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PubMed2003

Discrete nonlinear dynamics of weakly coupled Bose-Einstein condensates.

The dynamics of a Bose-Einstein condensate trapped in a periodic potential is governed by a discrete nonlinear equation. The interplay/competition between discreteness (introduced by the lattice) and nonlinearity (due to the interatomic interaction) manifests itself on nontrivial dynamical regimes which disappear in the continuum (translationally invariant) limit, and have been recently observed experimentally. We review some recent efforts on this highly interdisciplinary field, with the goal of stimulating interexchanges among the communities of condensed matter, quantum optics, and nonlinear physics.

Journal Article↗
PubMed2003

Scalings of mixed-mode regimes in a simple polynomial three-variable model of nonlinear dynamical systems.

We describe scaling laws for a control parameter for various sequences of bifurcations of the LSn mixed-mode regimes consisting of single large amplitude maximum followed by n small amplitude peaks. These regimes are obtained in a normalized version of a simple three-variable polynomial model that contains only one nonlinear cubic term. The period adding bifurcations for LSn patterns scales as 1/n at low n and as 1/n2 at sufficiently large values of n. Similar scaling laws 1/k at low k and 1/k2 at sufficiently high values of k describe the period adding bifurcations for complex k(LSn)(LS(n + 1)) patterns. A finite number of basic LSn patterns and infinite sequences of complex k(LSn)(LS(n + 1)) patterns exist in the model. Each periodic pattern loses its stability by the period doubling bifurcations scaled by the Feigenbaum law. Also an infinite number of the broken Farey trees exists between complex periodic orbits. A family of 1D return maps constructed from appropriate Poincaré sections is a very fruitful tool in studies of the dynamical system. Analysis of this family of maps supports the scaling laws found using the numerical integration of the model.

Models, Theoretical↗
PubMed2001

[The usefulness of the application of nonlinear dynamics in the analysis of electrocardiograms in Chagas' disease patients].

INTRODUCTION AND OBJECTIVES: The application of nonlinear techniques allows the definition of early risk markers in patients with Chagas infection and without any evidence of cardiac involvement evaluated by standard diagnostic test. Nonlinear modeling techniques have proved to be effective in cardiac rhythm analysis, thereby justifying its use in Chagas' disease. PATIENTS AND METHOD: The routine noninvasive test and heart rate variability analysis were performed in Chagas' disease patients and in a group of healthy subjects. In a second phase we used nonlinear analysis in the evaluation of patients with Chagas infection and no evidence of heart disease, Chagasic patients with minimal electrocardiographic abnormalities and healthy controls. RESULTS: Twenty-four-hour electrocardiographic ambulatory monitoring and heart rate variability allowed us to establish differences between the healthy subjects and patients with Chagas infection without evidence of cardiac disease (p c 0.05 and p <0.005). In sharp contrast nonlinear analysis characterized 4 subgroups in Chagasic patients without cardiac involvement (sensitivity and specificity of 1 00%). CONCLUSIONS: Our findings suggest that nonlinear modeling techniques have a high sensitivity and specificity in the early detection of cardiac involvement and very early autonomic disturbance. We recommend that these techniques be applied to patients with high risk of cardiac disease other than Chagasic myocarditis. Our findings should be corroborated with studies in larger populations. We are currently developing a prospective study to this end.

Adult↗
PubMed2006

Nonlinear dynamics in one dimension: a criterion for coarsening and its temporal law.

We develop a general criterion about coarsening for some classes of nonlinear evolution equations describing one-dimensional pattern-forming systems. This criterion allows one to discriminate between the situation where a coarsening process takes place and the one where the wavelength is fixed in the course of time. An intermediate scenario may occur, namely "interrupted coarsening." The power of the criterion on which a brief account has been given [Politi and Misbah, Phys. Rev. Lett. 92, 090601 (2004)], and which we extend here to more general equations, lies in the fact that the statement about the occurrence of coarsening, or selection of a length scale, can be made by only inspecting the behavior of the branch of steady state periodic solutions. The criterion states that coarsening occurs if lambda'(A)>0 while a length scale selection prevails if lambda'(A)<0, where lambda is the wavelength of the pattern and A is the amplitude of the profile (prime refers to differentiation). This criterion is established thanks to the analysis of the phase diffusion equation of the pattern. We connect the phase diffusion coefficient D(lambda) (which carries a kinetic information) to lambda'(A), which refers to a pure steady state property. The relationship between kinetics and the behavior of the branch of steady state solutions is established fully analytically. Another important and new result which emerges here is that the exploitation of the phase diffusion coefficient enables us to determine in a rather straightforward manner the dynamical coarsening exponent. Our calculation, based on the idea that |D(lambda)| approximately lambda2/t, is exemplified on several nonlinear equations, showing that the exact exponent is captured. We are not aware of another method that so systematically provides the coarsening exponent. Contrary to many situations where the one-dimensional character has proven essential for the derivation of the coarsening exponent, this idea can be used, in principle, at any dimension. Some speculations about the extension of the present results are outlined.

