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Results for “Nonlinear Dynamics”

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At least 469 records · Page 26Linked to original sources

PubMed2000

Transverse and longitudinal dynamics of nonlinear intramolecular excitations on multileg ladder lattices.

A model of nonlinear intramolecular excitations on a multileg ladder lattice integrable by the inverse scattering transform is elaborated. The principal question of how to include the interchain linear coupling between excitations in the inverse scattering scheme is solved, and a detailed outline of the inverse scattering technique transforming the initially nonlinear problem into a linear one is given. The model permits a number of physically interesting applications related to striplike and bunchlike biological and condensed matter systems and in its partially continuous form to arrays of linearly and nonlinearly coupled optical fibers. The soliton dynamics across and along the chains for the cases of two-leg and three-leg ladder lattices is analyzed. The effect of an external magnetic field on the transverse dynamics of charged excitations on a three-leg ladder lattice with triangular cross section is studied and circular traveling as well as standing modes supporting the oscillating redistribution of soliton density between the chains are described. From the physical point of view it is reasonable to treat all transverse modes caused by interchain linear couplings as breathing modes, insofar as they correspond to the intrinsic degrees of freedom of a spatially constricted nonlinear wave packet moving uniformly as a whole along the chains.

DNA↗

PubMed2005

Influence of implant/abutment joint designs on abutment screw loosening in a dental implant system.

The objective of this study was to investigate the influence of implant/abutment joint designs on abutment screw loosening in a dental implant system, using nonlinear dynamic analysis of the finite element method (FEM). This finite element simulation study used two dental implant systems: the Ankylos implant system (Degusa Dental, Hanau, German) with a taper joint (taper joint-type model), and the Bränemark implant system (Nobel Biocare, Gothenburg, Sweden) with an external hex joint (external hex joint-type model). The nonlinear dynamic analysis was performed using three-dimensional finite element analysis. In comparing the movement of the taper type-joint model and external hex type-joint model, it was found that the external hex type-joint model had greater movement than the taper type-joint model. The external hex joint-type model showed rotation movement, whereas the movement of the taper joint-type model showed no rotation. It was concluded that the nonlinear dynamic analysis used in this study clearly demonstrated the differences in rotation of components in dental implant systems with taper or external hex joints.

Biocompatible Materials↗

PubMed1989

Signal transformation and coding in neural systems.

The subject of signal transformation and coding in neural systems is fundamental in understanding information processing by the nervous system. This paper addresses this issue at the level of neural units (neurons) using nonparametric nonlinear dynamic models. These models are variants of the general Wiener-Bose model, adapted to this problem as to represent the nonlinear dynamics of neural signal transformation using a set of parallel filters (neuron modes) followed by a binary operator with multiple real-valued operands (equal in number to the number of modes). The postulated model constitutes a reasonable compromise between mathematical complexity and current neurophysiological evidence. It incorporates nonlinear dynamics and spike generation mechanisms in a fairly general, yet parsimonious manner. Although this study has objectives limited to a single unit and represents a small contribution in a vast and complex research area, it is hoped that it will facilitate progress in the systematic study of the functional organization of neural systems with multiple units.

Action Potentials↗

PubMed2001

[Prognostication of the outcome of heart valve prosthesis implantation by the method of nonlinear chaos dynamics of the heart rate].

An examination of 39 patients with heart diseases was performed before and after operations by the method of geometrical analysis of the nonlinear chaos (fractal) variability of the cardiac rhythm on the basis of the apparatus-programmed complex "Poly-spectrum". Five-minute-long registrations of ECG were carried on. On the basis of the data of examination of 195 healthy volunteers the reference norm of this method parameters was determined. Reliably lower parameters were found in patients with the acquired valvular disease. A dynamic investigation of the geometrical nonlinear structure of the cardiac rhythm has shown the possibility to make a prognosis of early complications after prosthetics of the heart valves.

Adult↗

PubMed1999

A characterization of HRV's nonlinear hidden dynamics by means of Markov models.

