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At least 451 records · Page 25Linked to original sources
PubMed2003

Modulational instability and space-time dynamics in nonlinear parabolic-index optical fibers.

Beam propagation in multimode graded-index parabolic optical fibers in the presence of group-velocity dispersion and Kerr nonlinearity is theoretically investigated. It is shown that a modulational instability arising from the periodic spatial focusing of the beam takes place regardless of the sign of fiber dispersion, leading to a highly nonlinear space-time dynamics and the generation of ultrashort optical pulses.

Journal Article↗
PubMed2004

A nonlinear discrete dynamical model for transcriptional regulation: construction and properties.

Transcriptional regulation is a fundamental mechanism of living cells, which allows them to determine their actions and properties, by selectively choosing which proteins to express and by dynamically controlling the amounts of those proteins. In this article, we revisit the problem of mathematically modeling transcriptional regulation. First, we adopt a biologically motivated continuous model for gene transcription and mRNA translation, based on first-order rate equations, coupled with a set of nonlinear equations that model cis-regulation. Then, we view the processes of transcription and translation as being discrete, which, together with the need to use computational techniques for large-scale analysis and simulation, motivates us to model transcriptional regulation by means of a nonlinear discrete dynamical system. Classical arguments from chemical kinetics allow us to specify the nonlinearities underlying cis-regulation and to include both activators and repressors as well as the notion of regulatory modules in our formulation. We show that the steady-state behavior of the proposed discrete dynamical system is identical to that of the continuous model. We discuss several aspects of our model, related to homeostatic and epigenetic regulation as well as to Boolean networks, and elaborate on their significance. Simulations of transcriptional regulation of a hypothetical metabolic pathway illustrate several properties of our model, and demonstrate that a nonlinear discrete dynamical system may be effectively used to model transcriptional regulation in a biologically relevant way.

Algorithms↗
PubMed1998

Periodic orbits: a new language for neuronal dynamics.

A new nonlinear dynamical analysis is applied to complex behavior from neuronal systems. The conceptual foundation of this analysis is the abstraction of observed neuronal activities into a dynamical landscape characterized by a hierarchy of "unstable periodic orbits" (UPOs). UPOs are rigorously identified in data sets representative of three different levels of organization in mammalian brain. An analysis based on UPOs affords a novel alternative method of decoding, predicting, and controlling these neuronal systems.

Action Potentials↗
PubMed2000

Linear inverse filtering improves spatial separation of nonlinear brain dynamics: a simulation study.

We examined topographic variations in nonlinear measures based on scalp voltages, which were generated by two simulated current dipoles each placed in a different hemisphere of a spherical volume conductor (three-shell model). Dipole dynamics were that of a three-torus and the x-component of the Lorenz-system and scalp voltage were calculated for a configuration of 29 electrode positions. Although estimates for correlation dimension D2 and Lyapunov exponent L1 were close to the theoretical values for the original time series, the simulated scalp voltage data showed almost no topographic resolution of dipole positions. In order to enhance topographic differentiation, we constructed linear inverse filters, to focus on brain activity from a specified brain region. It turned out that the nonlinear measures for the inversely filtered time series were much closer to the expected values (with respect to the location of the dipoles used in the simulation) than when using unfiltered data. Our preliminary results indicate that inverse filtering can improve the topographic resolution of nonlinear scalp EEG estimates.

Brain↗
PubMed2000

A new approach to uncover dynamic phase coordination and synchronization.

Phase attractive maps are an essential mechanism of multi-stable systems such as found in coupled neuronal oscillators. An essential feature of this type of dynamic nonlinear coordination is dynamic phase synchronization. The identification of dynamic phase synchronizations is complicated due to changing frequency ratios of synchronized intervals, other nonstationarities, and noise. In order to overcome these problems the momentary phase relations and their statistics were analyzed by several authors. In this way phase synchronizations also in chaotic and noisy oscillating systems could be uncovered. We propose a novel method which avoids one essential limitation of these approaches, namely the necessity of presetting particular frequency ratios of interest. The proposed novel method was validated by its application to a simulated driven neuronal generator during the transition period between different synchronization modes and to dynamically coupled components of sympathetic nerve discharges.

