Search PubMed⌕ Search

SEARCH · Search PubMed

Results for “Nonlinear Dynamics”

Search indexed PubMed citations on genomics, clinical trials, systematic reviews and public health. Explore titles, authors and supplied subject terms, then open the PubMed record.

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

At least 199 records · Page 11Linked to original sources
PubMed2001

Spatial heterogeneity of the nonlinear dynamics in the FMRI BOLD response.

Recent studies of blood oxygenation level dependent (BOLD) signal responses averaged over a region of interest have demonstrated that the response is nonlinear with respect to stimulus duration. Specifically, shorter duration stimuli produce signal changes larger than expected from a linear system. The focus of this study is to characterize the spatial heterogeneity of this nonlinear effect. A series of MR images of the visual and motor cortexes were acquired during visual stimulation and finger tapping, respectively, at five different stimulus durations (SD). The nonlinearity was assessed by fitting ideal linear responses to the responses at each SD. This amplitude, which is constant for different SD in a linear system, was normalized by the amplitude of the response to a blocked design, thus describing the amount by which the stimulus is larger than predicted from a linear extrapolation of the response to the long duration stimulus. The amplitude of the BOLD response showed a nonlinear behavior that varied considerably and consistently over space, ranging from almost linear to 10 times larger than a linear prediction at short SD. In the motor cortex different nonlinear behavior was found in the primary and supplementary motor cortexes.

Adult↗
PubMed2003

Dynamic nonlinear effect on lasing in a random medium.

We have studied both experimentally and numerically the dynamic effect of nonlinearity on lasing in disordered medium. The third-order nonlinearity not only changes the frequency and size of lasing modes, but also modifies the laser emission intensity and laser pulse width. When the nonlinear response time is longer than the lifetime of the lasing mode, the nonlinearity changes the laser output through modifying the size of the lasing mode. When the nonlinear response is faster than the buildup of the lasing mode, positive nonlinearity always extracts more laser emission from the random medium due to the enhancement of single particle scattering.

Journal Article↗
PubMed2006

Nonlinear dynamic range compression deconvolution.

We introduce a dynamic range image compression technique for nonlinear deconvolution; the impulse response of the distortion function and the noisy distorted image are jointly transformed to pump a clean reference beam in a two-beam coupling arrangement. The Fourier transform of the pumped reference beam contains the deconvolved image and its conjugate. In contrast to standard deconvolution approaches, for which noise can be a limiting factor in the performance, this approach allows the retrieval of distorted signals embedded in a very high-noise environment.

Journal Article↗
PubMedDate not supplied

Exploring the nonlinear dynamics of the brain.

The growing need for a better understanding of large-scale brain dynamics has stimulated in the last decade the development of new and more advanced data analysis techniques. Progress in this domain has greatly benefited from developments in nonlinear time series analysis. This review gives a short overview of some of the nonlinear properties one may wish to infer from brain recordings and presents some examples and recent applications.

Brain↗
PubMed1991

Classical chaos and nonlinear dynamics of rays in inhomogeneous media.

An investigation is made of the classical nonlinear resonance and the classical stochastic dynamics of rays in waveguide media with irregular inhomogeneities. Analytic and numerical methods are used to study the characteristics of the ray trajectories, their confinement in a nonlinear resonance, and the development of chaotic behavior in waveguides with longitudinal periodic inhomogeneities. It is established that the localization of the rays has fractal properties; in particular, the cycle length of a ray and the time and velocity of propagation of a signal depend on the initial parameters of the ray in the form of a "devil's staircase." A waveguide with an inhomogeneous index of refraction and a periodically corrugated wall is considered.

Journal Article↗
PubMedDate not supplied

Characterization of state transitions in spatially distributed, chaotic, nonlinear, dynamical systems in cerebral cortex.

The neurons of cerebral cortex are largely autonomous and generate activity that is manifested in trains of microscopic axonal action potentials. The neurons interact by sparse but numerous synaptic connections to generate macroscopic dendritic activity patterns that are observed in electroencephalographic (EEG) waves. The macroscopic patterns are constructed by the populations and they shape the output of cortical neurons in parallel arrays. Sensory cortexes receive sensory information in the form of microscopic action potentials, which induce state transitions in population dynamics. Each state transition transforms sensory information to perceptual meaning. The EEG reflects both kinds of activity. The sensory input is accessed by time ensemble averaging, whereas the perceptual output is found by spatial ensemble averaging. Spatial phase gradients in the EEG are useful for identifying EEG segments in a sequence of state transitions in response to sensory input. The rapidity and flexibility with which they take place give strong reason to postulate that the mechanism for the construction of these sequences of patterns is a dynamical system operating in a chaotic domain.

Action Potentials↗
PubMed2006

Nonlinear dynamics of blood pressure variability after caffeine consumption.

OBJECTIVES: The occurrence of continuous blood pressure (BP) fluctuations is an intrinsic feature of the cardiovascular system and is related to complex cardiovascular mechanisms and environmental stimulations or daily habits such as coffee drinking. The aim of this study was to investigate the effect of caffeine on indices expressing the complex and "chaotic" nonlinear characteristics of BP variability. DESIGN: Fourteen healthy subjects consumed 240 mg of caffeine or placebo according to a randomized, double-blind, crossover design. Continuous radial pressure waveforms were recorded by applanation tonometry at baseline and at 30, 60, 90 and 120 minutes after ingestion of caffeine or placebo. METHODS: Approximate entropy (ApEn) was determined to assess BP irregularity. Detrended fluctuation analysis was also used to quantify the fractal correlation properties of the BP data by estimating the scaling (self-similarity) exponent alpha. Analysis of variance for repeated measurements was used to detect significant changes in the measured variables at 30, 60, 90 and 120 minutes after ingestion of caffeine or placebo. RESULTS: BP fluctuations demonstrated high regularity and predictability as indicated by the low values of ApEn (0.2 +/- 0.3), and they remained unchanged after caffeine ingestion. In contrast, the long-term scaling exponent alpha of the BP time series was significantly increased from 0.99 to 1.04 (p=0.01) after caffeine ingestion, while the placebo induced no significant change. CONCLUSIONS: Caffeine induced greater "randomness" in BP fluctuations, possibly by triggering cardiovascular mechanisms that could not be directly specified but should be investigated in future studies.

Adult↗
PubMed2005

Precise fabrication of nanomaterials: a nonlinear dynamics approach.

Modeling of the precise fabrication in the self-assembling of particles is studied using the nonlinear Langevin equation system. The numerical simulation showed a marked ordering of the particles as a function of time after some induction period. The abnormally enlarged fluctuation was found around the start of the evident ordering. After the fluctuation, a sudden increase of the cluster size was observed. The results corresponded well to the dynamics due to the formation of the critical cluster. The shape of the critical cluster around the enlarged fluctuation was not compact and showed fractal-like structures. The fluctuation of the cluster size around the formation of the critical cluster was explained by the anomalous fluctuation theorem for the generalized Langevin equation. The characterization of the stochastic dynamics of the critical clusters rationalized the concept of dynamic templating for the fabrication technique of the self-assembling of nanoparticles, that is, the structural constraint on the particle assembly by externally adding the resonance frequencies that match with the localized nonlinear vibrational modes of the target structures originating from thermal (Brownian) activation.

Computer Simulation↗