗

PubMed1998

Stabilizing unstable steady states using extended time-delay autosynchronization.

We describe a method for stabilizing unstable steady states in nonlinear dynamical systems using a form of extended time-delay autosynchronization. Specifically, stabilization is achieved by applying a feedback signal generated by high-pass-filtering in real time the dynamical state of the system to an accessible system parameter or variables. Our technique is easy to implement, does not require knowledge of the unstable steady state coordinates in phase space, automatically tracks changes in the system parameters, and is more robust to broadband noise than previous schemes. We demonstrate the controller's efficacy by stabilizing unstable steady states in an electronic circuit exhibiting low-dimensional temporal chaos. The simplicity and robustness of the scheme suggests that it is ideally suited for stabilizing unstable steady states in ultra-high-speed systems. (c) 1998 American Institute of Physics.

Journal Article↗

PubMed2000

Investigation of determinism in heart rate variability.

The article searches for the possible presence of determinism in heart rate variability (HRV) signals by using a new approach based on NARMA (nonlinear autoregressive moving average) modeling and free-run prediction. Thirty-three 256-point HRV time series obtained from Wistar rats submitted to different autonomic blockade protocols are considered, and a collection of surrogate data sets are generated from each one of them. These surrogate sequences are assumed to be nondeterministic and therefore they may not be predictable. The original HRV time series and related surrogates are submitted to NARMA modeling and prediction. Special attention has been paid to the problem of stationarity. The results consistently show that the surrogate data sets cannot be predicted better than the trivial predictor-the mean-while most of the HRV control sequences are predictable to a certain degree. This suggests that the normal HRV signals have a deterministic signature. The HRV time series derived from the autonomic blockade segments of the experimental protocols do not show the same predictability performance, albeit the physiological interpretation is not obvious. These results have important implications to the methodology of HRV analysis, indicating that techniques from nonlinear dynamics and deterministic chaos may be applied to elicit more information about the autonomic modulation of the cardiovascular activity. (c) 2000 American Institute of Physics.

Journal Article↗

PubMed2004

Dynamics of caged ions in glassy ionic conductors.

At sufficiently high frequency and low temperature, the dielectric responses of glassy, crystalline, and molten ionic conductors all invariably exhibit nearly constant loss. This ubiquitous characteristic occurs in the short-time regime when the ions are still caged, indicating that it could be a determining factor of the mobility of the ions in conduction at longer times. An improved understanding of its origin should benefit the research of ion conducting materials for portable energy source as well as the resolution of the fundamental problem of the dynamics of ions. We perform molecular dynamics simulations of glassy lithium metasilicate (Li2SiO3) and find that the length scales of the caged Li+ ions motions are distributed according to a Levy distribution that has a long tail. These results suggest that the nearly constant loss originates from "dynamic anharmonicity" experienced by the moving but caged Li+ ions and provided by the surrounding matrix atoms executing correlated movements. The results pave the way for rigorous treatments of caged ion dynamics by nonlinear Hamiltonian dynamics.

Journal Article↗

PubMed2005

Fingering of exothermic reaction-diffusion fronts in Hele-Shaw cells with conducting walls.

We consider the influence of heat losses through the walls of a Hele-Shaw cell on the linear stability and nonlinear dynamics of exothermic chemical fronts whose solutal and thermal contributions to density changes have the same signs. Our analysis is based on the reaction-diffusion-convection equations obtained from the Darcy-Boussinesq approximation. The parameters governing the equations are the Damkohler number, a kinetic parameter d, the Lewis number Le, the thermal-expansion coefficient gammaT, and a heat-transfer coefficient alpha which measures heat losses through the walls. We show that for thermally insulating walls, the temperature profile is a front that follows the concentration profile, while in the presence of heat losses, the temperature profile becomes a pulse that leads to a nonmonotonic density profile which in turn may lead to a destabilization of an otherwise stable front.

Journal Article↗

PubMed2006

The size of the sync basin.

We suggest a new line of research that we hope will appeal to the nonlinear dynamics community, especially the readers of this Focus Issue. Consider a network of identical oscillators. Suppose the synchronous state is locally stable but not globally stable; it competes with other attractors for the available phase space. How likely is the system to synchronize, starting from a random initial condition? And how does the probability of synchronization depend on the way the network is connected? On the one hand, such questions are inherently difficult because they require calculation of a global geometric quantity, the size of the "sync basin" (or, more formally, the measure of the basin of attraction for the synchronous state). On the other hand, these questions are wide open, important in many real-world settings, and approachable by numerical experiments on various combinations of dynamical systems and network topologies. To give a case study in this direction, we report results on the sync basin for a ring of n >> 1 identical phase oscillators with sinusoidal coupling. Each oscillator interacts equally with its k nearest neighbors on either side. For k/n greater than a critical value (approximately 0.34, obtained analytically), we show that the sync basin is the whole phase space, except for a set of measure zero. As k/n passes below this critical value, coexisting attractors are born in a well-defined sequence. These take the form of uniformly twisted waves, each characterized by an integer winding number q, the number of complete phase twists in one circuit around the ring. The maximum stable twist is proportional to n/k; the constant of proportionality is also obtained analytically. For large values of n/k, corresponding to large rings or short-range coupling, many different twisted states compete for their share of phase space. Our simulations reveal that their basin sizes obey a tantalizingly simple statistical law: the probability that the final state has q twists follows a Gaussian distribution with respect to q. Furthermore, as n/k increases, the standard deviation of this distribution grows linearly with square root of n/k. We have been unable to explain either of these last two results by anything beyond a hand-waving argument.

