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Results for “Nonlinear Dynamics”

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At least 181 records · Page 10Linked to original sources
PubMed2004

Periodic precursors of nonlinear dynamical transitions.

We study the resonant response of a nonlinear system to external periodic perturbations. We show by numerical simulation that the periodic resonance curve may anticipate the dynamical instability of the unperturbed nonlinear periodic system, at parameter values far away from the bifurcation points. In the presence of noise, the buried intrinsic periodic dynamics can be picked out by analyzing the system's response to periodic modulation of appropriate intensity.

Journal Article↗
PubMed2000

Nonlinear dynamics of heart rate variability during experimental hemorrhage in ketamine-anesthetized rats.

Indexes of heart rate variability (HRV) based on linear stochastic models are independent risk factors for arrhythmic death (AD). An index based on a nonlinear deterministic model, a reduction in the point correlation dimension (PD2i), has been shown in both animal and human studies to have a higher sensitivity and specificity for predicting AD. Dimensional reduction subsequent to transient ischemia was examined previously in a simple model system, the intrinsic nervous system of the isolated rabbit heart. The present study presents a new model system in which the higher cerebral centers are blocked chemically (ketamine inhibition of N-methyl-D-aspartate receptors) and the system is perturbed over a longer 15-min interval by continuous hemorrhage. The hypothesis tested was that dimensional reduction would again be evoked, but in association with a more complex relationship between the system variables. The hypothesis was supported, and we interpret the greater response complexity to result from the larger autonomic superstructure attached to the heart. The complexities observed in the nonlinear heartbeat dynamics constitute a new genre of autonomic response, one clearly distinct from a hardwired reflex or a cerebrally determined defensive reaction.

Anesthesia↗
PubMed2005

Nonlinear dynamics of homeothermic temperature control in skunk cabbage, Symplocarpus foetidus.

Certain primitive plants undergo orchestrated temperature control during flowering. Skunk cabbage, Symplocarpus foetidus, has been demonstrated to maintain an internal temperature of around 20 degrees C even when the ambient temperature drops below freezing. However, it is not clear whether a unique algorithm controls the homeothermic behavior of S. foetidus, or whether such an algorithm might exhibit linear or nonlinear thermoregulatory dynamics. Here we report the underlying dynamics of temperature control in S. foetidus using nonlinear forecasting, attractor and correlation dimension analyses. It was shown that thermoregulation in S. foetidus was governed by low-dimensional chaotic dynamics, the geometry of which showed a strange attractor named the "Zazen attractor." Our data suggest that the chaotic thermoregulation in S. foetidus is inherent and that it is an adaptive response to the natural environment.

Araceae↗
PubMed2001

Nonlinear dynamic analysis of the EEG in patients with Alzheimer's disease and vascular dementia.

To assess nonlinear EEG activity in patients with Alzheimer's disease (AD) and vascular dementia (VaD), the authors estimated the correlation dimension (D2) and the first positive Lyapunov exponent (L1) of the EEGs in both patients and age-matched healthy control subjects. EEGs were recorded in 15 electrodes from 12 AD patients, 12 VaD patients, and 14 healthy subjects. The AD patients had significantly lower D2 values than the normal control subjects, (P < H > 0.05), except at the F7 and the O1 electrodes, and the VaD patients, except at the C3 and the C4 electrodes. The VaD patients had relatively increased values of D2 and L1 compared with the AD patients, and rather higher values of D2 than the normal control subjects at the F7, F4, F8, Fp2, O1, and O2 electrodes. The L1 values of the EEGs were also lower for the AD patients than for the normal control subjects, except in the O1 and the O2 channels, and for the VaD patients at all electrodes. The L1 values were higher for the VaD patients than for the normal control subjects (F3, F4, F8, O1, and O2). In addition, the authors detected that the VaD patients had an uneven distribution of D2 values over the regions than the AD patients and the normal control subjects, although the statistics do not confirm this. By contrast, AD patients had uniformly lower D2 values in most regions, indicating that AD patients have less complex temporal characteristics of the EEG in entire regions. These nonlinear analyses of the EEG may be helpful in understanding the nonlinear EEG activity in AD and VaD.

Aged↗
PubMed1998

Linear and nonlinear dynamics and the pathophysiology of shock.