A study of the 24-h heart rate variability's (HRV) hidden dynamic is performed hour by hour, in order to investigate the evolution of the nonlinear structure of the underlying nervous system. A hierarchy of null hypotheses of nonlinear Markov models with increasing order n is tested against the hidden dynamic of the HRV time series. The minimum accepted Markov order supplies information about the nonlinearity of the HRV's hidden dynamic and consequently of the underlying nervous system. The Markov model with minimum order is detected for each hour of the RR time series extracted from seven 24-h electrocardiogram records of patients in different pathophysiological conditions, some including ventricular tachycardia episodes. Heart rate, pNN30, and LF/HF index plots are reported to serve as a reference for the description of the patient's cardiovascular frame during each examined hour. The minimum Markov order shows to be a promising index for quantifying the average nonlinearity of the autonomic nervous system's activity.

Aged↗

PubMed2004

EEG dynamics in patients with Alzheimer's disease.

Alzheimer's disease (AD) is the most common neurodegenerative disorder characterized by cognitive and intellectual deficits and behavior disturbance. The electroencephalogram (EEG) has been used as a tool for diagnosing AD for several decades. The hallmark of EEG abnormalities in AD patients is a shift of the power spectrum to lower frequencies and a decrease in coherence of fast rhythms. These abnormalities are thought to be associated with functional disconnections among cortical areas resulting from death of cortical neurons, axonal pathology, cholinergic deficits, etc. This article reviews main findings of EEG abnormalities in AD patients obtained from conventional spectral analysis and nonlinear dynamical methods. In particular, nonlinear alterations in the EEG of AD patients, i.e. a decreased complexity of EEG patterns and reduced information transmission among cortical areas, and their clinical implications are discussed. For future studies, improvement of the accuracy of differential diagnosis and early detection of AD based on multimodal approaches, longitudinal studies on nonlinear dynamics of the EEG, drug effects on the EEG dynamics, and linear and nonlinear functional connectivity among cortical regions in AD are proposed to be investigated. EEG abnormalities of AD patients are characterized by slowed mean frequency, less complex activity, and reduced coherences among cortical regions. These abnormalities suggest that the EEG has utility as a valuable tool for differential and early diagnosis of AD.

Alzheimer Disease↗

PubMed2006

Strongly nonlinear wave dynamics in a chain of polymer coated beads.

Strongly nonlinear phononic crystals were assembled from a chain of Parylene-C coated steel spheres in a polytetrafluoroethylene holder. This system exhibits strongly nonlinear properties and extends the range of materials supporting sonic-vacuum-type behavior. The combination of a high density core and a soft (low elastic modulus) coating ensures a relatively low velocity of wave propagation. The bead contact interaction caused by the deformation of the Parylene coating can be described by classical nonlinear elastic Hertz theory with an effective value of the elastic modulus equal to 15 GPa for the contact interaction. Strongly nonlinear solitary waves excited by impacts were investigated experimentally and compared to chains composed of uniform steel beads. Fracture of the polymer coating was detected under relatively large pulse amplitude.

Journal Article↗

PubMed1992

Order and chaos in fixed-interval schedules of reinforcement.

Fixed-interval schedule performance is characterized by high levels of variability. Responding is absent at the onset of the interval and gradually increases in frequency until reinforcer delivery. Measures of behavior also vary drastically and unpredictably between successive intervals. Recent advances in the study of nonlinear dynamics have allowed researchers to study irregular and unpredictable behavior in a number of fields. This paper reviews several concepts and techniques from nonlinear dynamics and examines their utility in predicting the behavior of pigeons responding to a fixed-interval schedule of reinforcement. The analysis provided fairly accurate a priori accounts of response rates, accounting for 92.8% of the variance when predicting response rate 1 second in the future and 64% of the variance when predicting response rates for each second over the entire next interreinforcer interval. The nonlinear dynamics account suggests that even the "noisiest" behavior might be the product of purely deterministic mechanisms.

Journal Article↗

PubMedDate not supplied

Models for diseases with vertical transmission and nonlinear population dynamics.

Vertical transmission, the direct transfer of a disease from an infective parent to a new born offspring, is an important aspect of many diseases. Most of what is known for vertical transmission models assumes birth rates proportional to population size. We consider models with nonlinear population dynamics and finite carrying capacity and analyze the stability of equilibria in the special case in which the overall birth rate does not depend on infective population size.

Female↗

PubMed2003

Signal detection via residence-time asymmetry in noisy bistable devices.

