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Results for “Nonlinear Dynamics”

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PubMed2000

Chaotic dynamics of coupled transverse-longitudinal plasma oscillations in magnetized plasmas.

The propagation of intense electromagnetic waves in cold magnetized plasma is tackled through a relativistic hydrodynamic approach. The analysis of coupled transverse-longitudinal plasma oscillations is performed for traveling plane waves. When these waves propagate perpendicularly to a static magnetic field, the model is describable in terms of a nonlinear dynamical system with 2 degrees of freedom. A constant of motion is obtained and the powerful classical mechanics methods can be used. A new class of solutions, i.e., the chaotic solutions, is discovered by the Poincaré surface of sections. As a result, coupled transverse-longitudinal plasma oscillations become aperiodically modulated.

Journal Article↗

PubMedDate not supplied

[The effect of microwaves on the bioelectric brain activity].

The experiments on rats have shown that the effect of millimeter range electromagnetic radiation on the bioelectric brain activity is dependent on the initial functional state of central nervous system. Microwaves are able to cause a nonspecific electroencephalographic reaction of synchronization and probably the lower the bioelectric brain process dynamics of active rats. Enrichment of electrocorticograms with high-frequency rhythms and increase in degree of bioelectric brain dynamics can be observed in narcosis conditions. The appearance of biological resonance in the brain of narcotized rats preliminary injected aminazin by pulse-modulated microwaves is noted. This is expressed as epileptiform convulsive activity in electrocorticogram. It has been shown that the nonlinear dynamics method may provide a reliable characterization of changing bioelectric brain activity under of nonionized electromagnetic fields. It is possible to modulate the bioelectric brain activity by microwaves to change the functional state of central nervous system and probably of the whole organism.

Alpha Rhythm↗

PubMed2004

Theory of gaseous detonations.

The objective of the present paper is to review some developments that have occurred in detonation theory over the last ten years. They concern nonlinear dynamics of detonation fronts, namely patterns of pulsating and/or cellular fronts, selection of the cell size, dynamical self-quenching, direct (blast) or spontaneous initiation, and transition from deflagration to detonation. These phenomena are all well documented by experiments since the sixties but remained unexplained until recently. In the first part of the paper, the patterns of cellular detonations are described by an asymptotic solution to nonlinear hyperbolic equations (reactive Euler equations) in the form of unsteady (sometime chaotic) and multidimensional traveling-waves. In the second part, turning points of quasi-steady solutions are shown to correspond to critical conditions of fully unsteady problems, either for (direct or spontaneous) initiation or for spontaneous failure (self-quenching). Physical insights are tentatively presented rather than technical aspects. The challenge is to identify the physical mechanisms with their relevant parameters, and more specifically to explain how the length-scales involved in detonation dynamics are larger by two order of magnitude (at least) than the length-scale involved in the steady planar traveling-wave solution (detonation thickness).

Journal Article↗

PubMed2006

Inertia and memory in ambiguous visual perception.

Perceptual multistability during ambiguous visual perception is an important clue to neural dynamics. We examined perceptual switching during ambiguous depth perception using a Necker cube stimulus, and also during binocular rivalry. Analysis of perceptual switching time series using variance-sample size analysis, spectral analysis and time series shuffling shows that switching times behave as a 1/f noise and possess very long range correlations. The long memory feature contrasts sharply with the traditional satiation models of multistability, where the memory is not incorporated, as well as with recently published models of multistability and neural processing, where memory is excluded. On the other hand, the long memory feature favors the concept of "dynamic core" or coalition of neurons, where neurons form transient coalitions. Perceptual switching then corresponds to replacement of one coalition of neurons by another. The inertia and memory measures the stability of a coalition: a strong and stable coalition has to be won over by another similarly strong and stable coalition, resulting in long switching times. The complicated transient dynamics of competing coalitions of neurons may be addressable using a combination of functional imaging, measurement of frequency-tagged magnetoencephalography and frequency-tagged encephalography, simultaneous recordings of groups of neurons in many areas of the brain, and concepts from statistical mechanics and nonlinear dynamics theory.