Journal Article↗
PubMed1991

Nonlinear dynamic behavior of the human knee joint--Part I: Postmortem frequency domain analyses.

Characteristics results of postmortem experiments on five knee-joint specimens are reported. The experiments were performed to investigate the applicability of a local linearization technique that would make it possible to describe the dynamic behavior of the joint in terms of transfer functions. The results indicate that the stiffness of the bracing wires, attached to muscle tendons to create a static equilibrium position, can be accounted for when determining the stiffness of the joint. Besides the static equilibrium configuration, the magnitude of the dynamic load and the type of dynamic load applied to the joint can be shown to have their influence. As the influence of the dynamic load is significant, it has to be concluded that in essence the knee joint has to be regarded as a nonlinear system, making application of a Local Linearization Technique questionable. However, when the magnitude of the dynamic load is included as an additional measurement parameter, an indication can be obtained about the behavior of the joint and the degree of nonlinearity.

Biomechanical Phenomena↗
PubMed1975

A topological theorem for nonlinear dynamics in chemical and ecological networks.

A topological theorem is given which places restrictions on the numbers and types of critical points in nonlinear chemical and ecological systems, provided certain stringent conditions on the flows on the boundary of the concentration space are satisfied. The sets of critical points that are found for stable and unstable oscillations, and for competitive exclusion, represent the simplest sets of critical points that satisfy the topological theorem. The restrictions that are imposed on bifurcations of the dynamics are discussed.

Journal Article↗
PubMed1987

Beef cattle feed intake and growth: empirical Bayes derivation of the Kalman filter applied to a nonlinear dynamic model.

Feed intake and growth rate of a single group of growing-finishing feedlot beef cattle are difficult to predict. Subsequent performance can be projected more precisely from past performance of a group of cattle. Using an adaptation of the statistical procedure called the empirical Bayes (EB) derivation of the Kalman filter, estimates from any dynamic model (M) can be adjusted based on past performance. The model may be either linear or nonlinear. With this procedure, predictions of intake and body weight gain are periodically updated by multiplying the estimates from M by statistically weighted factors. These factors are derived from the ratio of performance in each period to the performance predicted by M. For comparison to the EB adjustment, weighting of factors by least-squares (LS) adjustment also was tested to predict subsequent feed intake and gain. The test data base consisted of periodic feed intake and gain observations (usually 28 d) for 200 pens of feedlot steers. Bias of prediction was lower for EB than for M or LS for feed intake and (usually) gain. Intake and gain prediction errors averaged for the whole feeding period were .42 kg/d for intake and .14 kg/d for gain by EB, being .84 and .18 kg/d more precise than M and .12 and .33 kg/d more precise than LS predictions. More than two observations were needed before LS produced accurate prediction but after about 80 d, LS and EB estimates converged. Accuracy of both estimates continued to improve as days on feed increased.(ABSTRACT TRUNCATED AT 250 WORDS)

Animals↗
PubMed1979

Nonlinear dynamics of paleocortex manifested in the olfactory EEG.

The olfactory bulb is the first central component in a highly sensitive yet markedly stable sensory system. It receives a surge of receptor activity with each inspiration and transmits output as a brief burst of oscillatory activity that is most clearly seen in the EEG. These properties together with the known anatomy and physiology of the bulb are used as design criteria to synthesize, evaluate and solve a set of nonlinear differential equations that represent lumped bulbar dynamics. According to the model bulbar processing is in two stages. In the outer layers the interneurons perform the operations of input range compression, integration, clipping, holding, and bias control. In the inner layers the input surge is converted to a burst, which is transmitted by the mitral cells as a pulse density wave. The phase, frequency duration and amplitude of the wave convey information centrally about both the input and the state of the system. The model suffices to replicate the forms of the EEG burst; the pulse probability distributions conditional on the EEG; the waveforms of averaged evoked potentials (AEPs) and post stimulus time (PST) histograms from the bulb and cortex; and the changes in waveform induced by behavioral control of attentiveness and habituation. It is inferred that with selective attention there is a permanent change in the strength of mutually excitatory connections among excitatory neurons, and that with habituation there is a reversible change in the effectiveness of excitatory synapses. The limitations and deficiencies of the model and the need for centrifugal controls of bulbocortical function are discussed.

