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PubMed1988

Nonlinear identification of stretch reflex dynamics.

The objective of this study was to use nonlinear identification techniques to study the dynamics of stretch reflexes in the human calf muscles (gastrocnemius-soleus). Stochastic perturbations of ankle position were applied while subjects maintained a constant, tonic contraction of gastrocnemius-soleus. Linear models of the relation between ankle velocity and the electromyographic (EMG) activity under these conditions typically accounted for less than 40% of the observed EMG variance. Nonlinear system identification techniques were then applied. The first- and second-order Wiener kernels were computed as the initial stage of this analysis. These did not provide an adequate description of system behavior; subsequent simulation studies showed that the major problem with the Wiener analysis was that the input spectrum was not adequately white. Nevertheless, the shape of the second-order Wiener kernel suggested that a Hammerstein structure consisting of a static nonlinearity followed by a dynamic linear system would be appropriate. Consequently, we used an iterative procedure for Hammerstein system identification to determine the form of the static nonlinearity and the associated linear dynamics. The resulting nonlinear model provided a much better description of the system's behavior than did the linear models (variance accounted for greater than 60%). Furthermore, they confirmed our previous empirical findings; the static nonlinearity closely resembled a half-wave rectifier while the dynamics were typified by a pure delay and a velocity filter. The application of nonlinear identification techniques thus produced a much improved, physically meaningful model of stretch reflex behavior.

Electromyography↗
PubMed1999

Transient nonlinear dielectric relaxation and dynamic Kerr effect from sudden changes of a strong dc electric field: polar and polarizable molecules.

The nonlinear transient response of polar and polarizable particles (macromolecules) diluted in a nonpolar solvent to a sudden change both in magnitude and in direction of a strong external dc field is considered. By averaging the underlying Langevin equation, the infinite hierarchy of differential-recurrence equations for ensemble averages of the spherical harmonics is derived for an assembly of polar and anisotropically polarizable molecules pertaining to the noninertial rotational Brownian motion. On solving this hierarchy, the relaxation functions and relaxation times appropriate to the transient dynamic Kerr effect and nonlinear dielectric relaxation are calculated. The calculations are accomplished using the matrix continued fraction method, which allows us to express exactly the solution of the infinite hierarchy of differential-recurrence relations for the first- and second-order transient responses of the ensemble averages of the spherical harmonics (relaxation functions). The results are then compared with available experimental data and solutions previously obtained for various particular cases.

Journal Article↗
PubMed1999

Nonlinear EEG analysis in early Alzheimer's disease.

Nonlinear EEG analysis attempts to characterize the dynamics of neural networks in the brain. Abnormalities in nonlinear EEG measures have been found repeatedly in Alzheimer's disease (AD). The present study was undertaken to investigate whether these abnormalities could already be found in the early stage of AD. In a representative sample of 49 community-dwelling elderly, Alzheimer's disease was diagnosed in 7 subjects. Correlation dimension (D2) and nonlinear prediction were measured at 16 electrodes and in two different activational states. Also, 10 surrogate data sets were generated for each EEG epoch in order to investigate the presence of nonlinear dynamics. Differences between nonlinear statistics derived from original and from surrogate data sets were expressed as Z-scores. We found lower D2 and higher predictability in the demented subjects compared to the normal subjects. The results obtained with the Z-scores pointed to changed nonlinear dynamics in frontal and temporal areas in demented subjects. However, the major differences between demented and healthy subjects are not due to nonlinearity. From this it appears that linear dynamics change first in the course of AD, followed by changes in nonlinear dynamics.

Aged↗
PubMed2003

Dynamical analysis of the nonlinear growth of the m = n = 1 resistive internal mode.

A dynamical analysis is presented that self-consistently takes into account the motion of the critical layer, in which the magnetic field reconnects, to describe how the m=n=1 resistive internal kink mode develops in the nonlinear regime. The amplitude threshold marking the onset of strong nonlinearities due to a balance between convective and mode coupling terms is identified. We predict quantitatively the early nonlinear growth rate of the m=n=1 mode below this threshold.