Journal Article↗

PubMed2004

Dimensional reduction for a Bayesian filter.

An adaptive strategy is proposed for reducing the number of unknowns in the calculation of a proposal distribution in a sequential Monte Carlo implementation of a Bayesian filter for nonlinear dynamics. The idea is to solve only in directions in which the dynamics is expanding, found adaptively; this strategy is suggested by earlier work on optimal prediction. The construction should be of value in data assimilation, for example, in geophysical fluid dynamics.

Journal Article↗

PubMed1988

Chemical oscillations in closed macromolecular systems.

A cycle of irreversible, first-order, autocatalytic reactions among different states of a polyfunctional macromolecule, subject to the conservation of mass, can display stable chemical oscillations. This introduces a class of nonlinear dynamic models for energy transduction in closed macromolecular systems.

Chemical Phenomena↗

PubMed1999

Self-organized defensive behavior in honeybees.

We investigated the defensive behavior of honeybees under controlled experimental conditions. During an attack on two identical targets, the spatial distribution of stings varied as a function of the total number of stings, evincing the classic "pitchfork bifurcation" phenomenon of nonlinear dynamics. The experimental results support a model of defensive behavior based on a self-organizing mechanism. The model helps to explain several of the characteristic features of the honeybee defensive response: (i) the ability of the colony to localize and focus its attack, (ii) the strong variability between different hives in the intensity of attack, as well as (iii) the variability observed within the same hive, and (iv) the ability of the colony to amplify small differences between the targets.

Journal Article↗

PubMed1989

On task and theory specificity.

One of the significant limitations of the motor control and skill acquisition domain is that the theories, models, and hypotheses are, in most cases, task specific. Many lines of theorizing fail to hold up under even small changes in task constraints, although clearly the field does have some robust phenomena. It is proposed that a broader consideration of the role of task constraints, which is grounded in the methodology of nonlinear dynamics, may help to formulate a more general action theory of coordination and control.

Journal Article↗

PubMedDate not supplied

The use of regularity as estimated by approximate entropy to distinguish saltatory growth.

A nonlinear dynamics metric, approximate entropy (ApEn), is investigated as a diagnostic method for distinguishing between mathematical models, and the underlying mechanistic hypotheses that purport to describe the same time series experimental observations. ApEn measures the occurrence of pattern regularity within a time series, and is used here to investigate growth patterns in daily length growth. The notion investigated is that ApEn distributions for competing time series patterns expressed as mathematical formulations can be modelled by Monte Carlo and bootstrap methods and compared to the ApEn values for an original experimental data series. If the ApEn values for the different models do not overlap, then it is expected that ApEn can be utilized to distinguish these models and hypotheses, and to provide statistical assessment for the underlying biological patterns in experimental data. The conclusion is that the ApEn metric is successful as a time series diagnostic tool. It is a model-independent statistic that clearly differentiates saltatory growth from slowly varying continuous models of growth and serves to further document the saltatory nature of growth. This is a unique application of approximate entropy, illustrating the broad applicability of ApEn to biological time series, with the specific example of discriminating a saltatory growth process in longitudinal growth data. Future investigations of regularity in longitudinal time series in human biology with ApEn statistics are suggested.

Data Interpretation, Statistical↗

PubMedDate not supplied

A developmental model of infantile nystagmus.

The possibility that infantile nystagmus (IN) may reflect a failure in early sensorimotor integration has been proposed for more than a century, but is only recently being borne out in animal studies. The underlying neural and genetic substrate for this plasticity is complex. We propose that, in most cases, IN develops as a developmental response to reduced contrast sensitivity to high-spatial frequencies in an early "critical period," however caused, whether by structural malformations (e.g. foveal hypoplasia) or poor optics (e.g. cataract). As shown by psychophysics, contrast sensitivity to low spatial frequencies is enhanced by motion of the image across the retina. Based on our previous theoretical study (Harris & Berry, Nonlinear Dynamics, 2006), we argue that the best compromise between moving the image and maintaining the image near the fovea (or its remnant) is to oscillate the eyes with jerk nystagmus with increasing velocity waveforms, as seen empirically. The generation of jerk waveforms relies heavily on the saccadic system, which is immature in infancy. Pendular waveforms may therefore provide an alternative to jerk waveforms, and may explain why they are seen more often in young infants. We discuss the implications of this developmental model for the need to synchronize sensory and motor developments in normal development. Failure of this synchronization may also explain some idiopathic cases.

