PubMed Health⌕ Search

SEARCH · PubMed Health

Results for “Nonlinear Dynamics”

Explore indexed PubMed citations for clinical trials, systematic reviews and public health research. Read source abstracts and follow each citation to its original PubMed record.

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

At least 397 records · Page 22Linked to original sources
PubMed2002

Quantum-classical transition in nonlinear dynamical systems.

Viewed as approximations to quantum mechanics, classical evolutions can violate the positive semidefiniteness of the density matrix. The nature of the violation suggests a classification of dynamical systems based on classical-quantum correspondence; we show that this can be used to identify when environmental interaction (decoherence) will be unsuccessful in inducing the quantum-classical transition. In particular, the late-time Wigner function can become positive without any corresponding approach to classical dynamics. In the light of these results, we emphasize key issues relevant for experiments studying the quantum-classical transition.

Journal Article↗
PubMed2005

Nonlinear dynamics of a flow-focusing bubble generator: an inverted dripping faucet.

We describe the rich dynamic behavior--including period-doubling and period-halving bifurcations, intermittency, and chaos--observed in the breakup of an inviscid fluid in a coflowing, viscous liquid, both confined in a microfabricated flow-focusing geometry. Experimental observations support inertia-dominated dynamics of the interface, and suggest the possible similarity to the dynamics of a topologically inverted counterpart of this system, that is, a dripping faucet.

Journal Article↗
PubMed2006

Conical emission, pulse splitting, and X-wave parametric amplification in nonlinear dynamics of ultrashort light pulses.

The precise observation of the angle-frequency spectrum of light filaments in water reveals a scenario incompatible with current models of conical emission (CE). Its description in terms of linear X-wave modes leads us to understand filamentation dynamics requiring a phase- and group-matched, Kerr-driven four-wave-mixing process that involves two highly localized pumps and two X waves. CE and temporal splitting arise naturally as two manifestations of this process.

Journal Article↗
PubMed1995

A nonlinear dynamical systems analysis of fricative consonants.

Acoustic waveforms of the strident fricatives /s/, /z/, /integral of/, and /3/ spoken by two native American English speakers are analyzed using modern chaotic analysis techniques. Fricative data are extracted from both intervocalic and sustained utterances. For comparison, acoustic waveforms of the vowels /a/, /i/, and /u/ are also analyzed. For 44% of the unvoiced fricative tokens in VCV contexts and 59% of the sustained voiced fricatives, indications of low-dimensional dynamics could be found with the given limitations of stationarity. The low-dimensional chaotic behavior is exhibited by a correlation dimension (D2) ranging between 3 and 7.2, and by positive maximum Lyapunov exponents (LEs). For the remaining fricatives, results suggest that the dimensional complexity therein is greater than the maximum D2 value that could be reliably estimated from the available data (about 7.8 for the intervocalic cases and 9 for the sustained cases). Intervocalic voiced fricatives are excluded from the analysis due to stationarity requirements. Analysis of vowels, on the other hand, indicates nonchaotic behavior demonstrated by folded limit cycles and nonpositive maximum LEs; this is consistent with results of previous studies. Findings are interpreted in terms of posited articulatory and aerodynamic parameters of turbulence in the production of fricative consonants.

Humans↗
PubMed1992

Three ways of abolishing automaticity in sinoatrial node: ionic modeling and nonlinear dynamics.

A review of the experimental literature reveals that there are essentially three qualitatively different ways in which spontaneous activity in the sinoatrial node can be abolished. We show that these three ways also occur in an ionic model of space-clamped nodal membrane. In one of these three ways, injection of a current pulse abolishes ("annihilates") spontaneous action potential generation. In the other two ways, as some parameter is changed, one sees a sequence of qualitative changes in the behavior of the membrane as it is brought to quiescence. In one of these two ways there are incrementing prepotentials intermixed with action potentials, with a maintained small-amplitude subthreshold oscillation being the limiting case of such behavior. Thus both experimental and modeling work indicate that the number of ways in which spontaneous activity can be abolished, or initiated, in the sinoatrial node is limited. The classification into three ways is based on ideas drawn from the qualitative theory of differential equations, which are introduced. The classification scheme can be extended to encompass behaviors seen in other cardiac oscillators.