Journal Article↗
PubMed1996

Identification of the nonlinear state-space dynamics of the action-perception cycle for visually induced postural sway.

Human subjects standing in a sinusoidally moving visual environment display postural sway with characteristic dynamical properties. We analyzed the spatiotemporal properties of this sway in an experiment in which the frequency of the visual motion was varied. We found a constant gain near 1, which implies that the sway motion matches the spatial parameters of the visual motion for a large range of frequencies. A linear dynamical model with constant parameters was compared quantitatively with the data. Its failure to describe correctly the spatiotemporal properties of the system led us to consider adaptive and nonlinear models. To differentiate between possible alternative structures we directly fitted nonlinear differential equations to the sway and visual motion trajectories on a trial-by-trial basis. We found that the eigenfrequency of the fitted model adapts strongly to the visual motion frequency. The damping coefficient decreases with increasing frequency. This indicates that the system destabilizes its postural state in the inertial frame. This leads to a faster internal dynamics which is capable of synchronizing posture with fast-moving visual environments. Using an algorithm which allows the identification of essentially nonlinear terms of the dynamics we found small nonlinear contributions. These nonlinearities are not consistent with a limit-cycle dynamics, accounting for the robustness of the amplitude of postural sway against frequency variations. We interpret out results in terms of active generation of postural sway specified by sensory information. We derive also a number of conclusions for a behavior-oriented analysis of the postural system.

Humans↗
PubMed2000

Dynamics of quasicollapse in nonlinear Schrodinger systems with nonlocal interactions

We study the effect of nonlocality on some dynamical properties of a self-focusing nonlocal nonlinear Schrodinger system. Using a combination of moment techniques, time dependent variational methods, and numerical simulations, we present evidence in support of the hypothesis that nonlocal attractively interacting condensates cannot collapse under very general forms of the interaction. Instead there appear oscillations of the wave packet with a localized component whose size is of the order of the range of interactions. We discuss the implications of the results to collapse phenomena in Bose-Einstein condensates.

Journal Article↗
PubMed2006

Nonlinear changes in brain dynamics during emergence from sevoflurane anesthesia: preliminary exploration using new software.

BACKGROUND: New software was used during a pilot study of nonlinear changes in the electroencephalogram during emergence from sevoflurane anesthesia. METHODS: Digitized electroencephalographic signals were recorded from bipolar forehead electrodes between 1.2 and 40 k s/sec. Trajectories derived from underlying attractors were displayed continuously, and attractor dimensions were estimated. Observations are reported from 13 patients emerging from sevoflurane anesthesia. RESULTS: Qualitative observations and quantitative analysis of the data demonstrated four dynamical stages during emergence from deep anesthesia to consciousness. CONCLUSIONS: The dynamical stages of emergence from sevoflurane anesthesia into consciousness demonstrate a classic route toward chaos, but the presence of chaos in the conscious state remains unproven. These stages are apparent both pictorially and analytically. Pre-emergent attractor patterns are usually distinctive; their real-time display could be a useful adjunct to depth of anesthesia monitors because they may provide warning of an imminent return to consciousness.

Adult↗
PubMed2002

Joint stiffness of the ankle and the knee in running.

The spring-mass model is a valid fundament to understand global dynamics of fast legged locomotion under gravity. The underlying concept of elasticity, implying leg stiffness as a crucial parameter, is also found on lower motor control levels, i.e. in muscle-reflex and muscle-tendon systems. Therefore, it seems reasonable that global leg stiffness emerges from local elasticity established by appropriate joint torques. A recently published model of an elastically operating, segmented leg predicts that proper adjustment of joint elasticities to the leg geometry and initial conditions of ground contact provides internal leg stability. Another recent study suggests that in turn the leg segmentation and the initial conditions may be a consequence of metabolic and bone stress constraints. In this study, the theoretical predictions were verified experimentally with respect to initial conditions and elastic joint characteristics in human running. Kinematics and kinetics were measured and the joint torques were estimated by inverse dynamics. Stiffnesses and elastic nonlinearities describing the resulting joint characteristics were extracted from parameter fits. Our results clearly support the theoretical predictions: the knee joint is always stiffer and more extended than the ankle joint. Moreover, the knee torque characteristic on the average shows the higher nonlinearity. According to literature, the leg geometry is a consequence of metabolic and material stress limitations. Adapted to this given geometry, the initial joint angle conditions in fast locomotion are a compromise between metabolic and control effort minimisation. Based on this adaptation, an appropriate joint stiffness ratio between ankle and knee passively safeguards the internal leg stability. The identified joint nonlinearities contribute to the linearisation of the leg spring.