Data Interpretation, Statistical↗

PubMed1999

Largest Lyapunov exponent in molecular systems. II: Quaternion coordinates and application to methane clusters.

We present a numerical procedure for extracting Lyapunov characteristic exponents from classical molecular-dynamics simulations of molecular systems. The theoretical frame chosen to describe the orientational degrees of freedom is the quaternions scheme. We apply the method to small methane clusters. Two different model potentials are used to investigate the role of internal molecular motion on the nonlinear dynamics, and several parameters are calculated to study the thermodynamics and chaotic dynamics of these clusters. Evidence is found for a solidlike to plasticlike phase transition occurring with the release of the orientational degrees of freedom, at low temperatures below the melting point. The largest Lyapunov exponent increases significantly during this transition, but it exhibits no particular variation during melting.

Journal Article↗

PubMed2005

Self-channeling of ultrashort laser pulses in materials with anomalous dispersion.

The nonlinear dynamics of femtosecond optical pulses propagating in solid media with anomalous group-velocity dispersion (GVD) is investigated. A map fixing the boundaries of collapse or noncollapse regimes for high-power beams versus the relative strength of GVD is first established. Next, from a nonlinear Schrödinger model accounting for higher-order dispersion, self-steepening, and plasma generation, the possibility of producing extended collapse events that promote a long self-guiding is confirmed, in agreement with recent experiments [K.D. Moll and A.L. Gaeta, Opt. Lett. 29, 995 (2004)]. Three-dimensional collapsing pulses are shown to propagate by emitting quasiperiodically bursts of temporally compressed light bullets, with durations close to the single cycle limit.

Journal Article↗

PubMed2006

Keeping up with bats: dynamic auditory tuning in a moth.

Many night-flying insects evolved ultrasound sensitive ears in response to acoustic predation by echolocating bats . Noctuid moths are most sensitive to frequencies at 20-40 kHz , the lower range of bat ultrasound . This may disadvantage the moth because noctuid-hunting bats in particular echolocate at higher frequencies shortly before prey capture and thus improve their echolocation and reduce their acoustic conspicuousness . Yet, moth hearing is not simple; the ear's nonlinear dynamic response shifts its mechanical sensitivity up to high frequencies. Dependent on incident sound intensity, the moth's ear mechanically tunes up and anticipates the high frequencies used by hunting bats. Surprisingly, this tuning is hysteretic, keeping the ear tuned up for the bat's possible return. A mathematical model is constructed for predicting a linear relationship between the ear's mechanical stiffness and sound intensity. This nonlinear mechanical response is a parametric amplitude dependence that may constitute a feature common to other sensory systems. Adding another twist to the coevolutionary arms race between moths and bats, these results reveal unexpected sophistication in one of the simplest ears known and a novel perspective for interpreting bat echolocation calls.

Acoustic Stimulation↗

PubMed2006

Coexistence of Josephson oscillations and a novel self-trapping regime in optical waveguide arrays.

Considering the coherent nonlinear dynamics between two weakly linked optical waveguide arrays, we find the first example of coexistence of Josephson oscillations with a novel self-trapping regime. This macroscopic bistability is explained by proving analytically the simultaneous existence of symmetric, antisymmetric, and asymmetric stationary solutions of the associated nonlinear Schrödinger equation. The effect is illustrated and confirmed by numerical simulations. This property allows us to conceive an optical switch based on the variation of the refractive index of the linking central waveguide.

Journal Article↗

PubMed2003

Enhancing nursing research with children and families using a developmental science perspective.