Action Potentials↗
PubMed1999

Decreased chaos of midbrain dopaminergic neurons after serotonin denervation.

Neuropharmacological investigations aimed at understanding the electrophysiological correlates between drug effect and action potential trains have usually been carried out with the analysis of firing rate and bursting activity. In this study, a selective alteration of neural circuits providing inputs to ventral tegmental area dopaminergic neurons has been produced, and the corresponding electrophysiological correlates have been investigated by nonlinear dynamical analysis. The nonlinear prediction method combined with Gaussian-scaled surrogate data has been used to show the chaotic structure in the time-series corresponding to the electrical activity of ventral tegmental area dopaminergic neurons, extracellularly recorded in vivo. A decrease in chaos of ventral tegmental area dopaminergic neurons was found in a group of rats lesioned with 5,7-dihydroxytryptamine, a neurotoxin which selectively destroys serotonergic terminals. The chaos content of ventral tegmental area dopaminergic neurons in the control group and the decrease of chaos in the lesioned group cannot be explained in terms of standard characteristics of neuronal activity (firing rate, bursting activity). Moreover, in the control group a positive correlation has been found between the density-power-spectrum of the interspike intervals and the chaos content measured by nonlinear prediction S score; this relation was lost in the lesioned group. It is concluded that the impaired serotonergic tone induced by 5,7-dihydroxytryptamine reduces the chaotic behaviour of the dopaminergic cell firing pattern, while retaining many standard interspike interval characteristics. The functional role of this behaviour in a neuronal coding problem context and the implications for the pathophysiology of some mental disorders are discussed.

5,7-Dihydroxytryptamine↗
PubMed1999

Spatiotemporal dynamics of electromagnetic pulses in saturating nonlinear optical media with normal group velocity dispersion.

The nonlinear dynamics of ultrashort optical pulses in nonlinear saturating media with normal group velocity dispersion is examined. The studied saturating nonlinearity changes the sign at the peak intensity of the laser pulses. In the bulk media and the planar wave guides the temporal collapse of the pulse is arrested by its splitting in spatial domain leading to rings formation. The wave collapse in one dimensional geometry cannot be arrested; the field singularity develops for a finite propagation distance.

Journal Article↗
PubMed1999

On the dynamics of nonlinear systems with input constraints.

In this work we deal with the dynamical analysis of nonlinear systems with input constraints. A characterization of the domain of attraction of the region of controllability of an equilibrium point under bounded control is provided and the concept of regions of invariance within such domains of attraction is introduced and characterized. The concepts and results are illustrated through case studies on chemical reactor models. (c) 1999 American Institute of Physics.

Journal Article↗
PubMed2006

Robust fuzzy filter design for nonlinear systems with persistent bounded disturbances.

To date, nonlinear Linfinity-gain filtering problems have not been solved by conventional methods for nonlinear dynamic systems with persistent bounded disturbances. This study introduces a fuzzy filtering design to deal with the nonlinear Linfinity-gain filtering problem. First, the Takagi and Sugeno fuzzy model is employed to approximate the nonlinear dynamic system. Next, based on the fuzzy model, a fuzzy filter is developed to minimize the upper bound of Linfinity-gain of the estimation error under some linear matrix inequality (LMI) constraints. Therefore, the nonlinear Linfinity-gain filtering problem is transformed into a suboptimal filtering problem, i.e., to minimize the upper bound of the Linfinity-gain of the estimation error subject to some LMI constraints. In this situation, the nonlinear Linfinity-gain filtering problem can be easily solved by an LMI-based optimization method. The proposed methods, which efficiently attenuate the peak of estimation error due to persistent bounded disturbances, extend the Linfinity-gain filtering problems from linear dynamic systems to nonlinear dynamic systems.

Algorithms↗
PubMed2006

Multiscale character of the nonlinear coherent dynamics in the Rayleigh-Taylor instability.