Adult↗
PubMed2003

Photoexcited breathers in conjugated polyenes: an excited-state molecular dynamics study.

pi-conjugated polymers have become an important class of materials for electronic devices. Design of these devices requires understanding such processes as photochemical reactions, spatial dynamics of photoexcitations, and energy and charge transport, which in turn involve complex coupled electron-vibrational dynamics. Here we study nonlinear photoexcitation dynamics in the polyene oligomers by using a quantum-chemical method suitable for the simulation of excited-state molecular dynamics in extended molecular systems with sizes up to hundreds of atoms. The method is based on the adiabatic propagation of the ground-state and transition single-electron density matrices along the trajectory. The simulations reveal formation of a self-localized vibronic excitation ("breather" or multiquanta bound state) with a typical period of 34 fs and allows us to identify specific slow and fast nuclear motions strongly coupled to the electronic degrees of freedom. The effect of chain imperfections and chemical defects on the dynamics is also investigated. A complementary two-dimensional analysis of corresponding transition density matrices provides an efficient way to monitor time-dependent real-space localization of the photoexcitation by identifying the underlying changes in charge densities and bond orders. Possible correlated electronic and vibrational spectroscopic signatures of photoexcited breathers are predicted, and generalizations to energy localization in complex macromolecules are discussed.

Algorithms↗
PubMed1981

Some aspects of modern population mathematics.

"The purpose of this paper is to survey a number of the technical tools and models that have found use in the study of human and other populations, and to indicate some problems of current interest. These tools and models are varied: integral equations, nonlinear oscillations, differential geometry, dynamical systems, nonlinear operation, bifurcation theory, semigroup theory, martingale theory, Markov processes, diffusion processes, branching processes, ergodic theory, prediction theory and state-space models. A fairly extensive bibliography is provided. Also an Appendix has been added describing the analysis of a classical entomological data set." (summary in FRE)

Demography↗
PubMed2003

Impulse response due to jumping on shoes of various stiffness and damping.

The human body is a dynamic system with dynamic behaviour. Linear and nonlinear models of a standing human are investigated. The models simulated the body by 15-lumped masses connected by springs and dampers. A square wave impulse input is applied at the shoes and the lumbar spine response is presented as an example. The results show that the mechanical response is affected by the kind of representation (linear or nonlinear model) and the shoes stiffness and damping coefficients.

Computer Simulation↗
PubMed2001

Coherent nonlinear spectroscopy: from femtosecond dynamics to control.

This review focuses on the study of the dynamics of isolated molecules and their control using coherent nonlinear spectroscopic methods. Emphasis is placed on topics such as bound-to-free excitation and the study of concerted elimination reactions, free-to-bound excitation and the study of bimolecular reactions, and bound-to-bound excitation and the study of intramolecular rovibrational dynamics and coherence relaxation. For each case the detailed time-resolved information reveals possible strategies to control the outcome. Experimental results are shown for each of the reactions discussed. The methods discussed include pump-probe and four-wave mixing processes such as transient grating and photon echo spectroscopy. Off-resonance transient-grating experiments are shown to be ideal for the study of ground state dynamics, molecular structure, and the molecular response to strong field excitation.

Journal Article↗
PubMedDate not supplied

[Nonlinear effects on population dynamics related to age structure and fishery impact].