Action Potentials↗
PubMed2002

Nonlinear dynamics of a zonal flow near marginal stability.

The predator-prey model of the coupled spectral dynamics of drift-wave-zonal-flow turbulence is extended to the regime near the instability threshold. The problem reduces to a nonlinear integral equation, which is similar to that for the mode-particle system [H. L. Berk, Phys. Rev. Lett. 76, 1256 (1996)]], but contains two additional terms due to drift-wave self-nonlinearity. The possibility of pulsating solutions of this equation is investigated. The critical parameter for the Hopf bifurcation and the pulsation period are in reasonable agreement with the bursting behavior recently observed in the global gyrokinetic simulations [Z. Lin, Phys. Rev. Lett. 83, 3545 (1999)]].

Journal Article↗
PubMed1998

Dynamic nonlinear vago-sympathetic interaction in regulating heart rate.

Although the characteristics of the static interactions between the sympathetic and parasympathetic nervous systems in regulating heart rate have been well established, how the dynamic interaction modulates the heart rate response remains unknown. Thus, we investigated the dynamic interaction by estimating the transfer function from nerve stimulation to heart rate, using band-limited Gaussian white noise, in anesthetized rabbits. Concomitant tonic vagal stimulation at 5 and 10 Hz increased the gain of the transfer function relating dynamic sympathetic stimulation to heart rate by 55.0%+/-40.1% and 80.7%+/-50.5%, respectively (P < 0.05). Concomitant tonic sympathetic stimulation at 5 and 10 Hz increased the gain of the transfer function relating dynamic vagal stimulation to heart rate by 18.2%+/-17.9% and 24.1%+/-18.0%, respectively (P < 0.05). Such bidirectional augmentation was also observed during simultaneous dynamic stimulation of the sympathetic and vagal nerves independent of their stimulation patterns. Because of these characteristics, changes in sympathetic or vagal tone alone can alter the dynamic heart rate response to stimulation of the other nerve. We explained this phenomenon by assuming a sigmoidal static relationship between autonomic nerve activity and heart rate. To confirm this assumption, we identified the static and dynamic characteristics of heart rate regulation by a neural network analysis, using large-amplitude Gaussian white noise input. To examine the mechanism involved in the bidirectional augmentation, we increased cytosolic adenosine 3',5'-cyclic monophosphate (cAMP) at the postjunctional effector site by applying pharmacological interventions. The cAMP accumulation increased the gain of the transfer function relating dynamic vagal stimulation to heart rate. Thus, accumulation of cAMP contributes, at least in part, to the sympathetic augmentation of the dynamic vagal control of heart rate.

Animals↗
PubMed1985

A dorsal spinal neural network in cat. III. Dynamic nonlinear analysis of responses to random stimulation of single type 1 cutaneous input fibers.

The input/output characteristics of a subset of dorsal horn neurons in laminae 3 and 4 [( L3,4:SA1,X], see INTRODUCTION; output cells) of cat have previously been examined in the resting unperturbed condition using single or paired input pulses introduced once every three seconds on single slowly adapting type 1 (SA1) cutaneous mechanoreceptor afferent fibers (1, 27, 28). The present study extends this description to the dynamic condition by use of a random-stimulation method developed for the characterization of multiport pulse-input/pulse-output nonlinear systems. A total of 58 SA1 receptor input channels to 29 [L3,4:SA1,X] network output cells were tested individually in 15 spinal cats with several random train stimuli of differing mean input rates [5, 10, 20, 30, 50 pulses per second (pps)]. Simultaneous stimulation of two input channels with independent random trains was performed in 16 units. In each case, zero-, first-, and second-order descriptions of network behavior were obtained; the second-order characteristics of interest were expressed in the form of excitability functions, which are directly comparable with those obtained from condition-test results. Preliminary testing with multiple input pulses suggested that, in addition to the strong second-order effects previously identified, third- and higher-order nonlinearities and effects with long time constants could generate significant rate effects. Nonetheless, first-order response characteristics obtained in the dynamic condition at the lowest mean input rate used (5 pps) were in each case qualitatively identical, though slightly smaller in magnitude, to the poststimulus time histograms (PST) obtained in the unperturbed condition. Second-order excitability functions were generally, but not always, similar to condition-test results in the eight cases in which comparisons were made. Furthermore, use of a complete second-order characterization to predict the output response to a different random input in five cases resulted in an average correlation with the observed output that was a 50% improvement over the linear model predictions. These results indicate strong second-order and weaker higher-order nonlinearities in the [L3,4:SA1,X] network. Three classes of channel-specific second-order excitability characteristics were identified into which the previous descriptions (28) can be incorporated. The general pattern was initial facilitation followed by inhibition. This was observed for both the early and late response components in about half the channels (class I).(ABSTRACT TRUNCATED AT 400 WORDS)

Afferent Pathways↗
PubMed2004

Generation and nonlinear dynamics of X waves of the Schrödinger equation.