Nursing scholarship on children and their families has increased rapidly over the past decades. This research focuses on infants, children, and adolescents and their families facing acute or chronic illness, as well as on promoting health and preventing disease in children. While the amount and scope of research in pediatric nursing has increased, the methods and theories used are diverse and are often not based on the most recent science in the broader fields of developmental research. Developmental science, which evolved over the past two decades into a new interdisciplinary framework for the study of human development, involves an integrated holistic, developmental, and systems-oriented perspective. According to this view, the individual functions and develops through dynamic and complex processes involving the integration of many systems within the individual, including mental, biological, and behavioral systems. In addition, individuals function and develop in a continuously ongoing, reciprocal process of interaction with their environment and, as such, have an influence on that environment. These nonlinear, dynamic processes demand complex conceptualizations and research designs if one is to truly understand human development, including health and illness. Key aspects of developmental science important in conceptualization, design, measurement, and data analysis are identified. By providing a framework for critiquing research and presenting recommendations for future research based on developmental science, we hope to move nursing research with children forward toward more developmentally sound knowledge of nursing practice.

Acute Disease↗

PubMed2005

Control-relevant modeling of the antitumor effects of 9-nitrocamptothecin in SCID mice bearing HT29 human colon xenografts.

The mathematical model structure selected to describe system behavior is at least partially dependent on the proposed use of the model. In this paper, a pharmacokinetic(PK)/pharmacodynamic (PD) model for use in drug delivery algorithm synthesis is developed. The antitumor agent 9-nitrocamptothecin (9NC) was administered orally to severe combined immunodeficient (SCID) mice bearing subcutaneously implanted HT29 human colon xenografts, and the effect of 9NC on those xenografts was characterized. Different PK model structures were considered in characterizing the dynamics of the drug concentration in the plasma. Akaike's Information Criterion (AIC) was used to select the model structure maximizing fit accuracy while simultaneously minimizing the number of model parameters. The resulting PK model was a set of coupled linear ordinary differential equations able to describe the nonlinear dynamic behavior (e.g. plateauing, etc.) of the drug concentrations observed in the plasma. Pharmacodynamics were modeled by characterizing tumor growth in both the untreated and drug-treated animals. The resulting PK/PD model related drug administration to effect, and this model has a structure that facilitates future control algorithm synthesis. Control algorithms in this context would directly utilize PK/PD model predictions. These predictions would be used to determine the amount and frequency of drug administration in order to reduce the tumor burden without violating clinically relevant constraints. This methodology could then be used to aid the clinician in selecting dose levels and schedules, and extension to patient tailored treatment may eventually be feasible with this approach.

Algorithms↗

PubMed2001

Complex AV nodal dynamics during ventricular-triggered atrial pacing in humans.

In vitro experiments have shown that the complexity of atrioventricular nodal (AVN) conduction dynamics increases with heart rate. Although complex AVN dynamics (e.g., alternans) have been observed clinically, human AVN dynamics during rapid pacing have not been systematically investigated. We studied such dynamics during ventricular-triggered atrial pacing in 37 patients with normal AVN function (18 patients with dual AVN pathway physiology and 19 patients without). Alternans, which always resulted from single pathway conduction, occurred in 18 patients. In 16 patients (3 of whom also had alternans), quasisinusoidal AVN conduction oscillations occurred (mean frequency 0.02 Hz); such oscillations have not been previously reported. There were no significant differences in the dynamics for patients with or without dual AVN pathways. To illuminate the governing dynamic mechanism, a second atrial pacing trial was performed on 12 patients after autonomic blockade. Blockade facilitated alternans but inhibited oscillations. This study suggests that rapid AVN excitation in vivo can lead to autonomically mediated AVN conduction oscillations or single pathway alternans that are a function of inherent nonlinear dynamic AVN tissue properties.

Atrioventricular Node↗

PubMed2004

Deterministic dynamics control oscillations of bone marrow cell proliferation.