Animals↗
PubMed1997

Nonlinear dynamics of the frequency locking of baroreceptor and sympathetic rhythms.

We used phase plane analysis to identify modes of frequency locking of the 10-Hz rhythm in sympathetic nerve discharge (SND) to the cardiac cycle in urethan-anesthetized, baroreceptor-innervated cats. Frequency locking occurred in rational ratios predicted by a generic mathematical construct called the Farey tree. Both simple harmonic ratios (e.g., 1:3) and complex ratios (e.g., 2:5) comprised of relatively prime integers (no common divisor) were identified under natural conditions. Frequency locking in such ratios is attributed to forcing of the 10-Hz oscillator by pulse-synchronous baroreceptor afferent nerve activity (BNA). Ventricular pacing changed the frequency of the 10-Hz rhythm as well as heart rate so as to maintain or change the ratio of frequency locking in a predictable way. Intriguingly, frequency locking of the 10-Hz rhythm to medullary raphe sympathoinhibitory stimuli in simple harmonic ratios was accompanied by increased power in the 10-Hz band of SND, whereas locking in complex ratios led to decreased 10-Hz power. These findings raise the possibility that pulse-synchronous BNA also exerts divergent actions on the 10-Hz rhythm depending on the ratio of frequency locking. Augmented 10-Hz power can be attributed to the resonant properties of oscillators that are periodically forced at the same phase in their cycle.

Activity Cycles↗
PubMed1990

Nonlinear dynamics of rate-dependent activation in models of single cardiac cells.

Recent studies in isolated cardiac tissue preparations have demonstrated the applicability of a one-dimensional difference equation model describing the global behavior of a driven nonpacemaker cell to the understanding of rate-dependent cardiac excitation. As a first approximation to providing an ionic basis to complex excitation patterns in cardiac cells, we have compared the predictions of the one-dimensional model with those of numerical simulations using a modified high-dimensional ionic model of the space-clamped myocyte. Stimulus-response ratios were recorded at various stimulus magnitudes, durations, and frequencies. Iteration of the difference equation model reproduced all important features of the ionic model results, including a wide spectrum of stimulus-response locking patterns, period doubling, and irregular (chaotic) dynamics. In addition, in the parameter plane, both models predict that the bifurcation structure of the cardiac cell must change as a function of stimulus duration, because stimulus duration modifies the type of supernormal excitability present at short diastolic interval. We conclude that, to a large extent, the bifurcation structure of the ionic model under repetitive stimulation can be understood by two functions: excitability and action potential duration. The characteristics of these functions depend on the stimulus duration.

Action Potentials↗
PubMed1994

Nonlinear dynamic processes in open single enzyme systems.

Chemical oscillations are predicted theoretically in single enzyme systems open to substrate containing a regulatory enzyme, which shows a slow substrate activation. The time-evolution of the system is well described by two ordinary differential equations. The conditions for oscillations or overshoot phenomena of the substrate concentration were analysed by numerical simulation. The existence of damped oscillations or overshoot phenomena in a regulatory enzyme reaction, open to substrate, has been proved experimentally in the pyruvate decarboxylase reaction and in the pyruvate dehydrogenase reaction. In both cases the concentration of the substrate pyruvate shows a strongly damped oscillation in a concentration range below the Km-value.

Binding Sites↗
PubMed2004

Nonlinear dynamic buckling of stiffened plates under in-plane impact load.

This paper presents a simple solution of the dynamic buckling of stiffened plates under in-plane impact loading. Based on large deflection theory, a discretely stiffened plate model has been used. The tangential stresses of stiffeners and in-plane displacement are neglected. Applying the Hamilton's principle, the motion equations of stiffened plates are obtained. The deflection of the plate is taken as Fourier series, and using Galerkin method the discrete equations can be deduced, which can be solved easily by Runge-Kutta method. The dynamic buckling loads of the stiffened plates are obtained form Budiansky-Roth criterion.

Journal Article↗