Eye Movements↗

PubMed1993

Fractals and foods.

Fractal geometry and related concepts have had only a very minor impact on food research. The very few reported food applications deal mainly with the characterization of the contours of agglomerated instant coffee particles, the surface morphology of treated starch particles, the microstructure of casein gels viewed as a product limited diffusion aggregation, and the jagged mechanical signatures of crunchy dry foods. Fractal geometry describes objects having morphological features that are scale invariant. A demonstration of the self-similarity of fractal objects can be found in the familiar morphology of cauliflower and broccoli, both foods. Processes regulated by nonlinear dynamics can exhibit a chaotic behavior that has fractal characteristics. Examples are mixing of viscous fluids, turbulence, crystallization, agglomeration, diffusion, and possibly food spoilage.

Chemical Phenomena↗

PubMed2006

Carmeli's S index assesses motion and muscle artefact reduction in rowers' electrocardiograms.

Electrocardiograms (ECG) suffer high perturbations from motion and muscle activities when measured on the chest of rowers. However, for cardiac assessment and sport performance measures, ECG complexes and their time occurrences contain information of great value. We thus propose to use electromyogram (EMG) sensors placed on the distal pectoral muscle to provide a reference signal for motion and muscle activity cancellation. The low frequencies of the EMG signal are conserved for motion cancellation. A combination of band-pass and adaptive filters allows us to recover ECG complexes. This specific scheme is intended to be used for advanced ECG sensors with on-board digital signal processing which requires low-power electronics. A validation of the method is performed based on a nonlinear dynamic model of the ECG and linear frequency modulated rowing movement for various input and output signal-to-noise ratios and adaptive filter gain parameters. Results show a good motion tracking cancellation of the adaptive filter. Finally, assessments of the method on the real recorded data from five subjects are presented. To this end, we have first computed estimates of the signal-to-noise ratio gain between the original and noise-reduced signals. Second, we have developed a modified synchronization index first proposed by Carmeli et al between a QRS template and the original and noise-reduced signals. Both assessment measures are complementary to each other.

Artifacts↗

PubMed2004

Investigating the complexity of respiratory patterns during recovery from severe hypoxia.

Progressive hypoxemia in anesthetized, peripherally chemodenervated piglets results in initial depression of the phrenic neurogram (PN) culminating in phrenic silence and, eventually, gasping. These changes reverse after the 30 min reoxygenation (recovery) period. To determine if changes in the PN patterns correspond to changes in temporal patterning, we have used the approximate entropy (ApEn) method to examine the effects of maturation on the complexity of breathing patterns in chemodenervated, vagotomized and decerebrated piglets during severe hypoxia and reoxygenation. The phrenic neurogram in piglets was recorded during eupnea (normal breathing), severe hypoxia (gasping) and recovery from severe hypoxia in 31 piglets (2-35 days). Nonlinear dynamical analysis of the phrenic neurogram was performed using the ApEn method. The mean ApEn values for a recording of five consecutive breaths during eupnea, a few phrenic neurogram signals during gasping, the beginning of the recovery period, and five consecutive breaths at every 5 min interval for the 30 min recovery period were calculated. Our data suggest that gasping resulted in reduced duration of the phrenic neurogram, and the gasp-like patterns exist at the beginning of the recovery. But, the durations of phrenic neurograms during recovery were increased after 10 min postreoxygenation, but were restored 30 min post recovery. The ApEn (complexity) values of the phrenic neurogram during eupnea were higher than those of gasping and the early (the onset of) recovery from severe hypoxia (p < 0.01), but were not statistically different than 5 min post recovery regardless of the maturation stages. These results suggest that hypoxia results in a reversible reconfiguration of the central respiratory pattern generator.

Adaptation, Physiological↗

PubMed2003

DNA sequence evolution with neighbor-dependent mutation.

We introduce a model of DNA sequence evolution which can account for biases in mutation rates that depend on the identity of the neighboring bases. An analytic solution for this class of models is developed by adopting well-known methods of nonlinear dynamics. Results are presented for the CpG-methylation-deamination process, which dominates point substitutions in vertebrates. The dinucleotide frequencies generated by the model (using empirically obtained mutation rates) match the overall pattern observed in noncoding DNA. A web-based tool has been constructed to compute single- and dinucleotide frequencies for arbitrary neighbor-dependent mutation rates. Also provided is the backward procedure to infer the mutation rates using maximum likelihood analysis given the observed single- and dinucleotide frequencies. Reasonable estimates of the mutation rates can be obtained very efficiently, using generic noncoding DNA sequences as input, after masking out long homonucleotide subsequences. Our method is much more convenient and versatile to use than the traditional method of deducing mutation rates by counting mutation events in carefully chosen sequences. More generally, our approach provides a more realistic but still tractable description of noncoding genomic DNA and may be used as a null model for various sequence analysis applications.

DNA↗