The generation of finite-energy packets of X waves is analyzed in normally dispersive cubic media by using an X-wave expansion. The three-dimensional nonlinear Schrödinger model is reduced to a one-dimensional equation with anomalous dispersion. Pulse splitting and beam replenishment as observed in experiments with water and Kerr media are explained in terms of a higher-order breathing soliton. The results presented also hold in periodic media and Bose-condensed gases.

Journal Article↗
PubMedDate not supplied

[The participation of nonlinear dynamic processes in the formation of the high-frequency EEG in the rabbit].

By means of a new method of the EEG analysis, suitable, in contrast to traditional correlative-spectral analysis, for description of nonlinear processes, the informativeness of high-frequency EEG is proved for evaluation of functional brain state. Evidences are obtained in favour to the hypothesis that in the rabbit neocortex and hippocampus EEG a determinate chaotic component is present whose parameters depend on the area of EEG recording and change together with the change of functional brain state.

Animals↗
PubMed1995

Nonlinear dynamics of the voice: Signal analysis and biomechanical modeling.

Irregularities in voiced speech are often observed as a consequence of vocal fold lesions, paralyses, and other pathological conditions. Many of these instabilities are related to the intrinsic nonlinearities in the vibrations of the vocal folds. In this paper, bifurcations in voice signals are analyzed using narrow-band spectrograms. We study sustained phonation of patients with laryngeal paralysis and data from an excised larynx experiment. These spectrograms are compared with computer simulations of an asymmetric 2-mass model of the vocal folds. (c) 1995 American Institute of Physics.

Journal Article↗
PubMed2002

Gap bifurcations in nonlinear dynamical systems.

We investigate the dynamics generated by a type of equation which is common to a variety of physical systems where the undesirable effects of a number of self-consistent nonlinear forces are balanced by an externally imposed controlling harmonic force. We show that the equation presents a new sequence of bifurcations where periodic orbits are created and destroyed in such a nonsimultaneous way that may leave the appropriate phase-space occasionally empty of fundamental harmonic orbits and confined trajectories. A generic analytical model is developed and compared with a concrete physical example.

Journal Article↗
PubMed2005

A quasi-dynamic nonlinear finite element model to investigate prosthetic interface stresses during walking for trans-tibial amputees.

BACKGROUND: To predict the interface pressure between residual limb and prosthetic socket for trans-tibial amputees during walking. METHODS: A quasi-dynamic finite element model was built based on the actual geometry of residual limb, internal bones and socket liner. To simulate the friction/slip boundary conditions between the skin and liner, automated surface-to-surface contact was used. Besides variable external loads and material inertia, the coupling between the large rigid displacement of knee joint and small elastic deformation of residual limb and prosthetic components were also considered. RESULTS: Interface pressure distribution was found to have the same profile during walking. The high pressures fall over popliteal depression, middle patella tendon, lateral tibia and medial tibia regions. Interface pressure predicted by static or quasi-dynamic analysis had the similar double-peaked waveform shape in stance phase. INTERPRETATION: The consideration of inertial effects and motion of knee joint cause 210% average variation of the area between the pressure curve and the horizontal line of pressure threshold between two cases, even though there is only a small change in the peak pressure. The findings in this paper show that the coupling dynamic effects of inertial loads and knee flexion must be considered to study interface pressure between residual limb and prosthetic socket during walking.

Artificial Limbs↗
PubMed2002

Comment on "Localized vortices with a semi-integer charge in nonlinear dynamical lattices".

In a recent paper by Kevrekidis, Malomed, Bishop, and Frantzeskakis [Phys. Rev. E 65, 016605 (2001)] the existence of localized vortices with semi-integer topological charge as exact stationary solutions in a two-dimensional discrete nonlinear Schrödinger model is claimed, as well as the existence of an analog solution in the one-dimensional model. We point out that the existence of such exact stationary solutions would violate fundamental conservation laws, and therefore these claims are erroneous and appear as a consequence of inaccurate numerics. We illustrate the origin of these errors by performing similar numerical calculations using more accurate numerics.

Comment↗