We report nonlinear solutions for a system of conservation laws describing the dynamics of the large-scale coherent structure of bubbles and spikes in the Rayleigh-Taylor instability (RTI) for fluids with a finite density ratio. Three-dimensional flows are considered with general type of symmetry in the plane normal to the direction of gravity. The nonlocal properties of the interface evolution are accounted for on the basis of group theory. It is shown that isotropic coherent structures are stable. For anisotropic structures, secondary instabilities develop with the growth rate determined by the density ratio. For stable structures, the curvature and velocity of the nonlinear bubble have nontrivial dependencies on the density ratio, yet their mutual dependence on one another has an invariant form independent of the density ratio. The process of bubble merge is not considered. Based on the obtained results we argue that the large-scale coherent dynamics in RTI has a multiscale character and is governed by two length scales: the period of the coherent structure and the bubble (spike) position.

Journal Article↗
PubMed2006

Target-mediated drug disposition and dynamics.

Nonlinear pharmacokinetics and pharmacodynamics may result from several capacity-limited processes and often represent complicating factors in characterizing the pharmacological properties of drugs. Target-mediated drug disposition (TMDD) corresponds to a special case wherein a significant proportion of a drug (relative to dose) is bound with high affinity to a pharmacological target, such that this interaction is reflected in the pharmacokinetic properties of the drug. Dose-dependent effects on apparent pharmacokinetic parameters may manifest, including the steady-state volume of distribution and total systemic clearance. Although a few small molecular weight compounds have been identified to exhibit TMDD, the incidence of TMDD is likely to increase particularly among emerging biotechnology pharmaceuticals. The goal of this commentary is to describe the basic tenets of TMDD and discuss several mathematical modeling approaches for characterizing this phenomenon. Whereas traditional pharmacokinetic/pharmacodynamic models assume that the amount of the drug-target complex is negligible relative to the total amount of drug in the body, integrated mechanism-based models of TMDD incorporate the binding and stoichiometry of drug-target binding. These models may be utilized to infer the time-course of inaccessible system variables, such as the in vivo density of the drug-target complex, and provide a suitable platform for ascertaining the apparent pharmacodynamic implications of TMDD.

Animals↗
PubMed2003

Linear and nonlinear photoexcitation dynamics in pi-conjugated polymers.

Linear and nonlinear recombination kinetics with various lifetime distributions were identified for long-lived photoexcitations in a series of pi-conjugated polymer films using modulation frequency and excitation intensity dependencies of the photoinduced absorption. This includes monomolecular, bimolecular, and defect-limited recombination processes that lead to saturation. Using generalized kinetics parameters, we found characteristic plots for all recombination processes. Specifically, the bimolecular recombination process shows superlinear intensity dependence away from the steady state; on the contrary, dispersive bimolecular recombination leads to sublinear dependence.

Journal Article↗
PubMed2005

Chaos in voice, from modeling to measurement.

Chaos has been observed in turbulence, chemical reactions, nonlinear circuits, the solar system, biological populations, and seems to be an essential aspect of most physical systems. Chaos may also be central to the interpretation of irregularity in voice disorders. This presentation will summarize the results from a series of our recent studies. These studies have demonstrated the prescence of chaos in computer models of vocal folds, experiments with excised larynges, and human voices. Methods based on nonlinear dynamics can be used to quantify chaos and irregularity in vocal fold vibration. Studies have suggested that disordered voices from laryngeal pathologies such as laryngeal paralysis, vocal polyps, and vocal nodules might exhibit chaotic behaviors. Conventional parameters, such as jitter and shimmer, may be unreliable for analysis of periodic and chaotic voice signals. Nonlinear dynamic methods, however, have differentiated between normal and pathological phonations and can describe the aperiodic or chaotic voice. Chaos theory and nonlinear dynamics can enchance our understanding and therefore our assessment of pathological phonation.

Analysis of Variance↗
PubMed1997

Nonlinear mathematical analysis of the hemodynamic parameters during left ventricular assistance with oscillated blood flow.