We introduce a dynamical readout description for a wide class of nonlinear dynamic sensors operating in a noisy environment. The presence of weak unknown signals is assessed via the monitoring of the residence time in the metastable attractors of the system, in the presence of a known, usually time-periodic, bias signal. This operational scenario can mitigate the effects of sensor noise, providing a greatly simplified readout scheme, as well as significantly reduced processing procedures. Such devices can also show a wide variety of interesting dynamical features. This scheme for quantifying the response of a nonlinear dynamic device has been implemented in experiments involving a simple laboratory version of a fluxgate magnetometer. We present the results of the experiments and demonstrate that they match the theoretical predictions reasonably well.

Journal Article↗

PubMed2004

Dynamics of gene regulatory networks with cell division cycle.

This paper focuses on modeling and analyzing the nonlinear dynamics of gene regulatory networks with the consideration of a cell division cycle with duplication process of DNA, in particular for switches and oscillators of synthetic networks. We derive two models that may correspond to the eukaryotic and prokaryotic cells, respectively. A biologically plausible three-gene model ( lac, tetR, and cI ) and a repressilator as switch and oscillator examples are used to illustrate our theoretical results. We show that the cell cycle may play a significant role in gene regulation due to the nonlinear dynamics of a gene regulatory network although gene expressions are usually tightly controlled by transcriptional factors.

Animals↗

PubMed2005

Neural network adaptive control for nonlinear nonnegative dynamical systems.

Nonnegative and compartmental dynamical system models are derived from mass and energy balance considerations that involve dynamic states whose values are nonnegative. These models are widespread in engineering and life sciences and typically involve the exchange of nonnegative quantities between subsystems or compartments wherein each compartment is assumed to be kinetically homogeneous. In this paper, we develop a full-state feedback neural adaptive control framework for adaptive set-point regulation of nonlinear uncertain nonnegative and compartmental systems. The proposed framework is Lyapunov-based and guarantees ultimate boundedness of the error signals corresponding to the physical system states and the neural network weighting gains. In addition, the neural adaptive controller guarantees that the physical system states remain in the nonnegative orthant of the state-space for nonnegative initial conditions.

Adaptation, Physiological↗

PubMed1995

Dynamical disease: Identification, temporal aspects and treatment strategies of human illness.

Dynamical diseases are characterized by sudden changes in the qualitative dynamics of physiological processes, leading to abnormal dynamics and disease. Thus, there is a natural matching between the mathematical field of nonlinear dynamics and medicine. This paper summarizes advances in the study of dynamical disease with emphasis on a NATO Advanced Research Worshop held in Mont Tremblant, Quebec, Canada in February 1994. We describe the international effort currently underway to identify dynamical diseases and to study these diseases from a perspective of nonlinear dynamics. Linear and nonlinear time series analysis combined with analysis of bifurcations in dynamics are being used to help understand mechanisms of pathological rhythms and offer the promise for better diagnostic and therapeutic techniques. (c) 1995 American Institute of Physics.

Journal Article↗

PubMed2000

Prediction of short cardiovascular variability signals based on conditional distribution.

A new approach measuring the predictability of a process is proposed. The predictor is defined as the median of the distribution conditioned by a sequence of L - 1 previous samples (i.e., a pattern). A function referred to as the corrected mean squared predictor error is defined to prevent the perfect adequacy to the data (i.e., the decrease to zero of the prediction error), thus avoiding to divide the whole set of data in learning and test sets. This function exhibits a minimum and this minimum is taken as a measure of predictability of the series. The use of the minimization procedure avoids to fix a priori the pattern length L. This approach permits one a reliable measure of predictability on short data sequences (around 300 samples). Moreover, this method, in connection with a surrogate data approach, is useful to detect nonlinear dynamics. The analysis indicates that, in simulated and real data, predictability and nonlinearity measures provide different information. The application of this approach to the analysis of cardiovascular variability series of the heart period (RR interval) and systolic arterial pressure (SAP) shows: 1) SAP series is more predictable than RR interval series; 2) predictability of the RR interval series is larger during tilt, during controlled respiration at 10 breaths/min (bpm) and after high-dose administration of atropine; 3) SAP series is dominated by linear correlation; 4) RR interval series exhibits nonlinear dynamics during controlled respiration at 10 bpm and after low-dose administration of atropine, while it is linear during sympathetic activation produced by tilt and after peripheral parasympathetic blockade caused by high-dose administration of atropine.