Rapid progress has been made in the use of linear and nonlinear time series analysis of heart rate and blood pressure variability as an indicator of disease severity and prognosis for patients in shock. Clinical and experimental studies have demonstrated the potential for linear and nonlinear measurements as a method for quantifying changes in neuroautonomic cardiovascular regulatory mechanisms. These measures have been demonstrated to correlate with severity of illness and outcome for critically ill and injured patients, including those with shock. These powerful mathematical techniques may allow for new insights into the pathophysiology of shock. In addition, these measures may also enable detection of early changes in neuroautonomic cardiovascular regulatory mechanisms during the development of shock before the onset of overt hypotension and inadequate tissue perfusion or may be used to assess the response to therapy. Further studies are needed to establish the role of these tools in clinical use.

Animals↗
PubMed1998

The role of nonlinear dynamics of the syrinx in the vocalizations of a songbird.

Birdsong is characterized by the modulation of sound properties over a wide image of timescales. Understanding the mechanisms by which the brain organizes this complex temporal behaviour is a central motivation in the study of the song control and learning system. Here we present evidence that, in addition to central neural control, a further level of temporal organization is provided by nonlinear oscillatory dynamics that are intrinsic to the avian vocal organ. A detailed temporal and spectral examination of song of the zebra finch (Taeniopygia guttata) reveals a class of rapid song modulations that are consistent with transitions in the dynamical state of the syrinx. Furthermore, in vitro experiments show that the syrinx can produce a sequence of oscillatory states that are both spectrally and temporally complex in response to the slow variation of respiratory or syringeal parameters. As a consequence, simple variations in a small number of neural signals can result in a complex acoustic sequence.

Animals↗
PubMed2001

Nonlinear dynamics of higher-order solitons near the oscillatory instability threshold.

Nonlinear theory describing the dynamics of solitons in the vicinity of oscillatory instability threshold with a low frequency offset is developed. The theory is tested on the example of parametric degenerate four-wave mixing. All major predictions of our theory are in agreement with the results of direct numerical modeling. This includes the position of oscillatory instability threshold, instability rates, and various instability development scenarios.

Journal Article↗
PubMed2004

Continuous weak measurement and nonlinear dynamics in a cold spin ensemble.

A weak continuous quantum measurement of an atomic spin ensemble can be implemented via Faraday rotation of an off-resonance probe beam, and may be used to create and probe nonclassical spin states and dynamics. We show that the probe light shift leads to nonlinearity in the spin dynamics and limits the useful Faraday measurement window. Removing the nonlinearity allows a nonperturbing measurement on the much longer time scale set by decoherence. The nonlinear spin Hamiltonian is of interest for studies of quantum chaos and real-time quantum state estimation.

Journal Article↗
PubMed1990

Comparisons of the nonlinear dynamics of electroencephalograms under various task loading conditions: a preliminary report.

Comparison of the characteristics of electroencephalogram (EEG) records treated as realizations from a nonlinear process were compared under four different conditions: eyes shut resting, and three silent observation instructions to predict the patterns of randomly generated lights which illuminated every 10 seconds. The correlation dimension of the EEG was calculated by a method involving finding the correlation integral in m-dimensional space, and found to show some variations within time series. The degree and directions of changes in the dimensionality of the process varied between observers and did not clearly confirm some earlier reported findings, but it is demonstrable that the measures of nonlinear brain dynamics can be correlated with psychological variables. Reasons for this are discussed.

Adult↗
PubMed1995

Nonlinear dynamics in pulsatile secretion of parathyroid hormone in normal human subjects.

In many biological systems, information is transferred by hormonal ligands, and it is assumed that these hormonal signals encode developmental and regulatory programs in mammalian organisms. In contrast to the dogma of endocrine homeostasis, it could be shown that the biological information in hormonal networks is not only present as a constant hormone concentration in the circulation pool. Recently, it has become apparent that hormone pulses contribute to this hormonal pool, which modulates the responsiveness of receptors within the cell membrane by regulation of the receptor synthesis, movement within the membrane layer, coupling to signal transduction proteins and internalization. Phase space analysis of dynamic parathyroid hormone (PTH) secretion allowed the definition of a (in comparison to normal subjects) relatively quiet "low dynamic" secretory pattern in osteoporosis, and a "high dynamic" state in hyperparathyroidism. We now investigate whether this pulsatile secretion of PTH in healthy men exhibits characteristics of nonlinear determinism. Our findings suggest that this is conceivable, although on the basis of presently available data and techniques, no proof can be established. Nevertheless, pulsatile secretion of PTH might be a first example of nonlinear deterministic dynamics in an apparently irregular hormonal rhythm in human physiology. (c) 1995 American Institute of Physics.

Journal Article↗