OBJECTIVE: The production of blood cells in vivo, both normal and tumoral, displays oscillatory dynamics. Many cells in long-term cultures also show large amplitude oscillations of proliferative rate. Therefore we examined the proliferation dynamics of mouse bone marrow cells (MBM) and their clonogenic progenitor production (BMP), in order to characterize these dynamics. METHODS: Five Dexter-type cultures of MBM cells and their clonogenic BMP production were examined for up to seven-months periods of time. The recorded time series exhibited a complex pattern of oscillations with variable amplitudes. We previously reported a method that allowed analysis of such nonlinear dynamics of hepatoma cell proliferation. We applied this method, based on the two-dimensional recurrent representation of data, to analyze the fluctuations of bone marrow cells proliferation. RESULTS: The proliferation rate of mouse bone marrow cells shows large amplitude oscillations every 2 to 3 weeks. Mathematical analysis revealed a deterministic mechanism that controls all proliferation local maxima of MBM cells. Dynamics for progenitor production resembled that of parental cells. This reflects a predominant negative feedback on bone marrow cell proliferation. CONCLUSION: These dynamics were opposite of that previously described for hepatoma cells where the dominant control is applied to the local minima (troughs of proliferation). Therefore, the complex system of cell proliferation is controlled by a bipolar mechanism, with a predominant dampening command depending on the cell type. We propose that the dominant dampening control of local maxima in bone marrow cells protects the stock of stem cells.

Animals↗

PubMed2006

Canard orbits in Fabry-Perot cavities induced by radiation pressure and photothermal effects.

A theoretical study of a high-finesse Fabry-Perot cavity considering radiation pressure and photothermal displacement is reported. We show that the competition between these two effects induces a different kind of dynamic behavior in such a system, consisting of canard orbits and excitability. The transition between the excitable regime and the canard oscillations, occurring through a supercritical Hopf bifurcation, appears in an order compatible with the van der Pol-FitzHugh-Nagumo equations. Besides its interest as a study of general nonlinear dynamics, the characterization of the effects described is critical for high sensitivity interferometric displacement measurements as those employed for gravitational waves detection.

Journal Article↗

PubMed2005

Eukaryotic cells are dynamically ordered or critical but not chaotic.

Two important theoretical approaches have been developed to generically characterize the relationship between the structure and function of large genetic networks: the continuous approach, based on reaction-kinetics differential equations, and the Boolean approach, based on difference equations and discrete logical rules. These two approaches do not always coincide in their predictions for the same system. Nonetheless, both of them predict that the highly nonlinear dynamics exhibited by genetic regulatory systems can be characterized into two broad regimes, to wit, an ordered regime where the system is robust against perturbations, and a chaotic regime where the system is extremely sensitive to perturbations. It has been a plausible and long-standing hypothesis that genomic regulatory networks of real cells operate in the ordered regime or at the border between order and chaos. This hypothesis is indirectly supported by the robustness and stability observed in the phenotypic traits of living organisms under genetic perturbations. However, there has been no systematic study to determine whether the gene-expression patterns of real cells are compatible with the dynamically ordered regimes predicted by theoretical models. Using the Boolean approach, here we show what we believe to be the first direct evidence that the underlying genetic network of HeLa cells appears to operate either in the ordered regime or at the border between order and chaos but does not appear to be chaotic.

Gene Expression Regulation↗

PubMed2006

On the attenuation and amplification of molecular noise in genetic regulatory networks.

BACKGROUND: Noise has many important roles in cellular genetic regulatory functions at the nanomolar scale. At present, no good theory exists for identifying all possible mechanisms of genetic regulatory networks to attenuate the molecular noise to achieve regulatory ability or to amplify the molecular noise to randomize outcomes to the advantage of diversity. Therefore, the noise filtering of genetic regulatory network is an important topic for gene networks under intrinsic fluctuation and extrinsic noise. RESULTS: Based on stochastic dynamic regulation equation, the intrinsic fluctuation in reaction rates is modeled as a state-dependent stochastic process, which will influence the stability of gene regulatory network, especially, with low concentrations of reacting species. Then the mechanisms of genetic regulatory network to attenuate or amplify extrinsic fluctuation are revealed from the nonlinear stochastic filtering point of view. Furthermore, a simple measure of attenuation level or amplification level of extrinsic noise for genetic regulatory networks is also introduced by nonlinear robust filtering method. Based on the global linearization scheme, a convenient method is introduced to measure noise attenuation or amplification for each gene of the nonlinear stochastic regulatory network by solving a set of filtering problems, which correspond to a set of linearized stochastic regulatory networks. Finally, by the proposed methods, several simulation examples of genetic regulatory networks are given to measure their robust stability under intrinsic fluctuations, and to estimate the genes' attenuation and amplification levels under extrinsic noises. CONCLUSION: In this study, a stochastic nonlinear dynamic model is developed for genetic regulatory networks under intrinsic fluctuation and extrinsic noise. By the method we proposed, we could determine the robust stability under intrinsic fluctuations and identify the genes that are significantly affected by extrinsic noises, which we call the weak structure of the network. This method will be potential for robust gene circuit design in future, on which a drug design could be based.