Adult↗

PubMed2001

Modeling of chaotic vibrations in symmetric vocal folds.

The chaos mechanism of above-range phonation was examined in symmetrically modeled vocal folds by using the traditional two-mass model assumption. The Poincaré map technique was used to display chaotic attractors. This method provided an effective description of irregular vocal-fold movements. The power spectrum, Lyapunov exponent, and Kaplan-Yorke dimension were employed to describe chaotic vibrations in the vocal-fold model. These nonlinear dynamic analyses suggested that, for the positive Lyapunov exponent, chaotic attractors contribute to irregular vocal-fold vibrations. Descriptions of complicated irregular vibrations of the vocal fold yielded evidence of chaos. To investigate the effects of independent parameters such as subglottal pressure, coupling stiffness, and phonation neutral area, bifurcation diagrams based on the Poincaré map were discussed. The results confirmed that the dynamics of the two-mass model was strongly influenced by independent parameters. Nonlinear dynamic methods were expected to provide useful information for better understanding of irregular vocal-fold vibrations as well as of the dynamic mechanism of above-range phonation in excised larynx experimentation.

Humans↗

PubMed2000

Dynamic, stochastic, and topological aspects of polyrhythmic performance.

Previous research on polyrhythmic performance can be broadly summarized in terms of 2 classes of models: timekeeper models and nonlinear dynamical models. In the former approach, research has been focused on patterns of covariance among time intervals, and in the latter approach, the concentration has been on pattern (in)stability and the spatiotemporal properties of oscillating limbs. It is suggested that one can achieve a more comprehensive theory that incorporates the strengths of each of these approaches by endowing timekeeper models with nonlinear dynamics or by endowing nonlinear oscillator models with stochastic variability. Additionally, those models are complemented by a topological description of performance based on knot theory. Knot theory provides a new index of difficulty for polyrhythmic tapping, a spatial interpretation of transitions between different stable rhythms, and a possible instantiation of N. A. Bernstein's (1967a) notion of a topological motor program.

Attention↗

PubMed1996

The nature of dominant Lyapunov exponent and attractor dimension curves of EEG in sleep.

The dynamical behaviour of the brain is currently being viewed from the perspective of nonlinear dynamics. There are several reports of low dimensional chaotic activity in various states of human behaviour. The time evolution of chaotic systems exhibit many transitional states and brain is known to undergo a number of transitions in sleep. It evolves from random looking states to almost periodic states with an increase in the depth of sleep. There occurs intermittent random-like behaviour in REM (rapid eye movement) sleep. In this paper, we examine the transitional processes of brain activity in sleep from the patterns of attractor dimension (D2) and its corresponding dominant Lyapunov exponent (lambda 1) curves of EEG signals. Results indicate the occurrence of different degrees of chaoticity in the transitional states that may be related to various sleep stages. The chaotic parameter curves yield an objective measure of the neurodynamics of sleep comparable to an hypnogram. The parallelism of D2 and lambda 1 curves implies the validity of Kaplan-Yorke conjecture for EEG. It is suggested that the nonlinear dynamical measures of EEG may yield information about the nature of underlying neural processes of brain in sleep.

Adolescent↗

PubMed2001

Nonlinear temporal dynamics of the cerebral blood flow response.

The linearity of the cerebral perfusion response relative to stimulus duration is an important consideration in the characterization of the relationship between regional cerebral blood flow (CBF), cerebral metabolism, and the blood oxygenation level dependent (BOLD) signal. It is also a critical component in the design and analysis of functional neuroimaging studies. To study the linearity of the CBF response to different duration stimuli, the perfusion response in primary motor and visual cortices was measured during stimulation using an arterial spin labeling technique with magnetic resonance imaging (MRI) that allows simultaneous measurement of CBF and BOLD changes. In each study, the perfusion response was measured for stimuli lasting 2, 6, and 18 sec. The CBF response was found in general to be nonlinearly related to stimulus duration, although the strength of nonlinearity varied between the motor and visual cortices. In contrast, the BOLD response was found to be strongly nonlinear in both regions studied, in agreement with previous findings. The observed nonlinearities are consistent with a model with a nonlinear step from stimulus to neural activity, a linear step from neural activity to CBF change, and a nonlinear step from CBF change to BOLD signal change.

Cerebrovascular Circulation↗