Population dynamics of commercial fish populations with an age structure was studied by the example of salmons. The relationship between the amount of catch on fishing efforts and total abundance of a stock fished is described by a nonlinear "trophic" function. Special attention is given to the analysis of population dynamics stability under conditions for maximum profit. Simulation results are compared to statistical data on the catch of Pacific salmon species in the Bering Sea.

Age Factors↗
PubMed2000

Pathological tremors: Deterministic chaos or nonlinear stochastic oscillators?

Pathological tremors exhibit a nonlinear oscillation that is not strictly periodic. We investigate whether the deviation from periodicity is due to nonlinear deterministic chaotic dynamics or due to nonlinear stochastic dynamics. To do so, we apply various methods from linear and nonlinear time series analysis to tremor time series. The results of the different methods suggest that the considered types of pathological tremors represent nonlinear stochastic second order processes. Finally, we evaluate whether two earlier proposed features capturing nonlinear effects in the time series allow for a discrimination between two pathological forms of tremor for a much larger sample of time series than previously investigated. (c) 2000 American Institute of Physics.

Journal Article↗
PubMed1995

Information processing in neural networks by means of controlled dynamic regimes.

This paper is concerned with the modeling of neural systems regarded as information processing entities. I investigate the various dynamic regimes that are accessible in neural networks considered as nonlinear adaptive dynamic systems. The possibilities of obtaining steady, oscillatory or chaotic regimes are illustrated with different neural network models. Some aspects of the dependence of the dynamic regimes upon the synaptic couplings are examined. I emphasize the role that the various regimes may play to support information processing abilities. I present an example where controlled transient evolutions in a neural network, are used to model the regulation of motor activities by the cerebellar cortex.

Cerebellum↗
PubMed2004

Freezing of nonlinear Bloch oscillations in the generalized discrete nonlinear Schrödinger equation.

The dynamics in a nonlinear Schrödinger chain in a homogeneous electric field is studied. We show that discrete translational invariant integrability-breaking terms can freeze the Bloch nonlinear oscillations and introduce new faster frequencies in their dynamics. These phenomena are studied by direct numerical integration and through an adiabatic approximation. The adiabatic approximation allows a description in terms of an effective potential that greatly clarifies the phenomena.

Journal Article↗
PubMed1994

Volume-pressure curve of the respiratory system predicts effects of PEEP in ARDS: "occlusion" versus "constant flow" technique.

The effects of positive end-expiratory pressure (PEEP) on static ("rapid airway occlusion" technique) and dynamic ("constant flow" technique) volume-pressure (V-P) curves were studied in 19 patients with adult respiratory distress syndrome (ARDS). To describe the shape of both curves, the nonlinear coefficient of a second-order polynomial equation fitted to the static (static nonlinear coefficient) and dynamic (dynamic nonlinear coefficient) V-P curves on zero end-expiratory pressure (ZEEP) was used. Two distinct patterns were observed: (1) in ten patients, the static and dynamic V-P curves on ZEEP exhibited a convex shape with a progressive decrease in slope with increasing inflation volume (nonlinear coefficients: negative). In these patients PEEP induced a volume displacement along the static and dynamic V-P curves on ZEEP (hyperinflation). (2) In nine patients, the static and dynamic V-P curves on ZEEP showed a concave shape with a progressive increase in slope with increasing volume (nonlinear coefficients: positive) and PEEP shifted both curves upward along the volume axis (alveolar recruitment). A correlation (p < 0.0001) between static and dynamic nonlinear coefficients was found at all levels of PEEP. Both static and dynamic nonlinear coefficients on ZEEP were correlated (p < 0.0001) with the amount of lung volume recruited with PEEP, and the variations of cardiac index (CI), O2 delivery (DO2), right-to-left venous admixture (Qs/Qt), and PaO2 with PEEP. Besides, the effects of PEEP on Cl, DO2, Qs/Qt, and PaO2 were less pronounced (p < 0.001) in patients with convex V-P curves than in patients with concave V-P curves.(ABSTRACT TRUNCATED AT 250 WORDS)

Aged↗