Animals↗

PubMed1993

Deterministic chaos and the sciences of complexity: psychoanalysis in the midst of a general scientific revolution.

A combination of new concepts and the enormous powers of computation now available have created the beginnings of a major new scientific revolution. It does not have to do with psychoanalysis per se, but with some basic assumptions among the sciences generally. The result is already showing in new visions of nature variously called "deterministic chaos," "nonlinear dynamics," or "sciences of complexity." For the first time it is possible to study complex systems in process, over time. This paper, especially attending to issues of separation and integration, focuses on two components of the new understandings, fractal geometry (part of the mathematics of topology) and deterministic chaos (the tendency of nonlinear systems to oscillate toward and away from absolute chaotic disorganization). In a diverse group of intellectual disciplines, it is now possible to describe systems in operation in detail, in terms of nonlinear differential equations. From these, computer models of multiple variables in interaction can be produced. In turn, this allows experimentation on the models by altering variables. At this time, psychoanalysis can only use deterministic chaos and fractals metaphorically, but in the future, especially if psychoanalysis is seen in terms of process or organismic theory, it is likely that such models can be produced.

Computer Simulation↗

PubMed2004

DNA dynamically directs its own transcription initiation.

It has long been known that double-stranded DNA is subject to temporary, localized openings of its two strands. Particular regions along a DNA polymer are destabilized structurally by available thermal energy in the system. The localized sequence of DNA determines the physical properties of a stretch of DNA, and that in turn determines the opening profile of that DNA fragment. We show that the Peyrard-Bishop nonlinear dynamical model of DNA, which has been used to simulate denaturation of short DNA fragments, gives an accurate representation of the instability profile of a defined sequence of DNA, as verified using S1 nuclease cleavage assays. By comparing results for a non-promoter DNA fragment, the adenovirus major late promoter, the adeno-associated viral P5 promoter and a known P5 mutant promoter that is inactive for transcription, we show that the predicted openings correlate almost exactly with the promoter transcriptional start sites and major regulatory sites. Physicists have speculated that localized melting of DNA might play a role in gene transcription and other processes. Our data link sequence-dependent opening behavior in DNA to transcriptional activity for the first time.

Adenoviridae↗

PubMed1993

Mapping the dynamics of a bursting neuron.

The anterior burster (AB) neuron of the lobster stomatogastric ganglion displays varied rhythmic behavior when treated with neuromodulators and channel-blocking toxins. We introduce a channel-based model for this neuron and show how bifurcation analysis can be used to investigate the response of this model to changes of its parameters. Two dimensional maps of the parameter space of the model were constructed using computational tools based on the theory of nonlinear dynamical systems. Changes in the intrinsic firing and oscillatory properties of the model AB neuron were correlated with the boundaries of Hopf and saddle-node bifurcations on these maps. Complex rhythmic patterns were observed, with a bounded region of the parameter plane producing bursting behavior of the model neuron. Experiments were performed by treating an isolated AB cell with 4-aminopyridine which selectively reduces gA, the conductance of the transient potassium channel. The model accurately predicts the qualitative changes in the neuronal voltage oscillations that are observed over a range of reduction of gA in the neuron. These results demonstrate the efficacy of dynamical systems theory as a means of determining the varied oscillatory behaviors inherent in a channel-based neural model. Further, the maps of bifurcations provide a useful tool for determining how these behaviors depend upon model parameters and comparing the model to a real neuron.

4-Aminopyridine↗