For the development of a totally implantable ventricular assist system (VAS), we have been developing the vibrating flow pump (VFP), which can generate oscillated blood flow with a relatively high frequency (10-50 Hz) for a totally implantable system. In this study, effects of left ventricular assistance with this unique oscillated blood flow were analyzed by nonlinear mathematics for evaluation as the entire circulatory regulatory system, not as a separate part of the system. Left heart bypasses using VFPs from the left atriums to the descending aortas were performed in chronic animal experiments using healthy adult goats. Electrocardiogram (ECG), arterial blood pressure, VFP pump flow, and flow of the descending aorta data taken while the goats were awake were recorded in the data recorder and analyzed in the personal computer system through the AD convertor. Using nonlinear mathematics, time series data were embedded into the phase space, and the Lyapunov numerical method, fractal dimension analysis, and power spectrum analysis were performed to evaluate the nonlinear dynamics. During left ventricular assistance with the VFP, Mayer wave fluctuations were decreased in the power spectrum, the fractal dimension of the hemodynamics was significantly decreased, and peripheral vascular resistance was significantly decreased. These results suggest that nonlinear dynamics, which mediate the cardiovascular dynamics, may be affected during LV bypass with oscillated flow. Decreased power of the Mayer wave in the spectrum caused the limit cycle attractor of the hemodynamics and decreased the peripheral resistance. Decreased sympathetic discharges may be the origin of the decreased Mayer wave and fractal dimension. These nonlinear dynamical analyses may be useful to design the optimal VAS control.

Animals↗
PubMed2003

Langevin description of speckle dynamics in nonlinear disordered media.

We formulate a Langevin description of dynamics of a speckle pattern resulting from the multiple scattering of a coherent wave in a nonlinear disordered medium. The speckle pattern exhibits instability with respect to periodic excitations at frequencies Omega below some Omega(max), provided that the nonlinearity exceeds some Omega-dependent threshold. A transition of the speckle pattern from a stationary state to the chaotic evolution is predicted upon increasing nonlinearity. The shortest typical time scale of chaotic intensity fluctuations is of the order of 1/Omega(max).

Journal Article↗
PubMed1999

Chaotic dynamics in circulation with Tohoku University vibrating flow pump.

For the development of a totally implantable ventricular assist system (VAS), we have been developing the vibrating flow pump (VFP), which can generate oscillated blood flow with a relative high frequency (10-50 Hz) for a totally implantable system. In this study, the effects of left ventricular assistance with this unique oscillated blood flow were analyzed by the use of nonlinear mathematics for evaluation as the whole circulatory regulatory system, not as the decomposed parts of the system. Left heart bypasses using the VFP from the left atrium to the descending aorta were performed in chronic animal experiments using healthy adult goats. The ECG, arterial blood pressure, VFP pump flow, and the flow of the descending aorta were recorded in the data recorder during awake conditions and analyzed in a personal computer system through an A-D convertor. By the use of nonlinear mathematics, time series data were embedded into the phase space, the Lyapunov numerical method, fractal dimension analysis, and power spectrum analysis were performed to evaluate nonlinear dynamics. During left ventricular assistance with the VFP, Mayer wave fluctuations were decreased in the power spectrum, the fractal dimension of the hemodynamics was significantly decreased, and peripheral vascular resistance was significantly decreased. These results suggest that nonlinear dynamics, which mediate the cardiovascular dynamics, may be affected during left ventricular (LV) bypass with oscillated flow. The decreased power of the Mayer wave in the spectrum caused the limit cycle attractor of the hemodynamics and decreased peripheral resistance. Decreased sympathetic discharges may be the origin of the decreased Mayer wave and fractal dimension. These nonlinear dynamic analyses may be useful to design optimal VAS control.

Analog-Digital Conversion↗
PubMed2003

Hilbert phase analysis of the dynamics of a semiconductor laser with optical feedback.

The nonlinear dynamics of a semiconductor laser with an optical feedback is studied using Hilbert phase analysis, which reveals interesting facets of the nonlinear dynamical behavior, including the formation and interaction of external cavity modes with increasing external feedback. Here we report measurements on two illustrative cases with very different dynamics; the laser is first biased just near threshold, and then far above threshold. We observe 2pi phase jumps at intervals that are multiples of the external cavity round-trip time, indicating the interaction and transfer of energy between external cavity modes.

Journal Article↗